Properties

Label 441.4.e.k.361.1
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.k.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-3.50000 - 6.06218i) q^{5} +24.0000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(2.00000 - 3.46410i) q^{4} +(-3.50000 - 6.06218i) q^{5} +24.0000 q^{8} +(7.00000 - 12.1244i) q^{10} +(-2.50000 + 4.33013i) q^{11} +14.0000 q^{13} +(8.00000 + 13.8564i) q^{16} +(10.5000 - 18.1865i) q^{17} +(24.5000 + 42.4352i) q^{19} -28.0000 q^{20} -10.0000 q^{22} +(-79.5000 - 137.698i) q^{23} +(38.0000 - 65.8179i) q^{25} +(14.0000 + 24.2487i) q^{26} -58.0000 q^{29} +(73.5000 - 127.306i) q^{31} +(80.0000 - 138.564i) q^{32} +42.0000 q^{34} +(-109.500 - 189.660i) q^{37} +(-49.0000 + 84.8705i) q^{38} +(-84.0000 - 145.492i) q^{40} +350.000 q^{41} -124.000 q^{43} +(10.0000 + 17.3205i) q^{44} +(159.000 - 275.396i) q^{46} +(-262.500 - 454.663i) q^{47} +152.000 q^{50} +(28.0000 - 48.4974i) q^{52} +(151.500 - 262.406i) q^{53} +35.0000 q^{55} +(-58.0000 - 100.459i) q^{58} +(52.5000 - 90.9327i) q^{59} +(-206.500 - 357.668i) q^{61} +294.000 q^{62} +448.000 q^{64} +(-49.0000 - 84.8705i) q^{65} +(-207.500 + 359.401i) q^{67} +(-42.0000 - 72.7461i) q^{68} +432.000 q^{71} +(-556.500 + 963.886i) q^{73} +(219.000 - 379.319i) q^{74} +196.000 q^{76} +(51.5000 + 89.2006i) q^{79} +(56.0000 - 96.9948i) q^{80} +(350.000 + 606.218i) q^{82} +1092.00 q^{83} -147.000 q^{85} +(-124.000 - 214.774i) q^{86} +(-60.0000 + 103.923i) q^{88} +(164.500 + 284.922i) q^{89} -636.000 q^{92} +(525.000 - 909.327i) q^{94} +(171.500 - 297.047i) q^{95} +882.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} + 4q^{4} - 7q^{5} + 48q^{8} + O(q^{10}) \) \( 2q + 2q^{2} + 4q^{4} - 7q^{5} + 48q^{8} + 14q^{10} - 5q^{11} + 28q^{13} + 16q^{16} + 21q^{17} + 49q^{19} - 56q^{20} - 20q^{22} - 159q^{23} + 76q^{25} + 28q^{26} - 116q^{29} + 147q^{31} + 160q^{32} + 84q^{34} - 219q^{37} - 98q^{38} - 168q^{40} + 700q^{41} - 248q^{43} + 20q^{44} + 318q^{46} - 525q^{47} + 304q^{50} + 56q^{52} + 303q^{53} + 70q^{55} - 116q^{58} + 105q^{59} - 413q^{61} + 588q^{62} + 896q^{64} - 98q^{65} - 415q^{67} - 84q^{68} + 864q^{71} - 1113q^{73} + 438q^{74} + 392q^{76} + 103q^{79} + 112q^{80} + 700q^{82} + 2184q^{83} - 294q^{85} - 248q^{86} - 120q^{88} + 329q^{89} - 1272q^{92} + 1050q^{94} + 343q^{95} + 1764q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 0 0
\(4\) 2.00000 3.46410i 0.250000 0.433013i
\(5\) −3.50000 6.06218i −0.313050 0.542218i 0.665971 0.745977i \(-0.268017\pi\)
−0.979021 + 0.203760i \(0.934684\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 24.0000 1.06066
\(9\) 0 0
\(10\) 7.00000 12.1244i 0.221359 0.383406i
\(11\) −2.50000 + 4.33013i −0.0685253 + 0.118689i −0.898252 0.439480i \(-0.855163\pi\)
0.829727 + 0.558169i \(0.188496\pi\)
\(12\) 0 0
\(13\) 14.0000 0.298685 0.149342 0.988786i \(-0.452284\pi\)
0.149342 + 0.988786i \(0.452284\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 8.00000 + 13.8564i 0.125000 + 0.216506i
\(17\) 10.5000 18.1865i 0.149801 0.259464i −0.781353 0.624090i \(-0.785470\pi\)
0.931154 + 0.364626i \(0.118803\pi\)
\(18\) 0 0
\(19\) 24.5000 + 42.4352i 0.295826 + 0.512385i 0.975177 0.221429i \(-0.0710720\pi\)
−0.679351 + 0.733813i \(0.737739\pi\)
\(20\) −28.0000 −0.313050
\(21\) 0 0
\(22\) −10.0000 −0.0969094
\(23\) −79.5000 137.698i −0.720735 1.24835i −0.960706 0.277569i \(-0.910471\pi\)
0.239971 0.970780i \(-0.422862\pi\)
\(24\) 0 0
\(25\) 38.0000 65.8179i 0.304000 0.526543i
\(26\) 14.0000 + 24.2487i 0.105601 + 0.182906i
\(27\) 0 0
\(28\) 0 0
\(29\) −58.0000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 73.5000 127.306i 0.425838 0.737574i −0.570660 0.821186i \(-0.693313\pi\)
0.996498 + 0.0836128i \(0.0266459\pi\)
\(32\) 80.0000 138.564i 0.441942 0.765466i
\(33\) 0 0
\(34\) 42.0000 0.211851
\(35\) 0 0
\(36\) 0 0
\(37\) −109.500 189.660i −0.486532 0.842698i 0.513348 0.858181i \(-0.328405\pi\)
−0.999880 + 0.0154821i \(0.995072\pi\)
\(38\) −49.0000 + 84.8705i −0.209180 + 0.362311i
\(39\) 0 0
\(40\) −84.0000 145.492i −0.332039 0.575109i
\(41\) 350.000 1.33319 0.666595 0.745420i \(-0.267751\pi\)
0.666595 + 0.745420i \(0.267751\pi\)
\(42\) 0 0
\(43\) −124.000 −0.439763 −0.219882 0.975527i \(-0.570567\pi\)
−0.219882 + 0.975527i \(0.570567\pi\)
\(44\) 10.0000 + 17.3205i 0.0342627 + 0.0593447i
\(45\) 0 0
\(46\) 159.000 275.396i 0.509636 0.882716i
