Properties

Label 6025.2.a.h.1.6
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.115670\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.115670 q^{2}\) \(+3.28295 q^{3}\) \(-1.98662 q^{4}\) \(-0.379739 q^{6}\) \(-3.19647 q^{7}\) \(+0.461133 q^{8}\) \(+7.77775 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.115670 q^{2}\) \(+3.28295 q^{3}\) \(-1.98662 q^{4}\) \(-0.379739 q^{6}\) \(-3.19647 q^{7}\) \(+0.461133 q^{8}\) \(+7.77775 q^{9}\) \(+1.38968 q^{11}\) \(-6.52197 q^{12}\) \(+5.87704 q^{13}\) \(+0.369736 q^{14}\) \(+3.91990 q^{16}\) \(-5.28927 q^{17}\) \(-0.899653 q^{18}\) \(+4.99913 q^{19}\) \(-10.4938 q^{21}\) \(-0.160744 q^{22}\) \(-3.07207 q^{23}\) \(+1.51387 q^{24}\) \(-0.679798 q^{26}\) \(+15.6851 q^{27}\) \(+6.35017 q^{28}\) \(+3.28657 q^{29}\) \(+0.672296 q^{31}\) \(-1.37568 q^{32}\) \(+4.56225 q^{33}\) \(+0.611810 q^{34}\) \(-15.4514 q^{36}\) \(+3.79547 q^{37}\) \(-0.578249 q^{38}\) \(+19.2940 q^{39}\) \(+0.970489 q^{41}\) \(+1.21382 q^{42}\) \(-7.93946 q^{43}\) \(-2.76077 q^{44}\) \(+0.355346 q^{46}\) \(-2.82021 q^{47}\) \(+12.8688 q^{48}\) \(+3.21740 q^{49}\) \(-17.3644 q^{51}\) \(-11.6754 q^{52}\) \(-8.45419 q^{53}\) \(-1.81430 q^{54}\) \(-1.47400 q^{56}\) \(+16.4119 q^{57}\) \(-0.380158 q^{58}\) \(+5.70844 q^{59}\) \(+0.717980 q^{61}\) \(-0.0777646 q^{62}\) \(-24.8613 q^{63}\) \(-7.68068 q^{64}\) \(-0.527716 q^{66}\) \(-8.81215 q^{67}\) \(+10.5078 q^{68}\) \(-10.0854 q^{69}\) \(+15.8552 q^{71}\) \(+3.58657 q^{72}\) \(+8.75018 q^{73}\) \(-0.439022 q^{74}\) \(-9.93137 q^{76}\) \(-4.44207 q^{77}\) \(-2.23174 q^{78}\) \(+11.4452 q^{79}\) \(+28.1601 q^{81}\) \(-0.112256 q^{82}\) \(+11.9246 q^{83}\) \(+20.8473 q^{84}\) \(+0.918358 q^{86}\) \(+10.7896 q^{87}\) \(+0.640827 q^{88}\) \(-11.9996 q^{89}\) \(-18.7858 q^{91}\) \(+6.10304 q^{92}\) \(+2.20711 q^{93}\) \(+0.326214 q^{94}\) \(-4.51629 q^{96}\) \(-1.18886 q^{97}\) \(-0.372157 q^{98}\) \(+10.8086 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 49q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 34q^{47} \) \(\mathstrut +\mathstrut 49q^{48} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 94q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 7q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 3q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 28q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.115670 −0.0817911 −0.0408955 0.999163i \(-0.513021\pi\)
−0.0408955 + 0.999163i \(0.513021\pi\)
\(3\) 3.28295 1.89541 0.947705 0.319146i \(-0.103396\pi\)
0.947705 + 0.319146i \(0.103396\pi\)
\(4\) −1.98662 −0.993310
\(5\) 0 0
\(6\) −0.379739 −0.155028
\(7\) −3.19647 −1.20815 −0.604076 0.796927i \(-0.706457\pi\)
−0.604076 + 0.796927i \(0.706457\pi\)
\(8\) 0.461133 0.163035
\(9\) 7.77775 2.59258
\(10\) 0 0
\(11\) 1.38968 0.419005 0.209502 0.977808i \(-0.432816\pi\)
0.209502 + 0.977808i \(0.432816\pi\)
\(12\) −6.52197 −1.88273
\(13\) 5.87704 1.63000 0.814999 0.579463i \(-0.196738\pi\)
0.814999 + 0.579463i \(0.196738\pi\)
\(14\) 0.369736 0.0988160
\(15\) 0 0
\(16\) 3.91990 0.979975
\(17\) −5.28927 −1.28284 −0.641418 0.767191i \(-0.721654\pi\)
−0.641418 + 0.767191i \(0.721654\pi\)
\(18\) −0.899653 −0.212050
\(19\) 4.99913 1.14688 0.573439 0.819248i \(-0.305609\pi\)
0.573439 + 0.819248i \(0.305609\pi\)
\(20\) 0 0
\(21\) −10.4938 −2.28994
\(22\) −0.160744 −0.0342708
\(23\) −3.07207 −0.640571 −0.320285 0.947321i \(-0.603779\pi\)
−0.320285 + 0.947321i \(0.603779\pi\)
\(24\) 1.51387 0.309018
\(25\) 0 0
\(26\) −0.679798 −0.133319
\(27\) 15.6851 3.01860
\(28\) 6.35017 1.20007
\(29\) 3.28657 0.610301 0.305150 0.952304i \(-0.401293\pi\)
0.305150 + 0.952304i \(0.401293\pi\)
\(30\) 0 0
\(31\) 0.672296 0.120748 0.0603740 0.998176i \(-0.480771\pi\)
0.0603740 + 0.998176i \(0.480771\pi\)
\(32\) −1.37568 −0.243188
\(33\) 4.56225 0.794186
\(34\) 0.611810 0.104925
\(35\) 0 0
\(36\) −15.4514 −2.57524
\(37\) 3.79547 0.623971 0.311986 0.950087i \(-0.399006\pi\)
0.311986 + 0.950087i \(0.399006\pi\)
\(38\) −0.578249 −0.0938044
\(39\) 19.2940 3.08952
\(40\) 0 0
\(41\) 0.970489 0.151565 0.0757824 0.997124i \(-0.475855\pi\)
0.0757824 + 0.997124i \(0.475855\pi\)
\(42\) 1.21382 0.187297
\(43\) −7.93946 −1.21076 −0.605378 0.795938i \(-0.706978\pi\)
−0.605378 + 0.795938i \(0.706978\pi\)
\(44\) −2.76077 −0.416201
\(45\) 0 0
\(46\) 0.355346 0.0523930
\(47\) −2.82021 −0.411370 −0.205685 0.978618i \(-0.565942\pi\)
−0.205685 + 0.978618i \(0.565942\pi\)
\(48\) 12.8688 1.85746
\(49\) 3.21740 0.459629
\(50\) 0 0
\(51\) −17.3644 −2.43150
\(52\) −11.6754 −1.61909
\(53\) −8.45419 −1.16127 −0.580636 0.814163i \(-0.697196\pi\)
−0.580636 + 0.814163i \(0.697196\pi\)
\(54\) −1.81430 −0.246894
\(55\) 0 0
\(56\) −1.47400 −0.196971
\(57\) 16.4119 2.17381
\(58\) −0.380158 −0.0499172
