Properties

Label 8015.2.a.l.1.9
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.20228 q^{2}\) \(-3.01220 q^{3}\) \(+2.85005 q^{4}\) \(-1.00000 q^{5}\) \(+6.63371 q^{6}\) \(-1.00000 q^{7}\) \(-1.87206 q^{8}\) \(+6.07333 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.20228 q^{2}\) \(-3.01220 q^{3}\) \(+2.85005 q^{4}\) \(-1.00000 q^{5}\) \(+6.63371 q^{6}\) \(-1.00000 q^{7}\) \(-1.87206 q^{8}\) \(+6.07333 q^{9}\) \(+2.20228 q^{10}\) \(-3.78158 q^{11}\) \(-8.58492 q^{12}\) \(+4.33541 q^{13}\) \(+2.20228 q^{14}\) \(+3.01220 q^{15}\) \(-1.57731 q^{16}\) \(+1.42225 q^{17}\) \(-13.3752 q^{18}\) \(-3.78650 q^{19}\) \(-2.85005 q^{20}\) \(+3.01220 q^{21}\) \(+8.32810 q^{22}\) \(-8.43662 q^{23}\) \(+5.63900 q^{24}\) \(+1.00000 q^{25}\) \(-9.54781 q^{26}\) \(-9.25749 q^{27}\) \(-2.85005 q^{28}\) \(-7.89528 q^{29}\) \(-6.63371 q^{30}\) \(-4.98465 q^{31}\) \(+7.21779 q^{32}\) \(+11.3909 q^{33}\) \(-3.13220 q^{34}\) \(+1.00000 q^{35}\) \(+17.3093 q^{36}\) \(-2.71137 q^{37}\) \(+8.33895 q^{38}\) \(-13.0591 q^{39}\) \(+1.87206 q^{40}\) \(-1.56428 q^{41}\) \(-6.63371 q^{42}\) \(+5.07248 q^{43}\) \(-10.7777 q^{44}\) \(-6.07333 q^{45}\) \(+18.5798 q^{46}\) \(-3.10936 q^{47}\) \(+4.75116 q^{48}\) \(+1.00000 q^{49}\) \(-2.20228 q^{50}\) \(-4.28410 q^{51}\) \(+12.3562 q^{52}\) \(+1.42151 q^{53}\) \(+20.3876 q^{54}\) \(+3.78158 q^{55}\) \(+1.87206 q^{56}\) \(+11.4057 q^{57}\) \(+17.3876 q^{58}\) \(-9.60495 q^{59}\) \(+8.58492 q^{60}\) \(-10.5797 q^{61}\) \(+10.9776 q^{62}\) \(-6.07333 q^{63}\) \(-12.7410 q^{64}\) \(-4.33541 q^{65}\) \(-25.0859 q^{66}\) \(-0.748661 q^{67}\) \(+4.05349 q^{68}\) \(+25.4128 q^{69}\) \(-2.20228 q^{70}\) \(+1.44871 q^{71}\) \(-11.3696 q^{72}\) \(+5.14212 q^{73}\) \(+5.97121 q^{74}\) \(-3.01220 q^{75}\) \(-10.7917 q^{76}\) \(+3.78158 q^{77}\) \(+28.7599 q^{78}\) \(+9.81951 q^{79}\) \(+1.57731 q^{80}\) \(+9.66538 q^{81}\) \(+3.44499 q^{82}\) \(+0.0758723 q^{83}\) \(+8.58492 q^{84}\) \(-1.42225 q^{85}\) \(-11.1710 q^{86}\) \(+23.7821 q^{87}\) \(+7.07932 q^{88}\) \(-14.5072 q^{89}\) \(+13.3752 q^{90}\) \(-4.33541 q^{91}\) \(-24.0448 q^{92}\) \(+15.0148 q^{93}\) \(+6.84769 q^{94}\) \(+3.78650 q^{95}\) \(-21.7414 q^{96}\) \(+8.60767 q^{97}\) \(-2.20228 q^{98}\) \(-22.9668 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.20228 −1.55725 −0.778625 0.627490i \(-0.784082\pi\)
−0.778625 + 0.627490i \(0.784082\pi\)
\(3\) −3.01220 −1.73909 −0.869547 0.493851i \(-0.835589\pi\)
−0.869547 + 0.493851i \(0.835589\pi\)
\(4\) 2.85005 1.42503
\(5\) −1.00000 −0.447214
\(6\) 6.63371 2.70820
\(7\) −1.00000 −0.377964
\(8\) −1.87206 −0.661872
\(9\) 6.07333 2.02444
\(10\) 2.20228 0.696423
\(11\) −3.78158 −1.14019 −0.570094 0.821580i \(-0.693093\pi\)
−0.570094 + 0.821580i \(0.693093\pi\)
\(12\) −8.58492 −2.47825
\(13\) 4.33541 1.20243 0.601214 0.799088i \(-0.294684\pi\)
0.601214 + 0.799088i \(0.294684\pi\)
\(14\) 2.20228 0.588585
\(15\) 3.01220 0.777746
\(16\) −1.57731 −0.394327
\(17\) 1.42225 0.344947 0.172473 0.985014i \(-0.444824\pi\)
0.172473 + 0.985014i \(0.444824\pi\)
\(18\) −13.3752 −3.15257
\(19\) −3.78650 −0.868683 −0.434341 0.900748i \(-0.643019\pi\)
−0.434341 + 0.900748i \(0.643019\pi\)
\(20\) −2.85005 −0.637291
\(21\) 3.01220 0.657315
\(22\) 8.32810 1.77556
\(23\) −8.43662 −1.75916 −0.879578 0.475754i \(-0.842175\pi\)
−0.879578 + 0.475754i \(0.842175\pi\)
\(24\) 5.63900 1.15106
\(25\) 1.00000 0.200000
\(26\) −9.54781 −1.87248
\(27\) −9.25749 −1.78160
\(28\) −2.85005 −0.538609
\(29\) −7.89528 −1.46612 −0.733058 0.680166i \(-0.761908\pi\)
−0.733058 + 0.680166i \(0.761908\pi\)
\(30\) −6.63371 −1.21114
\(31\) −4.98465 −0.895270 −0.447635 0.894216i \(-0.647734\pi\)
−0.447635 + 0.894216i \(0.647734\pi\)
\(32\) 7.21779 1.27594
\(33\) 11.3909 1.98289
\(34\) −3.13220 −0.537168
\(35\) 1.00000 0.169031
\(36\) 17.3093 2.88489
\(37\) −2.71137 −0.445747 −0.222873 0.974847i \(-0.571544\pi\)
−0.222873 + 0.974847i \(0.571544\pi\)
\(38\) 8.33895 1.35276
\(39\) −13.0591 −2.09113
\(40\) 1.87206 0.295998
\(41\) −1.56428 −0.244299 −0.122150 0.992512i \(-0.538979\pi\)
−0.122150 + 0.992512i \(0.538979\pi\)
\(42\) −6.63371 −1.02360
\(43\) 5.07248 0.773545 0.386773 0.922175i \(-0.373590\pi\)
0.386773 + 0.922175i \(0.373590\pi\)
\(44\) −10.7777 −1.62480
\(45\) −6.07333 −0.905359
\(46\) 18.5798 2.73945
\(47\) −3.10936 −0.453547 −0.226773 0.973948i \(-0.572818\pi\)
−0.226773 + 0.973948i \(0.572818\pi\)
\(48\) 4.75116 0.685771
\(49\) 1.00000 0.142857
\(50\) −2.20228 −0.311450
\(51\) −4.28410 −0.599894
\(52\) 12.3562 1.71349
\(53\) 1.42151 0.195259 0.0976295 0.995223i \(-0.468874\pi\)
0.0976295 + 0.995223i \(0.468874\pi\)
\(54\) 20.3876 2.77440
\(55\) 3.78158 0.509908
\(56\) 1.87206 0.250164
\(57\) 11.4057 1.51072
\(58\) 17.3876 2.28311
\(59\) −9.60495 −1.25046 −0.625229 0.780441i \(-0.714994\pi\)
−0.625229 + 0.780441i \(0.714994\pi\)
\(60\) 8.58492 1.10831
\(61\) −10.5797 −1.35460 −0.677299 0.735708i \(-0.736850\pi\)
−0.677299 + 0.735708i \(0.736850\pi\)
\(62\) 10.9776 1.39416
\(63\) −6.07333 −0.765168
\(64\) −12.7410 −1.59263
\(65\) −4.33541 −0.537742
