Properties

Label 8035.2.a.e.1.16
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

Related objects

Downloads

Learn more about

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 1.16
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.32037 q^{2}\) \(+2.64444 q^{3}\) \(+3.38410 q^{4}\) \(+1.00000 q^{5}\) \(-6.13607 q^{6}\) \(+4.54944 q^{7}\) \(-3.21162 q^{8}\) \(+3.99307 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.32037 q^{2}\) \(+2.64444 q^{3}\) \(+3.38410 q^{4}\) \(+1.00000 q^{5}\) \(-6.13607 q^{6}\) \(+4.54944 q^{7}\) \(-3.21162 q^{8}\) \(+3.99307 q^{9}\) \(-2.32037 q^{10}\) \(+4.33503 q^{11}\) \(+8.94905 q^{12}\) \(-1.34544 q^{13}\) \(-10.5564 q^{14}\) \(+2.64444 q^{15}\) \(+0.683929 q^{16}\) \(-2.85566 q^{17}\) \(-9.26540 q^{18}\) \(-2.45105 q^{19}\) \(+3.38410 q^{20}\) \(+12.0307 q^{21}\) \(-10.0588 q^{22}\) \(+3.22525 q^{23}\) \(-8.49294 q^{24}\) \(+1.00000 q^{25}\) \(+3.12192 q^{26}\) \(+2.62613 q^{27}\) \(+15.3958 q^{28}\) \(+3.53723 q^{29}\) \(-6.13607 q^{30}\) \(+6.72082 q^{31}\) \(+4.83627 q^{32}\) \(+11.4637 q^{33}\) \(+6.62618 q^{34}\) \(+4.54944 q^{35}\) \(+13.5130 q^{36}\) \(+5.60838 q^{37}\) \(+5.68734 q^{38}\) \(-3.55794 q^{39}\) \(-3.21162 q^{40}\) \(-2.64781 q^{41}\) \(-27.9157 q^{42}\) \(-1.92594 q^{43}\) \(+14.6702 q^{44}\) \(+3.99307 q^{45}\) \(-7.48377 q^{46}\) \(+1.58251 q^{47}\) \(+1.80861 q^{48}\) \(+13.6974 q^{49}\) \(-2.32037 q^{50}\) \(-7.55164 q^{51}\) \(-4.55310 q^{52}\) \(-9.57516 q^{53}\) \(-6.09358 q^{54}\) \(+4.33503 q^{55}\) \(-14.6111 q^{56}\) \(-6.48166 q^{57}\) \(-8.20767 q^{58}\) \(+4.60243 q^{59}\) \(+8.94905 q^{60}\) \(-6.26088 q^{61}\) \(-15.5948 q^{62}\) \(+18.1663 q^{63}\) \(-12.5898 q^{64}\) \(-1.34544 q^{65}\) \(-26.6000 q^{66}\) \(-13.8298 q^{67}\) \(-9.66385 q^{68}\) \(+8.52900 q^{69}\) \(-10.5564 q^{70}\) \(-10.7191 q^{71}\) \(-12.8242 q^{72}\) \(+6.51080 q^{73}\) \(-13.0135 q^{74}\) \(+2.64444 q^{75}\) \(-8.29460 q^{76}\) \(+19.7219 q^{77}\) \(+8.25572 q^{78}\) \(-7.44392 q^{79}\) \(+0.683929 q^{80}\) \(-5.03458 q^{81}\) \(+6.14389 q^{82}\) \(+6.50425 q^{83}\) \(+40.7132 q^{84}\) \(-2.85566 q^{85}\) \(+4.46889 q^{86}\) \(+9.35401 q^{87}\) \(-13.9224 q^{88}\) \(+12.0542 q^{89}\) \(-9.26540 q^{90}\) \(-6.12100 q^{91}\) \(+10.9146 q^{92}\) \(+17.7728 q^{93}\) \(-3.67200 q^{94}\) \(-2.45105 q^{95}\) \(+12.7892 q^{96}\) \(+8.75566 q^{97}\) \(-31.7830 q^{98}\) \(+17.3101 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.32037 −1.64075 −0.820373 0.571828i \(-0.806234\pi\)
−0.820373 + 0.571828i \(0.806234\pi\)
\(3\) 2.64444 1.52677 0.763385 0.645944i \(-0.223536\pi\)
0.763385 + 0.645944i \(0.223536\pi\)
\(4\) 3.38410 1.69205
\(5\) 1.00000 0.447214
\(6\) −6.13607 −2.50504
\(7\) 4.54944 1.71953 0.859763 0.510693i \(-0.170611\pi\)
0.859763 + 0.510693i \(0.170611\pi\)
\(8\) −3.21162 −1.13548
\(9\) 3.99307 1.33102
\(10\) −2.32037 −0.733764
\(11\) 4.33503 1.30706 0.653530 0.756901i \(-0.273287\pi\)
0.653530 + 0.756901i \(0.273287\pi\)
\(12\) 8.94905 2.58337
\(13\) −1.34544 −0.373158 −0.186579 0.982440i \(-0.559740\pi\)
−0.186579 + 0.982440i \(0.559740\pi\)
\(14\) −10.5564 −2.82131
\(15\) 2.64444 0.682792
\(16\) 0.683929 0.170982
\(17\) −2.85566 −0.692600 −0.346300 0.938124i \(-0.612562\pi\)
−0.346300 + 0.938124i \(0.612562\pi\)
\(18\) −9.26540 −2.18387
\(19\) −2.45105 −0.562310 −0.281155 0.959662i \(-0.590717\pi\)
−0.281155 + 0.959662i \(0.590717\pi\)
\(20\) 3.38410 0.756708
\(21\) 12.0307 2.62532
\(22\) −10.0588 −2.14455
\(23\) 3.22525 0.672512 0.336256 0.941771i \(-0.390839\pi\)
0.336256 + 0.941771i \(0.390839\pi\)
\(24\) −8.49294 −1.73361
\(25\) 1.00000 0.200000
\(26\) 3.12192 0.612258
\(27\) 2.62613 0.505399
\(28\) 15.3958 2.90952
\(29\) 3.53723 0.656847 0.328424 0.944530i \(-0.393483\pi\)
0.328424 + 0.944530i \(0.393483\pi\)
\(30\) −6.13607 −1.12029
\(31\) 6.72082 1.20709 0.603547 0.797327i \(-0.293753\pi\)
0.603547 + 0.797327i \(0.293753\pi\)
\(32\) 4.83627 0.854939
\(33\) 11.4637 1.99558
\(34\) 6.62618 1.13638
\(35\) 4.54944 0.768996
\(36\) 13.5130 2.25216
\(37\) 5.60838 0.922013 0.461006 0.887397i \(-0.347489\pi\)
0.461006 + 0.887397i \(0.347489\pi\)
\(38\) 5.68734 0.922608
\(39\) −3.55794 −0.569726
\(40\) −3.21162 −0.507801
\(41\) −2.64781 −0.413519 −0.206759 0.978392i \(-0.566292\pi\)
−0.206759 + 0.978392i \(0.566292\pi\)
\(42\) −27.9157 −4.30749
\(43\) −1.92594 −0.293703 −0.146852 0.989159i \(-0.546914\pi\)
−0.146852 + 0.989159i \(0.546914\pi\)
\(44\) 14.6702 2.21161
\(45\) 3.99307 0.595252
\(46\) −7.48377 −1.10342
\(47\) 1.58251 0.230833 0.115416 0.993317i \(-0.463180\pi\)
0.115416 + 0.993317i \(0.463180\pi\)
\(48\) 1.80861 0.261051
\(49\) 13.6974 1.95677
\(50\) −2.32037 −0.328149
\(51\) −7.55164 −1.05744
\(52\) −4.55310 −0.631402
\(53\) −9.57516 −1.31525 −0.657625 0.753345i \(-0.728439\pi\)
−0.657625 + 0.753345i \(0.728439\pi\)
\(54\) −6.09358 −0.829231
\(55\) 4.33503 0.584535
\(56\) −14.6111 −1.95248
\(57\) −6.48166 −0.858517
\(58\) −8.20767 −1.07772
\(59\) 4.60243 0.599185 0.299593 0.954067i \(-0.403149\pi\)
0.299593 + 0.954067i \(0.403149\pi\)
\(60\) 8.94905 1.15532
