Properties

Label 630.4.g.a.379.1
Level $630$
Weight $4$
Character 630.379
Analytic conductor $37.171$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 630.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(37.1712033036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 379.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 630.379
Dual form 630.4.g.a.379.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000i q^{2} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +7.00000i q^{7} +8.00000i q^{8} +O(q^{10})\) \(q-2.00000i q^{2} -4.00000 q^{4} +(-10.0000 - 5.00000i) q^{5} +7.00000i q^{7} +8.00000i q^{8} +(-10.0000 + 20.0000i) q^{10} +37.0000 q^{11} -51.0000i q^{13} +14.0000 q^{14} +16.0000 q^{16} -41.0000i q^{17} +108.000 q^{19} +(40.0000 + 20.0000i) q^{20} -74.0000i q^{22} -70.0000i q^{23} +(75.0000 + 100.000i) q^{25} -102.000 q^{26} -28.0000i q^{28} -249.000 q^{29} -134.000 q^{31} -32.0000i q^{32} -82.0000 q^{34} +(35.0000 - 70.0000i) q^{35} -334.000i q^{37} -216.000i q^{38} +(40.0000 - 80.0000i) q^{40} -206.000 q^{41} +376.000i q^{43} -148.000 q^{44} -140.000 q^{46} +287.000i q^{47} -49.0000 q^{49} +(200.000 - 150.000i) q^{50} +204.000i q^{52} -6.00000i q^{53} +(-370.000 - 185.000i) q^{55} -56.0000 q^{56} +498.000i q^{58} -2.00000 q^{59} -940.000 q^{61} +268.000i q^{62} -64.0000 q^{64} +(-255.000 + 510.000i) q^{65} +106.000i q^{67} +164.000i q^{68} +(-140.000 - 70.0000i) q^{70} -456.000 q^{71} -650.000i q^{73} -668.000 q^{74} -432.000 q^{76} +259.000i q^{77} +1239.00 q^{79} +(-160.000 - 80.0000i) q^{80} +412.000i q^{82} +428.000i q^{83} +(-205.000 + 410.000i) q^{85} +752.000 q^{86} +296.000i q^{88} -220.000 q^{89} +357.000 q^{91} +280.000i q^{92} +574.000 q^{94} +(-1080.00 - 540.000i) q^{95} -1055.00i q^{97} +98.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{4} - 20 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 8 q^{4} - 20 q^{5} - 20 q^{10} + 74 q^{11} + 28 q^{14} + 32 q^{16} + 216 q^{19} + 80 q^{20} + 150 q^{25} - 204 q^{26} - 498 q^{29} - 268 q^{31} - 164 q^{34} + 70 q^{35} + 80 q^{40} - 412 q^{41} - 296 q^{44} - 280 q^{46} - 98 q^{49} + 400 q^{50} - 740 q^{55} - 112 q^{56} - 4 q^{59} - 1880 q^{61} - 128 q^{64} - 510 q^{65} - 280 q^{70} - 912 q^{71} - 1336 q^{74} - 864 q^{76} + 2478 q^{79} - 320 q^{80} - 410 q^{85} + 1504 q^{86} - 440 q^{89} + 714 q^{91} + 1148 q^{94} - 2160 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 0 0
\(4\) −4.00000 −0.500000
\(5\) −10.0000 5.00000i −0.894427 0.447214i
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 8.00000i 0.353553i
\(9\) 0 0
\(10\) −10.0000 + 20.0000i −0.316228 + 0.632456i
\(11\) 37.0000 1.01417 0.507087 0.861895i \(-0.330722\pi\)
0.507087 + 0.861895i \(0.330722\pi\)
\(12\) 0 0
\(13\) 51.0000i 1.08807i −0.839064 0.544033i \(-0.816897\pi\)
0.839064 0.544033i \(-0.183103\pi\)
\(14\) 14.0000 0.267261
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) 41.0000i 0.584939i −0.956275 0.292469i \(-0.905523\pi\)
0.956275 0.292469i \(-0.0944770\pi\)
\(18\) 0 0
\(19\) 108.000 1.30405 0.652024 0.758199i \(-0.273920\pi\)
0.652024 + 0.758199i \(0.273920\pi\)
\(20\) 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 \(-0.102778\pi\)
\(24\) 0 0
\(25\) 75.0000 + 100.000i 0.600000 + 0.800000i
\(26\) −102.000 −0.769379
\(27\) 0 0
\(28\) 28.0000i 0.188982i
\(29\) −249.000 −1.59442 −0.797209 0.603703i \(-0.793691\pi\)
−0.797209 + 0.603703i \(0.793691\pi\)
\(30\) 0 0
\(31\) −134.000 −0.776358 −0.388179 0.921584i \(-0.626896\pi\)
