Properties

Label 6034.2.a.n.1.17
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 1.17
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.52105 q^{3}\) \(+1.00000 q^{4}\) \(-3.19164 q^{5}\) \(-1.52105 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-0.686407 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.52105 q^{3}\) \(+1.00000 q^{4}\) \(-3.19164 q^{5}\) \(-1.52105 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-0.686407 q^{9}\) \(+3.19164 q^{10}\) \(-1.28860 q^{11}\) \(+1.52105 q^{12}\) \(+1.34956 q^{13}\) \(+1.00000 q^{14}\) \(-4.85464 q^{15}\) \(+1.00000 q^{16}\) \(+5.77216 q^{17}\) \(+0.686407 q^{18}\) \(-7.04424 q^{19}\) \(-3.19164 q^{20}\) \(-1.52105 q^{21}\) \(+1.28860 q^{22}\) \(-5.21023 q^{23}\) \(-1.52105 q^{24}\) \(+5.18656 q^{25}\) \(-1.34956 q^{26}\) \(-5.60721 q^{27}\) \(-1.00000 q^{28}\) \(-2.06455 q^{29}\) \(+4.85464 q^{30}\) \(-1.05869 q^{31}\) \(-1.00000 q^{32}\) \(-1.96003 q^{33}\) \(-5.77216 q^{34}\) \(+3.19164 q^{35}\) \(-0.686407 q^{36}\) \(+0.620197 q^{37}\) \(+7.04424 q^{38}\) \(+2.05275 q^{39}\) \(+3.19164 q^{40}\) \(-6.09301 q^{41}\) \(+1.52105 q^{42}\) \(-9.64795 q^{43}\) \(-1.28860 q^{44}\) \(+2.19076 q^{45}\) \(+5.21023 q^{46}\) \(+11.2768 q^{47}\) \(+1.52105 q^{48}\) \(+1.00000 q^{49}\) \(-5.18656 q^{50}\) \(+8.77974 q^{51}\) \(+1.34956 q^{52}\) \(+11.5691 q^{53}\) \(+5.60721 q^{54}\) \(+4.11276 q^{55}\) \(+1.00000 q^{56}\) \(-10.7146 q^{57}\) \(+2.06455 q^{58}\) \(-2.46795 q^{59}\) \(-4.85464 q^{60}\) \(-9.99054 q^{61}\) \(+1.05869 q^{62}\) \(+0.686407 q^{63}\) \(+1.00000 q^{64}\) \(-4.30731 q^{65}\) \(+1.96003 q^{66}\) \(+15.7014 q^{67}\) \(+5.77216 q^{68}\) \(-7.92502 q^{69}\) \(-3.19164 q^{70}\) \(+7.43814 q^{71}\) \(+0.686407 q^{72}\) \(+5.84106 q^{73}\) \(-0.620197 q^{74}\) \(+7.88902 q^{75}\) \(-7.04424 q^{76}\) \(+1.28860 q^{77}\) \(-2.05275 q^{78}\) \(-2.91941 q^{79}\) \(-3.19164 q^{80}\) \(-6.46962 q^{81}\) \(+6.09301 q^{82}\) \(-2.31837 q^{83}\) \(-1.52105 q^{84}\) \(-18.4226 q^{85}\) \(+9.64795 q^{86}\) \(-3.14028 q^{87}\) \(+1.28860 q^{88}\) \(+14.5030 q^{89}\) \(-2.19076 q^{90}\) \(-1.34956 q^{91}\) \(-5.21023 q^{92}\) \(-1.61032 q^{93}\) \(-11.2768 q^{94}\) \(+22.4827 q^{95}\) \(-1.52105 q^{96}\) \(+9.65031 q^{97}\) \(-1.00000 q^{98}\) \(+0.884507 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.52105 0.878179 0.439089 0.898443i \(-0.355301\pi\)
0.439089 + 0.898443i \(0.355301\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.19164 −1.42734 −0.713672 0.700480i \(-0.752969\pi\)
−0.713672 + 0.700480i \(0.752969\pi\)
\(6\) −1.52105 −0.620966
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −0.686407 −0.228802
\(10\) 3.19164 1.00928
\(11\) −1.28860 −0.388529 −0.194264 0.980949i \(-0.562232\pi\)
−0.194264 + 0.980949i \(0.562232\pi\)
\(12\) 1.52105 0.439089
\(13\) 1.34956 0.374301 0.187150 0.982331i \(-0.440075\pi\)
0.187150 + 0.982331i \(0.440075\pi\)
\(14\) 1.00000 0.267261
\(15\) −4.85464 −1.25346
\(16\) 1.00000 0.250000
\(17\) 5.77216 1.39995 0.699977 0.714165i \(-0.253194\pi\)
0.699977 + 0.714165i \(0.253194\pi\)
\(18\) 0.686407 0.161788
\(19\) −7.04424 −1.61606 −0.808029 0.589142i \(-0.799466\pi\)
−0.808029 + 0.589142i \(0.799466\pi\)
\(20\) −3.19164 −0.713672
\(21\) −1.52105 −0.331920
\(22\) 1.28860 0.274731
\(23\) −5.21023 −1.08641 −0.543204 0.839601i \(-0.682789\pi\)
−0.543204 + 0.839601i \(0.682789\pi\)
\(24\) −1.52105 −0.310483
\(25\) 5.18656 1.03731
\(26\) −1.34956 −0.264671
\(27\) −5.60721 −1.07911
\(28\) −1.00000 −0.188982
\(29\) −2.06455 −0.383377 −0.191689 0.981456i \(-0.561396\pi\)
−0.191689 + 0.981456i \(0.561396\pi\)
\(30\) 4.85464 0.886332
\(31\) −1.05869 −0.190146 −0.0950730 0.995470i \(-0.530308\pi\)
−0.0950730 + 0.995470i \(0.530308\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.96003 −0.341197
\(34\) −5.77216 −0.989917
\(35\) 3.19164 0.539485
\(36\) −0.686407 −0.114401
\(37\) 0.620197 0.101960 0.0509799 0.998700i \(-0.483766\pi\)
0.0509799 + 0.998700i \(0.483766\pi\)
\(38\) 7.04424 1.14273
\(39\) 2.05275 0.328703
\(40\) 3.19164 0.504642
\(41\) −6.09301 −0.951569 −0.475784 0.879562i \(-0.657836\pi\)
−0.475784 + 0.879562i \(0.657836\pi\)
\(42\) 1.52105 0.234703
\(43\) −9.64795 −1.47130 −0.735649 0.677363i \(-0.763123\pi\)
−0.735649 + 0.677363i \(0.763123\pi\)
\(44\) −1.28860 −0.194264
\(45\) 2.19076 0.326580
\(46\) 5.21023 0.768207
\(47\) 11.2768 1.64489 0.822445 0.568844i \(-0.192609\pi\)
0.822445 + 0.568844i \(0.192609\pi\)
\(48\) 1.52105 0.219545
\(49\) 1.00000 0.142857
\(50\) −5.18656 −0.733490
\(51\) 8.77974 1.22941
\(52\) 1.34956 0.187150
\(53\) 11.5691 1.58914 0.794571 0.607172i \(-0.207696\pi\)
0.794571 + 0.607172i \(0.207696\pi\)
\(54\) 5.60721 0.763045
\(55\) 4.11276 0.554564
\(56\) 1.00000 0.133631
\(57\) −10.7146 −1.41919
\(58\) 2.06455 0.271089
\(59\) −2.46795 −0.321299 −0.160650 0.987011i \(-0.551359\pi\)
−0.160650 + 0.987011i \(0.551359\pi\)
\(60\) −4.85464 −0.626732
\(61\) −9.99054 −1.27916 −0.639579 0.768726i \(-0.720891\pi\)
−0.639579 + 0.768726i \(0.720891\pi\)
\(62\) 1.05869 0.134454
\(63\) 0.686407 0.0864792
\(64\) 1.00000 0.125000
