Properties

Label 6017.2.a.c.1.9
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.47702 q^{2}\) \(+3.19961 q^{3}\) \(+4.13562 q^{4}\) \(-3.89998 q^{5}\) \(-7.92550 q^{6}\) \(-4.57915 q^{7}\) \(-5.28996 q^{8}\) \(+7.23752 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.47702 q^{2}\) \(+3.19961 q^{3}\) \(+4.13562 q^{4}\) \(-3.89998 q^{5}\) \(-7.92550 q^{6}\) \(-4.57915 q^{7}\) \(-5.28996 q^{8}\) \(+7.23752 q^{9}\) \(+9.66032 q^{10}\) \(+1.00000 q^{11}\) \(+13.2324 q^{12}\) \(+2.88643 q^{13}\) \(+11.3426 q^{14}\) \(-12.4784 q^{15}\) \(+4.83209 q^{16}\) \(+0.354961 q^{17}\) \(-17.9275 q^{18}\) \(-2.08115 q^{19}\) \(-16.1288 q^{20}\) \(-14.6515 q^{21}\) \(-2.47702 q^{22}\) \(+2.89822 q^{23}\) \(-16.9258 q^{24}\) \(+10.2098 q^{25}\) \(-7.14973 q^{26}\) \(+13.5584 q^{27}\) \(-18.9376 q^{28}\) \(-5.27832 q^{29}\) \(+30.9093 q^{30}\) \(-7.89839 q^{31}\) \(-1.38925 q^{32}\) \(+3.19961 q^{33}\) \(-0.879245 q^{34}\) \(+17.8586 q^{35}\) \(+29.9316 q^{36}\) \(-0.709403 q^{37}\) \(+5.15504 q^{38}\) \(+9.23545 q^{39}\) \(+20.6307 q^{40}\) \(+10.7338 q^{41}\) \(+36.2920 q^{42}\) \(-0.999145 q^{43}\) \(+4.13562 q^{44}\) \(-28.2262 q^{45}\) \(-7.17893 q^{46}\) \(-3.46035 q^{47}\) \(+15.4608 q^{48}\) \(+13.9686 q^{49}\) \(-25.2900 q^{50}\) \(+1.13574 q^{51}\) \(+11.9372 q^{52}\) \(+12.9768 q^{53}\) \(-33.5845 q^{54}\) \(-3.89998 q^{55}\) \(+24.2235 q^{56}\) \(-6.65887 q^{57}\) \(+13.0745 q^{58}\) \(-2.13636 q^{59}\) \(-51.6060 q^{60}\) \(-6.20113 q^{61}\) \(+19.5644 q^{62}\) \(-33.1417 q^{63}\) \(-6.22298 q^{64}\) \(-11.2570 q^{65}\) \(-7.92550 q^{66}\) \(-3.71458 q^{67}\) \(+1.46798 q^{68}\) \(+9.27317 q^{69}\) \(-44.2360 q^{70}\) \(+5.24113 q^{71}\) \(-38.2862 q^{72}\) \(-13.4599 q^{73}\) \(+1.75720 q^{74}\) \(+32.6676 q^{75}\) \(-8.60683 q^{76}\) \(-4.57915 q^{77}\) \(-22.8764 q^{78}\) \(-0.525188 q^{79}\) \(-18.8450 q^{80}\) \(+21.6691 q^{81}\) \(-26.5877 q^{82}\) \(-12.0963 q^{83}\) \(-60.5930 q^{84}\) \(-1.38434 q^{85}\) \(+2.47490 q^{86}\) \(-16.8886 q^{87}\) \(-5.28996 q^{88}\) \(+14.4254 q^{89}\) \(+69.9168 q^{90}\) \(-13.2174 q^{91}\) \(+11.9859 q^{92}\) \(-25.2718 q^{93}\) \(+8.57134 q^{94}\) \(+8.11644 q^{95}\) \(-4.44506 q^{96}\) \(+11.7333 q^{97}\) \(-34.6005 q^{98}\) \(+7.23752 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47702 −1.75152 −0.875758 0.482750i \(-0.839638\pi\)
−0.875758 + 0.482750i \(0.839638\pi\)
\(3\) 3.19961 1.84730 0.923649 0.383240i \(-0.125192\pi\)
0.923649 + 0.383240i \(0.125192\pi\)
\(4\) 4.13562 2.06781
\(5\) −3.89998 −1.74412 −0.872062 0.489395i \(-0.837218\pi\)
−0.872062 + 0.489395i \(0.837218\pi\)
\(6\) −7.92550 −3.23557
\(7\) −4.57915 −1.73076 −0.865378 0.501120i \(-0.832921\pi\)
−0.865378 + 0.501120i \(0.832921\pi\)
\(8\) −5.28996 −1.87028
\(9\) 7.23752 2.41251
\(10\) 9.66032 3.05486
\(11\) 1.00000 0.301511
\(12\) 13.2324 3.81986
\(13\) 2.88643 0.800551 0.400276 0.916395i \(-0.368914\pi\)
0.400276 + 0.916395i \(0.368914\pi\)
\(14\) 11.3426 3.03145
\(15\) −12.4784 −3.22192
\(16\) 4.83209 1.20802
\(17\) 0.354961 0.0860907 0.0430454 0.999073i \(-0.486294\pi\)
0.0430454 + 0.999073i \(0.486294\pi\)
\(18\) −17.9275 −4.22554
\(19\) −2.08115 −0.477448 −0.238724 0.971087i \(-0.576729\pi\)
−0.238724 + 0.971087i \(0.576729\pi\)
\(20\) −16.1288 −3.60651
\(21\) −14.6515 −3.19722
\(22\) −2.47702 −0.528102
\(23\) 2.89822 0.604320 0.302160 0.953257i \(-0.402292\pi\)
0.302160 + 0.953257i \(0.402292\pi\)
\(24\) −16.9258 −3.45497
\(25\) 10.2098 2.04197
\(26\) −7.14973 −1.40218
\(27\) 13.5584 2.60932
\(28\) −18.9376 −3.57887
\(29\) −5.27832 −0.980159 −0.490079 0.871678i \(-0.663032\pi\)
−0.490079 + 0.871678i \(0.663032\pi\)
\(30\) 30.9093 5.64324
\(31\) −7.89839 −1.41859 −0.709296 0.704910i \(-0.750987\pi\)
−0.709296 + 0.704910i \(0.750987\pi\)
\(32\) −1.38925 −0.245587
\(33\) 3.19961 0.556981
\(34\) −0.879245 −0.150789
\(35\) 17.8586 3.01865
\(36\) 29.9316 4.98860
\(37\) −0.709403 −0.116625 −0.0583126 0.998298i \(-0.518572\pi\)
−0.0583126 + 0.998298i \(0.518572\pi\)
\(38\) 5.15504 0.836259
\(39\) 9.23545 1.47886
\(40\) 20.6307 3.26201
\(41\) 10.7338 1.67633 0.838165 0.545416i \(-0.183628\pi\)
0.838165 + 0.545416i \(0.183628\pi\)
\(42\) 36.2920 5.59998
\(43\) −0.999145 −0.152368 −0.0761841 0.997094i \(-0.524274\pi\)
−0.0761841 + 0.997094i \(0.524274\pi\)
\(44\) 4.13562 0.623468
\(45\) −28.2262 −4.20771
\(46\) −7.17893 −1.05848
\(47\) −3.46035 −0.504743 −0.252372 0.967630i \(-0.581211\pi\)
−0.252372 + 0.967630i \(0.581211\pi\)
\(48\) 15.4608 2.23158
\(49\) 13.9686 1.99551
\(50\) −25.2900 −3.57654
\(51\) 1.13574 0.159035
\(52\) 11.9372 1.65539
\(53\) 12.9768 1.78250 0.891250 0.453512i \(-0.149829\pi\)
0.891250 + 0.453512i \(0.149829\pi\)
\(54\) −33.5845 −4.57027
\(55\) −3.89998 −0.525873
\(56\) 24.2235 3.23700
\(57\) −6.65887 −0.881989
\(58\) 13.0745 1.71676
\(59\) −2.13636 −0.278130 −0.139065 0.990283i \(-0.544410\pi\)
−0.139065 + 0.990283i \(0.544410\pi\)
\(60\) −51.6060 −6.66230
\(61\) −6.20113 −0.793973 −0.396987 0.917824i \(-0.629944\pi\)
−0.396987 + 0.917824i \(0.629944\pi\)
