Properties

Label 8021.2.a.a.1.15
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.26323 q^{2}\) \(+2.87488 q^{3}\) \(+3.12222 q^{4}\) \(+0.727126 q^{5}\) \(-6.50652 q^{6}\) \(+0.231070 q^{7}\) \(-2.53984 q^{8}\) \(+5.26494 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.26323 q^{2}\) \(+2.87488 q^{3}\) \(+3.12222 q^{4}\) \(+0.727126 q^{5}\) \(-6.50652 q^{6}\) \(+0.231070 q^{7}\) \(-2.53984 q^{8}\) \(+5.26494 q^{9}\) \(-1.64565 q^{10}\) \(-3.33792 q^{11}\) \(+8.97600 q^{12}\) \(+1.00000 q^{13}\) \(-0.522964 q^{14}\) \(+2.09040 q^{15}\) \(-0.496194 q^{16}\) \(-3.22094 q^{17}\) \(-11.9158 q^{18}\) \(+6.87412 q^{19}\) \(+2.27025 q^{20}\) \(+0.664297 q^{21}\) \(+7.55448 q^{22}\) \(+5.68451 q^{23}\) \(-7.30173 q^{24}\) \(-4.47129 q^{25}\) \(-2.26323 q^{26}\) \(+6.51144 q^{27}\) \(+0.721449 q^{28}\) \(-4.07676 q^{29}\) \(-4.73106 q^{30}\) \(-7.88925 q^{31}\) \(+6.20268 q^{32}\) \(-9.59611 q^{33}\) \(+7.28974 q^{34}\) \(+0.168017 q^{35}\) \(+16.4383 q^{36}\) \(-0.678172 q^{37}\) \(-15.5577 q^{38}\) \(+2.87488 q^{39}\) \(-1.84678 q^{40}\) \(-1.78071 q^{41}\) \(-1.50346 q^{42}\) \(-10.7329 q^{43}\) \(-10.4217 q^{44}\) \(+3.82828 q^{45}\) \(-12.8654 q^{46}\) \(-6.89821 q^{47}\) \(-1.42650 q^{48}\) \(-6.94661 q^{49}\) \(+10.1196 q^{50}\) \(-9.25983 q^{51}\) \(+3.12222 q^{52}\) \(-13.4534 q^{53}\) \(-14.7369 q^{54}\) \(-2.42709 q^{55}\) \(-0.586879 q^{56}\) \(+19.7623 q^{57}\) \(+9.22666 q^{58}\) \(+3.71415 q^{59}\) \(+6.52669 q^{60}\) \(-11.1669 q^{61}\) \(+17.8552 q^{62}\) \(+1.21657 q^{63}\) \(-13.0457 q^{64}\) \(+0.727126 q^{65}\) \(+21.7182 q^{66}\) \(-2.94515 q^{67}\) \(-10.0565 q^{68}\) \(+16.3423 q^{69}\) \(-0.380261 q^{70}\) \(+4.67416 q^{71}\) \(-13.3721 q^{72}\) \(-9.34443 q^{73}\) \(+1.53486 q^{74}\) \(-12.8544 q^{75}\) \(+21.4625 q^{76}\) \(-0.771291 q^{77}\) \(-6.50652 q^{78}\) \(-10.8175 q^{79}\) \(-0.360796 q^{80}\) \(+2.92479 q^{81}\) \(+4.03016 q^{82}\) \(+1.49211 q^{83}\) \(+2.07408 q^{84}\) \(-2.34203 q^{85}\) \(+24.2911 q^{86}\) \(-11.7202 q^{87}\) \(+8.47776 q^{88}\) \(-7.30224 q^{89}\) \(-8.66428 q^{90}\) \(+0.231070 q^{91}\) \(+17.7483 q^{92}\) \(-22.6807 q^{93}\) \(+15.6122 q^{94}\) \(+4.99835 q^{95}\) \(+17.8320 q^{96}\) \(+5.41826 q^{97}\) \(+15.7218 q^{98}\) \(-17.5739 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.26323 −1.60035 −0.800173 0.599769i \(-0.795259\pi\)
−0.800173 + 0.599769i \(0.795259\pi\)
\(3\) 2.87488 1.65981 0.829907 0.557902i \(-0.188394\pi\)
0.829907 + 0.557902i \(0.188394\pi\)
\(4\) 3.12222 1.56111
\(5\) 0.727126 0.325181 0.162590 0.986694i \(-0.448015\pi\)
0.162590 + 0.986694i \(0.448015\pi\)
\(6\) −6.50652 −2.65628
\(7\) 0.231070 0.0873361 0.0436680 0.999046i \(-0.486096\pi\)
0.0436680 + 0.999046i \(0.486096\pi\)
\(8\) −2.53984 −0.897968
\(9\) 5.26494 1.75498
\(10\) −1.64565 −0.520402
\(11\) −3.33792 −1.00642 −0.503210 0.864164i \(-0.667848\pi\)
−0.503210 + 0.864164i \(0.667848\pi\)
\(12\) 8.97600 2.59115
\(13\) 1.00000 0.277350
\(14\) −0.522964 −0.139768
\(15\) 2.09040 0.539739
\(16\) −0.496194 −0.124049
\(17\) −3.22094 −0.781194 −0.390597 0.920562i \(-0.627731\pi\)
−0.390597 + 0.920562i \(0.627731\pi\)
\(18\) −11.9158 −2.80858
\(19\) 6.87412 1.57703 0.788516 0.615015i \(-0.210850\pi\)
0.788516 + 0.615015i \(0.210850\pi\)
\(20\) 2.27025 0.507642
\(21\) 0.664297 0.144962
\(22\) 7.55448 1.61062
\(23\) 5.68451 1.18530 0.592652 0.805459i \(-0.298081\pi\)
0.592652 + 0.805459i \(0.298081\pi\)
\(24\) −7.30173 −1.49046
\(25\) −4.47129 −0.894258
\(26\) −2.26323 −0.443856
\(27\) 6.51144 1.25313
\(28\) 0.721449 0.136341
\(29\) −4.07676 −0.757036 −0.378518 0.925594i \(-0.623566\pi\)
−0.378518 + 0.925594i \(0.623566\pi\)
\(30\) −4.73106 −0.863770
\(31\) −7.88925 −1.41695 −0.708476 0.705735i \(-0.750617\pi\)
−0.708476 + 0.705735i \(0.750617\pi\)
\(32\) 6.20268 1.09649
\(33\) −9.59611 −1.67047
\(34\) 7.28974 1.25018
\(35\) 0.168017 0.0284000
\(36\) 16.4383 2.73972
\(37\) −0.678172 −0.111491 −0.0557454 0.998445i \(-0.517754\pi\)
−0.0557454 + 0.998445i \(0.517754\pi\)
\(38\) −15.5577 −2.52380
\(39\) 2.87488 0.460349
\(40\) −1.84678 −0.292002
\(41\) −1.78071 −0.278100 −0.139050 0.990285i \(-0.544405\pi\)
−0.139050 + 0.990285i \(0.544405\pi\)
\(42\) −1.50346 −0.231989
\(43\) −10.7329 −1.63676 −0.818379 0.574679i \(-0.805127\pi\)
−0.818379 + 0.574679i \(0.805127\pi\)
\(44\) −10.4217 −1.57113
\(45\) 3.82828 0.570686
\(46\) −12.8654 −1.89690
\(47\) −6.89821 −1.00621 −0.503103 0.864226i \(-0.667809\pi\)
−0.503103 + 0.864226i \(0.667809\pi\)
\(48\) −1.42650 −0.205898
\(49\) −6.94661 −0.992372
\(50\) 10.1196 1.43112
\(51\) −9.25983 −1.29664
\(52\) 3.12222 0.432974
\(53\) −13.4534 −1.84796 −0.923981 0.382439i \(-0.875084\pi\)
−0.923981 + 0.382439i \(0.875084\pi\)
\(54\) −14.7369 −2.00544
\(55\) −2.42709 −0.327268
\(56\) −0.586879 −0.0784250
\(57\) 19.7623 2.61758
\(58\) 9.22666 1.21152
\(59\) 3.71415 0.483541 0.241771 0.970333i \(-0.422272\pi\)
0.241771 + 0.970333i \(0.422272\pi\)
\(60\) 6.52669 0.842592
\(61\) −11.1669 −1.42978 −0.714888 0.699239i \(-0.753522\pi\)
−0.714888 + 0.699239i \(0.753522\pi\)
\(62\) 17.8552 2.26761
