Properties

Label 6047.2.a.a.1.19
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.45739 q^{2}\) \(+0.0299595 q^{3}\) \(+4.03876 q^{4}\) \(-2.30057 q^{5}\) \(-0.0736221 q^{6}\) \(-3.67314 q^{7}\) \(-5.01004 q^{8}\) \(-2.99910 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.45739 q^{2}\) \(+0.0299595 q^{3}\) \(+4.03876 q^{4}\) \(-2.30057 q^{5}\) \(-0.0736221 q^{6}\) \(-3.67314 q^{7}\) \(-5.01004 q^{8}\) \(-2.99910 q^{9}\) \(+5.65341 q^{10}\) \(+3.96870 q^{11}\) \(+0.120999 q^{12}\) \(-4.41626 q^{13}\) \(+9.02634 q^{14}\) \(-0.0689240 q^{15}\) \(+4.23409 q^{16}\) \(-4.45195 q^{17}\) \(+7.36996 q^{18}\) \(+3.64597 q^{19}\) \(-9.29148 q^{20}\) \(-0.110045 q^{21}\) \(-9.75264 q^{22}\) \(+0.433976 q^{23}\) \(-0.150098 q^{24}\) \(+0.292644 q^{25}\) \(+10.8525 q^{26}\) \(-0.179730 q^{27}\) \(-14.8350 q^{28}\) \(-2.33443 q^{29}\) \(+0.169373 q^{30}\) \(+7.37324 q^{31}\) \(-0.384728 q^{32}\) \(+0.118900 q^{33}\) \(+10.9402 q^{34}\) \(+8.45034 q^{35}\) \(-12.1127 q^{36}\) \(+2.28378 q^{37}\) \(-8.95958 q^{38}\) \(-0.132309 q^{39}\) \(+11.5260 q^{40}\) \(-0.467077 q^{41}\) \(+0.270424 q^{42}\) \(-1.26591 q^{43}\) \(+16.0286 q^{44}\) \(+6.89966 q^{45}\) \(-1.06645 q^{46}\) \(+2.01157 q^{47}\) \(+0.126851 q^{48}\) \(+6.49197 q^{49}\) \(-0.719140 q^{50}\) \(-0.133378 q^{51}\) \(-17.8362 q^{52}\) \(+3.87564 q^{53}\) \(+0.441666 q^{54}\) \(-9.13028 q^{55}\) \(+18.4026 q^{56}\) \(+0.109231 q^{57}\) \(+5.73660 q^{58}\) \(-5.23852 q^{59}\) \(-0.278368 q^{60}\) \(-1.65719 q^{61}\) \(-18.1189 q^{62}\) \(+11.0161 q^{63}\) \(-7.52275 q^{64}\) \(+10.1599 q^{65}\) \(-0.292184 q^{66}\) \(+1.83199 q^{67}\) \(-17.9804 q^{68}\) \(+0.0130017 q^{69}\) \(-20.7658 q^{70}\) \(-0.430424 q^{71}\) \(+15.0256 q^{72}\) \(+8.72962 q^{73}\) \(-5.61213 q^{74}\) \(+0.00876745 q^{75}\) \(+14.7252 q^{76}\) \(-14.5776 q^{77}\) \(+0.325135 q^{78}\) \(+2.67184 q^{79}\) \(-9.74084 q^{80}\) \(+8.99192 q^{81}\) \(+1.14779 q^{82}\) \(-0.878878 q^{83}\) \(-0.444447 q^{84}\) \(+10.2420 q^{85}\) \(+3.11084 q^{86}\) \(-0.0699383 q^{87}\) \(-19.8833 q^{88}\) \(+11.7431 q^{89}\) \(-16.9552 q^{90}\) \(+16.2216 q^{91}\) \(+1.75273 q^{92}\) \(+0.220898 q^{93}\) \(-4.94321 q^{94}\) \(-8.38783 q^{95}\) \(-0.0115262 q^{96}\) \(-4.51612 q^{97}\) \(-15.9533 q^{98}\) \(-11.9025 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45739 −1.73764 −0.868818 0.495131i \(-0.835120\pi\)
−0.868818 + 0.495131i \(0.835120\pi\)
\(3\) 0.0299595 0.0172971 0.00864855 0.999963i \(-0.497247\pi\)
0.00864855 + 0.999963i \(0.497247\pi\)
\(4\) 4.03876 2.01938
\(5\) −2.30057 −1.02885 −0.514424 0.857536i \(-0.671994\pi\)
−0.514424 + 0.857536i \(0.671994\pi\)
\(6\) −0.0736221 −0.0300561
\(7\) −3.67314 −1.38832 −0.694159 0.719822i \(-0.744223\pi\)
−0.694159 + 0.719822i \(0.744223\pi\)
\(8\) −5.01004 −1.77132
\(9\) −2.99910 −0.999701