\(61\) −6.26088 −0.801623 −0.400812 0.916160i \(-0.631272\pi\)
−0.400812 + 0.916160i \(0.631272\pi\)
\(62\) −15.5948 −1.98054
\(63\) 18.1663 2.28873
\(64\) −12.5898 −1.57372
\(65\) −1.34544 −0.166881
\(66\) −26.6000 −3.27424
\(67\) −13.8298 −1.68958 −0.844792 0.535094i \(-0.820276\pi\)
−0.844792 + 0.535094i \(0.820276\pi\)
\(68\) −9.66385 −1.17191
\(69\) 8.52900 1.02677
\(70\) −10.5564 −1.26173
\(71\) −10.7191 −1.27213 −0.636064 0.771636i \(-0.719439\pi\)
−0.636064 + 0.771636i \(0.719439\pi\)
\(72\) −12.8242 −1.51135
\(73\) 6.51080 0.762032 0.381016 0.924569i \(-0.375574\pi\)
0.381016 + 0.924569i \(0.375574\pi\)
\(74\) −13.0135 −1.51279
\(75\) 2.64444 0.305354
\(76\) −8.29460 −0.951456
\(77\) 19.7219 2.24752
\(78\) 8.25572 0.934777
\(79\) −7.44392 −0.837506 −0.418753 0.908100i \(-0.637533\pi\)
−0.418753 + 0.908100i \(0.637533\pi\)
\(80\) 0.683929 0.0764656
\(81\) −5.03458 −0.559398
\(82\) 6.14389 0.678479
\(83\) 6.50425 0.713934 0.356967 0.934117i \(-0.383811\pi\)
0.356967 + 0.934117i \(0.383811\pi\)
\(84\) 40.7132 4.44217
\(85\) −2.85566 −0.309740
\(86\) 4.46889 0.481892
\(87\) 9.35401 1.00285
\(88\) −13.9224 −1.48414
\(89\) 12.0542 1.27774 0.638870 0.769315i \(-0.279402\pi\)
0.638870 + 0.769315i \(0.279402\pi\)
\(90\) −9.26540 −0.976658
\(91\) −6.12100 −0.641655
\(92\) 10.9146 1.13792
\(93\) 17.7728 1.84295
\(94\) −3.67200 −0.378738
\(95\) −2.45105 −0.251473
\(96\) 12.7892 1.30530
\(97\) 8.75566 0.889002 0.444501 0.895778i \(-0.353381\pi\)
0.444501 + 0.895778i \(0.353381\pi\)
\(98\) −31.7830 −3.21057
\(99\) 17.3101 1.73973
\(100\) 3.38410 0.338410
\(101\) 14.8576 1.47839 0.739194 0.673493i \(-0.235207\pi\)
0.739194 + 0.673493i \(0.235207\pi\)
\(102\) 17.5226 1.73499
\(103\) −13.6659 −1.34654 −0.673270 0.739397i \(-0.735111\pi\)
−0.673270 + 0.739397i \(0.735111\pi\)
\(104\) 4.32104 0.423713
\(105\) 12.0307 1.17408
\(106\) 22.2179 2.15799
\(107\) 9.71118 0.938815 0.469408 0.882982i \(-0.344467\pi\)
0.469408 + 0.882982i \(0.344467\pi\)
\(108\) 8.88708 0.855160
\(109\) 2.49497 0.238975 0.119487 0.992836i \(-0.461875\pi\)
0.119487 + 0.992836i \(0.461875\pi\)
\(110\) −10.0588 −0.959073
\(111\) 14.8310 1.40770
\(112\) 3.11150 0.294009
\(113\) 8.81959 0.829677 0.414839 0.909895i \(-0.363838\pi\)
0.414839 + 0.909895i \(0.363838\pi\)
\(114\) 15.0398 1.40861
\(115\) 3.22525 0.300756
\(116\) 11.9703 1.11142
\(117\) −5.37245 −0.496683
\(118\) −10.6793 −0.983111
\(119\) −12.9917 −1.19094
\(120\) −8.49294 −0.775295
\(121\) 7.79245 0.708405
\(122\) 14.5275 1.31526
\(123\) −7.00198 −0.631348
\(124\) 22.7439 2.04246
\(125\) 1.00000 0.0894427
\(126\) −42.1524 −3.75523
\(127\) −2.91396 −0.258572 −0.129286 0.991607i \(-0.541269\pi\)
−0.129286 + 0.991607i \(0.541269\pi\)
\(128\) 19.5403 1.72714
\(129\) −5.09304 −0.448417
\(130\) 3.12192 0.273810
\(131\) −1.90961 −0.166843 −0.0834217 0.996514i \(-0.526585\pi\)
−0.0834217 + 0.996514i \(0.526585\pi\)
\(132\) 38.7944 3.37662
\(133\) −11.1509 −0.966906
\(134\) 32.0903 2.77218
\(135\) 2.62613 0.226021
\(136\) 9.17130 0.786432
\(137\) −9.97449 −0.852178 −0.426089 0.904681i \(-0.640109\pi\)
−0.426089 + 0.904681i \(0.640109\pi\)
\(138\) −19.7904 −1.68467
\(139\) 0.250117 0.0212146 0.0106073 0.999944i \(-0.496624\pi\)
0.0106073 + 0.999944i \(0.496624\pi\)
\(140\) 15.3958 1.30118
\(141\) 4.18485 0.352428
\(142\) 24.8723 2.08724
\(143\) −5.83252 −0.487740
\(144\) 2.73098 0.227582
\(145\) 3.53723 0.293751
\(146\) −15.1074 −1.25030
\(147\) 36.2220 2.98754
\(148\) 18.9793 1.56009
\(149\) 0.955480 0.0782760 0.0391380 0.999234i \(-0.487539\pi\)
0.0391380 + 0.999234i \(0.487539\pi\)
\(150\) −6.13607 −0.501008
\(151\) 21.5986 1.75767 0.878835 0.477126i \(-0.158321\pi\)
0.878835 + 0.477126i \(0.158321\pi\)
\(152\) 7.87184 0.638490
\(153\) −11.4029 −0.921868
\(154\) −45.7621 −3.68762
\(155\) 6.72082 0.539829
\(156\) −12.0404 −0.964005
\(157\) 2.59811 0.207352 0.103676 0.994611i \(-0.466940\pi\)
0.103676 + 0.994611i \(0.466940\pi\)
\(158\) 17.2726 1.37414
\(159\) −25.3210 −2.00808
\(160\) 4.83627 0.382341
\(161\) 14.6731 1.15640
\(162\) 11.6821 0.917830
\(163\) 2.04576 0.160236 0.0801181 0.996785i \(-0.474470\pi\)
0.0801181 + 0.996785i \(0.474470\pi\)
\(164\) −8.96045 −0.699694
\(165\) 11.4637 0.892450
\(166\) −15.0922 −1.17138
\(167\) 4.60394 0.356264 0.178132 0.984007i \(-0.442995\pi\)
0.178132 + 0.984007i \(0.442995\pi\)
\(168\) −38.6381 −2.98099
\(169\) −11.1898 −0.860753
\(170\) 6.62618 0.508205
\(171\) −9.78723 −0.748448
\(172\) −6.51757 −0.496960
\(173\) 3.25271 0.247299 0.123649 0.992326i \(-0.460540\pi\)
0.123649 + 0.992326i \(0.460540\pi\)
\(174\) −21.7047 −1.64543
\(175\) 4.54944 0.343905
\(176\) 2.96485 0.223484
\(177\) 12.1709 0.914817
\(178\) −27.9701 −2.09645
\(179\) 13.8170 1.03273 0.516366 0.856368i \(-0.327285\pi\)
0.516366 + 0.856368i \(0.327285\pi\)
\(180\) 13.5130 1.00720
\(181\) 4.62251 0.343588 0.171794 0.985133i \(-0.445044\pi\)
0.171794 + 0.985133i \(0.445044\pi\)
\(182\) 14.2030 1.05279
\(183\) −16.5565 −1.22389
\(184\) −10.3583 −0.763622
\(185\) 5.60838 0.412337
\(186\) −41.2394 −3.02382
