Properties

Label 4010.2.a.k.1.9
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.79590\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.154802 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.154802 q^{6} -4.41535 q^{7} -1.00000 q^{8} -2.97604 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.154802 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.154802 q^{6} -4.41535 q^{7} -1.00000 q^{8} -2.97604 q^{9} +1.00000 q^{10} -3.07208 q^{11} -0.154802 q^{12} +6.08938 q^{13} +4.41535 q^{14} +0.154802 q^{15} +1.00000 q^{16} +6.99132 q^{17} +2.97604 q^{18} -0.745971 q^{19} -1.00000 q^{20} +0.683507 q^{21} +3.07208 q^{22} -2.22179 q^{23} +0.154802 q^{24} +1.00000 q^{25} -6.08938 q^{26} +0.925104 q^{27} -4.41535 q^{28} +2.48268 q^{29} -0.154802 q^{30} +2.52786 q^{31} -1.00000 q^{32} +0.475565 q^{33} -6.99132 q^{34} +4.41535 q^{35} -2.97604 q^{36} -3.01023 q^{37} +0.745971 q^{38} -0.942651 q^{39} +1.00000 q^{40} +6.07906 q^{41} -0.683507 q^{42} +1.67837 q^{43} -3.07208 q^{44} +2.97604 q^{45} +2.22179 q^{46} +2.53479 q^{47} -0.154802 q^{48} +12.4953 q^{49} -1.00000 q^{50} -1.08227 q^{51} +6.08938 q^{52} -0.745448 q^{53} -0.925104 q^{54} +3.07208 q^{55} +4.41535 q^{56} +0.115478 q^{57} -2.48268 q^{58} -3.79594 q^{59} +0.154802 q^{60} +4.16103 q^{61} -2.52786 q^{62} +13.1402 q^{63} +1.00000 q^{64} -6.08938 q^{65} -0.475565 q^{66} -13.0017 q^{67} +6.99132 q^{68} +0.343938 q^{69} -4.41535 q^{70} +8.13964 q^{71} +2.97604 q^{72} +1.02853 q^{73} +3.01023 q^{74} -0.154802 q^{75} -0.745971 q^{76} +13.5643 q^{77} +0.942651 q^{78} -7.95012 q^{79} -1.00000 q^{80} +8.78490 q^{81} -6.07906 q^{82} -6.71915 q^{83} +0.683507 q^{84} -6.99132 q^{85} -1.67837 q^{86} -0.384325 q^{87} +3.07208 q^{88} +8.62004 q^{89} -2.97604 q^{90} -26.8868 q^{91} -2.22179 q^{92} -0.391319 q^{93} -2.53479 q^{94} +0.745971 q^{95} +0.154802 q^{96} -16.4913 q^{97} -12.4953 q^{98} +9.14262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

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
\(3\) −0.154802 −0.0893752 −0.0446876 0.999001i \(-0.514229\pi\)
−0.0446876 + 0.999001i \(0.514229\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 0.154802 0.0631978
\(7\) −4.41535 −1.66885 −0.834423 0.551125i \(-0.814199\pi\)
−0.834423 + 0.551125i \(0.814199\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.97604 −0.992012
\(10\) 1.00000 0.316228
\(11\) −3.07208 −0.926267 −0.463133 0.886289i \(-0.653275\pi\)
−0.463133 + 0.886289i \(0.653275\pi\)
\(12\) −0.154802 −0.0446876
\(13\) 6.08938 1.68889 0.844446 0.535641i \(-0.179930\pi\)
0.844446 + 0.535641i \(0.179930\pi\)
\(14\) 4.41535 1.18005
\(15\) 0.154802 0.0399698
\(16\) 1.00000 0.250000
\(17\) 6.99132 1.69565 0.847823 0.530280i \(-0.177913\pi\)
0.847823 + 0.530280i \(0.177913\pi\)
\(18\) 2.97604 0.701458
\(19\) −0.745971 −0.171138 −0.0855688 0.996332i \(-0.527271\pi\)
−0.0855688 + 0.996332i \(0.527271\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0.683507 0.149153
\(22\) 3.07208 0.654969
\(23\) −2.22179 −0.463274 −0.231637 0.972802i \(-0.574408\pi\)
−0.231637 + 0.972802i \(0.574408\pi\)
\(24\) 0.154802 0.0315989
\(25\) 1.00000 0.200000
\(26\) −6.08938 −1.19423
\(27\) 0.925104 0.178036
\(28\) −4.41535 −0.834423
\(29\) 2.48268 0.461023 0.230511 0.973070i \(-0.425960\pi\)
0.230511 + 0.973070i \(0.425960\pi\)
\(30\) −0.154802 −0.0282629
\(31\) 2.52786 0.454017 0.227009 0.973893i \(-0.427105\pi\)
0.227009 + 0.973893i \(0.427105\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.475565 0.0827852
\(34\) −6.99132 −1.19900
\(35\) 4.41535 0.746330
\(36\) −2.97604 −0.496006
\(37\) −3.01023 −0.494878 −0.247439 0.968903i \(-0.579589\pi\)
−0.247439 + 0.968903i \(0.579589\pi\)
\(38\) 0.745971 0.121013
\(39\) −0.942651 −0.150945
\(40\) 1.00000 0.158114
\(41\) 6.07906 0.949389 0.474694 0.880151i \(-0.342559\pi\)
0.474694 + 0.880151i \(0.342559\pi\)
\(42\) −0.683507 −0.105467
\(43\) 1.67837 0.255948 0.127974 0.991777i \(-0.459153\pi\)
0.127974 + 0.991777i \(0.459153\pi\)
\(44\) −3.07208 −0.463133
\(45\) 2.97604 0.443641
\(46\) 2.22179 0.327584
\(47\) 2.53479 0.369737 0.184868 0.982763i \(-0.440814\pi\)
0.184868 + 0.982763i \(0.440814\pi\)
\(48\) −0.154802 −0.0223438
\(49\) 12.4953 1.78504
\(50\) −1.00000 −0.141421
\(51\) −1.08227 −0.151549
\(52\) 6.08938 0.844446
\(53\) −0.745448 −0.102395 −0.0511976 0.998689i \(-0.516304\pi\)
−0.0511976 + 0.998689i \(0.516304\pi\)
\(54\) −0.925104 −0.125891
\(55\) 3.07208 0.414239
\(56\) 4.41535 0.590026
\(57\) 0.115478 0.0152954
\(58\) −2.48268 −0.325992
\(59\) −3.79594 −0.494189 −0.247095 0.968991i \(-0.579476\pi\)
−0.247095 + 0.968991i \(0.579476\pi\)
\(60\) 0.154802 0.0199849
\(61\) 4.16103 0.532766 0.266383 0.963867i \(-0.414171\pi\)
0.266383 + 0.963867i \(0.414171\pi\)
\(62\) −2.52786 −0.321039
\(63\) 13.1402 1.65551
\(64\) 1.00000 0.125000
\(65\) −6.08938 −0.755295
\(66\) −0.475565 −0.0585380
\(67\) −13.0017 −1.58841 −0.794203 0.607653i \(-0.792111\pi\)
−0.794203 + 0.607653i \(0.792111\pi\)
\(68\) 6.99132 0.847823
\(69\) 0.343938 0.0414052
\(70\) −4.41535 −0.527735
\(71\) 8.13964 0.965998 0.482999 0.875621i \(-0.339548\pi\)