\(59\) 5.70844 0.743176 0.371588 0.928398i \(-0.378813\pi\)
0.371588 + 0.928398i \(0.378813\pi\)
\(60\) 0 0
\(61\) 0.717980 0.0919279 0.0459639 0.998943i \(-0.485364\pi\)
0.0459639 + 0.998943i \(0.485364\pi\)
\(62\) −0.0777646 −0.00987611
\(63\) −24.8613 −3.13223
\(64\) −7.68068 −0.960085
\(65\) 0 0
\(66\) −0.527716 −0.0649573
\(67\) −8.81215 −1.07658 −0.538288 0.842761i \(-0.680929\pi\)
−0.538288 + 0.842761i \(0.680929\pi\)
\(68\) 10.5078 1.27425
\(69\) −10.0854 −1.21414
\(70\) 0 0
\(71\) 15.8552 1.88166 0.940832 0.338874i \(-0.110046\pi\)
0.940832 + 0.338874i \(0.110046\pi\)
\(72\) 3.58657 0.422682
\(73\) 8.75018 1.02413 0.512066 0.858946i \(-0.328880\pi\)
0.512066 + 0.858946i \(0.328880\pi\)
\(74\) −0.439022 −0.0510353
\(75\) 0 0
\(76\) −9.93137 −1.13921
\(77\) −4.44207 −0.506221
\(78\) −2.23174 −0.252695
\(79\) 11.4452 1.28769 0.643843 0.765158i \(-0.277339\pi\)
0.643843 + 0.765158i \(0.277339\pi\)
\(80\) 0 0
\(81\) 28.1601 3.12890
\(82\) −0.112256 −0.0123967
\(83\) 11.9246 1.30889 0.654446 0.756109i \(-0.272902\pi\)
0.654446 + 0.756109i \(0.272902\pi\)
\(84\) 20.8473 2.27462
\(85\) 0 0
\(86\) 0.918358 0.0990291
\(87\) 10.7896 1.15677
\(88\) 0.640827 0.0683124
\(89\) −11.9996 −1.27195 −0.635975 0.771709i \(-0.719402\pi\)
−0.635975 + 0.771709i \(0.719402\pi\)
\(90\) 0 0
\(91\) −18.7858 −1.96928
\(92\) 6.10304 0.636285
\(93\) 2.20711 0.228867
\(94\) 0.326214 0.0336464
\(95\) 0 0
\(96\) −4.51629 −0.460942
\(97\) −1.18886 −0.120710 −0.0603550 0.998177i \(-0.519223\pi\)
−0.0603550 + 0.998177i \(0.519223\pi\)
\(98\) −0.372157 −0.0375936
\(99\) 10.8086 1.08630
\(100\) 0 0
\(101\) 19.9051 1.98064 0.990318 0.138820i \(-0.0443311\pi\)
0.990318 + 0.138820i \(0.0443311\pi\)
\(102\) 2.00854 0.198875
\(103\) 2.74129 0.270108 0.135054 0.990838i \(-0.456879\pi\)
0.135054 + 0.990838i \(0.456879\pi\)
\(104\) 2.71010 0.265747
\(105\) 0 0
\(106\) 0.977897 0.0949817
\(107\) 9.95829 0.962704 0.481352 0.876527i \(-0.340146\pi\)
0.481352 + 0.876527i \(0.340146\pi\)
\(108\) −31.1603 −2.99840
\(109\) −5.65622 −0.541768 −0.270884 0.962612i \(-0.587316\pi\)
−0.270884 + 0.962612i \(0.587316\pi\)
\(110\) 0 0
\(111\) 12.4603 1.18268
\(112\) −12.5298 −1.18396
\(113\) 12.9604 1.21921 0.609604 0.792706i \(-0.291329\pi\)
0.609604 + 0.792706i \(0.291329\pi\)
\(114\) −1.89836 −0.177798
\(115\) 0 0
\(116\) −6.52917 −0.606218
\(117\) 45.7101 4.22590
\(118\) −0.660296 −0.0607852
\(119\) 16.9070 1.54986
\(120\) 0 0
\(121\) −9.06879 −0.824435
\(122\) −0.0830488 −0.00751888
\(123\) 3.18606 0.287278
\(124\) −1.33560 −0.119940
\(125\) 0 0
\(126\) 2.87571 0.256189
\(127\) 10.4647 0.928593 0.464297 0.885680i \(-0.346307\pi\)
0.464297 + 0.885680i \(0.346307\pi\)
\(128\) 3.63979 0.321715
\(129\) −26.0648 −2.29488
\(130\) 0 0
\(131\) 12.9607 1.13238 0.566190 0.824275i \(-0.308417\pi\)
0.566190 + 0.824275i \(0.308417\pi\)
\(132\) −9.06346 −0.788873
\(133\) −15.9795 −1.38560
\(134\) 1.01930 0.0880543
\(135\) 0 0
\(136\) −2.43906 −0.209147
\(137\) −14.1420 −1.20824 −0.604118 0.796895i \(-0.706474\pi\)
−0.604118 + 0.796895i \(0.706474\pi\)
\(138\) 1.16658 0.0993062
\(139\) −16.8589 −1.42996 −0.714978 0.699147i \(-0.753563\pi\)
−0.714978 + 0.699147i \(0.753563\pi\)
\(140\) 0 0
\(141\) −9.25861 −0.779716
\(142\) −1.83397 −0.153903
\(143\) 8.16721 0.682976
\(144\) 30.4880 2.54067
\(145\) 0 0
\(146\) −1.01213 −0.0837648
\(147\) 10.5626 0.871186
\(148\) −7.54015 −0.619797
\(149\) 16.2523 1.33144 0.665722 0.746200i \(-0.268124\pi\)
0.665722 + 0.746200i \(0.268124\pi\)
\(150\) 0 0
\(151\) −10.4085 −0.847035 −0.423517 0.905888i \(-0.639205\pi\)
−0.423517 + 0.905888i \(0.639205\pi\)
\(152\) 2.30526 0.186981
\(153\) −41.1386 −3.32586
\(154\) 0.513814 0.0414043
\(155\) 0 0
\(156\) −38.3299 −3.06885
\(157\) 18.9894 1.51552 0.757758 0.652535i \(-0.226295\pi\)
0.757758 + 0.652535i \(0.226295\pi\)
\(158\) −1.32387 −0.105321
\(159\) −27.7547 −2.20109
\(160\) 0 0
\(161\) 9.81977 0.773906
\(162\) −3.25728 −0.255916
\(163\) −7.43947 −0.582704 −0.291352 0.956616i \(-0.594105\pi\)
−0.291352 + 0.956616i \(0.594105\pi\)
\(164\) −1.92799 −0.150551
\(165\) 0 0
\(166\) −1.37932 −0.107056
\(167\) −13.4159 −1.03815 −0.519076 0.854728i \(-0.673724\pi\)
−0.519076 + 0.854728i \(0.673724\pi\)
\(168\) −4.83905 −0.373341
\(169\) 21.5396 1.65689
\(170\) 0 0
\(171\) 38.8819 2.97338
\(172\) 15.7727 1.20266
\(173\) 3.18442 0.242107 0.121053 0.992646i \(-0.461373\pi\)
0.121053 + 0.992646i \(0.461373\pi\)
\(174\) −1.24804 −0.0946135
\(175\) 0 0
\(176\) 5.44741 0.410614
\(177\) 18.7405 1.40862
\(178\) 1.38799 0.104034
\(179\) 11.8290 0.884142 0.442071 0.896980i \(-0.354244\pi\)
0.442071 + 0.896980i \(0.354244\pi\)
\(180\) 0 0
\(181\) −3.92038 −0.291399 −0.145700 0.989329i \(-0.546543\pi\)
−0.145700 + 0.989329i \(0.546543\pi\)
\(182\) 2.17295 0.161070
