Properties

Label 6025.2.a.h.1.12
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-2.59703\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.59703 q^{2} +1.20534 q^{3} +4.74454 q^{4} +3.13029 q^{6} +0.744578 q^{7} +7.12764 q^{8} -1.54716 q^{9} +O(q^{10})\) \(q+2.59703 q^{2} +1.20534 q^{3} +4.74454 q^{4} +3.13029 q^{6} +0.744578 q^{7} +7.12764 q^{8} -1.54716 q^{9} +6.28793 q^{11} +5.71878 q^{12} +4.06994 q^{13} +1.93369 q^{14} +9.02158 q^{16} +1.60034 q^{17} -4.01801 q^{18} +2.14421 q^{19} +0.897468 q^{21} +16.3299 q^{22} -9.25572 q^{23} +8.59122 q^{24} +10.5697 q^{26} -5.48087 q^{27} +3.53268 q^{28} +3.13090 q^{29} -3.15223 q^{31} +9.17399 q^{32} +7.57908 q^{33} +4.15612 q^{34} -7.34056 q^{36} -4.19928 q^{37} +5.56857 q^{38} +4.90566 q^{39} -4.52694 q^{41} +2.33075 q^{42} -6.99535 q^{43} +29.8333 q^{44} -24.0373 q^{46} +4.82023 q^{47} +10.8741 q^{48} -6.44560 q^{49} +1.92895 q^{51} +19.3100 q^{52} -3.71179 q^{53} -14.2339 q^{54} +5.30708 q^{56} +2.58450 q^{57} +8.13103 q^{58} +3.34128 q^{59} +10.8630 q^{61} -8.18643 q^{62} -1.15198 q^{63} +5.78192 q^{64} +19.6831 q^{66} -5.80682 q^{67} +7.59287 q^{68} -11.1563 q^{69} +15.7805 q^{71} -11.0276 q^{72} +1.64682 q^{73} -10.9056 q^{74} +10.1733 q^{76} +4.68186 q^{77} +12.7401 q^{78} -11.4813 q^{79} -1.96482 q^{81} -11.7566 q^{82} +4.74454 q^{83} +4.25807 q^{84} -18.1671 q^{86} +3.77380 q^{87} +44.8181 q^{88} -7.95332 q^{89} +3.03039 q^{91} -43.9141 q^{92} -3.79951 q^{93} +12.5182 q^{94} +11.0578 q^{96} +5.49759 q^{97} -16.7394 q^{98} -9.72843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{2} - q^{3} + 13q^{4} - q^{6} - 3q^{7} - 9q^{8} + 15q^{9} + O(q^{10}) \) \( 12q - 3q^{2} - q^{3} + 13q^{4} - q^{6} - 3q^{7} - 9q^{8} + 15q^{9} + 22q^{11} + 7q^{12} + 5q^{13} + 6q^{14} + 15q^{16} + 4q^{17} + q^{18} - 6q^{19} - 14q^{21} + 12q^{22} - 32q^{23} - 15q^{24} + 8q^{26} + 5q^{27} + 11q^{28} + 6q^{29} + 8q^{31} - q^{32} + 24q^{33} - 19q^{34} - 8q^{36} + 8q^{37} + 10q^{38} + 31q^{39} - q^{41} + 49q^{42} + 2q^{43} + 42q^{44} - 25q^{46} - 34q^{47} + 49q^{48} - 9q^{49} - 3q^{51} + 41q^{52} - 5q^{53} - 40q^{54} + q^{56} + 22q^{57} + 33q^{58} + 26q^{59} - 26q^{61} + 17q^{62} + 4q^{63} + 13q^{64} - 2q^{66} - 6q^{67} + 35q^{68} - 2q^{69} + 94q^{71} - 17q^{72} + 22q^{73} + 26q^{74} - 20q^{76} + 7q^{77} - 54q^{78} + 9q^{79} + 4q^{81} - 15q^{82} + 8q^{83} + 2q^{84} + 9q^{86} - 4q^{87} - 6q^{88} - 3q^{89} - 20q^{91} - 36q^{92} - 12q^{93} + 48q^{94} - 23q^{96} + 29q^{97} - 28q^{98} + 36q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.59703 1.83637 0.918187 0.396147i \(-0.129653\pi\)
0.918187 + 0.396147i \(0.129653\pi\)
\(3\) 1.20534 0.695902 0.347951 0.937513i \(-0.386877\pi\)
0.347951 + 0.937513i \(0.386877\pi\)
\(4\) 4.74454 2.37227
\(5\) 0 0
\(6\) 3.13029 1.27794
\(7\) 0.744578 0.281424 0.140712 0.990051i \(-0.455061\pi\)
0.140712 + 0.990051i \(0.455061\pi\)
\(8\) 7.12764 2.52000
\(9\) −1.54716 −0.515720
\(10\) 0 0
\(11\) 6.28793 1.89588 0.947941 0.318445i \(-0.103161\pi\)
0.947941 + 0.318445i \(0.103161\pi\)
\(12\) 5.71878 1.65087
\(13\) 4.06994 1.12880 0.564399 0.825502i \(-0.309108\pi\)
0.564399 + 0.825502i \(0.309108\pi\)
\(14\) 1.93369 0.516800
\(15\) 0 0
\(16\) 9.02158 2.25539
\(17\) 1.60034 0.388139 0.194070 0.980988i \(-0.437831\pi\)
0.194070 + 0.980988i \(0.437831\pi\)
\(18\) −4.01801 −0.947055
\(19\) 2.14421 0.491916 0.245958 0.969280i \(-0.420897\pi\)
0.245958 + 0.969280i \(0.420897\pi\)
\(20\) 0 0
\(21\) 0.897468 0.195844
\(22\) 16.3299 3.48155
\(23\) −9.25572 −1.92995 −0.964975 0.262340i \(-0.915506\pi\)
−0.964975 + 0.262340i \(0.915506\pi\)
\(24\) 8.59122 1.75367
\(25\) 0 0
\(26\) 10.5697 2.07290
\(27\) −5.48087 −1.05479
\(28\) 3.53268 0.667614
\(29\) 3.13090 0.581394 0.290697 0.956815i \(-0.406113\pi\)
0.290697 + 0.956815i \(0.406113\pi\)
\(30\) 0 0
\(31\) −3.15223 −0.566158 −0.283079 0.959097i \(-0.591356\pi\)
−0.283079 + 0.959097i \(0.591356\pi\)
\(32\) 9.17399 1.62175
\(33\) 7.57908 1.31935
\(34\) 4.15612 0.712769
\(35\) 0 0
\(36\) −7.34056 −1.22343
\(37\) −4.19928 −0.690358 −0.345179 0.938537i \(-0.612182\pi\)
−0.345179 + 0.938537i \(0.612182\pi\)
\(38\) 5.56857 0.903342
\(39\) 4.90566 0.785534
\(40\) 0 0
\(41\) −4.52694 −0.706990 −0.353495 0.935436i \(-0.615007\pi\)
−0.353495 + 0.935436i \(0.615007\pi\)
\(42\) 2.33075 0.359642
\(43\) −6.99535 −1.06678 −0.533391 0.845869i \(-0.679082\pi\)
−0.533391 + 0.845869i \(0.679082\pi\)
\(44\) 29.8333 4.49754
\(45\) 0 0
\(46\) −24.0373 −3.54411
\(47\) 4.82023 0.703102 0.351551 0.936169i \(-0.385654\pi\)
0.351551 + 0.936169i \(0.385654\pi\)
\(48\) 10.8741 1.56953
\(49\) −6.44560 −0.920800
\(50\) 0 0
\(51\) 1.92895 0.270107
\(52\) 19.3100 2.67782
\(53\) −3.71179 −0.509853 −0.254927 0.966960i \(-0.582051\pi\)
