Properties

Label 882.4.g.bf.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
Defining polynomial: \(x^{4} - x^{3} + 337 x^{2} + 336 x + 112896\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(9.41856 + 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.bf.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-10.4186 - 18.0455i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-10.4186 - 18.0455i) q^{5} -8.00000 q^{8} +(20.8371 - 36.0910i) q^{10} +(7.58144 - 13.1314i) q^{11} -2.16288 q^{13} +(-8.00000 - 13.8564i) q^{16} +(59.6742 - 103.359i) q^{17} +(-16.7557 - 29.0217i) q^{19} +83.3485 q^{20} +30.3258 q^{22} +(0.325758 + 0.564230i) q^{23} +(-154.593 + 267.763i) q^{25} +(-2.16288 - 3.74622i) q^{26} +163.208 q^{29} +(-111.663 + 193.406i) q^{31} +(16.0000 - 27.7128i) q^{32} +238.697 q^{34} +(-84.2670 - 145.955i) q^{37} +(33.5114 - 58.0434i) q^{38} +(83.3485 + 144.364i) q^{40} -323.023 q^{41} +221.557 q^{43} +(30.3258 + 52.5258i) q^{44} +(-0.651517 + 1.12846i) q^{46} +(-254.023 - 439.980i) q^{47} -618.371 q^{50} +(4.32576 - 7.49243i) q^{52} +(-88.2557 + 152.863i) q^{53} -315.951 q^{55} +(163.208 + 282.685i) q^{58} +(-227.464 + 393.979i) q^{59} +(19.3258 + 33.4732i) q^{61} -446.652 q^{62} +64.0000 q^{64} +(22.5341 + 39.0302i) q^{65} +(-70.8958 + 122.795i) q^{67} +(238.697 + 413.435i) q^{68} -602.742 q^{71} +(-551.150 + 954.619i) q^{73} +(168.534 - 291.910i) q^{74} +134.045 q^{76} +(58.1515 + 100.721i) q^{79} +(-166.697 + 288.728i) q^{80} +(-323.023 - 559.492i) q^{82} -568.928 q^{83} -2486.88 q^{85} +(221.557 + 383.748i) q^{86} +(-60.6515 + 105.052i) q^{88} +(191.580 + 331.825i) q^{89} -2.60607 q^{92} +(508.045 - 879.961i) q^{94} +(-349.140 + 604.728i) q^{95} -334.701 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} - 5q^{5} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} - 5q^{5} - 32q^{8} + 10q^{10} + 67q^{11} - 82q^{13} - 32q^{16} + 92q^{17} + 43q^{19} + 40q^{20} + 268q^{22} + 148q^{23} - 435q^{25} - 82q^{26} - 154q^{29} - 520q^{31} + 64q^{32} + 368q^{34} - 7q^{37} - 86q^{38} + 40q^{40} - 852q^{41} - 214q^{43} + 268q^{44} - 296q^{46} - 576q^{47} - 1740q^{50} + 164q^{52} - 243q^{53} + 1010q^{55} - 154q^{58} + 7q^{59} + 224q^{61} - 2080q^{62} + 256q^{64} - 570q^{65} - 687q^{67} + 368q^{68} - 944q^{71} - 921q^{73} + 14q^{74} - 344q^{76} + 526q^{79} - 80q^{80} - 852q^{82} - 442q^{83} - 5840q^{85} - 214q^{86} - 536q^{88} - 774q^{89} - 1184q^{92} + 1152q^{94} - 1910q^{95} - 3906q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −10.4186 18.0455i −0.931864 1.61404i −0.780132 0.625615i \(-0.784848\pi\)
−0.151732 0.988422i \(-0.548485\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) 20.8371 36.0910i 0.658928 1.14130i
\(11\) 7.58144 13.1314i 0.207808 0.359934i −0.743216 0.669052i \(-0.766700\pi\)
0.951024 + 0.309118i \(0.100034\pi\)
\(12\) 0 0
\(13\) −2.16288 −0.0461442 −0.0230721 0.999734i \(-0.507345\pi\)
−0.0230721 + 0.999734i \(0.507345\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 59.6742 103.359i 0.851361 1.47460i −0.0286202 0.999590i \(-0.509111\pi\)
0.879981 0.475009i \(-0.157555\pi\)
\(18\) 0 0
\(19\) −16.7557 29.0217i −0.202317 0.350423i 0.746958 0.664871i \(-0.231514\pi\)
−0.949274 + 0.314449i \(0.898180\pi\)
\(20\) 83.3485 0.931864
\(21\) 0 0
\(22\) 30.3258 0.293885
\(23\) 0.325758 + 0.564230i 0.00295327 + 0.00511522i 0.867498 0.497440i \(-0.165727\pi\)
−0.864545 + 0.502555i \(0.832393\pi\)
\(24\) 0 0
\(25\) −154.593 + 267.763i −1.23674 + 2.14210i
\(26\) −2.16288 3.74622i −0.0163144 0.0282574i
\(27\) 0 0
\(28\) 0 0
\(29\) 163.208 1.04507 0.522535 0.852618i \(-0.324986\pi\)
0.522535 + 0.852618i \(0.324986\pi\)
\(30\) 0 0
\(31\) −111.663 + 193.406i −0.646943 + 1.12054i 0.336906 + 0.941538i \(0.390620\pi\)
−0.983849 + 0.179000i \(0.942714\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 238.697 1.20401
\(35\) 0 0
\(36\) 0 0
\(37\) −84.2670 145.955i −0.374417 0.648509i 0.615823 0.787885i \(-0.288824\pi\)
−0.990240 + 0.139376i \(0.955490\pi\)
\(38\) 33.5114 58.0434i 0.143059 0.247786i
\(39\) 0 0
\(40\) 83.3485 + 144.364i 0.329464 + 0.570648i
\(41\) −323.023 −1.23043 −0.615216 0.788359i \(-0.710931\pi\)
−0.615216 + 0.788359i \(0.710931\pi\)
\(42\) 0 0
\(43\) 221.557 0.785746 0.392873 0.919593i \(-0.371481\pi\)
0.392873 + 0.919593i \(0.371481\pi\)
\(44\) 30.3258 + 52.5258i 0.103904 + 0.179967i
\(45\) 0 0