\(187\) −12.3794 −0.905269
\(188\) 5.35536 0.390580
\(189\) 11.9474 0.869046
\(190\) 5.68734 0.412603
\(191\) −5.17864 −0.374713 −0.187357 0.982292i \(-0.559992\pi\)
−0.187357 + 0.982292i \(0.559992\pi\)
\(192\) −33.2929 −2.40271
\(193\) 19.6064 1.41130 0.705650 0.708561i \(-0.250655\pi\)
0.705650 + 0.708561i \(0.250655\pi\)
\(194\) −20.3163 −1.45863
\(195\) −3.55794 −0.254789
\(196\) 46.3534 3.31095
\(197\) 13.3605 0.951898 0.475949 0.879473i \(-0.342105\pi\)
0.475949 + 0.879473i \(0.342105\pi\)
\(198\) −40.1657 −2.85445
\(199\) −17.2051 −1.21964 −0.609820 0.792540i \(-0.708758\pi\)
−0.609820 + 0.792540i \(0.708758\pi\)
\(200\) −3.21162 −0.227096
\(201\) −36.5722 −2.57961
\(202\) −34.4751 −2.42566
\(203\) 16.0924 1.12947
\(204\) −25.5555 −1.78924
\(205\) −2.64781 −0.184931
\(206\) 31.7099 2.20933
\(207\) 12.8787 0.895130
\(208\) −0.920186 −0.0638034
\(209\) −10.6254 −0.734972
\(210\) −27.9157 −1.92637
\(211\) −15.1596 −1.04363 −0.521814 0.853059i \(-0.674744\pi\)
−0.521814 + 0.853059i \(0.674744\pi\)
\(212\) −32.4033 −2.22547
\(213\) −28.3462 −1.94225
\(214\) −22.5335 −1.54036
\(215\) −1.92594 −0.131348
\(216\) −8.43412 −0.573869
\(217\) 30.5760 2.07563
\(218\) −5.78925 −0.392097
\(219\) 17.2174 1.16345
\(220\) 14.6702 0.989062
\(221\) 3.84213 0.258449
\(222\) −34.4135 −2.30968
\(223\) 11.6371 0.779280 0.389640 0.920967i \(-0.372599\pi\)
0.389640 + 0.920967i \(0.372599\pi\)
\(224\) 22.0023 1.47009
\(225\) 3.99307 0.266205
\(226\) −20.4647 −1.36129
\(227\) −5.71826 −0.379534 −0.189767 0.981829i \(-0.560773\pi\)
−0.189767 + 0.981829i \(0.560773\pi\)
\(228\) −21.9346 −1.45265
\(229\) −14.6751 −0.969759 −0.484880 0.874581i \(-0.661137\pi\)
−0.484880 + 0.874581i \(0.661137\pi\)
\(230\) −7.48377 −0.493465
\(231\) 52.1535 3.43145
\(232\) −11.3602 −0.745836
\(233\) −13.7583 −0.901337 −0.450668 0.892691i \(-0.648814\pi\)
−0.450668 + 0.892691i \(0.648814\pi\)
\(234\) 12.4660 0.814931
\(235\) 1.58251 0.103231
\(236\) 15.5751 1.01385
\(237\) −19.6850 −1.27868
\(238\) 30.1454 1.95404
\(239\) 5.73906 0.371229 0.185614 0.982623i \(-0.440572\pi\)
0.185614 + 0.982623i \(0.440572\pi\)
\(240\) 1.80861 0.116745
\(241\) 2.82335 0.181868 0.0909339 0.995857i \(-0.471015\pi\)
0.0909339 + 0.995857i \(0.471015\pi\)
\(242\) −18.0813 −1.16231
\(243\) −21.1920 −1.35947
\(244\) −21.1874 −1.35639
\(245\) 13.6974 0.875095
\(246\) 16.2472 1.03588
\(247\) 3.29774 0.209830
\(248\) −21.5847 −1.37063
\(249\) 17.2001 1.09001
\(250\) −2.32037 −0.146753
\(251\) −15.3933 −0.971618 −0.485809 0.874065i \(-0.661475\pi\)
−0.485809 + 0.874065i \(0.661475\pi\)
\(252\) 61.4764 3.87265
\(253\) 13.9816 0.879013
\(254\) 6.76146 0.424252
\(255\) −7.55164 −0.472902
\(256\) −20.1612 −1.26008
\(257\) −14.6277 −0.912449 −0.456224 0.889865i \(-0.650799\pi\)
−0.456224 + 0.889865i \(0.650799\pi\)
\(258\) 11.8177 0.735739
\(259\) 25.5150 1.58543
\(260\) −4.55310 −0.282372
\(261\) 14.1244 0.874280
\(262\) 4.43099 0.273748
\(263\) 24.6072 1.51734 0.758672 0.651472i \(-0.225848\pi\)
0.758672 + 0.651472i \(0.225848\pi\)
\(264\) −36.8171 −2.26594
\(265\) −9.57516 −0.588198
\(266\) 25.8742 1.58645
\(267\) 31.8766 1.95082
\(268\) −46.8016 −2.85886
\(269\) −26.9657 −1.64413 −0.822063 0.569397i \(-0.807177\pi\)
−0.822063 + 0.569397i \(0.807177\pi\)
\(270\) −6.09358 −0.370843
\(271\) 15.7753 0.958284 0.479142 0.877737i \(-0.340948\pi\)
0.479142 + 0.877737i \(0.340948\pi\)
\(272\) −1.95307 −0.118422
\(273\) −16.1866 −0.979660
\(274\) 23.1445 1.39821
\(275\) 4.33503 0.261412
\(276\) 28.8630 1.73735
\(277\) −6.24037 −0.374948 −0.187474 0.982270i \(-0.560030\pi\)
−0.187474 + 0.982270i \(0.560030\pi\)
\(278\) −0.580363 −0.0348078
\(279\) 26.8367 1.60667
\(280\) −14.6111 −0.873178
\(281\) 22.1505 1.32139 0.660695 0.750654i \(-0.270262\pi\)
0.660695 + 0.750654i \(0.270262\pi\)
\(282\) −9.71039 −0.578245
\(283\) −6.06473 −0.360511 −0.180255 0.983620i \(-0.557692\pi\)
−0.180255 + 0.983620i \(0.557692\pi\)
\(284\) −36.2747 −2.15251
\(285\) −6.48166 −0.383941
\(286\) 13.5336 0.800258
\(287\) −12.0461 −0.711056
\(288\) 19.3116 1.13795
\(289\) −8.84519 −0.520305
\(290\) −8.20767 −0.481971
\(291\) 23.1538 1.35730
\(292\) 22.0332 1.28940
\(293\) 14.4061 0.841614 0.420807 0.907150i \(-0.361747\pi\)
0.420807 + 0.907150i \(0.361747\pi\)
\(294\) −84.0483 −4.90179
\(295\) 4.60243 0.267964
\(296\) −18.0120 −1.04693
\(297\) 11.3843 0.660586
\(298\) −2.21706 −0.128431
\(299\) −4.33939 −0.250953
\(300\) 8.94905 0.516674
\(301\) −8.76195 −0.505030
\(302\) −50.1167 −2.88389
\(303\) 39.2901 2.25716
\(304\) −1.67635 −0.0961450
\(305\) −6.26088 −0.358497
\(306\) 26.4588 1.51255
\(307\) −11.7899 −0.672884 −0.336442 0.941704i \(-0.609224\pi\)
−0.336442 + 0.941704i \(0.609224\pi\)
\(308\) 66.7410 3.80292
\(309\) −36.1387 −2.05586
\(310\) −15.5948 −0.885723
\(311\) 1.67991 0.0952588 0.0476294 0.998865i \(-0.484833\pi\)
0.0476294 + 0.998865i \(0.484833\pi\)
\(312\) 11.4267 0.646912
\(313\) −12.0379 −0.680421 −0.340210 0.940349i \(-0.610498\pi\)
−0.340210 + 0.940349i \(0.610498\pi\)
\(314\) −6.02856 −0.340211
\(315\) 18.1663 1.02355
\(316\) −25.1910 −1.41710
