Properties

Label 4009.2.a.c.1.2
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70369 q^{2}\) \(+1.93926 q^{3}\) \(+5.30992 q^{4}\) \(+1.68888 q^{5}\) \(-5.24315 q^{6}\) \(+4.83108 q^{7}\) \(-8.94900 q^{8}\) \(+0.760725 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70369 q^{2}\) \(+1.93926 q^{3}\) \(+5.30992 q^{4}\) \(+1.68888 q^{5}\) \(-5.24315 q^{6}\) \(+4.83108 q^{7}\) \(-8.94900 q^{8}\) \(+0.760725 q^{9}\) \(-4.56619 q^{10}\) \(-3.10973 q^{11}\) \(+10.2973 q^{12}\) \(-3.06975 q^{13}\) \(-13.0617 q^{14}\) \(+3.27517 q^{15}\) \(+13.5754 q^{16}\) \(-6.37810 q^{17}\) \(-2.05676 q^{18}\) \(+1.00000 q^{19}\) \(+8.96780 q^{20}\) \(+9.36872 q^{21}\) \(+8.40773 q^{22}\) \(-5.89111 q^{23}\) \(-17.3544 q^{24}\) \(-2.14770 q^{25}\) \(+8.29965 q^{26}\) \(-4.34253 q^{27}\) \(+25.6527 q^{28}\) \(-10.1889 q^{29}\) \(-8.85503 q^{30}\) \(-7.88562 q^{31}\) \(-18.8058 q^{32}\) \(-6.03057 q^{33}\) \(+17.2444 q^{34}\) \(+8.15910 q^{35}\) \(+4.03939 q^{36}\) \(+6.79489 q^{37}\) \(-2.70369 q^{38}\) \(-5.95304 q^{39}\) \(-15.1138 q^{40}\) \(+6.98418 q^{41}\) \(-25.3301 q^{42}\) \(-6.77347 q^{43}\) \(-16.5124 q^{44}\) \(+1.28477 q^{45}\) \(+15.9277 q^{46}\) \(+12.4136 q^{47}\) \(+26.3263 q^{48}\) \(+16.3393 q^{49}\) \(+5.80670 q^{50}\) \(-12.3688 q^{51}\) \(-16.3001 q^{52}\) \(-9.18206 q^{53}\) \(+11.7409 q^{54}\) \(-5.25194 q^{55}\) \(-43.2333 q^{56}\) \(+1.93926 q^{57}\) \(+27.5475 q^{58}\) \(-3.55429 q^{59}\) \(+17.3909 q^{60}\) \(+5.04153 q^{61}\) \(+21.3202 q^{62}\) \(+3.67512 q^{63}\) \(+23.6940 q^{64}\) \(-5.18443 q^{65}\) \(+16.3048 q^{66}\) \(-3.69827 q^{67}\) \(-33.8672 q^{68}\) \(-11.4244 q^{69}\) \(-22.0596 q^{70}\) \(+0.0274348 q^{71}\) \(-6.80773 q^{72}\) \(+1.57094 q^{73}\) \(-18.3712 q^{74}\) \(-4.16494 q^{75}\) \(+5.30992 q^{76}\) \(-15.0233 q^{77}\) \(+16.0952 q^{78}\) \(-16.4961 q^{79}\) \(+22.9273 q^{80}\) \(-10.7035 q^{81}\) \(-18.8830 q^{82}\) \(+7.74228 q^{83}\) \(+49.7472 q^{84}\) \(-10.7718 q^{85}\) \(+18.3134 q^{86}\) \(-19.7588 q^{87}\) \(+27.8290 q^{88}\) \(+2.26865 q^{89}\) \(-3.47362 q^{90}\) \(-14.8302 q^{91}\) \(-31.2813 q^{92}\) \(-15.2922 q^{93}\) \(-33.5626 q^{94}\) \(+1.68888 q^{95}\) \(-36.4693 q^{96}\) \(+0.814711 q^{97}\) \(-44.1765 q^{98}\) \(-2.36565 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70369 −1.91180 −0.955898 0.293700i \(-0.905113\pi\)
−0.955898 + 0.293700i \(0.905113\pi\)
\(3\) 1.93926 1.11963 0.559816 0.828617i \(-0.310872\pi\)
0.559816 + 0.828617i \(0.310872\pi\)
\(4\) 5.30992 2.65496
\(5\) 1.68888 0.755288 0.377644 0.925951i \(-0.376734\pi\)
0.377644 + 0.925951i \(0.376734\pi\)
\(6\) −5.24315 −2.14051
\(7\) 4.83108 1.82598 0.912989 0.407985i \(-0.133769\pi\)
0.912989 + 0.407985i \(0.133769\pi\)
\(8\) −8.94900 −3.16395
\(9\) 0.760725 0.253575
\(10\) −4.56619 −1.44396
\(11\) −3.10973 −0.937618 −0.468809 0.883300i \(-0.655317\pi\)
−0.468809 + 0.883300i \(0.655317\pi\)
\(12\) 10.2973 2.97258
\(13\) −3.06975 −0.851396 −0.425698 0.904865i \(-0.639971\pi\)
−0.425698 + 0.904865i \(0.639971\pi\)
\(14\) −13.0617 −3.49089
\(15\) 3.27517 0.845645
\(16\) 13.5754 3.39386
\(17\) −6.37810 −1.54692 −0.773459 0.633847i \(-0.781475\pi\)
−0.773459 + 0.633847i \(0.781475\pi\)
\(18\) −2.05676 −0.484784
\(19\) 1.00000 0.229416
\(20\) 8.96780 2.00526
\(21\) 9.36872 2.04442
\(22\) 8.40773 1.79253
\(23\) −5.89111 −1.22838 −0.614190 0.789158i \(-0.710517\pi\)
−0.614190 + 0.789158i \(0.710517\pi\)
\(24\) −17.3544 −3.54246
\(25\) −2.14770 −0.429539
\(26\) 8.29965 1.62769
\(27\) −4.34253 −0.835721
\(28\) 25.6527 4.84790
\(29\) −10.1889 −1.89202 −0.946011 0.324134i \(-0.894927\pi\)
−0.946011 + 0.324134i \(0.894927\pi\)
\(30\) −8.85503 −1.61670
\(31\) −7.88562 −1.41630 −0.708149 0.706063i \(-0.750470\pi\)
−0.708149 + 0.706063i \(0.750470\pi\)
\(32\) −18.8058 −3.32442
\(33\) −6.03057 −1.04979
\(34\) 17.2444 2.95739
\(35\) 8.15910 1.37914
\(36\) 4.03939 0.673232
\(37\) 6.79489 1.11707 0.558536 0.829480i \(-0.311363\pi\)
0.558536 + 0.829480i \(0.311363\pi\)
\(38\) −2.70369 −0.438596
\(39\) −5.95304 −0.953250
\(40\) −15.1138 −2.38969
\(41\) 6.98418 1.09075 0.545373 0.838194i \(-0.316388\pi\)
0.545373 + 0.838194i \(0.316388\pi\)
\(42\) −25.3301 −3.90852
\(43\) −6.77347 −1.03294 −0.516472 0.856304i \(-0.672755\pi\)
−0.516472 + 0.856304i \(0.672755\pi\)
\(44\) −16.5124 −2.48934
\(45\) 1.28477 0.191522
\(46\) 15.9277 2.34841
\(47\) 12.4136 1.81071 0.905357 0.424651i \(-0.139603\pi\)
0.905357 + 0.424651i \(0.139603\pi\)
\(48\) 26.3263 3.79988
\(49\) 16.3393 2.33419
\(50\) 5.80670 0.821192
\(51\) −12.3688 −1.73198
\(52\) −16.3001 −2.26042
\(53\) −9.18206 −1.26125 −0.630627 0.776086i \(-0.717202\pi\)
−0.630627 + 0.776086i \(0.717202\pi\)
\(54\) 11.7409 1.59773
\(55\) −5.25194 −0.708172
\(56\) −43.2333 −5.77730
\(57\) 1.93926 0.256861
\(58\) 27.5475 3.61716
\(59\) −3.55429 −0.462729 −0.231365 0.972867i \(-0.574319\pi\)
−0.231365 + 0.972867i \(0.574319\pi\)
\(60\) 17.3909 2.24515
\(61\) 5.04153 0.645501 0.322751 0.946484i \(-0.395392\pi\)
0.322751 + 0.946484i \(0.395392\pi\)
\(62\) 21.3202 2.70767
