Properties

Label 882.4.g.s.667.1
Level $882$
Weight $4$
Character 882.667
Analytic conductor $52.040$
Analytic rank $1$
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: \(1\)
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 42)
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.s.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(1.00000 - 1.73205i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(1.00000 - 1.73205i) q^{5} -8.00000 q^{8} +(-2.00000 - 3.46410i) q^{10} +(-4.00000 - 6.92820i) q^{11} -42.0000 q^{13} +(-8.00000 + 13.8564i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(62.0000 - 107.387i) q^{19} -8.00000 q^{20} -16.0000 q^{22} +(38.0000 - 65.8179i) q^{23} +(60.5000 + 104.789i) q^{25} +(-42.0000 + 72.7461i) q^{26} -254.000 q^{29} +(36.0000 + 62.3538i) q^{31} +(16.0000 + 27.7128i) q^{32} -4.00000 q^{34} +(-199.000 + 344.678i) q^{37} +(-124.000 - 214.774i) q^{38} +(-8.00000 + 13.8564i) q^{40} -462.000 q^{41} +212.000 q^{43} +(-16.0000 + 27.7128i) q^{44} +(-76.0000 - 131.636i) q^{46} +(-132.000 + 228.631i) q^{47} +242.000 q^{50} +(84.0000 + 145.492i) q^{52} +(-81.0000 - 140.296i) q^{53} -16.0000 q^{55} +(-254.000 + 439.941i) q^{58} +(-386.000 - 668.572i) q^{59} +(-15.0000 + 25.9808i) q^{61} +144.000 q^{62} +64.0000 q^{64} +(-42.0000 + 72.7461i) q^{65} +(382.000 + 661.643i) q^{67} +(-4.00000 + 6.92820i) q^{68} +236.000 q^{71} +(-209.000 - 361.999i) q^{73} +(398.000 + 689.356i) q^{74} -496.000 q^{76} +(-276.000 + 478.046i) q^{79} +(16.0000 + 27.7128i) q^{80} +(-462.000 + 800.207i) q^{82} -1036.00 q^{83} -4.00000 q^{85} +(212.000 - 367.195i) q^{86} +(32.0000 + 55.4256i) q^{88} +(15.0000 - 25.9808i) q^{89} -304.000 q^{92} +(264.000 + 457.261i) q^{94} +(-124.000 - 214.774i) q^{95} -1190.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 4q^{4} + 2q^{5} - 16q^{8} + O(q^{10}) \) \( 2q + 2q^{2} - 4q^{4} + 2q^{5} - 16q^{8} - 4q^{10} - 8q^{11} - 84q^{13} - 16q^{16} - 2q^{17} + 124q^{19} - 16q^{20} - 32q^{22} + 76q^{23} + 121q^{25} - 84q^{26} - 508q^{29} + 72q^{31} + 32q^{32} - 8q^{34} - 398q^{37} - 248q^{38} - 16q^{40} - 924q^{41} + 424q^{43} - 32q^{44} - 152q^{46} - 264q^{47} + 484q^{50} + 168q^{52} - 162q^{53} - 32q^{55} - 508q^{58} - 772q^{59} - 30q^{61} + 288q^{62} + 128q^{64} - 84q^{65} + 764q^{67} - 8q^{68} + 472q^{71} - 418q^{73} + 796q^{74} - 992q^{76} - 552q^{79} + 32q^{80} - 924q^{82} - 2072q^{83} - 8q^{85} + 424q^{86} + 64q^{88} + 30q^{89} - 608q^{92} + 528q^{94} - 248q^{95} - 2380q^{97} + O(q^{100}) \)

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
\(5\) 1.00000 1.73205i 0.0894427 0.154919i −0.817833 0.575456i \(-0.804825\pi\)
0.907276 + 0.420536i \(0.138158\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −2.00000 3.46410i −0.0632456 0.109545i
\(11\) −4.00000 6.92820i −0.109640 0.189903i 0.805984 0.591937i \(-0.201637\pi\)
−0.915625 + 0.402034i \(0.868303\pi\)
\(12\) 0 0
\(13\) −42.0000 −0.896054 −0.448027 0.894020i \(-0.647873\pi\)
−0.448027 + 0.894020i \(0.647873\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −1.00000 1.73205i −0.0142668 0.0247108i 0.858804 0.512305i \(-0.171208\pi\)
−0.873071 + 0.487594i \(0.837875\pi\)
\(18\) 0 0
\(19\) 62.0000 107.387i 0.748620 1.29665i −0.199865 0.979824i \(-0.564050\pi\)
0.948484 0.316824i \(-0.102616\pi\)
\(20\) −8.00000 −0.0894427
\(21\) 0 0
\(22\) −16.0000 −0.155055
\(23\) 38.0000 65.8179i 0.344502 0.596695i −0.640761 0.767740i \(-0.721381\pi\)
0.985263 + 0.171045i \(0.0547144\pi\)
\(24\) 0 0
\(25\) 60.5000 + 104.789i 0.484000 + 0.838313i
\(26\) −42.0000 + 72.7461i −0.316803 + 0.548719i
\(27\) 0 0
\(28\) 0 0
\(29\) −254.000 −1.62644 −0.813218 0.581960i \(-0.802286\pi\)
−0.813218 + 0.581960i \(0.802286\pi\)
\(30\) 0 0
\(31\) 36.0000 + 62.3538i 0.208574 + 0.361261i 0.951266 0.308373i \(-0.0997845\pi\)
−0.742692 + 0.669634i \(0.766451\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −4.00000 −0.0201763
\(35\) 0 0
\(36\) 0 0
\(37\) −199.000 + 344.678i −0.884200 + 1.53148i −0.0375721 + 0.999294i \(0.511962\pi\)
−0.846628 + 0.532185i \(0.821371\pi\)
\(38\) −124.000 214.774i −0.529354 0.916868i
\(39\) 0 0
\(40\) −8.00000 + 13.8564i −0.0316228 + 0.0547723i
\(41\) −462.000 −1.75981 −0.879906 0.475148i \(-0.842394\pi\)
−0.879906 + 0.475148i \(0.842394\pi\)
\(42\) 0 0
\(43\) 212.000 0.751853 0.375927 0.926649i \(-0.377324\pi\)
0.375927 + 0.926649i \(0.377324\pi\)
\(44\) −16.0000 + 27.7128i −0.0548202 + 0.0949514i
