Properties

Label 4033.2.a.d.1.11
Level 4033
Weight 2
Character 4033.1
Self dual Yes
Analytic conductor 32.204
Analytic rank 1
Dimension 79
CM No

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(79\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.27855 q^{2}\) \(-2.02568 q^{3}\) \(+3.19181 q^{4}\) \(-1.32967 q^{5}\) \(+4.61563 q^{6}\) \(+2.20899 q^{7}\) \(-2.71560 q^{8}\) \(+1.10340 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.27855 q^{2}\) \(-2.02568 q^{3}\) \(+3.19181 q^{4}\) \(-1.32967 q^{5}\) \(+4.61563 q^{6}\) \(+2.20899 q^{7}\) \(-2.71560 q^{8}\) \(+1.10340 q^{9}\) \(+3.02972 q^{10}\) \(+3.01218 q^{11}\) \(-6.46560 q^{12}\) \(+3.26538 q^{13}\) \(-5.03331 q^{14}\) \(+2.69349 q^{15}\) \(-0.195977 q^{16}\) \(-3.42969 q^{17}\) \(-2.51415 q^{18}\) \(+7.40650 q^{19}\) \(-4.24404 q^{20}\) \(-4.47472 q^{21}\) \(-6.86341 q^{22}\) \(-3.27201 q^{23}\) \(+5.50095 q^{24}\) \(-3.23198 q^{25}\) \(-7.44035 q^{26}\) \(+3.84192 q^{27}\) \(+7.05068 q^{28}\) \(-6.08679 q^{29}\) \(-6.13726 q^{30}\) \(+9.24208 q^{31}\) \(+5.87774 q^{32}\) \(-6.10172 q^{33}\) \(+7.81473 q^{34}\) \(-2.93723 q^{35}\) \(+3.52184 q^{36}\) \(-1.00000 q^{37}\) \(-16.8761 q^{38}\) \(-6.61463 q^{39}\) \(+3.61084 q^{40}\) \(-5.52935 q^{41}\) \(+10.1959 q^{42}\) \(-8.51355 q^{43}\) \(+9.61429 q^{44}\) \(-1.46715 q^{45}\) \(+7.45545 q^{46}\) \(+0.687745 q^{47}\) \(+0.396987 q^{48}\) \(-2.12035 q^{49}\) \(+7.36425 q^{50}\) \(+6.94747 q^{51}\) \(+10.4225 q^{52}\) \(-11.3154 q^{53}\) \(-8.75401 q^{54}\) \(-4.00519 q^{55}\) \(-5.99874 q^{56}\) \(-15.0032 q^{57}\) \(+13.8691 q^{58}\) \(-2.57226 q^{59}\) \(+8.59709 q^{60}\) \(-3.70675 q^{61}\) \(-21.0586 q^{62}\) \(+2.43740 q^{63}\) \(-13.0008 q^{64}\) \(-4.34187 q^{65}\) \(+13.9031 q^{66}\) \(-10.1990 q^{67}\) \(-10.9469 q^{68}\) \(+6.62806 q^{69}\) \(+6.69263 q^{70}\) \(+14.6737 q^{71}\) \(-2.99639 q^{72}\) \(+1.15575 q^{73}\) \(+2.27855 q^{74}\) \(+6.54698 q^{75}\) \(+23.6401 q^{76}\) \(+6.65388 q^{77}\) \(+15.0718 q^{78}\) \(+7.31062 q^{79}\) \(+0.260584 q^{80}\) \(-11.0927 q^{81}\) \(+12.5989 q^{82}\) \(+7.03276 q^{83}\) \(-14.2825 q^{84}\) \(+4.56034 q^{85}\) \(+19.3986 q^{86}\) \(+12.3299 q^{87}\) \(-8.17987 q^{88}\) \(-16.7495 q^{89}\) \(+3.34299 q^{90}\) \(+7.21321 q^{91}\) \(-10.4436 q^{92}\) \(-18.7215 q^{93}\) \(-1.56706 q^{94}\) \(-9.84818 q^{95}\) \(-11.9065 q^{96}\) \(-2.27322 q^{97}\) \(+4.83133 q^{98}\) \(+3.32363 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 14q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut -\mathstrut 42q^{8} \) \(\mathstrut +\mathstrut 76q^{9} \) \(\mathstrut -\mathstrut 13q^{10} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 40q^{12} \) \(\mathstrut -\mathstrut 18q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 49q^{15} \) \(\mathstrut +\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 62q^{17} \) \(\mathstrut -\mathstrut 33q^{18} \) \(\mathstrut -\mathstrut 25q^{19} \) \(\mathstrut -\mathstrut 39q^{20} \) \(\mathstrut -\mathstrut 15q^{21} \) \(\mathstrut -\mathstrut 31q^{22} \) \(\mathstrut -\mathstrut 94q^{23} \) \(\mathstrut -\mathstrut 39q^{24} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut -\mathstrut 35q^{26} \) \(\mathstrut -\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 13q^{28} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 37q^{31} \) \(\mathstrut -\mathstrut 105q^{32} \) \(\mathstrut -\mathstrut 60q^{33} \) \(\mathstrut +\mathstrut 9q^{34} \) \(\mathstrut -\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 79q^{37} \) \(\mathstrut -\mathstrut 80q^{38} \) \(\mathstrut -\mathstrut 41q^{39} \) \(\mathstrut -\mathstrut 64q^{40} \) \(\mathstrut -\mathstrut 37q^{41} \) \(\mathstrut -\mathstrut 30q^{42} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 61q^{46} \) \(\mathstrut -\mathstrut 148q^{47} \) \(\mathstrut -\mathstrut 39q^{48} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut 90q^{50} \) \(\mathstrut -\mathstrut 45q^{51} \) \(\mathstrut -\mathstrut 27q^{52} \) \(\mathstrut -\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 41q^{54} \) \(\mathstrut -\mathstrut 105q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut -\mathstrut 96q^{59} \) \(\mathstrut -\mathstrut 74q^{60} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut -\mathstrut 60q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 71q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 166q^{68} \) \(\mathstrut -\mathstrut 72q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut -\mathstrut 55q^{71} \) \(\mathstrut -\mathstrut 126q^{72} \) \(\mathstrut -\mathstrut 27q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut -\mathstrut 39q^{75} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut -\mathstrut 104q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut -\mathstrut 49q^{79} \) \(\mathstrut -\mathstrut 82q^{80} \) \(\mathstrut +\mathstrut 55q^{81} \) \(\mathstrut +\mathstrut 20q^{82} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 29q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 113q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 39q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 179q^{92} \) \(\mathstrut -\mathstrut 53q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 86q^{95} \) \(\mathstrut +\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut -\mathstrut 116q^{98} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27855 −1.61118 −0.805590 0.592473i \(-0.798152\pi\)