\(66\) −25.0859 −3.08786
\(67\) −0.748661 −0.0914636 −0.0457318 0.998954i \(-0.514562\pi\)
−0.0457318 + 0.998954i \(0.514562\pi\)
\(68\) 4.05349 0.491558
\(69\) 25.4128 3.05934
\(70\) −2.20228 −0.263223
\(71\) 1.44871 0.171930 0.0859650 0.996298i \(-0.472603\pi\)
0.0859650 + 0.996298i \(0.472603\pi\)
\(72\) −11.3696 −1.33992
\(73\) 5.14212 0.601840 0.300920 0.953649i \(-0.402706\pi\)
0.300920 + 0.953649i \(0.402706\pi\)
\(74\) 5.97121 0.694139
\(75\) −3.01220 −0.347819
\(76\) −10.7917 −1.23790
\(77\) 3.78158 0.430950
\(78\) 28.7599 3.25642
\(79\) 9.81951 1.10478 0.552391 0.833585i \(-0.313716\pi\)
0.552391 + 0.833585i \(0.313716\pi\)
\(80\) 1.57731 0.176348
\(81\) 9.66538 1.07393
\(82\) 3.44499 0.380435
\(83\) 0.0758723 0.00832807 0.00416403 0.999991i \(-0.498675\pi\)
0.00416403 + 0.999991i \(0.498675\pi\)
\(84\) 8.58492 0.936692
\(85\) −1.42225 −0.154265
\(86\) −11.1710 −1.20460
\(87\) 23.7821 2.54971
\(88\) 7.07932 0.754658
\(89\) −14.5072 −1.53776 −0.768879 0.639395i \(-0.779185\pi\)
−0.768879 + 0.639395i \(0.779185\pi\)
\(90\) 13.3752 1.40987
\(91\) −4.33541 −0.454475
\(92\) −24.0448 −2.50684
\(93\) 15.0148 1.55696
\(94\) 6.84769 0.706285
\(95\) 3.78650 0.388487
\(96\) −21.7414 −2.21897
\(97\) 8.60767 0.873976 0.436988 0.899467i \(-0.356045\pi\)
0.436988 + 0.899467i \(0.356045\pi\)
\(98\) −2.20228 −0.222464
\(99\) −22.9668 −2.30825
\(100\) 2.85005 0.285005
\(101\) −1.83398 −0.182488 −0.0912442 0.995829i \(-0.529084\pi\)
−0.0912442 + 0.995829i \(0.529084\pi\)
\(102\) 9.43481 0.934185
\(103\) −9.46639 −0.932751 −0.466375 0.884587i \(-0.654440\pi\)
−0.466375 + 0.884587i \(0.654440\pi\)
\(104\) −8.11614 −0.795853
\(105\) −3.01220 −0.293960
\(106\) −3.13056 −0.304067
\(107\) 0.955305 0.0923528 0.0461764 0.998933i \(-0.485296\pi\)
0.0461764 + 0.998933i \(0.485296\pi\)
\(108\) −26.3843 −2.53883
\(109\) 3.03723 0.290913 0.145457 0.989365i \(-0.453535\pi\)
0.145457 + 0.989365i \(0.453535\pi\)
\(110\) −8.32810 −0.794053
\(111\) 8.16719 0.775195
\(112\) 1.57731 0.149041
\(113\) 9.05115 0.851461 0.425730 0.904850i \(-0.360017\pi\)
0.425730 + 0.904850i \(0.360017\pi\)
\(114\) −25.1186 −2.35257
\(115\) 8.43662 0.786719
\(116\) −22.5020 −2.08925
\(117\) 26.3304 2.43425
\(118\) 21.1528 1.94728
\(119\) −1.42225 −0.130378
\(120\) −5.63900 −0.514768
\(121\) 3.30031 0.300028
\(122\) 23.2996 2.10945
\(123\) 4.71192 0.424859
\(124\) −14.2065 −1.27578
\(125\) −1.00000 −0.0894427
\(126\) 13.3752 1.19156
\(127\) −15.2615 −1.35424 −0.677122 0.735871i \(-0.736773\pi\)
−0.677122 + 0.735871i \(0.736773\pi\)
\(128\) 13.6237 1.20418
\(129\) −15.2793 −1.34527
\(130\) 9.54781 0.837398
\(131\) 3.03144 0.264858 0.132429 0.991192i \(-0.457722\pi\)
0.132429 + 0.991192i \(0.457722\pi\)
\(132\) 32.4645 2.82567
\(133\) 3.78650 0.328331
\(134\) 1.64876 0.142432
\(135\) 9.25749 0.796758
\(136\) −2.66254 −0.228311
\(137\) 3.14462 0.268663 0.134332 0.990936i \(-0.457111\pi\)
0.134332 + 0.990936i \(0.457111\pi\)
\(138\) −55.9661 −4.76415
\(139\) −11.8717 −1.00695 −0.503473 0.864011i \(-0.667945\pi\)
−0.503473 + 0.864011i \(0.667945\pi\)
\(140\) 2.85005 0.240873
\(141\) 9.36600 0.788760
\(142\) −3.19046 −0.267738
\(143\) −16.3947 −1.37099
\(144\) −9.57951 −0.798292
\(145\) 7.89528 0.655667
\(146\) −11.3244 −0.937215
\(147\) −3.01220 −0.248442
\(148\) −7.72755 −0.635201
\(149\) −18.1012 −1.48291 −0.741454 0.671004i \(-0.765863\pi\)
−0.741454 + 0.671004i \(0.765863\pi\)
\(150\) 6.63371 0.541640
\(151\) −6.14969 −0.500455 −0.250227 0.968187i \(-0.580505\pi\)
−0.250227 + 0.968187i \(0.580505\pi\)
\(152\) 7.08854 0.574957
\(153\) 8.63781 0.698326
\(154\) −8.32810 −0.671097
\(155\) 4.98465 0.400377
\(156\) −37.2192 −2.97992
\(157\) 17.3907 1.38793 0.693964 0.720009i \(-0.255863\pi\)
0.693964 + 0.720009i \(0.255863\pi\)
\(158\) −21.6253 −1.72042
\(159\) −4.28186 −0.339573
\(160\) −7.21779 −0.570616
\(161\) 8.43662 0.664899
\(162\) −21.2859 −1.67238
\(163\) −6.62045 −0.518554 −0.259277 0.965803i \(-0.583484\pi\)
−0.259277 + 0.965803i \(0.583484\pi\)
\(164\) −4.45828 −0.348133
\(165\) −11.3909 −0.886777
\(166\) −0.167092 −0.0129689
\(167\) −20.9967 −1.62478 −0.812388 0.583118i \(-0.801833\pi\)
−0.812388 + 0.583118i \(0.801833\pi\)
\(168\) −5.63900 −0.435058
\(169\) 5.79580 0.445831
\(170\) 3.13220 0.240229
\(171\) −22.9967 −1.75860
\(172\) 14.4568 1.10232
\(173\) −15.8812 −1.20742 −0.603712 0.797202i \(-0.706312\pi\)
−0.603712 + 0.797202i \(0.706312\pi\)
\(174\) −52.3750 −3.97054
\(175\) −1.00000 −0.0755929
\(176\) 5.96470 0.449606
\(177\) 28.9320 2.17466
\(178\) 31.9489 2.39467
\(179\) 8.25045 0.616668 0.308334 0.951278i \(-0.400229\pi\)
0.308334 + 0.951278i \(0.400229\pi\)
\(180\) −17.3093 −1.29016
\(181\) 13.4586 1.00037 0.500184 0.865919i \(-0.333266\pi\)
0.500184 + 0.865919i \(0.333266\pi\)
\(182\) 9.54781 0.707731
\(183\) 31.8683 2.35577
\(184\) 15.7938 1.16434
\(185\) 2.71137 0.199344
\(186\) −33.0667 −2.42457
\(187\) −5.37835 −0.393304
\(188\) −8.86184 −0.646316
\(189\) 9.25749 0.673383
\(190\) −8.33895 −0.604971
\(191\) 9.46567 0.684912 0.342456 0.939534i \(-0.388741\pi\)