−0.254927 + 0.966960i \(0.582051\pi\)
\(54\) −14.2339 −1.93699
\(55\) 0 0
\(56\) 5.30708 0.709189
\(57\) 2.58450 0.342325
\(58\) 8.13103 1.06766
\(59\) 3.34128 0.434997 0.217499 0.976061i \(-0.430210\pi\)
0.217499 + 0.976061i \(0.430210\pi\)
\(60\) 0 0
\(61\) 10.8630 1.39087 0.695434 0.718590i \(-0.255212\pi\)
0.695434 + 0.718590i \(0.255212\pi\)
\(62\) −8.18643 −1.03968
\(63\) −1.15198 −0.145136
\(64\) 5.78192 0.722740
\(65\) 0 0
\(66\) 19.6831 2.42282
\(67\) −5.80682 −0.709416 −0.354708 0.934977i \(-0.615420\pi\)
−0.354708 + 0.934977i \(0.615420\pi\)
\(68\) 7.59287 0.920771
\(69\) −11.1563 −1.34306
\(70\) 0 0
\(71\) 15.7805 1.87281 0.936403 0.350927i \(-0.114134\pi\)
0.936403 + 0.350927i \(0.114134\pi\)
\(72\) −11.0276 −1.29961
\(73\) 1.64682 0.192745 0.0963727 0.995345i \(-0.469276\pi\)
0.0963727 + 0.995345i \(0.469276\pi\)
\(74\) −10.9056 −1.26775
\(75\) 0 0
\(76\) 10.1733 1.16696
\(77\) 4.68186 0.533547
\(78\) 12.7401 1.44253
\(79\) −11.4813 −1.29174 −0.645872 0.763446i \(-0.723506\pi\)
−0.645872 + 0.763446i \(0.723506\pi\)
\(80\) 0 0
\(81\) −1.96482 −0.218313
\(82\) −11.7566 −1.29830
\(83\) 4.74454 0.520781 0.260390 0.965503i \(-0.416149\pi\)
0.260390 + 0.965503i \(0.416149\pi\)
\(84\) 4.25807 0.464594
\(85\) 0 0
\(86\) −18.1671 −1.95901
\(87\) 3.77380 0.404594
\(88\) 44.8181 4.77762
\(89\) −7.95332 −0.843050 −0.421525 0.906817i \(-0.638505\pi\)
−0.421525 + 0.906817i \(0.638505\pi\)
\(90\) 0 0
\(91\) 3.03039 0.317671
\(92\) −43.9141 −4.57836
\(93\) −3.79951 −0.393991
\(94\) 12.5182 1.29116
\(95\) 0 0
\(96\) 11.0578 1.12858
\(97\) 5.49759 0.558195 0.279098 0.960263i \(-0.409965\pi\)
0.279098 + 0.960263i \(0.409965\pi\)
\(98\) −16.7394 −1.69093
\(99\) −9.72843 −0.977744
\(100\) 0 0
\(101\) −10.4008 −1.03492 −0.517459 0.855708i \(-0.673122\pi\)
−0.517459 + 0.855708i \(0.673122\pi\)
\(102\) 5.00953 0.496018
\(103\) 16.9464 1.66978 0.834888 0.550420i \(-0.185532\pi\)
0.834888 + 0.550420i \(0.185532\pi\)
\(104\) 29.0091 2.84457
\(105\) 0 0
\(106\) −9.63961 −0.936281
\(107\) 0.873633 0.0844573 0.0422287 0.999108i \(-0.486554\pi\)
0.0422287 + 0.999108i \(0.486554\pi\)
\(108\) −26.0042 −2.50225
\(109\) −9.90349 −0.948582 −0.474291 0.880368i \(-0.657296\pi\)
−0.474291 + 0.880368i \(0.657296\pi\)
\(110\) 0 0
\(111\) −5.06155 −0.480421
\(112\) 6.71727 0.634722
\(113\) −5.23192 −0.492177 −0.246089 0.969247i \(-0.579145\pi\)
−0.246089 + 0.969247i \(0.579145\pi\)
\(114\) 6.71201 0.628638
\(115\) 0 0
\(116\) 14.8547 1.37922
\(117\) −6.29685 −0.582144
\(118\) 8.67738 0.798818
\(119\) 1.19158 0.109232
\(120\) 0 0
\(121\) 28.5381 2.59437
\(122\) 28.2115 2.55415
\(123\) −5.45650 −0.491996
\(124\) −14.9559 −1.34308
\(125\) 0 0
\(126\) −2.99172 −0.266524
\(127\) 3.50226 0.310775 0.155388 0.987854i \(-0.450337\pi\)
0.155388 + 0.987854i \(0.450337\pi\)
\(128\) −3.33219 −0.294527
\(129\) −8.43177 −0.742376
\(130\) 0 0
\(131\) −13.2883 −1.16100 −0.580500 0.814260i \(-0.697143\pi\)
−0.580500 + 0.814260i \(0.697143\pi\)
\(132\) 35.9593 3.12985
\(133\) 1.59653 0.138437
\(134\) −15.0805 −1.30275
\(135\) 0 0
\(136\) 11.4066 0.978111
\(137\) 9.37803 0.801219 0.400610 0.916249i \(-0.368798\pi\)
0.400610 + 0.916249i \(0.368798\pi\)
\(138\) −28.9731 −2.46636
\(139\) 3.48685 0.295751 0.147875 0.989006i \(-0.452757\pi\)
0.147875 + 0.989006i \(0.452757\pi\)
\(140\) 0 0
\(141\) 5.81000 0.489291
\(142\) 40.9825 3.43917
\(143\) 25.5915 2.14007
\(144\) −13.9578 −1.16315
\(145\) 0 0
\(146\) 4.27683 0.353953
\(147\) −7.76913 −0.640787
\(148\) −19.9237 −1.63771
\(149\) −8.39873 −0.688051 −0.344025 0.938960i \(-0.611791\pi\)
−0.344025 + 0.938960i \(0.611791\pi\)
\(150\) 0 0
\(151\) −6.68837 −0.544292 −0.272146 0.962256i \(-0.587733\pi\)
−0.272146 + 0.962256i \(0.587733\pi\)
\(152\) 15.2832 1.23963
\(153\) −2.47598 −0.200171
\(154\) 12.1589 0.979792
\(155\) 0 0
\(156\) 23.2751 1.86350
\(157\) 11.9755 0.955752 0.477876 0.878427i \(-0.341407\pi\)
0.477876 + 0.878427i \(0.341407\pi\)
\(158\) −29.8171 −2.37213
\(159\) −4.47396 −0.354808
\(160\) 0 0
\(161\) −6.89161 −0.543135
\(162\) −5.10268 −0.400905
\(163\) 13.7742 1.07888 0.539438 0.842025i \(-0.318637\pi\)
0.539438 + 0.842025i \(0.318637\pi\)
\(164\) −21.4783 −1.67717
\(165\) 0 0
\(166\) 12.3217 0.956348
\(167\) −7.34847 −0.568642 −0.284321 0.958729i \(-0.591768\pi\)
−0.284321 + 0.958729i \(0.591768\pi\)
\(168\) 6.39683 0.493526
\(169\) 3.56442 0.274187
\(170\) 0 0
\(171\) −3.31744 −0.253691
\(172\) −33.1897 −2.53069
\(173\) −14.4542 −1.09893 −0.549467 0.835515i \(-0.685169\pi\)
−0.549467 + 0.835515i \(0.685169\pi\)
\(174\) 9.80065 0.742985
\(175\) 0 0
\(176\) 56.7270 4.27596
\(177\) 4.02737 0.302716
\(178\) −20.6550 −1.54816
\(179\) 10.4351 0.779953 0.389976 0.920825i \(-0.372483\pi\)