\(317\) −33.8585 −1.90169 −0.950843 0.309675i \(-0.899780\pi\)
−0.950843 + 0.309675i \(0.899780\pi\)
\(318\) 58.7539 3.29476
\(319\) 15.3340 0.858539
\(320\) −12.5898 −0.703790
\(321\) 25.6807 1.43335
\(322\) −34.0470 −1.89736
\(323\) 6.99938 0.389456
\(324\) −17.0375 −0.946529
\(325\) −1.34544 −0.0746316
\(326\) −4.74691 −0.262907
\(327\) 6.59781 0.364859
\(328\) 8.50375 0.469541
\(329\) 7.19952 0.396923
\(330\) −26.6000 −1.46428
\(331\) 7.54252 0.414574 0.207287 0.978280i \(-0.433537\pi\)
0.207287 + 0.978280i \(0.433537\pi\)
\(332\) 22.0110 1.20801
\(333\) 22.3947 1.22722
\(334\) −10.6828 −0.584539
\(335\) −13.8298 −0.755605
\(336\) 8.22817 0.448883
\(337\) −23.7388 −1.29314 −0.646568 0.762856i \(-0.723796\pi\)
−0.646568 + 0.762856i \(0.723796\pi\)
\(338\) 25.9644 1.41228
\(339\) 23.3229 1.26673
\(340\) −9.66385 −0.524096
\(341\) 29.1349 1.57774
\(342\) 22.7100 1.22801
\(343\) 30.4694 1.64519
\(344\) 6.18538 0.333494
\(345\) 8.52900 0.459186
\(346\) −7.54748 −0.405755
\(347\) 2.99093 0.160562 0.0802809 0.996772i \(-0.474418\pi\)
0.0802809 + 0.996772i \(0.474418\pi\)
\(348\) 31.6549 1.69688
\(349\) 23.6467 1.26578 0.632890 0.774242i \(-0.281868\pi\)
0.632890 + 0.774242i \(0.281868\pi\)
\(350\) −10.5564 −0.564261
\(351\) −3.53330 −0.188594
\(352\) 20.9653 1.11746
\(353\) 29.6987 1.58070 0.790351 0.612654i \(-0.209898\pi\)
0.790351 + 0.612654i \(0.209898\pi\)
\(354\) −28.2408 −1.50098
\(355\) −10.7191 −0.568913
\(356\) 40.7925 2.16200
\(357\) −34.3557 −1.81830
\(358\) −32.0605 −1.69445
\(359\) −29.3925 −1.55128 −0.775639 0.631176i \(-0.782572\pi\)
−0.775639 + 0.631176i \(0.782572\pi\)
\(360\) −12.8242 −0.675896
\(361\) −12.9923 −0.683808
\(362\) −10.7259 −0.563741
\(363\) 20.6067 1.08157
\(364\) −20.7141 −1.08571
\(365\) 6.51080 0.340791
\(366\) 38.4172 2.00810
\(367\) −27.8774 −1.45519 −0.727594 0.686008i \(-0.759362\pi\)
−0.727594 + 0.686008i \(0.759362\pi\)
\(368\) 2.20585 0.114988
\(369\) −10.5729 −0.550403
\(370\) −13.0135 −0.676540
\(371\) −43.5616 −2.26161
\(372\) 60.1450 3.11837
\(373\) −30.9115 −1.60053 −0.800267 0.599643i \(-0.795309\pi\)
−0.800267 + 0.599643i \(0.795309\pi\)
\(374\) 28.7247 1.48532
\(375\) 2.64444 0.136558
\(376\) −5.08241 −0.262105
\(377\) −4.75914 −0.245108
\(378\) −27.7224 −1.42588
\(379\) −22.6232 −1.16207 −0.581037 0.813877i \(-0.697353\pi\)
−0.581037 + 0.813877i \(0.697353\pi\)
\(380\) −8.29460 −0.425504
\(381\) −7.70581 −0.394780
\(382\) 12.0163 0.614809
\(383\) −2.18637 −0.111718 −0.0558592 0.998439i \(-0.517790\pi\)
−0.0558592 + 0.998439i \(0.517790\pi\)
\(384\) 51.6733 2.63694
\(385\) 19.7219 1.00512
\(386\) −45.4940 −2.31558
\(387\) −7.69042 −0.390926
\(388\) 29.6300 1.50424
\(389\) −3.00667 −0.152444 −0.0762221 0.997091i \(-0.524286\pi\)
−0.0762221 + 0.997091i \(0.524286\pi\)
\(390\) 8.25572 0.418045
\(391\) −9.21024 −0.465782
\(392\) −43.9908 −2.22187
\(393\) −5.04985 −0.254731
\(394\) −31.0013 −1.56182
\(395\) −7.44392 −0.374544
\(396\) 58.5790 2.94371
\(397\) −20.0766 −1.00762 −0.503808 0.863816i \(-0.668068\pi\)
−0.503808 + 0.863816i \(0.668068\pi\)
\(398\) 39.9222 2.00112
\(399\) −29.4879 −1.47624
\(400\) 0.683929 0.0341965
\(401\) 11.9906 0.598781 0.299391 0.954131i \(-0.403217\pi\)
0.299391 + 0.954131i \(0.403217\pi\)
\(402\) 84.8610 4.23248
\(403\) −9.04246 −0.450437
\(404\) 50.2796 2.50150
\(405\) −5.03458 −0.250170
\(406\) −37.3403 −1.85317
\(407\) 24.3125 1.20513
\(408\) 24.2530 1.20070
\(409\) −10.9065 −0.539290 −0.269645 0.962960i \(-0.586906\pi\)
−0.269645 + 0.962960i \(0.586906\pi\)
\(410\) 6.14389 0.303425
\(411\) −26.3770 −1.30108
\(412\) −46.2467 −2.27841
\(413\) 20.9385 1.03031
\(414\) −29.8832 −1.46868
\(415\) 6.50425 0.319281
\(416\) −6.50691 −0.319028
\(417\) 0.661419 0.0323898
\(418\) 24.6547 1.20590
\(419\) 31.4908 1.53843 0.769214 0.638991i \(-0.220648\pi\)
0.769214 + 0.638991i \(0.220648\pi\)
\(420\) 40.7132 1.98660
\(421\) 39.1240 1.90679 0.953394 0.301727i \(-0.0975630\pi\)
0.953394 + 0.301727i \(0.0975630\pi\)
\(422\) 35.1758 1.71233
\(423\) 6.31907 0.307244
\(424\) 30.7518 1.49344
\(425\) −2.85566 −0.138520
\(426\) 65.7735 3.18674
\(427\) −28.4835 −1.37841
\(428\) 32.8636 1.58852
\(429\) −15.4238 −0.744666
\(430\) 4.46889 0.215509
\(431\) 1.49541 0.0720315 0.0360157 0.999351i \(-0.488533\pi\)
0.0360157 + 0.999351i \(0.488533\pi\)
\(432\) 1.79609 0.0864142
\(433\) 26.9556 1.29540 0.647701 0.761895i \(-0.275731\pi\)
0.647701 + 0.761895i \(0.275731\pi\)
\(434\) −70.9474 −3.40558
\(435\) 9.35401 0.448490
\(436\) 8.44323 0.404357
\(437\) −7.90526 −0.378160
\(438\) −39.9508 −1.90892
\(439\) −4.13259 −0.197238 −0.0986189 0.995125i \(-0.531442\pi\)
−0.0986189 + 0.995125i \(0.531442\pi\)
\(440\) −13.9224 −0.663726
\(441\) 54.6947 2.60451
\(442\) −8.91514 −0.424050
\(443\) 3.53038 0.167733 0.0838667 0.996477i \(-0.473273\pi\)
0.0838667 + 0.996477i \(0.473273\pi\)
\(444\) 50.1897 2.38190
\(445\) 12.0542 0.571423
\(446\) −27.0024 −1.27860
\(447\) 2.52671 0.119509
\(448\) −57.2764 −2.70606
\(449\) 4.00427 0.188973 0.0944867 0.995526i \(-0.469879\pi\)
0.0944867 + 0.995526i \(0.469879\pi\)