\(46\) −0.651517 + 1.12846i −0.00208828 + 0.00361701i
\(47\) −254.023 439.980i −0.788362 1.36548i −0.926970 0.375136i \(-0.877596\pi\)
0.138608 0.990347i \(-0.455737\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −618.371 −1.74902
\(51\) 0 0
\(52\) 4.32576 7.49243i 0.0115361 0.0199810i
\(53\) −88.2557 + 152.863i −0.228733 + 0.396177i −0.957433 0.288656i \(-0.906792\pi\)
0.728700 + 0.684833i \(0.240125\pi\)
\(54\) 0 0
\(55\) −315.951 −0.774596
\(56\) 0 0
\(57\) 0 0
\(58\) 163.208 + 282.685i 0.369488 + 0.639972i
\(59\) −227.464 + 393.979i −0.501920 + 0.869351i 0.498077 + 0.867133i \(0.334040\pi\)
−0.999998 + 0.00221868i \(0.999294\pi\)
\(60\) 0 0
\(61\) 19.3258 + 33.4732i 0.0405641 + 0.0702591i 0.885595 0.464459i \(-0.153751\pi\)
−0.845031 + 0.534718i \(0.820418\pi\)
\(62\) −446.652 −0.914916
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 22.5341 + 39.0302i 0.0430001 + 0.0744784i
\(66\) 0 0
\(67\) −70.8958 + 122.795i −0.129273 + 0.223908i −0.923395 0.383851i \(-0.874598\pi\)
0.794122 + 0.607758i \(0.207931\pi\)
\(68\) 238.697 + 413.435i 0.425680 + 0.737300i
\(69\) 0 0
\(70\) 0 0
\(71\) −602.742 −1.00750 −0.503749 0.863850i \(-0.668046\pi\)
−0.503749 + 0.863850i \(0.668046\pi\)
\(72\) 0 0
\(73\) −551.150 + 954.619i −0.883660 + 1.53054i −0.0364183 + 0.999337i \(0.511595\pi\)
−0.847242 + 0.531207i \(0.821738\pi\)
\(74\) 168.534 291.910i 0.264753 0.458565i
\(75\) 0 0
\(76\) 134.045 0.202317
\(77\) 0 0
\(78\) 0 0
\(79\) 58.1515 + 100.721i 0.0828172 + 0.143444i 0.904459 0.426561i \(-0.140275\pi\)
−0.821642 + 0.570004i \(0.806942\pi\)
\(80\) −166.697 + 288.728i −0.232966 + 0.403509i
\(81\) 0 0
\(82\) −323.023 559.492i −0.435023 0.753482i
\(83\) −568.928 −0.752385 −0.376193 0.926542i \(-0.622767\pi\)
−0.376193 + 0.926542i \(0.622767\pi\)
\(84\) 0 0
\(85\) −2486.88 −3.17341
\(86\) 221.557 + 383.748i 0.277803 + 0.481169i
\(87\) 0 0
\(88\) −60.6515 + 105.052i −0.0734713 + 0.127256i
\(89\) 191.580 + 331.825i 0.228173 + 0.395207i 0.957267 0.289207i \(-0.0933915\pi\)
−0.729094 + 0.684414i \(0.760058\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.60607 −0.00295327
\(93\) 0 0
\(94\) 508.045 879.961i 0.557456 0.965543i
\(95\) −349.140 + 604.728i −0.377063 + 0.653093i
\(96\) 0 0
\(97\) −334.701 −0.350348 −0.175174 0.984538i \(-0.556049\pi\)
−0.175174 + 0.984538i \(0.556049\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −618.371 1071.05i −0.618371 1.07105i
\(101\) 7.37121 12.7673i 0.00726201 0.0125782i −0.862372 0.506276i \(-0.831022\pi\)
0.869634 + 0.493698i \(0.164355\pi\)
\(102\) 0 0
\(103\) −420.710 728.691i −0.402464 0.697088i 0.591559 0.806262i \(-0.298513\pi\)
−0.994023 + 0.109174i \(0.965180\pi\)
\(104\) 17.3030 0.0163144
\(105\) 0 0
\(106\) −353.023 −0.323477
\(107\) −357.835 619.789i −0.323301 0.559974i 0.657866 0.753135i \(-0.271459\pi\)
−0.981167 + 0.193161i \(0.938126\pi\)
\(108\) 0 0
\(109\) −300.009 + 519.632i −0.263630 + 0.456621i −0.967204 0.254001i \(-0.918253\pi\)
0.703574 + 0.710622i \(0.251587\pi\)
\(110\) −315.951 547.243i −0.273861 0.474341i
\(111\) 0 0
\(112\) 0 0
\(113\) −622.644 −0.518349 −0.259174 0.965831i \(-0.583450\pi\)
−0.259174 + 0.965831i \(0.583450\pi\)
\(114\) 0 0
\(115\) 6.78787 11.7569i 0.00550410 0.00953339i
\(116\) −326.417 + 565.370i −0.261267 + 0.452529i
\(117\) 0 0
\(118\) −909.856 −0.709822
\(119\) 0 0
\(120\) 0 0
\(121\) 550.544 + 953.569i 0.413632 + 0.716431i
\(122\) −38.6515 + 66.9464i −0.0286831 + 0.0496807i
\(123\) 0 0
\(124\) −446.652 773.623i −0.323472 0.560269i
\(125\) 3837.90 2.74618
\(126\) 0 0
\(127\) −180.076 −0.125820 −0.0629100 0.998019i \(-0.520038\pi\)
−0.0629100 + 0.998019i \(0.520038\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −45.0682 + 78.0604i −0.0304057 + 0.0526642i
\(131\) −108.930 188.672i −0.0726508 0.125835i 0.827411 0.561596i \(-0.189813\pi\)
−0.900062 + 0.435761i \(0.856479\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −283.583 −0.182820
\(135\) 0 0
\(136\) −477.394 + 826.871i −0.301001 + 0.521350i
\(137\) −1300.93 + 2253.27i −0.811283 + 1.40518i 0.100683 + 0.994919i \(0.467897\pi\)
−0.911966 + 0.410265i \(0.865436\pi\)
\(138\) 0 0
\(139\) 2651.55 1.61800 0.808998 0.587811i \(-0.200010\pi\)
0.808998 + 0.587811i \(0.200010\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −602.742 1043.98i −0.356204 0.616964i
\(143\) −16.3977 + 28.4017i −0.00958914 + 0.0166089i
\(144\) 0 0
