Properties

Label 1050.3.f.e.601.6
Level $1050$
Weight $3$
Character 1050.601
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 8 x^{15} + 88 x^{14} - 476 x^{13} + 2744 x^{12} - 10640 x^{11} + 39126 x^{10} - 108488 x^{9} + 259514 x^{8} - 486436 x^{7} + 690168 x^{6} - 725188 x^{5} + \cdots + 33124 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 601.6
Root \(-0.207107 + 0.264184i\) of defining polynomial
Character \(\chi\) \(=\) 1050.601
Dual form 1050.3.f.e.601.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(-0.853218 - 6.94781i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +1.73205i q^{3} +2.00000 q^{4} -2.44949i q^{6} +(-0.853218 - 6.94781i) q^{7} -2.82843 q^{8} -3.00000 q^{9} +2.88097 q^{11} +3.46410i q^{12} +13.8145i q^{13} +(1.20663 + 9.82568i) q^{14} +4.00000 q^{16} -24.1754i q^{17} +4.24264 q^{18} +6.53403i q^{19} +(12.0340 - 1.47782i) q^{21} -4.07430 q^{22} -28.8420 q^{23} -4.89898i q^{24} -19.5367i q^{26} -5.19615i q^{27} +(-1.70644 - 13.8956i) q^{28} +32.9589 q^{29} +2.43276i q^{31} -5.65685 q^{32} +4.98998i q^{33} +34.1892i q^{34} -6.00000 q^{36} -50.9799 q^{37} -9.24052i q^{38} -23.9275 q^{39} +21.5225i q^{41} +(-17.0186 + 2.08995i) q^{42} -13.5554 q^{43} +5.76193 q^{44} +40.7887 q^{46} +40.7305i q^{47} +6.92820i q^{48} +(-47.5440 + 11.8560i) q^{49} +41.8730 q^{51} +27.6291i q^{52} +17.2758 q^{53} +7.34847i q^{54} +(2.41326 + 19.6514i) q^{56} -11.3173 q^{57} -46.6109 q^{58} -1.47488i q^{59} +111.568i q^{61} -3.44045i q^{62} +(2.55965 + 20.8434i) q^{63} +8.00000 q^{64} -7.05690i q^{66} -120.293 q^{67} -48.3508i q^{68} -49.9558i q^{69} -90.3855 q^{71} +8.48528 q^{72} -21.4890i q^{73} +72.0964 q^{74} +13.0681i q^{76} +(-2.45809 - 20.0164i) q^{77} +33.8385 q^{78} +66.1324 q^{79} +9.00000 q^{81} -30.4375i q^{82} -78.5172i q^{83} +(24.0679 - 2.95563i) q^{84} +19.1703 q^{86} +57.0865i q^{87} -8.14861 q^{88} -90.9724i q^{89} +(95.9807 - 11.7868i) q^{91} -57.6840 q^{92} -4.21367 q^{93} -57.6016i q^{94} -9.79796i q^{96} +44.1972i q^{97} +(67.2374 - 16.7669i) q^{98} -8.64290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 32 q^{4} - 48 q^{9} + 96 q^{11} - 16 q^{14} + 64 q^{16} + 24 q^{21} - 64 q^{29} - 96 q^{36} + 144 q^{39} + 192 q^{44} - 176 q^{46} - 224 q^{49} - 48 q^{51} - 32 q^{56} + 128 q^{64} - 384 q^{71} - 224 q^{74} + 608 q^{79} + 144 q^{81} + 48 q^{84} + 416 q^{86} + 224 q^{91} - 288 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) 1.73205i 0.577350i
\(4\) 2.00000 0.500000
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) −0.853218 6.94781i −0.121888 0.992544i
\(8\) −2.82843 −0.353553
\(9\) −3.00000 −0.333333
\(10\) 0 0
\(11\) 2.88097 0.261906 0.130953 0.991389i \(-0.458196\pi\)
0.130953 + 0.991389i \(0.458196\pi\)
\(12\) 3.46410i 0.288675i
\(13\) 13.8145i 1.06266i 0.847166 + 0.531328i \(0.178307\pi\)
−0.847166 + 0.531328i \(0.821693\pi\)
\(14\) 1.20663 + 9.82568i 0.0861880 + 0.701834i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 24.1754i 1.42208i −0.703150 0.711041i \(-0.748224\pi\)
0.703150 0.711041i \(-0.251776\pi\)
\(18\) 4.24264 0.235702
\(19\) 6.53403i 0.343896i 0.985106 + 0.171948i \(0.0550062\pi\)
−0.985106 + 0.171948i \(0.944994\pi\)
\(20\) 0 0
\(21\) 12.0340 1.47782i 0.573045 0.0703722i
\(22\) −4.07430 −0.185196
\(23\) −28.8420 −1.25400 −0.627000 0.779019i \(-0.715717\pi\)
−0.627000 + 0.779019i \(0.715717\pi\)
\(24\) 4.89898i 0.204124i
\(25\) 0 0
\(26\) 19.5367i 0.751411i
\(27\) 5.19615i 0.192450i
\(28\) −1.70644 13.8956i −0.0609441 0.496272i
\(29\) 32.9589 1.13651 0.568257 0.822851i \(-0.307618\pi\)
0.568257 + 0.822851i \(0.307618\pi\)
\(30\) 0 0
\(31\) 2.43276i 0.0784762i 0.999230 + 0.0392381i \(0.0124931\pi\)
−0.999230 + 0.0392381i \(0.987507\pi\)
\(32\) −5.65685 −0.176777
\(33\) 4.98998i 0.151212i
\(34\) 34.1892i 1.00556i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −50.9799 −1.37783 −0.688917 0.724840i \(-0.741914\pi\)
−0.688917 + 0.724840i \(0.741914\pi\)
\(38\) 9.24052i 0.243171i
\(39\) −23.9275 −0.613525
\(40\) 0 0
\(41\) 21.5225i 0.524940i 0.964940 + 0.262470i \(0.0845371\pi\)
−0.964940 + 0.262470i \(0.915463\pi\)
\(42\) −17.0186 + 2.08995i −0.405204 + 0.0497607i
