Properties

Label 8034.2.a.o.1.2
Level 8034
Weight 2
Character 8034.1
Self dual Yes
Analytic conductor 64.152
Analytic rank 1
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.16681\)
Character \(\chi\) = 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.61702 q^{5}\) \(+1.00000 q^{6}\) \(-0.977840 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.61702 q^{5}\) \(+1.00000 q^{6}\) \(-0.977840 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+2.61702 q^{10}\) \(-0.240785 q^{11}\) \(-1.00000 q^{12}\) \(+1.00000 q^{13}\) \(+0.977840 q^{14}\) \(+2.61702 q^{15}\) \(+1.00000 q^{16}\) \(-4.91508 q^{17}\) \(-1.00000 q^{18}\) \(-1.97784 q^{19}\) \(-2.61702 q^{20}\) \(+0.977840 q^{21}\) \(+0.240785 q^{22}\) \(-0.244868 q^{23}\) \(+1.00000 q^{24}\) \(+1.84882 q^{25}\) \(-1.00000 q^{26}\) \(-1.00000 q^{27}\) \(-0.977840 q^{28}\) \(+8.09791 q^{29}\) \(-2.61702 q^{30}\) \(-7.15427 q^{31}\) \(-1.00000 q^{32}\) \(+0.240785 q^{33}\) \(+4.91508 q^{34}\) \(+2.55903 q^{35}\) \(+1.00000 q^{36}\) \(+5.41686 q^{37}\) \(+1.97784 q^{38}\) \(-1.00000 q^{39}\) \(+2.61702 q^{40}\) \(+10.7554 q^{41}\) \(-0.977840 q^{42}\) \(-5.03820 q^{43}\) \(-0.240785 q^{44}\) \(-2.61702 q^{45}\) \(+0.244868 q^{46}\) \(+9.26343 q^{47}\) \(-1.00000 q^{48}\) \(-6.04383 q^{49}\) \(-1.84882 q^{50}\) \(+4.91508 q^{51}\) \(+1.00000 q^{52}\) \(+9.79000 q^{53}\) \(+1.00000 q^{54}\) \(+0.630140 q^{55}\) \(+0.977840 q^{56}\) \(+1.97784 q^{57}\) \(-8.09791 q^{58}\) \(-7.05375 q^{59}\) \(+2.61702 q^{60}\) \(+3.55737 q^{61}\) \(+7.15427 q^{62}\) \(-0.977840 q^{63}\) \(+1.00000 q^{64}\) \(-2.61702 q^{65}\) \(-0.240785 q^{66}\) \(-14.2272 q^{67}\) \(-4.91508 q^{68}\) \(+0.244868 q^{69}\) \(-2.55903 q^{70}\) \(+9.42409 q^{71}\) \(-1.00000 q^{72}\) \(+0.976521 q^{73}\) \(-5.41686 q^{74}\) \(-1.84882 q^{75}\) \(-1.97784 q^{76}\) \(+0.235449 q^{77}\) \(+1.00000 q^{78}\) \(-8.87366 q^{79}\) \(-2.61702 q^{80}\) \(+1.00000 q^{81}\) \(-10.7554 q^{82}\) \(+13.3970 q^{83}\) \(+0.977840 q^{84}\) \(+12.8629 q^{85}\) \(+5.03820 q^{86}\) \(-8.09791 q^{87}\) \(+0.240785 q^{88}\) \(-0.490697 q^{89}\) \(+2.61702 q^{90}\) \(-0.977840 q^{91}\) \(-0.244868 q^{92}\) \(+7.15427 q^{93}\) \(-9.26343 q^{94}\) \(+5.17606 q^{95}\) \(+1.00000 q^{96}\) \(+14.7754 q^{97}\) \(+6.04383 q^{98}\) \(-0.240785 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 17q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −2.61702 −1.17037 −0.585184 0.810900i \(-0.698978\pi\)
−0.585184 + 0.810900i \(0.698978\pi\)
\(6\) 1.00000 0.408248
\(7\) −0.977840 −0.369589 −0.184794 0.982777i \(-0.559162\pi\)
−0.184794 + 0.982777i \(0.559162\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.61702 0.827576
\(11\) −0.240785 −0.0725993 −0.0362997 0.999341i \(-0.511557\pi\)
−0.0362997 + 0.999341i \(0.511557\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 0.977840 0.261339
\(15\) 2.61702 0.675713
\(16\) 1.00000 0.250000
\(17\) −4.91508 −1.19208 −0.596041 0.802954i \(-0.703261\pi\)
−0.596041 + 0.802954i \(0.703261\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.97784 −0.453748 −0.226874 0.973924i \(-0.572851\pi\)
−0.226874 + 0.973924i \(0.572851\pi\)
\(20\) −2.61702 −0.585184
\(21\) 0.977840 0.213382
\(22\) 0.240785 0.0513355
\(23\) −0.244868 −0.0510585 −0.0255292 0.999674i \(-0.508127\pi\)
−0.0255292 + 0.999674i \(0.508127\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.84882 0.369763
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −0.977840 −0.184794
\(29\) 8.09791 1.50374 0.751872 0.659309i \(-0.229151\pi\)
0.751872 + 0.659309i \(0.229151\pi\)
\(30\) −2.61702 −0.477801
\(31\) −7.15427 −1.28494 −0.642472 0.766309i \(-0.722091\pi\)
−0.642472 + 0.766309i \(0.722091\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.240785 0.0419152
\(34\) 4.91508 0.842930
\(35\) 2.55903 0.432555
\(36\) 1.00000 0.166667
\(37\) 5.41686 0.890526 0.445263 0.895400i \(-0.353110\pi\)
0.445263 + 0.895400i \(0.353110\pi\)
\(38\) 1.97784 0.320848
\(39\) −1.00000 −0.160128
\(40\) 2.61702 0.413788
\(41\) 10.7554 1.67971 0.839855 0.542811i \(-0.182640\pi\)
0.839855 + 0.542811i \(0.182640\pi\)
\(42\) −0.977840 −0.150884
\(43\) −5.03820 −0.768318 −0.384159 0.923267i \(-0.625509\pi\)
−0.384159 + 0.923267i \(0.625509\pi\)
\(44\) −0.240785 −0.0362997
\(45\) −2.61702 −0.390123
\(46\) 0.244868 0.0361038
\(47\) 9.26343 1.35121 0.675605 0.737264i \(-0.263882\pi\)
0.675605 + 0.737264i \(0.263882\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.04383 −0.863404
\(50\) −1.84882 −0.261462
\(51\) 4.91508 0.688249
\(52\) 1.00000 0.138675
\(53\) 9.79000 1.34476 0.672380 0.740206i \(-0.265272\pi\)
0.672380 + 0.740206i \(0.265272\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.630140 0.0849680
\(56\) 0.977840 0.130669
\(57\) 1.97784 0.261971
\(58\) −8.09791 −1.06331
\(59\) −7.05375 −0.918320 −0.459160 0.888353i \(-0.651850\pi\)
−0.459160 + 0.888353i \(0.651850\pi\)
\(60\) 2.61702 0.337856
\(61\) 3.55737 0.455474 0.227737 0.973723i \(-0.426867\pi\)
0.227737 + 0.973723i \(0.426867\pi\)
\(62\) 7.15427 0.908593
\(63\) −0.977840 −0.123196
\(64\) 1.00000 0.125000
\(65\) −2.61702 −0.324602
\(66\) −0.240785 −0.0296386