\(145\) −1700.40 2945.17i −0.973863 1.68678i
\(146\) −2204.60 −1.24968
\(147\) 0 0
\(148\) 674.136 0.374417
\(149\) 290.511 + 503.180i 0.159729 + 0.276659i 0.934771 0.355251i \(-0.115605\pi\)
−0.775042 + 0.631910i \(0.782271\pi\)
\(150\) 0 0
\(151\) 307.695 532.943i 0.165827 0.287221i −0.771122 0.636688i \(-0.780304\pi\)
0.936949 + 0.349467i \(0.113637\pi\)
\(152\) 134.045 + 232.174i 0.0715297 + 0.123893i
\(153\) 0 0
\(154\) 0 0
\(155\) 4653.47 2.41145
\(156\) 0 0
\(157\) −153.466 + 265.811i −0.0780122 + 0.135121i −0.902392 0.430916i \(-0.858191\pi\)
0.824380 + 0.566037i \(0.191524\pi\)
\(158\) −116.303 + 201.443i −0.0585606 + 0.101430i
\(159\) 0 0
\(160\) −666.788 −0.329464
\(161\) 0 0
\(162\) 0 0
\(163\) −1757.25 3043.65i −0.844408 1.46256i −0.886135 0.463428i \(-0.846619\pi\)
0.0417271 0.999129i \(-0.486714\pi\)
\(164\) 646.045 1118.98i 0.307608 0.532792i
\(165\) 0 0
\(166\) −568.928 985.412i −0.266008 0.460740i
\(167\) 1123.30 0.520502 0.260251 0.965541i \(-0.416195\pi\)
0.260251 + 0.965541i \(0.416195\pi\)
\(168\) 0 0
\(169\) −2192.32 −0.997871
\(170\) −2486.88 4307.40i −1.12197 1.94331i
\(171\) 0 0
\(172\) −443.114 + 767.495i −0.196437 + 0.340238i
\(173\) −765.299 1325.54i −0.336327 0.582536i 0.647412 0.762141i \(-0.275852\pi\)
−0.983739 + 0.179605i \(0.942518\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −242.606 −0.103904
\(177\) 0 0
\(178\) −383.159 + 663.651i −0.161343 + 0.279454i
\(179\) 1706.72 2956.12i 0.712659 1.23436i −0.251197 0.967936i \(-0.580824\pi\)
0.963856 0.266425i \(-0.0858426\pi\)
\(180\) 0 0
\(181\) −1286.71 −0.528399 −0.264200 0.964468i \(-0.585108\pi\)
−0.264200 + 0.964468i \(0.585108\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.60607 4.51384i −0.00104414 0.00180850i
\(185\) −1755.88 + 3041.28i −0.697811 + 1.20864i
\(186\) 0 0
\(187\) −904.833 1567.22i −0.353839 0.612868i
\(188\) 2032.18 0.788362
\(189\) 0 0
\(190\) −1396.56 −0.533248
\(191\) 527.648 + 913.913i 0.199891 + 0.346222i 0.948493 0.316798i \(-0.102608\pi\)
−0.748602 + 0.663020i \(0.769274\pi\)
\(192\) 0 0
\(193\) 2385.42 4131.67i 0.889670 1.54095i 0.0494044 0.998779i \(-0.484268\pi\)
0.840266 0.542175i \(-0.182399\pi\)
\(194\) −334.701 579.719i −0.123867 0.214543i
\(195\) 0 0
\(196\) 0 0
\(197\) −1622.31 −0.586725 −0.293363 0.956001i \(-0.594774\pi\)
−0.293363 + 0.956001i \(0.594774\pi\)
\(198\) 0 0
\(199\) −1775.07 + 3074.51i −0.632318 + 1.09521i 0.354759 + 0.934958i \(0.384563\pi\)
−0.987077 + 0.160249i \(0.948770\pi\)
\(200\) 1236.74 2142.10i 0.437254 0.757347i
\(201\) 0 0
\(202\) 29.4848 0.0102700
\(203\) 0 0
\(204\) 0 0
\(205\) 3365.43 + 5829.10i 1.14659 + 1.98596i
\(206\) 841.420 1457.38i 0.284585 0.492916i
\(207\) 0 0
\(208\) 17.3030 + 29.9697i 0.00576803 + 0.00999051i
\(209\) −508.129 −0.168172
\(210\) 0 0
\(211\) 4653.39 1.51826 0.759129 0.650941i \(-0.225625\pi\)
0.759129 + 0.650941i \(0.225625\pi\)
\(212\) −353.023 611.453i −0.114367 0.198089i
\(213\) 0 0
\(214\) 715.670 1239.58i 0.228609 0.395962i
\(215\) −2308.30 3998.10i −0.732209 1.26822i
\(216\) 0 0
\(217\) 0 0
\(218\) −1200.04 −0.372829
\(219\) 0 0
\(220\) 631.901 1094.49i 0.193649 0.335410i
\(221\) −129.068 + 223.553i −0.0392854 + 0.0680442i
\(222\) 0 0
\(223\) 4649.53 1.39621 0.698107 0.715993i \(-0.254026\pi\)
0.698107 + 0.715993i \(0.254026\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −622.644 1078.45i −0.183264 0.317423i
\(227\) −2075.86 + 3595.49i −0.606958 + 1.05128i 0.384780 + 0.923008i \(0.374277\pi\)
−0.991739 + 0.128274i \(0.959056\pi\)
\(228\) 0 0
\(229\) 2131.82 + 3692.41i 0.615172 + 1.06551i 0.990354 + 0.138558i \(0.0442468\pi\)
−0.375182 + 0.926951i \(0.622420\pi\)
\(230\) 27.1515 0.00778398
\(231\) 0 0
\(232\) −1305.67 −0.369488
\(233\) 1524.95 + 2641.29i 0.428768 + 0.742647i 0.996764 0.0803838i \(-0.0256146\pi\)
−0.567996 + 0.823031i \(0.692281\pi\)
\(234\) 0 0
\(235\) −5293.10 + 9167.92i −1.46929 + 2.54489i
\(236\) −909.856 1575.92i −0.250960 0.434676i
\(237\) 0 0
\(238\) 0 0
\(239\) −3987.20 −1.07912 −0.539562 0.841946i \(-0.681410\pi\)
−0.539562 + 0.841946i \(0.681410\pi\)
\(240\) 0 0
\(241\) −312.324 + 540.961i −0.0834795 + 0.144591i −0.904742 0.425959i \(-0.859937\pi\)
0.821263 + 0.570550i \(0.193270\pi\)
\(242\) −1101.09 + 1907.14i −0.292482 + 0.506593i
\(243\) 0 0
\(244\) −154.606 −0.0405641
\(245\) 0 0
\(246\) 0 0
\(247\) 36.2405 + 62.7704i 0.00933574 + 0.0161700i