\(45\) 0 0
\(46\) −76.0000 131.636i −0.243600 0.421927i
\(47\) −132.000 + 228.631i −0.409663 + 0.709558i −0.994852 0.101339i \(-0.967687\pi\)
0.585189 + 0.810897i \(0.301021\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 242.000 0.684479
\(51\) 0 0
\(52\) 84.0000 + 145.492i 0.224014 + 0.388003i
\(53\) −81.0000 140.296i −0.209928 0.363607i 0.741763 0.670662i \(-0.233990\pi\)
−0.951692 + 0.307055i \(0.900656\pi\)
\(54\) 0 0
\(55\) −16.0000 −0.0392262
\(56\) 0 0
\(57\) 0 0
\(58\) −254.000 + 439.941i −0.575032 + 0.995984i
\(59\) −386.000 668.572i −0.851744 1.47526i −0.879633 0.475654i \(-0.842212\pi\)
0.0278883 0.999611i \(-0.491122\pi\)
\(60\) 0 0
\(61\) −15.0000 + 25.9808i −0.0314845 + 0.0545327i −0.881338 0.472486i \(-0.843357\pi\)
0.849854 + 0.527018i \(0.176690\pi\)
\(62\) 144.000 0.294968
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −42.0000 + 72.7461i −0.0801455 + 0.138816i
\(66\) 0 0
\(67\) 382.000 + 661.643i 0.696548 + 1.20646i 0.969656 + 0.244473i \(0.0786151\pi\)
−0.273108 + 0.961983i \(0.588052\pi\)
\(68\) −4.00000 + 6.92820i −0.00713340 + 0.0123554i
\(69\) 0 0
\(70\) 0 0
\(71\) 236.000 0.394480 0.197240 0.980355i \(-0.436802\pi\)
0.197240 + 0.980355i \(0.436802\pi\)
\(72\) 0 0
\(73\) −209.000 361.999i −0.335090 0.580394i 0.648412 0.761290i \(-0.275434\pi\)
−0.983502 + 0.180896i \(0.942100\pi\)
\(74\) 398.000 + 689.356i 0.625224 + 1.08292i
\(75\) 0 0
\(76\) −496.000 −0.748620
\(77\) 0 0
\(78\) 0 0
\(79\) −276.000 + 478.046i −0.393069 + 0.680815i −0.992853 0.119347i \(-0.961920\pi\)
0.599784 + 0.800162i \(0.295253\pi\)
\(80\) 16.0000 + 27.7128i 0.0223607 + 0.0387298i
\(81\) 0 0
\(82\) −462.000 + 800.207i −0.622187 + 1.07766i
\(83\) −1036.00 −1.37007 −0.685035 0.728510i \(-0.740213\pi\)
−0.685035 + 0.728510i \(0.740213\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.00510425
\(86\) 212.000 367.195i 0.265820 0.460414i
\(87\) 0 0
\(88\) 32.0000 + 55.4256i 0.0387638 + 0.0671408i
\(89\) 15.0000 25.9808i 0.0178651 0.0309433i −0.856955 0.515392i \(-0.827646\pi\)
0.874820 + 0.484449i \(0.160980\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −304.000 −0.344502
\(93\) 0 0
\(94\) 264.000 + 457.261i 0.289676 + 0.501733i
\(95\) −124.000 214.774i −0.133917 0.231951i
\(96\) 0 0
\(97\) −1190.00 −1.24563 −0.622815 0.782369i \(-0.714011\pi\)
−0.622815 + 0.782369i \(0.714011\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 242.000 419.156i 0.242000 0.419156i
\(101\) 685.000 + 1186.45i 0.674852 + 1.16888i 0.976512 + 0.215462i \(0.0691259\pi\)
−0.301660 + 0.953416i \(0.597541\pi\)
\(102\) 0 0
\(103\) −232.000 + 401.836i −0.221938 + 0.384408i −0.955396 0.295326i \(-0.904572\pi\)
0.733458 + 0.679735i \(0.237905\pi\)
\(104\) 336.000 0.316803
\(105\) 0 0
\(106\) −324.000 −0.296884
\(107\) −1068.00 + 1849.83i −0.964930 + 1.67131i −0.255125 + 0.966908i \(0.582117\pi\)
−0.709804 + 0.704399i \(0.751217\pi\)
\(108\) 0 0
\(109\) 613.000 + 1061.75i 0.538667 + 0.932999i 0.998976 + 0.0452405i \(0.0144054\pi\)
−0.460309 + 0.887759i \(0.652261\pi\)
\(110\) −16.0000 + 27.7128i −0.0138685 + 0.0240210i
\(111\) 0 0
\(112\) 0 0
\(113\) −338.000 −0.281384 −0.140692 0.990053i \(-0.544933\pi\)
−0.140692 + 0.990053i \(0.544933\pi\)
\(114\) 0 0
\(115\) −76.0000 131.636i −0.0616264 0.106740i
\(116\) 508.000 + 879.882i 0.406609 + 0.704267i
\(117\) 0 0
\(118\) −1544.00 −1.20455
\(119\) 0 0
\(120\) 0 0
\(121\) 633.500 1097.25i 0.475958 0.824383i
\(122\) 30.0000 + 51.9615i 0.0222629 + 0.0385605i
\(123\) 0 0
\(124\) 144.000 249.415i 0.104287 0.180630i
\(125\) 492.000 0.352047
\(126\) 0 0
\(127\) 2088.00 1.45890 0.729449 0.684035i \(-0.239777\pi\)
0.729449 + 0.684035i \(0.239777\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 84.0000 + 145.492i 0.0566714 + 0.0981578i
\(131\) −146.000 + 252.879i −0.0973747 + 0.168658i −0.910597 0.413295i \(-0.864378\pi\)
0.813223 + 0.581953i \(0.197711\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1528.00 0.985068
\(135\) 0 0
\(136\) 8.00000 + 13.8564i 0.00504408 + 0.00873660i
\(137\) 409.000 + 708.409i 0.255060 + 0.441777i 0.964912 0.262574i \(-0.0845714\pi\)
−0.709852 + 0.704351i \(0.751238\pi\)
\(138\) 0 0
\(139\) −2156.00 −1.31561 −0.657804 0.753189i \(-0.728515\pi\)
−0.657804 + 0.753189i \(0.728515\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 236.000 408.764i 0.139470 0.241568i
\(143\) 168.000 + 290.985i 0.0982438 + 0.170163i
\(144\) 0 0
