Properties

Label 882.4.g.bf.667.1
Level $882$
Weight $4$
Character 882.667
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 667.1
Root \(9.41856 - 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.bf.361.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 −0.151732 + 0.988422i \(0.548485\pi\)
−0.780132 + 0.625615i \(0.784848\pi\)
\(6\) 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 0.951024 0.309118i \(-0.100034\pi\)
−0.743216 + 0.669052i \(0.766700\pi\)
\(12\) 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 0.879981 + 0.475009i \(0.157555\pi\)
−0.0286202 + 0.999590i \(0.509111\pi\)
\(18\) 0 0
\(19\) −16.7557 + 29.0217i −0.202317 + 0.350423i −0.949274 0.314449i \(-0.898180\pi\)
0.746958 + 0.664871i \(0.231514\pi\)
\(20\) 83.3485 0.931864
\(21\) 0 0
\(22\) 30.3258 0.293885
\(23\) 0.325758 0.564230i 0.00295327 0.00511522i −0.864545 0.502555i \(-0.832393\pi\)
0.867498 + 0.497440i \(0.165727\pi\)
\(24\) 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 −0.983849 0.179000i \(-0.942714\pi\)
0.336906 0.941538i \(-0.390620\pi\)
\(32\) 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 −0.990240 0.139376i \(-0.955490\pi\)
0.615823 + 0.787885i \(0.288824\pi\)
\(38\) 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 0.138608 + 0.990347i \(0.455737\pi\)
−0.926970 + 0.375136i \(0.877596\pi\)
\(48\) 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 0.728700 0.684833i \(-0.240125\pi\)
−0.957433 + 0.288656i \(0.906792\pi\)
\(54\) 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 −0.999998 0.00221868i \(-0.999294\pi\)
0.498077 0.867133i \(-0.334040\pi\)
\(60\) 0 0
\(61\) 19.3258 33.4732i 0.0405641 0.0702591i −0.845031 0.534718i \(-0.820418\pi\)
0.885595 + 0.464459i \(0.153751\pi\)
\(62\) −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 0.794122 0.607758i \(-0.207931\pi\)
−0.923395 + 0.383851i \(0.874598\pi\)
\(68\) 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 −0.847242 0.531207i \(-0.821738\pi\)
−0.0364183 0.999337i \(-0.511595\pi\)
\(74\) 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 −0.821642 0.570004i \(-0.806942\pi\)
0.904459 + 0.426561i \(0.140275\pi\)
\(80\) −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 −0.729094 0.684414i \(-0.760058\pi\)
0.957267 + 0.289207i \(0.0933915\pi\)
\(90\) 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 0.869634 0.493698i \(-0.164355\pi\)
−0.862372 + 0.506276i \(0.831022\pi\)
\(102\) 0 0
\(103\) −420.710 + 728.691i −0.402464 + 0.697088i −0.994023 0.109174i \(-0.965180\pi\)
0.591559 + 0.806262i \(0.298513\pi\)
\(104\) 17.3030 0.0163144
\(105\) 0 0
\(106\) −353.023 −0.323477
\(107\) −357.835 + 619.789i −0.323301 + 0.559974i −0.981167 0.193161i \(-0.938126\pi\)
0.657866 + 0.753135i \(0.271459\pi\)
\(108\) 0 0
\(109\) −300.009 519.632i −0.263630 0.456621i 0.703574 0.710622i \(-0.251587\pi\)
−0.967204 + 0.254001i \(0.918253\pi\)
\(110\) −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 −0.900062 0.435761i \(-0.856479\pi\)
0.827411 + 0.561596i \(0.189813\pi\)
\(132\) 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 −0.911966 0.410265i \(-0.865436\pi\)
0.100683 0.994919i \(-0.467897\pi\)
\(138\) 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 −0.775042 0.631910i \(-0.782271\pi\)
0.934771 + 0.355251i \(0.115605\pi\)
\(150\) 0 0
\(151\) 307.695 + 532.943i 0.165827 + 0.287221i 0.936949 0.349467i \(-0.113637\pi\)
−0.771122 + 0.636688i \(0.780304\pi\)
\(152\) 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 0.824380 0.566037i \(-0.191524\pi\)
−0.902392 + 0.430916i \(0.858191\pi\)
\(158\) −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 0.0417271 + 0.999129i \(0.486714\pi\)
−0.886135 + 0.463428i \(0.846619\pi\)
\(164\) 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 −0.983739 0.179605i \(-0.942518\pi\)
0.647412 + 0.762141i \(0.275852\pi\)
\(174\) 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 0.963856 + 0.266425i \(0.0858426\pi\)
−0.251197 + 0.967936i \(0.580824\pi\)
\(180\) 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 −0.748602 0.663020i \(-0.769274\pi\)
0.948493 + 0.316798i \(0.102608\pi\)
\(192\) 0 0
\(193\) 2385.42 + 4131.67i 0.889670 + 1.54095i 0.840266 + 0.542175i \(0.182399\pi\)
0.0494044 + 0.998779i \(0.484268\pi\)
\(194\) −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 −0.987077 0.160249i \(-0.948770\pi\)
