Properties

Label 4005.2.a.l.1.4
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 0
Dimension 4
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.725.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.09529\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.39026 q^{2} +3.71333 q^{4} +1.00000 q^{5} +1.95452 q^{7} +4.09529 q^{8} +O(q^{10})\) \(q+2.39026 q^{2} +3.71333 q^{4} +1.00000 q^{5} +1.95452 q^{7} +4.09529 q^{8} +2.39026 q^{10} +4.29496 q^{11} +1.05377 q^{13} +4.67180 q^{14} +2.36215 q^{16} -3.65443 q^{17} -3.07792 q^{19} +3.71333 q^{20} +10.2661 q^{22} +1.46385 q^{23} +1.00000 q^{25} +2.51878 q^{26} +7.25777 q^{28} +8.44007 q^{29} +4.24040 q^{31} -2.54445 q^{32} -8.73503 q^{34} +1.95452 q^{35} -4.61163 q^{37} -7.35702 q^{38} +4.09529 q^{40} -0.785638 q^{41} -3.60895 q^{43} +15.9486 q^{44} +3.49897 q^{46} +10.8220 q^{47} -3.17985 q^{49} +2.39026 q^{50} +3.91300 q^{52} +9.07035 q^{53} +4.29496 q^{55} +8.00433 q^{56} +20.1739 q^{58} +5.36459 q^{59} -5.59950 q^{61} +10.1356 q^{62} -10.8062 q^{64} +1.05377 q^{65} -7.92129 q^{67} -13.5701 q^{68} +4.67180 q^{70} -10.0621 q^{71} +2.47330 q^{73} -11.0230 q^{74} -11.4293 q^{76} +8.39459 q^{77} -11.6532 q^{79} +2.36215 q^{80} -1.87788 q^{82} -12.5329 q^{83} -3.65443 q^{85} -8.62632 q^{86} +17.5891 q^{88} +1.00000 q^{89} +2.05962 q^{91} +5.43574 q^{92} +25.8674 q^{94} -3.07792 q^{95} +5.96756 q^{97} -7.60066 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} + 3q^{4} + 4q^{5} + 2q^{7} + 9q^{8} + O(q^{10}) \) \( 4q - q^{2} + 3q^{4} + 4q^{5} + 2q^{7} + 9q^{8} - q^{10} + 14q^{11} - 5q^{13} + 5q^{14} - 3q^{16} + 3q^{17} - q^{19} + 3q^{20} + 2q^{22} + 3q^{23} + 4q^{25} + 9q^{26} + 5q^{28} + 10q^{29} - 11q^{31} + 2q^{32} - 8q^{34} + 2q^{35} + 3q^{37} - 2q^{38} + 9q^{40} + 3q^{41} + 9q^{43} + 9q^{44} - 4q^{46} + 24q^{47} - q^{50} + 8q^{52} - 3q^{53} + 14q^{55} + 13q^{56} + 19q^{58} + 22q^{59} - 3q^{61} + 24q^{62} - 11q^{64} - 5q^{65} - 9q^{67} - 31q^{68} + 5q^{70} - 16q^{71} + 3q^{73} - 31q^{74} - 24q^{76} + 4q^{77} - 27q^{79} - 3q^{80} - 15q^{82} - 6q^{83} + 3q^{85} - 15q^{86} + 30q^{88} + 4q^{89} - 29q^{91} + 17q^{92} + 13q^{94} - q^{95} + 41q^{97} - 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.39026 1.69017 0.845083 0.534634i \(-0.179551\pi\)
0.845083 + 0.534634i \(0.179551\pi\)
\(3\) 0 0
\(4\) 3.71333 1.85666
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.95452 0.738739 0.369370 0.929283i \(-0.379574\pi\)
0.369370 + 0.929283i \(0.379574\pi\)
\(8\) 4.09529 1.44791
\(9\) 0 0
\(10\) 2.39026 0.755866
\(11\) 4.29496 1.29498 0.647490 0.762074i \(-0.275819\pi\)
0.647490 + 0.762074i \(0.275819\pi\)
\(12\) 0 0
\(13\) 1.05377 0.292263 0.146132 0.989265i \(-0.453318\pi\)
0.146132 + 0.989265i \(0.453318\pi\)
\(14\) 4.67180 1.24859
\(15\) 0 0
\(16\) 2.36215 0.590537
\(17\) −3.65443 −0.886330 −0.443165 0.896440i \(-0.646144\pi\)
−0.443165 + 0.896440i \(0.646144\pi\)
\(18\) 0 0
\(19\) −3.07792 −0.706124 −0.353062 0.935600i \(-0.614859\pi\)
−0.353062 + 0.935600i \(0.614859\pi\)
\(20\) 3.71333 0.830325
\(21\) 0 0
\(22\) 10.2661 2.18873
\(23\) 1.46385 0.305233 0.152616 0.988286i \(-0.451230\pi\)
0.152616 + 0.988286i \(0.451230\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 2.51878 0.493974
\(27\) 0 0
\(28\) 7.25777 1.37159
\(29\) 8.44007 1.56728 0.783641 0.621214i \(-0.213360\pi\)
0.783641 + 0.621214i \(0.213360\pi\)
\(30\) 0 0
\(31\) 4.24040 0.761599 0.380799 0.924658i \(-0.375649\pi\)
0.380799 + 0.924658i \(0.375649\pi\)
\(32\) −2.54445 −0.449799
\(33\) 0 0
\(34\) −8.73503 −1.49805
\(35\) 1.95452 0.330374
\(36\) 0 0
\(37\) −4.61163 −0.758148 −0.379074 0.925366i \(-0.623757\pi\)
−0.379074 + 0.925366i \(0.623757\pi\)
\(38\) −7.35702 −1.19347
\(39\) 0 0
\(40\) 4.09529 0.647523
\(41\) −0.785638 −0.122696 −0.0613480 0.998116i \(-0.519540\pi\)
−0.0613480 + 0.998116i \(0.519540\pi\)
\(42\) 0 0
\(43\) −3.60895 −0.550360 −0.275180 0.961393i \(-0.588737\pi\)
−0.275180 + 0.961393i \(0.588737\pi\)
\(44\) 15.9486 2.40434
\(45\) 0 0
\(46\) 3.49897 0.515894
\(47\) 10.8220 1.57856 0.789278 0.614036i \(-0.210455\pi\)
0.789278 + 0.614036i \(0.210455\pi\)
\(48\) 0 0
\(49\) −3.17985 −0.454265
\(50\) 2.39026 0.338033
\(51\) 0 0
\(52\) 3.91300 0.542635
\(53\) 9.07035 1.24591 0.622954 0.782258i \(-0.285932\pi\)
0.622954 + 0.782258i \(0.285932\pi\)
\(54\) 0 0
\(55\) 4.29496 0.579133
\(56\) 8.00433 1.06962
\(57\) 0 0
\(58\) 20.1739 2.64897
\(59\) 5.36459 0.698411 0.349205 0.937046i \(-0.386452\pi\)