\(67\) −14.2272 −1.73813 −0.869067 0.494694i \(-0.835280\pi\)
−0.869067 + 0.494694i \(0.835280\pi\)
\(68\) −4.91508 −0.596041
\(69\) 0.244868 0.0294786
\(70\) −2.55903 −0.305863
\(71\) 9.42409 1.11843 0.559217 0.829021i \(-0.311102\pi\)
0.559217 + 0.829021i \(0.311102\pi\)
\(72\) −1.00000 −0.117851
\(73\) 0.976521 0.114293 0.0571466 0.998366i \(-0.481800\pi\)
0.0571466 + 0.998366i \(0.481800\pi\)
\(74\) −5.41686 −0.629697
\(75\) −1.84882 −0.213483
\(76\) −1.97784 −0.226874
\(77\) 0.235449 0.0268319
\(78\) 1.00000 0.113228
\(79\) −8.87366 −0.998365 −0.499182 0.866497i \(-0.666366\pi\)
−0.499182 + 0.866497i \(0.666366\pi\)
\(80\) −2.61702 −0.292592
\(81\) 1.00000 0.111111
\(82\) −10.7554 −1.18773
\(83\) 13.3970 1.47051 0.735253 0.677792i \(-0.237063\pi\)
0.735253 + 0.677792i \(0.237063\pi\)
\(84\) 0.977840 0.106691
\(85\) 12.8629 1.39518
\(86\) 5.03820 0.543283
\(87\) −8.09791 −0.868187
\(88\) 0.240785 0.0256677
\(89\) −0.490697 −0.0520138 −0.0260069 0.999662i \(-0.508279\pi\)
−0.0260069 + 0.999662i \(0.508279\pi\)
\(90\) 2.61702 0.275859
\(91\) −0.977840 −0.102506
\(92\) −0.244868 −0.0255292
\(93\) 7.15427 0.741863
\(94\) −9.26343 −0.955450
\(95\) 5.17606 0.531052
\(96\) 1.00000 0.102062
\(97\) 14.7754 1.50021 0.750107 0.661317i \(-0.230002\pi\)
0.750107 + 0.661317i \(0.230002\pi\)
\(98\) 6.04383 0.610519
\(99\) −0.240785 −0.0241998
\(100\) 1.84882 0.184882
\(101\) −10.7141 −1.06609 −0.533045 0.846087i \(-0.678953\pi\)
−0.533045 + 0.846087i \(0.678953\pi\)
\(102\) −4.91508 −0.486666
\(103\) 1.00000 0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −2.55903 −0.249736
\(106\) −9.79000 −0.950889
\(107\) −12.2317 −1.18248 −0.591241 0.806495i \(-0.701362\pi\)
−0.591241 + 0.806495i \(0.701362\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −15.0495 −1.44148 −0.720740 0.693206i \(-0.756198\pi\)
−0.720740 + 0.693206i \(0.756198\pi\)
\(110\) −0.630140 −0.0600814
\(111\) −5.41686 −0.514145
\(112\) −0.977840 −0.0923972
\(113\) 15.2767 1.43711 0.718557 0.695468i \(-0.244803\pi\)
0.718557 + 0.695468i \(0.244803\pi\)
\(114\) −1.97784 −0.185242
\(115\) 0.640825 0.0597572
\(116\) 8.09791 0.751872
\(117\) 1.00000 0.0924500
\(118\) 7.05375 0.649351
\(119\) 4.80617 0.440581
\(120\) −2.61702 −0.238901
\(121\) −10.9420 −0.994729
\(122\) −3.55737 −0.322069
\(123\) −10.7554 −0.969781
\(124\) −7.15427 −0.642472
\(125\) 8.24672 0.737609
\(126\) 0.977840 0.0871129
\(127\) −5.61363 −0.498129 −0.249065 0.968487i \(-0.580123\pi\)
−0.249065 + 0.968487i \(0.580123\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.03820 0.443589
\(130\) 2.61702 0.229528
\(131\) 3.87103 0.338214 0.169107 0.985598i \(-0.445912\pi\)
0.169107 + 0.985598i \(0.445912\pi\)
\(132\) 0.240785 0.0209576
\(133\) 1.93401 0.167700
\(134\) 14.2272 1.22905
\(135\) 2.61702 0.225238
\(136\) 4.91508 0.421465
\(137\) 8.32317 0.711097 0.355548 0.934658i \(-0.384294\pi\)
0.355548 + 0.934658i \(0.384294\pi\)
\(138\) −0.244868 −0.0208445
\(139\) 1.62532 0.137857 0.0689287 0.997622i \(-0.478042\pi\)
0.0689287 + 0.997622i \(0.478042\pi\)
\(140\) 2.55903 0.216278
\(141\) −9.26343 −0.780122
\(142\) −9.42409 −0.790852
\(143\) −0.240785 −0.0201354
\(144\) 1.00000 0.0833333
\(145\) −21.1924 −1.75994
\(146\) −0.976521 −0.0808174
\(147\) 6.04383 0.498487
\(148\) 5.41686 0.445263
\(149\) −6.63099 −0.543232 −0.271616 0.962406i \(-0.587558\pi\)
−0.271616 + 0.962406i \(0.587558\pi\)
\(150\) 1.84882 0.150955
\(151\) 7.91264 0.643922 0.321961 0.946753i \(-0.395658\pi\)
0.321961 + 0.946753i \(0.395658\pi\)
\(152\) 1.97784 0.160424
\(153\) −4.91508 −0.397361
\(154\) −0.235449 −0.0189730
\(155\) 18.7229 1.50386
\(156\) −1.00000 −0.0800641
\(157\) 5.70092 0.454983 0.227492 0.973780i \(-0.426948\pi\)
0.227492 + 0.973780i \(0.426948\pi\)
\(158\) 8.87366 0.705950
\(159\) −9.79000 −0.776398
\(160\) 2.61702 0.206894
\(161\) 0.239442 0.0188706
\(162\) −1.00000 −0.0785674
\(163\) 11.8922 0.931469 0.465734 0.884925i \(-0.345790\pi\)
0.465734 + 0.884925i \(0.345790\pi\)
\(164\) 10.7554 0.839855
\(165\) −0.630140 −0.0490563
\(166\) −13.3970 −1.03981
\(167\) 7.73384 0.598462 0.299231 0.954181i \(-0.403270\pi\)
0.299231 + 0.954181i \(0.403270\pi\)
\(168\) −0.977840 −0.0754420
\(169\) 1.00000 0.0769231
\(170\) −12.8629 −0.986539
\(171\) −1.97784 −0.151249
\(172\) −5.03820 −0.384159
\(173\) 0.659015 0.0501040 0.0250520 0.999686i \(-0.492025\pi\)
0.0250520 + 0.999686i \(0.492025\pi\)
\(174\) 8.09791 0.613901
\(175\) −1.80785 −0.136660
\(176\) −0.240785 −0.0181498
\(177\) 7.05375 0.530193
\(178\) 0.490697 0.0367793
\(179\) 20.3333 1.51978 0.759891 0.650051i \(-0.225253\pi\)
0.759891 + 0.650051i \(0.225253\pi\)
\(180\) −2.61702 −0.195061
\(181\) 11.7556 0.873786 0.436893 0.899514i \(-0.356079\pi\)
0.436893 + 0.899514i \(0.356079\pi\)
\(182\) 0.977840 0.0724823
\(183\) −3.55737 −0.262968
\(184\) 0.244868 0.0180519
\(185\) −14.1760 −1.04224
\(186\) −7.15427 −0.524576
\(187\) 1.18348 0.0865444
\(188\) 9.26343 0.675605
\(189\) 0.977840 0.0711274
\(190\) −5.17606 −0.375511
\(191\) 6.63399 0.480019 0.240009 0.970771i \(-0.422849\pi\)
0.240009 + 0.970771i \(0.422849\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 7.61732 0.548306 0.274153 0.961686i \(-0.411602\pi\)