\(43\) −13.5554 −0.315243 −0.157621 0.987500i \(-0.550383\pi\)
−0.157621 + 0.987500i \(0.550383\pi\)
\(44\) 5.76193 0.130953
\(45\) 0 0
\(46\) 40.7887 0.886712
\(47\) 40.7305i 0.866605i 0.901248 + 0.433303i \(0.142652\pi\)
−0.901248 + 0.433303i \(0.857348\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −47.5440 + 11.8560i −0.970287 + 0.241959i
\(50\) 0 0
\(51\) 41.8730 0.821040
\(52\) 27.6291i 0.531328i
\(53\) 17.2758 0.325959 0.162979 0.986629i \(-0.447890\pi\)
0.162979 + 0.986629i \(0.447890\pi\)
\(54\) 7.34847i 0.136083i
\(55\) 0 0
\(56\) 2.41326 + 19.6514i 0.0430940 + 0.350917i
\(57\) −11.3173 −0.198549
\(58\) −46.6109 −0.803636
\(59\) 1.47488i 0.0249980i −0.999922 0.0124990i \(-0.996021\pi\)
0.999922 0.0124990i \(-0.00397867\pi\)
\(60\) 0 0
\(61\) 111.568i 1.82898i 0.404609 + 0.914490i \(0.367408\pi\)
−0.404609 + 0.914490i \(0.632592\pi\)
\(62\) 3.44045i 0.0554911i
\(63\) 2.55965 + 20.8434i 0.0406294 + 0.330848i
\(64\) 8.00000 0.125000
\(65\) 0 0
\(66\) 7.05690i 0.106923i
\(67\) −120.293 −1.79542 −0.897709 0.440590i \(-0.854769\pi\)
−0.897709 + 0.440590i \(0.854769\pi\)
\(68\) 48.3508i 0.711041i
\(69\) 49.9558i 0.723997i
\(70\) 0 0
\(71\) −90.3855 −1.27304 −0.636518 0.771262i \(-0.719626\pi\)
−0.636518 + 0.771262i \(0.719626\pi\)
\(72\) 8.48528 0.117851
\(73\) 21.4890i 0.294370i −0.989109 0.147185i \(-0.952979\pi\)
0.989109 0.147185i \(-0.0470212\pi\)
\(74\) 72.0964 0.974276
\(75\) 0 0
\(76\) 13.0681i 0.171948i
\(77\) −2.45809 20.0164i −0.0319233 0.259953i
\(78\) 33.8385 0.433827
\(79\) 66.1324 0.837119 0.418559 0.908189i \(-0.362535\pi\)
0.418559 + 0.908189i \(0.362535\pi\)
\(80\) 0 0
\(81\) 9.00000 0.111111
\(82\) 30.4375i 0.371189i
\(83\) 78.5172i 0.945990i −0.881065 0.472995i \(-0.843173\pi\)
0.881065 0.472995i \(-0.156827\pi\)
\(84\) 24.0679 2.95563i 0.286523 0.0351861i
\(85\) 0 0
\(86\) 19.1703 0.222910
\(87\) 57.0865i 0.656166i
\(88\) −8.14861 −0.0925978
\(89\) 90.9724i 1.02216i −0.859533 0.511081i \(-0.829245\pi\)
0.859533 0.511081i \(-0.170755\pi\)
\(90\) 0 0
\(91\) 95.9807 11.7868i 1.05473 0.129525i
\(92\) −57.6840 −0.627000
\(93\) −4.21367 −0.0453083
\(94\) 57.6016i 0.612783i
\(95\) 0 0
\(96\) 9.79796i 0.102062i
\(97\) 44.1972i 0.455642i 0.973703 + 0.227821i \(0.0731600\pi\)
−0.973703 + 0.227821i \(0.926840\pi\)
\(98\) 67.2374 16.7669i 0.686096 0.171091i
\(99\) −8.64290 −0.0873020
\(100\) 0 0
\(101\) 180.052i 1.78269i −0.453326 0.891345i \(-0.649763\pi\)
0.453326 0.891345i \(-0.350237\pi\)
\(102\) −59.2174 −0.580563
\(103\) 107.208i 1.04086i 0.853906 + 0.520428i \(0.174228\pi\)
−0.853906 + 0.520428i \(0.825772\pi\)
\(104\) 39.0734i 0.375706i
\(105\) 0 0
\(106\) −24.4317 −0.230488
\(107\) −33.1521 −0.309833 −0.154917 0.987928i \(-0.549511\pi\)
−0.154917 + 0.987928i \(0.549511\pi\)
\(108\) 10.3923i 0.0962250i
\(109\) −108.819 −0.998338 −0.499169 0.866505i \(-0.666361\pi\)
−0.499169 + 0.866505i \(0.666361\pi\)
\(110\) 0 0
\(111\) 88.2997i 0.795493i
\(112\) −3.41287 27.7912i −0.0304721 0.248136i
\(113\) −157.658 −1.39520 −0.697600 0.716488i \(-0.745749\pi\)
−0.697600 + 0.716488i \(0.745749\pi\)
\(114\) 16.0050 0.140395
\(115\) 0 0
\(116\) 65.9178 0.568257
\(117\) 41.4436i 0.354219i
\(118\) 2.08580i 0.0176763i
\(119\) −167.966 + 20.6269i −1.41148 + 0.173335i
\(120\) 0 0
\(121\) −112.700 −0.931405
\(122\) 157.781i 1.29328i
\(123\) −37.2781 −0.303074
\(124\) 4.86553i 0.0392381i
\(125\) 0 0
\(126\) −3.61990 29.4770i −0.0287293 0.233945i
\(127\) −28.2047 −0.222085 −0.111042 0.993816i \(-0.535419\pi\)
−0.111042 + 0.993816i \(0.535419\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 23.4787i 0.182006i
\(130\) 0 0
\(131\) 157.620i 1.20321i −0.798795 0.601604i \(-0.794529\pi\)
0.798795 0.601604i \(-0.205471\pi\)
\(132\) 9.97996i 0.0756058i
\(133\) 45.3972 5.57495i 0.341332 0.0419169i
\(134\) 170.120 1.26955
\(135\) 0 0
\(136\) 68.3784i 0.502782i
\(137\) −244.855 −1.78726 −0.893632 0.448800i \(-0.851852\pi\)
−0.893632 + 0.448800i \(0.851852\pi\)
\(138\) 70.6482i 0.511943i
\(139\) 238.245i 1.71399i 0.515325 + 0.856995i \(0.327671\pi\)
−0.515325 + 0.856995i \(0.672329\pi\)
\(140\) 0 0
\(141\) −70.5472 −0.500335
\(142\) 127.824 0.900172
