Properties

Label 4030.2.a.f.1.3
Level 4030
Weight 2
Character 4030.1
Self dual Yes
Analytic conductor 32.180
Analytic rank 1
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4030.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1797120146\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.4418197.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.67370\)
Character \(\chi\) = 4030.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.33263 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.33263 q^{6} +1.60759 q^{7} +1.00000 q^{8} -1.22409 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.33263 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.33263 q^{6} +1.60759 q^{7} +1.00000 q^{8} -1.22409 q^{9} -1.00000 q^{10} +3.78207 q^{11} -1.33263 q^{12} +1.00000 q^{13} +1.60759 q^{14} +1.33263 q^{15} +1.00000 q^{16} -7.50664 q^{17} -1.22409 q^{18} +1.98730 q^{19} -1.00000 q^{20} -2.14232 q^{21} +3.78207 q^{22} -7.33848 q^{23} -1.33263 q^{24} +1.00000 q^{25} +1.00000 q^{26} +5.62916 q^{27} +1.60759 q^{28} -9.25022 q^{29} +1.33263 q^{30} -1.00000 q^{31} +1.00000 q^{32} -5.04011 q^{33} -7.50664 q^{34} -1.60759 q^{35} -1.22409 q^{36} -2.62790 q^{37} +1.98730 q^{38} -1.33263 q^{39} -1.00000 q^{40} -6.29946 q^{41} -2.14232 q^{42} +12.8464 q^{43} +3.78207 q^{44} +1.22409 q^{45} -7.33848 q^{46} +0.235941 q^{47} -1.33263 q^{48} -4.41566 q^{49} +1.00000 q^{50} +10.0036 q^{51} +1.00000 q^{52} +5.87278 q^{53} +5.62916 q^{54} -3.78207 q^{55} +1.60759 q^{56} -2.64834 q^{57} -9.25022 q^{58} +0.614367 q^{59} +1.33263 q^{60} +6.39470 q^{61} -1.00000 q^{62} -1.96784 q^{63} +1.00000 q^{64} -1.00000 q^{65} -5.04011 q^{66} -0.858063 q^{67} -7.50664 q^{68} +9.77949 q^{69} -1.60759 q^{70} -2.99244 q^{71} -1.22409 q^{72} -0.697694 q^{73} -2.62790 q^{74} -1.33263 q^{75} +1.98730 q^{76} +6.08002 q^{77} -1.33263 q^{78} -9.61181 q^{79} -1.00000 q^{80} -3.82932 q^{81} -6.29946 q^{82} +11.1875 q^{83} -2.14232 q^{84} +7.50664 q^{85} +12.8464 q^{86} +12.3271 q^{87} +3.78207 q^{88} -6.48047 q^{89} +1.22409 q^{90} +1.60759 q^{91} -7.33848 q^{92} +1.33263 q^{93} +0.235941 q^{94} -1.98730 q^{95} -1.33263 q^{96} +0.423705 q^{97} -4.41566 q^{98} -4.62961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} + O(q^{10}) \) \( 6q + 6q^{2} - 3q^{3} + 6q^{4} - 6q^{5} - 3q^{6} - 2q^{7} + 6q^{8} - q^{9} - 6q^{10} - 4q^{11} - 3q^{12} + 6q^{13} - 2q^{14} + 3q^{15} + 6q^{16} - 8q^{17} - q^{18} - 9q^{19} - 6q^{20} - 5q^{21} - 4q^{22} - 7q^{23} - 3q^{24} + 6q^{25} + 6q^{26} + 9q^{27} - 2q^{28} - 14q^{29} + 3q^{30} - 6q^{31} + 6q^{32} - 6q^{33} - 8q^{34} + 2q^{35} - q^{36} - 9q^{38} - 3q^{39} - 6q^{40} + 2q^{41} - 5q^{42} - 7q^{43} - 4q^{44} + q^{45} - 7q^{46} - 8q^{47} - 3q^{48} - 14q^{49} + 6q^{50} - 5q^{51} + 6q^{52} - 24q^{53} + 9q^{54} + 4q^{55} - 2q^{56} - 15q^{57} - 14q^{58} - 5q^{59} + 3q^{60} - 5q^{61} - 6q^{62} - 19q^{63} + 6q^{64} - 6q^{65} - 6q^{66} - 12q^{67} - 8q^{68} + 2q^{70} - 10q^{71} - q^{72} + 5q^{73} - 3q^{75} - 9q^{76} - q^{77} - 3q^{78} - 16q^{79} - 6q^{80} - 10q^{81} + 2q^{82} - 22q^{83} - 5q^{84} + 8q^{85} - 7q^{86} - 31q^{87} - 4q^{88} + 14q^{89} + q^{90} - 2q^{91} - 7q^{92} + 3q^{93} - 8q^{94} + 9q^{95} - 3q^{96} - 9q^{97} - 14q^{98} - 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.33263 −0.769395 −0.384698 0.923043i \(-0.625694\pi\)
−0.384698 + 0.923043i \(0.625694\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.33263 −0.544045
\(7\) 1.60759 0.607611 0.303806 0.952734i \(-0.401743\pi\)
0.303806 + 0.952734i \(0.401743\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.22409 −0.408031
\(10\) −1.00000 −0.316228
\(11\) 3.78207 1.14034 0.570169 0.821527i \(-0.306878\pi\)
0.570169 + 0.821527i \(0.306878\pi\)
\(12\) −1.33263 −0.384698
\(13\) 1.00000 0.277350
\(14\) 1.60759 0.429646
\(15\) 1.33263 0.344084
\(16\) 1.00000 0.250000
\(17\) −7.50664 −1.82063 −0.910313 0.413920i \(-0.864159\pi\)
−0.910313 + 0.413920i \(0.864159\pi\)
\(18\) −1.22409 −0.288521
\(19\) 1.98730 0.455919 0.227959 0.973671i \(-0.426795\pi\)
0.227959 + 0.973671i \(0.426795\pi\)
\(20\) −1.00000 −0.223607
\(21\) −2.14232 −0.467493
\(22\) 3.78207 0.806341
\(23\) −7.33848 −1.53018 −0.765089 0.643924i \(-0.777305\pi\)
−0.765089 + 0.643924i \(0.777305\pi\)
\(24\) −1.33263 −0.272022
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) 5.62916 1.08333
\(28\) 1.60759 0.303806
\(29\) −9.25022 −1.71772 −0.858861 0.512208i \(-0.828828\pi\)
−0.858861 + 0.512208i \(0.828828\pi\)
\(30\) 1.33263 0.243304
\(31\) −1.00000 −0.179605
\(32\) 1.00000 0.176777
\(33\) −5.04011 −0.877371
\(34\) −7.50664 −1.28738
\(35\) −1.60759 −0.271732
\(36\) −1.22409 −0.204015
\(37\) −2.62790 −0.432024 −0.216012 0.976391i \(-0.569305\pi\)
−0.216012 + 0.976391i \(0.569305\pi\)
\(38\) 1.98730 0.322383
\(39\) −1.33263 −0.213392
\(40\) −1.00000 −0.158114
\(41\) −6.29946 −0.983811 −0.491905 0.870649i \(-0.663699\pi\)
−0.491905 + 0.870649i \(0.663699\pi\)
\(42\) −2.14232 −0.330568
\(43\) 12.8464 1.95906 0.979529 0.201303i \(-0.0645176\pi\)
0.979529 + 0.201303i \(0.0645176\pi\)
\(44\) 3.78207 0.570169
\(45\) 1.22409 0.182477
\(46\) −7.33848 −1.08200
\(47\) 0.235941 0.0344156 0.0172078 0.999852i \(-0.494522\pi\)
0.0172078 + 0.999852i \(0.494522\pi\)