\(10\) 5.65341 1.78776
\(11\) 3.96870 1.19661 0.598304 0.801269i \(-0.295842\pi\)
0.598304 + 0.801269i \(0.295842\pi\)
\(12\) 0.120999 0.0349295
\(13\) −4.41626 −1.22485 −0.612426 0.790528i \(-0.709806\pi\)
−0.612426 + 0.790528i \(0.709806\pi\)
\(14\) 9.02634 2.41239
\(15\) −0.0689240 −0.0177961
\(16\) 4.23409 1.05852
\(17\) −4.45195 −1.07976 −0.539878 0.841743i \(-0.681530\pi\)
−0.539878 + 0.841743i \(0.681530\pi\)
\(18\) 7.36996 1.73712
\(19\) 3.64597 0.836444 0.418222 0.908345i \(-0.362653\pi\)
0.418222 + 0.908345i \(0.362653\pi\)
\(20\) −9.29148 −2.07764
\(21\) −0.110045 −0.0240139
\(22\) −9.75264 −2.07927
\(23\) 0.433976 0.0904903 0.0452451 0.998976i \(-0.485593\pi\)
0.0452451 + 0.998976i \(0.485593\pi\)
\(24\) −0.150098 −0.0306386
\(25\) 0.292644 0.0585287
\(26\) 10.8525 2.12835
\(27\) −0.179730 −0.0345890
\(28\) −14.8350 −2.80354
\(29\) −2.33443 −0.433493 −0.216746 0.976228i \(-0.569544\pi\)
−0.216746 + 0.976228i \(0.569544\pi\)
\(30\) 0.169373 0.0309232
\(31\) 7.37324 1.32427 0.662137 0.749383i \(-0.269650\pi\)
0.662137 + 0.749383i \(0.269650\pi\)
\(32\) −0.384728 −0.0680110
\(33\) 0.118900 0.0206978
\(34\) 10.9402 1.87622
\(35\) 8.45034 1.42837
\(36\) −12.1127 −2.01878
\(37\) 2.28378 0.375451 0.187725 0.982222i \(-0.439888\pi\)
0.187725 + 0.982222i \(0.439888\pi\)
\(38\) −8.95958 −1.45344
\(39\) −0.132309 −0.0211864
\(40\) 11.5260 1.82242
\(41\) −0.467077 −0.0729452 −0.0364726 0.999335i \(-0.511612\pi\)
−0.0364726 + 0.999335i \(0.511612\pi\)
\(42\) 0.270424 0.0417274
\(43\) −1.26591 −0.193050 −0.0965251 0.995331i \(-0.530773\pi\)
−0.0965251 + 0.995331i \(0.530773\pi\)
\(44\) 16.0286 2.41641
\(45\) 6.89966 1.02854
\(46\) −1.06645 −0.157239
\(47\) 2.01157 0.293417 0.146709 0.989180i \(-0.453132\pi\)
0.146709 + 0.989180i \(0.453132\pi\)
\(48\) 0.126851 0.0183094
\(49\) 6.49197 0.927425
\(50\) −0.719140 −0.101702
\(51\) −0.133378 −0.0186767
\(52\) −17.8362 −2.47344
\(53\) 3.87564 0.532361 0.266180 0.963923i \(-0.414238\pi\)
0.266180 + 0.963923i \(0.414238\pi\)
\(54\) 0.441666 0.0601032
\(55\) −9.13028 −1.23113
\(56\) 18.4026 2.45915
\(57\) 0.109231 0.0144681
\(58\) 5.73660 0.753253
\(59\) −5.23852 −0.681997 −0.340998 0.940064i \(-0.610765\pi\)
−0.340998 + 0.940064i \(0.610765\pi\)
\(60\) −0.278368 −0.0359371
\(61\) −1.65719 −0.212182 −0.106091 0.994356i \(-0.533833\pi\)
−0.106091 + 0.994356i \(0.533833\pi\)
\(62\) −18.1189 −2.30111
\(63\) 11.0161 1.38790
\(64\) −7.52275 −0.940344
\(65\) 10.1599 1.26019
\(66\) −0.292184 −0.0359653
\(67\) 1.83199 0.223813 0.111906 0.993719i \(-0.464304\pi\)
0.111906 + 0.993719i \(0.464304\pi\)
\(68\) −17.9804 −2.18044
\(69\) 0.0130017 0.00156522
\(70\) −20.7658 −2.48198
\(71\) −0.430424 −0.0510819 −0.0255410 0.999674i \(-0.508131\pi\)
−0.0255410 + 0.999674i \(0.508131\pi\)
\(72\) 15.0256 1.77079