\(65\) −4.30731 −0.534256
\(66\) 1.96003 0.241263
\(67\) 15.7014 1.91823 0.959114 0.283019i \(-0.0913361\pi\)
0.959114 + 0.283019i \(0.0913361\pi\)
\(68\) 5.77216 0.699977
\(69\) −7.92502 −0.954060
\(70\) −3.19164 −0.381474
\(71\) 7.43814 0.882745 0.441373 0.897324i \(-0.354492\pi\)
0.441373 + 0.897324i \(0.354492\pi\)
\(72\) 0.686407 0.0808939
\(73\) 5.84106 0.683645 0.341822 0.939765i \(-0.388956\pi\)
0.341822 + 0.939765i \(0.388956\pi\)
\(74\) −0.620197 −0.0720964
\(75\) 7.88902 0.910945
\(76\) −7.04424 −0.808029
\(77\) 1.28860 0.146850
\(78\) −2.05275 −0.232428
\(79\) −2.91941 −0.328459 −0.164229 0.986422i \(-0.552514\pi\)
−0.164229 + 0.986422i \(0.552514\pi\)
\(80\) −3.19164 −0.356836
\(81\) −6.46962 −0.718847
\(82\) 6.09301 0.672861
\(83\) −2.31837 −0.254475 −0.127237 0.991872i \(-0.540611\pi\)
−0.127237 + 0.991872i \(0.540611\pi\)
\(84\) −1.52105 −0.165960
\(85\) −18.4226 −1.99822
\(86\) 9.64795 1.04037
\(87\) −3.14028 −0.336674
\(88\) 1.28860 0.137366
\(89\) 14.5030 1.53732 0.768658 0.639660i \(-0.220925\pi\)
0.768658 + 0.639660i \(0.220925\pi\)
\(90\) −2.19076 −0.230927
\(91\) −1.34956 −0.141472
\(92\) −5.21023 −0.543204
\(93\) −1.61032 −0.166982
\(94\) −11.2768 −1.16311
\(95\) 22.4827 2.30667
\(96\) −1.52105 −0.155242
\(97\) 9.65031 0.979840 0.489920 0.871767i \(-0.337026\pi\)
0.489920 + 0.871767i \(0.337026\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0.884507 0.0888963
\(100\) 5.18656 0.518656
\(101\) −17.2580 −1.71724 −0.858620 0.512613i \(-0.828678\pi\)
−0.858620 + 0.512613i \(0.828678\pi\)
\(102\) −8.77974 −0.869324
\(103\) 8.12280 0.800364 0.400182 0.916436i \(-0.368947\pi\)
0.400182 + 0.916436i \(0.368947\pi\)
\(104\) −1.34956 −0.132335
\(105\) 4.85464 0.473765
\(106\) −11.5691 −1.12369
\(107\) −7.61685 −0.736349 −0.368174 0.929757i \(-0.620017\pi\)
−0.368174 + 0.929757i \(0.620017\pi\)
\(108\) −5.60721 −0.539554
\(109\) −14.9452 −1.43150 −0.715748 0.698359i \(-0.753914\pi\)
−0.715748 + 0.698359i \(0.753914\pi\)
\(110\) −4.11276 −0.392136
\(111\) 0.943351 0.0895389
\(112\) −1.00000 −0.0944911
\(113\) 5.90534 0.555528 0.277764 0.960649i \(-0.410407\pi\)
0.277764 + 0.960649i \(0.410407\pi\)
\(114\) 10.7146 1.00352
\(115\) 16.6292 1.55068
\(116\) −2.06455 −0.191689
\(117\) −0.926348 −0.0856409
\(118\) 2.46795 0.227193
\(119\) −5.77216 −0.529133
\(120\) 4.85464 0.443166
\(121\) −9.33950 −0.849046
\(122\) 9.99054 0.904501
\(123\) −9.26778 −0.835647
\(124\) −1.05869 −0.0950730
\(125\) −0.595431 −0.0532570
\(126\) −0.686407 −0.0611500
\(127\) 5.92583 0.525833 0.262916 0.964819i \(-0.415316\pi\)
0.262916 + 0.964819i \(0.415316\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −14.6750 −1.29206
\(130\) 4.30731 0.377776
\(131\) −7.13803 −0.623653 −0.311826 0.950139i \(-0.600941\pi\)
−0.311826 + 0.950139i \(0.600941\pi\)
\(132\) −1.96003 −0.170599
\(133\) 7.04424 0.610813
\(134\) −15.7014 −1.35639
\(135\) 17.8962 1.54026
\(136\) −5.77216 −0.494958
\(137\) 8.51425 0.727421 0.363711 0.931512i \(-0.381510\pi\)
0.363711 + 0.931512i \(0.381510\pi\)
\(138\) 7.92502 0.674623
\(139\) −8.10576 −0.687522 −0.343761 0.939057i \(-0.611701\pi\)
−0.343761 + 0.939057i \(0.611701\pi\)
\(140\) 3.19164 0.269743
\(141\) 17.1526 1.44451
\(142\) −7.43814 −0.624195
\(143\) −1.73905 −0.145426
\(144\) −0.686407 −0.0572006
\(145\) 6.58930 0.547211
\(146\) −5.84106 −0.483410
\(147\) 1.52105 0.125454
\(148\) 0.620197 0.0509799
\(149\) −13.2557 −1.08595 −0.542973 0.839750i \(-0.682701\pi\)
−0.542973 + 0.839750i \(0.682701\pi\)
\(150\) −7.88902 −0.644135
\(151\) 11.8253 0.962331 0.481165 0.876630i \(-0.340214\pi\)
0.481165 + 0.876630i \(0.340214\pi\)
\(152\) 7.04424 0.571363
\(153\) −3.96205 −0.320313
\(154\) −1.28860 −0.103839
\(155\) 3.37895 0.271404
\(156\) 2.05275 0.164351
\(157\) −10.4632 −0.835057 −0.417529 0.908664i \(-0.637104\pi\)
−0.417529 + 0.908664i \(0.637104\pi\)
\(158\) 2.91941 0.232256
\(159\) 17.5972 1.39555
\(160\) 3.19164 0.252321
\(161\) 5.21023 0.410624
\(162\) 6.46962 0.508302
\(163\) 2.15221 0.168574 0.0842870 0.996442i \(-0.473139\pi\)
0.0842870 + 0.996442i \(0.473139\pi\)
\(164\) −6.09301 −0.475784
\(165\) 6.25571 0.487006
\(166\) 2.31837 0.179941
\(167\) 22.9023 1.77224 0.886118 0.463461i \(-0.153392\pi\)
0.886118 + 0.463461i \(0.153392\pi\)
\(168\) 1.52105 0.117352
\(169\) −11.1787 −0.859899
\(170\) 18.4226 1.41295
\(171\) 4.83522 0.369758
\(172\) −9.64795 −0.735649
\(173\) 3.05284 0.232103 0.116051 0.993243i \(-0.462976\pi\)
0.116051 + 0.993243i \(0.462976\pi\)
\(174\) 3.14028 0.238064
\(175\) −5.18656 −0.392067
\(176\) −1.28860 −0.0971321
\(177\) −3.75387 −0.282158
\(178\) −14.5030 −1.08705
\(179\) 10.9370 0.817466 0.408733 0.912654i \(-0.365971\pi\)
0.408733 + 0.912654i \(0.365971\pi\)
\(180\) 2.19076 0.163290
\(181\) −7.20674 −0.535673 −0.267836 0.963464i \(-0.586309\pi\)
−0.267836 + 0.963464i \(0.586309\pi\)
\(182\) 1.34956 0.100036
\(183\) −15.1961 −1.12333
\(184\) 5.21023 0.384103
\(185\) −1.97944 −0.145532
\(186\) 1.61032 0.118074
\(187\) −7.43802 −0.543922
\(188\) 11.2768 0.822445
\(189\) 5.60721 0.407864
\(190\) −22.4827 −1.63106