\(248\) 893.303 1547.25i 0.228729 0.396170i
\(249\) 0 0
\(250\) 3837.90 + 6647.43i 0.970920 + 1.68168i
\(251\) −1328.78 −0.334152 −0.167076 0.985944i \(-0.553432\pi\)
−0.167076 + 0.985944i \(0.553432\pi\)
\(252\) 0 0
\(253\) 9.87887 0.00245486
\(254\) −180.076 311.900i −0.0444841 0.0770487i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 1613.09 + 2793.96i 0.391525 + 0.678141i 0.992651 0.121013i \(-0.0386144\pi\)
−0.601126 + 0.799154i \(0.705281\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −180.273 −0.0430001
\(261\) 0 0
\(262\) 217.860 377.344i 0.0513719 0.0889787i
\(263\) 1625.31 2815.11i 0.381067 0.660028i −0.610148 0.792288i \(-0.708890\pi\)
0.991215 + 0.132260i \(0.0422233\pi\)
\(264\) 0 0
\(265\) 3677.99 0.852593
\(266\) 0 0
\(267\) 0 0
\(268\) −283.583 491.181i −0.0646366 0.111954i
\(269\) −1413.02 + 2447.42i −0.320273 + 0.554729i −0.980544 0.196298i \(-0.937108\pi\)
0.660271 + 0.751027i \(0.270441\pi\)
\(270\) 0 0
\(271\) −1198.38 2075.66i −0.268622 0.465268i 0.699884 0.714257i \(-0.253235\pi\)
−0.968506 + 0.248989i \(0.919902\pi\)
\(272\) −1909.58 −0.425680
\(273\) 0 0
\(274\) −5203.71 −1.14733
\(275\) 2344.07 + 4060.05i 0.514010 + 0.890292i
\(276\) 0 0
\(277\) −910.233 + 1576.57i −0.197439 + 0.341974i −0.947697 0.319170i \(-0.896596\pi\)
0.750258 + 0.661145i \(0.229929\pi\)
\(278\) 2651.55 + 4592.62i 0.572048 + 0.990816i
\(279\) 0 0
\(280\) 0 0
\(281\) −3083.81 −0.654679 −0.327339 0.944907i \(-0.606152\pi\)
−0.327339 + 0.944907i \(0.606152\pi\)
\(282\) 0 0
\(283\) 1277.38 2212.49i 0.268313 0.464732i −0.700113 0.714032i \(-0.746867\pi\)
0.968426 + 0.249300i \(0.0802005\pi\)
\(284\) 1205.48 2087.96i 0.251875 0.436259i
\(285\) 0 0
\(286\) −65.5910 −0.0135611
\(287\) 0 0
\(288\) 0 0
\(289\) −4665.53 8080.94i −0.949630 1.64481i
\(290\) 3400.79 5890.34i 0.688625 1.19273i
\(291\) 0 0
\(292\) −2204.60 3818.48i −0.441830 0.765272i
\(293\) −1846.47 −0.368163 −0.184081 0.982911i \(-0.558931\pi\)
−0.184081 + 0.982911i \(0.558931\pi\)
\(294\) 0 0
\(295\) 9479.39 1.87089
\(296\) 674.136 + 1167.64i 0.132376 + 0.229282i
\(297\) 0 0
\(298\) −581.023 + 1006.36i −0.112945 + 0.195627i
\(299\) −0.704576 1.22036i −0.000136277 0.000236038i
\(300\) 0 0
\(301\) 0 0
\(302\) 1230.78 0.234515
\(303\) 0 0
\(304\) −268.091 + 464.347i −0.0505792 + 0.0876057i
\(305\) 402.693 697.485i 0.0756005 0.130944i
\(306\) 0 0
\(307\) −7041.50 −1.30905 −0.654527 0.756039i \(-0.727132\pi\)
−0.654527 + 0.756039i \(0.727132\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4653.47 + 8060.04i 0.852578 + 1.47671i
\(311\) 1343.00 2326.14i 0.244869 0.424126i −0.717226 0.696841i \(-0.754588\pi\)
0.962095 + 0.272715i \(0.0879216\pi\)
\(312\) 0 0
\(313\) 1109.59 + 1921.87i 0.200377 + 0.347063i 0.948650 0.316328i \(-0.102450\pi\)
−0.748273 + 0.663391i \(0.769117\pi\)
\(314\) −613.864 −0.110326
\(315\) 0 0
\(316\) −465.212 −0.0828172
\(317\) 1110.63 + 1923.67i 0.196780 + 0.340833i 0.947483 0.319807i \(-0.103618\pi\)
−0.750703 + 0.660640i \(0.770285\pi\)
\(318\) 0 0
\(319\) 1237.35 2143.16i 0.217174 0.376157i
\(320\) −666.788 1154.91i −0.116483 0.201755i
\(321\) 0 0
\(322\) 0 0
\(323\) −3999.53 −0.688978
\(324\) 0 0
\(325\) 334.366 579.138i 0.0570685 0.0988455i
\(326\) 3514.50 6087.29i 0.597086 1.03418i
\(327\) 0 0
\(328\) 2584.18 0.435023
\(329\) 0 0
\(330\) 0 0
\(331\) −2077.03 3597.52i −0.344906 0.597394i 0.640431 0.768016i \(-0.278756\pi\)
−0.985337 + 0.170622i \(0.945422\pi\)
\(332\) 1137.86 1970.82i 0.188096 0.325792i
\(333\) 0 0
\(334\) 1123.30 + 1945.62i 0.184025 + 0.318741i
\(335\) 2954.53 0.481860
\(336\) 0 0
\(337\) −254.167 −0.0410841 −0.0205420 0.999789i \(-0.506539\pi\)
−0.0205420 + 0.999789i \(0.506539\pi\)
\(338\) −2192.32 3797.21i −0.352801 0.611069i
\(339\) 0 0
\(340\) 4973.76 8614.80i 0.793353 1.37413i
\(341\) 1693.13 + 2932.59i 0.268880 + 0.465714i
\(342\) 0 0
\(343\) 0 0
\(344\) −1772.45 −0.277803
\(345\) 0 0
\(346\) 1530.60 2651.07i 0.237819 0.411915i
\(347\) −3112.32 + 5390.69i −0.481493 + 0.833970i −0.999774 0.0212401i \(-0.993239\pi\)
0.518282 + 0.855210i \(0.326572\pi\)
\(348\) 0 0
\(349\) −9732.21 −1.49270 −0.746352 0.665552i \(-0.768196\pi\)
−0.746352 + 0.665552i \(0.768196\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −242.606 420.206i −0.0367356 0.0636280i
\(353\) −712.807 + 1234.62i −0.107476 + 0.186153i −0.914747 0.404027i \(-0.867610\pi\)
0.807271 + 0.590180i \(0.200943\pi\)
