Properties

Label 882.4.g.a.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.a.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-11.0000 + 19.0526i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(-11.0000 + 19.0526i) q^{5} +8.00000 q^{8} +(-22.0000 - 38.1051i) q^{10} +(13.0000 + 22.5167i) q^{11} +54.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-37.0000 - 64.0859i) q^{17} +(58.0000 - 100.459i) q^{19} +88.0000 q^{20} -52.0000 q^{22} +(-29.0000 + 50.2295i) q^{23} +(-179.500 - 310.903i) q^{25} +(-54.0000 + 93.5307i) q^{26} -208.000 q^{29} +(-126.000 - 218.238i) q^{31} +(-16.0000 - 27.7128i) q^{32} +148.000 q^{34} +(-25.0000 + 43.3013i) q^{37} +(116.000 + 200.918i) q^{38} +(-88.0000 + 152.420i) q^{40} +126.000 q^{41} +164.000 q^{43} +(52.0000 - 90.0666i) q^{44} +(-58.0000 - 100.459i) q^{46} +(222.000 - 384.515i) q^{47} +718.000 q^{50} +(-108.000 - 187.061i) q^{52} +(6.00000 + 10.3923i) q^{53} -572.000 q^{55} +(208.000 - 360.267i) q^{58} +(-62.0000 - 107.387i) q^{59} +(-81.0000 + 140.296i) q^{61} +504.000 q^{62} +64.0000 q^{64} +(-594.000 + 1028.84i) q^{65} +(430.000 + 744.782i) q^{67} +(-148.000 + 256.344i) q^{68} +238.000 q^{71} +(-73.0000 - 126.440i) q^{73} +(-50.0000 - 86.6025i) q^{74} -464.000 q^{76} +(492.000 - 852.169i) q^{79} +(-176.000 - 304.841i) q^{80} +(-126.000 + 218.238i) q^{82} +656.000 q^{83} +1628.00 q^{85} +(-164.000 + 284.056i) q^{86} +(104.000 + 180.133i) q^{88} +(477.000 - 826.188i) q^{89} +232.000 q^{92} +(444.000 + 769.031i) q^{94} +(1276.00 + 2210.10i) q^{95} -526.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} - 22q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} - 22q^{5} + 16q^{8} - 44q^{10} + 26q^{11} + 108q^{13} - 16q^{16} - 74q^{17} + 116q^{19} + 176q^{20} - 104q^{22} - 58q^{23} - 359q^{25} - 108q^{26} - 416q^{29} - 252q^{31} - 32q^{32} + 296q^{34} - 50q^{37} + 232q^{38} - 176q^{40} + 252q^{41} + 328q^{43} + 104q^{44} - 116q^{46} + 444q^{47} + 1436q^{50} - 216q^{52} + 12q^{53} - 1144q^{55} + 416q^{58} - 124q^{59} - 162q^{61} + 1008q^{62} + 128q^{64} - 1188q^{65} + 860q^{67} - 296q^{68} + 476q^{71} - 146q^{73} - 100q^{74} - 928q^{76} + 984q^{79} - 352q^{80} - 252q^{82} + 1312q^{83} + 3256q^{85} - 328q^{86} + 208q^{88} + 954q^{89} + 464q^{92} + 888q^{94} + 2552q^{95} - 1052q^{97} + O(q^{100}) \)

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
\(5\) −11.0000 + 19.0526i −0.983870 + 1.70411i −0.337016 + 0.941499i \(0.609418\pi\)
−0.646854 + 0.762614i \(0.723916\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) −22.0000 38.1051i −0.695701 1.20499i
\(11\) 13.0000 + 22.5167i 0.356332 + 0.617184i 0.987345 0.158588i \(-0.0506940\pi\)
−0.631013 + 0.775772i \(0.717361\pi\)
\(12\) 0 0
\(13\) 54.0000 1.15207 0.576035 0.817425i \(-0.304599\pi\)
0.576035 + 0.817425i \(0.304599\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −37.0000 64.0859i −0.527872 0.914301i −0.999472 0.0324882i \(-0.989657\pi\)
0.471600 0.881812i \(-0.343676\pi\)
\(18\) 0 0
\(19\) 58.0000 100.459i 0.700322 1.21299i −0.268032 0.963410i \(-0.586373\pi\)
0.968353 0.249583i \(-0.0802934\pi\)
\(20\) 88.0000 0.983870
\(21\) 0 0
\(22\) −52.0000 −0.503929
\(23\) −29.0000 + 50.2295i −0.262909 + 0.455373i −0.967014 0.254724i \(-0.918015\pi\)
0.704104 + 0.710097i \(0.251349\pi\)
\(24\) 0 0
\(25\) −179.500 310.903i −1.43600 2.48722i
\(26\) −54.0000 + 93.5307i −0.407318 + 0.705496i
\(27\) 0 0
\(28\) 0 0
\(29\) −208.000 −1.33188 −0.665942 0.746004i \(-0.731970\pi\)
−0.665942 + 0.746004i \(0.731970\pi\)
\(30\) 0 0
\(31\) −126.000 218.238i −0.730009 1.26441i −0.956879 0.290487i \(-0.906183\pi\)
0.226870 0.973925i \(-0.427151\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 148.000 0.746523
\(35\) 0 0
\(36\) 0 0
\(37\) −25.0000 + 43.3013i −0.111080 + 0.192397i −0.916206 0.400707i \(-0.868764\pi\)
0.805126 + 0.593104i \(0.202098\pi\)
\(38\) 116.000 + 200.918i 0.495202 + 0.857715i
\(39\) 0 0
\(40\) −88.0000 + 152.420i −0.347851 + 0.602495i
\(41\) 126.000 0.479949 0.239974 0.970779i \(-0.422861\pi\)
0.239974 + 0.970779i \(0.422861\pi\)
\(42\) 0 0
\(43\) 164.000 0.581622 0.290811 0.956780i \(-0.406075\pi\)
0.290811 + 0.956780i \(0.406075\pi\)
\(44\) 52.0000 90.0666i 0.178166 0.308592i
\(45\) 0 0
\(46\) −58.0000 100.459i −0.185905 0.321997i
\(47\) 222.000 384.515i 0.688979 1.19335i −0.283189 0.959064i \(-0.591392\pi\)