\(191\) 4.94052 0.357483 0.178742 0.983896i \(-0.442797\pi\)
0.178742 + 0.983896i \(0.442797\pi\)
\(192\) 1.52105 0.109772
\(193\) 0.189080 0.0136102 0.00680512 0.999977i \(-0.497834\pi\)
0.00680512 + 0.999977i \(0.497834\pi\)
\(194\) −9.65031 −0.692852
\(195\) −6.55163 −0.469172
\(196\) 1.00000 0.0714286
\(197\) −2.30403 −0.164155 −0.0820776 0.996626i \(-0.526156\pi\)
−0.0820776 + 0.996626i \(0.526156\pi\)
\(198\) −0.884507 −0.0628592
\(199\) 22.6764 1.60749 0.803744 0.594975i \(-0.202838\pi\)
0.803744 + 0.594975i \(0.202838\pi\)
\(200\) −5.18656 −0.366745
\(201\) 23.8826 1.68455
\(202\) 17.2580 1.21427
\(203\) 2.06455 0.144903
\(204\) 8.77974 0.614705
\(205\) 19.4467 1.35822
\(206\) −8.12280 −0.565943
\(207\) 3.57634 0.248573
\(208\) 1.34956 0.0935752
\(209\) 9.07723 0.627885
\(210\) −4.85464 −0.335002
\(211\) 12.5303 0.862620 0.431310 0.902204i \(-0.358052\pi\)
0.431310 + 0.902204i \(0.358052\pi\)
\(212\) 11.5691 0.794571
\(213\) 11.3138 0.775208
\(214\) 7.61685 0.520677
\(215\) 30.7928 2.10005
\(216\) 5.60721 0.381522
\(217\) 1.05869 0.0718684
\(218\) 14.9452 1.01222
\(219\) 8.88455 0.600362
\(220\) 4.11276 0.277282
\(221\) 7.78987 0.524004
\(222\) −0.943351 −0.0633135
\(223\) −12.9727 −0.868717 −0.434359 0.900740i \(-0.643025\pi\)
−0.434359 + 0.900740i \(0.643025\pi\)
\(224\) 1.00000 0.0668153
\(225\) −3.56009 −0.237339
\(226\) −5.90534 −0.392817
\(227\) 7.24109 0.480608 0.240304 0.970698i \(-0.422753\pi\)
0.240304 + 0.970698i \(0.422753\pi\)
\(228\) −10.7146 −0.709594
\(229\) 3.79306 0.250653 0.125326 0.992116i \(-0.460002\pi\)
0.125326 + 0.992116i \(0.460002\pi\)
\(230\) −16.6292 −1.09650
\(231\) 1.96003 0.128961
\(232\) 2.06455 0.135544
\(233\) 14.4348 0.945656 0.472828 0.881155i \(-0.343233\pi\)
0.472828 + 0.881155i \(0.343233\pi\)
\(234\) 0.926348 0.0605573
\(235\) −35.9915 −2.34783
\(236\) −2.46795 −0.160650
\(237\) −4.44056 −0.288446
\(238\) 5.77216 0.374153
\(239\) 18.6684 1.20756 0.603779 0.797151i \(-0.293661\pi\)
0.603779 + 0.797151i \(0.293661\pi\)
\(240\) −4.85464 −0.313366
\(241\) −28.5089 −1.83642 −0.918209 0.396097i \(-0.870364\pi\)
−0.918209 + 0.396097i \(0.870364\pi\)
\(242\) 9.33950 0.600366
\(243\) 6.98101 0.447832
\(244\) −9.99054 −0.639579
\(245\) −3.19164 −0.203906
\(246\) 9.26778 0.590892
\(247\) −9.50662 −0.604892
\(248\) 1.05869 0.0672268
\(249\) −3.52636 −0.223474
\(250\) 0.595431 0.0376584
\(251\) 26.8629 1.69557 0.847786 0.530339i \(-0.177935\pi\)
0.847786 + 0.530339i \(0.177935\pi\)
\(252\) 0.686407 0.0432396
\(253\) 6.71392 0.422101
\(254\) −5.92583 −0.371820
\(255\) −28.0218 −1.75479
\(256\) 1.00000 0.0625000
\(257\) −10.6919 −0.666943 −0.333472 0.942760i \(-0.608220\pi\)
−0.333472 + 0.942760i \(0.608220\pi\)
\(258\) 14.6750 0.913627
\(259\) −0.620197 −0.0385372
\(260\) −4.30731 −0.267128
\(261\) 1.41712 0.0877176
\(262\) 7.13803 0.440989
\(263\) 12.9105 0.796094 0.398047 0.917365i \(-0.369688\pi\)
0.398047 + 0.917365i \(0.369688\pi\)
\(264\) 1.96003 0.120632
\(265\) −36.9245 −2.26825
\(266\) −7.04424 −0.431910
\(267\) 22.0598 1.35004
\(268\) 15.7014 0.959114
\(269\) 12.8847 0.785596 0.392798 0.919625i \(-0.371507\pi\)
0.392798 + 0.919625i \(0.371507\pi\)
\(270\) −17.8962 −1.08913
\(271\) −6.74674 −0.409835 −0.204918 0.978779i \(-0.565693\pi\)
−0.204918 + 0.978779i \(0.565693\pi\)
\(272\) 5.77216 0.349988
\(273\) −2.05275 −0.124238
\(274\) −8.51425 −0.514365
\(275\) −6.68342 −0.403025
\(276\) −7.92502 −0.477030
\(277\) 6.70796 0.403042 0.201521 0.979484i \(-0.435412\pi\)
0.201521 + 0.979484i \(0.435412\pi\)
\(278\) 8.10576 0.486151
\(279\) 0.726691 0.0435059
\(280\) −3.19164 −0.190737
\(281\) 23.7571 1.41723 0.708616 0.705594i \(-0.249320\pi\)
0.708616 + 0.705594i \(0.249320\pi\)
\(282\) −17.1526 −1.02142
\(283\) 0.277722 0.0165089 0.00825444 0.999966i \(-0.497373\pi\)
0.00825444 + 0.999966i \(0.497373\pi\)
\(284\) 7.43814 0.441373
\(285\) 34.1973 2.02567
\(286\) 1.73905 0.102832
\(287\) 6.09301 0.359659
\(288\) 0.686407 0.0404469
\(289\) 16.3178 0.959871
\(290\) −6.58930 −0.386937
\(291\) 14.6786 0.860475
\(292\) 5.84106 0.341822
\(293\) 2.33289 0.136289 0.0681443 0.997675i \(-0.478292\pi\)
0.0681443 + 0.997675i \(0.478292\pi\)
\(294\) −1.52105 −0.0887094
\(295\) 7.87680 0.458605
\(296\) −0.620197 −0.0360482
\(297\) 7.22547 0.419264
\(298\) 13.2557 0.767880
\(299\) −7.03152 −0.406643
\(300\) 7.88902 0.455473
\(301\) 9.64795 0.556099
\(302\) −11.8253 −0.680471
\(303\) −26.2503 −1.50804
\(304\) −7.04424 −0.404015
\(305\) 31.8862 1.82580
\(306\) 3.96205 0.226495
\(307\) 11.9231 0.680488 0.340244 0.940337i \(-0.389490\pi\)
0.340244 + 0.940337i \(0.389490\pi\)
\(308\) 1.28860 0.0734250
\(309\) 12.3552 0.702862
\(310\) −3.37895 −0.191912
\(311\) 13.8823 0.787196 0.393598 0.919283i \(-0.371230\pi\)
0.393598 + 0.919283i \(0.371230\pi\)
\(312\) −2.05275 −0.116214
\(313\) −0.493548 −0.0278970 −0.0139485 0.999903i \(-0.504440\pi\)
−0.0139485 + 0.999903i \(0.504440\pi\)
\(314\) 10.4632 0.590475
\(315\) −2.19076 −0.123436
\(316\) −2.91941 −0.164229
\(317\) 5.58340 0.313595 0.156798 0.987631i \(-0.449883\pi\)
0.156798 + 0.987631i \(0.449883\pi\)
\(318\) −17.5972 −0.986803