\(63\) 3.67512 0.463022
\(64\) 23.6940 2.96175
\(65\) −5.18443 −0.643049
\(66\) 16.3048 2.00698
\(67\) −3.69827 −0.451816 −0.225908 0.974149i \(-0.572535\pi\)
−0.225908 + 0.974149i \(0.572535\pi\)
\(68\) −33.8672 −4.10701
\(69\) −11.4244 −1.37533
\(70\) −22.0596 −2.63663
\(71\) 0.0274348 0.00325591 0.00162795 0.999999i \(-0.499482\pi\)
0.00162795 + 0.999999i \(0.499482\pi\)
\(72\) −6.80773 −0.802298
\(73\) 1.57094 0.183864 0.0919321 0.995765i \(-0.470696\pi\)
0.0919321 + 0.995765i \(0.470696\pi\)
\(74\) −18.3712 −2.13561
\(75\) −4.16494 −0.480926
\(76\) 5.30992 0.609090
\(77\) −15.0233 −1.71207
\(78\) 16.0952 1.82242
\(79\) −16.4961 −1.85596 −0.927979 0.372632i \(-0.878456\pi\)
−0.927979 + 0.372632i \(0.878456\pi\)
\(80\) 22.9273 2.56334
\(81\) −10.7035 −1.18927
\(82\) −18.8830 −2.08528
\(83\) 7.74228 0.849826 0.424913 0.905234i \(-0.360305\pi\)
0.424913 + 0.905234i \(0.360305\pi\)
\(84\) 49.7472 5.42786
\(85\) −10.7718 −1.16837
\(86\) 18.3134 1.97478
\(87\) −19.7588 −2.11837
\(88\) 27.8290 2.96658
\(89\) 2.26865 0.240476 0.120238 0.992745i \(-0.461634\pi\)
0.120238 + 0.992745i \(0.461634\pi\)
\(90\) −3.47362 −0.366151
\(91\) −14.8302 −1.55463
\(92\) −31.2813 −3.26130
\(93\) −15.2922 −1.58573
\(94\) −33.5626 −3.46172
\(95\) 1.68888 0.173275
\(96\) −36.4693 −3.72213
\(97\) 0.814711 0.0827214 0.0413607 0.999144i \(-0.486831\pi\)
0.0413607 + 0.999144i \(0.486831\pi\)
\(98\) −44.1765 −4.46250
\(99\) −2.36565 −0.237756
\(100\) −11.4041 −1.14041
\(101\) −4.21383 −0.419291 −0.209646 0.977777i \(-0.567231\pi\)
−0.209646 + 0.977777i \(0.567231\pi\)
\(102\) 33.4413 3.31119
\(103\) 17.4058 1.71504 0.857522 0.514448i \(-0.172003\pi\)
0.857522 + 0.514448i \(0.172003\pi\)
\(104\) 27.4712 2.69377
\(105\) 15.8226 1.54413
\(106\) 24.8254 2.41126
\(107\) −17.2405 −1.66670 −0.833351 0.552745i \(-0.813581\pi\)
−0.833351 + 0.552745i \(0.813581\pi\)
\(108\) −23.0585 −2.21881
\(109\) −3.40367 −0.326012 −0.163006 0.986625i \(-0.552119\pi\)
−0.163006 + 0.986625i \(0.552119\pi\)
\(110\) 14.1996 1.35388
\(111\) 13.1770 1.25071
\(112\) 65.5841 6.19711
\(113\) 5.36054 0.504277 0.252138 0.967691i \(-0.418866\pi\)
0.252138 + 0.967691i \(0.418866\pi\)
\(114\) −5.24315 −0.491066
\(115\) −9.94935 −0.927782
\(116\) −54.1020 −5.02325
\(117\) −2.33524 −0.215893
\(118\) 9.60969 0.884644
\(119\) −30.8131 −2.82464
\(120\) −29.3095 −2.67558
\(121\) −1.32960 −0.120872
\(122\) −13.6307 −1.23407
\(123\) 13.5441 1.22123
\(124\) −41.8720 −3.76022
\(125\) −12.0716 −1.07971
\(126\) −9.93639 −0.885204
\(127\) −9.28280 −0.823715 −0.411858 0.911248i \(-0.635120\pi\)
−0.411858 + 0.911248i \(0.635120\pi\)
\(128\) −26.4497 −2.33784
\(129\) −13.1355 −1.15652
\(130\) 14.0171 1.22938
\(131\) 9.21365 0.805000 0.402500 0.915420i \(-0.368141\pi\)
0.402500 + 0.915420i \(0.368141\pi\)
\(132\) −32.0219 −2.78714
\(133\) 4.83108 0.418908
\(134\) 9.99898 0.863780
\(135\) −7.33400 −0.631210
\(136\) 57.0777 4.89437
\(137\) −0.919109 −0.0785248 −0.0392624 0.999229i \(-0.512501\pi\)
−0.0392624 + 0.999229i \(0.512501\pi\)
\(138\) 30.8880 2.62936
\(139\) 5.62081 0.476751 0.238376 0.971173i \(-0.423385\pi\)
0.238376 + 0.971173i \(0.423385\pi\)
\(140\) 43.3242 3.66156
\(141\) 24.0732 2.02733
\(142\) −0.0741750 −0.00622463
\(143\) 9.54609 0.798284
\(144\) 10.3272 0.860599
\(145\) −17.2077 −1.42902
\(146\) −4.24732 −0.351511
\(147\) 31.6862 2.61344
\(148\) 36.0803 2.96579
\(149\) −0.930135 −0.0761996 −0.0380998 0.999274i \(-0.512130\pi\)
−0.0380998 + 0.999274i \(0.512130\pi\)
\(150\) 11.2607 0.919432
\(151\) −1.42515 −0.115977 −0.0579887 0.998317i \(-0.518469\pi\)
−0.0579887 + 0.998317i \(0.518469\pi\)
\(152\) −8.94900 −0.725860
\(153\) −4.85198 −0.392260
\(154\) 40.6184 3.27313
\(155\) −13.3178 −1.06971
\(156\) −31.6102 −2.53084
\(157\) −16.4956 −1.31649 −0.658246 0.752803i \(-0.728701\pi\)
−0.658246 + 0.752803i \(0.728701\pi\)
\(158\) 44.6004 3.54821
\(159\) −17.8064 −1.41214
\(160\) −31.7606 −2.51090
\(161\) −28.4604 −2.24300
\(162\) 28.9388 2.27365
\(163\) 8.10033 0.634467 0.317233 0.948347i \(-0.397246\pi\)
0.317233 + 0.948347i \(0.397246\pi\)
\(164\) 37.0855 2.89589
\(165\) −10.1849 −0.792892
\(166\) −20.9327 −1.62469
\(167\) −9.27610 −0.717806 −0.358903 0.933375i \(-0.616849\pi\)
−0.358903 + 0.933375i \(0.616849\pi\)
\(168\) −83.8407 −6.46845
\(169\) −3.57663 −0.275125
\(170\) 29.1237 2.23368
\(171\) 0.760725 0.0581741
\(172\) −35.9666 −2.74243
\(173\) 5.72964 0.435616 0.217808 0.975992i \(-0.430109\pi\)
0.217808 + 0.975992i \(0.430109\pi\)
\(174\) 53.4217 4.04989
\(175\) −10.3757 −0.784329
\(176\) −42.2159 −3.18215
\(177\) −6.89269 −0.518086
\(178\) −6.13371 −0.459741
\(179\) −1.35140 −0.101008 −0.0505041 0.998724i \(-0.516083\pi\)
−0.0505041 + 0.998724i \(0.516083\pi\)
\(180\) 6.82203 0.508484
\(181\) 12.1641 0.904150 0.452075 0.891980i \(-0.350684\pi\)
0.452075 + 0.891980i \(0.350684\pi\)
\(182\) 40.0963 2.97213
\(183\) 9.77683 0.722724
\(184\) 52.7195 3.88653
\(185\) 11.4757 0.843712
\(186\) 41.3455 3.03160
\(187\) 19.8342 1.45042
\(188\) 65.9154 4.80738
\(189\) −20.9791 −1.52601