\(48\) −1.33263 −0.192349
\(49\) −4.41566 −0.630808
\(50\) 1.00000 0.141421
\(51\) 10.0036 1.40078
\(52\) 1.00000 0.138675
\(53\) 5.87278 0.806689 0.403344 0.915048i \(-0.367848\pi\)
0.403344 + 0.915048i \(0.367848\pi\)
\(54\) 5.62916 0.766032
\(55\) −3.78207 −0.509975
\(56\) 1.60759 0.214823
\(57\) −2.64834 −0.350782
\(58\) −9.25022 −1.21461
\(59\) 0.614367 0.0799838 0.0399919 0.999200i \(-0.487267\pi\)
0.0399919 + 0.999200i \(0.487267\pi\)
\(60\) 1.33263 0.172042
\(61\) 6.39470 0.818758 0.409379 0.912364i \(-0.365745\pi\)
0.409379 + 0.912364i \(0.365745\pi\)
\(62\) −1.00000 −0.127000
\(63\) −1.96784 −0.247924
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −5.04011 −0.620395
\(67\) −0.858063 −0.104829 −0.0524145 0.998625i \(-0.516692\pi\)
−0.0524145 + 0.998625i \(0.516692\pi\)
\(68\) −7.50664 −0.910313
\(69\) 9.77949 1.17731
\(70\) −1.60759 −0.192144
\(71\) −2.99244 −0.355137 −0.177569 0.984108i \(-0.556823\pi\)
−0.177569 + 0.984108i \(0.556823\pi\)
\(72\) −1.22409 −0.144261
\(73\) −0.697694 −0.0816589 −0.0408295 0.999166i \(-0.513000\pi\)
−0.0408295 + 0.999166i \(0.513000\pi\)
\(74\) −2.62790 −0.305487
\(75\) −1.33263 −0.153879
\(76\) 1.98730 0.227959
\(77\) 6.08002 0.692883
\(78\) −1.33263 −0.150891
\(79\) −9.61181 −1.08141 −0.540707 0.841211i \(-0.681843\pi\)
−0.540707 + 0.841211i \(0.681843\pi\)
\(80\) −1.00000 −0.111803
\(81\) −3.82932 −0.425480
\(82\) −6.29946 −0.695659
\(83\) 11.1875 1.22798 0.613992 0.789312i \(-0.289563\pi\)
0.613992 + 0.789312i \(0.289563\pi\)
\(84\) −2.14232 −0.233747
\(85\) 7.50664 0.814209
\(86\) 12.8464 1.38526
\(87\) 12.3271 1.32161
\(88\) 3.78207 0.403171
\(89\) −6.48047 −0.686928 −0.343464 0.939166i \(-0.611600\pi\)
−0.343464 + 0.939166i \(0.611600\pi\)
\(90\) 1.22409 0.129031
\(91\) 1.60759 0.168521
\(92\) −7.33848 −0.765089
\(93\) 1.33263 0.138187
\(94\) 0.235941 0.0243355
\(95\) −1.98730 −0.203893
\(96\) −1.33263 −0.136011
\(97\) 0.423705 0.0430207 0.0215103 0.999769i \(-0.493153\pi\)
0.0215103 + 0.999769i \(0.493153\pi\)
\(98\) −4.41566 −0.446049
\(99\) −4.62961 −0.465293
\(100\) 1.00000 0.100000
\(101\) −16.8595 −1.67758 −0.838791 0.544454i \(-0.816737\pi\)
−0.838791 + 0.544454i \(0.816737\pi\)
\(102\) 10.0036 0.990502
\(103\) −5.77995 −0.569515 −0.284758 0.958600i \(-0.591913\pi\)
−0.284758 + 0.958600i \(0.591913\pi\)
\(104\) 1.00000 0.0980581
\(105\) 2.14232 0.209069
\(106\) 5.87278 0.570415
\(107\) −6.73092 −0.650703 −0.325351 0.945593i \(-0.605483\pi\)
−0.325351 + 0.945593i \(0.605483\pi\)
\(108\) 5.62916 0.541666
\(109\) −6.70105 −0.641844 −0.320922 0.947106i \(-0.603993\pi\)
−0.320922 + 0.947106i \(0.603993\pi\)
\(110\) −3.78207 −0.360607
\(111\) 3.50203 0.332398
\(112\) 1.60759 0.151903
\(113\) −20.7037 −1.94764 −0.973820 0.227321i \(-0.927003\pi\)
−0.973820 + 0.227321i \(0.927003\pi\)
\(114\) −2.64834 −0.248040
\(115\) 7.33848 0.684317
\(116\) −9.25022 −0.858861
\(117\) −1.22409 −0.113167
\(118\) 0.614367 0.0565571
\(119\) −12.0676 −1.10623
\(120\) 1.33263 0.121652
\(121\) 3.30409 0.300372
\(122\) 6.39470 0.578949
\(123\) 8.39486 0.756939
\(124\) −1.00000 −0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −1.96784 −0.175309
\(127\) −1.59487 −0.141522 −0.0707608 0.997493i \(-0.522543\pi\)
−0.0707608 + 0.997493i \(0.522543\pi\)
\(128\) 1.00000 0.0883883
\(129\) −17.1195 −1.50729
\(130\) −1.00000 −0.0877058
\(131\) −4.22674 −0.369292 −0.184646 0.982805i \(-0.559114\pi\)
−0.184646 + 0.982805i \(0.559114\pi\)
\(132\) −5.04011 −0.438686
\(133\) 3.19477 0.277021
\(134\) −0.858063 −0.0741253
\(135\) −5.62916 −0.484481
\(136\) −7.50664 −0.643689
\(137\) −20.2651 −1.73136 −0.865680 0.500597i \(-0.833114\pi\)
−0.865680 + 0.500597i \(0.833114\pi\)
\(138\) 9.77949 0.832485
\(139\) 15.8944 1.34815 0.674073 0.738665i \(-0.264543\pi\)
0.674073 + 0.738665i \(0.264543\pi\)
\(140\) −1.60759 −0.135866
\(141\) −0.314423 −0.0264792
\(142\) −2.99244 −0.251120
\(143\) 3.78207 0.316273
\(144\) −1.22409 −0.102008
\(145\) 9.25022 0.768189
\(146\) −0.697694 −0.0577416
\(147\) 5.88445 0.485341
\(148\) −2.62790 −0.216012
\(149\) −23.3186 −1.91034 −0.955168 0.296065i \(-0.904326\pi\)
−0.955168 + 0.296065i \(0.904326\pi\)
\(150\) −1.33263 −0.108809
\(151\) −8.39218 −0.682946 −0.341473 0.939892i \(-0.610926\pi\)
−0.341473 + 0.939892i \(0.610926\pi\)
\(152\) 1.98730 0.161192
\(153\) 9.18882 0.742872
\(154\) 6.08002 0.489942
\(155\) 1.00000 0.0803219
\(156\) −1.33263 −0.106696
\(157\) −10.2898 −0.821219 −0.410609 0.911811i \(-0.634684\pi\)
−0.410609 + 0.911811i \(0.634684\pi\)
\(158\) −9.61181 −0.764675
\(159\) −7.82626 −0.620663
\(160\) −1.00000 −0.0790569
\(161\) −11.7973 −0.929754
\(162\) −3.82932 −0.300860
\(163\) −2.40960 −0.188734 −0.0943672 0.995537i \(-0.530083\pi\)
−0.0943672 + 0.995537i \(0.530083\pi\)
\(164\) −6.29946 −0.491905
\(165\) 5.04011 0.392372
\(166\) 11.1875 0.868316
\(167\) 13.6758 1.05827 0.529134 0.848539i \(-0.322517\pi\)
0.529134 + 0.848539i \(0.322517\pi\)
\(168\) −2.14232 −0.165284
\(169\) 1.00000 0.0769231
\(170\) 7.50664 0.575733
\(171\) −2.43264 −0.186029
\(172\) 12.8464 0.979529
\(173\) 18.3393 1.39431 0.697154 0.716922i \(-0.254449\pi\)
0.697154 + 0.716922i \(0.254449\pi\)
\(174\) 12.3271 0.934518
\(175\) 1.60759 0.121522
\(176\) 3.78207 0.285085