\(47\) −262.500 454.663i −0.814671 1.41105i −0.909564 0.415565i \(-0.863584\pi\)
0.0948921 0.995488i \(-0.469749\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 152.000 0.429921
\(51\) 0 0
\(52\) 28.0000 48.4974i 0.0746712 0.129334i
\(53\) 151.500 262.406i 0.392644 0.680079i −0.600153 0.799885i \(-0.704894\pi\)
0.992797 + 0.119806i \(0.0382272\pi\)
\(54\) 0 0
\(55\) 35.0000 0.0858073
\(56\) 0 0
\(57\) 0 0
\(58\) −58.0000 100.459i −0.131306 0.227429i
\(59\) 52.5000 90.9327i 0.115846 0.200651i −0.802272 0.596959i \(-0.796375\pi\)
0.918118 + 0.396308i \(0.129709\pi\)
\(60\) 0 0
\(61\) −206.500 357.668i −0.433436 0.750734i 0.563730 0.825959i \(-0.309366\pi\)
−0.997167 + 0.0752252i \(0.976032\pi\)
\(62\) 294.000 0.602226
\(63\) 0 0
\(64\) 448.000 0.875000
\(65\) −49.0000 84.8705i −0.0935031 0.161952i
\(66\) 0 0
\(67\) −207.500 + 359.401i −0.378361 + 0.655340i −0.990824 0.135159i \(-0.956845\pi\)
0.612463 + 0.790499i \(0.290179\pi\)
\(68\) −42.0000 72.7461i −0.0749007 0.129732i
\(69\) 0 0
\(70\) 0 0
\(71\) 432.000 0.722098 0.361049 0.932547i \(-0.382419\pi\)
0.361049 + 0.932547i \(0.382419\pi\)
\(72\) 0 0
\(73\) −556.500 + 963.886i −0.892238 + 1.54540i −0.0550526 + 0.998483i \(0.517533\pi\)
−0.837186 + 0.546919i \(0.815801\pi\)
\(74\) 219.000 379.319i 0.344030 0.595878i
\(75\) 0 0
\(76\) 196.000 0.295826
\(77\) 0 0
\(78\) 0 0
\(79\) 51.5000 + 89.2006i 0.0733443 + 0.127036i 0.900365 0.435135i \(-0.143299\pi\)
−0.827021 + 0.562171i \(0.809966\pi\)
\(80\) 56.0000 96.9948i 0.0782624 0.135554i
\(81\) 0 0
\(82\) 350.000 + 606.218i 0.471354 + 0.816409i
\(83\) 1092.00 1.44413 0.722064 0.691827i \(-0.243194\pi\)
0.722064 + 0.691827i \(0.243194\pi\)
\(84\) 0 0
\(85\) −147.000 −0.187581
\(86\) −124.000 214.774i −0.155480 0.269299i
\(87\) 0 0
\(88\) −60.0000 + 103.923i −0.0726821 + 0.125889i
\(89\) 164.500 + 284.922i 0.195921 + 0.339345i 0.947202 0.320637i \(-0.103897\pi\)
−0.751281 + 0.659982i \(0.770564\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −636.000 −0.720735
\(93\) 0 0
\(94\) 525.000 909.327i 0.576060 0.997765i
\(95\) 171.500 297.047i 0.185216 0.320804i
\(96\) 0 0
\(97\) 882.000 0.923232 0.461616 0.887080i \(-0.347270\pi\)
0.461616 + 0.887080i \(0.347270\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −152.000 263.272i −0.152000 0.263272i
\(101\) −689.500 + 1194.25i −0.679285 + 1.17656i 0.295911 + 0.955215i \(0.404377\pi\)
−0.975196 + 0.221341i \(0.928957\pi\)
\(102\) 0 0
\(103\) −339.500 588.031i −0.324776 0.562529i 0.656691 0.754160i \(-0.271956\pi\)
−0.981467 + 0.191631i \(0.938622\pi\)
\(104\) 336.000 0.316803
\(105\) 0 0
\(106\) 606.000 0.555282
\(107\) 228.500 + 395.774i 0.206448 + 0.357578i 0.950593 0.310440i \(-0.100476\pi\)
−0.744145 + 0.668018i \(0.767143\pi\)
\(108\) 0 0
\(109\) 562.500 974.279i 0.494291 0.856137i −0.505687 0.862717i \(-0.668761\pi\)
0.999978 + 0.00657959i \(0.00209436\pi\)
\(110\) 35.0000 + 60.6218i 0.0303374 + 0.0525460i
\(111\) 0 0
\(112\) 0 0
\(113\) 1538.00 1.28038 0.640190 0.768217i \(-0.278856\pi\)
0.640190 + 0.768217i \(0.278856\pi\)
\(114\) 0 0
\(115\) −556.500 + 963.886i −0.451251 + 0.781590i
\(116\) −116.000 + 200.918i −0.0928477 + 0.160817i
\(117\) 0 0
\(118\) 210.000 0.163831
\(119\) 0 0
\(120\) 0 0
\(121\) 653.000 + 1131.03i 0.490609 + 0.849759i
\(122\) 413.000 715.337i 0.306486 0.530849i
\(123\) 0 0
\(124\) −294.000 509.223i −0.212919 0.368787i
\(125\) −1407.00 −1.00677
\(126\) 0 0
\(127\) 72.0000 0.0503068 0.0251534 0.999684i \(-0.491993\pi\)
0.0251534 + 0.999684i \(0.491993\pi\)
\(128\) −192.000 332.554i −0.132583 0.229640i
\(129\) 0 0
\(130\) 98.0000 169.741i 0.0661167 0.114517i
\(131\) −1074.50 1861.09i −0.716637 1.24125i −0.962325 0.271903i \(-0.912347\pi\)
0.245687 0.969349i \(-0.420986\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −830.000 −0.535083
\(135\) 0 0
\(136\) 252.000 436.477i 0.158888 0.275203i
\(137\) −562.500 + 974.279i −0.350786 + 0.607578i −0.986387 0.164439i \(-0.947419\pi\)
0.635602 + 0.772017i \(0.280752\pi\)
\(138\) 0 0
\(139\) −252.000 −0.153772 −0.0768862 0.997040i \(-0.524498\pi\)
−0.0768862 + 0.997040i \(0.524498\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 432.000 + 748.246i 0.255300 + 0.442193i
\(143\) −35.0000 + 60.6218i −0.0204675 + 0.0354507i
\(144\) 0 0
\(145\) 203.000 + 351.606i 0.116264 + 0.201375i
\(146\) −2226.00 −1.26182
\(147\) 0 0
\(148\) −876.000 −0.486532