0.972168 0.234283i \(-0.0752743\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 718.000 2.03081
\(51\) 0 0
\(52\) −108.000 187.061i −0.288017 0.498861i
\(53\) 6.00000 + 10.3923i 0.0155503 + 0.0269338i 0.873696 0.486473i \(-0.161717\pi\)
−0.858146 + 0.513406i \(0.828383\pi\)
\(54\) 0 0
\(55\) −572.000 −1.40234
\(56\) 0 0
\(57\) 0 0
\(58\) 208.000 360.267i 0.470892 0.815609i
\(59\) −62.0000 107.387i −0.136809 0.236960i 0.789478 0.613779i \(-0.210351\pi\)
−0.926287 + 0.376819i \(0.877018\pi\)
\(60\) 0 0
\(61\) −81.0000 + 140.296i −0.170016 + 0.294477i −0.938425 0.345482i \(-0.887715\pi\)
0.768409 + 0.639959i \(0.221049\pi\)
\(62\) 504.000 1.03239
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −594.000 + 1028.84i −1.13349 + 1.96326i
\(66\) 0 0
\(67\) 430.000 + 744.782i 0.784073 + 1.35805i 0.929552 + 0.368692i \(0.120194\pi\)
−0.145479 + 0.989361i \(0.546472\pi\)
\(68\) −148.000 + 256.344i −0.263936 + 0.457150i
\(69\) 0 0
\(70\) 0 0
\(71\) 238.000 0.397823 0.198911 0.980017i \(-0.436259\pi\)
0.198911 + 0.980017i \(0.436259\pi\)
\(72\) 0 0
\(73\) −73.0000 126.440i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) −50.0000 86.6025i −0.0785457 0.136045i
\(75\) 0 0
\(76\) −464.000 −0.700322
\(77\) 0 0
\(78\) 0 0
\(79\) 492.000 852.169i 0.700688 1.21363i −0.267538 0.963547i \(-0.586210\pi\)
0.968225 0.250079i \(-0.0804567\pi\)
\(80\) −176.000 304.841i −0.245967 0.426028i
\(81\) 0 0
\(82\) −126.000 + 218.238i −0.169687 + 0.293907i
\(83\) 656.000 0.867534 0.433767 0.901025i \(-0.357184\pi\)
0.433767 + 0.901025i \(0.357184\pi\)
\(84\) 0 0
\(85\) 1628.00 2.07743
\(86\) −164.000 + 284.056i −0.205635 + 0.356170i
\(87\) 0 0
\(88\) 104.000 + 180.133i 0.125982 + 0.218208i
\(89\) 477.000 826.188i 0.568111 0.983998i −0.428642 0.903475i \(-0.641008\pi\)
0.996753 0.0805229i \(-0.0256590\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 232.000 0.262909
\(93\) 0 0
\(94\) 444.000 + 769.031i 0.487182 + 0.843824i
\(95\) 1276.00 + 2210.10i 1.37805 + 2.38685i
\(96\) 0 0
\(97\) −526.000 −0.550590 −0.275295 0.961360i \(-0.588775\pi\)
−0.275295 + 0.961360i \(0.588775\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −718.000 + 1243.61i −0.718000 + 1.24361i
\(101\) −653.000 1131.03i −0.643326 1.11427i −0.984685 0.174341i \(-0.944221\pi\)
0.341359 0.939933i \(-0.389113\pi\)
\(102\) 0 0
\(103\) −254.000 + 439.941i −0.242984 + 0.420861i −0.961563 0.274585i \(-0.911460\pi\)
0.718579 + 0.695446i \(0.244793\pi\)
\(104\) 432.000 0.407318
\(105\) 0 0
\(106\) −24.0000 −0.0219914
\(107\) 249.000 431.281i 0.224970 0.389659i −0.731341 0.682012i \(-0.761105\pi\)
0.956310 + 0.292354i \(0.0944384\pi\)
\(108\) 0 0
\(109\) 307.000 + 531.740i 0.269773 + 0.467261i 0.968803 0.247832i \(-0.0797180\pi\)
−0.699030 + 0.715092i \(0.746385\pi\)
\(110\) 572.000 990.733i 0.495801 0.858752i
\(111\) 0 0
\(112\) 0 0
\(113\) 1232.00 1.02564 0.512818 0.858498i \(-0.328602\pi\)
0.512818 + 0.858498i \(0.328602\pi\)
\(114\) 0 0
\(115\) −638.000 1105.05i −0.517337 0.896055i
\(116\) 416.000 + 720.533i 0.332971 + 0.576723i
\(117\) 0 0
\(118\) 248.000 0.193477
\(119\) 0 0
\(120\) 0 0
\(121\) 327.500 567.247i 0.246056 0.426181i
\(122\) −162.000 280.592i −0.120220 0.208226i
\(123\) 0 0
\(124\) −504.000 + 872.954i −0.365004 + 0.632206i
\(125\) 5148.00 3.68361
\(126\) 0 0
\(127\) −2808.00 −1.96197 −0.980983 0.194093i \(-0.937824\pi\)
−0.980983 + 0.194093i \(0.937824\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1188.00 2057.68i −0.801496 1.38823i
\(131\) −260.000 + 450.333i −0.173407 + 0.300350i −0.939609 0.342250i \(-0.888811\pi\)
0.766202 + 0.642600i \(0.222144\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1720.00 −1.10885
\(135\) 0 0
\(136\) −296.000 512.687i −0.186631 0.323254i
\(137\) −1258.00 2178.92i −0.784512 1.35882i −0.929290 0.369351i \(-0.879580\pi\)
0.144778 0.989464i \(-0.453753\pi\)
\(138\) 0 0
\(139\) 2672.00 1.63048 0.815238 0.579126i \(-0.196606\pi\)
0.815238 + 0.579126i \(0.196606\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −238.000 + 412.228i −0.140652 + 0.243616i
\(143\) 702.000 + 1215.90i 0.410519 + 0.711039i
\(144\) 0 0
\(145\) 2288.00 3962.93i 1.31040 2.26968i
\(146\) 292.000 0.165521
\(147\) 0 0
\(148\) 200.000 0.111080
\(149\) −582.000 + 1008.05i −0.319995 + 0.554248i −0.980487 0.196586i \(-0.937015\pi\)