\(177\) −0.818725 −0.0615392
\(178\) −6.48047 −0.485732
\(179\) −7.36796 −0.550707 −0.275354 0.961343i \(-0.588795\pi\)
−0.275354 + 0.961343i \(0.588795\pi\)
\(180\) 1.22409 0.0912385
\(181\) −0.113739 −0.00845414 −0.00422707 0.999991i \(-0.501346\pi\)
−0.00422707 + 0.999991i \(0.501346\pi\)
\(182\) 1.60759 0.119162
\(183\) −8.52178 −0.629948
\(184\) −7.33848 −0.541000
\(185\) 2.62790 0.193207
\(186\) 1.33263 0.0977133
\(187\) −28.3907 −2.07613
\(188\) 0.235941 0.0172078
\(189\) 9.04937 0.658245
\(190\) −1.98730 −0.144174
\(191\) −18.3453 −1.32742 −0.663710 0.747990i \(-0.731019\pi\)
−0.663710 + 0.747990i \(0.731019\pi\)
\(192\) −1.33263 −0.0961744
\(193\) 15.1604 1.09127 0.545635 0.838023i \(-0.316289\pi\)
0.545635 + 0.838023i \(0.316289\pi\)
\(194\) 0.423705 0.0304202
\(195\) 1.33263 0.0954317
\(196\) −4.41566 −0.315404
\(197\) −6.46630 −0.460705 −0.230352 0.973107i \(-0.573988\pi\)
−0.230352 + 0.973107i \(0.573988\pi\)
\(198\) −4.62961 −0.329012
\(199\) −1.74394 −0.123625 −0.0618123 0.998088i \(-0.519688\pi\)
−0.0618123 + 0.998088i \(0.519688\pi\)
\(200\) 1.00000 0.0707107
\(201\) 1.14348 0.0806550
\(202\) −16.8595 −1.18623
\(203\) −14.8706 −1.04371
\(204\) 10.0036 0.700391
\(205\) 6.29946 0.439973
\(206\) −5.77995 −0.402708
\(207\) 8.98298 0.624360
\(208\) 1.00000 0.0693375
\(209\) 7.51613 0.519902
\(210\) 2.14232 0.147834
\(211\) 5.59671 0.385293 0.192647 0.981268i \(-0.438293\pi\)
0.192647 + 0.981268i \(0.438293\pi\)
\(212\) 5.87278 0.403344
\(213\) 3.98782 0.273241
\(214\) −6.73092 −0.460116
\(215\) −12.8464 −0.876117
\(216\) 5.62916 0.383016
\(217\) −1.60759 −0.109130
\(218\) −6.70105 −0.453852
\(219\) 0.929769 0.0628280
\(220\) −3.78207 −0.254987
\(221\) −7.50664 −0.504951
\(222\) 3.50203 0.235041
\(223\) −24.7089 −1.65463 −0.827316 0.561737i \(-0.810133\pi\)
−0.827316 + 0.561737i \(0.810133\pi\)
\(224\) 1.60759 0.107412
\(225\) −1.22409 −0.0816062
\(226\) −20.7037 −1.37719
\(227\) −8.97325 −0.595576 −0.297788 0.954632i \(-0.596249\pi\)
−0.297788 + 0.954632i \(0.596249\pi\)
\(228\) −2.64834 −0.175391
\(229\) −2.94499 −0.194610 −0.0973052 0.995255i \(-0.531022\pi\)
−0.0973052 + 0.995255i \(0.531022\pi\)
\(230\) 7.33848 0.483885
\(231\) −8.10243 −0.533101
\(232\) −9.25022 −0.607307
\(233\) 15.0687 0.987182 0.493591 0.869694i \(-0.335684\pi\)
0.493591 + 0.869694i \(0.335684\pi\)
\(234\) −1.22409 −0.0800214
\(235\) −0.235941 −0.0153911
\(236\) 0.614367 0.0399919
\(237\) 12.8090 0.832034
\(238\) −12.0676 −0.782225
\(239\) −24.6433 −1.59404 −0.797021 0.603951i \(-0.793592\pi\)
−0.797021 + 0.603951i \(0.793592\pi\)
\(240\) 1.33263 0.0860210
\(241\) 10.4708 0.674486 0.337243 0.941418i \(-0.390506\pi\)
0.337243 + 0.941418i \(0.390506\pi\)
\(242\) 3.30409 0.212395
\(243\) −11.7844 −0.755970
\(244\) 6.39470 0.409379
\(245\) 4.41566 0.282106
\(246\) 8.39486 0.535237
\(247\) 1.98730 0.126449
\(248\) −1.00000 −0.0635001
\(249\) −14.9088 −0.944805
\(250\) −1.00000 −0.0632456
\(251\) 6.08626 0.384161 0.192081 0.981379i \(-0.438476\pi\)
0.192081 + 0.981379i \(0.438476\pi\)
\(252\) −1.96784 −0.123962
\(253\) −27.7547 −1.74492
\(254\) −1.59487 −0.100071
\(255\) −10.0036 −0.626449
\(256\) 1.00000 0.0625000
\(257\) −14.5157 −0.905465 −0.452732 0.891647i \(-0.649551\pi\)
−0.452732 + 0.891647i \(0.649551\pi\)
\(258\) −17.1195 −1.06581
\(259\) −4.22459 −0.262503
\(260\) −1.00000 −0.0620174
\(261\) 11.3231 0.700884
\(262\) −4.22674 −0.261129
\(263\) 13.6068 0.839028 0.419514 0.907749i \(-0.362200\pi\)
0.419514 + 0.907749i \(0.362200\pi\)
\(264\) −5.04011 −0.310197
\(265\) −5.87278 −0.360762
\(266\) 3.19477 0.195884
\(267\) 8.63608 0.528519
\(268\) −0.858063 −0.0524145
\(269\) 16.3470 0.996696 0.498348 0.866977i \(-0.333940\pi\)
0.498348 + 0.866977i \(0.333940\pi\)
\(270\) −5.62916 −0.342580
\(271\) 8.70647 0.528880 0.264440 0.964402i \(-0.414813\pi\)
0.264440 + 0.964402i \(0.414813\pi\)
\(272\) −7.50664 −0.455157
\(273\) −2.14232 −0.129659
\(274\) −20.2651 −1.22426
\(275\) 3.78207 0.228068
\(276\) 9.77949 0.588656
\(277\) −23.2021 −1.39408 −0.697040 0.717032i \(-0.745500\pi\)
−0.697040 + 0.717032i \(0.745500\pi\)
\(278\) 15.8944 0.953283
\(279\) 1.22409 0.0732845
\(280\) −1.60759 −0.0960718
\(281\) 32.6834 1.94973 0.974864 0.222802i \(-0.0715205\pi\)
0.974864 + 0.222802i \(0.0715205\pi\)
\(282\) −0.314423 −0.0187236
\(283\) 31.2336 1.85664 0.928322 0.371777i \(-0.121251\pi\)
0.928322 + 0.371777i \(0.121251\pi\)
\(284\) −2.99244 −0.177569
\(285\) 2.64834 0.156874
\(286\) 3.78207 0.223639
\(287\) −10.1269 −0.597775
\(288\) −1.22409 −0.0721304
\(289\) 39.3496 2.31468
\(290\) 9.25022 0.543192
\(291\) −0.564642 −0.0330999
\(292\) −0.697694 −0.0408295
\(293\) 21.0438 1.22939 0.614696 0.788764i \(-0.289279\pi\)
0.614696 + 0.788764i \(0.289279\pi\)
\(294\) 5.88445 0.343188
\(295\) −0.614367 −0.0357698
\(296\) −2.62790 −0.152744
\(297\) 21.2899 1.23537
\(298\) −23.3186 −1.35081
\(299\) −7.33848 −0.424395
\(300\) −1.33263 −0.0769395
\(301\) 20.6517 1.19035
\(302\) −8.39218 −0.482916
\(303\) 22.4675 1.29072
\(304\) 1.98730 0.113980
\(305\) −6.39470 −0.366160
\(306\) 9.18882 0.525290
\(307\) −33.2724 −1.89896 −0.949478 0.313832i \(-0.898387\pi\)
−0.949478 + 0.313832i \(0.898387\pi\)
\(308\) 6.08002 0.346441