\(145\) −254.000 + 439.941i −0.145473 + 0.251966i
\(146\) −836.000 −0.473889
\(147\) 0 0
\(148\) 1592.00 0.884200
\(149\) −1425.00 + 2468.17i −0.783494 + 1.35705i 0.146401 + 0.989225i \(0.453231\pi\)
−0.929895 + 0.367825i \(0.880102\pi\)
\(150\) 0 0
\(151\) −836.000 1447.99i −0.450548 0.780372i 0.547872 0.836562i \(-0.315438\pi\)
−0.998420 + 0.0561903i \(0.982105\pi\)
\(152\) −496.000 + 859.097i −0.264677 + 0.458434i
\(153\) 0 0
\(154\) 0 0
\(155\) 144.000 0.0746217
\(156\) 0 0
\(157\) −223.000 386.247i −0.113359 0.196343i 0.803764 0.594949i \(-0.202828\pi\)
−0.917123 + 0.398605i \(0.869494\pi\)
\(158\) 552.000 + 956.092i 0.277942 + 0.481409i
\(159\) 0 0
\(160\) 64.0000 0.0316228
\(161\) 0 0
\(162\) 0 0
\(163\) −1354.00 + 2345.20i −0.650635 + 1.12693i 0.332334 + 0.943162i \(0.392164\pi\)
−0.982969 + 0.183771i \(0.941170\pi\)
\(164\) 924.000 + 1600.41i 0.439953 + 0.762021i
\(165\) 0 0
\(166\) −1036.00 + 1794.40i −0.484393 + 0.838993i
\(167\) −896.000 −0.415177 −0.207589 0.978216i \(-0.566561\pi\)
−0.207589 + 0.978216i \(0.566561\pi\)
\(168\) 0 0
\(169\) −433.000 −0.197087
\(170\) −4.00000 + 6.92820i −0.00180462 + 0.00312570i
\(171\) 0 0
\(172\) −424.000 734.390i −0.187963 0.325562i
\(173\) 2017.00 3493.55i 0.886414 1.53531i 0.0423302 0.999104i \(-0.486522\pi\)
0.844084 0.536211i \(-0.180145\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 128.000 0.0548202
\(177\) 0 0
\(178\) −30.0000 51.9615i −0.0126326 0.0218802i
\(179\) −1740.00 3013.77i −0.726557 1.25843i −0.958330 0.285664i \(-0.907786\pi\)
0.231773 0.972770i \(-0.425547\pi\)
\(180\) 0 0
\(181\) −2898.00 −1.19009 −0.595046 0.803692i \(-0.702866\pi\)
−0.595046 + 0.803692i \(0.702866\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −304.000 + 526.543i −0.121800 + 0.210964i
\(185\) 398.000 + 689.356i 0.158170 + 0.273959i
\(186\) 0 0
\(187\) −8.00000 + 13.8564i −0.00312844 + 0.00541861i
\(188\) 1056.00 0.409663
\(189\) 0 0
\(190\) −496.000 −0.189387
\(191\) 1326.00 2296.70i 0.502335 0.870070i −0.497661 0.867371i \(-0.665808\pi\)
0.999996 0.00269837i \(-0.000858920\pi\)
\(192\) 0 0
\(193\) −73.0000 126.440i −0.0272262 0.0471571i 0.852091 0.523393i \(-0.175334\pi\)
−0.879317 + 0.476236i \(0.842001\pi\)
\(194\) −1190.00 + 2061.14i −0.440397 + 0.762790i
\(195\) 0 0
\(196\) 0 0
\(197\) 2546.00 0.920787 0.460393 0.887715i \(-0.347708\pi\)
0.460393 + 0.887715i \(0.347708\pi\)
\(198\) 0 0
\(199\) 1268.00 + 2196.24i 0.451689 + 0.782349i 0.998491 0.0549134i \(-0.0174883\pi\)
−0.546802 + 0.837262i \(0.684155\pi\)
\(200\) −484.000 838.313i −0.171120 0.296388i
\(201\) 0 0
\(202\) 2740.00 0.954385
\(203\) 0 0
\(204\) 0 0
\(205\) −462.000 + 800.207i −0.157402 + 0.272629i
\(206\) 464.000 + 803.672i 0.156934 + 0.271818i
\(207\) 0 0
\(208\) 336.000 581.969i 0.112007 0.194001i
\(209\) −992.000 −0.328316
\(210\) 0 0
\(211\) −1300.00 −0.424150 −0.212075 0.977253i \(-0.568022\pi\)
−0.212075 + 0.977253i \(0.568022\pi\)
\(212\) −324.000 + 561.184i −0.104964 + 0.181803i
\(213\) 0 0
\(214\) 2136.00 + 3699.66i 0.682308 + 1.18179i
\(215\) 212.000 367.195i 0.0672478 0.116477i
\(216\) 0 0
\(217\) 0 0
\(218\) 2452.00 0.761791
\(219\) 0 0
\(220\) 32.0000 + 55.4256i 0.00980654 + 0.0169854i
\(221\) 42.0000 + 72.7461i 0.0127838 + 0.0221422i
\(222\) 0 0
\(223\) 2576.00 0.773550 0.386775 0.922174i \(-0.373589\pi\)
0.386775 + 0.922174i \(0.373589\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −338.000 + 585.433i −0.0994842 + 0.172312i
\(227\) −918.000 1590.02i −0.268413 0.464905i 0.700039 0.714105i \(-0.253166\pi\)
−0.968452 + 0.249199i \(0.919833\pi\)
\(228\) 0 0
\(229\) 937.000 1622.93i 0.270387 0.468325i −0.698574 0.715538i \(-0.746182\pi\)
0.968961 + 0.247213i \(0.0795149\pi\)
\(230\) −304.000 −0.0871529
\(231\) 0 0
\(232\) 2032.00 0.575032
\(233\) 1865.00 3230.27i 0.524379 0.908250i −0.475219 0.879868i \(-0.657631\pi\)
0.999597 0.0283826i \(-0.00903567\pi\)
\(234\) 0 0
\(235\) 264.000 + 457.261i 0.0732828 + 0.126930i
\(236\) −1544.00 + 2674.29i −0.425872 + 0.737632i
\(237\) 0 0
\(238\) 0 0
\(239\) −2004.00 −0.542377 −0.271188 0.962526i \(-0.587417\pi\)
−0.271188 + 0.962526i \(0.587417\pi\)
\(240\) 0 0
\(241\) 323.000 + 559.452i 0.0863330 + 0.149533i 0.905958 0.423367i \(-0.139152\pi\)
−0.819625 + 0.572900i \(0.805818\pi\)
\(242\) −1267.00 2194.51i −0.336553 0.582927i
\(243\) 0 0
\(244\) 120.000 0.0314845
\(245\) 0 0
\(246\) 0 0
\(247\) −2604.00 + 4510.26i −0.670804 + 1.16187i