0.482999 + 0.875621i \(0.339548\pi\)
\(72\) 2.97604 0.350729
\(73\) 1.02853 0.120380 0.0601902 0.998187i \(-0.480829\pi\)
0.0601902 + 0.998187i \(0.480829\pi\)
\(74\) 3.01023 0.349932
\(75\) −0.154802 −0.0178750
\(76\) −0.745971 −0.0855688
\(77\) 13.5643 1.54580
\(78\) 0.942651 0.106734
\(79\) −7.95012 −0.894459 −0.447229 0.894419i \(-0.647589\pi\)
−0.447229 + 0.894419i \(0.647589\pi\)
\(80\) −1.00000 −0.111803
\(81\) 8.78490 0.976100
\(82\) −6.07906 −0.671319
\(83\) −6.71915 −0.737522 −0.368761 0.929524i \(-0.620218\pi\)
−0.368761 + 0.929524i \(0.620218\pi\)
\(84\) 0.683507 0.0745767
\(85\) −6.99132 −0.758316
\(86\) −1.67837 −0.180983
\(87\) −0.384325 −0.0412040
\(88\) 3.07208 0.327485
\(89\) 8.62004 0.913722 0.456861 0.889538i \(-0.348974\pi\)
0.456861 + 0.889538i \(0.348974\pi\)
\(90\) −2.97604 −0.313702
\(91\) −26.8868 −2.81850
\(92\) −2.22179 −0.231637
\(93\) −0.391319 −0.0405779
\(94\) −2.53479 −0.261443
\(95\) 0.745971 0.0765350
\(96\) 0.154802 0.0157994
\(97\) −16.4913 −1.67444 −0.837218 0.546870i \(-0.815819\pi\)
−0.837218 + 0.546870i \(0.815819\pi\)
\(98\) −12.4953 −1.26222
\(99\) 9.14262 0.918868
\(100\) 1.00000 0.100000
\(101\) −11.6975 −1.16394 −0.581970 0.813210i \(-0.697718\pi\)
−0.581970 + 0.813210i \(0.697718\pi\)
\(102\) 1.08227 0.107161
\(103\) 2.10592 0.207503 0.103751 0.994603i \(-0.466915\pi\)
0.103751 + 0.994603i \(0.466915\pi\)
\(104\) −6.08938 −0.597113
\(105\) −0.683507 −0.0667034
\(106\) 0.745448 0.0724043
\(107\) −11.0502 −1.06826 −0.534130 0.845402i \(-0.679361\pi\)
−0.534130 + 0.845402i \(0.679361\pi\)
\(108\) 0.925104 0.0890182
\(109\) −3.08659 −0.295642 −0.147821 0.989014i \(-0.547226\pi\)
−0.147821 + 0.989014i \(0.547226\pi\)
\(110\) −3.07208 −0.292911
\(111\) 0.465990 0.0442299
\(112\) −4.41535 −0.417211
\(113\) 12.8891 1.21250 0.606250 0.795274i \(-0.292673\pi\)
0.606250 + 0.795274i \(0.292673\pi\)
\(114\) −0.115478 −0.0108155
\(115\) 2.22179 0.207183
\(116\) 2.48268 0.230511
\(117\) −18.1222 −1.67540
\(118\) 3.79594 0.349444
\(119\) −30.8691 −2.82977
\(120\) −0.154802 −0.0141315
\(121\) −1.56233 −0.142030
\(122\) −4.16103 −0.376722
\(123\) −0.941052 −0.0848518
\(124\) 2.52786 0.227009
\(125\) −1.00000 −0.0894427
\(126\) −13.1402 −1.17063
\(127\) −11.2095 −0.994681 −0.497340 0.867556i \(-0.665690\pi\)
−0.497340 + 0.867556i \(0.665690\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.259815 −0.0228754
\(130\) 6.08938 0.534074
\(131\) 6.16032 0.538230 0.269115 0.963108i \(-0.413269\pi\)
0.269115 + 0.963108i \(0.413269\pi\)
\(132\) 0.475565 0.0413926
\(133\) 3.29372 0.285602
\(134\) 13.0017 1.12317
\(135\) −0.925104 −0.0796203
\(136\) −6.99132 −0.599501
\(137\) −16.4405 −1.40460 −0.702302 0.711879i \(-0.747844\pi\)
−0.702302 + 0.711879i \(0.747844\pi\)
\(138\) −0.343938 −0.0292779
\(139\) 5.10643 0.433122 0.216561 0.976269i \(-0.430516\pi\)
0.216561 + 0.976269i \(0.430516\pi\)
\(140\) 4.41535 0.373165
\(141\) −0.392391 −0.0330453
\(142\) −8.13964 −0.683063
\(143\) −18.7071 −1.56436
\(144\) −2.97604 −0.248003
\(145\) −2.48268 −0.206176
\(146\) −1.02853 −0.0851217
\(147\) −1.93430 −0.159539
\(148\) −3.01023 −0.247439
\(149\) 8.47553 0.694342 0.347171 0.937802i \(-0.387142\pi\)
0.347171 + 0.937802i \(0.387142\pi\)
\(150\) 0.154802 0.0126396
\(151\) −20.8152 −1.69391 −0.846957 0.531661i \(-0.821568\pi\)
−0.846957 + 0.531661i \(0.821568\pi\)
\(152\) 0.745971 0.0605063
\(153\) −20.8064 −1.68210
\(154\) −13.5643 −1.09304
\(155\) −2.52786 −0.203043
\(156\) −0.942651 −0.0754725
\(157\) 6.57637 0.524851 0.262426 0.964952i \(-0.415478\pi\)
0.262426 + 0.964952i \(0.415478\pi\)
\(158\) 7.95012 0.632478
\(159\) 0.115397 0.00915159
\(160\) 1.00000 0.0790569
\(161\) 9.80996 0.773133
\(162\) −8.78490 −0.690207
\(163\) −7.48490 −0.586263 −0.293131 0.956072i \(-0.594697\pi\)
−0.293131 + 0.956072i \(0.594697\pi\)
\(164\) 6.07906 0.474694
\(165\) −0.475565 −0.0370227
\(166\) 6.71915 0.521507
\(167\) −8.85429 −0.685166 −0.342583 0.939488i \(-0.611302\pi\)
−0.342583 + 0.939488i \(0.611302\pi\)
\(168\) −0.683507 −0.0527337
\(169\) 24.0806 1.85235
\(170\) 6.99132 0.536210
\(171\) 2.22004 0.169770
\(172\) 1.67837 0.127974
\(173\) −12.4239 −0.944571 −0.472285 0.881446i \(-0.656571\pi\)
−0.472285 + 0.881446i \(0.656571\pi\)
\(174\) 0.384325 0.0291356
\(175\) −4.41535 −0.333769
\(176\) −3.07208 −0.231567
\(177\) 0.587620 0.0441682
\(178\) −8.62004 −0.646099
\(179\) 4.44563 0.332282 0.166141 0.986102i \(-0.446869\pi\)
0.166141 + 0.986102i \(0.446869\pi\)
\(180\) 2.97604 0.221821
\(181\) −16.4715 −1.22431 −0.612157 0.790736i \(-0.709698\pi\)
−0.612157 + 0.790736i \(0.709698\pi\)
\(182\) 26.8868 1.99298
\(183\) −0.644138 −0.0476160
\(184\) 2.22179 0.163792
\(185\) 3.01023 0.221316
\(186\) 0.391319 0.0286929
\(187\) −21.4779 −1.57062
\(188\) 2.53479 0.184868
\(189\) −4.08466 −0.297115
\(190\) −0.745971 −0.0541184
\(191\) 5.80047 0.419707 0.209853 0.977733i \(-0.432701\pi\)
0.209853 + 0.977733i \(0.432701\pi\)
\(192\) −0.154802 −0.0111719
\(193\) 17.6844 1.27295 0.636475 0.771297i \(-0.280392\pi\)
0.636475 + 0.771297i \(0.280392\pi\)
\(194\) 16.4913 1.18400