−0.805590 + 0.592473i \(0.798152\pi\)
\(3\) −2.02568 −1.16953 −0.584765 0.811203i \(-0.698813\pi\)
−0.584765 + 0.811203i \(0.698813\pi\)
\(4\) 3.19181 1.59590
\(5\) −1.32967 −0.594645 −0.297323 0.954777i \(-0.596094\pi\)
−0.297323 + 0.954777i \(0.596094\pi\)
\(6\) 4.61563 1.88432
\(7\) 2.20899 0.834921 0.417461 0.908695i \(-0.362920\pi\)
0.417461 + 0.908695i \(0.362920\pi\)
\(8\) −2.71560 −0.960109
\(9\) 1.10340 0.367800
\(10\) 3.02972 0.958081
\(11\) 3.01218 0.908206 0.454103 0.890949i \(-0.349960\pi\)
0.454103 + 0.890949i \(0.349960\pi\)
\(12\) −6.46560 −1.86646
\(13\) 3.26538 0.905654 0.452827 0.891598i \(-0.350416\pi\)
0.452827 + 0.891598i \(0.350416\pi\)
\(14\) −5.03331 −1.34521
\(15\) 2.69349 0.695455
\(16\) −0.195977 −0.0489941
\(17\) −3.42969 −0.831822 −0.415911 0.909405i \(-0.636537\pi\)
−0.415911 + 0.909405i \(0.636537\pi\)
\(18\) −2.51415 −0.592592
\(19\) 7.40650 1.69917 0.849583 0.527454i \(-0.176853\pi\)
0.849583 + 0.527454i \(0.176853\pi\)
\(20\) −4.24404 −0.948997
\(21\) −4.47472 −0.976465
\(22\) −6.86341 −1.46328
\(23\) −3.27201 −0.682261 −0.341130 0.940016i \(-0.610810\pi\)
−0.341130 + 0.940016i \(0.610810\pi\)
\(24\) 5.50095 1.12288
\(25\) −3.23198 −0.646397
\(26\) −7.44035 −1.45917
\(27\) 3.84192 0.739377
\(28\) 7.05068 1.33245
\(29\) −6.08679 −1.13029 −0.565144 0.824992i \(-0.691180\pi\)
−0.565144 + 0.824992i \(0.691180\pi\)
\(30\) −6.13726 −1.12050
\(31\) 9.24208 1.65993 0.829963 0.557819i \(-0.188362\pi\)
0.829963 + 0.557819i \(0.188362\pi\)
\(32\) 5.87774 1.03905
\(33\) −6.10172 −1.06217
\(34\) 7.81473 1.34022
\(35\) −2.93723 −0.496482
\(36\) 3.52184 0.586973
\(37\) −1.00000 −0.164399
\(38\) −16.8761 −2.73767
\(39\) −6.61463 −1.05919
\(40\) 3.61084 0.570925
\(41\) −5.52935 −0.863539 −0.431770 0.901984i \(-0.642111\pi\)
−0.431770 + 0.901984i \(0.642111\pi\)
\(42\) 10.1959 1.57326
\(43\) −8.51355 −1.29830 −0.649152 0.760658i \(-0.724876\pi\)
−0.649152 + 0.760658i \(0.724876\pi\)
\(44\) 9.61429 1.44941
\(45\) −1.46715 −0.218710
\(46\) 7.45545 1.09925
\(47\) 0.687745 0.100318 0.0501590 0.998741i \(-0.484027\pi\)
0.0501590 + 0.998741i \(0.484027\pi\)
\(48\) 0.396987 0.0573001
\(49\) −2.12035 −0.302907
\(50\) 7.36425 1.04146
\(51\) 6.94747 0.972840
\(52\) 10.4225 1.44534
\(53\) −11.3154 −1.55430 −0.777148 0.629318i \(-0.783334\pi\)
−0.777148 + 0.629318i \(0.783334\pi\)
\(54\) −8.75401 −1.19127
\(55\) −4.00519 −0.540060
\(56\) −5.99874 −0.801616
\(57\) −15.0032 −1.98723
\(58\) 13.8691 1.82110
\(59\) −2.57226 −0.334880 −0.167440 0.985882i \(-0.553550\pi\)
−0.167440 + 0.985882i \(0.553550\pi\)
\(60\) 8.59709 1.10988
\(61\) −3.70675 −0.474601 −0.237300 0.971436i \(-0.576263\pi\)
−0.237300 + 0.971436i \(0.576263\pi\)
\(62\) −21.0586 −2.67444
\(63\) 2.43740 0.307084
\(64\) −13.0008 −1.62510
\(65\) −4.34187 −0.538543
\(66\) 13.9031 1.71135
\(67\) −10.1990 −1.24601 −0.623004 0.782219i \(-0.714088\pi\)
−0.623004 + 0.782219i \(0.714088\pi\)
\(68\) −10.9469 −1.32751
\(69\) 6.62806 0.797924
\(70\) 6.69263 0.799922
\(71\) 14.6737 1.74144 0.870722 0.491776i \(-0.163652\pi\)
0.870722 + 0.491776i \(0.163652\pi\)
\(72\) −2.99639 −0.353128
\(73\) 1.15575 0.135271 0.0676353 0.997710i \(-0.478455\pi\)
0.0676353 + 0.997710i \(0.478455\pi\)
\(74\) 2.27855 0.264877
\(75\) 6.54698 0.755980
\(76\) 23.6401 2.71171
\(77\) 6.65388 0.758280
\(78\) 15.0718 1.70655
\(79\) 7.31062 0.822509 0.411255 0.911520i \(-0.365091\pi\)
0.411255 + 0.911520i \(0.365091\pi\)
\(80\) 0.260584 0.0291341
\(81\) −11.0927 −1.23252
\(82\) 12.5989 1.39132
\(83\) 7.03276 0.771945 0.385973 0.922510i \(-0.373866\pi\)
0.385973 + 0.922510i \(0.373866\pi\)
\(84\) −14.2825 −1.55834
\(85\) 4.56034 0.494639
\(86\) 19.3986 2.09180
\(87\) 12.3299 1.32191
\(88\) −8.17987 −0.871977
\(89\) −16.7495 −1.77544 −0.887720 0.460384i \(-0.847712\pi\)
−0.887720 + 0.460384i \(0.847712\pi\)
\(90\) 3.34299 0.352382
\(91\) 7.21321 0.756149
\(92\) −10.4436 −1.08882
\(93\) −18.7215 −1.94133
\(94\) −1.56706 −0.161630
\(95\) −9.84818 −1.01040
\(96\) −11.9065 −1.21520
\(97\) −2.27322 −0.230811 −0.115405 0.993318i \(-0.536817\pi\)
−0.115405 + 0.993318i \(0.536817\pi\)
\(98\) 4.83133 0.488038
\(99\) 3.32363 0.334038
\(100\) −10.3159 −1.03159
\(101\) 12.0462 1.19864 0.599322 0.800508i \(-0.295437\pi\)
0.599322 + 0.800508i \(0.295437\pi\)
\(102\) −15.8302 −1.56742
\(103\) 9.62249 0.948132 0.474066 0.880489i \(-0.342786\pi\)
0.474066 + 0.880489i \(0.342786\pi\)
\(104\) −8.86747 −0.869527
\(105\) 5.94990 0.580650
\(106\) 25.7829 2.50425
\(107\) −7.26039 −0.701889 −0.350944 0.936396i \(-0.614139\pi\)
−0.350944 + 0.936396i \(0.614139\pi\)
\(108\) 12.2627 1.17997
\(109\) −1.00000 −0.0957826
\(110\) 9.12605 0.870135
\(111\) 2.02568 0.192269
\(112\) −0.432911 −0.0409062
\(113\) −1.67006 −0.157106 −0.0785530 0.996910i \(-0.525030\pi\)
−0.0785530 + 0.996910i \(0.525030\pi\)
\(114\) 34.1857 3.20178
\(115\) 4.35068 0.405703
\(116\) −19.4279 −1.80383
\(117\) 3.60302 0.333099
\(118\) 5.86104 0.539553
\(119\) −7.57616 −0.694505
\(120\) −7.31443 −0.667713
\(121\) −1.92679 −0.175163
\(122\) 8.44603 0.764667
\(123\) 11.2007 1.00993
\(124\) 29.4989 2.64908
\(125\) 10.9458 0.979022
\(126\) −5.55375 −0.494767
\(127\) 15.3448 1.36163 0.680813 0.732457i \(-0.261626\pi\)
0.680813 + 0.732457i \(0.261626\pi\)
\(128\) 17.8675 1.57928
\(129\) 17.2458 1.51841
\(130\) 9.89319 0.867690
\(131\) −0.952744 −0.0832416 −0.0416208 0.999133i \(-0.513252\pi\)
−0.0416208 + 0.999133i \(0.513252\pi\)