\(450\) −9.26540 −0.436775
\(451\) −11.4783 −0.540493
\(452\) 29.8464 1.40386
\(453\) 57.1163 2.68356
\(454\) 13.2685 0.622720
\(455\) −6.12100 −0.286957
\(456\) 20.8166 0.974827
\(457\) −20.2031 −0.945059 −0.472530 0.881315i \(-0.656659\pi\)
−0.472530 + 0.881315i \(0.656659\pi\)
\(458\) 34.0516 1.59113
\(459\) −7.49934 −0.350039
\(460\) 10.9146 0.508895
\(461\) 24.8642 1.15804 0.579022 0.815312i \(-0.303435\pi\)
0.579022 + 0.815312i \(0.303435\pi\)
\(462\) −121.015 −5.63014
\(463\) −4.56220 −0.212024 −0.106012 0.994365i \(-0.533808\pi\)
−0.106012 + 0.994365i \(0.533808\pi\)
\(464\) 2.41922 0.112309
\(465\) 17.7728 0.824194
\(466\) 31.9243 1.47887
\(467\) 23.4269 1.08407 0.542034 0.840357i \(-0.317654\pi\)
0.542034 + 0.840357i \(0.317654\pi\)
\(468\) −18.1809 −0.840412
\(469\) −62.9181 −2.90529
\(470\) −3.67200 −0.169377
\(471\) 6.87055 0.316578
\(472\) −14.7812 −0.680362
\(473\) −8.34900 −0.383887
\(474\) 45.6764 2.09799
\(475\) −2.45105 −0.112462
\(476\) −43.9651 −2.01514
\(477\) −38.2343 −1.75063
\(478\) −13.3167 −0.609092
\(479\) −35.1980 −1.60824 −0.804118 0.594469i \(-0.797362\pi\)
−0.804118 + 0.594469i \(0.797362\pi\)
\(480\) 12.7892 0.583746
\(481\) −7.54575 −0.344057
\(482\) −6.55120 −0.298399
\(483\) 38.8022 1.76556
\(484\) 26.3704 1.19866
\(485\) 8.75566 0.397574
\(486\) 49.1733 2.23055
\(487\) −10.1913 −0.461813 −0.230906 0.972976i \(-0.574169\pi\)
−0.230906 + 0.972976i \(0.574169\pi\)
\(488\) 20.1075 0.910226
\(489\) 5.40989 0.244644
\(490\) −31.7830 −1.43581
\(491\) 15.9025 0.717669 0.358834 0.933401i \(-0.383174\pi\)
0.358834 + 0.933401i \(0.383174\pi\)
\(492\) −23.6954 −1.06827
\(493\) −10.1011 −0.454933
\(494\) −7.65197 −0.344279
\(495\) 17.3101 0.778030
\(496\) 4.59656 0.206392
\(497\) −48.7661 −2.18746
\(498\) −39.9106 −1.78843
\(499\) 3.12949 0.140095 0.0700476 0.997544i \(-0.477685\pi\)
0.0700476 + 0.997544i \(0.477685\pi\)
\(500\) 3.38410 0.151342
\(501\) 12.1749 0.543933
\(502\) 35.7182 1.59418
\(503\) −11.8563 −0.528648 −0.264324 0.964434i \(-0.585149\pi\)
−0.264324 + 0.964434i \(0.585149\pi\)
\(504\) −58.3430 −2.59881
\(505\) 14.8576 0.661155
\(506\) −32.4423 −1.44224
\(507\) −29.5908 −1.31417
\(508\) −9.86114 −0.437517
\(509\) 36.2396 1.60629 0.803146 0.595783i \(-0.203158\pi\)
0.803146 + 0.595783i \(0.203158\pi\)
\(510\) 17.5226 0.775912
\(511\) 29.6205 1.31033
\(512\) 7.70070 0.340326
\(513\) −6.43677 −0.284191
\(514\) 33.9415 1.49710
\(515\) −13.6659 −0.602191
\(516\) −17.2353 −0.758744
\(517\) 6.86021 0.301712
\(518\) −59.2042 −2.60128
\(519\) 8.60160 0.377568
\(520\) 4.32104 0.189490
\(521\) 25.3687 1.11142 0.555712 0.831375i \(-0.312446\pi\)
0.555712 + 0.831375i \(0.312446\pi\)
\(522\) −32.7739 −1.43447
\(523\) −25.2585 −1.10448 −0.552239 0.833686i \(-0.686226\pi\)
−0.552239 + 0.833686i \(0.686226\pi\)
\(524\) −6.46231 −0.282307
\(525\) 12.0307 0.525064
\(526\) −57.0977 −2.48958
\(527\) −19.1924 −0.836034
\(528\) 7.84038 0.341209
\(529\) −12.5977 −0.547728
\(530\) 22.2179 0.965083
\(531\) 18.3778 0.797530
\(532\) −37.7358 −1.63605
\(533\) 3.56247 0.154308
\(534\) −73.9653 −3.20079
\(535\) 9.71118 0.419851
\(536\) 44.4162 1.91849
\(537\) 36.5383 1.57674
\(538\) 62.5702 2.69759
\(539\) 59.3786 2.55762
\(540\) 8.88708 0.382439
\(541\) −24.9068 −1.07083 −0.535414 0.844590i \(-0.679844\pi\)
−0.535414 + 0.844590i \(0.679844\pi\)
\(542\) −36.6046 −1.57230
\(543\) 12.2240 0.524580
\(544\) −13.8108 −0.592131
\(545\) 2.49497 0.106873
\(546\) 37.5589 1.60737
\(547\) 26.6515 1.13954 0.569768 0.821805i \(-0.307033\pi\)
0.569768 + 0.821805i \(0.307033\pi\)
\(548\) −33.7547 −1.44193
\(549\) −25.0002 −1.06698
\(550\) −10.0588 −0.428911
\(551\) −8.66993 −0.369352
\(552\) −27.3919 −1.16588
\(553\) −33.8657 −1.44011
\(554\) 14.4800 0.615194
\(555\) 14.8310 0.629543
\(556\) 0.846420 0.0358962
\(557\) −3.92451 −0.166287 −0.0831434 0.996538i \(-0.526496\pi\)
−0.0831434 + 0.996538i \(0.526496\pi\)
\(558\) −62.2710 −2.63614
\(559\) 2.59124 0.109598
\(560\) 3.11150 0.131485
\(561\) −32.7365 −1.38214
\(562\) −51.3974 −2.16807
\(563\) −19.9387 −0.840317 −0.420159 0.907451i \(-0.638026\pi\)
−0.420159 + 0.907451i \(0.638026\pi\)
\(564\) 14.1620 0.596326
\(565\) 8.81959 0.371043
\(566\) 14.0724 0.591507
\(567\) −22.9045 −0.961899
\(568\) 34.4258 1.44447
\(569\) −22.6758 −0.950621 −0.475310 0.879818i \(-0.657664\pi\)
−0.475310 + 0.879818i \(0.657664\pi\)
\(570\) 15.0398 0.629949
\(571\) −5.36019 −0.224317 −0.112158 0.993690i \(-0.535776\pi\)
−0.112158 + 0.993690i \(0.535776\pi\)
\(572\) −19.7378 −0.825280
\(573\) −13.6946 −0.572100
\(574\) 27.9513 1.16666
\(575\) 3.22525 0.134502
\(576\) −50.2719 −2.09466
\(577\) −43.3315 −1.80391 −0.901956 0.431828i \(-0.857869\pi\)
−0.901956 + 0.431828i \(0.857869\pi\)
\(578\) 20.5241 0.853689
\(579\) 51.8480 2.15473
\(580\) 11.9703 0.497041
\(581\) 29.5907 1.22763
\(582\) −53.7254 −2.22699
\(583\) −41.5086 −1.71911
\(584\) −20.9102 −0.865270
\(585\) −5.37245 −0.222123
\(586\) −33.4274 −1.38088
\(587\) 5.08639 0.209938 0.104969 0.994476i \(-0.466526\pi\)
0.104969 + 0.994476i \(0.466526\pi\)