\(195\) 0.942651 0.0675046
\(196\) 12.4953 0.892522
\(197\) 0.207977 0.0148178 0.00740888 0.999973i \(-0.497642\pi\)
0.00740888 + 0.999973i \(0.497642\pi\)
\(198\) −9.14262 −0.649738
\(199\) 20.8974 1.48138 0.740688 0.671849i \(-0.234500\pi\)
0.740688 + 0.671849i \(0.234500\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 2.01269 0.141964
\(202\) 11.6975 0.823030
\(203\) −10.9619 −0.769375
\(204\) −1.08227 −0.0757743
\(205\) −6.07906 −0.424580
\(206\) −2.10592 −0.146727
\(207\) 6.61212 0.459574
\(208\) 6.08938 0.422223
\(209\) 2.29168 0.158519
\(210\) 0.683507 0.0471664
\(211\) 18.2355 1.25538 0.627691 0.778463i \(-0.284000\pi\)
0.627691 + 0.778463i \(0.284000\pi\)
\(212\) −0.745448 −0.0511976
\(213\) −1.26004 −0.0863362
\(214\) 11.0502 0.755374
\(215\) −1.67837 −0.114464
\(216\) −0.925104 −0.0629454
\(217\) −11.1614 −0.757685
\(218\) 3.08659 0.209050
\(219\) −0.159219 −0.0107590
\(220\) 3.07208 0.207120
\(221\) 42.5729 2.86376
\(222\) −0.465990 −0.0312752
\(223\) −0.115780 −0.00775320 −0.00387660 0.999992i \(-0.501234\pi\)
−0.00387660 + 0.999992i \(0.501234\pi\)
\(224\) 4.41535 0.295013
\(225\) −2.97604 −0.198402
\(226\) −12.8891 −0.857367
\(227\) −29.4485 −1.95457 −0.977284 0.211935i \(-0.932024\pi\)
−0.977284 + 0.211935i \(0.932024\pi\)
\(228\) 0.115478 0.00764772
\(229\) −6.16106 −0.407134 −0.203567 0.979061i \(-0.565254\pi\)
−0.203567 + 0.979061i \(0.565254\pi\)
\(230\) −2.22179 −0.146500
\(231\) −2.09979 −0.138156
\(232\) −2.48268 −0.162996
\(233\) 8.87040 0.581119 0.290560 0.956857i \(-0.406159\pi\)
0.290560 + 0.956857i \(0.406159\pi\)
\(234\) 18.1222 1.18469
\(235\) −2.53479 −0.165351
\(236\) −3.79594 −0.247095
\(237\) 1.23070 0.0799424
\(238\) 30.8691 2.00095
\(239\) 7.53613 0.487472 0.243736 0.969842i \(-0.421627\pi\)
0.243736 + 0.969842i \(0.421627\pi\)
\(240\) 0.154802 0.00999245
\(241\) −25.3180 −1.63088 −0.815439 0.578844i \(-0.803504\pi\)
−0.815439 + 0.578844i \(0.803504\pi\)
\(242\) 1.56233 0.100430
\(243\) −4.13524 −0.265276
\(244\) 4.16103 0.266383
\(245\) −12.4953 −0.798296
\(246\) 0.941052 0.0599993
\(247\) −4.54251 −0.289033
\(248\) −2.52786 −0.160519
\(249\) 1.04014 0.0659162
\(250\) 1.00000 0.0632456
\(251\) 18.4613 1.16527 0.582633 0.812735i \(-0.302022\pi\)
0.582633 + 0.812735i \(0.302022\pi\)
\(252\) 13.1402 0.827757
\(253\) 6.82550 0.429116
\(254\) 11.2095 0.703345
\(255\) 1.08227 0.0677746
\(256\) 1.00000 0.0625000
\(257\) −28.3938 −1.77116 −0.885578 0.464491i \(-0.846237\pi\)
−0.885578 + 0.464491i \(0.846237\pi\)
\(258\) 0.259815 0.0161754
\(259\) 13.2912 0.825876
\(260\) −6.08938 −0.377648
\(261\) −7.38855 −0.457340
\(262\) −6.16032 −0.380586
\(263\) 15.6425 0.964559 0.482280 0.876017i \(-0.339809\pi\)
0.482280 + 0.876017i \(0.339809\pi\)
\(264\) −0.475565 −0.0292690
\(265\) 0.745448 0.0457925
\(266\) −3.29372 −0.201951
\(267\) −1.33440 −0.0816641
\(268\) −13.0017 −0.794203
\(269\) 12.6077 0.768704 0.384352 0.923187i \(-0.374425\pi\)
0.384352 + 0.923187i \(0.374425\pi\)
\(270\) 0.925104 0.0563001
\(271\) −25.6235 −1.55651 −0.778257 0.627946i \(-0.783896\pi\)
−0.778257 + 0.627946i \(0.783896\pi\)
\(272\) 6.99132 0.423911
\(273\) 4.16213 0.251904
\(274\) 16.4405 0.993205
\(275\) −3.07208 −0.185253
\(276\) 0.343938 0.0207026
\(277\) 29.5108 1.77313 0.886565 0.462604i \(-0.153085\pi\)
0.886565 + 0.462604i \(0.153085\pi\)
\(278\) −5.10643 −0.306263
\(279\) −7.52301 −0.450391
\(280\) −4.41535 −0.263868
\(281\) −11.9491 −0.712824 −0.356412 0.934329i \(-0.616000\pi\)
−0.356412 + 0.934329i \(0.616000\pi\)
\(282\) 0.392391 0.0233666
\(283\) −29.0019 −1.72398 −0.861991 0.506923i \(-0.830783\pi\)
−0.861991 + 0.506923i \(0.830783\pi\)
\(284\) 8.13964 0.482999
\(285\) −0.115478 −0.00684033
\(286\) 18.7071 1.10617
\(287\) −26.8412 −1.58438
\(288\) 2.97604 0.175365
\(289\) 31.8786 1.87521
\(290\) 2.48268 0.145788
\(291\) 2.55289 0.149653
\(292\) 1.02853 0.0601902
\(293\) −7.99449 −0.467043 −0.233521 0.972352i \(-0.575025\pi\)
−0.233521 + 0.972352i \(0.575025\pi\)
\(294\) 1.93430 0.112811
\(295\) 3.79594 0.221008
\(296\) 3.01023 0.174966
\(297\) −2.84199 −0.164909
\(298\) −8.47553 −0.490974
\(299\) −13.5293 −0.782420
\(300\) −0.154802 −0.00893752
\(301\) −7.41058 −0.427138
\(302\) 20.8152 1.19778
\(303\) 1.81079 0.104027
\(304\) −0.745971 −0.0427844
\(305\) −4.16103 −0.238260
\(306\) 20.8064 1.18942
\(307\) 24.2347 1.38315 0.691574 0.722306i \(-0.256918\pi\)
0.691574 + 0.722306i \(0.256918\pi\)
\(308\) 13.5643 0.772898
\(309\) −0.326002 −0.0185456
\(310\) 2.52786 0.143573
\(311\) 25.0016 1.41771 0.708854 0.705355i \(-0.249212\pi\)
0.708854 + 0.705355i \(0.249212\pi\)
\(312\) 0.942651 0.0533671
\(313\) −22.7439 −1.28556 −0.642780 0.766051i \(-0.722219\pi\)
−0.642780 + 0.766051i \(0.722219\pi\)
\(314\) −6.57637 −0.371126
\(315\) −13.1402 −0.740369
\(316\) −7.95012 −0.447229
\(317\) −5.43701 −0.305373 −0.152686 0.988275i \(-0.548792\pi\)
−0.152686 + 0.988275i \(0.548792\pi\)
\(318\) −0.115397 −0.00647115
\(319\) −7.62700 −0.427030
\(320\) −1.00000 −0.0559017
\(321\) 1.71059 0.0954760
\(322\) −9.80996 −0.546688
\(323\) −5.21533 −0.290188
\(324\) 8.78490 0.488050