−0.388179 + 0.921584i \(0.626896\pi\)
\(32\) 32.0000i 0.176777i
\(33\) 0 0
\(34\) −82.0000 −0.413614
\(35\) 35.0000 70.0000i 0.169031 0.338062i
\(36\) 0 0
\(37\) 334.000i 1.48403i −0.670381 0.742017i \(-0.733869\pi\)
0.670381 0.742017i \(-0.266131\pi\)
\(38\) 216.000i 0.922101i
\(39\) 0 0
\(40\) 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 \(0.232310\pi\)
−0.745292 + 0.666738i \(0.767690\pi\)
\(44\) −148.000 −0.507087
\(45\) 0 0
\(46\) −140.000 −0.448736
\(47\) 287.000i 0.890708i 0.895355 + 0.445354i \(0.146922\pi\)
−0.895355 + 0.445354i \(0.853078\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 200.000 150.000i 0.565685 0.424264i
\(51\) 0 0
\(52\) 204.000i 0.544033i
\(53\) 6.00000i 0.0155503i −0.999970 0.00777513i \(-0.997525\pi\)
0.999970 0.00777513i \(-0.00247492\pi\)
\(54\) 0 0
\(55\) −370.000 185.000i −0.907105 0.453553i
\(56\) −56.0000 −0.133631
\(57\) 0 0
\(58\) 498.000i 1.12742i
\(59\) −2.00000 −0.00441318 −0.00220659 0.999998i \(-0.500702\pi\)
−0.00220659 + 0.999998i \(0.500702\pi\)
\(60\) 0 0
\(61\) −940.000 −1.97303 −0.986514 0.163679i \(-0.947664\pi\)
−0.986514 + 0.163679i \(0.947664\pi\)
\(62\) 268.000i 0.548968i
\(63\) 0 0
\(64\) −64.0000 −0.125000
\(65\) −255.000 + 510.000i −0.486598 + 0.973196i
\(66\) 0 0
\(67\) 106.000i 0.193283i 0.995319 + 0.0966415i \(0.0308100\pi\)
−0.995319 + 0.0966415i \(0.969190\pi\)
\(68\) 164.000i 0.292469i
\(69\) 0 0
\(70\) −140.000 70.0000i −0.239046 0.119523i
\(71\) −456.000 −0.762215 −0.381107 0.924531i \(-0.624457\pi\)
−0.381107 + 0.924531i \(0.624457\pi\)
\(72\) 0 0
\(73\) 650.000i 1.04215i −0.853512 0.521074i \(-0.825532\pi\)
0.853512 0.521074i \(-0.174468\pi\)
\(74\) −668.000 −1.04937
\(75\) 0 0
\(76\) −432.000 −0.652024
\(77\) 259.000i 0.383322i
\(78\) 0 0
\(79\) 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
\(81\) 0 0
\(82\) 412.000i 0.554851i
\(83\) 428.000i 0.566013i 0.959118 + 0.283007i \(0.0913319\pi\)
−0.959118 + 0.283007i \(0.908668\pi\)
\(84\) 0 0
\(85\) −205.000 + 410.000i −0.261593 + 0.523185i
\(86\) 752.000 0.942910
\(87\) 0 0
\(88\) 296.000i 0.358565i
\(89\) −220.000 −0.262022 −0.131011 0.991381i \(-0.541822\pi\)
−0.131011 + 0.991381i \(0.541822\pi\)
\(90\) 0 0
\(91\) 357.000 0.411250
\(92\) 280.000i 0.317305i
\(93\) 0 0
\(94\) 574.000 0.629825
\(95\) −1080.00 540.000i −1.16638 0.583188i
\(96\) 0 0
\(97\) 1055.00i 1.10432i −0.833738 0.552160i \(-0.813804\pi\)
0.833738 0.552160i \(-0.186196\pi\)
\(98\) 98.0000i 0.101015i
\(99\) 0 0
\(100\) −300.000 400.000i −0.300000 0.400000i
\(101\) −1960.00 −1.93096 −0.965482 0.260471i \(-0.916122\pi\)
−0.965482 + 0.260471i \(0.916122\pi\)
\(102\) 0 0
\(103\) 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 \(0.979279\pi\)
\(108\) 0 0
\(109\) −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
\(111\) 0 0
\(112\) 112.000i 0.0944911i
\(113\) 798.000i 0.664332i 0.943221 + 0.332166i \(0.107779\pi\)
−0.943221 + 0.332166i \(0.892221\pi\)
\(114\) 0 0
\(115\) −350.000 + 700.000i −0.283806 + 0.567612i
\(116\) 996.000 0.797209
\(117\) 0 0
\(118\) 4.00000i 0.00312059i
\(119\) 287.000 0.221086
\(120\) 0 0
\(121\) 38.0000 0.0285500
\(122\) 1880.00i 1.39514i
\(123\) 0 0
\(124\) 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 \(0.0484487\pi\)
−0.988439 + 0.151619i \(0.951551\pi\)
\(128\) 128.000i 0.0883883i
\(129\) 0 0
\(130\) 1020.00 + 510.000i 0.688153 + 0.344077i
\(131\) 1290.00 0.860365 0.430183 0.902742i \(-0.358449\pi\)
0.430183 + 0.902742i \(0.358449\pi\)