0.274153 + 0.961686i \(0.411602\pi\)
\(194\) −14.7754 −1.06081
\(195\) 2.61702 0.187409
\(196\) −6.04383 −0.431702
\(197\) −5.85181 −0.416924 −0.208462 0.978030i \(-0.566846\pi\)
−0.208462 + 0.978030i \(0.566846\pi\)
\(198\) 0.240785 0.0171118
\(199\) −1.15345 −0.0817656 −0.0408828 0.999164i \(-0.513017\pi\)
−0.0408828 + 0.999164i \(0.513017\pi\)
\(200\) −1.84882 −0.130731
\(201\) 14.2272 1.00351
\(202\) 10.7141 0.753840
\(203\) −7.91847 −0.555767
\(204\) 4.91508 0.344125
\(205\) −28.1471 −1.96588
\(206\) −1.00000 −0.0696733
\(207\) −0.244868 −0.0170195
\(208\) 1.00000 0.0693375
\(209\) 0.476234 0.0329418
\(210\) 2.55903 0.176590
\(211\) 0.706007 0.0486035 0.0243018 0.999705i \(-0.492264\pi\)
0.0243018 + 0.999705i \(0.492264\pi\)
\(212\) 9.79000 0.672380
\(213\) −9.42409 −0.645728
\(214\) 12.2317 0.836141
\(215\) 13.1851 0.899216
\(216\) 1.00000 0.0680414
\(217\) 6.99573 0.474901
\(218\) 15.0495 1.01928
\(219\) −0.976521 −0.0659872
\(220\) 0.630140 0.0424840
\(221\) −4.91508 −0.330624
\(222\) 5.41686 0.363556
\(223\) 14.3345 0.959906 0.479953 0.877294i \(-0.340654\pi\)
0.479953 + 0.877294i \(0.340654\pi\)
\(224\) 0.977840 0.0653347
\(225\) 1.84882 0.123254
\(226\) −15.2767 −1.01619
\(227\) 12.2428 0.812586 0.406293 0.913743i \(-0.366821\pi\)
0.406293 + 0.913743i \(0.366821\pi\)
\(228\) 1.97784 0.130986
\(229\) 26.8538 1.77455 0.887274 0.461242i \(-0.152596\pi\)
0.887274 + 0.461242i \(0.152596\pi\)
\(230\) −0.640825 −0.0422547
\(231\) −0.235449 −0.0154914
\(232\) −8.09791 −0.531654
\(233\) −11.9179 −0.780769 −0.390384 0.920652i \(-0.627658\pi\)
−0.390384 + 0.920652i \(0.627658\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −24.2426 −1.58141
\(236\) −7.05375 −0.459160
\(237\) 8.87366 0.576406
\(238\) −4.80617 −0.311538
\(239\) −8.42147 −0.544739 −0.272370 0.962193i \(-0.587807\pi\)
−0.272370 + 0.962193i \(0.587807\pi\)
\(240\) 2.61702 0.168928
\(241\) 4.39928 0.283382 0.141691 0.989911i \(-0.454746\pi\)
0.141691 + 0.989911i \(0.454746\pi\)
\(242\) 10.9420 0.703380
\(243\) −1.00000 −0.0641500
\(244\) 3.55737 0.227737
\(245\) 15.8168 1.01050
\(246\) 10.7554 0.685739
\(247\) −1.97784 −0.125847
\(248\) 7.15427 0.454297
\(249\) −13.3970 −0.848997
\(250\) −8.24672 −0.521569
\(251\) −22.7613 −1.43668 −0.718339 0.695693i \(-0.755097\pi\)
−0.718339 + 0.695693i \(0.755097\pi\)
\(252\) −0.977840 −0.0615982
\(253\) 0.0589604 0.00370681
\(254\) 5.61363 0.352230
\(255\) −12.8629 −0.805506
\(256\) 1.00000 0.0625000
\(257\) −29.1047 −1.81550 −0.907752 0.419507i \(-0.862203\pi\)
−0.907752 + 0.419507i \(0.862203\pi\)
\(258\) −5.03820 −0.313665
\(259\) −5.29682 −0.329128
\(260\) −2.61702 −0.162301
\(261\) 8.09791 0.501248
\(262\) −3.87103 −0.239153
\(263\) −6.72826 −0.414882 −0.207441 0.978247i \(-0.566514\pi\)
−0.207441 + 0.978247i \(0.566514\pi\)
\(264\) −0.240785 −0.0148193
\(265\) −25.6207 −1.57387
\(266\) −1.93401 −0.118582
\(267\) 0.490697 0.0300302
\(268\) −14.2272 −0.869067
\(269\) −14.7972 −0.902204 −0.451102 0.892472i \(-0.648969\pi\)
−0.451102 + 0.892472i \(0.648969\pi\)
\(270\) −2.61702 −0.159267
\(271\) −1.96999 −0.119669 −0.0598343 0.998208i \(-0.519057\pi\)
−0.0598343 + 0.998208i \(0.519057\pi\)
\(272\) −4.91508 −0.298021
\(273\) 0.977840 0.0591816
\(274\) −8.32317 −0.502821
\(275\) −0.445167 −0.0268446
\(276\) 0.244868 0.0147393
\(277\) −16.6946 −1.00308 −0.501541 0.865134i \(-0.667233\pi\)
−0.501541 + 0.865134i \(0.667233\pi\)
\(278\) −1.62532 −0.0974800
\(279\) −7.15427 −0.428315
\(280\) −2.55903 −0.152931
\(281\) −27.9085 −1.66488 −0.832440 0.554115i \(-0.813057\pi\)
−0.832440 + 0.554115i \(0.813057\pi\)
\(282\) 9.26343 0.551629
\(283\) −0.449681 −0.0267307 −0.0133654 0.999911i \(-0.504254\pi\)
−0.0133654 + 0.999911i \(0.504254\pi\)
\(284\) 9.42409 0.559217
\(285\) −5.17606 −0.306603
\(286\) 0.240785 0.0142379
\(287\) −10.5171 −0.620802
\(288\) −1.00000 −0.0589256
\(289\) 7.15805 0.421062
\(290\) 21.1924 1.24446
\(291\) −14.7754 −0.866149
\(292\) 0.976521 0.0571466
\(293\) 2.83914 0.165864 0.0829322 0.996555i \(-0.473572\pi\)
0.0829322 + 0.996555i \(0.473572\pi\)
\(294\) −6.04383 −0.352483
\(295\) 18.4598 1.07477
\(296\) −5.41686 −0.314848
\(297\) 0.240785 0.0139717
\(298\) 6.63099 0.384123
\(299\) −0.244868 −0.0141611
\(300\) −1.84882 −0.106741
\(301\) 4.92655 0.283962
\(302\) −7.91264 −0.455321
\(303\) 10.7141 0.615508
\(304\) −1.97784 −0.113437
\(305\) −9.30972 −0.533073
\(306\) 4.91508 0.280977
\(307\) 22.4489 1.28123 0.640614 0.767863i \(-0.278680\pi\)
0.640614 + 0.767863i \(0.278680\pi\)
\(308\) 0.235449 0.0134160
\(309\) −1.00000 −0.0568880
\(310\) −18.7229 −1.06339
\(311\) −4.91789 −0.278868 −0.139434 0.990231i \(-0.544528\pi\)
−0.139434 + 0.990231i \(0.544528\pi\)
\(312\) 1.00000 0.0566139
\(313\) 14.2027 0.802781 0.401391 0.915907i \(-0.368527\pi\)
0.401391 + 0.915907i \(0.368527\pi\)
\(314\) −5.70092 −0.321722
\(315\) 2.55903 0.144185
\(316\) −8.87366 −0.499182
\(317\) 1.83459 0.103041 0.0515205 0.998672i \(-0.483593\pi\)
0.0515205 + 0.998672i \(0.483593\pi\)
\(318\) 9.79000 0.548996
\(319\) −1.94985 −0.109171
\(320\) −2.61702 −0.146296
\(321\) 12.2317 0.682706