\(132\) −19.4755 −1.69513
\(133\) 16.3609 1.41867
\(134\) 23.2390 2.00754
\(135\) −5.10847 −0.439667
\(136\) 9.31366 0.798640
\(137\) −8.13948 −0.695403 −0.347701 0.937605i \(-0.613038\pi\)
−0.347701 + 0.937605i \(0.613038\pi\)
\(138\) −15.1024 −1.28560
\(139\) −8.21718 −0.696972 −0.348486 0.937314i \(-0.613304\pi\)
−0.348486 + 0.937314i \(0.613304\pi\)
\(140\) −9.37506 −0.792338
\(141\) −1.39315 −0.117325
\(142\) −33.4347 −2.80578
\(143\) 9.83591 0.822520
\(144\) −0.216240 −0.0180200
\(145\) 8.09341 0.672121
\(146\) −2.63345 −0.217946
\(147\) 4.29516 0.354258
\(148\) −3.19181 −0.262365
\(149\) −5.03263 −0.412289 −0.206145 0.978522i \(-0.566092\pi\)
−0.206145 + 0.978522i \(0.566092\pi\)
\(150\) −14.9177 −1.21802
\(151\) 3.95007 0.321452 0.160726 0.986999i \(-0.448616\pi\)
0.160726 + 0.986999i \(0.448616\pi\)
\(152\) −20.1131 −1.63139
\(153\) −3.78431 −0.305944
\(154\) −15.1612 −1.22173
\(155\) −12.2889 −0.987067
\(156\) −21.1126 −1.69036
\(157\) −2.14937 −0.171538 −0.0857692 0.996315i \(-0.527335\pi\)
−0.0857692 + 0.996315i \(0.527335\pi\)
\(158\) −16.6576 −1.32521
\(159\) 22.9215 1.81780
\(160\) −7.81544 −0.617865
\(161\) −7.22784 −0.569634
\(162\) 25.2753 1.98582
\(163\) −21.8714 −1.71310 −0.856550 0.516064i \(-0.827397\pi\)
−0.856550 + 0.516064i \(0.827397\pi\)
\(164\) −17.6486 −1.37813
\(165\) 8.11326 0.631616
\(166\) −16.0245 −1.24374
\(167\) −5.73252 −0.443596 −0.221798 0.975093i \(-0.571193\pi\)
−0.221798 + 0.975093i \(0.571193\pi\)
\(168\) 12.1516 0.937513
\(169\) −2.33729 −0.179791
\(170\) −10.3910 −0.796953
\(171\) 8.17232 0.624953
\(172\) −27.1736 −2.07197
\(173\) 11.8926 0.904177 0.452089 0.891973i \(-0.350679\pi\)
0.452089 + 0.891973i \(0.350679\pi\)
\(174\) −28.0944 −2.12983
\(175\) −7.13943 −0.539690
\(176\) −0.590316 −0.0444967
\(177\) 5.21060 0.391652
\(178\) 38.1646 2.86055
\(179\) 8.58866 0.641947 0.320973 0.947088i \(-0.395990\pi\)
0.320973 + 0.947088i \(0.395990\pi\)
\(180\) −4.68287 −0.349041
\(181\) 2.86228 0.212752 0.106376 0.994326i \(-0.466075\pi\)
0.106376 + 0.994326i \(0.466075\pi\)
\(182\) −16.4357 −1.21829
\(183\) 7.50870 0.555059
\(184\) 8.88546 0.655045
\(185\) 1.32967 0.0977591
\(186\) 42.6580 3.12784
\(187\) −10.3308 −0.755465
\(188\) 2.19515 0.160098
\(189\) 8.48677 0.617322
\(190\) 22.4396 1.62794
\(191\) 10.6560 0.771045 0.385522 0.922699i \(-0.374021\pi\)
0.385522 + 0.922699i \(0.374021\pi\)
\(192\) 26.3355 1.90060
\(193\) 5.31819 0.382811 0.191406 0.981511i \(-0.438695\pi\)
0.191406 + 0.981511i \(0.438695\pi\)
\(194\) 5.17966 0.371878
\(195\) 8.79526 0.629842
\(196\) −6.76774 −0.483410
\(197\) 13.3860 0.953712 0.476856 0.878981i \(-0.341776\pi\)
0.476856 + 0.878981i \(0.341776\pi\)
\(198\) −7.57308 −0.538195
\(199\) 19.3494 1.37165 0.685823 0.727769i \(-0.259443\pi\)
0.685823 + 0.727769i \(0.259443\pi\)
\(200\) 8.77678 0.620612
\(201\) 20.6600 1.45724
\(202\) −27.4480 −1.93123
\(203\) −13.4457 −0.943702
\(204\) 22.1750 1.55256
\(205\) 7.35220 0.513500
\(206\) −21.9254 −1.52761
\(207\) −3.61033 −0.250935
\(208\) −0.639938 −0.0443717
\(209\) 22.3097 1.54319
\(210\) −13.5572 −0.935533
\(211\) −12.1549 −0.836777 −0.418388 0.908268i \(-0.637405\pi\)
−0.418388 + 0.908268i \(0.637405\pi\)
\(212\) −36.1167 −2.48051
\(213\) −29.7242 −2.03667
\(214\) 16.5432 1.13087
\(215\) 11.3202 0.772031
\(216\) −10.4331 −0.709883
\(217\) 20.4157 1.38591
\(218\) 2.27855 0.154323
\(219\) −2.34119 −0.158203
\(220\) −12.7838 −0.861884
\(221\) −11.1992 −0.753342
\(222\) −4.61563 −0.309781
\(223\) 3.88466 0.260136 0.130068 0.991505i \(-0.458480\pi\)
0.130068 + 0.991505i \(0.458480\pi\)
\(224\) 12.9839 0.867523
\(225\) −3.56617 −0.237745
\(226\) 3.80532 0.253126
\(227\) −16.7237 −1.10999 −0.554996 0.831853i \(-0.687280\pi\)
−0.554996 + 0.831853i \(0.687280\pi\)
\(228\) −47.8874 −3.17142
\(229\) 13.5835 0.897624 0.448812 0.893626i \(-0.351847\pi\)
0.448812 + 0.893626i \(0.351847\pi\)
\(230\) −9.91326 −0.653661
\(231\) −13.4787 −0.886831
\(232\) 16.5293 1.08520
\(233\) 0.657731 0.0430894 0.0215447 0.999768i \(-0.493142\pi\)
0.0215447 + 0.999768i \(0.493142\pi\)
\(234\) −8.20967 −0.536683
\(235\) −0.914472 −0.0596536
\(236\) −8.21017 −0.534437
\(237\) −14.8090 −0.961949
\(238\) 17.2627 1.11897
\(239\) −9.00287 −0.582347 −0.291174 0.956670i \(-0.594046\pi\)
−0.291174 + 0.956670i \(0.594046\pi\)
\(240\) −0.527860 −0.0340732
\(241\) 6.30220 0.405960 0.202980 0.979183i \(-0.434937\pi\)
0.202980 + 0.979183i \(0.434937\pi\)
\(242\) 4.39029 0.282219
\(243\) 10.9446 0.702095
\(244\) −11.8312 −0.757417
\(245\) 2.81936 0.180122
\(246\) −25.5214 −1.62719
\(247\) 24.1850 1.53886
\(248\) −25.0978 −1.59371
\(249\) −14.2461 −0.902813
\(250\) −24.9406 −1.57738
\(251\) 12.4969 0.788796 0.394398 0.918940i \(-0.370953\pi\)
0.394398 + 0.918940i \(0.370953\pi\)
\(252\) 7.77972 0.490076
\(253\) −9.85587 −0.619633
\(254\) −34.9638 −2.19383
\(255\) −9.23782 −0.578495
\(256\) −14.7106 −0.919410
\(257\) −11.7281 −0.731580 −0.365790 0.930697i \(-0.619201\pi\)
−0.365790 + 0.930697i \(0.619201\pi\)
\(258\) −39.2954 −2.44643
\(259\) −2.20899 −0.137260
\(260\) −13.8584 −0.859463
\(261\) −6.71616 −0.415720
\(262\) 2.17088 0.134117
\(263\) −6.44448 −0.397383 −0.198692 0.980062i \(-0.563669\pi\)
−0.198692 + 0.980062i \(0.563669\pi\)
\(264\) 16.5698 1.01980
\(265\) 15.0458 0.924255
\(266\) −37.2792 −2.28573
\(267\) 33.9291 2.07643
\(268\) −32.5533 −1.98851
\(269\) 6.33179 0.386056 0.193028 0.981193i \(-0.438169\pi\)
0.193028 + 0.981193i \(0.438169\pi\)
