Properties

Label 8013.2.a.d.1.13
Level 8013
Weight 2
Character 8013.1
Self dual Yes
Analytic conductor 63.984
Analytic rank 0
Dimension 129
CM No

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Newspace parameters

Level: \( N \) = \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8013.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(129\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8013.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.41059 q^{2}\) \(+1.00000 q^{3}\) \(+3.81094 q^{4}\) \(-0.0291843 q^{5}\) \(-2.41059 q^{6}\) \(-4.28110 q^{7}\) \(-4.36543 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.41059 q^{2}\) \(+1.00000 q^{3}\) \(+3.81094 q^{4}\) \(-0.0291843 q^{5}\) \(-2.41059 q^{6}\) \(-4.28110 q^{7}\) \(-4.36543 q^{8}\) \(+1.00000 q^{9}\) \(+0.0703514 q^{10}\) \(-2.79864 q^{11}\) \(+3.81094 q^{12}\) \(-0.529671 q^{13}\) \(+10.3200 q^{14}\) \(-0.0291843 q^{15}\) \(+2.90137 q^{16}\) \(-6.45533 q^{17}\) \(-2.41059 q^{18}\) \(+3.36076 q^{19}\) \(-0.111220 q^{20}\) \(-4.28110 q^{21}\) \(+6.74637 q^{22}\) \(+1.83835 q^{23}\) \(-4.36543 q^{24}\) \(-4.99915 q^{25}\) \(+1.27682 q^{26}\) \(+1.00000 q^{27}\) \(-16.3150 q^{28}\) \(+9.38740 q^{29}\) \(+0.0703514 q^{30}\) \(-8.61633 q^{31}\) \(+1.73684 q^{32}\) \(-2.79864 q^{33}\) \(+15.5611 q^{34}\) \(+0.124941 q^{35}\) \(+3.81094 q^{36}\) \(+6.02920 q^{37}\) \(-8.10140 q^{38}\) \(-0.529671 q^{39}\) \(+0.127402 q^{40}\) \(-5.62171 q^{41}\) \(+10.3200 q^{42}\) \(+4.91765 q^{43}\) \(-10.6654 q^{44}\) \(-0.0291843 q^{45}\) \(-4.43152 q^{46}\) \(-12.7556 q^{47}\) \(+2.90137 q^{48}\) \(+11.3278 q^{49}\) \(+12.0509 q^{50}\) \(-6.45533 q^{51}\) \(-2.01854 q^{52}\) \(-3.08474 q^{53}\) \(-2.41059 q^{54}\) \(+0.0816764 q^{55}\) \(+18.6888 q^{56}\) \(+3.36076 q^{57}\) \(-22.6292 q^{58}\) \(-0.386347 q^{59}\) \(-0.111220 q^{60}\) \(-13.8054 q^{61}\) \(+20.7704 q^{62}\) \(-4.28110 q^{63}\) \(-9.98955 q^{64}\) \(+0.0154581 q^{65}\) \(+6.74637 q^{66}\) \(+12.4931 q^{67}\) \(-24.6008 q^{68}\) \(+1.83835 q^{69}\) \(-0.301181 q^{70}\) \(-8.82238 q^{71}\) \(-4.36543 q^{72}\) \(+8.57246 q^{73}\) \(-14.5339 q^{74}\) \(-4.99915 q^{75}\) \(+12.8076 q^{76}\) \(+11.9812 q^{77}\) \(+1.27682 q^{78}\) \(-4.68356 q^{79}\) \(-0.0846745 q^{80}\) \(+1.00000 q^{81}\) \(+13.5516 q^{82}\) \(+3.14380 q^{83}\) \(-16.3150 q^{84}\) \(+0.188394 q^{85}\) \(-11.8544 q^{86}\) \(+9.38740 q^{87}\) \(+12.2172 q^{88}\) \(-13.1700 q^{89}\) \(+0.0703514 q^{90}\) \(+2.26757 q^{91}\) \(+7.00585 q^{92}\) \(-8.61633 q^{93}\) \(+30.7486 q^{94}\) \(-0.0980815 q^{95}\) \(+1.73684 q^{96}\) \(+12.5415 q^{97}\) \(-27.3066 q^{98}\) \(-2.79864 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(129q \) \(\mathstrut +\mathstrut 15q^{2} \) \(\mathstrut +\mathstrut 129q^{3} \) \(\mathstrut +\mathstrut 151q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 15q^{6} \) \(\mathstrut +\mathstrut 61q^{7} \) \(\mathstrut +\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 129q^{9} \) \(\mathstrut +\mathstrut 41q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 151q^{12} \) \(\mathstrut +\mathstrut 56q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 195q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 15q^{18} \) \(\mathstrut +\mathstrut 93q^{19} \) \(\mathstrut +\mathstrut 44q^{20} \) \(\mathstrut +\mathstrut 61q^{21} \) \(\mathstrut +\mathstrut 46q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 42q^{24} \) \(\mathstrut +\mathstrut 193q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut 129q^{27} \) \(\mathstrut +\mathstrut 145q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 41q^{30} \) \(\mathstrut +\mathstrut 67q^{31} \) \(\mathstrut +\mathstrut 89q^{32} \) \(\mathstrut +\mathstrut 51q^{33} \) \(\mathstrut +\mathstrut 73q^{34} \) \(\mathstrut +\mathstrut 56q^{35} \) \(\mathstrut +\mathstrut 151q^{36} \) \(\mathstrut +\mathstrut 95q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 103q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 150q^{43} \) \(\mathstrut +\mathstrut 69q^{44} \) \(\mathstrut +\mathstrut 16q^{45} \) \(\mathstrut +\mathstrut 72q^{46} \) \(\mathstrut +\mathstrut 53q^{47} \) \(\mathstrut +\mathstrut 195q^{48} \) \(\mathstrut +\mathstrut 240q^{49} \) \(\mathstrut +\mathstrut 17q^{50} \) \(\mathstrut +\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 124q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut +\mathstrut 15q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 17q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 57q^{58} \) \(\mathstrut +\mathstrut 49q^{59} \) \(\mathstrut +\mathstrut 44q^{60} \) \(\mathstrut +\mathstrut 113q^{61} \) \(\mathstrut +\mathstrut 27q^{62} \) \(\mathstrut +\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 262q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 46q^{66} \) \(\mathstrut +\mathstrut 185q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 50q^{69} \) \(\mathstrut +\mathstrut 25q^{70} \) \(\mathstrut +\mathstrut 41q^{71} \) \(\mathstrut +\mathstrut 42q^{72} \) \(\mathstrut +\mathstrut 153q^{73} \) \(\mathstrut -\mathstrut q^{74} \) \(\mathstrut +\mathstrut 193q^{75} \) \(\mathstrut +\mathstrut 190q^{76} \) \(\mathstrut +\mathstrut 39q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 101q^{79} \) \(\mathstrut +\mathstrut 48q^{80} \) \(\mathstrut +\mathstrut 129q^{81} \) \(\mathstrut +\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 162q^{83} \) \(\mathstrut +\mathstrut 145q^{84} \) \(\mathstrut +\mathstrut 99q^{85} \) \(\mathstrut +\mathstrut 13q^{86} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut +\mathstrut 86q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 117q^{91} \) \(\mathstrut +\mathstrut 56q^{92} \) \(\mathstrut +\mathstrut 67q^{93} \) \(\mathstrut +\mathstrut 49q^{94} \) \(\mathstrut +\mathstrut 71q^{95} \) \(\mathstrut +\mathstrut 89q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut +\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41059 −1.70454 −0.852272 0.523099i \(-0.824776\pi\)