\(73\) 8.72962 1.02173 0.510863 0.859662i \(-0.329326\pi\)
0.510863 + 0.859662i \(0.329326\pi\)
\(74\) −5.61213 −0.652397
\(75\) 0.00876745 0.00101238
\(76\) 14.7252 1.68910
\(77\) −14.5776 −1.66127
\(78\) 0.325135 0.0368142
\(79\) 2.67184 0.300605 0.150303 0.988640i \(-0.451975\pi\)
0.150303 + 0.988640i \(0.451975\pi\)
\(80\) −9.74084 −1.08906
\(81\) 8.99192 0.999103
\(82\) 1.14779 0.126752
\(83\) −0.878878 −0.0964693 −0.0482347 0.998836i \(-0.515360\pi\)
−0.0482347 + 0.998836i \(0.515360\pi\)
\(84\) −0.444447 −0.0484932
\(85\) 10.2420 1.11091
\(86\) 3.11084 0.335451
\(87\) −0.0699383 −0.00749817
\(88\) −19.8833 −2.11957
\(89\) 11.7431 1.24476 0.622382 0.782713i \(-0.286165\pi\)
0.622382 + 0.782713i \(0.286165\pi\)
\(90\) −16.9552 −1.78723
\(91\) 16.2216 1.70048
\(92\) 1.75273 0.182734
\(93\) 0.220898 0.0229061
\(94\) −4.94321 −0.509853
\(95\) −8.38783 −0.860574
\(96\) −0.0115262 −0.00117639
\(97\) −4.51612 −0.458542 −0.229271 0.973363i \(-0.573634\pi\)
−0.229271 + 0.973363i \(0.573634\pi\)
\(98\) −15.9533 −1.61153
\(99\) −11.9025 −1.19625
\(100\) 1.18192 0.118192
\(101\) 10.3677 1.03163 0.515814 0.856701i \(-0.327490\pi\)
0.515814 + 0.856701i \(0.327490\pi\)
\(102\) 0.327762 0.0324533
\(103\) −4.94178 −0.486928 −0.243464 0.969910i \(-0.578284\pi\)
−0.243464 + 0.969910i \(0.578284\pi\)
\(104\) 22.1257 2.16960
\(105\) 0.253168 0.0247066
\(106\) −9.52397 −0.925050
\(107\) 18.0684 1.74674 0.873371 0.487055i \(-0.161929\pi\)
0.873371 + 0.487055i \(0.161929\pi\)
\(108\) −0.725887 −0.0698485
\(109\) 12.5145 1.19867 0.599336 0.800498i \(-0.295431\pi\)
0.599336 + 0.800498i \(0.295431\pi\)
\(110\) 22.4367 2.13925
\(111\) 0.0684208 0.00649421
\(112\) −15.5524 −1.46956
\(113\) 8.61282 0.810226 0.405113 0.914267i \(-0.367232\pi\)
0.405113 + 0.914267i \(0.367232\pi\)
\(114\) −0.268424 −0.0251402
\(115\) −0.998394 −0.0931007
\(116\) −9.42821 −0.875388
\(117\) 13.2448 1.22448
\(118\) 12.8731 1.18506
\(119\) 16.3526 1.49904
\(120\) 0.345312 0.0315225
\(121\) 4.75056 0.431869
\(122\) 4.07237 0.368695
\(123\) −0.0139934 −0.00126174
\(124\) 29.7788 2.67421
\(125\) 10.8296 0.968631
\(126\) −27.0709 −2.41167
\(127\) −12.1161 −1.07513 −0.537565 0.843222i \(-0.680656\pi\)
−0.537565 + 0.843222i \(0.680656\pi\)
\(128\) 19.2558 1.70199
\(129\) −0.0379261 −0.00333921
\(130\) −24.9669 −2.18975
\(131\) 0.235248 0.0205537 0.0102768 0.999947i \(-0.496729\pi\)
0.0102768 + 0.999947i \(0.496729\pi\)
\(132\) 0.480209 0.0417969
\(133\) −13.3922 −1.16125
\(134\) −4.50190 −0.388905
\(135\) 0.413482 0.0355869
\(136\) 22.3044 1.91259
\(137\) −19.7097 −1.68391 −0.841956 0.539547i \(-0.818596\pi\)
−0.841956 + 0.539547i \(0.818596\pi\)
\(138\) −0.0319502 −0.00271978
\(139\) −8.64297 −0.733087 −0.366543 0.930401i \(-0.619459\pi\)
−0.366543 + 0.930401i \(0.619459\pi\)
\(140\) 34.1289 2.88442
\(141\) 0.0602655 0.00507527