\(132\) 0 0
\(133\) 756.000i 0.492884i
\(134\) 212.000 0.136672
\(135\) 0 0
\(136\) 328.000 0.206807
\(137\) 192.000i 0.119735i −0.998206 0.0598674i \(-0.980932\pi\)
0.998206 0.0598674i \(-0.0190678\pi\)
\(138\) 0 0
\(139\) −1402.00 −0.855511 −0.427756 0.903894i \(-0.640696\pi\)
−0.427756 + 0.903894i \(0.640696\pi\)
\(140\) −140.000 + 280.000i −0.0845154 + 0.169031i
\(141\) 0 0
\(142\) 912.000i 0.538967i
\(143\) 1887.00i 1.10349i
\(144\) 0 0
\(145\) 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 \(-0.526457\pi\)
−0.0830228 + 0.996548i \(0.526457\pi\)
\(150\) 0 0
\(151\) −3167.00 −1.70680 −0.853400 0.521257i \(-0.825463\pi\)
−0.853400 + 0.521257i \(0.825463\pi\)
\(152\) 864.000i 0.461050i
\(153\) 0 0
\(154\) 518.000 0.271050
\(155\) 1340.00 + 670.000i 0.694396 + 0.347198i
\(156\) 0 0
\(157\) 470.000i 0.238918i −0.992839 0.119459i \(-0.961884\pi\)
0.992839 0.119459i \(-0.0381160\pi\)
\(158\) 2478.00i 1.24772i
\(159\) 0 0
\(160\) −160.000 + 320.000i −0.0790569 + 0.158114i
\(161\) 490.000 0.239860
\(162\) 0 0
\(163\) 2390.00i 1.14846i 0.818693 + 0.574231i \(0.194699\pi\)
−0.818693 + 0.574231i \(0.805301\pi\)
\(164\) 824.000 0.392339
\(165\) 0 0
\(166\) 856.000 0.400232
\(167\) 2631.00i 1.21912i 0.792740 + 0.609560i \(0.208654\pi\)
−0.792740 + 0.609560i \(0.791346\pi\)
\(168\) 0 0
\(169\) −404.000 −0.183887
\(170\) 820.000 + 410.000i 0.369948 + 0.184974i
\(171\) 0 0
\(172\) 1504.00i 0.666738i
\(173\) 2243.00i 0.985735i −0.870104 0.492867i \(-0.835949\pi\)
0.870104 0.492867i \(-0.164051\pi\)
\(174\) 0 0
\(175\) −700.000 + 525.000i −0.302372 + 0.226779i
\(176\) 592.000 0.253544
\(177\) 0 0
\(178\) 440.000i 0.185277i
\(179\) 52.0000 0.0217132 0.0108566 0.999941i \(-0.496544\pi\)
0.0108566 + 0.999941i \(0.496544\pi\)
\(180\) 0 0
\(181\) 2462.00 1.01104 0.505522 0.862814i \(-0.331300\pi\)
0.505522 + 0.862814i \(0.331300\pi\)
\(182\) 714.000i 0.290798i
\(183\) 0 0
\(184\) 560.000 0.224368
\(185\) −1670.00 + 3340.00i −0.663680 + 1.32736i
\(186\) 0 0
\(187\) 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 \(-0.704185\pi\)
−0.598370 + 0.801220i \(0.704185\pi\)
\(192\) 0 0
\(193\) 2060.00i 0.768301i −0.923271 0.384150i \(-0.874494\pi\)
0.923271 0.384150i \(-0.125506\pi\)
\(194\) −2110.00 −0.780872
\(195\) 0 0
\(196\) 196.000 0.0714286
\(197\) 1738.00i 0.628565i −0.949329 0.314283i \(-0.898236\pi\)
0.949329 0.314283i \(-0.101764\pi\)
\(198\) 0 0
\(199\) 894.000 0.318462 0.159231 0.987241i \(-0.449099\pi\)
0.159231 + 0.987241i \(0.449099\pi\)
\(200\) −800.000 + 600.000i −0.282843 + 0.212132i
\(201\) 0 0
\(202\) 3920.00i 1.36540i
\(203\) 1743.00i 0.602634i
\(204\) 0 0
\(205\) 2060.00 + 1030.00i 0.701837 + 0.350919i
\(206\) −3650.00 −1.23450
\(207\) 0 0
\(208\) 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
\(213\) 0 0
\(214\) 288.000 0.0919966
\(215\) 1880.00 3760.00i 0.596349 1.19270i
\(216\) 0 0
\(217\) 938.000i 0.293436i
\(218\) 3362.00i 1.04451i
\(219\) 0 0
\(220\) 1480.00 + 740.000i 0.453553 + 0.226776i
\(221\) −2091.00 −0.636452
\(222\) 0 0
\(223\) 377.000i 0.113210i −0.998397 0.0566049i \(-0.981972\pi\)
0.998397 0.0566049i \(-0.0180275\pi\)
\(224\) 224.000 0.0668153
\(225\) 0 0
\(226\) 1596.00 0.469754
\(227\) 2551.00i 0.745885i 0.927855 + 0.372942i \(0.121651\pi\)
−0.927855 + 0.372942i \(0.878349\pi\)
\(228\) 0 0
\(229\) −74.0000 −0.0213540 −0.0106770 0.999943i \(-0.503399\pi\)
−0.0106770 + 0.999943i \(0.503399\pi\)
\(230\) 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 \(0.914488\pi\)