\(270\) 11.6399 0.708383
\(271\) −1.28736 −0.0782014 −0.0391007 0.999235i \(-0.512449\pi\)
−0.0391007 + 0.999235i \(0.512449\pi\)
\(272\) 0.672138 0.0407544
\(273\) −14.6117 −0.884339
\(274\) 18.5462 1.12042
\(275\) −9.73531 −0.587061
\(276\) 21.1555 1.27341
\(277\) −23.2025 −1.39410 −0.697051 0.717021i \(-0.745505\pi\)
−0.697051 + 0.717021i \(0.745505\pi\)
\(278\) 18.7233 1.12295
\(279\) 10.1977 0.610520
\(280\) 7.97633 0.476677
\(281\) −11.5857 −0.691144 −0.345572 0.938392i \(-0.612315\pi\)
−0.345572 + 0.938392i \(0.612315\pi\)
\(282\) 3.17438 0.189031
\(283\) −11.5051 −0.683907 −0.341954 0.939717i \(-0.611089\pi\)
−0.341954 + 0.939717i \(0.611089\pi\)
\(284\) 46.8355 2.77918
\(285\) 19.9493 1.18169
\(286\) −22.4116 −1.32523
\(287\) −12.2143 −0.720987
\(288\) 6.48549 0.382161
\(289\) −5.23724 −0.308073
\(290\) −18.4413 −1.08291
\(291\) 4.60483 0.269940
\(292\) 3.68894 0.215879
\(293\) 29.6626 1.73291 0.866455 0.499255i \(-0.166393\pi\)
0.866455 + 0.499255i \(0.166393\pi\)
\(294\) −9.78674 −0.570774
\(295\) 3.42026 0.199135
\(296\) 2.71560 0.157841
\(297\) 11.5725 0.671506
\(298\) 11.4671 0.664273
\(299\) −10.6844 −0.617892
\(300\) 20.8967 1.20647
\(301\) −18.8064 −1.08398
\(302\) −9.00045 −0.517917
\(303\) −24.4019 −1.40185
\(304\) −1.45150 −0.0832492
\(305\) 4.92874 0.282219
\(306\) 8.62277 0.492931
\(307\) −7.26778 −0.414794 −0.207397 0.978257i \(-0.566499\pi\)
−0.207397 + 0.978257i \(0.566499\pi\)
\(308\) 21.2379 1.21014
\(309\) −19.4921 −1.10887
\(310\) 28.0009 1.59034
\(311\) −25.9585 −1.47197 −0.735986 0.676997i \(-0.763281\pi\)
−0.735986 + 0.676997i \(0.763281\pi\)
\(312\) 17.9627 1.01694
\(313\) −15.3192 −0.865892 −0.432946 0.901420i \(-0.642526\pi\)
−0.432946 + 0.901420i \(0.642526\pi\)
\(314\) 4.89746 0.276379
\(315\) −3.24093 −0.182606
\(316\) 23.3341 1.31265
\(317\) −18.1478 −1.01928 −0.509642 0.860386i \(-0.670222\pi\)
−0.509642 + 0.860386i \(0.670222\pi\)
\(318\) −52.2279 −2.92880
\(319\) −18.3345 −1.02653
\(320\) 17.2867 0.966358
\(321\) 14.7073 0.820880
\(322\) 16.4690 0.917783
\(323\) −25.4020 −1.41340
\(324\) −35.4058 −1.96699
\(325\) −10.5537 −0.585412
\(326\) 49.8352 2.76011
\(327\) 2.02568 0.112021
\(328\) 15.0155 0.829092
\(329\) 1.51922 0.0837576
\(330\) −18.4865 −1.01765
\(331\) 10.9990 0.604558 0.302279 0.953219i \(-0.402253\pi\)
0.302279 + 0.953219i \(0.402253\pi\)
\(332\) 22.4472 1.23195
\(333\) −1.10340 −0.0604659
\(334\) 13.0619 0.714714
\(335\) 13.5613 0.740933
\(336\) 0.876941 0.0478411
\(337\) 16.0753 0.875680 0.437840 0.899053i \(-0.355744\pi\)
0.437840 + 0.899053i \(0.355744\pi\)
\(338\) 5.32563 0.289676
\(339\) 3.38301 0.183740
\(340\) 14.5557 0.789396
\(341\) 27.8388 1.50755
\(342\) −18.6211 −1.00691
\(343\) −20.1468 −1.08782
\(344\) 23.1194 1.24651
\(345\) −8.81311 −0.474482
\(346\) −27.0979 −1.45679
\(347\) −10.7209 −0.575528 −0.287764 0.957701i \(-0.592912\pi\)
−0.287764 + 0.957701i \(0.592912\pi\)
\(348\) 39.3547 2.10964
\(349\) −30.8818 −1.65306 −0.826531 0.562891i \(-0.809689\pi\)
−0.826531 + 0.562891i \(0.809689\pi\)
\(350\) 16.2676 0.869539
\(351\) 12.5453 0.669620
\(352\) 17.7048 0.943669
\(353\) −22.7095 −1.20870 −0.604352 0.796717i \(-0.706568\pi\)
−0.604352 + 0.796717i \(0.706568\pi\)
\(354\) −11.8726 −0.631023
\(355\) −19.5111 −1.03554
\(356\) −53.4611 −2.83343
\(357\) 15.3469 0.812245
\(358\) −19.5697 −1.03429
\(359\) 6.74457 0.355965 0.177982 0.984034i \(-0.443043\pi\)
0.177982 + 0.984034i \(0.443043\pi\)
\(360\) 3.98420 0.209986
\(361\) 35.8562 1.88717
\(362\) −6.52186 −0.342781
\(363\) 3.90307 0.204858
\(364\) 23.0232 1.20674
\(365\) −1.53677 −0.0804381
\(366\) −17.1090 −0.894301
\(367\) 6.25311 0.326410 0.163205 0.986592i \(-0.447817\pi\)
0.163205 + 0.986592i \(0.447817\pi\)
\(368\) 0.641237 0.0334268
\(369\) −6.10108 −0.317609
\(370\) −3.02972 −0.157508
\(371\) −24.9957 −1.29771
\(372\) −59.7555 −3.09818
\(373\) −25.9620 −1.34426 −0.672130 0.740433i \(-0.734620\pi\)
−0.672130 + 0.740433i \(0.734620\pi\)
\(374\) 23.5394 1.21719
\(375\) −22.1727 −1.14500
\(376\) −1.86764 −0.0963162
\(377\) −19.8757 −1.02365
\(378\) −19.3376 −0.994617
\(379\) 26.2988 1.35088 0.675439 0.737416i \(-0.263954\pi\)
0.675439 + 0.737416i \(0.263954\pi\)
\(380\) −31.4335 −1.61250
\(381\) −31.0836 −1.59246
\(382\) −24.2804 −1.24229
\(383\) −29.1346 −1.48871 −0.744353 0.667786i \(-0.767242\pi\)
−0.744353 + 0.667786i \(0.767242\pi\)
\(384\) −36.1940 −1.84702
\(385\) −8.84745 −0.450908
\(386\) −12.1178 −0.616778
\(387\) −9.39385 −0.477516
\(388\) −7.25569 −0.368352
\(389\) 8.37378 0.424567 0.212284 0.977208i \(-0.431910\pi\)
0.212284 + 0.977208i \(0.431910\pi\)
\(390\) −20.0405 −1.01479
\(391\) 11.2220 0.567519
\(392\) 5.75801 0.290824
\(393\) 1.92996 0.0973535
\(394\) −30.5007 −1.53660
\(395\) −9.72070 −0.489101
\(396\) 10.6084 0.533092
\(397\) −25.8696 −1.29836 −0.649178 0.760636i \(-0.724887\pi\)
−0.649178 + 0.760636i \(0.724887\pi\)
\(398\) −44.0887 −2.20997
\(399\) −33.1420 −1.65918
\(400\) 0.633393 0.0316697
\(401\) −27.3623 −1.36641 −0.683204 0.730228i \(-0.739414\pi\)
−0.683204 + 0.730228i \(0.739414\pi\)
\(402\) −47.0749 −2.34788
\(403\) 30.1789 1.50332
\(404\) 38.4492 1.91292
\(405\) 14.7496 0.732914
\(406\) 30.6367 1.52047
\(407\) −3.01218 −0.149308
\(408\) −18.8665 −0.934033
\(409\) −1.60723 −0.0794726 −0.0397363 0.999210i \(-0.512652\pi\)
−0.0397363 + 0.999210i \(0.512652\pi\)
\(410\) −16.7524 −0.827341
\(411\) 16.4880 0.813294
\(412\) 30.7132 1.51313
\(413\) −5.68211 −0.279599
