Properties

Label 8007.2.a.e.1.6
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.38281 q^{2}\) \(+1.00000 q^{3}\) \(+3.67776 q^{4}\) \(-2.44898 q^{5}\) \(-2.38281 q^{6}\) \(-2.76989 q^{7}\) \(-3.99778 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.38281 q^{2}\) \(+1.00000 q^{3}\) \(+3.67776 q^{4}\) \(-2.44898 q^{5}\) \(-2.38281 q^{6}\) \(-2.76989 q^{7}\) \(-3.99778 q^{8}\) \(+1.00000 q^{9}\) \(+5.83545 q^{10}\) \(+5.16191 q^{11}\) \(+3.67776 q^{12}\) \(+5.84979 q^{13}\) \(+6.60012 q^{14}\) \(-2.44898 q^{15}\) \(+2.17041 q^{16}\) \(-1.00000 q^{17}\) \(-2.38281 q^{18}\) \(+7.85558 q^{19}\) \(-9.00677 q^{20}\) \(-2.76989 q^{21}\) \(-12.2998 q^{22}\) \(-7.69237 q^{23}\) \(-3.99778 q^{24}\) \(+0.997513 q^{25}\) \(-13.9389 q^{26}\) \(+1.00000 q^{27}\) \(-10.1870 q^{28}\) \(-0.463832 q^{29}\) \(+5.83545 q^{30}\) \(-0.798135 q^{31}\) \(+2.82389 q^{32}\) \(+5.16191 q^{33}\) \(+2.38281 q^{34}\) \(+6.78342 q^{35}\) \(+3.67776 q^{36}\) \(-2.00510 q^{37}\) \(-18.7183 q^{38}\) \(+5.84979 q^{39}\) \(+9.79050 q^{40}\) \(-12.4259 q^{41}\) \(+6.60012 q^{42}\) \(-7.76567 q^{43}\) \(+18.9843 q^{44}\) \(-2.44898 q^{45}\) \(+18.3294 q^{46}\) \(+2.81407 q^{47}\) \(+2.17041 q^{48}\) \(+0.672308 q^{49}\) \(-2.37688 q^{50}\) \(-1.00000 q^{51}\) \(+21.5142 q^{52}\) \(+10.3695 q^{53}\) \(-2.38281 q^{54}\) \(-12.6414 q^{55}\) \(+11.0734 q^{56}\) \(+7.85558 q^{57}\) \(+1.10522 q^{58}\) \(-4.14917 q^{59}\) \(-9.00677 q^{60}\) \(+0.116552 q^{61}\) \(+1.90180 q^{62}\) \(-2.76989 q^{63}\) \(-11.0696 q^{64}\) \(-14.3260 q^{65}\) \(-12.2998 q^{66}\) \(+1.94065 q^{67}\) \(-3.67776 q^{68}\) \(-7.69237 q^{69}\) \(-16.1636 q^{70}\) \(-13.9424 q^{71}\) \(-3.99778 q^{72}\) \(-13.9824 q^{73}\) \(+4.77776 q^{74}\) \(+0.997513 q^{75}\) \(+28.8910 q^{76}\) \(-14.2980 q^{77}\) \(-13.9389 q^{78}\) \(+4.88266 q^{79}\) \(-5.31530 q^{80}\) \(+1.00000 q^{81}\) \(+29.6086 q^{82}\) \(-9.14988 q^{83}\) \(-10.1870 q^{84}\) \(+2.44898 q^{85}\) \(+18.5041 q^{86}\) \(-0.463832 q^{87}\) \(-20.6362 q^{88}\) \(-2.81073 q^{89}\) \(+5.83545 q^{90}\) \(-16.2033 q^{91}\) \(-28.2907 q^{92}\) \(-0.798135 q^{93}\) \(-6.70538 q^{94}\) \(-19.2382 q^{95}\) \(+2.82389 q^{96}\) \(+15.3999 q^{97}\) \(-1.60198 q^{98}\) \(+5.16191 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38281 −1.68490 −0.842449 0.538776i \(-0.818887\pi\)
−0.842449 + 0.538776i \(0.818887\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.67776 1.83888
\(5\) −2.44898 −1.09522 −0.547609 0.836734i \(-0.684462\pi\)
−0.547609 + 0.836734i \(0.684462\pi\)
\(6\) −2.38281 −0.972776
\(7\) −2.76989 −1.04692 −0.523461 0.852050i \(-0.675359\pi\)
−0.523461 + 0.852050i \(0.675359\pi\)
\(8\) −3.99778 −1.41343
\(9\) 1.00000 0.333333
\(10\) 5.83545 1.84533
\(11\) 5.16191 1.55638 0.778188 0.628032i \(-0.216139\pi\)
0.778188 + 0.628032i \(0.216139\pi\)
\(12\) 3.67776 1.06168
\(13\) 5.84979 1.62244 0.811220 0.584741i \(-0.198804\pi\)
0.811220 + 0.584741i \(0.198804\pi\)
\(14\) 6.60012 1.76396
\(15\) −2.44898 −0.632324
\(16\) 2.17041 0.542603
\(17\) −1.00000 −0.242536
\(18\) −2.38281 −0.561633
\(19\) 7.85558 1.80219 0.901097 0.433618i \(-0.142763\pi\)
0.901097 + 0.433618i \(0.142763\pi\)
\(20\) −9.00677 −2.01398
\(21\) −2.76989 −0.604440
\(22\) −12.2998 −2.62233
\(23\) −7.69237 −1.60397 −0.801985 0.597344i \(-0.796223\pi\)
−0.801985 + 0.597344i \(0.796223\pi\)
\(24\) −3.99778 −0.816044
\(25\) 0.997513 0.199503
\(26\) −13.9389 −2.73365
\(27\) 1.00000 0.192450
\(28\) −10.1870 −1.92516
\(29\) −0.463832 −0.0861315 −0.0430658 0.999072i \(-0.513712\pi\)
−0.0430658 + 0.999072i \(0.513712\pi\)
\(30\) 5.83545 1.06540
\(31\) −0.798135 −0.143349 −0.0716746 0.997428i \(-0.522834\pi\)
−0.0716746 + 0.997428i \(0.522834\pi\)
\(32\) 2.82389 0.499199
\(33\) 5.16191 0.898574
\(34\) 2.38281 0.408648
\(35\) 6.78342 1.14661
\(36\) 3.67776 0.612960
\(37\) −2.00510 −0.329636 −0.164818 0.986324i \(-0.552704\pi\)
−0.164818 + 0.986324i \(0.552704\pi\)
\(38\) −18.7183 −3.03651
\(39\) 5.84979 0.936717
\(40\) 9.79050 1.54801
\(41\) −12.4259 −1.94060 −0.970301 0.241899i \(-0.922230\pi\)
−0.970301 + 0.241899i \(0.922230\pi\)
\(42\) 6.60012 1.01842
\(43\) −7.76567 −1.18425 −0.592127 0.805845i \(-0.701712\pi\)
−0.592127 + 0.805845i \(0.701712\pi\)
\(44\) 18.9843 2.86199
\(45\) −2.44898 −0.365073
\(46\) 18.3294 2.70253
\(47\) 2.81407 0.410474 0.205237 0.978712i \(-0.434203\pi\)
0.205237 + 0.978712i \(0.434203\pi\)
\(48\) 2.17041 0.313272
\(49\) 0.672308 0.0960439
\(50\) −2.37688 −0.336142
\(51\) −1.00000 −0.140028
\(52\) 21.5142 2.98348
\(53\) 10.3695 1.42436 0.712182 0.701995i \(-0.247707\pi\)
0.712182 + 0.701995i \(0.247707\pi\)
\(54\) −2.38281 −0.324259
\(55\) −12.6414 −1.70457
\(56\) 11.0734 1.47975
\(57\) 7.85558 1.04050
\(58\) 1.10522 0.145123
\(59\) −4.14917 −0.540175 −0.270088 0.962836i \(-0.587053\pi\)
−0.270088 + 0.962836i \(0.587053\pi\)
\(60\) −9.00677 −1.16277
\(61\) 0.116552 0.0149230 0.00746148 0.999972i \(-0.497625\pi\)
0.00746148 + 0.999972i \(0.497625\pi\)
\(62\) 1.90180 0.241529
\(63\) −2.76989 −0.348974
\(64\) −11.0696 −1.38370
\(65\) −14.3260 −1.77693