−0.852272 + 0.523099i \(0.824776\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.81094 1.90547
\(5\) −0.0291843 −0.0130516 −0.00652582 0.999979i \(-0.502077\pi\)
−0.00652582 + 0.999979i \(0.502077\pi\)
\(6\) −2.41059 −0.984119
\(7\) −4.28110 −1.61810 −0.809051 0.587738i \(-0.800018\pi\)
−0.809051 + 0.587738i \(0.800018\pi\)
\(8\) −4.36543 −1.54341
\(9\) 1.00000 0.333333
\(10\) 0.0703514 0.0222471
\(11\) −2.79864 −0.843821 −0.421911 0.906637i \(-0.638640\pi\)
−0.421911 + 0.906637i \(0.638640\pi\)
\(12\) 3.81094 1.10012
\(13\) −0.529671 −0.146904 −0.0734522 0.997299i \(-0.523402\pi\)
−0.0734522 + 0.997299i \(0.523402\pi\)
\(14\) 10.3200 2.75813
\(15\) −0.0291843 −0.00753536
\(16\) 2.90137 0.725342
\(17\) −6.45533 −1.56565 −0.782823 0.622244i \(-0.786221\pi\)
−0.782823 + 0.622244i \(0.786221\pi\)
\(18\) −2.41059 −0.568181
\(19\) 3.36076 0.771011 0.385505 0.922706i \(-0.374027\pi\)
0.385505 + 0.922706i \(0.374027\pi\)
\(20\) −0.111220 −0.0248695
\(21\) −4.28110 −0.934212
\(22\) 6.74637 1.43833
\(23\) 1.83835 0.383323 0.191662 0.981461i \(-0.438612\pi\)
0.191662 + 0.981461i \(0.438612\pi\)
\(24\) −4.36543 −0.891089
\(25\) −4.99915 −0.999830
\(26\) 1.27682 0.250405
\(27\) 1.00000 0.192450
\(28\) −16.3150 −3.08324
\(29\) 9.38740 1.74320 0.871599 0.490220i \(-0.163084\pi\)
0.871599 + 0.490220i \(0.163084\pi\)
\(30\) 0.0703514 0.0128444
\(31\) −8.61633 −1.54754 −0.773769 0.633468i \(-0.781631\pi\)
−0.773769 + 0.633468i \(0.781631\pi\)
\(32\) 1.73684 0.307033
\(33\) −2.79864 −0.487181
\(34\) 15.5611 2.66871
\(35\) 0.124941 0.0211189
\(36\) 3.81094 0.635156
\(37\) 6.02920 0.991195 0.495598 0.868552i \(-0.334949\pi\)
0.495598 + 0.868552i \(0.334949\pi\)
\(38\) −8.10140 −1.31422
\(39\) −0.529671 −0.0848153
\(40\) 0.127402 0.0201440
\(41\) −5.62171 −0.877964 −0.438982 0.898496i \(-0.644661\pi\)
−0.438982 + 0.898496i \(0.644661\pi\)
\(42\) 10.3200 1.59240
\(43\) 4.91765 0.749935 0.374968 0.927038i \(-0.377654\pi\)
0.374968 + 0.927038i \(0.377654\pi\)
\(44\) −10.6654 −1.60788
\(45\) −0.0291843 −0.00435054
\(46\) −4.43152 −0.653392
\(47\) −12.7556 −1.86060 −0.930301 0.366797i \(-0.880455\pi\)
−0.930301 + 0.366797i \(0.880455\pi\)
\(48\) 2.90137 0.418777
\(49\) 11.3278 1.61825
\(50\) 12.0509 1.70425
\(51\) −6.45533 −0.903926
\(52\) −2.01854 −0.279922
\(53\) −3.08474 −0.423722 −0.211861 0.977300i \(-0.567952\pi\)
−0.211861 + 0.977300i \(0.567952\pi\)
\(54\) −2.41059 −0.328040
\(55\) 0.0816764 0.0110132
\(56\) 18.6888 2.49740
\(57\) 3.36076 0.445143
\(58\) −22.6292 −2.97136
\(59\) −0.386347 −0.0502981 −0.0251490 0.999684i \(-0.508006\pi\)
−0.0251490 + 0.999684i \(0.508006\pi\)
\(60\) −0.111220 −0.0143584
\(61\) −13.8054 −1.76760 −0.883802 0.467861i \(-0.845025\pi\)
−0.883802 + 0.467861i \(0.845025\pi\)
\(62\) 20.7704 2.63785
\(63\) −4.28110 −0.539367
\(64\) −9.98955 −1.24869
\(65\) 0.0154581 0.00191734
\(66\) 6.74637 0.830420
\(67\) 12.4931 1.52628 0.763139 0.646234i \(-0.223657\pi\)
0.763139 + 0.646234i \(0.223657\pi\)
\(68\) −24.6008 −2.98329
\(69\) 1.83835 0.221312
\(70\) −0.301181 −0.0359980
\(71\) −8.82238 −1.04702 −0.523512 0.852018i \(-0.675379\pi\)
−0.523512 + 0.852018i \(0.675379\pi\)
\(72\) −4.36543 −0.514470
\(73\) 8.57246 1.00333 0.501665 0.865062i \(-0.332721\pi\)
0.501665 + 0.865062i \(0.332721\pi\)
\(74\) −14.5339 −1.68954
\(75\) −4.99915 −0.577252
\(76\) 12.8076 1.46914
\(77\) 11.9812 1.36539
\(78\) 1.27682 0.144571
\(79\) −4.68356 −0.526942 −0.263471 0.964667i \(-0.584867\pi\)
−0.263471 + 0.964667i \(0.584867\pi\)
\(80\) −0.0846745 −0.00946690
\(81\) 1.00000 0.111111
\(82\) 13.5516 1.49653
\(83\) 3.14380 0.345077 0.172538 0.985003i \(-0.444803\pi\)
0.172538 + 0.985003i \(0.444803\pi\)
\(84\) −16.3150 −1.78011
\(85\) 0.188394 0.0204342
\(86\) −11.8544 −1.27830
\(87\) 9.38740 1.00644
\(88\) 12.2172 1.30236
\(89\) −13.1700 −1.39601 −0.698007 0.716091i \(-0.745930\pi\)
−0.698007 + 0.716091i \(0.745930\pi\)
\(90\) 0.0703514 0.00741569
\(91\) 2.26757 0.237706
\(92\) 7.00585 0.730411
\(93\) −8.61633 −0.893471
\(94\) 30.7486 3.17148
\(95\) −0.0980815 −0.0100629
\(96\) 1.73684 0.177266
\(97\) 12.5415 1.27340 0.636698 0.771113i \(-0.280300\pi\)
0.636698 + 0.771113i \(0.280300\pi\)
\(98\) −27.3066 −2.75839
\(99\) −2.79864 −0.281274
\(100\) −19.0514 −1.90514
\(101\) −1.13220 −0.112658 −0.0563292 0.998412i \(-0.517940\pi\)
−0.0563292 + 0.998412i \(0.517940\pi\)
\(102\) 15.5611 1.54078
\(103\) −10.8243 −1.06655 −0.533276 0.845941i \(-0.679039\pi\)
−0.533276 + 0.845941i \(0.679039\pi\)
\(104\) 2.31224 0.226734
\(105\) 0.124941 0.0121930
\(106\) 7.43604 0.722252
\(107\) −16.3976 −1.58522 −0.792610 0.609729i \(-0.791278\pi\)
−0.792610 + 0.609729i \(0.791278\pi\)
\(108\) 3.81094 0.366708
\(109\) −4.83098 −0.462724 −0.231362 0.972868i \(-0.574318\pi\)
−0.231362 + 0.972868i \(0.574318\pi\)
\(110\) −0.196888 −0.0187726
\(111\) 6.02920 0.572267
\(112\) −12.4210 −1.17368
\(113\) −11.4476 −1.07690 −0.538448 0.842659i \(-0.680989\pi\)
−0.538448 + 0.842659i \(0.680989\pi\)
\(114\) −8.10140 −0.758766
\(115\) −0.0536512 −0.00500300
\(116\) 35.7748 3.32161
\(117\) −0.529671 −0.0489681
\(118\) 0.931323 0.0857352
\(119\) 27.6359 2.53338