\(322\) −0.239442 −0.0133436
\(323\) 9.72125 0.540905
\(324\) 1.00000 0.0555556
\(325\) 1.84882 0.102554
\(326\) −11.8922 −0.658648
\(327\) 15.0495 0.832239
\(328\) −10.7554 −0.593867
\(329\) −9.05816 −0.499392
\(330\) 0.630140 0.0346880
\(331\) −22.7353 −1.24965 −0.624823 0.780767i \(-0.714829\pi\)
−0.624823 + 0.780767i \(0.714829\pi\)
\(332\) 13.3970 0.735253
\(333\) 5.41686 0.296842
\(334\) −7.73384 −0.423177
\(335\) 37.2330 2.03426
\(336\) 0.977840 0.0533456
\(337\) 1.40532 0.0765528 0.0382764 0.999267i \(-0.487813\pi\)
0.0382764 + 0.999267i \(0.487813\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −15.2767 −0.829718
\(340\) 12.8629 0.697588
\(341\) 1.72264 0.0932861
\(342\) 1.97784 0.106949
\(343\) 12.7548 0.688693
\(344\) 5.03820 0.271641
\(345\) −0.640825 −0.0345008
\(346\) −0.659015 −0.0354289
\(347\) −28.8724 −1.54995 −0.774977 0.631989i \(-0.782239\pi\)
−0.774977 + 0.631989i \(0.782239\pi\)
\(348\) −8.09791 −0.434094
\(349\) −22.1867 −1.18763 −0.593813 0.804603i \(-0.702378\pi\)
−0.593813 + 0.804603i \(0.702378\pi\)
\(350\) 1.80785 0.0966335
\(351\) −1.00000 −0.0533761
\(352\) 0.240785 0.0128339
\(353\) −5.73114 −0.305038 −0.152519 0.988301i \(-0.548738\pi\)
−0.152519 + 0.988301i \(0.548738\pi\)
\(354\) −7.05375 −0.374903
\(355\) −24.6631 −1.30898
\(356\) −0.490697 −0.0260069
\(357\) −4.80617 −0.254369
\(358\) −20.3333 −1.07465
\(359\) −16.9988 −0.897164 −0.448582 0.893742i \(-0.648071\pi\)
−0.448582 + 0.893742i \(0.648071\pi\)
\(360\) 2.61702 0.137929
\(361\) −15.0881 −0.794113
\(362\) −11.7556 −0.617860
\(363\) 10.9420 0.574307
\(364\) −0.977840 −0.0512528
\(365\) −2.55558 −0.133765
\(366\) 3.55737 0.185947
\(367\) −8.06954 −0.421226 −0.210613 0.977569i \(-0.567546\pi\)
−0.210613 + 0.977569i \(0.567546\pi\)
\(368\) −0.244868 −0.0127646
\(369\) 10.7554 0.559903
\(370\) 14.1760 0.736978
\(371\) −9.57306 −0.497008
\(372\) 7.15427 0.370932
\(373\) −9.23667 −0.478257 −0.239128 0.970988i \(-0.576862\pi\)
−0.239128 + 0.970988i \(0.576862\pi\)
\(374\) −1.18348 −0.0611962
\(375\) −8.24672 −0.425859
\(376\) −9.26343 −0.477725
\(377\) 8.09791 0.417064
\(378\) −0.977840 −0.0502947
\(379\) −16.8755 −0.866834 −0.433417 0.901193i \(-0.642692\pi\)
−0.433417 + 0.901193i \(0.642692\pi\)
\(380\) 5.17606 0.265526
\(381\) 5.61363 0.287595
\(382\) −6.63399 −0.339425
\(383\) −10.8901 −0.556460 −0.278230 0.960514i \(-0.589748\pi\)
−0.278230 + 0.960514i \(0.589748\pi\)
\(384\) 1.00000 0.0510310
\(385\) −0.616176 −0.0314032
\(386\) −7.61732 −0.387711
\(387\) −5.03820 −0.256106
\(388\) 14.7754 0.750107
\(389\) 23.2979 1.18125 0.590626 0.806945i \(-0.298881\pi\)
0.590626 + 0.806945i \(0.298881\pi\)
\(390\) −2.61702 −0.132518
\(391\) 1.20355 0.0608659
\(392\) 6.04383 0.305259
\(393\) −3.87103 −0.195268
\(394\) 5.85181 0.294810
\(395\) 23.2226 1.16845
\(396\) −0.240785 −0.0120999
\(397\) 12.2264 0.613624 0.306812 0.951770i \(-0.400738\pi\)
0.306812 + 0.951770i \(0.400738\pi\)
\(398\) 1.15345 0.0578170
\(399\) −1.93401 −0.0968217
\(400\) 1.84882 0.0924408
\(401\) 8.14554 0.406769 0.203385 0.979099i \(-0.434806\pi\)
0.203385 + 0.979099i \(0.434806\pi\)
\(402\) −14.2272 −0.709590
\(403\) −7.15427 −0.356380
\(404\) −10.7141 −0.533045
\(405\) −2.61702 −0.130041
\(406\) 7.91847 0.392987
\(407\) −1.30430 −0.0646516
\(408\) −4.91508 −0.243333
\(409\) −23.0045 −1.13750 −0.568749 0.822511i \(-0.692572\pi\)
−0.568749 + 0.822511i \(0.692572\pi\)
\(410\) 28.1471 1.39009
\(411\) −8.32317 −0.410552
\(412\) 1.00000 0.0492665
\(413\) 6.89744 0.339401
\(414\) 0.244868 0.0120346
\(415\) −35.0602 −1.72104
\(416\) −1.00000 −0.0490290
\(417\) −1.62532 −0.0795921
\(418\) −0.476234 −0.0232934
\(419\) 17.7485 0.867070 0.433535 0.901137i \(-0.357266\pi\)
0.433535 + 0.901137i \(0.357266\pi\)
\(420\) −2.55903 −0.124868
\(421\) 9.92884 0.483902 0.241951 0.970288i \(-0.422213\pi\)
0.241951 + 0.970288i \(0.422213\pi\)
\(422\) −0.706007 −0.0343679
\(423\) 9.26343 0.450403
\(424\) −9.79000 −0.475445
\(425\) −9.08709 −0.440788
\(426\) 9.42409 0.456599
\(427\) −3.47854 −0.168338
\(428\) −12.2317 −0.591241
\(429\) 0.240785 0.0116252
\(430\) −13.1851 −0.635841
\(431\) 7.53987 0.363183 0.181591 0.983374i \(-0.441875\pi\)
0.181591 + 0.983374i \(0.441875\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −9.84043 −0.472901 −0.236451 0.971644i \(-0.575984\pi\)
−0.236451 + 0.971644i \(0.575984\pi\)
\(434\) −6.99573 −0.335806
\(435\) 21.1924 1.01610
\(436\) −15.0495 −0.720740
\(437\) 0.484309 0.0231677
\(438\) 0.976521 0.0466600
\(439\) −18.5120 −0.883528 −0.441764 0.897131i \(-0.645647\pi\)
−0.441764 + 0.897131i \(0.645647\pi\)
\(440\) −0.630140 −0.0300407
\(441\) −6.04383 −0.287801
\(442\) 4.91508 0.233787
\(443\) −19.4535 −0.924264 −0.462132 0.886811i \(-0.652915\pi\)
−0.462132 + 0.886811i \(0.652915\pi\)
\(444\) −5.41686 −0.257073
\(445\) 1.28417 0.0608753
\(446\) −14.3345 −0.678756
\(447\) 6.63099 0.313635
\(448\) −0.977840 −0.0461986
\(449\) −42.1339 −1.98842 −0.994211 0.107445i \(-0.965733\pi\)
−0.994211 + 0.107445i \(0.965733\pi\)
\(450\) −1.84882 −0.0871540
\(451\) −2.58973 −0.121946
\(452\) 15.2767 0.718557
\(453\) −7.91264 −0.371768
\(454\) −12.2428 −0.574585
