Properties

Label 6034.2.a.n.1.7
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.44122 q^{3}\) \(+1.00000 q^{4}\) \(-2.06061 q^{5}\) \(+1.44122 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-0.922894 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.44122 q^{3}\) \(+1.00000 q^{4}\) \(-2.06061 q^{5}\) \(+1.44122 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-0.922894 q^{9}\) \(+2.06061 q^{10}\) \(+5.36187 q^{11}\) \(-1.44122 q^{12}\) \(-1.30949 q^{13}\) \(+1.00000 q^{14}\) \(+2.96979 q^{15}\) \(+1.00000 q^{16}\) \(+0.952708 q^{17}\) \(+0.922894 q^{18}\) \(+0.858033 q^{19}\) \(-2.06061 q^{20}\) \(+1.44122 q^{21}\) \(-5.36187 q^{22}\) \(-3.31160 q^{23}\) \(+1.44122 q^{24}\) \(-0.753879 q^{25}\) \(+1.30949 q^{26}\) \(+5.65374 q^{27}\) \(-1.00000 q^{28}\) \(-6.46534 q^{29}\) \(-2.96979 q^{30}\) \(-1.34002 q^{31}\) \(-1.00000 q^{32}\) \(-7.72761 q^{33}\) \(-0.952708 q^{34}\) \(+2.06061 q^{35}\) \(-0.922894 q^{36}\) \(+10.6717 q^{37}\) \(-0.858033 q^{38}\) \(+1.88725 q^{39}\) \(+2.06061 q^{40}\) \(+10.3312 q^{41}\) \(-1.44122 q^{42}\) \(-12.4429 q^{43}\) \(+5.36187 q^{44}\) \(+1.90173 q^{45}\) \(+3.31160 q^{46}\) \(-0.731597 q^{47}\) \(-1.44122 q^{48}\) \(+1.00000 q^{49}\) \(+0.753879 q^{50}\) \(-1.37306 q^{51}\) \(-1.30949 q^{52}\) \(-5.33616 q^{53}\) \(-5.65374 q^{54}\) \(-11.0487 q^{55}\) \(+1.00000 q^{56}\) \(-1.23661 q^{57}\) \(+6.46534 q^{58}\) \(+3.54084 q^{59}\) \(+2.96979 q^{60}\) \(+10.5771 q^{61}\) \(+1.34002 q^{62}\) \(+0.922894 q^{63}\) \(+1.00000 q^{64}\) \(+2.69834 q^{65}\) \(+7.72761 q^{66}\) \(+5.59410 q^{67}\) \(+0.952708 q^{68}\) \(+4.77274 q^{69}\) \(-2.06061 q^{70}\) \(-6.54641 q^{71}\) \(+0.922894 q^{72}\) \(-14.5970 q^{73}\) \(-10.6717 q^{74}\) \(+1.08650 q^{75}\) \(+0.858033 q^{76}\) \(-5.36187 q^{77}\) \(-1.88725 q^{78}\) \(+7.82490 q^{79}\) \(-2.06061 q^{80}\) \(-5.37959 q^{81}\) \(-10.3312 q^{82}\) \(-8.16771 q^{83}\) \(+1.44122 q^{84}\) \(-1.96316 q^{85}\) \(+12.4429 q^{86}\) \(+9.31796 q^{87}\) \(-5.36187 q^{88}\) \(-9.24161 q^{89}\) \(-1.90173 q^{90}\) \(+1.30949 q^{91}\) \(-3.31160 q^{92}\) \(+1.93126 q^{93}\) \(+0.731597 q^{94}\) \(-1.76807 q^{95}\) \(+1.44122 q^{96}\) \(-7.78207 q^{97}\) \(-1.00000 q^{98}\) \(-4.94844 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.44122 −0.832087 −0.416043 0.909345i \(-0.636584\pi\)
−0.416043 + 0.909345i \(0.636584\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.06061 −0.921534 −0.460767 0.887521i \(-0.652426\pi\)
−0.460767 + 0.887521i \(0.652426\pi\)
\(6\) 1.44122 0.588374
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −0.922894 −0.307631
\(10\) 2.06061 0.651623
\(11\) 5.36187 1.61666 0.808332 0.588727i \(-0.200371\pi\)
0.808332 + 0.588727i \(0.200371\pi\)
\(12\) −1.44122 −0.416043
\(13\) −1.30949 −0.363186 −0.181593 0.983374i \(-0.558125\pi\)
−0.181593 + 0.983374i \(0.558125\pi\)
\(14\) 1.00000 0.267261
\(15\) 2.96979 0.766796
\(16\) 1.00000 0.250000
\(17\) 0.952708 0.231066 0.115533 0.993304i \(-0.463142\pi\)
0.115533 + 0.993304i \(0.463142\pi\)
\(18\) 0.922894 0.217528
\(19\) 0.858033 0.196846 0.0984231 0.995145i \(-0.468620\pi\)
0.0984231 + 0.995145i \(0.468620\pi\)
\(20\) −2.06061 −0.460767
\(21\) 1.44122 0.314499
\(22\) −5.36187 −1.14315
\(23\) −3.31160 −0.690517 −0.345258 0.938508i \(-0.612209\pi\)
−0.345258 + 0.938508i \(0.612209\pi\)
\(24\) 1.44122 0.294187
\(25\) −0.753879 −0.150776
\(26\) 1.30949 0.256811
\(27\) 5.65374 1.08806
\(28\) −1.00000 −0.188982
\(29\) −6.46534 −1.20058 −0.600292 0.799781i \(-0.704949\pi\)
−0.600292 + 0.799781i \(0.704949\pi\)
\(30\) −2.96979 −0.542207
\(31\) −1.34002 −0.240674 −0.120337 0.992733i \(-0.538398\pi\)
−0.120337 + 0.992733i \(0.538398\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.72761 −1.34520
\(34\) −0.952708 −0.163388
\(35\) 2.06061 0.348307
\(36\) −0.922894 −0.153816
\(37\) 10.6717 1.75441 0.877205 0.480115i \(-0.159405\pi\)
0.877205 + 0.480115i \(0.159405\pi\)
\(38\) −0.858033 −0.139191
\(39\) 1.88725 0.302202
\(40\) 2.06061 0.325811
\(41\) 10.3312 1.61346 0.806729 0.590921i \(-0.201236\pi\)
0.806729 + 0.590921i \(0.201236\pi\)
\(42\) −1.44122 −0.222385
\(43\) −12.4429 −1.89753 −0.948765 0.315984i \(-0.897665\pi\)
−0.948765 + 0.315984i \(0.897665\pi\)
\(44\) 5.36187 0.808332
\(45\) 1.90173 0.283493
\(46\) 3.31160 0.488269
\(47\) −0.731597 −0.106714 −0.0533572 0.998575i \(-0.516992\pi\)
−0.0533572 + 0.998575i \(0.516992\pi\)
\(48\) −1.44122 −0.208022
\(49\) 1.00000 0.142857
\(50\) 0.753879 0.106615
\(51\) −1.37306 −0.192267
\(52\) −1.30949 −0.181593
\(53\) −5.33616 −0.732978 −0.366489 0.930422i \(-0.619440\pi\)
−0.366489 + 0.930422i \(0.619440\pi\)
\(54\) −5.65374 −0.769377
\(55\) −11.0487 −1.48981
\(56\) 1.00000 0.133631
\(57\) −1.23661 −0.163793
\(58\) 6.46534 0.848941
\(59\) 3.54084 0.460978 0.230489 0.973075i \(-0.425967\pi\)
0.230489 + 0.973075i \(0.425967\pi\)
\(60\) 2.96979 0.383398
\(61\) 10.5771 1.35426 0.677132 0.735862i \(-0.263223\pi\)
0.677132 + 0.735862i \(0.263223\pi\)
\(62\) 1.34002 0.170182
\(63\) 0.922894 0.116274
\(64\) 1.00000 0.125000
\(65\) 2.69834 0.334688
\(66\) 7.72761 0.951204