\(183\) 2.35709 0.174241
\(184\) −1.41663 −0.104435
\(185\) 0 0
\(186\) −0.255297 −0.0187193
\(187\) −7.35040 −0.537514
\(188\) 5.60269 0.408618
\(189\) −50.1369 −3.64692
\(190\) 0 0
\(191\) 1.27094 0.0919617 0.0459809 0.998942i \(-0.485359\pi\)
0.0459809 + 0.998942i \(0.485359\pi\)
\(192\) −25.2153 −1.81976
\(193\) 7.18460 0.517159 0.258580 0.965990i \(-0.416746\pi\)
0.258580 + 0.965990i \(0.416746\pi\)
\(194\) 0.137515 0.00987300
\(195\) 0 0
\(196\) −6.39176 −0.456554
\(197\) −6.64645 −0.473540 −0.236770 0.971566i \(-0.576089\pi\)
−0.236770 + 0.971566i \(0.576089\pi\)
\(198\) −1.25023 −0.0888500
\(199\) 12.7358 0.902819 0.451410 0.892317i \(-0.350921\pi\)
0.451410 + 0.892317i \(0.350921\pi\)
\(200\) 0 0
\(201\) −28.9298 −2.04055
\(202\) −2.30243 −0.161998
\(203\) −10.5054 −0.737336
\(204\) 34.4965 2.41524
\(205\) 0 0
\(206\) −0.317085 −0.0220924
\(207\) −23.8938 −1.66073
\(208\) 23.0374 1.59736
\(209\) 6.94719 0.480547
\(210\) 0 0
\(211\) 5.22527 0.359722 0.179861 0.983692i \(-0.442435\pi\)
0.179861 + 0.983692i \(0.442435\pi\)
\(212\) 16.7953 1.15350
\(213\) 52.0517 3.56653
\(214\) −1.15188 −0.0787406
\(215\) 0 0
\(216\) 7.23291 0.492137
\(217\) −2.14897 −0.145882
\(218\) 0.654256 0.0443118
\(219\) 28.7264 1.94115
\(220\) 0 0
\(221\) −31.0853 −2.09102
\(222\) −1.44129 −0.0967328
\(223\) 1.68503 0.112838 0.0564191 0.998407i \(-0.482032\pi\)
0.0564191 + 0.998407i \(0.482032\pi\)
\(224\) 4.39732 0.293808
\(225\) 0 0
\(226\) −1.49913 −0.0997203
\(227\) 1.27020 0.0843064 0.0421532 0.999111i \(-0.486578\pi\)
0.0421532 + 0.999111i \(0.486578\pi\)
\(228\) −32.6042 −2.15926
\(229\) 24.4833 1.61790 0.808950 0.587877i \(-0.200036\pi\)
0.808950 + 0.587877i \(0.200036\pi\)
\(230\) 0 0
\(231\) −14.5831 −0.959496
\(232\) 1.51554 0.0995004
\(233\) −3.58351 −0.234764 −0.117382 0.993087i \(-0.537450\pi\)
−0.117382 + 0.993087i \(0.537450\pi\)
\(234\) −5.28729 −0.345641
\(235\) 0 0
\(236\) −11.3405 −0.738204
\(237\) 37.5740 2.44069
\(238\) −1.95563 −0.126765
\(239\) −27.0261 −1.74817 −0.874087 0.485769i \(-0.838540\pi\)
−0.874087 + 0.485769i \(0.838540\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 1.04899 0.0674315
\(243\) 45.3929 2.91195
\(244\) −1.42635 −0.0913129
\(245\) 0 0
\(246\) −0.368532 −0.0234968
\(247\) 29.3801 1.86941
\(248\) 0.310018 0.0196862
\(249\) 39.1478 2.48089
\(250\) 0 0
\(251\) −19.0710 −1.20375 −0.601874 0.798591i \(-0.705579\pi\)
−0.601874 + 0.798591i \(0.705579\pi\)
\(252\) 49.3900 3.11128
\(253\) −4.26920 −0.268402
\(254\) −1.21045 −0.0759506
\(255\) 0 0
\(256\) 14.9403 0.933771
\(257\) 29.8662 1.86300 0.931502 0.363736i \(-0.118499\pi\)
0.931502 + 0.363736i \(0.118499\pi\)
\(258\) 3.01492 0.187701
\(259\) −12.1321 −0.753851
\(260\) 0 0
\(261\) 25.5621 1.58225
\(262\) −1.49916 −0.0926186
\(263\) 14.4912 0.893563 0.446781 0.894643i \(-0.352570\pi\)
0.446781 + 0.894643i \(0.352570\pi\)
\(264\) 2.10380 0.129480
\(265\) 0 0
\(266\) 1.84835 0.113330
\(267\) −39.3939 −2.41087
\(268\) 17.5064 1.06937
\(269\) 9.73320 0.593444 0.296722 0.954964i \(-0.404107\pi\)
0.296722 + 0.954964i \(0.404107\pi\)
\(270\) 0 0
\(271\) 17.7984 1.08117 0.540587 0.841288i \(-0.318202\pi\)
0.540587 + 0.841288i \(0.318202\pi\)
\(272\) −20.7334 −1.25715
\(273\) −61.6727 −3.73260
\(274\) 1.63581 0.0988229
\(275\) 0 0
\(276\) 20.0359 1.20602
\(277\) −2.28565 −0.137332 −0.0686658 0.997640i \(-0.521874\pi\)
−0.0686658 + 0.997640i \(0.521874\pi\)
\(278\) 1.95007 0.116958
\(279\) 5.22895 0.313049
\(280\) 0 0
\(281\) 9.34433 0.557436 0.278718 0.960373i \(-0.410090\pi\)
0.278718 + 0.960373i \(0.410090\pi\)
\(282\) 1.07094 0.0637738
\(283\) −8.86628 −0.527045 −0.263523 0.964653i \(-0.584884\pi\)
−0.263523 + 0.964653i \(0.584884\pi\)
\(284\) −31.4982 −1.86908
\(285\) 0 0
\(286\) −0.944702 −0.0558614
\(287\) −3.10214 −0.183113
\(288\) −10.6997 −0.630486
\(289\) 10.9764 0.645670
\(290\) 0 0
\(291\) −3.90295 −0.228795
\(292\) −17.3833 −1.01728
\(293\) −17.1228 −1.00032 −0.500161 0.865932i \(-0.666726\pi\)
−0.500161 + 0.865932i \(0.666726\pi\)
\(294\) −1.22177 −0.0712552
\(295\) 0 0
\(296\) 1.75021 0.101729
\(297\) 21.7973 1.26481
\(298\) −1.87991 −0.108900
\(299\) −18.0547 −1.04413
\(300\) 0 0
\(301\) 25.3782 1.46278
\(302\) 1.20396 0.0692799
\(303\) 65.3475 3.75412
\(304\) 19.5961 1.12391
\(305\) 0 0
\(306\) 4.75851 0.272026
\(307\) −5.03009 −0.287082 −0.143541 0.989644i \(-0.545849\pi\)
−0.143541 + 0.989644i \(0.545849\pi\)
\(308\) 8.82471 0.502834
\(309\) 8.99952 0.511965
\(310\) 0 0
\(311\) 9.99750 0.566906 0.283453 0.958986i \(-0.408520\pi\)
0.283453 + 0.958986i \(0.408520\pi\)
\(312\) 8.89710 0.503699
\(313\) −28.1466 −1.59094 −0.795471 0.605992i \(-0.792776\pi\)
−0.795471 + 0.605992i \(0.792776\pi\)
\(314\) −2.19650 −0.123956
\(315\) 0 0
\(316\) −22.7373 −1.27907