\(234\) 0 0
\(235\) 1435.00 2870.00i 0.398337 0.796673i
\(236\) 8.00000 0.00220659
\(237\) 0 0
\(238\) 574.000i 0.156331i
\(239\) 4997.00 1.35242 0.676211 0.736708i \(-0.263621\pi\)
0.676211 + 0.736708i \(0.263621\pi\)
\(240\) 0 0
\(241\) −3830.00 −1.02370 −0.511851 0.859074i \(-0.671040\pi\)
−0.511851 + 0.859074i \(0.671040\pi\)
\(242\) 76.0000i 0.0201879i
\(243\) 0 0
\(244\) 3760.00 0.986514
\(245\) 490.000 + 245.000i 0.127775 + 0.0638877i
\(246\) 0 0
\(247\) 5508.00i 1.41889i
\(248\) 1072.00i 0.274484i
\(249\) 0 0
\(250\) −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
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 7170.00i 1.74028i −0.492803 0.870141i \(-0.664028\pi\)
0.492803 0.870141i \(-0.335972\pi\)
\(258\) 0 0
\(259\) 2338.00 0.560912
\(260\) 1020.00 2040.00i 0.243299 0.486598i
\(261\) 0 0
\(262\) 2580.00i 0.608370i
\(263\) 7672.00i 1.79877i −0.437160 0.899384i \(-0.644016\pi\)
0.437160 0.899384i \(-0.355984\pi\)
\(264\) 0 0
\(265\) −30.0000 + 60.0000i −0.00695428 + 0.0139086i
\(266\) 1512.00 0.348521
\(267\) 0 0
\(268\) 424.000i 0.0966415i
\(269\) −54.0000 −0.0122395 −0.00611977 0.999981i \(-0.501948\pi\)
−0.00611977 + 0.999981i \(0.501948\pi\)
\(270\) 0 0
\(271\) 2932.00 0.657219 0.328609 0.944466i \(-0.393420\pi\)
0.328609 + 0.944466i \(0.393420\pi\)
\(272\) 656.000i 0.146235i
\(273\) 0 0
\(274\) −384.000 −0.0846653
\(275\) 2775.00 + 3700.00i 0.608505 + 0.811340i
\(276\) 0 0
\(277\) 3254.00i 0.705826i 0.935656 + 0.352913i \(0.114809\pi\)
−0.935656 + 0.352913i \(0.885191\pi\)
\(278\) 2804.00i 0.604938i
\(279\) 0 0
\(280\) 560.000 + 280.000i 0.119523 + 0.0597614i
\(281\) −3327.00 −0.706307 −0.353153 0.935565i \(-0.614891\pi\)
−0.353153 + 0.935565i \(0.614891\pi\)
\(282\) 0 0
\(283\) 4627.00i 0.971896i −0.873988 0.485948i \(-0.838474\pi\)
0.873988 0.485948i \(-0.161526\pi\)
\(284\) 1824.00 0.381107
\(285\) 0 0
\(286\) −3774.00 −0.780284
\(287\) 1442.00i 0.296580i
\(288\) 0 0
\(289\) 3232.00 0.657847
\(290\) 2490.00 4980.00i 0.504199 1.00840i
\(291\) 0 0
\(292\) 2600.00i 0.521074i
\(293\) 4083.00i 0.814100i −0.913406 0.407050i \(-0.866557\pi\)
0.913406 0.407050i \(-0.133443\pi\)
\(294\) 0 0
\(295\) 20.0000 + 10.0000i 0.00394727 + 0.00197364i
\(296\) 2672.00 0.524685
\(297\) 0 0
\(298\) 604.000i 0.117412i
\(299\) −3570.00 −0.690496
\(300\) 0 0
\(301\) −2632.00 −0.504007
\(302\) 6334.00i 1.20689i
\(303\) 0 0
\(304\) 1728.00 0.326012
\(305\) 9400.00 + 4700.00i 1.76473 + 0.882365i
\(306\) 0 0
\(307\) 4089.00i 0.760168i −0.924952 0.380084i \(-0.875895\pi\)
0.924952 0.380084i \(-0.124105\pi\)
\(308\) 1036.00i 0.191661i
\(309\) 0 0
\(310\) 1340.00 2680.00i 0.245506 0.491012i
\(311\) 4008.00 0.730781 0.365390 0.930854i \(-0.380935\pi\)
0.365390 + 0.930854i \(0.380935\pi\)
\(312\) 0 0
\(313\) 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 \(0.952335\pi\)
\(318\) 0 0
\(319\) −9213.00 −1.61702
\(320\) 640.000 + 320.000i 0.111803 + 0.0559017i
\(321\) 0 0
\(322\) 980.000i 0.169606i
\(323\) 4428.00i 0.762788i
\(324\) 0 0
\(325\) 5100.00 3825.00i 0.870453 0.652839i
\(326\) 4780.00 0.812085
\(327\) 0 0
\(328\) 1648.00i 0.277426i
\(329\) −2009.00 −0.336656
\(330\) 0 0
\(331\) −1460.00 −0.242444 −0.121222 0.992625i \(-0.538681\pi\)
−0.121222 + 0.992625i \(0.538681\pi\)
\(332\) 1712.00i 0.283007i
\(333\) 0 0
\(334\) 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 \(0.207744\pi\)
−0.794480 + 0.607290i \(0.792256\pi\)
\(338\) 808.000i 0.130028i