\(66\) −12.2998 −1.51401
\(67\) 1.94065 0.237088 0.118544 0.992949i \(-0.462177\pi\)
0.118544 + 0.992949i \(0.462177\pi\)
\(68\) −3.67776 −0.445994
\(69\) −7.69237 −0.926052
\(70\) −16.1636 −1.93192
\(71\) −13.9424 −1.65466 −0.827329 0.561717i \(-0.810141\pi\)
−0.827329 + 0.561717i \(0.810141\pi\)
\(72\) −3.99778 −0.471143
\(73\) −13.9824 −1.63652 −0.818259 0.574850i \(-0.805060\pi\)
−0.818259 + 0.574850i \(0.805060\pi\)
\(74\) 4.77776 0.555403
\(75\) 0.997513 0.115183
\(76\) 28.8910 3.31402
\(77\) −14.2980 −1.62940
\(78\) −13.9389 −1.57827
\(79\) 4.88266 0.549342 0.274671 0.961538i \(-0.411431\pi\)
0.274671 + 0.961538i \(0.411431\pi\)
\(80\) −5.31530 −0.594269
\(81\) 1.00000 0.111111
\(82\) 29.6086 3.26972
\(83\) −9.14988 −1.00433 −0.502165 0.864772i \(-0.667463\pi\)
−0.502165 + 0.864772i \(0.667463\pi\)
\(84\) −10.1870 −1.11149
\(85\) 2.44898 0.265629
\(86\) 18.5041 1.99535
\(87\) −0.463832 −0.0497281
\(88\) −20.6362 −2.19983
\(89\) −2.81073 −0.297937 −0.148968 0.988842i \(-0.547595\pi\)
−0.148968 + 0.988842i \(0.547595\pi\)
\(90\) 5.83545 0.615110
\(91\) −16.2033 −1.69857
\(92\) −28.2907 −2.94951
\(93\) −0.798135 −0.0827627
\(94\) −6.70538 −0.691607
\(95\) −19.2382 −1.97379
\(96\) 2.82389 0.288212
\(97\) 15.3999 1.56362 0.781811 0.623515i \(-0.214296\pi\)
0.781811 + 0.623515i \(0.214296\pi\)
\(98\) −1.60198 −0.161824
\(99\) 5.16191 0.518792
\(100\) 3.66862 0.366862
\(101\) 12.2940 1.22330 0.611652 0.791127i \(-0.290505\pi\)
0.611652 + 0.791127i \(0.290505\pi\)
\(102\) 2.38281 0.235933
\(103\) 14.6573 1.44423 0.722114 0.691774i \(-0.243170\pi\)
0.722114 + 0.691774i \(0.243170\pi\)
\(104\) −23.3862 −2.29321
\(105\) 6.78342 0.661994
\(106\) −24.7086 −2.39991
\(107\) −0.457810 −0.0442582 −0.0221291 0.999755i \(-0.507044\pi\)
−0.0221291 + 0.999755i \(0.507044\pi\)
\(108\) 3.67776 0.353893
\(109\) −8.89691 −0.852169 −0.426085 0.904683i \(-0.640107\pi\)
−0.426085 + 0.904683i \(0.640107\pi\)
\(110\) 30.1221 2.87203
\(111\) −2.00510 −0.190315
\(112\) −6.01181 −0.568063
\(113\) −19.9970 −1.88116 −0.940578 0.339578i \(-0.889716\pi\)
−0.940578 + 0.339578i \(0.889716\pi\)
\(114\) −18.7183 −1.75313
\(115\) 18.8385 1.75670
\(116\) −1.70587 −0.158386
\(117\) 5.84979 0.540814
\(118\) 9.88666 0.910140
\(119\) 2.76989 0.253916
\(120\) 9.79050 0.893746
\(121\) 15.6454 1.42231
\(122\) −0.277721 −0.0251437
\(123\) −12.4259 −1.12041
\(124\) −2.93535 −0.263602
\(125\) 9.80202 0.876719
\(126\) 6.60012 0.587985
\(127\) 11.0946 0.984490 0.492245 0.870457i \(-0.336176\pi\)
0.492245 + 0.870457i \(0.336176\pi\)
\(128\) 20.7290 1.83220
\(129\) −7.76567 −0.683730
\(130\) 34.1362 2.99394
\(131\) −9.22883 −0.806327 −0.403164 0.915128i \(-0.632089\pi\)
−0.403164 + 0.915128i \(0.632089\pi\)
\(132\) 18.9843 1.65237
\(133\) −21.7591 −1.88675
\(134\) −4.62418 −0.399469
\(135\) −2.44898 −0.210775
\(136\) 3.99778 0.342807
\(137\) −12.5510 −1.07231 −0.536154 0.844120i \(-0.680123\pi\)
−0.536154 + 0.844120i \(0.680123\pi\)
\(138\) 18.3294 1.56030
\(139\) 8.41286 0.713569 0.356785 0.934187i \(-0.383873\pi\)
0.356785 + 0.934187i \(0.383873\pi\)
\(140\) 24.9478 2.10847
\(141\) 2.81407 0.236987
\(142\) 33.2220 2.78793
\(143\) 30.1961 2.52513
\(144\) 2.17041 0.180868
\(145\) 1.13592 0.0943328
\(146\) 33.3174 2.75736
\(147\) 0.672308 0.0554510
\(148\) −7.37428 −0.606162
\(149\) 19.9930 1.63789 0.818946 0.573871i \(-0.194559\pi\)
0.818946 + 0.573871i \(0.194559\pi\)
\(150\) −2.37688 −0.194071
\(151\) −4.91248 −0.399772 −0.199886 0.979819i \(-0.564057\pi\)
−0.199886 + 0.979819i \(0.564057\pi\)
\(152\) −31.4049 −2.54727
\(153\) −1.00000 −0.0808452
\(154\) 34.0692 2.74538
\(155\) 1.95462 0.156999
\(156\) 21.5142 1.72251
\(157\) 1.00000 0.0798087
\(158\) −11.6344 −0.925586
\(159\) 10.3695 0.822357
\(160\) −6.91566 −0.546731
\(161\) 21.3070 1.67923
\(162\) −2.38281 −0.187211
\(163\) 7.89454 0.618348 0.309174 0.951005i \(-0.399947\pi\)
0.309174 + 0.951005i \(0.399947\pi\)
\(164\) −45.6996 −3.56854
\(165\) −12.6414 −0.984135
\(166\) 21.8024 1.69219
\(167\) −7.88959 −0.610514 −0.305257 0.952270i \(-0.598742\pi\)
−0.305257 + 0.952270i \(0.598742\pi\)
\(168\) 11.0734 0.854334
\(169\) 21.2201 1.63231
\(170\) −5.83545 −0.447558
\(171\) 7.85558 0.600731
\(172\) −28.5603 −2.17770
\(173\) −12.4726 −0.948274 −0.474137 0.880451i \(-0.657240\pi\)
−0.474137 + 0.880451i \(0.657240\pi\)
\(174\) 1.10522 0.0837867
\(175\) −2.76301 −0.208864
\(176\) 11.2035 0.844494
\(177\) −4.14917 −0.311870
\(178\) 6.69742 0.501993
\(179\) −1.14945 −0.0859141 −0.0429571 0.999077i \(-0.513678\pi\)
−0.0429571 + 0.999077i \(0.513678\pi\)
\(180\) −9.00677 −0.671325
\(181\) 21.2259 1.57771 0.788855 0.614579i \(-0.210674\pi\)
0.788855 + 0.614579i \(0.210674\pi\)
\(182\) 38.6093 2.86191
\(183\) 0.116552 0.00861578
\(184\) 30.7524 2.26710
\(185\) 4.91045 0.361023
\(186\) 1.90180 0.139447
\(187\) −5.16191 −0.377477
\(188\) 10.3495 0.754813
\(189\) −2.76989 −0.201480
\(190\) 45.8408 3.32564
\(191\) 8.34597 0.603893 0.301947 0.953325i \(-0.402364\pi\)
0.301947 + 0.953325i \(0.402364\pi\)
\(192\) −11.0696 −0.798881