\(317\) 5.66871 0.318387 0.159193 0.987247i \(-0.449111\pi\)
0.159193 + 0.987247i \(0.449111\pi\)
\(318\) 3.21038 0.180029
\(319\) 4.56728 0.255719
\(320\) 0 0
\(321\) 32.6925 1.82472
\(322\) −1.13585 −0.0632986
\(323\) −26.4417 −1.47126
\(324\) −55.9434 −3.10797
\(325\) 0 0
\(326\) 0.860524 0.0476600
\(327\) −18.5691 −1.02687
\(328\) 0.447524 0.0247104
\(329\) 9.01472 0.496998
\(330\) 0 0
\(331\) −14.8950 −0.818701 −0.409350 0.912377i \(-0.634245\pi\)
−0.409350 + 0.912377i \(0.634245\pi\)
\(332\) −23.6896 −1.30014
\(333\) 29.5202 1.61770
\(334\) 1.55181 0.0849115
\(335\) 0 0
\(336\) −41.1348 −2.24409
\(337\) −21.4134 −1.16646 −0.583231 0.812306i \(-0.698212\pi\)
−0.583231 + 0.812306i \(0.698212\pi\)
\(338\) −2.49149 −0.135519
\(339\) 42.5482 2.31090
\(340\) 0 0
\(341\) 0.934278 0.0505940
\(342\) −4.49748 −0.243196
\(343\) 12.0909 0.652850
\(344\) −3.66115 −0.197396
\(345\) 0 0
\(346\) −0.368342 −0.0198022
\(347\) 6.12740 0.328936 0.164468 0.986382i \(-0.447409\pi\)
0.164468 + 0.986382i \(0.447409\pi\)
\(348\) −21.4349 −1.14903
\(349\) −7.15661 −0.383085 −0.191542 0.981484i \(-0.561349\pi\)
−0.191542 + 0.981484i \(0.561349\pi\)
\(350\) 0 0
\(351\) 92.1819 4.92031
\(352\) −1.91176 −0.101897
\(353\) 9.47379 0.504239 0.252120 0.967696i \(-0.418872\pi\)
0.252120 + 0.967696i \(0.418872\pi\)
\(354\) −2.16772 −0.115213
\(355\) 0 0
\(356\) 23.8386 1.26344
\(357\) 55.5047 2.93762
\(358\) −1.36826 −0.0723149
\(359\) 7.14694 0.377201 0.188601 0.982054i \(-0.439605\pi\)
0.188601 + 0.982054i \(0.439605\pi\)
\(360\) 0 0
\(361\) 5.99126 0.315330
\(362\) 0.453470 0.0238339
\(363\) −29.7724 −1.56264
\(364\) 37.3202 1.95611
\(365\) 0 0
\(366\) −0.272645 −0.0142514
\(367\) −2.63925 −0.137767 −0.0688837 0.997625i \(-0.521944\pi\)
−0.0688837 + 0.997625i \(0.521944\pi\)
\(368\) −12.0422 −0.627744
\(369\) 7.54822 0.392944
\(370\) 0 0
\(371\) 27.0235 1.40299
\(372\) −4.38470 −0.227336
\(373\) −20.5114 −1.06204 −0.531020 0.847360i \(-0.678191\pi\)
−0.531020 + 0.847360i \(0.678191\pi\)
\(374\) 0.850221 0.0439639
\(375\) 0 0
\(376\) −1.30049 −0.0670678
\(377\) 19.3153 0.994789
\(378\) 5.79934 0.298286
\(379\) −24.7263 −1.27010 −0.635051 0.772470i \(-0.719021\pi\)
−0.635051 + 0.772470i \(0.719021\pi\)
\(380\) 0 0
\(381\) 34.3551 1.76007
\(382\) −0.147009 −0.00752165
\(383\) 33.2690 1.69997 0.849983 0.526810i \(-0.176612\pi\)
0.849983 + 0.526810i \(0.176612\pi\)
\(384\) 11.9492 0.609781
\(385\) 0 0
\(386\) −0.831044 −0.0422990
\(387\) −61.7511 −3.13899
\(388\) 2.36181 0.119902
\(389\) −11.2024 −0.567985 −0.283992 0.958827i \(-0.591659\pi\)
−0.283992 + 0.958827i \(0.591659\pi\)
\(390\) 0 0
\(391\) 16.2490 0.821748
\(392\) 1.48365 0.0749356
\(393\) 42.5493 2.14633
\(394\) 0.768796 0.0387314
\(395\) 0 0
\(396\) −21.4726 −1.07904
\(397\) −5.20629 −0.261296 −0.130648 0.991429i \(-0.541706\pi\)
−0.130648 + 0.991429i \(0.541706\pi\)
\(398\) −1.47315 −0.0738426
\(399\) −52.4600 −2.62629
\(400\) 0 0
\(401\) −2.79646 −0.139649 −0.0698243 0.997559i \(-0.522244\pi\)
−0.0698243 + 0.997559i \(0.522244\pi\)
\(402\) 3.34632 0.166899
\(403\) 3.95111 0.196819
\(404\) −39.5440 −1.96739
\(405\) 0 0
\(406\) 1.21516 0.0603075
\(407\) 5.27449 0.261447
\(408\) −8.00729 −0.396420
\(409\) 0.743107 0.0367443 0.0183721 0.999831i \(-0.494152\pi\)
0.0183721 + 0.999831i \(0.494152\pi\)
\(410\) 0 0
\(411\) −46.4276 −2.29010
\(412\) −5.44591 −0.268301
\(413\) −18.2469 −0.897869
\(414\) 2.76379 0.135833
\(415\) 0 0
\(416\) −8.08493 −0.396396
\(417\) −55.3470 −2.71035
\(418\) −0.803582 −0.0393045
\(419\) −11.8016 −0.576544 −0.288272 0.957549i \(-0.593081\pi\)
−0.288272 + 0.957549i \(0.593081\pi\)
\(420\) 0 0
\(421\) −9.89956 −0.482475 −0.241237 0.970466i \(-0.577553\pi\)
−0.241237 + 0.970466i \(0.577553\pi\)
\(422\) −0.604407 −0.0294221
\(423\) −21.9349 −1.06651
\(424\) −3.89850 −0.189328
\(425\) 0 0
\(426\) −6.02083 −0.291710
\(427\) −2.29500 −0.111063
\(428\) −19.7833 −0.956264
\(429\) 26.8125 1.29452
\(430\) 0 0
\(431\) 9.64934 0.464793 0.232396 0.972621i \(-0.425343\pi\)
0.232396 + 0.972621i \(0.425343\pi\)
\(432\) 61.4840 2.95815
\(433\) 38.9496 1.87180 0.935900 0.352265i \(-0.114588\pi\)
0.935900 + 0.352265i \(0.114588\pi\)
\(434\) 0.248572 0.0119318
\(435\) 0 0
\(436\) 11.2368 0.538144
\(437\) −15.3577 −0.734657
\(438\) −3.32278 −0.158769
\(439\) −16.8089 −0.802243 −0.401121 0.916025i \(-0.631379\pi\)
−0.401121 + 0.916025i \(0.631379\pi\)
\(440\) 0 0
\(441\) 25.0241 1.19163
\(442\) 3.59563 0.171027
\(443\) 0.438324 0.0208254 0.0104127 0.999946i \(-0.496685\pi\)
0.0104127 + 0.999946i \(0.496685\pi\)
\(444\) −24.7539 −1.17477
\(445\) 0 0
\(446\) −0.194908 −0.00922917
\(447\) 53.3556 2.52363
\(448\) 24.5510 1.15993
\(449\) −31.7722 −1.49942 −0.749711 0.661766i \(-0.769807\pi\)