\(588\) 122.579 5.05506
\(589\) −16.4731 −0.678761
\(590\) −10.6793 −0.439661
\(591\) 35.3311 1.45333
\(592\) 3.83574 0.157648
\(593\) −18.9775 −0.779311 −0.389655 0.920961i \(-0.627406\pi\)
−0.389655 + 0.920961i \(0.627406\pi\)
\(594\) −26.4158 −1.08385
\(595\) −12.9917 −0.532606
\(596\) 3.23344 0.132447
\(597\) −45.4980 −1.86211
\(598\) 10.0690 0.411751
\(599\) −34.5583 −1.41201 −0.706007 0.708205i \(-0.749505\pi\)
−0.706007 + 0.708205i \(0.749505\pi\)
\(600\) −8.49294 −0.346723
\(601\) 25.0349 1.02119 0.510597 0.859820i \(-0.329424\pi\)
0.510597 + 0.859820i \(0.329424\pi\)
\(602\) 20.3309 0.828627
\(603\) −55.2236 −2.24888
\(604\) 73.0918 2.97406
\(605\) 7.79245 0.316808
\(606\) −91.1674 −3.70342
\(607\) 0.469295 0.0190481 0.00952406 0.999955i \(-0.496968\pi\)
0.00952406 + 0.999955i \(0.496968\pi\)
\(608\) −11.8539 −0.480741
\(609\) 42.5555 1.72444
\(610\) 14.5275 0.588202
\(611\) −2.12917 −0.0861370
\(612\) −38.5885 −1.55985
\(613\) −15.6484 −0.632035 −0.316017 0.948753i \(-0.602346\pi\)
−0.316017 + 0.948753i \(0.602346\pi\)
\(614\) 27.3569 1.10403
\(615\) −7.00198 −0.282347
\(616\) −63.3393 −2.55201
\(617\) −36.6104 −1.47388 −0.736939 0.675959i \(-0.763729\pi\)
−0.736939 + 0.675959i \(0.763729\pi\)
\(618\) 83.8549 3.37314
\(619\) −13.5619 −0.545097 −0.272549 0.962142i \(-0.587867\pi\)
−0.272549 + 0.962142i \(0.587867\pi\)
\(620\) 22.7439 0.913417
\(621\) 8.46993 0.339887
\(622\) −3.89800 −0.156296
\(623\) 54.8398 2.19711
\(624\) −2.43338 −0.0974132
\(625\) 1.00000 0.0400000
\(626\) 27.9323 1.11640
\(627\) −28.0982 −1.12213
\(628\) 8.79225 0.350849
\(629\) −16.0157 −0.638586
\(630\) −42.1524 −1.67939
\(631\) −7.44155 −0.296243 −0.148122 0.988969i \(-0.547323\pi\)
−0.148122 + 0.988969i \(0.547323\pi\)
\(632\) 23.9070 0.950970
\(633\) −40.0886 −1.59338
\(634\) 78.5642 3.12018
\(635\) −2.91396 −0.115637
\(636\) −85.6887 −3.39778
\(637\) −18.4290 −0.730185
\(638\) −35.5805 −1.40864
\(639\) −42.8024 −1.69324
\(640\) 19.5403 0.772400
\(641\) 30.6232 1.20954 0.604771 0.796399i \(-0.293264\pi\)
0.604771 + 0.796399i \(0.293264\pi\)
\(642\) −59.5885 −2.35177
\(643\) 30.7851 1.21405 0.607024 0.794684i \(-0.292363\pi\)
0.607024 + 0.794684i \(0.292363\pi\)
\(644\) 49.6552 1.95669
\(645\) −5.09304 −0.200538
\(646\) −16.2411 −0.638998
\(647\) −7.25823 −0.285350 −0.142675 0.989770i \(-0.545570\pi\)
−0.142675 + 0.989770i \(0.545570\pi\)
\(648\) 16.1691 0.635184
\(649\) 19.9516 0.783171
\(650\) 3.12192 0.122452
\(651\) 80.8563 3.16901
\(652\) 6.92305 0.271128
\(653\) −32.3115 −1.26445 −0.632223 0.774786i \(-0.717857\pi\)
−0.632223 + 0.774786i \(0.717857\pi\)
\(654\) −15.3093 −0.598642
\(655\) −1.90961 −0.0746146
\(656\) −1.81092 −0.0707044
\(657\) 25.9981 1.01428
\(658\) −16.7055 −0.651249
\(659\) −20.3727 −0.793606 −0.396803 0.917904i \(-0.629880\pi\)
−0.396803 + 0.917904i \(0.629880\pi\)
\(660\) 38.7944 1.51007
\(661\) −30.5661 −1.18888 −0.594441 0.804139i \(-0.702627\pi\)
−0.594441 + 0.804139i \(0.702627\pi\)
\(662\) −17.5014 −0.680212
\(663\) 10.1603 0.394593
\(664\) −20.8892 −0.810656
\(665\) −11.1509 −0.432414
\(666\) −51.9639 −2.01356
\(667\) 11.4085 0.441738
\(668\) 15.5802 0.602816
\(669\) 30.7737 1.18978
\(670\) 32.0903 1.23976
\(671\) −27.1411 −1.04777
\(672\) 58.1838 2.24449
\(673\) −3.16739 −0.122094 −0.0610469 0.998135i \(-0.519444\pi\)
−0.0610469 + 0.998135i \(0.519444\pi\)
\(674\) 55.0828 2.12171
\(675\) 2.62613 0.101080
\(676\) −37.8674 −1.45644
\(677\) 4.30938 0.165623 0.0828115 0.996565i \(-0.473610\pi\)
0.0828115 + 0.996565i \(0.473610\pi\)
\(678\) −54.1177 −2.07838
\(679\) 39.8333 1.52866
\(680\) 9.17130 0.351703
\(681\) −15.1216 −0.579461
\(682\) −67.6037 −2.58868
\(683\) 14.4689 0.553636 0.276818 0.960922i \(-0.410720\pi\)
0.276818 + 0.960922i \(0.410720\pi\)
\(684\) −33.1210 −1.26641
\(685\) −9.97449 −0.381106
\(686\) −70.7002 −2.69935
\(687\) −38.8075 −1.48060
\(688\) −1.31721 −0.0502181
\(689\) 12.8828 0.490796
\(690\) −19.7904 −0.753407
\(691\) 16.4279 0.624947 0.312474 0.949926i \(-0.398842\pi\)
0.312474 + 0.949926i \(0.398842\pi\)
\(692\) 11.0075 0.418442
\(693\) 78.7512 2.99151
\(694\) −6.94006 −0.263441
\(695\) 0.250117 0.00948747
\(696\) −30.0415 −1.13872
\(697\) 7.56126 0.286403
\(698\) −54.8691 −2.07683
\(699\) −36.3831 −1.37613
\(700\) 15.3958 0.581905
\(701\) 36.6139 1.38289 0.691443 0.722431i \(-0.256975\pi\)
0.691443 + 0.722431i \(0.256975\pi\)
\(702\) 8.19855 0.309434
\(703\) −13.7464 −0.518457
\(704\) −54.5770 −2.05695
\(705\) 4.18485 0.157611
\(706\) −68.9119 −2.59353
\(707\) 67.5938 2.54213
\(708\) 41.1874 1.54792
\(709\) 1.94397 0.0730074 0.0365037 0.999334i \(-0.488378\pi\)
0.0365037 + 0.999334i \(0.488378\pi\)
\(710\) 24.8723 0.933443
\(711\) −29.7241 −1.11474
\(712\) −38.7134 −1.45085
\(713\) 21.6763 0.811785
\(714\) 79.7178 2.98336
\(715\) −5.83252 −0.218124
\(716\) 46.7581 1.74743
\(717\) 15.1766 0.566781
\(718\) 68.2015 2.54526
\(719\) −35.6397 −1.32914 −0.664568 0.747228i \(-0.731384\pi\)
−0.664568 + 0.747228i \(0.731384\pi\)
\(720\) 2.73098 0.101778
\(721\) −62.1722 −2.31541
\(722\) 30.1470 1.12196
\(723\) 7.46618 0.277670
