Properties

Label 490.4.c.a.99.1
Level $490$
Weight $4$
Character 490.99
Analytic conductor $28.911$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 490.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.9109359028\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 490.99
Dual form 490.4.c.a.99.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000i q^{2} +7.00000i q^{3} -4.00000 q^{4} +(-10.0000 + 5.00000i) q^{5} +14.0000 q^{6} +8.00000i q^{8} -22.0000 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} +7.00000i q^{3} -4.00000 q^{4} +(-10.0000 + 5.00000i) q^{5} +14.0000 q^{6} +8.00000i q^{8} -22.0000 q^{9} +(10.0000 + 20.0000i) q^{10} -37.0000 q^{11} -28.0000i q^{12} -51.0000i q^{13} +(-35.0000 - 70.0000i) q^{15} +16.0000 q^{16} +41.0000i q^{17} +44.0000i q^{18} -108.000 q^{19} +(40.0000 - 20.0000i) q^{20} +74.0000i q^{22} -70.0000i q^{23} -56.0000 q^{24} +(75.0000 - 100.000i) q^{25} -102.000 q^{26} +35.0000i q^{27} +249.000 q^{29} +(-140.000 + 70.0000i) q^{30} +134.000 q^{31} -32.0000i q^{32} -259.000i q^{33} +82.0000 q^{34} +88.0000 q^{36} +334.000i q^{37} +216.000i q^{38} +357.000 q^{39} +(-40.0000 - 80.0000i) q^{40} -206.000 q^{41} -376.000i q^{43} +148.000 q^{44} +(220.000 - 110.000i) q^{45} -140.000 q^{46} -287.000i q^{47} +112.000i q^{48} +(-200.000 - 150.000i) q^{50} -287.000 q^{51} +204.000i q^{52} -6.00000i q^{53} +70.0000 q^{54} +(370.000 - 185.000i) q^{55} -756.000i q^{57} -498.000i q^{58} -2.00000 q^{59} +(140.000 + 280.000i) q^{60} +940.000 q^{61} -268.000i q^{62} -64.0000 q^{64} +(255.000 + 510.000i) q^{65} -518.000 q^{66} -106.000i q^{67} -164.000i q^{68} +490.000 q^{69} +456.000 q^{71} -176.000i q^{72} -650.000i q^{73} +668.000 q^{74} +(700.000 + 525.000i) q^{75} +432.000 q^{76} -714.000i q^{78} +1239.00 q^{79} +(-160.000 + 80.0000i) q^{80} -839.000 q^{81} +412.000i q^{82} -428.000i q^{83} +(-205.000 - 410.000i) q^{85} -752.000 q^{86} +1743.00i q^{87} -296.000i q^{88} -220.000 q^{89} +(-220.000 - 440.000i) q^{90} +280.000i q^{92} +938.000i q^{93} -574.000 q^{94} +(1080.00 - 540.000i) q^{95} +224.000 q^{96} -1055.00i q^{97} +814.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{4} - 20 q^{5} + 28 q^{6} - 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 8 q^{4} - 20 q^{5} + 28 q^{6} - 44 q^{9} + 20 q^{10} - 74 q^{11} - 70 q^{15} + 32 q^{16} - 216 q^{19} + 80 q^{20} - 112 q^{24} + 150 q^{25} - 204 q^{26} + 498 q^{29} - 280 q^{30} + 268 q^{31} + 164 q^{34} + 176 q^{36} + 714 q^{39} - 80 q^{40} - 412 q^{41} + 296 q^{44} + 440 q^{45} - 280 q^{46} - 400 q^{50} - 574 q^{51} + 140 q^{54} + 740 q^{55} - 4 q^{59} + 280 q^{60} + 1880 q^{61} - 128 q^{64} + 510 q^{65} - 1036 q^{66} + 980 q^{69} + 912 q^{71} + 1336 q^{74} + 1400 q^{75} + 864 q^{76} + 2478 q^{79} - 320 q^{80} - 1678 q^{81} - 410 q^{85} - 1504 q^{86} - 440 q^{89} - 440 q^{90} - 1148 q^{94} + 2160 q^{95} + 448 q^{96} + 1628 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 0.707107i
\(3\) 7.00000i 1.34715i 0.739119 + 0.673575i \(0.235242\pi\)
−0.739119 + 0.673575i \(0.764758\pi\)
\(4\) −4.00000 −0.500000
\(5\) −10.0000 + 5.00000i −0.894427 + 0.447214i
\(6\) 14.0000 0.952579
\(7\) 0 0
\(8\) 8.00000i 0.353553i
\(9\) −22.0000 −0.814815
\(10\) 10.0000 + 20.0000i 0.316228 + 0.632456i
\(11\) −37.0000 −1.01417 −0.507087 0.861895i \(-0.669278\pi\)
−0.507087 + 0.861895i \(0.669278\pi\)
\(12\) 28.0000i 0.673575i
\(13\) 51.0000i 1.08807i −0.839064 0.544033i \(-0.816897\pi\)
0.839064 0.544033i \(-0.183103\pi\)
\(14\) 0 0
\(15\) −35.0000 70.0000i −0.602464 1.20493i
\(16\) 16.0000 0.250000
\(17\) 41.0000i 0.584939i 0.956275 + 0.292469i \(0.0944770\pi\)
−0.956275 + 0.292469i \(0.905523\pi\)
\(18\) 44.0000i 0.576161i
\(19\) −108.000 −1.30405 −0.652024 0.758199i \(-0.726080\pi\)
−0.652024 + 0.758199i \(0.726080\pi\)
\(20\) 40.0000 20.0000i 0.447214 0.223607i
\(21\) 0 0
\(22\) 74.0000i 0.717130i
\(23\) 70.0000i 0.634609i −0.948324 0.317305i \(-0.897222\pi\)
0.948324 0.317305i \(-0.102778\pi\)
\(24\) −56.0000 −0.476290
\(25\) 75.0000 100.000i 0.600000 0.800000i
\(26\) −102.000 −0.769379
\(27\) 35.0000i 0.249472i
\(28\) 0 0
\(29\) 249.000 1.59442 0.797209 0.603703i \(-0.206309\pi\)
0.797209 + 0.603703i \(0.206309\pi\)
\(30\) −140.000 + 70.0000i −0.852013 + 0.426006i
\(31\) 134.000 0.776358 0.388179 0.921584i \(-0.373104\pi\)
0.388179 + 0.921584i \(0.373104\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 259.000i 1.36625i