0.342456 + 0.939534i \(0.388741\pi\)
\(192\) 38.3784 2.76972
\(193\) −16.0525 −1.15549 −0.577743 0.816219i \(-0.696066\pi\)
−0.577743 + 0.816219i \(0.696066\pi\)
\(194\) −18.9565 −1.36100
\(195\) 13.0591 0.935183
\(196\) 2.85005 0.203575
\(197\) −22.5002 −1.60307 −0.801535 0.597948i \(-0.795983\pi\)
−0.801535 + 0.597948i \(0.795983\pi\)
\(198\) 50.5793 3.59452
\(199\) −9.28637 −0.658293 −0.329147 0.944279i \(-0.606761\pi\)
−0.329147 + 0.944279i \(0.606761\pi\)
\(200\) −1.87206 −0.132374
\(201\) 2.25512 0.159064
\(202\) 4.03895 0.284180
\(203\) 7.89528 0.554140
\(204\) −12.2099 −0.854865
\(205\) 1.56428 0.109254
\(206\) 20.8477 1.45253
\(207\) −51.2384 −3.56132
\(208\) −6.83827 −0.474149
\(209\) 14.3189 0.990462
\(210\) 6.63371 0.457770
\(211\) −15.1645 −1.04397 −0.521985 0.852955i \(-0.674808\pi\)
−0.521985 + 0.852955i \(0.674808\pi\)
\(212\) 4.05137 0.278249
\(213\) −4.36379 −0.299002
\(214\) −2.10385 −0.143816
\(215\) −5.07248 −0.345940
\(216\) 17.3305 1.17919
\(217\) 4.98465 0.338380
\(218\) −6.68883 −0.453025
\(219\) −15.4891 −1.04666
\(220\) 10.7777 0.726632
\(221\) 6.16605 0.414773
\(222\) −17.9865 −1.20717
\(223\) −4.53894 −0.303950 −0.151975 0.988384i \(-0.548563\pi\)
−0.151975 + 0.988384i \(0.548563\pi\)
\(224\) −7.21779 −0.482259
\(225\) 6.07333 0.404889
\(226\) −19.9332 −1.32594
\(227\) 3.67431 0.243873 0.121936 0.992538i \(-0.461090\pi\)
0.121936 + 0.992538i \(0.461090\pi\)
\(228\) 32.5068 2.15282
\(229\) 1.00000 0.0660819
\(230\) −18.5798 −1.22512
\(231\) −11.3909 −0.749463
\(232\) 14.7804 0.970381
\(233\) −16.8132 −1.10147 −0.550734 0.834681i \(-0.685652\pi\)
−0.550734 + 0.834681i \(0.685652\pi\)
\(234\) −57.9870 −3.79073
\(235\) 3.10936 0.202832
\(236\) −27.3746 −1.78194
\(237\) −29.5783 −1.92132
\(238\) 3.13220 0.203030
\(239\) 17.7248 1.14652 0.573262 0.819372i \(-0.305678\pi\)
0.573262 + 0.819372i \(0.305678\pi\)
\(240\) −4.75116 −0.306686
\(241\) 18.8485 1.21414 0.607070 0.794649i \(-0.292345\pi\)
0.607070 + 0.794649i \(0.292345\pi\)
\(242\) −7.26822 −0.467219
\(243\) −1.34157 −0.0860617
\(244\) −30.1528 −1.93034
\(245\) −1.00000 −0.0638877
\(246\) −10.3770 −0.661612
\(247\) −16.4160 −1.04453
\(248\) 9.33155 0.592554
\(249\) −0.228542 −0.0144833
\(250\) 2.20228 0.139285
\(251\) −4.97088 −0.313759 −0.156880 0.987618i \(-0.550143\pi\)
−0.156880 + 0.987618i \(0.550143\pi\)
\(252\) −17.3093 −1.09038
\(253\) 31.9037 2.00577
\(254\) 33.6103 2.10889
\(255\) 4.28410 0.268281
\(256\) −4.52129 −0.282581
\(257\) 2.41699 0.150768 0.0753840 0.997155i \(-0.475982\pi\)
0.0753840 + 0.997155i \(0.475982\pi\)
\(258\) 33.6493 2.09492
\(259\) 2.71137 0.168476
\(260\) −12.3562 −0.766296
\(261\) −47.9507 −2.96807
\(262\) −6.67608 −0.412450
\(263\) −7.57986 −0.467394 −0.233697 0.972309i \(-0.575082\pi\)
−0.233697 + 0.972309i \(0.575082\pi\)
\(264\) −21.3243 −1.31242
\(265\) −1.42151 −0.0873224
\(266\) −8.33895 −0.511294
\(267\) 43.6985 2.67430
\(268\) −2.13372 −0.130338
\(269\) −15.2830 −0.931820 −0.465910 0.884832i \(-0.654273\pi\)
−0.465910 + 0.884832i \(0.654273\pi\)
\(270\) −20.3876 −1.24075
\(271\) 1.98963 0.120861 0.0604307 0.998172i \(-0.480753\pi\)
0.0604307 + 0.998172i \(0.480753\pi\)
\(272\) −2.24333 −0.136022
\(273\) 13.0591 0.790374
\(274\) −6.92535 −0.418376
\(275\) −3.78158 −0.228038
\(276\) 72.4277 4.35964
\(277\) −25.7457 −1.54691 −0.773455 0.633852i \(-0.781473\pi\)
−0.773455 + 0.633852i \(0.781473\pi\)
\(278\) 26.1449 1.56807
\(279\) −30.2734 −1.81242
\(280\) −1.87206 −0.111877
\(281\) 22.8797 1.36489 0.682445 0.730937i \(-0.260917\pi\)
0.682445 + 0.730937i \(0.260917\pi\)
\(282\) −20.6266 −1.22830
\(283\) −6.63277 −0.394277 −0.197139 0.980376i \(-0.563165\pi\)
−0.197139 + 0.980376i \(0.563165\pi\)
\(284\) 4.12889 0.245005
\(285\) −11.4057 −0.675615
\(286\) 36.1057 2.13498
\(287\) 1.56428 0.0923365
\(288\) 43.8360 2.58306
\(289\) −14.9772 −0.881012
\(290\) −17.3876 −1.02104
\(291\) −25.9280 −1.51993
\(292\) 14.6553 0.857638
\(293\) −6.88190 −0.402045 −0.201023 0.979587i \(-0.564426\pi\)
−0.201023 + 0.979587i \(0.564426\pi\)
\(294\) 6.63371 0.386886
\(295\) 9.60495 0.559222
\(296\) 5.07584 0.295027
\(297\) 35.0079 2.03136
\(298\) 39.8640 2.30926
\(299\) −36.5762 −2.11526
\(300\) −8.58492 −0.495651
\(301\) −5.07248 −0.292373
\(302\) 13.5434 0.779333
\(303\) 5.52432 0.317364
\(304\) 5.97247 0.342545
\(305\) 10.5797 0.605795
\(306\) −19.0229 −1.08747
\(307\) 9.02278 0.514957 0.257479 0.966284i \(-0.417108\pi\)
0.257479 + 0.966284i \(0.417108\pi\)
\(308\) 10.7777 0.614116
\(309\) 28.5146 1.62214
\(310\) −10.9776 −0.623487
\(311\) −24.3545 −1.38102 −0.690510 0.723323i \(-0.742614\pi\)
−0.690510 + 0.723323i \(0.742614\pi\)
\(312\) 24.4474 1.38406
\(313\) 2.98681 0.168824 0.0844122 0.996431i \(-0.473099\pi\)
0.0844122 + 0.996431i \(0.473099\pi\)
\(314\) −38.2992 −2.16135
\(315\) 6.07333 0.342194
\(316\) 27.9861 1.57434
\(317\) −20.6349 −1.15897 −0.579487 0.814982i \(-0.696747\pi\)
−0.579487 + 0.814982i \(0.696747\pi\)
\(318\) 9.42986 0.528801
\(319\) 29.8566 1.67165
\(320\) 12.7410 0.712244
\(321\) −2.87757 −0.160610