\(319\) 2.66039 0.148953
\(320\) −3.19164 −0.178418
\(321\) −11.5856 −0.646646
\(322\) −5.21023 −0.290355
\(323\) −40.6604 −2.26241
\(324\) −6.46962 −0.359424
\(325\) 6.99957 0.388267
\(326\) −2.15221 −0.119200
\(327\) −22.7325 −1.25711
\(328\) 6.09301 0.336430
\(329\) −11.2768 −0.621710
\(330\) −6.25571 −0.344365
\(331\) 20.1655 1.10840 0.554198 0.832385i \(-0.313025\pi\)
0.554198 + 0.832385i \(0.313025\pi\)
\(332\) −2.31837 −0.127237
\(333\) −0.425708 −0.0233286
\(334\) −22.9023 −1.25316
\(335\) −50.1131 −2.73797
\(336\) −1.52105 −0.0829801
\(337\) −12.4429 −0.677809 −0.338904 0.940821i \(-0.610056\pi\)
−0.338904 + 0.940821i \(0.610056\pi\)
\(338\) 11.1787 0.608040
\(339\) 8.98232 0.487852
\(340\) −18.4226 −0.999108
\(341\) 1.36423 0.0738772
\(342\) −4.83522 −0.261459
\(343\) −1.00000 −0.0539949
\(344\) 9.64795 0.520183
\(345\) 25.2938 1.36177
\(346\) −3.05284 −0.164122
\(347\) −4.20130 −0.225537 −0.112769 0.993621i \(-0.535972\pi\)
−0.112769 + 0.993621i \(0.535972\pi\)
\(348\) −3.14028 −0.168337
\(349\) 33.7381 1.80596 0.902981 0.429681i \(-0.141374\pi\)
0.902981 + 0.429681i \(0.141374\pi\)
\(350\) 5.18656 0.277233
\(351\) −7.56727 −0.403911
\(352\) 1.28860 0.0686828
\(353\) 25.2469 1.34376 0.671880 0.740660i \(-0.265487\pi\)
0.671880 + 0.740660i \(0.265487\pi\)
\(354\) 3.75387 0.199516
\(355\) −23.7399 −1.25998
\(356\) 14.5030 0.768658
\(357\) −8.77974 −0.464673
\(358\) −10.9370 −0.578036
\(359\) −9.59978 −0.506657 −0.253328 0.967380i \(-0.581525\pi\)
−0.253328 + 0.967380i \(0.581525\pi\)
\(360\) −2.19076 −0.115463
\(361\) 30.6213 1.61165
\(362\) 7.20674 0.378778
\(363\) −14.2058 −0.745614
\(364\) −1.34956 −0.0707362
\(365\) −18.6426 −0.975797
\(366\) 15.1961 0.794313
\(367\) 11.8428 0.618192 0.309096 0.951031i \(-0.399974\pi\)
0.309096 + 0.951031i \(0.399974\pi\)
\(368\) −5.21023 −0.271602
\(369\) 4.18229 0.217721
\(370\) 1.97944 0.102906
\(371\) −11.5691 −0.600639
\(372\) −1.61032 −0.0834911
\(373\) 24.7385 1.28091 0.640456 0.767995i \(-0.278745\pi\)
0.640456 + 0.767995i \(0.278745\pi\)
\(374\) 7.43802 0.384611
\(375\) −0.905681 −0.0467692
\(376\) −11.2768 −0.581557
\(377\) −2.78623 −0.143498
\(378\) −5.60721 −0.288404
\(379\) 8.42862 0.432949 0.216475 0.976288i \(-0.430544\pi\)
0.216475 + 0.976288i \(0.430544\pi\)
\(380\) 22.4827 1.15334
\(381\) 9.01349 0.461775
\(382\) −4.94052 −0.252779
\(383\) 22.2967 1.13931 0.569653 0.821885i \(-0.307078\pi\)
0.569653 + 0.821885i \(0.307078\pi\)
\(384\) −1.52105 −0.0776208
\(385\) −4.11276 −0.209606
\(386\) −0.189080 −0.00962390
\(387\) 6.62242 0.336637
\(388\) 9.65031 0.489920
\(389\) 6.43268 0.326150 0.163075 0.986614i \(-0.447859\pi\)
0.163075 + 0.986614i \(0.447859\pi\)
\(390\) 6.55163 0.331755
\(391\) −30.0743 −1.52092
\(392\) −1.00000 −0.0505076
\(393\) −10.8573 −0.547678
\(394\) 2.30403 0.116075
\(395\) 9.31769 0.468824
\(396\) 0.884507 0.0444481
\(397\) 18.5004 0.928509 0.464254 0.885702i \(-0.346322\pi\)
0.464254 + 0.885702i \(0.346322\pi\)
\(398\) −22.6764 −1.13667
\(399\) 10.7146 0.536403
\(400\) 5.18656 0.259328
\(401\) −9.81363 −0.490069 −0.245035 0.969514i \(-0.578799\pi\)
−0.245035 + 0.969514i \(0.578799\pi\)
\(402\) −23.8826 −1.19115
\(403\) −1.42876 −0.0711718
\(404\) −17.2580 −0.858620
\(405\) 20.6487 1.02604
\(406\) −2.06455 −0.102462
\(407\) −0.799188 −0.0396143
\(408\) −8.77974 −0.434662
\(409\) −21.6181 −1.06895 −0.534474 0.845185i \(-0.679490\pi\)
−0.534474 + 0.845185i \(0.679490\pi\)
\(410\) −19.4467 −0.960404
\(411\) 12.9506 0.638806
\(412\) 8.12280 0.400182
\(413\) 2.46795 0.121440
\(414\) −3.57634 −0.175768
\(415\) 7.39941 0.363223
\(416\) −1.34956 −0.0661676
\(417\) −12.3293 −0.603767
\(418\) −9.07723 −0.443982
\(419\) 13.3692 0.653126 0.326563 0.945175i \(-0.394109\pi\)
0.326563 + 0.945175i \(0.394109\pi\)
\(420\) 4.85464 0.236882
\(421\) 8.21394 0.400323 0.200162 0.979763i \(-0.435853\pi\)
0.200162 + 0.979763i \(0.435853\pi\)
\(422\) −12.5303 −0.609964
\(423\) −7.74048 −0.376355
\(424\) −11.5691 −0.561846
\(425\) 29.9376 1.45219
\(426\) −11.3138 −0.548155
\(427\) 9.99054 0.483476
\(428\) −7.61685 −0.368174
\(429\) −2.64518 −0.127710
\(430\) −30.7928 −1.48496
\(431\) 1.00000 0.0481683
\(432\) −5.60721 −0.269777
\(433\) −7.69393 −0.369747 −0.184873 0.982762i \(-0.559187\pi\)
−0.184873 + 0.982762i \(0.559187\pi\)
\(434\) −1.05869 −0.0508187
\(435\) 10.0226 0.480549
\(436\) −14.9452 −0.715748
\(437\) 36.7021 1.75570
\(438\) −8.88455 −0.424520
\(439\) −13.8335 −0.660236 −0.330118 0.943940i \(-0.607089\pi\)
−0.330118 + 0.943940i \(0.607089\pi\)
\(440\) −4.11276 −0.196068
\(441\) −0.686407 −0.0326861
\(442\) −7.78987 −0.370526
\(443\) −16.9069 −0.803271 −0.401636 0.915800i \(-0.631558\pi\)
−0.401636 + 0.915800i \(0.631558\pi\)
\(444\) 0.943351 0.0447694
\(445\) −46.2884 −2.19428
\(446\) 12.9727 0.614276
\(447\) −20.1625 −0.953655
\(448\) −1.00000 −0.0472456
\(449\) −20.4743 −0.966244 −0.483122 0.875553i \(-0.660497\pi\)
−0.483122 + 0.875553i \(0.660497\pi\)
\(450\) 3.56009 0.167824
\(451\) 7.85148 0.369712
\(452\) 5.90534 0.277764
\(453\) 17.9869 0.845098
\(454\) −7.24109 −0.339841