0.349205 + 0.937046i \(0.386452\pi\)
\(60\) 0 0
\(61\) −5.59950 −0.716942 −0.358471 0.933541i \(-0.616702\pi\)
−0.358471 + 0.933541i \(0.616702\pi\)
\(62\) 10.1356 1.28723
\(63\) 0 0
\(64\) −10.8062 −1.35077
\(65\) 1.05377 0.130704
\(66\) 0 0
\(67\) −7.92129 −0.967739 −0.483870 0.875140i \(-0.660769\pi\)
−0.483870 + 0.875140i \(0.660769\pi\)
\(68\) −13.5701 −1.64562
\(69\) 0 0
\(70\) 4.67180 0.558387
\(71\) −10.0621 −1.19415 −0.597074 0.802187i \(-0.703670\pi\)
−0.597074 + 0.802187i \(0.703670\pi\)
\(72\) 0 0
\(73\) 2.47330 0.289478 0.144739 0.989470i \(-0.453766\pi\)
0.144739 + 0.989470i \(0.453766\pi\)
\(74\) −11.0230 −1.28140
\(75\) 0 0
\(76\) −11.4293 −1.31103
\(77\) 8.39459 0.956652
\(78\) 0 0
\(79\) −11.6532 −1.31108 −0.655541 0.755159i \(-0.727559\pi\)
−0.655541 + 0.755159i \(0.727559\pi\)
\(80\) 2.36215 0.264096
\(81\) 0 0
\(82\) −1.87788 −0.207377
\(83\) −12.5329 −1.37567 −0.687833 0.725869i \(-0.741438\pi\)
−0.687833 + 0.725869i \(0.741438\pi\)
\(84\) 0 0
\(85\) −3.65443 −0.396379
\(86\) −8.62632 −0.930201
\(87\) 0 0
\(88\) 17.5891 1.87501
\(89\) 1.00000 0.106000
\(90\) 0 0
\(91\) 2.05962 0.215906
\(92\) 5.43574 0.566715
\(93\) 0 0
\(94\) 25.8674 2.66802
\(95\) −3.07792 −0.315788
\(96\) 0 0
\(97\) 5.96756 0.605914 0.302957 0.953004i \(-0.402026\pi\)
0.302957 + 0.953004i \(0.402026\pi\)
\(98\) −7.60066 −0.767783
\(99\) 0 0
\(100\) 3.71333 0.371333
\(101\) −6.15863 −0.612807 −0.306403 0.951902i \(-0.599126\pi\)
−0.306403 + 0.951902i \(0.599126\pi\)
\(102\) 0 0
\(103\) 15.0166 1.47963 0.739814 0.672812i \(-0.234914\pi\)
0.739814 + 0.672812i \(0.234914\pi\)
\(104\) 4.31550 0.423170
\(105\) 0 0
\(106\) 21.6805 2.10579
\(107\) −2.68955 −0.260009 −0.130004 0.991513i \(-0.541499\pi\)
−0.130004 + 0.991513i \(0.541499\pi\)
\(108\) 0 0
\(109\) −0.671805 −0.0643472 −0.0321736 0.999482i \(-0.510243\pi\)
−0.0321736 + 0.999482i \(0.510243\pi\)
\(110\) 10.2661 0.978831
\(111\) 0 0
\(112\) 4.61687 0.436253
\(113\) 8.72825 0.821085 0.410543 0.911841i \(-0.365339\pi\)
0.410543 + 0.911841i \(0.365339\pi\)
\(114\) 0 0
\(115\) 1.46385 0.136504
\(116\) 31.3408 2.90992
\(117\) 0 0
\(118\) 12.8228 1.18043
\(119\) −7.14266 −0.654767
\(120\) 0 0
\(121\) 7.44671 0.676973
\(122\) −13.3842 −1.21175
\(123\) 0 0
\(124\) 15.7460 1.41403
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −4.55006 −0.403752 −0.201876 0.979411i \(-0.564704\pi\)
−0.201876 + 0.979411i \(0.564704\pi\)
\(128\) −20.7406 −1.83323
\(129\) 0 0
\(130\) 2.51878 0.220912
\(131\) 9.12736 0.797461 0.398731 0.917068i \(-0.369451\pi\)
0.398731 + 0.917068i \(0.369451\pi\)
\(132\) 0 0
\(133\) −6.01586 −0.521641
\(134\) −18.9339 −1.63564
\(135\) 0 0
\(136\) −14.9660 −1.28332
\(137\) −16.8521 −1.43978 −0.719888 0.694090i \(-0.755807\pi\)
−0.719888 + 0.694090i \(0.755807\pi\)
\(138\) 0 0
\(139\) 3.20205 0.271594 0.135797 0.990737i \(-0.456641\pi\)
0.135797 + 0.990737i \(0.456641\pi\)
\(140\) 7.25777 0.613394
\(141\) 0 0
\(142\) −24.0509 −2.01831
\(143\) 4.52591 0.378475
\(144\) 0 0
\(145\) 8.44007 0.700910
\(146\) 5.91183 0.489267
\(147\) 0 0
\(148\) −17.1245 −1.40763
\(149\) −14.6448 −1.19975 −0.599874 0.800094i \(-0.704783\pi\)
−0.599874 + 0.800094i \(0.704783\pi\)
\(150\) 0 0
\(151\) −17.8411 −1.45189 −0.725943 0.687755i \(-0.758596\pi\)
−0.725943 + 0.687755i \(0.758596\pi\)
\(152\) −12.6050 −1.02240
\(153\) 0 0
\(154\) 20.0652 1.61690
\(155\) 4.24040 0.340597
\(156\) 0 0
\(157\) 15.4767 1.23518 0.617588 0.786502i \(-0.288110\pi\)
0.617588 + 0.786502i \(0.288110\pi\)
\(158\) −27.8540 −2.21595
\(159\) 0 0
\(160\) −2.54445 −0.201156
\(161\) 2.86111 0.225487
\(162\) 0 0
\(163\) −2.39177 −0.187338 −0.0936689 0.995603i \(-0.529860\pi\)
−0.0936689 + 0.995603i \(0.529860\pi\)
\(164\) −2.91733 −0.227805
\(165\) 0 0
\(166\) −29.9569 −2.32511
\(167\) −0.644864 −0.0499011 −0.0249505 0.999689i \(-0.507943\pi\)
−0.0249505 + 0.999689i \(0.507943\pi\)
\(168\) 0 0
\(169\) −11.8896 −0.914582
\(170\) −8.73503 −0.669947
\(171\) 0 0
\(172\) −13.4012 −1.02183
\(173\) 19.2152 1.46091 0.730453 0.682963i \(-0.239309\pi\)
0.730453 + 0.682963i \(0.239309\pi\)
\(174\) 0 0
\(175\) 1.95452 0.147748
\(176\) 10.1453 0.764734
\(177\) 0 0
\(178\) 2.39026 0.179157
\(179\) 14.9898 1.12039 0.560193 0.828362i \(-0.310727\pi\)
0.560193 + 0.828362i \(0.310727\pi\)
\(180\) 0 0
\(181\) 23.1716 1.72233 0.861167 0.508322i \(-0.169734\pi\)
0.861167 + 0.508322i \(0.169734\pi\)
\(182\) 4.92301 0.364918
\(183\) 0 0
\(184\) 5.99488 0.441948
\(185\) −4.61163 −0.339054
\(186\) 0 0