\(248\) −288.000 498.831i −0.0737420 0.127725i
\(249\) 0 0
\(250\) 492.000 852.169i 0.124467 0.215584i
\(251\) −1260.00 −0.316855 −0.158427 0.987371i \(-0.550642\pi\)
−0.158427 + 0.987371i \(0.550642\pi\)
\(252\) 0 0
\(253\) −608.000 −0.151086
\(254\) 2088.00 3616.52i 0.515798 0.893389i
\(255\) 0 0
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2955.00 5118.21i 0.717229 1.24228i −0.244865 0.969557i \(-0.578744\pi\)
0.962094 0.272720i \(-0.0879232\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 336.000 0.0801455
\(261\) 0 0
\(262\) 292.000 + 505.759i 0.0688543 + 0.119259i
\(263\) 1494.00 + 2587.68i 0.350281 + 0.606705i 0.986299 0.164970i \(-0.0527527\pi\)
−0.636017 + 0.771675i \(0.719419\pi\)
\(264\) 0 0
\(265\) −324.000 −0.0751063
\(266\) 0 0
\(267\) 0 0
\(268\) 1528.00 2646.57i 0.348274 0.603228i
\(269\) −659.000 1141.42i −0.149368 0.258713i 0.781626 0.623747i \(-0.214391\pi\)
−0.930994 + 0.365035i \(0.881057\pi\)
\(270\) 0 0
\(271\) 2820.00 4884.38i 0.632114 1.09485i −0.355005 0.934864i \(-0.615521\pi\)
0.987119 0.159989i \(-0.0511458\pi\)
\(272\) 32.0000 0.00713340
\(273\) 0 0
\(274\) 1636.00 0.360709
\(275\) 484.000 838.313i 0.106132 0.183826i
\(276\) 0 0
\(277\) −3223.00 5582.40i −0.699102 1.21088i −0.968778 0.247929i \(-0.920250\pi\)
0.269676 0.962951i \(-0.413083\pi\)
\(278\) −2156.00 + 3734.30i −0.465138 + 0.805642i
\(279\) 0 0
\(280\) 0 0
\(281\) −4930.00 −1.04662 −0.523308 0.852144i \(-0.675302\pi\)
−0.523308 + 0.852144i \(0.675302\pi\)
\(282\) 0 0
\(283\) 3130.00 + 5421.32i 0.657453 + 1.13874i 0.981273 + 0.192623i \(0.0616995\pi\)
−0.323820 + 0.946119i \(0.604967\pi\)
\(284\) −472.000 817.528i −0.0986199 0.170815i
\(285\) 0 0
\(286\) 672.000 0.138938
\(287\) 0 0
\(288\) 0 0
\(289\) 2454.50 4251.32i 0.499593 0.865320i
\(290\) 508.000 + 879.882i 0.102865 + 0.178167i
\(291\) 0 0
\(292\) −836.000 + 1447.99i −0.167545 + 0.290197i
\(293\) 2310.00 0.460586 0.230293 0.973121i \(-0.426032\pi\)
0.230293 + 0.973121i \(0.426032\pi\)
\(294\) 0 0
\(295\) −1544.00 −0.304729
\(296\) 1592.00 2757.42i 0.312612 0.541460i
\(297\) 0 0
\(298\) 2850.00 + 4936.34i 0.554014 + 0.959580i
\(299\) −1596.00 + 2764.35i −0.308693 + 0.534671i
\(300\) 0 0
\(301\) 0 0
\(302\) −3344.00 −0.637171
\(303\) 0 0
\(304\) 992.000 + 1718.19i 0.187155 + 0.324162i
\(305\) 30.0000 + 51.9615i 0.00563211 + 0.00975511i
\(306\) 0 0
\(307\) 196.000 0.0364375 0.0182187 0.999834i \(-0.494200\pi\)
0.0182187 + 0.999834i \(0.494200\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 144.000 249.415i 0.0263827 0.0456963i
\(311\) −3368.00 5833.55i −0.614089 1.06363i −0.990544 0.137199i \(-0.956190\pi\)
0.376454 0.926435i \(-0.377143\pi\)
\(312\) 0 0
\(313\) −197.000 + 341.214i −0.0355754 + 0.0616184i −0.883265 0.468874i \(-0.844660\pi\)
0.847690 + 0.530493i \(0.177993\pi\)
\(314\) −892.000 −0.160314
\(315\) 0 0
\(316\) 2208.00 0.393069
\(317\) −3357.00 + 5814.49i −0.594788 + 1.03020i 0.398788 + 0.917043i \(0.369431\pi\)
−0.993577 + 0.113161i \(0.963903\pi\)
\(318\) 0 0
\(319\) 1016.00 + 1759.76i 0.178323 + 0.308865i
\(320\) 64.0000 110.851i 0.0111803 0.0193649i
\(321\) 0 0
\(322\) 0 0
\(323\) −248.000 −0.0427216
\(324\) 0 0
\(325\) −2541.00 4401.14i −0.433690 0.751173i
\(326\) 2708.00 + 4690.39i 0.460068 + 0.796862i
\(327\) 0 0
\(328\) 3696.00 0.622187
\(329\) 0 0
\(330\) 0 0
\(331\) −346.000 + 599.290i −0.0574558 + 0.0995164i −0.893323 0.449416i \(-0.851632\pi\)
0.835867 + 0.548932i \(0.184966\pi\)
\(332\) 2072.00 + 3588.81i 0.342517 + 0.593258i
\(333\) 0 0
\(334\) −896.000 + 1551.92i −0.146787 + 0.254243i
\(335\) 1528.00 0.249205
\(336\) 0 0
\(337\) −1566.00 −0.253132 −0.126566 0.991958i \(-0.540396\pi\)
−0.126566 + 0.991958i \(0.540396\pi\)
\(338\) −433.000 + 749.978i −0.0696808 + 0.120691i
\(339\) 0 0
\(340\) 8.00000 + 13.8564i 0.00127606 + 0.00221020i
\(341\) 288.000 498.831i 0.0457363 0.0792176i
\(342\) 0 0
\(343\) 0 0
\(344\) −1696.00 −0.265820
\(345\) 0 0
\(346\) −4034.00 6987.09i −0.626790 1.08563i
\(347\) −2664.00 4614.18i −0.412135 0.713840i 0.582988 0.812481i \(-0.301884\pi\)
−0.995123 + 0.0986415i \(0.968550\pi\)
\(348\) 0 0
\(349\) 11326.0 1.73715 0.868577 0.495554i \(-0.165035\pi\)
0.868577 + 0.495554i \(0.165035\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 128.000 221.703i 0.0193819 0.0335704i
\(353\) −1065.00 1844.63i −0.160579 0.278130i 0.774498 0.632577i \(-0.218003\pi\)