\(455\) 4.30731 0.201930
\(456\) 10.7146 0.501759
\(457\) 8.32894 0.389611 0.194806 0.980842i \(-0.437592\pi\)
0.194806 + 0.980842i \(0.437592\pi\)
\(458\) −3.79306 −0.177238
\(459\) −32.3657 −1.51070
\(460\) 16.6292 0.775339
\(461\) −30.3206 −1.41217 −0.706084 0.708128i \(-0.749540\pi\)
−0.706084 + 0.708128i \(0.749540\pi\)
\(462\) −1.96003 −0.0911888
\(463\) 12.7482 0.592461 0.296230 0.955117i \(-0.404270\pi\)
0.296230 + 0.955117i \(0.404270\pi\)
\(464\) −2.06455 −0.0958443
\(465\) 5.13955 0.238341
\(466\) −14.4348 −0.668680
\(467\) 19.7315 0.913065 0.456533 0.889707i \(-0.349091\pi\)
0.456533 + 0.889707i \(0.349091\pi\)
\(468\) −0.926348 −0.0428204
\(469\) −15.7014 −0.725022
\(470\) 35.9915 1.66016
\(471\) −15.9151 −0.733330
\(472\) 2.46795 0.113596
\(473\) 12.4324 0.571642
\(474\) 4.44056 0.203962
\(475\) −36.5354 −1.67636
\(476\) −5.77216 −0.264566
\(477\) −7.94113 −0.363599
\(478\) −18.6684 −0.853873
\(479\) −30.1114 −1.37583 −0.687913 0.725793i \(-0.741473\pi\)
−0.687913 + 0.725793i \(0.741473\pi\)
\(480\) 4.85464 0.221583
\(481\) 0.836993 0.0381636
\(482\) 28.5089 1.29854
\(483\) 7.92502 0.360601
\(484\) −9.33950 −0.424523
\(485\) −30.8003 −1.39857
\(486\) −6.98101 −0.316665
\(487\) −1.44157 −0.0653236 −0.0326618 0.999466i \(-0.510398\pi\)
−0.0326618 + 0.999466i \(0.510398\pi\)
\(488\) 9.99054 0.452250
\(489\) 3.27362 0.148038
\(490\) 3.19164 0.144184
\(491\) −8.76940 −0.395757 −0.197879 0.980227i \(-0.563405\pi\)
−0.197879 + 0.980227i \(0.563405\pi\)
\(492\) −9.26778 −0.417824
\(493\) −11.9169 −0.536710
\(494\) 9.50662 0.427723
\(495\) −2.82303 −0.126886
\(496\) −1.05869 −0.0475365
\(497\) −7.43814 −0.333646
\(498\) 3.52636 0.158020
\(499\) −9.82796 −0.439960 −0.219980 0.975504i \(-0.570599\pi\)
−0.219980 + 0.975504i \(0.570599\pi\)
\(500\) −0.595431 −0.0266285
\(501\) 34.8356 1.55634
\(502\) −26.8629 −1.19895
\(503\) 4.66012 0.207785 0.103892 0.994589i \(-0.466870\pi\)
0.103892 + 0.994589i \(0.466870\pi\)
\(504\) −0.686407 −0.0305750
\(505\) 55.0814 2.45109
\(506\) −6.71392 −0.298470
\(507\) −17.0033 −0.755145
\(508\) 5.92583 0.262916
\(509\) 13.4419 0.595801 0.297900 0.954597i \(-0.403714\pi\)
0.297900 + 0.954597i \(0.403714\pi\)
\(510\) 28.0218 1.24082
\(511\) −5.84106 −0.258393
\(512\) −1.00000 −0.0441942
\(513\) 39.4985 1.74390
\(514\) 10.6919 0.471600
\(515\) −25.9251 −1.14239
\(516\) −14.6750 −0.646032
\(517\) −14.5313 −0.639087
\(518\) 0.620197 0.0272499
\(519\) 4.64352 0.203828
\(520\) 4.30731 0.188888
\(521\) −26.6330 −1.16681 −0.583407 0.812180i \(-0.698281\pi\)
−0.583407 + 0.812180i \(0.698281\pi\)
\(522\) −1.41712 −0.0620257
\(523\) −26.6902 −1.16708 −0.583540 0.812085i \(-0.698333\pi\)
−0.583540 + 0.812085i \(0.698333\pi\)
\(524\) −7.13803 −0.311826
\(525\) −7.88902 −0.344305
\(526\) −12.9105 −0.562923
\(527\) −6.11092 −0.266196
\(528\) −1.96003 −0.0852994
\(529\) 4.14650 0.180283
\(530\) 36.9245 1.60390
\(531\) 1.69402 0.0735141
\(532\) 7.04424 0.305406
\(533\) −8.22289 −0.356173
\(534\) −22.0598 −0.954621
\(535\) 24.3102 1.05102
\(536\) −15.7014 −0.678196
\(537\) 16.6356 0.717881
\(538\) −12.8847 −0.555500
\(539\) −1.28860 −0.0555041
\(540\) 17.8962 0.770129
\(541\) 0.262978 0.0113063 0.00565316 0.999984i \(-0.498201\pi\)
0.00565316 + 0.999984i \(0.498201\pi\)
\(542\) 6.74674 0.289797
\(543\) −10.9618 −0.470416
\(544\) −5.77216 −0.247479
\(545\) 47.6998 2.04324
\(546\) 2.05275 0.0878495
\(547\) −15.6346 −0.668488 −0.334244 0.942487i \(-0.608481\pi\)
−0.334244 + 0.942487i \(0.608481\pi\)
\(548\) 8.51425 0.363711
\(549\) 6.85758 0.292674
\(550\) 6.68342 0.284982
\(551\) 14.5432 0.619560
\(552\) 7.92502 0.337311
\(553\) 2.91941 0.124146
\(554\) −6.70796 −0.284994
\(555\) −3.01083 −0.127803
\(556\) −8.10576 −0.343761
\(557\) 33.9298 1.43765 0.718826 0.695190i \(-0.244680\pi\)
0.718826 + 0.695190i \(0.244680\pi\)
\(558\) −0.726691 −0.0307633
\(559\) −13.0205 −0.550708
\(560\) 3.19164 0.134871
\(561\) −11.3136 −0.477661
\(562\) −23.7571 −1.00213
\(563\) −12.5560 −0.529172 −0.264586 0.964362i \(-0.585235\pi\)
−0.264586 + 0.964362i \(0.585235\pi\)
\(564\) 17.1526 0.722254
\(565\) −18.8477 −0.792929
\(566\) −0.277722 −0.0116735
\(567\) 6.46962 0.271699
\(568\) −7.43814 −0.312098
\(569\) −6.75825 −0.283321 −0.141660 0.989915i \(-0.545244\pi\)
−0.141660 + 0.989915i \(0.545244\pi\)
\(570\) −34.1973 −1.43237
\(571\) −11.7875 −0.493292 −0.246646 0.969106i \(-0.579329\pi\)
−0.246646 + 0.969106i \(0.579329\pi\)
\(572\) −1.73905 −0.0727132
\(573\) 7.51478 0.313934
\(574\) −6.09301 −0.254317
\(575\) −27.0232 −1.12694
\(576\) −0.686407 −0.0286003
\(577\) −1.79260 −0.0746270 −0.0373135 0.999304i \(-0.511880\pi\)
−0.0373135 + 0.999304i \(0.511880\pi\)
\(578\) −16.3178 −0.678731
\(579\) 0.287599 0.0119522
\(580\) 6.58930 0.273606
\(581\) 2.31837 0.0961824
\(582\) −14.6786 −0.608447
\(583\) −14.9080 −0.617427
\(584\) −5.84106 −0.241705
\(585\) 2.95657 0.122239
\(586\) −2.33289 −0.0963706
\(587\) −22.3933 −0.924271 −0.462136 0.886809i \(-0.652917\pi\)
−0.462136 + 0.886809i \(0.652917\pi\)
\(588\) 1.52105 0.0627270
\(589\) 7.45765 0.307287
\(590\) −7.87680 −0.324283