\(190\) −4.56619 −0.331266
\(191\) 21.4709 1.55358 0.776791 0.629759i \(-0.216846\pi\)
0.776791 + 0.629759i \(0.216846\pi\)
\(192\) 45.9488 3.31607
\(193\) −1.28063 −0.0921816 −0.0460908 0.998937i \(-0.514676\pi\)
−0.0460908 + 0.998937i \(0.514676\pi\)
\(194\) −2.20272 −0.158146
\(195\) −10.0540 −0.719978
\(196\) 86.7607 6.19719
\(197\) 21.2115 1.51126 0.755628 0.655000i \(-0.227332\pi\)
0.755628 + 0.655000i \(0.227332\pi\)
\(198\) 6.39597 0.454542
\(199\) −15.6379 −1.10854 −0.554271 0.832337i \(-0.687003\pi\)
−0.554271 + 0.832337i \(0.687003\pi\)
\(200\) 19.2197 1.35904
\(201\) −7.17191 −0.505868
\(202\) 11.3929 0.801599
\(203\) −49.2232 −3.45479
\(204\) −65.6774 −4.59834
\(205\) 11.7954 0.823827
\(206\) −47.0598 −3.27881
\(207\) −4.48151 −0.311487
\(208\) −41.6733 −2.88952
\(209\) −3.10973 −0.215104
\(210\) −42.7794 −2.95206
\(211\) 1.00000 0.0688428
\(212\) −48.7561 −3.34858
\(213\) 0.0532031 0.00364542
\(214\) 46.6129 3.18639
\(215\) −11.4396 −0.780171
\(216\) 38.8613 2.64418
\(217\) −38.0960 −2.58613
\(218\) 9.20246 0.623269
\(219\) 3.04645 0.205860
\(220\) −27.8874 −1.88017
\(221\) 19.5792 1.31704
\(222\) −35.6266 −2.39110
\(223\) 16.5049 1.10525 0.552626 0.833429i \(-0.313626\pi\)
0.552626 + 0.833429i \(0.313626\pi\)
\(224\) −90.8522 −6.07032
\(225\) −1.63381 −0.108920
\(226\) −14.4932 −0.964074
\(227\) 13.6090 0.903259 0.451629 0.892206i \(-0.350843\pi\)
0.451629 + 0.892206i \(0.350843\pi\)
\(228\) 10.2973 0.681957
\(229\) 6.67579 0.441149 0.220574 0.975370i \(-0.429207\pi\)
0.220574 + 0.975370i \(0.429207\pi\)
\(230\) 26.8999 1.77373
\(231\) −29.1342 −1.91689
\(232\) 91.1801 5.98626
\(233\) −28.3415 −1.85672 −0.928358 0.371687i \(-0.878779\pi\)
−0.928358 + 0.371687i \(0.878779\pi\)
\(234\) 6.31375 0.412743
\(235\) 20.9651 1.36761
\(236\) −18.8730 −1.22853
\(237\) −31.9903 −2.07799
\(238\) 83.3091 5.40013
\(239\) 8.59965 0.556265 0.278132 0.960543i \(-0.410285\pi\)
0.278132 + 0.960543i \(0.410285\pi\)
\(240\) 44.4619 2.87000
\(241\) −20.7898 −1.33919 −0.669594 0.742727i \(-0.733532\pi\)
−0.669594 + 0.742727i \(0.733532\pi\)
\(242\) 3.59481 0.231083
\(243\) −7.72920 −0.495829
\(244\) 26.7701 1.71378
\(245\) 27.5951 1.76299
\(246\) −36.6191 −2.33475
\(247\) −3.06975 −0.195324
\(248\) 70.5684 4.48110
\(249\) 15.0143 0.951492
\(250\) 32.6378 2.06419
\(251\) 30.1707 1.90436 0.952180 0.305538i \(-0.0988363\pi\)
0.952180 + 0.305538i \(0.0988363\pi\)
\(252\) 19.5146 1.22931
\(253\) 18.3197 1.15175
\(254\) 25.0978 1.57478
\(255\) −20.8894 −1.30814
\(256\) 24.1236 1.50773
\(257\) −8.84419 −0.551685 −0.275843 0.961203i \(-0.588957\pi\)
−0.275843 + 0.961203i \(0.588957\pi\)
\(258\) 35.5143 2.21103
\(259\) 32.8267 2.03975
\(260\) −27.5289 −1.70727
\(261\) −7.75092 −0.479770
\(262\) −24.9108 −1.53900
\(263\) 11.5914 0.714757 0.357378 0.933960i \(-0.383671\pi\)
0.357378 + 0.933960i \(0.383671\pi\)
\(264\) 53.9675 3.32147
\(265\) −15.5074 −0.952610
\(266\) −13.0617 −0.800866
\(267\) 4.39949 0.269245
\(268\) −19.6376 −1.19955
\(269\) 26.6346 1.62394 0.811972 0.583697i \(-0.198394\pi\)
0.811972 + 0.583697i \(0.198394\pi\)
\(270\) 19.8288 1.20675
\(271\) −4.54285 −0.275958 −0.137979 0.990435i \(-0.544061\pi\)
−0.137979 + 0.990435i \(0.544061\pi\)
\(272\) −86.5856 −5.25002
\(273\) −28.7596 −1.74061
\(274\) 2.48498 0.150123
\(275\) 6.67875 0.402744
\(276\) −60.6626 −3.65146
\(277\) −17.1463 −1.03022 −0.515112 0.857123i \(-0.672250\pi\)
−0.515112 + 0.857123i \(0.672250\pi\)
\(278\) −15.1969 −0.911451
\(279\) −5.99878 −0.359138
\(280\) −73.0158 −4.36353
\(281\) 27.1929 1.62219 0.811097 0.584912i \(-0.198871\pi\)
0.811097 + 0.584912i \(0.198871\pi\)
\(282\) −65.0865 −3.87585
\(283\) 8.18221 0.486382 0.243191 0.969978i \(-0.421806\pi\)
0.243191 + 0.969978i \(0.421806\pi\)
\(284\) 0.145677 0.00864431
\(285\) 3.27517 0.194004
\(286\) −25.8096 −1.52616
\(287\) 33.7411 1.99168
\(288\) −14.3060 −0.842990
\(289\) 23.6802 1.39295
\(290\) 46.5243 2.73200
\(291\) 1.57994 0.0926175
\(292\) 8.34156 0.488153
\(293\) −3.24484 −0.189566 −0.0947828 0.995498i \(-0.530216\pi\)
−0.0947828 + 0.995498i \(0.530216\pi\)
\(294\) −85.6696 −4.99635
\(295\) −6.00276 −0.349494
\(296\) −60.8074 −3.53436
\(297\) 13.5041 0.783587
\(298\) 2.51479 0.145678
\(299\) 18.0842 1.04584
\(300\) −22.1155 −1.27684
\(301\) −32.7232 −1.88613
\(302\) 3.85317 0.221725
\(303\) −8.17170 −0.469452
\(304\) 13.5754 0.778605
\(305\) 8.51452 0.487540
\(306\) 13.1182 0.749920
\(307\) −13.3760 −0.763408 −0.381704 0.924285i \(-0.624663\pi\)
−0.381704 + 0.924285i \(0.624663\pi\)
\(308\) −79.7728 −4.54548
\(309\) 33.7543 1.92022
\(310\) 36.0072 2.04507
\(311\) −14.1492 −0.802327 −0.401163 0.916007i \(-0.631394\pi\)
−0.401163 + 0.916007i \(0.631394\pi\)
\(312\) 53.2738 3.01603
\(313\) −14.3166 −0.809219 −0.404610 0.914489i \(-0.632593\pi\)
−0.404610 + 0.914489i \(0.632593\pi\)
\(314\) 44.5989 2.51686
\(315\) 6.20683 0.349715
\(316\) −87.5932 −4.92750
\(317\) 1.13777 0.0639033 0.0319517 0.999489i \(-0.489828\pi\)
0.0319517 + 0.999489i \(0.489828\pi\)
\(318\) 48.1429 2.69972
\(319\) 31.6846 1.77399