\(67\) 5.59410 0.683429 0.341714 0.939804i \(-0.388992\pi\)
0.341714 + 0.939804i \(0.388992\pi\)
\(68\) 0.952708 0.115533
\(69\) 4.77274 0.574570
\(70\) −2.06061 −0.246290
\(71\) −6.54641 −0.776916 −0.388458 0.921467i \(-0.626992\pi\)
−0.388458 + 0.921467i \(0.626992\pi\)
\(72\) 0.922894 0.108764
\(73\) −14.5970 −1.70845 −0.854224 0.519905i \(-0.825967\pi\)
−0.854224 + 0.519905i \(0.825967\pi\)
\(74\) −10.6717 −1.24056
\(75\) 1.08650 0.125459
\(76\) 0.858033 0.0984231
\(77\) −5.36187 −0.611042
\(78\) −1.88725 −0.213689
\(79\) 7.82490 0.880370 0.440185 0.897907i \(-0.354913\pi\)
0.440185 + 0.897907i \(0.354913\pi\)
\(80\) −2.06061 −0.230383
\(81\) −5.37959 −0.597732
\(82\) −10.3312 −1.14089
\(83\) −8.16771 −0.896522 −0.448261 0.893903i \(-0.647957\pi\)
−0.448261 + 0.893903i \(0.647957\pi\)
\(84\) 1.44122 0.157250
\(85\) −1.96316 −0.212935
\(86\) 12.4429 1.34176
\(87\) 9.31796 0.998990
\(88\) −5.36187 −0.571577
\(89\) −9.24161 −0.979609 −0.489804 0.871832i \(-0.662932\pi\)
−0.489804 + 0.871832i \(0.662932\pi\)
\(90\) −1.90173 −0.200460
\(91\) 1.30949 0.137271
\(92\) −3.31160 −0.345258
\(93\) 1.93126 0.200262
\(94\) 0.731597 0.0754585
\(95\) −1.76807 −0.181400
\(96\) 1.44122 0.147094
\(97\) −7.78207 −0.790150 −0.395075 0.918649i \(-0.629281\pi\)
−0.395075 + 0.918649i \(0.629281\pi\)
\(98\) −1.00000 −0.101015
\(99\) −4.94844 −0.497336
\(100\) −0.753879 −0.0753879
\(101\) 2.58345 0.257063 0.128532 0.991705i \(-0.458974\pi\)
0.128532 + 0.991705i \(0.458974\pi\)
\(102\) 1.37306 0.135953
\(103\) −7.45659 −0.734720 −0.367360 0.930079i \(-0.619738\pi\)
−0.367360 + 0.930079i \(0.619738\pi\)
\(104\) 1.30949 0.128406
\(105\) −2.96979 −0.289822
\(106\) 5.33616 0.518294
\(107\) −15.1193 −1.46164 −0.730819 0.682571i \(-0.760862\pi\)
−0.730819 + 0.682571i \(0.760862\pi\)
\(108\) 5.65374 0.544031
\(109\) −11.0227 −1.05578 −0.527892 0.849311i \(-0.677017\pi\)
−0.527892 + 0.849311i \(0.677017\pi\)
\(110\) 11.0487 1.05345
\(111\) −15.3802 −1.45982
\(112\) −1.00000 −0.0944911
\(113\) 7.36105 0.692469 0.346235 0.938148i \(-0.387460\pi\)
0.346235 + 0.938148i \(0.387460\pi\)
\(114\) 1.23661 0.115819
\(115\) 6.82393 0.636334
\(116\) −6.46534 −0.600292
\(117\) 1.20852 0.111727
\(118\) −3.54084 −0.325961
\(119\) −0.952708 −0.0873346
\(120\) −2.96979 −0.271103
\(121\) 17.7496 1.61360
\(122\) −10.5771 −0.957609
\(123\) −14.8895 −1.34254
\(124\) −1.34002 −0.120337
\(125\) 11.8565 1.06048
\(126\) −0.922894 −0.0822179
\(127\) 1.48055 0.131378 0.0656888 0.997840i \(-0.479076\pi\)
0.0656888 + 0.997840i \(0.479076\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 17.9330 1.57891
\(130\) −2.69834 −0.236660
\(131\) 10.7800 0.941849 0.470924 0.882174i \(-0.343920\pi\)
0.470924 + 0.882174i \(0.343920\pi\)
\(132\) −7.72761 −0.672602
\(133\) −0.858033 −0.0744009
\(134\) −5.59410 −0.483257
\(135\) −11.6502 −1.00269
\(136\) −0.952708 −0.0816940
\(137\) −1.96379 −0.167778 −0.0838891 0.996475i \(-0.526734\pi\)
−0.0838891 + 0.996475i \(0.526734\pi\)
\(138\) −4.77274 −0.406282
\(139\) −19.5278 −1.65632 −0.828162 0.560489i \(-0.810613\pi\)
−0.828162 + 0.560489i \(0.810613\pi\)
\(140\) 2.06061 0.174153
\(141\) 1.05439 0.0887957
\(142\) 6.54641 0.549362
\(143\) −7.02129 −0.587149
\(144\) −0.922894 −0.0769078
\(145\) 13.3226 1.10638
\(146\) 14.5970 1.20806
\(147\) −1.44122 −0.118870
\(148\) 10.6717 0.877205
\(149\) −12.5231 −1.02593 −0.512967 0.858408i \(-0.671454\pi\)
−0.512967 + 0.858408i \(0.671454\pi\)
\(150\) −1.08650 −0.0887126
\(151\) 7.93284 0.645565 0.322783 0.946473i \(-0.395382\pi\)
0.322783 + 0.946473i \(0.395382\pi\)
\(152\) −0.858033 −0.0695956
\(153\) −0.879248 −0.0710830
\(154\) 5.36187 0.432072
\(155\) 2.76126 0.221789
\(156\) 1.88725 0.151101
\(157\) −20.4111 −1.62898 −0.814491 0.580176i \(-0.802984\pi\)
−0.814491 + 0.580176i \(0.802984\pi\)
\(158\) −7.82490 −0.622516
\(159\) 7.69057 0.609902
\(160\) 2.06061 0.162906
\(161\) 3.31160 0.260991
\(162\) 5.37959 0.422660
\(163\) 11.7522 0.920505 0.460252 0.887788i \(-0.347759\pi\)
0.460252 + 0.887788i \(0.347759\pi\)
\(164\) 10.3312 0.806729
\(165\) 15.9236 1.23965
\(166\) 8.16771 0.633937
\(167\) 4.08743 0.316295 0.158148 0.987415i \(-0.449448\pi\)
0.158148 + 0.987415i \(0.449448\pi\)
\(168\) −1.44122 −0.111192
\(169\) −11.2852 −0.868096
\(170\) 1.96316 0.150568
\(171\) −0.791873 −0.0605561
\(172\) −12.4429 −0.948765
\(173\) 12.9144 0.981862 0.490931 0.871198i \(-0.336657\pi\)
0.490931 + 0.871198i \(0.336657\pi\)
\(174\) −9.31796 −0.706393
\(175\) 0.753879 0.0569879
\(176\) 5.36187 0.404166
\(177\) −5.10312 −0.383574
\(178\) 9.24161 0.692688
\(179\) −14.0782 −1.05225 −0.526127 0.850406i \(-0.676356\pi\)
−0.526127 + 0.850406i \(0.676356\pi\)
\(180\) 1.90173 0.141746
\(181\) 14.5243 1.07958 0.539790 0.841800i \(-0.318504\pi\)
0.539790 + 0.841800i \(0.318504\pi\)
\(182\) −1.30949 −0.0970655
\(183\) −15.2440 −1.12687
\(184\) 3.31160 0.244135
\(185\) −21.9902 −1.61675
\(186\) −1.93126 −0.141607
\(187\) 5.10829 0.373555
\(188\) −0.731597 −0.0533572
\(189\) −5.65374 −0.411249
\(190\) 1.76807 0.128269
\(191\) 16.4301 1.18884 0.594421 0.804154i \(-0.297381\pi\)