\(143\) 39.7992i 0.278316i
\(144\) −12.0000 −0.0833333
\(145\) 0 0
\(146\) 30.3900i 0.208151i
\(147\) −20.5352 82.3487i −0.139695 0.560195i
\(148\) −101.960 −0.688917
\(149\) −10.8398 −0.0727503 −0.0363751 0.999338i \(-0.511581\pi\)
−0.0363751 + 0.999338i \(0.511581\pi\)
\(150\) 0 0
\(151\) −112.999 −0.748340 −0.374170 0.927360i \(-0.622072\pi\)
−0.374170 + 0.927360i \(0.622072\pi\)
\(152\) 18.4810i 0.121586i
\(153\) 72.5262i 0.474027i
\(154\) 3.47627 + 28.3075i 0.0225732 + 0.183815i
\(155\) 0 0
\(156\) −47.8549 −0.306762
\(157\) 103.693i 0.660462i −0.943900 0.330231i \(-0.892873\pi\)
0.943900 0.330231i \(-0.107127\pi\)
\(158\) −93.5253 −0.591932
\(159\) 29.9226i 0.188193i
\(160\) 0 0
\(161\) 24.6085 + 200.389i 0.152848 + 1.24465i
\(162\) −12.7279 −0.0785674
\(163\) 199.576 1.22439 0.612196 0.790706i \(-0.290287\pi\)
0.612196 + 0.790706i \(0.290287\pi\)
\(164\) 43.0451i 0.262470i
\(165\) 0 0
\(166\) 111.040i 0.668916i
\(167\) 87.0777i 0.521424i 0.965417 + 0.260712i \(0.0839572\pi\)
−0.965417 + 0.260712i \(0.916043\pi\)
\(168\) −34.0372 + 4.17990i −0.202602 + 0.0248803i
\(169\) −21.8411 −0.129237
\(170\) 0 0
\(171\) 19.6021i 0.114632i
\(172\) −27.1109 −0.157621
\(173\) 106.597i 0.616166i −0.951359 0.308083i \(-0.900313\pi\)
0.951359 0.308083i \(-0.0996875\pi\)
\(174\) 80.7325i 0.463980i
\(175\) 0 0
\(176\) 11.5239 0.0654765
\(177\) 2.55458 0.0144326
\(178\) 128.654i 0.722778i
\(179\) −275.881 −1.54123 −0.770617 0.637298i \(-0.780052\pi\)
−0.770617 + 0.637298i \(0.780052\pi\)
\(180\) 0 0
\(181\) 186.431i 1.03000i 0.857189 + 0.515002i \(0.172209\pi\)
−0.857189 + 0.515002i \(0.827791\pi\)
\(182\) −135.737 + 16.6690i −0.745808 + 0.0915882i
\(183\) −193.241 −1.05596
\(184\) 81.5775 0.443356
\(185\) 0 0
\(186\) 5.95903 0.0320378
\(187\) 69.6485i 0.372452i
\(188\) 81.4609i 0.433303i
\(189\) −36.1019 + 4.43345i −0.191015 + 0.0234574i
\(190\) 0 0
\(191\) −177.076 −0.927102 −0.463551 0.886070i \(-0.653425\pi\)
−0.463551 + 0.886070i \(0.653425\pi\)
\(192\) 13.8564i 0.0721688i
\(193\) −153.453 −0.795092 −0.397546 0.917582i \(-0.630138\pi\)
−0.397546 + 0.917582i \(0.630138\pi\)
\(194\) 62.5043i 0.322187i
\(195\) 0 0
\(196\) −95.0881 + 23.7120i −0.485143 + 0.120979i
\(197\) 214.041 1.08650 0.543252 0.839570i \(-0.317193\pi\)
0.543252 + 0.839570i \(0.317193\pi\)
\(198\) 12.2229 0.0617319
\(199\) 178.176i 0.895359i −0.894194 0.447679i \(-0.852251\pi\)
0.894194 0.447679i \(-0.147749\pi\)
\(200\) 0 0
\(201\) 208.354i 1.03658i
\(202\) 254.631i 1.26055i
\(203\) −28.1211 228.992i −0.138528 1.12804i
\(204\) 83.7460 0.410520
\(205\) 0 0
\(206\) 151.615i 0.735996i
\(207\) 86.5260 0.418000
\(208\) 55.2581i 0.265664i
\(209\) 18.8243i 0.0900686i
\(210\) 0 0
\(211\) −398.012 −1.88631 −0.943156 0.332350i \(-0.892158\pi\)
−0.943156 + 0.332350i \(0.892158\pi\)
\(212\) 34.5517 0.162979
\(213\) 156.552i 0.734987i
\(214\) 46.8842 0.219085
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 16.9024 2.07568i 0.0778911 0.00956533i
\(218\) 153.893 0.705932
\(219\) 37.2200 0.169954
\(220\) 0 0
\(221\) 333.972 1.51118
\(222\) 124.875i 0.562499i
\(223\) 6.96741i 0.0312440i 0.999878 + 0.0156220i \(0.00497284\pi\)
−0.999878 + 0.0156220i \(0.995027\pi\)
\(224\) 4.82653 + 39.3027i 0.0215470 + 0.175459i
\(225\) 0 0
\(226\) 222.961 0.986555
\(227\) 242.118i 1.06660i −0.845927 0.533299i \(-0.820952\pi\)
0.845927 0.533299i \(-0.179048\pi\)
\(228\) −22.6345 −0.0992743
\(229\) 225.586i 0.985093i −0.870286 0.492547i \(-0.836066\pi\)
0.870286 0.492547i \(-0.163934\pi\)
\(230\) 0 0
\(231\) 34.6694 4.25754i 0.150084 0.0184309i
\(232\) −93.2218 −0.401818
\(233\) 435.850 1.87060 0.935300 0.353856i \(-0.115130\pi\)
0.935300 + 0.353856i \(0.115130\pi\)
\(234\) 58.6101i 0.250470i
\(235\) 0 0
\(236\) 2.94977i 0.0124990i
\(237\) 114.545i 0.483311i
\(238\) 237.540 29.1708i 0.998066 0.122566i
\(239\) −194.711 −0.814690 −0.407345 0.913274i \(-0.633545\pi\)
−0.407345 + 0.913274i \(0.633545\pi\)
\(240\) 0 0
\(241\) 245.810i 1.01996i 0.860186 + 0.509980i \(0.170347\pi\)
−0.860186 + 0.509980i \(0.829653\pi\)
\(242\) 159.382 0.658603
\(243\) 15.5885i 0.0641500i
\(244\) 223.136i 0.914490i
\(245\) 0 0