\(320\) 40.0163 2.23698
\(321\) −33.4338 −1.86609
\(322\) 76.9481 4.28815
\(323\) −6.37810 −0.354887
\(324\) −56.8346 −3.15748
\(325\) 6.59290 0.365708
\(326\) −21.9008 −1.21297
\(327\) −6.60060 −0.365014
\(328\) −62.5014 −3.45106
\(329\) 59.9713 3.30632
\(330\) 27.5367 1.51585
\(331\) 27.0806 1.48849 0.744243 0.667909i \(-0.232810\pi\)
0.744243 + 0.667909i \(0.232810\pi\)
\(332\) 41.1109 2.25626
\(333\) 5.16904 0.283262
\(334\) 25.0797 1.37230
\(335\) −6.24593 −0.341251
\(336\) 127.185 6.93849
\(337\) −17.7083 −0.964634 −0.482317 0.875997i \(-0.660205\pi\)
−0.482317 + 0.875997i \(0.660205\pi\)
\(338\) 9.67008 0.525983
\(339\) 10.3955 0.564604
\(340\) −57.1976 −3.10197
\(341\) 24.5221 1.32795
\(342\) −2.05676 −0.111217
\(343\) 45.1191 2.43620
\(344\) 60.6158 3.26819
\(345\) −19.2944 −1.03877
\(346\) −15.4912 −0.832810
\(347\) 8.60374 0.461873 0.230937 0.972969i \(-0.425821\pi\)
0.230937 + 0.972969i \(0.425821\pi\)
\(348\) −104.918 −5.62419
\(349\) −24.3516 −1.30351 −0.651755 0.758430i \(-0.725967\pi\)
−0.651755 + 0.758430i \(0.725967\pi\)
\(350\) 28.0526 1.49948
\(351\) 13.3305 0.711529
\(352\) 58.4808 3.11704
\(353\) −1.22951 −0.0654402 −0.0327201 0.999465i \(-0.510417\pi\)
−0.0327201 + 0.999465i \(0.510417\pi\)
\(354\) 18.6357 0.990475
\(355\) 0.0463339 0.00245915
\(356\) 12.0463 0.638455
\(357\) −59.7546 −3.16255
\(358\) 3.65376 0.193107
\(359\) −0.967710 −0.0510738 −0.0255369 0.999674i \(-0.508130\pi\)
−0.0255369 + 0.999674i \(0.508130\pi\)
\(360\) −11.4974 −0.605967
\(361\) 1.00000 0.0526316
\(362\) −32.8879 −1.72855
\(363\) −2.57843 −0.135333
\(364\) −78.7473 −4.12748
\(365\) 2.65312 0.138871
\(366\) −26.4335 −1.38170
\(367\) 15.4235 0.805099 0.402550 0.915398i \(-0.368124\pi\)
0.402550 + 0.915398i \(0.368124\pi\)
\(368\) −79.9744 −4.16896
\(369\) 5.31304 0.276586
\(370\) −31.0268 −1.61300
\(371\) −44.3593 −2.30302
\(372\) −81.2007 −4.21006
\(373\) 20.8775 1.08100 0.540498 0.841345i \(-0.318236\pi\)
0.540498 + 0.841345i \(0.318236\pi\)
\(374\) −53.6254 −2.77290
\(375\) −23.4099 −1.20888
\(376\) −111.090 −5.72901
\(377\) 31.2772 1.61086
\(378\) 56.7210 2.91741
\(379\) 21.2132 1.08965 0.544824 0.838550i \(-0.316596\pi\)
0.544824 + 0.838550i \(0.316596\pi\)
\(380\) 8.96780 0.460039
\(381\) −18.0018 −0.922258
\(382\) −58.0507 −2.97013
\(383\) −36.6112 −1.87075 −0.935373 0.353663i \(-0.884936\pi\)
−0.935373 + 0.353663i \(0.884936\pi\)
\(384\) −51.2928 −2.61752
\(385\) −25.3726 −1.29311
\(386\) 3.46242 0.176232
\(387\) −5.15275 −0.261929
\(388\) 4.32605 0.219622
\(389\) −9.77670 −0.495698 −0.247849 0.968799i \(-0.579724\pi\)
−0.247849 + 0.968799i \(0.579724\pi\)
\(390\) 27.1827 1.37645
\(391\) 37.5741 1.90020
\(392\) −146.221 −7.38527
\(393\) 17.8676 0.901304
\(394\) −57.3493 −2.88921
\(395\) −27.8599 −1.40178
\(396\) −12.5614 −0.631235
\(397\) 11.3260 0.568438 0.284219 0.958759i \(-0.408266\pi\)
0.284219 + 0.958759i \(0.408266\pi\)
\(398\) 42.2800 2.11930
\(399\) 9.36872 0.469022
\(400\) −29.1560 −1.45780
\(401\) −22.0850 −1.10287 −0.551436 0.834217i \(-0.685920\pi\)
−0.551436 + 0.834217i \(0.685920\pi\)
\(402\) 19.3906 0.967115
\(403\) 24.2069 1.20583
\(404\) −22.3751 −1.11320
\(405\) −18.0768 −0.898245
\(406\) 133.084 6.60485
\(407\) −21.1302 −1.04739
\(408\) 110.688 5.47989
\(409\) −10.8790 −0.537931 −0.268966 0.963150i \(-0.586682\pi\)
−0.268966 + 0.963150i \(0.586682\pi\)
\(410\) −31.8911 −1.57499
\(411\) −1.78239 −0.0879188
\(412\) 92.4234 4.55338
\(413\) −17.1711 −0.844933
\(414\) 12.1166 0.595499
\(415\) 13.0758 0.641863
\(416\) 57.7290 2.83040
\(417\) 10.9002 0.533786
\(418\) 8.40773 0.411236
\(419\) −25.5771 −1.24952 −0.624762 0.780815i \(-0.714804\pi\)
−0.624762 + 0.780815i \(0.714804\pi\)
\(420\) 84.0168 4.09960
\(421\) −7.61403 −0.371085 −0.185543 0.982636i \(-0.559404\pi\)
−0.185543 + 0.982636i \(0.559404\pi\)
\(422\) −2.70369 −0.131613
\(423\) 9.44336 0.459152
\(424\) 82.1703 3.99054
\(425\) 13.6982 0.664462
\(426\) −0.143845 −0.00696929
\(427\) 24.3560 1.17867
\(428\) −91.5457 −4.42503
\(429\) 18.5123 0.893784
\(430\) 30.9290 1.49153
\(431\) 1.00617 0.0484657 0.0242329 0.999706i \(-0.492286\pi\)
0.0242329 + 0.999706i \(0.492286\pi\)
\(432\) −58.9518 −2.83632
\(433\) −21.3721 −1.02708 −0.513540 0.858066i \(-0.671666\pi\)
−0.513540 + 0.858066i \(0.671666\pi\)
\(434\) 103.000 4.94415
\(435\) −33.3702 −1.59998
\(436\) −18.0732 −0.865551
\(437\) −5.89111 −0.281810
\(438\) −8.23666 −0.393563
\(439\) −14.3007 −0.682536 −0.341268 0.939966i \(-0.610856\pi\)
−0.341268 + 0.939966i \(0.610856\pi\)
\(440\) 46.9997 2.24062
\(441\) 12.4297 0.591893
\(442\) −52.9360 −2.51791
\(443\) −0.899710 −0.0427465 −0.0213732 0.999772i \(-0.506804\pi\)
−0.0213732 + 0.999772i \(0.506804\pi\)
\(444\) 69.9691 3.32059
\(445\) 3.83146 0.181629
\(446\) −44.6242 −2.11302
\(447\) −1.80377 −0.0853155
\(448\) 114.468 5.40809
\(449\) 6.11687 0.288673 0.144336 0.989529i \(-0.453895\pi\)
0.144336 + 0.989529i \(0.453895\pi\)
\(450\) 4.41730 0.208234
\(451\) −21.7189 −1.02270
\(452\) 28.4640 1.33884
\(453\) −2.76374 −0.129852
\(454\) −36.7944 −1.72685