\(142\) 1.05772 0.0887619
\(143\) −17.5268 −1.46567
\(144\) −12.6985 −1.05821
\(145\) 5.37053 0.445998
\(146\) −21.4521 −1.77539
\(147\) 0.194496 0.0160418
\(148\) 9.22364 0.758179
\(149\) 12.8144 1.04980 0.524898 0.851165i \(-0.324103\pi\)
0.524898 + 0.851165i \(0.324103\pi\)
\(150\) −0.0215450 −0.00175915
\(151\) 8.00201 0.651194 0.325597 0.945509i \(-0.394435\pi\)
0.325597 + 0.945509i \(0.394435\pi\)
\(152\) −18.2665 −1.48161
\(153\) 13.3519 1.07943
\(154\) 35.8228 2.88668
\(155\) −16.9627 −1.36248
\(156\) −0.534365 −0.0427834
\(157\) −17.7755 −1.41864 −0.709320 0.704886i \(-0.750998\pi\)
−0.709320 + 0.704886i \(0.750998\pi\)
\(158\) −6.56575 −0.522343
\(159\) 0.116112 0.00920830
\(160\) 0.885096 0.0699730
\(161\) −1.59406 −0.125629
\(162\) −22.0967 −1.73608
\(163\) −11.5339 −0.903404 −0.451702 0.892169i \(-0.649183\pi\)
−0.451702 + 0.892169i \(0.649183\pi\)
\(164\) −1.88642 −0.147304
\(165\) −0.273538 −0.0212949
\(166\) 2.15974 0.167629
\(167\) −1.71315 −0.132568 −0.0662838 0.997801i \(-0.521114\pi\)
−0.0662838 + 0.997801i \(0.521114\pi\)
\(168\) 0.551332 0.0425362
\(169\) 6.50339 0.500261
\(170\) −25.1687 −1.93035
\(171\) −10.9346 −0.836193
\(172\) −5.11273 −0.389842
\(173\) 0.696083 0.0529222 0.0264611 0.999650i \(-0.491576\pi\)
0.0264611 + 0.999650i \(0.491576\pi\)
\(174\) 0.171866 0.0130291
\(175\) −1.07492 −0.0812565
\(176\) 16.8038 1.26664
\(177\) −0.156943 −0.0117966
\(178\) −28.8573 −2.16295
\(179\) −25.5763 −1.91167 −0.955833 0.293910i \(-0.905043\pi\)
−0.955833 + 0.293910i \(0.905043\pi\)
\(180\) 27.8661 2.07702
\(181\) 21.4620 1.59526 0.797629 0.603149i \(-0.206087\pi\)
0.797629 + 0.603149i \(0.206087\pi\)
\(182\) −39.8627 −2.95482
\(183\) −0.0496486 −0.00367013
\(184\) −2.17424 −0.160287
\(185\) −5.25400 −0.386282
\(186\) −0.542833 −0.0398025
\(187\) −17.6684 −1.29204
\(188\) 8.12425 0.592522
\(189\) 0.660173 0.0480206
\(190\) 20.6122 1.49536
\(191\) 2.42770 0.175662 0.0878310 0.996135i \(-0.472006\pi\)
0.0878310 + 0.996135i \(0.472006\pi\)
\(192\) −0.225378 −0.0162652
\(193\) −17.0805 −1.22948 −0.614739 0.788731i \(-0.710739\pi\)
−0.614739 + 0.788731i \(0.710739\pi\)
\(194\) 11.0979 0.796780
\(195\) 0.304387 0.0217976
\(196\) 26.2195 1.87282
\(197\) 24.3559 1.73529 0.867644 0.497186i \(-0.165633\pi\)
0.867644 + 0.497186i \(0.165633\pi\)
\(198\) 29.2492 2.07865
\(199\) −9.38482 −0.665272 −0.332636 0.943055i \(-0.607938\pi\)
−0.332636 + 0.943055i \(0.607938\pi\)
\(200\) −1.46616 −0.103673
\(201\) 0.0548853 0.00387131
\(202\) −25.4776 −1.79259
\(203\) 8.57469 0.601825
\(204\) −0.538682 −0.0377153
\(205\) 1.07455 0.0750496
\(206\) 12.1439 0.846104
\(207\) −1.30154 −0.0904632
\(208\) −18.6989 −1.29653
\(209\) 14.4698 1.00089
\(210\) −0.622131 −0.0429311
\(211\) −10.8129 −0.744387 −0.372194 0.928155i \(-0.621394\pi\)