\(246\) 52.7192 0.214306
\(247\) −90.2645 −0.365443
\(248\) 6.88089i 0.0277455i
\(249\) 135.996 0.546168
\(250\) 0 0
\(251\) 147.023i 0.585749i −0.956151 0.292875i \(-0.905388\pi\)
0.956151 0.292875i \(-0.0946118\pi\)
\(252\) 5.11931 + 41.6868i 0.0203147 + 0.165424i
\(253\) −83.0928 −0.328430
\(254\) 39.8875 0.157038
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 421.734i 1.64099i 0.571654 + 0.820495i \(0.306302\pi\)
−0.571654 + 0.820495i \(0.693698\pi\)
\(258\) 33.2039i 0.128697i
\(259\) 43.4969 + 354.198i 0.167942 + 1.36756i
\(260\) 0 0
\(261\) −98.8767 −0.378838
\(262\) 222.909i 0.850796i
\(263\) −68.6354 −0.260971 −0.130486 0.991450i \(-0.541654\pi\)
−0.130486 + 0.991450i \(0.541654\pi\)
\(264\) 14.1138i 0.0534614i
\(265\) 0 0
\(266\) −64.2013 + 7.88417i −0.241358 + 0.0296397i
\(267\) 157.569 0.590145
\(268\) −240.586 −0.897709
\(269\) 93.2991i 0.346837i 0.984848 + 0.173418i \(0.0554813\pi\)
−0.984848 + 0.173418i \(0.944519\pi\)
\(270\) 0 0
\(271\) 288.317i 1.06390i 0.846776 + 0.531949i \(0.178540\pi\)
−0.846776 + 0.531949i \(0.821460\pi\)
\(272\) 96.7016i 0.355521i
\(273\) 20.4153 + 166.243i 0.0747814 + 0.608950i
\(274\) 346.278 1.26379
\(275\) 0 0
\(276\) 99.9116i 0.361999i
\(277\) 385.440 1.39148 0.695740 0.718294i \(-0.255077\pi\)
0.695740 + 0.718294i \(0.255077\pi\)
\(278\) 336.929i 1.21197i
\(279\) 7.29829i 0.0261587i
\(280\) 0 0
\(281\) 243.958 0.868179 0.434090 0.900870i \(-0.357070\pi\)
0.434090 + 0.900870i \(0.357070\pi\)
\(282\) 99.7688 0.353790
\(283\) 501.435i 1.77185i −0.463825 0.885927i \(-0.653523\pi\)
0.463825 0.885927i \(-0.346477\pi\)
\(284\) −180.771 −0.636518
\(285\) 0 0
\(286\) 56.2846i 0.196799i
\(287\) 149.534 18.3634i 0.521026 0.0639840i
\(288\) 16.9706 0.0589256
\(289\) −295.450 −1.02232
\(290\) 0 0
\(291\) −76.5519 −0.263065
\(292\) 42.9780i 0.147185i
\(293\) 337.308i 1.15122i 0.817724 + 0.575611i \(0.195236\pi\)
−0.817724 + 0.575611i \(0.804764\pi\)
\(294\) 29.0411 + 116.459i 0.0987793 + 0.396118i
\(295\) 0 0
\(296\) 144.193 0.487138
\(297\) 14.9699i 0.0504039i
\(298\) 15.3298 0.0514422
\(299\) 398.438i 1.33257i
\(300\) 0 0
\(301\) 11.5657 + 94.1806i 0.0384244 + 0.312892i
\(302\) 159.805 0.529156
\(303\) 311.859 1.02924
\(304\) 26.1361i 0.0859741i
\(305\) 0 0
\(306\) 102.568i 0.335188i
\(307\) 112.285i 0.365751i 0.983136 + 0.182875i \(0.0585405\pi\)
−0.983136 + 0.182875i \(0.941460\pi\)
\(308\) −4.91618 40.0328i −0.0159616 0.129977i
\(309\) −185.690 −0.600938
\(310\) 0 0
\(311\) 146.478i 0.470990i −0.971876 0.235495i \(-0.924329\pi\)
0.971876 0.235495i \(-0.0756711\pi\)
\(312\) 67.6771 0.216914
\(313\) 139.927i 0.447052i 0.974698 + 0.223526i \(0.0717568\pi\)
−0.974698 + 0.223526i \(0.928243\pi\)
\(314\) 146.643i 0.467017i
\(315\) 0 0
\(316\) 132.265 0.418559
\(317\) −39.7776 −0.125481 −0.0627407 0.998030i \(-0.519984\pi\)
−0.0627407 + 0.998030i \(0.519984\pi\)
\(318\) 42.3170i 0.133072i
\(319\) 94.9535 0.297660
\(320\) 0 0
\(321\) 57.4212i 0.178882i
\(322\) −34.8017 283.392i −0.108080 0.880100i
\(323\) 157.963 0.489049
\(324\) 18.0000 0.0555556
\(325\) 0 0
\(326\) −282.243 −0.865775
\(327\) 188.480i 0.576391i
\(328\) 60.8749i 0.185594i
\(329\) 282.987 34.7519i 0.860144 0.105629i
\(330\) 0 0
\(331\) −13.6736 −0.0413101 −0.0206550 0.999787i \(-0.506575\pi\)
−0.0206550 + 0.999787i \(0.506575\pi\)
\(332\) 157.034i 0.472995i
\(333\) 152.940 0.459278
\(334\) 123.147i 0.368702i
\(335\) 0 0
\(336\) 48.1358 5.91127i 0.143261 0.0175931i
\(337\) 364.873 1.08271 0.541354 0.840795i \(-0.317912\pi\)
0.541354 + 0.840795i \(0.317912\pi\)
\(338\) 30.8880 0.0913846
\(339\) 273.071i 0.805519i
\(340\) 0 0
\(341\) 7.00871i 0.0205534i
\(342\) 27.7215i 0.0810572i
\(343\) 122.938 + 320.211i 0.358421 + 0.933560i
\(344\) 38.3406 0.111455
\(345\) 0 0
\(346\) 150.751i 0.435695i
\(347\) 469.783 1.35384 0.676920 0.736056i \(-0.263314\pi\)
0.676920 + 0.736056i \(0.263314\pi\)
\(348\) 114.173i 0.328083i
\(349\) 26.7504i 0.0766487i 0.999265 + 0.0383244i \(0.0122020\pi\)
−0.999265 + 0.0383244i \(0.987798\pi\)
\(350\) 0 0
\(351\) 71.7824 0.204508
\(352\) −16.2972 −0.0462989
\(353\) 473.408i 1.34110i 0.741864 + 0.670550i \(0.233942\pi\)
