Properties

Label 8035.2.a.e.1.10
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.54388 q^{2}\) \(+1.32249 q^{3}\) \(+4.47134 q^{4}\) \(+1.00000 q^{5}\) \(-3.36426 q^{6}\) \(+2.08615 q^{7}\) \(-6.28679 q^{8}\) \(-1.25102 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.54388 q^{2}\) \(+1.32249 q^{3}\) \(+4.47134 q^{4}\) \(+1.00000 q^{5}\) \(-3.36426 q^{6}\) \(+2.08615 q^{7}\) \(-6.28679 q^{8}\) \(-1.25102 q^{9}\) \(-2.54388 q^{10}\) \(+0.221908 q^{11}\) \(+5.91330 q^{12}\) \(+6.62780 q^{13}\) \(-5.30692 q^{14}\) \(+1.32249 q^{15}\) \(+7.05017 q^{16}\) \(+6.05401 q^{17}\) \(+3.18244 q^{18}\) \(-5.99797 q^{19}\) \(+4.47134 q^{20}\) \(+2.75891 q^{21}\) \(-0.564507 q^{22}\) \(+6.32410 q^{23}\) \(-8.31422 q^{24}\) \(+1.00000 q^{25}\) \(-16.8603 q^{26}\) \(-5.62193 q^{27}\) \(+9.32787 q^{28}\) \(-1.35243 q^{29}\) \(-3.36426 q^{30}\) \(+2.37765 q^{31}\) \(-5.36124 q^{32}\) \(+0.293471 q^{33}\) \(-15.4007 q^{34}\) \(+2.08615 q^{35}\) \(-5.59372 q^{36}\) \(+4.89059 q^{37}\) \(+15.2581 q^{38}\) \(+8.76520 q^{39}\) \(-6.28679 q^{40}\) \(+4.94423 q^{41}\) \(-7.01835 q^{42}\) \(+2.04258 q^{43}\) \(+0.992223 q^{44}\) \(-1.25102 q^{45}\) \(-16.0878 q^{46}\) \(-6.47533 q^{47}\) \(+9.32379 q^{48}\) \(-2.64798 q^{49}\) \(-2.54388 q^{50}\) \(+8.00637 q^{51}\) \(+29.6351 q^{52}\) \(+8.72719 q^{53}\) \(+14.3015 q^{54}\) \(+0.221908 q^{55}\) \(-13.1152 q^{56}\) \(-7.93225 q^{57}\) \(+3.44042 q^{58}\) \(+8.15836 q^{59}\) \(+5.91330 q^{60}\) \(-0.446960 q^{61}\) \(-6.04847 q^{62}\) \(-2.60981 q^{63}\) \(-0.461994 q^{64}\) \(+6.62780 q^{65}\) \(-0.746555 q^{66}\) \(-3.27388 q^{67}\) \(+27.0695 q^{68}\) \(+8.36357 q^{69}\) \(-5.30692 q^{70}\) \(+1.68463 q^{71}\) \(+7.86488 q^{72}\) \(-7.86727 q^{73}\) \(-12.4411 q^{74}\) \(+1.32249 q^{75}\) \(-26.8189 q^{76}\) \(+0.462932 q^{77}\) \(-22.2976 q^{78}\) \(+6.87089 q^{79}\) \(+7.05017 q^{80}\) \(-3.68190 q^{81}\) \(-12.5775 q^{82}\) \(+16.1977 q^{83}\) \(+12.3360 q^{84}\) \(+6.05401 q^{85}\) \(-5.19607 q^{86}\) \(-1.78858 q^{87}\) \(-1.39509 q^{88}\) \(-10.5008 q^{89}\) \(+3.18244 q^{90}\) \(+13.8266 q^{91}\) \(+28.2772 q^{92}\) \(+3.14443 q^{93}\) \(+16.4725 q^{94}\) \(-5.99797 q^{95}\) \(-7.09019 q^{96}\) \(+14.6847 q^{97}\) \(+6.73616 q^{98}\) \(-0.277610 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54388 −1.79880 −0.899398 0.437130i \(-0.855995\pi\)
−0.899398 + 0.437130i \(0.855995\pi\)
\(3\) 1.32249 0.763540 0.381770 0.924257i \(-0.375315\pi\)
0.381770 + 0.924257i \(0.375315\pi\)
\(4\) 4.47134 2.23567
\(5\) 1.00000 0.447214
\(6\) −3.36426 −1.37345
\(7\) 2.08615 0.788490 0.394245 0.919005i \(-0.371006\pi\)
0.394245 + 0.919005i \(0.371006\pi\)
\(8\) −6.28679 −2.22272
\(9\) −1.25102 −0.417006
\(10\) −2.54388 −0.804446
\(11\) 0.221908 0.0669076 0.0334538 0.999440i \(-0.489349\pi\)
0.0334538 + 0.999440i \(0.489349\pi\)
\(12\) 5.91330 1.70702
\(13\) 6.62780 1.83822 0.919110 0.394000i \(-0.128909\pi\)
0.919110 + 0.394000i \(0.128909\pi\)
\(14\) −5.30692 −1.41833
\(15\) 1.32249 0.341466
\(16\) 7.05017 1.76254
\(17\) 6.05401 1.46831 0.734156 0.678981i \(-0.237578\pi\)
0.734156 + 0.678981i \(0.237578\pi\)
\(18\) 3.18244 0.750109
\(19\) −5.99797 −1.37603 −0.688014 0.725698i \(-0.741517\pi\)
−0.688014 + 0.725698i \(0.741517\pi\)
\(20\) 4.47134 0.999821
\(21\) 2.75891 0.602044
\(22\) −0.564507 −0.120353
\(23\) 6.32410 1.31867 0.659333 0.751851i \(-0.270839\pi\)
0.659333 + 0.751851i \(0.270839\pi\)
\(24\) −8.31422 −1.69713
\(25\) 1.00000 0.200000
\(26\) −16.8603 −3.30658
\(27\) −5.62193 −1.08194
\(28\) 9.32787 1.76280
\(29\) −1.35243 −0.251140 −0.125570 0.992085i \(-0.540076\pi\)
−0.125570 + 0.992085i \(0.540076\pi\)
\(30\) −3.36426 −0.614227
\(31\) 2.37765 0.427039 0.213520 0.976939i \(-0.431507\pi\)
0.213520 + 0.976939i \(0.431507\pi\)
\(32\) −5.36124 −0.947742
\(33\) 0.293471 0.0510867
\(34\) −15.4007 −2.64119
\(35\) 2.08615 0.352623
\(36\) −5.59372 −0.932287
\(37\) 4.89059 0.804008 0.402004 0.915638i \(-0.368314\pi\)
0.402004 + 0.915638i \(0.368314\pi\)
\(38\) 15.2581 2.47519
\(39\) 8.76520 1.40356
\(40\) −6.28679 −0.994028
\(41\) 4.94423 0.772159 0.386079 0.922466i \(-0.373829\pi\)
0.386079 + 0.922466i \(0.373829\pi\)
\(42\) −7.01835 −1.08295
\(43\) 2.04258 0.311490 0.155745 0.987797i \(-0.450222\pi\)
0.155745 + 0.987797i \(0.450222\pi\)
\(44\) 0.992223 0.149583
\(45\) −1.25102 −0.186491
\(46\) −16.0878 −2.37201
\(47\) −6.47533 −0.944524 −0.472262 0.881458i \(-0.656562\pi\)
−0.472262 + 0.881458i \(0.656562\pi\)
\(48\) 9.32379 1.34577
\(49\) −2.64798 −0.378283
\(50\) −2.54388 −0.359759
\(51\) 8.00637 1.12112
\(52\) 29.6351 4.10965
\(53\) 8.72719 1.19877 0.599386 0.800460i \(-0.295411\pi\)
0.599386 + 0.800460i \(0.295411\pi\)
\(54\) 14.3015 1.94619
\(55\) 0.221908 0.0299220
\(56\) −13.1152 −1.75259
\(57\) −7.93225 −1.05065
\(58\) 3.44042 0.451750
\(59\) 8.15836 1.06213 0.531064 0.847332i \(-0.321792\pi\)
0.531064 + 0.847332i \(0.321792\pi\)
\(60\) 5.91330 0.763404
\(61\) −0.446960 −0.0572273 −0.0286137 0.999591i \(-0.509109\pi\)
−0.0286137 + 0.999591i \(0.509109\pi\)
\(62\) −6.04847 −0.768157
\(63\) −2.60981 −0.328805