0.389976 + 0.920825i \(0.372483\pi\)
\(180\) 0 0
\(181\) 25.3704 1.88577 0.942883 0.333125i \(-0.108103\pi\)
0.942883 + 0.333125i \(0.108103\pi\)
\(182\) 7.87000 0.583363
\(183\) 13.0936 0.967908
\(184\) −65.9714 −4.86348
\(185\) 0 0
\(186\) −9.86741 −0.723514
\(187\) 10.0628 0.735867
\(188\) 22.8698 1.66795
\(189\) −4.08093 −0.296844
\(190\) 0 0
\(191\) −16.4111 −1.18747 −0.593733 0.804662i \(-0.702346\pi\)
−0.593733 + 0.804662i \(0.702346\pi\)
\(192\) 6.96916 0.502956
\(193\) 8.05553 0.579850 0.289925 0.957049i \(-0.406370\pi\)
0.289925 + 0.957049i \(0.406370\pi\)
\(194\) 14.2774 1.02506
\(195\) 0 0
\(196\) −30.5814 −2.18439
\(197\) −1.16210 −0.0827963 −0.0413981 0.999143i \(-0.513181\pi\)
−0.0413981 + 0.999143i \(0.513181\pi\)
\(198\) −25.2650 −1.79550
\(199\) −15.8123 −1.12090 −0.560451 0.828188i \(-0.689372\pi\)
−0.560451 + 0.828188i \(0.689372\pi\)
\(200\) 0 0
\(201\) −6.99918 −0.493684
\(202\) −27.0112 −1.90050
\(203\) 2.33120 0.163618
\(204\) 9.15198 0.640767
\(205\) 0 0
\(206\) 44.0102 3.06633
\(207\) 14.3201 0.995314
\(208\) 36.7173 2.54589
\(209\) 13.4827 0.932615
\(210\) 0 0
\(211\) −6.41779 −0.441819 −0.220910 0.975294i \(-0.570903\pi\)
−0.220910 + 0.975294i \(0.570903\pi\)
\(212\) −17.6107 −1.20951
\(213\) 19.0209 1.30329
\(214\) 2.26885 0.155095
\(215\) 0 0
\(216\) −39.0656 −2.65808
\(217\) −2.34708 −0.159330
\(218\) −25.7196 −1.74195
\(219\) 1.98497 0.134132
\(220\) 0 0
\(221\) 6.51329 0.438131
\(222\) −13.1450 −0.882234
\(223\) −15.6352 −1.04701 −0.523506 0.852022i \(-0.675376\pi\)
−0.523506 + 0.852022i \(0.675376\pi\)
\(224\) 6.83075 0.456399
\(225\) 0 0
\(226\) −13.5874 −0.903821
\(227\) 6.01020 0.398911 0.199456 0.979907i \(-0.436083\pi\)
0.199456 + 0.979907i \(0.436083\pi\)
\(228\) 12.2623 0.812088
\(229\) −10.7079 −0.707595 −0.353798 0.935322i \(-0.615110\pi\)
−0.353798 + 0.935322i \(0.615110\pi\)
\(230\) 0 0
\(231\) 5.64322 0.371297
\(232\) 22.3159 1.46511
\(233\) −2.77571 −0.181843 −0.0909214 0.995858i \(-0.528981\pi\)
−0.0909214 + 0.995858i \(0.528981\pi\)
\(234\) −16.3531 −1.06903
\(235\) 0 0
\(236\) 15.8528 1.03193
\(237\) −13.8388 −0.898928
\(238\) 3.09456 0.200590
\(239\) 9.74488 0.630344 0.315172 0.949035i \(-0.397938\pi\)
0.315172 + 0.949035i \(0.397938\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 74.1141 4.76423
\(243\) 14.0743 0.902868
\(244\) 51.5400 3.29951
\(245\) 0 0
\(246\) −14.1707 −0.903489
\(247\) 8.72682 0.555274
\(248\) −22.4680 −1.42672
\(249\) 5.71877 0.362413
\(250\) 0 0
\(251\) 1.47018 0.0927970 0.0463985 0.998923i \(-0.485226\pi\)
0.0463985 + 0.998923i \(0.485226\pi\)
\(252\) −5.46562 −0.344302
\(253\) −58.1993 −3.65896
\(254\) 9.09545 0.570699
\(255\) 0 0
\(256\) −20.2176 −1.26360
\(257\) −19.0717 −1.18966 −0.594829 0.803852i \(-0.702780\pi\)
−0.594829 + 0.803852i \(0.702780\pi\)
\(258\) −21.8975 −1.36328
\(259\) −3.12669 −0.194283
\(260\) 0 0
\(261\) −4.84401 −0.299836
\(262\) −34.5099 −2.13203
\(263\) 11.0150 0.679217 0.339608 0.940567i \(-0.389705\pi\)
0.339608 + 0.940567i \(0.389705\pi\)
\(264\) 54.0210 3.32476
\(265\) 0 0
\(266\) 4.14624 0.254222
\(267\) −9.58644 −0.586681
\(268\) −27.5507 −1.68293
\(269\) −9.48636 −0.578393 −0.289197 0.957270i \(-0.593388\pi\)
−0.289197 + 0.957270i \(0.593388\pi\)
\(270\) 0 0
\(271\) 21.3477 1.29678 0.648390 0.761308i \(-0.275443\pi\)
0.648390 + 0.761308i \(0.275443\pi\)
\(272\) 14.4376 0.875407
\(273\) 3.65264 0.221068
\(274\) 24.3550 1.47134
\(275\) 0 0
\(276\) −52.9314 −3.18609
\(277\) 18.2788 1.09827 0.549135 0.835734i \(-0.314957\pi\)
0.549135 + 0.835734i \(0.314957\pi\)
\(278\) 9.05544 0.543109
\(279\) 4.87701 0.291979
\(280\) 0 0
\(281\) 11.5147 0.686909 0.343454 0.939169i \(-0.388403\pi\)
0.343454 + 0.939169i \(0.388403\pi\)
\(282\) 15.0887 0.898521
\(283\) −25.1735 −1.49641 −0.748205 0.663468i \(-0.769084\pi\)
−0.748205 + 0.663468i \(0.769084\pi\)
\(284\) 74.8714 4.44280
\(285\) 0 0
\(286\) 66.4618 3.92997
\(287\) −3.37066 −0.198964
\(288\) −14.1936 −0.836367
\(289\) −14.4389 −0.849348
\(290\) 0 0
\(291\) 6.62645 0.388449
\(292\) 7.81339 0.457244
\(293\) 0.319785 0.0186820 0.00934102 0.999956i \(-0.497027\pi\)
0.00934102 + 0.999956i \(0.497027\pi\)
\(294\) −20.1766 −1.17673
\(295\) 0 0
\(296\) −29.9310 −1.73970
\(297\) −34.4633 −1.99976
\(298\) −21.8117 −1.26352
\(299\) −37.6702 −2.17853
\(300\) 0 0
\(301\) −5.20859 −0.300218
\(302\) −17.3699 −0.999523
\(303\) −12.5365 −0.720202
\(304\) 19.3442 1.10946
\(305\) 0 0
\(306\) −6.43018 −0.367589
\(307\) 8.24844 0.470763 0.235382 0.971903i \(-0.424366\pi\)
0.235382 + 0.971903i \(0.424366\pi\)
\(308\) 22.2132 1.26572
\(309\) 20.4261 1.16200
\(310\) 0 0
\(311\) −11.0098 −0.624306 −0.312153 0.950032i \(-0.601050\pi\)
−0.312153 + 0.950032i \(0.601050\pi\)
\(312\) 34.9657 1.97955