\(193\) −20.2571 −1.45814 −0.729070 0.684439i \(-0.760047\pi\)
−0.729070 + 0.684439i \(0.760047\pi\)
\(194\) −36.6950 −2.63454
\(195\) −14.3260 −1.02591
\(196\) 2.47259 0.176613
\(197\) 10.3346 0.736311 0.368155 0.929764i \(-0.379989\pi\)
0.368155 + 0.929764i \(0.379989\pi\)
\(198\) −12.2998 −0.874112
\(199\) 11.0351 0.782258 0.391129 0.920336i \(-0.372085\pi\)
0.391129 + 0.920336i \(0.372085\pi\)
\(200\) −3.98784 −0.281983
\(201\) 1.94065 0.136883
\(202\) −29.2943 −2.06114
\(203\) 1.28477 0.0901729
\(204\) −3.67776 −0.257495
\(205\) 30.4309 2.12538
\(206\) −34.9256 −2.43338
\(207\) −7.69237 −0.534657
\(208\) 12.6965 0.880341
\(209\) 40.5498 2.80489
\(210\) −16.1636 −1.11539
\(211\) −6.17433 −0.425058 −0.212529 0.977155i \(-0.568170\pi\)
−0.212529 + 0.977155i \(0.568170\pi\)
\(212\) 38.1366 2.61924
\(213\) −13.9424 −0.955318
\(214\) 1.09087 0.0745705
\(215\) 19.0180 1.29702
\(216\) −3.99778 −0.272015
\(217\) 2.21075 0.150075
\(218\) 21.1996 1.43582
\(219\) −13.9824 −0.944844
\(220\) −46.4922 −3.13450
\(221\) −5.84979 −0.393500
\(222\) 4.77776 0.320662
\(223\) −9.75096 −0.652972 −0.326486 0.945202i \(-0.605865\pi\)
−0.326486 + 0.945202i \(0.605865\pi\)
\(224\) −7.82188 −0.522622
\(225\) 0.997513 0.0665009
\(226\) 47.6489 3.16956
\(227\) 9.73180 0.645922 0.322961 0.946412i \(-0.395322\pi\)
0.322961 + 0.946412i \(0.395322\pi\)
\(228\) 28.8910 1.91335
\(229\) −9.11556 −0.602373 −0.301186 0.953565i \(-0.597383\pi\)
−0.301186 + 0.953565i \(0.597383\pi\)
\(230\) −44.8884 −2.95986
\(231\) −14.2980 −0.940736
\(232\) 1.85430 0.121741
\(233\) −9.51003 −0.623022 −0.311511 0.950242i \(-0.600835\pi\)
−0.311511 + 0.950242i \(0.600835\pi\)
\(234\) −13.9389 −0.911216
\(235\) −6.89160 −0.449559
\(236\) −15.2596 −0.993318
\(237\) 4.88266 0.317163
\(238\) −6.60012 −0.427822
\(239\) −16.5345 −1.06953 −0.534763 0.845002i \(-0.679599\pi\)
−0.534763 + 0.845002i \(0.679599\pi\)
\(240\) −5.31530 −0.343101
\(241\) 8.55357 0.550984 0.275492 0.961303i \(-0.411159\pi\)
0.275492 + 0.961303i \(0.411159\pi\)
\(242\) −37.2799 −2.39644
\(243\) 1.00000 0.0641500
\(244\) 0.428651 0.0274416
\(245\) −1.64647 −0.105189
\(246\) 29.6086 1.88777
\(247\) 45.9535 2.92395
\(248\) 3.19077 0.202614
\(249\) −9.14988 −0.579850
\(250\) −23.3563 −1.47718
\(251\) −4.39216 −0.277231 −0.138615 0.990346i \(-0.544265\pi\)
−0.138615 + 0.990346i \(0.544265\pi\)
\(252\) −10.1870 −0.641721
\(253\) −39.7074 −2.49638
\(254\) −26.4364 −1.65877
\(255\) 2.44898 0.153361
\(256\) −27.2538 −1.70336
\(257\) −24.4415 −1.52462 −0.762310 0.647212i \(-0.775935\pi\)
−0.762310 + 0.647212i \(0.775935\pi\)
\(258\) 18.5041 1.15201
\(259\) 5.55391 0.345103
\(260\) −52.6878 −3.26756
\(261\) −0.463832 −0.0287105
\(262\) 21.9905 1.35858
\(263\) −17.0012 −1.04834 −0.524170 0.851614i \(-0.675624\pi\)
−0.524170 + 0.851614i \(0.675624\pi\)
\(264\) −20.6362 −1.27007
\(265\) −25.3948 −1.55999
\(266\) 51.8477 3.17899
\(267\) −2.81073 −0.172014
\(268\) 7.13724 0.435976
\(269\) −5.38491 −0.328324 −0.164162 0.986433i \(-0.552492\pi\)
−0.164162 + 0.986433i \(0.552492\pi\)
\(270\) 5.83545 0.355134
\(271\) −26.0857 −1.58459 −0.792295 0.610138i \(-0.791114\pi\)
−0.792295 + 0.610138i \(0.791114\pi\)
\(272\) −2.17041 −0.131601
\(273\) −16.2033 −0.980668
\(274\) 29.9067 1.80673
\(275\) 5.14908 0.310501
\(276\) −28.2907 −1.70290
\(277\) −18.4041 −1.10580 −0.552899 0.833249i \(-0.686478\pi\)
−0.552899 + 0.833249i \(0.686478\pi\)
\(278\) −20.0462 −1.20229
\(279\) −0.798135 −0.0477831
\(280\) −27.1186 −1.62065
\(281\) 21.2812 1.26953 0.634766 0.772704i \(-0.281096\pi\)
0.634766 + 0.772704i \(0.281096\pi\)
\(282\) −6.70538 −0.399299
\(283\) −20.5187 −1.21971 −0.609854 0.792514i \(-0.708772\pi\)
−0.609854 + 0.792514i \(0.708772\pi\)
\(284\) −51.2768 −3.04272
\(285\) −19.2382 −1.13957
\(286\) −71.9515 −4.25458
\(287\) 34.4185 2.03166
\(288\) 2.82389 0.166400
\(289\) 1.00000 0.0588235
\(290\) −2.70667 −0.158941
\(291\) 15.3999 0.902758
\(292\) −51.4240 −3.00936
\(293\) 14.6928 0.858360 0.429180 0.903219i \(-0.358803\pi\)
0.429180 + 0.903219i \(0.358803\pi\)
\(294\) −1.60198 −0.0934293
\(295\) 10.1612 0.591610
\(296\) 8.01595 0.465917
\(297\) 5.16191 0.299525
\(298\) −47.6395 −2.75968
\(299\) −44.9988 −2.60235
\(300\) 3.66862 0.211808
\(301\) 21.5101 1.23982
\(302\) 11.7055 0.673574
\(303\) 12.2940 0.706274
\(304\) 17.0498 0.977876
\(305\) −0.285434 −0.0163439
\(306\) 2.38281 0.136216
\(307\) −13.2264 −0.754872 −0.377436 0.926036i \(-0.623194\pi\)
−0.377436 + 0.926036i \(0.623194\pi\)
\(308\) −52.5845 −2.99628
\(309\) 14.6573 0.833826
\(310\) −4.65748 −0.264527
\(311\) 1.56495 0.0887401 0.0443701 0.999015i \(-0.485872\pi\)
0.0443701 + 0.999015i \(0.485872\pi\)
\(312\) −23.3862 −1.32398
\(313\) −0.612868 −0.0346414 −0.0173207 0.999850i \(-0.505514\pi\)
−0.0173207 + 0.999850i \(0.505514\pi\)
\(314\) −2.38281 −0.134469
\(315\) 6.78342 0.382202
\(316\) 17.9573 1.01018
\(317\) −21.1489 −1.18784 −0.593920 0.804524i \(-0.702421\pi\)
−0.593920 + 0.804524i \(0.702421\pi\)
\(318\) −24.7086 −1.38559
\(319\) −2.39426 −0.134053
\(320\) 27.1093 1.51546