\(63\) 1.21657 0.153273
\(64\) −13.0457 −1.63071
\(65\) 0.727126 0.0901889
\(66\) 21.7182 2.67333
\(67\) −2.94515 −0.359807 −0.179904 0.983684i \(-0.557579\pi\)
−0.179904 + 0.983684i \(0.557579\pi\)
\(68\) −10.0565 −1.21953
\(69\) 16.3423 1.96738
\(70\) −0.380261 −0.0454498
\(71\) 4.67416 0.554720 0.277360 0.960766i \(-0.410540\pi\)
0.277360 + 0.960766i \(0.410540\pi\)
\(72\) −13.3721 −1.57592
\(73\) −9.34443 −1.09368 −0.546841 0.837236i \(-0.684170\pi\)
−0.546841 + 0.837236i \(0.684170\pi\)
\(74\) 1.53486 0.178424
\(75\) −12.8544 −1.48430
\(76\) 21.4625 2.46192
\(77\) −0.771291 −0.0878967
\(78\) −6.50652 −0.736719
\(79\) −10.8175 −1.21707 −0.608534 0.793527i \(-0.708242\pi\)
−0.608534 + 0.793527i \(0.708242\pi\)
\(80\) −0.360796 −0.0403382
\(81\) 2.92479 0.324977
\(82\) 4.03016 0.445057
\(83\) 1.49211 0.163780 0.0818902 0.996641i \(-0.473904\pi\)
0.0818902 + 0.996641i \(0.473904\pi\)
\(84\) 2.07408 0.226301
\(85\) −2.34203 −0.254029
\(86\) 24.2911 2.61938
\(87\) −11.7202 −1.25654
\(88\) 8.47776 0.903733
\(89\) −7.30224 −0.774036 −0.387018 0.922072i \(-0.626495\pi\)
−0.387018 + 0.922072i \(0.626495\pi\)
\(90\) −8.66428 −0.913295
\(91\) 0.231070 0.0242227
\(92\) 17.7483 1.85039
\(93\) −22.6807 −2.35187
\(94\) 15.6122 1.61028
\(95\) 4.99835 0.512820
\(96\) 17.8320 1.81997
\(97\) 5.41826 0.550141 0.275070 0.961424i \(-0.411299\pi\)
0.275070 + 0.961424i \(0.411299\pi\)
\(98\) 15.7218 1.58814
\(99\) −17.5739 −1.76625
\(100\) −13.9603 −1.39603
\(101\) 10.0455 0.999565 0.499782 0.866151i \(-0.333413\pi\)
0.499782 + 0.866151i \(0.333413\pi\)
\(102\) 20.9571 2.07507
\(103\) 12.4191 1.22369 0.611844 0.790979i \(-0.290428\pi\)
0.611844 + 0.790979i \(0.290428\pi\)
\(104\) −2.53984 −0.249052
\(105\) 0.483028 0.0471387
\(106\) 30.4481 2.95738
\(107\) −14.9574 −1.44598 −0.722992 0.690857i \(-0.757234\pi\)
−0.722992 + 0.690857i \(0.757234\pi\)
\(108\) 20.3301 1.95627
\(109\) −4.23403 −0.405546 −0.202773 0.979226i \(-0.564995\pi\)
−0.202773 + 0.979226i \(0.564995\pi\)
\(110\) 5.49306 0.523742
\(111\) −1.94966 −0.185054
\(112\) −0.114655 −0.0108339
\(113\) 15.7265 1.47943 0.739713 0.672922i \(-0.234961\pi\)
0.739713 + 0.672922i \(0.234961\pi\)
\(114\) −44.7266 −4.18903
\(115\) 4.13336 0.385438
\(116\) −12.7285 −1.18182
\(117\) 5.26494 0.486744
\(118\) −8.40599 −0.773834
\(119\) −0.744262 −0.0682264
\(120\) −5.30928 −0.484669
\(121\) 0.141686 0.0128805
\(122\) 25.2733 2.28814
\(123\) −5.11934 −0.461595
\(124\) −24.6320 −2.21201
\(125\) −6.88682 −0.615976
\(126\) −2.75337 −0.245290
\(127\) −17.2316 −1.52906 −0.764529 0.644589i \(-0.777028\pi\)
−0.764529 + 0.644589i \(0.777028\pi\)
\(128\) 17.1201 1.51322
\(129\) −30.8559 −2.71671
\(130\) −1.64565 −0.144333
\(131\) 21.0173 1.83629 0.918147 0.396240i \(-0.129685\pi\)
0.918147 + 0.396240i \(0.129685\pi\)
\(132\) −29.9611 −2.60778
\(133\) 1.58840 0.137732
\(134\) 6.66556 0.575816
\(135\) 4.73464 0.407493
\(136\) 8.18067 0.701487
\(137\) 4.18841 0.357840 0.178920 0.983864i \(-0.442740\pi\)
0.178920 + 0.983864i \(0.442740\pi\)
\(138\) −36.9864 −3.14849
\(139\) −1.64264 −0.139327 −0.0696636 0.997571i \(-0.522193\pi\)
−0.0696636 + 0.997571i \(0.522193\pi\)
\(140\) 0.524585 0.0443355
\(141\) −19.8315 −1.67012
\(142\) −10.5787 −0.887745
\(143\) −3.33792 −0.279131
\(144\) −2.61243 −0.217703
\(145\) −2.96432 −0.246173
\(146\) 21.1486 1.75027
\(147\) −19.9707 −1.64715
\(148\) −2.11740 −0.174049
\(149\) 0.782707 0.0641219 0.0320609 0.999486i \(-0.489793\pi\)
0.0320609 + 0.999486i \(0.489793\pi\)
\(150\) 29.0925 2.37540
\(151\) 8.82419 0.718102 0.359051 0.933318i \(-0.383100\pi\)
0.359051 + 0.933318i \(0.383100\pi\)
\(152\) −17.4591 −1.41612
\(153\) −16.9581 −1.37098
\(154\) 1.74561 0.140665
\(155\) −5.73648 −0.460765
\(156\) 8.97600 0.718655
\(157\) −10.5723 −0.843763 −0.421882 0.906651i \(-0.638630\pi\)
−0.421882 + 0.906651i \(0.638630\pi\)
\(158\) 24.4826 1.94773
\(159\) −38.6768 −3.06727
\(160\) 4.51013 0.356557
\(161\) 1.31352 0.103520
\(162\) −6.61948 −0.520075
\(163\) 4.52550 0.354464 0.177232 0.984169i \(-0.443286\pi\)
0.177232 + 0.984169i \(0.443286\pi\)
\(164\) −5.55977 −0.434145
\(165\) −6.97758 −0.543204
\(166\) −3.37699 −0.262105
\(167\) 23.7812 1.84024 0.920122 0.391632i \(-0.128089\pi\)
0.920122 + 0.391632i \(0.128089\pi\)
\(168\) −1.68721 −0.130171
\(169\) 1.00000 0.0769231
\(170\) 5.30056 0.406535
\(171\) 36.1919 2.76766
\(172\) −33.5106 −2.55516
\(173\) 8.48460 0.645072 0.322536 0.946557i \(-0.395465\pi\)
0.322536 + 0.946557i \(0.395465\pi\)
\(174\) 26.5255 2.01090
\(175\) −1.03318 −0.0781009
\(176\) 1.65626 0.124845
\(177\) 10.6777 0.802589
\(178\) 16.5267 1.23873
\(179\) −3.70508 −0.276931 −0.138465 0.990367i \(-0.544217\pi\)
−0.138465 + 0.990367i \(0.544217\pi\)
\(180\) 11.9527 0.890902
\(181\) 20.9145 1.55456 0.777281 0.629154i \(-0.216598\pi\)
0.777281 + 0.629154i \(0.216598\pi\)
\(182\) −0.522964 −0.0387647
\(183\) −32.1035 −2.37316
\(184\) −14.4377 −1.06436
\(185\) −0.493116 −0.0362546
\(186\) 51.3316 3.76381
\(187\) 10.7512 0.786209
\(188\) −21.5377 −1.57080
\(189\) 1.50460 0.109443
\(190\) −11.3124 −0.820690