0.660491 + 0.750834i \(0.270348\pi\)
\(150\) 0 0
\(151\) −836.000 1447.99i −0.450548 0.780372i 0.547872 0.836562i \(-0.315438\pi\)
−0.998420 + 0.0561903i \(0.982105\pi\)
\(152\) 464.000 803.672i 0.247601 0.428858i
\(153\) 0 0
\(154\) 0 0
\(155\) 5544.00 2.87293
\(156\) 0 0
\(157\) 223.000 + 386.247i 0.113359 + 0.196343i 0.917123 0.398605i \(-0.130506\pi\)
−0.803764 + 0.594949i \(0.797172\pi\)
\(158\) 984.000 + 1704.34i 0.495461 + 0.858164i
\(159\) 0 0
\(160\) 704.000 0.347851
\(161\) 0 0
\(162\) 0 0
\(163\) −214.000 + 370.659i −0.102833 + 0.178112i −0.912851 0.408293i \(-0.866124\pi\)
0.810018 + 0.586405i \(0.199457\pi\)
\(164\) −252.000 436.477i −0.119987 0.207824i
\(165\) 0 0
\(166\) −656.000 + 1136.23i −0.306720 + 0.531254i
\(167\) 4.00000 0.00185347 0.000926734 1.00000i \(-0.499705\pi\)
0.000926734 1.00000i \(0.499705\pi\)
\(168\) 0 0
\(169\) 719.000 0.327264
\(170\) −1628.00 + 2819.78i −0.734482 + 1.27216i
\(171\) 0 0
\(172\) −328.000 568.113i −0.145406 0.251850i
\(173\) 295.000 510.955i 0.129644 0.224550i −0.793895 0.608055i \(-0.791950\pi\)
0.923539 + 0.383505i \(0.125283\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −416.000 −0.178166
\(177\) 0 0
\(178\) 954.000 + 1652.38i 0.401715 + 0.695791i
\(179\) 1767.00 + 3060.53i 0.737831 + 1.27796i 0.953470 + 0.301488i \(0.0974833\pi\)
−0.215639 + 0.976473i \(0.569183\pi\)
\(180\) 0 0
\(181\) −1098.00 −0.450904 −0.225452 0.974254i \(-0.572386\pi\)
−0.225452 + 0.974254i \(0.572386\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −232.000 + 401.836i −0.0929525 + 0.160999i
\(185\) −550.000 952.628i −0.218577 0.378587i
\(186\) 0 0
\(187\) 962.000 1666.23i 0.376195 0.651588i
\(188\) −1776.00 −0.688979
\(189\) 0 0
\(190\) −5104.00 −1.94886
\(191\) −2427.00 + 4203.69i −0.919432 + 1.59250i −0.119153 + 0.992876i \(0.538018\pi\)
−0.800279 + 0.599627i \(0.795315\pi\)
\(192\) 0 0
\(193\) 749.000 + 1297.31i 0.279348 + 0.483845i 0.971223 0.238172i \(-0.0765483\pi\)
−0.691875 + 0.722018i \(0.743215\pi\)
\(194\) 526.000 911.059i 0.194663 0.337166i
\(195\) 0 0
\(196\) 0 0
\(197\) −620.000 −0.224229 −0.112115 0.993695i \(-0.535762\pi\)
−0.112115 + 0.993695i \(0.535762\pi\)
\(198\) 0 0
\(199\) 16.0000 + 27.7128i 0.00569955 + 0.00987191i 0.868861 0.495056i \(-0.164852\pi\)
−0.863162 + 0.504928i \(0.831519\pi\)
\(200\) −1436.00 2487.22i −0.507703 0.879367i
\(201\) 0 0
\(202\) 2612.00 0.909800
\(203\) 0 0
\(204\) 0 0
\(205\) −1386.00 + 2400.62i −0.472207 + 0.817887i
\(206\) −508.000 879.882i −0.171816 0.297594i
\(207\) 0 0
\(208\) −432.000 + 748.246i −0.144009 + 0.249430i
\(209\) 3016.00 0.998187
\(210\) 0 0
\(211\) 4268.00 1.39252 0.696259 0.717791i \(-0.254847\pi\)
0.696259 + 0.717791i \(0.254847\pi\)
\(212\) 24.0000 41.5692i 0.00777513 0.0134669i
\(213\) 0 0
\(214\) 498.000 + 862.561i 0.159077 + 0.275530i
\(215\) −1804.00 + 3124.62i −0.572241 + 0.991150i
\(216\) 0 0
\(217\) 0 0
\(218\) −1228.00 −0.381517
\(219\) 0 0
\(220\) 1144.00 + 1981.47i 0.350584 + 0.607229i
\(221\) −1998.00 3460.64i −0.608145 1.05334i
\(222\) 0 0
\(223\) −3464.00 −1.04021 −0.520104 0.854103i \(-0.674107\pi\)
−0.520104 + 0.854103i \(0.674107\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1232.00 + 2133.89i −0.362617 + 0.628071i
\(227\) 1626.00 + 2816.31i 0.475425 + 0.823460i 0.999604 0.0281483i \(-0.00896107\pi\)
−0.524179 + 0.851608i \(0.675628\pi\)
\(228\) 0 0
\(229\) 209.000 361.999i 0.0603105 0.104461i −0.834294 0.551320i \(-0.814124\pi\)
0.894604 + 0.446859i \(0.147458\pi\)
\(230\) 2552.00 0.731626
\(231\) 0 0
\(232\) −1664.00 −0.470892
\(233\) 1042.00 1804.80i 0.292977 0.507451i −0.681535 0.731785i \(-0.738687\pi\)
0.974512 + 0.224334i \(0.0720207\pi\)
\(234\) 0 0
\(235\) 4884.00 + 8459.34i 1.35573 + 2.34820i
\(236\) −248.000 + 429.549i −0.0684043 + 0.118480i
\(237\) 0 0
\(238\) 0 0
\(239\) −1662.00 −0.449815 −0.224908 0.974380i \(-0.572208\pi\)
−0.224908 + 0.974380i \(0.572208\pi\)
\(240\) 0 0
\(241\) 3091.00 + 5353.77i 0.826178 + 1.43098i 0.901016 + 0.433786i \(0.142823\pi\)
−0.0748383 + 0.997196i \(0.523844\pi\)
\(242\) 655.000 + 1134.49i 0.173988 + 0.301355i
\(243\) 0 0
\(244\) 648.000 0.170016
\(245\) 0 0
\(246\) 0 0
\(247\) 3132.00 5424.78i 0.806819 1.39745i
\(248\) −1008.00 1745.91i −0.258097 0.447037i
\(249\) 0 0
\(250\) −5148.00 + 8916.60i −1.30235 + 2.25574i
\(251\) −996.000 −0.250466 −0.125233 0.992127i \(-0.539968\pi\)