\(64\) −0.461994 −0.0577492
\(65\) 6.62780 0.822077
\(66\) −0.746555 −0.0918946
\(67\) −3.27388 −0.399968 −0.199984 0.979799i \(-0.564089\pi\)
−0.199984 + 0.979799i \(0.564089\pi\)
\(68\) 27.0695 3.28266
\(69\) 8.36357 1.00686
\(70\) −5.30692 −0.634298
\(71\) 1.68463 0.199929 0.0999643 0.994991i \(-0.468127\pi\)
0.0999643 + 0.994991i \(0.468127\pi\)
\(72\) 7.86488 0.926885
\(73\) −7.86727 −0.920795 −0.460397 0.887713i \(-0.652293\pi\)
−0.460397 + 0.887713i \(0.652293\pi\)
\(74\) −12.4411 −1.44625
\(75\) 1.32249 0.152708
\(76\) −26.8189 −3.07634
\(77\) 0.462932 0.0527560
\(78\) −22.2976 −2.52471
\(79\) 6.87089 0.773035 0.386518 0.922282i \(-0.373678\pi\)
0.386518 + 0.922282i \(0.373678\pi\)
\(80\) 7.05017 0.788233
\(81\) −3.68190 −0.409100
\(82\) −12.5775 −1.38896
\(83\) 16.1977 1.77793 0.888963 0.457979i \(-0.151426\pi\)
0.888963 + 0.457979i \(0.151426\pi\)
\(84\) 12.3360 1.34597
\(85\) 6.05401 0.656649
\(86\) −5.19607 −0.560307
\(87\) −1.78858 −0.191756
\(88\) −1.39509 −0.148717
\(89\) −10.5008 −1.11308 −0.556540 0.830821i \(-0.687872\pi\)
−0.556540 + 0.830821i \(0.687872\pi\)
\(90\) 3.18244 0.335459
\(91\) 13.8266 1.44942
\(92\) 28.2772 2.94810
\(93\) 3.14443 0.326062
\(94\) 16.4725 1.69901
\(95\) −5.99797 −0.615378
\(96\) −7.09019 −0.723639
\(97\) 14.6847 1.49101 0.745504 0.666501i \(-0.232209\pi\)
0.745504 + 0.666501i \(0.232209\pi\)
\(98\) 6.73616 0.680455
\(99\) −0.277610 −0.0279009
\(100\) 4.47134 0.447134
\(101\) 13.3893 1.33229 0.666145 0.745822i \(-0.267943\pi\)
0.666145 + 0.745822i \(0.267943\pi\)
\(102\) −20.3673 −2.01666
\(103\) −6.67503 −0.657710 −0.328855 0.944380i \(-0.606663\pi\)
−0.328855 + 0.944380i \(0.606663\pi\)
\(104\) −41.6676 −4.08584
\(105\) 2.75891 0.269242
\(106\) −22.2010 −2.15635
\(107\) −14.1506 −1.36799 −0.683997 0.729485i \(-0.739760\pi\)
−0.683997 + 0.729485i \(0.739760\pi\)
\(108\) −25.1375 −2.41886
\(109\) −17.0881 −1.63674 −0.818371 0.574691i \(-0.805122\pi\)
−0.818371 + 0.574691i \(0.805122\pi\)
\(110\) −0.564507 −0.0538236
\(111\) 6.46776 0.613892
\(112\) 14.7077 1.38975
\(113\) −7.51791 −0.707225 −0.353613 0.935392i \(-0.615047\pi\)
−0.353613 + 0.935392i \(0.615047\pi\)
\(114\) 20.1787 1.88991
\(115\) 6.32410 0.589726
\(116\) −6.04717 −0.561466
\(117\) −8.29149 −0.766549
\(118\) −20.7539 −1.91055
\(119\) 12.6296 1.15775
\(120\) −8.31422 −0.758981
\(121\) −10.9508 −0.995523
\(122\) 1.13701 0.102940
\(123\) 6.53870 0.589575
\(124\) 10.6313 0.954718
\(125\) 1.00000 0.0894427
\(126\) 6.63905 0.591453
\(127\) −17.2947 −1.53466 −0.767328 0.641255i \(-0.778414\pi\)
−0.767328 + 0.641255i \(0.778414\pi\)
\(128\) 11.8977 1.05162
\(129\) 2.70129 0.237835
\(130\) −16.8603 −1.47875
\(131\) 8.65582 0.756262 0.378131 0.925752i \(-0.376567\pi\)
0.378131 + 0.925752i \(0.376567\pi\)
\(132\) 1.31221 0.114213
\(133\) −12.5126 −1.08498
\(134\) 8.32836 0.719461
\(135\) −5.62193 −0.483859
\(136\) −38.0602 −3.26364
\(137\) 17.8284 1.52319 0.761593 0.648055i \(-0.224417\pi\)
0.761593 + 0.648055i \(0.224417\pi\)
\(138\) −21.2759 −1.81113
\(139\) −11.2816 −0.956895 −0.478448 0.878116i \(-0.658800\pi\)
−0.478448 + 0.878116i \(0.658800\pi\)
\(140\) 9.32787 0.788349
\(141\) −8.56356 −0.721182
\(142\) −4.28550 −0.359631
\(143\) 1.47076 0.122991
\(144\) −8.81989 −0.734991
\(145\) −1.35243 −0.112313
\(146\) 20.0134 1.65632
\(147\) −3.50193 −0.288835
\(148\) 21.8675 1.79749
\(149\) −18.9699 −1.55408 −0.777039 0.629453i \(-0.783279\pi\)
−0.777039 + 0.629453i \(0.783279\pi\)
\(150\) −3.36426 −0.274691
\(151\) 4.83210 0.393230 0.196615 0.980481i \(-0.437005\pi\)
0.196615 + 0.980481i \(0.437005\pi\)
\(152\) 37.7079 3.05852
\(153\) −7.57367 −0.612295
\(154\) −1.17764 −0.0948973
\(155\) 2.37765 0.190978
\(156\) 39.1922 3.13788
\(157\) 15.0206 1.19877 0.599387 0.800460i \(-0.295411\pi\)
0.599387 + 0.800460i \(0.295411\pi\)
\(158\) −17.4787 −1.39053
\(159\) 11.5416 0.915311
\(160\) −5.36124 −0.423843
\(161\) 13.1930 1.03976
\(162\) 9.36632 0.735888
\(163\) −12.1542 −0.951987 −0.475994 0.879449i \(-0.657911\pi\)
−0.475994 + 0.879449i \(0.657911\pi\)
\(164\) 22.1073 1.72629
\(165\) 0.293471 0.0228467
\(166\) −41.2050 −3.19813
\(167\) 17.8328 1.37994 0.689970 0.723838i \(-0.257624\pi\)
0.689970 + 0.723838i \(0.257624\pi\)
\(168\) −17.3447 −1.33817
\(169\) 30.9277 2.37905
\(170\) −15.4007 −1.18118
\(171\) 7.50356 0.573812
\(172\) 9.13305 0.696388
\(173\) −13.9536 −1.06087 −0.530436 0.847725i \(-0.677972\pi\)
−0.530436 + 0.847725i \(0.677972\pi\)
\(174\) 4.54993 0.344929
\(175\) 2.08615 0.157698
\(176\) 1.56449 0.117928
\(177\) 10.7894 0.810978
\(178\) 26.7128 2.00221
\(179\) −16.6736 −1.24624 −0.623122 0.782125i \(-0.714136\pi\)
−0.623122 + 0.782125i \(0.714136\pi\)
\(180\) −5.59372 −0.416931
\(181\) 13.8655 1.03061 0.515306 0.857006i \(-0.327678\pi\)
0.515306 + 0.857006i \(0.327678\pi\)
\(182\) −35.1732 −2.60721
\(183\) −0.591100 −0.0436954
\(184\) −39.7583 −2.93102
\(185\) 4.89059 0.359563
\(186\) −7.99905 −0.586519
\(187\) 1.34343 0.0982413
\(188\) −28.9534 −2.11164
\(189\) −11.7282 −0.853100
\(190\) 15.2581 1.10694