\(354\) 0 0
\(355\) 6279.71 + 10876.8i 0.938852 + 1.62614i
\(356\) −1532.64 −0.228173
\(357\) 0 0
\(358\) 6826.86 1.00785
\(359\) −2883.25 4993.93i −0.423877 0.734177i 0.572438 0.819948i \(-0.305998\pi\)
−0.996315 + 0.0857714i \(0.972665\pi\)
\(360\) 0 0
\(361\) 2867.99 4967.51i 0.418136 0.724233i
\(362\) −1286.71 2228.64i −0.186817 0.323577i
\(363\) 0 0
\(364\) 0 0
\(365\) 22968.7 3.29381
\(366\) 0 0
\(367\) 5772.67 9998.56i 0.821065 1.42213i −0.0838244 0.996481i \(-0.526713\pi\)
0.904890 0.425646i \(-0.139953\pi\)
\(368\) 5.21213 9.02768i 0.000738319 0.00127881i
\(369\) 0 0
\(370\) −7023.53 −0.986854
\(371\) 0 0
\(372\) 0 0
\(373\) 3239.79 + 5611.47i 0.449731 + 0.778957i 0.998368 0.0571033i \(-0.0181864\pi\)
−0.548637 + 0.836061i \(0.684853\pi\)
\(374\) 1809.67 3134.43i 0.250202 0.433363i
\(375\) 0 0
\(376\) 2032.18 + 3519.84i 0.278728 + 0.482771i
\(377\) −353.000 −0.0482239
\(378\) 0 0
\(379\) 611.996 0.0829449 0.0414725 0.999140i \(-0.486795\pi\)
0.0414725 + 0.999140i \(0.486795\pi\)
\(380\) −1396.56 2418.91i −0.188532 0.326546i
\(381\) 0 0
\(382\) −1055.30 + 1827.83i −0.141345 + 0.244816i
\(383\) −2180.41 3776.57i −0.290897 0.503848i 0.683125 0.730301i \(-0.260620\pi\)
−0.974022 + 0.226453i \(0.927287\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9541.68 1.25818
\(387\) 0 0
\(388\) 669.402 1159.44i 0.0875869 0.151705i
\(389\) −6573.46 + 11385.6i −0.856781 + 1.48399i 0.0182021 + 0.999834i \(0.494206\pi\)
−0.874983 + 0.484154i \(0.839128\pi\)
\(390\) 0 0
\(391\) 77.7575 0.0100572
\(392\) 0 0
\(393\) 0 0
\(394\) −1622.31 2809.92i −0.207439 0.359294i
\(395\) 1211.71 2098.74i 0.154349 0.267340i
\(396\) 0 0
\(397\) −4239.02 7342.20i −0.535895 0.928198i −0.999119 0.0419565i \(-0.986641\pi\)
0.463224 0.886241i \(-0.346692\pi\)
\(398\) −7100.27 −0.894232
\(399\) 0 0
\(400\) 4946.97 0.618371
\(401\) 1401.50 + 2427.47i 0.174533 + 0.302299i 0.939999 0.341176i \(-0.110825\pi\)
−0.765467 + 0.643475i \(0.777492\pi\)
\(402\) 0 0
\(403\) 241.513 418.313i 0.0298527 0.0517064i
\(404\) 29.4848 + 51.0692i 0.00363100 + 0.00628908i
\(405\) 0 0
\(406\) 0 0
\(407\) −2555.46 −0.311227
\(408\) 0 0
\(409\) −3192.69 + 5529.91i −0.385987 + 0.668548i −0.991906 0.126978i \(-0.959472\pi\)
0.605919 + 0.795526i \(0.292806\pi\)
\(410\) −6730.86 + 11658.2i −0.810765 + 1.40429i
\(411\) 0 0
\(412\) 3365.68 0.402464
\(413\) 0 0
\(414\) 0 0
\(415\) 5927.41 + 10266.6i 0.701121 + 1.21438i
\(416\) −34.6061 + 59.9395i −0.00407861 + 0.00706436i
\(417\) 0 0
\(418\) −508.129 880.105i −0.0594579 0.102984i
\(419\) 4831.66 0.563346 0.281673 0.959510i \(-0.409111\pi\)
0.281673 + 0.959510i \(0.409111\pi\)
\(420\) 0 0
\(421\) 7475.37 0.865385 0.432693 0.901542i \(-0.357564\pi\)
0.432693 + 0.901542i \(0.357564\pi\)
\(422\) 4653.39 + 8059.90i 0.536785 + 0.929739i
\(423\) 0 0
\(424\) 706.045 1222.91i 0.0808693 0.140070i
\(425\) 18450.4 + 31957.1i 2.10583 + 3.64740i
\(426\) 0 0
\(427\) 0 0
\(428\) 2862.68 0.323301
\(429\) 0 0
\(430\) 4616.61 7996.20i 0.517750 0.896769i
\(431\) 3495.97 6055.19i 0.390707 0.676725i −0.601836 0.798620i \(-0.705564\pi\)
0.992543 + 0.121895i \(0.0388972\pi\)
\(432\) 0 0
\(433\) 7699.26 0.854510 0.427255 0.904131i \(-0.359481\pi\)
0.427255 + 0.904131i \(0.359481\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1200.04 2078.53i −0.131815 0.228310i
\(437\) 10.9166 18.9081i 0.00119499 0.00206979i
\(438\) 0 0
\(439\) 4706.16 + 8151.31i 0.511646 + 0.886198i 0.999909 + 0.0135008i \(0.00429758\pi\)
−0.488262 + 0.872697i \(0.662369\pi\)
\(440\) 2527.61 0.273861
\(441\) 0 0
\(442\) −516.273 −0.0555579
\(443\) −3129.09 5419.74i −0.335593 0.581263i 0.648006 0.761635i \(-0.275603\pi\)
−0.983598 + 0.180372i \(0.942270\pi\)
\(444\) 0 0
\(445\) 3991.97 6914.29i 0.425252 0.736559i
\(446\) 4649.53 + 8053.23i 0.493636 + 0.855003i
\(447\) 0 0
\(448\) 0 0
\(449\) 11633.8 1.22279 0.611396 0.791325i \(-0.290608\pi\)
0.611396 + 0.791325i \(0.290608\pi\)
\(450\) 0 0
\(451\) −2448.98 + 4241.75i −0.255694 + 0.442874i
\(452\) 1245.29 2156.90i 0.129587 0.224452i
\(453\) 0 0
\(454\) −8303.43 −0.858369
\(455\) 0 0
\(456\) 0 0
\(457\) 6552.31 + 11348.9i 0.670688 + 1.16167i 0.977709 + 0.209963i \(0.0673343\pi\)
−0.307022 + 0.951703i \(0.599332\pi\)
\(458\) −4263.63 + 7384.83i −0.434992 + 0.753429i
\(459\) 0 0
\(460\) 27.1515 + 47.0277i 0.00275205 + 0.00476669i
\(461\) −2594.63 −0.262134 −0.131067 0.991373i \(-0.541840\pi\)