\(321\) −0.457810 −0.0255525
\(322\) −50.7705 −2.82933
\(323\) −7.85558 −0.437096
\(324\) 3.67776 0.204320
\(325\) 5.83525 0.323681
\(326\) −18.8112 −1.04185
\(327\) −8.89691 −0.492000
\(328\) 49.6761 2.74290
\(329\) −7.79467 −0.429734
\(330\) 30.1221 1.65817
\(331\) 20.0255 1.10070 0.550350 0.834934i \(-0.314494\pi\)
0.550350 + 0.834934i \(0.314494\pi\)
\(332\) −33.6511 −1.84684
\(333\) −2.00510 −0.109879
\(334\) 18.7993 1.02865
\(335\) −4.75261 −0.259663
\(336\) −6.01181 −0.327971
\(337\) −8.74188 −0.476201 −0.238100 0.971241i \(-0.576525\pi\)
−0.238100 + 0.971241i \(0.576525\pi\)
\(338\) −50.5633 −2.75028
\(339\) −19.9970 −1.08609
\(340\) 9.00677 0.488461
\(341\) −4.11990 −0.223105
\(342\) −18.7183 −1.01217
\(343\) 17.5270 0.946371
\(344\) 31.0455 1.67386
\(345\) 18.8385 1.01423
\(346\) 29.7198 1.59774
\(347\) −21.7473 −1.16745 −0.583727 0.811950i \(-0.698406\pi\)
−0.583727 + 0.811950i \(0.698406\pi\)
\(348\) −1.70587 −0.0914440
\(349\) −8.87129 −0.474870 −0.237435 0.971403i \(-0.576307\pi\)
−0.237435 + 0.971403i \(0.576307\pi\)
\(350\) 6.58370 0.351914
\(351\) 5.84979 0.312239
\(352\) 14.5767 0.776941
\(353\) 8.89442 0.473402 0.236701 0.971583i \(-0.423934\pi\)
0.236701 + 0.971583i \(0.423934\pi\)
\(354\) 9.88666 0.525470
\(355\) 34.1447 1.81221
\(356\) −10.3372 −0.547870
\(357\) 2.76989 0.146598
\(358\) 2.73892 0.144757
\(359\) −9.34646 −0.493287 −0.246644 0.969106i \(-0.579328\pi\)
−0.246644 + 0.969106i \(0.579328\pi\)
\(360\) 9.79050 0.516004
\(361\) 42.7101 2.24790
\(362\) −50.5773 −2.65828
\(363\) 15.6454 0.821169
\(364\) −59.5919 −3.12346
\(365\) 34.2427 1.79234
\(366\) −0.277721 −0.0145167
\(367\) −26.4190 −1.37906 −0.689529 0.724258i \(-0.742182\pi\)
−0.689529 + 0.724258i \(0.742182\pi\)
\(368\) −16.6956 −0.870319
\(369\) −12.4259 −0.646868
\(370\) −11.7006 −0.608288
\(371\) −28.7225 −1.49120
\(372\) −2.93535 −0.152191
\(373\) 7.26255 0.376041 0.188020 0.982165i \(-0.439793\pi\)
0.188020 + 0.982165i \(0.439793\pi\)
\(374\) 12.2998 0.636010
\(375\) 9.80202 0.506174
\(376\) −11.2500 −0.580176
\(377\) −2.71332 −0.139743
\(378\) 6.60012 0.339473
\(379\) 21.9845 1.12927 0.564633 0.825342i \(-0.309018\pi\)
0.564633 + 0.825342i \(0.309018\pi\)
\(380\) −70.7534 −3.62957
\(381\) 11.0946 0.568396
\(382\) −19.8868 −1.01750
\(383\) −6.83081 −0.349038 −0.174519 0.984654i \(-0.555837\pi\)
−0.174519 + 0.984654i \(0.555837\pi\)
\(384\) 20.7290 1.05782
\(385\) 35.0154 1.78455
\(386\) 48.2688 2.45682
\(387\) −7.76567 −0.394751
\(388\) 56.6372 2.87532
\(389\) 18.4303 0.934452 0.467226 0.884138i \(-0.345254\pi\)
0.467226 + 0.884138i \(0.345254\pi\)
\(390\) 34.1362 1.72855
\(391\) 7.69237 0.389020
\(392\) −2.68774 −0.135751
\(393\) −9.22883 −0.465533
\(394\) −24.6254 −1.24061
\(395\) −11.9575 −0.601650
\(396\) 18.9843 0.953997
\(397\) −22.5851 −1.13351 −0.566756 0.823886i \(-0.691802\pi\)
−0.566756 + 0.823886i \(0.691802\pi\)
\(398\) −26.2945 −1.31803
\(399\) −21.7591 −1.08932
\(400\) 2.16502 0.108251
\(401\) 34.3084 1.71328 0.856641 0.515914i \(-0.172547\pi\)
0.856641 + 0.515914i \(0.172547\pi\)
\(402\) −4.62418 −0.230633
\(403\) −4.66892 −0.232576
\(404\) 45.2146 2.24951
\(405\) −2.44898 −0.121691
\(406\) −3.06135 −0.151932
\(407\) −10.3501 −0.513038
\(408\) 3.99778 0.197920
\(409\) −30.8318 −1.52453 −0.762267 0.647262i \(-0.775914\pi\)
−0.762267 + 0.647262i \(0.775914\pi\)
\(410\) −72.5108 −3.58105
\(411\) −12.5510 −0.619097
\(412\) 53.9062 2.65577
\(413\) 11.4927 0.565521
\(414\) 18.3294 0.900842
\(415\) 22.4079 1.09996
\(416\) 16.5192 0.809920
\(417\) 8.41286 0.411980
\(418\) −96.6223 −4.72595
\(419\) −39.6518 −1.93712 −0.968559 0.248783i \(-0.919969\pi\)
−0.968559 + 0.248783i \(0.919969\pi\)
\(420\) 24.9478 1.21733
\(421\) 29.6186 1.44352 0.721760 0.692143i \(-0.243333\pi\)
0.721760 + 0.692143i \(0.243333\pi\)
\(422\) 14.7122 0.716180
\(423\) 2.81407 0.136825
\(424\) −41.4551 −2.01324
\(425\) −0.997513 −0.0483865
\(426\) 33.2220 1.60961
\(427\) −0.322837 −0.0156232
\(428\) −1.68372 −0.0813855
\(429\) 30.1961 1.45788
\(430\) −45.3162 −2.18534
\(431\) 1.65307 0.0796255 0.0398127 0.999207i \(-0.487324\pi\)
0.0398127 + 0.999207i \(0.487324\pi\)
\(432\) 2.17041 0.104424
\(433\) −29.9909 −1.44127 −0.720636 0.693314i \(-0.756150\pi\)
−0.720636 + 0.693314i \(0.756150\pi\)
\(434\) −5.26778 −0.252862
\(435\) 1.13592 0.0544631
\(436\) −32.7207 −1.56704
\(437\) −60.4280 −2.89066
\(438\) 33.3174 1.59197
\(439\) 12.4187 0.592712 0.296356 0.955078i \(-0.404229\pi\)
0.296356 + 0.955078i \(0.404229\pi\)
\(440\) 50.5377 2.40929
\(441\) 0.672308 0.0320146
\(442\) 13.9389 0.663007
\(443\) −18.5035 −0.879128 −0.439564 0.898211i \(-0.644867\pi\)
−0.439564 + 0.898211i \(0.644867\pi\)
\(444\) −7.37428 −0.349968
\(445\) 6.88343 0.326306
\(446\) 23.2346 1.10019
\(447\) 19.9930 0.945637
\(448\) 30.6616 1.44863
\(449\) −26.9879 −1.27364 −0.636820 0.771013i \(-0.719750\pi\)
−0.636820 + 0.771013i \(0.719750\pi\)
\(450\) −2.37688 −0.112047
\(451\) −64.1415 −3.02031
\(452\) −73.5441 −3.45922
\(453\) −4.91248 −0.230808
\(454\) −23.1890 −1.08831
\(455\) 39.6816 1.86030