\(414\) 8.22633 0.404302
\(415\) −9.35123 −0.459034
\(416\) 19.1931 0.941018
\(417\) 16.6454 0.815129
\(418\) −50.8338 −2.48636
\(419\) 21.2476 1.03801 0.519007 0.854770i \(-0.326302\pi\)
0.519007 + 0.854770i \(0.326302\pi\)
\(420\) 18.9909 0.926662
\(421\) 21.2541 1.03586 0.517931 0.855423i \(-0.326702\pi\)
0.517931 + 0.855423i \(0.326702\pi\)
\(422\) 27.6956 1.34820
\(423\) 0.758857 0.0368969
\(424\) 30.7282 1.49229
\(425\) 11.0847 0.537687
\(426\) 67.7282 3.28144
\(427\) −8.18818 −0.396254
\(428\) −23.1738 −1.12015
\(429\) −19.9244 −0.961961
\(430\) −25.7937 −1.24388
\(431\) −34.9924 −1.68553 −0.842763 0.538285i \(-0.819072\pi\)
−0.842763 + 0.538285i \(0.819072\pi\)
\(432\) −0.752925 −0.0362251
\(433\) −37.8076 −1.81692 −0.908458 0.417977i \(-0.862739\pi\)
−0.908458 + 0.417977i \(0.862739\pi\)
\(434\) −46.5182 −2.23295
\(435\) −16.3947 −0.786065
\(436\) −3.19181 −0.152860
\(437\) −24.2341 −1.15927
\(438\) 5.33453 0.254894
\(439\) 22.5208 1.07486 0.537430 0.843309i \(-0.319395\pi\)
0.537430 + 0.843309i \(0.319395\pi\)
\(440\) 10.8765 0.518517
\(441\) −2.33959 −0.111409
\(442\) 25.5181 1.21377
\(443\) −8.81901 −0.419004 −0.209502 0.977808i \(-0.567184\pi\)
−0.209502 + 0.977808i \(0.567184\pi\)
\(444\) 6.46560 0.306844
\(445\) 22.2712 1.05576
\(446\) −8.85141 −0.419126
\(447\) 10.1945 0.482185
\(448\) −28.7187 −1.35683
\(449\) −24.1815 −1.14120 −0.570598 0.821229i \(-0.693289\pi\)
−0.570598 + 0.821229i \(0.693289\pi\)
\(450\) 8.12571 0.383050
\(451\) −16.6554 −0.784271
\(452\) −5.33051 −0.250726
\(453\) −8.00159 −0.375948
\(454\) 38.1059 1.78840
\(455\) −9.59116 −0.449641
\(456\) 40.7428 1.90795
\(457\) −21.8843 −1.02370 −0.511852 0.859074i \(-0.671040\pi\)
−0.511852 + 0.859074i \(0.671040\pi\)
\(458\) −30.9508 −1.44623
\(459\) −13.1766 −0.615030
\(460\) 13.8865 0.647463
\(461\) 0.0156943 0.000730956 0 0.000365478 1.00000i \(-0.499884\pi\)
0.000365478 1.00000i \(0.499884\pi\)
\(462\) 30.7119 1.42885
\(463\) 42.2851 1.96515 0.982577 0.185857i \(-0.0595060\pi\)
0.982577 + 0.185857i \(0.0595060\pi\)
\(464\) 1.19287 0.0553775
\(465\) 24.8934 1.15440
\(466\) −1.49867 −0.0694248
\(467\) 21.7149 1.00484 0.502422 0.864622i \(-0.332442\pi\)
0.502422 + 0.864622i \(0.332442\pi\)
\(468\) 11.5001 0.531594
\(469\) −22.5295 −1.04032
\(470\) 2.08367 0.0961127
\(471\) 4.35395 0.200619
\(472\) 6.98524 0.321522
\(473\) −25.6443 −1.17913
\(474\) 33.7431 1.54987
\(475\) −23.9377 −1.09834
\(476\) −24.1817 −1.10836
\(477\) −12.4854 −0.571669
\(478\) 20.5135 0.938267
\(479\) 11.9819 0.547468 0.273734 0.961805i \(-0.411741\pi\)
0.273734 + 0.961805i \(0.411741\pi\)
\(480\) 15.8316 0.722611
\(481\) −3.26538 −0.148889
\(482\) −14.3599 −0.654075
\(483\) 14.6413 0.666204
\(484\) −6.14994 −0.279543
\(485\) 3.02263 0.137250
\(486\) −24.9378 −1.13120
\(487\) 5.92913 0.268674 0.134337 0.990936i \(-0.457109\pi\)
0.134337 + 0.990936i \(0.457109\pi\)
\(488\) 10.0660 0.455668
\(489\) 44.3046 2.00352
\(490\) −6.42406 −0.290209
\(491\) −13.1771 −0.594672 −0.297336 0.954773i \(-0.596098\pi\)
−0.297336 + 0.954773i \(0.596098\pi\)
\(492\) 35.7506 1.61176
\(493\) 20.8758 0.940199
\(494\) −55.1069 −2.47938
\(495\) −4.41933 −0.198634
\(496\) −1.81123 −0.0813266
\(497\) 32.4140 1.45397
\(498\) 32.4606 1.45459
\(499\) −26.6542 −1.19321 −0.596603 0.802537i \(-0.703483\pi\)
−0.596603 + 0.802537i \(0.703483\pi\)
\(500\) 34.9369 1.56243
\(501\) 11.6123 0.518799
\(502\) −28.4748 −1.27089
\(503\) −22.0724 −0.984159 −0.492080 0.870550i \(-0.663763\pi\)
−0.492080 + 0.870550i \(0.663763\pi\)
\(504\) −6.61901 −0.294834
\(505\) −16.0175 −0.712768
\(506\) 22.4571 0.998341
\(507\) 4.73461 0.210271
\(508\) 48.9775 2.17303
\(509\) −16.8509 −0.746905 −0.373453 0.927649i \(-0.621826\pi\)
−0.373453 + 0.927649i \(0.621826\pi\)
\(510\) 21.0489 0.932060
\(511\) 2.55305 0.112940
\(512\) −2.21629 −0.0979470
\(513\) 28.4551 1.25632
\(514\) 26.7232 1.17871
\(515\) −12.7947 −0.563803
\(516\) 55.0452 2.42323
\(517\) 2.07161 0.0911093
\(518\) 5.03331 0.221151
\(519\) −24.0906 −1.05746
\(520\) 11.7908 0.517060
\(521\) 20.1149 0.881249 0.440625 0.897691i \(-0.354757\pi\)
0.440625 + 0.897691i \(0.354757\pi\)
\(522\) 15.3031 0.669800
\(523\) −18.5804 −0.812464 −0.406232 0.913770i \(-0.633158\pi\)
−0.406232 + 0.913770i \(0.633158\pi\)
\(524\) −3.04098 −0.132846
\(525\) 14.4622 0.631184
\(526\) 14.6841 0.640257
\(527\) −31.6974 −1.38076
\(528\) 1.19579 0.0520403
\(529\) −12.2940 −0.534520
\(530\) −34.2826 −1.48914
\(531\) −2.83823 −0.123169
\(532\) 52.2209 2.26406
\(533\) −18.0554 −0.782068
\(534\) −77.3094 −3.34550
\(535\) 9.65391 0.417375
\(536\) 27.6964 1.19630
\(537\) −17.3979 −0.750776
\(538\) −14.4273 −0.622006
\(539\) −6.38686 −0.275102
\(540\) −16.3053 −0.701667
\(541\) 26.7444 1.14983 0.574916 0.818213i \(-0.305035\pi\)
0.574916 + 0.818213i \(0.305035\pi\)
\(542\) 2.93332 0.125997
\(543\) −5.79808 −0.248819
\(544\) −20.1588 −0.864302
\(545\) 1.32967 0.0569567
\(546\) 33.2935 1.42483
\(547\) 4.33001 0.185138 0.0925688 0.995706i \(-0.470492\pi\)
0.0925688 + 0.995706i \(0.470492\pi\)
\(548\) −25.9797 −1.10980
\(549\) −4.09002 −0.174558
\(550\) 22.1824 0.945862
\(551\) −45.0818 −1.92055
\(552\) −17.9991 −0.766095
\(553\) 16.1491 0.686730
\(554\) 52.8681 2.24615
\(555\) −2.69349 −0.114332
\(556\) −26.2277 −1.11230
\(557\) −7.47786 −0.316847 −0.158424 0.987371i \(-0.550641\pi\)
−0.158424 + 0.987371i \(0.550641\pi\)
\(558\) −23.2360 −0.983658
\(559\) −27.8000 −1.17581
\(560\) 0.575627 0.0243247