\(313\) 10.3244 0.583570 0.291785 0.956484i \(-0.405751\pi\)
0.291785 + 0.956484i \(0.405751\pi\)
\(314\) 31.1008 1.75512
\(315\) 0 0
\(316\) −54.4733 −3.06437
\(317\) 29.1691 1.63830 0.819149 0.573581i \(-0.194446\pi\)
0.819149 + 0.573581i \(0.194446\pi\)
\(318\) −11.6190 −0.651560
\(319\) 19.6869 1.10225
\(320\) 0 0
\(321\) 1.05302 0.0587740
\(322\) −17.8977 −0.997398
\(323\) 3.43147 0.190932
\(324\) −9.32216 −0.517898
\(325\) 0 0
\(326\) 35.7719 1.98122
\(327\) −11.9371 −0.660121
\(328\) −32.2664 −1.78162
\(329\) 3.58903 0.197870
\(330\) 0 0
\(331\) 14.3362 0.787988 0.393994 0.919113i \(-0.371093\pi\)
0.393994 + 0.919113i \(0.371093\pi\)
\(332\) 22.5107 1.23543
\(333\) 6.49696 0.356031
\(334\) −19.0842 −1.04424
\(335\) 0 0
\(336\) 8.09658 0.441705
\(337\) −5.47393 −0.298184 −0.149092 0.988823i \(-0.547635\pi\)
−0.149092 + 0.988823i \(0.547635\pi\)
\(338\) 9.25690 0.503509
\(339\) −6.30623 −0.342507
\(340\) 0 0
\(341\) −19.8210 −1.07337
\(342\) −8.61547 −0.465871
\(343\) −10.0113 −0.540559
\(344\) −49.8604 −2.68829
\(345\) 0 0
\(346\) −37.5380 −2.01805
\(347\) 24.3460 1.30696 0.653480 0.756944i \(-0.273309\pi\)
0.653480 + 0.756944i \(0.273309\pi\)
\(348\) 17.9049 0.959805
\(349\) −32.0868 −1.71757 −0.858783 0.512339i \(-0.828779\pi\)
−0.858783 + 0.512339i \(0.828779\pi\)
\(350\) 0 0
\(351\) −22.3068 −1.19065
\(352\) 57.6854 3.07464
\(353\) −13.4079 −0.713631 −0.356816 0.934175i \(-0.616138\pi\)
−0.356816 + 0.934175i \(0.616138\pi\)
\(354\) 10.4592 0.555899
\(355\) 0 0
\(356\) −37.7348 −1.99994
\(357\) 1.43625 0.0760146
\(358\) 27.1001 1.43228
\(359\) 26.1416 1.37970 0.689851 0.723951i \(-0.257676\pi\)
0.689851 + 0.723951i \(0.257676\pi\)
\(360\) 0 0
\(361\) −14.4024 −0.758019
\(362\) 65.8875 3.46297
\(363\) 34.3980 1.80543
\(364\) 14.3778 0.753602
\(365\) 0 0
\(366\) 34.0044 1.77744
\(367\) −4.22872 −0.220737 −0.110369 0.993891i \(-0.535203\pi\)
−0.110369 + 0.993891i \(0.535203\pi\)
\(368\) −83.5012 −4.35280
\(369\) 7.00391 0.364609
\(370\) 0 0
\(371\) −2.76372 −0.143485
\(372\) −18.0269 −0.934652
\(373\) 35.5776 1.84214 0.921070 0.389398i \(-0.127317\pi\)
0.921070 + 0.389398i \(0.127317\pi\)
\(374\) 26.1334 1.35133
\(375\) 0 0
\(376\) 34.3568 1.77182
\(377\) 12.7426 0.656277
\(378\) −10.5983 −0.545117
\(379\) −10.5187 −0.540310 −0.270155 0.962817i \(-0.587075\pi\)
−0.270155 + 0.962817i \(0.587075\pi\)
\(380\) 0 0
\(381\) 4.22140 0.216269
\(382\) −42.6201 −2.18063
\(383\) −14.8054 −0.756519 −0.378260 0.925700i \(-0.623477\pi\)
−0.378260 + 0.925700i \(0.623477\pi\)
\(384\) −4.01641 −0.204962
\(385\) 0 0
\(386\) 20.9204 1.06482
\(387\) 10.8229 0.550160
\(388\) 26.0835 1.32419
\(389\) −8.90749 −0.451628 −0.225814 0.974170i \(-0.572504\pi\)
−0.225814 + 0.974170i \(0.572504\pi\)
\(390\) 0 0
\(391\) −14.8123 −0.749090
\(392\) −45.9419 −2.32042
\(393\) −16.0168 −0.807943
\(394\) −3.01801 −0.152045
\(395\) 0 0
\(396\) −46.1569 −2.31947
\(397\) −32.7082 −1.64158 −0.820789 0.571232i \(-0.806466\pi\)
−0.820789 + 0.571232i \(0.806466\pi\)
\(398\) −41.0648 −2.05839
\(399\) 1.92436 0.0963386
\(400\) 0 0
\(401\) −16.3591 −0.816933 −0.408467 0.912773i \(-0.633936\pi\)
−0.408467 + 0.912773i \(0.633936\pi\)
\(402\) −18.1771 −0.906589
\(403\) −12.8294 −0.639078
\(404\) −49.3470 −2.45511
\(405\) 0 0
\(406\) 6.05419 0.300464
\(407\) −26.4048 −1.30884
\(408\) 13.7489 0.680670
\(409\) −27.1198 −1.34099 −0.670494 0.741915i \(-0.733918\pi\)
−0.670494 + 0.741915i \(0.733918\pi\)
\(410\) 0 0
\(411\) 11.3037 0.557570
\(412\) 80.4028 3.96116
\(413\) 2.48784 0.122419
\(414\) 37.1896 1.82777
\(415\) 0 0
\(416\) 37.3376 1.83063
\(417\) 4.20284 0.205814
\(418\) 35.0148 1.71263
\(419\) −1.69471 −0.0827921 −0.0413960 0.999143i \(-0.513181\pi\)
−0.0413960 + 0.999143i \(0.513181\pi\)
\(420\) 0 0
\(421\) 6.27194 0.305676 0.152838 0.988251i \(-0.451159\pi\)
0.152838 + 0.988251i \(0.451159\pi\)
\(422\) −16.6672 −0.811345
\(423\) −7.45766 −0.362604
\(424\) −26.4563 −1.28483
\(425\) 0 0
\(426\) 49.3977 2.39333
\(427\) 8.08837 0.391424
\(428\) 4.14499 0.200356
\(429\) 30.8464 1.48928
\(430\) 0 0
\(431\) 26.2043 1.26222 0.631108 0.775695i \(-0.282600\pi\)
0.631108 + 0.775695i \(0.282600\pi\)
\(432\) −49.4460 −2.37897
\(433\) 1.61920 0.0778136 0.0389068 0.999243i \(-0.487612\pi\)
0.0389068 + 0.999243i \(0.487612\pi\)
\(434\) −6.09543 −0.292590
\(435\) 0 0
\(436\) −46.9875 −2.25029
\(437\) −19.8462 −0.949374
\(438\) 5.15502 0.246316
\(439\) −35.8451 −1.71080 −0.855398 0.517972i \(-0.826687\pi\)
−0.855398 + 0.517972i \(0.826687\pi\)
\(440\) 0 0
\(441\) 9.97238 0.474875
\(442\) 16.9152 0.804573
\(443\) −19.6847 −0.935250 −0.467625 0.883927i \(-0.654890\pi\)
−0.467625 + 0.883927i \(0.654890\pi\)
\(444\) −24.0147 −1.13969
\(445\) 0 0
\(446\) −40.6051 −1.92271