−0.749711 + 0.661766i \(0.769807\pi\)
\(450\) 0 0
\(451\) 1.34867 0.0635064
\(452\) −25.7473 −1.21105
\(453\) −34.1707 −1.60548
\(454\) −0.146925 −0.00689551
\(455\) 0 0
\(456\) 7.56805 0.354406
\(457\) −17.1543 −0.802444 −0.401222 0.915981i \(-0.631414\pi\)
−0.401222 + 0.915981i \(0.631414\pi\)
\(458\) −2.83198 −0.132330
\(459\) −82.9627 −3.87237
\(460\) 0 0
\(461\) −30.9242 −1.44028 −0.720141 0.693827i \(-0.755923\pi\)
−0.720141 + 0.693827i \(0.755923\pi\)
\(462\) 1.68683 0.0784783
\(463\) −15.6931 −0.729319 −0.364659 0.931141i \(-0.618815\pi\)
−0.364659 + 0.931141i \(0.618815\pi\)
\(464\) 12.8830 0.598080
\(465\) 0 0
\(466\) 0.414505 0.0192016
\(467\) −21.3617 −0.988501 −0.494250 0.869320i \(-0.664557\pi\)
−0.494250 + 0.869320i \(0.664557\pi\)
\(468\) −90.8087 −4.19763
\(469\) 28.1678 1.30067
\(470\) 0 0
\(471\) 62.3411 2.87253
\(472\) 2.63235 0.121164
\(473\) −11.0333 −0.507313
\(474\) −4.34619 −0.199627
\(475\) 0 0
\(476\) −33.5878 −1.53949
\(477\) −65.7545 −3.01069
\(478\) 3.12611 0.142985
\(479\) 27.3633 1.25026 0.625130 0.780521i \(-0.285046\pi\)
0.625130 + 0.780521i \(0.285046\pi\)
\(480\) 0 0
\(481\) 22.3061 1.01707
\(482\) −0.115670 −0.00526863
\(483\) 32.2378 1.46687
\(484\) 18.0162 0.818920
\(485\) 0 0
\(486\) −5.25060 −0.238172
\(487\) 9.12015 0.413274 0.206637 0.978418i \(-0.433748\pi\)
0.206637 + 0.978418i \(0.433748\pi\)
\(488\) 0.331084 0.0149875
\(489\) −24.4234 −1.10446
\(490\) 0 0
\(491\) −7.29684 −0.329302 −0.164651 0.986352i \(-0.552650\pi\)
−0.164651 + 0.986352i \(0.552650\pi\)
\(492\) −6.32950 −0.285356
\(493\) −17.3836 −0.782916
\(494\) −3.39839 −0.152901
\(495\) 0 0
\(496\) 2.63534 0.118330
\(497\) −50.6806 −2.27333
\(498\) −4.52822 −0.202915
\(499\) 1.98278 0.0887613 0.0443807 0.999015i \(-0.485869\pi\)
0.0443807 + 0.999015i \(0.485869\pi\)
\(500\) 0 0
\(501\) −44.0436 −1.96772
\(502\) 2.20594 0.0984559
\(503\) −7.01318 −0.312702 −0.156351 0.987702i \(-0.549973\pi\)
−0.156351 + 0.987702i \(0.549973\pi\)
\(504\) −11.4644 −0.510663
\(505\) 0 0
\(506\) 0.493818 0.0219529
\(507\) 70.7134 3.14049
\(508\) −20.7894 −0.922381
\(509\) −28.5738 −1.26651 −0.633256 0.773943i \(-0.718282\pi\)
−0.633256 + 0.773943i \(0.718282\pi\)
\(510\) 0 0
\(511\) −27.9697 −1.23731
\(512\) −9.00772 −0.398089
\(513\) 78.4118 3.46196
\(514\) −3.45463 −0.152377
\(515\) 0 0
\(516\) 51.7809 2.27953
\(517\) −3.91920 −0.172366
\(518\) 1.40332 0.0616583
\(519\) 10.4543 0.458892
\(520\) 0 0
\(521\) −13.1589 −0.576501 −0.288250 0.957555i \(-0.593074\pi\)
−0.288250 + 0.957555i \(0.593074\pi\)
\(522\) −2.95677 −0.129414
\(523\) −23.8792 −1.04416 −0.522082 0.852895i \(-0.674845\pi\)
−0.522082 + 0.852895i \(0.674845\pi\)
\(524\) −25.7480 −1.12480
\(525\) 0 0
\(526\) −1.67619 −0.0730855
\(527\) −3.55596 −0.154900
\(528\) 17.8836 0.778282
\(529\) −13.5624 −0.589669
\(530\) 0 0
\(531\) 44.3988 1.92674
\(532\) 31.7453 1.37633
\(533\) 5.70360 0.247050
\(534\) 4.55670 0.197188
\(535\) 0 0
\(536\) −4.06357 −0.175520
\(537\) 38.8340 1.67581
\(538\) −1.12584 −0.0485384
\(539\) 4.47116 0.192587
\(540\) 0 0
\(541\) −7.11389 −0.305850 −0.152925 0.988238i \(-0.548869\pi\)
−0.152925 + 0.988238i \(0.548869\pi\)
\(542\) −2.05874 −0.0884304
\(543\) −12.8704 −0.552321
\(544\) 7.27635 0.311971
\(545\) 0 0
\(546\) 7.13368 0.305294
\(547\) −2.10736 −0.0901044 −0.0450522 0.998985i \(-0.514345\pi\)
−0.0450522 + 0.998985i \(0.514345\pi\)
\(548\) 28.0949 1.20015
\(549\) 5.58426 0.238331
\(550\) 0 0
\(551\) 16.4300 0.699941
\(552\) −4.65073 −0.197948
\(553\) −36.5842 −1.55572
\(554\) 0.264382 0.0112325
\(555\) 0 0
\(556\) 33.4923 1.42039
\(557\) 9.69468 0.410777 0.205388 0.978681i \(-0.434154\pi\)
0.205388 + 0.978681i \(0.434154\pi\)
\(558\) −0.604833 −0.0256046
\(559\) −46.6605 −1.97353
\(560\) 0 0
\(561\) −24.1310 −1.01881
\(562\) −1.08086 −0.0455933
\(563\) 12.6385 0.532647 0.266324 0.963884i \(-0.414191\pi\)
0.266324 + 0.963884i \(0.414191\pi\)
\(564\) 18.3933 0.774500
\(565\) 0 0
\(566\) 1.02556 0.0431076
\(567\) −90.0129 −3.78018
\(568\) 7.31134 0.306777
\(569\) 17.6815 0.741245 0.370622 0.928784i \(-0.379144\pi\)
0.370622 + 0.928784i \(0.379144\pi\)
\(570\) 0 0
\(571\) −24.5248 −1.02633 −0.513166 0.858289i \(-0.671527\pi\)
−0.513166 + 0.858289i \(0.671527\pi\)
\(572\) −16.2251 −0.678407
\(573\) 4.17242 0.174305
\(574\) 0.358824 0.0149770
\(575\) 0 0
\(576\) −59.7384 −2.48910
\(577\) 35.7883 1.48988 0.744942 0.667129i \(-0.232477\pi\)
0.744942 + 0.667129i \(0.232477\pi\)
\(578\) −1.26964 −0.0528101
\(579\) 23.5867 0.980229
\(580\) 0 0
\(581\) −38.1165 −1.58134
\(582\) 0.451455 0.0187134
\(583\) −11.7486 −0.486578
\(584\) 4.03500 0.166969
\(585\) 0 0
\(586\) 1.98059 0.0818175
\(587\) 42.4486 1.75204 0.876021 0.482273i \(-0.160189\pi\)
0.876021 + 0.482273i \(0.160189\pi\)