\(120\) 0.127402 0.0116302
\(121\) −3.16762 −0.287965
\(122\) 33.2792 3.01296
\(123\) −5.62171 −0.506893
\(124\) −32.8363 −2.94878
\(125\) 0.291818 0.0261010
\(126\) 10.3200 0.919375
\(127\) −5.91982 −0.525299 −0.262649 0.964891i \(-0.584596\pi\)
−0.262649 + 0.964891i \(0.584596\pi\)
\(128\) 20.6070 1.82142
\(129\) 4.91765 0.432975
\(130\) −0.0372631 −0.00326819
\(131\) 11.0327 0.963929 0.481965 0.876191i \(-0.339923\pi\)
0.481965 + 0.876191i \(0.339923\pi\)
\(132\) −10.6654 −0.928307
\(133\) −14.3877 −1.24757
\(134\) −30.1158 −2.60161
\(135\) −0.0291843 −0.00251179
\(136\) 28.1802 2.41644
\(137\) −9.59424 −0.819691 −0.409846 0.912155i \(-0.634417\pi\)
−0.409846 + 0.912155i \(0.634417\pi\)
\(138\) −4.43152 −0.377236
\(139\) −15.7442 −1.33541 −0.667705 0.744426i \(-0.732723\pi\)
−0.667705 + 0.744426i \(0.732723\pi\)
\(140\) 0.476142 0.0402414
\(141\) −12.7556 −1.07422
\(142\) 21.2671 1.78470
\(143\) 1.48236 0.123961
\(144\) 2.90137 0.241781
\(145\) −0.273965 −0.0227516
\(146\) −20.6647 −1.71022
\(147\) 11.3278 0.934300
\(148\) 22.9769 1.88869
\(149\) −20.2264 −1.65701 −0.828504 0.559983i \(-0.810808\pi\)
−0.828504 + 0.559983i \(0.810808\pi\)
\(150\) 12.0509 0.983951
\(151\) 10.0513 0.817962 0.408981 0.912543i \(-0.365884\pi\)
0.408981 + 0.912543i \(0.365884\pi\)
\(152\) −14.6711 −1.18999
\(153\) −6.45533 −0.521882
\(154\) −28.8818 −2.32737
\(155\) 0.251462 0.0201979
\(156\) −2.01854 −0.161613
\(157\) 11.6302 0.928191 0.464096 0.885785i \(-0.346379\pi\)
0.464096 + 0.885785i \(0.346379\pi\)
\(158\) 11.2901 0.898195
\(159\) −3.08474 −0.244636
\(160\) −0.0506886 −0.00400729
\(161\) −7.87017 −0.620257
\(162\) −2.41059 −0.189394
\(163\) 23.1152 1.81052 0.905262 0.424854i \(-0.139675\pi\)
0.905262 + 0.424854i \(0.139675\pi\)
\(164\) −21.4240 −1.67293
\(165\) 0.0816764 0.00635850
\(166\) −7.57841 −0.588199
\(167\) 12.0948 0.935924 0.467962 0.883749i \(-0.344988\pi\)
0.467962 + 0.883749i \(0.344988\pi\)
\(168\) 18.6888 1.44187
\(169\) −12.7194 −0.978419
\(170\) −0.454141 −0.0348311
\(171\) 3.36076 0.257004
\(172\) 18.7409 1.42898
\(173\) −14.0029 −1.06462 −0.532309 0.846550i \(-0.678676\pi\)
−0.532309 + 0.846550i \(0.678676\pi\)
\(174\) −22.6292 −1.71551
\(175\) 21.4018 1.61783
\(176\) −8.11988 −0.612059
\(177\) −0.386347 −0.0290396
\(178\) 31.7474 2.37957
\(179\) 7.71284 0.576485 0.288243 0.957557i \(-0.406929\pi\)
0.288243 + 0.957557i \(0.406929\pi\)
\(180\) −0.111220 −0.00828982
\(181\) −16.7560 −1.24547 −0.622733 0.782434i \(-0.713978\pi\)
−0.622733 + 0.782434i \(0.713978\pi\)
\(182\) −5.46619 −0.405181
\(183\) −13.8054 −1.02053
\(184\) −8.02520 −0.591626
\(185\) −0.175958 −0.0129367
\(186\) 20.7704 1.52296
\(187\) 18.0661 1.32113
\(188\) −48.6110 −3.54532
\(189\) −4.28110 −0.311404
\(190\) 0.236434 0.0171527
\(191\) −2.11723 −0.153197 −0.0765985 0.997062i \(-0.524406\pi\)
−0.0765985 + 0.997062i \(0.524406\pi\)
\(192\) −9.98955 −0.720934
\(193\) 21.7998 1.56919 0.784593 0.620011i \(-0.212872\pi\)
0.784593 + 0.620011i \(0.212872\pi\)
\(194\) −30.2324 −2.17056
\(195\) 0.0154581 0.00110698
\(196\) 43.1695 3.08353
\(197\) 12.6763 0.903151 0.451575 0.892233i \(-0.350862\pi\)
0.451575 + 0.892233i \(0.350862\pi\)
\(198\) 6.74637 0.479443
\(199\) −2.54320 −0.180283 −0.0901413 0.995929i \(-0.528732\pi\)
−0.0901413 + 0.995929i \(0.528732\pi\)
\(200\) 21.8234 1.54315
\(201\) 12.4931 0.881197
\(202\) 2.72927 0.192031
\(203\) −40.1884 −2.82067
\(204\) −24.6008 −1.72240
\(205\) 0.164066 0.0114589
\(206\) 26.0930 1.81798
\(207\) 1.83835 0.127774
\(208\) −1.53677 −0.106556
\(209\) −9.40555 −0.650595
\(210\) −0.301181 −0.0207835
\(211\) 13.6475 0.939535 0.469768 0.882790i \(-0.344338\pi\)
0.469768 + 0.882790i \(0.344338\pi\)
\(212\) −11.7557 −0.807388
\(213\) −8.82238 −0.604500
\(214\) 39.5280 2.70208
\(215\) −0.143518 −0.00978788
\(216\) −4.36543 −0.297030
\(217\) 36.8873 2.50407
\(218\) 11.6455 0.788733
\(219\) 8.57246 0.579273
\(220\) 0.311264 0.0209854
\(221\) 3.41920 0.230000
\(222\) −14.5339 −0.975454
\(223\) 15.0731 1.00937 0.504683 0.863305i \(-0.331609\pi\)
0.504683 + 0.863305i \(0.331609\pi\)
\(224\) −7.43559 −0.496811
\(225\) −4.99915 −0.333277
\(226\) 27.5954 1.83562
\(227\) 23.3873 1.55227 0.776134 0.630568i \(-0.217178\pi\)
0.776134 + 0.630568i \(0.217178\pi\)
\(228\) 12.8076 0.848206
\(229\) 29.9193 1.97712 0.988562 0.150812i \(-0.0481889\pi\)
0.988562 + 0.150812i \(0.0481889\pi\)
\(230\) 0.129331 0.00852782
\(231\) 11.9812 0.788308
\(232\) −40.9800 −2.69047
\(233\) −13.7713 −0.902185 −0.451092 0.892477i \(-0.648965\pi\)
−0.451092 + 0.892477i \(0.648965\pi\)
\(234\) 1.27682 0.0834683
\(235\) 0.372265 0.0242839
\(236\) −1.47234 −0.0958414
\(237\) −4.68356 −0.304230
\(238\) −66.6187 −4.31825
\(239\) 10.4291 0.674604 0.337302 0.941397i \(-0.390486\pi\)
0.337302 + 0.941397i \(0.390486\pi\)
\(240\) −0.0846745 −0.00546572
\(241\) −6.11450 −0.393870 −0.196935 0.980417i \(-0.563099\pi\)
−0.196935 + 0.980417i \(0.563099\pi\)
\(242\) 7.63583 0.490850
\(243\) 1.00000 0.0641500
\(244\) −52.6116 −3.36811
\(245\) −0.330594 −0.0211209
\(246\) 13.5516 0.864021
\(247\) −1.78010 −0.113265
\(248\) 37.6139 2.38849
\(249\) 3.14380 0.199230
\(250\) −0.703454 −0.0444904
\(251\) 20.3582 1.28500 0.642500 0.766285i \(-0.277897\pi\)
0.642500 + 0.766285i \(0.277897\pi\)
\(252\) −16.3150 −1.02775
\(253\) −5.14489 −0.323457
\(254\) 14.2702 0.895395
\(255\) 0.188394 0.0117977
\(256\) −29.6959 −1.85600
\(257\) −11.1357 −0.694624 −0.347312 0.937750i \(-0.612906\pi\)
−0.347312 + 0.937750i \(0.612906\pi\)
\(258\) −11.8544 −0.738025
\(259\) −25.8116 −1.60386
\(260\) 0.0589098 0.00365343