\(561\) 20.9270 0.883539
\(562\) 26.3986 1.11356
\(563\) 32.1159 1.35353 0.676763 0.736201i \(-0.263382\pi\)
0.676763 + 0.736201i \(0.263382\pi\)
\(564\) −4.44668 −0.187239
\(565\) 2.22062 0.0934224
\(566\) 26.2150 1.10190
\(567\) −24.5037 −1.02906
\(568\) −39.8478 −1.67198
\(569\) −27.2656 −1.14303 −0.571516 0.820591i \(-0.693644\pi\)
−0.571516 + 0.820591i \(0.693644\pi\)
\(570\) −45.4556 −1.90392
\(571\) 22.7540 0.952227 0.476114 0.879384i \(-0.342045\pi\)
0.476114 + 0.879384i \(0.342045\pi\)
\(572\) 31.3943 1.31266
\(573\) −21.5858 −0.901760
\(574\) 27.8309 1.16164
\(575\) 10.5751 0.441011
\(576\) −14.3451 −0.597711
\(577\) −9.64440 −0.401502 −0.200751 0.979642i \(-0.564338\pi\)
−0.200751 + 0.979642i \(0.564338\pi\)
\(578\) 11.9333 0.496361
\(579\) −10.7730 −0.447709
\(580\) 25.8326 1.07264
\(581\) 15.5353 0.644513
\(582\) −10.4924 −0.434922
\(583\) −34.0841 −1.41162
\(584\) −3.13856 −0.129875
\(585\) −4.79082 −0.198076
\(586\) −67.5879 −2.79203
\(587\) 0.417407 0.0172282 0.00861411 0.999963i \(-0.497258\pi\)
0.00861411 + 0.999963i \(0.497258\pi\)
\(588\) 13.7093 0.565362
\(589\) 68.4514 2.82049
\(590\) −7.79324 −0.320842
\(591\) −27.1158 −1.11539
\(592\) 0.195977 0.00805459
\(593\) 10.2890 0.422520 0.211260 0.977430i \(-0.432243\pi\)
0.211260 + 0.977430i \(0.432243\pi\)
\(594\) −26.3686 −1.08192
\(595\) 10.0738 0.412984
\(596\) −16.0632 −0.657974
\(597\) −39.1959 −1.60418
\(598\) 24.3449 0.995536
\(599\) 18.2932 0.747439 0.373719 0.927542i \(-0.378082\pi\)
0.373719 + 0.927542i \(0.378082\pi\)
\(600\) −17.7790 −0.725824
\(601\) −16.7823 −0.684564 −0.342282 0.939597i \(-0.611200\pi\)
−0.342282 + 0.939597i \(0.611200\pi\)
\(602\) 42.8514 1.74649
\(603\) −11.2536 −0.458281
\(604\) 12.6079 0.513007
\(605\) 2.56199 0.104160
\(606\) 55.6009 2.25863
\(607\) −27.4739 −1.11513 −0.557566 0.830132i \(-0.688265\pi\)
−0.557566 + 0.830132i \(0.688265\pi\)
\(608\) 43.5335 1.76552
\(609\) 27.2367 1.10369
\(610\) −11.2304 −0.454706
\(611\) 2.24575 0.0908533
\(612\) −12.0788 −0.488257
\(613\) 21.0839 0.851569 0.425785 0.904825i \(-0.359998\pi\)
0.425785 + 0.904825i \(0.359998\pi\)
\(614\) 16.5600 0.668308
\(615\) −14.8932 −0.600553
\(616\) −18.0693 −0.728032
\(617\) 7.26400 0.292437 0.146219 0.989252i \(-0.453290\pi\)
0.146219 + 0.989252i \(0.453290\pi\)
\(618\) 44.4139 1.78659
\(619\) 45.2965 1.82062 0.910310 0.413927i \(-0.135843\pi\)
0.910310 + 0.413927i \(0.135843\pi\)
\(620\) −39.2238 −1.57526
\(621\) −12.5708 −0.504448
\(622\) 59.1479 2.37161
\(623\) −36.9995 −1.48235
\(624\) 1.29631 0.0518940
\(625\) 1.60565 0.0642260
\(626\) 34.9056 1.39511
\(627\) −45.1924 −1.80481
\(628\) −6.86038 −0.273759
\(629\) 3.42969 0.136751
\(630\) 7.38464 0.294211
\(631\) 10.3181 0.410757 0.205378 0.978683i \(-0.434158\pi\)
0.205378 + 0.978683i \(0.434158\pi\)
\(632\) −19.8527 −0.789699
\(633\) 24.6220 0.978635
\(634\) 41.3508 1.64225
\(635\) −20.4034 −0.809685
\(636\) 73.1611 2.90103
\(637\) −6.92374 −0.274329
\(638\) 41.7761 1.65393
\(639\) 16.1909 0.640502
\(640\) −23.7579 −0.939113
\(641\) 2.91433 0.115109 0.0575545 0.998342i \(-0.481670\pi\)
0.0575545 + 0.998342i \(0.481670\pi\)
\(642\) −33.5113 −1.32259
\(643\) −24.5561 −0.968399 −0.484200 0.874958i \(-0.660889\pi\)
−0.484200 + 0.874958i \(0.660889\pi\)
\(644\) −23.0699 −0.909081
\(645\) −22.9311 −0.902913
\(646\) 57.8798 2.27725
\(647\) −27.2420 −1.07099 −0.535496 0.844538i \(-0.679875\pi\)
−0.535496 + 0.844538i \(0.679875\pi\)
\(648\) 30.1234 1.18336
\(649\) −7.74811 −0.304140
\(650\) 24.0471 0.943204
\(651\) −41.3557 −1.62086
\(652\) −69.8093 −2.73394
\(653\) −28.1153 −1.10024 −0.550118 0.835087i \(-0.685417\pi\)
−0.550118 + 0.835087i \(0.685417\pi\)
\(654\) −4.61563 −0.180486
\(655\) 1.26683 0.0494992
\(656\) 1.08362 0.0423084
\(657\) 1.27526 0.0497525
\(658\) −3.46164 −0.134949
\(659\) 11.5646 0.450494 0.225247 0.974302i \(-0.427681\pi\)
0.225247 + 0.974302i \(0.427681\pi\)
\(660\) 25.8960 1.00800
\(661\) 28.3169 1.10140 0.550699 0.834704i \(-0.314361\pi\)
0.550699 + 0.834704i \(0.314361\pi\)
\(662\) −25.0618 −0.974053
\(663\) 22.6861 0.881056
\(664\) −19.0981 −0.741152
\(665\) −21.7546 −0.843606
\(666\) 2.51415 0.0974215
\(667\) 19.9160 0.771152
\(668\) −18.2971 −0.707937
\(669\) −7.86910 −0.304237
\(670\) −30.9001 −1.19378
\(671\) −11.1654 −0.431035
\(672\) −26.3013 −1.01459
\(673\) −0.149299 −0.00575506 −0.00287753 0.999996i \(-0.500916\pi\)
−0.00287753 + 0.999996i \(0.500916\pi\)
\(674\) −36.6285 −1.41088
\(675\) −12.4170 −0.477931
\(676\) −7.46017 −0.286930
\(677\) −16.4402 −0.631847 −0.315923 0.948785i \(-0.602314\pi\)
−0.315923 + 0.948785i \(0.602314\pi\)
\(678\) −7.70838 −0.296039
\(679\) −5.02153 −0.192709
\(680\) −12.3841 −0.474907
\(681\) 33.8770 1.29817
\(682\) −63.4321 −2.42894
\(683\) −16.9704 −0.649352 −0.324676 0.945825i \(-0.605255\pi\)
−0.324676 + 0.945825i \(0.605255\pi\)
\(684\) 26.0845 0.997365
\(685\) 10.8228 0.413518
\(686\) 45.9055 1.75268
\(687\) −27.5159 −1.04980
\(688\) 1.66846 0.0636093
\(689\) −36.9492 −1.40765
\(690\) 20.0811 0.764476
\(691\) 11.1449 0.423973 0.211986 0.977273i \(-0.432007\pi\)
0.211986 + 0.977273i \(0.432007\pi\)
\(692\) 37.9589 1.44298
\(693\) 7.34188 0.278895
\(694\) 24.4281 0.927280
\(695\) 10.9261 0.414451
\(696\) −33.4831 −1.26917
\(697\) 18.9639 0.718311
\(698\) 70.3658 2.66338
\(699\) −1.33235 −0.0503943
\(700\) −22.7877 −0.861294
\(701\) 36.8255 1.39088 0.695441 0.718583i \(-0.255209\pi\)
0.695441 + 0.718583i \(0.255209\pi\)