\(62\) 19.5644 2.48469
\(63\) −33.1417 −4.17546
\(64\) −6.22298 −0.777873
\(65\) −11.2570 −1.39626
\(66\) −7.92550 −0.975561
\(67\) −3.71458 −0.453808 −0.226904 0.973917i \(-0.572860\pi\)
−0.226904 + 0.973917i \(0.572860\pi\)
\(68\) 1.46798 0.178019
\(69\) 9.27317 1.11636
\(70\) −44.2360 −5.28722
\(71\) 5.24113 0.622008 0.311004 0.950409i \(-0.399335\pi\)
0.311004 + 0.950409i \(0.399335\pi\)
\(72\) −38.2862 −4.51207
\(73\) −13.4599 −1.57537 −0.787683 0.616081i \(-0.788719\pi\)
−0.787683 + 0.616081i \(0.788719\pi\)
\(74\) 1.75720 0.204271
\(75\) 32.6676 3.77212
\(76\) −8.60683 −0.987272
\(77\) −4.57915 −0.521842
\(78\) −22.8764 −2.59024
\(79\) −0.525188 −0.0590883 −0.0295441 0.999563i \(-0.509406\pi\)
−0.0295441 + 0.999563i \(0.509406\pi\)
\(80\) −18.8450 −2.10694
\(81\) 21.6691 2.40768
\(82\) −26.5877 −2.93612
\(83\) −12.0963 −1.32774 −0.663872 0.747846i \(-0.731088\pi\)
−0.663872 + 0.747846i \(0.731088\pi\)
\(84\) −60.5930 −6.61124
\(85\) −1.38434 −0.150153
\(86\) 2.47490 0.266875
\(87\) −16.8886 −1.81064
\(88\) −5.28996 −0.563911
\(89\) 14.4254 1.52909 0.764547 0.644568i \(-0.222963\pi\)
0.764547 + 0.644568i \(0.222963\pi\)
\(90\) 69.9168 7.36987
\(91\) −13.2174 −1.38556
\(92\) 11.9859 1.24962
\(93\) −25.2718 −2.62056
\(94\) 8.57134 0.884066
\(95\) 8.11644 0.832729
\(96\) −4.44506 −0.453672
\(97\) 11.7333 1.19133 0.595666 0.803232i \(-0.296888\pi\)
0.595666 + 0.803232i \(0.296888\pi\)
\(98\) −34.6005 −3.49518
\(99\) 7.23752 0.727398
\(100\) 42.2240 4.22240
\(101\) −14.8987 −1.48248 −0.741240 0.671240i \(-0.765762\pi\)
−0.741240 + 0.671240i \(0.765762\pi\)
\(102\) −2.81324 −0.278553
\(103\) 8.34891 0.822642 0.411321 0.911490i \(-0.365067\pi\)
0.411321 + 0.911490i \(0.365067\pi\)
\(104\) −15.2691 −1.49726
\(105\) 57.1406 5.57635
\(106\) −32.1438 −3.12208
\(107\) 16.3045 1.57622 0.788110 0.615535i \(-0.211060\pi\)
0.788110 + 0.615535i \(0.211060\pi\)
\(108\) 56.0724 5.39557
\(109\) 8.90399 0.852847 0.426424 0.904524i \(-0.359773\pi\)
0.426424 + 0.904524i \(0.359773\pi\)
\(110\) 9.66032 0.921075
\(111\) −2.26981 −0.215441
\(112\) −22.1268 −2.09079
\(113\) −13.4001 −1.26057 −0.630285 0.776364i \(-0.717062\pi\)
−0.630285 + 0.776364i \(0.717062\pi\)
\(114\) 16.4941 1.54482
\(115\) −11.3030 −1.05401
\(116\) −21.8291 −2.02678
\(117\) 20.8906 1.93134
\(118\) 5.29180 0.487150
\(119\) −1.62542 −0.149002
\(120\) 66.0104 6.02589
\(121\) 1.00000 0.0909091
\(122\) 15.3603 1.39066
\(123\) 34.3439 3.09668
\(124\) −32.6647 −2.93338
\(125\) −20.3183 −1.81732
\(126\) 82.0925 7.31338
\(127\) −16.3797 −1.45346 −0.726732 0.686921i \(-0.758962\pi\)
−0.726732 + 0.686921i \(0.758962\pi\)
\(128\) 18.1929 1.60804
\(129\) −3.19688 −0.281469
\(130\) 27.8838 2.44557
\(131\) −16.1832 −1.41393 −0.706966 0.707248i \(-0.749937\pi\)
−0.706966 + 0.707248i \(0.749937\pi\)
\(132\) 13.2324 1.15173
\(133\) 9.52989 0.826346
\(134\) 9.20108 0.794852
\(135\) −52.8776 −4.55098
\(136\) −1.87773 −0.161014
\(137\) 7.94361 0.678668 0.339334 0.940666i \(-0.389798\pi\)
0.339334 + 0.940666i \(0.389798\pi\)
\(138\) −22.9698 −1.95532
\(139\) 10.1432 0.860335 0.430168 0.902749i \(-0.358454\pi\)
0.430168 + 0.902749i \(0.358454\pi\)
\(140\) 73.8563 6.24199
\(141\) −11.0718 −0.932411
\(142\) −12.9824 −1.08946
\(143\) 2.88643 0.241375
\(144\) 34.9723 2.91436
\(145\) 20.5853 1.70952
\(146\) 33.3405 2.75928
\(147\) 44.6941 3.68631
\(148\) −2.93382 −0.241158
\(149\) 16.1523 1.32325 0.661624 0.749836i \(-0.269868\pi\)
0.661624 + 0.749836i \(0.269868\pi\)
\(150\) −80.9181 −6.60694
\(151\) −11.9771 −0.974686 −0.487343 0.873211i \(-0.662034\pi\)
−0.487343 + 0.873211i \(0.662034\pi\)
\(152\) 11.0092 0.892964
\(153\) 2.56904 0.207695
\(154\) 11.3426 0.914015
\(155\) 30.8036 2.47420
\(156\) 38.1943 3.05799
\(157\) −18.7756 −1.49846 −0.749228 0.662312i \(-0.769575\pi\)
−0.749228 + 0.662312i \(0.769575\pi\)
\(158\) 1.30090 0.103494
\(159\) 41.5207 3.29281
\(160\) 5.41805 0.428334
\(161\) −13.2714 −1.04593
\(162\) −53.6749 −4.21710
\(163\) −5.83591 −0.457104 −0.228552 0.973532i \(-0.573399\pi\)
−0.228552 + 0.973532i \(0.573399\pi\)
\(164\) 44.3907 3.46633
\(165\) −12.4784 −0.971444
\(166\) 29.9628 2.32556
\(167\) 8.91224 0.689650 0.344825 0.938667i \(-0.387938\pi\)
0.344825 + 0.938667i \(0.387938\pi\)
\(168\) 77.5058 5.97970
\(169\) −4.66853 −0.359118
\(170\) 3.42904 0.262995
\(171\) −15.0624 −1.15185
\(172\) −4.13208 −0.315068
\(173\) −24.1041 −1.83260 −0.916301 0.400490i \(-0.868840\pi\)
−0.916301 + 0.400490i \(0.868840\pi\)
\(174\) 41.8333 3.17137
\(175\) −46.7524 −3.53415
\(176\) 4.83209 0.364232
\(177\) −6.83552 −0.513789
\(178\) −35.7321 −2.67823
\(179\) −7.16747 −0.535722 −0.267861 0.963458i \(-0.586317\pi\)
−0.267861 + 0.963458i \(0.586317\pi\)
\(180\) −116.733 −8.70074
\(181\) 1.50477 0.111849 0.0559245 0.998435i \(-0.482189\pi\)
0.0559245 + 0.998435i \(0.482189\pi\)
\(182\) 32.7397 2.42683
\(183\) −19.8412 −1.46670
\(184\) −15.3314 −1.13025
\(185\) 2.76666 0.203409
\(186\) 62.5987 4.58996
\(187\) 0.354961 0.0259573
\(188\) −14.3107 −1.04371
\(189\) −62.0860 −4.51610