\(455\) 2.55903 0.119969
\(456\) −1.97784 −0.0926209
\(457\) 22.9184 1.07208 0.536038 0.844194i \(-0.319920\pi\)
0.536038 + 0.844194i \(0.319920\pi\)
\(458\) −26.8538 −1.25480
\(459\) 4.91508 0.229416
\(460\) 0.640825 0.0298786
\(461\) −6.85452 −0.319247 −0.159623 0.987178i \(-0.551028\pi\)
−0.159623 + 0.987178i \(0.551028\pi\)
\(462\) 0.235449 0.0109541
\(463\) −20.9881 −0.975399 −0.487699 0.873012i \(-0.662164\pi\)
−0.487699 + 0.873012i \(0.662164\pi\)
\(464\) 8.09791 0.375936
\(465\) −18.7229 −0.868254
\(466\) 11.9179 0.552087
\(467\) 25.5979 1.18453 0.592264 0.805744i \(-0.298234\pi\)
0.592264 + 0.805744i \(0.298234\pi\)
\(468\) 1.00000 0.0462250
\(469\) 13.9120 0.642395
\(470\) 24.2426 1.11823
\(471\) −5.70092 −0.262685
\(472\) 7.05375 0.324675
\(473\) 1.21312 0.0557794
\(474\) −8.87366 −0.407581
\(475\) −3.65666 −0.167779
\(476\) 4.80617 0.220290
\(477\) 9.79000 0.448253
\(478\) 8.42147 0.385189
\(479\) −27.7457 −1.26773 −0.633867 0.773442i \(-0.718533\pi\)
−0.633867 + 0.773442i \(0.718533\pi\)
\(480\) −2.61702 −0.119450
\(481\) 5.41686 0.246987
\(482\) −4.39928 −0.200382
\(483\) −0.239442 −0.0108950
\(484\) −10.9420 −0.497365
\(485\) −38.6676 −1.75580
\(486\) 1.00000 0.0453609
\(487\) 20.8544 0.945004 0.472502 0.881330i \(-0.343351\pi\)
0.472502 + 0.881330i \(0.343351\pi\)
\(488\) −3.55737 −0.161034
\(489\) −11.8922 −0.537784
\(490\) −15.8168 −0.714532
\(491\) −29.1552 −1.31576 −0.657879 0.753124i \(-0.728546\pi\)
−0.657879 + 0.753124i \(0.728546\pi\)
\(492\) −10.7554 −0.484891
\(493\) −39.8019 −1.79259
\(494\) 1.97784 0.0889872
\(495\) 0.630140 0.0283227
\(496\) −7.15427 −0.321236
\(497\) −9.21526 −0.413361
\(498\) 13.3970 0.600332
\(499\) −22.6831 −1.01543 −0.507717 0.861524i \(-0.669511\pi\)
−0.507717 + 0.861524i \(0.669511\pi\)
\(500\) 8.24672 0.368805
\(501\) −7.73384 −0.345522
\(502\) 22.7613 1.01588
\(503\) −8.39406 −0.374272 −0.187136 0.982334i \(-0.559921\pi\)
−0.187136 + 0.982334i \(0.559921\pi\)
\(504\) 0.977840 0.0435565
\(505\) 28.0390 1.24772
\(506\) −0.0589604 −0.00262111
\(507\) −1.00000 −0.0444116
\(508\) −5.61363 −0.249065
\(509\) 15.2631 0.676526 0.338263 0.941052i \(-0.390161\pi\)
0.338263 + 0.941052i \(0.390161\pi\)
\(510\) 12.8629 0.569579
\(511\) −0.954881 −0.0422415
\(512\) −1.00000 −0.0441942
\(513\) 1.97784 0.0873238
\(514\) 29.1047 1.28376
\(515\) −2.61702 −0.115320
\(516\) 5.03820 0.221794
\(517\) −2.23049 −0.0980970
\(518\) 5.29682 0.232729
\(519\) −0.659015 −0.0289275
\(520\) 2.61702 0.114764
\(521\) 13.5364 0.593041 0.296521 0.955026i \(-0.404174\pi\)
0.296521 + 0.955026i \(0.404174\pi\)
\(522\) −8.09791 −0.354436
\(523\) −14.4599 −0.632288 −0.316144 0.948711i \(-0.602388\pi\)
−0.316144 + 0.948711i \(0.602388\pi\)
\(524\) 3.87103 0.169107
\(525\) 1.80785 0.0789009
\(526\) 6.72826 0.293366
\(527\) 35.1638 1.53176
\(528\) 0.240785 0.0104788
\(529\) −22.9400 −0.997393
\(530\) 25.6207 1.11289
\(531\) −7.05375 −0.306107
\(532\) 1.93401 0.0838501
\(533\) 10.7554 0.465868
\(534\) −0.490697 −0.0212345
\(535\) 32.0106 1.38394
\(536\) 14.2272 0.614523
\(537\) −20.3333 −0.877446
\(538\) 14.7972 0.637954
\(539\) 1.45526 0.0626826
\(540\) 2.61702 0.112619
\(541\) −34.3574 −1.47714 −0.738571 0.674176i \(-0.764499\pi\)
−0.738571 + 0.674176i \(0.764499\pi\)
\(542\) 1.96999 0.0846185
\(543\) −11.7556 −0.504480
\(544\) 4.91508 0.210732
\(545\) 39.3849 1.68706
\(546\) −0.977840 −0.0418477
\(547\) −7.44242 −0.318215 −0.159107 0.987261i \(-0.550862\pi\)
−0.159107 + 0.987261i \(0.550862\pi\)
\(548\) 8.32317 0.355548
\(549\) 3.55737 0.151825
\(550\) 0.445167 0.0189820
\(551\) −16.0164 −0.682321
\(552\) −0.244868 −0.0104223
\(553\) 8.67702 0.368984
\(554\) 16.6946 0.709286
\(555\) 14.1760 0.601740
\(556\) 1.62532 0.0689287
\(557\) 19.7550 0.837045 0.418522 0.908207i \(-0.362548\pi\)
0.418522 + 0.908207i \(0.362548\pi\)
\(558\) 7.15427 0.302864
\(559\) −5.03820 −0.213093
\(560\) 2.55903 0.108139
\(561\) −1.18348 −0.0499664
\(562\) 27.9085 1.17725
\(563\) −12.0479 −0.507757 −0.253878 0.967236i \(-0.581706\pi\)
−0.253878 + 0.967236i \(0.581706\pi\)
\(564\) −9.26343 −0.390061
\(565\) −39.9796 −1.68195
\(566\) 0.449681 0.0189015
\(567\) −0.977840 −0.0410654
\(568\) −9.42409 −0.395426
\(569\) −5.93297 −0.248723 −0.124362 0.992237i \(-0.539688\pi\)
−0.124362 + 0.992237i \(0.539688\pi\)
\(570\) 5.17606 0.216801
\(571\) −5.79958 −0.242705 −0.121352 0.992609i \(-0.538723\pi\)
−0.121352 + 0.992609i \(0.538723\pi\)
\(572\) −0.240785 −0.0100677
\(573\) −6.63399 −0.277139
\(574\) 10.5171 0.438973
\(575\) −0.452715 −0.0188795
\(576\) 1.00000 0.0416667
\(577\) 3.70002 0.154034 0.0770169 0.997030i \(-0.475460\pi\)
0.0770169 + 0.997030i \(0.475460\pi\)
\(578\) −7.15805 −0.297736
\(579\) −7.61732 −0.316565
\(580\) −21.1924 −0.879968
\(581\) −13.1001 −0.543483
\(582\) 14.7754 0.612460
\(583\) −2.35728 −0.0976287
\(584\) −0.976521 −0.0404087
\(585\) −2.61702 −0.108201
\(586\) −2.83914 −0.117284
\(587\) 18.7108 0.772278 0.386139 0.922441i \(-0.373808\pi\)
0.386139 + 0.922441i \(0.373808\pi\)
\(588\) 6.04383 0.249243
\(589\) 14.1500 0.583041
\(590\) −18.4598 −0.759980
\(591\) 5.85181 0.240711
\(592\) 5.41686 0.222631