\(191\) −9.99153 −0.722962 −0.361481 0.932380i \(-0.617729\pi\)
−0.361481 + 0.932380i \(0.617729\pi\)
\(192\) −37.5049 −2.70668
\(193\) 19.9574 1.43656 0.718282 0.695752i \(-0.244929\pi\)
0.718282 + 0.695752i \(0.244929\pi\)
\(194\) −12.2628 −0.880416
\(195\) 2.09040 0.149697
\(196\) −21.6888 −1.54920
\(197\) 11.2148 0.799023 0.399512 0.916728i \(-0.369180\pi\)
0.399512 + 0.916728i \(0.369180\pi\)
\(198\) 39.7739 2.82661
\(199\) 4.80276 0.340459 0.170229 0.985404i \(-0.445549\pi\)
0.170229 + 0.985404i \(0.445549\pi\)
\(200\) 11.3563 0.803015
\(201\) −8.46696 −0.597213
\(202\) −22.7353 −1.59965
\(203\) −0.942016 −0.0661165
\(204\) −28.9112 −2.02419
\(205\) −1.29480 −0.0904329
\(206\) −28.1072 −1.95832
\(207\) 29.9286 2.08018
\(208\) −0.496194 −0.0344049
\(209\) −22.9452 −1.58716
\(210\) −1.09320 −0.0754383
\(211\) −6.46430 −0.445021 −0.222510 0.974930i \(-0.571425\pi\)
−0.222510 + 0.974930i \(0.571425\pi\)
\(212\) −42.0043 −2.88487
\(213\) 13.4376 0.920732
\(214\) 33.8520 2.31407
\(215\) −7.80420 −0.532242
\(216\) −16.5380 −1.12527
\(217\) −1.82297 −0.123751
\(218\) 9.58258 0.649015
\(219\) −26.8641 −1.81531
\(220\) −7.57789 −0.510901
\(221\) −3.22094 −0.216664
\(222\) 4.41254 0.296150
\(223\) −1.79459 −0.120175 −0.0600874 0.998193i \(-0.519138\pi\)
−0.0600874 + 0.998193i \(0.519138\pi\)
\(224\) 1.43325 0.0957630
\(225\) −23.5411 −1.56940
\(226\) −35.5928 −2.36760
\(227\) 9.79583 0.650172 0.325086 0.945684i \(-0.394607\pi\)
0.325086 + 0.945684i \(0.394607\pi\)
\(228\) 61.7021 4.08632
\(229\) −19.8591 −1.31232 −0.656162 0.754620i \(-0.727821\pi\)
−0.656162 + 0.754620i \(0.727821\pi\)
\(230\) −9.35475 −0.616834
\(231\) −2.21737 −0.145892
\(232\) 10.3543 0.679794
\(233\) −21.0746 −1.38064 −0.690322 0.723502i \(-0.742531\pi\)
−0.690322 + 0.723502i \(0.742531\pi\)
\(234\) −11.9158 −0.778959
\(235\) −5.01587 −0.327199
\(236\) 11.5964 0.754861
\(237\) −31.0992 −2.02011
\(238\) 1.68444 0.109186
\(239\) 29.6582 1.91843 0.959213 0.282684i \(-0.0912247\pi\)
0.959213 + 0.282684i \(0.0912247\pi\)
\(240\) −1.03725 −0.0669539
\(241\) 5.26925 0.339422 0.169711 0.985494i \(-0.445717\pi\)
0.169711 + 0.985494i \(0.445717\pi\)
\(242\) −0.320668 −0.0206133
\(243\) −11.1259 −0.713727
\(244\) −34.8655 −2.23203
\(245\) −5.05106 −0.322700
\(246\) 11.5862 0.738712
\(247\) 6.87412 0.437390
\(248\) 20.0374 1.27238
\(249\) 4.28964 0.271845
\(250\) 15.5865 0.985775
\(251\) 6.16806 0.389324 0.194662 0.980870i \(-0.437639\pi\)
0.194662 + 0.980870i \(0.437639\pi\)
\(252\) 3.79839 0.239276
\(253\) −18.9744 −1.19291
\(254\) 38.9991 2.44702
\(255\) −6.73306 −0.421641
\(256\) −12.6553 −0.790959
\(257\) −3.02385 −0.188623 −0.0943113 0.995543i \(-0.530065\pi\)
−0.0943113 + 0.995543i \(0.530065\pi\)
\(258\) 69.8341 4.34768
\(259\) −0.156705 −0.00973716
\(260\) 2.27025 0.140795
\(261\) −21.4639 −1.32858
\(262\) −47.5671 −2.93871
\(263\) 12.9573 0.798984 0.399492 0.916737i \(-0.369187\pi\)
0.399492 + 0.916737i \(0.369187\pi\)
\(264\) 24.3726 1.50003
\(265\) −9.78229 −0.600921
\(266\) −3.59492 −0.220419
\(267\) −20.9931 −1.28476
\(268\) −9.19540 −0.561698
\(269\) −5.52691 −0.336982 −0.168491 0.985703i \(-0.553889\pi\)
−0.168491 + 0.985703i \(0.553889\pi\)
\(270\) −10.7156 −0.652129
\(271\) −4.95257 −0.300847 −0.150424 0.988622i \(-0.548064\pi\)
−0.150424 + 0.988622i \(0.548064\pi\)
\(272\) 1.59821 0.0969060
\(273\) 0.664297 0.0402051
\(274\) −9.47935 −0.572668
\(275\) 14.9248 0.899998
\(276\) 51.0242 3.07130
\(277\) −10.4964 −0.630670 −0.315335 0.948980i \(-0.602117\pi\)
−0.315335 + 0.948980i \(0.602117\pi\)
\(278\) 3.71768 0.222972
\(279\) −41.5365 −2.48672
\(280\) −0.426735 −0.0255023
\(281\) 10.4408 0.622846 0.311423 0.950271i \(-0.399194\pi\)
0.311423 + 0.950271i \(0.399194\pi\)
\(282\) 44.8833 2.67276
\(283\) 13.5942 0.808094 0.404047 0.914738i \(-0.367603\pi\)
0.404047 + 0.914738i \(0.367603\pi\)
\(284\) 14.5937 0.865979
\(285\) 14.3697 0.851186
\(286\) 7.55448 0.446706
\(287\) −0.411468 −0.0242882
\(288\) 32.6567 1.92432
\(289\) −6.62552 −0.389736
\(290\) 6.70894 0.393963
\(291\) 15.5769 0.913131
\(292\) −29.1753 −1.70736
\(293\) −17.8775 −1.04441 −0.522207 0.852818i \(-0.674891\pi\)
−0.522207 + 0.852818i \(0.674891\pi\)
\(294\) 45.1983 2.63602
\(295\) 2.70066 0.157238
\(296\) 1.72245 0.100115
\(297\) −21.7346 −1.26117
\(298\) −1.77145 −0.102617
\(299\) 5.68451 0.328744
\(300\) −40.1343 −2.31715
\(301\) −2.48005 −0.142948
\(302\) −19.9712 −1.14921
\(303\) 28.8796 1.65909
\(304\) −3.41090 −0.195629
\(305\) −8.11974 −0.464935
\(306\) 38.3801 2.19404
\(307\) −8.81980 −0.503372 −0.251686 0.967809i \(-0.580985\pi\)
−0.251686 + 0.967809i \(0.580985\pi\)
\(308\) −2.40814 −0.137216
\(309\) 35.7033 2.03109
\(310\) 12.9830 0.737384
\(311\) 12.7692 0.724074 0.362037 0.932164i \(-0.382081\pi\)
0.362037 + 0.932164i \(0.382081\pi\)
\(312\) −7.30173 −0.413379
\(313\) −15.3799 −0.869323 −0.434662 0.900594i \(-0.643132\pi\)
−0.434662 + 0.900594i \(0.643132\pi\)
\(314\) 23.9276 1.35031
\(315\) 0.884598 0.0498415
\(316\) −33.7747 −1.89998
\(317\) −25.1672 −1.41353 −0.706764 0.707449i \(-0.749846\pi\)