\(34\) 82.0000 0.413614
\(35\) 0 0
\(36\) 88.0000 0.407407
\(37\) 334.000i 1.48403i 0.670381 + 0.742017i \(0.266131\pi\)
−0.670381 + 0.742017i \(0.733869\pi\)
\(38\) 216.000i 0.922101i
\(39\) 357.000 1.46579
\(40\) −40.0000 80.0000i −0.158114 0.316228i
\(41\) −206.000 −0.784678 −0.392339 0.919821i \(-0.628334\pi\)
−0.392339 + 0.919821i \(0.628334\pi\)
\(42\) 0 0
\(43\) 376.000i 1.33348i −0.745292 0.666738i \(-0.767690\pi\)
0.745292 0.666738i \(-0.232310\pi\)
\(44\) 148.000 0.507087
\(45\) 220.000 110.000i 0.728793 0.364396i
\(46\) −140.000 −0.448736
\(47\) 287.000i 0.890708i −0.895355 0.445354i \(-0.853078\pi\)
0.895355 0.445354i \(-0.146922\pi\)
\(48\) 112.000i 0.336788i
\(49\) 0 0
\(50\) −200.000 150.000i −0.565685 0.424264i
\(51\) −287.000 −0.788001
\(52\) 204.000i 0.544033i
\(53\) 6.00000i 0.0155503i −0.999970 0.00777513i \(-0.997525\pi\)
0.999970 0.00777513i \(-0.00247492\pi\)
\(54\) 70.0000 0.176404
\(55\) 370.000 185.000i 0.907105 0.453553i
\(56\) 0 0
\(57\) 756.000i 1.75675i
\(58\) 498.000i 1.12742i
\(59\) −2.00000 −0.00441318 −0.00220659 0.999998i \(-0.500702\pi\)
−0.00220659 + 0.999998i \(0.500702\pi\)
\(60\) 140.000 + 280.000i 0.301232 + 0.602464i
\(61\) 940.000 1.97303 0.986514 0.163679i \(-0.0523361\pi\)
0.986514 + 0.163679i \(0.0523361\pi\)
\(62\) 268.000i 0.548968i
\(63\) 0 0
\(64\) −64.0000 −0.125000
\(65\) 255.000 + 510.000i 0.486598 + 0.973196i
\(66\) −518.000 −0.966082
\(67\) 106.000i 0.193283i −0.995319 0.0966415i \(-0.969190\pi\)
0.995319 0.0966415i \(-0.0308100\pi\)
\(68\) 164.000i 0.292469i
\(69\) 490.000 0.854914
\(70\) 0 0
\(71\) 456.000 0.762215 0.381107 0.924531i \(-0.375543\pi\)
0.381107 + 0.924531i \(0.375543\pi\)
\(72\) 176.000i 0.288081i
\(73\) 650.000i 1.04215i −0.853512 0.521074i \(-0.825532\pi\)
0.853512 0.521074i \(-0.174468\pi\)
\(74\) 668.000 1.04937
\(75\) 700.000 + 525.000i 1.07772 + 0.808290i
\(76\) 432.000 0.652024
\(77\) 0 0
\(78\) 714.000i 1.03647i
\(79\) 1239.00 1.76454 0.882268 0.470747i \(-0.156016\pi\)
0.882268 + 0.470747i \(0.156016\pi\)
\(80\) −160.000 + 80.0000i −0.223607 + 0.111803i
\(81\) −839.000 −1.15089
\(82\) 412.000i 0.554851i
\(83\) 428.000i 0.566013i −0.959118 0.283007i \(-0.908668\pi\)
0.959118 0.283007i \(-0.0913319\pi\)
\(84\) 0 0
\(85\) −205.000 410.000i −0.261593 0.523185i
\(86\) −752.000 −0.942910
\(87\) 1743.00i 2.14792i
\(88\) 296.000i 0.358565i
\(89\) −220.000 −0.262022 −0.131011 0.991381i \(-0.541822\pi\)
−0.131011 + 0.991381i \(0.541822\pi\)
\(90\) −220.000 440.000i −0.257667 0.515334i
\(91\) 0 0
\(92\) 280.000i 0.317305i
\(93\) 938.000i 1.04587i
\(94\) −574.000 −0.629825
\(95\) 1080.00 540.000i 1.16638 0.583188i
\(96\) 224.000 0.238145
\(97\) 1055.00i 1.10432i −0.833738 0.552160i \(-0.813804\pi\)
0.833738 0.552160i \(-0.186196\pi\)
\(98\) 0 0
\(99\) 814.000 0.826364
\(100\) −300.000 + 400.000i −0.300000 + 0.400000i
\(101\) −1960.00 −1.93096 −0.965482 0.260471i \(-0.916122\pi\)
−0.965482 + 0.260471i \(0.916122\pi\)
\(102\) 574.000i 0.557201i
\(103\) 1825.00i 1.74585i −0.487854 0.872925i \(-0.662220\pi\)
0.487854 0.872925i \(-0.337780\pi\)
\(104\) 408.000 0.384689
\(105\) 0 0
\(106\) −12.0000 −0.0109957
\(107\) 144.000i 0.130103i 0.997882 + 0.0650514i \(0.0207211\pi\)
−0.997882 + 0.0650514i \(0.979279\pi\)
\(108\) 140.000i 0.124736i
\(109\) −1681.00 −1.47716 −0.738581 0.674165i \(-0.764504\pi\)
−0.738581 + 0.674165i \(0.764504\pi\)
\(110\) −370.000 740.000i −0.320710 0.641420i
\(111\) −2338.00 −1.99922
\(112\) 0 0
\(113\) 798.000i 0.664332i 0.943221 + 0.332166i \(0.107779\pi\)
−0.943221 + 0.332166i \(0.892221\pi\)
\(114\) −1512.00 −1.24221
\(115\) 350.000 + 700.000i 0.283806 + 0.567612i
\(116\) −996.000 −0.797209
\(117\) 1122.00i 0.886572i
\(118\) 4.00000i 0.00312059i
\(119\) 0 0
\(120\) 560.000 280.000i 0.426006 0.213003i
\(121\) 38.0000 0.0285500
\(122\) 1880.00i 1.39514i
\(123\) 1442.00i 1.05708i
\(124\) −536.000 −0.388179
\(125\) −250.000 + 1375.00i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) 434.000i 0.303238i −0.988439 0.151619i \(-0.951551\pi\)
0.988439 0.151619i \(-0.0484487\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 2632.00 1.79639
\(130\) 1020.00 510.000i 0.688153 0.344077i
\(131\) 1290.00 0.860365 0.430183 0.902742i \(-0.358449\pi\)
0.430183 + 0.902742i \(0.358449\pi\)
\(132\) 1036.00i 0.683123i
\(133\) 0 0