−0.741864 + 0.670550i \(0.766058\pi\)
\(354\) −3.61272 −0.0102054
\(355\) 0 0
\(356\) 181.945i 0.511081i
\(357\) −35.7268 290.926i −0.100075 0.814918i
\(358\) 390.155 1.08982
\(359\) 98.8174 0.275257 0.137629 0.990484i \(-0.456052\pi\)
0.137629 + 0.990484i \(0.456052\pi\)
\(360\) 0 0
\(361\) 318.306 0.881735
\(362\) 263.653i 0.728323i
\(363\) 195.202i 0.537747i
\(364\) 191.961 23.5736i 0.527366 0.0647626i
\(365\) 0 0
\(366\) 273.284 0.746678
\(367\) 331.526i 0.903341i −0.892185 0.451671i \(-0.850828\pi\)
0.892185 0.451671i \(-0.149172\pi\)
\(368\) −115.368 −0.313500
\(369\) 64.5676i 0.174980i
\(370\) 0 0
\(371\) −14.7400 120.029i −0.0397306 0.323529i
\(372\) −8.42734 −0.0226541
\(373\) −416.519 −1.11667 −0.558337 0.829614i \(-0.688560\pi\)
−0.558337 + 0.829614i \(0.688560\pi\)
\(374\) 98.4979i 0.263363i
\(375\) 0 0
\(376\) 115.203i 0.306391i
\(377\) 455.311i 1.20772i
\(378\) 51.0557 6.26984i 0.135068 0.0165869i
\(379\) −560.942 −1.48006 −0.740028 0.672576i \(-0.765188\pi\)
−0.740028 + 0.672576i \(0.765188\pi\)
\(380\) 0 0
\(381\) 48.8520i 0.128221i
\(382\) 250.424 0.655560
\(383\) 135.702i 0.354314i 0.984183 + 0.177157i \(0.0566900\pi\)
−0.984183 + 0.177157i \(0.943310\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) 217.015 0.562215
\(387\) 40.6663 0.105081
\(388\) 88.3945i 0.227821i
\(389\) 703.375 1.80816 0.904081 0.427361i \(-0.140557\pi\)
0.904081 + 0.427361i \(0.140557\pi\)
\(390\) 0 0
\(391\) 697.267i 1.78329i
\(392\) 134.475 33.5338i 0.343048 0.0855454i
\(393\) 273.006 0.694672
\(394\) −302.700 −0.768274
\(395\) 0 0
\(396\) −17.2858 −0.0436510
\(397\) 2.16495i 0.00545326i −0.999996 0.00272663i \(-0.999132\pi\)
0.999996 0.00272663i \(-0.000867915\pi\)
\(398\) 251.979i 0.633114i
\(399\) 9.65610 + 78.6302i 0.0242007 + 0.197068i
\(400\) 0 0
\(401\) −227.907 −0.568347 −0.284174 0.958773i \(-0.591719\pi\)
−0.284174 + 0.958773i \(0.591719\pi\)
\(402\) 294.656i 0.732976i
\(403\) −33.6075 −0.0833932
\(404\) 360.103i 0.891345i
\(405\) 0 0
\(406\) 39.7693 + 323.844i 0.0979538 + 0.797644i
\(407\) −146.871 −0.360863
\(408\) −118.435 −0.290281
\(409\) 219.271i 0.536116i 0.963403 + 0.268058i \(0.0863818\pi\)
−0.963403 + 0.268058i \(0.913618\pi\)
\(410\) 0 0
\(411\) 424.102i 1.03188i
\(412\) 214.416i 0.520428i
\(413\) −10.2472 + 1.25840i −0.0248117 + 0.00304697i
\(414\) −122.366 −0.295571
\(415\) 0 0
\(416\) 78.1468i 0.187853i
\(417\) −412.652 −0.989572
\(418\) 26.6216i 0.0636881i
\(419\) 636.723i 1.51963i 0.650141 + 0.759813i \(0.274710\pi\)
−0.650141 + 0.759813i \(0.725290\pi\)
\(420\) 0 0
\(421\) 816.589 1.93964 0.969821 0.243819i \(-0.0784003\pi\)
0.969821 + 0.243819i \(0.0784003\pi\)
\(422\) 562.874 1.33382
\(423\) 122.191i 0.288868i
\(424\) −48.8634 −0.115244
\(425\) 0 0
\(426\) 221.398i 0.519714i
\(427\) 775.151 95.1916i 1.81534 0.222931i
\(428\) −66.3043 −0.154917
\(429\) −68.9342 −0.160686
\(430\) 0 0
\(431\) −288.911 −0.670328 −0.335164 0.942160i \(-0.608792\pi\)
−0.335164 + 0.942160i \(0.608792\pi\)
\(432\) 20.7846i 0.0481125i
\(433\) 114.744i 0.264997i 0.991183 + 0.132498i \(0.0423000\pi\)
−0.991183 + 0.132498i \(0.957700\pi\)
\(434\) −23.9036 + 2.93545i −0.0550773 + 0.00676371i
\(435\) 0 0
\(436\) −217.638 −0.499169
\(437\) 188.454i 0.431246i
\(438\) −52.6371 −0.120176
\(439\) 637.443i 1.45203i −0.687677 0.726017i \(-0.741369\pi\)
0.687677 0.726017i \(-0.258631\pi\)
\(440\) 0 0
\(441\) 142.632 35.5679i 0.323429 0.0806529i
\(442\) −472.307 −1.06857
\(443\) −184.901 −0.417384 −0.208692 0.977981i \(-0.566921\pi\)
−0.208692 + 0.977981i \(0.566921\pi\)
\(444\) 176.599i 0.397747i
\(445\) 0 0
\(446\) 9.85341i 0.0220928i
\(447\) 18.7751i 0.0420024i
\(448\) −6.82574 55.5825i −0.0152360 0.124068i
\(449\) 313.278 0.697723 0.348862 0.937174i \(-0.386568\pi\)
0.348862 + 0.937174i \(0.386568\pi\)
\(450\) 0 0
\(451\) 62.0057i 0.137485i
\(452\) −315.315 −0.697600
\(453\) 195.721i 0.432054i
\(454\) 342.406i 0.754198i
\(455\) 0 0
\(456\) 32.0101 0.0701976
\(457\) 174.826 0.382551 0.191275 0.981536i \(-0.438738\pi\)
0.191275 + 0.981536i \(0.438738\pi\)
\(458\) 319.027i 0.696566i
\(459\) −125.619 −0.273680
\(460\) 0 0
\(461\) 379.263i 0.822695i −0.911479 0.411348i \(-0.865058\pi\)