−0.706764 + 0.707449i \(0.749846\pi\)
\(318\) 87.5346 4.90870
\(319\) 13.6079 0.761896
\(320\) −9.48587 −0.530276
\(321\) −43.0007 −2.40006
\(322\) −2.97280 −0.165667
\(323\) −22.1412 −1.23197
\(324\) 9.13183 0.507324
\(325\) −4.47129 −0.248022
\(326\) −10.2423 −0.567266
\(327\) −12.1723 −0.673131
\(328\) 4.52272 0.249725
\(329\) −1.59397 −0.0878782
\(330\) 15.7919 0.869315
\(331\) −6.56601 −0.360901 −0.180450 0.983584i \(-0.557756\pi\)
−0.180450 + 0.983584i \(0.557756\pi\)
\(332\) 4.65869 0.255679
\(333\) −3.57053 −0.195664
\(334\) −53.8223 −2.94503
\(335\) −2.14150 −0.117002
\(336\) −0.329621 −0.0179823
\(337\) −5.94918 −0.324072 −0.162036 0.986785i \(-0.551806\pi\)
−0.162036 + 0.986785i \(0.551806\pi\)
\(338\) −2.26323 −0.123104
\(339\) 45.2119 2.45557
\(340\) −7.31233 −0.396567
\(341\) 26.3337 1.42605
\(342\) −81.9105 −4.42921
\(343\) −3.22264 −0.174006
\(344\) 27.2599 1.46976
\(345\) 11.8829 0.639755
\(346\) −19.2026 −1.03234
\(347\) −10.7969 −0.579610 −0.289805 0.957086i \(-0.593590\pi\)
−0.289805 + 0.957086i \(0.593590\pi\)
\(348\) −36.5930 −1.96159
\(349\) 6.09456 0.326234 0.163117 0.986607i \(-0.447845\pi\)
0.163117 + 0.986607i \(0.447845\pi\)
\(350\) 2.33832 0.124989
\(351\) 6.51144 0.347555
\(352\) −20.7040 −1.10353
\(353\) −14.3485 −0.763693 −0.381846 0.924226i \(-0.624712\pi\)
−0.381846 + 0.924226i \(0.624712\pi\)
\(354\) −24.1662 −1.28442
\(355\) 3.39870 0.180384
\(356\) −22.7992 −1.20835
\(357\) −2.13967 −0.113243
\(358\) 8.38546 0.443185
\(359\) −7.22186 −0.381155 −0.190578 0.981672i \(-0.561036\pi\)
−0.190578 + 0.981672i \(0.561036\pi\)
\(360\) −9.72320 −0.512458
\(361\) 28.2535 1.48703
\(362\) −47.3343 −2.48784
\(363\) 0.407330 0.0213793
\(364\) 0.721449 0.0378142
\(365\) −6.79458 −0.355644
\(366\) 72.6577 3.79788
\(367\) 24.6065 1.28445 0.642224 0.766517i \(-0.278012\pi\)
0.642224 + 0.766517i \(0.278012\pi\)
\(368\) −2.82062 −0.147035
\(369\) −9.37535 −0.488061
\(370\) 1.11604 0.0580200
\(371\) −3.10866 −0.161394
\(372\) −70.8139 −3.67153
\(373\) 15.4082 0.797806 0.398903 0.916993i \(-0.369391\pi\)
0.398903 + 0.916993i \(0.369391\pi\)
\(374\) −24.3326 −1.25821
\(375\) −19.7988 −1.02241
\(376\) 17.5203 0.903542
\(377\) −4.07676 −0.209964
\(378\) −3.40525 −0.175147
\(379\) 16.8279 0.864391 0.432195 0.901780i \(-0.357739\pi\)
0.432195 + 0.901780i \(0.357739\pi\)
\(380\) 15.6059 0.800568
\(381\) −49.5388 −2.53795
\(382\) 22.6131 1.15699
\(383\) 1.67797 0.0857405 0.0428702 0.999081i \(-0.486350\pi\)
0.0428702 + 0.999081i \(0.486350\pi\)
\(384\) 49.2183 2.51166
\(385\) −0.560826 −0.0285823
\(386\) −45.1682 −2.29900
\(387\) −56.5083 −2.87248
\(388\) 16.9170 0.858830
\(389\) 4.70040 0.238320 0.119160 0.992875i \(-0.461980\pi\)
0.119160 + 0.992875i \(0.461980\pi\)
\(390\) −4.73106 −0.239567
\(391\) −18.3095 −0.925951
\(392\) 17.6433 0.891119
\(393\) 60.4224 3.04791
\(394\) −25.3818 −1.27871
\(395\) −7.86572 −0.395767
\(396\) −54.8696 −2.75730
\(397\) −11.8147 −0.592965 −0.296482 0.955038i \(-0.595814\pi\)
−0.296482 + 0.955038i \(0.595814\pi\)
\(398\) −10.8698 −0.544852
\(399\) 4.56646 0.228609
\(400\) 2.21863 0.110931
\(401\) −28.4064 −1.41855 −0.709273 0.704934i \(-0.750977\pi\)
−0.709273 + 0.704934i \(0.750977\pi\)
\(402\) 19.1627 0.955748
\(403\) −7.88925 −0.392992
\(404\) 31.3642 1.56043
\(405\) 2.12669 0.105676
\(406\) 2.13200 0.105809
\(407\) 2.26368 0.112206
\(408\) 23.5185 1.16434
\(409\) −6.04617 −0.298964 −0.149482 0.988764i \(-0.547761\pi\)
−0.149482 + 0.988764i \(0.547761\pi\)
\(410\) 2.93044 0.144724
\(411\) 12.0412 0.593948
\(412\) 38.7750 1.91031
\(413\) 0.858227 0.0422306
\(414\) −67.7354 −3.32902
\(415\) 1.08495 0.0532582
\(416\) 6.20268 0.304111
\(417\) −4.72240 −0.231257
\(418\) 51.9304 2.54000
\(419\) −29.6068 −1.44639 −0.723194 0.690644i \(-0.757327\pi\)
−0.723194 + 0.690644i \(0.757327\pi\)
\(420\) 1.50812 0.0735886
\(421\) 5.27427 0.257052 0.128526 0.991706i \(-0.458975\pi\)
0.128526 + 0.991706i \(0.458975\pi\)
\(422\) 14.6302 0.712188
\(423\) −36.3187 −1.76587
\(424\) 34.1694 1.65941
\(425\) 14.4018 0.698588
\(426\) −30.4125 −1.47349
\(427\) −2.58033 −0.124871
\(428\) −46.7002 −2.25734
\(429\) −9.59611 −0.463305
\(430\) 17.6627 0.851771
\(431\) 2.20419 0.106172 0.0530859 0.998590i \(-0.483094\pi\)
0.0530859 + 0.998590i \(0.483094\pi\)
\(432\) −3.23094 −0.155449
\(433\) −30.8102 −1.48064 −0.740322 0.672252i \(-0.765327\pi\)
−0.740322 + 0.672252i \(0.765327\pi\)
\(434\) 4.12579 0.198044
\(435\) −8.52207 −0.408602
\(436\) −13.2196 −0.633102
\(437\) 39.0760 1.86926
\(438\) 60.7997 2.90512
\(439\) −1.74225 −0.0831531 −0.0415766 0.999135i \(-0.513238\pi\)
−0.0415766 + 0.999135i \(0.513238\pi\)
\(440\) 6.16440 0.293876
\(441\) −36.5735 −1.74159
\(442\) 7.28974 0.346738
\(443\) −7.07615 −0.336198 −0.168099 0.985770i \(-0.553763\pi\)
−0.168099 + 0.985770i \(0.553763\pi\)
\(444\) −6.08727 −0.288889
\(445\) −5.30965 −0.251702
\(446\) 4.06158 0.192321
\(447\) 2.25019 0.106430
\(448\) −3.01447 −0.142420
\(449\) 3.08120 0.145411 0.0727054 0.997353i \(-0.476837\pi\)
0.0727054 + 0.997353i \(0.476837\pi\)
\(450\) 53.2789 2.51159