−0.935076 + 0.354446i \(0.884669\pi\)
\(354\) 0 0
\(355\) 236.000 408.764i 0.0352833 0.0611125i
\(356\) −120.000 −0.0178651
\(357\) 0 0
\(358\) −6960.00 −1.02751
\(359\) 1522.00 2636.18i 0.223755 0.387555i −0.732190 0.681100i \(-0.761502\pi\)
0.955945 + 0.293545i \(0.0948351\pi\)
\(360\) 0 0
\(361\) −4258.50 7375.94i −0.620863 1.07537i
\(362\) −2898.00 + 5019.48i −0.420761 + 0.728780i
\(363\) 0 0
\(364\) 0 0
\(365\) −836.000 −0.119886
\(366\) 0 0
\(367\) −6208.00 10752.6i −0.882984 1.52937i −0.848008 0.529984i \(-0.822198\pi\)
−0.0349760 0.999388i \(-0.511135\pi\)
\(368\) 608.000 + 1053.09i 0.0861255 + 0.149174i
\(369\) 0 0
\(370\) 1592.00 0.223687
\(371\) 0 0
\(372\) 0 0
\(373\) 3721.00 6444.96i 0.516531 0.894658i −0.483285 0.875463i \(-0.660556\pi\)
0.999816 0.0191948i \(-0.00611026\pi\)
\(374\) 16.0000 + 27.7128i 0.00221214 + 0.00383154i
\(375\) 0 0
\(376\) 1056.00 1829.05i 0.144838 0.250867i
\(377\) 10668.0 1.45737
\(378\) 0 0
\(379\) 100.000 0.0135532 0.00677659 0.999977i \(-0.497843\pi\)
0.00677659 + 0.999977i \(0.497843\pi\)
\(380\) −496.000 + 859.097i −0.0669586 + 0.115976i
\(381\) 0 0
\(382\) −2652.00 4593.40i −0.355205 0.615232i
\(383\) 4040.00 6997.49i 0.538993 0.933563i −0.459965 0.887937i \(-0.652138\pi\)
0.998959 0.0456266i \(-0.0145284\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −292.000 −0.0385036
\(387\) 0 0
\(388\) 2380.00 + 4122.28i 0.311408 + 0.539374i
\(389\) −2741.00 4747.55i −0.357260 0.618793i 0.630242 0.776399i \(-0.282956\pi\)
−0.987502 + 0.157606i \(0.949622\pi\)
\(390\) 0 0
\(391\) −152.000 −0.0196598
\(392\) 0 0
\(393\) 0 0
\(394\) 2546.00 4409.80i 0.325547 0.563864i
\(395\) 552.000 + 956.092i 0.0703143 + 0.121788i
\(396\) 0 0
\(397\) −5223.00 + 9046.50i −0.660289 + 1.14365i 0.320250 + 0.947333i \(0.396233\pi\)
−0.980540 + 0.196322i \(0.937100\pi\)
\(398\) 5072.00 0.638785
\(399\) 0 0
\(400\) −1936.00 −0.242000
\(401\) −5667.00 + 9815.53i −0.705727 + 1.22235i 0.260702 + 0.965419i \(0.416046\pi\)
−0.966429 + 0.256935i \(0.917287\pi\)
\(402\) 0 0
\(403\) −1512.00 2618.86i −0.186894 0.323709i
\(404\) 2740.00 4745.82i 0.337426 0.584439i
\(405\) 0 0
\(406\) 0 0
\(407\) 3184.00 0.387776
\(408\) 0 0
\(409\) −4297.00 7442.62i −0.519494 0.899790i −0.999743 0.0226578i \(-0.992787\pi\)
0.480249 0.877132i \(-0.340546\pi\)
\(410\) 924.000 + 1600.41i 0.111300 + 0.192778i
\(411\) 0 0
\(412\) 1856.00 0.221938
\(413\) 0 0
\(414\) 0 0
\(415\) −1036.00 + 1794.40i −0.122543 + 0.212250i
\(416\) −672.000 1163.94i −0.0792007 0.137180i
\(417\) 0 0
\(418\) −992.000 + 1718.19i −0.116077 + 0.201052i
\(419\) −10500.0 −1.22424 −0.612122 0.790763i \(-0.709684\pi\)
−0.612122 + 0.790763i \(0.709684\pi\)
\(420\) 0 0
\(421\) −12066.0 −1.39682 −0.698410 0.715698i \(-0.746109\pi\)
−0.698410 + 0.715698i \(0.746109\pi\)
\(422\) −1300.00 + 2251.67i −0.149960 + 0.259738i
\(423\) 0 0
\(424\) 648.000 + 1122.37i 0.0742209 + 0.128554i
\(425\) 121.000 209.578i 0.0138103 0.0239201i
\(426\) 0 0
\(427\) 0 0
\(428\) 8544.00 0.964930
\(429\) 0 0
\(430\) −424.000 734.390i −0.0475514 0.0823614i
\(431\) 2166.00 + 3751.62i 0.242071 + 0.419279i 0.961304 0.275490i \(-0.0888400\pi\)
−0.719233 + 0.694769i \(0.755507\pi\)
\(432\) 0 0
\(433\) −1918.00 −0.212871 −0.106436 0.994320i \(-0.533944\pi\)
−0.106436 + 0.994320i \(0.533944\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 2452.00 4246.99i 0.269334 0.466500i
\(437\) −4712.00 8161.42i −0.515802 0.893395i
\(438\) 0 0
\(439\) 3996.00 6921.28i 0.434439 0.752470i −0.562811 0.826586i \(-0.690280\pi\)
0.997250 + 0.0741155i \(0.0236134\pi\)
\(440\) 128.000 0.0138685
\(441\) 0 0
\(442\) 168.000 0.0180791
\(443\) 1592.00 2757.42i 0.170741 0.295732i −0.767938 0.640524i \(-0.778717\pi\)
0.938679 + 0.344792i \(0.112051\pi\)
\(444\) 0 0
\(445\) −30.0000 51.9615i −0.00319581 0.00553531i
\(446\) 2576.00 4461.76i 0.273491 0.473701i
\(447\) 0 0
\(448\) 0 0
\(449\) −11426.0 −1.20095 −0.600475 0.799644i \(-0.705022\pi\)
−0.600475 + 0.799644i \(0.705022\pi\)
\(450\) 0 0
\(451\) 1848.00 + 3200.83i 0.192947 + 0.334193i
\(452\) 676.000 + 1170.87i 0.0703459 + 0.121843i
\(453\) 0 0
\(454\) −3672.00 −0.379594
\(455\) 0 0
\(456\) 0 0
\(457\) 8467.00 14665.3i 0.866673 1.50112i 0.00129662 0.999999i \(-0.499587\pi\)
0.865376 0.501122i \(-0.167079\pi\)
\(458\) −1874.00 3245.86i −0.191193 0.331156i
\(459\) 0 0
\(460\) −304.000 + 526.543i −0.0308132 + 0.0533700i
\(461\) 17038.0 1.72134 0.860671 0.509161i \(-0.170044\pi\)