\(134\) −212.000 −0.136672
\(135\) −175.000 350.000i −0.111567 0.223135i
\(136\) −328.000 −0.206807
\(137\) 192.000i 0.119735i −0.998206 0.0598674i \(-0.980932\pi\)
0.998206 0.0598674i \(-0.0190678\pi\)
\(138\) 980.000i 0.604516i
\(139\) 1402.00 0.855511 0.427756 0.903894i \(-0.359304\pi\)
0.427756 + 0.903894i \(0.359304\pi\)
\(140\) 0 0
\(141\) 2009.00 1.19992
\(142\) 912.000i 0.538967i
\(143\) 1887.00i 1.10349i
\(144\) −352.000 −0.203704
\(145\) −2490.00 + 1245.00i −1.42609 + 0.713046i
\(146\) −1300.00 −0.736909
\(147\) 0 0
\(148\) 1336.00i 0.742017i
\(149\) 302.000 0.166046 0.0830228 0.996548i \(-0.473543\pi\)
0.0830228 + 0.996548i \(0.473543\pi\)
\(150\) 1050.00 1400.00i 0.571548 0.762063i
\(151\) −3167.00 −1.70680 −0.853400 0.521257i \(-0.825463\pi\)
−0.853400 + 0.521257i \(0.825463\pi\)
\(152\) 864.000i 0.461050i
\(153\) 902.000i 0.476617i
\(154\) 0 0
\(155\) −1340.00 + 670.000i −0.694396 + 0.347198i
\(156\) −1428.00 −0.732894
\(157\) 470.000i 0.238918i −0.992839 0.119459i \(-0.961884\pi\)
0.992839 0.119459i \(-0.0381160\pi\)
\(158\) 2478.00i 1.24772i
\(159\) 42.0000 0.0209485
\(160\) 160.000 + 320.000i 0.0790569 + 0.158114i
\(161\) 0 0
\(162\) 1678.00i 0.813803i
\(163\) 2390.00i 1.14846i −0.818693 0.574231i \(-0.805301\pi\)
0.818693 0.574231i \(-0.194699\pi\)
\(164\) 824.000 0.392339
\(165\) 1295.00 + 2590.00i 0.611004 + 1.22201i
\(166\) −856.000 −0.400232
\(167\) 2631.00i 1.21912i −0.792740 0.609560i \(-0.791346\pi\)
0.792740 0.609560i \(-0.208654\pi\)
\(168\) 0 0
\(169\) −404.000 −0.183887
\(170\) −820.000 + 410.000i −0.369948 + 0.184974i
\(171\) 2376.00 1.06256
\(172\) 1504.00i 0.666738i
\(173\) 2243.00i 0.985735i 0.870104 + 0.492867i \(0.164051\pi\)
−0.870104 + 0.492867i \(0.835949\pi\)
\(174\) 3486.00 1.51881
\(175\) 0 0
\(176\) −592.000 −0.253544
\(177\) 14.0000i 0.00594522i
\(178\) 440.000i 0.185277i
\(179\) −52.0000 −0.0217132 −0.0108566 0.999941i \(-0.503456\pi\)
−0.0108566 + 0.999941i \(0.503456\pi\)
\(180\) −880.000 + 440.000i −0.364396 + 0.182198i
\(181\) −2462.00 −1.01104 −0.505522 0.862814i \(-0.668700\pi\)
−0.505522 + 0.862814i \(0.668700\pi\)
\(182\) 0 0
\(183\) 6580.00i 2.65797i
\(184\) 560.000 0.224368
\(185\) −1670.00 3340.00i −0.663680 1.32736i
\(186\) 1876.00 0.739543
\(187\) 1517.00i 0.593230i
\(188\) 1148.00i 0.445354i
\(189\) 0 0
\(190\) −1080.00 2160.00i −0.412376 0.824752i
\(191\) 3159.00 1.19674 0.598370 0.801220i \(-0.295815\pi\)
0.598370 + 0.801220i \(0.295815\pi\)
\(192\) 448.000i 0.168394i
\(193\) 2060.00i 0.768301i 0.923271 + 0.384150i \(0.125506\pi\)
−0.923271 + 0.384150i \(0.874494\pi\)
\(194\) −2110.00 −0.780872
\(195\) −3570.00 + 1785.00i −1.31104 + 0.655521i
\(196\) 0 0
\(197\) 1738.00i 0.628565i −0.949329 0.314283i \(-0.898236\pi\)
0.949329 0.314283i \(-0.101764\pi\)
\(198\) 1628.00i 0.584328i
\(199\) −894.000 −0.318462 −0.159231 0.987241i \(-0.550901\pi\)
−0.159231 + 0.987241i \(0.550901\pi\)
\(200\) 800.000 + 600.000i 0.282843 + 0.212132i
\(201\) 742.000 0.260381
\(202\) 3920.00i 1.36540i
\(203\) 0 0
\(204\) 1148.00 0.394000
\(205\) 2060.00 1030.00i 0.701837 0.350919i
\(206\) −3650.00 −1.23450
\(207\) 1540.00i 0.517089i
\(208\) 816.000i 0.272016i
\(209\) 3996.00 1.32253
\(210\) 0 0
\(211\) −4083.00 −1.33216 −0.666079 0.745881i \(-0.732029\pi\)
−0.666079 + 0.745881i \(0.732029\pi\)
\(212\) 24.0000i 0.00777513i
\(213\) 3192.00i 1.02682i
\(214\) 288.000 0.0919966
\(215\) 1880.00 + 3760.00i 0.596349 + 1.19270i
\(216\) −280.000 −0.0882018
\(217\) 0 0
\(218\) 3362.00i 1.04451i
\(219\) 4550.00 1.40393
\(220\) −1480.00 + 740.000i −0.453553 + 0.226776i
\(221\) 2091.00 0.636452
\(222\) 4676.00i 1.41366i
\(223\) 377.000i 0.113210i −0.998397 0.0566049i \(-0.981972\pi\)
0.998397 0.0566049i \(-0.0180275\pi\)
\(224\) 0 0
\(225\) −1650.00 + 2200.00i −0.488889 + 0.651852i
\(226\) 1596.00 0.469754
\(227\) 2551.00i 0.745885i −0.927855 0.372942i \(-0.878349\pi\)
0.927855 0.372942i \(-0.121651\pi\)
\(228\) 3024.00i 0.878374i
\(229\) 74.0000 0.0213540 0.0106770 0.999943i \(-0.496601\pi\)
0.0106770 + 0.999943i \(0.496601\pi\)
\(230\) 1400.00 700.000i 0.401362 0.200681i
\(231\) 0 0
\(232\) 1992.00i 0.563712i
\(233\) 1888.00i 0.530845i 0.964132 + 0.265423i \(0.0855115\pi\)
−0.964132 + 0.265423i \(0.914488\pi\)
\(234\) 2244.00 0.626901
\(235\) 1435.00 + 2870.00i 0.398337 + 0.796673i
\(236\) 8.00000 0.00220659
\(237\) 8673.00i 2.37710i