\(451\) 5.94387 0.279886
\(452\) 49.1016 2.30955
\(453\) 25.3685 1.19192
\(454\) −22.1702 −1.04050
\(455\) 0.168017 0.00787674
\(456\) −50.1930 −2.35050
\(457\) 29.2582 1.36864 0.684321 0.729181i \(-0.260099\pi\)
0.684321 + 0.729181i \(0.260099\pi\)
\(458\) 44.9457 2.10017
\(459\) −20.9730 −0.978935
\(460\) 12.9052 0.601710
\(461\) −21.4103 −0.997177 −0.498589 0.866839i \(-0.666148\pi\)
−0.498589 + 0.866839i \(0.666148\pi\)
\(462\) 5.01842 0.233478
\(463\) −0.171564 −0.00797325 −0.00398662 0.999992i \(-0.501269\pi\)
−0.00398662 + 0.999992i \(0.501269\pi\)
\(464\) 2.02287 0.0939092
\(465\) −16.4917 −0.764784
\(466\) 47.6967 2.20951
\(467\) 0.438115 0.0202736 0.0101368 0.999949i \(-0.496773\pi\)
0.0101368 + 0.999949i \(0.496773\pi\)
\(468\) 16.4383 0.759860
\(469\) −0.680534 −0.0314242
\(470\) 11.3521 0.523632
\(471\) −30.3942 −1.40049
\(472\) −9.43334 −0.434205
\(473\) 35.8256 1.64726
\(474\) 70.3846 3.23287
\(475\) −30.7362 −1.41027
\(476\) −2.32375 −0.106509
\(477\) −70.8312 −3.24314
\(478\) −67.1233 −3.07015
\(479\) 22.0409 1.00707 0.503537 0.863973i \(-0.332032\pi\)
0.503537 + 0.863973i \(0.332032\pi\)
\(480\) 12.9661 0.591818
\(481\) −0.678172 −0.0309220
\(482\) −11.9255 −0.543193
\(483\) 3.77621 0.171823
\(484\) 0.442374 0.0201079
\(485\) 3.93976 0.178895
\(486\) 25.1805 1.14221
\(487\) 3.21183 0.145542 0.0727709 0.997349i \(-0.476816\pi\)
0.0727709 + 0.997349i \(0.476816\pi\)
\(488\) 28.3621 1.28389
\(489\) 13.0103 0.588345
\(490\) 11.4317 0.516432
\(491\) 39.8075 1.79649 0.898243 0.439500i \(-0.144844\pi\)
0.898243 + 0.439500i \(0.144844\pi\)
\(492\) −15.9837 −0.720600
\(493\) 13.1310 0.591392
\(494\) −15.5577 −0.699975
\(495\) −12.7785 −0.574349
\(496\) 3.91460 0.175771
\(497\) 1.08006 0.0484471
\(498\) −9.70845 −0.435046
\(499\) −20.5000 −0.917708 −0.458854 0.888512i \(-0.651740\pi\)
−0.458854 + 0.888512i \(0.651740\pi\)
\(500\) −21.5021 −0.961605
\(501\) 68.3681 3.05446
\(502\) −13.9597 −0.623054
\(503\) 38.2808 1.70686 0.853429 0.521209i \(-0.174519\pi\)
0.853429 + 0.521209i \(0.174519\pi\)
\(504\) −3.08988 −0.137634
\(505\) 7.30435 0.325039
\(506\) 42.9435 1.90907
\(507\) 2.87488 0.127678
\(508\) −53.8008 −2.38703
\(509\) 9.77141 0.433110 0.216555 0.976270i \(-0.430518\pi\)
0.216555 + 0.976270i \(0.430518\pi\)
\(510\) 15.2385 0.674771
\(511\) −2.15921 −0.0955179
\(512\) −5.59824 −0.247410
\(513\) 44.7604 1.97622
\(514\) 6.84367 0.301862
\(515\) 9.03023 0.397919
\(516\) −96.3389 −4.24108
\(517\) 23.0256 1.01267
\(518\) 0.354659 0.0155828
\(519\) 24.3922 1.07070
\(520\) −1.84678 −0.0809867
\(521\) 7.79097 0.341328 0.170664 0.985329i \(-0.445409\pi\)
0.170664 + 0.985329i \(0.445409\pi\)
\(522\) 48.5778 2.12619
\(523\) −10.7245 −0.468947 −0.234474 0.972122i \(-0.575337\pi\)
−0.234474 + 0.972122i \(0.575337\pi\)
\(524\) 65.6207 2.86665
\(525\) −2.97027 −0.129633
\(526\) −29.3255 −1.27865
\(527\) 25.4108 1.10691
\(528\) 4.76154 0.207219
\(529\) 9.31370 0.404943
\(530\) 22.1396 0.961682
\(531\) 19.5548 0.848606
\(532\) 4.95933 0.215014
\(533\) −1.78071 −0.0771312
\(534\) 47.5122 2.05605
\(535\) −10.8759 −0.470206
\(536\) 7.48020 0.323096
\(537\) −10.6517 −0.459654
\(538\) 12.5087 0.539288
\(539\) 23.1872 0.998743
\(540\) 14.7826 0.636140
\(541\) 38.4437 1.65282 0.826411 0.563067i \(-0.190379\pi\)
0.826411 + 0.563067i \(0.190379\pi\)
\(542\) 11.2088 0.481460
\(543\) 60.1267 2.58028
\(544\) −19.9785 −0.856570
\(545\) −3.07867 −0.131876
\(546\) −1.50346 −0.0643421
\(547\) 0.255008 0.0109034 0.00545168 0.999985i \(-0.498265\pi\)
0.00545168 + 0.999985i \(0.498265\pi\)
\(548\) 13.0771 0.558627
\(549\) −58.7931 −2.50923
\(550\) −33.7782 −1.44031
\(551\) −28.0242 −1.19387
\(552\) −41.5068 −1.76665
\(553\) −2.49961 −0.106294
\(554\) 23.7559 1.00929
\(555\) −1.41765 −0.0601759
\(556\) −5.12869 −0.217505
\(557\) −3.93264 −0.166631 −0.0833157 0.996523i \(-0.526551\pi\)
−0.0833157 + 0.996523i \(0.526551\pi\)
\(558\) 94.0066 3.97962
\(559\) −10.7329 −0.453955
\(560\) −0.0833689 −0.00352298
\(561\) 30.9085 1.30496
\(562\) −23.6300 −0.996770
\(563\) −5.44011 −0.229274 −0.114637 0.993407i \(-0.536570\pi\)
−0.114637 + 0.993407i \(0.536570\pi\)
\(564\) −61.9183 −2.60723
\(565\) 11.4352 0.481081
\(566\) −30.7669 −1.29323
\(567\) 0.675830 0.0283822
\(568\) −11.8716 −0.498121
\(569\) 13.0844 0.548528 0.274264 0.961654i \(-0.411566\pi\)
0.274264 + 0.961654i \(0.411566\pi\)
\(570\) −32.5219 −1.36219
\(571\) 35.9286 1.50356 0.751782 0.659412i \(-0.229195\pi\)
0.751782 + 0.659412i \(0.229195\pi\)
\(572\) −10.4217 −0.435753
\(573\) −28.7245 −1.19998
\(574\) 0.931248 0.0388695
\(575\) −25.4171 −1.05997
\(576\) −68.6849 −2.86187
\(577\) −34.1241 −1.42060 −0.710302 0.703897i \(-0.751441\pi\)
−0.710302 + 0.703897i \(0.751441\pi\)
\(578\) 14.9951 0.623713
\(579\) 57.3751 2.38443
\(580\) −9.25525 −0.384303
\(581\) 0.344781 0.0143039
\(582\) −35.2540 −1.46133
\(583\) 44.9062 1.85982
\(584\) 23.7333 0.982092
\(585\) 3.82828 0.158280
\(586\) 40.4609 1.67143
\(587\) 18.9242 0.781087 0.390543 0.920584i \(-0.372287\pi\)
0.390543 + 0.920584i \(0.372287\pi\)
\(588\) −62.3528 −2.57138