\(309\) 7.70254 0.438182
\(310\) 1.00000 0.0567962
\(311\) 25.7628 1.46087 0.730436 0.682981i \(-0.239317\pi\)
0.730436 + 0.682981i \(0.239317\pi\)
\(312\) −1.33263 −0.0754454
\(313\) −17.2712 −0.976226 −0.488113 0.872780i \(-0.662315\pi\)
−0.488113 + 0.872780i \(0.662315\pi\)
\(314\) −10.2898 −0.580689
\(315\) 1.96784 0.110875
\(316\) −9.61181 −0.540707
\(317\) −16.1651 −0.907924 −0.453962 0.891021i \(-0.649990\pi\)
−0.453962 + 0.891021i \(0.649990\pi\)
\(318\) −7.82626 −0.438875
\(319\) −34.9850 −1.95879
\(320\) −1.00000 −0.0559017
\(321\) 8.96984 0.500648
\(322\) −11.7973 −0.657435
\(323\) −14.9180 −0.830058
\(324\) −3.82932 −0.212740
\(325\) 1.00000 0.0554700
\(326\) −2.40960 −0.133455
\(327\) 8.93003 0.493832
\(328\) −6.29946 −0.347830
\(329\) 0.379297 0.0209113
\(330\) 5.04011 0.277449
\(331\) 2.27168 0.124863 0.0624314 0.998049i \(-0.480115\pi\)
0.0624314 + 0.998049i \(0.480115\pi\)
\(332\) 11.1875 0.613992
\(333\) 3.21680 0.176279
\(334\) 13.6758 0.748308
\(335\) 0.858063 0.0468810
\(336\) −2.14232 −0.116873
\(337\) 26.5368 1.44555 0.722775 0.691084i \(-0.242866\pi\)
0.722775 + 0.691084i \(0.242866\pi\)
\(338\) 1.00000 0.0543928
\(339\) 27.5904 1.49850
\(340\) 7.50664 0.407104
\(341\) −3.78207 −0.204811
\(342\) −2.43264 −0.131542
\(343\) −18.3517 −0.990898
\(344\) 12.8464 0.692632
\(345\) −9.77949 −0.526510
\(346\) 18.3393 0.985924
\(347\) 35.4079 1.90080 0.950399 0.311033i \(-0.100675\pi\)
0.950399 + 0.311033i \(0.100675\pi\)
\(348\) 12.3271 0.660804
\(349\) −33.0019 −1.76655 −0.883275 0.468856i \(-0.844666\pi\)
−0.883275 + 0.468856i \(0.844666\pi\)
\(350\) 1.60759 0.0859292
\(351\) 5.62916 0.300462
\(352\) 3.78207 0.201585
\(353\) 3.54019 0.188425 0.0942127 0.995552i \(-0.469967\pi\)
0.0942127 + 0.995552i \(0.469967\pi\)
\(354\) −0.818725 −0.0435148
\(355\) 2.99244 0.158822
\(356\) −6.48047 −0.343464
\(357\) 16.0816 0.851131
\(358\) −7.36796 −0.389409
\(359\) 0.305070 0.0161010 0.00805048 0.999968i \(-0.497437\pi\)
0.00805048 + 0.999968i \(0.497437\pi\)
\(360\) 1.22409 0.0645154
\(361\) −15.0506 −0.792138
\(362\) −0.113739 −0.00597798
\(363\) −4.40313 −0.231105
\(364\) 1.60759 0.0842605
\(365\) 0.697694 0.0365190
\(366\) −8.52178 −0.445441
\(367\) 19.0805 0.995992 0.497996 0.867179i \(-0.334069\pi\)
0.497996 + 0.867179i \(0.334069\pi\)
\(368\) −7.33848 −0.382545
\(369\) 7.71113 0.401425
\(370\) 2.62790 0.136618
\(371\) 9.44102 0.490153
\(372\) 1.33263 0.0690937
\(373\) 6.62044 0.342793 0.171397 0.985202i \(-0.445172\pi\)
0.171397 + 0.985202i \(0.445172\pi\)
\(374\) −28.3907 −1.46805
\(375\) 1.33263 0.0688168
\(376\) 0.235941 0.0121678
\(377\) −9.25022 −0.476411
\(378\) 9.04937 0.465450
\(379\) −12.8868 −0.661949 −0.330974 0.943640i \(-0.607377\pi\)
−0.330974 + 0.943640i \(0.607377\pi\)
\(380\) −1.98730 −0.101947
\(381\) 2.12537 0.108886
\(382\) −18.3453 −0.938628
\(383\) 0.170091 0.00869126 0.00434563 0.999991i \(-0.498617\pi\)
0.00434563 + 0.999991i \(0.498617\pi\)
\(384\) −1.33263 −0.0680056
\(385\) −6.08002 −0.309867
\(386\) 15.1604 0.771644
\(387\) −15.7252 −0.799356
\(388\) 0.423705 0.0215103
\(389\) −25.1888 −1.27712 −0.638560 0.769572i \(-0.720470\pi\)
−0.638560 + 0.769572i \(0.720470\pi\)
\(390\) 1.33263 0.0674804
\(391\) 55.0873 2.78588
\(392\) −4.41566 −0.223024
\(393\) 5.63269 0.284132
\(394\) −6.46630 −0.325767
\(395\) 9.61181 0.483623
\(396\) −4.62961 −0.232647
\(397\) 6.54529 0.328499 0.164249 0.986419i \(-0.447480\pi\)
0.164249 + 0.986419i \(0.447480\pi\)
\(398\) −1.74394 −0.0874157
\(399\) −4.25745 −0.213139
\(400\) 1.00000 0.0500000
\(401\) 19.3588 0.966733 0.483366 0.875418i \(-0.339414\pi\)
0.483366 + 0.875418i \(0.339414\pi\)
\(402\) 1.14348 0.0570317
\(403\) −1.00000 −0.0498135
\(404\) −16.8595 −0.838791
\(405\) 3.82932 0.190280
\(406\) −14.8706 −0.738013
\(407\) −9.93892 −0.492654
\(408\) 10.0036 0.495251
\(409\) 3.72518 0.184199 0.0920993 0.995750i \(-0.470642\pi\)
0.0920993 + 0.995750i \(0.470642\pi\)
\(410\) 6.29946 0.311108
\(411\) 27.0059 1.33210
\(412\) −5.77995 −0.284758
\(413\) 0.987650 0.0485991
\(414\) 8.98298 0.441489
\(415\) −11.1875 −0.549171
\(416\) 1.00000 0.0490290
\(417\) −21.1814 −1.03726
\(418\) 7.51613 0.367626
\(419\) 9.56328 0.467197 0.233598 0.972333i \(-0.424950\pi\)
0.233598 + 0.972333i \(0.424950\pi\)
\(420\) 2.14232 0.104535
\(421\) −15.4149 −0.751275 −0.375638 0.926767i \(-0.622576\pi\)
−0.375638 + 0.926767i \(0.622576\pi\)
\(422\) 5.59671 0.272444
\(423\) −0.288814 −0.0140426
\(424\) 5.87278 0.285208
\(425\) −7.50664 −0.364125
\(426\) 3.98782 0.193210
\(427\) 10.2801 0.497487
\(428\) −6.73092 −0.325351
\(429\) −5.04011 −0.243339
\(430\) −12.8464 −0.619509
\(431\) 32.3013 1.55590 0.777951 0.628325i \(-0.216259\pi\)
0.777951 + 0.628325i \(0.216259\pi\)
\(432\) 5.62916 0.270833
\(433\) 30.7989 1.48010 0.740051 0.672550i \(-0.234801\pi\)
0.740051 + 0.672550i \(0.234801\pi\)
\(434\) −1.60759 −0.0771667
\(435\) −12.3271 −0.591041
\(436\) −6.70105 −0.320922
\(437\) −14.5838 −0.697637
\(438\) 0.929769 0.0444261
\(439\) −24.7611 −1.18178 −0.590891 0.806752i \(-0.701223\pi\)
−0.590891 + 0.806752i \(0.701223\pi\)
\(440\) −3.78207 −0.180303
\(441\) 5.40518 0.257389
\(442\) −7.50664 −0.357054
\(443\) −3.21255 −0.152633 −0.0763165 0.997084i \(-0.524316\pi\)