−0.125233 + 0.992127i \(0.539968\pi\)
\(252\) 0 0
\(253\) −1508.00 −0.374732
\(254\) 2808.00 4863.60i 0.693660 1.20145i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2997.00 5190.96i 0.727423 1.25993i −0.230546 0.973061i \(-0.574051\pi\)
0.957969 0.286872i \(-0.0926155\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 4752.00 1.13349
\(261\) 0 0
\(262\) −520.000 900.666i −0.122617 0.212379i
\(263\) 3207.00 + 5554.69i 0.751909 + 1.30234i 0.946896 + 0.321539i \(0.104200\pi\)
−0.194987 + 0.980806i \(0.562467\pi\)
\(264\) 0 0
\(265\) −264.000 −0.0611977
\(266\) 0 0
\(267\) 0 0
\(268\) 1720.00 2979.13i 0.392036 0.679027i
\(269\) −1343.00 2326.14i −0.304402 0.527240i 0.672726 0.739892i \(-0.265123\pi\)
−0.977128 + 0.212652i \(0.931790\pi\)
\(270\) 0 0
\(271\) 2550.00 4416.73i 0.571592 0.990027i −0.424811 0.905282i \(-0.639659\pi\)
0.996403 0.0847444i \(-0.0270074\pi\)
\(272\) 1184.00 0.263936
\(273\) 0 0
\(274\) 5032.00 1.10947
\(275\) 4667.00 8083.48i 1.02338 1.77255i
\(276\) 0 0
\(277\) 2213.00 + 3833.03i 0.480023 + 0.831424i 0.999737 0.0229162i \(-0.00729509\pi\)
−0.519715 + 0.854340i \(0.673962\pi\)
\(278\) −2672.00 + 4628.04i −0.576460 + 0.998458i
\(279\) 0 0
\(280\) 0 0
\(281\) −7508.00 −1.59391 −0.796957 0.604036i \(-0.793558\pi\)
−0.796957 + 0.604036i \(0.793558\pi\)
\(282\) 0 0
\(283\) 1706.00 + 2954.88i 0.358343 + 0.620669i 0.987684 0.156460i \(-0.0500084\pi\)
−0.629341 + 0.777129i \(0.716675\pi\)
\(284\) −476.000 824.456i −0.0994556 0.172262i
\(285\) 0 0
\(286\) −2808.00 −0.580561
\(287\) 0 0
\(288\) 0 0
\(289\) −281.500 + 487.572i −0.0572970 + 0.0992413i
\(290\) 4576.00 + 7925.86i 0.926593 + 1.60491i
\(291\) 0 0
\(292\) −292.000 + 505.759i −0.0585206 + 0.101361i
\(293\) −4734.00 −0.943902 −0.471951 0.881625i \(-0.656450\pi\)
−0.471951 + 0.881625i \(0.656450\pi\)
\(294\) 0 0
\(295\) 2728.00 0.538408
\(296\) −200.000 + 346.410i −0.0392729 + 0.0680226i
\(297\) 0 0
\(298\) −1164.00 2016.11i −0.226271 0.391913i
\(299\) −1566.00 + 2712.39i −0.302890 + 0.524621i
\(300\) 0 0
\(301\) 0 0
\(302\) 3344.00 0.637171
\(303\) 0 0
\(304\) 928.000 + 1607.34i 0.175080 + 0.303248i
\(305\) −1782.00 3086.51i −0.334548 0.579453i
\(306\) 0 0
\(307\) −5836.00 −1.08494 −0.542472 0.840074i \(-0.682512\pi\)
−0.542472 + 0.840074i \(0.682512\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −5544.00 + 9602.49i −1.01574 + 1.75931i
\(311\) −2810.00 4867.06i −0.512349 0.887414i −0.999897 0.0143184i \(-0.995442\pi\)
0.487549 0.873096i \(-0.337891\pi\)
\(312\) 0 0
\(313\) 3041.00 5267.17i 0.549161 0.951175i −0.449171 0.893446i \(-0.648281\pi\)
0.998332 0.0577294i \(-0.0183861\pi\)
\(314\) −892.000 −0.160314
\(315\) 0 0
\(316\) −3936.00 −0.700688
\(317\) −3654.00 + 6328.91i −0.647410 + 1.12135i 0.336329 + 0.941745i \(0.390815\pi\)
−0.983739 + 0.179603i \(0.942519\pi\)
\(318\) 0 0
\(319\) −2704.00 4683.47i −0.474592 0.822018i
\(320\) −704.000 + 1219.36i −0.122984 + 0.213014i
\(321\) 0 0
\(322\) 0 0
\(323\) −8584.00 −1.47872
\(324\) 0 0
\(325\) −9693.00 16788.8i −1.65437 2.86546i
\(326\) −428.000 741.318i −0.0727139 0.125944i
\(327\) 0 0
\(328\) 1008.00 0.169687
\(329\) 0 0
\(330\) 0 0
\(331\) 4010.00 6945.52i 0.665890 1.15336i −0.313153 0.949703i \(-0.601385\pi\)
0.979043 0.203652i \(-0.0652813\pi\)
\(332\) −1312.00 2272.45i −0.216884 0.375653i
\(333\) 0 0
\(334\) −4.00000 + 6.92820i −0.000655300 + 0.00113501i
\(335\) −18920.0 −3.08570
\(336\) 0 0
\(337\) 4590.00 0.741938 0.370969 0.928645i \(-0.379026\pi\)
0.370969 + 0.928645i \(0.379026\pi\)
\(338\) −719.000 + 1245.34i −0.115705 + 0.200408i
\(339\) 0 0
\(340\) −3256.00 5639.56i −0.519357 0.899553i
\(341\) 3276.00 5674.20i 0.520250 0.901100i
\(342\) 0 0
\(343\) 0 0
\(344\) 1312.00 0.205635
\(345\) 0 0
\(346\) 590.000 + 1021.91i 0.0916722 + 0.158781i
\(347\) −3273.00 5669.00i −0.506351 0.877026i −0.999973 0.00734926i \(-0.997661\pi\)
0.493622 0.869677i \(-0.335673\pi\)
\(348\) 0 0
\(349\) 7994.00 1.22610 0.613050 0.790044i \(-0.289942\pi\)
0.613050 + 0.790044i \(0.289942\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 416.000 720.533i 0.0629911 0.109104i
\(353\) −2325.00 4027.02i −0.350559 0.607186i 0.635789 0.771863i \(-0.280675\pi\)
−0.986347 + 0.164678i \(0.947342\pi\)
\(354\) 0 0
\(355\) −2618.00 + 4534.51i −0.391406 + 0.677935i
\(356\) −3816.00 −0.568111