\(261\) 9.38740 0.581066
\(262\) −26.5952 −1.64306
\(263\) 22.0849 1.36181 0.680906 0.732371i \(-0.261586\pi\)
0.680906 + 0.732371i \(0.261586\pi\)
\(264\) 12.2172 0.751920
\(265\) 0.0900261 0.00553026
\(266\) 34.6829 2.12654
\(267\) −13.1700 −0.805989
\(268\) 47.6105 2.90828
\(269\) −24.7147 −1.50688 −0.753441 0.657516i \(-0.771607\pi\)
−0.753441 + 0.657516i \(0.771607\pi\)
\(270\) 0.0703514 0.00428145
\(271\) 19.4297 1.18027 0.590134 0.807305i \(-0.299075\pi\)
0.590134 + 0.807305i \(0.299075\pi\)
\(272\) −18.7293 −1.13563
\(273\) 2.26757 0.137240
\(274\) 23.1278 1.39720
\(275\) 13.9908 0.843678
\(276\) 7.00585 0.421703
\(277\) 19.7316 1.18556 0.592778 0.805366i \(-0.298031\pi\)
0.592778 + 0.805366i \(0.298031\pi\)
\(278\) 37.9529 2.27626
\(279\) −8.61633 −0.515846
\(280\) −0.545420 −0.0325951
\(281\) 15.5789 0.929361 0.464680 0.885478i \(-0.346169\pi\)
0.464680 + 0.885478i \(0.346169\pi\)
\(282\) 30.7486 1.83105
\(283\) 22.0000 1.30776 0.653882 0.756597i \(-0.273139\pi\)
0.653882 + 0.756597i \(0.273139\pi\)
\(284\) −33.6216 −1.99507
\(285\) −0.0980815 −0.00580984
\(286\) −3.57336 −0.211297
\(287\) 24.0671 1.42064
\(288\) 1.73684 0.102344
\(289\) 24.6712 1.45125
\(290\) 0.660417 0.0387810
\(291\) 12.5415 0.735196
\(292\) 32.6691 1.91182
\(293\) 30.8227 1.80068 0.900342 0.435183i \(-0.143316\pi\)
0.900342 + 0.435183i \(0.143316\pi\)
\(294\) −27.3066 −1.59255
\(295\) 0.0112753 0.000656472 0
\(296\) −26.3200 −1.52982
\(297\) −2.79864 −0.162394
\(298\) 48.7574 2.82444
\(299\) −0.973723 −0.0563119
\(300\) −19.0514 −1.09994
\(301\) −21.0530 −1.21347
\(302\) −24.2295 −1.39425
\(303\) −1.13220 −0.0650433
\(304\) 9.75080 0.559247
\(305\) 0.402902 0.0230701
\(306\) 15.5611 0.889571
\(307\) −9.68555 −0.552783 −0.276392 0.961045i \(-0.589139\pi\)
−0.276392 + 0.961045i \(0.589139\pi\)
\(308\) 45.6598 2.60171
\(309\) −10.8243 −0.615774
\(310\) −0.606171 −0.0344282
\(311\) 4.90114 0.277918 0.138959 0.990298i \(-0.455624\pi\)
0.138959 + 0.990298i \(0.455624\pi\)
\(312\) 2.31224 0.130905
\(313\) 5.44833 0.307958 0.153979 0.988074i \(-0.450791\pi\)
0.153979 + 0.988074i \(0.450791\pi\)
\(314\) −28.0356 −1.58214
\(315\) 0.124941 0.00703962
\(316\) −17.8488 −1.00407
\(317\) 13.9208 0.781868 0.390934 0.920419i \(-0.372152\pi\)
0.390934 + 0.920419i \(0.372152\pi\)
\(318\) 7.43604 0.416992
\(319\) −26.2720 −1.47095
\(320\) 0.291538 0.0162975
\(321\) −16.3976 −0.915227
\(322\) 18.9717 1.05725
\(323\) −21.6948 −1.20713
\(324\) 3.81094 0.211719
\(325\) 2.64790 0.146879
\(326\) −55.7213 −3.08612
\(327\) −4.83098 −0.267154
\(328\) 24.5412 1.35506
\(329\) 54.6082 3.01064
\(330\) −0.196888 −0.0108383
\(331\) −20.0851 −1.10398 −0.551989 0.833852i \(-0.686131\pi\)
−0.551989 + 0.833852i \(0.686131\pi\)
\(332\) 11.9808 0.657533
\(333\) 6.02920 0.330398
\(334\) −29.1556 −1.59532
\(335\) −0.364604 −0.0199204
\(336\) −12.4210 −0.677623
\(337\) 12.3695 0.673808 0.336904 0.941539i \(-0.390620\pi\)
0.336904 + 0.941539i \(0.390620\pi\)
\(338\) 30.6614 1.66776
\(339\) −11.4476 −0.621746
\(340\) 0.717959 0.0389368
\(341\) 24.1140 1.30585
\(342\) −8.10140 −0.438074
\(343\) −18.5277 −1.00040
\(344\) −21.4677 −1.15746
\(345\) −0.0536512 −0.00288848
\(346\) 33.7552 1.81469
\(347\) −23.5795 −1.26582 −0.632908 0.774227i \(-0.718139\pi\)
−0.632908 + 0.774227i \(0.718139\pi\)
\(348\) 35.7748 1.91773
\(349\) 10.7755 0.576798 0.288399 0.957510i \(-0.406877\pi\)
0.288399 + 0.957510i \(0.406877\pi\)
\(350\) −51.5910 −2.75766
\(351\) −0.529671 −0.0282718
\(352\) −4.86080 −0.259081
\(353\) 9.91438 0.527689 0.263845 0.964565i \(-0.415009\pi\)
0.263845 + 0.964565i \(0.415009\pi\)
\(354\) 0.931323 0.0494993
\(355\) 0.257475 0.0136654
\(356\) −50.1899 −2.66006
\(357\) 27.6359 1.46265
\(358\) −18.5925 −0.982644
\(359\) −29.9928 −1.58296 −0.791480 0.611196i \(-0.790689\pi\)
−0.791480 + 0.611196i \(0.790689\pi\)
\(360\) 0.127402 0.00671468
\(361\) −7.70531 −0.405543
\(362\) 40.3919 2.12295
\(363\) −3.16762 −0.166257
\(364\) 8.64158 0.452942
\(365\) −0.250182 −0.0130951
\(366\) 33.2792 1.73953
\(367\) 27.9195 1.45738 0.728692 0.684842i \(-0.240129\pi\)
0.728692 + 0.684842i \(0.240129\pi\)
\(368\) 5.33375 0.278041
\(369\) −5.62171 −0.292655
\(370\) 0.424163 0.0220512
\(371\) 13.2061 0.685625
\(372\) −32.8363 −1.70248
\(373\) 6.98536 0.361688 0.180844 0.983512i \(-0.442117\pi\)
0.180844 + 0.983512i \(0.442117\pi\)
\(374\) −43.5500 −2.25192
\(375\) 0.291818 0.0150694
\(376\) 55.6838 2.87167
\(377\) −4.97224 −0.256083
\(378\) 10.3200 0.530802
\(379\) −3.13295 −0.160929 −0.0804644 0.996757i \(-0.525640\pi\)
−0.0804644 + 0.996757i \(0.525640\pi\)
\(380\) −0.373782 −0.0191746
\(381\) −5.91982 −0.303281
\(382\) 5.10376 0.261131
\(383\) −7.43540 −0.379931 −0.189966 0.981791i \(-0.560838\pi\)
−0.189966 + 0.981791i \(0.560838\pi\)
\(384\) 20.6070 1.05160
\(385\) −0.349665 −0.0178206
\(386\) −52.5504 −2.67475
\(387\) 4.91765 0.249978
\(388\) 47.7949 2.42642
\(389\) −11.1293 −0.564277 −0.282139 0.959374i \(-0.591044\pi\)
−0.282139 + 0.959374i \(0.591044\pi\)
\(390\) −0.0372631 −0.00188689
\(391\) −11.8672 −0.600149
\(392\) −49.4506 −2.49763
\(393\) 11.0327 0.556525
\(394\) −30.5574 −1.53946
\(395\) 0.136687 0.00687745
\(396\) −10.6654 −0.535958
\(397\) −4.70184 −0.235979 −0.117989 0.993015i \(-0.537645\pi\)
−0.117989 + 0.993015i \(0.537645\pi\)
\(398\) 6.13060 0.307299
\(399\) −14.3877 −0.720287
\(400\) −14.5044 −0.725219
\(401\) 13.0422 0.651297 0.325649 0.945491i \(-0.394417\pi\)
0.325649 + 0.945491i \(0.394417\pi\)
\(402\) −30.1158 −1.50204
\(403\) 4.56382 0.227340
\(404\) −4.31475 −0.214667
\(405\) −0.0291843 −0.00145018