\(149\) −100.500 174.071i −0.0552569 0.0957078i 0.837074 0.547090i \(-0.184264\pi\)
−0.892331 + 0.451382i \(0.850931\pi\)
\(150\) 0 0
\(151\) −809.500 + 1402.10i −0.436266 + 0.755635i −0.997398 0.0720914i \(-0.977033\pi\)
0.561132 + 0.827726i \(0.310366\pi\)
\(152\) 588.000 + 1018.45i 0.313770 + 0.543466i
\(153\) 0 0
\(154\) 0 0
\(155\) −1029.00 −0.533234
\(156\) 0 0
\(157\) 339.500 588.031i 0.172580 0.298917i −0.766741 0.641956i \(-0.778123\pi\)
0.939321 + 0.343039i \(0.111456\pi\)
\(158\) −103.000 + 178.401i −0.0518623 + 0.0898281i
\(159\) 0 0
\(160\) −1120.00 −0.553399
\(161\) 0 0
\(162\) 0 0
\(163\) 233.500 + 404.434i 0.112203 + 0.194342i 0.916658 0.399672i \(-0.130876\pi\)
−0.804455 + 0.594014i \(0.797543\pi\)
\(164\) 700.000 1212.44i 0.333298 0.577288i
\(165\) 0 0
\(166\) 1092.00 + 1891.40i 0.510576 + 0.884344i
\(167\) 1204.00 0.557894 0.278947 0.960306i \(-0.410015\pi\)
0.278947 + 0.960306i \(0.410015\pi\)
\(168\) 0 0
\(169\) −2001.00 −0.910787
\(170\) −147.000 254.611i −0.0663199 0.114869i
\(171\) 0 0
\(172\) −248.000 + 429.549i −0.109941 + 0.190423i
\(173\) 1410.50 + 2443.06i 0.619875 + 1.07365i 0.989508 + 0.144477i \(0.0461499\pi\)
−0.369633 + 0.929178i \(0.620517\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −80.0000 −0.0342627
\(177\) 0 0
\(178\) −329.000 + 569.845i −0.138537 + 0.239953i
\(179\) −1626.50 + 2817.18i −0.679164 + 1.17635i 0.296069 + 0.955166i \(0.404324\pi\)
−0.975233 + 0.221180i \(0.929009\pi\)
\(180\) 0 0
\(181\) −1582.00 −0.649664 −0.324832 0.945772i \(-0.605308\pi\)
−0.324832 + 0.945772i \(0.605308\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1908.00 3304.75i −0.764454 1.32407i
\(185\) −766.500 + 1327.62i −0.304617 + 0.527613i
\(186\) 0 0
\(187\) 52.5000 + 90.9327i 0.0205304 + 0.0355597i
\(188\) −2100.00 −0.814671
\(189\) 0 0
\(190\) 686.000 0.261935
\(191\) 1278.50 + 2214.43i 0.484340 + 0.838902i 0.999838 0.0179887i \(-0.00572630\pi\)
−0.515498 + 0.856891i \(0.672393\pi\)
\(192\) 0 0
\(193\) 198.500 343.812i 0.0740329 0.128229i −0.826632 0.562742i \(-0.809746\pi\)
0.900665 + 0.434514i \(0.143080\pi\)
\(194\) 882.000 + 1527.67i 0.326412 + 0.565362i
\(195\) 0 0
\(196\) 0 0
\(197\) −2914.00 −1.05388 −0.526939 0.849903i \(-0.676660\pi\)
−0.526939 + 0.849903i \(0.676660\pi\)
\(198\) 0 0
\(199\) 1669.50 2891.66i 0.594712 1.03007i −0.398875 0.917005i \(-0.630599\pi\)
0.993587 0.113066i \(-0.0360673\pi\)
\(200\) 912.000 1579.63i 0.322441 0.558484i
\(201\) 0 0
\(202\) −2758.00 −0.960654
\(203\) 0 0
\(204\) 0 0
\(205\) −1225.00 2121.76i −0.417355 0.722880i
\(206\) 679.000 1176.06i 0.229651 0.397768i
\(207\) 0 0
\(208\) 112.000 + 193.990i 0.0373356 + 0.0646671i
\(209\) −245.000 −0.0810861
\(210\) 0 0
\(211\) 1780.00 0.580759 0.290380 0.956911i \(-0.406218\pi\)
0.290380 + 0.956911i \(0.406218\pi\)
\(212\) −606.000 1049.62i −0.196322 0.340040i
\(213\) 0 0
\(214\) −457.000 + 791.547i −0.145981 + 0.252846i
\(215\) 434.000 + 751.710i 0.137668 + 0.238447i
\(216\) 0 0
\(217\) 0 0
\(218\) 2250.00 0.699033
\(219\) 0 0
\(220\) 70.0000 121.244i 0.0214518 0.0371556i
\(221\) 147.000 254.611i 0.0447434 0.0774978i
\(222\) 0 0
\(223\) 1400.00 0.420408 0.210204 0.977658i \(-0.432587\pi\)
0.210204 + 0.977658i \(0.432587\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1538.00 + 2663.89i 0.452682 + 0.784069i
\(227\) 1102.50 1909.59i 0.322359 0.558342i −0.658615 0.752480i \(-0.728858\pi\)
0.980974 + 0.194138i \(0.0621908\pi\)
\(228\) 0 0
\(229\) 143.500 + 248.549i 0.0414094 + 0.0717231i 0.885987 0.463710i \(-0.153482\pi\)
−0.844578 + 0.535433i \(0.820149\pi\)
\(230\) −2226.00 −0.638166
\(231\) 0 0
\(232\) −1392.00 −0.393919
\(233\) 2293.50 + 3972.46i 0.644859 + 1.11693i 0.984334 + 0.176314i \(0.0564173\pi\)
−0.339475 + 0.940615i \(0.610249\pi\)
\(234\) 0 0
\(235\) −1837.50 + 3182.64i −0.510065 + 0.883459i
\(236\) −210.000 363.731i −0.0579230 0.100326i
\(237\) 0 0
\(238\) 0 0
\(239\) −1668.00 −0.451439 −0.225720 0.974192i \(-0.572473\pi\)
−0.225720 + 0.974192i \(0.572473\pi\)
\(240\) 0 0
\(241\) −1704.50 + 2952.28i −0.455587 + 0.789100i −0.998722 0.0505456i \(-0.983904\pi\)
0.543135 + 0.839646i \(0.317237\pi\)
\(242\) −1306.00 + 2262.06i −0.346913 + 0.600870i
\(243\) 0 0
\(244\) −1652.00 −0.433436
\(245\) 0 0
\(246\) 0 0
\(247\) 343.000 + 594.093i 0.0883586 + 0.153042i
\(248\) 1764.00 3055.34i 0.451670 0.782315i
\(249\) 0 0
\(250\) −1407.00 2437.00i −0.355946 0.616517i