\(724\) 15.6430 0.581368
\(725\) 3.53723 0.131369
\(726\) −47.8150 −1.77458
\(727\) 16.2009 0.600860 0.300430 0.953804i \(-0.402870\pi\)
0.300430 + 0.953804i \(0.402870\pi\)
\(728\) 19.6583 0.728586
\(729\) −40.9374 −1.51620
\(730\) −15.1074 −0.559152
\(731\) 5.49984 0.203419
\(732\) −56.0289 −2.07089
\(733\) −51.4687 −1.90104 −0.950521 0.310661i \(-0.899450\pi\)
−0.950521 + 0.310661i \(0.899450\pi\)
\(734\) 64.6858 2.38760
\(735\) 36.2220 1.33607
\(736\) 15.5982 0.574957
\(737\) −59.9528 −2.20839
\(738\) 24.5330 0.903073
\(739\) 36.1962 1.33150 0.665749 0.746176i \(-0.268112\pi\)
0.665749 + 0.746176i \(0.268112\pi\)
\(740\) 18.9793 0.697694
\(741\) 8.72069 0.320363
\(742\) 101.079 3.71072
\(743\) 37.7260 1.38403 0.692017 0.721881i \(-0.256722\pi\)
0.692017 + 0.721881i \(0.256722\pi\)
\(744\) −57.0795 −2.09263
\(745\) 0.955480 0.0350061
\(746\) 71.7259 2.62607
\(747\) 25.9719 0.950264
\(748\) −41.8930 −1.53176
\(749\) 44.1804 1.61432
\(750\) −6.13607 −0.224058
\(751\) 50.6770 1.84923 0.924615 0.380904i \(-0.124387\pi\)
0.924615 + 0.380904i \(0.124387\pi\)
\(752\) 1.08232 0.0394683
\(753\) −40.7068 −1.48344
\(754\) 11.0429 0.402160
\(755\) 21.5986 0.786054
\(756\) 40.4312 1.47047
\(757\) −39.9617 −1.45243 −0.726217 0.687465i \(-0.758723\pi\)
−0.726217 + 0.687465i \(0.758723\pi\)
\(758\) 52.4940 1.90667
\(759\) 36.9734 1.34205
\(760\) 7.87184 0.285542
\(761\) 23.4731 0.850900 0.425450 0.904982i \(-0.360116\pi\)
0.425450 + 0.904982i \(0.360116\pi\)
\(762\) 17.8803 0.647735
\(763\) 11.3507 0.410924
\(764\) −17.5250 −0.634033
\(765\) −11.4029 −0.412272
\(766\) 5.07318 0.183302
\(767\) −6.19229 −0.223591
\(768\) −53.3152 −1.92384
\(769\) −13.6008 −0.490458 −0.245229 0.969465i \(-0.578863\pi\)
−0.245229 + 0.969465i \(0.578863\pi\)
\(770\) −45.7621 −1.64915
\(771\) −38.6820 −1.39310
\(772\) 66.3500 2.38799
\(773\) −26.7691 −0.962817 −0.481408 0.876496i \(-0.659875\pi\)
−0.481408 + 0.876496i \(0.659875\pi\)
\(774\) 17.8446 0.641411
\(775\) 6.72082 0.241419
\(776\) −28.1198 −1.00944
\(777\) 67.4730 2.42058
\(778\) 6.97658 0.250122
\(779\) 6.48992 0.232525
\(780\) −12.0404 −0.431116
\(781\) −46.4678 −1.66275
\(782\) 21.3711 0.764230
\(783\) 9.28922 0.331970
\(784\) 9.36805 0.334573
\(785\) 2.59811 0.0927304
\(786\) 11.7175 0.417950
\(787\) 15.1146 0.538776 0.269388 0.963032i \(-0.413179\pi\)
0.269388 + 0.963032i \(0.413179\pi\)
\(788\) 45.2133 1.61066
\(789\) 65.0723 2.31664
\(790\) 17.2726 0.614532
\(791\) 40.1242 1.42665
\(792\) −55.5934 −1.97542
\(793\) 8.42364 0.299132
\(794\) 46.5850 1.65324
\(795\) −25.3210 −0.898042
\(796\) −58.2239 −2.06369
\(797\) 9.34859 0.331144 0.165572 0.986198i \(-0.447053\pi\)
0.165572 + 0.986198i \(0.447053\pi\)
\(798\) 68.4228 2.42214
\(799\) −4.51911 −0.159875
\(800\) 4.83627 0.170988
\(801\) 48.1332 1.70070
\(802\) −27.8225 −0.982448
\(803\) 28.2245 0.996021
\(804\) −123.764 −4.36482
\(805\) 14.6731 0.517159
\(806\) 20.9818 0.739053
\(807\) −71.3091 −2.51020
\(808\) −47.7169 −1.67868
\(809\) 7.00155 0.246161 0.123081 0.992397i \(-0.460723\pi\)
0.123081 + 0.992397i \(0.460723\pi\)
\(810\) 11.6821 0.410466
\(811\) 4.44382 0.156044 0.0780218 0.996952i \(-0.475140\pi\)
0.0780218 + 0.996952i \(0.475140\pi\)
\(812\) 54.4584 1.91111
\(813\) 41.7170 1.46308
\(814\) −56.4139 −1.97731
\(815\) 2.04576 0.0716598
\(816\) −5.16479 −0.180804
\(817\) 4.72058 0.165152
\(818\) 25.3070 0.884838
\(819\) −24.4416 −0.854059
\(820\) −8.96045 −0.312913
\(821\) 29.7236 1.03736 0.518680 0.854968i \(-0.326423\pi\)
0.518680 + 0.854968i \(0.326423\pi\)
\(822\) 61.2042 2.13474
\(823\) −10.5331 −0.367163 −0.183581 0.983005i \(-0.558769\pi\)
−0.183581 + 0.983005i \(0.558769\pi\)
\(824\) 43.8896 1.52897
\(825\) 11.4637 0.399116
\(826\) −48.5849 −1.69049
\(827\) 2.46758 0.0858060 0.0429030 0.999079i \(-0.486339\pi\)
0.0429030 + 0.999079i \(0.486339\pi\)
\(828\) 43.5827 1.51460
\(829\) 14.3389 0.498011 0.249005 0.968502i \(-0.419896\pi\)
0.249005 + 0.968502i \(0.419896\pi\)
\(830\) −15.0922 −0.523859
\(831\) −16.5023 −0.572459
\(832\) 16.9388 0.587247
\(833\) −39.1152 −1.35526
\(834\) −1.53474 −0.0531435
\(835\) 4.60394 0.159326
\(836\) −35.9573 −1.24361
\(837\) 17.6497 0.610064
\(838\) −73.0703 −2.52417
\(839\) 28.5870 0.986932 0.493466 0.869765i \(-0.335730\pi\)
0.493466 + 0.869765i \(0.335730\pi\)
\(840\) −38.6381 −1.33314
\(841\) −16.4880 −0.568551
\(842\) −90.7821 −3.12856
\(843\) 58.5758 2.01746
\(844\) −51.3015 −1.76587
\(845\) −11.1898 −0.384940
\(846\) −14.6626 −0.504109
\(847\) 35.4513 1.21812
\(848\) −6.54874 −0.224885
\(849\) −16.0378 −0.550417
\(850\) 6.62618 0.227276
\(851\) 18.0885 0.620064
\(852\) −95.9262 −3.28638
\(853\) 0.727424 0.0249065 0.0124533 0.999922i \(-0.496036\pi\)
0.0124533 + 0.999922i \(0.496036\pi\)
\(854\) 66.0921 2.26163
\(855\) −9.78723 −0.334716
\(856\) −31.1886 −1.06600
\(857\) −52.0075 −1.77654 −0.888270 0.459321i \(-0.848093\pi\)
−0.888270 + 0.459321i \(0.848093\pi\)
\(858\) 35.7888 1.22181
\(859\) 12.3236 0.420474 0.210237 0.977650i \(-0.432576\pi\)
0.210237 + 0.977650i \(0.432576\pi\)
\(860\) −6.51757 −0.222247