\(588\) −20.9838 −0.865358
\(589\) 3.36089 0.138483
\(590\) 0 0
\(591\) −21.8200 −0.897553
\(592\) 14.8779 0.611476
\(593\) −17.8382 −0.732527 −0.366263 0.930511i \(-0.619363\pi\)
−0.366263 + 0.930511i \(0.619363\pi\)
\(594\) −2.52129 −0.103450
\(595\) 0 0
\(596\) −32.2872 −1.32254
\(597\) 41.8111 1.71121
\(598\) 2.08839 0.0854004
\(599\) 21.3734 0.873291 0.436646 0.899634i \(-0.356166\pi\)
0.436646 + 0.899634i \(0.356166\pi\)
\(600\) 0 0
\(601\) −42.3095 −1.72584 −0.862920 0.505341i \(-0.831367\pi\)
−0.862920 + 0.505341i \(0.831367\pi\)
\(602\) −2.93550 −0.119642
\(603\) −68.5387 −2.79111
\(604\) 20.6778 0.841368
\(605\) 0 0
\(606\) −7.55875 −0.307053
\(607\) −1.51410 −0.0614552 −0.0307276 0.999528i \(-0.509782\pi\)
−0.0307276 + 0.999528i \(0.509782\pi\)
\(608\) −6.87720 −0.278907
\(609\) −34.4887 −1.39755
\(610\) 0 0
\(611\) −16.5745 −0.670533
\(612\) 81.7268 3.30361
\(613\) 15.4991 0.626001 0.313000 0.949753i \(-0.398666\pi\)
0.313000 + 0.949753i \(0.398666\pi\)
\(614\) 0.581830 0.0234808
\(615\) 0 0
\(616\) −2.04838 −0.0825317
\(617\) −22.9695 −0.924718 −0.462359 0.886693i \(-0.652997\pi\)
−0.462359 + 0.886693i \(0.652997\pi\)
\(618\) −1.04097 −0.0418742
\(619\) 36.7503 1.47712 0.738559 0.674189i \(-0.235507\pi\)
0.738559 + 0.674189i \(0.235507\pi\)
\(620\) 0 0
\(621\) −48.1857 −1.93363
\(622\) −1.15641 −0.0463679
\(623\) 38.3562 1.53671
\(624\) 75.6306 3.02765
\(625\) 0 0
\(626\) 3.25572 0.130125
\(627\) 22.8073 0.910834
\(628\) −37.7247 −1.50538
\(629\) −20.0753 −0.800453
\(630\) 0 0
\(631\) −16.5412 −0.658494 −0.329247 0.944244i \(-0.606795\pi\)
−0.329247 + 0.944244i \(0.606795\pi\)
\(632\) 5.27775 0.209938
\(633\) 17.1543 0.681821
\(634\) −0.655700 −0.0260412
\(635\) 0 0
\(636\) 55.1380 2.18636
\(637\) 18.9088 0.749194
\(638\) −0.528298 −0.0209155
\(639\) 123.318 4.87837
\(640\) 0 0
\(641\) 1.70611 0.0673873 0.0336937 0.999432i \(-0.489273\pi\)
0.0336937 + 0.999432i \(0.489273\pi\)
\(642\) −3.78155 −0.149246
\(643\) 12.2046 0.481302 0.240651 0.970612i \(-0.422639\pi\)
0.240651 + 0.970612i \(0.422639\pi\)
\(644\) −19.5082 −0.768729
\(645\) 0 0
\(646\) 3.05852 0.120336
\(647\) −28.0548 −1.10295 −0.551473 0.834193i \(-0.685934\pi\)
−0.551473 + 0.834193i \(0.685934\pi\)
\(648\) 12.9855 0.510120
\(649\) 7.93291 0.311394
\(650\) 0 0
\(651\) −7.05497 −0.276506
\(652\) 14.7794 0.578806
\(653\) −5.68400 −0.222432 −0.111216 0.993796i \(-0.535475\pi\)
−0.111216 + 0.993796i \(0.535475\pi\)
\(654\) 2.14789 0.0839891
\(655\) 0 0
\(656\) 3.80422 0.148530
\(657\) 68.0567 2.65515
\(658\) −1.04273 −0.0406500
\(659\) −30.6811 −1.19517 −0.597584 0.801806i \(-0.703873\pi\)
−0.597584 + 0.801806i \(0.703873\pi\)
\(660\) 0 0
\(661\) −13.8208 −0.537568 −0.268784 0.963200i \(-0.586622\pi\)
−0.268784 + 0.963200i \(0.586622\pi\)
\(662\) 1.72290 0.0669624
\(663\) −102.051 −3.96334
\(664\) 5.49881 0.213395
\(665\) 0 0
\(666\) −3.41460 −0.132313
\(667\) −10.0966 −0.390941
\(668\) 26.6522 1.03121
\(669\) 5.53188 0.213875
\(670\) 0 0
\(671\) 0.997763 0.0385182
\(672\) 14.4362 0.556887
\(673\) −19.2294 −0.741240 −0.370620 0.928785i \(-0.620855\pi\)
−0.370620 + 0.928785i \(0.620855\pi\)
\(674\) 2.47689 0.0954062
\(675\) 0 0
\(676\) −42.7910 −1.64581
\(677\) −34.7093 −1.33399 −0.666994 0.745063i \(-0.732419\pi\)
−0.666994 + 0.745063i \(0.732419\pi\)
\(678\) −4.92155 −0.189011
\(679\) 3.80014 0.145836
\(680\) 0 0
\(681\) 4.17001 0.159795
\(682\) −0.108068 −0.00413814
\(683\) −2.16428 −0.0828139 −0.0414069 0.999142i \(-0.513184\pi\)
−0.0414069 + 0.999142i \(0.513184\pi\)
\(684\) −77.2437 −2.95348
\(685\) 0 0
\(686\) −1.39856 −0.0533973
\(687\) 80.3773 3.06659
\(688\) −31.1219 −1.18651
\(689\) −49.6856 −1.89287
\(690\) 0 0
\(691\) 22.7388 0.865025 0.432513 0.901628i \(-0.357627\pi\)
0.432513 + 0.901628i \(0.357627\pi\)
\(692\) −6.32623 −0.240487
\(693\) −34.5493 −1.31242
\(694\) −0.708756 −0.0269040
\(695\) 0 0
\(696\) 4.97545 0.188594
\(697\) −5.13318 −0.194433
\(698\) 0.827806 0.0313329
\(699\) −11.7645 −0.444974
\(700\) 0 0
\(701\) −21.4836 −0.811424 −0.405712 0.914001i \(-0.632976\pi\)
−0.405712 + 0.914001i \(0.632976\pi\)
\(702\) −10.6627 −0.402437
\(703\) 18.9740 0.715619
\(704\) −10.6737 −0.402280
\(705\) 0 0
\(706\) −1.09583 −0.0412423
\(707\) −63.6261 −2.39291
\(708\) −37.2303 −1.39920
\(709\) −4.43026 −0.166382 −0.0831910 0.996534i \(-0.526511\pi\)
−0.0831910 + 0.996534i \(0.526511\pi\)
\(710\) 0 0
\(711\) 89.0178 3.33843
\(712\) −5.53339 −0.207373
\(713\) −2.06534 −0.0773476
\(714\) −6.42024 −0.240271
\(715\) 0 0
\(716\) −23.4998 −0.878227
\(717\) −88.7254 −3.31351
\(718\) −0.826688 −0.0308517
\(719\) 37.8736 1.41245 0.706224 0.707989i \(-0.250397\pi\)
0.706224 + 0.707989i \(0.250397\pi\)
\(720\) 0 0
\(721\) −8.76245 −0.326331
\(722\) −0.693010 −0.0257912
\(723\) 3.28295 0.122094