\(251\) −4760.00 −1.19701 −0.598503 0.801121i \(-0.704238\pi\)
−0.598503 + 0.801121i \(0.704238\pi\)
\(252\) 0 0
\(253\) 795.000 0.197554
\(254\) 72.0000 + 124.708i 0.0177861 + 0.0308065i
\(255\) 0 0
\(256\) 2176.00 3768.94i 0.531250 0.920152i
\(257\) 402.500 + 697.150i 0.0976936 + 0.169210i 0.910730 0.413003i \(-0.135520\pi\)
−0.813036 + 0.582213i \(0.802187\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −392.000 −0.0935031
\(261\) 0 0
\(262\) 2149.00 3722.18i 0.506739 0.877698i
\(263\) −128.500 + 222.569i −0.0301279 + 0.0521831i −0.880696 0.473681i \(-0.842925\pi\)
0.850568 + 0.525865i \(0.176258\pi\)
\(264\) 0 0
\(265\) −2121.00 −0.491668
\(266\) 0 0
\(267\) 0 0
\(268\) 830.000 + 1437.60i 0.189180 + 0.327670i
\(269\) −1795.50 + 3109.90i −0.406965 + 0.704884i −0.994548 0.104280i \(-0.966746\pi\)
0.587583 + 0.809164i \(0.300080\pi\)
\(270\) 0 0
\(271\) 696.500 + 1206.37i 0.156123 + 0.270413i 0.933467 0.358662i \(-0.116767\pi\)
−0.777344 + 0.629075i \(0.783434\pi\)
\(272\) 336.000 0.0749007
\(273\) 0 0
\(274\) −2250.00 −0.496086
\(275\) 190.000 + 329.090i 0.0416634 + 0.0721631i
\(276\) 0 0
\(277\) −207.500 + 359.401i −0.0450089 + 0.0779577i −0.887652 0.460514i \(-0.847665\pi\)
0.842643 + 0.538472i \(0.180998\pi\)
\(278\) −252.000 436.477i −0.0543667 0.0941660i
\(279\) 0 0
\(280\) 0 0
\(281\) 4954.00 1.05171 0.525856 0.850574i \(-0.323745\pi\)
0.525856 + 0.850574i \(0.323745\pi\)
\(282\) 0 0
\(283\) −2138.50 + 3703.99i −0.449190 + 0.778019i −0.998333 0.0577087i \(-0.981621\pi\)
0.549144 + 0.835728i \(0.314954\pi\)
\(284\) 864.000 1496.49i 0.180525 0.312678i
\(285\) 0 0
\(286\) −140.000 −0.0289454
\(287\) 0 0
\(288\) 0 0
\(289\) 2236.00 + 3872.87i 0.455119 + 0.788289i
\(290\) −406.000 + 703.213i −0.0822108 + 0.142393i
\(291\) 0 0
\(292\) 2226.00 + 3855.55i 0.446119 + 0.772701i
\(293\) 7742.00 1.54366 0.771830 0.635829i \(-0.219342\pi\)
0.771830 + 0.635829i \(0.219342\pi\)
\(294\) 0 0
\(295\) −735.000 −0.145062
\(296\) −2628.00 4551.83i −0.516045 0.893817i
\(297\) 0 0
\(298\) 201.000 348.142i 0.0390725 0.0676756i
\(299\) −1113.00 1927.77i −0.215272 0.372863i
\(300\) 0 0
\(301\) 0 0
\(302\) −3238.00 −0.616973
\(303\) 0 0
\(304\) −392.000 + 678.964i −0.0739564 + 0.128096i
\(305\) −1445.50 + 2503.68i −0.271374 + 0.470034i
\(306\) 0 0
\(307\) 7364.00 1.36901 0.684504 0.729009i \(-0.260019\pi\)
0.684504 + 0.729009i \(0.260019\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1029.00 1782.28i −0.188527 0.326538i
\(311\) −4987.50 + 8638.60i −0.909374 + 1.57508i −0.0944372 + 0.995531i \(0.530105\pi\)
−0.814936 + 0.579550i \(0.803228\pi\)
\(312\) 0 0
\(313\) −2376.50 4116.22i −0.429162 0.743330i 0.567637 0.823279i \(-0.307858\pi\)
−0.996799 + 0.0799485i \(0.974524\pi\)
\(314\) 1358.00 0.244065
\(315\) 0 0
\(316\) 412.000 0.0733443
\(317\) −1738.50 3011.17i −0.308025 0.533515i 0.669905 0.742447i \(-0.266335\pi\)
−0.977930 + 0.208932i \(0.933001\pi\)
\(318\) 0 0
\(319\) 145.000 251.147i 0.0254497 0.0440801i
\(320\) −1568.00 2715.86i −0.273918 0.474440i
\(321\) 0 0
\(322\) 0 0
\(323\) 1029.00 0.177260
\(324\) 0 0
\(325\) 532.000 921.451i 0.0908002 0.157270i
\(326\) −467.000 + 808.868i −0.0793397 + 0.137420i
\(327\) 0 0
\(328\) 8400.00 1.41406
\(329\) 0 0
\(330\) 0 0
\(331\) −1670.50 2893.39i −0.277399 0.480469i 0.693339 0.720612i \(-0.256139\pi\)
−0.970738 + 0.240143i \(0.922806\pi\)
\(332\) 2184.00 3782.80i 0.361032 0.625325i
\(333\) 0 0
\(334\) 1204.00 + 2085.39i 0.197245 + 0.341639i
\(335\) 2905.00 0.473782
\(336\) 0 0
\(337\) 7366.00 1.19066 0.595329 0.803482i \(-0.297022\pi\)
0.595329 + 0.803482i \(0.297022\pi\)
\(338\) −2001.00 3465.83i −0.322012 0.557741i
\(339\) 0 0
\(340\) −294.000 + 509.223i −0.0468953 + 0.0812250i
\(341\) 367.500 + 636.529i 0.0583614 + 0.101085i
\(342\) 0 0
\(343\) 0 0
\(344\) −2976.00 −0.466439
\(345\) 0 0
\(346\) −2821.00 + 4886.12i −0.438318 + 0.759188i
\(347\) 3707.50 6421.58i 0.573571 0.993454i −0.422625 0.906305i \(-0.638891\pi\)
0.996195 0.0871487i \(-0.0277755\pi\)
\(348\) 0 0
\(349\) 3878.00 0.594798 0.297399 0.954753i \(-0.403881\pi\)
0.297399 + 0.954753i \(0.403881\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 400.000 + 692.820i 0.0605684 + 0.104908i
\(353\) −633.500 + 1097.25i −0.0955179 + 0.165442i −0.909825 0.414993i \(-0.863784\pi\)
0.814307 + 0.580435i \(0.197117\pi\)
\(354\) 0 0
\(355\) −1512.00 2618.86i −0.226052 0.391534i
\(356\) 1316.00 0.195921