\(455\) −25.0464 −1.17419
\(456\) −17.3544 −0.812696
\(457\) 23.3192 1.09083 0.545413 0.838168i \(-0.316373\pi\)
0.545413 + 0.838168i \(0.316373\pi\)
\(458\) −18.0493 −0.843387
\(459\) 27.6971 1.29279
\(460\) −52.8303 −2.46323
\(461\) 6.24650 0.290928 0.145464 0.989364i \(-0.453532\pi\)
0.145464 + 0.989364i \(0.453532\pi\)
\(462\) 78.7696 3.66470
\(463\) 12.8265 0.596098 0.298049 0.954551i \(-0.403664\pi\)
0.298049 + 0.954551i \(0.403664\pi\)
\(464\) −138.318 −6.42126
\(465\) −25.8267 −1.19769
\(466\) 76.6267 3.54966
\(467\) 4.93835 0.228520 0.114260 0.993451i \(-0.463550\pi\)
0.114260 + 0.993451i \(0.463550\pi\)
\(468\) −12.3999 −0.573187
\(469\) −17.8667 −0.825006
\(470\) −56.6830 −2.61459
\(471\) −31.9892 −1.47399
\(472\) 31.8073 1.46405
\(473\) 21.0637 0.968508
\(474\) 86.4916 3.97269
\(475\) −2.14770 −0.0985431
\(476\) −163.615 −7.49930
\(477\) −6.98503 −0.319822
\(478\) −23.2508 −1.06346
\(479\) −2.97377 −0.135875 −0.0679374 0.997690i \(-0.521642\pi\)
−0.0679374 + 0.997690i \(0.521642\pi\)
\(480\) −61.5920 −2.81128
\(481\) −20.8586 −0.951071
\(482\) 56.2091 2.56025
\(483\) −55.1921 −2.51133
\(484\) −7.06006 −0.320912
\(485\) 1.37595 0.0624785
\(486\) 20.8973 0.947923
\(487\) −14.6507 −0.663888 −0.331944 0.943299i \(-0.607704\pi\)
−0.331944 + 0.943299i \(0.607704\pi\)
\(488\) −45.1166 −2.04233
\(489\) 15.7086 0.710369
\(490\) −74.6086 −3.37047
\(491\) −16.8368 −0.759835 −0.379918 0.925020i \(-0.624048\pi\)
−0.379918 + 0.925020i \(0.624048\pi\)
\(492\) 71.9183 3.24233
\(493\) 64.9856 2.92680
\(494\) 8.29965 0.373419
\(495\) −3.99529 −0.179575
\(496\) −107.051 −4.80672
\(497\) 0.132540 0.00594521
\(498\) −40.5939 −1.81906
\(499\) 28.0698 1.25657 0.628287 0.777981i \(-0.283756\pi\)
0.628287 + 0.777981i \(0.283756\pi\)
\(500\) −64.0992 −2.86660
\(501\) −17.9888 −0.803678
\(502\) −81.5722 −3.64075
\(503\) 26.3219 1.17364 0.586818 0.809719i \(-0.300381\pi\)
0.586818 + 0.809719i \(0.300381\pi\)
\(504\) −32.8887 −1.46498
\(505\) −7.11663 −0.316686
\(506\) −49.5308 −2.20191
\(507\) −6.93601 −0.308039
\(508\) −49.2910 −2.18693
\(509\) −14.2330 −0.630865 −0.315432 0.948948i \(-0.602150\pi\)
−0.315432 + 0.948948i \(0.602150\pi\)
\(510\) 56.4783 2.50090
\(511\) 7.58932 0.335732
\(512\) −12.3233 −0.544620
\(513\) −4.34253 −0.191728
\(514\) 23.9119 1.05471
\(515\) 29.3962 1.29535
\(516\) −69.7486 −3.07051
\(517\) −38.6030 −1.69776
\(518\) −88.7530 −3.89958
\(519\) 11.1113 0.487730
\(520\) 46.3955 2.03458
\(521\) −23.6952 −1.03811 −0.519053 0.854742i \(-0.673715\pi\)
−0.519053 + 0.854742i \(0.673715\pi\)
\(522\) 20.9561 0.917221
\(523\) −19.8050 −0.866010 −0.433005 0.901391i \(-0.642547\pi\)
−0.433005 + 0.901391i \(0.642547\pi\)
\(524\) 48.9238 2.13724
\(525\) −20.1212 −0.878160
\(526\) −31.3395 −1.36647
\(527\) 50.2953 2.19090
\(528\) −81.8676 −3.56283
\(529\) 11.7051 0.508920
\(530\) 41.9271 1.82120
\(531\) −2.70384 −0.117337
\(532\) 25.6527 1.11218
\(533\) −21.4397 −0.928656
\(534\) −11.8949 −0.514741
\(535\) −29.1171 −1.25884
\(536\) 33.0959 1.42952
\(537\) −2.62071 −0.113092
\(538\) −72.0118 −3.10465
\(539\) −50.8109 −2.18858
\(540\) −38.9430 −1.67584
\(541\) −0.823610 −0.0354098 −0.0177049 0.999843i \(-0.505636\pi\)
−0.0177049 + 0.999843i \(0.505636\pi\)
\(542\) 12.2824 0.527576
\(543\) 23.5893 1.01231
\(544\) 119.945 5.14261
\(545\) −5.74838 −0.246233
\(546\) 77.7570 3.32769
\(547\) −9.33900 −0.399307 −0.199653 0.979867i \(-0.563982\pi\)
−0.199653 + 0.979867i \(0.563982\pi\)
\(548\) −4.88040 −0.208480
\(549\) 3.83522 0.163683
\(550\) −18.0573 −0.769964
\(551\) −10.1889 −0.434060
\(552\) 102.237 4.35149
\(553\) −79.6941 −3.38894
\(554\) 46.3584 1.96958
\(555\) 22.2544 0.944647
\(556\) 29.8461 1.26576
\(557\) 7.81568 0.331161 0.165580 0.986196i \(-0.447050\pi\)
0.165580 + 0.986196i \(0.447050\pi\)
\(558\) 16.2188 0.686598
\(559\) 20.7929 0.879445
\(560\) 110.763 4.68061
\(561\) 38.4636 1.62393
\(562\) −73.5212 −3.10130
\(563\) 3.82521 0.161213 0.0806067 0.996746i \(-0.474314\pi\)
0.0806067 + 0.996746i \(0.474314\pi\)
\(564\) 127.827 5.38249
\(565\) 9.05328 0.380875
\(566\) −22.1221 −0.929862
\(567\) −51.7093 −2.17159
\(568\) −0.245514 −0.0103015
\(569\) −40.5066 −1.69813 −0.849063 0.528291i \(-0.822833\pi\)
−0.849063 + 0.528291i \(0.822833\pi\)
\(570\) −8.85503 −0.370896
\(571\) −11.6873 −0.489099 −0.244549 0.969637i \(-0.578640\pi\)
−0.244549 + 0.969637i \(0.578640\pi\)
\(572\) 50.6890 2.11941
\(573\) 41.6377 1.73944
\(574\) −91.2255 −3.80768
\(575\) 12.6523 0.527638
\(576\) 18.0246 0.751026
\(577\) 6.50862 0.270958 0.135479 0.990780i \(-0.456743\pi\)
0.135479 + 0.990780i \(0.456743\pi\)
\(578\) −64.0239 −2.66304
\(579\) −2.48347 −0.103209
\(580\) −91.3716 −3.79400
\(581\) 37.4036 1.55176
\(582\) −4.27165 −0.177066
\(583\) 28.5537 1.18257
\(584\) −14.0583 −0.581737
\(585\) −3.94393 −0.163061
\(586\) 8.77303 0.362411
\(587\) −2.69292 −0.111149 −0.0555743 0.998455i \(-0.517699\pi\)
−0.0555743 + 0.998455i \(0.517699\pi\)
\(588\) 168.251 6.93857
\(589\) −7.88562 −0.324921
\(590\) 16.2296 0.668161
\(591\) 41.1346 1.69205