\(191\) −5.14084 −0.371978 −0.185989 0.982552i \(-0.559549\pi\)
−0.185989 + 0.982552i \(0.559549\pi\)
\(192\) −0.610982 −0.0440939
\(193\) −5.87316 −0.422759 −0.211380 0.977404i \(-0.567796\pi\)
−0.211380 + 0.977404i \(0.567796\pi\)
\(194\) −37.3562 −2.68202
\(195\) 8.76520 0.627689
\(196\) −11.8400 −0.845716
\(197\) 23.3208 1.66154 0.830771 0.556615i \(-0.187900\pi\)
0.830771 + 0.556615i \(0.187900\pi\)
\(198\) 0.706208 0.0501880
\(199\) 23.6505 1.67654 0.838269 0.545256i \(-0.183568\pi\)
0.838269 + 0.545256i \(0.183568\pi\)
\(200\) −6.28679 −0.444543
\(201\) −4.32967 −0.305392
\(202\) −34.0609 −2.39652
\(203\) −2.82137 −0.198021
\(204\) 35.7992 2.50644
\(205\) 4.94423 0.345320
\(206\) 16.9805 1.18309
\(207\) −7.91157 −0.549892
\(208\) 46.7271 3.23994
\(209\) −1.33099 −0.0920668
\(210\) −7.01835 −0.484312
\(211\) 9.68877 0.667002 0.333501 0.942750i \(-0.391770\pi\)
0.333501 + 0.942750i \(0.391770\pi\)
\(212\) 39.0222 2.68006
\(213\) 2.22791 0.152654
\(214\) 35.9976 2.46074
\(215\) 2.04258 0.139303
\(216\) 35.3439 2.40485
\(217\) 4.96014 0.336716
\(218\) 43.4701 2.94416
\(219\) −10.4044 −0.703064
\(220\) 0.992223 0.0668957
\(221\) 40.1247 2.69908
\(222\) −16.4532 −1.10427
\(223\) −12.0672 −0.808081 −0.404040 0.914741i \(-0.632394\pi\)
−0.404040 + 0.914741i \(0.632394\pi\)
\(224\) −11.1843 −0.747285
\(225\) −1.25102 −0.0834012
\(226\) 19.1247 1.27215
\(227\) −23.5017 −1.55986 −0.779931 0.625866i \(-0.784746\pi\)
−0.779931 + 0.625866i \(0.784746\pi\)
\(228\) −35.4678 −2.34891
\(229\) −11.8415 −0.782510 −0.391255 0.920282i \(-0.627959\pi\)
−0.391255 + 0.920282i \(0.627959\pi\)
\(230\) −16.0878 −1.06080
\(231\) 0.612224 0.0402814
\(232\) 8.50244 0.558213
\(233\) −6.14611 −0.402645 −0.201323 0.979525i \(-0.564524\pi\)
−0.201323 + 0.979525i \(0.564524\pi\)
\(234\) 21.0926 1.37887
\(235\) −6.47533 −0.422404
\(236\) 36.4788 2.37457
\(237\) 9.08669 0.590244
\(238\) −32.1281 −2.08256
\(239\) 1.35031 0.0873443 0.0436722 0.999046i \(-0.486094\pi\)
0.0436722 + 0.999046i \(0.486094\pi\)
\(240\) 9.32379 0.601848
\(241\) 11.1840 0.720424 0.360212 0.932871i \(-0.382704\pi\)
0.360212 + 0.932871i \(0.382704\pi\)
\(242\) 27.8574 1.79074
\(243\) 11.9965 0.769577
\(244\) −1.99851 −0.127941
\(245\) −2.64798 −0.169173
\(246\) −16.6337 −1.06052
\(247\) −39.7533 −2.52944
\(248\) −14.9478 −0.949187
\(249\) 21.4213 1.35752
\(250\) −2.54388 −0.160889
\(251\) 10.3920 0.655935 0.327967 0.944689i \(-0.393636\pi\)
0.327967 + 0.944689i \(0.393636\pi\)
\(252\) −11.6693 −0.735099
\(253\) 1.40337 0.0882289
\(254\) 43.9956 2.76053
\(255\) 8.00637 0.501378
\(256\) −29.3424 −1.83390
\(257\) 21.2233 1.32387 0.661937 0.749559i \(-0.269735\pi\)
0.661937 + 0.749559i \(0.269735\pi\)
\(258\) −6.87176 −0.427817
\(259\) 10.2025 0.633952
\(260\) 29.6351 1.83789
\(261\) 1.69192 0.104727
\(262\) −22.0194 −1.36036
\(263\) −8.13847 −0.501840 −0.250920 0.968008i \(-0.580733\pi\)
−0.250920 + 0.968008i \(0.580733\pi\)
\(264\) −1.84499 −0.113551
\(265\) 8.72719 0.536107
\(266\) 31.8307 1.95167
\(267\) −13.8872 −0.849882
\(268\) −14.6386 −0.894196
\(269\) 23.3291 1.42240 0.711201 0.702989i \(-0.248152\pi\)
0.711201 + 0.702989i \(0.248152\pi\)
\(270\) 14.3015 0.870364
\(271\) 2.08322 0.126547 0.0632734 0.997996i \(-0.479846\pi\)
0.0632734 + 0.997996i \(0.479846\pi\)
\(272\) 42.6818 2.58796
\(273\) 18.2855 1.10669
\(274\) −45.3535 −2.73990
\(275\) 0.221908 0.0133815
\(276\) 37.3963 2.25099
\(277\) −9.38720 −0.564022 −0.282011 0.959411i \(-0.591002\pi\)
−0.282011 + 0.959411i \(0.591002\pi\)
\(278\) 28.6991 1.72126
\(279\) −2.97449 −0.178078
\(280\) −13.1152 −0.783782
\(281\) 17.3632 1.03580 0.517902 0.855440i \(-0.326713\pi\)
0.517902 + 0.855440i \(0.326713\pi\)
\(282\) 21.7847 1.29726
\(283\) 21.6699 1.28814 0.644071 0.764966i \(-0.277244\pi\)
0.644071 + 0.764966i \(0.277244\pi\)
\(284\) 7.53254 0.446974
\(285\) −7.93225 −0.469866
\(286\) −3.74144 −0.221236
\(287\) 10.3144 0.608840
\(288\) 6.70700 0.395214
\(289\) 19.6510 1.15594
\(290\) 3.44042 0.202029
\(291\) 19.4204 1.13845
\(292\) −35.1772 −2.05859
\(293\) 19.5291 1.14090 0.570450 0.821332i \(-0.306769\pi\)
0.570450 + 0.821332i \(0.306769\pi\)
\(294\) 8.90851 0.519555
\(295\) 8.15836 0.474998
\(296\) −30.7461 −1.78708
\(297\) −1.24755 −0.0723902
\(298\) 48.2573 2.79547
\(299\) 41.9149 2.42400
\(300\) 5.91330 0.341405
\(301\) 4.26112 0.245607
\(302\) −12.2923 −0.707341
\(303\) 17.7073 1.01726
\(304\) −42.2867 −2.42531
\(305\) −0.446960 −0.0255928
\(306\) 19.2665 1.10139
\(307\) −23.0121 −1.31337 −0.656684 0.754166i \(-0.728042\pi\)
−0.656684 + 0.754166i \(0.728042\pi\)
\(308\) 2.06993 0.117945
\(309\) −8.82766 −0.502188
\(310\) −6.04847 −0.343530
\(311\) −11.9586 −0.678112 −0.339056 0.940766i \(-0.610108\pi\)
−0.339056 + 0.940766i \(0.610108\pi\)
\(312\) −55.1050 −3.11970
\(313\) −23.4843 −1.32741 −0.663704 0.747995i \(-0.731017\pi\)
−0.663704 + 0.747995i \(0.731017\pi\)
\(314\) −38.2106 −2.15635
\(315\) −2.60981 −0.147046
\(316\) 30.7221 1.72825
\(317\) 19.6593 1.10417 0.552087 0.833787i \(-0.313832\pi\)
0.552087 + 0.833787i \(0.313832\pi\)
\(318\) −29.3606 −1.64646