−0.131067 + 0.991373i \(0.541840\pi\)
\(462\) 0 0
\(463\) −14136.2 −1.41893 −0.709465 0.704741i \(-0.751063\pi\)
−0.709465 + 0.704741i \(0.751063\pi\)
\(464\) −1305.67 2261.48i −0.130634 0.226264i
\(465\) 0 0
\(466\) −3049.90 + 5282.58i −0.303184 + 0.525131i
\(467\) −7795.12 13501.5i −0.772409 1.33785i −0.936239 0.351363i \(-0.885718\pi\)
0.163830 0.986489i \(-0.447615\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −21172.4 −2.07789
\(471\) 0 0
\(472\) 1819.71 3151.83i 0.177456 0.307362i
\(473\) 1679.72 2909.36i 0.163285 0.282817i
\(474\) 0 0
\(475\) 10361.2 1.00085
\(476\) 0 0
\(477\) 0 0
\(478\) −3987.20 6906.04i −0.381528 0.660826i
\(479\) 4226.75 7320.95i 0.403184 0.698336i −0.590924 0.806727i \(-0.701237\pi\)
0.994108 + 0.108391i \(0.0345700\pi\)
\(480\) 0 0
\(481\) 182.259 + 315.683i 0.0172772 + 0.0299249i
\(482\) −1249.30 −0.118058
\(483\) 0 0
\(484\) −4404.35 −0.413632
\(485\) 3487.10 + 6039.83i 0.326476 + 0.565474i
\(486\) 0 0
\(487\) 2005.53 3473.69i 0.186611 0.323219i −0.757507 0.652827i \(-0.773583\pi\)
0.944118 + 0.329607i \(0.106916\pi\)
\(488\) −154.606 267.786i −0.0143416 0.0248403i
\(489\) 0 0
\(490\) 0 0
\(491\) −13927.9 −1.28016 −0.640079 0.768309i \(-0.721098\pi\)
−0.640079 + 0.768309i \(0.721098\pi\)
\(492\) 0 0
\(493\) 9739.33 16869.0i 0.889731 1.54106i
\(494\) −72.4810 + 125.541i −0.00660137 + 0.0114339i
\(495\) 0 0
\(496\) 3573.21 0.323472
\(497\) 0 0
\(498\) 0 0
\(499\) 1973.77 + 3418.68i 0.177071 + 0.306695i 0.940876 0.338751i \(-0.110005\pi\)
−0.763805 + 0.645447i \(0.776671\pi\)
\(500\) −7675.80 + 13294.9i −0.686544 + 1.18913i
\(501\) 0 0
\(502\) −1328.78 2301.52i −0.118141 0.204625i
\(503\) −13725.3 −1.21666 −0.608331 0.793684i \(-0.708161\pi\)
−0.608331 + 0.793684i \(0.708161\pi\)
\(504\) 0 0
\(505\) −307.190 −0.0270688
\(506\) 9.87887 + 17.1107i 0.000867924 + 0.00150329i
\(507\) 0 0
\(508\) 360.152 623.801i 0.0314550 0.0544817i
\(509\) −3915.05 6781.07i −0.340926 0.590502i 0.643679 0.765296i \(-0.277407\pi\)
−0.984605 + 0.174794i \(0.944074\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −3226.18 + 5587.91i −0.276850 + 0.479518i
\(515\) −8766.39 + 15183.8i −0.750084 + 1.29918i
\(516\) 0 0
\(517\) −7703.43 −0.655312
\(518\) 0 0
\(519\) 0 0
\(520\) −180.273 312.241i −0.0152028 0.0263321i
\(521\) 2953.69 5115.95i 0.248376 0.430199i −0.714700 0.699431i \(-0.753437\pi\)
0.963075 + 0.269232i \(0.0867700\pi\)
\(522\) 0 0
\(523\) 3954.03 + 6848.58i 0.330588 + 0.572595i 0.982627 0.185590i \(-0.0594196\pi\)
−0.652039 + 0.758185i \(0.726086\pi\)
\(524\) 871.439 0.0726508
\(525\) 0 0
\(526\) 6501.23 0.538911
\(527\) 13326.8 + 23082.7i 1.10156 + 1.90797i
\(528\) 0 0
\(529\) 6083.29 10536.6i 0.499983 0.865995i
\(530\) 3677.99 + 6370.46i 0.301437 + 0.522104i
\(531\) 0 0
\(532\) 0 0
\(533\) 698.659 0.0567773
\(534\) 0 0
\(535\) −7456.26 + 12914.6i −0.602546 + 1.04364i
\(536\) 567.167 982.362i 0.0457050 0.0791633i
\(537\) 0 0
\(538\) −5652.08 −0.452934
\(539\) 0 0
\(540\) 0 0
\(541\) 1970.52 + 3413.04i 0.156598 + 0.271235i 0.933640 0.358214i \(-0.116614\pi\)
−0.777042 + 0.629449i \(0.783281\pi\)
\(542\) 2396.77 4151.33i 0.189945 0.328994i
\(543\) 0 0
\(544\) −1909.58 3307.48i −0.150501 0.260675i
\(545\) 12502.7 0.982670
\(546\) 0 0
\(547\) −1828.71 −0.142943 −0.0714717 0.997443i \(-0.522770\pi\)
−0.0714717 + 0.997443i \(0.522770\pi\)
\(548\) −5203.71 9013.09i −0.405642 0.702592i
\(549\) 0 0
\(550\) −4688.14 + 8120.10i −0.363460 + 0.629532i
\(551\) −2734.67 4736.58i −0.211435 0.366216i
\(552\) 0 0
\(553\) 0 0
\(554\) −3640.93 −0.279221
\(555\) 0 0
\(556\) −5303.10 + 9185.24i −0.404499 + 0.700613i
\(557\) 11266.0 19513.3i 0.857011 1.48439i −0.0177556 0.999842i \(-0.505652\pi\)
0.874767 0.484544i \(-0.161015\pi\)
\(558\) 0 0
\(559\) −479.201 −0.0362577
\(560\) 0 0
\(561\) 0 0
\(562\) −3083.81 5341.32i −0.231464 0.400907i
\(563\) −11677.9 + 20226.6i −0.874179 + 1.51412i −0.0165446 + 0.999863i \(0.505267\pi\)
−0.857635 + 0.514260i \(0.828067\pi\)
\(564\) 0 0
\(565\) 6487.05 + 11235.9i 0.483031 + 0.836634i
\(566\) 5109.54 0.379452
\(567\) 0 0
\(568\) 4821.94 0.356204
\(569\) −10443.8 18089.2i −0.769468 1.33276i −0.937852 0.347036i \(-0.887188\pi\)
0.168384 0.985721i \(-0.446145\pi\)
\(570\) 0 0
\(571\) −11872.6 + 20564.0i −0.870147 + 1.50714i −0.00830301 + 0.999966i \(0.502643\pi\)
−0.861844 + 0.507173i \(0.830690\pi\)