\(592\) 92.2436 3.79119
\(593\) −42.8992 −1.76166 −0.880829 0.473434i \(-0.843014\pi\)
−0.880829 + 0.473434i \(0.843014\pi\)
\(594\) −36.5109 −1.49806
\(595\) −52.0396 −2.13341
\(596\) −4.93895 −0.202307
\(597\) −30.3259 −1.24116
\(598\) −48.8941 −1.99943
\(599\) −26.9412 −1.10079 −0.550394 0.834905i \(-0.685522\pi\)
−0.550394 + 0.834905i \(0.685522\pi\)
\(600\) 37.2721 1.52163
\(601\) −27.3720 −1.11653 −0.558264 0.829663i \(-0.688532\pi\)
−0.558264 + 0.829663i \(0.688532\pi\)
\(602\) 88.4733 3.60590
\(603\) −2.81337 −0.114569
\(604\) −7.56746 −0.307915
\(605\) −2.24552 −0.0912935
\(606\) 22.0937 0.897496
\(607\) −6.84939 −0.278008 −0.139004 0.990292i \(-0.544390\pi\)
−0.139004 + 0.990292i \(0.544390\pi\)
\(608\) −18.8058 −0.762675
\(609\) −95.4565 −3.86809
\(610\) −23.0206 −0.932076
\(611\) −38.1068 −1.54163
\(612\) −25.7637 −1.04143
\(613\) 39.6831 1.60279 0.801393 0.598138i \(-0.204093\pi\)
0.801393 + 0.598138i \(0.204093\pi\)
\(614\) 36.1645 1.45948
\(615\) 22.8744 0.922383
\(616\) 134.444 5.41690
\(617\) −3.24438 −0.130614 −0.0653068 0.997865i \(-0.520803\pi\)
−0.0653068 + 0.997865i \(0.520803\pi\)
\(618\) −91.2612 −3.67106
\(619\) −33.6128 −1.35101 −0.675506 0.737355i \(-0.736075\pi\)
−0.675506 + 0.737355i \(0.736075\pi\)
\(620\) −70.7167 −2.84005
\(621\) 25.5823 1.02658
\(622\) 38.2550 1.53388
\(623\) 10.9600 0.439104
\(624\) −80.8152 −3.23520
\(625\) −9.64891 −0.385956
\(626\) 38.7075 1.54706
\(627\) −6.03057 −0.240838
\(628\) −87.5903 −3.49523
\(629\) −43.3385 −1.72802
\(630\) −16.7813 −0.668584
\(631\) 21.0771 0.839065 0.419533 0.907740i \(-0.362194\pi\)
0.419533 + 0.907740i \(0.362194\pi\)
\(632\) 147.624 5.87216
\(633\) 1.93926 0.0770786
\(634\) −3.07616 −0.122170
\(635\) −15.6775 −0.622143
\(636\) −94.5506 −3.74918
\(637\) −50.1577 −1.98732
\(638\) −85.6651 −3.39151
\(639\) 0.0208703 0.000825617 0
\(640\) −44.6702 −1.76575
\(641\) 18.3880 0.726282 0.363141 0.931734i \(-0.381704\pi\)
0.363141 + 0.931734i \(0.381704\pi\)
\(642\) 90.3945 3.56759
\(643\) 25.2660 0.996393 0.498197 0.867064i \(-0.333996\pi\)
0.498197 + 0.867064i \(0.333996\pi\)
\(644\) −151.123 −5.95507
\(645\) −22.1843 −0.873504
\(646\) 17.2444 0.678472
\(647\) −34.5925 −1.35997 −0.679987 0.733224i \(-0.738014\pi\)
−0.679987 + 0.733224i \(0.738014\pi\)
\(648\) 95.7854 3.76281
\(649\) 11.0529 0.433863
\(650\) −17.8251 −0.699159
\(651\) −73.8781 −2.89551
\(652\) 43.0122 1.68449
\(653\) 47.1087 1.84350 0.921752 0.387779i \(-0.126758\pi\)
0.921752 + 0.387779i \(0.126758\pi\)
\(654\) 17.8459 0.697832
\(655\) 15.5607 0.608007
\(656\) 94.8133 3.70184
\(657\) 1.19505 0.0466234
\(658\) −162.144 −6.32101
\(659\) −31.5202 −1.22785 −0.613927 0.789363i \(-0.710411\pi\)
−0.613927 + 0.789363i \(0.710411\pi\)
\(660\) −54.0809 −2.10510
\(661\) −39.7020 −1.54423 −0.772114 0.635484i \(-0.780801\pi\)
−0.772114 + 0.635484i \(0.780801\pi\)
\(662\) −73.2176 −2.84568
\(663\) 37.9691 1.47460
\(664\) −69.2857 −2.68881
\(665\) 8.15910 0.316396
\(666\) −13.9755 −0.541538
\(667\) 60.0236 2.32412
\(668\) −49.2554 −1.90575
\(669\) 32.0074 1.23748
\(670\) 16.8870 0.652403
\(671\) −15.6778 −0.605234
\(672\) −176.186 −6.79652
\(673\) 44.3464 1.70943 0.854714 0.519100i \(-0.173733\pi\)
0.854714 + 0.519100i \(0.173733\pi\)
\(674\) 47.8778 1.84418
\(675\) 9.32645 0.358975
\(676\) −18.9916 −0.730447
\(677\) −4.79223 −0.184180 −0.0920902 0.995751i \(-0.529355\pi\)
−0.0920902 + 0.995751i \(0.529355\pi\)
\(678\) −28.1061 −1.07941
\(679\) 3.93594 0.151047
\(680\) 96.3971 3.69666
\(681\) 26.3913 1.01132
\(682\) −66.3001 −2.53876
\(683\) 10.5939 0.405364 0.202682 0.979245i \(-0.435034\pi\)
0.202682 + 0.979245i \(0.435034\pi\)
\(684\) 4.03939 0.154450
\(685\) −1.55226 −0.0593089
\(686\) −121.988 −4.65752
\(687\) 12.9461 0.493924
\(688\) −91.9529 −3.50567
\(689\) 28.1867 1.07383
\(690\) 52.1659 1.98592
\(691\) −36.1210 −1.37411 −0.687054 0.726607i \(-0.741096\pi\)
−0.687054 + 0.726607i \(0.741096\pi\)
\(692\) 30.4240 1.15655
\(693\) −11.4286 −0.434138
\(694\) −23.2618 −0.883007
\(695\) 9.49286 0.360085
\(696\) 176.822 6.70241
\(697\) −44.5458 −1.68729
\(698\) 65.8390 2.49204
\(699\) −54.9616 −2.07884
\(700\) −55.0942 −2.08236
\(701\) 13.5453 0.511598 0.255799 0.966730i \(-0.417661\pi\)
0.255799 + 0.966730i \(0.417661\pi\)
\(702\) −36.0415 −1.36030
\(703\) 6.79489 0.256274
\(704\) −73.6819 −2.77699
\(705\) 40.6567 1.53122
\(706\) 3.32421 0.125108
\(707\) −20.3573 −0.765616
\(708\) −36.5997 −1.37550
\(709\) 12.1210 0.455215 0.227608 0.973753i \(-0.426910\pi\)
0.227608 + 0.973753i \(0.426910\pi\)
\(710\) −0.125272 −0.00470139
\(711\) −12.5490 −0.470625
\(712\) −20.3021 −0.760854
\(713\) 46.4550 1.73975
\(714\) 161.558 6.04615
\(715\) 16.1222 0.602935
\(716\) −7.17582 −0.268173
\(717\) 16.6769 0.622812
\(718\) 2.61639 0.0976426
\(719\) 34.8151 1.29838 0.649192 0.760625i \(-0.275107\pi\)
0.649192 + 0.760625i \(0.275107\pi\)
\(720\) 17.4413 0.650000
\(721\) 84.0888 3.13163
\(722\) −2.70369 −0.100621
\(723\) −40.3168 −1.49940
\(724\) 64.5904 2.40048
\(725\) 21.8826 0.812698