\(357\) 0 0
\(358\) −6506.00 −0.960483
\(359\) 2342.50 + 4057.33i 0.344380 + 0.596484i 0.985241 0.171173i \(-0.0547558\pi\)
−0.640861 + 0.767657i \(0.721422\pi\)
\(360\) 0 0
\(361\) 2229.00 3860.74i 0.324974 0.562872i
\(362\) −1582.00 2740.10i −0.229691 0.397836i
\(363\) 0 0
\(364\) 0 0
\(365\) 7791.00 1.11726
\(366\) 0 0
\(367\) −2320.50 + 4019.22i −0.330052 + 0.571667i −0.982522 0.186148i \(-0.940400\pi\)
0.652470 + 0.757815i \(0.273733\pi\)
\(368\) 1272.00 2203.17i 0.180184 0.312087i
\(369\) 0 0
\(370\) −3066.00 −0.430794
\(371\) 0 0
\(372\) 0 0
\(373\) 4398.50 + 7618.43i 0.610578 + 1.05755i 0.991143 + 0.132798i \(0.0423963\pi\)
−0.380565 + 0.924754i \(0.624270\pi\)
\(374\) −105.000 + 181.865i −0.0145172 + 0.0251445i
\(375\) 0 0
\(376\) −6300.00 10911.9i −0.864090 1.49665i
\(377\) −812.000 −0.110929
\(378\) 0 0
\(379\) 13680.0 1.85407 0.927037 0.374969i \(-0.122347\pi\)
0.927037 + 0.374969i \(0.122347\pi\)
\(380\) −686.000 1188.19i −0.0926080 0.160402i
\(381\) 0 0
\(382\) −2557.00 + 4428.85i −0.342480 + 0.593193i
\(383\) −4882.50 8456.74i −0.651395 1.12825i −0.982785 0.184755i \(-0.940851\pi\)
0.331390 0.943494i \(-0.392482\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 794.000 0.104698
\(387\) 0 0
\(388\) 1764.00 3055.34i 0.230808 0.399771i
\(389\) 865.500 1499.09i 0.112809 0.195390i −0.804093 0.594504i \(-0.797349\pi\)
0.916902 + 0.399113i \(0.130682\pi\)
\(390\) 0 0
\(391\) −3339.00 −0.431868
\(392\) 0 0
\(393\) 0 0
\(394\) −2914.00 5047.20i −0.372602 0.645366i
\(395\) 360.500 624.404i 0.0459208 0.0795372i
\(396\) 0 0
\(397\) 5491.50 + 9511.56i 0.694233 + 1.20245i 0.970439 + 0.241348i \(0.0775896\pi\)
−0.276206 + 0.961099i \(0.589077\pi\)
\(398\) 6678.00 0.841050
\(399\) 0 0
\(400\) 1216.00 0.152000
\(401\) 3301.50 + 5718.37i 0.411145 + 0.712124i 0.995015 0.0997232i \(-0.0317957\pi\)
−0.583870 + 0.811847i \(0.698462\pi\)
\(402\) 0 0
\(403\) 1029.00 1782.28i 0.127191 0.220302i
\(404\) 2758.00 + 4777.00i 0.339643 + 0.588278i
\(405\) 0 0
\(406\) 0 0
\(407\) 1095.00 0.133359
\(408\) 0 0
\(409\) 5477.50 9487.31i 0.662213 1.14699i −0.317820 0.948151i \(-0.602951\pi\)
0.980033 0.198835i \(-0.0637158\pi\)
\(410\) 2450.00 4243.52i 0.295114 0.511153i
\(411\) 0 0
\(412\) −2716.00 −0.324776
\(413\) 0 0
\(414\) 0 0
\(415\) −3822.00 6619.90i −0.452083 0.783031i
\(416\) 1120.00 1939.90i 0.132001 0.228633i
\(417\) 0 0
\(418\) −245.000 424.352i −0.0286683 0.0496549i
\(419\) 6636.00 0.773723 0.386861 0.922138i \(-0.373559\pi\)
0.386861 + 0.922138i \(0.373559\pi\)
\(420\) 0 0
\(421\) −16630.0 −1.92517 −0.962585 0.270980i \(-0.912652\pi\)
−0.962585 + 0.270980i \(0.912652\pi\)
\(422\) 1780.00 + 3083.05i 0.205329 + 0.355641i
\(423\) 0 0
\(424\) 3636.00 6297.74i 0.416462 0.721333i
\(425\) −798.000 1382.18i −0.0910793 0.157754i
\(426\) 0 0
\(427\) 0 0
\(428\) 1828.00 0.206448
\(429\) 0 0
\(430\) −868.000 + 1503.42i −0.0973458 + 0.168608i
\(431\) 2461.50 4263.44i 0.275096 0.476480i −0.695064 0.718948i \(-0.744624\pi\)
0.970159 + 0.242468i \(0.0779571\pi\)
\(432\) 0 0
\(433\) −8974.00 −0.995988 −0.497994 0.867180i \(-0.665930\pi\)
−0.497994 + 0.867180i \(0.665930\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2250.00 3897.11i −0.247146 0.428069i
\(437\) 3895.50 6747.20i 0.426423 0.738587i
\(438\) 0 0
\(439\) −2089.50 3619.12i −0.227167 0.393465i 0.729800 0.683660i \(-0.239613\pi\)
−0.956967 + 0.290195i \(0.906280\pi\)
\(440\) 840.000 0.0910123
\(441\) 0 0
\(442\) 588.000 0.0632767
\(443\) −6463.50 11195.1i −0.693206 1.20067i −0.970782 0.239964i \(-0.922864\pi\)
0.277576 0.960704i \(-0.410469\pi\)
\(444\) 0 0
\(445\) 1151.50 1994.46i 0.122666 0.212464i
\(446\) 1400.00 + 2424.87i 0.148637 + 0.257446i
\(447\) 0 0
\(448\) 0 0
\(449\) 2826.00 0.297032 0.148516 0.988910i \(-0.452550\pi\)
0.148516 + 0.988910i \(0.452550\pi\)
\(450\) 0 0
\(451\) −875.000 + 1515.54i −0.0913573 + 0.158235i
\(452\) 3076.00 5327.79i 0.320095 0.554421i
\(453\) 0 0
\(454\) 4410.00 0.455884
\(455\) 0 0
\(456\) 0 0
\(457\) −4239.50 7343.03i −0.433951 0.751625i 0.563259 0.826281i \(-0.309547\pi\)
−0.997209 + 0.0746560i \(0.976214\pi\)
\(458\) −287.000 + 497.099i −0.0292808 + 0.0507159i
\(459\) 0 0
\(460\) 2226.00 + 3855.55i 0.225626 + 0.390795i
\(461\) 9338.00 0.943414 0.471707 0.881755i \(-0.343638\pi\)
0.471707 + 0.881755i \(0.343638\pi\)
\(462\) 0 0
\(463\) −4016.00 −0.403109 −0.201554 0.979477i \(-0.564599\pi\)