0.354759 0.934958i \(-0.384563\pi\)
\(200\) 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 −0.991739 0.128274i \(-0.959056\pi\)
0.384780 0.923008i \(-0.374277\pi\)
\(228\) 0 0
\(229\) 2131.82 3692.41i 0.615172 1.06551i −0.375182 0.926951i \(-0.622420\pi\)
0.990354 0.138558i \(-0.0442468\pi\)
\(230\) 27.1515 0.00778398
\(231\) 0 0
\(232\) −1305.67 −0.369488
\(233\) 1524.95 2641.29i 0.428768 0.742647i −0.567996 0.823031i \(-0.692281\pi\)
0.996764 + 0.0803838i \(0.0256146\pi\)
\(234\) 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 0.821263 0.570550i \(-0.193270\pi\)
−0.904742 + 0.425959i \(0.859937\pi\)
\(242\) −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 −0.601126 0.799154i \(-0.705281\pi\)
0.992651 + 0.121013i \(0.0386144\pi\)
\(258\) 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 0.991215 0.132260i \(-0.0422233\pi\)
−0.610148 + 0.792288i \(0.708890\pi\)
\(264\) 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 0.660271 0.751027i \(-0.270441\pi\)
−0.980544 + 0.196298i \(0.937108\pi\)
\(270\) 0 0
\(271\) −1198.38 + 2075.66i −0.268622 + 0.465268i −0.968506 0.248989i \(-0.919902\pi\)
0.699884 + 0.714257i \(0.253235\pi\)
\(272\) −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 0.750258 0.661145i \(-0.229929\pi\)
−0.947697 + 0.319170i \(0.896596\pi\)
\(278\) 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 0.968426 0.249300i \(-0.0802005\pi\)
−0.700113 + 0.714032i \(0.746867\pi\)
\(284\) 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 0.962095 0.272715i \(-0.0879216\pi\)
−0.717226 + 0.696841i \(0.754588\pi\)
\(312\) 0 0
\(313\) 1109.59 1921.87i 0.200377 0.347063i −0.748273 0.663391i \(-0.769117\pi\)
0.948650 + 0.316328i \(0.102450\pi\)
\(314\) −613.864 −0.110326
\(315\) 0 0
\(316\) −465.212 −0.0828172
\(317\) 1110.63 1923.67i 0.196780 0.340833i −0.750703 0.660640i \(-0.770285\pi\)
0.947483 + 0.319807i \(0.103618\pi\)
\(318\) 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 −0.985337 0.170622i \(-0.945422\pi\)
0.640431 + 0.768016i \(0.278756\pi\)
\(332\) 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 0.518282 0.855210i \(-0.326572\pi\)
−0.999774 + 0.0212401i \(0.993239\pi\)
\(348\) 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 0.807271 0.590180i \(-0.200943\pi\)
−0.914747 + 0.404027i \(0.867610\pi\)
\(354\) 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 −0.996315 0.0857714i \(-0.972665\pi\)
0.572438 + 0.819948i \(0.305998\pi\)
\(360\) 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 0.904890 + 0.425646i \(0.139953\pi\)
−0.0838244 + 0.996481i \(0.526713\pi\)
\(368\) 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 −0.548637 0.836061i \(-0.684853\pi\)
0.998368 + 0.0571033i \(0.0181864\pi\)
\(374\) 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 −0.974022 0.226453i \(-0.927287\pi\)
0.683125 + 0.730301i \(0.260620\pi\)
\(384\) 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 −0.874983 0.484154i \(-0.839128\pi\)
0.0182021 0.999834i \(-0.494206\pi\)
\(390\) 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 0.463224 + 0.886241i \(0.346692\pi\)
−0.999119 + 0.0419565i \(0.986641\pi\)
\(398\) −7100.27 −0.894232
\(399\) 0 0
\(400\) 4946.97 0.618371
\(401\) 1401.50 2427.47i 0.174533 0.302299i −0.765467 0.643475i \(-0.777492\pi\)
0.939999 + 0.341176i \(0.110825\pi\)
\(402\) 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 0.605919 0.795526i \(-0.292806\pi\)
−0.991906 + 0.126978i \(0.959472\pi\)
\(410\) −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 0.992543 0.121895i \(-0.0388972\pi\)
−0.601836 + 0.798620i \(0.705564\pi\)
\(432\) 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 −0.488262 0.872697i \(-0.662369\pi\)
0.999909 0.0135008i \(-0.00429758\pi\)
\(440\) 2527.61 0.273861
\(441\) 0 0
\(442\) −516.273 −0.0555579
\(443\) −3129.09 + 5419.74i −0.335593 + 0.581263i −0.983598 0.180372i \(-0.942270\pi\)
0.648006 + 0.761635i \(0.275603\pi\)
\(444\) 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 −0.307022 0.951703i \(-0.599332\pi\)
0.977709 0.209963i \(-0.0673343\pi\)
\(458\) −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 0.163830 + 0.986489i \(0.447615\pi\)
−0.936239 + 0.351363i \(0.885718\pi\)
\(468\) 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 0.994108 0.108391i \(-0.0345700\pi\)
−0.590924 + 0.806727i \(0.701237\pi\)