\(447\) −10.1233 −0.478816
\(448\) 4.30509 0.203396
\(449\) 23.0445 1.08754 0.543769 0.839235i \(-0.316997\pi\)
0.543769 + 0.839235i \(0.316997\pi\)
\(450\) 0 0
\(451\) −28.4651 −1.34037
\(452\) −24.8230 −1.16758
\(453\) −8.06175 −0.378774
\(454\) 15.6086 0.732550
\(455\) 0 0
\(456\) 18.4214 0.862660
\(457\) −9.75545 −0.456341 −0.228170 0.973621i \(-0.573274\pi\)
−0.228170 + 0.973621i \(0.573274\pi\)
\(458\) −27.8086 −1.29941
\(459\) −8.77125 −0.409407
\(460\) 0 0
\(461\) 29.0597 1.35345 0.676724 0.736237i \(-0.263399\pi\)
0.676724 + 0.736237i \(0.263399\pi\)
\(462\) 14.6556 0.681839
\(463\) −34.1246 −1.58591 −0.792953 0.609282i \(-0.791458\pi\)
−0.792953 + 0.609282i \(0.791458\pi\)
\(464\) 28.2457 1.31127
\(465\) 0 0
\(466\) −7.20859 −0.333931
\(467\) 12.0061 0.555577 0.277789 0.960642i \(-0.410399\pi\)
0.277789 + 0.960642i \(0.410399\pi\)
\(468\) −29.8757 −1.38100
\(469\) −4.32363 −0.199647
\(470\) 0 0
\(471\) 14.4346 0.665110
\(472\) 23.8154 1.09619
\(473\) −43.9863 −2.02249
\(474\) −35.9398 −1.65077
\(475\) 0 0
\(476\) 5.65349 0.259127
\(477\) 5.74273 0.262941
\(478\) 25.3077 1.15755
\(479\) 7.47517 0.341549 0.170775 0.985310i \(-0.445373\pi\)
0.170775 + 0.985310i \(0.445373\pi\)
\(480\) 0 0
\(481\) −17.0908 −0.779275
\(482\) 2.59703 0.118291
\(483\) −8.30672 −0.377969
\(484\) 135.400 6.15455
\(485\) 0 0
\(486\) 36.5514 1.65800
\(487\) −21.7985 −0.987783 −0.493891 0.869524i \(-0.664426\pi\)
−0.493891 + 0.869524i \(0.664426\pi\)
\(488\) 77.4277 3.50499
\(489\) 16.6025 0.750793
\(490\) 0 0
\(491\) −12.8909 −0.581758 −0.290879 0.956760i \(-0.593948\pi\)
−0.290879 + 0.956760i \(0.593948\pi\)
\(492\) −25.8886 −1.16715
\(493\) 5.01051 0.225662
\(494\) 22.6638 1.01969
\(495\) 0 0
\(496\) −28.4381 −1.27691
\(497\) 11.7498 0.527053
\(498\) 14.8518 0.665525
\(499\) −24.9744 −1.11801 −0.559004 0.829165i \(-0.688816\pi\)
−0.559004 + 0.829165i \(0.688816\pi\)
\(500\) 0 0
\(501\) −8.85740 −0.395719
\(502\) 3.81810 0.170410
\(503\) −11.1640 −0.497779 −0.248890 0.968532i \(-0.580066\pi\)
−0.248890 + 0.968532i \(0.580066\pi\)
\(504\) −8.21090 −0.365743
\(505\) 0 0
\(506\) −151.145 −6.71922
\(507\) 4.29634 0.190807
\(508\) 16.6166 0.737242
\(509\) 18.6656 0.827337 0.413668 0.910428i \(-0.364247\pi\)
0.413668 + 0.910428i \(0.364247\pi\)
\(510\) 0 0
\(511\) 1.22618 0.0542432
\(512\) −45.8413 −2.02592
\(513\) −11.7521 −0.518870
\(514\) −49.5296 −2.18466
\(515\) 0 0
\(516\) −40.0049 −1.76112
\(517\) 30.3092 1.33300
\(518\) −8.12010 −0.356777
\(519\) −17.4222 −0.764751
\(520\) 0 0
\(521\) −37.9249 −1.66152 −0.830760 0.556631i \(-0.812094\pi\)
−0.830760 + 0.556631i \(0.812094\pi\)
\(522\) −12.5800 −0.550612
\(523\) −23.8400 −1.04245 −0.521225 0.853419i \(-0.674525\pi\)
−0.521225 + 0.853419i \(0.674525\pi\)
\(524\) −63.0467 −2.75421
\(525\) 0 0
\(526\) 28.6063 1.24730
\(527\) −5.04464 −0.219748
\(528\) 68.3753 2.97565
\(529\) 62.6683 2.72471
\(530\) 0 0
\(531\) −5.16949 −0.224337
\(532\) 7.57482 0.328410
\(533\) −18.4244 −0.798049
\(534\) −24.8962 −1.07737
\(535\) 0 0
\(536\) −41.3889 −1.78773
\(537\) 12.5778 0.542771
\(538\) −24.6363 −1.06215
\(539\) −40.5295 −1.74573
\(540\) 0 0
\(541\) 37.7424 1.62267 0.811337 0.584579i \(-0.198740\pi\)
0.811337 + 0.584579i \(0.198740\pi\)
\(542\) 55.4405 2.38137
\(543\) 30.5799 1.31231
\(544\) 14.6815 0.629464
\(545\) 0 0
\(546\) 9.48601 0.405964
\(547\) 22.1817 0.948423 0.474211 0.880411i \(-0.342733\pi\)
0.474211 + 0.880411i \(0.342733\pi\)
\(548\) 44.4944 1.90071
\(549\) −16.8068 −0.717298
\(550\) 0 0
\(551\) 6.71332 0.285997
\(552\) −79.5179 −3.38451
\(553\) −8.54870 −0.363528
\(554\) 47.4706 2.01683
\(555\) 0 0
\(556\) 16.5435 0.701601
\(557\) −4.36041 −0.184757 −0.0923783 0.995724i \(-0.529447\pi\)
−0.0923783 + 0.995724i \(0.529447\pi\)
\(558\) 12.6657 0.536182
\(559\) −28.4707 −1.20418
\(560\) 0 0
\(561\) 12.1291 0.512091
\(562\) 29.9039 1.26142
\(563\) −5.45151 −0.229754 −0.114877 0.993380i \(-0.536647\pi\)
−0.114877 + 0.993380i \(0.536647\pi\)
\(564\) 27.5658 1.16073
\(565\) 0 0
\(566\) −65.3762 −2.74797
\(567\) −1.46296 −0.0614386
\(568\) 112.478 4.71947
\(569\) −17.0647 −0.715388 −0.357694 0.933839i \(-0.616437\pi\)
−0.357694 + 0.933839i \(0.616437\pi\)
\(570\) 0 0
\(571\) −12.7567 −0.533853 −0.266926 0.963717i \(-0.586008\pi\)
−0.266926 + 0.963717i \(0.586008\pi\)
\(572\) 121.420 5.07682
\(573\) −19.7809 −0.826360
\(574\) −8.75370 −0.365372
\(575\) 0 0
\(576\) −8.94555 −0.372731
\(577\) 28.2866 1.17759 0.588794 0.808283i \(-0.299603\pi\)
0.588794 + 0.808283i \(0.299603\pi\)
\(578\) −37.4982 −1.55972
\(579\) 9.70964 0.403519
\(580\) 0 0
\(581\) 3.53268 0.146560
\(582\) 17.2091 0.713339
\(583\) −23.3395 −0.966622
\(584\) 11.7379 0.485718
\(585\) 0 0
\(586\) 0.830490 0.0343072