\(406\) 96.8776 4.80796
\(407\) −16.8736 −0.836392
\(408\) 28.1802 1.39513
\(409\) 18.5050 0.915011 0.457505 0.889207i \(-0.348743\pi\)
0.457505 + 0.889207i \(0.348743\pi\)
\(410\) −0.395495 −0.0195321
\(411\) −9.59424 −0.473249
\(412\) −41.2508 −2.03228
\(413\) 1.65399 0.0813874
\(414\) −4.43152 −0.217797
\(415\) −0.0917497 −0.00450382
\(416\) −0.919955 −0.0451045
\(417\) −15.7442 −0.770999
\(418\) 22.6729 1.10897
\(419\) −21.6029 −1.05537 −0.527686 0.849439i \(-0.676940\pi\)
−0.527686 + 0.849439i \(0.676940\pi\)
\(420\) 0.476142 0.0232334
\(421\) −13.6903 −0.667222 −0.333611 0.942711i \(-0.608267\pi\)
−0.333611 + 0.942711i \(0.608267\pi\)
\(422\) −32.8986 −1.60148
\(423\) −12.7556 −0.620201
\(424\) 13.4662 0.653976
\(425\) 32.2711 1.56538
\(426\) 21.2671 1.03040
\(427\) 59.1024 2.86016
\(428\) −62.4904 −3.02059
\(429\) 1.48236 0.0715689
\(430\) 0.345964 0.0166839
\(431\) 8.11749 0.391006 0.195503 0.980703i \(-0.437366\pi\)
0.195503 + 0.980703i \(0.437366\pi\)
\(432\) 2.90137 0.139592
\(433\) −1.57598 −0.0757367 −0.0378684 0.999283i \(-0.512057\pi\)
−0.0378684 + 0.999283i \(0.512057\pi\)
\(434\) −88.9202 −4.26830
\(435\) −0.273965 −0.0131356
\(436\) −18.4106 −0.881706
\(437\) 6.17826 0.295546
\(438\) −20.6647 −0.987397
\(439\) 18.3362 0.875139 0.437570 0.899185i \(-0.355839\pi\)
0.437570 + 0.899185i \(0.355839\pi\)
\(440\) −0.356552 −0.0169980
\(441\) 11.3278 0.539418
\(442\) −8.24228 −0.392045
\(443\) −34.6421 −1.64590 −0.822948 0.568117i \(-0.807672\pi\)
−0.822948 + 0.568117i \(0.807672\pi\)
\(444\) 22.9769 1.09044
\(445\) 0.384357 0.0182203
\(446\) −36.3349 −1.72051
\(447\) −20.2264 −0.956674
\(448\) 42.7662 2.02051
\(449\) 2.54242 0.119984 0.0599922 0.998199i \(-0.480892\pi\)
0.0599922 + 0.998199i \(0.480892\pi\)
\(450\) 12.0509 0.568084
\(451\) 15.7331 0.740845
\(452\) −43.6259 −2.05199
\(453\) 10.0513 0.472251
\(454\) −56.3771 −2.64591
\(455\) −0.0661776 −0.00310245
\(456\) −14.6711 −0.687039
\(457\) −18.9791 −0.887805 −0.443902 0.896075i \(-0.646406\pi\)
−0.443902 + 0.896075i \(0.646406\pi\)
\(458\) −72.1232 −3.37010
\(459\) −6.45533 −0.301309
\(460\) −0.204461 −0.00953305
\(461\) −9.74527 −0.453882 −0.226941 0.973908i \(-0.572873\pi\)
−0.226941 + 0.973908i \(0.572873\pi\)
\(462\) −28.8818 −1.34371
\(463\) 26.6543 1.23873 0.619366 0.785102i \(-0.287390\pi\)
0.619366 + 0.785102i \(0.287390\pi\)
\(464\) 27.2363 1.26441
\(465\) 0.251462 0.0116613
\(466\) 33.1968 1.53781
\(467\) −1.80488 −0.0835201 −0.0417600 0.999128i \(-0.513296\pi\)
−0.0417600 + 0.999128i \(0.513296\pi\)
\(468\) −2.01854 −0.0933072
\(469\) −53.4843 −2.46967
\(470\) −0.897378 −0.0413930
\(471\) 11.6302 0.535891
\(472\) 1.68657 0.0776306
\(473\) −13.7627 −0.632811
\(474\) 11.2901 0.518573
\(475\) −16.8009 −0.770879
\(476\) 105.319 4.82727
\(477\) −3.08474 −0.141241
\(478\) −25.1403 −1.14989
\(479\) 35.0893 1.60327 0.801636 0.597813i \(-0.203963\pi\)
0.801636 + 0.597813i \(0.203963\pi\)
\(480\) −0.0506886 −0.00231361
\(481\) −3.19350 −0.145611
\(482\) 14.7396 0.671368
\(483\) −7.87017 −0.358105
\(484\) −12.0716 −0.548709
\(485\) −0.366015 −0.0166199
\(486\) −2.41059 −0.109347
\(487\) −12.0195 −0.544653 −0.272327 0.962205i \(-0.587793\pi\)
−0.272327 + 0.962205i \(0.587793\pi\)
\(488\) 60.2666 2.72814
\(489\) 23.1152 1.04531
\(490\) 0.796926 0.0360014
\(491\) −10.3636 −0.467704 −0.233852 0.972272i \(-0.575133\pi\)
−0.233852 + 0.972272i \(0.575133\pi\)
\(492\) −21.4240 −0.965868
\(493\) −60.5988 −2.72923
\(494\) 4.29108 0.193065
\(495\) 0.0816764 0.00367108
\(496\) −24.9991 −1.12249
\(497\) 37.7695 1.69419
\(498\) −7.57841 −0.339597
\(499\) 10.4650 0.468479 0.234239 0.972179i \(-0.424740\pi\)
0.234239 + 0.972179i \(0.424740\pi\)
\(500\) 1.11210 0.0497347
\(501\) 12.0948 0.540356
\(502\) −49.0753 −2.19034
\(503\) −42.0914 −1.87676 −0.938380 0.345604i \(-0.887674\pi\)
−0.938380 + 0.345604i \(0.887674\pi\)
\(504\) 18.6888 0.832465
\(505\) 0.0330426 0.00147037
\(506\) 12.4022 0.551346
\(507\) −12.7194 −0.564891
\(508\) −22.5601 −1.00094
\(509\) 9.02358 0.399963 0.199982 0.979800i \(-0.435912\pi\)
0.199982 + 0.979800i \(0.435912\pi\)
\(510\) −0.454141 −0.0201097
\(511\) −36.6995 −1.62349
\(512\) 30.3706 1.34221
\(513\) 3.36076 0.148381
\(514\) 26.8435 1.18402
\(515\) 0.315900 0.0139202
\(516\) 18.7409 0.825021
\(517\) 35.6985 1.57002
\(518\) 62.2212 2.73384
\(519\) −14.0029 −0.614658
\(520\) −0.0674812 −0.00295924
\(521\) 13.1280 0.575150 0.287575 0.957758i \(-0.407151\pi\)
0.287575 + 0.957758i \(0.407151\pi\)
\(522\) −22.6292 −0.990452
\(523\) 18.3421 0.802046 0.401023 0.916068i \(-0.368655\pi\)
0.401023 + 0.916068i \(0.368655\pi\)
\(524\) 42.0448 1.83674
\(525\) 21.4018 0.934053
\(526\) −53.2375 −2.32127
\(527\) 55.6212 2.42290
\(528\) −8.11988 −0.353373
\(529\) −19.6205 −0.853063
\(530\) −0.217016 −0.00942656
\(531\) −0.386347 −0.0167660
\(532\) −54.8307 −2.37721
\(533\) 2.97766 0.128977
\(534\) 31.7474 1.37384
\(535\) 0.478554 0.0206897
\(536\) −54.5378 −2.35567
\(537\) 7.71284 0.332834
\(538\) 59.5770 2.56855
\(539\) −31.7024 −1.36552
\(540\) −0.111220 −0.00478613
\(541\) −36.9626 −1.58915 −0.794573 0.607168i \(-0.792305\pi\)
−0.794573 + 0.607168i \(0.792305\pi\)
\(542\) −46.8369 −2.01182
\(543\) −16.7560 −0.719070
\(544\) −11.2119 −0.480706
\(545\) 0.140989 0.00603930
\(546\) −5.46619 −0.233931
\(547\) 15.8891 0.679370 0.339685 0.940539i \(-0.389680\pi\)
0.339685 + 0.940539i \(0.389680\pi\)
\(548\) −36.5631 −1.56190
\(549\) −13.8054 −0.589201
\(550\) −33.7261 −1.43809
\(551\) 31.5488 1.34402
\(552\) −8.02520 −0.341575
\(553\) 20.0508 0.852646
\(554\) −47.5647 −2.02083