\(589\) −54.2317 −2.23458
\(590\) −6.11221 −0.251636
\(591\) 32.2413 1.32623
\(592\) 0.336505 0.0138303
\(593\) 32.0440 1.31589 0.657944 0.753067i \(-0.271426\pi\)
0.657944 + 0.753067i \(0.271426\pi\)
\(594\) 49.1905 2.01831
\(595\) −0.541172 −0.0221859
\(596\) 2.44378 0.100101
\(597\) 13.8074 0.565098
\(598\) −12.8654 −0.526104
\(599\) −43.6287 −1.78262 −0.891311 0.453393i \(-0.850213\pi\)
−0.891311 + 0.453393i \(0.850213\pi\)
\(600\) 32.6481 1.33285
\(601\) 21.5082 0.877339 0.438670 0.898648i \(-0.355450\pi\)
0.438670 + 0.898648i \(0.355450\pi\)
\(602\) 5.61294 0.228766
\(603\) −15.5060 −0.631455
\(604\) 27.5510 1.12104
\(605\) 0.103024 0.00418850
\(606\) −65.3613 −2.65512
\(607\) −43.7596 −1.77615 −0.888073 0.459702i \(-0.847956\pi\)
−0.888073 + 0.459702i \(0.847956\pi\)
\(608\) 42.6380 1.72920
\(609\) −2.70818 −0.109741
\(610\) 18.3769 0.744057
\(611\) −6.89821 −0.279072
\(612\) −52.9468 −2.14025
\(613\) −40.7041 −1.64402 −0.822012 0.569471i \(-0.807148\pi\)
−0.822012 + 0.569471i \(0.807148\pi\)
\(614\) 19.9612 0.805570
\(615\) −3.72240 −0.150102
\(616\) 1.95895 0.0789285
\(617\) 1.00000 0.0402585
\(618\) −80.8049 −3.25045
\(619\) −11.0672 −0.444828 −0.222414 0.974952i \(-0.571394\pi\)
−0.222414 + 0.974952i \(0.571394\pi\)
\(620\) −17.9105 −0.719304
\(621\) 37.0144 1.48534
\(622\) −28.8996 −1.15877
\(623\) −1.68733 −0.0676013
\(624\) −1.42650 −0.0571057
\(625\) 17.3489 0.693954
\(626\) 34.8083 1.39122
\(627\) −65.9648 −2.63438
\(628\) −33.0091 −1.31721
\(629\) 2.18435 0.0870958
\(630\) −2.00205 −0.0797636
\(631\) 42.4297 1.68910 0.844550 0.535477i \(-0.179868\pi\)
0.844550 + 0.535477i \(0.179868\pi\)
\(632\) 27.4748 1.09289
\(633\) −18.5841 −0.738652
\(634\) 56.9591 2.26213
\(635\) −12.5295 −0.497220
\(636\) −120.757 −4.78834
\(637\) −6.94661 −0.275235
\(638\) −30.7978 −1.21930
\(639\) 24.6092 0.973523
\(640\) 12.4485 0.492069
\(641\) 30.2692 1.19556 0.597782 0.801659i \(-0.296049\pi\)
0.597782 + 0.801659i \(0.296049\pi\)
\(642\) 97.3205 3.84093
\(643\) 41.8938 1.65213 0.826065 0.563575i \(-0.190574\pi\)
0.826065 + 0.563575i \(0.190574\pi\)
\(644\) 4.10109 0.161606
\(645\) −22.4361 −0.883422
\(646\) 50.1106 1.97157
\(647\) 22.0340 0.866246 0.433123 0.901335i \(-0.357412\pi\)
0.433123 + 0.901335i \(0.357412\pi\)
\(648\) −7.42849 −0.291819
\(649\) −12.3975 −0.486646
\(650\) 10.1196 0.396922
\(651\) −5.24081 −0.205404
\(652\) 14.1296 0.553358
\(653\) −40.6267 −1.58985 −0.794923 0.606710i \(-0.792489\pi\)
−0.794923 + 0.606710i \(0.792489\pi\)
\(654\) 27.5488 1.07724
\(655\) 15.2823 0.597127
\(656\) 0.883579 0.0344980
\(657\) −49.1979 −1.91939
\(658\) 3.60751 0.140636
\(659\) −29.4560 −1.14744 −0.573721 0.819051i \(-0.694501\pi\)
−0.573721 + 0.819051i \(0.694501\pi\)
\(660\) −21.7855 −0.848001
\(661\) −19.2038 −0.746940 −0.373470 0.927642i \(-0.621832\pi\)
−0.373470 + 0.927642i \(0.621832\pi\)
\(662\) 14.8604 0.577566
\(663\) −9.25983 −0.359622
\(664\) −3.78972 −0.147070
\(665\) 1.15497 0.0447877
\(666\) 8.08095 0.313130
\(667\) −23.1744 −0.897317
\(668\) 74.2500 2.87282
\(669\) −5.15924 −0.199468
\(670\) 4.84670 0.187244
\(671\) 37.2742 1.43895
\(672\) 4.12042 0.158949
\(673\) 24.0230 0.926018 0.463009 0.886353i \(-0.346770\pi\)
0.463009 + 0.886353i \(0.346770\pi\)
\(674\) 13.4644 0.518628
\(675\) −29.1145 −1.12062
\(676\) 3.12222 0.120085
\(677\) −31.2762 −1.20204 −0.601022 0.799233i \(-0.705240\pi\)
−0.601022 + 0.799233i \(0.705240\pi\)
\(678\) −102.325 −3.92977
\(679\) 1.25199 0.0480471
\(680\) 5.94838 0.228110
\(681\) 28.1618 1.07916
\(682\) −59.5992 −2.28217
\(683\) 27.7739 1.06274 0.531368 0.847141i \(-0.321678\pi\)
0.531368 + 0.847141i \(0.321678\pi\)
\(684\) 112.999 4.32062
\(685\) 3.04550 0.116363
\(686\) 7.29357 0.278470
\(687\) −57.0925 −2.17821
\(688\) 5.32562 0.203037
\(689\) −13.4534 −0.512532
\(690\) −26.8938 −1.02383
\(691\) 17.4490 0.663791 0.331896 0.943316i \(-0.392312\pi\)
0.331896 + 0.943316i \(0.392312\pi\)
\(692\) 26.4908 1.00703
\(693\) −4.06080 −0.154257
\(694\) 24.4360 0.927576
\(695\) −1.19441 −0.0453065
\(696\) 29.7674 1.12833
\(697\) 5.73557 0.217250
\(698\) −13.7934 −0.522088
\(699\) −60.5870 −2.29161
\(700\) −3.22581 −0.121924
\(701\) 34.0334 1.28542 0.642712 0.766108i \(-0.277809\pi\)
0.642712 + 0.766108i \(0.277809\pi\)
\(702\) −14.7369 −0.556208
\(703\) −4.66183 −0.175824
\(704\) 43.5455 1.64118
\(705\) −14.4200 −0.543089
\(706\) 32.4740 1.22217
\(707\) 2.32121 0.0872981
\(708\) 33.3382 1.25293
\(709\) −9.92587 −0.372774 −0.186387 0.982476i \(-0.559678\pi\)
−0.186387 + 0.982476i \(0.559678\pi\)
\(710\) −7.69205 −0.288677
\(711\) −56.9537 −2.13593
\(712\) 18.5465 0.695060
\(713\) −44.8466 −1.67952
\(714\) 4.84256 0.181228
\(715\) −2.42709 −0.0907679
\(716\) −11.5681 −0.432319
\(717\) 85.2637 3.18423
\(718\) 16.3447 0.609980
\(719\) −22.7950 −0.850110 −0.425055 0.905168i \(-0.639745\pi\)
−0.425055 + 0.905168i \(0.639745\pi\)
\(720\) −1.89957 −0.0707928
\(721\) 2.86967 0.106872
\(722\) −63.9443 −2.37976
\(723\) 15.1485 0.563377
\(724\) 65.2996 2.42684
\(725\) 18.2284 0.676985
\(726\) −0.921883 −0.0342143