−0.201554 + 0.979477i \(0.564599\pi\)
\(464\) −464.000 803.672i −0.0464238 0.0804084i
\(465\) 0 0
\(466\) −4587.00 + 7944.92i −0.455984 + 0.789788i
\(467\) 2929.50 + 5074.04i 0.290281 + 0.502781i 0.973876 0.227080i \(-0.0729180\pi\)
−0.683595 + 0.729861i \(0.739585\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −7350.00 −0.721341
\(471\) 0 0
\(472\) 1260.00 2182.38i 0.122873 0.212823i
\(473\) 310.000 536.936i 0.0301349 0.0521952i
\(474\) 0 0
\(475\) 3724.00 0.359724
\(476\) 0 0
\(477\) 0 0
\(478\) −1668.00 2889.06i −0.159608 0.276449i
\(479\) −3251.50 + 5631.76i −0.310156 + 0.537206i −0.978396 0.206740i \(-0.933715\pi\)
0.668240 + 0.743946i \(0.267048\pi\)
\(480\) 0 0
\(481\) −1533.00 2655.23i −0.145320 0.251701i
\(482\) −6818.00 −0.644297
\(483\) 0 0
\(484\) 5224.00 0.490609
\(485\) −3087.00 5346.84i −0.289017 0.500593i
\(486\) 0 0
\(487\) 8024.50 13898.8i 0.746663 1.29326i −0.202751 0.979230i \(-0.564988\pi\)
0.949414 0.314028i \(-0.101678\pi\)
\(488\) −4956.00 8584.04i −0.459729 0.796273i
\(489\) 0 0
\(490\) 0 0
\(491\) −8864.00 −0.814718 −0.407359 0.913268i \(-0.633550\pi\)
−0.407359 + 0.913268i \(0.633550\pi\)
\(492\) 0 0
\(493\) −609.000 + 1054.82i −0.0556348 + 0.0963624i
\(494\) −686.000 + 1188.19i −0.0624789 + 0.108217i
\(495\) 0 0
\(496\) 2352.00 0.212919
\(497\) 0 0
\(498\) 0 0
\(499\) 5105.50 + 8842.99i 0.458023 + 0.793319i 0.998856 0.0478104i \(-0.0152243\pi\)
−0.540833 + 0.841130i \(0.681891\pi\)
\(500\) −2814.00 + 4873.99i −0.251692 + 0.435943i
\(501\) 0 0
\(502\) −4760.00 8244.56i −0.423206 0.733014i
\(503\) −1680.00 −0.148921 −0.0744607 0.997224i \(-0.523724\pi\)
−0.0744607 + 0.997224i \(0.523724\pi\)
\(504\) 0 0
\(505\) 9653.00 0.850600
\(506\) 795.000 + 1376.98i 0.0698460 + 0.120977i
\(507\) 0 0
\(508\) 144.000 249.415i 0.0125767 0.0217835i
\(509\) 4728.50 + 8190.00i 0.411762 + 0.713193i 0.995083 0.0990489i \(-0.0315800\pi\)
−0.583320 + 0.812242i \(0.698247\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 5632.00 0.486136
\(513\) 0 0
\(514\) −805.000 + 1394.30i −0.0690798 + 0.119650i
\(515\) −2376.50 + 4116.22i −0.203342 + 0.352199i
\(516\) 0 0
\(517\) 2625.00 0.223302
\(518\) 0 0
\(519\) 0 0
\(520\) −1176.00 2036.89i −0.0991750 0.171776i
\(521\) 9040.50 15658.6i 0.760214 1.31673i −0.182526 0.983201i \(-0.558427\pi\)
0.942740 0.333528i \(-0.108239\pi\)
\(522\) 0 0
\(523\) 10188.5 + 17647.0i 0.851839 + 1.47543i 0.879546 + 0.475813i \(0.157846\pi\)
−0.0277071 + 0.999616i \(0.508821\pi\)
\(524\) −8596.00 −0.716637
\(525\) 0 0
\(526\) −514.000 −0.0426073
\(527\) −1543.50 2673.42i −0.127582 0.220979i
\(528\) 0 0
\(529\) −6557.00 + 11357.1i −0.538917 + 0.933431i
\(530\) −2121.00 3673.68i −0.173831 0.301084i
\(531\) 0 0
\(532\) 0 0
\(533\) 4900.00 0.398204
\(534\) 0 0
\(535\) 1599.50 2770.42i 0.129257 0.223879i
\(536\) −4980.00 + 8625.61i −0.401312 + 0.695093i
\(537\) 0 0
\(538\) −7182.00 −0.575535
\(539\) 0 0
\(540\) 0 0
\(541\) 3096.50 + 5363.30i 0.246079 + 0.426222i 0.962435 0.271514i \(-0.0875243\pi\)
−0.716355 + 0.697736i \(0.754191\pi\)
\(542\) −1393.00 + 2412.75i −0.110396 + 0.191211i
\(543\) 0 0
\(544\) −1680.00 2909.85i −0.132407 0.229336i
\(545\) −7875.00 −0.618950
\(546\) 0 0
\(547\) −18464.0 −1.44326 −0.721630 0.692279i \(-0.756607\pi\)
−0.721630 + 0.692279i \(0.756607\pi\)
\(548\) 2250.00 + 3897.11i 0.175393 + 0.303789i
\(549\) 0 0
\(550\) −380.000 + 658.179i −0.0294605 + 0.0510270i
\(551\) −1421.00 2461.24i −0.109867 0.190295i
\(552\) 0 0
\(553\) 0 0
\(554\) −830.000 −0.0636522
\(555\) 0 0
\(556\) −504.000 + 872.954i −0.0384431 + 0.0665854i
\(557\) −4706.50 + 8151.90i −0.358027 + 0.620120i −0.987631 0.156796i \(-0.949884\pi\)
0.629604 + 0.776916i \(0.283217\pi\)
\(558\) 0 0
\(559\) −1736.00 −0.131351
\(560\) 0 0
\(561\) 0 0
\(562\) 4954.00 + 8580.58i 0.371836 + 0.644039i
\(563\) −1599.50 + 2770.42i −0.119735 + 0.207387i −0.919663 0.392709i \(-0.871538\pi\)
0.799928 + 0.600097i \(0.204871\pi\)
\(564\) 0 0
\(565\) −5383.00 9323.63i −0.400822 0.694244i
\(566\) −8554.00 −0.635250
\(567\) 0 0
\(568\) 10368.0 0.765901
\(569\) 10791.5 + 18691.4i 0.795085 + 1.37713i 0.922785 + 0.385314i \(0.125907\pi\)
−0.127701 + 0.991813i \(0.540760\pi\)
\(570\) 0 0
\(571\) −10133.5 + 17551.7i −0.742686 + 1.28637i 0.208582 + 0.978005i \(0.433115\pi\)
−0.951268 + 0.308365i \(0.900218\pi\)
\(572\) 140.000 + 242.487i 0.0102337 + 0.0177253i
\(573\) 0 0