\(572\) −65.5910 113.607i −0.00479457 0.00830444i
\(573\) 0 0
\(574\) 0 0
\(575\) −201.440 −0.0146098
\(576\) 0 0
\(577\) 1227.20 2125.57i 0.0885422 0.153360i −0.818353 0.574716i \(-0.805113\pi\)
0.906895 + 0.421356i \(0.138446\pi\)
\(578\) 9331.06 16161.9i 0.671490 1.16305i
\(579\) 0 0
\(580\) 13603.2 0.973863
\(581\) 0 0
\(582\) 0 0
\(583\) 1338.21 + 2317.85i 0.0950652 + 0.164658i
\(584\) 4409.20 7636.95i 0.312421 0.541129i
\(585\) 0 0
\(586\) −1846.47 3198.17i −0.130165 0.225453i
\(587\) 18567.5 1.30556 0.652780 0.757547i \(-0.273603\pi\)
0.652780 + 0.757547i \(0.273603\pi\)
\(588\) 0 0
\(589\) 7483.95 0.523550
\(590\) 9479.39 + 16418.8i 0.661458 + 1.14568i
\(591\) 0 0
\(592\) −1348.27 + 2335.28i −0.0936042 + 0.162127i
\(593\) −8556.47 14820.2i −0.592533 1.02630i −0.993890 0.110375i \(-0.964795\pi\)
0.401357 0.915922i \(-0.368539\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2324.09 −0.159729
\(597\) 0 0
\(598\) 1.40915 2.44072i 9.63621e−5 0.000166904i
\(599\) 11632.4 20147.9i 0.793469 1.37433i −0.130338 0.991470i \(-0.541606\pi\)
0.923807 0.382859i \(-0.125060\pi\)
\(600\) 0 0
\(601\) −25322.3 −1.71867 −0.859334 0.511416i \(-0.829121\pi\)
−0.859334 + 0.511416i \(0.829121\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 1230.78 + 2131.77i 0.0829135 + 0.143610i
\(605\) 11471.7 19869.6i 0.770897 1.33523i
\(606\) 0 0
\(607\) −10867.2 18822.5i −0.726665 1.25862i −0.958285 0.285814i \(-0.907736\pi\)
0.231620 0.972806i \(-0.425597\pi\)
\(608\) −1072.36 −0.0715297
\(609\) 0 0
\(610\) 1610.77 0.106915
\(611\) 549.420 + 951.624i 0.0363784 + 0.0630092i
\(612\) 0 0
\(613\) 6786.19 11754.0i 0.447131 0.774454i −0.551067 0.834461i \(-0.685779\pi\)
0.998198 + 0.0600072i \(0.0191124\pi\)
\(614\) −7041.50 12196.2i −0.462820 0.801628i
\(615\) 0 0
\(616\) 0 0
\(617\) 8497.12 0.554427 0.277213 0.960808i \(-0.410589\pi\)
0.277213 + 0.960808i \(0.410589\pi\)
\(618\) 0 0
\(619\) −11491.5 + 19903.8i −0.746173 + 1.29241i 0.203472 + 0.979081i \(0.434777\pi\)
−0.949645 + 0.313329i \(0.898556\pi\)
\(620\) −9306.93 + 16120.1i −0.602863 + 1.04419i
\(621\) 0 0
\(622\) 5371.98 0.346297
\(623\) 0 0
\(624\) 0 0
\(625\) −20661.3 35786.4i −1.32232 2.29033i
\(626\) −2219.19 + 3843.75i −0.141688 + 0.245411i
\(627\) 0 0
\(628\) −613.864 1063.24i −0.0390061 0.0675605i
\(629\) −20114.3 −1.27505
\(630\) 0 0
\(631\) −15717.9 −0.991635 −0.495817 0.868427i \(-0.665131\pi\)
−0.495817 + 0.868427i \(0.665131\pi\)
\(632\) −465.212 805.771i −0.0292803 0.0507150i
\(633\) 0 0
\(634\) −2221.26 + 3847.34i −0.139144 + 0.241005i
\(635\) 1876.13 + 3249.55i 0.117247 + 0.203078i
\(636\) 0 0
\(637\) 0 0
\(638\) 4949.42 0.307131
\(639\) 0 0
\(640\) 1333.58 2309.82i 0.0823660 0.142662i
\(641\) 14553.7 25207.7i 0.896780 1.55327i 0.0651930 0.997873i \(-0.479234\pi\)
0.831587 0.555395i \(-0.187433\pi\)
\(642\) 0 0
\(643\) 3112.26 0.190880 0.0954398 0.995435i \(-0.469574\pi\)
0.0954398 + 0.995435i \(0.469574\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3999.53 6927.39i −0.243590 0.421911i
\(647\) 3928.80 6804.87i 0.238728 0.413489i −0.721622 0.692288i \(-0.756603\pi\)
0.960349 + 0.278799i \(0.0899363\pi\)
\(648\) 0 0
\(649\) 3449.01 + 5973.86i 0.208606 + 0.361317i
\(650\) 1337.46 0.0807071
\(651\) 0 0
\(652\) 14058.0 0.844408
\(653\) −9761.01 16906.6i −0.584958 1.01318i −0.994881 0.101057i \(-0.967778\pi\)
0.409923 0.912120i \(-0.365556\pi\)
\(654\) 0 0
\(655\) −2269.79 + 3931.38i −0.135401 + 0.234522i
\(656\) 2584.18 + 4475.93i 0.153804 + 0.266396i
\(657\) 0 0
\(658\) 0 0
\(659\) −664.061 −0.0392536 −0.0196268 0.999807i \(-0.506248\pi\)
−0.0196268 + 0.999807i \(0.506248\pi\)
\(660\) 0 0
\(661\) 7960.82 13788.5i 0.468442 0.811365i −0.530908 0.847430i \(-0.678149\pi\)
0.999349 + 0.0360650i \(0.0114823\pi\)
\(662\) 4154.06 7195.04i 0.243885 0.422422i
\(663\) 0 0
\(664\) 4551.42 0.266008
\(665\) 0 0
\(666\) 0 0
\(667\) 53.1665 + 92.0870i 0.00308638 + 0.00534576i
\(668\) −2246.61 + 3891.24i −0.130125 + 0.225384i
\(669\) 0 0
\(670\) 2954.53 + 5117.40i 0.170363 + 0.295078i
\(671\) 586.068 0.0337182
\(672\) 0 0
\(673\) 24631.0 1.41078 0.705391 0.708819i \(-0.250771\pi\)
0.705391 + 0.708819i \(0.250771\pi\)
\(674\) −254.167 440.230i −0.0145254 0.0251588i
\(675\) 0 0
\(676\) 4384.64 7594.43i 0.249468 0.432091i
\(677\) −8546.39 14802.8i −0.485177 0.840350i 0.514678 0.857383i \(-0.327911\pi\)