\(555\) −0.175958 −0.00746902
\(556\) −60.0003 −2.54458
\(557\) 1.39247 0.0590010 0.0295005 0.999565i \(-0.490608\pi\)
0.0295005 + 0.999565i \(0.490608\pi\)
\(558\) 20.7704 0.879282
\(559\) −2.60474 −0.110169
\(560\) 0.362500 0.0153184
\(561\) 18.0661 0.762753
\(562\) −37.5544 −1.58414
\(563\) −2.08672 −0.0879446 −0.0439723 0.999033i \(-0.514001\pi\)
−0.0439723 + 0.999033i \(0.514001\pi\)
\(564\) −48.6110 −2.04689
\(565\) 0.334090 0.0140553
\(566\) −53.0329 −2.22914
\(567\) −4.28110 −0.179789
\(568\) 38.5135 1.61599
\(569\) 4.35134 0.182418 0.0912088 0.995832i \(-0.470927\pi\)
0.0912088 + 0.995832i \(0.470927\pi\)
\(570\) 0.236434 0.00990313
\(571\) 32.5669 1.36288 0.681442 0.731872i \(-0.261353\pi\)
0.681442 + 0.731872i \(0.261353\pi\)
\(572\) 5.64917 0.236204
\(573\) −2.11723 −0.0884483
\(574\) −58.0158 −2.42153
\(575\) −9.19021 −0.383258
\(576\) −9.98955 −0.416231
\(577\) 12.2346 0.509332 0.254666 0.967029i \(-0.418034\pi\)
0.254666 + 0.967029i \(0.418034\pi\)
\(578\) −59.4722 −2.47372
\(579\) 21.7998 0.905970
\(580\) −1.04406 −0.0433524
\(581\) −13.4589 −0.558370
\(582\) −30.2324 −1.25317
\(583\) 8.63307 0.357545
\(584\) −37.4224 −1.54855
\(585\) 0.0154581 0.000639114 0
\(586\) −74.3010 −3.06934
\(587\) 13.3537 0.551166 0.275583 0.961277i \(-0.411129\pi\)
0.275583 + 0.961277i \(0.411129\pi\)
\(588\) 43.1695 1.78028
\(589\) −28.9574 −1.19317
\(590\) −0.0271800 −0.00111898
\(591\) 12.6763 0.521434
\(592\) 17.4929 0.718956
\(593\) −26.6548 −1.09458 −0.547290 0.836943i \(-0.684341\pi\)
−0.547290 + 0.836943i \(0.684341\pi\)
\(594\) 6.74637 0.276807
\(595\) −0.806535 −0.0330647
\(596\) −77.0814 −3.15738
\(597\) −2.54320 −0.104086
\(598\) 2.34725 0.0959860
\(599\) −25.5806 −1.04519 −0.522597 0.852580i \(-0.675037\pi\)
−0.522597 + 0.852580i \(0.675037\pi\)
\(600\) 21.8234 0.890937
\(601\) 14.1037 0.575301 0.287650 0.957735i \(-0.407126\pi\)
0.287650 + 0.957735i \(0.407126\pi\)
\(602\) 50.7500 2.06842
\(603\) 12.4931 0.508760
\(604\) 38.3048 1.55860
\(605\) 0.0924449 0.00375842
\(606\) 2.72927 0.110869
\(607\) 28.9805 1.17628 0.588141 0.808759i \(-0.299860\pi\)
0.588141 + 0.808759i \(0.299860\pi\)
\(608\) 5.83711 0.236726
\(609\) −40.1884 −1.62852
\(610\) −0.971232 −0.0393240
\(611\) 6.75630 0.273331
\(612\) −24.6008 −0.994430
\(613\) −9.41225 −0.380157 −0.190079 0.981769i \(-0.560874\pi\)
−0.190079 + 0.981769i \(0.560874\pi\)
\(614\) 23.3479 0.942244
\(615\) 0.164066 0.00661578
\(616\) −52.3032 −2.10736
\(617\) 27.4211 1.10393 0.551965 0.833867i \(-0.313878\pi\)
0.551965 + 0.833867i \(0.313878\pi\)
\(618\) 26.0930 1.04961
\(619\) −2.44299 −0.0981921 −0.0490961 0.998794i \(-0.515634\pi\)
−0.0490961 + 0.998794i \(0.515634\pi\)
\(620\) 0.958305 0.0384865
\(621\) 1.83835 0.0737706
\(622\) −11.8146 −0.473723
\(623\) 56.3819 2.25889
\(624\) −1.53677 −0.0615201
\(625\) 24.9872 0.999489
\(626\) −13.1337 −0.524927
\(627\) −9.40555 −0.375621
\(628\) 44.3220 1.76864
\(629\) −38.9205 −1.55186
\(630\) −0.301181 −0.0119993
\(631\) 17.0681 0.679469 0.339734 0.940521i \(-0.389663\pi\)
0.339734 + 0.940521i \(0.389663\pi\)
\(632\) 20.4457 0.813288
\(633\) 13.6475 0.542441
\(634\) −33.5572 −1.33273
\(635\) 0.172766 0.00685601
\(636\) −11.7557 −0.466146
\(637\) −6.00000 −0.237729
\(638\) 63.3309 2.50729
\(639\) −8.82238 −0.349008
\(640\) −0.601402 −0.0237725
\(641\) −2.09322 −0.0826772 −0.0413386 0.999145i \(-0.513162\pi\)
−0.0413386 + 0.999145i \(0.513162\pi\)
\(642\) 39.5280 1.56004
\(643\) −42.4852 −1.67545 −0.837726 0.546090i \(-0.816116\pi\)
−0.837726 + 0.546090i \(0.816116\pi\)
\(644\) −29.9927 −1.18188
\(645\) −0.143518 −0.00565103
\(646\) 52.2972 2.05761
\(647\) −15.3077 −0.601806 −0.300903 0.953655i \(-0.597288\pi\)
−0.300903 + 0.953655i \(0.597288\pi\)
\(648\) −4.36543 −0.171490
\(649\) 1.08125 0.0424426
\(650\) −6.38301 −0.250362
\(651\) 36.8873 1.44573
\(652\) 88.0907 3.44990
\(653\) 11.8262 0.462796 0.231398 0.972859i \(-0.425670\pi\)
0.231398 + 0.972859i \(0.425670\pi\)
\(654\) 11.6455 0.455375
\(655\) −0.321981 −0.0125808
\(656\) −16.3107 −0.636824
\(657\) 8.57246 0.334444
\(658\) −131.638 −5.13178
\(659\) 48.4642 1.88790 0.943949 0.330090i \(-0.107079\pi\)
0.943949 + 0.330090i \(0.107079\pi\)
\(660\) 0.311264 0.0121159
\(661\) −10.2091 −0.397089 −0.198544 0.980092i \(-0.563621\pi\)
−0.198544 + 0.980092i \(0.563621\pi\)
\(662\) 48.4169 1.88178
\(663\) 3.41920 0.132791
\(664\) −13.7240 −0.532595
\(665\) 0.419896 0.0162829
\(666\) −14.5339 −0.563178
\(667\) 17.2574 0.668208
\(668\) 46.0925 1.78337
\(669\) 15.0731 0.582758
\(670\) 0.878909 0.0339552
\(671\) 38.6364 1.49154
\(672\) −7.43559 −0.286834
\(673\) 49.9748 1.92639 0.963193 0.268812i \(-0.0866310\pi\)
0.963193 + 0.268812i \(0.0866310\pi\)
\(674\) −29.8177 −1.14853
\(675\) −4.99915 −0.192417
\(676\) −48.4730 −1.86435
\(677\) 31.1471 1.19708 0.598540 0.801093i \(-0.295748\pi\)
0.598540 + 0.801093i \(0.295748\pi\)
\(678\) 27.5954 1.05979
\(679\) −53.6914 −2.06049
\(680\) −0.822422 −0.0315384
\(681\) 23.3873 0.896202
\(682\) −58.1289 −2.22587
\(683\) 31.1306 1.19118 0.595590 0.803288i \(-0.296918\pi\)
0.595590 + 0.803288i \(0.296918\pi\)
\(684\) 12.8076 0.489712
\(685\) 0.280002 0.0106983
\(686\) 44.6626 1.70522
\(687\) 29.9193 1.14149
\(688\) 14.2679 0.543960
\(689\) 1.63390 0.0622465
\(690\) 0.129331 0.00492354
\(691\) −45.6611 −1.73703 −0.868515 0.495664i \(-0.834925\pi\)
−0.868515 + 0.495664i \(0.834925\pi\)
\(692\) −53.3641 −2.02860
\(693\) 11.9812 0.455130
\(694\) 56.8406 2.15764
\(695\) 0.459485 0.0174293
\(696\) −40.9800 −1.55334
\(697\) 36.2900 1.37458
\(698\) −25.9752 −0.983176
\(699\) −13.7713 −0.520877