\(574\) 0 0
\(575\) −12084.0 −0.876413
\(576\) 0 0
\(577\) 6975.50 12081.9i 0.503282 0.871710i −0.496711 0.867916i \(-0.665459\pi\)
0.999993 0.00379418i \(-0.00120773\pi\)
\(578\) −4472.00 + 7745.73i −0.321818 + 0.557405i
\(579\) 0 0
\(580\) 1624.00 0.116264
\(581\) 0 0
\(582\) 0 0
\(583\) 757.500 + 1312.03i 0.0538121 + 0.0932053i
\(584\) −13356.0 + 23133.3i −0.946362 + 1.63915i
\(585\) 0 0
\(586\) 7742.00 + 13409.5i 0.545766 + 0.945295i
\(587\) −20972.0 −1.47463 −0.737314 0.675550i \(-0.763906\pi\)
−0.737314 + 0.675550i \(0.763906\pi\)
\(588\) 0 0
\(589\) 7203.00 0.503895
\(590\) −735.000 1273.06i −0.0512872 0.0888321i
\(591\) 0 0
\(592\) 1752.00 3034.55i 0.121633 0.210675i
\(593\) 94.5000 + 163.679i 0.00654410 + 0.0113347i 0.869279 0.494322i \(-0.164584\pi\)
−0.862735 + 0.505657i \(0.831250\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −804.000 −0.0552569
\(597\) 0 0
\(598\) 2226.00 3855.55i 0.152221 0.263654i
\(599\) −5140.50 + 8903.61i −0.350643 + 0.607331i −0.986362 0.164589i \(-0.947370\pi\)
0.635719 + 0.771920i \(0.280704\pi\)
\(600\) 0 0
\(601\) 6090.00 0.413338 0.206669 0.978411i \(-0.433738\pi\)
0.206669 + 0.978411i \(0.433738\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3238.00 + 5608.38i 0.218133 + 0.377817i
\(605\) 4571.00 7917.20i 0.307170 0.532033i
\(606\) 0 0
\(607\) 2474.50 + 4285.96i 0.165464 + 0.286593i 0.936820 0.349812i \(-0.113754\pi\)
−0.771356 + 0.636404i \(0.780421\pi\)
\(608\) 7840.00 0.522951
\(609\) 0 0
\(610\) −5782.00 −0.383781
\(611\) −3675.00 6365.29i −0.243330 0.421460i
\(612\) 0 0
\(613\) 7898.50 13680.6i 0.520420 0.901394i −0.479298 0.877652i \(-0.659109\pi\)
0.999718 0.0237416i \(-0.00755791\pi\)
\(614\) 7364.00 + 12754.8i 0.484018 + 0.838343i
\(615\) 0 0
\(616\) 0 0
\(617\) 9378.00 0.611903 0.305951 0.952047i \(-0.401025\pi\)
0.305951 + 0.952047i \(0.401025\pi\)
\(618\) 0 0
\(619\) −12176.5 + 21090.3i −0.790654 + 1.36945i 0.134908 + 0.990858i \(0.456926\pi\)
−0.925562 + 0.378595i \(0.876407\pi\)
\(620\) −2058.00 + 3564.56i −0.133308 + 0.230897i
\(621\) 0 0
\(622\) −19950.0 −1.28605
\(623\) 0 0
\(624\) 0 0
\(625\) 174.500 + 302.243i 0.0111680 + 0.0193435i
\(626\) 4753.00 8232.44i 0.303463 0.525614i
\(627\) 0 0
\(628\) −1358.00 2352.12i −0.0862900 0.149459i
\(629\) −4599.00 −0.291533
\(630\) 0 0
\(631\) −12640.0 −0.797449 −0.398725 0.917071i \(-0.630547\pi\)
−0.398725 + 0.917071i \(0.630547\pi\)
\(632\) 1236.00 + 2140.81i 0.0777934 + 0.134742i
\(633\) 0 0
\(634\) 3477.00 6022.34i 0.217806 0.377252i
\(635\) −252.000 436.477i −0.0157485 0.0272772i
\(636\) 0 0
\(637\) 0 0
\(638\) 580.000 0.0359913
\(639\) 0 0
\(640\) −1344.00 + 2327.88i −0.0830098 + 0.143777i
\(641\) −520.500 + 901.532i −0.0320726 + 0.0555513i −0.881616 0.471967i \(-0.843544\pi\)
0.849544 + 0.527518i \(0.176877\pi\)
\(642\) 0 0
\(643\) −9548.00 −0.585593 −0.292797 0.956175i \(-0.594586\pi\)
−0.292797 + 0.956175i \(0.594586\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1029.00 + 1782.28i 0.0626710 + 0.108549i
\(647\) 1620.50 2806.79i 0.0984674 0.170551i −0.812583 0.582845i \(-0.801939\pi\)
0.911050 + 0.412295i \(0.135273\pi\)
\(648\) 0 0
\(649\) 262.500 + 454.663i 0.0158768 + 0.0274994i
\(650\) 2128.00 0.128411
\(651\) 0 0
\(652\) 1868.00 0.112203
\(653\) −4426.50 7666.92i −0.265272 0.459464i 0.702363 0.711819i \(-0.252128\pi\)
−0.967635 + 0.252355i \(0.918795\pi\)
\(654\) 0 0
\(655\) −7521.50 + 13027.6i −0.448686 + 0.777147i
\(656\) 2800.00 + 4849.74i 0.166649 + 0.288644i
\(657\) 0 0
\(658\) 0 0
\(659\) −7044.00 −0.416381 −0.208191 0.978088i \(-0.566757\pi\)
−0.208191 + 0.978088i \(0.566757\pi\)
\(660\) 0 0
\(661\) −6044.50 + 10469.4i −0.355679 + 0.616054i −0.987234 0.159277i \(-0.949084\pi\)
0.631555 + 0.775331i \(0.282417\pi\)
\(662\) 3341.00 5786.78i 0.196151 0.339743i
\(663\) 0 0
\(664\) 26208.0 1.53173
\(665\) 0 0
\(666\) 0 0
\(667\) 4611.00 + 7986.49i 0.267674 + 0.463625i
\(668\) 2408.00 4170.78i 0.139474 0.241575i
\(669\) 0 0
\(670\) 2905.00 + 5031.61i 0.167507 + 0.290131i
\(671\) 2065.00 0.118805
\(672\) 0 0
\(673\) 982.000 0.0562456 0.0281228 0.999604i \(-0.491047\pi\)
0.0281228 + 0.999604i \(0.491047\pi\)
\(674\) 7366.00 + 12758.3i 0.420961 + 0.729126i
\(675\) 0 0
\(676\) −4002.00 + 6931.67i −0.227697 + 0.394383i
\(677\) 15256.5 + 26425.0i 0.866108 + 1.50014i 0.865943 + 0.500143i \(0.166719\pi\)