\(238\) 0 0
\(239\) −4997.00 −1.35242 −0.676211 0.736708i \(-0.736379\pi\)
−0.676211 + 0.736708i \(0.736379\pi\)
\(240\) −560.000 1120.00i −0.150616 0.301232i
\(241\) 3830.00 1.02370 0.511851 0.859074i \(-0.328960\pi\)
0.511851 + 0.859074i \(0.328960\pi\)
\(242\) 76.0000i 0.0201879i
\(243\) 4928.00i 1.30095i
\(244\) −3760.00 −0.986514
\(245\) 0 0
\(246\) −2884.00 −0.747468
\(247\) 5508.00i 1.41889i
\(248\) 1072.00i 0.274484i
\(249\) 2996.00 0.762505
\(250\) 2750.00 + 500.000i 0.695701 + 0.126491i
\(251\) 3390.00 0.852490 0.426245 0.904608i \(-0.359836\pi\)
0.426245 + 0.904608i \(0.359836\pi\)
\(252\) 0 0
\(253\) 2590.00i 0.643604i
\(254\) −868.000 −0.214422
\(255\) 2870.00 1435.00i 0.704809 0.352405i
\(256\) 256.000 0.0625000
\(257\) 7170.00i 1.74028i 0.492803 + 0.870141i \(0.335972\pi\)
−0.492803 + 0.870141i \(0.664028\pi\)
\(258\) 5264.00i 1.27024i
\(259\) 0 0
\(260\) −1020.00 2040.00i −0.243299 0.486598i
\(261\) −5478.00 −1.29916
\(262\) 2580.00i 0.608370i
\(263\) 7672.00i 1.79877i −0.437160 0.899384i \(-0.644016\pi\)
0.437160 0.899384i \(-0.355984\pi\)
\(264\) 2072.00 0.483041
\(265\) 30.0000 + 60.0000i 0.00695428 + 0.0139086i
\(266\) 0 0
\(267\) 1540.00i 0.352983i
\(268\) 424.000i 0.0966415i
\(269\) −54.0000 −0.0122395 −0.00611977 0.999981i \(-0.501948\pi\)
−0.00611977 + 0.999981i \(0.501948\pi\)
\(270\) −700.000 + 350.000i −0.157780 + 0.0788901i
\(271\) −2932.00 −0.657219 −0.328609 0.944466i \(-0.606580\pi\)
−0.328609 + 0.944466i \(0.606580\pi\)
\(272\) 656.000i 0.146235i
\(273\) 0 0
\(274\) −384.000 −0.0846653
\(275\) −2775.00 + 3700.00i −0.608505 + 0.811340i
\(276\) −1960.00 −0.427457
\(277\) 3254.00i 0.705826i −0.935656 0.352913i \(-0.885191\pi\)
0.935656 0.352913i \(-0.114809\pi\)
\(278\) 2804.00i 0.604938i
\(279\) −2948.00 −0.632588
\(280\) 0 0
\(281\) 3327.00 0.706307 0.353153 0.935565i \(-0.385109\pi\)
0.353153 + 0.935565i \(0.385109\pi\)
\(282\) 4018.00i 0.848470i
\(283\) 4627.00i 0.971896i −0.873988 0.485948i \(-0.838474\pi\)
0.873988 0.485948i \(-0.161526\pi\)
\(284\) −1824.00 −0.381107
\(285\) 3780.00 + 7560.00i 0.785642 + 1.57128i
\(286\) 3774.00 0.780284
\(287\) 0 0
\(288\) 704.000i 0.144040i
\(289\) 3232.00 0.657847
\(290\) 2490.00 + 4980.00i 0.504199 + 1.00840i
\(291\) 7385.00 1.48769
\(292\) 2600.00i 0.521074i
\(293\) 4083.00i 0.814100i 0.913406 + 0.407050i \(0.133443\pi\)
−0.913406 + 0.407050i \(0.866557\pi\)
\(294\) 0 0
\(295\) 20.0000 10.0000i 0.00394727 0.00197364i
\(296\) −2672.00 −0.524685
\(297\) 1295.00i 0.253008i
\(298\) 604.000i 0.117412i
\(299\) −3570.00 −0.690496
\(300\) −2800.00 2100.00i −0.538860 0.404145i
\(301\) 0 0
\(302\) 6334.00i 1.20689i
\(303\) 13720.0i 2.60130i
\(304\) −1728.00 −0.326012
\(305\) −9400.00 + 4700.00i −1.76473 + 0.882365i
\(306\) −1804.00 −0.337019
\(307\) 4089.00i 0.760168i −0.924952 0.380084i \(-0.875895\pi\)
0.924952 0.380084i \(-0.124105\pi\)
\(308\) 0 0
\(309\) 12775.0 2.35192
\(310\) 1340.00 + 2680.00i 0.245506 + 0.491012i
\(311\) 4008.00 0.730781 0.365390 0.930854i \(-0.380935\pi\)
0.365390 + 0.930854i \(0.380935\pi\)
\(312\) 2856.00i 0.518234i
\(313\) 7355.00i 1.32821i −0.747640 0.664104i \(-0.768813\pi\)
0.747640 0.664104i \(-0.231187\pi\)
\(314\) −940.000 −0.168940
\(315\) 0 0
\(316\) −4956.00 −0.882268
\(317\) 1684.00i 0.298369i 0.988809 + 0.149184i \(0.0476648\pi\)
−0.988809 + 0.149184i \(0.952335\pi\)
\(318\) 84.0000i 0.0148128i
\(319\) −9213.00 −1.61702
\(320\) 640.000 320.000i 0.111803 0.0559017i
\(321\) −1008.00 −0.175268
\(322\) 0 0
\(323\) 4428.00i 0.762788i
\(324\) 3356.00 0.575446
\(325\) −5100.00 3825.00i −0.870453 0.652839i
\(326\) −4780.00 −0.812085
\(327\) 11767.0i 1.98996i
\(328\) 1648.00i 0.277426i
\(329\) 0 0
\(330\) 5180.00 2590.00i 0.864090 0.432045i
\(331\) −1460.00 −0.242444 −0.121222 0.992625i \(-0.538681\pi\)
−0.121222 + 0.992625i \(0.538681\pi\)
\(332\) 1712.00i 0.283007i
\(333\) 7348.00i 1.20921i
\(334\) −5262.00 −0.862047
\(335\) 530.000 + 1060.00i 0.0864388 + 0.172878i
\(336\) 0 0
\(337\) 7514.00i 1.21458i −0.794480 0.607290i \(-0.792256\pi\)
0.794480 0.607290i \(-0.207744\pi\)
\(338\) 808.000i 0.130028i
\(339\) −5586.00 −0.894955
\(340\) 820.000 + 1640.00i 0.130796 + 0.261593i
\(341\) −4958.00 −0.787363
\(342\) 4752.00i 0.751341i
\(343\) 0 0
\(344\) 3008.00 0.471455
\(345\) −4900.00 + 2450.00i −0.764658 + 0.382329i
\(346\) 4486.00 0.697020