\(861\) −31.8551 −1.08562
\(862\) −3.46990 −0.118185
\(863\) −15.9895 −0.544288 −0.272144 0.962257i \(-0.587733\pi\)
−0.272144 + 0.962257i \(0.587733\pi\)
\(864\) 12.7007 0.432085
\(865\) 3.25271 0.110595
\(866\) −62.5468 −2.12543
\(867\) −23.3906 −0.794386
\(868\) 103.472 3.51207
\(869\) −32.2696 −1.09467
\(870\) −21.7047 −0.735859
\(871\) 18.6072 0.630482
\(872\) −8.01289 −0.271351
\(873\) 34.9620 1.18328
\(874\) 18.3431 0.620465
\(875\) 4.54944 0.153799
\(876\) 58.2655 1.96861
\(877\) −28.3157 −0.956154 −0.478077 0.878318i \(-0.658666\pi\)
−0.478077 + 0.878318i \(0.658666\pi\)
\(878\) 9.58913 0.323617
\(879\) 38.0961 1.28495
\(880\) 2.96485 0.0999451
\(881\) 5.90164 0.198831 0.0994156 0.995046i \(-0.468303\pi\)
0.0994156 + 0.995046i \(0.468303\pi\)
\(882\) −126.912 −4.27334
\(883\) −9.69872 −0.326388 −0.163194 0.986594i \(-0.552180\pi\)
−0.163194 + 0.986594i \(0.552180\pi\)
\(884\) 13.0021 0.437309
\(885\) 12.1709 0.409119
\(886\) −8.19178 −0.275208
\(887\) −26.5324 −0.890872 −0.445436 0.895314i \(-0.646951\pi\)
−0.445436 + 0.895314i \(0.646951\pi\)
\(888\) −47.6317 −1.59841
\(889\) −13.2569 −0.444622
\(890\) −27.9701 −0.937560
\(891\) −21.8250 −0.731166
\(892\) 39.3812 1.31858
\(893\) −3.87881 −0.129799
\(894\) −5.86290 −0.196085
\(895\) 13.8170 0.461852
\(896\) 88.8976 2.96986
\(897\) −11.4753 −0.383148
\(898\) −9.29138 −0.310057
\(899\) 23.7731 0.792877
\(900\) 13.5130 0.450432
\(901\) 27.3434 0.910942
\(902\) 26.6339 0.886813
\(903\) −23.1705 −0.771065
\(904\) −28.3252 −0.942081
\(905\) 4.62251 0.153657
\(906\) −132.531 −4.40304
\(907\) 5.13863 0.170625 0.0853127 0.996354i \(-0.472811\pi\)
0.0853127 + 0.996354i \(0.472811\pi\)
\(908\) −19.3512 −0.642191
\(909\) 59.3275 1.96777
\(910\) 14.2030 0.470824
\(911\) −17.6236 −0.583896 −0.291948 0.956434i \(-0.594303\pi\)
−0.291948 + 0.956434i \(0.594303\pi\)
\(912\) −4.43300 −0.146791
\(913\) 28.1961 0.933154
\(914\) 46.8785 1.55060
\(915\) −16.5565 −0.547342
\(916\) −49.6621 −1.64088
\(917\) −8.68765 −0.286892
\(918\) 17.4012 0.574326
\(919\) −47.7484 −1.57508 −0.787538 0.616267i \(-0.788644\pi\)
−0.787538 + 0.616267i \(0.788644\pi\)
\(920\) −10.3583 −0.341502
\(921\) −31.1777 −1.02734
\(922\) −57.6941 −1.90006
\(923\) 14.4220 0.474705
\(924\) 176.493 5.80618
\(925\) 5.60838 0.184403
\(926\) 10.5860 0.347877
\(927\) −54.5689 −1.79228
\(928\) 17.1070 0.561565
\(929\) 31.7089 1.04033 0.520167 0.854064i \(-0.325870\pi\)
0.520167 + 0.854064i \(0.325870\pi\)
\(930\) −41.2394 −1.35229
\(931\) −33.5730 −1.10031
\(932\) −46.5595 −1.52511
\(933\) 4.44242 0.145438
\(934\) −54.3590 −1.77868
\(935\) −12.3794 −0.404849
\(936\) 17.2542 0.563972
\(937\) −51.9131 −1.69593 −0.847964 0.530055i \(-0.822171\pi\)
−0.847964 + 0.530055i \(0.822171\pi\)
\(938\) 145.993 4.76684
\(939\) −31.8335 −1.03885
\(940\) 5.35536 0.174673
\(941\) 27.2287 0.887629 0.443815 0.896119i \(-0.353625\pi\)
0.443815 + 0.896119i \(0.353625\pi\)
\(942\) −15.9422 −0.519424
\(943\) −8.53986 −0.278096
\(944\) 3.14774 0.102450
\(945\) 11.9474 0.388649
\(946\) 19.3727 0.629862
\(947\) 45.5752 1.48100 0.740498 0.672059i \(-0.234590\pi\)
0.740498 + 0.672059i \(0.234590\pi\)
\(948\) −66.6160 −2.16359
\(949\) −8.75990 −0.284358
\(950\) 5.68734 0.184522
\(951\) −89.5370 −2.90343
\(952\) 41.7243 1.35229
\(953\) 43.8420 1.42018 0.710091 0.704110i \(-0.248654\pi\)
0.710091 + 0.704110i \(0.248654\pi\)
\(954\) 88.7177 2.87234
\(955\) −5.17864 −0.167577
\(956\) 19.4215 0.628137
\(957\) 40.5499 1.31079
\(958\) 81.6722 2.63871
\(959\) −45.3783 −1.46534
\(960\) −33.2929 −1.07452
\(961\) 14.1694 0.457077
\(962\) 17.5089 0.564510
\(963\) 38.7775 1.24959
\(964\) 9.55449 0.307729
\(965\) 19.6064 0.631152
\(966\) −90.0352 −2.89684
\(967\) 23.8995 0.768556 0.384278 0.923217i \(-0.374450\pi\)
0.384278 + 0.923217i \(0.374450\pi\)
\(968\) −25.0264 −0.804378
\(969\) 18.5094 0.594609
\(970\) −20.3163 −0.652318
\(971\) 31.5030 1.01098 0.505489 0.862833i \(-0.331312\pi\)
0.505489 + 0.862833i \(0.331312\pi\)
\(972\) −71.7160 −2.30029
\(973\) 1.13789 0.0364791
\(974\) 23.6476 0.757718
\(975\) −3.55794 −0.113945
\(976\) −4.28200 −0.137063
\(977\) 24.9857 0.799362 0.399681 0.916654i \(-0.369121\pi\)
0.399681 + 0.916654i \(0.369121\pi\)
\(978\) −12.5529 −0.401399
\(979\) 52.2552 1.67008
\(980\) 46.3534 1.48070
\(981\) 9.96260 0.318081
\(982\) −36.8996 −1.17751
\(983\) 28.3870 0.905406 0.452703 0.891661i \(-0.350460\pi\)
0.452703 + 0.891661i \(0.350460\pi\)
\(984\) 22.4877 0.716881
\(985\) 13.3605 0.425702
\(986\) 23.4383 0.746429
\(987\) 19.0387 0.606009
\(988\) 11.1599 0.355043
\(989\) −6.21165 −0.197519
\(990\) −40.1657 −1.27655
\(991\) −14.0053 −0.444893 −0.222446 0.974945i \(-0.571404\pi\)
−0.222446 + 0.974945i \(0.571404\pi\)
\(992\) 32.5037 1.03199
\(993\) 19.9458 0.632960
\(994\) 113.155 3.58907
\(995\) −17.2051 −0.545439
\(996\) 58.2069 1.84436
\(997\) −59.2548 −1.87662 −0.938309 0.345797i \(-0.887609\pi\)
−0.938309 + 0.345797i \(0.887609\pi\)
\(998\) −7.26156 −0.229861
\(999\) 14.7283 0.465984
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 \(a_p\))