\(593\) −23.9001 −0.981460 −0.490730 0.871312i \(-0.663270\pi\)
−0.490730 + 0.871312i \(0.663270\pi\)
\(594\) −0.240785 −0.00987952
\(595\) −12.5779 −0.515642
\(596\) −6.63099 −0.271616
\(597\) 1.15345 0.0472074
\(598\) 0.244868 0.0100134
\(599\) 12.7785 0.522114 0.261057 0.965323i \(-0.415929\pi\)
0.261057 + 0.965323i \(0.415929\pi\)
\(600\) 1.84882 0.0754776
\(601\) −2.45569 −0.100170 −0.0500848 0.998745i \(-0.515949\pi\)
−0.0500848 + 0.998745i \(0.515949\pi\)
\(602\) −4.92655 −0.200791
\(603\) −14.2272 −0.579378
\(604\) 7.91264 0.321961
\(605\) 28.6355 1.16420
\(606\) −10.7141 −0.435230
\(607\) 37.5049 1.52228 0.761138 0.648590i \(-0.224641\pi\)
0.761138 + 0.648590i \(0.224641\pi\)
\(608\) 1.97784 0.0802120
\(609\) 7.91847 0.320872
\(610\) 9.30972 0.376939
\(611\) 9.26343 0.374758
\(612\) −4.91508 −0.198680
\(613\) 21.6188 0.873176 0.436588 0.899662i \(-0.356187\pi\)
0.436588 + 0.899662i \(0.356187\pi\)
\(614\) −22.4489 −0.905964
\(615\) 28.1471 1.13500
\(616\) −0.235449 −0.00948651
\(617\) −7.98471 −0.321452 −0.160726 0.986999i \(-0.551384\pi\)
−0.160726 + 0.986999i \(0.551384\pi\)
\(618\) 1.00000 0.0402259
\(619\) −15.5740 −0.625972 −0.312986 0.949758i \(-0.601329\pi\)
−0.312986 + 0.949758i \(0.601329\pi\)
\(620\) 18.7229 0.751930
\(621\) 0.244868 0.00982620
\(622\) 4.91789 0.197189
\(623\) 0.479823 0.0192237
\(624\) −1.00000 −0.0400320
\(625\) −30.8260 −1.23304
\(626\) −14.2027 −0.567652
\(627\) −0.476234 −0.0190189
\(628\) 5.70092 0.227492
\(629\) −26.6243 −1.06158
\(630\) −2.55903 −0.101954
\(631\) −19.6398 −0.781847 −0.390923 0.920423i \(-0.627844\pi\)
−0.390923 + 0.920423i \(0.627844\pi\)
\(632\) 8.87366 0.352975
\(633\) −0.706007 −0.0280613
\(634\) −1.83459 −0.0728609
\(635\) 14.6910 0.582995
\(636\) −9.79000 −0.388199
\(637\) −6.04383 −0.239465
\(638\) 1.94985 0.0771955
\(639\) 9.42409 0.372811
\(640\) 2.61702 0.103447
\(641\) −1.62764 −0.0642879 −0.0321439 0.999483i \(-0.510233\pi\)
−0.0321439 + 0.999483i \(0.510233\pi\)
\(642\) −12.2317 −0.482746
\(643\) −29.8776 −1.17826 −0.589128 0.808040i \(-0.700529\pi\)
−0.589128 + 0.808040i \(0.700529\pi\)
\(644\) 0.239442 0.00943532
\(645\) −13.1851 −0.519162
\(646\) −9.72125 −0.382478
\(647\) −11.9039 −0.467989 −0.233995 0.972238i \(-0.575180\pi\)
−0.233995 + 0.972238i \(0.575180\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 1.69844 0.0666695
\(650\) −1.84882 −0.0725165
\(651\) −6.99573 −0.274184
\(652\) 11.8922 0.465734
\(653\) 13.2976 0.520374 0.260187 0.965558i \(-0.416216\pi\)
0.260187 + 0.965558i \(0.416216\pi\)
\(654\) −15.0495 −0.588482
\(655\) −10.1306 −0.395835
\(656\) 10.7554 0.419928
\(657\) 0.976521 0.0380977
\(658\) 9.05816 0.353124
\(659\) 0.0282496 0.00110045 0.000550223 1.00000i \(-0.499825\pi\)
0.000550223 1.00000i \(0.499825\pi\)
\(660\) −0.630140 −0.0245281
\(661\) 11.7375 0.456536 0.228268 0.973598i \(-0.426694\pi\)
0.228268 + 0.973598i \(0.426694\pi\)
\(662\) 22.7353 0.883633
\(663\) 4.91508 0.190886
\(664\) −13.3970 −0.519903
\(665\) −5.06136 −0.196271
\(666\) −5.41686 −0.209899
\(667\) −1.98292 −0.0767789
\(668\) 7.73384 0.299231
\(669\) −14.3345 −0.554202
\(670\) −37.2330 −1.43844
\(671\) −0.856560 −0.0330671
\(672\) −0.977840 −0.0377210
\(673\) −3.55254 −0.136940 −0.0684702 0.997653i \(-0.521812\pi\)
−0.0684702 + 0.997653i \(0.521812\pi\)
\(674\) −1.40532 −0.0541310
\(675\) −1.84882 −0.0711610
\(676\) 1.00000 0.0384615
\(677\) −31.6198 −1.21525 −0.607623 0.794226i \(-0.707877\pi\)
−0.607623 + 0.794226i \(0.707877\pi\)
\(678\) 15.2767 0.586699
\(679\) −14.4480 −0.554462
\(680\) −12.8629 −0.493269
\(681\) −12.2428 −0.469147
\(682\) −1.72264 −0.0659633
\(683\) 10.8767 0.416184 0.208092 0.978109i \(-0.433275\pi\)
0.208092 + 0.978109i \(0.433275\pi\)
\(684\) −1.97784 −0.0756246
\(685\) −21.7819 −0.832245
\(686\) −12.7548 −0.486980
\(687\) −26.8538 −1.02454
\(688\) −5.03820 −0.192080
\(689\) 9.79000 0.372969
\(690\) 0.640825 0.0243958
\(691\) 34.5054 1.31265 0.656324 0.754479i \(-0.272110\pi\)
0.656324 + 0.754479i \(0.272110\pi\)
\(692\) 0.659015 0.0250520
\(693\) 0.235449 0.00894397
\(694\) 28.8724 1.09598
\(695\) −4.25349 −0.161344
\(696\) 8.09791 0.306951
\(697\) −52.8637 −2.00235
\(698\) 22.1867 0.839778
\(699\) 11.9179 0.450777
\(700\) −1.80785 −0.0683302
\(701\) −7.94945 −0.300247 −0.150123 0.988667i \(-0.547967\pi\)
−0.150123 + 0.988667i \(0.547967\pi\)
\(702\) 1.00000 0.0377426
\(703\) −10.7137 −0.404074
\(704\) −0.240785 −0.00907492
\(705\) 24.2426 0.913030
\(706\) 5.73114 0.215694
\(707\) 10.4767 0.394015
\(708\) 7.05375 0.265096
\(709\) −38.7513 −1.45534 −0.727668 0.685930i \(-0.759396\pi\)
−0.727668 + 0.685930i \(0.759396\pi\)
\(710\) 24.6631 0.925589
\(711\) −8.87366 −0.332788
\(712\) 0.490697 0.0183896
\(713\) 1.75185 0.0656073
\(714\) 4.80617 0.179866
\(715\) 0.630140 0.0235659
\(716\) 20.3333 0.759891
\(717\) 8.42147 0.314505
\(718\) 16.9988 0.634391
\(719\) 11.9026 0.443894 0.221947 0.975059i \(-0.428759\pi\)
0.221947 + 0.975059i \(0.428759\pi\)
\(720\) −2.61702 −0.0975307
\(721\) −0.977840 −0.0364167
\(722\) 15.0881 0.561523
\(723\) −4.39928 −0.163611
\(724\) 11.7556 0.436893
\(725\) 14.9716 0.556030
\(726\) −10.9420 −0.406097