−0.999855 + 0.0170329i \(0.994578\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 19895.0 1.12197
\(681\) 0 0
\(682\) −3386.26 + 5865.18i −0.190127 + 0.329310i
\(683\) −9581.79 + 16596.1i −0.536804 + 0.929771i 0.462270 + 0.886739i \(0.347035\pi\)
−0.999074 + 0.0430322i \(0.986298\pi\)
\(684\) 0 0
\(685\) 54215.2 3.02402
\(686\) 0 0
\(687\) 0 0
\(688\) −1772.45 3069.98i −0.0982183 0.170119i
\(689\) 190.886 330.625i 0.0105547 0.0182813i
\(690\) 0 0
\(691\) 4047.94 + 7011.23i 0.222852 + 0.385991i 0.955673 0.294431i \(-0.0951300\pi\)
−0.732821 + 0.680422i \(0.761797\pi\)
\(692\) 6122.39 0.336327
\(693\) 0 0
\(694\) −12449.3 −0.680934
\(695\) −27625.3 47848.5i −1.50775 2.61150i
\(696\) 0 0
\(697\) −19276.1 + 33387.2i −1.04754 + 1.81439i
\(698\) −9732.21 16856.7i −0.527750 0.914090i
\(699\) 0 0
\(700\) 0 0
\(701\) −12354.7 −0.665664 −0.332832 0.942986i \(-0.608004\pi\)
−0.332832 + 0.942986i \(0.608004\pi\)
\(702\) 0 0
\(703\) −2823.90 + 4891.14i −0.151501 + 0.262408i
\(704\) 485.212 840.412i 0.0259760 0.0449918i
\(705\) 0 0
\(706\) −2851.23 −0.151993
\(707\) 0 0
\(708\) 0 0
\(709\) −1914.41 3315.85i −0.101406 0.175641i 0.810858 0.585243i \(-0.199001\pi\)
−0.912264 + 0.409602i \(0.865668\pi\)
\(710\) −12559.4 + 21753.5i −0.663868 + 1.14985i
\(711\) 0 0
\(712\) −1532.64 2654.60i −0.0806713 0.139727i
\(713\) −145.500 −0.00764241
\(714\) 0 0
\(715\) 683.363 0.0357431
\(716\) 6826.86 + 11824.5i 0.356329 + 0.617181i
\(717\) 0 0
\(718\) 5766.49 9987.86i 0.299726 0.519141i
\(719\) −611.500 1059.15i −0.0317178 0.0549368i 0.849731 0.527217i \(-0.176764\pi\)
−0.881449 + 0.472280i \(0.843431\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 11472.0 0.591333
\(723\) 0 0
\(724\) 2573.42 4457.29i 0.132100 0.228804i
\(725\) −25230.8 + 43701.1i −1.29248 + 2.23864i
\(726\) 0 0
\(727\) −6368.21 −0.324875 −0.162437 0.986719i \(-0.551936\pi\)
−0.162437 + 0.986719i \(0.551936\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 22968.7 + 39783.0i 1.16454 + 2.01704i
\(731\) 13221.2 22899.9i 0.668954 1.15866i
\(732\) 0 0
\(733\) −12577.0 21784.0i −0.633753 1.09769i −0.986778 0.162079i \(-0.948180\pi\)
0.353024 0.935614i \(-0.385153\pi\)
\(734\) 23090.7 1.16116
\(735\) 0 0
\(736\) 20.8485 0.00104414
\(737\) 1074.98 + 1861.93i 0.0537281 + 0.0930597i
\(738\) 0 0
\(739\) 5369.55 9300.34i 0.267283 0.462948i −0.700876 0.713283i \(-0.747207\pi\)
0.968159 + 0.250335i \(0.0805408\pi\)
\(740\) −7023.53 12165.1i −0.348906 0.604322i
\(741\) 0 0
\(742\) 0 0
\(743\) −28166.3 −1.39074 −0.695370 0.718652i \(-0.744760\pi\)
−0.695370 + 0.718652i \(0.744760\pi\)
\(744\) 0 0
\(745\) 6053.42 10484.8i 0.297691 0.515617i
\(746\) −6479.57 + 11222.9i −0.318008 + 0.550806i
\(747\) 0 0
\(748\) 7238.67 0.353839
\(749\) 0 0
\(750\) 0 0
\(751\) −14328.5 24817.7i −0.696211 1.20587i −0.969771 0.244018i \(-0.921534\pi\)
0.273559 0.961855i \(-0.411799\pi\)
\(752\) −4064.36 + 7039.68i −0.197091 + 0.341371i
\(753\) 0 0
\(754\) −353.000 611.414i −0.0170497 0.0295310i
\(755\) −12823.0 −0.618113
\(756\) 0 0
\(757\) −23604.1 −1.13330 −0.566648 0.823960i \(-0.691760\pi\)
−0.566648 + 0.823960i \(0.691760\pi\)
\(758\) 611.996 + 1060.01i 0.0293255 + 0.0507932i
\(759\) 0 0
\(760\) 2793.12 4837.83i 0.133312 0.230903i
\(761\) −2315.48 4010.54i −0.110297 0.191041i 0.805593 0.592470i \(-0.201847\pi\)
−0.915890 + 0.401429i \(0.868514\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4221.18 −0.199891
\(765\) 0 0
\(766\) 4360.81 7553.15i 0.205695 0.356274i
\(767\) 491.977 852.129i 0.0231607 0.0401155i
\(768\) 0 0
\(769\) −33276.8 −1.56046 −0.780228 0.625495i \(-0.784897\pi\)
−0.780228 + 0.625495i \(0.784897\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 9541.68 + 16526.7i 0.444835 + 0.770477i
\(773\) 11469.4 19865.6i 0.533668 0.924340i −0.465558 0.885017i \(-0.654147\pi\)
0.999227 0.0393231i \(-0.0125202\pi\)
\(774\) 0 0
\(775\) −34524.6 59798.3i −1.60020 2.77164i
\(776\) 2677.61 0.123867
\(777\) 0 0
\(778\) −26293.8 −1.21167
\(779\) 5412.47 + 9374.67i 0.248937 + 0.431171i
\(780\) 0 0
\(781\) −4569.66 + 7914.88i −0.209366 + 0.362633i
\(782\) 77.7575 + 134.680i 0.00355576 + 0.00615876i
\(783\) 0 0
\(784\) 0 0
\(785\) 6395.58 0.290787
\(786\) 0 0
\(787\) −6757.23 + 11703.9i −0.306060 + 0.530112i −0.977497 0.210950i \(-0.932344\pi\)
0.671437 + 0.741062i \(0.265678\pi\)
\(788\) 3244.62 5619.85i 0.146681 0.254059i
\(789\) 0 0
\(790\) 4846.84 0.218282