\(319\) −0.300115 −0.0168032
\(320\) −0.461994 −0.0258262
\(321\) −18.7141 −1.04452
\(322\) −33.5615 −1.87031
\(323\) −36.3117 −2.02044
\(324\) −16.4630 −0.914612
\(325\) 6.62780 0.367644
\(326\) 30.9188 1.71243
\(327\) −22.5988 −1.24972
\(328\) −31.0833 −1.71629
\(329\) −13.5085 −0.744748
\(330\) −0.746555 −0.0410965
\(331\) −16.4886 −0.906294 −0.453147 0.891436i \(-0.649699\pi\)
−0.453147 + 0.891436i \(0.649699\pi\)
\(332\) 72.4253 3.97485
\(333\) −6.11821 −0.335276
\(334\) −45.3644 −2.48223
\(335\) −3.27388 −0.178871
\(336\) 19.4508 1.06113
\(337\) −9.93274 −0.541071 −0.270536 0.962710i \(-0.587201\pi\)
−0.270536 + 0.962710i \(0.587201\pi\)
\(338\) −78.6764 −4.27943
\(339\) −9.94236 −0.539995
\(340\) 27.0695 1.46805
\(341\) 0.527619 0.0285722
\(342\) −19.0882 −1.03217
\(343\) −20.1271 −1.08676
\(344\) −12.8412 −0.692354
\(345\) 8.36357 0.450279
\(346\) 35.4963 1.90829
\(347\) −14.9882 −0.804608 −0.402304 0.915506i \(-0.631790\pi\)
−0.402304 + 0.915506i \(0.631790\pi\)
\(348\) −7.99733 −0.428702
\(349\) −30.1832 −1.61567 −0.807836 0.589408i \(-0.799361\pi\)
−0.807836 + 0.589408i \(0.799361\pi\)
\(350\) −5.30692 −0.283667
\(351\) −37.2610 −1.98885
\(352\) −1.18970 −0.0634112
\(353\) 2.33863 0.124473 0.0622364 0.998061i \(-0.480177\pi\)
0.0622364 + 0.998061i \(0.480177\pi\)
\(354\) −27.4469 −1.45878
\(355\) 1.68463 0.0894108
\(356\) −46.9525 −2.48848
\(357\) 16.7025 0.883989
\(358\) 42.4157 2.24174
\(359\) −1.13090 −0.0596864 −0.0298432 0.999555i \(-0.509501\pi\)
−0.0298432 + 0.999555i \(0.509501\pi\)
\(360\) 7.86488 0.414516
\(361\) 16.9756 0.893452
\(362\) −35.2721 −1.85386
\(363\) −14.4823 −0.760122
\(364\) 61.8233 3.24042
\(365\) −7.86727 −0.411792
\(366\) 1.50369 0.0785991
\(367\) 9.67636 0.505102 0.252551 0.967584i \(-0.418730\pi\)
0.252551 + 0.967584i \(0.418730\pi\)
\(368\) 44.5860 2.32421
\(369\) −6.18532 −0.321995
\(370\) −12.4411 −0.646781
\(371\) 18.2062 0.945220
\(372\) 14.0598 0.728966
\(373\) −12.7644 −0.660917 −0.330458 0.943821i \(-0.607203\pi\)
−0.330458 + 0.943821i \(0.607203\pi\)
\(374\) −3.41753 −0.176716
\(375\) 1.32249 0.0682931
\(376\) 40.7090 2.09941
\(377\) −8.96364 −0.461651
\(378\) 29.8351 1.53455
\(379\) −16.0201 −0.822898 −0.411449 0.911433i \(-0.634977\pi\)
−0.411449 + 0.911433i \(0.634977\pi\)
\(380\) −26.8189 −1.37578
\(381\) −22.8721 −1.17177
\(382\) 13.0777 0.669113
\(383\) −9.79174 −0.500335 −0.250167 0.968203i \(-0.580486\pi\)
−0.250167 + 0.968203i \(0.580486\pi\)
\(384\) 15.7346 0.802955
\(385\) 0.462932 0.0235932
\(386\) 14.9406 0.760458
\(387\) −2.55530 −0.129893
\(388\) 65.6604 3.33340
\(389\) −14.4035 −0.730287 −0.365144 0.930951i \(-0.618980\pi\)
−0.365144 + 0.930951i \(0.618980\pi\)
\(390\) −22.2976 −1.12908
\(391\) 38.2862 1.93621
\(392\) 16.6473 0.840816
\(393\) 11.4472 0.577437
\(394\) −59.3255 −2.98877
\(395\) 6.87089 0.345712
\(396\) −1.24129 −0.0623771
\(397\) 25.4763 1.27862 0.639310 0.768949i \(-0.279220\pi\)
0.639310 + 0.768949i \(0.279220\pi\)
\(398\) −60.1641 −3.01575
\(399\) −16.5479 −0.828429
\(400\) 7.05017 0.352509
\(401\) 18.7393 0.935795 0.467897 0.883783i \(-0.345012\pi\)
0.467897 + 0.883783i \(0.345012\pi\)
\(402\) 11.0142 0.549337
\(403\) 15.7586 0.784992
\(404\) 59.8683 2.97856
\(405\) −3.68190 −0.182955
\(406\) 7.17724 0.356200
\(407\) 1.08526 0.0537943
\(408\) −50.3343 −2.49192
\(409\) 34.6318 1.71243 0.856217 0.516616i \(-0.172808\pi\)
0.856217 + 0.516616i \(0.172808\pi\)
\(410\) −12.5775 −0.621160
\(411\) 23.5780 1.16301
\(412\) −29.8463 −1.47042
\(413\) 17.0196 0.837477
\(414\) 20.1261 0.989143
\(415\) 16.1977 0.795113
\(416\) −35.5332 −1.74216
\(417\) −14.9199 −0.730628
\(418\) 3.38589 0.165609
\(419\) 26.2544 1.28261 0.641306 0.767285i \(-0.278393\pi\)
0.641306 + 0.767285i \(0.278393\pi\)
\(420\) 12.3360 0.601936
\(421\) −3.03988 −0.148155 −0.0740773 0.997253i \(-0.523601\pi\)
−0.0740773 + 0.997253i \(0.523601\pi\)
\(422\) −24.6471 −1.19980
\(423\) 8.10075 0.393872
\(424\) −54.8660 −2.66453
\(425\) 6.05401 0.293662
\(426\) −5.66753 −0.274593
\(427\) −0.932425 −0.0451232
\(428\) −63.2723 −3.05838
\(429\) 1.94506 0.0939086
\(430\) −5.19607 −0.250577
\(431\) −7.38388 −0.355669 −0.177835 0.984060i \(-0.556909\pi\)
−0.177835 + 0.984060i \(0.556909\pi\)
\(432\) −39.6356 −1.90697
\(433\) 19.7002 0.946733 0.473367 0.880866i \(-0.343039\pi\)
0.473367 + 0.880866i \(0.343039\pi\)
\(434\) −12.6180 −0.605684
\(435\) −1.78858 −0.0857557
\(436\) −76.4065 −3.65921
\(437\) −37.9318 −1.81452
\(438\) 26.4676 1.26467
\(439\) −3.45150 −0.164731 −0.0823655 0.996602i \(-0.526248\pi\)
−0.0823655 + 0.996602i \(0.526248\pi\)
\(440\) −1.39509 −0.0665081
\(441\) 3.31268 0.157746
\(442\) −102.073 −4.85510
\(443\) −7.00964 −0.333038 −0.166519 0.986038i \(-0.553253\pi\)
−0.166519 + 0.986038i \(0.553253\pi\)
\(444\) 28.9195 1.37246
\(445\) −10.5008 −0.497785
\(446\) 30.6976 1.45357
\(447\) −25.0876 −1.18660
\(448\) −0.963788 −0.0455347
\(449\) −29.1690 −1.37657 −0.688285 0.725441i \(-0.741636\pi\)
−0.688285 + 0.725441i \(0.741636\pi\)
\(450\) 3.18244 0.150022
\(451\) 1.09716 0.0516633