\(724\) 7.78830 0.289450
\(725\) 0 0
\(726\) 3.44377 0.127810
\(727\) 0.346692 0.0128581 0.00642904 0.999979i \(-0.497954\pi\)
0.00642904 + 0.999979i \(0.497954\pi\)
\(728\) −8.66273 −0.321062
\(729\) 64.5421 2.39045
\(730\) 0 0
\(731\) 41.9940 1.55320
\(732\) −4.68264 −0.173075
\(733\) −4.28244 −0.158176 −0.0790878 0.996868i \(-0.525201\pi\)
−0.0790878 + 0.996868i \(0.525201\pi\)
\(734\) 0.305282 0.0112682
\(735\) 0 0
\(736\) 4.22619 0.155779
\(737\) −12.2461 −0.451090
\(738\) −0.873103 −0.0321394
\(739\) 4.52351 0.166400 0.0832000 0.996533i \(-0.473486\pi\)
0.0832000 + 0.996533i \(0.473486\pi\)
\(740\) 0 0
\(741\) 96.4532 3.54330
\(742\) −3.12581 −0.114752
\(743\) −14.4360 −0.529606 −0.264803 0.964303i \(-0.585307\pi\)
−0.264803 + 0.964303i \(0.585307\pi\)
\(744\) 1.01777 0.0373133
\(745\) 0 0
\(746\) 2.37255 0.0868653
\(747\) 92.7463 3.39341
\(748\) 14.6025 0.533919
\(749\) −31.8313 −1.16309
\(750\) 0 0
\(751\) −18.6022 −0.678804 −0.339402 0.940641i \(-0.610225\pi\)
−0.339402 + 0.940641i \(0.610225\pi\)
\(752\) −11.0550 −0.403133
\(753\) −62.6090 −2.28160
\(754\) −2.23420 −0.0813649
\(755\) 0 0
\(756\) 99.6030 3.62252
\(757\) −1.36472 −0.0496015 −0.0248007 0.999692i \(-0.507895\pi\)
−0.0248007 + 0.999692i \(0.507895\pi\)
\(758\) 2.86009 0.103883
\(759\) −14.0155 −0.508732
\(760\) 0 0
\(761\) −32.0391 −1.16142 −0.580709 0.814111i \(-0.697224\pi\)
−0.580709 + 0.814111i \(0.697224\pi\)
\(762\) −3.97386 −0.143958
\(763\) 18.0799 0.654538
\(764\) −2.52487 −0.0913465
\(765\) 0 0
\(766\) −3.84823 −0.139042
\(767\) 33.5487 1.21138
\(768\) 49.0484 1.76988
\(769\) −7.53070 −0.271564 −0.135782 0.990739i \(-0.543355\pi\)
−0.135782 + 0.990739i \(0.543355\pi\)
\(770\) 0 0
\(771\) 98.0493 3.53116
\(772\) −14.2731 −0.513699
\(773\) 23.1144 0.831368 0.415684 0.909509i \(-0.363542\pi\)
0.415684 + 0.909509i \(0.363542\pi\)
\(774\) 7.14276 0.256741
\(775\) 0 0
\(776\) −0.548220 −0.0196800
\(777\) −39.8290 −1.42886
\(778\) 1.29578 0.0464561
\(779\) 4.85160 0.173826
\(780\) 0 0
\(781\) 22.0336 0.788426
\(782\) −1.87952 −0.0672116
\(783\) 51.5502 1.84225
\(784\) 12.6119 0.450425
\(785\) 0 0
\(786\) −4.92167 −0.175550
\(787\) −14.4891 −0.516479 −0.258240 0.966081i \(-0.583142\pi\)
−0.258240 + 0.966081i \(0.583142\pi\)
\(788\) 13.2040 0.470372
\(789\) 47.5737 1.69367
\(790\) 0 0
\(791\) −41.4274 −1.47299
\(792\) 4.98419 0.177106
\(793\) 4.21960 0.149842
\(794\) 0.602212 0.0213717
\(795\) 0 0
\(796\) −25.3013 −0.896780
\(797\) 13.1633 0.466267 0.233133 0.972445i \(-0.425102\pi\)
0.233133 + 0.972445i \(0.425102\pi\)
\(798\) 6.06805 0.214807
\(799\) 14.9169 0.527721
\(800\) 0 0
\(801\) −93.3296 −3.29764
\(802\) 0.323467 0.0114220
\(803\) 12.1600 0.429116
\(804\) 57.4726 2.02690
\(805\) 0 0
\(806\) −0.457026 −0.0160980
\(807\) 31.9536 1.12482
\(808\) 9.17891 0.322913
\(809\) −33.0845 −1.16319 −0.581595 0.813479i \(-0.697571\pi\)
−0.581595 + 0.813479i \(0.697571\pi\)
\(810\) 0 0
\(811\) −4.74569 −0.166644 −0.0833219 0.996523i \(-0.526553\pi\)
−0.0833219 + 0.996523i \(0.526553\pi\)
\(812\) 20.8703 0.732403
\(813\) 58.4311 2.04927
\(814\) −0.610101 −0.0213840
\(815\) 0 0
\(816\) −68.0668 −2.38281
\(817\) −39.6904 −1.38859
\(818\) −0.0859553 −0.00300536
\(819\) −146.111 −5.10553
\(820\) 0 0
\(821\) −33.6149 −1.17317 −0.586584 0.809888i \(-0.699528\pi\)
−0.586584 + 0.809888i \(0.699528\pi\)
\(822\) 5.37028 0.187310
\(823\) −45.7636 −1.59522 −0.797609 0.603175i \(-0.793902\pi\)
−0.797609 + 0.603175i \(0.793902\pi\)
\(824\) 1.26410 0.0440370
\(825\) 0 0
\(826\) 2.11061 0.0734377
\(827\) −29.9837 −1.04264 −0.521318 0.853363i \(-0.674559\pi\)
−0.521318 + 0.853363i \(0.674559\pi\)
\(828\) 47.4679 1.64962
\(829\) −2.23933 −0.0777753 −0.0388876 0.999244i \(-0.512381\pi\)
−0.0388876 + 0.999244i \(0.512381\pi\)
\(830\) 0 0
\(831\) −7.50368 −0.260300
\(832\) −45.1397 −1.56494
\(833\) −17.0177 −0.589629
\(834\) 6.40199 0.221683
\(835\) 0 0
\(836\) −13.8014 −0.477332
\(837\) 10.5450 0.364490
\(838\) 1.36509 0.0471561
\(839\) −31.0203 −1.07094 −0.535469 0.844555i \(-0.679865\pi\)
−0.535469 + 0.844555i \(0.679865\pi\)
\(840\) 0 0
\(841\) −18.1985 −0.627533
\(842\) 1.14508 0.0394621
\(843\) 30.6770 1.05657
\(844\) −10.3806 −0.357316
\(845\) 0 0
\(846\) 2.53721 0.0872311
\(847\) 28.9881 0.996042
\(848\) −33.1396 −1.13802
\(849\) −29.1075 −0.998968
\(850\) 0 0
\(851\) −11.6599 −0.399698
\(852\) −103.407 −3.54267
\(853\) 13.7603 0.471142 0.235571 0.971857i \(-0.424304\pi\)
0.235571 + 0.971857i \(0.424304\pi\)
\(854\) 0.265463 0.00908395
\(855\) 0 0
\(856\) 4.59209 0.156954
\(857\) −31.2228 −1.06655 −0.533276 0.845941i \(-0.679039\pi\)
−0.533276 + 0.845941i \(0.679039\pi\)
\(858\) −3.10141 −0.105880
\(859\) −55.8137 −1.90434 −0.952170 0.305569i \(-0.901153\pi\)