0.911479 0.411348i \(-0.134942\pi\)
\(462\) −49.0300 + 6.02107i −0.106125 + 0.0130326i
\(463\) 403.499 0.871489 0.435744 0.900071i \(-0.356485\pi\)
0.435744 + 0.900071i \(0.356485\pi\)
\(464\) 131.836 0.284128
\(465\) 0 0
\(466\) −616.385 −1.32271
\(467\) 807.901i 1.72998i 0.501788 + 0.864991i \(0.332676\pi\)
−0.501788 + 0.864991i \(0.667324\pi\)
\(468\) 82.8872i 0.177109i
\(469\) 102.636 + 835.772i 0.218840 + 1.78203i
\(470\) 0 0
\(471\) 179.601 0.381318
\(472\) 4.17160i 0.00883815i
\(473\) −39.0528 −0.0825640
\(474\) 161.991i 0.341752i
\(475\) 0 0
\(476\) −335.932 + 41.2538i −0.705740 + 0.0866675i
\(477\) −51.8275 −0.108653
\(478\) 275.363 0.576073
\(479\) 439.564i 0.917671i −0.888521 0.458835i \(-0.848267\pi\)
0.888521 0.458835i \(-0.151733\pi\)
\(480\) 0 0
\(481\) 704.263i 1.46416i
\(482\) 347.628i 0.721220i
\(483\) −347.083 + 42.6232i −0.718599 + 0.0882467i
\(484\) −225.400 −0.465703
\(485\) 0 0
\(486\) 22.0454i 0.0453609i
\(487\) −37.9665 −0.0779599 −0.0389799 0.999240i \(-0.512411\pi\)
−0.0389799 + 0.999240i \(0.512411\pi\)
\(488\) 315.561i 0.646642i
\(489\) 345.675i 0.706903i
\(490\) 0 0
\(491\) −7.32753 −0.0149237 −0.00746184 0.999972i \(-0.502375\pi\)
−0.00746184 + 0.999972i \(0.502375\pi\)
\(492\) −74.5563 −0.151537
\(493\) 796.794i 1.61622i
\(494\) 127.653 0.258408
\(495\) 0 0
\(496\) 9.73105i 0.0196191i
\(497\) 77.1185 + 627.981i 0.155168 + 1.26354i
\(498\) −192.327 −0.386199
\(499\) 397.886 0.797366 0.398683 0.917089i \(-0.369467\pi\)
0.398683 + 0.917089i \(0.369467\pi\)
\(500\) 0 0
\(501\) −150.823 −0.301044
\(502\) 207.922i 0.414187i
\(503\) 70.5081i 0.140175i 0.997541 + 0.0700876i \(0.0223279\pi\)
−0.997541 + 0.0700876i \(0.977672\pi\)
\(504\) −7.23979 58.9541i −0.0143647 0.116972i
\(505\) 0 0
\(506\) 117.511 0.232235
\(507\) 37.8299i 0.0746152i
\(508\) −56.4095 −0.111042
\(509\) 505.073i 0.992285i −0.868241 0.496143i \(-0.834749\pi\)
0.868241 0.496143i \(-0.165251\pi\)
\(510\) 0 0
\(511\) −149.301 + 18.3348i −0.292175 + 0.0358802i
\(512\) −22.6274 −0.0441942
\(513\) 33.9518 0.0661829
\(514\) 596.422i 1.16035i
\(515\) 0 0
\(516\) 46.9574i 0.0910028i
\(517\) 117.343i 0.226969i
\(518\) −61.5139 500.912i −0.118753 0.967012i
\(519\) 184.631 0.355744
\(520\) 0 0
\(521\) 214.185i 0.411104i −0.978646 0.205552i \(-0.934101\pi\)
0.978646 0.205552i \(-0.0658990\pi\)
\(522\) 139.833 0.267879
\(523\) 121.732i 0.232757i 0.993205 + 0.116379i \(0.0371286\pi\)
−0.993205 + 0.116379i \(0.962871\pi\)
\(524\) 315.240i 0.601604i
\(525\) 0 0
\(526\) 97.0651 0.184534
\(527\) 58.8130 0.111600
\(528\) 19.9599i 0.0378029i
\(529\) 302.861 0.572515
\(530\) 0 0
\(531\) 4.42465i 0.00833268i
\(532\) 90.7944 11.1499i 0.170666 0.0209585i
\(533\) −297.324 −0.557830
\(534\) −222.836 −0.417296
\(535\) 0 0
\(536\) 340.240 0.634776
\(537\) 477.840i 0.889832i
\(538\) 131.945i 0.245251i
\(539\) −136.973 + 34.1567i −0.254124 + 0.0633705i
\(540\) 0 0
\(541\) 600.626 1.11021 0.555107 0.831779i \(-0.312677\pi\)
0.555107 + 0.831779i \(0.312677\pi\)
\(542\) 407.741i 0.752290i
\(543\) −322.908 −0.594674
\(544\) 136.757i 0.251391i
\(545\) 0 0
\(546\) −28.8716 235.104i −0.0528785 0.430593i
\(547\) −1045.16 −1.91071 −0.955356 0.295457i \(-0.904528\pi\)
−0.955356 + 0.295457i \(0.904528\pi\)
\(548\) −489.711 −0.893632
\(549\) 334.703i 0.609660i
\(550\) 0 0
\(551\) 215.354i 0.390843i
\(552\) 141.296i 0.255972i
\(553\) −56.4253 459.475i −0.102035 0.830877i
\(554\) −545.094 −0.983924
\(555\) 0 0
\(556\) 476.489i 0.856995i
\(557\) −601.731 −1.08031 −0.540154 0.841566i \(-0.681634\pi\)
−0.540154 + 0.841566i \(0.681634\pi\)
\(558\) 10.3213i 0.0184970i
\(559\) 187.262i 0.334995i
\(560\) 0 0
\(561\) 120.635 0.215035
\(562\) −345.009 −0.613896
\(563\) 363.871i 0.646308i 0.946346 + 0.323154i \(0.104743\pi\)
−0.946346 + 0.323154i \(0.895257\pi\)
\(564\) −141.094 −0.250167
\(565\) 0 0
\(566\) 709.136i 1.25289i
\(567\) −7.67896 62.5303i −0.0135431 0.110283i
\(568\) 255.649 0.450086
\(569\) −902.900 −1.58682 −0.793410 0.608688i \(-0.791696\pi\)
−0.793410 + 0.608688i \(0.791696\pi\)
\(570\) 0 0
\(571\) −847.207 −1.48372 −0.741862 0.670552i \(-0.766057\pi\)
−0.741862 + 0.670552i \(0.766057\pi\)