\(187\) −15.6957 −1.14778
\(188\) 40.1858 2.93085
\(189\) 0 0
\(190\) −7.35702 −0.533735
\(191\) −0.390024 −0.0282211 −0.0141106 0.999900i \(-0.504492\pi\)
−0.0141106 + 0.999900i \(0.504492\pi\)
\(192\) 0 0
\(193\) 9.91428 0.713645 0.356823 0.934172i \(-0.383860\pi\)
0.356823 + 0.934172i \(0.383860\pi\)
\(194\) 14.2640 1.02410
\(195\) 0 0
\(196\) −11.8078 −0.843417
\(197\) 1.01097 0.0720286 0.0360143 0.999351i \(-0.488534\pi\)
0.0360143 + 0.999351i \(0.488534\pi\)
\(198\) 0 0
\(199\) −13.3504 −0.946384 −0.473192 0.880959i \(-0.656898\pi\)
−0.473192 + 0.880959i \(0.656898\pi\)
\(200\) 4.09529 0.289581
\(201\) 0 0
\(202\) −14.7207 −1.03575
\(203\) 16.4963 1.15781
\(204\) 0 0
\(205\) −0.785638 −0.0548713
\(206\) 35.8935 2.50082
\(207\) 0 0
\(208\) 2.48916 0.172592
\(209\) −13.2196 −0.914416
\(210\) 0 0
\(211\) −25.4818 −1.75424 −0.877118 0.480274i \(-0.840537\pi\)
−0.877118 + 0.480274i \(0.840537\pi\)
\(212\) 33.6812 2.31323
\(213\) 0 0
\(214\) −6.42872 −0.439459
\(215\) −3.60895 −0.246129
\(216\) 0 0
\(217\) 8.28795 0.562623
\(218\) −1.60579 −0.108758
\(219\) 0 0
\(220\) 15.9486 1.07525
\(221\) −3.85094 −0.259042
\(222\) 0 0
\(223\) 20.3456 1.36244 0.681222 0.732076i \(-0.261449\pi\)
0.681222 + 0.732076i \(0.261449\pi\)
\(224\) −4.97317 −0.332284
\(225\) 0 0
\(226\) 20.8628 1.38777
\(227\) −16.0605 −1.06597 −0.532986 0.846124i \(-0.678930\pi\)
−0.532986 + 0.846124i \(0.678930\pi\)
\(228\) 0 0
\(229\) 15.2661 1.00881 0.504405 0.863467i \(-0.331712\pi\)
0.504405 + 0.863467i \(0.331712\pi\)
\(230\) 3.49897 0.230715
\(231\) 0 0
\(232\) 34.5646 2.26928
\(233\) −18.5117 −1.21274 −0.606371 0.795182i \(-0.707375\pi\)
−0.606371 + 0.795182i \(0.707375\pi\)
\(234\) 0 0
\(235\) 10.8220 0.705952
\(236\) 19.9205 1.29671
\(237\) 0 0
\(238\) −17.0728 −1.10667
\(239\) 27.6511 1.78860 0.894300 0.447468i \(-0.147674\pi\)
0.894300 + 0.447468i \(0.147674\pi\)
\(240\) 0 0
\(241\) 27.2269 1.75384 0.876920 0.480636i \(-0.159594\pi\)
0.876920 + 0.480636i \(0.159594\pi\)
\(242\) 17.7995 1.14420
\(243\) 0 0
\(244\) −20.7928 −1.33112
\(245\) −3.17985 −0.203153
\(246\) 0 0
\(247\) −3.24342 −0.206374
\(248\) 17.3657 1.10272
\(249\) 0 0
\(250\) 2.39026 0.151173
\(251\) −12.9645 −0.818310 −0.409155 0.912465i \(-0.634176\pi\)
−0.409155 + 0.912465i \(0.634176\pi\)
\(252\) 0 0
\(253\) 6.28716 0.395270
\(254\) −10.8758 −0.682409
\(255\) 0 0
\(256\) −27.9631 −1.74769
\(257\) −18.9552 −1.18240 −0.591198 0.806527i \(-0.701345\pi\)
−0.591198 + 0.806527i \(0.701345\pi\)
\(258\) 0 0
\(259\) −9.01353 −0.560073
\(260\) 3.91300 0.242674
\(261\) 0 0
\(262\) 21.8167 1.34784
\(263\) 16.4109 1.01194 0.505971 0.862551i \(-0.331134\pi\)
0.505971 + 0.862551i \(0.331134\pi\)
\(264\) 0 0
\(265\) 9.07035 0.557187
\(266\) −14.3795 −0.881661
\(267\) 0 0
\(268\) −29.4143 −1.79677
\(269\) −28.9069 −1.76248 −0.881242 0.472664i \(-0.843292\pi\)
−0.881242 + 0.472664i \(0.843292\pi\)
\(270\) 0 0
\(271\) 6.39573 0.388513 0.194256 0.980951i \(-0.437771\pi\)
0.194256 + 0.980951i \(0.437771\pi\)
\(272\) −8.63231 −0.523411
\(273\) 0 0
\(274\) −40.2810 −2.43346
\(275\) 4.29496 0.258996
\(276\) 0 0
\(277\) −2.90811 −0.174731 −0.0873656 0.996176i \(-0.527845\pi\)
−0.0873656 + 0.996176i \(0.527845\pi\)
\(278\) 7.65371 0.459039
\(279\) 0 0
\(280\) 8.00433 0.478350
\(281\) 6.27691 0.374449 0.187225 0.982317i \(-0.440051\pi\)
0.187225 + 0.982317i \(0.440051\pi\)
\(282\) 0 0
\(283\) 11.8814 0.706277 0.353139 0.935571i \(-0.385114\pi\)
0.353139 + 0.935571i \(0.385114\pi\)
\(284\) −37.3637 −2.21713
\(285\) 0 0
\(286\) 10.8181 0.639686
\(287\) −1.53554 −0.0906403
\(288\) 0 0
\(289\) −3.64512 −0.214419
\(290\) 20.1739 1.18465
\(291\) 0 0
\(292\) 9.18419 0.537464
\(293\) 15.4163 0.900630 0.450315 0.892870i \(-0.351312\pi\)
0.450315 + 0.892870i \(0.351312\pi\)
\(294\) 0 0
\(295\) 5.36459 0.312339
\(296\) −18.8860 −1.09773
\(297\) 0 0
\(298\) −35.0048 −2.02777
\(299\) 1.54256 0.0892084
\(300\) 0 0
\(301\) −7.05377 −0.406573
\(302\) −42.6447 −2.45393
\(303\) 0 0
\(304\) −7.27051 −0.416992
\(305\) −5.59950 −0.320626
\(306\) 0 0
\(307\) −13.1695 −0.751623 −0.375811 0.926696i \(-0.622636\pi\)
−0.375811 + 0.926696i \(0.622636\pi\)
\(308\) 31.1719 1.77618
\(309\) 0 0
\(310\) 10.1356 0.575666
\(311\) −13.6116 −0.771841 −0.385920 0.922532i \(-0.626116\pi\)
−0.385920 + 0.922532i \(0.626116\pi\)
\(312\) 0 0
\(313\) −20.0023 −1.13059 −0.565297 0.824887i \(-0.691239\pi\)
−0.565297 + 0.824887i \(0.691239\pi\)
\(314\) 36.9933 2.08765
\(315\) 0 0