\(726\) 6.97127 0.258728
\(727\) 23.6593 0.877474 0.438737 0.898616i \(-0.355426\pi\)
0.438737 + 0.898616i \(0.355426\pi\)
\(728\) 132.716 4.91877
\(729\) 17.1215 0.634129
\(730\) −7.17320 −0.265492
\(731\) 43.2019 1.59788
\(732\) 51.9142 1.91880
\(733\) 5.18279 0.191431 0.0957153 0.995409i \(-0.469486\pi\)
0.0957153 + 0.995409i \(0.469486\pi\)
\(734\) −41.7003 −1.53918
\(735\) 53.5141 1.97390
\(736\) 110.787 4.08366
\(737\) 11.5006 0.423631
\(738\) −14.3648 −0.528775
\(739\) −39.7187 −1.46108 −0.730538 0.682872i \(-0.760731\pi\)
−0.730538 + 0.682872i \(0.760731\pi\)
\(740\) 60.9352 2.24002
\(741\) −5.95304 −0.218690
\(742\) 119.934 4.40290
\(743\) −12.1228 −0.444741 −0.222370 0.974962i \(-0.571379\pi\)
−0.222370 + 0.974962i \(0.571379\pi\)
\(744\) 136.850 5.01718
\(745\) −1.57088 −0.0575527
\(746\) −56.4463 −2.06665
\(747\) 5.88975 0.215495
\(748\) 105.318 3.85080
\(749\) −83.2902 −3.04336
\(750\) 63.2931 2.31114
\(751\) 24.8330 0.906171 0.453085 0.891467i \(-0.350323\pi\)
0.453085 + 0.891467i \(0.350323\pi\)
\(752\) 168.521 6.14532
\(753\) 58.5089 2.13218
\(754\) −84.5639 −3.07964
\(755\) −2.40691 −0.0875963
\(756\) −111.398 −4.05149
\(757\) 13.3690 0.485906 0.242953 0.970038i \(-0.421884\pi\)
0.242953 + 0.970038i \(0.421884\pi\)
\(758\) −57.3538 −2.08318
\(759\) 35.5267 1.28954
\(760\) −15.1138 −0.548233
\(761\) −19.9923 −0.724720 −0.362360 0.932038i \(-0.618029\pi\)
−0.362360 + 0.932038i \(0.618029\pi\)
\(762\) 48.6711 1.76317
\(763\) −16.4434 −0.595291
\(764\) 114.009 4.12470
\(765\) −8.19440 −0.296269
\(766\) 98.9853 3.57648
\(767\) 10.9108 0.393966
\(768\) 46.7819 1.68810
\(769\) −3.48179 −0.125557 −0.0627784 0.998027i \(-0.519996\pi\)
−0.0627784 + 0.998027i \(0.519996\pi\)
\(770\) 68.5995 2.47215
\(771\) −17.1512 −0.617684
\(772\) −6.80004 −0.244739
\(773\) 19.6712 0.707523 0.353761 0.935336i \(-0.384903\pi\)
0.353761 + 0.935336i \(0.384903\pi\)
\(774\) 13.9314 0.500755
\(775\) 16.9359 0.608356
\(776\) −7.29085 −0.261726
\(777\) 63.6594 2.28377
\(778\) 26.4331 0.947674
\(779\) 6.98418 0.250234
\(780\) −53.3857 −1.91152
\(781\) −0.0853146 −0.00305280
\(782\) −101.589 −3.63280
\(783\) 44.2454 1.58120
\(784\) 221.814 7.92193
\(785\) −27.8590 −0.994331
\(786\) −48.3085 −1.72311
\(787\) 14.6941 0.523787 0.261893 0.965097i \(-0.415653\pi\)
0.261893 + 0.965097i \(0.415653\pi\)
\(788\) 112.631 4.01233
\(789\) 22.4787 0.800264
\(790\) 75.3245 2.67992
\(791\) 25.8972 0.920798
\(792\) 21.1702 0.752250
\(793\) −15.4762 −0.549577
\(794\) −30.6221 −1.08674
\(795\) −30.0728 −1.06657
\(796\) −83.0361 −2.94314
\(797\) −27.8038 −0.984860 −0.492430 0.870352i \(-0.663891\pi\)
−0.492430 + 0.870352i \(0.663891\pi\)
\(798\) −25.3301 −0.896675
\(799\) −79.1754 −2.80103
\(800\) 40.3891 1.42797
\(801\) 1.72582 0.0609787
\(802\) 59.7109 2.10846
\(803\) −4.88518 −0.172394
\(804\) −38.0823 −1.34306
\(805\) −48.0661 −1.69411
\(806\) −65.4478 −2.30530
\(807\) 51.6515 1.81822
\(808\) 37.7095 1.32662
\(809\) −1.19402 −0.0419797 −0.0209898 0.999780i \(-0.506682\pi\)
−0.0209898 + 0.999780i \(0.506682\pi\)
\(810\) 48.8741 1.71726
\(811\) −26.3752 −0.926157 −0.463078 0.886317i \(-0.653255\pi\)
−0.463078 + 0.886317i \(0.653255\pi\)
\(812\) −261.371 −9.17234
\(813\) −8.80976 −0.308972
\(814\) 57.1296 2.00239
\(815\) 13.6805 0.479206
\(816\) −167.912 −5.87809
\(817\) −6.77347 −0.236974
\(818\) 29.4134 1.02841
\(819\) −11.2817 −0.394215
\(820\) 62.6327 2.18723
\(821\) −4.05064 −0.141368 −0.0706841 0.997499i \(-0.522518\pi\)
−0.0706841 + 0.997499i \(0.522518\pi\)
\(822\) 4.81903 0.168083
\(823\) 46.8677 1.63371 0.816853 0.576846i \(-0.195717\pi\)
0.816853 + 0.576846i \(0.195717\pi\)
\(824\) −155.764 −5.42631
\(825\) 12.9518 0.450925
\(826\) 46.4252 1.61534
\(827\) 3.72316 0.129467 0.0647335 0.997903i \(-0.479380\pi\)
0.0647335 + 0.997903i \(0.479380\pi\)
\(828\) −23.7965 −0.826985
\(829\) −44.3216 −1.53935 −0.769677 0.638434i \(-0.779583\pi\)
−0.769677 + 0.638434i \(0.779583\pi\)
\(830\) −35.3527 −1.22711
\(831\) −33.2512 −1.15347
\(832\) −72.7347 −2.52162
\(833\) −104.214 −3.61080
\(834\) −29.4708 −1.02049
\(835\) −15.6662 −0.542151
\(836\) −16.5124 −0.571094
\(837\) 34.2436 1.18363
\(838\) 69.1525 2.38883
\(839\) −5.24491 −0.181075 −0.0905373 0.995893i \(-0.528858\pi\)
−0.0905373 + 0.995893i \(0.528858\pi\)
\(840\) −141.596 −4.88554
\(841\) 74.8127 2.57975
\(842\) 20.5860 0.709439
\(843\) 52.7341 1.81626
\(844\) 5.30992 0.182775
\(845\) −6.04048 −0.207799
\(846\) −25.5319 −0.877805
\(847\) −6.42339 −0.220710
\(848\) −124.651 −4.28052
\(849\) 15.8674 0.544568
\(850\) −37.0357 −1.27032
\(851\) −40.0294 −1.37219
\(852\) 0.282505 0.00967845
\(853\) −17.4012 −0.595807 −0.297903 0.954596i \(-0.596287\pi\)
−0.297903 + 0.954596i \(0.596287\pi\)
\(854\) −65.8511 −2.25338
\(855\) 1.28477 0.0439382
\(856\) 154.285 5.27336
\(857\) 32.8660 1.12268 0.561340 0.827585i \(-0.310286\pi\)
0.561340 + 0.827585i \(0.310286\pi\)
\(858\) −50.0516 −1.70873
\(859\) −24.3426 −0.830558 −0.415279 0.909694i \(-0.636316\pi\)
−0.415279 + 0.909694i \(0.636316\pi\)
\(860\) −60.7432 −2.07133