\(357\) 0 0
\(358\) −7068.00 −1.04345
\(359\) 173.000 299.645i 0.0254334 0.0440519i −0.853029 0.521864i \(-0.825237\pi\)
0.878462 + 0.477812i \(0.158570\pi\)
\(360\) 0 0
\(361\) −3298.50 5713.17i −0.480901 0.832945i
\(362\) 1098.00 1901.79i 0.159419 0.276121i
\(363\) 0 0
\(364\) 0 0
\(365\) 3212.00 0.460613
\(366\) 0 0
\(367\) −3392.00 5875.12i −0.482455 0.835636i 0.517342 0.855779i \(-0.326921\pi\)
−0.999797 + 0.0201422i \(0.993588\pi\)
\(368\) −464.000 803.672i −0.0657274 0.113843i
\(369\) 0 0
\(370\) 2200.00 0.309115
\(371\) 0 0
\(372\) 0 0
\(373\) 3049.00 5281.02i 0.423247 0.733086i −0.573008 0.819550i \(-0.694223\pi\)
0.996255 + 0.0864642i \(0.0275568\pi\)
\(374\) 1924.00 + 3332.47i 0.266010 + 0.460743i
\(375\) 0 0
\(376\) 1776.00 3076.12i 0.243591 0.421912i
\(377\) −11232.0 −1.53442
\(378\) 0 0
\(379\) −2660.00 −0.360515 −0.180257 0.983619i \(-0.557693\pi\)
−0.180257 + 0.983619i \(0.557693\pi\)
\(380\) 5104.00 8840.39i 0.689025 1.19343i
\(381\) 0 0
\(382\) −4854.00 8407.37i −0.650137 1.12607i
\(383\) 380.000 658.179i 0.0506974 0.0878104i −0.839563 0.543262i \(-0.817189\pi\)
0.890260 + 0.455452i \(0.150522\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2996.00 −0.395058
\(387\) 0 0
\(388\) 1052.00 + 1822.12i 0.137647 + 0.238412i
\(389\) −52.0000 90.0666i −0.00677765 0.0117392i 0.862617 0.505858i \(-0.168824\pi\)
−0.869394 + 0.494119i \(0.835491\pi\)
\(390\) 0 0
\(391\) 4292.00 0.555130
\(392\) 0 0
\(393\) 0 0
\(394\) 620.000 1073.87i 0.0792770 0.137312i
\(395\) 10824.0 + 18747.7i 1.37877 + 2.38810i
\(396\) 0 0
\(397\) 2199.00 3808.78i 0.277997 0.481504i −0.692890 0.721043i \(-0.743663\pi\)
0.970887 + 0.239539i \(0.0769963\pi\)
\(398\) −64.0000 −0.00806038
\(399\) 0 0
\(400\) 5744.00 0.718000
\(401\) 6618.00 11462.7i 0.824157 1.42748i −0.0784040 0.996922i \(-0.524982\pi\)
0.902561 0.430561i \(-0.141684\pi\)
\(402\) 0 0
\(403\) −6804.00 11784.9i −0.841021 1.45669i
\(404\) −2612.00 + 4524.12i −0.321663 + 0.557137i
\(405\) 0 0
\(406\) 0 0
\(407\) −1300.00 −0.158326
\(408\) 0 0
\(409\) −4745.00 8218.58i −0.573656 0.993601i −0.996186 0.0872520i \(-0.972191\pi\)
0.422531 0.906349i \(-0.361142\pi\)
\(410\) −2772.00 4801.24i −0.333901 0.578333i
\(411\) 0 0
\(412\) 2032.00 0.242984
\(413\) 0 0
\(414\) 0 0
\(415\) −7216.00 + 12498.5i −0.853541 + 1.47838i
\(416\) −864.000 1496.49i −0.101830 0.176374i
\(417\) 0 0
\(418\) −3016.00 + 5223.87i −0.352912 + 0.611262i
\(419\) 4236.00 0.493895 0.246948 0.969029i \(-0.420572\pi\)
0.246948 + 0.969029i \(0.420572\pi\)
\(420\) 0 0
\(421\) 918.000 0.106272 0.0531361 0.998587i \(-0.483078\pi\)
0.0531361 + 0.998587i \(0.483078\pi\)
\(422\) −4268.00 + 7392.39i −0.492329 + 0.852739i
\(423\) 0 0
\(424\) 48.0000 + 83.1384i 0.00549784 + 0.00952255i
\(425\) −13283.0 + 23006.8i −1.51605 + 2.62587i
\(426\) 0 0
\(427\) 0 0
\(428\) −1992.00 −0.224970
\(429\) 0 0
\(430\) −3608.00 6249.24i −0.404635 0.700849i
\(431\) −5907.00 10231.2i −0.660163 1.14344i −0.980573 0.196157i \(-0.937154\pi\)
0.320410 0.947279i \(-0.396179\pi\)
\(432\) 0 0
\(433\) 8374.00 0.929397 0.464698 0.885469i \(-0.346163\pi\)
0.464698 + 0.885469i \(0.346163\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1228.00 2126.96i 0.134887 0.233630i
\(437\) 3364.00 + 5826.62i 0.368242 + 0.637815i
\(438\) 0 0
\(439\) 1920.00 3325.54i 0.208739 0.361547i −0.742578 0.669759i \(-0.766397\pi\)
0.951318 + 0.308212i \(0.0997306\pi\)
\(440\) −4576.00 −0.495801
\(441\) 0 0
\(442\) 7992.00 0.860047
\(443\) 5083.00 8804.01i 0.545148 0.944224i −0.453449 0.891282i \(-0.649807\pi\)
0.998598 0.0529423i \(-0.0168599\pi\)
\(444\) 0 0
\(445\) 10494.0 + 18176.1i 1.11790 + 1.93625i
\(446\) 3464.00 5999.82i 0.367769 0.636995i
\(447\) 0 0
\(448\) 0 0
\(449\) −8200.00 −0.861875 −0.430938 0.902382i \(-0.641817\pi\)
−0.430938 + 0.902382i \(0.641817\pi\)
\(450\) 0 0
\(451\) 1638.00 + 2837.10i 0.171021 + 0.296217i
\(452\) −2464.00 4267.77i −0.256409 0.444113i
\(453\) 0 0
\(454\) −6504.00 −0.672352
\(455\) 0 0
\(456\) 0 0
\(457\) 3037.00 5260.24i 0.310864 0.538432i −0.667686 0.744443i \(-0.732715\pi\)
0.978550 + 0.206011i \(0.0660483\pi\)
\(458\) 418.000 + 723.997i 0.0426460 + 0.0738650i
\(459\) 0 0
\(460\) −2552.00 + 4420.19i −0.258669 + 0.448027i
\(461\) −2006.00 −0.202665 −0.101333 0.994853i \(-0.532311\pi\)
−0.101333 + 0.994853i \(0.532311\pi\)
\(462\) 0 0