\(325\) 6.08938 0.337778
\(326\) 7.48490 0.414551
\(327\) 0.477811 0.0264230
\(328\) −6.07906 −0.335660
\(329\) −11.1920 −0.617034
\(330\) 0.475565 0.0261790
\(331\) 19.8682 1.09206 0.546028 0.837767i \(-0.316139\pi\)
0.546028 + 0.837767i \(0.316139\pi\)
\(332\) −6.71915 −0.368761
\(333\) 8.95855 0.490925
\(334\) 8.85429 0.484485
\(335\) 13.0017 0.710356
\(336\) 0.683507 0.0372883
\(337\) −9.36919 −0.510372 −0.255186 0.966892i \(-0.582137\pi\)
−0.255186 + 0.966892i \(0.582137\pi\)
\(338\) −24.0806 −1.30981
\(339\) −1.99526 −0.108367
\(340\) −6.99132 −0.379158
\(341\) −7.76579 −0.420541
\(342\) −2.22004 −0.120046
\(343\) −24.2637 −1.31012
\(344\) −1.67837 −0.0904915
\(345\) −0.343938 −0.0185170
\(346\) 12.4239 0.667912
\(347\) −8.04989 −0.432141 −0.216070 0.976378i \(-0.569324\pi\)
−0.216070 + 0.976378i \(0.569324\pi\)
\(348\) −0.384325 −0.0206020
\(349\) −14.1691 −0.758456 −0.379228 0.925303i \(-0.623810\pi\)
−0.379228 + 0.925303i \(0.623810\pi\)
\(350\) 4.41535 0.236010
\(351\) 5.63332 0.300684
\(352\) 3.07208 0.163742
\(353\) 29.1375 1.55083 0.775417 0.631449i \(-0.217539\pi\)
0.775417 + 0.631449i \(0.217539\pi\)
\(354\) −0.587620 −0.0312317
\(355\) −8.13964 −0.432007
\(356\) 8.62004 0.456861
\(357\) 4.77862 0.252911
\(358\) −4.44563 −0.234959
\(359\) −1.74842 −0.0922780 −0.0461390 0.998935i \(-0.514692\pi\)
−0.0461390 + 0.998935i \(0.514692\pi\)
\(360\) −2.97604 −0.156851
\(361\) −18.4435 −0.970712
\(362\) 16.4715 0.865721
\(363\) 0.241853 0.0126940
\(364\) −26.8868 −1.40925
\(365\) −1.02853 −0.0538357
\(366\) 0.644138 0.0336696
\(367\) −13.1991 −0.688986 −0.344493 0.938789i \(-0.611949\pi\)
−0.344493 + 0.938789i \(0.611949\pi\)
\(368\) −2.22179 −0.115819
\(369\) −18.0915 −0.941805
\(370\) −3.01023 −0.156494
\(371\) 3.29141 0.170882
\(372\) −0.391319 −0.0202889
\(373\) −35.7076 −1.84887 −0.924434 0.381341i \(-0.875462\pi\)
−0.924434 + 0.381341i \(0.875462\pi\)
\(374\) 21.4779 1.11060
\(375\) 0.154802 0.00799396
\(376\) −2.53479 −0.130722
\(377\) 15.1180 0.778617
\(378\) 4.08466 0.210092
\(379\) 20.2654 1.04096 0.520481 0.853873i \(-0.325753\pi\)
0.520481 + 0.853873i \(0.325753\pi\)
\(380\) 0.745971 0.0382675
\(381\) 1.73525 0.0888998
\(382\) −5.80047 −0.296778
\(383\) −35.0482 −1.79088 −0.895439 0.445183i \(-0.853139\pi\)
−0.895439 + 0.445183i \(0.853139\pi\)
\(384\) 0.154802 0.00789972
\(385\) −13.5643 −0.691301
\(386\) −17.6844 −0.900111
\(387\) −4.99488 −0.253904
\(388\) −16.4913 −0.837218
\(389\) −16.6478 −0.844078 −0.422039 0.906578i \(-0.638686\pi\)
−0.422039 + 0.906578i \(0.638686\pi\)
\(390\) −0.942651 −0.0477330
\(391\) −15.5332 −0.785549
\(392\) −12.4953 −0.631109
\(393\) −0.953633 −0.0481044
\(394\) −0.207977 −0.0104777
\(395\) 7.95012 0.400014
\(396\) 9.14262 0.459434
\(397\) 3.46731 0.174019 0.0870095 0.996207i \(-0.472269\pi\)
0.0870095 + 0.996207i \(0.472269\pi\)
\(398\) −20.8974 −1.04749
\(399\) −0.509876 −0.0255257
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) −2.01269 −0.100384
\(403\) 15.3931 0.766786
\(404\) −11.6975 −0.581970
\(405\) −8.78490 −0.436525
\(406\) 10.9619 0.544031
\(407\) 9.24766 0.458389
\(408\) 1.08227 0.0535805
\(409\) −39.8306 −1.96949 −0.984747 0.173990i \(-0.944334\pi\)
−0.984747 + 0.173990i \(0.944334\pi\)
\(410\) 6.07906 0.300223
\(411\) 2.54502 0.125537
\(412\) 2.10592 0.103751
\(413\) 16.7604 0.824725
\(414\) −6.61212 −0.324968
\(415\) 6.71915 0.329830
\(416\) −6.08938 −0.298557
\(417\) −0.790487 −0.0387103
\(418\) −2.29168 −0.112090
\(419\) 25.3727 1.23954 0.619768 0.784785i \(-0.287227\pi\)
0.619768 + 0.784785i \(0.287227\pi\)
\(420\) −0.683507 −0.0333517
\(421\) −21.5568 −1.05062 −0.525308 0.850912i \(-0.676050\pi\)
−0.525308 + 0.850912i \(0.676050\pi\)
\(422\) −18.2355 −0.887689
\(423\) −7.54362 −0.366783
\(424\) 0.745448 0.0362022
\(425\) 6.99132 0.339129
\(426\) 1.26004 0.0610489
\(427\) −18.3724 −0.889103
\(428\) −11.0502 −0.534130
\(429\) 2.89590 0.139815
\(430\) 1.67837 0.0809380
\(431\) −3.17088 −0.152736 −0.0763679 0.997080i \(-0.524332\pi\)
−0.0763679 + 0.997080i \(0.524332\pi\)
\(432\) 0.925104 0.0445091
\(433\) −13.6613 −0.656520 −0.328260 0.944587i \(-0.606462\pi\)
−0.328260 + 0.944587i \(0.606462\pi\)
\(434\) 11.1614 0.535764
\(435\) 0.384325 0.0184270
\(436\) −3.08659 −0.147821
\(437\) 1.65739 0.0792836
\(438\) 0.159219 0.00760777
\(439\) −12.4747 −0.595386 −0.297693 0.954662i \(-0.596217\pi\)
−0.297693 + 0.954662i \(0.596217\pi\)
\(440\) −3.07208 −0.146456
\(441\) −37.1865 −1.77079
\(442\) −42.5729 −2.02498
\(443\) −14.6634 −0.696677 −0.348338 0.937369i \(-0.613254\pi\)
−0.348338 + 0.937369i \(0.613254\pi\)
\(444\) 0.465990 0.0221149
\(445\) −8.62004 −0.408629
\(446\) 0.115780 0.00548234
\(447\) −1.31203 −0.0620570
\(448\) −4.41535 −0.208606
\(449\) −10.8612 −0.512573 −0.256286 0.966601i \(-0.582499\pi\)
−0.256286 + 0.966601i \(0.582499\pi\)
\(450\) 2.97604 0.140292
\(451\) −18.6753 −0.879387
\(452\) 12.8891 0.606250
\(453\) 3.22224 0.151394
\(454\) 29.4485 1.38209
\(455\) 26.8868 1.26047
\(456\) −0.115478 −0.00540776
\(457\) −18.3430 −0.858050 −0.429025 0.903293i \(-0.641143\pi\)
−0.429025 + 0.903293i \(0.641143\pi\)