\(322\) −18.5798 −1.03541
\(323\) −5.38536 −0.299649
\(324\) 27.5468 1.53038
\(325\) 4.33541 0.240485
\(326\) 14.5801 0.807517
\(327\) −9.14872 −0.505926
\(328\) 2.92842 0.161695
\(329\) 3.10936 0.171425
\(330\) 25.0859 1.38093
\(331\) −33.8801 −1.86222 −0.931110 0.364739i \(-0.881158\pi\)
−0.931110 + 0.364739i \(0.881158\pi\)
\(332\) 0.216240 0.0118677
\(333\) −16.4671 −0.902389
\(334\) 46.2407 2.53018
\(335\) 0.748661 0.0409037
\(336\) −4.75116 −0.259197
\(337\) −20.9479 −1.14110 −0.570552 0.821261i \(-0.693271\pi\)
−0.570552 + 0.821261i \(0.693271\pi\)
\(338\) −12.7640 −0.694270
\(339\) −27.2639 −1.48077
\(340\) −4.05349 −0.219831
\(341\) 18.8498 1.02078
\(342\) 50.6452 2.73858
\(343\) −1.00000 −0.0539949
\(344\) −9.49596 −0.511988
\(345\) −25.4128 −1.36818
\(346\) 34.9749 1.88026
\(347\) −19.5114 −1.04743 −0.523714 0.851894i \(-0.675454\pi\)
−0.523714 + 0.851894i \(0.675454\pi\)
\(348\) 67.7803 3.63341
\(349\) 7.17450 0.384042 0.192021 0.981391i \(-0.438496\pi\)
0.192021 + 0.981391i \(0.438496\pi\)
\(350\) 2.20228 0.117717
\(351\) −40.1350 −2.14225
\(352\) −27.2946 −1.45481
\(353\) 9.41706 0.501219 0.250610 0.968088i \(-0.419369\pi\)
0.250610 + 0.968088i \(0.419369\pi\)
\(354\) −63.7165 −3.38649
\(355\) −1.44871 −0.0768894
\(356\) −41.3462 −2.19134
\(357\) 4.28410 0.226739
\(358\) −18.1698 −0.960306
\(359\) 9.33033 0.492436 0.246218 0.969214i \(-0.420812\pi\)
0.246218 + 0.969214i \(0.420812\pi\)
\(360\) 11.3696 0.599232
\(361\) −4.66241 −0.245390
\(362\) −29.6396 −1.55782
\(363\) −9.94119 −0.521777
\(364\) −12.3562 −0.647638
\(365\) −5.14212 −0.269151
\(366\) −70.1830 −3.66852
\(367\) 18.0824 0.943895 0.471948 0.881627i \(-0.343551\pi\)
0.471948 + 0.881627i \(0.343551\pi\)
\(368\) 13.3071 0.693682
\(369\) −9.50039 −0.494571
\(370\) −5.97121 −0.310428
\(371\) −1.42151 −0.0738009
\(372\) 42.7928 2.21871
\(373\) 5.68094 0.294148 0.147074 0.989125i \(-0.453014\pi\)
0.147074 + 0.989125i \(0.453014\pi\)
\(374\) 11.8447 0.612473
\(375\) 3.01220 0.155549
\(376\) 5.82090 0.300190
\(377\) −34.2293 −1.76290
\(378\) −20.3876 −1.04863
\(379\) −18.6051 −0.955681 −0.477841 0.878447i \(-0.658580\pi\)
−0.477841 + 0.878447i \(0.658580\pi\)
\(380\) 10.7917 0.553604
\(381\) 45.9708 2.35516
\(382\) −20.8461 −1.06658
\(383\) −21.3436 −1.09060 −0.545302 0.838239i \(-0.683585\pi\)
−0.545302 + 0.838239i \(0.683585\pi\)
\(384\) −41.0373 −2.09418
\(385\) −3.78158 −0.192727
\(386\) 35.3522 1.79938
\(387\) 30.8068 1.56600
\(388\) 24.5323 1.24544
\(389\) −33.8583 −1.71668 −0.858341 0.513079i \(-0.828505\pi\)
−0.858341 + 0.513079i \(0.828505\pi\)
\(390\) −28.7599 −1.45631
\(391\) −11.9990 −0.606815
\(392\) −1.87206 −0.0945531
\(393\) −9.13129 −0.460613
\(394\) 49.5517 2.49638
\(395\) −9.81951 −0.494073
\(396\) −65.4565 −3.28931
\(397\) 17.2818 0.867351 0.433675 0.901069i \(-0.357216\pi\)
0.433675 + 0.901069i \(0.357216\pi\)
\(398\) 20.4512 1.02513
\(399\) −11.4057 −0.570999
\(400\) −1.57731 −0.0788653
\(401\) −34.5449 −1.72509 −0.862545 0.505980i \(-0.831131\pi\)
−0.862545 + 0.505980i \(0.831131\pi\)
\(402\) −4.96641 −0.247702
\(403\) −21.6105 −1.07650
\(404\) −5.22695 −0.260051
\(405\) −9.66538 −0.480277
\(406\) −17.3876 −0.862934
\(407\) 10.2533 0.508235
\(408\) 8.02008 0.397053
\(409\) 23.5760 1.16576 0.582879 0.812559i \(-0.301926\pi\)
0.582879 + 0.812559i \(0.301926\pi\)
\(410\) −3.44499 −0.170136
\(411\) −9.47222 −0.467230
\(412\) −26.9797 −1.32919
\(413\) 9.60495 0.472629
\(414\) 112.841 5.54586
\(415\) −0.0758723 −0.00372442
\(416\) 31.2921 1.53422
\(417\) 35.7600 1.75117
\(418\) −31.5344 −1.54240
\(419\) −36.7564 −1.79567 −0.897833 0.440336i \(-0.854859\pi\)
−0.897833 + 0.440336i \(0.854859\pi\)
\(420\) −8.58492 −0.418901
\(421\) 1.34267 0.0654375 0.0327188 0.999465i \(-0.489583\pi\)
0.0327188 + 0.999465i \(0.489583\pi\)
\(422\) 33.3966 1.62572
\(423\) −18.8842 −0.918180
\(424\) −2.66114 −0.129236
\(425\) 1.42225 0.0689893
\(426\) 9.61031 0.465621
\(427\) 10.5797 0.511990
\(428\) 2.72267 0.131605
\(429\) 49.3840 2.38428
\(430\) 11.1710 0.538715
\(431\) −7.49466 −0.361005 −0.180503 0.983575i \(-0.557772\pi\)
−0.180503 + 0.983575i \(0.557772\pi\)
\(432\) 14.6019 0.702534
\(433\) −7.35574 −0.353495 −0.176747 0.984256i \(-0.556558\pi\)
−0.176747 + 0.984256i \(0.556558\pi\)
\(434\) −10.9776 −0.526942
\(435\) −23.7821 −1.14027
\(436\) 8.65625 0.414559
\(437\) 31.9453 1.52815
\(438\) 34.1114 1.62990
\(439\) −9.15590 −0.436987 −0.218494 0.975838i \(-0.570114\pi\)
−0.218494 + 0.975838i \(0.570114\pi\)
\(440\) −7.07932 −0.337493
\(441\) 6.07333 0.289206
\(442\) −13.5794 −0.645906
\(443\) 17.1794 0.816216 0.408108 0.912934i \(-0.366189\pi\)
0.408108 + 0.912934i \(0.366189\pi\)
\(444\) 23.2769 1.10467
\(445\) 14.5072 0.687706
\(446\) 9.99602 0.473325
\(447\) 54.5244 2.57892
\(448\) 12.7410 0.601956
\(449\) −4.72940 −0.223194 −0.111597 0.993754i \(-0.535597\pi\)
−0.111597 + 0.993754i \(0.535597\pi\)
\(450\) −13.3752 −0.630513
\(451\) 5.91544 0.278547
\(452\) 25.7963 1.21335
\(453\) 18.5241 0.870337
\(454\) −8.09188 −0.379771
\(455\) 4.33541 0.203247