\(316\) −43.2720 −2.43424
\(317\) −17.9215 −1.00657 −0.503286 0.864120i \(-0.667876\pi\)
−0.503286 + 0.864120i \(0.667876\pi\)
\(318\) 0 0
\(319\) 36.2498 2.02960
\(320\) −10.8062 −0.604084
\(321\) 0 0
\(322\) 6.83880 0.381111
\(323\) 11.2481 0.625859
\(324\) 0 0
\(325\) 1.05377 0.0584527
\(326\) −5.71694 −0.316632
\(327\) 0 0
\(328\) −3.21742 −0.177652
\(329\) 21.1519 1.16614
\(330\) 0 0
\(331\) −20.2646 −1.11384 −0.556920 0.830566i \(-0.688017\pi\)
−0.556920 + 0.830566i \(0.688017\pi\)
\(332\) −46.5388 −2.55415
\(333\) 0 0
\(334\) −1.54139 −0.0843411
\(335\) −7.92129 −0.432786
\(336\) 0 0
\(337\) −16.1392 −0.879158 −0.439579 0.898204i \(-0.644872\pi\)
−0.439579 + 0.898204i \(0.644872\pi\)
\(338\) −28.4191 −1.54580
\(339\) 0 0
\(340\) −13.5701 −0.735942
\(341\) 18.2124 0.986255
\(342\) 0 0
\(343\) −19.8967 −1.07432
\(344\) −14.7797 −0.796869
\(345\) 0 0
\(346\) 45.9293 2.46918
\(347\) −14.3396 −0.769789 −0.384895 0.922961i \(-0.625762\pi\)
−0.384895 + 0.922961i \(0.625762\pi\)
\(348\) 0 0
\(349\) −31.8954 −1.70732 −0.853660 0.520830i \(-0.825622\pi\)
−0.853660 + 0.520830i \(0.825622\pi\)
\(350\) 4.67180 0.249718
\(351\) 0 0
\(352\) −10.9283 −0.582480
\(353\) −2.46050 −0.130959 −0.0654796 0.997854i \(-0.520858\pi\)
−0.0654796 + 0.997854i \(0.520858\pi\)
\(354\) 0 0
\(355\) −10.0621 −0.534039
\(356\) 3.71333 0.196806
\(357\) 0 0
\(358\) 35.8294 1.89364
\(359\) −4.79276 −0.252952 −0.126476 0.991970i \(-0.540367\pi\)
−0.126476 + 0.991970i \(0.540367\pi\)
\(360\) 0 0
\(361\) −9.52640 −0.501389
\(362\) 55.3862 2.91103
\(363\) 0 0
\(364\) 7.64803 0.400866
\(365\) 2.47330 0.129459
\(366\) 0 0
\(367\) −23.3647 −1.21963 −0.609813 0.792545i \(-0.708755\pi\)
−0.609813 + 0.792545i \(0.708755\pi\)
\(368\) 3.45782 0.180251
\(369\) 0 0
\(370\) −11.0230 −0.573058
\(371\) 17.7282 0.920402
\(372\) 0 0
\(373\) 23.7500 1.22973 0.614863 0.788634i \(-0.289211\pi\)
0.614863 + 0.788634i \(0.289211\pi\)
\(374\) −37.5166 −1.93994
\(375\) 0 0
\(376\) 44.3194 2.28560
\(377\) 8.89390 0.458059
\(378\) 0 0
\(379\) −27.7001 −1.42286 −0.711429 0.702758i \(-0.751952\pi\)
−0.711429 + 0.702758i \(0.751952\pi\)
\(380\) −11.4293 −0.586312
\(381\) 0 0
\(382\) −0.932257 −0.0476984
\(383\) −6.03526 −0.308388 −0.154194 0.988041i \(-0.549278\pi\)
−0.154194 + 0.988041i \(0.549278\pi\)
\(384\) 0 0
\(385\) 8.39459 0.427828
\(386\) 23.6977 1.20618
\(387\) 0 0
\(388\) 22.1595 1.12498
\(389\) −8.53031 −0.432504 −0.216252 0.976338i \(-0.569383\pi\)
−0.216252 + 0.976338i \(0.569383\pi\)
\(390\) 0 0
\(391\) −5.34952 −0.270537
\(392\) −13.0224 −0.657732
\(393\) 0 0
\(394\) 2.41648 0.121740
\(395\) −11.6532 −0.586334
\(396\) 0 0
\(397\) −14.6163 −0.733572 −0.366786 0.930305i \(-0.619542\pi\)
−0.366786 + 0.930305i \(0.619542\pi\)
\(398\) −31.9109 −1.59955
\(399\) 0 0
\(400\) 2.36215 0.118107
\(401\) −17.2987 −0.863858 −0.431929 0.901908i \(-0.642167\pi\)
−0.431929 + 0.901908i \(0.642167\pi\)
\(402\) 0 0
\(403\) 4.46841 0.222587
\(404\) −22.8690 −1.13778
\(405\) 0 0
\(406\) 39.4304 1.95690
\(407\) −19.8068 −0.981786
\(408\) 0 0
\(409\) −2.78264 −0.137592 −0.0687962 0.997631i \(-0.521916\pi\)
−0.0687962 + 0.997631i \(0.521916\pi\)
\(410\) −1.87788 −0.0927417
\(411\) 0 0
\(412\) 55.7615 2.74717
\(413\) 10.4852 0.515943
\(414\) 0 0
\(415\) −12.5329 −0.615217
\(416\) −2.68126 −0.131460
\(417\) 0 0
\(418\) −31.5981 −1.54552
\(419\) 4.20691 0.205521 0.102761 0.994706i \(-0.467232\pi\)
0.102761 + 0.994706i \(0.467232\pi\)
\(420\) 0 0
\(421\) 19.0766 0.929737 0.464869 0.885380i \(-0.346102\pi\)
0.464869 + 0.885380i \(0.346102\pi\)
\(422\) −60.9079 −2.96495
\(423\) 0 0
\(424\) 37.1458 1.80396
\(425\) −3.65443 −0.177266
\(426\) 0 0
\(427\) −10.9443 −0.529633
\(428\) −9.98720 −0.482749
\(429\) 0 0
\(430\) −8.62632 −0.415998
\(431\) 4.11651 0.198285 0.0991427 0.995073i \(-0.468390\pi\)
0.0991427 + 0.995073i \(0.468390\pi\)
\(432\) 0 0
\(433\) −34.4248 −1.65435 −0.827176 0.561943i \(-0.810054\pi\)
−0.827176 + 0.561943i \(0.810054\pi\)
\(434\) 19.8103 0.950926
\(435\) 0 0
\(436\) −2.49463 −0.119471
\(437\) −4.50560 −0.215532
\(438\) 0 0
\(439\) 15.1883 0.724896 0.362448 0.932004i \(-0.381941\pi\)
0.362448 + 0.932004i \(0.381941\pi\)
\(440\) 17.5891 0.838529
\(441\) 0 0
\(442\) −9.20472 −0.437824
\(443\) −2.14752 −0.102032 −0.0510159 0.998698i \(-0.516246\pi\)
−0.0510159 + 0.998698i \(0.516246\pi\)
\(444\) 0 0
\(445\) 1.00000 0.0474045
\(446\) 48.6313 2.30276
\(447\) 0 0
\(448\) −21.1209 −0.997868