\(347\) 2862.00i 0.442767i 0.975187 + 0.221384i \(0.0710573\pi\)
−0.975187 + 0.221384i \(0.928943\pi\)
\(348\) 6972.00i 1.07396i
\(349\) −6368.00 −0.976708 −0.488354 0.872646i \(-0.662403\pi\)
−0.488354 + 0.872646i \(0.662403\pi\)
\(350\) 0 0
\(351\) 1785.00 0.271442
\(352\) 1184.00i 0.179282i
\(353\) 3635.00i 0.548078i 0.961719 + 0.274039i \(0.0883597\pi\)
−0.961719 + 0.274039i \(0.911640\pi\)
\(354\) −28.0000 −0.00420391
\(355\) −4560.00 + 2280.00i −0.681746 + 0.340873i
\(356\) 880.000 0.131011
\(357\) 0 0
\(358\) 104.000i 0.0153535i
\(359\) −7116.00 −1.04615 −0.523075 0.852286i \(-0.675215\pi\)
−0.523075 + 0.852286i \(0.675215\pi\)
\(360\) 880.000 + 1760.00i 0.128834 + 0.257667i
\(361\) 4805.00 0.700539
\(362\) 4924.00i 0.714916i
\(363\) 266.000i 0.0384611i
\(364\) 0 0
\(365\) 3250.00 + 6500.00i 0.466062 + 0.932125i
\(366\) 13160.0 1.87947
\(367\) 319.000i 0.0453724i −0.999743 0.0226862i \(-0.992778\pi\)
0.999743 0.0226862i \(-0.00722186\pi\)
\(368\) 1120.00i 0.158652i
\(369\) 4532.00 0.639367
\(370\) −6680.00 + 3340.00i −0.938586 + 0.469293i
\(371\) 0 0
\(372\) 3752.00i 0.522936i
\(373\) 11652.0i 1.61747i −0.588171 0.808737i \(-0.700152\pi\)
0.588171 0.808737i \(-0.299848\pi\)
\(374\) −3034.00 −0.419477
\(375\) −9625.00 1750.00i −1.32542 0.240986i
\(376\) 2296.00 0.314913
\(377\) 12699.0i 1.73483i
\(378\) 0 0
\(379\) −7748.00 −1.05010 −0.525050 0.851071i \(-0.675953\pi\)
−0.525050 + 0.851071i \(0.675953\pi\)
\(380\) −4320.00 + 2160.00i −0.583188 + 0.291594i
\(381\) 3038.00 0.408508
\(382\) 6318.00i 0.846223i
\(383\) 8680.00i 1.15803i −0.815315 0.579017i \(-0.803436\pi\)
0.815315 0.579017i \(-0.196564\pi\)
\(384\) −896.000 −0.119072
\(385\) 0 0
\(386\) 4120.00 0.543271
\(387\) 8272.00i 1.08654i
\(388\) 4220.00i 0.552160i
\(389\) 1711.00 0.223011 0.111505 0.993764i \(-0.464433\pi\)
0.111505 + 0.993764i \(0.464433\pi\)
\(390\) 3570.00 + 7140.00i 0.463523 + 0.927046i
\(391\) 2870.00 0.371208
\(392\) 0 0
\(393\) 9030.00i 1.15904i
\(394\) −3476.00 −0.444463
\(395\) −12390.0 + 6195.00i −1.57825 + 0.789125i
\(396\) −3256.00 −0.413182
\(397\) 1589.00i 0.200881i 0.994943 + 0.100440i \(0.0320252\pi\)
−0.994943 + 0.100440i \(0.967975\pi\)
\(398\) 1788.00i 0.225187i
\(399\) 0 0
\(400\) 1200.00 1600.00i 0.150000 0.200000i
\(401\) −5147.00 −0.640970 −0.320485 0.947254i \(-0.603846\pi\)
−0.320485 + 0.947254i \(0.603846\pi\)
\(402\) 1484.00i 0.184117i
\(403\) 6834.00i 0.844729i
\(404\) 7840.00 0.965482
\(405\) 8390.00 4195.00i 1.02939 0.514694i
\(406\) 0 0
\(407\) 12358.0i 1.50507i
\(408\) 2296.00i 0.278600i
\(409\) −9100.00 −1.10016 −0.550081 0.835111i \(-0.685403\pi\)
−0.550081 + 0.835111i \(0.685403\pi\)
\(410\) −2060.00 4120.00i −0.248137 0.496274i
\(411\) 1344.00 0.161301
\(412\) 7300.00i 0.872925i
\(413\) 0 0
\(414\) 3080.00 0.365637
\(415\) 2140.00 + 4280.00i 0.253129 + 0.506258i
\(416\) −1632.00 −0.192345
\(417\) 9814.00i 1.15250i
\(418\) 7992.00i 0.935171i
\(419\) 2618.00 0.305245 0.152623 0.988285i \(-0.451228\pi\)
0.152623 + 0.988285i \(0.451228\pi\)
\(420\) 0 0
\(421\) −3695.00 −0.427751 −0.213876 0.976861i \(-0.568609\pi\)
−0.213876 + 0.976861i \(0.568609\pi\)
\(422\) 8166.00i 0.941978i
\(423\) 6314.00i 0.725762i
\(424\) 48.0000 0.00549784
\(425\) 4100.00 + 3075.00i 0.467951 + 0.350963i
\(426\) 6384.00 0.726070
\(427\) 0 0
\(428\) 576.000i 0.0650514i
\(429\) −13209.0 −1.48657
\(430\) 7520.00 3760.00i 0.843364 0.421682i
\(431\) 15779.0 1.76345 0.881726 0.471762i \(-0.156382\pi\)
0.881726 + 0.471762i \(0.156382\pi\)
\(432\) 560.000i 0.0623681i
\(433\) 7238.00i 0.803317i −0.915790 0.401658i \(-0.868434\pi\)
0.915790 0.401658i \(-0.131566\pi\)
\(434\) 0 0
\(435\) −8715.00 17430.0i −0.960580 1.92116i
\(436\) 6724.00 0.738581
\(437\) 7560.00i 0.827560i
\(438\) 9100.00i 0.992728i
\(439\) −2646.00 −0.287669 −0.143834 0.989602i \(-0.545943\pi\)
−0.143834 + 0.989602i \(0.545943\pi\)
\(440\) 1480.00 + 2960.00i 0.160355 + 0.320710i
\(441\) 0 0
\(442\) 4182.00i 0.450039i
\(443\) 5688.00i 0.610034i 0.952347 + 0.305017i \(0.0986621\pi\)
−0.952347 + 0.305017i \(0.901338\pi\)
\(444\) 9352.00 0.999609
\(445\) 2200.00 1100.00i 0.234360 0.117180i
\(446\) −754.000 −0.0800514
\(447\) 2114.00i 0.223689i
\(448\) 0 0
\(449\) 3285.00 0.345276 0.172638 0.984985i \(-0.444771\pi\)
0.172638 + 0.984985i \(0.444771\pi\)
\(450\) 4400.00 + 3300.00i 0.460929 + 0.345697i
\(451\) 7622.00 0.795800
\(452\) 3192.00i 0.332166i