\(190\) −20.1046 −1.45854
\(191\) 3.61116 0.261295 0.130647 0.991429i \(-0.458294\pi\)
0.130647 + 0.991429i \(0.458294\pi\)
\(192\) −19.9111 −1.43696
\(193\) −19.3554 −1.39323 −0.696615 0.717445i \(-0.745311\pi\)
−0.696615 + 0.717445i \(0.745311\pi\)
\(194\) −29.0635 −2.08664
\(195\) −36.0181 −2.57931
\(196\) 57.7688 4.12634
\(197\) 19.1707 1.36586 0.682929 0.730485i \(-0.260706\pi\)
0.682929 + 0.730485i \(0.260706\pi\)
\(198\) −17.9275 −1.27405
\(199\) −9.42513 −0.668130 −0.334065 0.942550i \(-0.608420\pi\)
−0.334065 + 0.942550i \(0.608420\pi\)
\(200\) −54.0097 −3.81906
\(201\) −11.8852 −0.838319
\(202\) 36.9044 2.59659
\(203\) 24.1702 1.69642
\(204\) 4.69698 0.328854
\(205\) −41.8614 −2.92373
\(206\) −20.6804 −1.44087
\(207\) 20.9759 1.45793
\(208\) 13.9475 0.967083
\(209\) −2.08115 −0.143956
\(210\) −141.538 −9.76706
\(211\) 2.46109 0.169428 0.0847141 0.996405i \(-0.473002\pi\)
0.0847141 + 0.996405i \(0.473002\pi\)
\(212\) 53.6671 3.68587
\(213\) 16.7696 1.14903
\(214\) −40.3866 −2.76077
\(215\) 3.89664 0.265749
\(216\) −71.7235 −4.88017
\(217\) 36.1679 2.45524
\(218\) −22.0553 −1.49378
\(219\) −43.0666 −2.91017
\(220\) −16.1288 −1.08740
\(221\) 1.02457 0.0689200
\(222\) 5.62237 0.377349
\(223\) −6.31624 −0.422967 −0.211483 0.977382i \(-0.567829\pi\)
−0.211483 + 0.977382i \(0.567829\pi\)
\(224\) 6.36158 0.425051
\(225\) 73.8940 4.92627
\(226\) 33.1922 2.20791
\(227\) −11.7037 −0.776799 −0.388399 0.921491i \(-0.626972\pi\)
−0.388399 + 0.921491i \(0.626972\pi\)
\(228\) −27.5385 −1.82378
\(229\) −3.80686 −0.251565 −0.125782 0.992058i \(-0.540144\pi\)
−0.125782 + 0.992058i \(0.540144\pi\)
\(230\) 27.9977 1.84611
\(231\) −14.6515 −0.963998
\(232\) 27.9221 1.83317
\(233\) −6.85111 −0.448831 −0.224416 0.974494i \(-0.572047\pi\)
−0.224416 + 0.974494i \(0.572047\pi\)
\(234\) −51.7463 −3.38276
\(235\) 13.4953 0.880335
\(236\) −8.83516 −0.575120
\(237\) −1.68040 −0.109154
\(238\) 4.02619 0.260979
\(239\) −14.5928 −0.943928 −0.471964 0.881618i \(-0.656455\pi\)
−0.471964 + 0.881618i \(0.656455\pi\)
\(240\) −60.2969 −3.89214
\(241\) 12.0719 0.777617 0.388809 0.921318i \(-0.372887\pi\)
0.388809 + 0.921318i \(0.372887\pi\)
\(242\) −2.47702 −0.159229
\(243\) 28.6576 1.83839
\(244\) −25.6455 −1.64178
\(245\) −54.4773 −3.48043
\(246\) −85.0703 −5.42389
\(247\) −6.00709 −0.382222
\(248\) 41.7822 2.65317
\(249\) −38.7035 −2.45274
\(250\) 50.3288 3.18307
\(251\) 25.5787 1.61451 0.807255 0.590202i \(-0.200952\pi\)
0.807255 + 0.590202i \(0.200952\pi\)
\(252\) −137.061 −8.63405
\(253\) 2.89822 0.182209
\(254\) 40.5728 2.54577
\(255\) −4.42936 −0.277377
\(256\) −32.6182 −2.03864
\(257\) −5.29055 −0.330015 −0.165008 0.986292i \(-0.552765\pi\)
−0.165008 + 0.986292i \(0.552765\pi\)
\(258\) 7.91872 0.492998
\(259\) 3.24846 0.201850
\(260\) −46.5547 −2.88720
\(261\) −38.2019 −2.36464
\(262\) 40.0860 2.47652
\(263\) −20.4231 −1.25934 −0.629670 0.776863i \(-0.716810\pi\)
−0.629670 + 0.776863i \(0.716810\pi\)
\(264\) −16.9258 −1.04171
\(265\) −50.6093 −3.10890
\(266\) −23.6057 −1.44736
\(267\) 46.1558 2.82469
\(268\) −15.3621 −0.938388
\(269\) −20.6456 −1.25878 −0.629392 0.777088i \(-0.716696\pi\)
−0.629392 + 0.777088i \(0.716696\pi\)
\(270\) 130.979 7.97111
\(271\) −18.6358 −1.13205 −0.566023 0.824390i \(-0.691518\pi\)
−0.566023 + 0.824390i \(0.691518\pi\)
\(272\) 1.71520 0.103999
\(273\) −42.2905 −2.55954
\(274\) −19.6765 −1.18870
\(275\) 10.2098 0.615677
\(276\) 38.3503 2.30841
\(277\) −19.6299 −1.17945 −0.589724 0.807605i \(-0.700763\pi\)
−0.589724 + 0.807605i \(0.700763\pi\)
\(278\) −25.1249 −1.50689
\(279\) −57.1648 −3.42236
\(280\) −94.4712 −5.64573
\(281\) −4.85728 −0.289761 −0.144880 0.989449i \(-0.546280\pi\)
−0.144880 + 0.989449i \(0.546280\pi\)
\(282\) 27.4250 1.63313
\(283\) −14.5164 −0.862911 −0.431455 0.902134i \(-0.642000\pi\)
−0.431455 + 0.902134i \(0.642000\pi\)
\(284\) 21.6753 1.28619
\(285\) 25.9695 1.53830
\(286\) −7.14973 −0.422773
\(287\) −49.1514 −2.90132
\(288\) −10.0547 −0.592480
\(289\) −16.8740 −0.992588
\(290\) −50.9902 −2.99425
\(291\) 37.5419 2.20075
\(292\) −55.6651 −3.25755
\(293\) 5.63997 0.329491 0.164745 0.986336i \(-0.447320\pi\)
0.164745 + 0.986336i \(0.447320\pi\)
\(294\) −110.708 −6.45663
\(295\) 8.33176 0.485094
\(296\) 3.75271 0.218122
\(297\) 13.5584 0.786740
\(298\) −40.0095 −2.31769
\(299\) 8.36549 0.483789
\(300\) 135.100 7.80003
\(301\) 4.57523 0.263712
\(302\) 29.6676 1.70718
\(303\) −47.6702 −2.73858
\(304\) −10.0563 −0.576768
\(305\) 24.1843 1.38479
\(306\) −6.36356 −0.363780
\(307\) −9.23958 −0.527331 −0.263665 0.964614i \(-0.584931\pi\)
−0.263665 + 0.964614i \(0.584931\pi\)
\(308\) −18.9376 −1.07907
\(309\) 26.7133 1.51966
\(310\) −76.3010 −4.33360
\(311\) 16.0768 0.911633 0.455816 0.890074i \(-0.349347\pi\)
0.455816 + 0.890074i \(0.349347\pi\)
\(312\) −48.8552 −2.76588
\(313\) 9.20398 0.520239 0.260120 0.965576i \(-0.416238\pi\)
0.260120 + 0.965576i \(0.416238\pi\)
\(314\) 46.5075 2.62457
\(315\) 129.252 7.28252
\(316\) −2.17198 −0.122183
\(317\) 10.3297 0.580172 0.290086 0.957001i \(-0.406316\pi\)