\(452\) −33.6151 −1.58112
\(453\) 6.39040 0.300247
\(454\) 59.7855 2.80587
\(455\) 13.8266 0.648200
\(456\) 49.8684 2.33530
\(457\) −23.0305 −1.07732 −0.538660 0.842523i \(-0.681069\pi\)
−0.538660 + 0.842523i \(0.681069\pi\)
\(458\) 30.1234 1.40758
\(459\) −34.0352 −1.58863
\(460\) 28.2772 1.31843
\(461\) −34.7680 −1.61931 −0.809654 0.586907i \(-0.800345\pi\)
−0.809654 + 0.586907i \(0.800345\pi\)
\(462\) −1.55742 −0.0724579
\(463\) −4.91327 −0.228339 −0.114169 0.993461i \(-0.536421\pi\)
−0.114169 + 0.993461i \(0.536421\pi\)
\(464\) −9.53487 −0.442645
\(465\) 3.14443 0.145819
\(466\) 15.6350 0.724277
\(467\) −24.8579 −1.15029 −0.575144 0.818052i \(-0.695054\pi\)
−0.575144 + 0.818052i \(0.695054\pi\)
\(468\) −37.0741 −1.71375
\(469\) −6.82980 −0.315371
\(470\) 16.4725 0.759818
\(471\) 19.8646 0.915312
\(472\) −51.2899 −2.36081
\(473\) 0.453263 0.0208411
\(474\) −23.1155 −1.06173
\(475\) −5.99797 −0.275206
\(476\) 56.4710 2.58834
\(477\) −10.9179 −0.499895
\(478\) −3.43503 −0.157115
\(479\) −20.1007 −0.918423 −0.459211 0.888327i \(-0.651868\pi\)
−0.459211 + 0.888327i \(0.651868\pi\)
\(480\) −7.09019 −0.323621
\(481\) 32.4138 1.47794
\(482\) −28.4507 −1.29590
\(483\) 17.4476 0.793895
\(484\) −48.9645 −2.22566
\(485\) 14.6847 0.666799
\(486\) −30.5177 −1.38431
\(487\) −29.3671 −1.33075 −0.665376 0.746509i \(-0.731729\pi\)
−0.665376 + 0.746509i \(0.731729\pi\)
\(488\) 2.80994 0.127200
\(489\) −16.0738 −0.726881
\(490\) 6.73616 0.304309
\(491\) 8.53562 0.385207 0.192603 0.981277i \(-0.438307\pi\)
0.192603 + 0.981277i \(0.438307\pi\)
\(492\) 29.2367 1.31809
\(493\) −8.18762 −0.368752
\(494\) 101.128 4.54995
\(495\) −0.277610 −0.0124777
\(496\) 16.7629 0.752675
\(497\) 3.51439 0.157642
\(498\) −54.4932 −2.44190
\(499\) −39.5805 −1.77186 −0.885932 0.463814i \(-0.846480\pi\)
−0.885932 + 0.463814i \(0.846480\pi\)
\(500\) 4.47134 0.199964
\(501\) 23.5837 1.05364
\(502\) −26.4359 −1.17989
\(503\) 37.0500 1.65198 0.825989 0.563686i \(-0.190617\pi\)
0.825989 + 0.563686i \(0.190617\pi\)
\(504\) 16.4073 0.730840
\(505\) 13.3893 0.595818
\(506\) −3.57000 −0.158706
\(507\) 40.9016 1.81650
\(508\) −77.3304 −3.43098
\(509\) −23.8825 −1.05857 −0.529286 0.848443i \(-0.677540\pi\)
−0.529286 + 0.848443i \(0.677540\pi\)
\(510\) −20.3673 −0.901877
\(511\) −16.4123 −0.726037
\(512\) 50.8482 2.24720
\(513\) 33.7202 1.48878
\(514\) −53.9896 −2.38138
\(515\) −6.67503 −0.294137
\(516\) 12.0784 0.531721
\(517\) −1.43692 −0.0631959
\(518\) −25.9539 −1.14035
\(519\) −18.4535 −0.810019
\(520\) −41.6676 −1.82724
\(521\) 3.96853 0.173865 0.0869323 0.996214i \(-0.472294\pi\)
0.0869323 + 0.996214i \(0.472294\pi\)
\(522\) −4.30403 −0.188382
\(523\) 16.2371 0.709997 0.354999 0.934867i \(-0.384481\pi\)
0.354999 + 0.934867i \(0.384481\pi\)
\(524\) 38.7031 1.69075
\(525\) 2.75891 0.120409
\(526\) 20.7033 0.902707
\(527\) 14.3943 0.627027
\(528\) 2.06902 0.0900425
\(529\) 16.9943 0.738882
\(530\) −22.2010 −0.964348
\(531\) −10.2063 −0.442914
\(532\) −55.9483 −2.42566
\(533\) 32.7694 1.41940
\(534\) 35.3274 1.52876
\(535\) −14.1506 −0.611786
\(536\) 20.5822 0.889015
\(537\) −22.0507 −0.951558
\(538\) −59.3466 −2.55861
\(539\) −0.587608 −0.0253101
\(540\) −25.1375 −1.08175
\(541\) 14.8097 0.636721 0.318360 0.947970i \(-0.396868\pi\)
0.318360 + 0.947970i \(0.396868\pi\)
\(542\) −5.29947 −0.227632
\(543\) 18.3370 0.786915
\(544\) −32.4570 −1.39158
\(545\) −17.0881 −0.731973
\(546\) −46.5162 −1.99071
\(547\) 32.6885 1.39766 0.698831 0.715287i \(-0.253704\pi\)
0.698831 + 0.715287i \(0.253704\pi\)
\(548\) 79.7170 3.40534
\(549\) 0.559155 0.0238641
\(550\) −0.564507 −0.0240706
\(551\) 8.11183 0.345576
\(552\) −52.5800 −2.23795
\(553\) 14.3337 0.609531
\(554\) 23.8799 1.01456
\(555\) 6.46776 0.274541
\(556\) −50.4440 −2.13930
\(557\) 8.81007 0.373295 0.186647 0.982427i \(-0.440238\pi\)
0.186647 + 0.982427i \(0.440238\pi\)
\(558\) 7.56675 0.320326
\(559\) 13.5378 0.572587
\(560\) 14.7077 0.621514
\(561\) 1.77667 0.0750112
\(562\) −44.1701 −1.86320
\(563\) 42.6698 1.79832 0.899158 0.437624i \(-0.144180\pi\)
0.899158 + 0.437624i \(0.144180\pi\)
\(564\) −38.2906 −1.61232
\(565\) −7.51791 −0.316281
\(566\) −55.1257 −2.31710
\(567\) −7.68099 −0.322571
\(568\) −10.5909 −0.444384
\(569\) 7.93659 0.332719 0.166360 0.986065i \(-0.446799\pi\)
0.166360 + 0.986065i \(0.446799\pi\)
\(570\) 20.1787 0.845194
\(571\) −12.8989 −0.539800 −0.269900 0.962888i \(-0.586991\pi\)
−0.269900 + 0.962888i \(0.586991\pi\)
\(572\) 6.57626 0.274967
\(573\) −6.79871 −0.284020
\(574\) −26.2386 −1.09518
\(575\) 6.32410 0.263733
\(576\) 0.577962 0.0240818
\(577\) −7.28590 −0.303316 −0.151658 0.988433i \(-0.548461\pi\)
−0.151658 + 0.988433i \(0.548461\pi\)
\(578\) −49.9898 −2.07930
\(579\) −7.76720 −0.322794
\(580\) −6.04717 −0.251095
\(581\) 33.7908 1.40188
\(582\) −49.4033 −2.04783
\(583\) 1.93663 0.0802070
\(584\) 49.4599 2.04666
\(585\) −8.29149 −0.342811
\(586\) −49.6796 −2.05225
\(587\) 36.4444 1.50422 0.752110 0.659038i \(-0.229036\pi\)
0.752110 + 0.659038i \(0.229036\pi\)
\(588\) −15.6583 −0.645738
\(589\) −14.2611 −0.587618