0.594421 + 0.804154i \(0.297381\pi\)
\(192\) −1.44122 −0.104011
\(193\) 1.84467 0.132782 0.0663912 0.997794i \(-0.478851\pi\)
0.0663912 + 0.997794i \(0.478851\pi\)
\(194\) 7.78207 0.558720
\(195\) −3.88889 −0.278489
\(196\) 1.00000 0.0714286
\(197\) 21.6830 1.54485 0.772424 0.635107i \(-0.219044\pi\)
0.772424 + 0.635107i \(0.219044\pi\)
\(198\) 4.94844 0.351670
\(199\) 2.47717 0.175602 0.0878008 0.996138i \(-0.472016\pi\)
0.0878008 + 0.996138i \(0.472016\pi\)
\(200\) 0.753879 0.0533073
\(201\) −8.06232 −0.568672
\(202\) −2.58345 −0.181771
\(203\) 6.46534 0.453778
\(204\) −1.37306 −0.0961333
\(205\) −21.2885 −1.48686
\(206\) 7.45659 0.519526
\(207\) 3.05626 0.212425
\(208\) −1.30949 −0.0907965
\(209\) 4.60066 0.318234
\(210\) 2.96979 0.204935
\(211\) −0.834672 −0.0574612 −0.0287306 0.999587i \(-0.509146\pi\)
−0.0287306 + 0.999587i \(0.509146\pi\)
\(212\) −5.33616 −0.366489
\(213\) 9.43479 0.646461
\(214\) 15.1193 1.03353
\(215\) 25.6400 1.74864
\(216\) −5.65374 −0.384688
\(217\) 1.34002 0.0909663
\(218\) 11.0227 0.746552
\(219\) 21.0374 1.42158
\(220\) −11.0487 −0.744905
\(221\) −1.24756 −0.0839197
\(222\) 15.3802 1.03225
\(223\) −10.1578 −0.680219 −0.340110 0.940386i \(-0.610464\pi\)
−0.340110 + 0.940386i \(0.610464\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0.695750 0.0463833
\(226\) −7.36105 −0.489650
\(227\) 6.81561 0.452368 0.226184 0.974085i \(-0.427375\pi\)
0.226184 + 0.974085i \(0.427375\pi\)
\(228\) −1.23661 −0.0818966
\(229\) 13.1381 0.868188 0.434094 0.900868i \(-0.357069\pi\)
0.434094 + 0.900868i \(0.357069\pi\)
\(230\) −6.82393 −0.449956
\(231\) 7.72761 0.508440
\(232\) 6.46534 0.424471
\(233\) 15.4705 1.01351 0.506753 0.862092i \(-0.330846\pi\)
0.506753 + 0.862092i \(0.330846\pi\)
\(234\) −1.20852 −0.0790032
\(235\) 1.50754 0.0983409
\(236\) 3.54084 0.230489
\(237\) −11.2774 −0.732545
\(238\) 0.952708 0.0617549
\(239\) −26.3858 −1.70675 −0.853376 0.521295i \(-0.825449\pi\)
−0.853376 + 0.521295i \(0.825449\pi\)
\(240\) 2.96979 0.191699
\(241\) −3.18617 −0.205240 −0.102620 0.994721i \(-0.532722\pi\)
−0.102620 + 0.994721i \(0.532722\pi\)
\(242\) −17.7496 −1.14099
\(243\) −9.20807 −0.590698
\(244\) 10.5771 0.677132
\(245\) −2.06061 −0.131648
\(246\) 14.8895 0.949318
\(247\) −1.12358 −0.0714918
\(248\) 1.34002 0.0850912
\(249\) 11.7714 0.745985
\(250\) −11.8565 −0.749872
\(251\) 26.4734 1.67099 0.835493 0.549501i \(-0.185182\pi\)
0.835493 + 0.549501i \(0.185182\pi\)
\(252\) 0.922894 0.0581369
\(253\) −17.7564 −1.11633
\(254\) −1.48055 −0.0928980
\(255\) 2.82934 0.177180
\(256\) 1.00000 0.0625000
\(257\) 23.9020 1.49097 0.745484 0.666524i \(-0.232219\pi\)
0.745484 + 0.666524i \(0.232219\pi\)
\(258\) −17.9330 −1.11646
\(259\) −10.6717 −0.663105
\(260\) 2.69834 0.167344
\(261\) 5.96683 0.369337
\(262\) −10.7800 −0.665988
\(263\) −11.0210 −0.679582 −0.339791 0.940501i \(-0.610356\pi\)
−0.339791 + 0.940501i \(0.610356\pi\)
\(264\) 7.72761 0.475602
\(265\) 10.9958 0.675464
\(266\) 0.858033 0.0526094
\(267\) 13.3192 0.815120
\(268\) 5.59410 0.341714
\(269\) 14.5455 0.886852 0.443426 0.896311i \(-0.353763\pi\)
0.443426 + 0.896311i \(0.353763\pi\)
\(270\) 11.6502 0.709007
\(271\) 8.59631 0.522189 0.261094 0.965313i \(-0.415917\pi\)
0.261094 + 0.965313i \(0.415917\pi\)
\(272\) 0.952708 0.0577664
\(273\) −1.88725 −0.114222
\(274\) 1.96379 0.118637
\(275\) −4.04220 −0.243754
\(276\) 4.77274 0.287285
\(277\) 15.0235 0.902674 0.451337 0.892354i \(-0.350947\pi\)
0.451337 + 0.892354i \(0.350947\pi\)
\(278\) 19.5278 1.17120
\(279\) 1.23669 0.0740390
\(280\) −2.06061 −0.123145
\(281\) −1.41898 −0.0846493 −0.0423247 0.999104i \(-0.513476\pi\)
−0.0423247 + 0.999104i \(0.513476\pi\)
\(282\) −1.05439 −0.0627880
\(283\) 27.0107 1.60562 0.802810 0.596235i \(-0.203337\pi\)
0.802810 + 0.596235i \(0.203337\pi\)
\(284\) −6.54641 −0.388458
\(285\) 2.54818 0.150941
\(286\) 7.02129 0.415177
\(287\) −10.3312 −0.609830
\(288\) 0.922894 0.0543820
\(289\) −16.0923 −0.946609
\(290\) −13.3226 −0.782328
\(291\) 11.2157 0.657473
\(292\) −14.5970 −0.854224
\(293\) 17.7650 1.03785 0.518923 0.854821i \(-0.326333\pi\)
0.518923 + 0.854821i \(0.326333\pi\)
\(294\) 1.44122 0.0840535
\(295\) −7.29630 −0.424807
\(296\) −10.6717 −0.620278
\(297\) 30.3146 1.75903
\(298\) 12.5231 0.725445
\(299\) 4.33649 0.250786
\(300\) 1.08650 0.0627293
\(301\) 12.4429 0.717199
\(302\) −7.93284 −0.456484
\(303\) −3.72332 −0.213899
\(304\) 0.858033 0.0492116
\(305\) −21.7954 −1.24800
\(306\) 0.879248 0.0502633
\(307\) −10.8429 −0.618836 −0.309418 0.950926i \(-0.600134\pi\)
−0.309418 + 0.950926i \(0.600134\pi\)
\(308\) −5.36187 −0.305521
\(309\) 10.7466 0.611351
\(310\) −2.76126 −0.156829
\(311\) 19.1207 1.08423 0.542117 0.840303i \(-0.317623\pi\)
0.542117 + 0.840303i \(0.317623\pi\)
\(312\) −1.88725 −0.106845
\(313\) 3.54610 0.200438 0.100219 0.994965i \(-0.468046\pi\)
0.100219 + 0.994965i \(0.468046\pi\)
\(314\) 20.4111 1.15186
\(315\) −1.90173 −0.107150
\(316\) 7.82490 0.440185
\(317\) 14.8345 0.833187 0.416594 0.909093i \(-0.363224\pi\)
0.416594 + 0.909093i \(0.363224\pi\)
\(318\) −7.69057 −0.431265
\(319\) −34.6663 −1.94094