0.290086 + 0.957001i \(0.406316\pi\)
\(318\) −102.848 −5.76741
\(319\) −5.27832 −0.295529
\(320\) 24.2695 1.35671
\(321\) 52.1682 2.91175
\(322\) 32.8734 1.83196
\(323\) −0.738727 −0.0411039
\(324\) 89.6153 4.97863
\(325\) 29.4700 1.63470
\(326\) 14.4556 0.800624
\(327\) 28.4893 1.57546
\(328\) −56.7811 −3.13521
\(329\) 15.8454 0.873587
\(330\) 30.9093 1.70150
\(331\) −33.8328 −1.85962 −0.929810 0.368039i \(-0.880029\pi\)
−0.929810 + 0.368039i \(0.880029\pi\)
\(332\) −50.0257 −2.74552
\(333\) −5.13432 −0.281359
\(334\) −22.0758 −1.20793
\(335\) 14.4868 0.791498
\(336\) −70.7973 −3.86231
\(337\) 28.0182 1.52625 0.763124 0.646253i \(-0.223665\pi\)
0.763124 + 0.646253i \(0.223665\pi\)
\(338\) 11.5640 0.629000
\(339\) −42.8750 −2.32865
\(340\) −5.72511 −0.310487
\(341\) −7.89839 −0.427722
\(342\) 37.3097 2.01748
\(343\) −31.9103 −1.72299
\(344\) 5.28543 0.284971
\(345\) −36.1652 −1.94707
\(346\) 59.7063 3.20983
\(347\) −21.6653 −1.16305 −0.581527 0.813527i \(-0.697545\pi\)
−0.581527 + 0.813527i \(0.697545\pi\)
\(348\) −69.8446 −3.74407
\(349\) 24.2650 1.29888 0.649438 0.760415i \(-0.275004\pi\)
0.649438 + 0.760415i \(0.275004\pi\)
\(350\) 115.807 6.19012
\(351\) 39.1354 2.08889
\(352\) −1.38925 −0.0740472
\(353\) −4.32955 −0.230439 −0.115219 0.993340i \(-0.536757\pi\)
−0.115219 + 0.993340i \(0.536757\pi\)
\(354\) 16.9317 0.899910
\(355\) −20.4403 −1.08486
\(356\) 59.6581 3.16187
\(357\) −5.20071 −0.275251
\(358\) 17.7540 0.938325
\(359\) 10.7073 0.565111 0.282555 0.959251i \(-0.408818\pi\)
0.282555 + 0.959251i \(0.408818\pi\)
\(360\) 149.315 7.86961
\(361\) −14.6688 −0.772043
\(362\) −3.72735 −0.195905
\(363\) 3.19961 0.167936
\(364\) −54.6620 −2.86507
\(365\) 52.4934 2.74763
\(366\) 49.1470 2.56896
\(367\) −21.8538 −1.14076 −0.570380 0.821381i \(-0.693204\pi\)
−0.570380 + 0.821381i \(0.693204\pi\)
\(368\) 14.0044 0.730032
\(369\) 77.6858 4.04416
\(370\) −6.85306 −0.356274
\(371\) −59.4227 −3.08507
\(372\) −104.514 −5.41882
\(373\) 19.5441 1.01195 0.505977 0.862547i \(-0.331132\pi\)
0.505977 + 0.862547i \(0.331132\pi\)
\(374\) −0.879245 −0.0454647
\(375\) −65.0107 −3.35714
\(376\) 18.3051 0.944013
\(377\) −15.2355 −0.784667
\(378\) 153.788 7.91001
\(379\) −37.0211 −1.90165 −0.950823 0.309736i \(-0.899759\pi\)
−0.950823 + 0.309736i \(0.899759\pi\)
\(380\) 33.5665 1.72192
\(381\) −52.4087 −2.68498
\(382\) −8.94491 −0.457662
\(383\) −26.4893 −1.35354 −0.676771 0.736193i \(-0.736621\pi\)
−0.676771 + 0.736193i \(0.736621\pi\)
\(384\) 58.2103 2.97053
\(385\) 17.8586 0.910158
\(386\) 47.9436 2.44026
\(387\) −7.23133 −0.367589
\(388\) 48.5243 2.46345
\(389\) 5.09480 0.258317 0.129158 0.991624i \(-0.458772\pi\)
0.129158 + 0.991624i \(0.458772\pi\)
\(390\) 89.2174 4.51770
\(391\) 1.02875 0.0520263
\(392\) −73.8933 −3.73218
\(393\) −51.7799 −2.61195
\(394\) −47.4862 −2.39232
\(395\) 2.04822 0.103057
\(396\) 29.9316 1.50412
\(397\) 27.4517 1.37776 0.688880 0.724876i \(-0.258103\pi\)
0.688880 + 0.724876i \(0.258103\pi\)
\(398\) 23.3462 1.17024
\(399\) 30.4920 1.52651
\(400\) 49.3349 2.46674
\(401\) −28.3552 −1.41599 −0.707995 0.706218i \(-0.750400\pi\)
−0.707995 + 0.706218i \(0.750400\pi\)
\(402\) 29.4399 1.46833
\(403\) −22.7981 −1.13566
\(404\) −61.6154 −3.06548
\(405\) −84.5093 −4.19930
\(406\) −59.8700 −2.97130
\(407\) −0.709403 −0.0351638
\(408\) −6.00801 −0.297441
\(409\) −30.3939 −1.50288 −0.751441 0.659801i \(-0.770641\pi\)
−0.751441 + 0.659801i \(0.770641\pi\)
\(410\) 103.691 5.12096
\(411\) 25.4165 1.25370
\(412\) 34.5279 1.70107
\(413\) 9.78270 0.481375
\(414\) −51.9577 −2.55358
\(415\) 47.1754 2.31575
\(416\) −4.00997 −0.196605
\(417\) 32.4543 1.58929
\(418\) 5.15504 0.252141
\(419\) 16.2748 0.795077 0.397538 0.917586i \(-0.369865\pi\)
0.397538 + 0.917586i \(0.369865\pi\)
\(420\) 236.311 11.5308
\(421\) 7.19941 0.350878 0.175439 0.984490i \(-0.443866\pi\)
0.175439 + 0.984490i \(0.443866\pi\)
\(422\) −6.09615 −0.296756
\(423\) −25.0443 −1.21770
\(424\) −68.6467 −3.33378
\(425\) 3.62410 0.175795
\(426\) −41.5386 −2.01255
\(427\) 28.3959 1.37417
\(428\) 67.4293 3.25932
\(429\) 9.23545 0.445892
\(430\) −9.65206 −0.465463
\(431\) 10.0527 0.484224 0.242112 0.970248i \(-0.422160\pi\)
0.242112 + 0.970248i \(0.422160\pi\)
\(432\) 65.5155 3.15212
\(433\) 10.6705 0.512794 0.256397 0.966572i \(-0.417465\pi\)
0.256397 + 0.966572i \(0.417465\pi\)
\(434\) −89.5885 −4.30039
\(435\) 65.8651 3.15799
\(436\) 36.8235 1.76352
\(437\) −6.03162 −0.288532
\(438\) 106.677 5.09721
\(439\) −4.04425 −0.193021 −0.0965107 0.995332i \(-0.530768\pi\)
−0.0965107 + 0.995332i \(0.530768\pi\)
\(440\) 20.6307 0.983532
\(441\) 101.098 4.81419
\(442\) −2.53788 −0.120715
\(443\) −30.6735 −1.45734 −0.728671 0.684864i \(-0.759861\pi\)
−0.728671 + 0.684864i \(0.759861\pi\)
\(444\) −9.38708 −0.445491
\(445\) −56.2589 −2.66693
\(446\) 15.6454 0.740833
\(447\) 51.6811 2.44443
\(448\) 28.4960 1.34631
\(449\) −6.71404 −0.316855 −0.158428 0.987371i \(-0.550642\pi\)
−0.158428 + 0.987371i \(0.550642\pi\)
\(450\) −183.037 −8.62843
\(451\) 10.7338 0.505433