\(727\) 12.8379 0.476132 0.238066 0.971249i \(-0.423487\pi\)
0.238066 + 0.971249i \(0.423487\pi\)
\(728\) −0.586879 −0.0217512
\(729\) −40.7600 −1.50963
\(730\) 15.3777 0.569154
\(731\) 34.5702 1.27862
\(732\) −100.234 −3.70476
\(733\) 31.0559 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(734\) −55.6901 −2.05556
\(735\) −14.5212 −0.535622
\(736\) 35.2592 1.29967
\(737\) 9.83066 0.362117
\(738\) 21.2186 0.781067
\(739\) −19.5811 −0.720302 −0.360151 0.932894i \(-0.617275\pi\)
−0.360151 + 0.932894i \(0.617275\pi\)
\(740\) −1.53962 −0.0565974
\(741\) 19.7623 0.725986
\(742\) 7.03562 0.258286
\(743\) 20.3408 0.746232 0.373116 0.927785i \(-0.378289\pi\)
0.373116 + 0.927785i \(0.378289\pi\)
\(744\) 57.6052 2.11191
\(745\) 0.569127 0.0208512
\(746\) −34.8723 −1.27677
\(747\) 7.85588 0.287432
\(748\) 33.5677 1.22736
\(749\) −3.45619 −0.126287
\(750\) 44.8092 1.63620
\(751\) −25.8205 −0.942204 −0.471102 0.882079i \(-0.656144\pi\)
−0.471102 + 0.882079i \(0.656144\pi\)
\(752\) 3.42285 0.124819
\(753\) 17.7324 0.646206
\(754\) 9.22666 0.336015
\(755\) 6.41630 0.233513
\(756\) 4.69767 0.170853
\(757\) 38.1845 1.38784 0.693920 0.720052i \(-0.255882\pi\)
0.693920 + 0.720052i \(0.255882\pi\)
\(758\) −38.0854 −1.38332
\(759\) −54.5492 −1.98001
\(760\) −12.6950 −0.460496
\(761\) −18.3843 −0.666432 −0.333216 0.942851i \(-0.608134\pi\)
−0.333216 + 0.942851i \(0.608134\pi\)
\(762\) 112.118 4.06160
\(763\) −0.978355 −0.0354188
\(764\) −31.1957 −1.12862
\(765\) −12.3307 −0.445816
\(766\) −3.79764 −0.137214
\(767\) 3.71415 0.134110
\(768\) −36.3826 −1.31284
\(769\) −41.9478 −1.51268 −0.756339 0.654180i \(-0.773014\pi\)
−0.756339 + 0.654180i \(0.773014\pi\)
\(770\) 1.26928 0.0457416
\(771\) −8.69321 −0.313078
\(772\) 62.3113 2.24263
\(773\) −2.88745 −0.103854 −0.0519272 0.998651i \(-0.516536\pi\)
−0.0519272 + 0.998651i \(0.516536\pi\)
\(774\) 127.891 4.59696
\(775\) 35.2751 1.26712
\(776\) −13.7615 −0.494009
\(777\) −0.450508 −0.0161619
\(778\) −10.6381 −0.381394
\(779\) −12.2408 −0.438573
\(780\) 6.52669 0.233693
\(781\) −15.6019 −0.558281
\(782\) 41.4386 1.48184
\(783\) −26.5456 −0.948662
\(784\) 3.44687 0.123102
\(785\) −7.68741 −0.274375
\(786\) −136.750 −4.87770
\(787\) −40.8556 −1.45634 −0.728172 0.685394i \(-0.759630\pi\)
−0.728172 + 0.685394i \(0.759630\pi\)
\(788\) 35.0151 1.24736
\(789\) 37.2508 1.32616
\(790\) 17.8019 0.633365
\(791\) 3.63392 0.129207
\(792\) 44.6349 1.58603
\(793\) −11.1669 −0.396548
\(794\) 26.7395 0.948949
\(795\) −28.1229 −0.997417
\(796\) 14.9953 0.531493
\(797\) −2.94119 −0.104182 −0.0520911 0.998642i \(-0.516589\pi\)
−0.0520911 + 0.998642i \(0.516589\pi\)
\(798\) −10.3350 −0.365854
\(799\) 22.2187 0.786043
\(800\) −27.7340 −0.980543
\(801\) −38.4459 −1.35842
\(802\) 64.2902 2.27017
\(803\) 31.1909 1.10070
\(804\) −26.4357 −0.932314
\(805\) 0.955093 0.0336626
\(806\) 17.8552 0.628923
\(807\) −15.8892 −0.559327
\(808\) −25.5139 −0.897577
\(809\) −36.1523 −1.27105 −0.635523 0.772082i \(-0.719215\pi\)
−0.635523 + 0.772082i \(0.719215\pi\)
\(810\) −4.81319 −0.169118
\(811\) 15.1272 0.531187 0.265593 0.964085i \(-0.414432\pi\)
0.265593 + 0.964085i \(0.414432\pi\)
\(812\) −2.94118 −0.103215
\(813\) −14.2381 −0.499350
\(814\) −5.12323 −0.179569
\(815\) 3.29061 0.115265
\(816\) 4.59468 0.160846
\(817\) −73.7795 −2.58122
\(818\) 13.6839 0.478446
\(819\) 1.21657 0.0425103
\(820\) −4.04265 −0.141176
\(821\) −53.7149 −1.87466 −0.937331 0.348440i \(-0.886711\pi\)
−0.937331 + 0.348440i \(0.886711\pi\)
\(822\) −27.2520 −0.950523
\(823\) −16.5464 −0.576771 −0.288385 0.957514i \(-0.593118\pi\)
−0.288385 + 0.957514i \(0.593118\pi\)
\(824\) −31.5424 −1.09883
\(825\) 42.9070 1.49383
\(826\) −1.94237 −0.0675836
\(827\) 32.1477 1.11788 0.558942 0.829207i \(-0.311208\pi\)
0.558942 + 0.829207i \(0.311208\pi\)
\(828\) 93.4437 3.24739
\(829\) 36.6747 1.27376 0.636882 0.770961i \(-0.280224\pi\)
0.636882 + 0.770961i \(0.280224\pi\)
\(830\) −2.45550 −0.0852316
\(831\) −30.1760 −1.04679
\(832\) −13.0457 −0.452278
\(833\) 22.3746 0.775235
\(834\) 10.6879 0.370091
\(835\) 17.2919 0.598412
\(836\) −71.6400 −2.47772
\(837\) −51.3704 −1.77562
\(838\) 67.0071 2.31472
\(839\) −24.5399 −0.847212 −0.423606 0.905846i \(-0.639236\pi\)
−0.423606 + 0.905846i \(0.639236\pi\)
\(840\) −1.22681 −0.0423291
\(841\) −12.3800 −0.426897
\(842\) −11.9369 −0.411372
\(843\) 30.0161 1.03381
\(844\) −20.1830 −0.694726
\(845\) 0.727126 0.0250139
\(846\) 82.1975 2.82601
\(847\) 0.0327393 0.00112494
\(848\) 6.67548 0.229237
\(849\) 39.0818 1.34129
\(850\) −32.5945 −1.11798
\(851\) −3.85508 −0.132150
\(852\) 41.9552 1.43736
\(853\) −47.5215 −1.62710 −0.813552 0.581492i \(-0.802469\pi\)
−0.813552 + 0.581492i \(0.802469\pi\)
\(854\) 5.83989 0.199837
\(855\) 26.3160 0.899989
\(856\) 37.9893 1.29845
\(857\) 56.4179 1.92720 0.963600 0.267349i \(-0.0861476\pi\)
0.963600 + 0.267349i \(0.0861476\pi\)
\(858\) 21.7182 0.741448
\(859\) −31.8299 −1.08602 −0.543011 0.839726i \(-0.682716\pi\)
−0.543011 + 0.839726i \(0.682716\pi\)
\(860\) −24.3664 −0.830887
\(861\) −1.18292 −0.0403139
\(862\) −4.98858 −0.169912