\(861\) 65.4328 2.22994
\(862\) −2.72038 −0.0926565
\(863\) 7.13513 0.242883 0.121441 0.992599i \(-0.461248\pi\)
0.121441 + 0.992599i \(0.461248\pi\)
\(864\) 81.6647 2.77829
\(865\) 9.67665 0.329016
\(866\) 57.7836 1.96357
\(867\) 45.9220 1.55959
\(868\) −202.287 −6.86607
\(869\) 51.2984 1.74018
\(870\) 90.2226 3.05883
\(871\) 11.3528 0.384674
\(872\) 30.4594 1.03149
\(873\) 0.619771 0.0209761
\(874\) 15.9277 0.538763
\(875\) −58.3188 −1.97153
\(876\) 16.1764 0.546551
\(877\) 58.0896 1.96155 0.980773 0.195153i \(-0.0625203\pi\)
0.980773 + 0.195153i \(0.0625203\pi\)
\(878\) 38.6647 1.30487
\(879\) −6.29258 −0.212244
\(880\) −71.2975 −2.40344
\(881\) 32.0010 1.07814 0.539071 0.842261i \(-0.318776\pi\)
0.539071 + 0.842261i \(0.318776\pi\)
\(882\) −33.6062 −1.13158
\(883\) −26.0480 −0.876586 −0.438293 0.898832i \(-0.644417\pi\)
−0.438293 + 0.898832i \(0.644417\pi\)
\(884\) 103.964 3.49669
\(885\) −11.6409 −0.391304
\(886\) 2.43253 0.0817226
\(887\) 52.1626 1.75145 0.875725 0.482811i \(-0.160384\pi\)
0.875725 + 0.482811i \(0.160384\pi\)
\(888\) −117.921 −3.95718
\(889\) −44.8460 −1.50409
\(890\) −10.3591 −0.347237
\(891\) 33.2849 1.11509
\(892\) 87.6400 2.93440
\(893\) 12.4136 0.415406
\(894\) 4.87684 0.163106
\(895\) −2.28234 −0.0762903
\(896\) −127.780 −4.26885
\(897\) 35.0700 1.17095
\(898\) −16.5381 −0.551884
\(899\) 80.3454 2.67967
\(900\) −8.67539 −0.289180
\(901\) 58.5642 1.95105
\(902\) 58.7211 1.95520
\(903\) −63.4588 −2.11178
\(904\) −47.9715 −1.59551
\(905\) 20.5436 0.682894
\(906\) 7.47229 0.248250
\(907\) 51.0635 1.69553 0.847767 0.530368i \(-0.177946\pi\)
0.847767 + 0.530368i \(0.177946\pi\)
\(908\) 72.2626 2.39812
\(909\) −3.20556 −0.106322
\(910\) 67.7176 2.24482
\(911\) −32.5104 −1.07712 −0.538559 0.842588i \(-0.681031\pi\)
−0.538559 + 0.842588i \(0.681031\pi\)
\(912\) 26.3263 0.871751
\(913\) −24.0764 −0.796812
\(914\) −63.0478 −2.08544
\(915\) 16.5118 0.545865
\(916\) 35.4480 1.17123
\(917\) 44.5119 1.46991
\(918\) −74.8844 −2.47155
\(919\) −52.3578 −1.72712 −0.863562 0.504243i \(-0.831772\pi\)
−0.863562 + 0.504243i \(0.831772\pi\)
\(920\) 89.0367 2.93545
\(921\) −25.9395 −0.854736
\(922\) −16.8886 −0.556196
\(923\) −0.0842179 −0.00277207
\(924\) −154.700 −5.08926
\(925\) −14.5934 −0.479827
\(926\) −34.6789 −1.13962
\(927\) 13.2410 0.434892
\(928\) 191.609 6.28988
\(929\) 48.3484 1.58626 0.793129 0.609053i \(-0.208450\pi\)
0.793129 + 0.609053i \(0.208450\pi\)
\(930\) 69.8274 2.28973
\(931\) 16.3393 0.535500
\(932\) −150.491 −4.92951
\(933\) −27.4389 −0.898310
\(934\) −13.3518 −0.436883
\(935\) 33.4974 1.09548
\(936\) 20.8980 0.683074
\(937\) 25.3696 0.828788 0.414394 0.910098i \(-0.363994\pi\)
0.414394 + 0.910098i \(0.363994\pi\)
\(938\) 48.3059 1.57724
\(939\) −27.7635 −0.906028
\(940\) 111.323 3.63096
\(941\) −22.3776 −0.729489 −0.364745 0.931108i \(-0.618844\pi\)
−0.364745 + 0.931108i \(0.618844\pi\)
\(942\) 86.4888 2.81796
\(943\) −41.1445 −1.33985
\(944\) −48.2511 −1.57044
\(945\) −35.4312 −1.15258
\(946\) −56.9495 −1.85159
\(947\) 9.70100 0.315240 0.157620 0.987500i \(-0.449618\pi\)
0.157620 + 0.987500i \(0.449618\pi\)
\(948\) −169.866 −5.51699
\(949\) −4.82238 −0.156541
\(950\) 5.80670 0.188394
\(951\) 2.20642 0.0715482
\(952\) 275.747 8.93700
\(953\) −56.5303 −1.83119 −0.915597 0.402096i \(-0.868282\pi\)
−0.915597 + 0.402096i \(0.868282\pi\)
\(954\) 18.8853 0.611435
\(955\) 36.2617 1.17340
\(956\) 45.6635 1.47686
\(957\) 61.4446 1.98622
\(958\) 8.04014 0.259765
\(959\) −4.44029 −0.143384
\(960\) 77.6019 2.50459
\(961\) 31.1829 1.00590
\(962\) 56.3952 1.81825
\(963\) −13.1153 −0.422634
\(964\) −110.392 −3.55549
\(965\) −2.16282 −0.0696237
\(966\) 149.222 4.80115
\(967\) −13.2578 −0.426343 −0.213172 0.977015i \(-0.568379\pi\)
−0.213172 + 0.977015i \(0.568379\pi\)
\(968\) 11.8986 0.382434
\(969\) −12.3688 −0.397343
\(970\) −3.72013 −0.119446
\(971\) −28.1519 −0.903438 −0.451719 0.892160i \(-0.649189\pi\)
−0.451719 + 0.892160i \(0.649189\pi\)
\(972\) −41.0415 −1.31641
\(973\) 27.1546 0.870537
\(974\) 39.6110 1.26922
\(975\) 12.7853 0.409458
\(976\) 68.4410 2.19074
\(977\) −35.8616 −1.14732 −0.573658 0.819095i \(-0.694476\pi\)
−0.573658 + 0.819095i \(0.694476\pi\)
\(978\) −42.4713 −1.35808
\(979\) −7.05487 −0.225475
\(980\) 146.528 4.68067
\(981\) −2.58926 −0.0826686
\(982\) 45.5215 1.45265
\(983\) −4.65839 −0.148580 −0.0742898 0.997237i \(-0.523669\pi\)
−0.0742898 + 0.997237i \(0.523669\pi\)
\(984\) −121.206 −3.86392
\(985\) 35.8236 1.14143
\(986\) −175.701 −5.59545
\(987\) 116.300 3.70186
\(988\) −16.3001 −0.518577
\(989\) 39.9033 1.26885
\(990\) 10.8020 0.343310
\(991\) −32.7571 −1.04056 −0.520281 0.853995i \(-0.674173\pi\)
−0.520281 + 0.853995i \(0.674173\pi\)
\(992\) 148.295 4.70837
\(993\) 52.5164 1.66656
\(994\) −0.358346 −0.0113660
\(995\) −26.4105 −0.837268
\(996\) 79.7247 2.52617
\(997\) 11.5364 0.365363 0.182681 0.983172i \(-0.441522\pi\)
0.182681 + 0.983172i \(0.441522\pi\)
\(998\) −75.8918 −2.40231
\(999\) −29.5070 −0.933561
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 \(a_p\))