\(452\) −55.4175 −2.60662
\(453\) −38.3222 −1.80053
\(454\) 28.9901 1.36058
\(455\) 51.5475 2.41659
\(456\) 35.2252 1.64957
\(457\) 5.02964 0.235277 0.117638 0.993057i \(-0.462468\pi\)
0.117638 + 0.993057i \(0.462468\pi\)
\(458\) 9.42967 0.440619
\(459\) 4.81272 0.224638
\(460\) −46.7448 −2.17949
\(461\) −21.1434 −0.984745 −0.492373 0.870384i \(-0.663870\pi\)
−0.492373 + 0.870384i \(0.663870\pi\)
\(462\) 36.2920 1.68846
\(463\) −23.2911 −1.08243 −0.541215 0.840885i \(-0.682035\pi\)
−0.541215 + 0.840885i \(0.682035\pi\)
\(464\) −25.5053 −1.18405
\(465\) 98.5595 4.57059
\(466\) 16.9703 0.786135
\(467\) −16.1214 −0.746008 −0.373004 0.927830i \(-0.621672\pi\)
−0.373004 + 0.927830i \(0.621672\pi\)
\(468\) 86.3954 3.99363
\(469\) 17.0096 0.785431
\(470\) −33.4280 −1.54192
\(471\) −60.0747 −2.76809
\(472\) 11.3012 0.520182
\(473\) −0.999145 −0.0459407
\(474\) 4.16238 0.191184
\(475\) −21.2482 −0.974935
\(476\) −6.72211 −0.308108
\(477\) 93.9199 4.30029
\(478\) 36.1465 1.65330
\(479\) −2.66835 −0.121920 −0.0609600 0.998140i \(-0.519416\pi\)
−0.0609600 + 0.998140i \(0.519416\pi\)
\(480\) 17.3356 0.791260
\(481\) −2.04764 −0.0933644
\(482\) −29.9022 −1.36201
\(483\) −42.4632 −1.93214
\(484\) 4.13562 0.187983
\(485\) −45.7595 −2.07783
\(486\) −70.9854 −3.21996
\(487\) −25.6670 −1.16308 −0.581541 0.813517i \(-0.697550\pi\)
−0.581541 + 0.813517i \(0.697550\pi\)
\(488\) 32.8037 1.48495
\(489\) −18.6726 −0.844406
\(490\) 134.941 6.09602
\(491\) −20.6623 −0.932475 −0.466237 0.884660i \(-0.654391\pi\)
−0.466237 + 0.884660i \(0.654391\pi\)
\(492\) 142.033 6.40334
\(493\) −1.87360 −0.0843826
\(494\) 14.8797 0.669468
\(495\) −28.2262 −1.26867
\(496\) −38.1657 −1.71369
\(497\) −23.9999 −1.07654
\(498\) 95.8693 4.29601
\(499\) 25.0080 1.11951 0.559756 0.828657i \(-0.310895\pi\)
0.559756 + 0.828657i \(0.310895\pi\)
\(500\) −84.0287 −3.75788
\(501\) 28.5157 1.27399
\(502\) −63.3588 −2.82784
\(503\) −10.7986 −0.481485 −0.240742 0.970589i \(-0.577391\pi\)
−0.240742 + 0.970589i \(0.577391\pi\)
\(504\) 175.318 7.80929
\(505\) 58.1048 2.58563
\(506\) −7.17893 −0.319142
\(507\) −14.9375 −0.663397
\(508\) −67.7402 −3.00549
\(509\) 29.9658 1.32821 0.664105 0.747639i \(-0.268813\pi\)
0.664105 + 0.747639i \(0.268813\pi\)
\(510\) 10.9716 0.485830
\(511\) 61.6350 2.72657
\(512\) 44.4101 1.96267
\(513\) −28.2171 −1.24582
\(514\) 13.1048 0.578027
\(515\) −32.5606 −1.43479
\(516\) −13.2210 −0.582024
\(517\) −3.46035 −0.152186
\(518\) −8.04649 −0.353543
\(519\) −77.1238 −3.38536
\(520\) 59.5491 2.61140
\(521\) −5.90976 −0.258911 −0.129456 0.991585i \(-0.541323\pi\)
−0.129456 + 0.991585i \(0.541323\pi\)
\(522\) 94.6268 4.14170
\(523\) −31.0399 −1.35728 −0.678640 0.734471i \(-0.737431\pi\)
−0.678640 + 0.734471i \(0.737431\pi\)
\(524\) −66.9275 −2.92374
\(525\) −149.590 −6.52862
\(526\) 50.5883 2.20575
\(527\) −2.80362 −0.122128
\(528\) 15.4608 0.672845
\(529\) −14.6003 −0.634798
\(530\) 125.360 5.44529
\(531\) −15.4619 −0.670991
\(532\) 39.4120 1.70873
\(533\) 30.9822 1.34199
\(534\) −114.329 −4.94749
\(535\) −63.5874 −2.74912
\(536\) 19.6500 0.848750
\(537\) −22.9331 −0.989638
\(538\) 51.1395 2.20478
\(539\) 13.9686 0.601670
\(540\) −218.681 −9.41055
\(541\) 37.7594 1.62340 0.811702 0.584072i \(-0.198541\pi\)
0.811702 + 0.584072i \(0.198541\pi\)
\(542\) 46.1612 1.98279
\(543\) 4.81470 0.206618
\(544\) −0.493130 −0.0211428
\(545\) −34.7254 −1.48747
\(546\) 104.754 4.48307
\(547\) 1.00000 0.0427569
\(548\) 32.8517 1.40336
\(549\) −44.8808 −1.91547
\(550\) −25.2900 −1.07837
\(551\) 10.9850 0.467975
\(552\) −49.0547 −2.08791
\(553\) 2.40492 0.102267
\(554\) 48.6237 2.06582
\(555\) 8.85223 0.375756
\(556\) 41.9484 1.77901
\(557\) −8.20405 −0.347617 −0.173808 0.984779i \(-0.555607\pi\)
−0.173808 + 0.984779i \(0.555607\pi\)
\(558\) 141.598 5.99433
\(559\) −2.88396 −0.121978
\(560\) 86.2943 3.64660
\(561\) 1.13574 0.0479509
\(562\) 12.0316 0.507521
\(563\) 1.29871 0.0547342 0.0273671 0.999625i \(-0.491288\pi\)
0.0273671 + 0.999625i \(0.491288\pi\)
\(564\) −45.7886 −1.92805
\(565\) 52.2599 2.19859
\(566\) 35.9574 1.51140
\(567\) −99.2263 −4.16711
\(568\) −27.7254 −1.16333
\(569\) −0.645479 −0.0270599 −0.0135300 0.999908i \(-0.504307\pi\)
−0.0135300 + 0.999908i \(0.504307\pi\)
\(570\) −64.3268 −2.69435
\(571\) −24.9695 −1.04494 −0.522472 0.852657i \(-0.674990\pi\)
−0.522472 + 0.852657i \(0.674990\pi\)
\(572\) 11.9372 0.499118
\(573\) 11.5543 0.482689
\(574\) 121.749 5.08171
\(575\) 29.5903 1.23400
\(576\) −45.0390 −1.87662
\(577\) −31.5561 −1.31370 −0.656849 0.754022i \(-0.728111\pi\)
−0.656849 + 0.754022i \(0.728111\pi\)
\(578\) 41.7972 1.73853
\(579\) −61.9297 −2.57371
\(580\) 85.1330 3.53496
\(581\) 55.3908 2.29800
\(582\) −92.9920 −3.85464
\(583\) 12.9768 0.537444
\(584\) 71.2025 2.94638
\(585\) −81.4729 −3.36849
\(586\) −13.9703 −0.577108
\(587\) −17.5995 −0.726409 −0.363204 0.931709i \(-0.618317\pi\)
−0.363204 + 0.931709i \(0.618317\pi\)
\(588\) 184.838 7.62258
\(589\) 16.4377 0.677305
\(590\) −20.6379 −0.849649
\(591\) 61.3389 2.52315