\(449\) −32.5132 −1.53439 −0.767197 0.641411i \(-0.778349\pi\)
−0.767197 + 0.641411i \(0.778349\pi\)
\(450\) 0 0
\(451\) −3.37429 −0.158889
\(452\) 32.4109 1.52448
\(453\) 0 0
\(454\) −38.3887 −1.80167
\(455\) 2.05962 0.0965563
\(456\) 0 0
\(457\) −15.9654 −0.746831 −0.373415 0.927664i \(-0.621813\pi\)
−0.373415 + 0.927664i \(0.621813\pi\)
\(458\) 36.4898 1.70506
\(459\) 0 0
\(460\) 5.43574 0.253443
\(461\) 0.406983 0.0189551 0.00947754 0.999955i \(-0.496983\pi\)
0.00947754 + 0.999955i \(0.496983\pi\)
\(462\) 0 0
\(463\) 28.6219 1.33017 0.665087 0.746766i \(-0.268395\pi\)
0.665087 + 0.746766i \(0.268395\pi\)
\(464\) 19.9367 0.925538
\(465\) 0 0
\(466\) −44.2477 −2.04974
\(467\) 38.5772 1.78514 0.892571 0.450907i \(-0.148900\pi\)
0.892571 + 0.450907i \(0.148900\pi\)
\(468\) 0 0
\(469\) −15.4823 −0.714907
\(470\) 25.8674 1.19318
\(471\) 0 0
\(472\) 21.9696 1.01123
\(473\) −15.5003 −0.712705
\(474\) 0 0
\(475\) −3.07792 −0.141225
\(476\) −26.5230 −1.21568
\(477\) 0 0
\(478\) 66.0932 3.02303
\(479\) 14.1350 0.645843 0.322922 0.946426i \(-0.395335\pi\)
0.322922 + 0.946426i \(0.395335\pi\)
\(480\) 0 0
\(481\) −4.85960 −0.221579
\(482\) 65.0793 2.96428
\(483\) 0 0
\(484\) 27.6521 1.25691
\(485\) 5.96756 0.270973
\(486\) 0 0
\(487\) −12.5869 −0.570369 −0.285184 0.958473i \(-0.592055\pi\)
−0.285184 + 0.958473i \(0.592055\pi\)
\(488\) −22.9316 −1.03806
\(489\) 0 0
\(490\) −7.60066 −0.343363
\(491\) 13.4541 0.607174 0.303587 0.952804i \(-0.401816\pi\)
0.303587 + 0.952804i \(0.401816\pi\)
\(492\) 0 0
\(493\) −30.8437 −1.38913
\(494\) −7.75262 −0.348807
\(495\) 0 0
\(496\) 10.0165 0.449752
\(497\) −19.6665 −0.882163
\(498\) 0 0
\(499\) 17.5343 0.784945 0.392472 0.919764i \(-0.371620\pi\)
0.392472 + 0.919764i \(0.371620\pi\)
\(500\) 3.71333 0.166065
\(501\) 0 0
\(502\) −30.9884 −1.38308
\(503\) 32.4398 1.44642 0.723209 0.690629i \(-0.242666\pi\)
0.723209 + 0.690629i \(0.242666\pi\)
\(504\) 0 0
\(505\) −6.15863 −0.274056
\(506\) 15.0279 0.668073
\(507\) 0 0
\(508\) −16.8959 −0.749632
\(509\) −37.9507 −1.68214 −0.841068 0.540929i \(-0.818073\pi\)
−0.841068 + 0.540929i \(0.818073\pi\)
\(510\) 0 0
\(511\) 4.83412 0.213849
\(512\) −25.3577 −1.12066
\(513\) 0 0
\(514\) −45.3079 −1.99845
\(515\) 15.0166 0.661710
\(516\) 0 0
\(517\) 46.4802 2.04420
\(518\) −21.5446 −0.946617
\(519\) 0 0
\(520\) 4.31550 0.189247
\(521\) 12.0211 0.526656 0.263328 0.964706i \(-0.415180\pi\)
0.263328 + 0.964706i \(0.415180\pi\)
\(522\) 0 0
\(523\) −23.7443 −1.03826 −0.519132 0.854694i \(-0.673745\pi\)
−0.519132 + 0.854694i \(0.673745\pi\)
\(524\) 33.8929 1.48062
\(525\) 0 0
\(526\) 39.2264 1.71035
\(527\) −15.4963 −0.675028
\(528\) 0 0
\(529\) −20.8572 −0.906833
\(530\) 21.6805 0.941740
\(531\) 0 0
\(532\) −22.3389 −0.968513
\(533\) −0.827882 −0.0358596
\(534\) 0 0
\(535\) −2.68955 −0.116280
\(536\) −32.4400 −1.40119
\(537\) 0 0
\(538\) −69.0949 −2.97889
\(539\) −13.6573 −0.588263
\(540\) 0 0
\(541\) 3.22247 0.138545 0.0692725 0.997598i \(-0.477932\pi\)
0.0692725 + 0.997598i \(0.477932\pi\)
\(542\) 15.2874 0.656651
\(543\) 0 0
\(544\) 9.29851 0.398670
\(545\) −0.671805 −0.0287770
\(546\) 0 0
\(547\) −0.363571 −0.0155452 −0.00777259 0.999970i \(-0.502474\pi\)
−0.00777259 + 0.999970i \(0.502474\pi\)
\(548\) −62.5775 −2.67318
\(549\) 0 0
\(550\) 10.2661 0.437746
\(551\) −25.9779 −1.10669
\(552\) 0 0
\(553\) −22.7763 −0.968548
\(554\) −6.95112 −0.295325
\(555\) 0 0
\(556\) 11.8902 0.504259
\(557\) 10.6808 0.452561 0.226280 0.974062i \(-0.427343\pi\)
0.226280 + 0.974062i \(0.427343\pi\)
\(558\) 0 0
\(559\) −3.80301 −0.160850
\(560\) 4.61687 0.195098
\(561\) 0 0
\(562\) 15.0034 0.632882
\(563\) 16.3376 0.688549 0.344274 0.938869i \(-0.388125\pi\)
0.344274 + 0.938869i \(0.388125\pi\)
\(564\) 0 0
\(565\) 8.72825 0.367200
\(566\) 28.3996 1.19373
\(567\) 0 0
\(568\) −41.2071 −1.72901
\(569\) 40.6357 1.70354 0.851768 0.523919i \(-0.175530\pi\)
0.851768 + 0.523919i \(0.175530\pi\)
\(570\) 0 0
\(571\) −38.8677 −1.62656 −0.813281 0.581871i \(-0.802321\pi\)
−0.813281 + 0.581871i \(0.802321\pi\)
\(572\) 16.8062 0.702702
\(573\) 0 0
\(574\) −3.67035 −0.153197
\(575\) 1.46385 0.0610466
\(576\) 0 0
\(577\) −29.1209 −1.21232 −0.606158 0.795344i \(-0.707290\pi\)
−0.606158 + 0.795344i \(0.707290\pi\)
\(578\) −8.71277 −0.362403
\(579\) 0 0
\(580\) 31.3408 1.30135
\(581\) −24.4958 −1.01626
\(582\) 0 0
\(583\) 38.9568 1.61343
\(584\) 10.1289 0.419137
\(585\) 0 0
\(586\) 36.8489 1.52221
\(587\) 11.3820 0.469787 0.234894 0.972021i \(-0.424526\pi\)