−0.0763165 + 0.997084i \(0.524316\pi\)
\(444\) 3.50203 0.166199
\(445\) 6.48047 0.307204
\(446\) −24.7089 −1.17000
\(447\) 31.0751 1.46980
\(448\) 1.60759 0.0759514
\(449\) −12.2838 −0.579707 −0.289853 0.957071i \(-0.593607\pi\)
−0.289853 + 0.957071i \(0.593607\pi\)
\(450\) −1.22409 −0.0577043
\(451\) −23.8250 −1.12188
\(452\) −20.7037 −0.973820
\(453\) 11.1837 0.525455
\(454\) −8.97325 −0.421136
\(455\) −1.60759 −0.0753649
\(456\) −2.64834 −0.124020
\(457\) −1.71695 −0.0803154 −0.0401577 0.999193i \(-0.512786\pi\)
−0.0401577 + 0.999193i \(0.512786\pi\)
\(458\) −2.94499 −0.137610
\(459\) −42.2561 −1.97234
\(460\) 7.33848 0.342158
\(461\) 21.8774 1.01893 0.509466 0.860491i \(-0.329843\pi\)
0.509466 + 0.860491i \(0.329843\pi\)
\(462\) −8.10243 −0.376959
\(463\) −17.6147 −0.818626 −0.409313 0.912394i \(-0.634232\pi\)
−0.409313 + 0.912394i \(0.634232\pi\)
\(464\) −9.25022 −0.429431
\(465\) −1.33263 −0.0617993
\(466\) 15.0687 0.698043
\(467\) 9.30031 0.430367 0.215183 0.976574i \(-0.430965\pi\)
0.215183 + 0.976574i \(0.430965\pi\)
\(468\) −1.22409 −0.0565837
\(469\) −1.37941 −0.0636953
\(470\) −0.235941 −0.0108832
\(471\) 13.7126 0.631842
\(472\) 0.614367 0.0282785
\(473\) 48.5861 2.23399
\(474\) 12.8090 0.588337
\(475\) 1.98730 0.0911838
\(476\) −12.0676 −0.553117
\(477\) −7.18883 −0.329154
\(478\) −24.6433 −1.12716
\(479\) −18.3745 −0.839551 −0.419776 0.907628i \(-0.637891\pi\)
−0.419776 + 0.907628i \(0.637891\pi\)
\(480\) 1.33263 0.0608260
\(481\) −2.62790 −0.119822
\(482\) 10.4708 0.476933
\(483\) 15.7214 0.715348
\(484\) 3.30409 0.150186
\(485\) −0.423705 −0.0192394
\(486\) −11.7844 −0.534552
\(487\) 37.3823 1.69395 0.846976 0.531630i \(-0.178420\pi\)
0.846976 + 0.531630i \(0.178420\pi\)
\(488\) 6.39470 0.289475
\(489\) 3.21111 0.145211
\(490\) 4.41566 0.199479
\(491\) −31.5304 −1.42295 −0.711473 0.702714i \(-0.751972\pi\)
−0.711473 + 0.702714i \(0.751972\pi\)
\(492\) 8.39486 0.378470
\(493\) 69.4380 3.12733
\(494\) 1.98730 0.0894130
\(495\) 4.62961 0.208086
\(496\) −1.00000 −0.0449013
\(497\) −4.81061 −0.215785
\(498\) −14.9088 −0.668078
\(499\) −40.8881 −1.83040 −0.915202 0.402996i \(-0.867969\pi\)
−0.915202 + 0.402996i \(0.867969\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −18.2248 −0.814226
\(502\) 6.08626 0.271643
\(503\) 4.14266 0.184712 0.0923560 0.995726i \(-0.470560\pi\)
0.0923560 + 0.995726i \(0.470560\pi\)
\(504\) −1.96784 −0.0876545
\(505\) 16.8595 0.750237
\(506\) −27.7547 −1.23385
\(507\) −1.33263 −0.0591843
\(508\) −1.59487 −0.0707608
\(509\) 29.5183 1.30837 0.654187 0.756333i \(-0.273011\pi\)
0.654187 + 0.756333i \(0.273011\pi\)
\(510\) −10.0036 −0.442966
\(511\) −1.12161 −0.0496169
\(512\) 1.00000 0.0441942
\(513\) 11.1869 0.493912
\(514\) −14.5157 −0.640260
\(515\) 5.77995 0.254695
\(516\) −17.1195 −0.753645
\(517\) 0.892348 0.0392454
\(518\) −4.22459 −0.185618
\(519\) −24.4395 −1.07277
\(520\) −1.00000 −0.0438529
\(521\) −30.0804 −1.31785 −0.658924 0.752210i \(-0.728988\pi\)
−0.658924 + 0.752210i \(0.728988\pi\)
\(522\) 11.3231 0.495600
\(523\) −1.39983 −0.0612101 −0.0306051 0.999532i \(-0.509743\pi\)
−0.0306051 + 0.999532i \(0.509743\pi\)
\(524\) −4.22674 −0.184646
\(525\) −2.14232 −0.0934987
\(526\) 13.6068 0.593283
\(527\) 7.50664 0.326994
\(528\) −5.04011 −0.219343
\(529\) 30.8533 1.34145
\(530\) −5.87278 −0.255097
\(531\) −0.752042 −0.0326359
\(532\) 3.19477 0.138511
\(533\) −6.29946 −0.272860
\(534\) 8.63608 0.373720
\(535\) 6.73092 0.291003
\(536\) −0.858063 −0.0370627
\(537\) 9.81878 0.423711
\(538\) 16.3470 0.704771
\(539\) −16.7003 −0.719335
\(540\) −5.62916 −0.242240
\(541\) −10.9426 −0.470460 −0.235230 0.971940i \(-0.575584\pi\)
−0.235230 + 0.971940i \(0.575584\pi\)
\(542\) 8.70647 0.373975
\(543\) 0.151572 0.00650458
\(544\) −7.50664 −0.321844
\(545\) 6.70105 0.287041
\(546\) −2.14232 −0.0916830
\(547\) 31.8026 1.35978 0.679889 0.733315i \(-0.262028\pi\)
0.679889 + 0.733315i \(0.262028\pi\)
\(548\) −20.2651 −0.865680
\(549\) −7.82771 −0.334078
\(550\) 3.78207 0.161268
\(551\) −18.3830 −0.783142
\(552\) 9.77949 0.416243
\(553\) −15.4518 −0.657079
\(554\) −23.2021 −0.985763
\(555\) −3.50203 −0.148653
\(556\) 15.8944 0.674073
\(557\) 0.291682 0.0123590 0.00617948 0.999981i \(-0.498033\pi\)
0.00617948 + 0.999981i \(0.498033\pi\)
\(558\) 1.22409 0.0518200
\(559\) 12.8464 0.543345
\(560\) −1.60759 −0.0679330
\(561\) 37.8343 1.59736
\(562\) 32.6834 1.37867
\(563\) 23.4509 0.988338 0.494169 0.869366i \(-0.335472\pi\)
0.494169 + 0.869366i \(0.335472\pi\)
\(564\) −0.314423 −0.0132396
\(565\) 20.7037 0.871011
\(566\) 31.2336 1.31285
\(567\) −6.15597 −0.258526
\(568\) −2.99244 −0.125560
\(569\) 30.7978 1.29111 0.645556 0.763713i \(-0.276626\pi\)
0.645556 + 0.763713i \(0.276626\pi\)
\(570\) 2.64834 0.110927
\(571\) −9.94394 −0.416141 −0.208070 0.978114i \(-0.566718\pi\)
−0.208070 + 0.978114i \(0.566718\pi\)
\(572\) 3.78207 0.158136
\(573\) 24.4475 1.02131
\(574\) −10.1269 −0.422690
\(575\) −7.33848 −0.306036
\(576\) −1.22409 −0.0510039
\(577\) −46.0243 −1.91602 −0.958008 0.286741i \(-0.907428\pi\)
−0.958008 + 0.286741i \(0.907428\pi\)
\(578\) 39.3496 1.63673
\(579\) −20.2032 −0.839617
\(580\) 9.25022 0.384094
\(581\) 17.9848 0.746137
\(582\) −0.564642 −0.0234052