\(592\) −3.42790 −0.140886
\(593\) 25.3881 1.04257 0.521283 0.853384i \(-0.325454\pi\)
0.521283 + 0.853384i \(0.325454\pi\)
\(594\) −33.5845 −1.37799
\(595\) 6.33911 0.259878
\(596\) 66.7997 2.73622
\(597\) −30.1568 −1.23423
\(598\) −20.7215 −0.847364
\(599\) 31.5592 1.28948 0.644738 0.764404i \(-0.276966\pi\)
0.644738 + 0.764404i \(0.276966\pi\)
\(600\) −172.810 −7.05494
\(601\) 33.9345 1.38422 0.692108 0.721794i \(-0.256682\pi\)
0.692108 + 0.721794i \(0.256682\pi\)
\(602\) −11.3329 −0.461896
\(603\) −26.8844 −1.09482
\(604\) −49.5328 −2.01546
\(605\) −3.89998 −0.158557
\(606\) 118.080 4.79667
\(607\) −25.3360 −1.02836 −0.514178 0.857684i \(-0.671903\pi\)
−0.514178 + 0.857684i \(0.671903\pi\)
\(608\) 2.89124 0.117255
\(609\) 77.3353 3.13378
\(610\) −59.9049 −2.42548
\(611\) −9.98804 −0.404073
\(612\) 10.6246 0.429472
\(613\) 11.7136 0.473106 0.236553 0.971619i \(-0.423982\pi\)
0.236553 + 0.971619i \(0.423982\pi\)
\(614\) 22.8866 0.923628
\(615\) −133.940 −5.40100
\(616\) 24.2235 0.975993
\(617\) −40.2143 −1.61897 −0.809484 0.587143i \(-0.800253\pi\)
−0.809484 + 0.587143i \(0.800253\pi\)
\(618\) −66.1692 −2.66172
\(619\) 5.95854 0.239494 0.119747 0.992804i \(-0.461792\pi\)
0.119747 + 0.992804i \(0.461792\pi\)
\(620\) 127.392 5.11617
\(621\) 39.2952 1.57686
\(622\) −39.8226 −1.59674
\(623\) −66.0562 −2.64649
\(624\) 44.6265 1.78649
\(625\) 28.1917 1.12767
\(626\) −22.7984 −0.911208
\(627\) −6.65887 −0.265930
\(628\) −77.6487 −3.09852
\(629\) −0.251810 −0.0100403
\(630\) −320.159 −12.7555
\(631\) 37.2582 1.48322 0.741612 0.670829i \(-0.234062\pi\)
0.741612 + 0.670829i \(0.234062\pi\)
\(632\) 2.77822 0.110512
\(633\) 7.87452 0.312984
\(634\) −25.5868 −1.01618
\(635\) 63.8806 2.53502
\(636\) 171.714 6.80889
\(637\) 40.3194 1.59751
\(638\) 13.0745 0.517624
\(639\) 37.9328 1.50060
\(640\) −70.9521 −2.80463
\(641\) 8.88454 0.350918 0.175459 0.984487i \(-0.443859\pi\)
0.175459 + 0.984487i \(0.443859\pi\)
\(642\) −129.222 −5.09997
\(643\) 0.0790906 0.00311903 0.00155951 0.999999i \(-0.499504\pi\)
0.00155951 + 0.999999i \(0.499504\pi\)
\(644\) −54.8853 −2.16278
\(645\) 12.4678 0.490917
\(646\) 1.82984 0.0719941
\(647\) −47.1582 −1.85398 −0.926991 0.375085i \(-0.877614\pi\)
−0.926991 + 0.375085i \(0.877614\pi\)
\(648\) −114.629 −4.50305
\(649\) −2.13636 −0.0838594
\(650\) −72.9977 −2.86320
\(651\) 115.723 4.53555
\(652\) −24.1351 −0.945202
\(653\) −6.52231 −0.255238 −0.127619 0.991823i \(-0.540733\pi\)
−0.127619 + 0.991823i \(0.540733\pi\)
\(654\) −70.5685 −2.75945
\(655\) 63.1141 2.46607
\(656\) 51.8664 2.02504
\(657\) −97.4165 −3.80058
\(658\) −39.2494 −1.53010
\(659\) 33.2205 1.29409 0.647044 0.762453i \(-0.276005\pi\)
0.647044 + 0.762453i \(0.276005\pi\)
\(660\) −51.6060 −2.00876
\(661\) 3.42551 0.133237 0.0666185 0.997779i \(-0.478779\pi\)
0.0666185 + 0.997779i \(0.478779\pi\)
\(662\) 83.8045 3.25715
\(663\) 3.27823 0.127316
\(664\) 63.9890 2.48326
\(665\) −37.1664 −1.44125
\(666\) 12.7178 0.492805
\(667\) −15.2977 −0.592329
\(668\) 36.8576 1.42606
\(669\) −20.2095 −0.781345
\(670\) −35.8840 −1.38632
\(671\) −6.20113 −0.239392
\(672\) 20.3546 0.785195
\(673\) 12.8196 0.494160 0.247080 0.968995i \(-0.420529\pi\)
0.247080 + 0.968995i \(0.420529\pi\)
\(674\) −69.4015 −2.67325
\(675\) 138.429 5.32815
\(676\) −19.3073 −0.742587
\(677\) −18.4034 −0.707302 −0.353651 0.935378i \(-0.615060\pi\)
−0.353651 + 0.935378i \(0.615060\pi\)
\(678\) 106.202 4.07867
\(679\) −53.7284 −2.06191
\(680\) 7.32311 0.280828
\(681\) −37.4471 −1.43498
\(682\) 19.5644 0.749161
\(683\) −5.66105 −0.216614 −0.108307 0.994118i \(-0.534543\pi\)
−0.108307 + 0.994118i \(0.534543\pi\)
\(684\) −62.2921 −2.38180
\(685\) −30.9799 −1.18368
\(686\) 79.0423 3.01785
\(687\) −12.1805 −0.464715
\(688\) −4.82795 −0.184064
\(689\) 37.4566 1.42698
\(690\) 89.5818 3.41032
\(691\) −1.70244 −0.0647637 −0.0323819 0.999476i \(-0.510309\pi\)
−0.0323819 + 0.999476i \(0.510309\pi\)
\(692\) −99.6854 −3.78947
\(693\) −33.1417 −1.25895
\(694\) 53.6653 2.03711
\(695\) −39.5583 −1.50053
\(696\) 89.3398 3.38642
\(697\) 3.81007 0.144317
\(698\) −60.1048 −2.27500
\(699\) −21.9209 −0.829124
\(700\) −193.350 −7.30794
\(701\) 5.47957 0.206960 0.103480 0.994632i \(-0.467002\pi\)
0.103480 + 0.994632i \(0.467002\pi\)
\(702\) −96.9391 −3.65873
\(703\) 1.47637 0.0556825
\(704\) −6.22298 −0.234537
\(705\) 43.1797 1.62624
\(706\) 10.7244 0.403617
\(707\) 68.2235 2.56581
\(708\) −28.2691 −1.06242
\(709\) −1.16914 −0.0439081 −0.0219541 0.999759i \(-0.506989\pi\)
−0.0219541 + 0.999759i \(0.506989\pi\)
\(710\) 50.6310 1.90015
\(711\) −3.80106 −0.142551
\(712\) −76.3100 −2.85984
\(713\) −22.8912 −0.857284
\(714\) 12.8823 0.482107
\(715\) −11.2570 −0.420988
\(716\) −29.6419 −1.10777
\(717\) −46.6912 −1.74371
\(718\) −26.5222 −0.989801
\(719\) 42.7487 1.59426 0.797129 0.603809i \(-0.206351\pi\)
0.797129 + 0.603809i \(0.206351\pi\)
\(720\) −136.391 −5.08301
\(721\) −38.2309 −1.42379
\(722\) 36.3349 1.35225
\(723\) 38.6253 1.43649
\(724\) 6.22317 0.231282
\(725\) −53.8908 −2.00145
\(726\) −7.92550 −0.294143