\(339\) 0 0
\(340\) 820.000 1640.00i 0.130796 0.261593i
\(341\) −4958.00 −0.787363
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) −3008.00 −0.471455
\(345\) 0 0
\(346\) −4486.00 −0.697020
\(347\) 2862.00i 0.442767i 0.975187 + 0.221384i \(0.0710573\pi\)
−0.975187 + 0.221384i \(0.928943\pi\)
\(348\) 0 0
\(349\) 6368.00 0.976708 0.488354 0.872646i \(-0.337597\pi\)
0.488354 + 0.872646i \(0.337597\pi\)
\(350\) 1050.00 + 1400.00i 0.160357 + 0.213809i
\(351\) 0 0
\(352\) 1184.00i 0.179282i
\(353\) 3635.00i 0.548078i −0.961719 0.274039i \(-0.911640\pi\)
0.961719 0.274039i \(-0.0883597\pi\)
\(354\) 0 0
\(355\) 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 \(-0.324785\pi\)
0.523075 + 0.852286i \(0.324785\pi\)
\(360\) 0 0
\(361\) 4805.00 0.700539
\(362\) 4924.00i 0.714916i
\(363\) 0 0
\(364\) −1428.00 −0.205625
\(365\) −3250.00 + 6500.00i −0.466062 + 0.932125i
\(366\) 0 0
\(367\) 319.000i 0.0453724i −0.999743 0.0226862i \(-0.992778\pi\)
0.999743 0.0226862i \(-0.00722186\pi\)
\(368\) 1120.00i 0.158652i
\(369\) 0 0
\(370\) 6680.00 + 3340.00i 0.938586 + 0.469293i
\(371\) 42.0000 0.00587744
\(372\) 0 0
\(373\) 11652.0i 1.61747i 0.588171 + 0.808737i \(0.299848\pi\)
−0.588171 + 0.808737i \(0.700152\pi\)
\(374\) −3034.00 −0.419477
\(375\) 0 0
\(376\) −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
\(381\) 0 0
\(382\) 6318.00i 0.846223i
\(383\) 8680.00i 1.15803i 0.815315 + 0.579017i \(0.196564\pi\)
−0.815315 + 0.579017i \(0.803436\pi\)
\(384\) 0 0
\(385\) 1295.00 2590.00i 0.171427 0.342854i
\(386\) −4120.00 −0.543271
\(387\) 0 0
\(388\) 4220.00i 0.552160i
\(389\) −1711.00 −0.223011 −0.111505 0.993764i \(-0.535567\pi\)
−0.111505 + 0.993764i \(0.535567\pi\)
\(390\) 0 0
\(391\) −2870.00 −0.371208
\(392\) 392.000i 0.0505076i
\(393\) 0 0
\(394\) −3476.00 −0.444463
\(395\) −12390.0 6195.00i −1.57825 0.789125i
\(396\) 0 0
\(397\) 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 \(-0.396154\pi\)
0.320485 + 0.947254i \(0.396154\pi\)
\(402\) 0 0
\(403\) 6834.00i 0.844729i
\(404\) 7840.00 0.965482
\(405\) 0 0
\(406\) −3486.00 −0.426126
\(407\) 12358.0i 1.50507i
\(408\) 0 0
\(409\) 9100.00 1.10016 0.550081 0.835111i \(-0.314597\pi\)
0.550081 + 0.835111i \(0.314597\pi\)
\(410\) 2060.00 4120.00i 0.248137 0.496274i
\(411\) 0 0
\(412\) 7300.00i 0.872925i
\(413\) 14.0000i 0.00166803i
\(414\) 0 0
\(415\) 2140.00 4280.00i 0.253129 0.506258i
\(416\) −1632.00 −0.192345
\(417\) 0 0
\(418\) 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
\(423\) 0 0
\(424\) 48.0000 0.00549784
\(425\) 4100.00 3075.00i 0.467951 0.350963i
\(426\) 0 0
\(427\) 6580.00i 0.745734i
\(428\) 576.000i 0.0650514i
\(429\) 0 0
\(430\) −7520.00 3760.00i −0.843364 0.421682i
\(431\) −15779.0 −1.76345 −0.881726 0.471762i \(-0.843618\pi\)
−0.881726 + 0.471762i \(0.843618\pi\)
\(432\) 0 0
\(433\) 7238.00i 0.803317i −0.915790 0.401658i \(-0.868434\pi\)
0.915790 0.401658i \(-0.131566\pi\)
\(434\) −1876.00 −0.207491
\(435\) 0 0
\(436\) 6724.00 0.738581
\(437\) 7560.00i 0.827560i
\(438\) 0 0
\(439\) 2646.00 0.287669 0.143834 0.989602i \(-0.454057\pi\)
0.143834 + 0.989602i \(0.454057\pi\)
\(440\) 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 \(0.901338\pi\)
\(444\) 0 0
\(445\) 2200.00 + 1100.00i 0.234360 + 0.117180i
\(446\) −754.000 −0.0800514
\(447\) 0 0
\(448\) 448.000i 0.0472456i
\(449\) −3285.00 −0.345276 −0.172638 0.984985i \(-0.555229\pi\)
−0.172638 + 0.984985i \(0.555229\pi\)
\(450\) 0 0
\(451\) −7622.00 −0.795800