\(702\) −28.5852 −1.07888
\(703\) −7.40650 −0.279341
\(704\) −39.1607 −1.47592
\(705\) 1.85243 0.0697666
\(706\) 51.7448 1.94744
\(707\) 26.6100 1.00077
\(708\) 16.6312 0.625040
\(709\) −29.4450 −1.10583 −0.552915 0.833237i \(-0.686485\pi\)
−0.552915 + 0.833237i \(0.686485\pi\)
\(710\) 44.4571 1.66844
\(711\) 8.06653 0.302519
\(712\) 45.4848 1.70462
\(713\) −30.2401 −1.13250
\(714\) −34.9688 −1.30867
\(715\) −13.0785 −0.489108
\(716\) 27.4134 1.02449
\(717\) 18.2370 0.681073
\(718\) −15.3679 −0.573523
\(719\) 0.395812 0.0147613 0.00738065 0.999973i \(-0.497651\pi\)
0.00738065 + 0.999973i \(0.497651\pi\)
\(720\) 0.287528 0.0107155
\(721\) 21.2560 0.791616
\(722\) −81.7002 −3.04057
\(723\) −12.7663 −0.474782
\(724\) 9.13585 0.339531
\(725\) 19.6724 0.730615
\(726\) −8.89335 −0.330063
\(727\) 46.8317 1.73689 0.868446 0.495783i \(-0.165119\pi\)
0.868446 + 0.495783i \(0.165119\pi\)
\(728\) −19.5882 −0.725986
\(729\) 11.1079 0.411402
\(730\) 3.50161 0.129600
\(731\) 29.1988 1.07996
\(732\) 23.9663 0.885822
\(733\) 14.4578 0.534011 0.267006 0.963695i \(-0.413966\pi\)
0.267006 + 0.963695i \(0.413966\pi\)
\(734\) −14.2481 −0.525905
\(735\) −5.71113 −0.210658
\(736\) −19.2320 −0.708902
\(737\) −30.7212 −1.13163
\(738\) 13.9016 0.511726
\(739\) −19.6171 −0.721627 −0.360813 0.932638i \(-0.617501\pi\)
−0.360813 + 0.932638i \(0.617501\pi\)
\(740\) 4.24404 0.156014
\(741\) −48.9913 −1.79974
\(742\) 56.9542 2.09085
\(743\) −44.4388 −1.63030 −0.815151 0.579248i \(-0.803346\pi\)
−0.815151 + 0.579248i \(0.803346\pi\)
\(744\) 50.8402 1.86389
\(745\) 6.69173 0.245166
\(746\) 59.1557 2.16585
\(747\) 7.75994 0.283921
\(748\) −32.9740 −1.20565
\(749\) −16.0382 −0.586022
\(750\) 50.5218 1.84480
\(751\) −37.1409 −1.35529 −0.677646 0.735388i \(-0.737000\pi\)
−0.677646 + 0.735388i \(0.737000\pi\)
\(752\) −0.134782 −0.00491499
\(753\) −25.3147 −0.922521
\(754\) 45.2878 1.64929
\(755\) −5.25228 −0.191150
\(756\) 27.0881 0.985186
\(757\) 10.8691 0.395042 0.197521 0.980299i \(-0.436711\pi\)
0.197521 + 0.980299i \(0.436711\pi\)
\(758\) −59.9232 −2.17651
\(759\) 19.9649 0.724679
\(760\) 26.7437 0.970096
\(761\) 24.2576 0.879336 0.439668 0.898160i \(-0.355096\pi\)
0.439668 + 0.898160i \(0.355096\pi\)
\(762\) 70.8257 2.56575
\(763\) −2.20899 −0.0799709
\(764\) 34.0121 1.23051
\(765\) 5.03188 0.181928
\(766\) 66.3847 2.39858
\(767\) −8.39942 −0.303286
\(768\) 29.7989 1.07528
\(769\) −12.6106 −0.454749 −0.227375 0.973807i \(-0.573014\pi\)
−0.227375 + 0.973807i \(0.573014\pi\)
\(770\) 20.1594 0.726494
\(771\) 23.7575 0.855605
\(772\) 16.9746 0.610930
\(773\) 22.7759 0.819193 0.409597 0.912267i \(-0.365669\pi\)
0.409597 + 0.912267i \(0.365669\pi\)
\(774\) 21.4044 0.769365
\(775\) −29.8702 −1.07297
\(776\) 6.17316 0.221603
\(777\) 4.47472 0.160530
\(778\) −19.0801 −0.684055
\(779\) −40.9531 −1.46730
\(780\) 28.0728 1.00517
\(781\) 44.1997 1.58159
\(782\) −25.5699 −0.914376
\(783\) −23.3849 −0.835710
\(784\) 0.415538 0.0148407
\(785\) 2.85795 0.102005
\(786\) −4.39751 −0.156854
\(787\) 31.8726 1.13614 0.568068 0.822982i \(-0.307691\pi\)
0.568068 + 0.822982i \(0.307691\pi\)
\(788\) 42.7255 1.52203
\(789\) 13.0545 0.464752
\(790\) 22.1491 0.788031
\(791\) −3.68915 −0.131171
\(792\) −9.02566 −0.320713
\(793\) −12.1039 −0.429824
\(794\) 58.9452 2.09189
\(795\) −30.4780 −1.08094
\(796\) 61.7597 2.18901
\(797\) 25.3339 0.897372 0.448686 0.893690i \(-0.351892\pi\)
0.448686 + 0.893690i \(0.351892\pi\)
\(798\) 75.5159 2.67323
\(799\) −2.35875 −0.0834466
\(800\) −18.9968 −0.671637
\(801\) −18.4813 −0.653006
\(802\) 62.3465 2.20153
\(803\) 3.48133 0.122854
\(804\) 65.9427 2.32562
\(805\) 9.61063 0.338730
\(806\) −68.7643 −2.42212
\(807\) −12.8262 −0.451504
\(808\) −32.7127 −1.15083
\(809\) 6.61829 0.232687 0.116343 0.993209i \(-0.462883\pi\)
0.116343 + 0.993209i \(0.462883\pi\)
\(810\) −33.6078 −1.18086
\(811\) 11.9125 0.418303 0.209151 0.977883i \(-0.432930\pi\)
0.209151 + 0.977883i \(0.432930\pi\)
\(812\) −42.9160 −1.50606
\(813\) 2.60778 0.0914589
\(814\) 6.86341 0.240562
\(815\) 29.0817 1.01869
\(816\) −1.36154 −0.0476635
\(817\) −63.0556 −2.20604
\(818\) 3.66217 0.128045
\(819\) 7.95904 0.278111
\(820\) 23.4668 0.819496
\(821\) 3.71471 0.129644 0.0648221 0.997897i \(-0.479352\pi\)
0.0648221 + 0.997897i \(0.479352\pi\)
\(822\) −37.5689 −1.31036
\(823\) −1.70002 −0.0592589 −0.0296295 0.999561i \(-0.509433\pi\)
−0.0296295 + 0.999561i \(0.509433\pi\)
\(824\) −26.1308 −0.910311
\(825\) 19.7207 0.686586
\(826\) 12.9470 0.450484
\(827\) −11.7542 −0.408733 −0.204366 0.978894i \(-0.565513\pi\)
−0.204366 + 0.978894i \(0.565513\pi\)
\(828\) −11.5235 −0.400469
\(829\) −12.5076 −0.434406 −0.217203 0.976127i \(-0.569693\pi\)
−0.217203 + 0.976127i \(0.569693\pi\)
\(830\) 21.3073 0.739586
\(831\) 47.0009 1.63044
\(832\) −42.4526 −1.47178
\(833\) 7.27213 0.251964
\(834\) −37.9275 −1.31332
\(835\) 7.62235 0.263782
\(836\) 71.2082 2.46279
\(837\) 35.5073 1.22731
\(838\) −48.4139 −1.67243
\(839\) 24.0395 0.829936 0.414968 0.909836i \(-0.363793\pi\)
0.414968 + 0.909836i \(0.363793\pi\)
\(840\) −16.1575 −0.557488
\(841\) 8.04902 0.277553
\(842\) −48.4286 −1.66896
\(843\) 23.4690 0.808314
\(844\) −38.7961 −1.33542
\(845\) 3.10781 0.106912
\(846\) −1.72910 −0.0594476
\(847\) −4.25626 −0.146247
\(848\) 2.21756 0.0761514
\(849\) 23.3057 0.799850
\(850\) −25.2571 −0.866311
\(851\) 3.27201 0.112163
\(852\) −94.8740 −3.25033
\(853\) −40.5273 −1.38763 −0.693814 0.720154i \(-0.744071\pi\)