\(590\) −20.7539 −0.854425
\(591\) 30.8416 1.26865
\(592\) 34.4795 1.41710
\(593\) −26.4906 −1.08784 −0.543920 0.839137i \(-0.683060\pi\)
−0.543920 + 0.839137i \(0.683060\pi\)
\(594\) 3.17362 0.130215
\(595\) 12.6296 0.517761
\(596\) −84.8209 −3.47440
\(597\) 31.2776 1.28011
\(598\) −106.627 −4.36028
\(599\) 34.8900 1.42557 0.712783 0.701385i \(-0.247435\pi\)
0.712783 + 0.701385i \(0.247435\pi\)
\(600\) −8.31422 −0.339427
\(601\) 21.2304 0.866007 0.433004 0.901392i \(-0.357454\pi\)
0.433004 + 0.901392i \(0.357454\pi\)
\(602\) −10.8398 −0.441797
\(603\) 4.09568 0.166789
\(604\) 21.6059 0.879133
\(605\) −10.9508 −0.445212
\(606\) −45.0453 −1.82984
\(607\) 3.03143 0.123042 0.0615209 0.998106i \(-0.480405\pi\)
0.0615209 + 0.998106i \(0.480405\pi\)
\(608\) 32.1565 1.30412
\(609\) −3.73124 −0.151197
\(610\) 1.13701 0.0460363
\(611\) −42.9172 −1.73624
\(612\) −33.8644 −1.36889
\(613\) 23.8629 0.963812 0.481906 0.876223i \(-0.339945\pi\)
0.481906 + 0.876223i \(0.339945\pi\)
\(614\) 58.5400 2.36248
\(615\) 6.53870 0.263666
\(616\) −2.91036 −0.117262
\(617\) −30.9732 −1.24693 −0.623467 0.781850i \(-0.714276\pi\)
−0.623467 + 0.781850i \(0.714276\pi\)
\(618\) 22.4565 0.903334
\(619\) 14.1381 0.568258 0.284129 0.958786i \(-0.408296\pi\)
0.284129 + 0.958786i \(0.408296\pi\)
\(620\) 10.6313 0.426963
\(621\) −35.5537 −1.42672
\(622\) 30.4214 1.21979
\(623\) −21.9062 −0.877653
\(624\) 61.7962 2.47383
\(625\) 1.00000 0.0400000
\(626\) 59.7412 2.38774
\(627\) −1.76023 −0.0702967
\(628\) 67.1621 2.68006
\(629\) 29.6076 1.18053
\(630\) 6.63905 0.264506
\(631\) −23.4726 −0.934431 −0.467215 0.884144i \(-0.654743\pi\)
−0.467215 + 0.884144i \(0.654743\pi\)
\(632\) −43.1958 −1.71824
\(633\) 12.8133 0.509283
\(634\) −50.0108 −1.98618
\(635\) −17.2947 −0.686319
\(636\) 51.6065 2.04633
\(637\) −17.5503 −0.695368
\(638\) 0.763456 0.0302255
\(639\) −2.10750 −0.0833714
\(640\) 11.8977 0.470299
\(641\) 0.0459485 0.00181486 0.000907428 1.00000i \(-0.499711\pi\)
0.000907428 1.00000i \(0.499711\pi\)
\(642\) 47.6065 1.87888
\(643\) −26.2476 −1.03510 −0.517552 0.855652i \(-0.673156\pi\)
−0.517552 + 0.855652i \(0.673156\pi\)
\(644\) 58.9904 2.32455
\(645\) 2.70129 0.106363
\(646\) 92.3727 3.63436
\(647\) −23.1078 −0.908462 −0.454231 0.890884i \(-0.650086\pi\)
−0.454231 + 0.890884i \(0.650086\pi\)
\(648\) 23.1473 0.909313
\(649\) 1.81040 0.0710645
\(650\) −16.8603 −0.661317
\(651\) 6.55974 0.257096
\(652\) −54.3453 −2.12833
\(653\) 26.6619 1.04336 0.521681 0.853141i \(-0.325305\pi\)
0.521681 + 0.853141i \(0.325305\pi\)
\(654\) 57.4888 2.24799
\(655\) 8.65582 0.338211
\(656\) 34.8577 1.36096
\(657\) 9.84210 0.383977
\(658\) 34.3640 1.33965
\(659\) 30.8921 1.20339 0.601693 0.798727i \(-0.294493\pi\)
0.601693 + 0.798727i \(0.294493\pi\)
\(660\) 1.31221 0.0510776
\(661\) −46.3873 −1.80426 −0.902128 0.431469i \(-0.857995\pi\)
−0.902128 + 0.431469i \(0.857995\pi\)
\(662\) 41.9450 1.63024
\(663\) 53.0646 2.06086
\(664\) −101.831 −3.95182
\(665\) −12.5126 −0.485220
\(666\) 15.5640 0.603093
\(667\) −8.55291 −0.331170
\(668\) 79.7363 3.08509
\(669\) −15.9588 −0.617002
\(670\) 8.32836 0.321753
\(671\) −0.0991838 −0.00382895
\(672\) −14.7912 −0.570582
\(673\) 38.4953 1.48388 0.741942 0.670465i \(-0.233905\pi\)
0.741942 + 0.670465i \(0.233905\pi\)
\(674\) 25.2677 0.973277
\(675\) −5.62193 −0.216388
\(676\) 138.288 5.31878
\(677\) −41.2878 −1.58682 −0.793410 0.608688i \(-0.791696\pi\)
−0.793410 + 0.608688i \(0.791696\pi\)
\(678\) 25.2922 0.971341
\(679\) 30.6345 1.17565
\(680\) −38.0602 −1.45954
\(681\) −31.0808 −1.19102
\(682\) −1.34220 −0.0513956
\(683\) −20.6255 −0.789213 −0.394607 0.918850i \(-0.629119\pi\)
−0.394607 + 0.918850i \(0.629119\pi\)
\(684\) 33.5509 1.28285
\(685\) 17.8284 0.681190
\(686\) 51.2010 1.95486
\(687\) −15.6603 −0.597478
\(688\) 14.4005 0.549015
\(689\) 57.8421 2.20361
\(690\) −21.2759 −0.809961
\(691\) 27.3094 1.03890 0.519450 0.854501i \(-0.326137\pi\)
0.519450 + 0.854501i \(0.326137\pi\)
\(692\) −62.3912 −2.37176
\(693\) −0.579136 −0.0219996
\(694\) 38.1282 1.44733
\(695\) −11.2816 −0.427937
\(696\) 11.2444 0.426218
\(697\) 29.9324 1.13377
\(698\) 76.7826 2.90626
\(699\) −8.12818 −0.307436
\(700\) 9.32787 0.352560
\(701\) −4.22255 −0.159484 −0.0797418 0.996816i \(-0.525410\pi\)
−0.0797418 + 0.996816i \(0.525410\pi\)
\(702\) 94.7877 3.57753
\(703\) −29.3336 −1.10634
\(704\) −0.102520 −0.00386386
\(705\) −8.56356 −0.322522
\(706\) −5.94920 −0.223901
\(707\) 27.9322 1.05050
\(708\) 48.2428 1.81308
\(709\) −6.71714 −0.252268 −0.126134 0.992013i \(-0.540257\pi\)
−0.126134 + 0.992013i \(0.540257\pi\)
\(710\) −4.28550 −0.160832
\(711\) −8.59561 −0.322360
\(712\) 66.0162 2.47406
\(713\) 15.0365 0.563122
\(714\) −42.4891 −1.59012
\(715\) 1.47076 0.0550033
\(716\) −74.5533 −2.78619
\(717\) 1.78577 0.0666909
\(718\) 2.87687 0.107364
\(719\) −34.9263 −1.30253 −0.651266 0.758850i \(-0.725762\pi\)
−0.651266 + 0.758850i \(0.725762\pi\)
\(720\) −8.81989 −0.328698
\(721\) −13.9251 −0.518598
\(722\) −43.1839 −1.60714
\(723\) 14.7907 0.550073
\(724\) 61.9972 2.30411
\(725\) −1.35243 −0.0502280