\(480\) 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 0.944118 0.329607i \(-0.106916\pi\)
−0.757507 + 0.652827i \(0.773583\pi\)
\(488\) −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 −0.763805 0.645447i \(-0.776671\pi\)
0.940876 + 0.338751i \(0.110005\pi\)
\(500\) −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 −0.984605 0.174794i \(-0.944074\pi\)
0.643679 + 0.765296i \(0.277407\pi\)
\(510\) 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 0.963075 0.269232i \(-0.0867700\pi\)
−0.714700 + 0.699431i \(0.753437\pi\)
\(522\) 0 0
\(523\) 3954.03 6848.58i 0.330588 0.572595i −0.652039 0.758185i \(-0.726086\pi\)
0.982627 + 0.185590i \(0.0594196\pi\)
\(524\) 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 −0.777042 0.629449i \(-0.783281\pi\)
0.933640 + 0.358214i \(0.116614\pi\)
\(542\) 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 0.874767 + 0.484544i \(0.161015\pi\)
−0.0177556 + 0.999842i \(0.505652\pi\)
\(558\) 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 −0.857635 0.514260i \(-0.828067\pi\)
−0.0165446 0.999863i \(-0.505267\pi\)
\(564\) 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 0.168384 + 0.985721i \(0.446145\pi\)
−0.937852 + 0.347036i \(0.887188\pi\)
\(570\) 0 0
\(571\) −11872.6 20564.0i −0.870147 1.50714i −0.861844 0.507173i \(-0.830690\pi\)
−0.00830301 0.999966i \(-0.502643\pi\)
\(572\) −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 0.906895 0.421356i \(-0.138446\pi\)
−0.818353 + 0.574716i \(0.805113\pi\)
\(578\) 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 0.401357 + 0.915922i \(0.368539\pi\)
−0.993890 + 0.110375i \(0.964795\pi\)
\(594\) 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 0.923807 + 0.382859i \(0.125060\pi\)
−0.130338 + 0.991470i \(0.541606\pi\)
\(600\) 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 0.231620 + 0.972806i \(0.425597\pi\)
−0.958285 + 0.285814i \(0.907736\pi\)
\(608\) −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 0.998198 0.0600072i \(-0.0191124\pi\)
−0.551067 + 0.834461i \(0.685779\pi\)
\(614\) −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 −0.949645 0.313329i \(-0.898556\pi\)
0.203472 0.979081i \(-0.434777\pi\)
\(620\) −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 0.831587 + 0.555395i \(0.187433\pi\)
0.0651930 + 0.997873i \(0.479234\pi\)
\(642\) 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 0.960349 0.278799i \(-0.0899363\pi\)
−0.721622 + 0.692288i \(0.756603\pi\)
\(648\) 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 0.409923 + 0.912120i \(0.365556\pi\)
−0.994881 + 0.101057i \(0.967778\pi\)
\(654\) 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 0.999349 0.0360650i \(-0.0114823\pi\)
−0.530908 + 0.847430i \(0.678149\pi\)
\(662\) 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 −0.999855 0.0170329i \(-0.994578\pi\)
0.514678 + 0.857383i \(0.327911\pi\)
\(678\) 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 −0.999074 0.0430322i \(-0.986298\pi\)
0.462270 0.886739i \(-0.347035\pi\)
\(684\) 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 −0.732821 0.680422i \(-0.761797\pi\)
0.955673 + 0.294431i \(0.0951300\pi\)
\(692\) 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 −0.912264 0.409602i \(-0.865668\pi\)
0.810858 + 0.585243i \(0.199001\pi\)
\(710\) −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 −0.881449 0.472280i \(-0.843431\pi\)
0.849731 + 0.527217i \(0.176764\pi\)
\(720\) 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 0.353024 + 0.935614i \(0.385153\pi\)
−0.986778 + 0.162079i \(0.948180\pi\)
\(734\) 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 0.968159 0.250335i \(-0.0805408\pi\)
−0.700876 + 0.713283i \(0.747207\pi\)
\(740\) −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 0.273559 + 0.961855i \(0.411799\pi\)
−0.969771 + 0.244018i \(0.921534\pi\)
\(752\) −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 −0.915890 0.401429i \(-0.868514\pi\)
0.805593 + 0.592470i \(0.201847\pi\)
\(762\) 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 0.999227 + 0.0393231i \(0.0125202\pi\)
−0.465558 + 0.885017i \(0.654147\pi\)
\(774\) 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 0.671437 0.741062i \(-0.265678\pi\)
−0.977497 + 0.210950i \(0.932344\pi\)
\(788\) 3244.62 + 5619.85i 0.146681 + 0.254059i
\(789\) 0 0
\(790\) 4846.84 0.218282
\(791\)