\(320\) −2.06061 −0.115192
\(321\) 21.7902 1.21621
\(322\) −3.31160 −0.184548
\(323\) 0.817454 0.0454844
\(324\) −5.37959 −0.298866
\(325\) 0.987193 0.0547596
\(326\) −11.7522 −0.650895
\(327\) 15.8861 0.878504
\(328\) −10.3312 −0.570444
\(329\) 0.731597 0.0403343
\(330\) −15.9236 −0.876566
\(331\) −5.85968 −0.322077 −0.161039 0.986948i \(-0.551484\pi\)
−0.161039 + 0.986948i \(0.551484\pi\)
\(332\) −8.16771 −0.448261
\(333\) −9.84881 −0.539712
\(334\) −4.08743 −0.223654
\(335\) −11.5273 −0.629802
\(336\) 1.44122 0.0786248
\(337\) −35.6583 −1.94243 −0.971216 0.238201i \(-0.923442\pi\)
−0.971216 + 0.238201i \(0.923442\pi\)
\(338\) 11.2852 0.613837
\(339\) −10.6089 −0.576195
\(340\) −1.96316 −0.106467
\(341\) −7.18500 −0.389090
\(342\) 0.791873 0.0428196
\(343\) −1.00000 −0.0539949
\(344\) 12.4429 0.670878
\(345\) −9.83476 −0.529486
\(346\) −12.9144 −0.694281
\(347\) −30.3916 −1.63151 −0.815753 0.578401i \(-0.803677\pi\)
−0.815753 + 0.578401i \(0.803677\pi\)
\(348\) 9.31796 0.499495
\(349\) 20.1347 1.07779 0.538894 0.842373i \(-0.318842\pi\)
0.538894 + 0.842373i \(0.318842\pi\)
\(350\) −0.753879 −0.0402965
\(351\) −7.40349 −0.395169
\(352\) −5.36187 −0.285789
\(353\) 2.93478 0.156202 0.0781012 0.996945i \(-0.475114\pi\)
0.0781012 + 0.996945i \(0.475114\pi\)
\(354\) 5.10312 0.271228
\(355\) 13.4896 0.715954
\(356\) −9.24161 −0.489804
\(357\) 1.37306 0.0726700
\(358\) 14.0782 0.744056
\(359\) 7.85580 0.414613 0.207307 0.978276i \(-0.433530\pi\)
0.207307 + 0.978276i \(0.433530\pi\)
\(360\) −1.90173 −0.100230
\(361\) −18.2638 −0.961252
\(362\) −14.5243 −0.763379
\(363\) −25.5811 −1.34266
\(364\) 1.30949 0.0686357
\(365\) 30.0787 1.57439
\(366\) 15.2440 0.796814
\(367\) 33.3337 1.74001 0.870004 0.493045i \(-0.164116\pi\)
0.870004 + 0.493045i \(0.164116\pi\)
\(368\) −3.31160 −0.172629
\(369\) −9.53458 −0.496350
\(370\) 21.9902 1.14321
\(371\) 5.33616 0.277040
\(372\) 1.93126 0.100131
\(373\) 3.92427 0.203191 0.101596 0.994826i \(-0.467605\pi\)
0.101596 + 0.994826i \(0.467605\pi\)
\(374\) −5.10829 −0.264144
\(375\) −17.0878 −0.882410
\(376\) 0.731597 0.0377292
\(377\) 8.46627 0.436035
\(378\) 5.65374 0.290797
\(379\) 10.4331 0.535913 0.267956 0.963431i \(-0.413652\pi\)
0.267956 + 0.963431i \(0.413652\pi\)
\(380\) −1.76807 −0.0907002
\(381\) −2.13379 −0.109318
\(382\) −16.4301 −0.840639
\(383\) −20.5998 −1.05260 −0.526301 0.850298i \(-0.676421\pi\)
−0.526301 + 0.850298i \(0.676421\pi\)
\(384\) 1.44122 0.0735468
\(385\) 11.0487 0.563095
\(386\) −1.84467 −0.0938913
\(387\) 11.4835 0.583739
\(388\) −7.78207 −0.395075
\(389\) 33.3523 1.69103 0.845515 0.533952i \(-0.179294\pi\)
0.845515 + 0.533952i \(0.179294\pi\)
\(390\) 3.88889 0.196922
\(391\) −3.15499 −0.159555
\(392\) −1.00000 −0.0505076
\(393\) −15.5363 −0.783700
\(394\) −21.6830 −1.09237
\(395\) −16.1241 −0.811291
\(396\) −4.94844 −0.248668
\(397\) −13.6159 −0.683363 −0.341681 0.939816i \(-0.610996\pi\)
−0.341681 + 0.939816i \(0.610996\pi\)
\(398\) −2.47717 −0.124169
\(399\) 1.23661 0.0619080
\(400\) −0.753879 −0.0376939
\(401\) −2.99379 −0.149503 −0.0747513 0.997202i \(-0.523816\pi\)
−0.0747513 + 0.997202i \(0.523816\pi\)
\(402\) 8.06232 0.402112
\(403\) 1.75473 0.0874095
\(404\) 2.58345 0.128532
\(405\) 11.0852 0.550830
\(406\) −6.46534 −0.320870
\(407\) 57.2201 2.83629
\(408\) 1.37306 0.0679765
\(409\) 3.45863 0.171018 0.0855091 0.996337i \(-0.472748\pi\)
0.0855091 + 0.996337i \(0.472748\pi\)
\(410\) 21.2885 1.05137
\(411\) 2.83025 0.139606
\(412\) −7.45659 −0.367360
\(413\) −3.54084 −0.174233
\(414\) −3.05626 −0.150207
\(415\) 16.8305 0.826176
\(416\) 1.30949 0.0642028
\(417\) 28.1438 1.37821
\(418\) −4.60066 −0.225026
\(419\) −0.276812 −0.0135231 −0.00676156 0.999977i \(-0.502152\pi\)
−0.00676156 + 0.999977i \(0.502152\pi\)
\(420\) −2.96979 −0.144911
\(421\) −22.1698 −1.08049 −0.540245 0.841508i \(-0.681668\pi\)
−0.540245 + 0.841508i \(0.681668\pi\)
\(422\) 0.834672 0.0406312
\(423\) 0.675187 0.0328287
\(424\) 5.33616 0.259147
\(425\) −0.718226 −0.0348391
\(426\) −9.43479 −0.457117
\(427\) −10.5771 −0.511864
\(428\) −15.1193 −0.730819
\(429\) 10.1192 0.488559
\(430\) −25.6400 −1.23647
\(431\) 1.00000 0.0481683
\(432\) 5.65374 0.272016
\(433\) 3.21212 0.154365 0.0771823 0.997017i \(-0.475408\pi\)
0.0771823 + 0.997017i \(0.475408\pi\)
\(434\) −1.34002 −0.0643229
\(435\) −19.2007 −0.920603
\(436\) −11.0227 −0.527892
\(437\) −2.84146 −0.135926
\(438\) −21.0374 −1.00521
\(439\) 24.6687 1.17737 0.588686 0.808362i \(-0.299645\pi\)
0.588686 + 0.808362i \(0.299645\pi\)
\(440\) 11.0487 0.526727
\(441\) −0.922894 −0.0439473
\(442\) 1.24756 0.0593402
\(443\) 11.4123 0.542215 0.271108 0.962549i \(-0.412610\pi\)
0.271108 + 0.962549i \(0.412610\pi\)
\(444\) −15.3802 −0.729911
\(445\) 19.0434 0.902742
\(446\) 10.1578 0.480988
\(447\) 18.0485 0.853666
\(448\) −1.00000 −0.0472456
\(449\) 12.3645 0.583518 0.291759 0.956492i \(-0.405760\pi\)
0.291759 + 0.956492i \(0.405760\pi\)
\(450\) −0.695750 −0.0327980
\(451\) 55.3944 2.60842
\(452\) 7.36105 0.346235
\(453\) −11.4329 −0.537166
\(454\) −6.81561 −0.319872
\(455\) −2.69834 −0.126500