\(456\) −21.3521 −0.999903
\(457\) 27.6705 1.29437 0.647185 0.762333i \(-0.275946\pi\)
0.647185 + 0.762333i \(0.275946\pi\)
\(458\) −2.20228 −0.102906
\(459\) −13.1665 −0.614559
\(460\) 24.0448 1.12109
\(461\) −29.1383 −1.35711 −0.678553 0.734551i \(-0.737393\pi\)
−0.678553 + 0.734551i \(0.737393\pi\)
\(462\) 25.0859 1.16710
\(463\) −34.8120 −1.61785 −0.808926 0.587910i \(-0.799951\pi\)
−0.808926 + 0.587910i \(0.799951\pi\)
\(464\) 12.4533 0.578129
\(465\) −15.0148 −0.696293
\(466\) 37.0274 1.71526
\(467\) −3.58396 −0.165846 −0.0829228 0.996556i \(-0.526426\pi\)
−0.0829228 + 0.996556i \(0.526426\pi\)
\(468\) 75.0430 3.46887
\(469\) 0.748661 0.0345700
\(470\) −6.84769 −0.315860
\(471\) −52.3842 −2.41374
\(472\) 17.9810 0.827643
\(473\) −19.1819 −0.881987
\(474\) 65.1398 2.99197
\(475\) −3.78650 −0.173737
\(476\) −4.05349 −0.185792
\(477\) 8.63328 0.395291
\(478\) −39.0351 −1.78543
\(479\) 24.9792 1.14133 0.570664 0.821184i \(-0.306686\pi\)
0.570664 + 0.821184i \(0.306686\pi\)
\(480\) 21.7414 0.992355
\(481\) −11.7549 −0.535978
\(482\) −41.5098 −1.89072
\(483\) −25.4128 −1.15632
\(484\) 9.40606 0.427548
\(485\) −8.60767 −0.390854
\(486\) 2.95451 0.134020
\(487\) 4.02620 0.182445 0.0912223 0.995831i \(-0.470923\pi\)
0.0912223 + 0.995831i \(0.470923\pi\)
\(488\) 19.8059 0.896570
\(489\) 19.9421 0.901813
\(490\) 2.20228 0.0994890
\(491\) −18.3784 −0.829407 −0.414703 0.909957i \(-0.636115\pi\)
−0.414703 + 0.909957i \(0.636115\pi\)
\(492\) 13.4292 0.605436
\(493\) −11.2291 −0.505732
\(494\) 36.1528 1.62659
\(495\) 22.9668 1.03228
\(496\) 7.86232 0.353029
\(497\) −1.44871 −0.0649834
\(498\) 0.503315 0.0225541
\(499\) −3.51102 −0.157175 −0.0785874 0.996907i \(-0.525041\pi\)
−0.0785874 + 0.996907i \(0.525041\pi\)
\(500\) −2.85005 −0.127458
\(501\) 63.2463 2.82564
\(502\) 10.9473 0.488601
\(503\) 19.7903 0.882405 0.441202 0.897408i \(-0.354552\pi\)
0.441202 + 0.897408i \(0.354552\pi\)
\(504\) 11.3696 0.506443
\(505\) 1.83398 0.0816113
\(506\) −70.2610 −3.12348
\(507\) −17.4581 −0.775341
\(508\) −43.4962 −1.92983
\(509\) 38.5748 1.70980 0.854899 0.518795i \(-0.173619\pi\)
0.854899 + 0.518795i \(0.173619\pi\)
\(510\) −9.43481 −0.417780
\(511\) −5.14212 −0.227474
\(512\) −17.2903 −0.764129
\(513\) 35.0535 1.54765
\(514\) −5.32291 −0.234783
\(515\) 9.46639 0.417139
\(516\) −43.5468 −1.91704
\(517\) 11.7583 0.517128
\(518\) −5.97121 −0.262360
\(519\) 47.8373 2.09982
\(520\) 8.11614 0.355916
\(521\) −27.2196 −1.19251 −0.596256 0.802794i \(-0.703346\pi\)
−0.596256 + 0.802794i \(0.703346\pi\)
\(522\) 105.601 4.62203
\(523\) 6.38232 0.279079 0.139540 0.990216i \(-0.455438\pi\)
0.139540 + 0.990216i \(0.455438\pi\)
\(524\) 8.63976 0.377429
\(525\) 3.01220 0.131463
\(526\) 16.6930 0.727849
\(527\) −7.08943 −0.308820
\(528\) −17.9669 −0.781907
\(529\) 48.1765 2.09463
\(530\) 3.13056 0.135983
\(531\) −58.3341 −2.53148
\(532\) 10.7917 0.467881
\(533\) −6.78180 −0.293752
\(534\) −96.2364 −4.16456
\(535\) −0.955305 −0.0413014
\(536\) 1.40154 0.0605371
\(537\) −24.8520 −1.07244
\(538\) 33.6575 1.45108
\(539\) −3.78158 −0.162884
\(540\) 26.3843 1.13540
\(541\) −26.9115 −1.15702 −0.578508 0.815677i \(-0.696365\pi\)
−0.578508 + 0.815677i \(0.696365\pi\)
\(542\) −4.38173 −0.188211
\(543\) −40.5399 −1.73973
\(544\) 10.2655 0.440130
\(545\) −3.03723 −0.130100
\(546\) −28.7599 −1.23081
\(547\) 28.9162 1.23637 0.618183 0.786034i \(-0.287869\pi\)
0.618183 + 0.786034i \(0.287869\pi\)
\(548\) 8.96234 0.382852
\(549\) −64.2543 −2.74231
\(550\) 8.32810 0.355111
\(551\) 29.8955 1.27359
\(552\) −47.5741 −2.02489
\(553\) −9.81951 −0.417568
\(554\) 56.6993 2.40892
\(555\) −8.16719 −0.346678
\(556\) −33.8350 −1.43493
\(557\) −14.7611 −0.625449 −0.312725 0.949844i \(-0.601242\pi\)
−0.312725 + 0.949844i \(0.601242\pi\)
\(558\) 66.6707 2.82240
\(559\) 21.9913 0.930132
\(560\) −1.57731 −0.0666534
\(561\) 16.2007 0.683992
\(562\) −50.3877 −2.12548
\(563\) −10.9805 −0.462774 −0.231387 0.972862i \(-0.574326\pi\)
−0.231387 + 0.972862i \(0.574326\pi\)
\(564\) 26.6936 1.12400
\(565\) −9.05115 −0.380785
\(566\) 14.6072 0.613988
\(567\) −9.66538 −0.405908
\(568\) −2.71206 −0.113796
\(569\) 33.1740 1.39073 0.695363 0.718659i \(-0.255244\pi\)
0.695363 + 0.718659i \(0.255244\pi\)
\(570\) 25.1186 1.05210
\(571\) −14.6394 −0.612640 −0.306320 0.951929i \(-0.599098\pi\)
−0.306320 + 0.951929i \(0.599098\pi\)
\(572\) −46.7257 −1.95370
\(573\) −28.5125 −1.19113
\(574\) −3.44499 −0.143791
\(575\) −8.43662 −0.351831
\(576\) −77.3804 −3.22418
\(577\) −36.5018 −1.51959 −0.759794 0.650164i \(-0.774700\pi\)
−0.759794 + 0.650164i \(0.774700\pi\)
\(578\) 32.9840 1.37196
\(579\) 48.3534 2.00950
\(580\) 22.5020 0.934343
\(581\) −0.0758723 −0.00314771
\(582\) 57.1008 2.36690
\(583\) −5.37553 −0.222632
\(584\) −9.62635 −0.398341
\(585\) −26.3304 −1.08863
\(586\) 15.1559 0.626085
\(587\) 10.5598 0.435848 0.217924 0.975966i \(-0.430071\pi\)
0.217924 + 0.975966i \(0.430071\pi\)
\(588\) −8.58492 −0.354036
\(589\) 18.8744 0.777705
\(590\) −21.1528 −0.870848
\(591\) 67.7749 2.78789
\(592\) 4.27666 0.175770