\(727\) −20.3323 −0.754082 −0.377041 0.926197i \(-0.623058\pi\)
−0.377041 + 0.926197i \(0.623058\pi\)
\(728\) 0.977840 0.0362412
\(729\) 1.00000 0.0370370
\(730\) 2.55558 0.0945862
\(731\) 24.7632 0.915899
\(732\) −3.55737 −0.131484
\(733\) 44.3842 1.63937 0.819684 0.572816i \(-0.194149\pi\)
0.819684 + 0.572816i \(0.194149\pi\)
\(734\) 8.06954 0.297852
\(735\) −15.8168 −0.583413
\(736\) 0.244868 0.00902594
\(737\) 3.42570 0.126187
\(738\) −10.7554 −0.395911
\(739\) −47.1876 −1.73582 −0.867912 0.496718i \(-0.834538\pi\)
−0.867912 + 0.496718i \(0.834538\pi\)
\(740\) −14.1760 −0.521122
\(741\) 1.97784 0.0726578
\(742\) 9.57306 0.351438
\(743\) −21.0148 −0.770957 −0.385478 0.922717i \(-0.625964\pi\)
−0.385478 + 0.922717i \(0.625964\pi\)
\(744\) −7.15427 −0.262288
\(745\) 17.3535 0.635782
\(746\) 9.23667 0.338179
\(747\) 13.3970 0.490169
\(748\) 1.18348 0.0432722
\(749\) 11.9606 0.437032
\(750\) 8.24672 0.301128
\(751\) 6.30191 0.229960 0.114980 0.993368i \(-0.463320\pi\)
0.114980 + 0.993368i \(0.463320\pi\)
\(752\) 9.26343 0.337803
\(753\) 22.7613 0.829467
\(754\) −8.09791 −0.294909
\(755\) −20.7076 −0.753626
\(756\) 0.977840 0.0355637
\(757\) 22.1721 0.805858 0.402929 0.915231i \(-0.367992\pi\)
0.402929 + 0.915231i \(0.367992\pi\)
\(758\) 16.8755 0.612945
\(759\) −0.0589604 −0.00214013
\(760\) −5.17606 −0.187755
\(761\) 11.4436 0.414830 0.207415 0.978253i \(-0.433495\pi\)
0.207415 + 0.978253i \(0.433495\pi\)
\(762\) −5.61363 −0.203360
\(763\) 14.7160 0.532755
\(764\) 6.63399 0.240009
\(765\) 12.8629 0.465059
\(766\) 10.8901 0.393477
\(767\) −7.05375 −0.254696
\(768\) −1.00000 −0.0360844
\(769\) 11.7434 0.423479 0.211739 0.977326i \(-0.432087\pi\)
0.211739 + 0.977326i \(0.432087\pi\)
\(770\) 0.616176 0.0222054
\(771\) 29.1047 1.04818
\(772\) 7.61732 0.274153
\(773\) −48.6889 −1.75122 −0.875608 0.483022i \(-0.839539\pi\)
−0.875608 + 0.483022i \(0.839539\pi\)
\(774\) 5.03820 0.181094
\(775\) −13.2269 −0.475125
\(776\) −14.7754 −0.530406
\(777\) 5.29682 0.190022
\(778\) −23.2979 −0.835271
\(779\) −21.2724 −0.762165
\(780\) 2.61702 0.0937045
\(781\) −2.26918 −0.0811975
\(782\) −1.20355 −0.0430387
\(783\) −8.09791 −0.289396
\(784\) −6.04383 −0.215851
\(785\) −14.9195 −0.532498
\(786\) 3.87103 0.138075
\(787\) 46.3481 1.65213 0.826066 0.563574i \(-0.190574\pi\)
0.826066 + 0.563574i \(0.190574\pi\)
\(788\) −5.85181 −0.208462
\(789\) 6.72826 0.239532
\(790\) −23.2226 −0.826222
\(791\) −14.9382 −0.531141
\(792\) 0.240785 0.00855591
\(793\) 3.55737 0.126326
\(794\) −12.2264 −0.433898
\(795\) 25.6207 0.908672
\(796\) −1.15345 −0.0408828
\(797\) −16.4711 −0.583438 −0.291719 0.956504i \(-0.594227\pi\)
−0.291719 + 0.956504i \(0.594227\pi\)
\(798\) 1.93401 0.0684633
\(799\) −45.5305 −1.61075
\(800\) −1.84882 −0.0653655
\(801\) −0.490697 −0.0173379
\(802\) −8.14554 −0.287629
\(803\) −0.235131 −0.00829760
\(804\) 14.2272 0.501756
\(805\) −0.626624 −0.0220856
\(806\) 7.15427 0.251998
\(807\) 14.7972 0.520888
\(808\) 10.7141 0.376920
\(809\) 23.2860 0.818692 0.409346 0.912379i \(-0.365757\pi\)
0.409346 + 0.912379i \(0.365757\pi\)
\(810\) 2.61702 0.0919529
\(811\) 2.52046 0.0885053 0.0442527 0.999020i \(-0.485909\pi\)
0.0442527 + 0.999020i \(0.485909\pi\)
\(812\) −7.91847 −0.277884
\(813\) 1.96999 0.0690907
\(814\) 1.30430 0.0457156
\(815\) −31.1222 −1.09016
\(816\) 4.91508 0.172062
\(817\) 9.96475 0.348623
\(818\) 23.0045 0.804333
\(819\) −0.977840 −0.0341685
\(820\) −28.1471 −0.982940
\(821\) 31.4193 1.09654 0.548270 0.836301i \(-0.315287\pi\)
0.548270 + 0.836301i \(0.315287\pi\)
\(822\) 8.32317 0.290304
\(823\) −36.9734 −1.28881 −0.644405 0.764684i \(-0.722895\pi\)
−0.644405 + 0.764684i \(0.722895\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 0.445167 0.0154987
\(826\) −6.89744 −0.239993
\(827\) −21.9835 −0.764440 −0.382220 0.924071i \(-0.624840\pi\)
−0.382220 + 0.924071i \(0.624840\pi\)
\(828\) −0.244868 −0.00850974
\(829\) 30.7938 1.06951 0.534757 0.845006i \(-0.320403\pi\)
0.534757 + 0.845006i \(0.320403\pi\)
\(830\) 35.0602 1.21696
\(831\) 16.6946 0.579130
\(832\) 1.00000 0.0346688
\(833\) 29.7059 1.02925
\(834\) 1.62532 0.0562801
\(835\) −20.2396 −0.700422
\(836\) 0.476234 0.0164709
\(837\) 7.15427 0.247288
\(838\) −17.7485 −0.613111
\(839\) −44.1131 −1.52295 −0.761477 0.648191i \(-0.775526\pi\)
−0.761477 + 0.648191i \(0.775526\pi\)
\(840\) 2.55903 0.0882950
\(841\) 36.5762 1.26125
\(842\) −9.92884 −0.342170
\(843\) 27.9085 0.961219
\(844\) 0.706007 0.0243018
\(845\) −2.61702 −0.0900284
\(846\) −9.26343 −0.318483
\(847\) 10.6996 0.367641
\(848\) 9.79000 0.336190
\(849\) 0.449681 0.0154330
\(850\) 9.08709 0.311685
\(851\) −1.32641 −0.0454689
\(852\) −9.42409 −0.322864
\(853\) −14.4974 −0.496381 −0.248191 0.968711i \(-0.579836\pi\)
−0.248191 + 0.968711i \(0.579836\pi\)
\(854\) 3.47854 0.119033
\(855\) 5.17606 0.177017
\(856\) 12.2317 0.418071
\(857\) 4.24844 0.145124 0.0725620 0.997364i \(-0.476882\pi\)
0.0725620 + 0.997364i \(0.476882\pi\)
\(858\) −0.240785 −0.00822026
\(859\) −15.3950 −0.525271 −0.262636 0.964895i \(-0.584592\pi\)
−0.262636 + 0.964895i \(0.584592\pi\)
\(860\) 13.1851 0.449608
\(861\) 10.5171 0.358420
\(862\) −7.53987 −0.256809