\(587\) −15.2711 −0.630308 −0.315154 0.949041i \(-0.602056\pi\)
−0.315154 + 0.949041i \(0.602056\pi\)
\(588\) −36.8610 −1.52012
\(589\) −6.75906 −0.278502
\(590\) 0 0
\(591\) −1.40072 −0.0576181
\(592\) −37.8841 −1.55703
\(593\) −14.5819 −0.598808 −0.299404 0.954126i \(-0.596788\pi\)
−0.299404 + 0.954126i \(0.596788\pi\)
\(594\) −89.5021 −3.67231
\(595\) 0 0
\(596\) −39.8481 −1.63224
\(597\) −19.0591 −0.780038
\(598\) −97.8305 −4.00059
\(599\) 24.4860 1.00047 0.500235 0.865890i \(-0.333247\pi\)
0.500235 + 0.865890i \(0.333247\pi\)
\(600\) 0 0
\(601\) 10.0479 0.409863 0.204931 0.978776i \(-0.434303\pi\)
0.204931 + 0.978776i \(0.434303\pi\)
\(602\) −13.5268 −0.551312
\(603\) 8.98408 0.365860
\(604\) −31.7332 −1.29121
\(605\) 0 0
\(606\) −32.5576 −1.32256
\(607\) 5.94024 0.241107 0.120553 0.992707i \(-0.461533\pi\)
0.120553 + 0.992707i \(0.461533\pi\)
\(608\) 19.6710 0.797763
\(609\) 2.80989 0.113862
\(610\) 0 0
\(611\) 19.6180 0.793661
\(612\) −11.7474 −0.474860
\(613\) −15.6857 −0.633539 −0.316769 0.948503i \(-0.602598\pi\)
−0.316769 + 0.948503i \(0.602598\pi\)
\(614\) 21.4214 0.864497
\(615\) 0 0
\(616\) 33.3706 1.34454
\(617\) 6.45067 0.259694 0.129847 0.991534i \(-0.458551\pi\)
0.129847 + 0.991534i \(0.458551\pi\)
\(618\) 53.0471 2.13387
\(619\) −3.10687 −0.124876 −0.0624379 0.998049i \(-0.519888\pi\)
−0.0624379 + 0.998049i \(0.519888\pi\)
\(620\) 0 0
\(621\) 50.7294 2.03570
\(622\) −28.5926 −1.14646
\(623\) −5.92187 −0.237255
\(624\) 44.2568 1.77169
\(625\) 0 0
\(626\) 26.8127 1.07165
\(627\) 16.2512 0.649009
\(628\) 56.8184 2.26730
\(629\) −6.72028 −0.267955
\(630\) 0 0
\(631\) −29.4635 −1.17292 −0.586462 0.809976i \(-0.699480\pi\)
−0.586462 + 0.809976i \(0.699480\pi\)
\(632\) −81.8343 −3.25520
\(633\) −7.73561 −0.307463
\(634\) 75.7528 3.00853
\(635\) 0 0
\(636\) −21.2269 −0.841700
\(637\) −26.2332 −1.03940
\(638\) 51.1274 2.02415
\(639\) −24.4150 −0.965843
\(640\) 0 0
\(641\) −48.1471 −1.90169 −0.950847 0.309660i \(-0.899785\pi\)
−0.950847 + 0.309660i \(0.899785\pi\)
\(642\) 2.73473 0.107931
\(643\) 44.2183 1.74380 0.871899 0.489686i \(-0.162888\pi\)
0.871899 + 0.489686i \(0.162888\pi\)
\(644\) −32.6975 −1.28846
\(645\) 0 0
\(646\) 8.91161 0.350622
\(647\) −45.0000 −1.76913 −0.884566 0.466415i \(-0.845546\pi\)
−0.884566 + 0.466415i \(0.845546\pi\)
\(648\) −14.0045 −0.550149
\(649\) 21.0097 0.824704
\(650\) 0 0
\(651\) −2.82903 −0.110878
\(652\) 65.3521 2.55939
\(653\) 32.3117 1.26445 0.632227 0.774784i \(-0.282141\pi\)
0.632227 + 0.774784i \(0.282141\pi\)
\(654\) −31.0008 −1.21223
\(655\) 0 0
\(656\) −40.8402 −1.59454
\(657\) −2.54789 −0.0994026
\(658\) 9.32081 0.363363
\(659\) 38.4217 1.49670 0.748349 0.663305i \(-0.230847\pi\)
0.748349 + 0.663305i \(0.230847\pi\)
\(660\) 0 0
\(661\) 18.8765 0.734210 0.367105 0.930179i \(-0.380349\pi\)
0.367105 + 0.930179i \(0.380349\pi\)
\(662\) 37.2315 1.44704
\(663\) 7.85072 0.304897
\(664\) 33.8174 1.31237
\(665\) 0 0
\(666\) 16.8728 0.653806
\(667\) −28.9788 −1.12206
\(668\) −34.8651 −1.34897
\(669\) −18.8457 −0.728618
\(670\) 0 0
\(671\) 68.3059 2.63692
\(672\) 8.23336 0.317609
\(673\) 4.88197 0.188186 0.0940931 0.995563i \(-0.470005\pi\)
0.0940931 + 0.995563i \(0.470005\pi\)
\(674\) −14.2159 −0.547577
\(675\) 0 0
\(676\) 16.9116 0.650444
\(677\) 14.1390 0.543405 0.271703 0.962381i \(-0.412413\pi\)
0.271703 + 0.962381i \(0.412413\pi\)
\(678\) −16.3774 −0.628972
\(679\) 4.09338 0.157090
\(680\) 0 0
\(681\) 7.24433 0.277603
\(682\) −51.4757 −1.97111
\(683\) 18.3055 0.700440 0.350220 0.936668i \(-0.386107\pi\)
0.350220 + 0.936668i \(0.386107\pi\)
\(684\) −15.7397 −0.601823
\(685\) 0 0
\(686\) −25.9996 −0.992669
\(687\) −12.9066 −0.492417
\(688\) −63.1091 −2.40601
\(689\) −15.1068 −0.575522
\(690\) 0 0
\(691\) 12.6938 0.482895 0.241448 0.970414i \(-0.422378\pi\)
0.241448 + 0.970414i \(0.422378\pi\)
\(692\) −68.5786 −2.60697
\(693\) −7.24358 −0.275161
\(694\) 63.2271 2.40007
\(695\) 0 0
\(696\) 26.8983 1.01958
\(697\) −7.24465 −0.274411
\(698\) −83.3302 −3.15409
\(699\) −3.34567 −0.126545
\(700\) 0 0
\(701\) 13.7325 0.518670 0.259335 0.965787i \(-0.416497\pi\)
0.259335 + 0.965787i \(0.416497\pi\)
\(702\) −57.9313 −2.18648
\(703\) −9.00415 −0.339598
\(704\) 36.3563 1.37023
\(705\) 0 0
\(706\) −34.8207 −1.31049
\(707\) −7.74421 −0.291251
\(708\) 19.1080 0.718123
\(709\) 37.0563 1.39168 0.695840 0.718197i \(-0.255032\pi\)
0.695840 + 0.718197i \(0.255032\pi\)
\(710\) 0 0
\(711\) 17.7634 0.666178
\(712\) −56.6884 −2.12449
\(713\) 29.1762 1.09266
\(714\) 3.72999 0.139591
\(715\) 0 0
\(716\) 49.5095 1.85026
\(717\) 11.7459 0.438658
\(718\) 67.8905 2.53365
\(719\) −21.7402 −0.810771 −0.405386 0.914146i \(-0.632863\pi\)
−0.405386 + 0.914146i \(0.632863\pi\)
\(720\) 0 0
\(721\) 12.6179 0.469915