\(593\) 36.9143 1.51589 0.757945 0.652318i \(-0.226203\pi\)
0.757945 + 0.652318i \(0.226203\pi\)
\(594\) −77.0973 −3.16334
\(595\) 1.42225 0.0583066
\(596\) −51.5894 −2.11318
\(597\) 27.9724 1.14483
\(598\) 80.5512 3.29398
\(599\) −32.5743 −1.33095 −0.665475 0.746420i \(-0.731771\pi\)
−0.665475 + 0.746420i \(0.731771\pi\)
\(600\) 5.63900 0.230211
\(601\) 18.4055 0.750776 0.375388 0.926868i \(-0.377509\pi\)
0.375388 + 0.926868i \(0.377509\pi\)
\(602\) 11.1710 0.455297
\(603\) −4.54687 −0.185163
\(604\) −17.5269 −0.713161
\(605\) −3.30031 −0.134177
\(606\) −12.1661 −0.494215
\(607\) −18.7941 −0.762830 −0.381415 0.924404i \(-0.624563\pi\)
−0.381415 + 0.924404i \(0.624563\pi\)
\(608\) −27.3302 −1.10838
\(609\) −23.7821 −0.963701
\(610\) −23.2996 −0.943373
\(611\) −13.4804 −0.545357
\(612\) 24.6182 0.995132
\(613\) 16.8509 0.680601 0.340300 0.940317i \(-0.389471\pi\)
0.340300 + 0.940317i \(0.389471\pi\)
\(614\) −19.8707 −0.801917
\(615\) −4.71192 −0.190003
\(616\) −7.07932 −0.285234
\(617\) 19.4653 0.783645 0.391822 0.920041i \(-0.371845\pi\)
0.391822 + 0.920041i \(0.371845\pi\)
\(618\) −62.7973 −2.52608
\(619\) 21.4252 0.861152 0.430576 0.902554i \(-0.358310\pi\)
0.430576 + 0.902554i \(0.358310\pi\)
\(620\) 14.2065 0.570547
\(621\) 78.1019 3.13412
\(622\) 53.6356 2.15059
\(623\) 14.5072 0.581218
\(624\) 20.5982 0.824589
\(625\) 1.00000 0.0400000
\(626\) −6.57780 −0.262902
\(627\) −43.1315 −1.72250
\(628\) 49.5644 1.97783
\(629\) −3.85625 −0.153759
\(630\) −13.3752 −0.532881
\(631\) 6.59963 0.262727 0.131364 0.991334i \(-0.458064\pi\)
0.131364 + 0.991334i \(0.458064\pi\)
\(632\) −18.3827 −0.731223
\(633\) 45.6786 1.81556
\(634\) 45.4440 1.80481
\(635\) 15.2615 0.605636
\(636\) −12.2035 −0.483901
\(637\) 4.33541 0.171775
\(638\) −65.7527 −2.60317
\(639\) 8.79848 0.348063
\(640\) −13.6237 −0.538525
\(641\) −1.68300 −0.0664747 −0.0332373 0.999447i \(-0.510582\pi\)
−0.0332373 + 0.999447i \(0.510582\pi\)
\(642\) 6.33722 0.250110
\(643\) 40.3837 1.59258 0.796289 0.604916i \(-0.206793\pi\)
0.796289 + 0.604916i \(0.206793\pi\)
\(644\) 24.0448 0.947498
\(645\) 15.2793 0.601622
\(646\) 11.8601 0.466629
\(647\) 20.9387 0.823183 0.411592 0.911368i \(-0.364973\pi\)
0.411592 + 0.911368i \(0.364973\pi\)
\(648\) −18.0941 −0.710805
\(649\) 36.3219 1.42576
\(650\) −9.54781 −0.374496
\(651\) −15.0148 −0.588475
\(652\) −18.8686 −0.738952
\(653\) −29.4081 −1.15083 −0.575414 0.817863i \(-0.695159\pi\)
−0.575414 + 0.817863i \(0.695159\pi\)
\(654\) 20.1481 0.787852
\(655\) −3.03144 −0.118448
\(656\) 2.46735 0.0963337
\(657\) 31.2298 1.21839
\(658\) −6.84769 −0.266951
\(659\) 16.2680 0.633712 0.316856 0.948474i \(-0.397373\pi\)
0.316856 + 0.948474i \(0.397373\pi\)
\(660\) −32.4645 −1.26368
\(661\) −23.2298 −0.903534 −0.451767 0.892136i \(-0.649206\pi\)
−0.451767 + 0.892136i \(0.649206\pi\)
\(662\) 74.6136 2.89994
\(663\) −18.5734 −0.721329
\(664\) −0.142037 −0.00551211
\(665\) −3.78650 −0.146834
\(666\) 36.2651 1.40525
\(667\) 66.6095 2.57913
\(668\) −59.8418 −2.31535
\(669\) 13.6722 0.528597
\(670\) −1.64876 −0.0636973
\(671\) 40.0081 1.54450
\(672\) 21.7414 0.838693
\(673\) 13.4306 0.517712 0.258856 0.965916i \(-0.416654\pi\)
0.258856 + 0.965916i \(0.416654\pi\)
\(674\) 46.1332 1.77698
\(675\) −9.25749 −0.356321
\(676\) 16.5183 0.635321
\(677\) 31.6062 1.21473 0.607363 0.794424i \(-0.292227\pi\)
0.607363 + 0.794424i \(0.292227\pi\)
\(678\) 60.0427 2.30593
\(679\) −8.60767 −0.330332
\(680\) 2.66254 0.102104
\(681\) −11.0678 −0.424118
\(682\) −41.5127 −1.58960
\(683\) 24.8793 0.951981 0.475991 0.879450i \(-0.342090\pi\)
0.475991 + 0.879450i \(0.342090\pi\)
\(684\) −65.5417 −2.50605
\(685\) −3.14462 −0.120150
\(686\) 2.20228 0.0840836
\(687\) −3.01220 −0.114923
\(688\) −8.00085 −0.305029
\(689\) 6.16282 0.234785
\(690\) 55.9661 2.13059
\(691\) 0.365424 0.0139014 0.00695069 0.999976i \(-0.497788\pi\)
0.00695069 + 0.999976i \(0.497788\pi\)
\(692\) −45.2622 −1.72061
\(693\) 22.9668 0.872435
\(694\) 42.9697 1.63111
\(695\) 11.8717 0.450320
\(696\) −44.5215 −1.68758
\(697\) −2.22480 −0.0842703
\(698\) −15.8003 −0.598050
\(699\) 50.6446 1.91556
\(700\) −2.85005 −0.107722
\(701\) 23.3790 0.883012 0.441506 0.897258i \(-0.354444\pi\)
0.441506 + 0.897258i \(0.354444\pi\)
\(702\) 88.3887 3.33602
\(703\) 10.2666 0.387212
\(704\) 48.1811 1.81589
\(705\) −9.36600 −0.352744
\(706\) −20.7390 −0.780524
\(707\) 1.83398 0.0689741
\(708\) 82.4578 3.09895
\(709\) 7.45475 0.279969 0.139984 0.990154i \(-0.455295\pi\)
0.139984 + 0.990154i \(0.455295\pi\)
\(710\) 3.19046 0.119736
\(711\) 59.6371 2.23657
\(712\) 27.1582 1.01780
\(713\) 42.0536 1.57492
\(714\) −9.43481 −0.353089
\(715\) 16.3947 0.613127
\(716\) 23.5142 0.878768
\(717\) −53.3907 −1.99391
\(718\) −20.5480 −0.766846
\(719\) −41.4309 −1.54511 −0.772555 0.634947i \(-0.781022\pi\)
−0.772555 + 0.634947i \(0.781022\pi\)
\(720\) 9.57951 0.357007
\(721\) 9.46639 0.352547
\(722\) 10.2680 0.382134
\(723\) −56.7754 −2.11150
\(724\) 38.3576 1.42555
\(725\) −7.89528 −0.293223
\(726\) 21.8933 0.812537