\(463\) −3728.00 −0.374201 −0.187100 0.982341i \(-0.559909\pi\)
−0.187100 + 0.982341i \(0.559909\pi\)
\(464\) 1664.00 2882.13i 0.166485 0.288361i
\(465\) 0 0
\(466\) 2084.00 + 3609.59i 0.207166 + 0.358822i
\(467\) 3190.00 5525.24i 0.316093 0.547490i −0.663576 0.748109i \(-0.730962\pi\)
0.979669 + 0.200619i \(0.0642954\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −19536.0 −1.91729
\(471\) 0 0
\(472\) −496.000 859.097i −0.0483692 0.0837779i
\(473\) 2132.00 + 3692.73i 0.207250 + 0.358968i
\(474\) 0 0
\(475\) −41644.0 −4.02265
\(476\) 0 0
\(477\) 0 0
\(478\) 1662.00 2878.67i 0.159034 0.275454i
\(479\) −8590.00 14878.3i −0.819389 1.41922i −0.906133 0.422992i \(-0.860980\pi\)
0.0867448 0.996231i \(-0.472354\pi\)
\(480\) 0 0
\(481\) −1350.00 + 2338.27i −0.127972 + 0.221655i
\(482\) −12364.0 −1.16839
\(483\) 0 0
\(484\) −2620.00 −0.246056
\(485\) 5786.00 10021.6i 0.541709 0.938267i
\(486\) 0 0
\(487\) 1364.00 + 2362.52i 0.126917 + 0.219827i 0.922481 0.386043i \(-0.126158\pi\)
−0.795563 + 0.605870i \(0.792825\pi\)
\(488\) −648.000 + 1122.37i −0.0601098 + 0.104113i
\(489\) 0 0
\(490\) 0 0
\(491\) −2574.00 −0.236585 −0.118292 0.992979i \(-0.537742\pi\)
−0.118292 + 0.992979i \(0.537742\pi\)
\(492\) 0 0
\(493\) 7696.00 + 13329.9i 0.703064 + 1.21774i
\(494\) 6264.00 + 10849.6i 0.570507 + 0.988148i
\(495\) 0 0
\(496\) 4032.00 0.365004
\(497\) 0 0
\(498\) 0 0
\(499\) 3742.00 6481.33i 0.335701 0.581452i −0.647918 0.761710i \(-0.724360\pi\)
0.983619 + 0.180258i \(0.0576934\pi\)
\(500\) −10296.0 17833.2i −0.920902 1.59505i
\(501\) 0 0
\(502\) 996.000 1725.12i 0.0885531 0.153378i
\(503\) 7920.00 0.702058 0.351029 0.936365i \(-0.385832\pi\)
0.351029 + 0.936365i \(0.385832\pi\)
\(504\) 0 0
\(505\) 28732.0 2.53180
\(506\) 1508.00 2611.93i 0.132488 0.229475i
\(507\) 0 0
\(508\) 5616.00 + 9727.20i 0.490492 + 0.849556i
\(509\) −3627.00 + 6282.15i −0.315843 + 0.547056i −0.979616 0.200878i \(-0.935621\pi\)
0.663774 + 0.747934i \(0.268954\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) 5994.00 + 10381.9i 0.514366 + 0.890908i
\(515\) −5588.00 9678.70i −0.478130 0.828145i
\(516\) 0 0
\(517\) 11544.0 0.982020
\(518\) 0 0
\(519\) 0 0
\(520\) −4752.00 + 8230.71i −0.400748 + 0.694116i
\(521\) 8931.00 + 15468.9i 0.751006 + 1.30078i 0.947335 + 0.320243i \(0.103765\pi\)
−0.196329 + 0.980538i \(0.562902\pi\)
\(522\) 0 0
\(523\) −296.000 + 512.687i −0.0247479 + 0.0428647i −0.878134 0.478415i \(-0.841212\pi\)
0.853386 + 0.521279i \(0.174545\pi\)
\(524\) 2080.00 0.173407
\(525\) 0 0
\(526\) −12828.0 −1.06336
\(527\) −9324.00 + 16149.6i −0.770702 + 1.33489i
\(528\) 0 0
\(529\) 4401.50 + 7623.62i 0.361757 + 0.626582i
\(530\) 264.000 457.261i 0.0216367 0.0374758i
\(531\) 0 0
\(532\) 0 0
\(533\) 6804.00 0.552934
\(534\) 0 0
\(535\) 5478.00 + 9488.17i 0.442681 + 0.766747i
\(536\) 3440.00 + 5958.25i 0.277212 + 0.480144i
\(537\) 0 0
\(538\) 5372.00 0.430490
\(539\) 0 0
\(540\) 0 0
\(541\) 3201.00 5544.29i 0.254384 0.440606i −0.710344 0.703855i \(-0.751461\pi\)
0.964728 + 0.263249i \(0.0847940\pi\)
\(542\) 5100.00 + 8833.46i 0.404177 + 0.700055i
\(543\) 0 0
\(544\) −1184.00 + 2050.75i −0.0933154 + 0.161627i
\(545\) −13508.0 −1.06169
\(546\) 0 0
\(547\) −8988.00 −0.702558 −0.351279 0.936271i \(-0.614253\pi\)
−0.351279 + 0.936271i \(0.614253\pi\)
\(548\) −5032.00 + 8715.68i −0.392256 + 0.679408i
\(549\) 0 0
\(550\) 9334.00 + 16167.0i 0.723642 + 1.25338i
\(551\) −12064.0 + 20895.5i −0.932747 + 1.61557i
\(552\) 0 0
\(553\) 0 0
\(554\) −8852.00 −0.678855
\(555\) 0 0
\(556\) −5344.00 9256.08i −0.407619 0.706017i
\(557\) 1622.00 + 2809.39i 0.123387 + 0.213712i 0.921101 0.389323i \(-0.127291\pi\)
−0.797715 + 0.603035i \(0.793958\pi\)
\(558\) 0 0
\(559\) 8856.00 0.670070
\(560\) 0 0
\(561\) 0 0
\(562\) 7508.00 13004.2i 0.563534 0.976069i
\(563\) −4906.00 8497.44i −0.367253 0.636100i 0.621882 0.783111i \(-0.286368\pi\)
−0.989135 + 0.147010i \(0.953035\pi\)
\(564\) 0 0
\(565\) −13552.0 + 23472.8i −1.00909 + 1.74780i
\(566\) −6824.00 −0.506774
\(567\) 0 0
\(568\) 1904.00 0.140652
\(569\) −6078.00 + 10527.4i −0.447808 + 0.775627i −0.998243 0.0592513i \(-0.981129\pi\)
0.550435 + 0.834878i \(0.314462\pi\)
\(570\) 0 0
\(571\) −3438.00 5954.79i −0.251972 0.436428i 0.712097 0.702081i \(-0.247746\pi\)
−0.964069 + 0.265653i \(0.914412\pi\)
\(572\) 2808.00 4863.60i 0.205259 0.355520i