\(591\) −3.50454 −0.144158
\(592\) 0.620197 0.0254899
\(593\) 41.3315 1.69728 0.848641 0.528969i \(-0.177421\pi\)
0.848641 + 0.528969i \(0.177421\pi\)
\(594\) −7.22547 −0.296465
\(595\) 18.4226 0.755255
\(596\) −13.2557 −0.542973
\(597\) 34.4920 1.41166
\(598\) 7.03152 0.287540
\(599\) 8.37665 0.342261 0.171130 0.985248i \(-0.445258\pi\)
0.171130 + 0.985248i \(0.445258\pi\)
\(600\) −7.88902 −0.322068
\(601\) −5.47057 −0.223149 −0.111575 0.993756i \(-0.535589\pi\)
−0.111575 + 0.993756i \(0.535589\pi\)
\(602\) −9.64795 −0.393221
\(603\) −10.7775 −0.438895
\(604\) 11.8253 0.481165
\(605\) 29.8083 1.21188
\(606\) 26.2503 1.06635
\(607\) −0.587193 −0.0238334 −0.0119167 0.999929i \(-0.503793\pi\)
−0.0119167 + 0.999929i \(0.503793\pi\)
\(608\) 7.04424 0.285682
\(609\) 3.14028 0.127251
\(610\) −31.8862 −1.29103
\(611\) 15.2187 0.615684
\(612\) −3.96205 −0.160156
\(613\) −11.6822 −0.471841 −0.235920 0.971772i \(-0.575810\pi\)
−0.235920 + 0.971772i \(0.575810\pi\)
\(614\) −11.9231 −0.481177
\(615\) 29.5794 1.19276
\(616\) −1.28860 −0.0519193
\(617\) −21.9608 −0.884108 −0.442054 0.896988i \(-0.645750\pi\)
−0.442054 + 0.896988i \(0.645750\pi\)
\(618\) −12.3552 −0.496999
\(619\) −12.8998 −0.518485 −0.259242 0.965812i \(-0.583473\pi\)
−0.259242 + 0.965812i \(0.583473\pi\)
\(620\) 3.37895 0.135702
\(621\) 29.2149 1.17235
\(622\) −13.8823 −0.556631
\(623\) −14.5030 −0.581051
\(624\) 2.05275 0.0821757
\(625\) −24.0324 −0.961296
\(626\) 0.493548 0.0197261
\(627\) 13.8069 0.551395
\(628\) −10.4632 −0.417529
\(629\) 3.57987 0.142739
\(630\) 2.19076 0.0872821
\(631\) 45.0367 1.79288 0.896442 0.443161i \(-0.146143\pi\)
0.896442 + 0.443161i \(0.146143\pi\)
\(632\) 2.91941 0.116128
\(633\) 19.0592 0.757534
\(634\) −5.58340 −0.221745
\(635\) −18.9131 −0.750544
\(636\) 17.5972 0.697775
\(637\) 1.34956 0.0534715
\(638\) −2.66039 −0.105326
\(639\) −5.10560 −0.201974
\(640\) 3.19164 0.126161
\(641\) 12.6284 0.498794 0.249397 0.968401i \(-0.419768\pi\)
0.249397 + 0.968401i \(0.419768\pi\)
\(642\) 11.5856 0.457248
\(643\) 25.7783 1.01660 0.508299 0.861181i \(-0.330274\pi\)
0.508299 + 0.861181i \(0.330274\pi\)
\(644\) 5.21023 0.205312
\(645\) 46.8374 1.84422
\(646\) 40.6604 1.59976
\(647\) 21.2392 0.835000 0.417500 0.908677i \(-0.362906\pi\)
0.417500 + 0.908677i \(0.362906\pi\)
\(648\) 6.46962 0.254151
\(649\) 3.18021 0.124834
\(650\) −6.99957 −0.274546
\(651\) 1.61032 0.0631133
\(652\) 2.15221 0.0842870
\(653\) −22.1599 −0.867182 −0.433591 0.901110i \(-0.642754\pi\)
−0.433591 + 0.901110i \(0.642754\pi\)
\(654\) 22.7325 0.888910
\(655\) 22.7820 0.890167
\(656\) −6.09301 −0.237892
\(657\) −4.00935 −0.156420
\(658\) 11.2768 0.439616
\(659\) 32.5969 1.26979 0.634897 0.772597i \(-0.281043\pi\)
0.634897 + 0.772597i \(0.281043\pi\)
\(660\) 6.25571 0.243503
\(661\) −28.1812 −1.09612 −0.548062 0.836438i \(-0.684634\pi\)
−0.548062 + 0.836438i \(0.684634\pi\)
\(662\) −20.1655 −0.783754
\(663\) 11.8488 0.460169
\(664\) 2.31837 0.0899704
\(665\) −22.4827 −0.871840
\(666\) 0.425708 0.0164958
\(667\) 10.7568 0.416504
\(668\) 22.9023 0.886118
\(669\) −19.7321 −0.762889
\(670\) 50.1131 1.93604
\(671\) 12.8738 0.496989
\(672\) 1.52105 0.0586758
\(673\) −28.0463 −1.08110 −0.540552 0.841311i \(-0.681785\pi\)
−0.540552 + 0.841311i \(0.681785\pi\)
\(674\) 12.4429 0.479283
\(675\) −29.0821 −1.11937
\(676\) −11.1787 −0.429950
\(677\) 34.7563 1.33579 0.667896 0.744255i \(-0.267195\pi\)
0.667896 + 0.744255i \(0.267195\pi\)
\(678\) −8.98232 −0.344964
\(679\) −9.65031 −0.370345
\(680\) 18.4226 0.706476
\(681\) 11.0141 0.422060
\(682\) −1.36423 −0.0522390
\(683\) 3.41569 0.130698 0.0653488 0.997862i \(-0.479184\pi\)
0.0653488 + 0.997862i \(0.479184\pi\)
\(684\) 4.83522 0.184879
\(685\) −27.1744 −1.03828
\(686\) 1.00000 0.0381802
\(687\) 5.76944 0.220118
\(688\) −9.64795 −0.367825
\(689\) 15.6132 0.594817
\(690\) −25.2938 −0.962919
\(691\) −11.6477 −0.443100 −0.221550 0.975149i \(-0.571112\pi\)
−0.221550 + 0.975149i \(0.571112\pi\)
\(692\) 3.05284 0.116051
\(693\) −0.884507 −0.0335996
\(694\) 4.20130 0.159479
\(695\) 25.8707 0.981330
\(696\) 3.14028 0.119032
\(697\) −35.1698 −1.33215
\(698\) −33.7381 −1.27701
\(699\) 21.9561 0.830455
\(700\) −5.18656 −0.196034
\(701\) −32.4282 −1.22480 −0.612398 0.790550i \(-0.709795\pi\)
−0.612398 + 0.790550i \(0.709795\pi\)
\(702\) 7.56727 0.285608
\(703\) −4.36881 −0.164773
\(704\) −1.28860 −0.0485661
\(705\) −54.7448 −2.06181
\(706\) −25.2469 −0.950181
\(707\) 17.2580 0.649056
\(708\) −3.75387 −0.141079
\(709\) −39.0374 −1.46608 −0.733040 0.680186i \(-0.761899\pi\)
−0.733040 + 0.680186i \(0.761899\pi\)
\(710\) 23.7399 0.890942
\(711\) 2.00390 0.0751522
\(712\) −14.5030 −0.543523
\(713\) 5.51601 0.206576
\(714\) 8.77974 0.328573
\(715\) 5.55041 0.207574
\(716\) 10.9370 0.408733
\(717\) 28.3956 1.06045
\(718\) 9.59978 0.358261
\(719\) 6.43215 0.239879 0.119939 0.992781i \(-0.461730\pi\)
0.119939 + 0.992781i \(0.461730\pi\)
\(720\) 2.19076 0.0816450
\(721\) −8.12280 −0.302509
\(722\) −30.6213 −1.13961
\(723\) −43.3634 −1.61270
\(724\) −7.20674 −0.267836
\(725\) −10.7079 −0.397682
\(726\) 14.2058 0.527228