\(456\) 1.23661 0.0579096
\(457\) 11.0586 0.517298 0.258649 0.965971i \(-0.416723\pi\)
0.258649 + 0.965971i \(0.416723\pi\)
\(458\) −13.1381 −0.613902
\(459\) 5.38636 0.251414
\(460\) 6.82393 0.318167
\(461\) 7.74473 0.360708 0.180354 0.983602i \(-0.442276\pi\)
0.180354 + 0.983602i \(0.442276\pi\)
\(462\) −7.72761 −0.359521
\(463\) 26.8388 1.24730 0.623652 0.781702i \(-0.285648\pi\)
0.623652 + 0.781702i \(0.285648\pi\)
\(464\) −6.46534 −0.300146
\(465\) −3.97957 −0.184548
\(466\) −15.4705 −0.716656
\(467\) 14.2019 0.657184 0.328592 0.944472i \(-0.393426\pi\)
0.328592 + 0.944472i \(0.393426\pi\)
\(468\) 1.20852 0.0558637
\(469\) −5.59410 −0.258312
\(470\) −1.50754 −0.0695375
\(471\) 29.4168 1.35545
\(472\) −3.54084 −0.162980
\(473\) −66.7173 −3.06767
\(474\) 11.2774 0.517987
\(475\) −0.646853 −0.0296796
\(476\) −0.952708 −0.0436673
\(477\) 4.92471 0.225487
\(478\) 26.3858 1.20686
\(479\) 25.3041 1.15617 0.578086 0.815976i \(-0.303800\pi\)
0.578086 + 0.815976i \(0.303800\pi\)
\(480\) −2.96979 −0.135552
\(481\) −13.9744 −0.637177
\(482\) 3.18617 0.145126
\(483\) −4.77274 −0.217167
\(484\) 17.7496 0.806801
\(485\) 16.0358 0.728150
\(486\) 9.20807 0.417687
\(487\) 6.27381 0.284293 0.142147 0.989846i \(-0.454600\pi\)
0.142147 + 0.989846i \(0.454600\pi\)
\(488\) −10.5771 −0.478805
\(489\) −16.9375 −0.765940
\(490\) 2.06061 0.0930890
\(491\) 38.7200 1.74741 0.873705 0.486456i \(-0.161711\pi\)
0.873705 + 0.486456i \(0.161711\pi\)
\(492\) −14.8895 −0.671269
\(493\) −6.15958 −0.277414
\(494\) 1.12358 0.0505523
\(495\) 10.1968 0.458312
\(496\) −1.34002 −0.0601686
\(497\) 6.54641 0.293647
\(498\) −11.7714 −0.527491
\(499\) −23.5779 −1.05549 −0.527745 0.849403i \(-0.676962\pi\)
−0.527745 + 0.849403i \(0.676962\pi\)
\(500\) 11.8565 0.530239
\(501\) −5.89088 −0.263185
\(502\) −26.4734 −1.18157
\(503\) 41.8306 1.86513 0.932566 0.360999i \(-0.117564\pi\)
0.932566 + 0.360999i \(0.117564\pi\)
\(504\) −0.922894 −0.0411090
\(505\) −5.32349 −0.236892
\(506\) 17.7564 0.789367
\(507\) 16.2645 0.722331
\(508\) 1.48055 0.0656888
\(509\) 28.4218 1.25978 0.629888 0.776686i \(-0.283101\pi\)
0.629888 + 0.776686i \(0.283101\pi\)
\(510\) −2.82934 −0.125285
\(511\) 14.5970 0.645733
\(512\) −1.00000 −0.0441942
\(513\) 4.85109 0.214181
\(514\) −23.9020 −1.05427
\(515\) 15.3651 0.677069
\(516\) 17.9330 0.789455
\(517\) −3.92273 −0.172521
\(518\) 10.6717 0.468886
\(519\) −18.6124 −0.816995
\(520\) −2.69834 −0.118330
\(521\) 31.0440 1.36006 0.680030 0.733184i \(-0.261967\pi\)
0.680030 + 0.733184i \(0.261967\pi\)
\(522\) −5.96683 −0.261161
\(523\) 3.22234 0.140903 0.0704516 0.997515i \(-0.477556\pi\)
0.0704516 + 0.997515i \(0.477556\pi\)
\(524\) 10.7800 0.470924
\(525\) −1.08650 −0.0474189
\(526\) 11.0210 0.480537
\(527\) −1.27665 −0.0556116
\(528\) −7.72761 −0.336301
\(529\) −12.0333 −0.523187
\(530\) −10.9958 −0.477625
\(531\) −3.26782 −0.141811
\(532\) −0.858033 −0.0372004
\(533\) −13.5285 −0.585985
\(534\) −13.3192 −0.576377
\(535\) 31.1550 1.34695
\(536\) −5.59410 −0.241629
\(537\) 20.2897 0.875567
\(538\) −14.5455 −0.627099
\(539\) 5.36187 0.230952
\(540\) −11.6502 −0.501343
\(541\) −6.35637 −0.273282 −0.136641 0.990621i \(-0.543631\pi\)
−0.136641 + 0.990621i \(0.543631\pi\)
\(542\) −8.59631 −0.369243
\(543\) −20.9326 −0.898305
\(544\) −0.952708 −0.0408470
\(545\) 22.7135 0.972941
\(546\) 1.88725 0.0807669
\(547\) −15.1207 −0.646513 −0.323257 0.946311i \(-0.604778\pi\)
−0.323257 + 0.946311i \(0.604778\pi\)
\(548\) −1.96379 −0.0838891
\(549\) −9.76158 −0.416614
\(550\) 4.04220 0.172360
\(551\) −5.54748 −0.236330
\(552\) −4.77274 −0.203141
\(553\) −7.82490 −0.332749
\(554\) −15.0235 −0.638287
\(555\) 31.6926 1.34528
\(556\) −19.5278 −0.828162
\(557\) −14.8428 −0.628909 −0.314454 0.949273i \(-0.601822\pi\)
−0.314454 + 0.949273i \(0.601822\pi\)
\(558\) −1.23669 −0.0523535
\(559\) 16.2938 0.689156
\(560\) 2.06061 0.0870767
\(561\) −7.36216 −0.310831
\(562\) 1.41898 0.0598561
\(563\) −24.0489 −1.01354 −0.506770 0.862081i \(-0.669161\pi\)
−0.506770 + 0.862081i \(0.669161\pi\)
\(564\) 1.05439 0.0443978
\(565\) −15.1683 −0.638134
\(566\) −27.0107 −1.13534
\(567\) 5.37959 0.225921
\(568\) 6.54641 0.274681
\(569\) −34.0739 −1.42845 −0.714226 0.699915i \(-0.753221\pi\)
−0.714226 + 0.699915i \(0.753221\pi\)
\(570\) −2.54818 −0.106731
\(571\) −11.9891 −0.501729 −0.250865 0.968022i \(-0.580715\pi\)
−0.250865 + 0.968022i \(0.580715\pi\)
\(572\) −7.02129 −0.293575
\(573\) −23.6794 −0.989221
\(574\) 10.3312 0.431215
\(575\) 2.49655 0.104113
\(576\) −0.922894 −0.0384539
\(577\) −31.6775 −1.31875 −0.659376 0.751814i \(-0.729179\pi\)
−0.659376 + 0.751814i \(0.729179\pi\)
\(578\) 16.0923 0.669353
\(579\) −2.65857 −0.110486
\(580\) 13.3226 0.553189
\(581\) 8.16771 0.338854
\(582\) −11.2157 −0.464904
\(583\) −28.6118 −1.18498
\(584\) 14.5970 0.604028
\(585\) −2.49028 −0.102960
\(586\) −17.7650 −0.733867
\(587\) 11.8890 0.490710 0.245355 0.969433i \(-0.421095\pi\)
0.245355 + 0.969433i \(0.421095\pi\)
\(588\) −1.44122 −0.0594348
\(589\) −1.14978 −0.0473758
\(590\) 7.29630 0.300384
\(591\) −31.2499 −1.28545
\(592\) 10.6717 0.438603