\(700\) 81.5610 3.08272
\(701\) 11.9171 0.450102 0.225051 0.974347i \(-0.427745\pi\)
0.225051 + 0.974347i \(0.427745\pi\)
\(702\) 1.27682 0.0481904
\(703\) 20.2627 0.764222
\(704\) 27.9571 1.05367
\(705\) 0.372265 0.0140203
\(706\) −23.8995 −0.899470
\(707\) 4.84707 0.182293
\(708\) −1.47234 −0.0553341
\(709\) −2.16116 −0.0811640 −0.0405820 0.999176i \(-0.512921\pi\)
−0.0405820 + 0.999176i \(0.512921\pi\)
\(710\) −0.620667 −0.0232932
\(711\) −4.68356 −0.175647
\(712\) 57.4925 2.15462
\(713\) −15.8399 −0.593208
\(714\) −66.6187 −2.49314
\(715\) −0.0432616 −0.00161789
\(716\) 29.3932 1.09847
\(717\) 10.4291 0.389483
\(718\) 72.3003 2.69822
\(719\) 1.95244 0.0728138 0.0364069 0.999337i \(-0.488409\pi\)
0.0364069 + 0.999337i \(0.488409\pi\)
\(720\) −0.0846745 −0.00315563
\(721\) 46.3399 1.72579
\(722\) 18.5743 0.691265
\(723\) −6.11450 −0.227401
\(724\) −63.8562 −2.37320
\(725\) −46.9290 −1.74290
\(726\) 7.63583 0.283392
\(727\) −14.0829 −0.522305 −0.261153 0.965298i \(-0.584103\pi\)
−0.261153 + 0.965298i \(0.584103\pi\)
\(728\) −9.89892 −0.366878
\(729\) 1.00000 0.0370370
\(730\) 0.603085 0.0223212
\(731\) −31.7451 −1.17413
\(732\) −52.6116 −1.94458
\(733\) 15.4869 0.572023 0.286011 0.958226i \(-0.407670\pi\)
0.286011 + 0.958226i \(0.407670\pi\)
\(734\) −67.3023 −2.48417
\(735\) −0.330594 −0.0121941
\(736\) 3.19293 0.117693
\(737\) −34.9638 −1.28791
\(738\) 13.5516 0.498843
\(739\) 35.3675 1.30101 0.650507 0.759501i \(-0.274557\pi\)
0.650507 + 0.759501i \(0.274557\pi\)
\(740\) −0.670566 −0.0246505
\(741\) −1.78010 −0.0653935
\(742\) −31.8344 −1.16868
\(743\) −12.9234 −0.474115 −0.237058 0.971496i \(-0.576183\pi\)
−0.237058 + 0.971496i \(0.576183\pi\)
\(744\) 37.6139 1.37899
\(745\) 0.590293 0.0216267
\(746\) −16.8388 −0.616514
\(747\) 3.14380 0.115026
\(748\) 68.8489 2.51736
\(749\) 70.1999 2.56505
\(750\) −0.703454 −0.0256865
\(751\) 33.6245 1.22698 0.613488 0.789704i \(-0.289766\pi\)
0.613488 + 0.789704i \(0.289766\pi\)
\(752\) −37.0088 −1.34957
\(753\) 20.3582 0.741896
\(754\) 11.9860 0.436505
\(755\) −0.293340 −0.0106757
\(756\) −16.3150 −0.593370
\(757\) −17.1319 −0.622669 −0.311335 0.950300i \(-0.600776\pi\)
−0.311335 + 0.950300i \(0.600776\pi\)
\(758\) 7.55225 0.274310
\(759\) −5.14489 −0.186748
\(760\) 0.428167 0.0155313
\(761\) −46.0391 −1.66892 −0.834458 0.551071i \(-0.814219\pi\)
−0.834458 + 0.551071i \(0.814219\pi\)
\(762\) 14.2702 0.516956
\(763\) 20.6819 0.748735
\(764\) −8.06861 −0.291912
\(765\) 0.188394 0.00681141
\(766\) 17.9237 0.647609
\(767\) 0.204637 0.00738900
\(768\) −29.6959 −1.07156
\(769\) 37.7773 1.36228 0.681142 0.732151i \(-0.261484\pi\)
0.681142 + 0.732151i \(0.261484\pi\)
\(770\) 0.842897 0.0303759
\(771\) −11.1357 −0.401042
\(772\) 83.0778 2.99004
\(773\) −10.8062 −0.388672 −0.194336 0.980935i \(-0.562255\pi\)
−0.194336 + 0.980935i \(0.562255\pi\)
\(774\) −11.8544 −0.426099
\(775\) 43.0743 1.54727
\(776\) −54.7490 −1.96537
\(777\) −25.8116 −0.925986
\(778\) 26.8281 0.961835
\(779\) −18.8932 −0.676919
\(780\) 0.0589098 0.00210931
\(781\) 24.6907 0.883502
\(782\) 28.6069 1.02298
\(783\) 9.38740 0.335478
\(784\) 32.8661 1.17379
\(785\) −0.339420 −0.0121144
\(786\) −26.5952 −0.948621
\(787\) −46.3487 −1.65215 −0.826076 0.563559i \(-0.809432\pi\)
−0.826076 + 0.563559i \(0.809432\pi\)
\(788\) 48.3087 1.72093
\(789\) 22.0849 0.786242
\(790\) −0.329495 −0.0117229
\(791\) 49.0081 1.74253
\(792\) 12.2172 0.434121
\(793\) 7.31234 0.259669
\(794\) 11.3342 0.402236
\(795\) 0.0900261 0.00319290
\(796\) −9.69197 −0.343523
\(797\) −18.0995 −0.641118 −0.320559 0.947229i \(-0.603871\pi\)
−0.320559 + 0.947229i \(0.603871\pi\)
\(798\) 34.6829 1.22776
\(799\) 82.3419 2.91305
\(800\) −8.68273 −0.306981
\(801\) −13.1700 −0.465338
\(802\) −31.4394 −1.11016
\(803\) −23.9912 −0.846632
\(804\) 47.6105 1.67909
\(805\) 0.229686 0.00809536
\(806\) −11.0015 −0.387511
\(807\) −24.7147 −0.869999
\(808\) 4.94254 0.173878
\(809\) −21.0268 −0.739264 −0.369632 0.929178i \(-0.620516\pi\)
−0.369632 + 0.929178i \(0.620516\pi\)
\(810\) 0.0703514 0.00247190
\(811\) −0.497548 −0.0174713 −0.00873563 0.999962i \(-0.502781\pi\)
−0.00873563 + 0.999962i \(0.502781\pi\)
\(812\) −153.155 −5.37470
\(813\) 19.4297 0.681428
\(814\) 40.6752 1.42567
\(815\) −0.674602 −0.0236303
\(816\) −18.7293 −0.655656
\(817\) 16.5270 0.578208
\(818\) −44.6078 −1.55968
\(819\) 2.26757 0.0792354
\(820\) 0.625245 0.0218345
\(821\) −42.3686 −1.47867 −0.739337 0.673335i \(-0.764861\pi\)
−0.739337 + 0.673335i \(0.764861\pi\)
\(822\) 23.1278 0.806674
\(823\) −36.5864 −1.27532 −0.637660 0.770318i \(-0.720098\pi\)
−0.637660 + 0.770318i \(0.720098\pi\)
\(824\) 47.2527 1.64613
\(825\) 13.9908 0.487098
\(826\) −3.98708 −0.138728
\(827\) 33.7534 1.17372 0.586861 0.809688i \(-0.300364\pi\)
0.586861 + 0.809688i \(0.300364\pi\)
\(828\) 7.00585 0.243470
\(829\) −27.0039 −0.937886 −0.468943 0.883229i \(-0.655365\pi\)
−0.468943 + 0.883229i \(0.655365\pi\)
\(830\) 0.221171 0.00767695
\(831\) 19.7316 0.684481
\(832\) 5.29118 0.183439
\(833\) −73.1245 −2.53362
\(834\) 37.9529 1.31420
\(835\) −0.352979 −0.0122153
\(836\) −35.8439 −1.23969
\(837\) −8.61633 −0.297824
\(838\) 52.0758 1.79893
\(839\) 30.4241 1.05036 0.525179 0.850992i \(-0.323998\pi\)
0.525179 + 0.850992i \(0.323998\pi\)
\(840\) −0.545420 −0.0188188
\(841\) 59.1233 2.03874
\(842\) 33.0016 1.13731
\(843\) 15.5789 0.536567
\(844\) 52.0099 1.79025
\(845\) 0.371209 0.0127700
\(846\) 30.7486 1.05716
\(847\) 13.5609 0.465957
\(848\) −8.94997 −0.307343
\(849\) 22.0000 0.755038
\(850\) −77.7924 −2.66826
\(851\) 11.0838 0.379948