\(727\) −17.5180 −0.649706 −0.324853 0.945765i \(-0.605315\pi\)
−0.324853 + 0.945765i \(0.605315\pi\)
\(728\) 69.9194 2.59139
\(729\) 26.6858 0.988362
\(730\) −130.027 −4.81252
\(731\) −0.354658 −0.0131175
\(732\) −82.0557 −3.03286
\(733\) −37.4860 −1.38458 −0.692289 0.721620i \(-0.743398\pi\)
−0.692289 + 0.721620i \(0.743398\pi\)
\(734\) 54.1323 1.99806
\(735\) −174.306 −6.42938
\(736\) −4.02635 −0.148413
\(737\) −3.71458 −0.136828
\(738\) −192.429 −7.08341
\(739\) 16.2715 0.598555 0.299278 0.954166i \(-0.403254\pi\)
0.299278 + 0.954166i \(0.403254\pi\)
\(740\) 11.4418 0.420610
\(741\) −19.2204 −0.706077
\(742\) 147.191 5.40355
\(743\) 43.9301 1.61164 0.805819 0.592162i \(-0.201725\pi\)
0.805819 + 0.592162i \(0.201725\pi\)
\(744\) 133.687 4.90119
\(745\) −62.9936 −2.30791
\(746\) −48.4111 −1.77245
\(747\) −87.5474 −3.20319
\(748\) 1.46798 0.0536748
\(749\) −74.6609 −2.72805
\(750\) 161.033 5.88008
\(751\) −21.8060 −0.795711 −0.397855 0.917448i \(-0.630245\pi\)
−0.397855 + 0.917448i \(0.630245\pi\)
\(752\) −16.7207 −0.609741
\(753\) 81.8418 2.98248
\(754\) 37.7386 1.37436
\(755\) 46.7106 1.69997
\(756\) −256.764 −9.33842
\(757\) 30.5735 1.11121 0.555606 0.831446i \(-0.312486\pi\)
0.555606 + 0.831446i \(0.312486\pi\)
\(758\) 91.7019 3.33076
\(759\) 9.27317 0.336595
\(760\) −42.9356 −1.55744
\(761\) −14.9373 −0.541478 −0.270739 0.962653i \(-0.587268\pi\)
−0.270739 + 0.962653i \(0.587268\pi\)
\(762\) 129.817 4.70279
\(763\) −40.7727 −1.47607
\(764\) 14.9344 0.540307
\(765\) −10.0192 −0.362245
\(766\) 65.6146 2.37075
\(767\) −6.16645 −0.222658
\(768\) −104.366 −3.76597
\(769\) 27.9378 1.00746 0.503732 0.863860i \(-0.331960\pi\)
0.503732 + 0.863860i \(0.331960\pi\)
\(770\) −44.2360 −1.59416
\(771\) −16.9277 −0.609636
\(772\) −80.0464 −2.88093
\(773\) −16.1741 −0.581741 −0.290871 0.956762i \(-0.593945\pi\)
−0.290871 + 0.956762i \(0.593945\pi\)
\(774\) 17.9121 0.643838
\(775\) −80.6413 −2.89672
\(776\) −62.0685 −2.22813
\(777\) 10.3938 0.372876
\(778\) −12.6199 −0.452446
\(779\) −22.3385 −0.800361
\(780\) −148.957 −5.33351
\(781\) 5.24113 0.187542
\(782\) −2.54824 −0.0911250
\(783\) −71.5657 −2.55755
\(784\) 67.4975 2.41063
\(785\) 73.2245 2.61349
\(786\) 128.260 4.57488
\(787\) 19.8586 0.707882 0.353941 0.935268i \(-0.384841\pi\)
0.353941 + 0.935268i \(0.384841\pi\)
\(788\) 79.2828 2.82433
\(789\) −65.3459 −2.32638
\(790\) −5.07349 −0.180507
\(791\) 61.3608 2.18174
\(792\) −38.2862 −1.36044
\(793\) −17.8991 −0.635616
\(794\) −67.9982 −2.41317
\(795\) −161.930 −5.74307
\(796\) −38.9787 −1.38156
\(797\) −13.4222 −0.475440 −0.237720 0.971334i \(-0.576400\pi\)
−0.237720 + 0.971334i \(0.576400\pi\)
\(798\) −75.5291 −2.67370
\(799\) −1.22829 −0.0434537
\(800\) −14.1840 −0.501481
\(801\) 104.404 3.68895
\(802\) 70.2363 2.48013
\(803\) −13.4599 −0.474990
\(804\) −49.1527 −1.73348
\(805\) 51.7581 1.82423
\(806\) 56.4714 1.98912
\(807\) −66.0579 −2.32535
\(808\) 78.8137 2.77266
\(809\) 31.1612 1.09557 0.547785 0.836619i \(-0.315471\pi\)
0.547785 + 0.836619i \(0.315471\pi\)
\(810\) 209.331 7.35514
\(811\) 48.0622 1.68769 0.843846 0.536585i \(-0.180286\pi\)
0.843846 + 0.536585i \(0.180286\pi\)
\(812\) 99.9587 3.50786
\(813\) −59.6274 −2.09122
\(814\) 1.75720 0.0615899
\(815\) 22.7599 0.797245
\(816\) 5.48799 0.192118
\(817\) 2.07937 0.0727479
\(818\) 75.2862 2.63232
\(819\) −95.6611 −3.34267
\(820\) −173.123 −6.04571
\(821\) 15.4395 0.538843 0.269421 0.963022i \(-0.413168\pi\)
0.269421 + 0.963022i \(0.413168\pi\)
\(822\) −62.9571 −2.19588
\(823\) 23.6321 0.823763 0.411881 0.911237i \(-0.364872\pi\)
0.411881 + 0.911237i \(0.364872\pi\)
\(824\) −44.1654 −1.53857
\(825\) 32.6676 1.13734
\(826\) −24.2319 −0.843137
\(827\) 11.8501 0.412068 0.206034 0.978545i \(-0.433944\pi\)
0.206034 + 0.978545i \(0.433944\pi\)
\(828\) 86.7483 3.01471
\(829\) −28.0115 −0.972881 −0.486441 0.873714i \(-0.661705\pi\)
−0.486441 + 0.873714i \(0.661705\pi\)
\(830\) −116.854 −4.05607
\(831\) −62.8081 −2.17879
\(832\) −17.9622 −0.622727
\(833\) 4.95831 0.171795
\(834\) −80.3899 −2.78367
\(835\) −34.7575 −1.20283
\(836\) −8.60683 −0.297674
\(837\) −107.090 −3.70156
\(838\) −40.3130 −1.39259
\(839\) −2.84150 −0.0980995 −0.0490498 0.998796i \(-0.515619\pi\)
−0.0490498 + 0.998796i \(0.515619\pi\)
\(840\) −302.271 −10.4293
\(841\) −1.13937 −0.0392888
\(842\) −17.8331 −0.614568
\(843\) −15.5414 −0.535274
\(844\) 10.1781 0.350345
\(845\) 18.2072 0.626346
\(846\) 62.0352 2.13282
\(847\) −4.57915 −0.157341
\(848\) 62.7050 2.15330
\(849\) −46.4469 −1.59405
\(850\) −8.97696 −0.307907
\(851\) −2.05600 −0.0704789
\(852\) 69.3526 2.37598
\(853\) −32.9155 −1.12701 −0.563503 0.826114i \(-0.690547\pi\)
−0.563503 + 0.826114i \(0.690547\pi\)
\(854\) −70.3371 −2.40689
\(855\) 58.7429 2.00897
\(856\) −86.2503 −2.94798
\(857\) −17.0339 −0.581868 −0.290934 0.956743i \(-0.593966\pi\)
−0.290934 + 0.956743i \(0.593966\pi\)
\(858\) −22.8764 −0.780987
\(859\) −25.4739 −0.869158 −0.434579 0.900634i \(-0.643103\pi\)
−0.434579 + 0.900634i \(0.643103\pi\)
\(860\) 16.1150 0.549518