0.234894 + 0.972021i \(0.424526\pi\)
\(588\) 0 0
\(589\) −13.0516 −0.537783
\(590\) 12.8228 0.527905
\(591\) 0 0
\(592\) −10.8934 −0.447714
\(593\) 5.10274 0.209544 0.104772 0.994496i \(-0.466589\pi\)
0.104772 + 0.994496i \(0.466589\pi\)
\(594\) 0 0
\(595\) −7.14266 −0.292821
\(596\) −54.3809 −2.22753
\(597\) 0 0
\(598\) 3.68711 0.150777
\(599\) −22.6299 −0.924631 −0.462316 0.886715i \(-0.652981\pi\)
−0.462316 + 0.886715i \(0.652981\pi\)
\(600\) 0 0
\(601\) 27.2940 1.11335 0.556673 0.830732i \(-0.312078\pi\)
0.556673 + 0.830732i \(0.312078\pi\)
\(602\) −16.8603 −0.687176
\(603\) 0 0
\(604\) −66.2497 −2.69566
\(605\) 7.44671 0.302752
\(606\) 0 0
\(607\) 34.1969 1.38801 0.694004 0.719971i \(-0.255845\pi\)
0.694004 + 0.719971i \(0.255845\pi\)
\(608\) 7.83161 0.317614
\(609\) 0 0
\(610\) −13.3842 −0.541912
\(611\) 11.4039 0.461354
\(612\) 0 0
\(613\) 24.2886 0.981009 0.490504 0.871439i \(-0.336813\pi\)
0.490504 + 0.871439i \(0.336813\pi\)
\(614\) −31.4785 −1.27037
\(615\) 0 0
\(616\) 34.3783 1.38514
\(617\) −31.9292 −1.28542 −0.642711 0.766109i \(-0.722190\pi\)
−0.642711 + 0.766109i \(0.722190\pi\)
\(618\) 0 0
\(619\) −29.1111 −1.17007 −0.585037 0.811007i \(-0.698920\pi\)
−0.585037 + 0.811007i \(0.698920\pi\)
\(620\) 15.7460 0.632375
\(621\) 0 0
\(622\) −32.5351 −1.30454
\(623\) 1.95452 0.0783062
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −47.8106 −1.91089
\(627\) 0 0
\(628\) 57.4701 2.29331
\(629\) 16.8529 0.671969
\(630\) 0 0
\(631\) 26.7634 1.06543 0.532717 0.846293i \(-0.321171\pi\)
0.532717 + 0.846293i \(0.321171\pi\)
\(632\) −47.7231 −1.89832
\(633\) 0 0
\(634\) −42.8370 −1.70128
\(635\) −4.55006 −0.180564
\(636\) 0 0
\(637\) −3.35084 −0.132765
\(638\) 86.6463 3.43036
\(639\) 0 0
\(640\) −20.7406 −0.819846
\(641\) 16.4357 0.649173 0.324586 0.945856i \(-0.394775\pi\)
0.324586 + 0.945856i \(0.394775\pi\)
\(642\) 0 0
\(643\) −28.2642 −1.11463 −0.557316 0.830300i \(-0.688169\pi\)
−0.557316 + 0.830300i \(0.688169\pi\)
\(644\) 10.6243 0.418654
\(645\) 0 0
\(646\) 26.8858 1.05781
\(647\) −16.9725 −0.667258 −0.333629 0.942704i \(-0.608273\pi\)
−0.333629 + 0.942704i \(0.608273\pi\)
\(648\) 0 0
\(649\) 23.0407 0.904428
\(650\) 2.51878 0.0987948
\(651\) 0 0
\(652\) −8.88142 −0.347823
\(653\) 39.2631 1.53648 0.768242 0.640160i \(-0.221132\pi\)
0.768242 + 0.640160i \(0.221132\pi\)
\(654\) 0 0
\(655\) 9.12736 0.356635
\(656\) −1.85579 −0.0724566
\(657\) 0 0
\(658\) 50.5584 1.97097
\(659\) −3.77282 −0.146968 −0.0734841 0.997296i \(-0.523412\pi\)
−0.0734841 + 0.997296i \(0.523412\pi\)
\(660\) 0 0
\(661\) 1.17732 0.0457923 0.0228962 0.999738i \(-0.492711\pi\)
0.0228962 + 0.999738i \(0.492711\pi\)
\(662\) −48.4375 −1.88258
\(663\) 0 0
\(664\) −51.3260 −1.99183
\(665\) −6.01586 −0.233285
\(666\) 0 0
\(667\) 12.3550 0.478386
\(668\) −2.39459 −0.0926495
\(669\) 0 0
\(670\) −18.9339 −0.731481
\(671\) −24.0496 −0.928425
\(672\) 0 0
\(673\) 45.6233 1.75865 0.879324 0.476224i \(-0.157995\pi\)
0.879324 + 0.476224i \(0.157995\pi\)
\(674\) −38.5768 −1.48592
\(675\) 0 0
\(676\) −44.1499 −1.69807
\(677\) 43.1019 1.65654 0.828270 0.560329i \(-0.189325\pi\)
0.828270 + 0.560329i \(0.189325\pi\)
\(678\) 0 0
\(679\) 11.6637 0.447612
\(680\) −14.9660 −0.573919
\(681\) 0 0
\(682\) 43.5322 1.66694
\(683\) −24.1509 −0.924108 −0.462054 0.886852i \(-0.652887\pi\)
−0.462054 + 0.886852i \(0.652887\pi\)
\(684\) 0 0
\(685\) −16.8521 −0.643887
\(686\) −47.5583 −1.81578
\(687\) 0 0
\(688\) −8.52488 −0.325008
\(689\) 9.55807 0.364134
\(690\) 0 0
\(691\) −31.4456 −1.19625 −0.598124 0.801404i \(-0.704087\pi\)
−0.598124 + 0.801404i \(0.704087\pi\)
\(692\) 71.3524 2.71241
\(693\) 0 0
\(694\) −34.2753 −1.30107
\(695\) 3.20205 0.121461
\(696\) 0 0
\(697\) 2.87106 0.108749
\(698\) −76.2381 −2.88566
\(699\) 0 0
\(700\) 7.25777 0.274318
\(701\) 45.2299 1.70831 0.854155 0.520019i \(-0.174075\pi\)
0.854155 + 0.520019i \(0.174075\pi\)
\(702\) 0 0
\(703\) 14.1942 0.535346
\(704\) −46.4121 −1.74922
\(705\) 0 0
\(706\) −5.88122 −0.221343
\(707\) −12.0372 −0.452705
\(708\) 0 0
\(709\) 11.5007 0.431919 0.215960 0.976402i \(-0.430712\pi\)
0.215960 + 0.976402i \(0.430712\pi\)
\(710\) −24.0509 −0.902615
\(711\) 0 0
\(712\) 4.09529 0.153478
\(713\) 6.20729 0.232465
\(714\) 0 0
\(715\) 4.52591 0.169259
\(716\) 55.6619 2.08018
\(717\) 0 0
\(718\) −11.4559 −0.427532
\(719\) 51.2805 1.91244 0.956220 0.292648i \(-0.0945365\pi\)
0.956220 + 0.292648i \(0.0945365\pi\)
\(720\) 0 0
\(721\) 29.3502 1.09306
\(722\) −22.7705 −0.847431