\(722\) −37.4033 −1.39201
\(723\) 1.20534 0.0448270
\(724\) 120.371 4.47354
\(725\) 0 0
\(726\) 89.3325 3.31544
\(727\) −22.3166 −0.827679 −0.413839 0.910350i \(-0.635812\pi\)
−0.413839 + 0.910350i \(0.635812\pi\)
\(728\) 21.5995 0.800531
\(729\) 22.8588 0.846621
\(730\) 0 0
\(731\) −11.1949 −0.414060
\(732\) 62.1232 2.29614
\(733\) 45.3568 1.67529 0.837645 0.546215i \(-0.183932\pi\)
0.837645 + 0.546215i \(0.183932\pi\)
\(734\) −10.9821 −0.405356
\(735\) 0 0
\(736\) −84.9118 −3.12989
\(737\) −36.5129 −1.34497
\(738\) 18.1893 0.669558
\(739\) −12.2783 −0.451663 −0.225831 0.974166i \(-0.572510\pi\)
−0.225831 + 0.974166i \(0.572510\pi\)
\(740\) 0 0
\(741\) 10.5188 0.386417
\(742\) −7.17744 −0.263492
\(743\) −23.7224 −0.870291 −0.435146 0.900360i \(-0.643303\pi\)
−0.435146 + 0.900360i \(0.643303\pi\)
\(744\) −27.0815 −0.992856
\(745\) 0 0
\(746\) 92.3960 3.38286
\(747\) −7.34056 −0.268577
\(748\) 47.7435 1.74567
\(749\) 0.650488 0.0237683
\(750\) 0 0
\(751\) 18.8204 0.686765 0.343383 0.939196i \(-0.388427\pi\)
0.343383 + 0.939196i \(0.388427\pi\)
\(752\) 43.4860 1.58577
\(753\) 1.77207 0.0645777
\(754\) 33.0928 1.20517
\(755\) 0 0
\(756\) −19.3621 −0.704194
\(757\) −20.4755 −0.744195 −0.372098 0.928194i \(-0.621361\pi\)
−0.372098 + 0.928194i \(0.621361\pi\)
\(758\) −27.3173 −0.992210
\(759\) −70.1499 −2.54628
\(760\) 0 0
\(761\) 6.54100 0.237111 0.118555 0.992947i \(-0.462174\pi\)
0.118555 + 0.992947i \(0.462174\pi\)
\(762\) 10.9631 0.397151
\(763\) −7.37392 −0.266954
\(764\) −77.8632 −2.81699
\(765\) 0 0
\(766\) −38.4499 −1.38925
\(767\) 13.5988 0.491024
\(768\) −24.3691 −0.879343
\(769\) −10.7564 −0.387885 −0.193942 0.981013i \(-0.562127\pi\)
−0.193942 + 0.981013i \(0.562127\pi\)
\(770\) 0 0
\(771\) −22.9878 −0.827886
\(772\) 38.2198 1.37556
\(773\) 24.6229 0.885624 0.442812 0.896614i \(-0.353981\pi\)
0.442812 + 0.896614i \(0.353981\pi\)
\(774\) 28.1074 1.01030
\(775\) 0 0
\(776\) 39.1848 1.40665
\(777\) −3.76872 −0.135202
\(778\) −23.1330 −0.829357
\(779\) −9.70673 −0.347780
\(780\) 0 0
\(781\) 99.2269 3.55062
\(782\) −38.4679 −1.37561
\(783\) −17.1601 −0.613250
\(784\) −58.1495 −2.07677
\(785\) 0 0
\(786\) −41.5961 −1.48369
\(787\) 10.1240 0.360883 0.180441 0.983586i \(-0.442247\pi\)
0.180441 + 0.983586i \(0.442247\pi\)
\(788\) −5.51363 −0.196415
\(789\) 13.2769 0.472669
\(790\) 0 0
\(791\) −3.89557 −0.138511
\(792\) −69.3407 −2.46392
\(793\) 44.2119 1.57001
\(794\) −84.9440 −3.01455
\(795\) 0 0
\(796\) −75.0219 −2.65908
\(797\) 8.60700 0.304876 0.152438 0.988313i \(-0.451288\pi\)
0.152438 + 0.988313i \(0.451288\pi\)
\(798\) 4.99762 0.176914
\(799\) 7.71400 0.272902
\(800\) 0 0
\(801\) 12.3051 0.434778
\(802\) −42.4849 −1.50020
\(803\) 10.3551 0.365423
\(804\) −33.2079 −1.17115
\(805\) 0 0
\(806\) −33.3183 −1.17359
\(807\) −11.4343 −0.402505
\(808\) −74.1332 −2.60800
\(809\) 23.7331 0.834411 0.417205 0.908812i \(-0.363010\pi\)
0.417205 + 0.908812i \(0.363010\pi\)
\(810\) 0 0
\(811\) 35.1374 1.23384 0.616920 0.787026i \(-0.288380\pi\)
0.616920 + 0.787026i \(0.288380\pi\)
\(812\) 11.0605 0.388147
\(813\) 25.7312 0.902432
\(814\) −68.5739 −2.40351
\(815\) 0 0
\(816\) 17.4022 0.609198
\(817\) −14.9995 −0.524767
\(818\) −70.4308 −2.46256
\(819\) −4.68850 −0.163829
\(820\) 0 0
\(821\) 18.3525 0.640508 0.320254 0.947332i \(-0.396232\pi\)
0.320254 + 0.947332i \(0.396232\pi\)
\(822\) 29.3560 1.02391
\(823\) 0.411745 0.0143525 0.00717626 0.999974i \(-0.497716\pi\)
0.00717626 + 0.999974i \(0.497716\pi\)
\(824\) 120.788 4.20784
\(825\) 0 0
\(826\) 6.46099 0.224807
\(827\) 10.9496 0.380756 0.190378 0.981711i \(-0.439029\pi\)
0.190378 + 0.981711i \(0.439029\pi\)
\(828\) 67.9422 2.36115
\(829\) 6.76398 0.234923 0.117461 0.993077i \(-0.462524\pi\)
0.117461 + 0.993077i \(0.462524\pi\)
\(830\) 0 0
\(831\) 22.0322 0.764288
\(832\) 23.5321 0.815827
\(833\) −10.3152 −0.357399
\(834\) 10.9149 0.377951
\(835\) 0 0
\(836\) 63.9690 2.21241
\(837\) 17.2770 0.597179
\(838\) −4.40121 −0.152037
\(839\) 3.28222 0.113315 0.0566574 0.998394i \(-0.481956\pi\)
0.0566574 + 0.998394i \(0.481956\pi\)
\(840\) 0 0
\(841\) −19.1974 −0.661981
\(842\) 16.2884 0.561335
\(843\) 13.8791 0.478021
\(844\) −30.4495 −1.04811
\(845\) 0 0
\(846\) −19.3677 −0.665876
\(847\) 21.2488 0.730118
\(848\) −33.4862 −1.14992
\(849\) −30.3426 −1.04136
\(850\) 0 0
\(851\) 38.8674 1.33236
\(852\) 90.2454 3.09175
\(853\) 36.1823 1.23886 0.619429 0.785053i \(-0.287364\pi\)
0.619429 + 0.785053i \(0.287364\pi\)
\(854\) 21.0057 0.718800
\(855\) 0 0
\(856\) 6.22694 0.212832
\(857\) 25.4700 0.870037 0.435019 0.900421i \(-0.356742\pi\)
0.435019 + 0.900421i \(0.356742\pi\)
\(858\) 80.1089 2.73487
\(859\) 3.88904 0.132692 0.0663461 0.997797i \(-0.478866\pi\)