\(593\) 5.09907 0.209394 0.104697 0.994504i \(-0.466613\pi\)
0.104697 + 0.994504i \(0.466613\pi\)
\(594\) −30.3146 −1.24382
\(595\) 1.96316 0.0804818
\(596\) −12.5231 −0.512967
\(597\) −3.57013 −0.146116
\(598\) −4.33649 −0.177332
\(599\) 23.2671 0.950668 0.475334 0.879805i \(-0.342327\pi\)
0.475334 + 0.879805i \(0.342327\pi\)
\(600\) −1.08650 −0.0443563
\(601\) −13.7735 −0.561834 −0.280917 0.959732i \(-0.590639\pi\)
−0.280917 + 0.959732i \(0.590639\pi\)
\(602\) −12.4429 −0.507136
\(603\) −5.16276 −0.210244
\(604\) 7.93284 0.322783
\(605\) −36.5751 −1.48699
\(606\) 3.72332 0.151249
\(607\) 29.9745 1.21663 0.608314 0.793697i \(-0.291846\pi\)
0.608314 + 0.793697i \(0.291846\pi\)
\(608\) −0.858033 −0.0347978
\(609\) −9.31796 −0.377583
\(610\) 21.7954 0.882469
\(611\) 0.958016 0.0387572
\(612\) −0.879248 −0.0355415
\(613\) 4.61196 0.186275 0.0931377 0.995653i \(-0.470310\pi\)
0.0931377 + 0.995653i \(0.470310\pi\)
\(614\) 10.8429 0.437583
\(615\) 30.6814 1.23719
\(616\) 5.36187 0.216036
\(617\) −0.189931 −0.00764632 −0.00382316 0.999993i \(-0.501217\pi\)
−0.00382316 + 0.999993i \(0.501217\pi\)
\(618\) −10.7466 −0.432290
\(619\) 26.2899 1.05668 0.528340 0.849033i \(-0.322815\pi\)
0.528340 + 0.849033i \(0.322815\pi\)
\(620\) 2.76126 0.110895
\(621\) −18.7229 −0.751326
\(622\) −19.1207 −0.766670
\(623\) 9.24161 0.370257
\(624\) 1.88725 0.0755505
\(625\) −20.6623 −0.826491
\(626\) −3.54610 −0.141731
\(627\) −6.63055 −0.264798
\(628\) −20.4111 −0.814491
\(629\) 10.1670 0.405384
\(630\) 1.90173 0.0757666
\(631\) 26.7760 1.06594 0.532968 0.846136i \(-0.321077\pi\)
0.532968 + 0.846136i \(0.321077\pi\)
\(632\) −7.82490 −0.311258
\(633\) 1.20294 0.0478127
\(634\) −14.8345 −0.589152
\(635\) −3.05084 −0.121069
\(636\) 7.69057 0.304951
\(637\) −1.30949 −0.0518837
\(638\) 34.6663 1.37245
\(639\) 6.04164 0.239004
\(640\) 2.06061 0.0814528
\(641\) 1.83176 0.0723502 0.0361751 0.999345i \(-0.488483\pi\)
0.0361751 + 0.999345i \(0.488483\pi\)
\(642\) −21.7902 −0.859991
\(643\) 42.4874 1.67554 0.837770 0.546024i \(-0.183859\pi\)
0.837770 + 0.546024i \(0.183859\pi\)
\(644\) 3.31160 0.130495
\(645\) −36.9529 −1.45502
\(646\) −0.817454 −0.0321623
\(647\) −10.3764 −0.407940 −0.203970 0.978977i \(-0.565385\pi\)
−0.203970 + 0.978977i \(0.565385\pi\)
\(648\) 5.37959 0.211330
\(649\) 18.9855 0.745247
\(650\) −0.987193 −0.0387209
\(651\) −1.93126 −0.0756919
\(652\) 11.7522 0.460252
\(653\) 13.8983 0.543881 0.271940 0.962314i \(-0.412335\pi\)
0.271940 + 0.962314i \(0.412335\pi\)
\(654\) −15.8861 −0.621196
\(655\) −22.2133 −0.867946
\(656\) 10.3312 0.403365
\(657\) 13.4715 0.525572
\(658\) −0.731597 −0.0285206
\(659\) 39.5933 1.54234 0.771168 0.636632i \(-0.219673\pi\)
0.771168 + 0.636632i \(0.219673\pi\)
\(660\) 15.9236 0.619826
\(661\) −45.8999 −1.78530 −0.892649 0.450752i \(-0.851156\pi\)
−0.892649 + 0.450752i \(0.851156\pi\)
\(662\) 5.85968 0.227743
\(663\) 1.79800 0.0698285
\(664\) 8.16771 0.316969
\(665\) 1.76807 0.0685629
\(666\) 9.84881 0.381634
\(667\) 21.4106 0.829023
\(668\) 4.08743 0.158148
\(669\) 14.6397 0.566002
\(670\) 11.5273 0.445338
\(671\) 56.7132 2.18939
\(672\) −1.44122 −0.0555961
\(673\) −34.4120 −1.32648 −0.663242 0.748405i \(-0.730820\pi\)
−0.663242 + 0.748405i \(0.730820\pi\)
\(674\) 35.6583 1.37351
\(675\) −4.26223 −0.164053
\(676\) −11.2852 −0.434048
\(677\) −1.23111 −0.0473152 −0.0236576 0.999720i \(-0.507531\pi\)
−0.0236576 + 0.999720i \(0.507531\pi\)
\(678\) 10.6089 0.407431
\(679\) 7.78207 0.298649
\(680\) 1.96316 0.0752838
\(681\) −9.82277 −0.376409
\(682\) 7.18500 0.275128
\(683\) −1.44557 −0.0553133 −0.0276566 0.999617i \(-0.508805\pi\)
−0.0276566 + 0.999617i \(0.508805\pi\)
\(684\) −0.791873 −0.0302780
\(685\) 4.04662 0.154613
\(686\) 1.00000 0.0381802
\(687\) −18.9348 −0.722408
\(688\) −12.4429 −0.474382
\(689\) 6.98762 0.266207
\(690\) 9.83476 0.374403
\(691\) −12.0649 −0.458970 −0.229485 0.973312i \(-0.573704\pi\)
−0.229485 + 0.973312i \(0.573704\pi\)
\(692\) 12.9144 0.490931
\(693\) 4.94844 0.187976
\(694\) 30.3916 1.15365
\(695\) 40.2392 1.52636
\(696\) −9.31796 −0.353196
\(697\) 9.84259 0.372815
\(698\) −20.1347 −0.762111
\(699\) −22.2963 −0.843324
\(700\) 0.753879 0.0284939
\(701\) −9.83329 −0.371398 −0.185699 0.982607i \(-0.559455\pi\)
−0.185699 + 0.982607i \(0.559455\pi\)
\(702\) 7.40349 0.279427
\(703\) 9.15664 0.345349
\(704\) 5.36187 0.202083
\(705\) −2.17269 −0.0818282
\(706\) −2.93478 −0.110452
\(707\) −2.58345 −0.0971607
\(708\) −5.10312 −0.191787
\(709\) 45.2023 1.69761 0.848804 0.528708i \(-0.177323\pi\)
0.848804 + 0.528708i \(0.177323\pi\)
\(710\) −13.4896 −0.506256
\(711\) −7.22156 −0.270829
\(712\) 9.24161 0.346344
\(713\) 4.43761 0.166190
\(714\) −1.37306 −0.0513854
\(715\) 14.4681 0.541078
\(716\) −14.0782 −0.526127
\(717\) 38.0276 1.42017
\(718\) −7.85580 −0.293176
\(719\) 10.7166 0.399662 0.199831 0.979830i \(-0.435961\pi\)
0.199831 + 0.979830i \(0.435961\pi\)
\(720\) 1.90173 0.0708731
\(721\) 7.45659 0.277698
\(722\) 18.2638 0.679708
\(723\) 4.59197 0.170777
\(724\) 14.5243 0.539790
\(725\) 4.87408 0.181019
\(726\) 25.5811 0.949402