−0.693814 + 0.720154i \(0.744071\pi\)
\(854\) 18.6572 0.638437
\(855\) −10.8665 −0.371625
\(856\) 19.7163 0.673890
\(857\) −44.8884 −1.53336 −0.766679 0.642030i \(-0.778092\pi\)
−0.766679 + 0.642030i \(0.778092\pi\)
\(858\) 45.3989 1.54989
\(859\) 4.29568 0.146567 0.0732833 0.997311i \(-0.476652\pi\)
0.0732833 + 0.997311i \(0.476652\pi\)
\(860\) 36.1319 1.23209
\(861\) 24.7423 0.843216
\(862\) 79.7321 2.71569
\(863\) −23.8712 −0.812585 −0.406293 0.913743i \(-0.633179\pi\)
−0.406293 + 0.913743i \(0.633179\pi\)
\(864\) 22.5818 0.768248
\(865\) −15.8132 −0.537665
\(866\) 86.1466 2.92738
\(867\) 10.6090 0.360300
\(868\) 65.1630 2.21177
\(869\) 22.0209 0.747008
\(870\) 37.3562 1.26649
\(871\) −33.3037 −1.12845
\(872\) 2.71560 0.0919618
\(873\) −2.50827 −0.0848921
\(874\) 55.2187 1.86780
\(875\) 24.1792 0.817406
\(876\) −7.47263 −0.252477
\(877\) −19.9793 −0.674653 −0.337327 0.941388i \(-0.609523\pi\)
−0.337327 + 0.941388i \(0.609523\pi\)
\(878\) −51.3149 −1.73179
\(879\) −60.0872 −2.02669
\(880\) 0.784924 0.0264598
\(881\) 17.0452 0.574269 0.287134 0.957890i \(-0.407297\pi\)
0.287134 + 0.957890i \(0.407297\pi\)
\(882\) 5.33088 0.179500
\(883\) −38.7495 −1.30402 −0.652012 0.758208i \(-0.726075\pi\)
−0.652012 + 0.758208i \(0.726075\pi\)
\(884\) −35.7458 −1.20226
\(885\) −6.92836 −0.232894
\(886\) 20.0946 0.675091
\(887\) −26.1564 −0.878247 −0.439124 0.898427i \(-0.644711\pi\)
−0.439124 + 0.898427i \(0.644711\pi\)
\(888\) −5.50095 −0.184600
\(889\) 33.8965 1.13685
\(890\) −50.7462 −1.70102
\(891\) −33.4132 −1.11938
\(892\) 12.3991 0.415152
\(893\) 5.09378 0.170457
\(894\) −23.2288 −0.776887
\(895\) −11.4201 −0.381731
\(896\) 39.4693 1.31858
\(897\) 21.6431 0.722643
\(898\) 55.0989 1.83867
\(899\) −56.2546 −1.87620
\(900\) −11.3825 −0.379418
\(901\) 38.8085 1.29290
\(902\) 37.9502 1.26360
\(903\) 38.0958 1.26775
\(904\) 4.53521 0.150839
\(905\) −3.80588 −0.126512
\(906\) 18.2321 0.605720
\(907\) −17.3010 −0.574469 −0.287235 0.957860i \(-0.592736\pi\)
−0.287235 + 0.957860i \(0.592736\pi\)
\(908\) −53.3789 −1.77144
\(909\) 13.2918 0.440861
\(910\) 21.8540 0.724453
\(911\) 1.31058 0.0434216 0.0217108 0.999764i \(-0.493089\pi\)
0.0217108 + 0.999764i \(0.493089\pi\)
\(912\) 2.94028 0.0973624
\(913\) 21.1839 0.701085
\(914\) 49.8645 1.64937
\(915\) −9.98408 −0.330063
\(916\) 43.3560 1.43252
\(917\) −2.10460 −0.0695002
\(918\) 30.0235 0.990924
\(919\) −54.6539 −1.80287 −0.901433 0.432919i \(-0.857484\pi\)
−0.901433 + 0.432919i \(0.857484\pi\)
\(920\) −11.8147 −0.389519
\(921\) 14.7222 0.485114
\(922\) −0.0357603 −0.00117770
\(923\) 47.9151 1.57715
\(924\) −43.0213 −1.41530
\(925\) 3.23198 0.106267
\(926\) −96.3488 −3.16622
\(927\) 10.6174 0.348723
\(928\) −35.7766 −1.17442
\(929\) −10.0083 −0.328360 −0.164180 0.986430i \(-0.552498\pi\)
−0.164180 + 0.986430i \(0.552498\pi\)
\(930\) −56.7210 −1.85995
\(931\) −15.7043 −0.514689
\(932\) 2.09935 0.0687665
\(933\) 52.5838 1.72151
\(934\) −49.4785 −1.61899
\(935\) 13.7366 0.449234
\(936\) −9.78435 −0.319812
\(937\) 37.5868 1.22791 0.613954 0.789342i \(-0.289578\pi\)
0.613954 + 0.789342i \(0.289578\pi\)
\(938\) 51.3348 1.67614
\(939\) 31.0319 1.01269
\(940\) −2.91882 −0.0952014
\(941\) −13.0015 −0.423837 −0.211918 0.977287i \(-0.567971\pi\)
−0.211918 + 0.977287i \(0.567971\pi\)
\(942\) −9.92070 −0.323234
\(943\) 18.0921 0.589159
\(944\) 0.504103 0.0164072
\(945\) −11.2846 −0.367087
\(946\) 58.4320 1.89979
\(947\) 13.9342 0.452800 0.226400 0.974034i \(-0.427304\pi\)
0.226400 + 0.974034i \(0.427304\pi\)
\(948\) −47.2675 −1.53518
\(949\) 3.77397 0.122508
\(950\) 54.5433 1.76962
\(951\) 36.7618 1.19208
\(952\) 20.5738 0.666801
\(953\) 30.4093 0.985053 0.492526 0.870298i \(-0.336074\pi\)
0.492526 + 0.870298i \(0.336074\pi\)
\(954\) 28.4488 0.921063
\(955\) −14.1690 −0.458498
\(956\) −28.7354 −0.929371
\(957\) 37.1399 1.20056
\(958\) −27.3015 −0.882071
\(959\) −17.9801 −0.580606
\(960\) −35.0175 −1.13018
\(961\) 54.4160 1.75535
\(962\) 7.44035 0.239886
\(963\) −8.01111 −0.258154
\(964\) 20.1154 0.647874
\(965\) −7.07142 −0.227637
\(966\) −33.3611 −1.07337
\(967\) 51.4531 1.65462 0.827310 0.561745i \(-0.189870\pi\)
0.827310 + 0.561745i \(0.189870\pi\)
\(968\) 5.23238 0.168175
\(969\) 51.4564 1.65302
\(970\) −6.88722 −0.221135
\(971\) 57.1482 1.83397 0.916986 0.398919i \(-0.130614\pi\)
0.916986 + 0.398919i \(0.130614\pi\)
\(972\) 34.9330 1.12048
\(973\) −18.1517 −0.581917
\(974\) −13.5098 −0.432883
\(975\) 21.3784 0.684657
\(976\) 0.726436 0.0232526
\(977\) −28.0599 −0.897716 −0.448858 0.893603i \(-0.648169\pi\)
−0.448858 + 0.893603i \(0.648169\pi\)
\(978\) −100.950 −3.22804
\(979\) −50.4523 −1.61246
\(980\) 8.99885 0.287458
\(981\) −1.10340 −0.0352288
\(982\) 30.0246 0.958124
\(983\) 60.1511 1.91852 0.959261 0.282523i \(-0.0911713\pi\)
0.959261 + 0.282523i \(0.0911713\pi\)
\(984\) −30.4167 −0.969648
\(985\) −17.7989 −0.567121
\(986\) −47.5666 −1.51483
\(987\) −3.07747 −0.0979570
\(988\) 77.1940 2.45587
\(989\) 27.8564 0.885783
\(990\) 10.0697 0.320035
\(991\) −4.54431 −0.144355 −0.0721775 0.997392i \(-0.522995\pi\)
−0.0721775 + 0.997392i \(0.522995\pi\)
\(992\) 54.3225 1.72474
\(993\) −22.2805 −0.707049
\(994\) −73.8571 −2.34261
\(995\) −25.7283 −0.815643
\(996\) −45.4710 −1.44080
\(997\) −35.1439 −1.11302 −0.556510 0.830841i \(-0.687860\pi\)
−0.556510 + 0.830841i \(0.687860\pi\)
\(998\) 60.7330 1.92247
\(999\) −3.84192 −0.121553
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 \(a_p\))