\(453\) 22169.0i 2.29932i
\(454\) −5102.00 −0.527420
\(455\) 0 0
\(456\) 6048.00 0.621104
\(457\) 14834.0i 1.51839i −0.650862 0.759196i \(-0.725592\pi\)
0.650862 0.759196i \(-0.274408\pi\)
\(458\) 148.000i 0.0150995i
\(459\) −1435.00 −0.145926
\(460\) −1400.00 2800.00i −0.141903 0.283806i
\(461\) 9972.00 1.00747 0.503734 0.863859i \(-0.331959\pi\)
0.503734 + 0.863859i \(0.331959\pi\)
\(462\) 0 0
\(463\) 9096.00i 0.913017i −0.889719 0.456509i \(-0.849100\pi\)
0.889719 0.456509i \(-0.150900\pi\)
\(464\) 3984.00 0.398605
\(465\) −4690.00 9380.00i −0.467728 0.935456i
\(466\) 3776.00 0.375364
\(467\) 15867.0i 1.57224i 0.618072 + 0.786121i \(0.287914\pi\)
−0.618072 + 0.786121i \(0.712086\pi\)
\(468\) 4488.00i 0.443286i
\(469\) 0 0
\(470\) 5740.00 2870.00i 0.563333 0.281666i
\(471\) 3290.00 0.321858
\(472\) 16.0000i 0.00156030i
\(473\) 13912.0i 1.35238i
\(474\) 17346.0 1.68086
\(475\) −8100.00 + 10800.0i −0.782428 + 1.04324i
\(476\) 0 0
\(477\) 132.000i 0.0126706i
\(478\) 9994.00i 0.956307i
\(479\) 242.000 0.0230841 0.0115420 0.999933i \(-0.496326\pi\)
0.0115420 + 0.999933i \(0.496326\pi\)
\(480\) −2240.00 + 1120.00i −0.213003 + 0.106502i
\(481\) 17034.0 1.61473
\(482\) 7660.00i 0.723866i
\(483\) 0 0
\(484\) −152.000 −0.0142750
\(485\) 5275.00 + 10550.0i 0.493867 + 0.987734i
\(486\) −9856.00 −0.919912
\(487\) 3558.00i 0.331064i 0.986204 + 0.165532i \(0.0529342\pi\)
−0.986204 + 0.165532i \(0.947066\pi\)
\(488\) 7520.00i 0.697571i
\(489\) 16730.0 1.54715
\(490\) 0 0
\(491\) 1473.00 0.135388 0.0676941 0.997706i \(-0.478436\pi\)
0.0676941 + 0.997706i \(0.478436\pi\)
\(492\) 5768.00i 0.528540i
\(493\) 10209.0i 0.932637i
\(494\) 11016.0 1.00331
\(495\) −8140.00 + 4070.00i −0.739123 + 0.369561i
\(496\) 2144.00 0.194090
\(497\) 0 0
\(498\) 5992.00i 0.539173i
\(499\) −603.000 −0.0540962 −0.0270481 0.999634i \(-0.508611\pi\)
−0.0270481 + 0.999634i \(0.508611\pi\)
\(500\) 1000.00 5500.00i 0.0894427 0.491935i
\(501\) 18417.0 1.64234
\(502\) 6780.00i 0.602801i
\(503\) 18387.0i 1.62989i −0.579537 0.814946i \(-0.696766\pi\)
0.579537 0.814946i \(-0.303234\pi\)
\(504\) 0 0
\(505\) 19600.0 9800.00i 1.72711 0.863553i
\(506\) 5180.00 0.455097
\(507\) 2828.00i 0.247724i
\(508\) 1736.00i 0.151619i
\(509\) 9018.00 0.785296 0.392648 0.919689i \(-0.371559\pi\)
0.392648 + 0.919689i \(0.371559\pi\)
\(510\) −2870.00 5740.00i −0.249188 0.498375i
\(511\) 0 0
\(512\) 512.000i 0.0441942i
\(513\) 3780.00i 0.325324i
\(514\) 14340.0 1.23056
\(515\) 9125.00 + 18250.0i 0.780768 + 1.56154i
\(516\) −10528.0 −0.898196
\(517\) 10619.0i 0.903333i
\(518\) 0 0
\(519\) −15701.0 −1.32793
\(520\) −4080.00 + 2040.00i −0.344077 + 0.172038i
\(521\) −4624.00 −0.388831 −0.194416 0.980919i \(-0.562281\pi\)
−0.194416 + 0.980919i \(0.562281\pi\)
\(522\) 10956.0i 0.918642i
\(523\) 5876.00i 0.491280i 0.969361 + 0.245640i \(0.0789981\pi\)
−0.969361 + 0.245640i \(0.921002\pi\)
\(524\) −5160.00 −0.430183
\(525\) 0 0
\(526\) −15344.0 −1.27192
\(527\) 5494.00i 0.454122i
\(528\) 4144.00i 0.341561i
\(529\) 7267.00 0.597271
\(530\) 120.000 60.0000i 0.00983484 0.00491742i
\(531\) 44.0000 0.00359593
\(532\) 0 0
\(533\) 10506.0i 0.853781i
\(534\) −3080.00 −0.249597
\(535\) −720.000 1440.00i −0.0581838 0.116368i
\(536\) 848.000 0.0683359
\(537\) 364.000i 0.0292509i
\(538\) 108.000i 0.00865467i
\(539\) 0 0
\(540\) 700.000 + 1400.00i 0.0557837 + 0.111567i
\(541\) −8537.00 −0.678437 −0.339218 0.940708i \(-0.610163\pi\)
−0.339218 + 0.940708i \(0.610163\pi\)
\(542\) 5864.00i 0.464724i
\(543\) 17234.0i 1.36203i
\(544\) 1312.00 0.103404
\(545\) 16810.0 8405.00i 1.32121 0.660607i
\(546\) 0 0
\(547\) 13060.0i 1.02085i 0.859922 + 0.510425i \(0.170512\pi\)
−0.859922 + 0.510425i \(0.829488\pi\)
\(548\) 768.000i 0.0598674i
\(549\) −20680.0 −1.60765
\(550\) 7400.00 + 5550.00i 0.573704 + 0.430278i
\(551\) −26892.0 −2.07920
\(552\) 3920.00i 0.302258i
\(553\) 0 0
\(554\) −6508.00 −0.499095
\(555\) 23380.0 11690.0i 1.78815 0.894077i
\(556\) −5608.00 −0.427756
\(557\) 21372.0i 1.62578i −0.582416 0.812891i \(-0.697892\pi\)
0.582416 0.812891i \(-0.302108\pi\)
\(558\) 5896.00i 0.447307i
\(559\) −19176.0 −1.45091
\(560\) 0 0
\(561\) 10619.0 0.799170
\(562\) 6654.00i 0.499434i
\(563\) 12704.0i 0.950994i 0.879717 + 0.475497i \(0.157732\pi\)
−0.879717 + 0.475497i \(0.842268\pi\)
\(564\) −8036.00 −0.599959
\(565\) −3990.00 7980.00i −0.297098 0.594197i