\(583\) 22.2113 0.919898
\(584\) −0.697694 −0.0288708
\(585\) 1.22409 0.0506100
\(586\) 21.0438 0.869311
\(587\) 25.8593 1.06733 0.533664 0.845696i \(-0.320815\pi\)
0.533664 + 0.845696i \(0.320815\pi\)
\(588\) 5.88445 0.242670
\(589\) −1.98730 −0.0818854
\(590\) −0.614367 −0.0252931
\(591\) 8.61719 0.354464
\(592\) −2.62790 −0.108006
\(593\) 23.4695 0.963777 0.481889 0.876232i \(-0.339951\pi\)
0.481889 + 0.876232i \(0.339951\pi\)
\(594\) 21.2899 0.873535
\(595\) 12.0676 0.494723
\(596\) −23.3186 −0.955168
\(597\) 2.32403 0.0951161
\(598\) −7.33848 −0.300093
\(599\) 12.9391 0.528679 0.264339 0.964430i \(-0.414846\pi\)
0.264339 + 0.964430i \(0.414846\pi\)
\(600\) −1.33263 −0.0544045
\(601\) 22.6735 0.924873 0.462436 0.886652i \(-0.346975\pi\)
0.462436 + 0.886652i \(0.346975\pi\)
\(602\) 20.6517 0.841702
\(603\) 1.05035 0.0427735
\(604\) −8.39218 −0.341473
\(605\) −3.30409 −0.134330
\(606\) 22.4675 0.912679
\(607\) −30.3552 −1.23208 −0.616039 0.787716i \(-0.711264\pi\)
−0.616039 + 0.787716i \(0.711264\pi\)
\(608\) 1.98730 0.0805958
\(609\) 19.8170 0.803024
\(610\) −6.39470 −0.258914
\(611\) 0.235941 0.00954517
\(612\) 9.18882 0.371436
\(613\) −43.8393 −1.77065 −0.885326 0.464971i \(-0.846065\pi\)
−0.885326 + 0.464971i \(0.846065\pi\)
\(614\) −33.2724 −1.34277
\(615\) −8.39486 −0.338514
\(616\) 6.08002 0.244971
\(617\) 22.1845 0.893114 0.446557 0.894755i \(-0.352650\pi\)
0.446557 + 0.894755i \(0.352650\pi\)
\(618\) 7.70254 0.309842
\(619\) 4.05899 0.163145 0.0815723 0.996667i \(-0.474006\pi\)
0.0815723 + 0.996667i \(0.474006\pi\)
\(620\) 1.00000 0.0401610
\(621\) −41.3095 −1.65769
\(622\) 25.7628 1.03299
\(623\) −10.4179 −0.417385
\(624\) −1.33263 −0.0533480
\(625\) 1.00000 0.0400000
\(626\) −17.2712 −0.690296
\(627\) −10.0162 −0.400010
\(628\) −10.2898 −0.410609
\(629\) 19.7267 0.786555
\(630\) 1.96784 0.0784005
\(631\) −10.1079 −0.402389 −0.201195 0.979551i \(-0.564482\pi\)
−0.201195 + 0.979551i \(0.564482\pi\)
\(632\) −9.61181 −0.382337
\(633\) −7.45835 −0.296443
\(634\) −16.1651 −0.641999
\(635\) 1.59487 0.0632904
\(636\) −7.82626 −0.310331
\(637\) −4.41566 −0.174955
\(638\) −34.9850 −1.38507
\(639\) 3.66302 0.144907
\(640\) −1.00000 −0.0395285
\(641\) −11.3771 −0.449368 −0.224684 0.974432i \(-0.572135\pi\)
−0.224684 + 0.974432i \(0.572135\pi\)
\(642\) 8.96984 0.354011
\(643\) 26.8150 1.05748 0.528740 0.848784i \(-0.322665\pi\)
0.528740 + 0.848784i \(0.322665\pi\)
\(644\) −11.7973 −0.464877
\(645\) 17.1195 0.674081
\(646\) −14.9180 −0.586940
\(647\) −16.3749 −0.643764 −0.321882 0.946780i \(-0.604315\pi\)
−0.321882 + 0.946780i \(0.604315\pi\)
\(648\) −3.82932 −0.150430
\(649\) 2.32358 0.0912086
\(650\) 1.00000 0.0392232
\(651\) 2.14232 0.0839643
\(652\) −2.40960 −0.0943672
\(653\) 19.0335 0.744839 0.372419 0.928065i \(-0.378528\pi\)
0.372419 + 0.928065i \(0.378528\pi\)
\(654\) 8.93003 0.349192
\(655\) 4.22674 0.165153
\(656\) −6.29946 −0.245953
\(657\) 0.854042 0.0333194
\(658\) 0.379297 0.0147865
\(659\) −41.1746 −1.60394 −0.801968 0.597367i \(-0.796214\pi\)
−0.801968 + 0.597367i \(0.796214\pi\)
\(660\) 5.04011 0.196186
\(661\) −25.2050 −0.980363 −0.490181 0.871620i \(-0.663069\pi\)
−0.490181 + 0.871620i \(0.663069\pi\)
\(662\) 2.27168 0.0882914
\(663\) 10.0036 0.388507
\(664\) 11.1875 0.434158
\(665\) −3.19477 −0.123888
\(666\) 3.21680 0.124648
\(667\) 67.8825 2.62842
\(668\) 13.6758 0.529134
\(669\) 32.9279 1.27307
\(670\) 0.858063 0.0331499
\(671\) 24.1852 0.933661
\(672\) −2.14232 −0.0826419
\(673\) −23.6889 −0.913140 −0.456570 0.889687i \(-0.650922\pi\)
−0.456570 + 0.889687i \(0.650922\pi\)
\(674\) 26.5368 1.02216
\(675\) 5.62916 0.216666
\(676\) 1.00000 0.0384615
\(677\) 14.2210 0.546556 0.273278 0.961935i \(-0.411892\pi\)
0.273278 + 0.961935i \(0.411892\pi\)
\(678\) 27.5904 1.05960
\(679\) 0.681143 0.0261399
\(680\) 7.50664 0.287866
\(681\) 11.9580 0.458233
\(682\) −3.78207 −0.144823
\(683\) −32.8833 −1.25824 −0.629122 0.777307i \(-0.716585\pi\)
−0.629122 + 0.777307i \(0.716585\pi\)
\(684\) −2.43264 −0.0930145
\(685\) 20.2651 0.774288
\(686\) −18.3517 −0.700671
\(687\) 3.92459 0.149732
\(688\) 12.8464 0.489764
\(689\) 5.87278 0.223735
\(690\) −9.77949 −0.372299
\(691\) −45.1640 −1.71812 −0.859059 0.511877i \(-0.828950\pi\)
−0.859059 + 0.511877i \(0.828950\pi\)
\(692\) 18.3393 0.697154
\(693\) −7.44251 −0.282718
\(694\) 35.4079 1.34407
\(695\) −15.8944 −0.602909
\(696\) 12.3271 0.467259
\(697\) 47.2878 1.79115
\(698\) −33.0019 −1.24914
\(699\) −20.0810 −0.759533
\(700\) 1.60759 0.0607611
\(701\) 19.6592 0.742519 0.371260 0.928529i \(-0.378926\pi\)
0.371260 + 0.928529i \(0.378926\pi\)
\(702\) 5.62916 0.212459
\(703\) −5.22244 −0.196968
\(704\) 3.78207 0.142542
\(705\) 0.314423 0.0118419
\(706\) 3.54019 0.133237
\(707\) −27.1031 −1.01932
\(708\) −0.818725 −0.0307696
\(709\) 20.6006 0.773670 0.386835 0.922149i \(-0.373568\pi\)
0.386835 + 0.922149i \(0.373568\pi\)
\(710\) 2.99244 0.112304
\(711\) 11.7657 0.441250
\(712\) −6.48047 −0.242866
\(713\) 7.33848 0.274828
\(714\) 16.0816 0.601840
\(715\) −3.78207 −0.141442
\(716\) −7.36796 −0.275354
\(717\) 32.8404 1.22645
\(718\) 0.305070 0.0113851
\(719\) 31.8647 1.18835 0.594176 0.804335i \(-0.297478\pi\)
0.594176 + 0.804335i \(0.297478\pi\)