0.0663461 + 0.997797i \(0.478866\pi\)
\(860\) 0 0
\(861\) −4.06279 −0.138459
\(862\) 68.0532 2.31790
\(863\) 4.43810 0.151075 0.0755373 0.997143i \(-0.475933\pi\)
0.0755373 + 0.997143i \(0.475933\pi\)
\(864\) −50.2814 −1.71061
\(865\) 0 0
\(866\) 4.20509 0.142895
\(867\) −17.4038 −0.591063
\(868\) −11.1358 −0.377975
\(869\) −72.1934 −2.44899
\(870\) 0 0
\(871\) −23.6334 −0.800788
\(872\) −70.5885 −2.39043
\(873\) −8.50564 −0.287872
\(874\) −51.5411 −1.74341
\(875\) 0 0
\(876\) 9.41778 0.318197
\(877\) −29.5579 −0.998101 −0.499050 0.866573i \(-0.666318\pi\)
−0.499050 + 0.866573i \(0.666318\pi\)
\(878\) −93.0907 −3.14166
\(879\) 0.385449 0.0130009
\(880\) 0 0
\(881\) −48.9852 −1.65035 −0.825177 0.564874i \(-0.808925\pi\)
−0.825177 + 0.564874i \(0.808925\pi\)
\(882\) 25.8985 0.872048
\(883\) −10.8101 −0.363790 −0.181895 0.983318i \(-0.558223\pi\)
−0.181895 + 0.983318i \(0.558223\pi\)
\(884\) 30.9026 1.03937
\(885\) 0 0
\(886\) −51.1218 −1.71747
\(887\) 13.9186 0.467340 0.233670 0.972316i \(-0.424926\pi\)
0.233670 + 0.972316i \(0.424926\pi\)
\(888\) −36.0769 −1.21066
\(889\) 2.60770 0.0874596
\(890\) 0 0
\(891\) −12.3546 −0.413896
\(892\) −74.1819 −2.48379
\(893\) 10.3356 0.345867
\(894\) −26.2905 −0.879286
\(895\) 0 0
\(896\) −2.48107 −0.0828869
\(897\) −45.4054 −1.51604
\(898\) 59.8472 1.99713
\(899\) −9.86933 −0.329161
\(900\) 0 0
\(901\) −5.94012 −0.197894
\(902\) −73.9246 −2.46142
\(903\) −6.27811 −0.208922
\(904\) −37.2912 −1.24029
\(905\) 0 0
\(906\) −20.9366 −0.695571
\(907\) 45.3560 1.50602 0.753011 0.658008i \(-0.228601\pi\)
0.753011 + 0.658008i \(0.228601\pi\)
\(908\) 28.5156 0.946325
\(909\) 16.0917 0.533728
\(910\) 0 0
\(911\) 3.51366 0.116413 0.0582064 0.998305i \(-0.481462\pi\)
0.0582064 + 0.998305i \(0.481462\pi\)
\(912\) 23.3163 0.772079
\(913\) 29.8333 0.987339
\(914\) −25.3352 −0.838013
\(915\) 0 0
\(916\) −50.8039 −1.67861
\(917\) −9.89414 −0.326733
\(918\) −22.7791 −0.751824
\(919\) 22.3344 0.736743 0.368372 0.929679i \(-0.379915\pi\)
0.368372 + 0.929679i \(0.379915\pi\)
\(920\) 0 0
\(921\) 9.94216 0.327605
\(922\) 75.4689 2.48544
\(923\) 64.2259 2.11402
\(924\) 26.7745 0.880816
\(925\) 0 0
\(926\) −88.6226 −2.91232
\(927\) −26.2187 −0.861137
\(928\) 28.7229 0.942874
\(929\) 18.1496 0.595470 0.297735 0.954648i \(-0.403769\pi\)
0.297735 + 0.954648i \(0.403769\pi\)
\(930\) 0 0
\(931\) −13.8207 −0.452956
\(932\) −13.1695 −0.431380
\(933\) −13.2705 −0.434456
\(934\) 31.1802 1.02025
\(935\) 0 0
\(936\) −44.8817 −1.46700
\(937\) −50.6507 −1.65469 −0.827343 0.561696i \(-0.810149\pi\)
−0.827343 + 0.561696i \(0.810149\pi\)
\(938\) −11.2286 −0.366626
\(939\) 12.4444 0.406107
\(940\) 0 0
\(941\) 44.9519 1.46539 0.732695 0.680558i \(-0.238262\pi\)
0.732695 + 0.680558i \(0.238262\pi\)
\(942\) 37.4869 1.22139
\(943\) 41.9001 1.36446
\(944\) 30.1436 0.981090
\(945\) 0 0
\(946\) −114.234 −3.71405
\(947\) −18.5204 −0.601832 −0.300916 0.953651i \(-0.597292\pi\)
−0.300916 + 0.953651i \(0.597292\pi\)
\(948\) −65.6588 −2.13250
\(949\) 6.70245 0.217571
\(950\) 0 0
\(951\) 35.1586 1.14010
\(952\) 8.49313 0.275264
\(953\) −4.77064 −0.154536 −0.0772681 0.997010i \(-0.524620\pi\)
−0.0772681 + 0.997010i \(0.524620\pi\)
\(954\) 14.9140 0.482859
\(955\) 0 0
\(956\) 46.2350 1.49535
\(957\) 23.7294 0.767062
\(958\) 19.4132 0.627212
\(959\) 6.98268 0.225482
\(960\) 0 0
\(961\) −21.0634 −0.679465
\(962\) −44.3853 −1.43104
\(963\) −1.35165 −0.0435563
\(964\) 4.74454 0.152811
\(965\) 0 0
\(966\) −21.5727 −0.694092
\(967\) 42.9853 1.38231 0.691157 0.722705i \(-0.257102\pi\)
0.691157 + 0.722705i \(0.257102\pi\)
\(968\) 203.409 6.53781
\(969\) 4.13608 0.132870
\(970\) 0 0
\(971\) 38.4332 1.23338 0.616690 0.787206i \(-0.288473\pi\)
0.616690 + 0.787206i \(0.288473\pi\)
\(972\) 66.7762 2.14185
\(973\) 2.59623 0.0832314
\(974\) −56.6112 −1.81394
\(975\) 0 0
\(976\) 98.0016 3.13695
\(977\) −11.7197 −0.374948 −0.187474 0.982270i \(-0.560030\pi\)
−0.187474 + 0.982270i \(0.560030\pi\)
\(978\) 43.1172 1.37874
\(979\) −50.0099 −1.59832
\(980\) 0 0
\(981\) 15.3223 0.489203
\(982\) −33.4780 −1.06832
\(983\) 24.4745 0.780615 0.390307 0.920685i \(-0.372369\pi\)
0.390307 + 0.920685i \(0.372369\pi\)
\(984\) −38.8920 −1.23983
\(985\) 0 0
\(986\) 13.0124 0.414400
\(987\) 4.32600 0.137698
\(988\) 41.4047 1.31726
\(989\) 64.7470 2.05884
\(990\) 0 0
\(991\) 22.7385 0.722313 0.361156 0.932505i \(-0.382382\pi\)
0.361156 + 0.932505i \(0.382382\pi\)
\(992\) −28.9185 −0.918164
\(993\) 17.2800 0.548363
\(994\) 30.5146 0.967866
\(995\) 0 0
\(996\) 27.1329 0.859740
\(997\) −51.7206 −1.63801 −0.819005 0.573787i \(-0.805474\pi\)
−0.819005 + 0.573787i \(0.805474\pi\)
\(998\) −64.8592 −2.05308
\(999\) 23.0157 0.728184
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 \(a_p\))