\(727\) 23.6351 0.876577 0.438288 0.898834i \(-0.355585\pi\)
0.438288 + 0.898834i \(0.355585\pi\)
\(728\) −1.30949 −0.0485327
\(729\) 29.4096 1.08924
\(730\) −30.0787 −1.11326
\(731\) −11.8545 −0.438454
\(732\) −15.2440 −0.563433
\(733\) 20.9517 0.773868 0.386934 0.922107i \(-0.373534\pi\)
0.386934 + 0.922107i \(0.373534\pi\)
\(734\) −33.3337 −1.23037
\(735\) 2.96979 0.109542
\(736\) 3.31160 0.122067
\(737\) 29.9948 1.10487
\(738\) 9.53458 0.350973
\(739\) −21.8405 −0.803417 −0.401708 0.915768i \(-0.631583\pi\)
−0.401708 + 0.915768i \(0.631583\pi\)
\(740\) −21.9902 −0.808374
\(741\) 1.61932 0.0594874
\(742\) −5.33616 −0.195897
\(743\) −13.4089 −0.491924 −0.245962 0.969279i \(-0.579104\pi\)
−0.245962 + 0.969279i \(0.579104\pi\)
\(744\) −1.93126 −0.0708033
\(745\) 25.8053 0.945433
\(746\) −3.92427 −0.143678
\(747\) 7.53793 0.275798
\(748\) 5.10829 0.186778
\(749\) 15.1193 0.552447
\(750\) 17.0878 0.623958
\(751\) 45.4168 1.65728 0.828642 0.559779i \(-0.189114\pi\)
0.828642 + 0.559779i \(0.189114\pi\)
\(752\) −0.731597 −0.0266786
\(753\) −38.1539 −1.39041
\(754\) −8.46627 −0.308323
\(755\) −16.3465 −0.594910
\(756\) −5.65374 −0.205625
\(757\) −16.7771 −0.609775 −0.304887 0.952388i \(-0.598619\pi\)
−0.304887 + 0.952388i \(0.598619\pi\)
\(758\) −10.4331 −0.378947
\(759\) 25.5908 0.928886
\(760\) 1.76807 0.0641347
\(761\) 9.96107 0.361089 0.180544 0.983567i \(-0.442214\pi\)
0.180544 + 0.983567i \(0.442214\pi\)
\(762\) 2.13379 0.0772992
\(763\) 11.0227 0.399049
\(764\) 16.4301 0.594421
\(765\) 1.81179 0.0655054
\(766\) 20.5998 0.744302
\(767\) −4.63668 −0.167421
\(768\) −1.44122 −0.0520054
\(769\) 26.1494 0.942971 0.471485 0.881874i \(-0.343718\pi\)
0.471485 + 0.881874i \(0.343718\pi\)
\(770\) −11.0487 −0.398169
\(771\) −34.4480 −1.24061
\(772\) 1.84467 0.0663912
\(773\) −10.2663 −0.369253 −0.184626 0.982809i \(-0.559108\pi\)
−0.184626 + 0.982809i \(0.559108\pi\)
\(774\) −11.4835 −0.412766
\(775\) 1.01021 0.0362878
\(776\) 7.78207 0.279360
\(777\) 15.3802 0.551761
\(778\) −33.3523 −1.19574
\(779\) 8.86449 0.317603
\(780\) −3.88889 −0.139245
\(781\) −35.1010 −1.25601
\(782\) 3.15499 0.112822
\(783\) −36.5534 −1.30631
\(784\) 1.00000 0.0357143
\(785\) 42.0593 1.50116
\(786\) 15.5363 0.554160
\(787\) −29.9952 −1.06922 −0.534608 0.845100i \(-0.679541\pi\)
−0.534608 + 0.845100i \(0.679541\pi\)
\(788\) 21.6830 0.772424
\(789\) 15.8836 0.565471
\(790\) 16.1241 0.573669
\(791\) −7.36105 −0.261729
\(792\) 4.94844 0.175835
\(793\) −13.8506 −0.491849
\(794\) 13.6159 0.483210
\(795\) −15.8473 −0.562045
\(796\) 2.47717 0.0878008
\(797\) −35.2420 −1.24833 −0.624167 0.781291i \(-0.714562\pi\)
−0.624167 + 0.781291i \(0.714562\pi\)
\(798\) −1.23661 −0.0437756
\(799\) −0.696998 −0.0246580
\(800\) 0.753879 0.0266536
\(801\) 8.52903 0.301358
\(802\) 2.99379 0.105714
\(803\) −78.2671 −2.76199
\(804\) −8.06232 −0.284336
\(805\) −6.82393 −0.240512
\(806\) −1.75473 −0.0618079
\(807\) −20.9632 −0.737938
\(808\) −2.58345 −0.0908855
\(809\) 49.1607 1.72840 0.864198 0.503151i \(-0.167826\pi\)
0.864198 + 0.503151i \(0.167826\pi\)
\(810\) −11.0852 −0.389496
\(811\) 14.9889 0.526333 0.263166 0.964750i \(-0.415233\pi\)
0.263166 + 0.964750i \(0.415233\pi\)
\(812\) 6.46534 0.226889
\(813\) −12.3891 −0.434506
\(814\) −57.2201 −2.00556
\(815\) −24.2168 −0.848276
\(816\) −1.37306 −0.0480667
\(817\) −10.6764 −0.373521
\(818\) −3.45863 −0.120928
\(819\) −1.20852 −0.0422290
\(820\) −21.2885 −0.743428
\(821\) −19.6250 −0.684919 −0.342459 0.939533i \(-0.611260\pi\)
−0.342459 + 0.939533i \(0.611260\pi\)
\(822\) −2.83025 −0.0987164
\(823\) −2.90579 −0.101289 −0.0506447 0.998717i \(-0.516128\pi\)
−0.0506447 + 0.998717i \(0.516128\pi\)
\(824\) 7.45659 0.259763
\(825\) 5.82568 0.202824
\(826\) 3.54084 0.123202
\(827\) 35.6584 1.23996 0.619981 0.784617i \(-0.287140\pi\)
0.619981 + 0.784617i \(0.287140\pi\)
\(828\) 3.05626 0.106212
\(829\) −28.9160 −1.00429 −0.502147 0.864782i \(-0.667456\pi\)
−0.502147 + 0.864782i \(0.667456\pi\)
\(830\) −16.8305 −0.584194
\(831\) −21.6521 −0.751103
\(832\) −1.30949 −0.0453982
\(833\) 0.952708 0.0330094
\(834\) −28.1438 −0.974539
\(835\) −8.42262 −0.291477
\(836\) 4.60066 0.159117
\(837\) −7.57611 −0.261869
\(838\) 0.276812 0.00956230
\(839\) 23.1069 0.797740 0.398870 0.917007i \(-0.369402\pi\)
0.398870 + 0.917007i \(0.369402\pi\)
\(840\) 2.96979 0.102467
\(841\) 12.8007 0.441402
\(842\) 22.1698 0.764022
\(843\) 2.04506 0.0704356
\(844\) −0.834672 −0.0287306
\(845\) 23.2545 0.799980
\(846\) −0.675187 −0.0232134
\(847\) −17.7496 −0.609884
\(848\) −5.33616 −0.183245
\(849\) −38.9283 −1.33602
\(850\) 0.718226 0.0246350
\(851\) −35.3403 −1.21145
\(852\) 9.43479 0.323231
\(853\) −42.3833 −1.45118 −0.725588 0.688130i \(-0.758432\pi\)
−0.725588 + 0.688130i \(0.758432\pi\)
\(854\) 10.5771 0.361942
\(855\) 1.63174 0.0558044
\(856\) 15.1193 0.516767
\(857\) −26.8447 −0.916999 −0.458499 0.888695i \(-0.651613\pi\)
−0.458499 + 0.888695i \(0.651613\pi\)
\(858\) −10.1192 −0.345464
\(859\) −23.2718 −0.794025 −0.397013 0.917813i \(-0.629953\pi\)
−0.397013 + 0.917813i \(0.629953\pi\)
\(860\) 25.6400 0.874318
\(861\) 14.8895 0.507432