\(456\) −31.4049 −1.47067
\(457\) −19.5559 −0.914788 −0.457394 0.889264i \(-0.651217\pi\)
−0.457394 + 0.889264i \(0.651217\pi\)
\(458\) 21.7206 1.01494
\(459\) −1.00000 −0.0466760
\(460\) 69.2834 3.23036
\(461\) −18.7797 −0.874659 −0.437330 0.899301i \(-0.644076\pi\)
−0.437330 + 0.899301i \(0.644076\pi\)
\(462\) 34.0692 1.58504
\(463\) 11.1471 0.518051 0.259025 0.965871i \(-0.416599\pi\)
0.259025 + 0.965871i \(0.416599\pi\)
\(464\) −1.00671 −0.0467352
\(465\) 1.95462 0.0906432
\(466\) 22.6605 1.04973
\(467\) −36.9729 −1.71090 −0.855451 0.517884i \(-0.826720\pi\)
−0.855451 + 0.517884i \(0.826720\pi\)
\(468\) 21.5142 0.994492
\(469\) −5.37538 −0.248212
\(470\) 16.4214 0.757460
\(471\) 1.00000 0.0460776
\(472\) 16.5875 0.763500
\(473\) −40.0858 −1.84314
\(474\) −11.6344 −0.534387
\(475\) 7.83604 0.359542
\(476\) 10.1870 0.466921
\(477\) 10.3695 0.474788
\(478\) 39.3985 1.80204
\(479\) 22.9894 1.05041 0.525206 0.850975i \(-0.323988\pi\)
0.525206 + 0.850975i \(0.323988\pi\)
\(480\) −6.91566 −0.315655
\(481\) −11.7294 −0.534815
\(482\) −20.3815 −0.928352
\(483\) 21.3070 0.969504
\(484\) 57.5399 2.61545
\(485\) −37.7141 −1.71251
\(486\) −2.38281 −0.108086
\(487\) 1.41970 0.0643328 0.0321664 0.999483i \(-0.489759\pi\)
0.0321664 + 0.999483i \(0.489759\pi\)
\(488\) −0.465950 −0.0210926
\(489\) 7.89454 0.357003
\(490\) 3.92322 0.177233
\(491\) 2.21101 0.0997814 0.0498907 0.998755i \(-0.484113\pi\)
0.0498907 + 0.998755i \(0.484113\pi\)
\(492\) −45.6996 −2.06030
\(493\) 0.463832 0.0208900
\(494\) −109.498 −4.92656
\(495\) −12.6414 −0.568190
\(496\) −1.73228 −0.0777818
\(497\) 38.6190 1.73230
\(498\) 21.8024 0.976988
\(499\) 28.6808 1.28393 0.641963 0.766735i \(-0.278120\pi\)
0.641963 + 0.766735i \(0.278120\pi\)
\(500\) 36.0495 1.61218
\(501\) −7.88959 −0.352481
\(502\) 10.4657 0.467105
\(503\) 5.46213 0.243544 0.121772 0.992558i \(-0.461142\pi\)
0.121772 + 0.992558i \(0.461142\pi\)
\(504\) 11.0734 0.493250
\(505\) −30.1079 −1.33978
\(506\) 94.6149 4.20615
\(507\) 21.2201 0.942417
\(508\) 40.8035 1.81036
\(509\) 27.6464 1.22540 0.612702 0.790314i \(-0.290082\pi\)
0.612702 + 0.790314i \(0.290082\pi\)
\(510\) −5.83545 −0.258398
\(511\) 38.7298 1.71330
\(512\) 23.4827 1.03780
\(513\) 7.85558 0.346832
\(514\) 58.2394 2.56883
\(515\) −35.8955 −1.58175
\(516\) −28.5603 −1.25730
\(517\) 14.5260 0.638852
\(518\) −13.2339 −0.581463
\(519\) −12.4726 −0.547486
\(520\) 57.2724 2.51156
\(521\) −43.4187 −1.90221 −0.951105 0.308869i \(-0.900049\pi\)
−0.951105 + 0.308869i \(0.900049\pi\)
\(522\) 1.10522 0.0483743
\(523\) 28.9843 1.26740 0.633698 0.773580i \(-0.281536\pi\)
0.633698 + 0.773580i \(0.281536\pi\)
\(524\) −33.9415 −1.48274
\(525\) −2.76301 −0.120587
\(526\) 40.5106 1.76634
\(527\) 0.798135 0.0347673
\(528\) 11.2035 0.487569
\(529\) 36.1725 1.57272
\(530\) 60.5108 2.62842
\(531\) −4.14917 −0.180058
\(532\) −80.0248 −3.46952
\(533\) −72.6891 −3.14851
\(534\) 6.69742 0.289826
\(535\) 1.12117 0.0484724
\(536\) −7.75828 −0.335107
\(537\) −1.14945 −0.0496025
\(538\) 12.8312 0.553192
\(539\) 3.47039 0.149480
\(540\) −9.00677 −0.387590
\(541\) −28.9030 −1.24264 −0.621319 0.783558i \(-0.713403\pi\)
−0.621319 + 0.783558i \(0.713403\pi\)
\(542\) 62.1570 2.66987
\(543\) 21.2259 0.910892
\(544\) −2.82389 −0.121073
\(545\) 21.7884 0.933311
\(546\) 38.6093 1.65233
\(547\) −16.5450 −0.707415 −0.353708 0.935356i \(-0.615079\pi\)
−0.353708 + 0.935356i \(0.615079\pi\)
\(548\) −46.1597 −1.97185
\(549\) 0.116552 0.00497432
\(550\) −12.2693 −0.523163
\(551\) −3.64367 −0.155226
\(552\) 30.7524 1.30891
\(553\) −13.5244 −0.575118
\(554\) 43.8535 1.86316
\(555\) 4.91045 0.208437
\(556\) 30.9405 1.31217
\(557\) 10.7749 0.456546 0.228273 0.973597i \(-0.426692\pi\)
0.228273 + 0.973597i \(0.426692\pi\)
\(558\) 1.90180 0.0805096
\(559\) −45.4276 −1.92138
\(560\) 14.7228 0.622153
\(561\) −5.16191 −0.217936
\(562\) −50.7091 −2.13903
\(563\) 1.94839 0.0821147 0.0410573 0.999157i \(-0.486927\pi\)
0.0410573 + 0.999157i \(0.486927\pi\)
\(564\) 10.3495 0.435792
\(565\) 48.9722 2.06028
\(566\) 48.8920 2.05508
\(567\) −2.76989 −0.116325
\(568\) 55.7387 2.33874
\(569\) 22.2616 0.933255 0.466627 0.884454i \(-0.345469\pi\)
0.466627 + 0.884454i \(0.345469\pi\)
\(570\) 45.8408 1.92006
\(571\) 24.4021 1.02119 0.510597 0.859820i \(-0.329424\pi\)
0.510597 + 0.859820i \(0.329424\pi\)
\(572\) 111.054 4.64341
\(573\) 8.34597 0.348658
\(574\) −82.0125 −3.42314
\(575\) −7.67324 −0.319996
\(576\) −11.0696 −0.461234
\(577\) −9.01116 −0.375140 −0.187570 0.982251i \(-0.560061\pi\)
−0.187570 + 0.982251i \(0.560061\pi\)
\(578\) −2.38281 −0.0991116
\(579\) −20.2571 −0.841858
\(580\) 4.17763 0.173467
\(581\) 25.3442 1.05145
\(582\) −36.6950 −1.52106
\(583\) 53.5266 2.21685
\(584\) 55.8986 2.31310
\(585\) −14.3260 −0.592309
\(586\) −35.0100 −1.44625
\(587\) −3.53678 −0.145979 −0.0729893 0.997333i \(-0.523254\pi\)
−0.0729893 + 0.997333i \(0.523254\pi\)
\(588\) 2.47259 0.101968
\(589\) −6.26981 −0.258343
\(590\) −24.2122 −0.996802
\(591\) 10.3346 0.425109
\(592\) −4.35189 −0.178862
\(593\) 34.2911 1.40817 0.704084 0.710117i \(-0.251358\pi\)