\(726\) 36.8412 1.36731
\(727\) 17.5334 0.650279 0.325140 0.945666i \(-0.394589\pi\)
0.325140 + 0.945666i \(0.394589\pi\)
\(728\) −86.9247 −3.22164
\(729\) 26.9110 0.996703
\(730\) 20.0134 0.740730
\(731\) 12.3658 0.457365
\(732\) −2.64301 −0.0976884
\(733\) 13.5415 0.500166 0.250083 0.968224i \(-0.419542\pi\)
0.250083 + 0.968224i \(0.419542\pi\)
\(734\) −24.6155 −0.908575
\(735\) −3.50193 −0.129171
\(736\) −33.9050 −1.24976
\(737\) −0.726498 −0.0267609
\(738\) 15.7347 0.579203
\(739\) −13.3757 −0.492032 −0.246016 0.969266i \(-0.579122\pi\)
−0.246016 + 0.969266i \(0.579122\pi\)
\(740\) 21.8675 0.803864
\(741\) −52.5734 −1.93133
\(742\) −46.3145 −1.70026
\(743\) −38.9047 −1.42728 −0.713638 0.700515i \(-0.752954\pi\)
−0.713638 + 0.700515i \(0.752954\pi\)
\(744\) −19.7683 −0.724742
\(745\) −18.9699 −0.695004
\(746\) 32.4712 1.18885
\(747\) −20.2636 −0.741406
\(748\) 6.00693 0.219635
\(749\) −29.5203 −1.07865
\(750\) −3.36426 −0.122845
\(751\) −32.6820 −1.19258 −0.596291 0.802768i \(-0.703360\pi\)
−0.596291 + 0.802768i \(0.703360\pi\)
\(752\) −45.6522 −1.66476
\(753\) 13.7433 0.500833
\(754\) 22.8024 0.830416
\(755\) 4.83210 0.175858
\(756\) −52.4407 −1.90725
\(757\) 0.666792 0.0242350 0.0121175 0.999927i \(-0.496143\pi\)
0.0121175 + 0.999927i \(0.496143\pi\)
\(758\) 40.7533 1.48023
\(759\) 1.85594 0.0673663
\(760\) 37.7079 1.36781
\(761\) 26.0070 0.942754 0.471377 0.881932i \(-0.343757\pi\)
0.471377 + 0.881932i \(0.343757\pi\)
\(762\) 58.1838 2.10778
\(763\) −35.6483 −1.29055
\(764\) −22.9864 −0.831620
\(765\) −7.57367 −0.273827
\(766\) 24.9090 0.900000
\(767\) 54.0720 1.95243
\(768\) −38.8051 −1.40026
\(769\) 27.8025 1.00259 0.501293 0.865278i \(-0.332858\pi\)
0.501293 + 0.865278i \(0.332858\pi\)
\(770\) −1.17764 −0.0424394
\(771\) 28.0676 1.01083
\(772\) −26.2609 −0.945149
\(773\) −18.3278 −0.659204 −0.329602 0.944120i \(-0.606915\pi\)
−0.329602 + 0.944120i \(0.606915\pi\)
\(774\) 6.50038 0.233651
\(775\) 2.37765 0.0854079
\(776\) −92.3198 −3.31409
\(777\) 13.4927 0.484048
\(778\) 36.6408 1.31364
\(779\) −29.6553 −1.06251
\(780\) 39.1922 1.40330
\(781\) 0.373832 0.0133768
\(782\) −97.3955 −3.48285
\(783\) 7.60327 0.271719
\(784\) −18.6687 −0.666741
\(785\) 15.0206 0.536108
\(786\) −29.1204 −1.03869
\(787\) 1.87212 0.0667340 0.0333670 0.999443i \(-0.489377\pi\)
0.0333670 + 0.999443i \(0.489377\pi\)
\(788\) 104.275 3.71465
\(789\) −10.7631 −0.383175
\(790\) −17.4787 −0.621865
\(791\) −15.6835 −0.557640
\(792\) 1.74528 0.0620157
\(793\) −2.96236 −0.105196
\(794\) −64.8087 −2.29998
\(795\) 11.5416 0.409340
\(796\) 105.749 3.74818
\(797\) 12.0415 0.426531 0.213265 0.976994i \(-0.431590\pi\)
0.213265 + 0.976994i \(0.431590\pi\)
\(798\) 42.0958 1.49018
\(799\) −39.2017 −1.38686
\(800\) −5.36124 −0.189548
\(801\) 13.1367 0.464161
\(802\) −47.6705 −1.68330
\(803\) −1.74581 −0.0616082
\(804\) −19.3594 −0.682755
\(805\) 13.1930 0.464993
\(806\) −40.0881 −1.41204
\(807\) 30.8526 1.08606
\(808\) −84.1760 −2.96130
\(809\) −10.0810 −0.354429 −0.177215 0.984172i \(-0.556709\pi\)
−0.177215 + 0.984172i \(0.556709\pi\)
\(810\) 9.36632 0.329099
\(811\) 39.9468 1.40272 0.701361 0.712806i \(-0.252576\pi\)
0.701361 + 0.712806i \(0.252576\pi\)
\(812\) −12.6153 −0.442710
\(813\) 2.75504 0.0966236
\(814\) −2.76077 −0.0967649
\(815\) −12.1542 −0.425742
\(816\) 56.4463 1.97602
\(817\) −12.2513 −0.428619
\(818\) −88.0993 −3.08032
\(819\) −17.2973 −0.604416
\(820\) 22.1073 0.772021
\(821\) 44.2350 1.54381 0.771907 0.635736i \(-0.219303\pi\)
0.771907 + 0.635736i \(0.219303\pi\)
\(822\) −59.9795 −2.09203
\(823\) 33.3225 1.16155 0.580774 0.814065i \(-0.302750\pi\)
0.580774 + 0.814065i \(0.302750\pi\)
\(824\) 41.9645 1.46190
\(825\) 0.293471 0.0102173
\(826\) −43.2957 −1.50645
\(827\) 9.66698 0.336154 0.168077 0.985774i \(-0.446244\pi\)
0.168077 + 0.985774i \(0.446244\pi\)
\(828\) −35.3753 −1.22938
\(829\) 29.7606 1.03363 0.516814 0.856098i \(-0.327118\pi\)
0.516814 + 0.856098i \(0.327118\pi\)
\(830\) −41.2050 −1.43025
\(831\) −12.4145 −0.430654
\(832\) −3.06200 −0.106156
\(833\) −16.0309 −0.555438
\(834\) 37.9543 1.31425
\(835\) 17.8328 0.617128
\(836\) −5.95132 −0.205831
\(837\) −13.3670 −0.462031
\(838\) −66.7881 −2.30716
\(839\) 28.0982 0.970059 0.485029 0.874498i \(-0.338809\pi\)
0.485029 + 0.874498i \(0.338809\pi\)
\(840\) −17.3447 −0.598449
\(841\) −27.1709 −0.936929
\(842\) 7.73309 0.266500
\(843\) 22.9627 0.790879
\(844\) 43.3217 1.49120
\(845\) 30.9277 1.06395
\(846\) −20.6074 −0.708496
\(847\) −22.8449 −0.784960
\(848\) 61.5282 2.11289
\(849\) 28.6582 0.983548
\(850\) −15.4007 −0.528239
\(851\) 30.9286 1.06022
\(852\) 9.96172 0.341283
\(853\) 16.4572 0.563484 0.281742 0.959490i \(-0.409088\pi\)
0.281742 + 0.959490i \(0.409088\pi\)
\(854\) 2.37198 0.0811674
\(855\) 7.50356 0.256616
\(856\) 88.9621 3.04066
\(857\) 24.6955 0.843582 0.421791 0.906693i \(-0.361402\pi\)
0.421791 + 0.906693i \(0.361402\pi\)
\(858\) −4.94802 −0.168922
\(859\) −12.2825 −0.419074 −0.209537 0.977801i \(-0.567196\pi\)
−0.209537 + 0.977801i \(0.567196\pi\)
\(860\) 9.13305 0.311434