\(566\) −9254.00 −0.687234
\(567\) 0 0
\(568\) 3648.00i 0.269484i
\(569\) −8762.00 −0.645557 −0.322779 0.946474i \(-0.604617\pi\)
−0.322779 + 0.946474i \(0.604617\pi\)
\(570\) 15120.0 7560.00i 1.11107 0.555533i
\(571\) −24764.0 −1.81496 −0.907479 0.420097i \(-0.861996\pi\)
−0.907479 + 0.420097i \(0.861996\pi\)
\(572\) 7548.00i 0.551744i
\(573\) 22113.0i 1.61219i
\(574\) 0 0
\(575\) −7000.00 5250.00i −0.507687 0.380765i
\(576\) 1408.00 0.101852
\(577\) 1811.00i 0.130664i 0.997864 + 0.0653318i \(0.0208106\pi\)
−0.997864 + 0.0653318i \(0.979189\pi\)
\(578\) 6464.00i 0.465168i
\(579\) −14420.0 −1.03502
\(580\) 9960.00 4980.00i 0.713046 0.356523i
\(581\) 0 0
\(582\) 14770.0i 1.05195i
\(583\) 222.000i 0.0157707i
\(584\) 5200.00 0.368455
\(585\) −5610.00 11220.0i −0.396487 0.792974i
\(586\) 8166.00 0.575656
\(587\) 10548.0i 0.741674i 0.928698 + 0.370837i \(0.120929\pi\)
−0.928698 + 0.370837i \(0.879071\pi\)
\(588\) 0 0
\(589\) −14472.0 −1.01241
\(590\) −20.0000 40.0000i −0.00139557 0.00279114i
\(591\) 12166.0 0.846772
\(592\) 5344.00i 0.371009i
\(593\) 17439.0i 1.20765i −0.797119 0.603823i \(-0.793643\pi\)
0.797119 0.603823i \(-0.206357\pi\)
\(594\) −2590.00 −0.178904
\(595\) 0 0
\(596\) −1208.00 −0.0830228
\(597\) 6258.00i 0.429017i
\(598\) 7140.00i 0.488255i
\(599\) −2451.00 −0.167187 −0.0835936 0.996500i \(-0.526640\pi\)
−0.0835936 + 0.996500i \(0.526640\pi\)
\(600\) −4200.00 + 5600.00i −0.285774 + 0.381032i
\(601\) 7792.00 0.528856 0.264428 0.964405i \(-0.414817\pi\)
0.264428 + 0.964405i \(0.414817\pi\)
\(602\) 0 0
\(603\) 2332.00i 0.157490i
\(604\) 12668.0 0.853400
\(605\) −380.000 + 190.000i −0.0255359 + 0.0127679i
\(606\) −27440.0 −1.83940
\(607\) 1937.00i 0.129523i −0.997901 0.0647615i \(-0.979371\pi\)
0.997901 0.0647615i \(-0.0206286\pi\)
\(608\) 3456.00i 0.230525i
\(609\) 0 0
\(610\) 9400.00 + 18800.0i 0.623926 + 1.24785i
\(611\) −14637.0 −0.969148
\(612\) 3608.00i 0.238308i
\(613\) 5036.00i 0.331814i 0.986141 + 0.165907i \(0.0530552\pi\)
−0.986141 + 0.165907i \(0.946945\pi\)
\(614\) −8178.00 −0.537520
\(615\) 7210.00 + 14420.0i 0.472740 + 0.945481i
\(616\) 0 0
\(617\) 27286.0i 1.78038i 0.455592 + 0.890189i \(0.349428\pi\)
−0.455592 + 0.890189i \(0.650572\pi\)
\(618\) 25550.0i 1.66306i
\(619\) 28538.0 1.85305 0.926526 0.376231i \(-0.122780\pi\)
0.926526 + 0.376231i \(0.122780\pi\)
\(620\) 5360.00 2680.00i 0.347198 0.173599i
\(621\) 2450.00 0.158317
\(622\) 8016.00i 0.516740i
\(623\) 0 0
\(624\) 5712.00 0.366447
\(625\) −4375.00 15000.0i −0.280000 0.960000i
\(626\) −14710.0 −0.939185
\(627\) 27972.0i 1.78165i
\(628\) 1880.00i 0.119459i
\(629\) −13694.0 −0.868069
\(630\) 0 0
\(631\) 25007.0 1.57768 0.788838 0.614602i \(-0.210683\pi\)
0.788838 + 0.614602i \(0.210683\pi\)
\(632\) 9912.00i 0.623858i
\(633\) 28581.0i 1.79462i
\(634\) 3368.00 0.210978
\(635\) 2170.00 + 4340.00i 0.135612 + 0.271225i
\(636\) −168.000 −0.0104743
\(637\) 0 0
\(638\) 18426.0i 1.14340i
\(639\) −10032.0 −0.621064
\(640\) −640.000 1280.00i −0.0395285 0.0790569i
\(641\) −12130.0 −0.747436 −0.373718 0.927542i \(-0.621917\pi\)
−0.373718 + 0.927542i \(0.621917\pi\)
\(642\) 2016.00i 0.123933i
\(643\) 14385.0i 0.882254i −0.897445 0.441127i \(-0.854579\pi\)
0.897445 0.441127i \(-0.145421\pi\)
\(644\) 0 0
\(645\) −26320.0 + 13160.0i −1.60674 + 0.803371i
\(646\) −8856.00 −0.539373
\(647\) 2208.00i 0.134166i −0.997747 0.0670830i \(-0.978631\pi\)
0.997747 0.0670830i \(-0.0213692\pi\)
\(648\) 6712.00i 0.406902i
\(649\) 74.0000 0.00447574
\(650\) −7650.00 + 10200.0i −0.461627 + 0.615503i
\(651\) 0 0
\(652\) 9560.00i 0.574231i
\(653\) 22448.0i 1.34527i 0.739977 + 0.672633i \(0.234837\pi\)
−0.739977 + 0.672633i \(0.765163\pi\)
\(654\) −23534.0 −1.40711
\(655\) −12900.0 + 6450.00i −0.769534 + 0.384767i
\(656\) −3296.00 −0.196169
\(657\) 14300.0i 0.849157i
\(658\) 0 0
\(659\) −8791.00 −0.519649 −0.259825 0.965656i \(-0.583665\pi\)
−0.259825 + 0.965656i \(0.583665\pi\)
\(660\) −5180.00 10360.0i −0.305502 0.611004i
\(661\) 13180.0 0.775556 0.387778 0.921753i \(-0.373243\pi\)
0.387778 + 0.921753i \(0.373243\pi\)
\(662\) 2920.00i 0.171434i
\(663\) 14637.0i 0.857397i
\(664\) 3424.00 0.200116
\(665\) 0 0
\(666\) −14696.0 −0.855043
\(667\) 17430.0i 1.01183i
\(668\) 10524.0i 0.609560i
\(669\) 2639.00 0.152511
\(670\) 2120.00 1060.00i 0.122243 0.0611215i
\(671\) −34780.0 −2.00099
\(672\) 0 0