0.704084 + 0.710117i \(0.251358\pi\)
\(594\) −12.2998 −0.504669
\(595\) −6.78342 −0.278093
\(596\) 73.5296 3.01189
\(597\) 11.0351 0.451637
\(598\) 107.223 4.38469
\(599\) 20.6764 0.844815 0.422407 0.906406i \(-0.361185\pi\)
0.422407 + 0.906406i \(0.361185\pi\)
\(600\) −3.98784 −0.162803
\(601\) 16.4467 0.670875 0.335438 0.942062i \(-0.391116\pi\)
0.335438 + 0.942062i \(0.391116\pi\)
\(602\) −51.2544 −2.08897
\(603\) 1.94065 0.0790292
\(604\) −18.0669 −0.735133
\(605\) −38.3152 −1.55773
\(606\) −29.2943 −1.19000
\(607\) −48.1981 −1.95630 −0.978151 0.207896i \(-0.933338\pi\)
−0.978151 + 0.207896i \(0.933338\pi\)
\(608\) 22.1833 0.899652
\(609\) 1.28477 0.0520614
\(610\) 0.680133 0.0275378
\(611\) 16.4617 0.665970
\(612\) −3.67776 −0.148665
\(613\) 19.9835 0.807126 0.403563 0.914952i \(-0.367772\pi\)
0.403563 + 0.914952i \(0.367772\pi\)
\(614\) 31.5160 1.27188
\(615\) 30.4309 1.22709
\(616\) 57.1601 2.30305
\(617\) 33.7523 1.35882 0.679408 0.733761i \(-0.262237\pi\)
0.679408 + 0.733761i \(0.262237\pi\)
\(618\) −34.9256 −1.40491
\(619\) −10.9193 −0.438882 −0.219441 0.975626i \(-0.570423\pi\)
−0.219441 + 0.975626i \(0.570423\pi\)
\(620\) 7.18862 0.288702
\(621\) −7.69237 −0.308684
\(622\) −3.72897 −0.149518
\(623\) 7.78542 0.311916
\(624\) 12.6965 0.508265
\(625\) −28.9925 −1.15970
\(626\) 1.46035 0.0583672
\(627\) 40.5498 1.61940
\(628\) 3.67776 0.146759
\(629\) 2.00510 0.0799485
\(630\) −16.1636 −0.643972
\(631\) −24.9206 −0.992075 −0.496037 0.868301i \(-0.665212\pi\)
−0.496037 + 0.868301i \(0.665212\pi\)
\(632\) −19.5198 −0.776456
\(633\) −6.17433 −0.245407
\(634\) 50.3937 2.00139
\(635\) −27.1706 −1.07823
\(636\) 38.1366 1.51222
\(637\) 3.93286 0.155826
\(638\) 5.70507 0.225866
\(639\) −13.9424 −0.551553
\(640\) −50.7648 −2.00666
\(641\) −37.7678 −1.49174 −0.745869 0.666093i \(-0.767965\pi\)
−0.745869 + 0.666093i \(0.767965\pi\)
\(642\) 1.09087 0.0430533
\(643\) −21.3845 −0.843323 −0.421662 0.906753i \(-0.638553\pi\)
−0.421662 + 0.906753i \(0.638553\pi\)
\(644\) 78.3622 3.08790
\(645\) 19.0180 0.748833
\(646\) 18.7183 0.736462
\(647\) 32.5394 1.27926 0.639629 0.768684i \(-0.279088\pi\)
0.639629 + 0.768684i \(0.279088\pi\)
\(648\) −3.99778 −0.157048
\(649\) −21.4176 −0.840716
\(650\) −13.9043 −0.545370
\(651\) 2.21075 0.0866461
\(652\) 29.0342 1.13707
\(653\) −31.2074 −1.22124 −0.610620 0.791924i \(-0.709080\pi\)
−0.610620 + 0.791924i \(0.709080\pi\)
\(654\) 21.1996 0.828970
\(655\) 22.6013 0.883104
\(656\) −26.9694 −1.05298
\(657\) −13.9824 −0.545506
\(658\) 18.5732 0.724058
\(659\) −10.2180 −0.398037 −0.199018 0.979996i \(-0.563775\pi\)
−0.199018 + 0.979996i \(0.563775\pi\)
\(660\) −46.4922 −1.80971
\(661\) −23.8465 −0.927522 −0.463761 0.885960i \(-0.653500\pi\)
−0.463761 + 0.885960i \(0.653500\pi\)
\(662\) −47.7169 −1.85457
\(663\) −5.84979 −0.227187
\(664\) 36.5792 1.41955
\(665\) 53.2877 2.06641
\(666\) 4.77776 0.185134
\(667\) 3.56797 0.138152
\(668\) −29.0160 −1.12266
\(669\) −9.75096 −0.376994
\(670\) 11.3245 0.437505
\(671\) 0.601632 0.0232257
\(672\) −7.82188 −0.301736
\(673\) 40.0371 1.54332 0.771658 0.636038i \(-0.219428\pi\)
0.771658 + 0.636038i \(0.219428\pi\)
\(674\) 20.8302 0.802349
\(675\) 0.997513 0.0383943
\(676\) 78.0424 3.00163
\(677\) 24.2092 0.930437 0.465218 0.885196i \(-0.345976\pi\)
0.465218 + 0.885196i \(0.345976\pi\)
\(678\) 47.6489 1.82994
\(679\) −42.6561 −1.63699
\(680\) −9.79050 −0.375448
\(681\) 9.73180 0.372923
\(682\) 9.81693 0.375910
\(683\) −10.8713 −0.415978 −0.207989 0.978131i \(-0.566692\pi\)
−0.207989 + 0.978131i \(0.566692\pi\)
\(684\) 28.8910 1.10467
\(685\) 30.7373 1.17441
\(686\) −41.7635 −1.59454
\(687\) −9.11556 −0.347780
\(688\) −16.8547 −0.642580
\(689\) 60.6596 2.31095
\(690\) −44.8884 −1.70887
\(691\) 24.9201 0.948004 0.474002 0.880524i \(-0.342809\pi\)
0.474002 + 0.880524i \(0.342809\pi\)
\(692\) −45.8712 −1.74376
\(693\) −14.2980 −0.543134
\(694\) 51.8195 1.96704
\(695\) −20.6029 −0.781514
\(696\) 1.85430 0.0702871
\(697\) 12.4259 0.470665
\(698\) 21.1386 0.800107
\(699\) −9.51003 −0.359702
\(700\) −10.1617 −0.384075
\(701\) −28.6359 −1.08156 −0.540782 0.841163i \(-0.681872\pi\)
−0.540782 + 0.841163i \(0.681872\pi\)
\(702\) −13.9389 −0.526091
\(703\) −15.7512 −0.594068
\(704\) −57.1404 −2.15356
\(705\) −6.89160 −0.259553
\(706\) −21.1937 −0.797634
\(707\) −34.0532 −1.28070
\(708\) −15.2596 −0.573493
\(709\) 25.0303 0.940033 0.470016 0.882658i \(-0.344248\pi\)
0.470016 + 0.882658i \(0.344248\pi\)
\(710\) −81.3602 −3.05339
\(711\) 4.88266 0.183114
\(712\) 11.2367 0.421113
\(713\) 6.13955 0.229928
\(714\) −6.60012 −0.247003
\(715\) −73.9498 −2.76557
\(716\) −4.22741 −0.157986
\(717\) −16.5345 −0.617492
\(718\) 22.2708 0.831139
\(719\) −4.11224 −0.153361 −0.0766803 0.997056i \(-0.524432\pi\)
−0.0766803 + 0.997056i \(0.524432\pi\)
\(720\) −5.31530 −0.198090
\(721\) −40.5992 −1.51199
\(722\) −101.770 −3.78748
\(723\) 8.55357 0.318111
\(724\) 78.0639 2.90122
\(725\) −0.462679 −0.0171835
\(726\) −37.2799 −1.38359
\(727\) −1.11930 −0.0415127 −0.0207563 0.999785i \(-0.506607\pi\)
