Properties

Label 441.4.e.z.226.2
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 226.2
Root \(-1.99285 + 3.45171i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.z.361.2

$q$-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 \(0.570360\pi\)
−0.735332 + 0.677707i \(0.762974\pi\)
\(3\) 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 0.559394 0.828902i \(-0.311034\pi\)
−0.997547 + 0.0699983i \(0.977701\pi\)
\(12\) 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 0.743717 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 \(0.394854\pi\)
−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 −0.713083 0.701079i \(-0.752702\pi\)
0.963694 + 0.267008i \(0.0860352\pi\)
\(24\) 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 \(-0.481915\pi\)
0.0567852 + 0.998386i \(0.481915\pi\)
\(30\) 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 \(-0.650159\pi\)
−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 0.641443 0.767170i \(-0.278336\pi\)
−0.985111 + 0.171921i \(0.945003\pi\)
\(54\) 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 −0.825272 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 \(-0.743173\pi\)
−0.691779 + 0.722110i \(0.743173\pi\)
\(72\) 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 \(-0.596865\pi\)
−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 \(-0.708625\pi\)
−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 \(-0.796496\pi\)
−0.115470 0.993311i \(-0.536837\pi\)
\(102\) 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 −0.665010 0.746835i \(-0.731573\pi\)
0.979283 + 0.202498i \(0.0649059\pi\)
\(108\) 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 \(-0.380949\pi\)
0.365350 + 0.930870i \(0.380949\pi\)
\(114\) 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 0.991134 0.132863i \(-0.0424171\pi\)
−0.610630 + 0.791916i \(0.709084\pi\)
\(138\) 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 \(-0.581013\pi\)
0.964013 0.265855i \(-0.0856541\pi\)
\(150\) 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 \(-0.773037\pi\)
−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 \(0.102283\pi\)
−0.200890 + 0.979614i \(0.564383\pi\)
\(180\) 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 \(0.346379\pi\)
−0.999160 + 0.0409717i \(0.986955\pi\)
\(192\) 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 \(-0.388926\pi\)
0.341909 + 0.939733i \(0.388926\pi\)
\(198\) 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 0.952240 0.305351i \(-0.0987737\pi\)
−0.740562 + 0.671989i \(0.765440\pi\)
\(228\) 0 0
\(229\) −808.774 + 1400.84i −0.233385 + 0.404235i −0.958802 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 \(-0.505996\pi\)
0.875290 0.483598i \(-0.160670\pi\)
\(234\) 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 \(-0.569289\pi\)
−0.215963 + 0.976401i \(0.569289\pi\)
\(240\) 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 \(-0.784755\pi\)
−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 0.560756 0.827981i \(-0.310511\pi\)
−0.997431 + 0.0716384i \(0.977177\pi\)
\(264\) 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 \(-0.631779\pi\)
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 \(-0.630922\pi\)
−0.399804 + 0.916601i \(0.630922\pi\)
\(282\) 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 \(-0.303133\pi\)
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 \(-0.558767\pi\)
−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 0.914010 0.405691i \(-0.132969\pi\)
−0.808344 + 0.588711i \(0.799636\pi\)
\(312\) 0 0
\(313\) −2246.84 + 3891.64i −0.405747 + 0.702774i −0.994408 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 −0.995363 0.0961925i \(-0.969334\pi\)
0.580987 + 0.813913i \(0.302667\pi\)
\(318\) 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 \(-0.944460\pi\)
0.342067 0.939676i \(-0.388873\pi\)
\(348\) 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 0.995053 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 \(0.344108\pi\)
−0.999427 + 0.0338425i \(0.989226\pi\)
\(360\) 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 −0.998791 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 0.647354 0.762189i \(-0.275875\pi\)
−0.983752 + 0.179531i \(0.942542\pi\)
\(390\) 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 −0.979963 0.199180i \(-0.936172\pi\)
0.662477 + 0.749083i \(0.269505\pi\)
\(402\) 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 \(-0.582879\pi\)
−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 0.816048 0.577984i \(-0.196160\pi\)
−0.908573 + 0.417726i \(0.862827\pi\)
\(432\) 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 −0.886840 0.462077i \(-0.847105\pi\)
0.843590 + 0.536988i \(0.180438\pi\)
\(444\) 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 \(-0.393417\pi\)
0.328618 + 0.944463i \(0.393417\pi\)
\(450\) 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 \(-0.0852937\pi\)
0.964313 + 0.264763i \(0.0852937\pi\)
\(492\) 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 −0.995467 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 0.938116 0.346322i \(-0.112570\pi\)
−0.768982 + 0.639271i \(0.779236\pi\)
\(558\) 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 −0.968649 0.248433i \(-0.920085\pi\)
0.699473 + 0.714659i \(0.253418\pi\)
\(570\) 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 \(-0.167172\pi\)
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 \(-0.917970\pi\)
0.262771 0.964858i \(-0.415363\pi\)
\(600\) 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 \(-0.446635\pi\)
0.166867 + 0.985979i \(0.446635\pi\)
\(618\) 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 0.998437 0.0558950i \(-0.0178012\pi\)
−0.547625 + 0.836724i \(0.684468\pi\)
\(642\) 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 \(-0.990254\pi\)
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 −0.910497 0.413515i \(-0.864301\pi\)
0.813363 + 0.581756i \(0.197634\pi\)
\(654\) 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 \(-0.339373\pi\)
0.483479 + 0.875356i \(0.339373\pi\)
\(660\) 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 \(-0.656034\pi\)
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 \(0.0850240\pi\)
−0.253685 + 0.967287i \(0.581643\pi\)
\(684\) 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 \(-0.583972\pi\)
−0.260757 + 0.965405i \(0.583972\pi\)
\(702\) 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 \(-0.287620\pi\)
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 \(-0.783158\pi\)
−0.776799 + 0.629749i \(0.783158\pi\)
\(744\) 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 \(-0.426774\pi\)
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 0.899757 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 \(0.00615065\pi\)
−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