\(727\) −10.5579 −0.391569 −0.195785 0.980647i \(-0.562725\pi\)
−0.195785 + 0.980647i \(0.562725\pi\)
\(728\) 8.11614 0.300804
\(729\) −24.9551 −0.924262
\(730\) 11.3244 0.419135
\(731\) 7.21434 0.266832
\(732\) 90.8263 3.35704
\(733\) 38.9965 1.44037 0.720184 0.693783i \(-0.244057\pi\)
0.720184 + 0.693783i \(0.244057\pi\)
\(734\) −39.8226 −1.46988
\(735\) 3.01220 0.111107
\(736\) −60.8937 −2.24457
\(737\) 2.83112 0.104286
\(738\) 20.9225 0.770170
\(739\) 6.56544 0.241514 0.120757 0.992682i \(-0.461468\pi\)
0.120757 + 0.992682i \(0.461468\pi\)
\(740\) 7.72755 0.284070
\(741\) 49.4484 1.81653
\(742\) 3.13056 0.114926
\(743\) 11.5345 0.423161 0.211581 0.977361i \(-0.432139\pi\)
0.211581 + 0.977361i \(0.432139\pi\)
\(744\) −28.1085 −1.03051
\(745\) 18.1012 0.663177
\(746\) −12.5110 −0.458062
\(747\) 0.460798 0.0168597
\(748\) −15.3286 −0.560469
\(749\) −0.955305 −0.0349061
\(750\) −6.63371 −0.242229
\(751\) 15.9499 0.582019 0.291010 0.956720i \(-0.406009\pi\)
0.291010 + 0.956720i \(0.406009\pi\)
\(752\) 4.90441 0.178846
\(753\) 14.9733 0.545657
\(754\) 75.3826 2.74527
\(755\) 6.14969 0.223810
\(756\) 26.3843 0.959589
\(757\) −36.4971 −1.32651 −0.663255 0.748394i \(-0.730825\pi\)
−0.663255 + 0.748394i \(0.730825\pi\)
\(758\) 40.9738 1.48823
\(759\) −96.1003 −3.48822
\(760\) −7.08854 −0.257128
\(761\) 29.2799 1.06140 0.530698 0.847561i \(-0.321930\pi\)
0.530698 + 0.847561i \(0.321930\pi\)
\(762\) −101.241 −3.66756
\(763\) −3.03723 −0.109955
\(764\) 26.9777 0.976017
\(765\) −8.63781 −0.312301
\(766\) 47.0046 1.69834
\(767\) −41.6414 −1.50358
\(768\) 13.6190 0.491434
\(769\) 31.3181 1.12936 0.564680 0.825310i \(-0.309000\pi\)
0.564680 + 0.825310i \(0.309000\pi\)
\(770\) 8.32810 0.300124
\(771\) −7.28046 −0.262199
\(772\) −45.7505 −1.64660
\(773\) 1.29537 0.0465911 0.0232956 0.999729i \(-0.492584\pi\)
0.0232956 + 0.999729i \(0.492584\pi\)
\(774\) −67.8454 −2.43865
\(775\) −4.98465 −0.179054
\(776\) −16.1140 −0.578460
\(777\) −8.16719 −0.292996
\(778\) 74.5655 2.67330
\(779\) 5.92314 0.212219
\(780\) 37.2192 1.33266
\(781\) −5.47840 −0.196032
\(782\) 26.4252 0.944963
\(783\) 73.0904 2.61204
\(784\) −1.57731 −0.0563324
\(785\) −17.3907 −0.620700
\(786\) 20.1097 0.717289
\(787\) 41.5502 1.48111 0.740553 0.671998i \(-0.234564\pi\)
0.740553 + 0.671998i \(0.234564\pi\)
\(788\) −64.1267 −2.28442
\(789\) 22.8320 0.812842
\(790\) 21.6253 0.769395
\(791\) −9.05115 −0.321822
\(792\) 42.9951 1.52776
\(793\) −45.8676 −1.62881
\(794\) −38.0595 −1.35068
\(795\) 4.28186 0.151862
\(796\) −26.4666 −0.938085
\(797\) −21.9005 −0.775756 −0.387878 0.921711i \(-0.626792\pi\)
−0.387878 + 0.921711i \(0.626792\pi\)
\(798\) 25.1186 0.889187
\(799\) −4.42229 −0.156449
\(800\) 7.21779 0.255187
\(801\) −88.1069 −3.11310
\(802\) 76.0777 2.68640
\(803\) −19.4453 −0.686211
\(804\) 6.42720 0.226670
\(805\) −8.43662 −0.297352
\(806\) 47.5925 1.67637
\(807\) 46.0354 1.62052
\(808\) 3.43332 0.120784
\(809\) 9.39275 0.330232 0.165116 0.986274i \(-0.447200\pi\)
0.165116 + 0.986274i \(0.447200\pi\)
\(810\) 21.2859 0.747910
\(811\) −31.7952 −1.11648 −0.558240 0.829680i \(-0.688523\pi\)
−0.558240 + 0.829680i \(0.688523\pi\)
\(812\) 22.5020 0.789664
\(813\) −5.99316 −0.210189
\(814\) −22.5806 −0.791449
\(815\) 6.62045 0.231904
\(816\) 6.75734 0.236554
\(817\) −19.2069 −0.671965
\(818\) −51.9210 −1.81538
\(819\) −26.3304 −0.920059
\(820\) 4.45828 0.155690
\(821\) −28.5619 −0.996818 −0.498409 0.866942i \(-0.666082\pi\)
−0.498409 + 0.866942i \(0.666082\pi\)
\(822\) 20.8605 0.727594
\(823\) −7.52021 −0.262138 −0.131069 0.991373i \(-0.541841\pi\)
−0.131069 + 0.991373i \(0.541841\pi\)
\(824\) 17.7216 0.617361
\(825\) 11.3909 0.396579
\(826\) −21.1528 −0.736001
\(827\) −29.9178 −1.04034 −0.520171 0.854062i \(-0.674132\pi\)
−0.520171 + 0.854062i \(0.674132\pi\)
\(828\) −146.032 −5.07497
\(829\) −30.9662 −1.07550 −0.537750 0.843104i \(-0.680726\pi\)
−0.537750 + 0.843104i \(0.680726\pi\)
\(830\) 0.167092 0.00579986
\(831\) 77.5511 2.69022
\(832\) −55.2375 −1.91502
\(833\) 1.42225 0.0492781
\(834\) −78.7536 −2.72701
\(835\) 20.9967 0.726622
\(836\) 40.8097 1.41143
\(837\) 46.1453 1.59502
\(838\) 80.9479 2.79630
\(839\) 29.6014 1.02196 0.510978 0.859594i \(-0.329284\pi\)
0.510978 + 0.859594i \(0.329284\pi\)
\(840\) 5.63900 0.194564
\(841\) 33.3354 1.14950
\(842\) −2.95693 −0.101903
\(843\) −68.9183 −2.37367
\(844\) −43.2197 −1.48768
\(845\) −5.79580 −0.199382
\(846\) 41.5883 1.42984
\(847\) −3.30031 −0.113400
\(848\) −2.24215 −0.0769958
\(849\) 19.9792 0.685685
\(850\) −3.13220 −0.107434
\(851\) 22.8748 0.784138
\(852\) −12.4370 −0.426086
\(853\) −3.48457 −0.119309 −0.0596547 0.998219i \(-0.519000\pi\)
−0.0596547 + 0.998219i \(0.519000\pi\)
\(854\) −23.2996 −0.797296
\(855\) 22.9967 0.786470
\(856\) −1.78838 −0.0611257
\(857\) −5.86120 −0.200215 −0.100107 0.994977i \(-0.531919\pi\)
−0.100107 + 0.994977i \(0.531919\pi\)
\(858\) −108.758 −3.71292
\(859\) −13.8263 −0.471746 −0.235873 0.971784i \(-0.575795\pi\)
−0.235873 + 0.971784i \(0.575795\pi\)
\(860\) −14.4568 −0.492973
\(861\) −4.71192 −0.160582