0.860671 + 0.509161i \(0.170044\pi\)
\(462\) 0 0
\(463\) −13592.0 −1.36431 −0.682153 0.731209i \(-0.738956\pi\)
−0.682153 + 0.731209i \(0.738956\pi\)
\(464\) 2032.00 3519.53i 0.203304 0.352134i
\(465\) 0 0
\(466\) −3730.00 6460.55i −0.370792 0.642230i
\(467\) 4306.00 7458.21i 0.426676 0.739025i −0.569899 0.821715i \(-0.693018\pi\)
0.996575 + 0.0826895i \(0.0263510\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1056.00 0.103638
\(471\) 0 0
\(472\) 3088.00 + 5348.57i 0.301137 + 0.521585i
\(473\) −848.000 1468.78i −0.0824336 0.142779i
\(474\) 0 0
\(475\) 15004.0 1.44933
\(476\) 0 0
\(477\) 0 0
\(478\) −2004.00 + 3471.03i −0.191759 + 0.332136i
\(479\) 3716.00 + 6436.30i 0.354464 + 0.613950i 0.987026 0.160560i \(-0.0513299\pi\)
−0.632562 + 0.774510i \(0.717997\pi\)
\(480\) 0 0
\(481\) 8358.00 14476.5i 0.792291 1.37229i
\(482\) 1292.00 0.122093
\(483\) 0 0
\(484\) −5068.00 −0.475958
\(485\) −1190.00 + 2061.14i −0.111413 + 0.192972i
\(486\) 0 0
\(487\) 3308.00 + 5729.62i 0.307802 + 0.533129i 0.977881 0.209160i \(-0.0670731\pi\)
−0.670079 + 0.742290i \(0.733740\pi\)
\(488\) 120.000 207.846i 0.0111314 0.0192802i
\(489\) 0 0
\(490\) 0 0
\(491\) −17040.0 −1.56620 −0.783100 0.621896i \(-0.786363\pi\)
−0.783100 + 0.621896i \(0.786363\pi\)
\(492\) 0 0
\(493\) 254.000 + 439.941i 0.0232040 + 0.0401906i
\(494\) 5208.00 + 9020.52i 0.474330 + 0.821564i
\(495\) 0 0
\(496\) −1152.00 −0.104287
\(497\) 0 0
\(498\) 0 0
\(499\) 1474.00 2553.04i 0.132235 0.229038i −0.792303 0.610128i \(-0.791118\pi\)
0.924538 + 0.381090i \(0.124451\pi\)
\(500\) −984.000 1704.34i −0.0880116 0.152441i
\(501\) 0 0
\(502\) −1260.00 + 2182.38i −0.112025 + 0.194033i
\(503\) −17304.0 −1.53389 −0.766946 0.641712i \(-0.778224\pi\)
−0.766946 + 0.641712i \(0.778224\pi\)
\(504\) 0 0
\(505\) 2740.00 0.241442
\(506\) −608.000 + 1053.09i −0.0534168 + 0.0925206i
\(507\) 0 0
\(508\) −4176.00 7233.04i −0.364724 0.631721i
\(509\) 2325.00 4027.02i 0.202463 0.350677i −0.746858 0.664983i \(-0.768439\pi\)
0.949322 + 0.314307i \(0.101772\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −5910.00 10236.4i −0.507157 0.878422i
\(515\) 464.000 + 803.672i 0.0397015 + 0.0687651i
\(516\) 0 0
\(517\) 2112.00 0.179663
\(518\) 0 0
\(519\) 0 0
\(520\) 336.000 581.969i 0.0283357 0.0490789i
\(521\) 8427.00 + 14596.0i 0.708625 + 1.22737i 0.965367 + 0.260894i \(0.0840175\pi\)
−0.256742 + 0.966480i \(0.582649\pi\)
\(522\) 0 0
\(523\) 62.0000 107.387i 0.00518369 0.00897842i −0.863422 0.504482i \(-0.831683\pi\)
0.868606 + 0.495504i \(0.165017\pi\)
\(524\) 1168.00 0.0973747
\(525\) 0 0
\(526\) 5976.00 0.495373
\(527\) 72.0000 124.708i 0.00595136 0.0103081i
\(528\) 0 0
\(529\) 3195.50 + 5534.77i 0.262637 + 0.454900i
\(530\) −324.000 + 561.184i −0.0265541 + 0.0459930i
\(531\) 0 0
\(532\) 0 0
\(533\) 19404.0 1.57689
\(534\) 0 0
\(535\) 2136.00 + 3699.66i 0.172612 + 0.298972i
\(536\) −3056.00 5293.15i −0.246267 0.426547i
\(537\) 0 0
\(538\) −2636.00 −0.211238
\(539\) 0 0
\(540\) 0 0
\(541\) −2691.00 + 4660.95i −0.213854 + 0.370406i −0.952918 0.303230i \(-0.901935\pi\)
0.739063 + 0.673636i \(0.235268\pi\)
\(542\) −5640.00 9768.77i −0.446972 0.774178i
\(543\) 0 0
\(544\) 32.0000 55.4256i 0.00252204 0.00436830i
\(545\) 2452.00 0.192720
\(546\) 0 0
\(547\) 17460.0 1.36478 0.682391 0.730987i \(-0.260940\pi\)
0.682391 + 0.730987i \(0.260940\pi\)
\(548\) 1636.00 2833.64i 0.127530 0.220888i
\(549\) 0 0
\(550\) −968.000 1676.63i −0.0750467 0.129985i
\(551\) −15748.0 + 27276.3i −1.21758 + 2.10891i
\(552\) 0 0
\(553\) 0 0
\(554\) −12892.0 −0.988680
\(555\) 0 0
\(556\) 4312.00 + 7468.60i 0.328902 + 0.569675i
\(557\) −4757.00 8239.37i −0.361868 0.626774i 0.626400 0.779502i \(-0.284528\pi\)
−0.988268 + 0.152728i \(0.951194\pi\)
\(558\) 0 0
\(559\) −8904.00 −0.673701
\(560\) 0 0
\(561\) 0 0
\(562\) −4930.00 + 8539.01i −0.370035 + 0.640919i
\(563\) 1994.00 + 3453.71i 0.149267 + 0.258537i 0.930957 0.365130i \(-0.118975\pi\)
−0.781690 + 0.623667i \(0.785642\pi\)
\(564\) 0 0
\(565\) −338.000 + 585.433i −0.0251677 + 0.0435918i
\(566\) 12520.0 0.929779
\(567\) 0 0
\(568\) −1888.00 −0.139470
\(569\) 5673.00 9825.92i 0.417969 0.723944i −0.577766 0.816203i \(-0.696075\pi\)
0.995735 + 0.0922585i \(0.0294086\pi\)
\(570\) 0 0
\(571\) 4218.00 + 7305.79i 0.309138 + 0.535443i 0.978174 0.207787i \(-0.0666262\pi\)
−0.669036 + 0.743230i \(0.733293\pi\)
\(572\) 672.000 1163.94i 0.0491219 0.0850816i