\(863\) 24.2821 0.826573 0.413287 0.910601i \(-0.364381\pi\)
0.413287 + 0.910601i \(0.364381\pi\)
\(864\) 1.00000 0.0340207
\(865\) −1.72466 −0.0586401
\(866\) 9.84043 0.334392
\(867\) −7.15805 −0.243100
\(868\) 6.99573 0.237451
\(869\) 2.13664 0.0724806
\(870\) −21.1924 −0.718491
\(871\) −14.2272 −0.482072
\(872\) 15.0495 0.509640
\(873\) 14.7754 0.500071
\(874\) −0.484309 −0.0163820
\(875\) −8.06398 −0.272612
\(876\) −0.976521 −0.0329936
\(877\) −1.83535 −0.0619752 −0.0309876 0.999520i \(-0.509865\pi\)
−0.0309876 + 0.999520i \(0.509865\pi\)
\(878\) 18.5120 0.624749
\(879\) −2.83914 −0.0957618
\(880\) 0.630140 0.0212420
\(881\) −31.1530 −1.04957 −0.524785 0.851235i \(-0.675854\pi\)
−0.524785 + 0.851235i \(0.675854\pi\)
\(882\) 6.04383 0.203506
\(883\) −21.5055 −0.723717 −0.361859 0.932233i \(-0.617858\pi\)
−0.361859 + 0.932233i \(0.617858\pi\)
\(884\) −4.91508 −0.165312
\(885\) −18.4598 −0.620521
\(886\) 19.4535 0.653553
\(887\) −5.17151 −0.173642 −0.0868211 0.996224i \(-0.527671\pi\)
−0.0868211 + 0.996224i \(0.527671\pi\)
\(888\) 5.41686 0.181778
\(889\) 5.48923 0.184103
\(890\) −1.28417 −0.0430453
\(891\) −0.240785 −0.00806659
\(892\) 14.3345 0.479953
\(893\) −18.3216 −0.613108
\(894\) −6.63099 −0.221773
\(895\) −53.2127 −1.77870
\(896\) 0.977840 0.0326674
\(897\) 0.244868 0.00817590
\(898\) 42.1339 1.40603
\(899\) −57.9346 −1.93223
\(900\) 1.84882 0.0616272
\(901\) −48.1187 −1.60307
\(902\) 2.58973 0.0862287
\(903\) −4.92655 −0.163945
\(904\) −15.2767 −0.508097
\(905\) −30.7647 −1.02265
\(906\) 7.91264 0.262880
\(907\) −44.7207 −1.48493 −0.742464 0.669886i \(-0.766343\pi\)
−0.742464 + 0.669886i \(0.766343\pi\)
\(908\) 12.2428 0.406293
\(909\) −10.7141 −0.355364
\(910\) −2.55903 −0.0848311
\(911\) 11.8184 0.391560 0.195780 0.980648i \(-0.437276\pi\)
0.195780 + 0.980648i \(0.437276\pi\)
\(912\) 1.97784 0.0654928
\(913\) −3.22578 −0.106758
\(914\) −22.9184 −0.758073
\(915\) 9.30972 0.307770
\(916\) 26.8538 0.887274
\(917\) −3.78525 −0.125000
\(918\) −4.91508 −0.162222
\(919\) −5.92090 −0.195313 −0.0976563 0.995220i \(-0.531135\pi\)
−0.0976563 + 0.995220i \(0.531135\pi\)
\(920\) −0.640825 −0.0211274
\(921\) −22.4489 −0.739717
\(922\) 6.85452 0.225742
\(923\) 9.42409 0.310198
\(924\) −0.235449 −0.00774570
\(925\) 10.0148 0.329284
\(926\) 20.9881 0.689711
\(927\) 1.00000 0.0328443
\(928\) −8.09791 −0.265827
\(929\) 48.9683 1.60660 0.803299 0.595576i \(-0.203076\pi\)
0.803299 + 0.595576i \(0.203076\pi\)
\(930\) 18.7229 0.613948
\(931\) 11.9537 0.391768
\(932\) −11.9179 −0.390384
\(933\) 4.91789 0.161004
\(934\) −25.5979 −0.837588
\(935\) −3.09719 −0.101289
\(936\) −1.00000 −0.0326860
\(937\) −2.99171 −0.0977350 −0.0488675 0.998805i \(-0.515561\pi\)
−0.0488675 + 0.998805i \(0.515561\pi\)
\(938\) −13.9120 −0.454242
\(939\) −14.2027 −0.463486
\(940\) −24.2426 −0.790707
\(941\) 53.2058 1.73446 0.867230 0.497908i \(-0.165898\pi\)
0.867230 + 0.497908i \(0.165898\pi\)
\(942\) 5.70092 0.185746
\(943\) −2.63365 −0.0857634
\(944\) −7.05375 −0.229580
\(945\) −2.55903 −0.0832453
\(946\) −1.21312 −0.0394420
\(947\) −37.0349 −1.20347 −0.601737 0.798694i \(-0.705524\pi\)
−0.601737 + 0.798694i \(0.705524\pi\)
\(948\) 8.87366 0.288203
\(949\) 0.976521 0.0316992
\(950\) 3.65666 0.118638
\(951\) −1.83459 −0.0594907
\(952\) −4.80617 −0.155769
\(953\) −6.97956 −0.226090 −0.113045 0.993590i \(-0.536060\pi\)
−0.113045 + 0.993590i \(0.536060\pi\)
\(954\) −9.79000 −0.316963
\(955\) −17.3613 −0.561799
\(956\) −8.42147 −0.272370
\(957\) 1.94985 0.0630298
\(958\) 27.7457 0.896423
\(959\) −8.13873 −0.262813
\(960\) 2.61702 0.0844641
\(961\) 20.1836 0.651083
\(962\) −5.41686 −0.174646
\(963\) −12.2317 −0.394161
\(964\) 4.39928 0.141691
\(965\) −19.9347 −0.641721
\(966\) 0.239442 0.00770391
\(967\) −22.8451 −0.734648 −0.367324 0.930093i \(-0.619726\pi\)
−0.367324 + 0.930093i \(0.619726\pi\)
\(968\) 10.9420 0.351690
\(969\) −9.72125 −0.312292
\(970\) 38.6676 1.24154
\(971\) −26.1693 −0.839812 −0.419906 0.907568i \(-0.637937\pi\)
−0.419906 + 0.907568i \(0.637937\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −1.58930 −0.0509506
\(974\) −20.8544 −0.668219
\(975\) −1.84882 −0.0592095
\(976\) 3.55737 0.113869
\(977\) −13.8230 −0.442235 −0.221118 0.975247i \(-0.570971\pi\)
−0.221118 + 0.975247i \(0.570971\pi\)
\(978\) 11.8922 0.380270
\(979\) 0.118152 0.00377617
\(980\) 15.8168 0.505251
\(981\) −15.0495 −0.480493
\(982\) 29.1552 0.930381
\(983\) −8.65886 −0.276175 −0.138087 0.990420i \(-0.544095\pi\)
−0.138087 + 0.990420i \(0.544095\pi\)
\(984\) 10.7554 0.342869
\(985\) 15.3143 0.487955
\(986\) 39.8019 1.26755
\(987\) 9.05816 0.288324
\(988\) −1.97784 −0.0629235
\(989\) 1.23369 0.0392291
\(990\) −0.630140 −0.0200271
\(991\) 4.05681 0.128869 0.0644344 0.997922i \(-0.479476\pi\)
0.0644344 + 0.997922i \(0.479476\pi\)
\(992\) 7.15427 0.227148
\(993\) 22.7353 0.721483
\(994\) 9.21526 0.292290
\(995\) 3.01859 0.0956959
\(996\) −13.3970 −0.424499
\(997\) −40.8563 −1.29393 −0.646966 0.762519i \(-0.723962\pi\)
−0.646966 + 0.762519i \(0.723962\pi\)
\(998\) 22.6831 0.718021
\(999\) −5.41686 −0.171382
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 \(a_p\))