−0.952170 + 0.305569i \(0.901153\pi\)
\(860\) 0 0
\(861\) −10.1841 −0.347075
\(862\) −1.11614 −0.0380159
\(863\) 0.720056 0.0245110 0.0122555 0.999925i \(-0.496099\pi\)
0.0122555 + 0.999925i \(0.496099\pi\)
\(864\) −21.5777 −0.734088
\(865\) 0 0
\(866\) −4.50531 −0.153097
\(867\) 36.0349 1.22381
\(868\) 4.26920 0.144906
\(869\) 15.9052 0.539546
\(870\) 0 0
\(871\) −51.7894 −1.75482
\(872\) −2.60827 −0.0883272
\(873\) −9.24662 −0.312951
\(874\) 1.77642 0.0600884
\(875\) 0 0
\(876\) −57.0685 −1.92816
\(877\) −48.3619 −1.63307 −0.816533 0.577298i \(-0.804107\pi\)
−0.816533 + 0.577298i \(0.804107\pi\)
\(878\) 1.94428 0.0656163
\(879\) −56.2132 −1.89602
\(880\) 0 0
\(881\) 36.2946 1.22279 0.611397 0.791324i \(-0.290608\pi\)
0.611397 + 0.791324i \(0.290608\pi\)
\(882\) −2.89454 −0.0974644
\(883\) 26.8840 0.904718 0.452359 0.891836i \(-0.350583\pi\)
0.452359 + 0.891836i \(0.350583\pi\)
\(884\) 61.7546 2.07703
\(885\) 0 0
\(886\) −0.0507010 −0.00170333
\(887\) −13.4296 −0.450923 −0.225461 0.974252i \(-0.572389\pi\)
−0.225461 + 0.974252i \(0.572389\pi\)
\(888\) 5.74586 0.192819
\(889\) −33.4501 −1.12188
\(890\) 0 0
\(891\) 39.1336 1.31102
\(892\) −3.34752 −0.112083
\(893\) −14.0986 −0.471792
\(894\) −6.17165 −0.206411
\(895\) 0 0
\(896\) −11.6345 −0.388680
\(897\) −59.2726 −1.97905
\(898\) 3.67509 0.122639
\(899\) 2.20955 0.0736926
\(900\) 0 0
\(901\) 44.7165 1.48972
\(902\) −0.156001 −0.00519426
\(903\) 83.3154 2.77256
\(904\) 5.97644 0.198774
\(905\) 0 0
\(906\) 3.95253 0.131314
\(907\) −7.62089 −0.253047 −0.126524 0.991964i \(-0.540382\pi\)
−0.126524 + 0.991964i \(0.540382\pi\)
\(908\) −2.52341 −0.0837424
\(909\) 154.817 5.13496
\(910\) 0 0
\(911\) −14.0113 −0.464214 −0.232107 0.972690i \(-0.574562\pi\)
−0.232107 + 0.972690i \(0.574562\pi\)
\(912\) 64.3329 2.13028
\(913\) 16.5714 0.548432
\(914\) 1.98424 0.0656327
\(915\) 0 0
\(916\) −48.6390 −1.60708
\(917\) −41.4284 −1.36809
\(918\) 9.59630 0.316725
\(919\) 12.5233 0.413107 0.206553 0.978435i \(-0.433775\pi\)
0.206553 + 0.978435i \(0.433775\pi\)
\(920\) 0 0
\(921\) −16.5135 −0.544139
\(922\) 3.57700 0.117802
\(923\) 93.1815 3.06711
\(924\) 28.9710 0.953078
\(925\) 0 0
\(926\) 1.81522 0.0596518
\(927\) 21.3211 0.700276
\(928\) −4.52127 −0.148418
\(929\) 14.3668 0.471359 0.235680 0.971831i \(-0.424268\pi\)
0.235680 + 0.971831i \(0.424268\pi\)
\(930\) 0 0
\(931\) 16.0842 0.527138
\(932\) 7.11908 0.233193
\(933\) 32.8213 1.07452
\(934\) 2.47091 0.0808505
\(935\) 0 0
\(936\) 21.0784 0.688970
\(937\) −57.2739 −1.87106 −0.935528 0.353253i \(-0.885075\pi\)
−0.935528 + 0.353253i \(0.885075\pi\)
\(938\) −3.25817 −0.106383
\(939\) −92.4039 −3.01549
\(940\) 0 0
\(941\) −2.50683 −0.0817202 −0.0408601 0.999165i \(-0.513010\pi\)
−0.0408601 + 0.999165i \(0.513010\pi\)
\(942\) −7.21100 −0.234947
\(943\) −2.98141 −0.0970880
\(944\) 22.3765 0.728294
\(945\) 0 0
\(946\) 1.27622 0.0414936
\(947\) 53.8904 1.75120 0.875601 0.483036i \(-0.160466\pi\)
0.875601 + 0.483036i \(0.160466\pi\)
\(948\) −74.6452 −2.42436
\(949\) 51.4252 1.66933
\(950\) 0 0
\(951\) 18.6101 0.603473
\(952\) 7.79636 0.252682
\(953\) 20.7256 0.671369 0.335684 0.941975i \(-0.391032\pi\)
0.335684 + 0.941975i \(0.391032\pi\)
\(954\) 7.60583 0.246248
\(955\) 0 0
\(956\) 53.6907 1.73648
\(957\) 14.9942 0.484692
\(958\) −3.16511 −0.102260
\(959\) 45.2046 1.45973
\(960\) 0 0
\(961\) −30.5480 −0.985420
\(962\) −2.58015 −0.0831874
\(963\) 77.4530 2.49589
\(964\) −1.98662 −0.0639847
\(965\) 0 0
\(966\) −3.72895 −0.119977
\(967\) −12.2723 −0.394652 −0.197326 0.980338i \(-0.563226\pi\)
−0.197326 + 0.980338i \(0.563226\pi\)
\(968\) −4.18191 −0.134412
\(969\) −86.8068 −2.78864
\(970\) 0 0
\(971\) 48.8599 1.56799 0.783994 0.620768i \(-0.213179\pi\)
0.783994 + 0.620768i \(0.213179\pi\)
\(972\) −90.1784 −2.89247
\(973\) 53.8890 1.72760
\(974\) −1.05493 −0.0338021
\(975\) 0 0
\(976\) 2.81441 0.0900871
\(977\) 29.7335 0.951260 0.475630 0.879645i \(-0.342220\pi\)
0.475630 + 0.879645i \(0.342220\pi\)
\(978\) 2.82506 0.0903353
\(979\) −16.6756 −0.532953
\(980\) 0 0
\(981\) −43.9927 −1.40458
\(982\) 0.844026 0.0269339
\(983\) −26.3255 −0.839655 −0.419827 0.907604i \(-0.637909\pi\)
−0.419827 + 0.907604i \(0.637909\pi\)
\(984\) 1.46920 0.0468363
\(985\) 0 0
\(986\) 2.01076 0.0640356
\(987\) 29.5949 0.942015
\(988\) −58.3670 −1.85690
\(989\) 24.3906 0.775575
\(990\) 0 0
\(991\) 44.7423 1.42129 0.710643 0.703552i \(-0.248404\pi\)
0.710643 + 0.703552i \(0.248404\pi\)
\(992\) −0.924865 −0.0293645
\(993\) −48.8994 −1.55177
\(994\) 5.86222 0.185938
\(995\) 0 0
\(996\) −77.7717 −2.46429
\(997\) 39.5818 1.25357 0.626784 0.779193i \(-0.284371\pi\)
0.626784 + 0.779193i \(0.284371\pi\)
\(998\) −0.229348 −0.00725988
\(999\) 59.5323 1.88352
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 \(a_p\))