\(572\) 79.5984i 0.139158i
\(573\) 306.705i 0.535263i
\(574\) −211.474 + 25.9698i −0.368421 + 0.0452435i
\(575\) 0 0
\(576\) −24.0000 −0.0416667
\(577\) 306.535i 0.531256i 0.964076 + 0.265628i \(0.0855793\pi\)
−0.964076 + 0.265628i \(0.914421\pi\)
\(578\) 417.829 0.722888
\(579\) 265.788i 0.459047i
\(580\) 0 0
\(581\) −545.522 + 66.9923i −0.938937 + 0.115305i
\(582\) 108.261 0.186015
\(583\) 49.7711 0.0853707
\(584\) 60.7801i 0.104075i
\(585\) 0 0
\(586\) 477.025i 0.814037i
\(587\) 467.524i 0.796463i 0.917285 + 0.398232i \(0.130376\pi\)
−0.917285 + 0.398232i \(0.869624\pi\)
\(588\) −41.0703 164.697i −0.0698475 0.280098i
\(589\) −15.8958 −0.0269877
\(590\) 0 0
\(591\) 370.730i 0.627293i
\(592\) −203.920 −0.344459
\(593\) 744.542i 1.25555i 0.778395 + 0.627775i \(0.216034\pi\)
−0.778395 + 0.627775i \(0.783966\pi\)
\(594\) 21.1707i 0.0356409i
\(595\) 0 0
\(596\) −21.6796 −0.0363751
\(597\) 308.611 0.516936
\(598\) 563.477i 0.942269i
\(599\) 276.145 0.461011 0.230505 0.973071i \(-0.425962\pi\)
0.230505 + 0.973071i \(0.425962\pi\)
\(600\) 0 0
\(601\) 779.606i 1.29718i 0.761137 + 0.648591i \(0.224641\pi\)
−0.761137 + 0.648591i \(0.775359\pi\)
\(602\) −16.3564 133.191i −0.0271702 0.221248i
\(603\) 360.879 0.598472
\(604\) −225.999 −0.374170
\(605\) 0 0
\(606\) −441.035 −0.727780
\(607\) 567.539i 0.934990i −0.883996 0.467495i \(-0.845157\pi\)
0.883996 0.467495i \(-0.154843\pi\)
\(608\) 36.9621i 0.0607929i
\(609\) 396.626 48.7072i 0.651274 0.0799790i
\(610\) 0 0
\(611\) −562.672 −0.920903
\(612\) 145.052i 0.237014i
\(613\) 801.088 1.30683 0.653416 0.756999i \(-0.273335\pi\)
0.653416 + 0.756999i \(0.273335\pi\)
\(614\) 158.796i 0.258625i
\(615\) 0 0
\(616\) 6.95253 + 56.6149i 0.0112866 + 0.0919074i
\(617\) −71.2583 −0.115492 −0.0577458 0.998331i \(-0.518391\pi\)
−0.0577458 + 0.998331i \(0.518391\pi\)
\(618\) 262.605 0.424928
\(619\) 821.793i 1.32761i 0.747904 + 0.663807i \(0.231060\pi\)
−0.747904 + 0.663807i \(0.768940\pi\)
\(620\) 0 0
\(621\) 149.867i 0.241332i
\(622\) 207.151i 0.333040i
\(623\) −632.059 + 77.6193i −1.01454 + 0.124590i
\(624\) −95.7098 −0.153381
\(625\) 0 0
\(626\) 197.887i 0.316114i
\(627\) −32.6047 −0.0520011
\(628\) 207.385i 0.330231i
\(629\) 1232.46i 1.95939i
\(630\) 0 0
\(631\) −916.907 −1.45310 −0.726551 0.687113i \(-0.758878\pi\)
−0.726551 + 0.687113i \(0.758878\pi\)
\(632\) −187.051 −0.295966
\(633\) 689.377i 1.08906i
\(634\) 56.2540 0.0887287
\(635\) 0 0
\(636\) 59.8452i 0.0940963i
\(637\) −163.785 656.798i −0.257119 1.03108i
\(638\) −134.285 −0.210477
\(639\) 271.156 0.424345
\(640\) 0 0
\(641\) 737.240 1.15014 0.575070 0.818104i \(-0.304975\pi\)
0.575070 + 0.818104i \(0.304975\pi\)
\(642\) 81.2058i 0.126489i
\(643\) 256.297i 0.398596i 0.979939 + 0.199298i \(0.0638661\pi\)
−0.979939 + 0.199298i \(0.936134\pi\)
\(644\) 49.2170 + 400.777i 0.0764239 + 0.622325i
\(645\) 0 0
\(646\) −223.393 −0.345810
\(647\) 689.147i 1.06514i −0.846385 0.532571i \(-0.821226\pi\)
0.846385 0.532571i \(-0.178774\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 4.24910i 0.00654714i
\(650\) 0 0
\(651\) 3.59518 + 29.2758i 0.00552255 + 0.0449705i
\(652\) 399.152 0.612196
\(653\) 395.775 0.606087 0.303044 0.952977i \(-0.401997\pi\)
0.303044 + 0.952977i \(0.401997\pi\)
\(654\) 266.551i 0.407570i
\(655\) 0 0
\(656\) 86.0902i 0.131235i
\(657\) 64.4670i 0.0981233i
\(658\) −400.205 + 49.1467i −0.608214 + 0.0746910i
\(659\) 47.8147 0.0725565 0.0362782 0.999342i \(-0.488450\pi\)
0.0362782 + 0.999342i \(0.488450\pi\)
\(660\) 0 0
\(661\) 89.9129i 0.136026i −0.997684 0.0680128i \(-0.978334\pi\)
0.997684 0.0680128i \(-0.0216659\pi\)
\(662\) 19.3374 0.0292106
\(663\) 578.456i 0.872482i
\(664\) 222.080i 0.334458i
\(665\) 0 0
\(666\) −216.289 −0.324759
\(667\) −950.600 −1.42519
\(668\) 174.155i 0.260712i
\(669\) −12.0679 −0.0180387
\(670\) 0 0
\(671\) 321.423i 0.479021i
\(672\) −68.0743 + 8.35979i −0.101301 + 0.0124402i
\(673\) −833.478 −1.23845 −0.619226 0.785213i \(-0.712553\pi\)
−0.619226 + 0.785213i \(0.712553\pi\)
\(674\) −516.008 −0.765590
\(675\) 0 0
\(676\) −43.6822 −0.0646187
\(677\) 44.1092i 0.0651540i 0.999469 + 0.0325770i \(0.0103714\pi\)