\(573\) 0 0
\(574\) 0 0
\(575\) 20822.0 1.51015
\(576\) 0 0
\(577\) 10001.0 + 17322.2i 0.721572 + 1.24980i 0.960369 + 0.278730i \(0.0899135\pi\)
−0.238797 + 0.971069i \(0.576753\pi\)
\(578\) −563.000 975.145i −0.0405151 0.0701742i
\(579\) 0 0
\(580\) −18304.0 −1.31040
\(581\) 0 0
\(582\) 0 0
\(583\) −156.000 + 270.200i −0.0110821 + 0.0191947i
\(584\) −584.000 1011.52i −0.0413803 0.0716728i
\(585\) 0 0
\(586\) 4734.00 8199.53i 0.333720 0.578019i
\(587\) 18404.0 1.29406 0.647031 0.762464i \(-0.276010\pi\)
0.647031 + 0.762464i \(0.276010\pi\)
\(588\) 0 0
\(589\) −29232.0 −2.04496
\(590\) −2728.00 + 4725.03i −0.190356 + 0.329706i
\(591\) 0 0
\(592\) −400.000 692.820i −0.0277701 0.0480992i
\(593\) 4923.00 8526.89i 0.340916 0.590484i −0.643687 0.765289i \(-0.722596\pi\)
0.984603 + 0.174805i \(0.0559294\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4656.00 0.319995
\(597\) 0 0
\(598\) −3132.00 5424.78i −0.214176 0.370963i
\(599\) 4617.00 + 7996.88i 0.314934 + 0.545482i 0.979423 0.201816i \(-0.0646843\pi\)
−0.664489 + 0.747298i \(0.731351\pi\)
\(600\) 0 0
\(601\) 1510.00 0.102486 0.0512431 0.998686i \(-0.483682\pi\)
0.0512431 + 0.998686i \(0.483682\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3344.00 + 5791.98i −0.225274 + 0.390186i
\(605\) 7205.00 + 12479.4i 0.484173 + 0.838613i
\(606\) 0 0
\(607\) 8772.00 15193.5i 0.586564 1.01596i −0.408114 0.912931i \(-0.633813\pi\)
0.994678 0.103028i \(-0.0328532\pi\)
\(608\) −3712.00 −0.247601
\(609\) 0 0
\(610\) 7128.00 0.473122
\(611\) 11988.0 20763.8i 0.793752 1.37482i
\(612\) 0 0
\(613\) −4623.00 8007.27i −0.304602 0.527587i 0.672570 0.740033i \(-0.265190\pi\)
−0.977173 + 0.212446i \(0.931857\pi\)
\(614\) 5836.00 10108.2i 0.383586 0.664390i
\(615\) 0 0
\(616\) 0 0
\(617\) 29212.0 1.90605 0.953023 0.302897i \(-0.0979537\pi\)
0.953023 + 0.302897i \(0.0979537\pi\)
\(618\) 0 0
\(619\) 3548.00 + 6145.32i 0.230382 + 0.399032i 0.957920 0.287034i \(-0.0926693\pi\)
−0.727539 + 0.686066i \(0.759336\pi\)
\(620\) −11088.0 19205.0i −0.718234 1.24402i
\(621\) 0 0
\(622\) 11240.0 0.724571
\(623\) 0 0
\(624\) 0 0
\(625\) −34190.5 + 59219.7i −2.18819 + 3.79006i
\(626\) 6082.00 + 10534.3i 0.388316 + 0.672582i
\(627\) 0 0
\(628\) 892.000 1544.99i 0.0566794 0.0981716i
\(629\) 3700.00 0.234545
\(630\) 0 0
\(631\) 488.000 0.0307876 0.0153938 0.999882i \(-0.495100\pi\)
0.0153938 + 0.999882i \(0.495100\pi\)
\(632\) 3936.00 6817.35i 0.247730 0.429082i
\(633\) 0 0
\(634\) −7308.00 12657.8i −0.457788 0.792913i
\(635\) 30888.0 53499.6i 1.93032 3.34341i
\(636\) 0 0
\(637\) 0 0
\(638\) 10816.0 0.671175
\(639\) 0 0
\(640\) −1408.00 2438.73i −0.0869626 0.150624i
\(641\) 4378.00 + 7582.92i 0.269767 + 0.467250i 0.968802 0.247838i \(-0.0797200\pi\)
−0.699035 + 0.715088i \(0.746387\pi\)
\(642\) 0 0
\(643\) 3364.00 0.206319 0.103160 0.994665i \(-0.467105\pi\)
0.103160 + 0.994665i \(0.467105\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 8584.00 14867.9i 0.522806 0.905527i
\(647\) −10902.0 18882.8i −0.662445 1.14739i −0.979971 0.199139i \(-0.936186\pi\)
0.317526 0.948249i \(-0.397148\pi\)
\(648\) 0 0
\(649\) 1612.00 2792.07i 0.0974985 0.168872i
\(650\) 38772.0 2.33964
\(651\) 0 0
\(652\) 1712.00 0.102833
\(653\) 6744.00 11681.0i 0.404155 0.700017i −0.590068 0.807354i \(-0.700899\pi\)
0.994223 + 0.107337i \(0.0342324\pi\)
\(654\) 0 0
\(655\) −5720.00 9907.33i −0.341220 0.591010i
\(656\) −1008.00 + 1745.91i −0.0599936 + 0.103912i
\(657\) 0 0
\(658\) 0 0
\(659\) −28946.0 −1.71104 −0.855521 0.517769i \(-0.826763\pi\)
−0.855521 + 0.517769i \(0.826763\pi\)
\(660\) 0 0
\(661\) −10321.0 17876.5i −0.607323 1.05191i −0.991680 0.128729i \(-0.958910\pi\)
0.384357 0.923185i \(-0.374423\pi\)
\(662\) 8020.00 + 13891.0i 0.470855 + 0.815545i
\(663\) 0 0
\(664\) 5248.00 0.306720
\(665\) 0 0
\(666\) 0 0
\(667\) 6032.00 10447.7i 0.350165 0.606503i
\(668\) −8.00000 13.8564i −0.000463367 0.000802576i
\(669\) 0 0
\(670\) 18920.0 32770.4i 1.09096 1.88960i
\(671\) −4212.00 −0.242329
\(672\) 0 0
\(673\) −17602.0 −1.00818 −0.504092 0.863650i \(-0.668173\pi\)
−0.504092 + 0.863650i \(0.668173\pi\)
\(674\) −4590.00 + 7950.11i −0.262315 + 0.454343i
\(675\) 0 0
\(676\) −1438.00 2490.69i −0.0818161 0.141710i
\(677\) −2133.00 + 3694.46i −0.121090 + 0.209734i −0.920198 0.391454i \(-0.871972\pi\)