\(863\) −20.4909 −0.697518 −0.348759 0.937212i \(-0.613397\pi\)
−0.348759 + 0.937212i \(0.613397\pi\)
\(864\) 40.3884 1.37404
\(865\) 6.16937 0.209765
\(866\) 69.7306 2.36954
\(867\) −19.0476 −0.646890
\(868\) −5.69169 −0.193189
\(869\) 36.1081 1.22488
\(870\) 19.2874 0.653905
\(871\) −2.94515 −0.0997926
\(872\) 10.7537 0.364168
\(873\) 28.5268 0.965487
\(874\) −88.4381 −2.99146
\(875\) −1.59133 −0.0537969
\(876\) −83.8756 −2.83389
\(877\) −12.5402 −0.423452 −0.211726 0.977329i \(-0.567908\pi\)
−0.211726 + 0.977329i \(0.567908\pi\)
\(878\) 3.94312 0.133074
\(879\) −51.3957 −1.73353
\(880\) 1.20431 0.0405972
\(881\) −7.60706 −0.256288 −0.128144 0.991756i \(-0.540902\pi\)
−0.128144 + 0.991756i \(0.540902\pi\)
\(882\) 82.7743 2.78715
\(883\) −38.5940 −1.29879 −0.649396 0.760450i \(-0.724978\pi\)
−0.649396 + 0.760450i \(0.724978\pi\)
\(884\) −10.0565 −0.338236
\(885\) 7.76407 0.260986
\(886\) 16.0150 0.538034
\(887\) −43.4524 −1.45899 −0.729495 0.683986i \(-0.760245\pi\)
−0.729495 + 0.683986i \(0.760245\pi\)
\(888\) 4.95183 0.166172
\(889\) −3.98170 −0.133542
\(890\) 12.0170 0.402810
\(891\) −9.76270 −0.327063
\(892\) −5.60311 −0.187606
\(893\) −47.4191 −1.58682
\(894\) −5.09270 −0.170325
\(895\) −2.69406 −0.0900526
\(896\) 3.95593 0.132158
\(897\) 16.3423 0.545654
\(898\) −6.97347 −0.232708
\(899\) 32.1626 1.07268
\(900\) −73.5003 −2.45001
\(901\) 43.3325 1.44362
\(902\) −13.4523 −0.447914
\(903\) −7.12986 −0.237267
\(904\) −39.9428 −1.32848
\(905\) 15.2075 0.505514
\(906\) −57.4148 −1.90748
\(907\) −4.21894 −0.140088 −0.0700439 0.997544i \(-0.522314\pi\)
−0.0700439 + 0.997544i \(0.522314\pi\)
\(908\) 30.5847 1.01499
\(909\) 52.8890 1.75422
\(910\) −0.380261 −0.0126055
\(911\) −29.4628 −0.976147 −0.488073 0.872803i \(-0.662300\pi\)
−0.488073 + 0.872803i \(0.662300\pi\)
\(912\) −9.80593 −0.324707
\(913\) −4.98054 −0.164832
\(914\) −66.2181 −2.19030
\(915\) −23.3433 −0.771706
\(916\) −62.0044 −2.04868
\(917\) 4.85647 0.160375
\(918\) 47.4667 1.56664
\(919\) −23.8998 −0.788382 −0.394191 0.919029i \(-0.628975\pi\)
−0.394191 + 0.919029i \(0.628975\pi\)
\(920\) −10.4981 −0.346111
\(921\) −25.3559 −0.835504
\(922\) 48.4565 1.59583
\(923\) 4.67416 0.153852
\(924\) −6.92311 −0.227754
\(925\) 3.03230 0.0997014
\(926\) 0.388289 0.0127600
\(927\) 65.3857 2.14755
\(928\) −25.2868 −0.830081
\(929\) 45.3090 1.48654 0.743271 0.668991i \(-0.233274\pi\)
0.743271 + 0.668991i \(0.233274\pi\)
\(930\) 37.3245 1.22392
\(931\) −47.7518 −1.56500
\(932\) −65.7995 −2.15533
\(933\) 36.7099 1.20183
\(934\) −0.991557 −0.0324447
\(935\) 7.81751 0.255660
\(936\) −13.3721 −0.437081
\(937\) −7.03101 −0.229693 −0.114847 0.993383i \(-0.536638\pi\)
−0.114847 + 0.993383i \(0.536638\pi\)
\(938\) 1.54021 0.0502895
\(939\) −44.2154 −1.44291
\(940\) −15.6606 −0.510793
\(941\) 45.0322 1.46801 0.734004 0.679146i \(-0.237650\pi\)
0.734004 + 0.679146i \(0.237650\pi\)
\(942\) 68.7890 2.24127
\(943\) −10.1225 −0.329633
\(944\) −1.84294 −0.0599826
\(945\) 1.09403 0.0355888
\(946\) −81.0817 −2.63619
\(947\) 16.5944 0.539246 0.269623 0.962966i \(-0.413101\pi\)
0.269623 + 0.962966i \(0.413101\pi\)
\(948\) −97.0983 −3.15361
\(949\) −9.34443 −0.303333
\(950\) 69.5631 2.25692
\(951\) −72.3526 −2.34619
\(952\) 1.89030 0.0612651
\(953\) −6.82136 −0.220965 −0.110483 0.993878i \(-0.535240\pi\)
−0.110483 + 0.993878i \(0.535240\pi\)
\(954\) 160.307 5.19014
\(955\) −7.26510 −0.235093
\(956\) 92.5992 2.99487
\(957\) 39.1211 1.26460
\(958\) −49.8837 −1.61167
\(959\) 0.967815 0.0312524
\(960\) −27.2708 −0.880160
\(961\) 31.2403 1.00775
\(962\) 1.53486 0.0494859
\(963\) −78.7497 −2.53767
\(964\) 16.4517 0.529874
\(965\) 14.5115 0.467143
\(966\) −8.54643 −0.274977
\(967\) −11.8405 −0.380764 −0.190382 0.981710i \(-0.560973\pi\)
−0.190382 + 0.981710i \(0.560973\pi\)
\(968\) −0.359859 −0.0115663
\(969\) −63.6532 −2.04484
\(970\) −8.91658 −0.286294
\(971\) −21.0574 −0.675764 −0.337882 0.941189i \(-0.609710\pi\)
−0.337882 + 0.941189i \(0.609710\pi\)
\(972\) −34.7375 −1.11420
\(973\) −0.379565 −0.0121683
\(974\) −7.26910 −0.232917
\(975\) −12.8544 −0.411671
\(976\) 5.54095 0.177362
\(977\) −26.8184 −0.857996 −0.428998 0.903305i \(-0.641133\pi\)
−0.428998 + 0.903305i \(0.641133\pi\)
\(978\) −29.4453 −0.941556
\(979\) 24.3743 0.779005
\(980\) −15.7705 −0.503770
\(981\) −22.2919 −0.711726
\(982\) −90.0935 −2.87500
\(983\) −10.5295 −0.335839 −0.167920 0.985801i \(-0.553705\pi\)
−0.167920 + 0.985801i \(0.553705\pi\)
\(984\) 13.0023 0.414497
\(985\) 8.15459 0.259827
\(986\) −29.7186 −0.946431
\(987\) −4.58246 −0.145861
\(988\) 21.4625 0.682813
\(989\) −61.0115 −1.94005
\(990\) 28.9206 0.919158
\(991\) −1.12636 −0.0357799 −0.0178900 0.999840i \(-0.505695\pi\)
−0.0178900 + 0.999840i \(0.505695\pi\)
\(992\) −48.9345 −1.55367
\(993\) −18.8765 −0.599028
\(994\) −2.44441 −0.0775321
\(995\) 3.49222 0.110711
\(996\) 13.3932 0.424380
\(997\) 28.5834 0.905247 0.452623 0.891702i \(-0.350488\pi\)
0.452623 + 0.891702i \(0.350488\pi\)
\(998\) 46.3964 1.46865
\(999\) −4.41587 −0.139712
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 \(a_p\))