\(852\) −33.6216 −1.15186
\(853\) −26.8765 −0.920232 −0.460116 0.887859i \(-0.652192\pi\)
−0.460116 + 0.887859i \(0.652192\pi\)
\(854\) −142.472 −4.87527
\(855\) −0.0980815 −0.00335431
\(856\) 71.5827 2.44665
\(857\) −3.71644 −0.126951 −0.0634755 0.997983i \(-0.520218\pi\)
−0.0634755 + 0.997983i \(0.520218\pi\)
\(858\) −3.57336 −0.121992
\(859\) −35.4170 −1.20841 −0.604206 0.796828i \(-0.706510\pi\)
−0.604206 + 0.796828i \(0.706510\pi\)
\(860\) −0.546940 −0.0186505
\(861\) 24.0671 0.820204
\(862\) −19.5679 −0.666486
\(863\) 15.5705 0.530027 0.265013 0.964245i \(-0.414624\pi\)
0.265013 + 0.964245i \(0.414624\pi\)
\(864\) 1.73684 0.0590886
\(865\) 0.408664 0.0138950
\(866\) 3.79904 0.129097
\(867\) 24.6712 0.837879
\(868\) 140.575 4.77144
\(869\) 13.1076 0.444645
\(870\) 0.660417 0.0223902
\(871\) −6.61725 −0.224217
\(872\) 21.0893 0.714173
\(873\) 12.5415 0.424466
\(874\) −14.8933 −0.503772
\(875\) −1.24930 −0.0422341
\(876\) 32.6691 1.10379
\(877\) −19.3818 −0.654478 −0.327239 0.944942i \(-0.606118\pi\)
−0.327239 + 0.944942i \(0.606118\pi\)
\(878\) −44.2010 −1.49171
\(879\) 30.8227 1.03963
\(880\) 0.236973 0.00798837
\(881\) −22.3823 −0.754080 −0.377040 0.926197i \(-0.623058\pi\)
−0.377040 + 0.926197i \(0.623058\pi\)
\(882\) −27.3066 −0.919462
\(883\) −45.7562 −1.53982 −0.769909 0.638154i \(-0.779698\pi\)
−0.769909 + 0.638154i \(0.779698\pi\)
\(884\) 13.0304 0.438258
\(885\) 0.0112753 0.000379014 0
\(886\) 83.5078 2.80550
\(887\) −7.67423 −0.257675 −0.128838 0.991666i \(-0.541125\pi\)
−0.128838 + 0.991666i \(0.541125\pi\)
\(888\) −26.3200 −0.883243
\(889\) 25.3433 0.849987
\(890\) −0.926526 −0.0310572
\(891\) −2.79864 −0.0937579
\(892\) 57.4425 1.92332
\(893\) −42.8686 −1.43454
\(894\) 48.7574 1.63069
\(895\) −0.225094 −0.00752407
\(896\) −88.2206 −2.94724
\(897\) −0.973723 −0.0325117
\(898\) −6.12874 −0.204519
\(899\) −80.8849 −2.69766
\(900\) −19.0514 −0.635048
\(901\) 19.9130 0.663398
\(902\) −37.9261 −1.26280
\(903\) −21.0530 −0.700598
\(904\) 49.9735 1.66209
\(905\) 0.489014 0.0162554
\(906\) −24.2295 −0.804972
\(907\) 22.3182 0.741064 0.370532 0.928820i \(-0.379175\pi\)
0.370532 + 0.928820i \(0.379175\pi\)
\(908\) 89.1274 2.95780
\(909\) −1.13220 −0.0375528
\(910\) 0.159527 0.00528827
\(911\) 56.8629 1.88395 0.941976 0.335681i \(-0.108966\pi\)
0.941976 + 0.335681i \(0.108966\pi\)
\(912\) 9.75080 0.322881
\(913\) −8.79836 −0.291183
\(914\) 45.7508 1.51330
\(915\) 0.402902 0.0133195
\(916\) 114.021 3.76735
\(917\) −47.2319 −1.55974
\(918\) 15.5611 0.513594
\(919\) 14.2808 0.471080 0.235540 0.971865i \(-0.424314\pi\)
0.235540 + 0.971865i \(0.424314\pi\)
\(920\) 0.234210 0.00772168
\(921\) −9.68555 −0.319150
\(922\) 23.4918 0.773662
\(923\) 4.67296 0.153812
\(924\) 45.6598 1.50210
\(925\) −30.1409 −0.991026
\(926\) −64.2526 −2.11147
\(927\) −10.8243 −0.355517
\(928\) 16.3044 0.535220
\(929\) 12.4699 0.409125 0.204563 0.978853i \(-0.434423\pi\)
0.204563 + 0.978853i \(0.434423\pi\)
\(930\) −0.606171 −0.0198771
\(931\) 38.0699 1.24769
\(932\) −52.4814 −1.71908
\(933\) 4.90114 0.160456
\(934\) 4.35083 0.142364
\(935\) −0.527248 −0.0172429
\(936\) 2.31224 0.0755779
\(937\) −54.6711 −1.78603 −0.893013 0.450030i \(-0.851413\pi\)
−0.893013 + 0.450030i \(0.851413\pi\)
\(938\) 128.929 4.20967
\(939\) 5.44833 0.177800
\(940\) 1.41868 0.0462722
\(941\) 14.5029 0.472780 0.236390 0.971658i \(-0.424036\pi\)
0.236390 + 0.971658i \(0.424036\pi\)
\(942\) −28.0356 −0.913450
\(943\) −10.3347 −0.336544
\(944\) −1.12093 −0.0364833
\(945\) 0.124941 0.00406433
\(946\) 33.1763 1.07865
\(947\) 42.9697 1.39633 0.698164 0.715938i \(-0.254001\pi\)
0.698164 + 0.715938i \(0.254001\pi\)
\(948\) −17.8488 −0.579701
\(949\) −4.54059 −0.147394
\(950\) 40.5001 1.31400
\(951\) 13.9208 0.451412
\(952\) −120.642 −3.91004
\(953\) −21.4599 −0.695155 −0.347578 0.937651i \(-0.612996\pi\)
−0.347578 + 0.937651i \(0.612996\pi\)
\(954\) 7.43604 0.240751
\(955\) 0.0617898 0.00199947
\(956\) 39.7447 1.28544
\(957\) −26.2720 −0.849252
\(958\) −84.5859 −2.73285
\(959\) 41.0739 1.32634
\(960\) 0.291538 0.00940936
\(961\) 43.2411 1.39487
\(962\) 7.69820 0.248200
\(963\) −16.3976 −0.528407
\(964\) −23.3020 −0.750506
\(965\) −0.636214 −0.0204804
\(966\) 18.9717 0.610406
\(967\) 46.9208 1.50887 0.754436 0.656373i \(-0.227910\pi\)
0.754436 + 0.656373i \(0.227910\pi\)
\(968\) 13.8280 0.444449
\(969\) −21.6948 −0.696937
\(970\) 0.882313 0.0283294
\(971\) −0.890351 −0.0285727 −0.0142864 0.999898i \(-0.504548\pi\)
−0.0142864 + 0.999898i \(0.504548\pi\)
\(972\) 3.81094 0.122236
\(973\) 67.4026 2.16083
\(974\) 28.9740 0.928385
\(975\) 2.64790 0.0848008
\(976\) −40.0546 −1.28212
\(977\) 40.7041 1.30224 0.651120 0.758974i \(-0.274299\pi\)
0.651120 + 0.758974i \(0.274299\pi\)
\(978\) −55.7213 −1.78177
\(979\) 36.8580 1.17799
\(980\) −1.25987 −0.0402451
\(981\) −4.83098 −0.154241
\(982\) 24.9824 0.797222
\(983\) −12.8908 −0.411153 −0.205576 0.978641i \(-0.565907\pi\)
−0.205576 + 0.978641i \(0.565907\pi\)
\(984\) 24.5412 0.782344
\(985\) −0.369950 −0.0117876
\(986\) 146.079 4.65209
\(987\) 54.6082 1.73820
\(988\) −6.78383 −0.215822
\(989\) 9.04039 0.287468
\(990\) −0.196888 −0.00625752
\(991\) 44.1812 1.40346 0.701731 0.712442i \(-0.252411\pi\)
0.701731 + 0.712442i \(0.252411\pi\)
\(992\) −14.9652 −0.475146
\(993\) −20.0851 −0.637382
\(994\) −91.0467 −2.88782
\(995\) 0.0742215 0.00235298
\(996\) 11.9808 0.379627
\(997\) 28.7888 0.911750 0.455875 0.890044i \(-0.349326\pi\)
0.455875 + 0.890044i \(0.349326\pi\)
\(998\) −25.2269 −0.798542
\(999\) 6.02920 0.190756
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 \(a_p\))