\(861\) −157.266 −5.35960
\(862\) −24.9008 −0.848126
\(863\) −7.02457 −0.239119 −0.119560 0.992827i \(-0.538148\pi\)
−0.119560 + 0.992827i \(0.538148\pi\)
\(864\) −18.8360 −0.640815
\(865\) 94.0056 3.19629
\(866\) −26.4311 −0.898166
\(867\) −53.9903 −1.83361
\(868\) 149.577 5.07696
\(869\) −0.525188 −0.0178158
\(870\) −163.149 −5.53127
\(871\) −10.7219 −0.363297
\(872\) −47.1017 −1.59507
\(873\) 84.9198 2.87410
\(874\) 14.9404 0.505368
\(875\) 93.0405 3.14534
\(876\) −178.107 −6.01767
\(877\) 54.2387 1.83151 0.915755 0.401738i \(-0.131594\pi\)
0.915755 + 0.401738i \(0.131594\pi\)
\(878\) 10.0177 0.338080
\(879\) 18.0457 0.608667
\(880\) −18.8450 −0.635266
\(881\) 55.0249 1.85384 0.926918 0.375265i \(-0.122448\pi\)
0.926918 + 0.375265i \(0.122448\pi\)
\(882\) −250.422 −8.43214
\(883\) 25.4826 0.857559 0.428779 0.903409i \(-0.358944\pi\)
0.428779 + 0.903409i \(0.358944\pi\)
\(884\) 4.23723 0.142513
\(885\) 26.6584 0.896112
\(886\) 75.9788 2.55256
\(887\) 12.7133 0.426870 0.213435 0.976957i \(-0.431535\pi\)
0.213435 + 0.976957i \(0.431535\pi\)
\(888\) 12.0072 0.402936
\(889\) 75.0052 2.51559
\(890\) 139.354 4.67117
\(891\) 21.6691 0.725944
\(892\) −26.1215 −0.874614
\(893\) 7.20150 0.240989
\(894\) −128.015 −4.28146
\(895\) 27.9530 0.934366
\(896\) −83.3081 −2.78313
\(897\) 26.7663 0.893702
\(898\) 16.6308 0.554977
\(899\) 41.6902 1.39045
\(900\) 305.597 10.1866
\(901\) 4.60626 0.153457
\(902\) −26.5877 −0.885273
\(903\) 14.6390 0.487154
\(904\) 70.8857 2.35762
\(905\) −5.86859 −0.195079
\(906\) 94.9248 3.15366
\(907\) 8.79982 0.292193 0.146097 0.989270i \(-0.453329\pi\)
0.146097 + 0.989270i \(0.453329\pi\)
\(908\) −48.4018 −1.60627
\(909\) −107.830 −3.57649
\(910\) −127.684 −4.23269
\(911\) −19.1267 −0.633697 −0.316849 0.948476i \(-0.602625\pi\)
−0.316849 + 0.948476i \(0.602625\pi\)
\(912\) −32.1763 −1.06546
\(913\) −12.0963 −0.400330
\(914\) −12.4585 −0.412091
\(915\) 77.3804 2.55812
\(916\) −15.7437 −0.520187
\(917\) 74.1052 2.44717
\(918\) −11.9212 −0.393458
\(919\) 32.4446 1.07025 0.535124 0.844774i \(-0.320265\pi\)
0.535124 + 0.844774i \(0.320265\pi\)
\(920\) 59.7923 1.97129
\(921\) −29.5631 −0.974137
\(922\) 52.3725 1.72480
\(923\) 15.1282 0.497949
\(924\) −60.5930 −1.99336
\(925\) −7.24289 −0.238145
\(926\) 57.6925 1.89589
\(927\) 60.4254 1.98463
\(928\) 7.33290 0.240714
\(929\) −52.3365 −1.71711 −0.858553 0.512725i \(-0.828636\pi\)
−0.858553 + 0.512725i \(0.828636\pi\)
\(930\) −244.134 −8.00545
\(931\) −29.0707 −0.952755
\(932\) −28.3336 −0.928096
\(933\) 51.4396 1.68406
\(934\) 39.9329 1.30665
\(935\) −1.38434 −0.0452728
\(936\) −110.510 −3.61214
\(937\) −17.0101 −0.555695 −0.277848 0.960625i \(-0.589621\pi\)
−0.277848 + 0.960625i \(0.589621\pi\)
\(938\) −42.1331 −1.37570
\(939\) 29.4492 0.961037
\(940\) 55.8113 1.82036
\(941\) 16.2164 0.528639 0.264320 0.964435i \(-0.414853\pi\)
0.264320 + 0.964435i \(0.414853\pi\)
\(942\) 148.806 4.84836
\(943\) 31.1087 1.01304
\(944\) −10.3231 −0.335987
\(945\) 242.134 7.87663
\(946\) 2.47490 0.0804659
\(947\) 28.9154 0.939624 0.469812 0.882767i \(-0.344322\pi\)
0.469812 + 0.882767i \(0.344322\pi\)
\(948\) −6.94949 −0.225709
\(949\) −38.8511 −1.26116
\(950\) 52.6322 1.70761
\(951\) 33.0509 1.07175
\(952\) 8.59840 0.278676
\(953\) 19.3700 0.627456 0.313728 0.949513i \(-0.398422\pi\)
0.313728 + 0.949513i \(0.398422\pi\)
\(954\) −232.641 −7.53203
\(955\) −14.0835 −0.455730
\(956\) −60.3501 −1.95186
\(957\) −16.8886 −0.545930
\(958\) 6.60955 0.213545
\(959\) −36.3750 −1.17461
\(960\) 77.6530 2.50624
\(961\) 31.3846 1.01241
\(962\) 5.07204 0.163529
\(963\) 118.004 3.80264
\(964\) 49.9246 1.60796
\(965\) 75.4855 2.42997
\(966\) 105.182 3.38418
\(967\) 6.75293 0.217160 0.108580 0.994088i \(-0.465370\pi\)
0.108580 + 0.994088i \(0.465370\pi\)
\(968\) −5.28996 −0.170026
\(969\) −2.36364 −0.0759311
\(970\) 113.347 3.63936
\(971\) −22.7375 −0.729683 −0.364841 0.931070i \(-0.618877\pi\)
−0.364841 + 0.931070i \(0.618877\pi\)
\(972\) 118.517 3.80143
\(973\) −46.4472 −1.48903
\(974\) 63.5775 2.03716
\(975\) 94.2926 3.01978
\(976\) −29.9644 −0.959137
\(977\) −52.3716 −1.67551 −0.837757 0.546043i \(-0.816134\pi\)
−0.837757 + 0.546043i \(0.816134\pi\)
\(978\) 46.2525 1.47899
\(979\) 14.4254 0.461039
\(980\) −225.297 −7.19685
\(981\) 64.4428 2.05750
\(982\) 51.1808 1.63324
\(983\) 34.2581 1.09266 0.546332 0.837569i \(-0.316024\pi\)
0.546332 + 0.837569i \(0.316024\pi\)
\(984\) −181.678 −5.79167
\(985\) −74.7655 −2.38223
\(986\) 4.64093 0.147797
\(987\) 50.6993 1.61378
\(988\) −24.8430 −0.790362
\(989\) −2.89574 −0.0920791
\(990\) 69.9168 2.22210
\(991\) 17.0063 0.540223 0.270112 0.962829i \(-0.412939\pi\)
0.270112 + 0.962829i \(0.412939\pi\)
\(992\) 10.9728 0.348388
\(993\) −108.252 −3.43527
\(994\) 59.4482 1.88558
\(995\) 36.7578 1.16530
\(996\) −160.063 −5.07179
\(997\) −27.2565 −0.863221 −0.431611 0.902060i \(-0.642055\pi\)
−0.431611 + 0.902060i \(0.642055\pi\)
\(998\) −61.9453 −1.96084
\(999\) −9.61839 −0.304312
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 \(a_p\))