\(452\) 3192.00i 0.332166i
\(453\) 0 0
\(454\) 5102.00 0.527420
\(455\) −3570.00 1785.00i −0.367833 0.183917i
\(456\) 0 0
\(457\) 14834.0i 1.51839i 0.650862 + 0.759196i \(0.274408\pi\)
−0.650862 + 0.759196i \(0.725592\pi\)
\(458\) 148.000i 0.0150995i
\(459\) 0 0
\(460\) 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 \(0.150900\pi\)
−0.889719 + 0.456509i \(0.849100\pi\)
\(464\) −3984.00 −0.398605
\(465\) 0 0
\(466\) 3776.00 0.375364
\(467\) 15867.0i 1.57224i −0.618072 0.786121i \(-0.712086\pi\)
0.618072 0.786121i \(-0.287914\pi\)
\(468\) 0 0
\(469\) −742.000 −0.0730541
\(470\) −5740.00 2870.00i −0.563333 0.281666i
\(471\) 0 0
\(472\) 16.0000i 0.00156030i
\(473\) 13912.0i 1.35238i
\(474\) 0 0
\(475\) 8100.00 + 10800.0i 0.782428 + 1.04324i
\(476\) −1148.00 −0.110543
\(477\) 0 0
\(478\) 9994.00i 0.956307i
\(479\) 242.000 0.0230841 0.0115420 0.999933i \(-0.496326\pi\)
0.0115420 + 0.999933i \(0.496326\pi\)
\(480\) 0 0
\(481\) −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
\(486\) 0 0
\(487\) 3558.00i 0.331064i −0.986204 0.165532i \(-0.947066\pi\)
0.986204 0.165532i \(-0.0529342\pi\)
\(488\) 7520.00i 0.697571i
\(489\) 0 0
\(490\) 490.000 980.000i 0.0451754 0.0903508i
\(491\) −1473.00 −0.135388 −0.0676941 0.997706i \(-0.521564\pi\)
−0.0676941 + 0.997706i \(0.521564\pi\)
\(492\) 0 0
\(493\) 10209.0i 0.932637i
\(494\) −11016.0 −1.00331
\(495\) 0 0
\(496\) −2144.00 −0.194090
\(497\) 3192.00i 0.288090i
\(498\) 0 0
\(499\) −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
\(501\) 0 0
\(502\) 6780.00i 0.602801i
\(503\) 18387.0i 1.62989i 0.579537 + 0.814946i \(0.303234\pi\)
−0.579537 + 0.814946i \(0.696766\pi\)
\(504\) 0 0
\(505\) 19600.0 + 9800.00i 1.72711 + 0.863553i
\(506\) −5180.00 −0.455097
\(507\) 0 0
\(508\) 1736.00i 0.151619i
\(509\) 9018.00 0.785296 0.392648 0.919689i \(-0.371559\pi\)
0.392648 + 0.919689i \(0.371559\pi\)
\(510\) 0 0
\(511\) 4550.00 0.393895
\(512\) 512.000i 0.0441942i
\(513\) 0 0
\(514\) −14340.0 −1.23056
\(515\) −9125.00 + 18250.0i −0.780768 + 1.56154i
\(516\) 0 0
\(517\) 10619.0i 0.903333i
\(518\) 4676.00i 0.396625i
\(519\) 0 0
\(520\) −4080.00 2040.00i −0.344077 0.172038i
\(521\) −4624.00 −0.388831 −0.194416 0.980919i \(-0.562281\pi\)
−0.194416 + 0.980919i \(0.562281\pi\)
\(522\) 0 0
\(523\) 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
\(528\) 0 0
\(529\) 7267.00 0.597271
\(530\) 120.000 + 60.0000i 0.00983484 + 0.00491742i
\(531\) 0 0
\(532\) 3024.00i 0.246442i
\(533\) 10506.0i 0.853781i
\(534\) 0 0
\(535\) 720.000 1440.00i 0.0581838 0.116368i
\(536\) −848.000 −0.0683359
\(537\) 0 0
\(538\) 108.000i 0.00865467i
\(539\) −1813.00 −0.144882
\(540\) 0 0
\(541\) −8537.00 −0.678437 −0.339218 0.940708i \(-0.610163\pi\)
−0.339218 + 0.940708i \(0.610163\pi\)
\(542\) 5864.00i 0.464724i
\(543\) 0 0
\(544\) −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 \(-0.829488\pi\)
0.859922 0.510425i \(-0.170512\pi\)
\(548\) 768.000i 0.0598674i
\(549\) 0 0
\(550\) 7400.00 5550.00i 0.573704 0.430278i
\(551\) −26892.0 −2.07920
\(552\) 0 0
\(553\) 8673.00i 0.666932i
\(554\) 6508.00 0.499095
\(555\) 0 0
\(556\) 5608.00 0.427756
\(557\) 21372.0i 1.62578i −0.582416 0.812891i \(-0.697892\pi\)
0.582416 0.812891i \(-0.302108\pi\)
\(558\) 0 0
\(559\) 19176.0 1.45091
\(560\) 560.000 1120.00i 0.0422577 0.0845154i
\(561\) 0 0
\(562\) 6654.00i 0.499434i
\(563\) 12704.0i 0.950994i −0.879717 0.475497i \(-0.842268\pi\)
0.879717 0.475497i \(-0.157732\pi\)
\(564\) 0 0