\(727\) −20.2201 −0.749920 −0.374960 0.927041i \(-0.622344\pi\)
−0.374960 + 0.927041i \(0.622344\pi\)
\(728\) 1.34956 0.0500180
\(729\) 30.0273 1.11212
\(730\) 18.6426 0.689992
\(731\) −55.6895 −2.05975
\(732\) −15.1961 −0.561664
\(733\) 4.53382 0.167460 0.0837302 0.996488i \(-0.473317\pi\)
0.0837302 + 0.996488i \(0.473317\pi\)
\(734\) −11.8428 −0.437128
\(735\) −4.85464 −0.179066
\(736\) 5.21023 0.192052
\(737\) −20.2328 −0.745286
\(738\) −4.18229 −0.153952
\(739\) −31.3707 −1.15399 −0.576996 0.816747i \(-0.695775\pi\)
−0.576996 + 0.816747i \(0.695775\pi\)
\(740\) −1.97944 −0.0727658
\(741\) −14.4600 −0.531203
\(742\) 11.5691 0.424716
\(743\) 46.7592 1.71543 0.857714 0.514127i \(-0.171884\pi\)
0.857714 + 0.514127i \(0.171884\pi\)
\(744\) 1.61032 0.0590371
\(745\) 42.3073 1.55002
\(746\) −24.7385 −0.905742
\(747\) 1.59135 0.0582244
\(748\) −7.43802 −0.271961
\(749\) 7.61685 0.278314
\(750\) 0.905681 0.0330708
\(751\) −33.0895 −1.20745 −0.603727 0.797191i \(-0.706318\pi\)
−0.603727 + 0.797191i \(0.706318\pi\)
\(752\) 11.2768 0.411223
\(753\) 40.8598 1.48901
\(754\) 2.78623 0.101469
\(755\) −37.7421 −1.37358
\(756\) 5.60721 0.203932
\(757\) −34.1041 −1.23954 −0.619768 0.784785i \(-0.712773\pi\)
−0.619768 + 0.784785i \(0.712773\pi\)
\(758\) −8.42862 −0.306141
\(759\) 10.2122 0.370680
\(760\) −22.4827 −0.815532
\(761\) 44.9328 1.62881 0.814406 0.580296i \(-0.197063\pi\)
0.814406 + 0.580296i \(0.197063\pi\)
\(762\) −9.01349 −0.326524
\(763\) 14.9452 0.541054
\(764\) 4.94052 0.178742
\(765\) 12.6454 0.457197
\(766\) −22.2967 −0.805611
\(767\) −3.33064 −0.120263
\(768\) 1.52105 0.0548862
\(769\) −27.4737 −0.990728 −0.495364 0.868686i \(-0.664965\pi\)
−0.495364 + 0.868686i \(0.664965\pi\)
\(770\) 4.11276 0.148213
\(771\) −16.2629 −0.585695
\(772\) 0.189080 0.00680512
\(773\) 32.8340 1.18096 0.590479 0.807053i \(-0.298939\pi\)
0.590479 + 0.807053i \(0.298939\pi\)
\(774\) −6.62242 −0.238038
\(775\) −5.49095 −0.197241
\(776\) −9.65031 −0.346426
\(777\) −0.943351 −0.0338425
\(778\) −6.43268 −0.230623
\(779\) 42.9206 1.53779
\(780\) −6.55163 −0.234586
\(781\) −9.58482 −0.342972
\(782\) 30.0743 1.07545
\(783\) 11.5764 0.413705
\(784\) 1.00000 0.0357143
\(785\) 33.3949 1.19191
\(786\) 10.8573 0.387267
\(787\) 31.2988 1.11568 0.557841 0.829948i \(-0.311630\pi\)
0.557841 + 0.829948i \(0.311630\pi\)
\(788\) −2.30403 −0.0820776
\(789\) 19.6375 0.699112
\(790\) −9.31769 −0.331509
\(791\) −5.90534 −0.209970
\(792\) −0.884507 −0.0314296
\(793\) −13.4828 −0.478789
\(794\) −18.5004 −0.656555
\(795\) −56.1640 −1.99193
\(796\) 22.6764 0.803744
\(797\) 46.1067 1.63318 0.816591 0.577217i \(-0.195861\pi\)
0.816591 + 0.577217i \(0.195861\pi\)
\(798\) −10.7146 −0.379294
\(799\) 65.0915 2.30277
\(800\) −5.18656 −0.183373
\(801\) −9.95497 −0.351742
\(802\) 9.81363 0.346531
\(803\) −7.52682 −0.265616
\(804\) 23.8826 0.842274
\(805\) −16.6292 −0.586101
\(806\) 1.42876 0.0503261
\(807\) 19.5983 0.689894
\(808\) 17.2580 0.607136
\(809\) −35.4448 −1.24617 −0.623087 0.782153i \(-0.714122\pi\)
−0.623087 + 0.782153i \(0.714122\pi\)
\(810\) −20.6487 −0.725521
\(811\) 0.677435 0.0237880 0.0118940 0.999929i \(-0.496214\pi\)
0.0118940 + 0.999929i \(0.496214\pi\)
\(812\) 2.06455 0.0724515
\(813\) −10.2621 −0.359908
\(814\) 0.799188 0.0280115
\(815\) −6.86908 −0.240613
\(816\) 8.77974 0.307352
\(817\) 67.9625 2.37771
\(818\) 21.6181 0.755860
\(819\) 0.926348 0.0323692
\(820\) 19.4467 0.679108
\(821\) −52.8303 −1.84379 −0.921896 0.387438i \(-0.873360\pi\)
−0.921896 + 0.387438i \(0.873360\pi\)
\(822\) −12.9506 −0.451704
\(823\) −12.5107 −0.436097 −0.218048 0.975938i \(-0.569969\pi\)
−0.218048 + 0.975938i \(0.569969\pi\)
\(824\) −8.12280 −0.282971
\(825\) −10.1658 −0.353928
\(826\) −2.46795 −0.0858709
\(827\) −44.5300 −1.54846 −0.774229 0.632905i \(-0.781862\pi\)
−0.774229 + 0.632905i \(0.781862\pi\)
\(828\) 3.57634 0.124286
\(829\) 10.3978 0.361130 0.180565 0.983563i \(-0.442207\pi\)
0.180565 + 0.983563i \(0.442207\pi\)
\(830\) −7.39941 −0.256837
\(831\) 10.2031 0.353943
\(832\) 1.34956 0.0467876
\(833\) 5.77216 0.199993
\(834\) 12.3293 0.426928
\(835\) −73.0960 −2.52959
\(836\) 9.07723 0.313942
\(837\) 5.93629 0.205188
\(838\) −13.3692 −0.461830
\(839\) 25.4430 0.878391 0.439195 0.898392i \(-0.355264\pi\)
0.439195 + 0.898392i \(0.355264\pi\)
\(840\) −4.85464 −0.167501
\(841\) −24.7376 −0.853022
\(842\) −8.21394 −0.283071
\(843\) 36.1358 1.24458
\(844\) 12.5303 0.431310
\(845\) 35.6783 1.22737
\(846\) 7.74048 0.266123
\(847\) 9.33950 0.320909
\(848\) 11.5691 0.397285
\(849\) 0.422429 0.0144977
\(850\) −29.9376 −1.02685
\(851\) −3.23137 −0.110770
\(852\) 11.3138 0.387604
\(853\) 20.1321 0.689309 0.344655 0.938730i \(-0.387996\pi\)
0.344655 + 0.938730i \(0.387996\pi\)
\(854\) −9.99054 −0.341869
\(855\) −15.4323 −0.527772
\(856\) 7.61685 0.260339
\(857\) −9.58377 −0.327375 −0.163688 0.986512i \(-0.552339\pi\)
−0.163688 + 0.986512i \(0.552339\pi\)
\(858\) 2.64518 0.0903049
\(859\) 38.3394 1.30812 0.654061 0.756442i \(-0.273064\pi\)
0.654061 + 0.756442i \(0.273064\pi\)
\(860\) 30.7928 1.05003
\(861\) 9.26778 0.315845