\(673\) 7164.00i 0.410330i −0.978727 0.205165i \(-0.934227\pi\)
0.978727 0.205165i \(-0.0657731\pi\)
\(674\) −15028.0 −0.858838
\(675\) 3500.00 + 2625.00i 0.199578 + 0.149683i
\(676\) 1616.00 0.0919436
\(677\) 12335.0i 0.700255i 0.936702 + 0.350127i \(0.113862\pi\)
−0.936702 + 0.350127i \(0.886138\pi\)
\(678\) 11172.0i 0.632829i
\(679\) 0 0
\(680\) 3280.00 1640.00i 0.184974 0.0924870i
\(681\) 17857.0 1.00482
\(682\) 9916.00i 0.556750i
\(683\) 15436.0i 0.864776i −0.901688 0.432388i \(-0.857671\pi\)
0.901688 0.432388i \(-0.142329\pi\)
\(684\) −9504.00 −0.531279
\(685\) 960.000 + 1920.00i 0.0535470 + 0.107094i
\(686\) 0 0
\(687\) 518.000i 0.0287670i
\(688\) 6016.00i 0.333369i
\(689\) −306.000 −0.0169197
\(690\) 4900.00 + 9800.00i 0.270348 + 0.540695i
\(691\) 19184.0 1.05614 0.528071 0.849200i \(-0.322916\pi\)
0.528071 + 0.849200i \(0.322916\pi\)
\(692\) 8972.00i 0.492867i
\(693\) 0 0
\(694\) 5724.00 0.313084
\(695\) −14020.0 + 7010.00i −0.765193 + 0.382596i
\(696\) −13944.0 −0.759405
\(697\) 8446.00i 0.458989i
\(698\) 12736.0i 0.690637i
\(699\) −13216.0 −0.715129
\(700\) 0 0
\(701\) 32975.0 1.77667 0.888337 0.459192i \(-0.151861\pi\)
0.888337 + 0.459192i \(0.151861\pi\)
\(702\) 3570.00i 0.191939i
\(703\) 36072.0i 1.93525i
\(704\) 2368.00 0.126772
\(705\) −20090.0 + 10045.0i −1.07324 + 0.536619i
\(706\) 7270.00 0.387550
\(707\) 0 0
\(708\) 56.0000i 0.00297261i
\(709\) 31497.0 1.66840 0.834199 0.551463i \(-0.185930\pi\)
0.834199 + 0.551463i \(0.185930\pi\)
\(710\) 4560.00 + 9120.00i 0.241033 + 0.482067i
\(711\) −27258.0 −1.43777
\(712\) 1760.00i 0.0926387i
\(713\) 9380.00i 0.492684i
\(714\) 0 0
\(715\) −9435.00 18870.0i −0.493495 0.986990i
\(716\) 208.000 0.0108566
\(717\) 34979.0i 1.82192i
\(718\) 14232.0i 0.739740i
\(719\) −18610.0 −0.965279 −0.482640 0.875819i \(-0.660322\pi\)
−0.482640 + 0.875819i \(0.660322\pi\)
\(720\) 3520.00 1760.00i 0.182198 0.0910991i
\(721\) 0 0
\(722\) 9610.00i 0.495356i
\(723\) 26810.0i 1.37908i
\(724\) 9848.00 0.505522
\(725\) 18675.0 24900.0i 0.956651 1.27553i
\(726\) 532.000 0.0271961
\(727\) 17508.0i 0.893172i −0.894741 0.446586i \(-0.852640\pi\)
0.894741 0.446586i \(-0.147360\pi\)
\(728\) 0 0
\(729\) 11843.0 0.601687
\(730\) 13000.0 6500.00i 0.659112 0.329556i
\(731\) 15416.0 0.780002
\(732\) 26320.0i 1.32898i
\(733\) 4685.00i 0.236077i 0.993009 + 0.118038i \(0.0376606\pi\)
−0.993009 + 0.118038i \(0.962339\pi\)
\(734\) −638.000 −0.0320831
\(735\) 0 0
\(736\) −2240.00 −0.112184
\(737\) 3922.00i 0.196023i
\(738\) 9064.00i 0.452101i
\(739\) 25925.0 1.29048 0.645241 0.763979i \(-0.276757\pi\)
0.645241 + 0.763979i \(0.276757\pi\)
\(740\) 6680.00 + 13360.0i 0.331840 + 0.663680i
\(741\) −38556.0 −1.91146
\(742\) 0 0
\(743\) 25578.0i 1.26294i 0.775400 + 0.631471i \(0.217548\pi\)
−0.775400 + 0.631471i \(0.782452\pi\)
\(744\) −7504.00 −0.369771
\(745\) −3020.00 + 1510.00i −0.148516 + 0.0742579i
\(746\) −23304.0 −1.14373
\(747\) 9416.00i 0.461196i
\(748\) 6068.00i 0.296615i
\(749\) 0 0
\(750\) −3500.00 + 19250.0i −0.170403 + 0.937214i
\(751\) −4291.00 −0.208496 −0.104248 0.994551i \(-0.533244\pi\)
−0.104248 + 0.994551i \(0.533244\pi\)
\(752\) 4592.00i 0.222677i
\(753\) 23730.0i 1.14843i
\(754\) −25398.0 −1.22671
\(755\) 31670.0 15835.0i 1.52661 0.763304i
\(756\) 0 0
\(757\) 31528.0i 1.51374i 0.653563 + 0.756872i \(0.273274\pi\)
−0.653563 + 0.756872i \(0.726726\pi\)
\(758\) 15496.0i 0.742533i
\(759\) −18130.0 −0.867032
\(760\) 4320.00 + 8640.00i 0.206188 + 0.412376i
\(761\) 23154.0 1.10293 0.551466 0.834197i \(-0.314068\pi\)
0.551466 + 0.834197i \(0.314068\pi\)
\(762\) 6076.00i 0.288859i
\(763\) 0 0
\(764\) −12636.0 −0.598370
\(765\) 4510.00 + 9020.00i 0.213150 + 0.426299i
\(766\) −17360.0 −0.818854
\(767\) 102.000i 0.00480183i
\(768\) 1792.00i 0.0841969i
\(769\) 13992.0 0.656131 0.328065 0.944655i \(-0.393603\pi\)
0.328065 + 0.944655i \(0.393603\pi\)
\(770\) 0 0
\(771\) −50190.0 −2.34442
\(772\) 8240.00i 0.384150i
\(773\) 21681.0i 1.00881i 0.863467 + 0.504406i \(0.168288\pi\)
−0.863467 + 0.504406i \(0.831712\pi\)
\(774\) 16544.0 0.768297
\(775\) 10050.0 13400.0i 0.465815 0.621087i
\(776\) 8440.00 0.390436
\(777\) 0 0
\(778\) 3422.00i 0.157692i
\(779\) 22248.0 1.02326
\(780\) 14280.0 7140.00i 0.655521 0.327760i
\(781\) −16872.0 −0.773019
\(782\) 5740.00i 0.262483i
\(783\) 8715.00i 0.397763i
\(784\) 0 0
\(785\) 2350.00 + 4700.00i 0.106847 + 0.213695i