\(565\) 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 \(-0.395383\pi\)
0.322779 + 0.946474i \(0.395383\pi\)
\(570\) 0 0
\(571\) −24764.0 −1.81496 −0.907479 0.420097i \(-0.861996\pi\)
−0.907479 + 0.420097i \(0.861996\pi\)
\(572\) 7548.00i 0.551744i
\(573\) 0 0
\(574\) −2884.00 −0.209714
\(575\) 7000.00 5250.00i 0.507687 0.380765i
\(576\) 0 0
\(577\) 1811.00i 0.130664i 0.997864 + 0.0653318i \(0.0208106\pi\)
−0.997864 + 0.0653318i \(0.979189\pi\)
\(578\) 6464.00i 0.465168i
\(579\) 0 0
\(580\) −9960.00 4980.00i −0.713046 0.356523i
\(581\) −2996.00 −0.213933
\(582\) 0 0
\(583\) 222.000i 0.0157707i
\(584\) 5200.00 0.368455
\(585\) 0 0
\(586\) −8166.00 −0.575656
\(587\) 10548.0i 0.741674i −0.928698 0.370837i \(-0.879071\pi\)
0.928698 0.370837i \(-0.120929\pi\)
\(588\) 0 0
\(589\) −14472.0 −1.01241
\(590\) 20.0000 40.0000i 0.00139557 0.00279114i
\(591\) 0 0
\(592\) 5344.00i 0.371009i
\(593\) 17439.0i 1.20765i 0.797119 + 0.603823i \(0.206357\pi\)
−0.797119 + 0.603823i \(0.793643\pi\)
\(594\) 0 0
\(595\) −2870.00 1435.00i −0.197745 0.0988727i
\(596\) 1208.00 0.0830228
\(597\) 0 0
\(598\) 7140.00i 0.488255i
\(599\) 2451.00 0.167187 0.0835936 0.996500i \(-0.473360\pi\)
0.0835936 + 0.996500i \(0.473360\pi\)
\(600\) 0 0
\(601\) −7792.00 −0.528856 −0.264428 0.964405i \(-0.585183\pi\)
−0.264428 + 0.964405i \(0.585183\pi\)
\(602\) 5264.00i 0.356386i
\(603\) 0 0
\(604\) 12668.0 0.853400
\(605\) −380.000 190.000i −0.0255359 0.0127679i
\(606\) 0 0
\(607\) 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
\(612\) 0 0
\(613\) 5036.00i 0.331814i −0.986141 0.165907i \(-0.946945\pi\)
0.986141 0.165907i \(-0.0530552\pi\)
\(614\) −8178.00 −0.537520
\(615\) 0 0
\(616\) −2072.00 −0.135525
\(617\) 27286.0i 1.78038i 0.455592 + 0.890189i \(0.349428\pi\)
−0.455592 + 0.890189i \(0.650572\pi\)
\(618\) 0 0
\(619\) −28538.0 −1.85305 −0.926526 0.376231i \(-0.877220\pi\)
−0.926526 + 0.376231i \(0.877220\pi\)
\(620\) −5360.00 2680.00i −0.347198 0.173599i
\(621\) 0 0
\(622\) 8016.00i 0.516740i
\(623\) 1540.00i 0.0990350i
\(624\) 0 0
\(625\) −4375.00 + 15000.0i −0.280000 + 0.960000i
\(626\) −14710.0 −0.939185
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 3368.00 0.210978
\(635\) 2170.00 4340.00i 0.135612 0.271225i
\(636\) 0 0
\(637\) 2499.00i 0.155438i
\(638\) 18426.0i 1.14340i
\(639\) 0 0
\(640\) 640.000 1280.00i 0.0395285 0.0790569i
\(641\) 12130.0 0.747436 0.373718 0.927542i \(-0.378083\pi\)
0.373718 + 0.927542i \(0.378083\pi\)
\(642\) 0 0
\(643\) 14385.0i 0.882254i −0.897445 0.441127i \(-0.854579\pi\)
0.897445 0.441127i \(-0.145421\pi\)
\(644\) −1960.00 −0.119930
\(645\) 0 0
\(646\) −8856.00 −0.539373
\(647\) 2208.00i 0.134166i 0.997747 + 0.0670830i \(0.0213692\pi\)
−0.997747 + 0.0670830i \(0.978631\pi\)
\(648\) 0 0
\(649\) −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 \(0.765163\pi\)
\(654\) 0 0
\(655\) −12900.0 6450.00i −0.769534 0.384767i
\(656\) −3296.00 −0.196169
\(657\) 0 0
\(658\) 4018.00i 0.238052i
\(659\) 8791.00 0.519649 0.259825 0.965656i \(-0.416335\pi\)
0.259825 + 0.965656i \(0.416335\pi\)
\(660\) 0 0
\(661\) −13180.0 −0.775556 −0.387778 0.921753i \(-0.626757\pi\)
−0.387778 + 0.921753i \(0.626757\pi\)
\(662\) 2920.00i 0.171434i
\(663\) 0 0
\(664\) −3424.00 −0.200116
\(665\) 3780.00 7560.00i 0.220424 0.440848i
\(666\) 0 0
\(667\) 17430.0i 1.01183i
\(668\) 10524.0i 0.609560i
\(669\) 0 0
\(670\) −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 \(0.0657731\pi\)
−0.978727 + 0.205165i \(0.934227\pi\)