\(458\) 6.16106 0.287888
\(459\) 6.46770 0.301887
\(460\) 2.22179 0.103591
\(461\) 38.6901 1.80198 0.900988 0.433844i \(-0.142843\pi\)
0.900988 + 0.433844i \(0.142843\pi\)
\(462\) 2.09979 0.0976909
\(463\) 23.1873 1.07760 0.538802 0.842433i \(-0.318877\pi\)
0.538802 + 0.842433i \(0.318877\pi\)
\(464\) 2.48268 0.115256
\(465\) 0.391319 0.0181470
\(466\) −8.87040 −0.410913
\(467\) 22.1349 1.02428 0.512140 0.858902i \(-0.328853\pi\)
0.512140 + 0.858902i \(0.328853\pi\)
\(468\) −18.1222 −0.837700
\(469\) 57.4069 2.65080
\(470\) 2.53479 0.116921
\(471\) −1.01804 −0.0469087
\(472\) 3.79594 0.174722
\(473\) −5.15607 −0.237077
\(474\) −1.23070 −0.0565278
\(475\) −0.745971 −0.0342275
\(476\) −30.8691 −1.41488
\(477\) 2.21848 0.101577
\(478\) −7.53613 −0.344695
\(479\) 16.5196 0.754799 0.377399 0.926051i \(-0.376818\pi\)
0.377399 + 0.926051i \(0.376818\pi\)
\(480\) −0.154802 −0.00706573
\(481\) −18.3304 −0.835796
\(482\) 25.3180 1.15320
\(483\) −1.51861 −0.0690989
\(484\) −1.56233 −0.0710151
\(485\) 16.4913 0.748830
\(486\) 4.13524 0.187578
\(487\) 29.4405 1.33407 0.667037 0.745024i \(-0.267562\pi\)
0.667037 + 0.745024i \(0.267562\pi\)
\(488\) −4.16103 −0.188361
\(489\) 1.15868 0.0523974
\(490\) 12.4953 0.564481
\(491\) 17.5779 0.793280 0.396640 0.917974i \(-0.370176\pi\)
0.396640 + 0.917974i \(0.370176\pi\)
\(492\) −0.941052 −0.0424259
\(493\) 17.3572 0.781731
\(494\) 4.54251 0.204377
\(495\) −9.14262 −0.410930
\(496\) 2.52786 0.113504
\(497\) −35.9394 −1.61210
\(498\) −1.04014 −0.0466098
\(499\) −35.8606 −1.60534 −0.802672 0.596421i \(-0.796589\pi\)
−0.802672 + 0.596421i \(0.796589\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 1.37067 0.0612368
\(502\) −18.4613 −0.823968
\(503\) −6.35538 −0.283372 −0.141686 0.989912i \(-0.545252\pi\)
−0.141686 + 0.989912i \(0.545252\pi\)
\(504\) −13.1402 −0.585313
\(505\) 11.6975 0.520530
\(506\) −6.82550 −0.303431
\(507\) −3.72773 −0.165554
\(508\) −11.2095 −0.497340
\(509\) −8.02027 −0.355492 −0.177746 0.984076i \(-0.556881\pi\)
−0.177746 + 0.984076i \(0.556881\pi\)
\(510\) −1.08227 −0.0479239
\(511\) −4.54132 −0.200896
\(512\) −1.00000 −0.0441942
\(513\) −0.690101 −0.0304687
\(514\) 28.3938 1.25240
\(515\) −2.10592 −0.0927981
\(516\) −0.259815 −0.0114377
\(517\) −7.78707 −0.342475
\(518\) −13.2912 −0.583982
\(519\) 1.92325 0.0844212
\(520\) 6.08938 0.267037
\(521\) −33.1875 −1.45397 −0.726986 0.686652i \(-0.759080\pi\)
−0.726986 + 0.686652i \(0.759080\pi\)
\(522\) 7.38855 0.323388
\(523\) −34.9210 −1.52699 −0.763494 0.645815i \(-0.776518\pi\)
−0.763494 + 0.645815i \(0.776518\pi\)
\(524\) 6.16032 0.269115
\(525\) 0.683507 0.0298307
\(526\) −15.6425 −0.682047
\(527\) 17.6731 0.769852
\(528\) 0.475565 0.0206963
\(529\) −18.0637 −0.785377
\(530\) −0.745448 −0.0323802
\(531\) 11.2969 0.490242
\(532\) 3.29372 0.142801
\(533\) 37.0177 1.60341
\(534\) 1.33440 0.0577452
\(535\) 11.0502 0.477741
\(536\) 13.0017 0.561586
\(537\) −0.688193 −0.0296977
\(538\) −12.6077 −0.543556
\(539\) −38.3866 −1.65343
\(540\) −0.925104 −0.0398102
\(541\) 5.86367 0.252099 0.126049 0.992024i \(-0.459770\pi\)
0.126049 + 0.992024i \(0.459770\pi\)
\(542\) 25.6235 1.10062
\(543\) 2.54982 0.109423
\(544\) −6.99132 −0.299751
\(545\) 3.08659 0.132215
\(546\) −4.16213 −0.178123
\(547\) 11.9297 0.510079 0.255039 0.966931i \(-0.417912\pi\)
0.255039 + 0.966931i \(0.417912\pi\)
\(548\) −16.4405 −0.702302
\(549\) −12.3834 −0.528510
\(550\) 3.07208 0.130994
\(551\) −1.85201 −0.0788983
\(552\) −0.343938 −0.0146390
\(553\) 35.1026 1.49271
\(554\) −29.5108 −1.25379
\(555\) −0.465990 −0.0197802
\(556\) 5.10643 0.216561
\(557\) 22.5121 0.953868 0.476934 0.878939i \(-0.341748\pi\)
0.476934 + 0.878939i \(0.341748\pi\)
\(558\) 7.52301 0.318474
\(559\) 10.2202 0.432269
\(560\) 4.41535 0.186583
\(561\) 3.32483 0.140374
\(562\) 11.9491 0.504042
\(563\) −5.22004 −0.219998 −0.109999 0.993932i \(-0.535085\pi\)
−0.109999 + 0.993932i \(0.535085\pi\)
\(564\) −0.392391 −0.0165226
\(565\) −12.8891 −0.542247
\(566\) 29.0019 1.21904
\(567\) −38.7884 −1.62896
\(568\) −8.13964 −0.341532
\(569\) −14.6065 −0.612335 −0.306168 0.951978i \(-0.599047\pi\)
−0.306168 + 0.951978i \(0.599047\pi\)
\(570\) 0.115478 0.00483685
\(571\) 2.78927 0.116727 0.0583636 0.998295i \(-0.481412\pi\)
0.0583636 + 0.998295i \(0.481412\pi\)
\(572\) −18.7071 −0.782182
\(573\) −0.897926 −0.0375114
\(574\) 26.8412 1.12033
\(575\) −2.22179 −0.0926549
\(576\) −2.97604 −0.124002
\(577\) −22.3981 −0.932447 −0.466223 0.884667i \(-0.654386\pi\)
−0.466223 + 0.884667i \(0.654386\pi\)
\(578\) −31.8786 −1.32598
\(579\) −2.73758 −0.113770
\(580\) −2.48268 −0.103088
\(581\) 29.6674 1.23081
\(582\) −2.55289 −0.105821
\(583\) 2.29008 0.0948452
\(584\) −1.02853 −0.0425609
\(585\) 18.1222 0.749262
\(586\) 7.99449 0.330249
\(587\) 17.3786 0.717292 0.358646 0.933474i \(-0.383239\pi\)
0.358646 + 0.933474i \(0.383239\pi\)
\(588\) −1.93430 −0.0797694
\(589\) −1.88571 −0.0776994
\(590\) −3.79594 −0.156276
\(591\) −0.0321954 −0.00132434
\(592\) −3.01023 −0.123720
\(593\) 30.3699 1.24714 0.623570 0.781767i \(-0.285681\pi\)
0.623570 + 0.781767i \(0.285681\pi\)