\(862\) 16.5054 0.562175
\(863\) −46.9250 −1.59735 −0.798673 0.601766i \(-0.794464\pi\)
−0.798673 + 0.601766i \(0.794464\pi\)
\(864\) −66.8186 −2.27321
\(865\) 15.8812 0.539977
\(866\) 16.1994 0.550479
\(867\) 45.1143 1.53216
\(868\) 14.2065 0.482201
\(869\) −37.1332 −1.25966
\(870\) 52.3750 1.77568
\(871\) −3.24576 −0.109978
\(872\) −5.68586 −0.192547
\(873\) 52.2772 1.76932
\(874\) −70.3525 −2.37971
\(875\) 1.00000 0.0338062
\(876\) −44.1447 −1.49151
\(877\) −49.1993 −1.66134 −0.830671 0.556763i \(-0.812043\pi\)
−0.830671 + 0.556763i \(0.812043\pi\)
\(878\) 20.1639 0.680498
\(879\) 20.7297 0.699194
\(880\) −5.96470 −0.201070
\(881\) 26.5334 0.893934 0.446967 0.894550i \(-0.352504\pi\)
0.446967 + 0.894550i \(0.352504\pi\)
\(882\) −13.3752 −0.450366
\(883\) 26.7806 0.901238 0.450619 0.892716i \(-0.351203\pi\)
0.450619 + 0.892716i \(0.351203\pi\)
\(884\) 17.5736 0.591063
\(885\) −28.9320 −0.972539
\(886\) −37.8338 −1.27105
\(887\) 22.7884 0.765158 0.382579 0.923923i \(-0.375036\pi\)
0.382579 + 0.923923i \(0.375036\pi\)
\(888\) −15.2894 −0.513080
\(889\) 15.2615 0.511856
\(890\) −31.9489 −1.07093
\(891\) −36.5504 −1.22448
\(892\) −12.9362 −0.433136
\(893\) 11.7736 0.393988
\(894\) −120.078 −4.01601
\(895\) −8.25045 −0.275782
\(896\) −13.6237 −0.455137
\(897\) 110.175 3.67863
\(898\) 10.4155 0.347569
\(899\) 39.3552 1.31257
\(900\) 17.3093 0.576977
\(901\) 2.02174 0.0673539
\(902\) −13.0275 −0.433767
\(903\) 15.2793 0.508463
\(904\) −16.9443 −0.563558
\(905\) −13.4586 −0.447378
\(906\) −40.7953 −1.35533
\(907\) −36.1619 −1.20074 −0.600368 0.799724i \(-0.704979\pi\)
−0.600368 + 0.799724i \(0.704979\pi\)
\(908\) 10.4720 0.347525
\(909\) −11.1384 −0.369437
\(910\) −9.54781 −0.316507
\(911\) −47.5345 −1.57489 −0.787444 0.616387i \(-0.788596\pi\)
−0.787444 + 0.616387i \(0.788596\pi\)
\(912\) −17.9903 −0.595717
\(913\) −0.286917 −0.00949556
\(914\) −60.9382 −2.01566
\(915\) −31.8683 −1.05353
\(916\) 2.85005 0.0941684
\(917\) −3.03144 −0.100107
\(918\) 28.9963 0.957021
\(919\) −7.87020 −0.259614 −0.129807 0.991539i \(-0.541436\pi\)
−0.129807 + 0.991539i \(0.541436\pi\)
\(920\) −15.7938 −0.520707
\(921\) −27.1784 −0.895558
\(922\) 64.1708 2.11335
\(923\) 6.28074 0.206733
\(924\) −32.4645 −1.06800
\(925\) −2.71137 −0.0891493
\(926\) 76.6660 2.51940
\(927\) −57.4925 −1.88830
\(928\) −56.9864 −1.87067
\(929\) 56.1990 1.84383 0.921915 0.387392i \(-0.126624\pi\)
0.921915 + 0.387392i \(0.126624\pi\)
\(930\) 33.0667 1.08430
\(931\) −3.78650 −0.124098
\(932\) −47.9185 −1.56962
\(933\) 73.3607 2.40172
\(934\) 7.89289 0.258263
\(935\) 5.37835 0.175891
\(936\) −49.2920 −1.61116
\(937\) 40.8418 1.33424 0.667122 0.744948i \(-0.267526\pi\)
0.667122 + 0.744948i \(0.267526\pi\)
\(938\) −1.64876 −0.0538341
\(939\) −8.99686 −0.293601
\(940\) 8.86184 0.289041
\(941\) −32.4457 −1.05770 −0.528850 0.848715i \(-0.677377\pi\)
−0.528850 + 0.848715i \(0.677377\pi\)
\(942\) 115.365 3.75879
\(943\) 13.1972 0.429761
\(944\) 15.1500 0.493089
\(945\) −9.25749 −0.301146
\(946\) 42.2441 1.37347
\(947\) 17.9499 0.583292 0.291646 0.956526i \(-0.405797\pi\)
0.291646 + 0.956526i \(0.405797\pi\)
\(948\) −84.2997 −2.73793
\(949\) 22.2932 0.723669
\(950\) 8.33895 0.270551
\(951\) 62.1565 2.01556
\(952\) 2.66254 0.0862933
\(953\) −1.98786 −0.0643929 −0.0321965 0.999482i \(-0.510250\pi\)
−0.0321965 + 0.999482i \(0.510250\pi\)
\(954\) −19.0129 −0.615566
\(955\) −9.46567 −0.306302
\(956\) 50.5167 1.63383
\(957\) −89.9339 −2.90715
\(958\) −55.0112 −1.77733
\(959\) −3.14462 −0.101545
\(960\) −38.3784 −1.23866
\(961\) −6.15325 −0.198492
\(962\) 25.8876 0.834651
\(963\) 5.80189 0.186963
\(964\) 53.7192 1.73018
\(965\) 16.0525 0.516749
\(966\) 55.9661 1.80068
\(967\) 47.0012 1.51146 0.755728 0.654885i \(-0.227283\pi\)
0.755728 + 0.654885i \(0.227283\pi\)
\(968\) −6.17837 −0.198580
\(969\) 16.2218 0.521118
\(970\) 18.9565 0.608657
\(971\) −53.3009 −1.71051 −0.855254 0.518210i \(-0.826599\pi\)
−0.855254 + 0.518210i \(0.826599\pi\)
\(972\) −3.82354 −0.122640
\(973\) 11.8717 0.380590
\(974\) −8.86684 −0.284112
\(975\) −13.0591 −0.418226
\(976\) 16.6875 0.534154
\(977\) −18.5001 −0.591871 −0.295935 0.955208i \(-0.595631\pi\)
−0.295935 + 0.955208i \(0.595631\pi\)
\(978\) −43.9182 −1.40435
\(979\) 54.8600 1.75333
\(980\) −2.85005 −0.0910416
\(981\) 18.4461 0.588938
\(982\) 40.4745 1.29159
\(983\) −38.3996 −1.22476 −0.612379 0.790564i \(-0.709787\pi\)
−0.612379 + 0.790564i \(0.709787\pi\)
\(984\) −8.82097 −0.281202
\(985\) 22.5002 0.716915
\(986\) 24.7296 0.787551
\(987\) −9.36600 −0.298123
\(988\) −46.7866 −1.48848
\(989\) −42.7945 −1.36079
\(990\) −50.5793 −1.60752
\(991\) −36.0994 −1.14673 −0.573367 0.819298i \(-0.694363\pi\)
−0.573367 + 0.819298i \(0.694363\pi\)
\(992\) −35.9782 −1.14231
\(993\) 102.054 3.23857
\(994\) 3.19046 0.101195
\(995\) 9.28637 0.294398
\(996\) −0.651358 −0.0206391
\(997\) 2.67421 0.0846931 0.0423465 0.999103i \(-0.486517\pi\)
0.0423465 + 0.999103i \(0.486517\pi\)
\(998\) 7.73226 0.244761
\(999\) 25.1005 0.794144
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 \(a_p\))