−0.999469 + 0.0325770i \(0.989629\pi\)
\(678\) 386.181i 0.569588i
\(679\) 307.074 37.7099i 0.452244 0.0555373i
\(680\) 0 0
\(681\) 419.360 0.615800
\(682\) 9.91182i 0.0145335i
\(683\) −130.146 −0.190550 −0.0952750 0.995451i \(-0.530373\pi\)
−0.0952750 + 0.995451i \(0.530373\pi\)
\(684\) 39.2042i 0.0573161i
\(685\) 0 0
\(686\) −173.861 452.847i −0.253442 0.660127i
\(687\) 390.727 0.568744
\(688\) −54.2218 −0.0788107
\(689\) 238.657i 0.346382i
\(690\) 0 0
\(691\) 714.724i 1.03433i −0.855885 0.517167i \(-0.826987\pi\)
0.855885 0.517167i \(-0.173013\pi\)
\(692\) 213.194i 0.308083i
\(693\) 7.37428 + 60.0492i 0.0106411 + 0.0866511i
\(694\) −664.373 −0.957310
\(695\) 0 0
\(696\) 161.465i 0.231990i
\(697\) 520.316 0.746508
\(698\) 37.8308i 0.0541988i
\(699\) 754.914i 1.07999i
\(700\) 0 0
\(701\) 463.854 0.661704 0.330852 0.943683i \(-0.392664\pi\)
0.330852 + 0.943683i \(0.392664\pi\)
\(702\) −101.516 −0.144609
\(703\) 333.104i 0.473832i
\(704\) 23.0477 0.0327383
\(705\) 0 0
\(706\) 669.500i 0.948301i
\(707\) −1250.96 + 153.623i −1.76940 + 0.217289i
\(708\) 5.10915 0.00721632
\(709\) 970.049 1.36819 0.684097 0.729391i \(-0.260197\pi\)
0.684097 + 0.729391i \(0.260197\pi\)
\(710\) 0 0
\(711\) −198.397 −0.279040
\(712\) 257.309i 0.361389i
\(713\) 70.1657i 0.0984092i
\(714\) 50.5253 + 411.431i 0.0707638 + 0.576234i
\(715\) 0 0
\(716\) −551.762 −0.770617
\(717\) 337.249i 0.470362i
\(718\) −139.749 −0.194636
\(719\) 1369.36i 1.90453i −0.305266 0.952267i \(-0.598745\pi\)
0.305266 0.952267i \(-0.401255\pi\)
\(720\) 0 0
\(721\) 744.861 91.4719i 1.03309 0.126868i
\(722\) −450.153 −0.623481
\(723\) −425.756 −0.588874
\(724\) 372.862i 0.515002i
\(725\) 0 0
\(726\) 276.058i 0.380245i
\(727\) 1106.85i 1.52249i −0.648463 0.761246i \(-0.724588\pi\)
0.648463 0.761246i \(-0.275412\pi\)
\(728\) −271.474 + 33.3381i −0.372904 + 0.0457941i
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) 327.708i 0.448301i
\(732\) −386.482 −0.527981
\(733\) 297.353i 0.405665i 0.979213 + 0.202833i \(0.0650147\pi\)
−0.979213 + 0.202833i \(0.934985\pi\)
\(734\) 468.849i 0.638759i
\(735\) 0 0
\(736\) 163.155 0.221678
\(737\) −346.560 −0.470231
\(738\) 91.3124i 0.123730i
\(739\) −604.951 −0.818608 −0.409304 0.912398i \(-0.634228\pi\)
−0.409304 + 0.912398i \(0.634228\pi\)
\(740\) 0 0
\(741\) 156.343i 0.210989i
\(742\) 20.8456 + 169.747i 0.0280938 + 0.228769i
\(743\) 733.877 0.987722 0.493861 0.869541i \(-0.335585\pi\)
0.493861 + 0.869541i \(0.335585\pi\)
\(744\) 11.9181 0.0160189
\(745\) 0 0
\(746\) 589.047 0.789608
\(747\) 235.552i 0.315330i
\(748\) 139.297i 0.186226i
\(749\) 28.2860 + 230.335i 0.0377650 + 0.307523i
\(750\) 0 0
\(751\) −71.0036 −0.0945455 −0.0472727 0.998882i \(-0.515053\pi\)
−0.0472727 + 0.998882i \(0.515053\pi\)
\(752\) 162.922i 0.216651i
\(753\) 254.651 0.338182
\(754\) 643.908i 0.853989i
\(755\) 0 0
\(756\) −72.2037 + 8.86690i −0.0955076 + 0.0117287i
\(757\) −708.172 −0.935497 −0.467749 0.883861i \(-0.654935\pi\)
−0.467749 + 0.883861i \(0.654935\pi\)
\(758\) 793.291 1.04656
\(759\) 143.921i 0.189619i
\(760\) 0 0
\(761\) 797.652i 1.04816i −0.851668 0.524081i \(-0.824409\pi\)
0.851668 0.524081i \(-0.175591\pi\)
\(762\) 69.0872i 0.0906657i
\(763\) 92.8462 + 756.052i 0.121686 + 0.990894i
\(764\) −354.153 −0.463551
\(765\) 0 0
\(766\) 191.912i 0.250538i
\(767\) 20.3748 0.0265643
\(768\) 27.7128i 0.0360844i
\(769\) 261.829i 0.340480i −0.985403 0.170240i \(-0.945546\pi\)
0.985403 0.170240i \(-0.0544543\pi\)
\(770\) 0 0
\(771\) −730.465 −0.947426
\(772\) −306.906 −0.397546
\(773\) 643.514i 0.832489i −0.909253 0.416245i \(-0.863346\pi\)
0.909253 0.416245i \(-0.136654\pi\)
\(774\) −57.5109 −0.0743035
\(775\) 0 0
\(776\) 125.009i 0.161094i
\(777\) −613.490 + 75.3389i −0.789562 + 0.0969613i
\(778\) −994.722 −1.27856
\(779\) −140.629 −0.180525
\(780\) 0 0
\(781\) −260.398 −0.333416
\(782\) 986.084i 1.26098i
\(783\) 171.259i 0.218722i
\(784\) −190.176 + 47.4239i −0.242572 + 0.0604897i
\(785\) 0 0
\(786\) −386.089 −0.491207
\(787\) 919.663i 1.16857i 0.811549 + 0.584284i \(0.198625\pi\)
−0.811549 + 0.584284i \(0.801375\pi\)
\(788\) 428.082 0.543252
\(789\) 118.880i 0.150672i
\(790\) 0 0