\(594\) 2.84199 0.116608
\(595\) 30.8691 1.26551
\(596\) 8.47553 0.347171
\(597\) −3.23497 −0.132398
\(598\) 13.5293 0.553255
\(599\) 38.9697 1.59226 0.796129 0.605127i \(-0.206878\pi\)
0.796129 + 0.605127i \(0.206878\pi\)
\(600\) 0.154802 0.00631978
\(601\) −17.3389 −0.707270 −0.353635 0.935383i \(-0.615055\pi\)
−0.353635 + 0.935383i \(0.615055\pi\)
\(602\) 7.41058 0.302033
\(603\) 38.6934 1.57572
\(604\) −20.8152 −0.846957
\(605\) 1.56233 0.0635178
\(606\) −1.81079 −0.0735585
\(607\) 16.2869 0.661066 0.330533 0.943794i \(-0.392772\pi\)
0.330533 + 0.943794i \(0.392772\pi\)
\(608\) 0.745971 0.0302531
\(609\) 1.69693 0.0687631
\(610\) 4.16103 0.168475
\(611\) 15.4353 0.624445
\(612\) −20.8064 −0.841050
\(613\) 8.14183 0.328845 0.164423 0.986390i \(-0.447424\pi\)
0.164423 + 0.986390i \(0.447424\pi\)
\(614\) −24.2347 −0.978033
\(615\) 0.941052 0.0379469
\(616\) −13.5643 −0.546521
\(617\) 25.3130 1.01906 0.509531 0.860452i \(-0.329819\pi\)
0.509531 + 0.860452i \(0.329819\pi\)
\(618\) 0.326002 0.0131137
\(619\) 27.8255 1.11840 0.559201 0.829032i \(-0.311108\pi\)
0.559201 + 0.829032i \(0.311108\pi\)
\(620\) −2.52786 −0.101521
\(621\) −2.05538 −0.0824797
\(622\) −25.0016 −1.00247
\(623\) −38.0605 −1.52486
\(624\) −0.942651 −0.0377362
\(625\) 1.00000 0.0400000
\(626\) 22.7439 0.909028
\(627\) −0.354758 −0.0141677
\(628\) 6.57637 0.262426
\(629\) −21.0455 −0.839138
\(630\) 13.1402 0.523520
\(631\) −13.7708 −0.548205 −0.274103 0.961700i \(-0.588381\pi\)
−0.274103 + 0.961700i \(0.588381\pi\)
\(632\) 7.95012 0.316239
\(633\) −2.82289 −0.112200
\(634\) 5.43701 0.215931
\(635\) 11.2095 0.444835
\(636\) 0.115397 0.00457579
\(637\) 76.0888 3.01475
\(638\) 7.62700 0.301956
\(639\) −24.2239 −0.958281
\(640\) 1.00000 0.0395285
\(641\) 7.82313 0.308995 0.154497 0.987993i \(-0.450624\pi\)
0.154497 + 0.987993i \(0.450624\pi\)
\(642\) −1.71059 −0.0675117
\(643\) −19.4985 −0.768948 −0.384474 0.923136i \(-0.625617\pi\)
−0.384474 + 0.923136i \(0.625617\pi\)
\(644\) 9.80996 0.386567
\(645\) 0.259815 0.0102302
\(646\) 5.21533 0.205194
\(647\) −20.7712 −0.816599 −0.408300 0.912848i \(-0.633878\pi\)
−0.408300 + 0.912848i \(0.633878\pi\)
\(648\) −8.78490 −0.345103
\(649\) 11.6614 0.457751
\(650\) −6.08938 −0.238845
\(651\) 1.72781 0.0677182
\(652\) −7.48490 −0.293131
\(653\) −14.9981 −0.586920 −0.293460 0.955971i \(-0.594807\pi\)
−0.293460 + 0.955971i \(0.594807\pi\)
\(654\) −0.477811 −0.0186839
\(655\) −6.16032 −0.240704
\(656\) 6.07906 0.237347
\(657\) −3.06094 −0.119419
\(658\) 11.1920 0.436309
\(659\) −48.6747 −1.89610 −0.948048 0.318127i \(-0.896946\pi\)
−0.948048 + 0.318127i \(0.896946\pi\)
\(660\) −0.475565 −0.0185113
\(661\) −23.0823 −0.897797 −0.448898 0.893583i \(-0.648184\pi\)
−0.448898 + 0.893583i \(0.648184\pi\)
\(662\) −19.8682 −0.772200
\(663\) −6.59038 −0.255949
\(664\) 6.71915 0.260753
\(665\) −3.29372 −0.127725
\(666\) −8.95855 −0.347137
\(667\) −5.51599 −0.213580
\(668\) −8.85429 −0.342583
\(669\) 0.0179230 0.000692944 0
\(670\) −13.0017 −0.502298
\(671\) −12.7830 −0.493483
\(672\) −0.683507 −0.0263668
\(673\) 24.1094 0.929349 0.464675 0.885482i \(-0.346171\pi\)
0.464675 + 0.885482i \(0.346171\pi\)
\(674\) 9.36919 0.360888
\(675\) 0.925104 0.0356073
\(676\) 24.0806 0.926177
\(677\) −32.1416 −1.23530 −0.617651 0.786452i \(-0.711916\pi\)
−0.617651 + 0.786452i \(0.711916\pi\)
\(678\) 1.99526 0.0766274
\(679\) 72.8147 2.79437
\(680\) 6.99132 0.268105
\(681\) 4.55870 0.174690
\(682\) 7.76579 0.297367
\(683\) −24.7150 −0.945692 −0.472846 0.881145i \(-0.656773\pi\)
−0.472846 + 0.881145i \(0.656773\pi\)
\(684\) 2.22004 0.0848852
\(685\) 16.4405 0.628158
\(686\) 24.2637 0.926394
\(687\) 0.953747 0.0363877
\(688\) 1.67837 0.0639871
\(689\) −4.53932 −0.172934
\(690\) 0.343938 0.0130935
\(691\) 8.28709 0.315256 0.157628 0.987499i \(-0.449615\pi\)
0.157628 + 0.987499i \(0.449615\pi\)
\(692\) −12.4239 −0.472285
\(693\) −40.3679 −1.53345
\(694\) 8.04989 0.305570
\(695\) −5.10643 −0.193698
\(696\) 0.384325 0.0145678
\(697\) 42.5006 1.60983
\(698\) 14.1691 0.536309
\(699\) −1.37316 −0.0519376
\(700\) −4.41535 −0.166885
\(701\) −34.6270 −1.30785 −0.653923 0.756561i \(-0.726878\pi\)
−0.653923 + 0.756561i \(0.726878\pi\)
\(702\) −5.63332 −0.212616
\(703\) 2.24554 0.0846923
\(704\) −3.07208 −0.115783
\(705\) 0.392391 0.0147783
\(706\) −29.1375 −1.09661
\(707\) 51.6484 1.94244
\(708\) 0.587620 0.0220841
\(709\) 31.5726 1.18574 0.592868 0.805300i \(-0.297996\pi\)
0.592868 + 0.805300i \(0.297996\pi\)
\(710\) 8.13964 0.305475
\(711\) 23.6599 0.887314
\(712\) −8.62004 −0.323050
\(713\) −5.61637 −0.210335
\(714\) −4.77862 −0.178835
\(715\) 18.7071 0.699605
\(716\) 4.44563 0.166141
\(717\) −1.16661 −0.0435679
\(718\) 1.74842 0.0652504
\(719\) −13.7600 −0.513163 −0.256581 0.966523i \(-0.582596\pi\)
−0.256581 + 0.966523i \(0.582596\pi\)
\(720\) 2.97604 0.110910
\(721\) −9.29839 −0.346290
\(722\) 18.4435 0.686397
\(723\) 3.91929 0.145760
\(724\) −16.4715 −0.612157
\(725\) 2.48268 0.0922045
\(726\) −0.241853 −0.00897599
\(727\) 5.15813 0.191304 0.0956522 0.995415i \(-0.469506\pi\)
0.0956522 + 0.995415i \(0.469506\pi\)