\(573\) 0 0
\(574\) 0 0
\(575\) 9196.00 0.666956
\(576\) 0 0
\(577\) −1049.00 1816.92i −0.0756853 0.131091i 0.825699 0.564111i \(-0.190781\pi\)
−0.901384 + 0.433020i \(0.857448\pi\)
\(578\) −4909.00 8502.64i −0.353266 0.611874i
\(579\) 0 0
\(580\) 2032.00 0.145473
\(581\) 0 0
\(582\) 0 0
\(583\) −648.000 + 1122.37i −0.0460333 + 0.0797320i
\(584\) 1672.00 + 2895.99i 0.118472 + 0.205200i
\(585\) 0 0
\(586\) 2310.00 4001.04i 0.162842 0.282050i
\(587\) −9436.00 −0.663484 −0.331742 0.943370i \(-0.607636\pi\)
−0.331742 + 0.943370i \(0.607636\pi\)
\(588\) 0 0
\(589\) 8928.00 0.624570
\(590\) −1544.00 + 2674.29i −0.107738 + 0.186608i
\(591\) 0 0
\(592\) −3184.00 5514.85i −0.221050 0.382870i
\(593\) −657.000 + 1137.96i −0.0454971 + 0.0788032i −0.887877 0.460081i \(-0.847820\pi\)
0.842380 + 0.538884i \(0.181154\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11400.0 0.783494
\(597\) 0 0
\(598\) 3192.00 + 5528.71i 0.218279 + 0.378070i
\(599\) −4470.00 7742.27i −0.304907 0.528114i 0.672334 0.740248i \(-0.265292\pi\)
−0.977241 + 0.212134i \(0.931959\pi\)
\(600\) 0 0
\(601\) 16058.0 1.08988 0.544941 0.838474i \(-0.316552\pi\)
0.544941 + 0.838474i \(0.316552\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3344.00 + 5791.98i −0.225274 + 0.390186i
\(605\) −1267.00 2194.51i −0.0851419 0.147470i
\(606\) 0 0
\(607\) −1968.00 + 3408.68i −0.131596 + 0.227931i −0.924292 0.381686i \(-0.875343\pi\)
0.792696 + 0.609617i \(0.208677\pi\)
\(608\) 3968.00 0.264677
\(609\) 0 0
\(610\) 120.000 0.00796501
\(611\) 5544.00 9602.49i 0.367081 0.635802i
\(612\) 0 0
\(613\) −87.0000 150.688i −0.00573230 0.00992863i 0.863145 0.504956i \(-0.168491\pi\)
−0.868877 + 0.495027i \(0.835158\pi\)
\(614\) 196.000 339.482i 0.0128826 0.0223133i
\(615\) 0 0
\(616\) 0 0
\(617\) −16018.0 −1.04515 −0.522577 0.852592i \(-0.675029\pi\)
−0.522577 + 0.852592i \(0.675029\pi\)
\(618\) 0 0
\(619\) 1534.00 + 2656.97i 0.0996069 + 0.172524i 0.911522 0.411251i \(-0.134908\pi\)
−0.811915 + 0.583776i \(0.801575\pi\)
\(620\) −288.000 498.831i −0.0186554 0.0323121i
\(621\) 0 0
\(622\) −13472.0 −0.868453
\(623\) 0 0
\(624\) 0 0
\(625\) −7070.50 + 12246.5i −0.452512 + 0.783774i
\(626\) 394.000 + 682.428i 0.0251556 + 0.0435708i
\(627\) 0 0
\(628\) −892.000 + 1544.99i −0.0566794 + 0.0981716i
\(629\) 796.000 0.0504588
\(630\) 0 0
\(631\) 24656.0 1.55553 0.777765 0.628555i \(-0.216353\pi\)
0.777765 + 0.628555i \(0.216353\pi\)
\(632\) 2208.00 3824.37i 0.138971 0.240704i
\(633\) 0 0
\(634\) 6714.00 + 11629.0i 0.420579 + 0.728464i
\(635\) 2088.00 3616.52i 0.130488 0.226011i
\(636\) 0 0
\(637\) 0 0
\(638\) 4064.00 0.252187
\(639\) 0 0
\(640\) −128.000 221.703i −0.00790569 0.0136931i
\(641\) 3797.00 + 6576.60i 0.233966 + 0.405242i 0.958972 0.283501i \(-0.0914961\pi\)
−0.725005 + 0.688743i \(0.758163\pi\)
\(642\) 0 0
\(643\) −3724.00 −0.228398 −0.114199 0.993458i \(-0.536430\pi\)
−0.114199 + 0.993458i \(0.536430\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −248.000 + 429.549i −0.0151044 + 0.0261616i
\(647\) 1896.00 + 3283.97i 0.115208 + 0.199546i 0.917863 0.396898i \(-0.129913\pi\)
−0.802655 + 0.596444i \(0.796580\pi\)
\(648\) 0 0
\(649\) −3088.00 + 5348.57i −0.186771 + 0.323497i
\(650\) −10164.0 −0.613331
\(651\) 0 0
\(652\) 10832.0 0.650635
\(653\) 12351.0 21392.6i 0.740171 1.28201i −0.212245 0.977216i \(-0.568078\pi\)
0.952417 0.304798i \(-0.0985890\pi\)
\(654\) 0 0
\(655\) 292.000 + 505.759i 0.0174189 + 0.0301704i
\(656\) 3696.00 6401.66i 0.219976 0.381010i
\(657\) 0 0
\(658\) 0 0
\(659\) 20144.0 1.19074 0.595371 0.803451i \(-0.297005\pi\)
0.595371 + 0.803451i \(0.297005\pi\)
\(660\) 0 0
\(661\) 1261.00 + 2184.12i 0.0742015 + 0.128521i 0.900739 0.434361i \(-0.143026\pi\)
−0.826537 + 0.562882i \(0.809693\pi\)
\(662\) 692.000 + 1198.58i 0.0406274 + 0.0703687i
\(663\) 0 0
\(664\) 8288.00 0.484393
\(665\) 0 0
\(666\) 0 0
\(667\) −9652.00 + 16717.8i −0.560310 + 0.970486i
\(668\) 1792.00 + 3103.84i 0.103794 + 0.179777i
\(669\) 0 0
\(670\) 1528.00 2646.57i 0.0881071 0.152606i
\(671\) 240.000 0.0138079
\(672\) 0 0
\(673\) −10414.0 −0.596479 −0.298239 0.954491i \(-0.596399\pi\)
−0.298239 + 0.954491i \(0.596399\pi\)
\(674\) −1566.00 + 2712.39i −0.0894956 + 0.155011i
\(675\) 0 0
\(676\) 866.000 + 1499.96i 0.0492717 + 0.0853411i
\(677\) −11115.0 + 19251.7i −0.630996 + 1.09292i 0.356353 + 0.934352i \(0.384020\pi\)