\(862\) −1.00000 −0.0340601
\(863\) 11.2400 0.382615 0.191307 0.981530i \(-0.438727\pi\)
0.191307 + 0.981530i \(0.438727\pi\)
\(864\) −5.65374 −0.192344
\(865\) −26.6115 −0.904819
\(866\) −3.21212 −0.109152
\(867\) 23.1926 0.787661
\(868\) 1.34002 0.0454832
\(869\) 41.9561 1.42326
\(870\) 19.2007 0.650965
\(871\) −7.32540 −0.248212
\(872\) 11.0227 0.373276
\(873\) 7.18203 0.243075
\(874\) 2.84146 0.0961139
\(875\) −11.8565 −0.400823
\(876\) 21.0374 0.710789
\(877\) 33.0853 1.11721 0.558605 0.829434i \(-0.311337\pi\)
0.558605 + 0.829434i \(0.311337\pi\)
\(878\) −24.6687 −0.832528
\(879\) −25.6033 −0.863577
\(880\) −11.0487 −0.372453
\(881\) 2.80931 0.0946480 0.0473240 0.998880i \(-0.484931\pi\)
0.0473240 + 0.998880i \(0.484931\pi\)
\(882\) 0.922894 0.0310755
\(883\) 47.4740 1.59763 0.798814 0.601578i \(-0.205461\pi\)
0.798814 + 0.601578i \(0.205461\pi\)
\(884\) −1.24756 −0.0419599
\(885\) 10.5156 0.353476
\(886\) −11.4123 −0.383404
\(887\) 19.3974 0.651301 0.325651 0.945490i \(-0.394417\pi\)
0.325651 + 0.945490i \(0.394417\pi\)
\(888\) 15.3802 0.516125
\(889\) −1.48055 −0.0496561
\(890\) −19.0434 −0.638335
\(891\) −28.8446 −0.966331
\(892\) −10.1578 −0.340110
\(893\) −0.627734 −0.0210063
\(894\) −18.0485 −0.603633
\(895\) 29.0097 0.969687
\(896\) 1.00000 0.0334077
\(897\) −6.24983 −0.208676
\(898\) −12.3645 −0.412609
\(899\) 8.66368 0.288950
\(900\) 0.695750 0.0231917
\(901\) −5.08380 −0.169366
\(902\) −55.3944 −1.84443
\(903\) −17.9330 −0.596772
\(904\) −7.36105 −0.244825
\(905\) −29.9289 −0.994870
\(906\) 11.4329 0.379834
\(907\) −7.54944 −0.250675 −0.125338 0.992114i \(-0.540001\pi\)
−0.125338 + 0.992114i \(0.540001\pi\)
\(908\) 6.81561 0.226184
\(909\) −2.38425 −0.0790807
\(910\) 2.69834 0.0894491
\(911\) 33.8218 1.12057 0.560283 0.828302i \(-0.310693\pi\)
0.560283 + 0.828302i \(0.310693\pi\)
\(912\) −1.23661 −0.0409483
\(913\) −43.7942 −1.44938
\(914\) −11.0586 −0.365785
\(915\) 31.4119 1.03844
\(916\) 13.1381 0.434094
\(917\) −10.7800 −0.355985
\(918\) −5.38636 −0.177776
\(919\) −27.9602 −0.922320 −0.461160 0.887317i \(-0.652567\pi\)
−0.461160 + 0.887317i \(0.652567\pi\)
\(920\) −6.82393 −0.224978
\(921\) 15.6269 0.514925
\(922\) −7.74473 −0.255059
\(923\) 8.57242 0.282165
\(924\) 7.72761 0.254220
\(925\) −8.04514 −0.264523
\(926\) −26.8388 −0.881976
\(927\) 6.88165 0.226023
\(928\) 6.46534 0.212235
\(929\) −14.7532 −0.484038 −0.242019 0.970271i \(-0.577810\pi\)
−0.242019 + 0.970271i \(0.577810\pi\)
\(930\) 3.97957 0.130495
\(931\) 0.858033 0.0281209
\(932\) 15.4705 0.506753
\(933\) −27.5571 −0.902178
\(934\) −14.2019 −0.464700
\(935\) −10.5262 −0.344244
\(936\) −1.20852 −0.0395016
\(937\) −29.6050 −0.967154 −0.483577 0.875302i \(-0.660663\pi\)
−0.483577 + 0.875302i \(0.660663\pi\)
\(938\) 5.59410 0.182654
\(939\) −5.11070 −0.166782
\(940\) 1.50754 0.0491705
\(941\) 17.2183 0.561301 0.280651 0.959810i \(-0.409450\pi\)
0.280651 + 0.959810i \(0.409450\pi\)
\(942\) −29.4168 −0.958451
\(943\) −34.2127 −1.11412
\(944\) 3.54084 0.115245
\(945\) 11.6502 0.378980
\(946\) 66.7173 2.16917
\(947\) −6.41790 −0.208554 −0.104277 0.994548i \(-0.533253\pi\)
−0.104277 + 0.994548i \(0.533253\pi\)
\(948\) −11.2774 −0.366272
\(949\) 19.1145 0.620484
\(950\) 0.646853 0.0209867
\(951\) −21.3797 −0.693284
\(952\) 0.952708 0.0308774
\(953\) 5.91434 0.191584 0.0957922 0.995401i \(-0.469462\pi\)
0.0957922 + 0.995401i \(0.469462\pi\)
\(954\) −4.92471 −0.159443
\(955\) −33.8561 −1.09556
\(956\) −26.3858 −0.853376
\(957\) 49.9617 1.61503
\(958\) −25.3041 −0.817537
\(959\) 1.96379 0.0634142
\(960\) 2.96979 0.0958495
\(961\) −29.2044 −0.942076
\(962\) 13.9744 0.450552
\(963\) 13.9535 0.449646
\(964\) −3.18617 −0.102620
\(965\) −3.80115 −0.122363
\(966\) 4.77274 0.153560
\(967\) 3.59789 0.115700 0.0578501 0.998325i \(-0.481575\pi\)
0.0578501 + 0.998325i \(0.481575\pi\)
\(968\) −17.7496 −0.570495
\(969\) −1.17813 −0.0378470
\(970\) −16.0358 −0.514879
\(971\) 6.16633 0.197887 0.0989434 0.995093i \(-0.468454\pi\)
0.0989434 + 0.995093i \(0.468454\pi\)
\(972\) −9.20807 −0.295349
\(973\) 19.5278 0.626032
\(974\) −6.27381 −0.201026
\(975\) −1.42276 −0.0455648
\(976\) 10.5771 0.338566
\(977\) 19.0140 0.608312 0.304156 0.952622i \(-0.401626\pi\)
0.304156 + 0.952622i \(0.401626\pi\)
\(978\) 16.9375 0.541601
\(979\) −49.5523 −1.58370
\(980\) −2.06061 −0.0658238
\(981\) 10.1728 0.324792
\(982\) −38.7200 −1.23561
\(983\) 42.9016 1.36835 0.684175 0.729318i \(-0.260163\pi\)
0.684175 + 0.729318i \(0.260163\pi\)
\(984\) 14.8895 0.474659
\(985\) −44.6802 −1.42363
\(986\) 6.15958 0.196161
\(987\) −1.05439 −0.0335616
\(988\) −1.12358 −0.0357459
\(989\) 41.2060 1.31028
\(990\) −10.1968 −0.324076
\(991\) 46.1663 1.46652 0.733260 0.679949i \(-0.237998\pi\)
0.733260 + 0.679949i \(0.237998\pi\)
\(992\) 1.34002 0.0425456
\(993\) 8.44507 0.267996
\(994\) −6.54641 −0.207639
\(995\) −5.10448 −0.161823
\(996\) 11.7714 0.372992
\(997\) 9.25911 0.293239 0.146619 0.989193i \(-0.453161\pi\)
0.146619 + 0.989193i \(0.453161\pi\)
\(998\) 23.5779 0.746345
\(999\) 60.3348 1.90891
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 \(a_p\))