\(728\) 26.8868 0.996490
\(729\) −25.7146 −0.952391
\(730\) 1.02853 0.0380676
\(731\) 11.7340 0.433998
\(732\) −0.644138 −0.0238080
\(733\) 3.56423 0.131648 0.0658239 0.997831i \(-0.479032\pi\)
0.0658239 + 0.997831i \(0.479032\pi\)
\(734\) 13.1991 0.487187
\(735\) 1.93430 0.0713479
\(736\) 2.22179 0.0818961
\(737\) 39.9421 1.47129
\(738\) 18.0915 0.665957
\(739\) −24.8946 −0.915763 −0.457882 0.889013i \(-0.651392\pi\)
−0.457882 + 0.889013i \(0.651392\pi\)
\(740\) 3.01023 0.110658
\(741\) 0.703191 0.0258324
\(742\) −3.29141 −0.120832
\(743\) 2.95294 0.108333 0.0541664 0.998532i \(-0.482750\pi\)
0.0541664 + 0.998532i \(0.482750\pi\)
\(744\) 0.391319 0.0143464
\(745\) −8.47553 −0.310519
\(746\) 35.7076 1.30735
\(747\) 19.9964 0.731631
\(748\) −21.4779 −0.785310
\(749\) 48.7904 1.78276
\(750\) −0.154802 −0.00565258
\(751\) −30.8730 −1.12657 −0.563286 0.826262i \(-0.690463\pi\)
−0.563286 + 0.826262i \(0.690463\pi\)
\(752\) 2.53479 0.0924342
\(753\) −2.85785 −0.104146
\(754\) −15.1180 −0.550565
\(755\) 20.8152 0.757542
\(756\) −4.08466 −0.148558
\(757\) −16.6834 −0.606368 −0.303184 0.952932i \(-0.598050\pi\)
−0.303184 + 0.952932i \(0.598050\pi\)
\(758\) −20.2654 −0.736072
\(759\) −1.05660 −0.0383523
\(760\) −0.745971 −0.0270592
\(761\) 4.46462 0.161843 0.0809213 0.996720i \(-0.474214\pi\)
0.0809213 + 0.996720i \(0.474214\pi\)
\(762\) −1.73525 −0.0628616
\(763\) 13.6284 0.493380
\(764\) 5.80047 0.209853
\(765\) 20.8064 0.752258
\(766\) 35.0482 1.26634
\(767\) −23.1149 −0.834632
\(768\) −0.154802 −0.00558595
\(769\) 14.1587 0.510577 0.255289 0.966865i \(-0.417830\pi\)
0.255289 + 0.966865i \(0.417830\pi\)
\(770\) 13.5643 0.488824
\(771\) 4.39542 0.158297
\(772\) 17.6844 0.636475
\(773\) 2.64733 0.0952179 0.0476090 0.998866i \(-0.484840\pi\)
0.0476090 + 0.998866i \(0.484840\pi\)
\(774\) 4.99488 0.179537
\(775\) 2.52786 0.0908035
\(776\) 16.4913 0.592002
\(777\) −2.05751 −0.0738128
\(778\) 16.6478 0.596853
\(779\) −4.53480 −0.162476
\(780\) 0.942651 0.0337523
\(781\) −25.0056 −0.894771
\(782\) 15.5332 0.555467
\(783\) 2.29674 0.0820788
\(784\) 12.4953 0.446261
\(785\) −6.57637 −0.234721
\(786\) 0.953633 0.0340149
\(787\) −19.8674 −0.708195 −0.354097 0.935209i \(-0.615212\pi\)
−0.354097 + 0.935209i \(0.615212\pi\)
\(788\) 0.207977 0.00740888
\(789\) −2.42150 −0.0862077
\(790\) −7.95012 −0.282853
\(791\) −56.9097 −2.02348
\(792\) −9.14262 −0.324869
\(793\) 25.3381 0.899783
\(794\) −3.46731 −0.123050
\(795\) −0.115397 −0.00409271
\(796\) 20.8974 0.740688
\(797\) −24.9638 −0.884263 −0.442131 0.896950i \(-0.645778\pi\)
−0.442131 + 0.896950i \(0.645778\pi\)
\(798\) 0.509876 0.0180494
\(799\) 17.7215 0.626942
\(800\) −1.00000 −0.0353553
\(801\) −25.6536 −0.906424
\(802\) 1.00000 0.0353112
\(803\) −3.15973 −0.111504
\(804\) 2.01269 0.0709820
\(805\) −9.80996 −0.345756
\(806\) −15.3931 −0.542200
\(807\) −1.95170 −0.0687030
\(808\) 11.6975 0.411515
\(809\) 36.0771 1.26840 0.634201 0.773168i \(-0.281329\pi\)
0.634201 + 0.773168i \(0.281329\pi\)
\(810\) 8.78490 0.308670
\(811\) −9.67711 −0.339809 −0.169905 0.985461i \(-0.554346\pi\)
−0.169905 + 0.985461i \(0.554346\pi\)
\(812\) −10.9619 −0.384688
\(813\) 3.96657 0.139114
\(814\) −9.24766 −0.324130
\(815\) 7.48490 0.262185
\(816\) −1.08227 −0.0378871
\(817\) −1.25201 −0.0438024
\(818\) 39.8306 1.39264
\(819\) 80.0160 2.79598
\(820\) −6.07906 −0.212290
\(821\) −54.0490 −1.88632 −0.943161 0.332335i \(-0.892163\pi\)
−0.943161 + 0.332335i \(0.892163\pi\)
\(822\) −2.54502 −0.0887678
\(823\) 6.13977 0.214019 0.107010 0.994258i \(-0.465872\pi\)
0.107010 + 0.994258i \(0.465872\pi\)
\(824\) −2.10592 −0.0733633
\(825\) 0.475565 0.0165570
\(826\) −16.7604 −0.583169
\(827\) −38.4233 −1.33611 −0.668055 0.744112i \(-0.732873\pi\)
−0.668055 + 0.744112i \(0.732873\pi\)
\(828\) 6.61212 0.229787
\(829\) −37.4537 −1.30082 −0.650411 0.759583i \(-0.725403\pi\)
−0.650411 + 0.759583i \(0.725403\pi\)
\(830\) −6.71915 −0.233225
\(831\) −4.56834 −0.158474
\(832\) 6.08938 0.211111
\(833\) 87.3588 3.02680
\(834\) 0.790487 0.0273723
\(835\) 8.85429 0.306415
\(836\) 2.29168 0.0792595
\(837\) 2.33854 0.0808316
\(838\) −25.3727 −0.876485
\(839\) 0.219915 0.00759230 0.00379615 0.999993i \(-0.498792\pi\)
0.00379615 + 0.999993i \(0.498792\pi\)
\(840\) 0.683507 0.0235832
\(841\) −22.8363 −0.787458
\(842\) 21.5568 0.742898
\(843\) 1.84975 0.0637087
\(844\) 18.2355 0.627691
\(845\) −24.0806 −0.828398
\(846\) 7.54362 0.259355
\(847\) 6.89824 0.237026
\(848\) −0.745448 −0.0255988
\(849\) 4.48956 0.154081
\(850\) −6.99132 −0.239800
\(851\) 6.68808 0.229265
\(852\) −1.26004 −0.0431681
\(853\) 1.66005 0.0568390 0.0284195 0.999596i \(-0.490953\pi\)
0.0284195 + 0.999596i \(0.490953\pi\)
\(854\) 18.3724 0.628691
\(855\) −2.22004 −0.0759237
\(856\) 11.0502 0.377687
\(857\) 24.0659 0.822074 0.411037 0.911619i \(-0.365167\pi\)
0.411037 + 0.911619i \(0.365167\pi\)
\(858\) −2.89590 −0.0988643
\(859\) 11.3191 0.386203 0.193102 0.981179i \(-0.438145\pi\)
0.193102 + 0.981179i \(0.438145\pi\)
\(860\) −1.67837 −0.0572318
\(861\) 4.15507 0.141605
\(862\) 3.17088 0.108001