−0.987348 + 0.158565i \(0.949313\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 32.0000 0.00180462
\(681\) 0 0
\(682\) −576.000 997.661i −0.0323404 0.0560153i
\(683\) 9096.00 + 15754.7i 0.509588 + 0.882633i 0.999938 + 0.0111072i \(0.00353559\pi\)
−0.490350 + 0.871526i \(0.663131\pi\)
\(684\) 0 0
\(685\) 1636.00 0.0912531
\(686\) 0 0
\(687\) 0 0
\(688\) −1696.00 + 2937.56i −0.0939817 + 0.162781i
\(689\) 3402.00 + 5892.44i 0.188107 + 0.325811i
\(690\) 0 0
\(691\) −4054.00 + 7021.73i −0.223186 + 0.386569i −0.955774 0.294103i \(-0.904979\pi\)
0.732588 + 0.680673i \(0.238312\pi\)
\(692\) −16136.0 −0.886414
\(693\) 0 0
\(694\) −10656.0 −0.582848
\(695\) −2156.00 + 3734.30i −0.117672 + 0.203813i
\(696\) 0 0
\(697\) 462.000 + 800.207i 0.0251069 + 0.0434864i
\(698\) 11326.0 19617.2i 0.614177 1.06379i
\(699\) 0 0
\(700\) 0 0
\(701\) 5794.00 0.312177 0.156089 0.987743i \(-0.450111\pi\)
0.156089 + 0.987743i \(0.450111\pi\)
\(702\) 0 0
\(703\) 24676.0 + 42740.1i 1.32386 + 2.29299i
\(704\) −256.000 443.405i −0.0137051 0.0237379i
\(705\) 0 0
\(706\) −4260.00 −0.227092
\(707\) 0 0
\(708\) 0 0
\(709\) 977.000 1692.21i 0.0517518 0.0896367i −0.838989 0.544148i \(-0.816853\pi\)
0.890741 + 0.454512i \(0.150186\pi\)
\(710\) −472.000 817.528i −0.0249491 0.0432131i
\(711\) 0 0
\(712\) −120.000 + 207.846i −0.00631628 + 0.0109401i
\(713\) 5472.00 0.287417
\(714\) 0 0
\(715\) 672.000 0.0351488
\(716\) −6960.00 + 12055.1i −0.363279 + 0.629217i
\(717\) 0 0
\(718\) −3044.00 5272.36i −0.158219 0.274043i
\(719\) −16008.0 + 27726.7i −0.830317 + 1.43815i 0.0674706 + 0.997721i \(0.478507\pi\)
−0.897787 + 0.440429i \(0.854826\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −17034.0 −0.878033
\(723\) 0 0
\(724\) 5796.00 + 10039.0i 0.297523 + 0.515325i
\(725\) −15367.0 26616.4i −0.787195 1.36346i
\(726\) 0 0
\(727\) −23072.0 −1.17702 −0.588510 0.808490i \(-0.700285\pi\)
−0.588510 + 0.808490i \(0.700285\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −836.000 + 1447.99i −0.0423860 + 0.0734146i
\(731\) −212.000 367.195i −0.0107265 0.0185789i
\(732\) 0 0
\(733\) −15891.0 + 27524.0i −0.800747 + 1.38693i 0.118378 + 0.992969i \(0.462230\pi\)
−0.919125 + 0.393966i \(0.871103\pi\)
\(734\) −24832.0 −1.24873
\(735\) 0 0
\(736\) 2432.00 0.121800
\(737\) 3056.00 5293.15i 0.152740 0.264553i
\(738\) 0 0
\(739\) 12198.0 + 21127.6i 0.607186 + 1.05168i 0.991702 + 0.128559i \(0.0410352\pi\)
−0.384516 + 0.923119i \(0.625631\pi\)
\(740\) 1592.00 2757.42i 0.0790852 0.136980i
\(741\) 0 0
\(742\) 0 0
\(743\) 32604.0 1.60986 0.804929 0.593371i \(-0.202203\pi\)
0.804929 + 0.593371i \(0.202203\pi\)
\(744\) 0 0
\(745\) 2850.00 + 4936.34i 0.140156 + 0.242757i
\(746\) −7442.00 12889.9i −0.365243 0.632619i
\(747\) 0 0
\(748\) 64.0000 0.00312844
\(749\) 0 0
\(750\) 0 0
\(751\) 3840.00 6651.08i 0.186583 0.323171i −0.757526 0.652805i \(-0.773592\pi\)
0.944109 + 0.329634i \(0.106925\pi\)
\(752\) −2112.00 3658.09i −0.102416 0.177389i
\(753\) 0 0
\(754\) 10668.0 18477.5i 0.515259 0.892456i
\(755\) −3344.00 −0.161193
\(756\) 0 0
\(757\) 366.000 0.0175727 0.00878633 0.999961i \(-0.497203\pi\)
0.00878633 + 0.999961i \(0.497203\pi\)
\(758\) 100.000 173.205i 0.00479177 0.00829959i
\(759\) 0 0
\(760\) 992.000 + 1718.19i 0.0473469 + 0.0820072i
\(761\) 14687.0 25438.6i 0.699610 1.21176i −0.268992 0.963143i \(-0.586690\pi\)
0.968602 0.248618i \(-0.0799763\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −10608.0 −0.502335
\(765\) 0 0
\(766\) −8080.00 13995.0i −0.381126 0.660129i
\(767\) 16212.0 + 28080.0i 0.763209 + 1.32192i
\(768\) 0 0
\(769\) −38990.0 −1.82837 −0.914184 0.405299i \(-0.867167\pi\)
−0.914184 + 0.405299i \(0.867167\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −292.000 + 505.759i −0.0136131 + 0.0235786i
\(773\) −10235.0 17727.5i −0.476232 0.824858i 0.523397 0.852089i \(-0.324664\pi\)
−0.999629 + 0.0272308i \(0.991331\pi\)
\(774\) 0 0
\(775\) −4356.00 + 7544.81i −0.201900 + 0.349700i
\(776\) 9520.00 0.440397
\(777\) 0 0
\(778\) −10964.0 −0.505242
\(779\) −28644.0 + 49612.9i −1.31743 + 2.28186i
\(780\) 0 0
\(781\) −944.000 1635.06i −0.0432509 0.0749128i
\(782\) −152.000 + 263.272i −0.00695078 + 0.0120391i
\(783\) 0 0
\(784\) 0 0
\(785\) −892.000 −0.0405565
\(786\) 0 0
\(787\) −14958.0 25908.0i −0.677503 1.17347i −0.975730 0.218975i \(-0.929729\pi\)
0.298227 0.954495i \(-0.403605\pi\)
\(788\) −5092.00 8819.60i −0.230197 0.398712i
\(789\) 0 0
\(790\) 2208.00 0.0994394
\(791\) 0