\(862\) −1.00000 −0.0340601
\(863\) −20.0896 −0.683856 −0.341928 0.939726i \(-0.611080\pi\)
−0.341928 + 0.939726i \(0.611080\pi\)
\(864\) 5.60721 0.190761
\(865\) −9.74355 −0.331291
\(866\) 7.69393 0.261450
\(867\) 24.8202 0.842938
\(868\) 1.05869 0.0359342
\(869\) 3.76196 0.127616
\(870\) −10.0226 −0.339800
\(871\) 21.1900 0.717994
\(872\) 14.9452 0.506110
\(873\) −6.62404 −0.224190
\(874\) −36.7021 −1.24147
\(875\) 0.595431 0.0201293
\(876\) 8.88455 0.300181
\(877\) 3.62986 0.122572 0.0612859 0.998120i \(-0.480480\pi\)
0.0612859 + 0.998120i \(0.480480\pi\)
\(878\) 13.8335 0.466857
\(879\) 3.54844 0.119686
\(880\) 4.11276 0.138641
\(881\) −12.2916 −0.414115 −0.207057 0.978329i \(-0.566389\pi\)
−0.207057 + 0.978329i \(0.566389\pi\)
\(882\) 0.686407 0.0231125
\(883\) −15.3722 −0.517316 −0.258658 0.965969i \(-0.583280\pi\)
−0.258658 + 0.965969i \(0.583280\pi\)
\(884\) 7.78987 0.262002
\(885\) 11.9810 0.402737
\(886\) 16.9069 0.567999
\(887\) 42.0265 1.41111 0.705556 0.708654i \(-0.250697\pi\)
0.705556 + 0.708654i \(0.250697\pi\)
\(888\) −0.943351 −0.0316568
\(889\) −5.92583 −0.198746
\(890\) 46.2884 1.55159
\(891\) 8.33678 0.279293
\(892\) −12.9727 −0.434359
\(893\) −79.4365 −2.65824
\(894\) 20.1625 0.674336
\(895\) −34.9068 −1.16681
\(896\) 1.00000 0.0334077
\(897\) −10.6953 −0.357105
\(898\) 20.4743 0.683238
\(899\) 2.18571 0.0728977
\(900\) −3.56009 −0.118670
\(901\) 66.7788 2.22472
\(902\) −7.85148 −0.261426
\(903\) 14.6750 0.488354
\(904\) −5.90534 −0.196409
\(905\) 23.0013 0.764589
\(906\) −17.9869 −0.597575
\(907\) −2.58213 −0.0857381 −0.0428690 0.999081i \(-0.513650\pi\)
−0.0428690 + 0.999081i \(0.513650\pi\)
\(908\) 7.24109 0.240304
\(909\) 11.8460 0.392909
\(910\) −4.30731 −0.142786
\(911\) −27.9289 −0.925327 −0.462663 0.886534i \(-0.653106\pi\)
−0.462663 + 0.886534i \(0.653106\pi\)
\(912\) −10.7146 −0.354797
\(913\) 2.98747 0.0988707
\(914\) −8.32894 −0.275497
\(915\) 48.5005 1.60338
\(916\) 3.79306 0.125326
\(917\) 7.13803 0.235719
\(918\) 32.3657 1.06823
\(919\) 42.6513 1.40694 0.703469 0.710726i \(-0.251634\pi\)
0.703469 + 0.710726i \(0.251634\pi\)
\(920\) −16.6292 −0.548248
\(921\) 18.1356 0.597590
\(922\) 30.3206 0.998554
\(923\) 10.0382 0.330412
\(924\) 1.96003 0.0644803
\(925\) 3.21669 0.105764
\(926\) −12.7482 −0.418933
\(927\) −5.57555 −0.183125
\(928\) 2.06455 0.0677722
\(929\) 23.5682 0.773248 0.386624 0.922237i \(-0.373641\pi\)
0.386624 + 0.922237i \(0.373641\pi\)
\(930\) −5.13955 −0.168533
\(931\) −7.04424 −0.230866
\(932\) 14.4348 0.472828
\(933\) 21.1157 0.691298
\(934\) −19.7315 −0.645635
\(935\) 23.7395 0.776364
\(936\) 0.926348 0.0302786
\(937\) −35.2042 −1.15007 −0.575036 0.818128i \(-0.695012\pi\)
−0.575036 + 0.818128i \(0.695012\pi\)
\(938\) 15.7014 0.512668
\(939\) −0.750711 −0.0244985
\(940\) −35.9915 −1.17391
\(941\) 4.75056 0.154864 0.0774319 0.996998i \(-0.475328\pi\)
0.0774319 + 0.996998i \(0.475328\pi\)
\(942\) 15.9151 0.518542
\(943\) 31.7460 1.03379
\(944\) −2.46795 −0.0803248
\(945\) −17.8962 −0.582163
\(946\) −12.4324 −0.404212
\(947\) 2.56404 0.0833202 0.0416601 0.999132i \(-0.486735\pi\)
0.0416601 + 0.999132i \(0.486735\pi\)
\(948\) −4.44056 −0.144223
\(949\) 7.88287 0.255889
\(950\) 36.5354 1.18536
\(951\) 8.49263 0.275392
\(952\) 5.77216 0.187077
\(953\) 45.1337 1.46202 0.731012 0.682365i \(-0.239048\pi\)
0.731012 + 0.682365i \(0.239048\pi\)
\(954\) 7.94113 0.257104
\(955\) −15.7684 −0.510252
\(956\) 18.6684 0.603779
\(957\) 4.04658 0.130807
\(958\) 30.1114 0.972856
\(959\) −8.51425 −0.274939
\(960\) −4.85464 −0.156683
\(961\) −29.8792 −0.963844
\(962\) −0.836993 −0.0269857
\(963\) 5.22826 0.168478
\(964\) −28.5089 −0.918209
\(965\) −0.603474 −0.0194265
\(966\) −7.92502 −0.254983
\(967\) −2.08878 −0.0671706 −0.0335853 0.999436i \(-0.510693\pi\)
−0.0335853 + 0.999436i \(0.510693\pi\)
\(968\) 9.33950 0.300183
\(969\) −61.8466 −1.98680
\(970\) 30.8003 0.988938
\(971\) −39.2254 −1.25880 −0.629401 0.777081i \(-0.716700\pi\)
−0.629401 + 0.777081i \(0.716700\pi\)
\(972\) 6.98101 0.223916
\(973\) 8.10576 0.259859
\(974\) 1.44157 0.0461907
\(975\) 10.6467 0.340967
\(976\) −9.99054 −0.319789
\(977\) −49.1802 −1.57341 −0.786706 0.617328i \(-0.788215\pi\)
−0.786706 + 0.617328i \(0.788215\pi\)
\(978\) −3.27362 −0.104679
\(979\) −18.6886 −0.597291
\(980\) −3.19164 −0.101953
\(981\) 10.2585 0.327530
\(982\) 8.76940 0.279843
\(983\) −25.9768 −0.828530 −0.414265 0.910156i \(-0.635961\pi\)
−0.414265 + 0.910156i \(0.635961\pi\)
\(984\) 9.26778 0.295446
\(985\) 7.35362 0.234306
\(986\) 11.9169 0.379512
\(987\) −17.1526 −0.545973
\(988\) −9.50662 −0.302446
\(989\) 50.2681 1.59843
\(990\) 2.82303 0.0897217
\(991\) 30.5926 0.971805 0.485903 0.874013i \(-0.338491\pi\)
0.485903 + 0.874013i \(0.338491\pi\)
\(992\) 1.05869 0.0336134
\(993\) 30.6727 0.973370
\(994\) 7.43814 0.235924
\(995\) −72.3750 −2.29444
\(996\) −3.52636 −0.111737
\(997\) 46.7080 1.47926 0.739628 0.673016i \(-0.235001\pi\)
0.739628 + 0.673016i \(0.235001\pi\)
\(998\) 9.82796 0.311099
\(999\) −3.47757 −0.110026
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 \(a_p\))