\(723\) 0 0
\(724\) 86.0439 3.19780
\(725\) 8.44007 0.313456
\(726\) 0 0
\(727\) 36.9416 1.37009 0.685044 0.728502i \(-0.259783\pi\)
0.685044 + 0.728502i \(0.259783\pi\)
\(728\) 8.43473 0.312612
\(729\) 0 0
\(730\) 5.91183 0.218807
\(731\) 13.1887 0.487801
\(732\) 0 0
\(733\) 14.0425 0.518673 0.259337 0.965787i \(-0.416496\pi\)
0.259337 + 0.965787i \(0.416496\pi\)
\(734\) −55.8476 −2.06137
\(735\) 0 0
\(736\) −3.72467 −0.137293
\(737\) −34.0216 −1.25320
\(738\) 0 0
\(739\) −18.4116 −0.677282 −0.338641 0.940916i \(-0.609967\pi\)
−0.338641 + 0.940916i \(0.609967\pi\)
\(740\) −17.1245 −0.629509
\(741\) 0 0
\(742\) 42.3749 1.55563
\(743\) 20.0671 0.736191 0.368096 0.929788i \(-0.380010\pi\)
0.368096 + 0.929788i \(0.380010\pi\)
\(744\) 0 0
\(745\) −14.6448 −0.536544
\(746\) 56.7685 2.07844
\(747\) 0 0
\(748\) −58.2831 −2.13104
\(749\) −5.25679 −0.192079
\(750\) 0 0
\(751\) −17.5280 −0.639607 −0.319803 0.947484i \(-0.603617\pi\)
−0.319803 + 0.947484i \(0.603617\pi\)
\(752\) 25.5633 0.932196
\(753\) 0 0
\(754\) 21.2587 0.774196
\(755\) −17.8411 −0.649303
\(756\) 0 0
\(757\) 21.0316 0.764406 0.382203 0.924078i \(-0.375166\pi\)
0.382203 + 0.924078i \(0.375166\pi\)
\(758\) −66.2103 −2.40487
\(759\) 0 0
\(760\) −12.6050 −0.457231
\(761\) 37.2035 1.34863 0.674313 0.738445i \(-0.264440\pi\)
0.674313 + 0.738445i \(0.264440\pi\)
\(762\) 0 0
\(763\) −1.31306 −0.0475358
\(764\) −1.44829 −0.0523972
\(765\) 0 0
\(766\) −14.4258 −0.521227
\(767\) 5.65305 0.204120
\(768\) 0 0
\(769\) −15.2246 −0.549013 −0.274507 0.961585i \(-0.588515\pi\)
−0.274507 + 0.961585i \(0.588515\pi\)
\(770\) 20.0652 0.723101
\(771\) 0 0
\(772\) 36.8150 1.32500
\(773\) −26.7520 −0.962202 −0.481101 0.876665i \(-0.659763\pi\)
−0.481101 + 0.876665i \(0.659763\pi\)
\(774\) 0 0
\(775\) 4.24040 0.152320
\(776\) 24.4389 0.877306
\(777\) 0 0
\(778\) −20.3896 −0.731004
\(779\) 2.41813 0.0866386
\(780\) 0 0
\(781\) −43.2162 −1.54640
\(782\) −12.7867 −0.457253
\(783\) 0 0
\(784\) −7.51128 −0.268260
\(785\) 15.4767 0.552387
\(786\) 0 0
\(787\) 28.4808 1.01523 0.507615 0.861584i \(-0.330527\pi\)
0.507615 + 0.861584i \(0.330527\pi\)
\(788\) 3.75406 0.133733
\(789\) 0 0
\(790\) −27.8540 −0.991002
\(791\) 17.0595 0.606568
\(792\) 0 0
\(793\) −5.90058 −0.209536
\(794\) −34.9367 −1.23986
\(795\) 0 0
\(796\) −49.5744 −1.75712
\(797\) −44.0413 −1.56002 −0.780012 0.625764i \(-0.784787\pi\)
−0.780012 + 0.625764i \(0.784787\pi\)
\(798\) 0 0
\(799\) −39.5484 −1.39912
\(800\) −2.54445 −0.0899597
\(801\) 0 0
\(802\) −41.3484 −1.46006
\(803\) 10.6227 0.374869
\(804\) 0 0
\(805\) 2.86111 0.100841
\(806\) 10.6807 0.376210
\(807\) 0 0
\(808\) −25.2214 −0.887286
\(809\) 30.2316 1.06289 0.531444 0.847094i \(-0.321650\pi\)
0.531444 + 0.847094i \(0.321650\pi\)
\(810\) 0 0
\(811\) −34.5210 −1.21220 −0.606099 0.795389i \(-0.707266\pi\)
−0.606099 + 0.795389i \(0.707266\pi\)
\(812\) 61.2561 2.14967
\(813\) 0 0
\(814\) −47.3433 −1.65938
\(815\) −2.39177 −0.0837800
\(816\) 0 0
\(817\) 11.1081 0.388622
\(818\) −6.65121 −0.232554
\(819\) 0 0
\(820\) −2.91733 −0.101878
\(821\) −35.2307 −1.22956 −0.614780 0.788698i \(-0.710755\pi\)
−0.614780 + 0.788698i \(0.710755\pi\)
\(822\) 0 0
\(823\) −40.5379 −1.41306 −0.706532 0.707681i \(-0.749741\pi\)
−0.706532 + 0.707681i \(0.749741\pi\)
\(824\) 61.4973 2.14236
\(825\) 0 0
\(826\) 25.0623 0.872030
\(827\) 30.0036 1.04333 0.521664 0.853151i \(-0.325312\pi\)
0.521664 + 0.853151i \(0.325312\pi\)
\(828\) 0 0
\(829\) 11.3949 0.395761 0.197881 0.980226i \(-0.436594\pi\)
0.197881 + 0.980226i \(0.436594\pi\)
\(830\) −29.9569 −1.03982
\(831\) 0 0
\(832\) −11.3872 −0.394781
\(833\) 11.6206 0.402628
\(834\) 0 0
\(835\) −0.644864 −0.0223164
\(836\) −49.0886 −1.69776
\(837\) 0 0
\(838\) 10.0556 0.347365
\(839\) −38.3055 −1.32245 −0.661226 0.750187i \(-0.729963\pi\)
−0.661226 + 0.750187i \(0.729963\pi\)
\(840\) 0 0
\(841\) 42.2348 1.45637
\(842\) 45.5980 1.57141
\(843\) 0 0
\(844\) −94.6221 −3.25703
\(845\) −11.8896 −0.409014
\(846\) 0 0
\(847\) 14.5547 0.500107
\(848\) 21.4255 0.735755
\(849\) 0 0
\(850\) −8.73503 −0.299609
\(851\) −6.75071 −0.231412
\(852\) 0 0
\(853\) −5.70914 −0.195477 −0.0977386 0.995212i \(-0.531161\pi\)
−0.0977386 + 0.995212i \(0.531161\pi\)
\(854\) −26.1597 −0.895168
\(855\) 0 0
\(856\) −11.0145 −0.376468
\(857\) 18.5138 0.632419 0.316210 0.948689i \(-0.397590\pi\)
0.316210 + 0.948689i \(0.397590\pi\)
\(858\) 0 0
\(859\) 36.1682 1.23404 0.617021 0.786947i \(-0.288339\pi\)