\(861\) 13.6407 0.464874
\(862\) 18.7837 0.639776
\(863\) −1.73921 −0.0592035 −0.0296017 0.999562i \(-0.509424\pi\)
−0.0296017 + 0.999562i \(0.509424\pi\)
\(864\) 30.1405 1.02540
\(865\) −13.9536 −0.474437
\(866\) −50.1151 −1.70298
\(867\) 25.9882 0.882607
\(868\) 22.1785 0.752786
\(869\) 1.52470 0.0517220
\(870\) 4.54993 0.154257
\(871\) −21.6986 −0.735229
\(872\) 107.429 3.63801
\(873\) −18.3709 −0.621760
\(874\) 96.4939 3.26395
\(875\) 2.08615 0.0705247
\(876\) −46.5215 −1.57182
\(877\) −21.5185 −0.726629 −0.363314 0.931667i \(-0.618355\pi\)
−0.363314 + 0.931667i \(0.618355\pi\)
\(878\) 8.78021 0.296318
\(879\) 25.8270 0.871123
\(880\) 1.56449 0.0527388
\(881\) 14.4446 0.486652 0.243326 0.969945i \(-0.421762\pi\)
0.243326 + 0.969945i \(0.421762\pi\)
\(882\) −8.42706 −0.283754
\(883\) 43.2706 1.45617 0.728085 0.685487i \(-0.240410\pi\)
0.728085 + 0.685487i \(0.240410\pi\)
\(884\) 179.411 6.03425
\(885\) 10.7894 0.362680
\(886\) 17.8317 0.599067
\(887\) −47.0060 −1.57831 −0.789154 0.614195i \(-0.789481\pi\)
−0.789154 + 0.614195i \(0.789481\pi\)
\(888\) −40.6614 −1.36451
\(889\) −36.0793 −1.21006
\(890\) 26.7128 0.895413
\(891\) −0.817041 −0.0273719
\(892\) −53.9566 −1.80660
\(893\) 38.8388 1.29969
\(894\) 63.8198 2.13445
\(895\) −16.6736 −0.557337
\(896\) 24.8204 0.829193
\(897\) 55.4320 1.85082
\(898\) 74.2024 2.47617
\(899\) −3.21561 −0.107247
\(900\) −5.59372 −0.186457
\(901\) 52.8345 1.76017
\(902\) −2.79105 −0.0929318
\(903\) 5.63529 0.187531
\(904\) 47.2635 1.57196
\(905\) 13.8655 0.460904
\(906\) −16.2564 −0.540084
\(907\) −8.56950 −0.284545 −0.142273 0.989827i \(-0.545441\pi\)
−0.142273 + 0.989827i \(0.545441\pi\)
\(908\) −105.084 −3.48733
\(909\) −16.7503 −0.555573
\(910\) −35.1732 −1.16598
\(911\) 9.03908 0.299478 0.149739 0.988726i \(-0.452157\pi\)
0.149739 + 0.988726i \(0.452157\pi\)
\(912\) −55.9238 −1.85182
\(913\) 3.59439 0.118957
\(914\) 58.5868 1.93788
\(915\) −0.591100 −0.0195412
\(916\) −52.9474 −1.74943
\(917\) 18.0573 0.596305
\(918\) 86.5816 2.85762
\(919\) −27.5248 −0.907961 −0.453980 0.891012i \(-0.649996\pi\)
−0.453980 + 0.891012i \(0.649996\pi\)
\(920\) −39.7583 −1.31079
\(921\) −30.4333 −1.00281
\(922\) 88.4458 2.91281
\(923\) 11.1654 0.367513
\(924\) 2.73746 0.0900557
\(925\) 4.89059 0.160802
\(926\) 12.4988 0.410735
\(927\) 8.35058 0.274269
\(928\) 7.25070 0.238016
\(929\) −57.4681 −1.88547 −0.942734 0.333544i \(-0.891755\pi\)
−0.942734 + 0.333544i \(0.891755\pi\)
\(930\) −7.99905 −0.262299
\(931\) 15.8825 0.520528
\(932\) −27.4813 −0.900181
\(933\) −15.8152 −0.517766
\(934\) 63.2356 2.06913
\(935\) 1.34343 0.0439348
\(936\) 52.1269 1.70382
\(937\) 16.2302 0.530217 0.265108 0.964219i \(-0.414592\pi\)
0.265108 + 0.964219i \(0.414592\pi\)
\(938\) 17.3742 0.567288
\(939\) −31.0577 −1.01353
\(940\) −28.9534 −0.944355
\(941\) −16.0621 −0.523611 −0.261805 0.965121i \(-0.584318\pi\)
−0.261805 + 0.965121i \(0.584318\pi\)
\(942\) −50.5332 −1.64646
\(943\) 31.2678 1.01822
\(944\) 57.5179 1.87205
\(945\) −11.7282 −0.381518
\(946\) −1.15305 −0.0374888
\(947\) −30.3942 −0.987678 −0.493839 0.869553i \(-0.664407\pi\)
−0.493839 + 0.869553i \(0.664407\pi\)
\(948\) 40.6296 1.31959
\(949\) −52.1427 −1.69262
\(950\) 15.2581 0.495039
\(951\) 25.9992 0.843081
\(952\) −79.3993 −2.57335
\(953\) 56.9325 1.84422 0.922112 0.386922i \(-0.126462\pi\)
0.922112 + 0.386922i \(0.126462\pi\)
\(954\) 27.7738 0.899210
\(955\) −5.14084 −0.166354
\(956\) 6.03769 0.195273
\(957\) −0.396899 −0.0128299
\(958\) 51.1337 1.65206
\(959\) 37.1928 1.20102
\(960\) −0.610982 −0.0197194
\(961\) −25.3468 −0.817637
\(962\) −82.4570 −2.65852
\(963\) 17.7027 0.570462
\(964\) 50.0074 1.61063
\(965\) −5.87316 −0.189064
\(966\) −44.3848 −1.42806
\(967\) 29.5291 0.949593 0.474796 0.880096i \(-0.342522\pi\)
0.474796 + 0.880096i \(0.342522\pi\)
\(968\) 68.8451 2.21276
\(969\) −48.0219 −1.54269
\(970\) −37.3562 −1.19944
\(971\) 31.0361 0.995997 0.497999 0.867178i \(-0.334068\pi\)
0.497999 + 0.867178i \(0.334068\pi\)
\(972\) 53.6405 1.72052
\(973\) −23.5352 −0.754503
\(974\) 74.7065 2.39375
\(975\) 8.76520 0.280711
\(976\) −3.15114 −0.100866
\(977\) 1.72349 0.0551393 0.0275696 0.999620i \(-0.491223\pi\)
0.0275696 + 0.999620i \(0.491223\pi\)
\(978\) 40.8898 1.30751
\(979\) −2.33020 −0.0744736
\(980\) −11.8400 −0.378216
\(981\) 21.3775 0.682531
\(982\) −21.7136 −0.692909
\(983\) −5.02593 −0.160302 −0.0801512 0.996783i \(-0.525540\pi\)
−0.0801512 + 0.996783i \(0.525540\pi\)
\(984\) −41.1074 −1.31046
\(985\) 23.3208 0.743064
\(986\) 20.8283 0.663310
\(987\) −17.8649 −0.568645
\(988\) −177.750 −5.65499
\(989\) 12.9175 0.410752
\(990\) 0.706208 0.0224448
\(991\) −36.6578 −1.16447 −0.582237 0.813019i \(-0.697822\pi\)
−0.582237 + 0.813019i \(0.697822\pi\)
\(992\) −12.7472 −0.404723
\(993\) −21.8060 −0.691992
\(994\) −8.94018 −0.283565
\(995\) 23.6505 0.749771
\(996\) 95.7818 3.03496
\(997\) 9.05228 0.286689 0.143344 0.989673i \(-0.454214\pi\)
0.143344 + 0.989673i \(0.454214\pi\)
\(998\) 100.688 3.18722
\(999\) −27.4946 −0.869889
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 \(a_p\))