−0.0207563 + 0.999785i \(0.506607\pi\)
\(728\) 64.7773 2.40081
\(729\) 1.00000 0.0370370
\(730\) −81.5936 −3.01992
\(731\) 7.76567 0.287224
\(732\) 0.428651 0.0158434
\(733\) −42.3378 −1.56378 −0.781892 0.623414i \(-0.785745\pi\)
−0.781892 + 0.623414i \(0.785745\pi\)
\(734\) 62.9512 2.32357
\(735\) −1.64647 −0.0607309
\(736\) −21.7224 −0.800699
\(737\) 10.0175 0.368998
\(738\) 29.6086 1.08991
\(739\) −20.4839 −0.753513 −0.376757 0.926312i \(-0.622961\pi\)
−0.376757 + 0.926312i \(0.622961\pi\)
\(740\) 18.0595 0.663879
\(741\) 45.9535 1.68814
\(742\) 68.4401 2.51251
\(743\) −12.5162 −0.459176 −0.229588 0.973288i \(-0.573738\pi\)
−0.229588 + 0.973288i \(0.573738\pi\)
\(744\) 3.19077 0.116979
\(745\) −48.9625 −1.79385
\(746\) −17.3053 −0.633590
\(747\) −9.14988 −0.334777
\(748\) −18.9843 −0.694135
\(749\) 1.26809 0.0463348
\(750\) −23.3563 −0.852852
\(751\) 15.5605 0.567810 0.283905 0.958852i \(-0.408370\pi\)
0.283905 + 0.958852i \(0.408370\pi\)
\(752\) 6.10769 0.222724
\(753\) −4.39216 −0.160059
\(754\) 6.46532 0.235453
\(755\) 12.0306 0.437837
\(756\) −10.1870 −0.370498
\(757\) −37.5956 −1.36644 −0.683218 0.730215i \(-0.739420\pi\)
−0.683218 + 0.730215i \(0.739420\pi\)
\(758\) −52.3847 −1.90270
\(759\) −39.7074 −1.44129
\(760\) 76.9100 2.78982
\(761\) −30.2747 −1.09746 −0.548729 0.836000i \(-0.684888\pi\)
−0.548729 + 0.836000i \(0.684888\pi\)
\(762\) −26.4364 −0.957689
\(763\) 24.6435 0.892154
\(764\) 30.6945 1.11049
\(765\) 2.44898 0.0885431
\(766\) 16.2765 0.588093
\(767\) −24.2718 −0.876403
\(768\) −27.2538 −0.983438
\(769\) 35.6966 1.28725 0.643626 0.765340i \(-0.277429\pi\)
0.643626 + 0.765340i \(0.277429\pi\)
\(770\) −83.4350 −3.00679
\(771\) −24.4415 −0.880240
\(772\) −74.5009 −2.68135
\(773\) −38.2027 −1.37405 −0.687027 0.726632i \(-0.741085\pi\)
−0.687027 + 0.726632i \(0.741085\pi\)
\(774\) 18.5041 0.665116
\(775\) −0.796150 −0.0285986
\(776\) −61.5654 −2.21007
\(777\) 5.55391 0.199245
\(778\) −43.9157 −1.57446
\(779\) −97.6128 −3.49734
\(780\) −52.6878 −1.88652
\(781\) −71.9695 −2.57527
\(782\) −18.3294 −0.655459
\(783\) −0.463832 −0.0165760
\(784\) 1.45918 0.0521137
\(785\) −2.44898 −0.0874079
\(786\) 21.9905 0.784376
\(787\) 18.5898 0.662656 0.331328 0.943516i \(-0.392503\pi\)
0.331328 + 0.943516i \(0.392503\pi\)
\(788\) 38.0083 1.35399
\(789\) −17.0012 −0.605259
\(790\) 28.4925 1.01372
\(791\) 55.3894 1.96942
\(792\) −20.6362 −0.733276
\(793\) 0.681805 0.0242116
\(794\) 53.8158 1.90985
\(795\) −25.3948 −0.900660
\(796\) 40.5845 1.43848
\(797\) −22.7691 −0.806523 −0.403262 0.915085i \(-0.632124\pi\)
−0.403262 + 0.915085i \(0.632124\pi\)
\(798\) 51.8477 1.83539
\(799\) −2.81407 −0.0995546
\(800\) 2.81687 0.0995914
\(801\) −2.81073 −0.0993123
\(802\) −81.7503 −2.88670
\(803\) −72.1760 −2.54704
\(804\) 7.13724 0.251711
\(805\) −52.1806 −1.83912
\(806\) 11.1251 0.391866
\(807\) −5.38491 −0.189558
\(808\) −49.1489 −1.72905
\(809\) 6.83394 0.240269 0.120134 0.992758i \(-0.461667\pi\)
0.120134 + 0.992758i \(0.461667\pi\)
\(810\) 5.83545 0.205037
\(811\) 2.52904 0.0888066 0.0444033 0.999014i \(-0.485861\pi\)
0.0444033 + 0.999014i \(0.485861\pi\)
\(812\) 4.72507 0.165817
\(813\) −26.0857 −0.914864
\(814\) 24.6624 0.864416
\(815\) −19.3336 −0.677226
\(816\) −2.17041 −0.0759796
\(817\) −61.0039 −2.13426
\(818\) 73.4662 2.56869
\(819\) −16.2033 −0.566189
\(820\) 111.917 3.90833
\(821\) 32.0958 1.12015 0.560076 0.828441i \(-0.310772\pi\)
0.560076 + 0.828441i \(0.310772\pi\)
\(822\) 29.9067 1.04312
\(823\) −15.7766 −0.549938 −0.274969 0.961453i \(-0.588668\pi\)
−0.274969 + 0.961453i \(0.588668\pi\)
\(824\) −58.5968 −2.04132
\(825\) 5.14908 0.179268
\(826\) −27.3850 −0.952845
\(827\) −4.58302 −0.159367 −0.0796835 0.996820i \(-0.525391\pi\)
−0.0796835 + 0.996820i \(0.525391\pi\)
\(828\) −28.2907 −0.983170
\(829\) −1.82672 −0.0634445 −0.0317223 0.999497i \(-0.510099\pi\)
−0.0317223 + 0.999497i \(0.510099\pi\)
\(830\) −53.3937 −1.85332
\(831\) −18.4041 −0.638432
\(832\) −64.7550 −2.24497
\(833\) −0.672308 −0.0232941
\(834\) −20.0462 −0.694143
\(835\) 19.3215 0.668646
\(836\) 149.133 5.15786
\(837\) −0.798135 −0.0275876
\(838\) 94.4826 3.26385
\(839\) 13.7577 0.474967 0.237484 0.971392i \(-0.423677\pi\)
0.237484 + 0.971392i \(0.423677\pi\)
\(840\) −27.1186 −0.935682
\(841\) −28.7849 −0.992581
\(842\) −70.5753 −2.43218
\(843\) 21.2812 0.732965
\(844\) −22.7077 −0.781632
\(845\) −51.9676 −1.78774
\(846\) −6.70538 −0.230536
\(847\) −43.3360 −1.48904
\(848\) 22.5061 0.772864
\(849\) −20.5187 −0.704199
\(850\) 2.37688 0.0815263
\(851\) 15.4240 0.528726
\(852\) −51.2768 −1.75672
\(853\) 23.5711 0.807058 0.403529 0.914967i \(-0.367783\pi\)
0.403529 + 0.914967i \(0.367783\pi\)
\(854\) 0.769257 0.0263234
\(855\) −19.2382 −0.657932
\(856\) 1.83023 0.0625558
\(857\) −21.0037 −0.717473 −0.358736 0.933439i \(-0.616792\pi\)
−0.358736 + 0.933439i \(0.616792\pi\)
\(858\) −71.9515 −2.45638
\(859\) −12.7840 −0.436184 −0.218092 0.975928i \(-0.569983\pi\)
−0.218092 + 0.975928i \(0.569983\pi\)
\(860\) 69.9437 2.38506
\(861\) 34.4185 1.17298