0.617021 + 0.786947i \(0.288339\pi\)
\(860\) −13.4012 −0.456978
\(861\) 0 0
\(862\) 9.83952 0.335135
\(863\) 48.1408 1.63873 0.819366 0.573271i \(-0.194326\pi\)
0.819366 + 0.573271i \(0.194326\pi\)
\(864\) 0 0
\(865\) 19.2152 0.653337
\(866\) −82.2842 −2.79613
\(867\) 0 0
\(868\) 30.7759 1.04460
\(869\) −50.0499 −1.69783
\(870\) 0 0
\(871\) −8.34722 −0.282835
\(872\) −2.75124 −0.0931687
\(873\) 0 0
\(874\) −10.7695 −0.364285
\(875\) 1.95452 0.0660748
\(876\) 0 0
\(877\) 16.7949 0.567122 0.283561 0.958954i \(-0.408484\pi\)
0.283561 + 0.958954i \(0.408484\pi\)
\(878\) 36.3038 1.22519
\(879\) 0 0
\(880\) 10.1453 0.341999
\(881\) −10.4309 −0.351425 −0.175713 0.984442i \(-0.556223\pi\)
−0.175713 + 0.984442i \(0.556223\pi\)
\(882\) 0 0
\(883\) 29.5575 0.994690 0.497345 0.867553i \(-0.334308\pi\)
0.497345 + 0.867553i \(0.334308\pi\)
\(884\) −14.2998 −0.480954
\(885\) 0 0
\(886\) −5.13313 −0.172451
\(887\) −30.1297 −1.01166 −0.505828 0.862634i \(-0.668813\pi\)
−0.505828 + 0.862634i \(0.668813\pi\)
\(888\) 0 0
\(889\) −8.89318 −0.298268
\(890\) 2.39026 0.0801216
\(891\) 0 0
\(892\) 75.5500 2.52960
\(893\) −33.3094 −1.11466
\(894\) 0 0
\(895\) 14.9898 0.501052
\(896\) −40.5380 −1.35428
\(897\) 0 0
\(898\) −77.7150 −2.59338
\(899\) 35.7893 1.19364
\(900\) 0 0
\(901\) −33.1470 −1.10429
\(902\) −8.06541 −0.268549
\(903\) 0 0
\(904\) 35.7448 1.18885
\(905\) 23.1716 0.770251
\(906\) 0 0
\(907\) 34.4041 1.14237 0.571185 0.820821i \(-0.306484\pi\)
0.571185 + 0.820821i \(0.306484\pi\)
\(908\) −59.6378 −1.97915
\(909\) 0 0
\(910\) 4.92301 0.163196
\(911\) 48.0626 1.59239 0.796193 0.605043i \(-0.206844\pi\)
0.796193 + 0.605043i \(0.206844\pi\)
\(912\) 0 0
\(913\) −53.8284 −1.78146
\(914\) −38.1615 −1.26227
\(915\) 0 0
\(916\) 56.6879 1.87302
\(917\) 17.8396 0.589116
\(918\) 0 0
\(919\) 9.64985 0.318319 0.159160 0.987253i \(-0.449122\pi\)
0.159160 + 0.987253i \(0.449122\pi\)
\(920\) 5.99488 0.197645
\(921\) 0 0
\(922\) 0.972793 0.0320372
\(923\) −10.6031 −0.349006
\(924\) 0 0
\(925\) −4.61163 −0.151630
\(926\) 68.4137 2.24822
\(927\) 0 0
\(928\) −21.4753 −0.704961
\(929\) 4.87453 0.159928 0.0799641 0.996798i \(-0.474519\pi\)
0.0799641 + 0.996798i \(0.474519\pi\)
\(930\) 0 0
\(931\) 9.78734 0.320767
\(932\) −68.7400 −2.25165
\(933\) 0 0
\(934\) 92.2095 3.01719
\(935\) −15.6957 −0.513303
\(936\) 0 0
\(937\) 6.79035 0.221831 0.110916 0.993830i \(-0.464622\pi\)
0.110916 + 0.993830i \(0.464622\pi\)
\(938\) −37.0067 −1.20831
\(939\) 0 0
\(940\) 40.1858 1.31072
\(941\) 26.9378 0.878147 0.439074 0.898451i \(-0.355307\pi\)
0.439074 + 0.898451i \(0.355307\pi\)
\(942\) 0 0
\(943\) −1.15005 −0.0374508
\(944\) 12.6720 0.412437
\(945\) 0 0
\(946\) −37.0497 −1.20459
\(947\) −0.0394219 −0.00128104 −0.000640519 1.00000i \(-0.500204\pi\)
−0.000640519 1.00000i \(0.500204\pi\)
\(948\) 0 0
\(949\) 2.60629 0.0846039
\(950\) −7.35702 −0.238693
\(951\) 0 0
\(952\) −29.2513 −0.948040
\(953\) 3.27013 0.105930 0.0529650 0.998596i \(-0.483133\pi\)
0.0529650 + 0.998596i \(0.483133\pi\)
\(954\) 0 0
\(955\) −0.390024 −0.0126209
\(956\) 102.678 3.32083
\(957\) 0 0
\(958\) 33.7862 1.09158
\(959\) −32.9379 −1.06362
\(960\) 0 0
\(961\) −13.0190 −0.419967
\(962\) −11.6157 −0.374505
\(963\) 0 0
\(964\) 101.102 3.25629
\(965\) 9.91428 0.319152
\(966\) 0 0
\(967\) 47.5329 1.52855 0.764277 0.644888i \(-0.223096\pi\)
0.764277 + 0.644888i \(0.223096\pi\)
\(968\) 30.4965 0.980193
\(969\) 0 0
\(970\) 14.2640 0.457989
\(971\) 25.1811 0.808101 0.404050 0.914737i \(-0.367602\pi\)
0.404050 + 0.914737i \(0.367602\pi\)
\(972\) 0 0
\(973\) 6.25846 0.200637
\(974\) −30.0860 −0.964019
\(975\) 0 0
\(976\) −13.2268 −0.423381
\(977\) 33.1228 1.05969 0.529846 0.848094i \(-0.322250\pi\)
0.529846 + 0.848094i \(0.322250\pi\)
\(978\) 0 0
\(979\) 4.29496 0.137268
\(980\) −11.8078 −0.377187
\(981\) 0 0
\(982\) 32.1587 1.02623
\(983\) 22.3428 0.712625 0.356313 0.934367i \(-0.384034\pi\)
0.356313 + 0.934367i \(0.384034\pi\)
\(984\) 0 0
\(985\) 1.01097 0.0322122
\(986\) −73.7243 −2.34786
\(987\) 0 0
\(988\) −12.0439 −0.383167
\(989\) −5.28295 −0.167988
\(990\) 0 0
\(991\) 37.5767 1.19366 0.596832 0.802366i \(-0.296426\pi\)
0.596832 + 0.802366i \(0.296426\pi\)
\(992\) −10.7895 −0.342566
\(993\) 0 0
\(994\) −47.0080 −1.49100
\(995\) −13.3504 −0.423236
\(996\) 0 0
\(997\) 21.4843 0.680416 0.340208 0.940350i \(-0.389502\pi\)
0.340208 + 0.940350i \(0.389502\pi\)
\(998\) 41.9116 1.32669
\(999\) 0 0
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 \(a_p\))