\(674\) 15028.0 0.858838
\(675\) 0 0
\(676\) 1616.00 0.0919436
\(677\) 12335.0i 0.700255i −0.936702 0.350127i \(-0.886138\pi\)
0.936702 0.350127i \(-0.113862\pi\)
\(678\) 0 0
\(679\) 7385.00 0.417394
\(680\) −3280.00 1640.00i −0.184974 0.0924870i
\(681\) 0 0
\(682\) 9916.00i 0.556750i
\(683\) 15436.0i 0.864776i −0.901688 0.432388i \(-0.857671\pi\)
0.901688 0.432388i \(-0.142329\pi\)
\(684\) 0 0
\(685\) −960.000 + 1920.00i −0.0535470 + 0.107094i
\(686\) −686.000 −0.0381802
\(687\) 0 0
\(688\) 6016.00i 0.333369i
\(689\) −306.000 −0.0169197
\(690\) 0 0
\(691\) −19184.0 −1.05614 −0.528071 0.849200i \(-0.677084\pi\)
−0.528071 + 0.849200i \(0.677084\pi\)
\(692\) 8972.00i 0.492867i
\(693\) 0 0
\(694\) 5724.00 0.313084
\(695\) 14020.0 + 7010.00i 0.765193 + 0.382596i
\(696\) 0 0
\(697\) 8446.00i 0.458989i
\(698\) 12736.0i 0.690637i
\(699\) 0 0
\(700\) 2800.00 2100.00i 0.151186 0.113389i
\(701\) −32975.0 −1.77667 −0.888337 0.459192i \(-0.848139\pi\)
−0.888337 + 0.459192i \(0.848139\pi\)
\(702\) 0 0
\(703\) 36072.0i 1.93525i
\(704\) −2368.00 −0.126772
\(705\) 0 0
\(706\) −7270.00 −0.387550
\(707\) 13720.0i 0.729836i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) 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
\(717\) 0 0
\(718\) 14232.0i 0.739740i
\(719\) −18610.0 −0.965279 −0.482640 0.875819i \(-0.660322\pi\)
−0.482640 + 0.875819i \(0.660322\pi\)
\(720\) 0 0
\(721\) 12775.0 0.659869
\(722\) 9610.00i 0.495356i
\(723\) 0 0
\(724\) −9848.00 −0.505522
\(725\) −18675.0 24900.0i −0.956651 1.27553i
\(726\) 0 0
\(727\) 17508.0i 0.893172i −0.894741 0.446586i \(-0.852640\pi\)
0.894741 0.446586i \(-0.147360\pi\)
\(728\) 2856.00i 0.145399i
\(729\) 0 0
\(730\) 13000.0 + 6500.00i 0.659112 + 0.329556i
\(731\) 15416.0 0.780002
\(732\) 0 0
\(733\) 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
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) 84.0000i 0.00415598i
\(743\) 25578.0i 1.26294i 0.775400 + 0.631471i \(0.217548\pi\)
−0.775400 + 0.631471i \(0.782452\pi\)
\(744\) 0 0
\(745\) 3020.00 + 1510.00i 0.148516 + 0.0742579i
\(746\) 23304.0 1.14373
\(747\) 0 0
\(748\) 6068.00i 0.296615i
\(749\) −1008.00 −0.0491743
\(750\) 0 0
\(751\) −4291.00 −0.208496 −0.104248 0.994551i \(-0.533244\pi\)
−0.104248 + 0.994551i \(0.533244\pi\)
\(752\) 4592.00i 0.222677i
\(753\) 0 0
\(754\) 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 \(-0.726726\pi\)
0.653563 0.756872i \(-0.273274\pi\)
\(758\) 15496.0i 0.742533i
\(759\) 0 0
\(760\) 4320.00 8640.00i 0.206188 0.412376i
\(761\) 23154.0 1.10293 0.551466 0.834197i \(-0.314068\pi\)
0.551466 + 0.834197i \(0.314068\pi\)
\(762\) 0 0
\(763\) 11767.0i 0.558315i
\(764\) 12636.0 0.598370
\(765\) 0 0
\(766\) 17360.0 0.818854
\(767\) 102.000i 0.00480183i
\(768\) 0 0
\(769\) −13992.0 −0.656131 −0.328065 0.944655i \(-0.606397\pi\)
−0.328065 + 0.944655i \(0.606397\pi\)
\(770\) −5180.00 2590.00i −0.242434 0.121217i
\(771\) 0 0
\(772\) 8240.00i 0.384150i
\(773\) 21681.0i 1.00881i −0.863467 0.504406i \(-0.831712\pi\)
0.863467 0.504406i \(-0.168288\pi\)
\(774\) 0 0
\(775\) −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
\(780\) 0 0
\(781\) −16872.0 −0.773019
\(782\) 5740.00i 0.262483i
\(783\) 0 0
\(784\) −784.000 −0.0357143
\(785\) −2350.00 + 4700.00i −0.106847 + 0.213695i
\(786\) 0 0
\(787\) 16903.0i 0.765600i −0.923831 0.382800i \(-0.874960\pi\)
0.923831 0.382800i \(-0.125040\pi\)
\(788\) 6952.00i 0.314283i
\(789\) 0 0
\(790\) −12390.0 + 24780.0i −0.557995 + 1.11599i