\(862\) −3.93894 −0.134161
\(863\) 37.7532 1.28513 0.642567 0.766230i \(-0.277869\pi\)
0.642567 + 0.766230i \(0.277869\pi\)
\(864\) 2.82389 0.0960708
\(865\) 30.5452 1.03857
\(866\) 71.4625 2.42839
\(867\) 1.00000 0.0339618
\(868\) 8.13061 0.275971
\(869\) 25.2039 0.854983
\(870\) −2.70667 −0.0917647
\(871\) 11.3524 0.384661
\(872\) 35.5679 1.20448
\(873\) 15.3999 0.521208
\(874\) 143.988 4.87047
\(875\) −27.1505 −0.917856
\(876\) −51.4240 −1.73746
\(877\) 26.5297 0.895843 0.447922 0.894073i \(-0.352164\pi\)
0.447922 + 0.894073i \(0.352164\pi\)
\(878\) −29.5913 −0.998659
\(879\) 14.6928 0.495574
\(880\) −27.4371 −0.924906
\(881\) 14.7168 0.495822 0.247911 0.968783i \(-0.420256\pi\)
0.247911 + 0.968783i \(0.420256\pi\)
\(882\) −1.60198 −0.0539414
\(883\) 40.6538 1.36811 0.684055 0.729430i \(-0.260215\pi\)
0.684055 + 0.729430i \(0.260215\pi\)
\(884\) −21.5142 −0.723599
\(885\) 10.1612 0.341566
\(886\) 44.0903 1.48124
\(887\) 20.8699 0.700742 0.350371 0.936611i \(-0.386055\pi\)
0.350371 + 0.936611i \(0.386055\pi\)
\(888\) 8.01595 0.268998
\(889\) −30.7310 −1.03068
\(890\) −16.4019 −0.549792
\(891\) 5.16191 0.172931
\(892\) −35.8617 −1.20074
\(893\) 22.1061 0.739754
\(894\) −47.6395 −1.59330
\(895\) 2.81499 0.0940947
\(896\) −57.4170 −1.91817
\(897\) −44.9988 −1.50247
\(898\) 64.3070 2.14595
\(899\) 0.370201 0.0123469
\(900\) 3.66862 0.122287
\(901\) −10.3695 −0.345459
\(902\) 152.837 5.08891
\(903\) 21.5101 0.715811
\(904\) 79.9435 2.65888
\(905\) −51.9819 −1.72794
\(906\) 11.7055 0.388888
\(907\) −51.0586 −1.69537 −0.847686 0.530499i \(-0.822005\pi\)
−0.847686 + 0.530499i \(0.822005\pi\)
\(908\) 35.7912 1.18777
\(909\) 12.2940 0.407768
\(910\) −94.5535 −3.13442
\(911\) 30.0849 0.996757 0.498379 0.866959i \(-0.333929\pi\)
0.498379 + 0.866959i \(0.333929\pi\)
\(912\) 17.0498 0.564577
\(913\) −47.2309 −1.56311
\(914\) 46.5980 1.54133
\(915\) −0.285434 −0.00943615
\(916\) −33.5249 −1.10769
\(917\) 25.5629 0.844161
\(918\) 2.38281 0.0786443
\(919\) −17.1111 −0.564443 −0.282221 0.959349i \(-0.591071\pi\)
−0.282221 + 0.959349i \(0.591071\pi\)
\(920\) −75.3121 −2.48297
\(921\) −13.2264 −0.435825
\(922\) 44.7484 1.47371
\(923\) −81.5602 −2.68459
\(924\) −52.5845 −1.72990
\(925\) −2.00011 −0.0657633
\(926\) −26.5614 −0.872862
\(927\) 14.6573 0.481410
\(928\) −1.30981 −0.0429967
\(929\) 27.0199 0.886494 0.443247 0.896399i \(-0.353826\pi\)
0.443247 + 0.896399i \(0.353826\pi\)
\(930\) −4.65748 −0.152725
\(931\) 5.28137 0.173090
\(932\) −34.9756 −1.14566
\(933\) 1.56495 0.0512341
\(934\) 88.0992 2.88269
\(935\) 12.6414 0.413419
\(936\) −23.3862 −0.764402
\(937\) −25.2258 −0.824092 −0.412046 0.911163i \(-0.635186\pi\)
−0.412046 + 0.911163i \(0.635186\pi\)
\(938\) 12.8085 0.418212
\(939\) −0.612868 −0.0200002
\(940\) −25.3457 −0.826685
\(941\) −29.4601 −0.960370 −0.480185 0.877167i \(-0.659431\pi\)
−0.480185 + 0.877167i \(0.659431\pi\)
\(942\) −2.38281 −0.0776360
\(943\) 95.5848 3.11267
\(944\) −9.00540 −0.293101
\(945\) 6.78342 0.220665
\(946\) 95.5166 3.10551
\(947\) 30.0159 0.975386 0.487693 0.873015i \(-0.337839\pi\)
0.487693 + 0.873015i \(0.337839\pi\)
\(948\) 17.9573 0.583225
\(949\) −81.7942 −2.65515
\(950\) −18.6718 −0.605792
\(951\) −21.1489 −0.685800
\(952\) −11.0734 −0.358892
\(953\) −36.6727 −1.18795 −0.593973 0.804485i \(-0.702442\pi\)
−0.593973 + 0.804485i \(0.702442\pi\)
\(954\) −24.7086 −0.799969
\(955\) −20.4391 −0.661395
\(956\) −60.8099 −1.96673
\(957\) −2.39426 −0.0773956
\(958\) −54.7793 −1.76984
\(959\) 34.7650 1.12262
\(960\) 27.1093 0.874948
\(961\) −30.3630 −0.979451
\(962\) 27.9489 0.901109
\(963\) −0.457810 −0.0147527
\(964\) 31.4580 1.01319
\(965\) 49.6094 1.59698
\(966\) −50.7705 −1.63352
\(967\) −38.2043 −1.22857 −0.614283 0.789086i \(-0.710555\pi\)
−0.614283 + 0.789086i \(0.710555\pi\)
\(968\) −62.5468 −2.01033
\(969\) −7.85558 −0.252358
\(970\) 89.8653 2.88540
\(971\) 12.4388 0.399179 0.199589 0.979880i \(-0.436039\pi\)
0.199589 + 0.979880i \(0.436039\pi\)
\(972\) 3.67776 0.117964
\(973\) −23.3027 −0.747051
\(974\) −3.38287 −0.108394
\(975\) 5.83525 0.186877
\(976\) 0.252966 0.00809725
\(977\) 39.4168 1.26105 0.630527 0.776167i \(-0.282839\pi\)
0.630527 + 0.776167i \(0.282839\pi\)
\(978\) −18.8112 −0.601514
\(979\) −14.5087 −0.463702
\(980\) −6.05532 −0.193430
\(981\) −8.89691 −0.284056
\(982\) −5.26840 −0.168122
\(983\) −34.0283 −1.08534 −0.542668 0.839948i \(-0.682586\pi\)
−0.542668 + 0.839948i \(0.682586\pi\)
\(984\) 49.6761 1.58362
\(985\) −25.3093 −0.806421
\(986\) −1.10522 −0.0351975
\(987\) −7.79467 −0.248107
\(988\) 169.006 5.37680
\(989\) 59.7364 1.89951
\(990\) 30.1221 0.957343
\(991\) 11.9205 0.378668 0.189334 0.981913i \(-0.439367\pi\)
0.189334 + 0.981913i \(0.439367\pi\)
\(992\) −2.25385 −0.0715597
\(993\) 20.0255 0.635490
\(994\) −92.0215 −2.91874
\(995\) −27.0248 −0.856743
\(996\) −33.6511 −1.06628
\(997\) 22.2485 0.704618 0.352309 0.935884i \(-0.385397\pi\)
0.352309 + 0.935884i \(0.385397\pi\)
\(998\) −68.3407 −2.16329
\(999\) −2.00510 −0.0634385
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 \(a_p\))