0.799108 + 0.601188i \(0.205306\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 13024.0 0.734482
\(681\) 0 0
\(682\) 6552.00 + 11348.4i 0.367873 + 0.637174i
\(683\) −13437.0 23273.6i −0.752786 1.30386i −0.946468 0.322798i \(-0.895376\pi\)
0.193682 0.981064i \(-0.437957\pi\)
\(684\) 0 0
\(685\) 55352.0 3.08743
\(686\) 0 0
\(687\) 0 0
\(688\) −1312.00 + 2272.45i −0.0727028 + 0.125925i
\(689\) 324.000 + 561.184i 0.0179150 + 0.0310296i
\(690\) 0 0
\(691\) −8564.00 + 14833.3i −0.471476 + 0.816620i −0.999468 0.0326293i \(-0.989612\pi\)
0.527992 + 0.849250i \(0.322945\pi\)
\(692\) −2360.00 −0.129644
\(693\) 0 0
\(694\) 13092.0 0.716089
\(695\) −29392.0 + 50908.4i −1.60418 + 2.77851i
\(696\) 0 0
\(697\) −4662.00 8074.82i −0.253351 0.438817i
\(698\) −7994.00 + 13846.0i −0.433492 + 0.750830i
\(699\) 0 0
\(700\) 0 0
\(701\) −11968.0 −0.644829 −0.322414 0.946599i \(-0.604494\pi\)
−0.322414 + 0.946599i \(0.604494\pi\)
\(702\) 0 0
\(703\) 2900.00 + 5022.95i 0.155584 + 0.269479i
\(704\) 832.000 + 1441.07i 0.0445414 + 0.0771481i
\(705\) 0 0
\(706\) 9300.00 0.495765
\(707\) 0 0
\(708\) 0 0
\(709\) 2639.00 4570.88i 0.139788 0.242120i −0.787628 0.616151i \(-0.788691\pi\)
0.927416 + 0.374031i \(0.122025\pi\)
\(710\) −5236.00 9069.02i −0.276766 0.479372i
\(711\) 0 0
\(712\) 3816.00 6609.51i 0.200858 0.347896i
\(713\) 14616.0 0.767705
\(714\) 0 0
\(715\) −30888.0 −1.61559
\(716\) 7068.00 12242.1i 0.368916 0.638981i
\(717\) 0 0
\(718\) 346.000 + 599.290i 0.0179841 + 0.0311494i
\(719\) −3360.00 + 5819.69i −0.174279 + 0.301861i −0.939912 0.341418i \(-0.889093\pi\)
0.765632 + 0.643278i \(0.222426\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13194.0 0.680097
\(723\) 0 0
\(724\) 2196.00 + 3803.58i 0.112726 + 0.195247i
\(725\) 37336.0 + 64667.8i 1.91259 + 3.31269i
\(726\) 0 0
\(727\) −16804.0 −0.857257 −0.428629 0.903481i \(-0.641003\pi\)
−0.428629 + 0.903481i \(0.641003\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −3212.00 + 5563.35i −0.162851 + 0.282067i
\(731\) −6068.00 10510.1i −0.307022 0.531778i
\(732\) 0 0
\(733\) 13761.0 23834.8i 0.693416 1.20103i −0.277295 0.960785i \(-0.589438\pi\)
0.970712 0.240248i \(-0.0772286\pi\)
\(734\) 13568.0 0.682294
\(735\) 0 0
\(736\) 1856.00 0.0929525
\(737\) −11180.0 + 19364.3i −0.558780 + 0.967835i
\(738\) 0 0
\(739\) −10566.0 18300.8i −0.525949 0.910971i −0.999543 0.0302276i \(-0.990377\pi\)
0.473594 0.880743i \(-0.342957\pi\)
\(740\) −2200.00 + 3810.51i −0.109289 + 0.189294i
\(741\) 0 0
\(742\) 0 0
\(743\) 30.0000 0.00148128 0.000740641 1.00000i \(-0.499764\pi\)
0.000740641 1.00000i \(0.499764\pi\)
\(744\) 0 0
\(745\) −12804.0 22177.2i −0.629667 1.09062i
\(746\) 6098.00 + 10562.0i 0.299281 + 0.518370i
\(747\) 0 0
\(748\) −7696.00 −0.376195
\(749\) 0 0
\(750\) 0 0
\(751\) 7740.00 13406.1i 0.376081 0.651391i −0.614407 0.788989i \(-0.710605\pi\)
0.990488 + 0.137598i \(0.0439382\pi\)
\(752\) 3552.00 + 6152.24i 0.172245 + 0.298337i
\(753\) 0 0
\(754\) 11232.0 19454.4i 0.542500 0.939638i
\(755\) 36784.0 1.77312
\(756\) 0 0
\(757\) 28770.0 1.38133 0.690663 0.723177i \(-0.257319\pi\)
0.690663 + 0.723177i \(0.257319\pi\)
\(758\) 2660.00 4607.26i 0.127461 0.220769i
\(759\) 0 0
\(760\) 10208.0 + 17680.8i 0.487215 + 0.843880i
\(761\) 6209.00 10754.3i 0.295764 0.512278i −0.679399 0.733769i \(-0.737759\pi\)
0.975162 + 0.221492i \(0.0710926\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 19416.0 0.919432
\(765\) 0 0
\(766\) 760.000 + 1316.36i 0.0358485 + 0.0620913i
\(767\) −3348.00 5798.91i −0.157613 0.272994i
\(768\) 0 0
\(769\) −12346.0 −0.578944 −0.289472 0.957186i \(-0.593480\pi\)
−0.289472 + 0.957186i \(0.593480\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2996.00 5189.22i 0.139674 0.241923i
\(773\) −19049.0 32993.8i −0.886345 1.53520i −0.844164 0.536085i \(-0.819903\pi\)
−0.0421813 0.999110i \(-0.513431\pi\)
\(774\) 0 0
\(775\) −45234.0 + 78347.6i −2.09658 + 3.63139i
\(776\) −4208.00 −0.194663
\(777\) 0 0
\(778\) 208.000 0.00958504
\(779\) 7308.00 12657.8i 0.336118 0.582174i
\(780\) 0 0
\(781\) 3094.00 + 5358.97i 0.141757 + 0.245530i
\(782\) −4292.00 + 7433.96i −0.196268 + 0.339946i
\(783\) 0 0
\(784\) 0 0
\(785\) −9812.00 −0.446121
\(786\) 0 0
\(787\) 6912.00 + 11971.9i 0.313070 + 0.542253i 0.979025 0.203738i \(-0.0653092\pi\)
−0.665955 + 0.745992i \(0.731976\pi\)
\(788\) 1240.00 + 2147.74i 0.0560573 + 0.0970941i
\(789\) 0 0