0.000164659 1.00000i \(0.499948\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3528.00 −0.198960
\(681\) 0 0
\(682\) −735.000 + 1273.06i −0.0412677 + 0.0714778i
\(683\) 5737.50 9937.64i 0.321434 0.556740i −0.659350 0.751836i \(-0.729169\pi\)
0.980784 + 0.195096i \(0.0625019\pi\)
\(684\) 0 0
\(685\) 7875.00 0.439253
\(686\) 0 0
\(687\) 0 0
\(688\) −992.000 1718.19i −0.0549704 0.0952116i
\(689\) 2121.00 3673.68i 0.117277 0.203129i
\(690\) 0 0
\(691\) −14157.5 24521.5i −0.779416 1.34999i −0.932279 0.361741i \(-0.882182\pi\)
0.152862 0.988248i \(-0.451151\pi\)
\(692\) 11284.0 0.619875
\(693\) 0 0
\(694\) 14830.0 0.811151
\(695\) 882.000 + 1527.67i 0.0481384 + 0.0833781i
\(696\) 0 0
\(697\) 3675.00 6365.29i 0.199714 0.345915i
\(698\) 3878.00 + 6716.89i 0.210293 + 0.364238i
\(699\) 0 0
\(700\) 0 0
\(701\) −10614.0 −0.571876 −0.285938 0.958248i \(-0.592305\pi\)
−0.285938 + 0.958248i \(0.592305\pi\)
\(702\) 0 0
\(703\) 5365.50 9293.32i 0.287857 0.498583i
\(704\) −1120.00 + 1939.90i −0.0599596 + 0.103853i
\(705\) 0 0
\(706\) −2534.00 −0.135083
\(707\) 0 0
\(708\) 0 0
\(709\) −5149.50 8919.20i −0.272769 0.472451i 0.696801 0.717265i \(-0.254606\pi\)
−0.969570 + 0.244814i \(0.921273\pi\)
\(710\) 3024.00 5237.72i 0.159843 0.276857i
\(711\) 0 0
\(712\) 3948.00 + 6838.14i 0.207806 + 0.359930i
\(713\) −23373.0 −1.22767
\(714\) 0 0
\(715\) 490.000 0.0256293
\(716\) 6506.00 + 11268.7i 0.339582 + 0.588173i
\(717\) 0 0
\(718\) −4685.00 + 8114.66i −0.243513 + 0.421778i
\(719\) −16264.5 28170.9i −0.843621 1.46119i −0.886813 0.462128i \(-0.847086\pi\)
0.0431924 0.999067i \(-0.486247\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 8916.00 0.459583
\(723\) 0 0
\(724\) −3164.00 + 5480.21i −0.162416 + 0.281313i
\(725\) −2204.00 + 3817.44i −0.112903 + 0.195553i
\(726\) 0 0
\(727\) −29456.0 −1.50270 −0.751350 0.659904i \(-0.770597\pi\)
−0.751350 + 0.659904i \(0.770597\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7791.00 + 13494.4i 0.395011 + 0.684179i
\(731\) −1302.00 + 2255.13i −0.0658772 + 0.114103i
\(732\) 0 0
\(733\) 13933.5 + 24133.5i 0.702109 + 1.21609i 0.967725 + 0.252009i \(0.0810912\pi\)
−0.265616 + 0.964079i \(0.585575\pi\)
\(734\) −9282.00 −0.466764
\(735\) 0 0
\(736\) −25440.0 −1.27409
\(737\) −1037.50 1797.00i −0.0518546 0.0898147i
\(738\) 0 0
\(739\) −9769.50 + 16921.3i −0.486302 + 0.842299i −0.999876 0.0157460i \(-0.994988\pi\)
0.513574 + 0.858045i \(0.328321\pi\)
\(740\) 3066.00 + 5310.47i 0.152309 + 0.263806i
\(741\) 0 0
\(742\) 0 0
\(743\) −1248.00 −0.0616214 −0.0308107 0.999525i \(-0.509809\pi\)
−0.0308107 + 0.999525i \(0.509809\pi\)
\(744\) 0 0
\(745\) −703.500 + 1218.50i −0.0345963 + 0.0599226i
\(746\) −8797.00 + 15236.9i −0.431744 + 0.747803i
\(747\) 0 0
\(748\) 420.000 0.0205304
\(749\) 0 0
\(750\) 0 0
\(751\) −14046.5 24329.3i −0.682509 1.18214i −0.974213 0.225631i \(-0.927556\pi\)
0.291704 0.956509i \(-0.405778\pi\)
\(752\) 4200.00 7274.61i 0.203668 0.352763i
\(753\) 0 0
\(754\) −812.000 1406.43i −0.0392192 0.0679297i
\(755\) 11333.0 0.546292
\(756\) 0 0
\(757\) 35954.0 1.72625 0.863124 0.504991i \(-0.168504\pi\)
0.863124 + 0.504991i \(0.168504\pi\)
\(758\) 13680.0 + 23694.5i 0.655514 + 1.13538i
\(759\) 0 0
\(760\) 4116.00 7129.12i 0.196451 0.340264i
\(761\) 430.500 + 745.648i 0.0205067 + 0.0355187i 0.876097 0.482136i \(-0.160139\pi\)
−0.855590 + 0.517654i \(0.826805\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 10228.0 0.484340
\(765\) 0 0
\(766\) 9765.00 16913.5i 0.460605 0.797792i
\(767\) 735.000 1273.06i 0.0346014 0.0599315i
\(768\) 0 0
\(769\) −24710.0 −1.15873 −0.579366 0.815067i \(-0.696700\pi\)
−0.579366 + 0.815067i \(0.696700\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −794.000 1375.25i −0.0370164 0.0641143i
\(773\) −8249.50 + 14288.6i −0.383847 + 0.664843i −0.991609 0.129277i \(-0.958734\pi\)
0.607761 + 0.794120i \(0.292068\pi\)
\(774\) 0 0
\(775\) −5586.00 9675.24i −0.258910 0.448445i
\(776\) 21168.0 0.979236
\(777\) 0 0
\(778\) 3462.00 0.159536
\(779\) 8575.00 + 14852.3i 0.394392 + 0.683107i
\(780\) 0 0
\(781\) −1080.00 + 1870.61i −0.0494820 + 0.0857053i
\(782\) −3339.00 5783.32i −0.152688 0.264464i
\(783\) 0 0
\(784\) 0 0
\(785\) −4753.00 −0.216104
\(786\) 0 0
\(787\) 8235.50 14264.3i 0.373016 0.646083i −0.617012 0.786954i \(-0.711657\pi\)
0.990028 + 0.140871i \(0.0449902\pi\)
\(788\) −5828.00 + 10094.4i −0.263469 + 0.456342i
\(789\) 0 0
\(790\) 1442.00 0.0649418
\(791\) 0