\(863\) −20.3884 −0.694029 −0.347015 0.937860i \(-0.612805\pi\)
−0.347015 + 0.937860i \(0.612805\pi\)
\(864\) −0.925104 −0.0314727
\(865\) 12.4239 0.422425
\(866\) 13.6613 0.464230
\(867\) −4.93488 −0.167597
\(868\) −11.1614 −0.378842
\(869\) 24.4234 0.828507
\(870\) −0.384325 −0.0130298
\(871\) −79.1721 −2.68264
\(872\) 3.08659 0.104525
\(873\) 49.0786 1.66106
\(874\) −1.65739 −0.0560620
\(875\) 4.41535 0.149266
\(876\) −0.159219 −0.00537951
\(877\) −8.71953 −0.294438 −0.147219 0.989104i \(-0.547032\pi\)
−0.147219 + 0.989104i \(0.547032\pi\)
\(878\) 12.4747 0.421001
\(879\) 1.23757 0.0417421
\(880\) 3.07208 0.103560
\(881\) −22.8663 −0.770386 −0.385193 0.922836i \(-0.625865\pi\)
−0.385193 + 0.922836i \(0.625865\pi\)
\(882\) 37.1865 1.25213
\(883\) 1.05873 0.0356292 0.0178146 0.999841i \(-0.494329\pi\)
0.0178146 + 0.999841i \(0.494329\pi\)
\(884\) 42.5729 1.43188
\(885\) −0.587620 −0.0197526
\(886\) 14.6634 0.492625
\(887\) 53.9716 1.81219 0.906094 0.423076i \(-0.139050\pi\)
0.906094 + 0.423076i \(0.139050\pi\)
\(888\) −0.465990 −0.0156376
\(889\) 49.4938 1.65997
\(890\) 8.62004 0.288944
\(891\) −26.9879 −0.904129
\(892\) −0.115780 −0.00387660
\(893\) −1.89088 −0.0632759
\(894\) 1.31203 0.0438809
\(895\) −4.44563 −0.148601
\(896\) 4.41535 0.147506
\(897\) 2.09437 0.0699289
\(898\) 10.8612 0.362444
\(899\) 6.27588 0.209312
\(900\) −2.97604 −0.0992012
\(901\) −5.21167 −0.173626
\(902\) 18.6753 0.621821
\(903\) 1.14717 0.0381756
\(904\) −12.8891 −0.428684
\(905\) 16.4715 0.547530
\(906\) −3.22224 −0.107052
\(907\) −42.0614 −1.39662 −0.698312 0.715793i \(-0.746065\pi\)
−0.698312 + 0.715793i \(0.746065\pi\)
\(908\) −29.4485 −0.977284
\(909\) 34.8120 1.15464
\(910\) −26.8868 −0.891287
\(911\) 17.5017 0.579858 0.289929 0.957048i \(-0.406368\pi\)
0.289929 + 0.957048i \(0.406368\pi\)
\(912\) 0.115478 0.00382386
\(913\) 20.6417 0.683142
\(914\) 18.3430 0.606733
\(915\) 0.644138 0.0212945
\(916\) −6.16106 −0.203567
\(917\) −27.2000 −0.898223
\(918\) −6.46770 −0.213466
\(919\) −23.6999 −0.781786 −0.390893 0.920436i \(-0.627834\pi\)
−0.390893 + 0.920436i \(0.627834\pi\)
\(920\) −2.22179 −0.0732501
\(921\) −3.75159 −0.123619
\(922\) −38.6901 −1.27419
\(923\) 49.5654 1.63146
\(924\) −2.09979 −0.0690779
\(925\) −3.01023 −0.0989757
\(926\) −23.1873 −0.761981
\(927\) −6.26731 −0.205845
\(928\) −2.48268 −0.0814980
\(929\) 21.2366 0.696751 0.348376 0.937355i \(-0.386733\pi\)
0.348376 + 0.937355i \(0.386733\pi\)
\(930\) −0.391319 −0.0128319
\(931\) −9.32114 −0.305488
\(932\) 8.87040 0.290560
\(933\) −3.87030 −0.126708
\(934\) −22.1349 −0.724275
\(935\) 21.4779 0.702402
\(936\) 18.1222 0.592344
\(937\) −38.9094 −1.27112 −0.635558 0.772053i \(-0.719230\pi\)
−0.635558 + 0.772053i \(0.719230\pi\)
\(938\) −57.4069 −1.87440
\(939\) 3.52081 0.114897
\(940\) −2.53479 −0.0826757
\(941\) 43.8295 1.42880 0.714401 0.699737i \(-0.246699\pi\)
0.714401 + 0.699737i \(0.246699\pi\)
\(942\) 1.01804 0.0331694
\(943\) −13.5064 −0.439828
\(944\) −3.79594 −0.123547
\(945\) 4.08466 0.132874
\(946\) 5.15607 0.167638
\(947\) 5.64650 0.183487 0.0917433 0.995783i \(-0.470756\pi\)
0.0917433 + 0.995783i \(0.470756\pi\)
\(948\) 1.23070 0.0399712
\(949\) 6.26311 0.203309
\(950\) 0.745971 0.0242025
\(951\) 0.841662 0.0272927
\(952\) 30.8691 1.00047
\(953\) 44.5998 1.44473 0.722364 0.691513i \(-0.243055\pi\)
0.722364 + 0.691513i \(0.243055\pi\)
\(954\) −2.21848 −0.0718260
\(955\) −5.80047 −0.187699
\(956\) 7.53613 0.243736
\(957\) 1.18068 0.0381659
\(958\) −16.5196 −0.533723
\(959\) 72.5904 2.34407
\(960\) 0.154802 0.00499622
\(961\) −24.6099 −0.793868
\(962\) 18.3304 0.590997
\(963\) 32.8857 1.05973
\(964\) −25.3180 −0.815439
\(965\) −17.6844 −0.569280
\(966\) 1.51861 0.0488603
\(967\) −1.31598 −0.0423192 −0.0211596 0.999776i \(-0.506736\pi\)
−0.0211596 + 0.999776i \(0.506736\pi\)
\(968\) 1.56233 0.0502152
\(969\) 0.807345 0.0259357
\(970\) −16.4913 −0.529503
\(971\) 6.26871 0.201173 0.100586 0.994928i \(-0.467928\pi\)
0.100586 + 0.994928i \(0.467928\pi\)
\(972\) −4.13524 −0.132638
\(973\) −22.5467 −0.722813
\(974\) −29.4405 −0.943333
\(975\) −0.942651 −0.0301890
\(976\) 4.16103 0.133191
\(977\) 10.8736 0.347878 0.173939 0.984756i \(-0.444350\pi\)
0.173939 + 0.984756i \(0.444350\pi\)
\(978\) −1.15868 −0.0370505
\(979\) −26.4814 −0.846351
\(980\) −12.4953 −0.399148
\(981\) 9.18580 0.293280
\(982\) −17.5779 −0.560933
\(983\) −22.8613 −0.729162 −0.364581 0.931172i \(-0.618788\pi\)
−0.364581 + 0.931172i \(0.618788\pi\)
\(984\) 0.941052 0.0299996
\(985\) −0.207977 −0.00662671
\(986\) −17.3572 −0.552767
\(987\) 1.73254 0.0551475
\(988\) −4.54251 −0.144516
\(989\) −3.72897 −0.118574
\(990\) 9.14262 0.290571
\(991\) −11.4088 −0.362413 −0.181206 0.983445i \(-0.558000\pi\)
−0.181206 + 0.983445i \(0.558000\pi\)
\(992\) −2.52786 −0.0802597
\(993\) −3.07565 −0.0976027
\(994\) 35.9394 1.13993
\(995\) −20.8974 −0.662492
\(996\) 1.04014 0.0329581
\(997\) −11.3329 −0.358917 −0.179458 0.983766i \(-0.557434\pi\)
−0.179458 + 0.983766i \(0.557434\pi\)
\(998\) 35.8606 1.13515
\(999\) −2.78478 −0.0881064
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 \(a_p\))