\(720\) 1.22409 0.0456192
\(721\) −9.29178 −0.346044
\(722\) −15.0506 −0.560126
\(723\) −13.9538 −0.518946
\(724\) −0.113739 −0.00422707
\(725\) −9.25022 −0.343545
\(726\) −4.40313 −0.163416
\(727\) −2.79504 −0.103662 −0.0518312 0.998656i \(-0.516506\pi\)
−0.0518312 + 0.998656i \(0.516506\pi\)
\(728\) 1.60759 0.0595812
\(729\) 27.1922 1.00712
\(730\) 0.697694 0.0258228
\(731\) −96.4333 −3.56671
\(732\) −8.52178 −0.314974
\(733\) 1.98182 0.0732001 0.0366000 0.999330i \(-0.488347\pi\)
0.0366000 + 0.999330i \(0.488347\pi\)
\(734\) 19.0805 0.704273
\(735\) −5.88445 −0.217051
\(736\) −7.33848 −0.270500
\(737\) −3.24526 −0.119541
\(738\) 7.71113 0.283850
\(739\) 52.6166 1.93553 0.967767 0.251848i \(-0.0810382\pi\)
0.967767 + 0.251848i \(0.0810382\pi\)
\(740\) 2.62790 0.0966036
\(741\) −2.64834 −0.0972894
\(742\) 9.44102 0.346591
\(743\) 6.82229 0.250286 0.125143 0.992139i \(-0.460061\pi\)
0.125143 + 0.992139i \(0.460061\pi\)
\(744\) 1.33263 0.0488566
\(745\) 23.3186 0.854328
\(746\) 6.62044 0.242391
\(747\) −13.6945 −0.501055
\(748\) −28.3907 −1.03807
\(749\) −10.8206 −0.395374
\(750\) 1.33263 0.0486608
\(751\) −30.5036 −1.11309 −0.556546 0.830817i \(-0.687874\pi\)
−0.556546 + 0.830817i \(0.687874\pi\)
\(752\) 0.235941 0.00860390
\(753\) −8.11074 −0.295572
\(754\) −9.25022 −0.336873
\(755\) 8.39218 0.305423
\(756\) 9.04937 0.329123
\(757\) 31.3110 1.13802 0.569009 0.822331i \(-0.307327\pi\)
0.569009 + 0.822331i \(0.307327\pi\)
\(758\) −12.8868 −0.468068
\(759\) 36.9868 1.34253
\(760\) −1.98730 −0.0720871
\(761\) −36.3495 −1.31767 −0.658835 0.752287i \(-0.728950\pi\)
−0.658835 + 0.752287i \(0.728950\pi\)
\(762\) 2.12537 0.0769941
\(763\) −10.7725 −0.389992
\(764\) −18.3453 −0.663710
\(765\) −9.18882 −0.332222
\(766\) 0.170091 0.00614565
\(767\) 0.614367 0.0221835
\(768\) −1.33263 −0.0480872
\(769\) −13.5460 −0.488482 −0.244241 0.969715i \(-0.578539\pi\)
−0.244241 + 0.969715i \(0.578539\pi\)
\(770\) −6.08002 −0.219109
\(771\) 19.3441 0.696660
\(772\) 15.1604 0.545635
\(773\) 9.64956 0.347071 0.173535 0.984828i \(-0.444481\pi\)
0.173535 + 0.984828i \(0.444481\pi\)
\(774\) −15.7252 −0.565230
\(775\) −1.00000 −0.0359211
\(776\) 0.423705 0.0152101
\(777\) 5.62982 0.201969
\(778\) −25.1888 −0.903061
\(779\) −12.5189 −0.448538
\(780\) 1.33263 0.0477159
\(781\) −11.3176 −0.404976
\(782\) 55.0873 1.96992
\(783\) −52.0710 −1.86086
\(784\) −4.41566 −0.157702
\(785\) 10.2898 0.367260
\(786\) 5.63269 0.200912
\(787\) −12.7149 −0.453237 −0.226619 0.973984i \(-0.572767\pi\)
−0.226619 + 0.973984i \(0.572767\pi\)
\(788\) −6.46630 −0.230352
\(789\) −18.1328 −0.645544
\(790\) 9.61181 0.341973
\(791\) −33.2830 −1.18341
\(792\) −4.62961 −0.164506
\(793\) 6.39470 0.227083
\(794\) 6.54529 0.232284
\(795\) 7.82626 0.277569
\(796\) −1.74394 −0.0618123
\(797\) 25.8807 0.916741 0.458371 0.888761i \(-0.348433\pi\)
0.458371 + 0.888761i \(0.348433\pi\)
\(798\) −4.25745 −0.150712
\(799\) −1.77113 −0.0626580
\(800\) 1.00000 0.0353553
\(801\) 7.93269 0.280288
\(802\) 19.3588 0.683583
\(803\) −2.63873 −0.0931188
\(804\) 1.14348 0.0403275
\(805\) 11.7973 0.415799
\(806\) −1.00000 −0.0352235
\(807\) −21.7846 −0.766853
\(808\) −16.8595 −0.593115
\(809\) −19.8834 −0.699062 −0.349531 0.936925i \(-0.613659\pi\)
−0.349531 + 0.936925i \(0.613659\pi\)
\(810\) 3.82932 0.134549
\(811\) 25.7884 0.905553 0.452776 0.891624i \(-0.350434\pi\)
0.452776 + 0.891624i \(0.350434\pi\)
\(812\) −14.8706 −0.521854
\(813\) −11.6025 −0.406918
\(814\) −9.93892 −0.348359
\(815\) 2.40960 0.0844046
\(816\) 10.0036 0.350195
\(817\) 25.5297 0.893171
\(818\) 3.72518 0.130248
\(819\) −1.96784 −0.0687618
\(820\) 6.29946 0.219987
\(821\) 11.1468 0.389027 0.194513 0.980900i \(-0.437687\pi\)
0.194513 + 0.980900i \(0.437687\pi\)
\(822\) 27.0059 0.941938
\(823\) 9.39920 0.327635 0.163818 0.986491i \(-0.447619\pi\)
0.163818 + 0.986491i \(0.447619\pi\)
\(824\) −5.77995 −0.201354
\(825\) −5.04011 −0.175474
\(826\) 0.987650 0.0343647
\(827\) −38.8186 −1.34985 −0.674927 0.737884i \(-0.735825\pi\)
−0.674927 + 0.737884i \(0.735825\pi\)
\(828\) 8.98298 0.312180
\(829\) 36.2401 1.25867 0.629336 0.777134i \(-0.283327\pi\)
0.629336 + 0.777134i \(0.283327\pi\)
\(830\) −11.1875 −0.388323
\(831\) 30.9199 1.07260
\(832\) 1.00000 0.0346688
\(833\) 33.1467 1.14847
\(834\) −21.1814 −0.733451
\(835\) −13.6758 −0.473271
\(836\) 7.51613 0.259951
\(837\) −5.62916 −0.194572
\(838\) 9.56328 0.330358
\(839\) 27.3225 0.943277 0.471638 0.881792i \(-0.343663\pi\)
0.471638 + 0.881792i \(0.343663\pi\)
\(840\) 2.14232 0.0739172
\(841\) 56.5666 1.95057
\(842\) −15.4149 −0.531232
\(843\) −43.5549 −1.50011
\(844\) 5.59671 0.192647
\(845\) −1.00000 −0.0344010
\(846\) −0.288814 −0.00992964
\(847\) 5.31162 0.182509
\(848\) 5.87278 0.201672
\(849\) −41.6229 −1.42849
\(850\) −7.50664 −0.257475
\(851\) 19.2848 0.661074
\(852\) 3.98782 0.136620
\(853\) 47.3193 1.62018 0.810091 0.586304i \(-0.199417\pi\)
0.810091 + 0.586304i \(0.199417\pi\)
\(854\) 10.2801 0.351776
\(855\) 2.43264 0.0831947
\(856\) −6.73092 −0.230058
\(857\) 2.99223 0.102213 0.0511064 0.998693i \(-0.483725\pi\)
0.0511064 + 0.998693i \(0.483725\pi\)
\(858\) −5.04011 −0.172067
\(859\) −25.9564 −0.885621 −0.442811 0.896615i \(-0.646019\pi\)
−0.442811 + 0.896615i \(0.646019\pi\)
\(860\) −12.8464 −0.438059
\(861\) 13.4955 0.459925
\(862\) 32.3013 1.10019
\(863\) 23.8018 0.810224 0.405112 0.914267i \(-0.367233\pi\)
0.405112 + 0.914267i \(0.367233\pi\)
\(864\) 5.62916 0.191508
\(865\) −18.3393 −0.623553
\(866\) 30.7989 1.04659
\(867\) −52.4385 −1.78090
\(868\) −1.60759 −0.0545651
\(869\) −36.3526 −1.23318
\(870\) −12.3271 −0.417929
\(871\) −0.858063 −0.0290743
\(872\) −6.70105 −0.226926
\(873\) −0.518654 −0.0175538
\(874\) −14.5838 −0.493304
\(875\) −1.60759 −0.0543464
\(876\) 0.929769 0.0314140
\(877\) 49.1750 1.66052 0.830261 0.557374i \(-0.188191\pi\)
0.830261 + 0.557374i \(0.188191\pi\)
\(878\) −24.7611 −0.835645
\(879\) −28.0436 −0.945888
\(880\) −3.78207 −0.127494
\(881\) −22.7367 −0.766020 −0.383010 0.923744i \(-0.625113\pi\)
−0.383010 + 0.923744i \(0.625113\pi\)
\(882\) 5.40518 0.182002
\(883\) 5.17174 0.174043 0.0870214 0.996206i \(-0.472265\pi\)
0.0870214 + 0.996206i \(0.472265\pi\)
\(884\) −7.50664 −0.252475
\(885\) 0.818725 0.0275211
\(886\) −3.21255 −0.107928
\(887\) 43.1654 1.44935 0.724677 0.689089i \(-0.241989\pi\)
0.724677 + 0.689089i \(0.241989\pi\)
\(888\) 3.50203 0.117520
\(889\) −2.56389 −0.0859902
\(890\) 6.48047 0.217226
\(891\) −14.4828 −0.485191
\(892\) −24.7089 −0.827316
\(893\) 0.468887 0.0156907
\(894\) 31.0751 1.03931
\(895\) 7.36796 0.246284
\(896\) 1.60759 0.0537058
\(897\) 9.77949 0.326528
\(898\) −12.2838 −0.409914
\(899\) 9.25022 0.308512
\(900\) −1.22409 −0.0408031
\(901\) −44.0848 −1.46868
\(902\) −23.8250 −0.793287
\(903\) −27.5212 −0.915847
\(904\) −20.7037 −0.688595
\(905\) 0.113739 0.00378081
\(906\) 11.1837 0.371553
\(907\) 18.9913 0.630597 0.315298 0.948993i \(-0.397895\pi\)
0.315298 + 0.948993i \(0.397895\pi\)
\(908\) −8.97325 −0.297788
\(909\) 20.6376 0.684505
\(910\) −1.60759 −0.0532910
\(911\) 17.0116 0.563619 0.281810 0.959470i \(-0.409065\pi\)
0.281810 + 0.959470i \(0.409065\pi\)
\(912\) −2.64834 −0.0876954
\(913\) 42.3118 1.40032
\(914\) −1.71695 −0.0567916
\(915\) 8.52178 0.281721
\(916\) −2.94499 −0.0973052
\(917\) −6.79487 −0.224386
\(918\) −42.2561 −1.39466
\(919\) 1.08728 0.0358661 0.0179330 0.999839i \(-0.494291\pi\)
0.0179330 + 0.999839i \(0.494291\pi\)
\(920\) 7.33848 0.241942
\(921\) 44.3399 1.46105
\(922\) 21.8774 0.720494
\(923\) −2.99244 −0.0984973
\(924\) −8.10243 −0.266550
\(925\) −2.62790 −0.0864049
\(926\) −17.6147 −0.578856
\(927\) 7.07519 0.232380
\(928\) −9.25022 −0.303653
\(929\) −55.7342 −1.82858 −0.914290 0.405060i \(-0.867251\pi\)
−0.914290 + 0.405060i \(0.867251\pi\)
\(930\) −1.33263 −0.0436987
\(931\) −8.77526 −0.287597
\(932\) 15.0687 0.493591
\(933\) −34.3323 −1.12399
\(934\) 9.30031 0.304315
\(935\) 28.3907 0.928474
\(936\) −1.22409 −0.0400107
\(937\) 17.4774 0.570963 0.285481 0.958384i \(-0.407847\pi\)
0.285481 + 0.958384i \(0.407847\pi\)
\(938\) −1.37941 −0.0450394
\(939\) 23.0162 0.751104
\(940\) −0.235941 −0.00769556
\(941\) 8.01048 0.261134 0.130567 0.991439i \(-0.458320\pi\)
0.130567 + 0.991439i \(0.458320\pi\)
\(942\) 13.7126 0.446780
\(943\) 46.2285 1.50541
\(944\) 0.614367 0.0199959
\(945\) −9.04937 −0.294376
\(946\) 48.5861 1.57967
\(947\) 42.3446 1.37602 0.688008 0.725703i \(-0.258486\pi\)
0.688008 + 0.725703i \(0.258486\pi\)
\(948\) 12.8090 0.416017
\(949\) −0.697694 −0.0226481
\(950\) 1.98730 0.0644767
\(951\) 21.5422 0.698552
\(952\) −12.0676 −0.391113
\(953\) −38.7034 −1.25372 −0.626862 0.779130i \(-0.715661\pi\)
−0.626862 + 0.779130i \(0.715661\pi\)
\(954\) −7.18883 −0.232747
\(955\) 18.3453 0.593640
\(956\) −24.6433 −0.797021
\(957\) 46.6222 1.50708
\(958\) −18.3745 −0.593653
\(959\) −32.5779 −1.05199
\(960\) 1.33263 0.0430105
\(961\) 1.00000 0.0322581
\(962\) −2.62790 −0.0847270
\(963\) 8.23927 0.265507
\(964\) 10.4708 0.337243
\(965\) −15.1604 −0.488030
\(966\) 15.7214 0.505828
\(967\) 47.4309 1.52527 0.762637 0.646827i \(-0.223904\pi\)
0.762637 + 0.646827i \(0.223904\pi\)
\(968\) 3.30409 0.106197
\(969\) 19.8802 0.638643
\(970\) −0.423705 −0.0136043
\(971\) 2.65825 0.0853074 0.0426537 0.999090i \(-0.486419\pi\)
0.0426537 + 0.999090i \(0.486419\pi\)
\(972\) −11.7844 −0.377985
\(973\) 25.5517 0.819149
\(974\) 37.3823 1.19781
\(975\) −1.33263 −0.0426784
\(976\) 6.39470 0.204689
\(977\) −37.4446 −1.19796 −0.598980 0.800764i \(-0.704427\pi\)
−0.598980 + 0.800764i \(0.704427\pi\)
\(978\) 3.21111 0.102680
\(979\) −24.5096 −0.783331
\(980\) 4.41566 0.141053
\(981\) 8.20270 0.261892
\(982\) −31.5304 −1.00617
\(983\) −30.9157 −0.986058 −0.493029 0.870013i \(-0.664110\pi\)
−0.493029 + 0.870013i \(0.664110\pi\)
\(984\) 8.39486 0.267618
\(985\) 6.46630 0.206033
\(986\) 69.4380 2.21136
\(987\) −0.505463 −0.0160891
\(988\) 1.98730 0.0632246
\(989\) −94.2730 −2.99771
\(990\) 4.62961 0.147139
\(991\) −26.7403 −0.849432 −0.424716 0.905327i \(-0.639626\pi\)
−0.424716 + 0.905327i \(0.639626\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −3.02731 −0.0960689
\(994\) −4.81061 −0.152583
\(995\) 1.74394 0.0552866
\(996\) −14.9088 −0.472403
\(997\) 24.0696 0.762293 0.381146 0.924515i \(-0.375529\pi\)
0.381146 + 0.924515i \(0.375529\pi\)
\(998\) −40.8881 −1.29429
\(999\) −14.7929 −0.468026
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 \(a_p\))