−0.372194 + 0.928155i \(0.621394\pi\)
\(212\) 15.6528 1.07504
\(213\) −0.0128953 −0.000883570 0
\(214\) −44.4012 −3.03520
\(215\) 2.91233 0.198619
\(216\) 0.900454 0.0612681
\(217\) −27.0830 −1.83851
\(218\) −30.7530 −2.08286
\(219\) 0.261535 0.0176729
\(220\) −36.8751 −2.48612
\(221\) 19.6610 1.32254
\(222\) −0.168137 −0.0112846
\(223\) 8.74930 0.585896 0.292948 0.956128i \(-0.405364\pi\)
0.292948 + 0.956128i \(0.405364\pi\)
\(224\) 1.41316 0.0944208
\(225\) −0.877669 −0.0585112
\(226\) −21.1651 −1.40788
\(227\) 10.5390 0.699497 0.349748 0.936844i \(-0.386267\pi\)
0.349748 + 0.936844i \(0.386267\pi\)
\(228\) 0.441160 0.0292165
\(229\) −24.7555 −1.63589 −0.817946 0.575295i \(-0.804887\pi\)
−0.817946 + 0.575295i \(0.804887\pi\)
\(230\) 2.45344 0.161775
\(231\) −0.436737 −0.0287352
\(232\) 11.6956 0.767853
\(233\) 1.69457 0.111015 0.0555075 0.998458i \(-0.482322\pi\)
0.0555075 + 0.998458i \(0.482322\pi\)
\(234\) −32.5477 −2.12771
\(235\) −4.62776 −0.301882
\(236\) −21.1571 −1.37721
\(237\) 0.0800468 0.00519960
\(238\) −40.1848 −2.60479
\(239\) 0.483451 0.0312719 0.0156359 0.999878i \(-0.495023\pi\)
0.0156359 + 0.999878i \(0.495023\pi\)
\(240\) −0.291830 −0.0188376
\(241\) 3.46950 0.223490 0.111745 0.993737i \(-0.464356\pi\)
0.111745 + 0.993737i \(0.464356\pi\)
\(242\) −11.6740 −0.750432
\(243\) 0.808583 0.0518706
\(244\) −6.69301 −0.428476
\(245\) −14.9353 −0.954179
\(246\) 0.0343872 0.00219245
\(247\) −16.1016 −1.02452
\(248\) −36.9402 −2.34571
\(249\) −0.0263307 −0.00166864
\(250\) −26.6126 −1.68313
\(251\) 8.04890 0.508042 0.254021 0.967199i \(-0.418247\pi\)
0.254021 + 0.967199i \(0.418247\pi\)
\(252\) 44.4915 2.80270
\(253\) 1.72232 0.108281
\(254\) 29.7740 1.86819
\(255\) 0.306846 0.0192155
\(256\) −32.2735 −2.01709
\(257\) 17.6413 1.10044 0.550219 0.835021i \(-0.314544\pi\)
0.550219 + 0.835021i \(0.314544\pi\)
\(258\) 0.0931992 0.00580233
\(259\) −8.38864 −0.521245
\(260\) 41.0336 2.54480
\(261\) 7.00119 0.433363
\(262\) −0.578096 −0.0357149
\(263\) 0.603599 0.0372195 0.0186098 0.999827i \(-0.494076\pi\)
0.0186098 + 0.999827i \(0.494076\pi\)
\(264\) −0.595694 −0.0366624
\(265\) −8.91621 −0.547718
\(266\) 32.9098 2.01783
\(267\) 0.351817 0.0215308
\(268\) 7.39896 0.451963
\(269\) 12.4266 0.757666 0.378833 0.925465i \(-0.376326\pi\)
0.378833 + 0.925465i \(0.376326\pi\)
\(270\) −1.01609 −0.0618371
\(271\) −12.9612 −0.787337 −0.393668 0.919253i \(-0.628794\pi\)
−0.393668 + 0.919253i \(0.628794\pi\)
\(272\) −18.8499 −1.14295
\(273\) 0.485989 0.0294134
\(274\) 48.4344 2.92603
\(275\) 1.16141 0.0700359
\(276\) 0.0525108 0.00316078
\(277\) 13.0113 0.781773 0.390886 0.920439i \(-0.372169\pi\)
0.390886 + 0.920439i \(0.372169\pi\)
\(278\) 21.2391 1.27384
\(279\) −22.1131 −1.32388
\(280\) −42.3365 −2.53009
\(281\) 11.4820 0.684957 0.342478 0.939526i \(-0.388734\pi\)
0.342478 + 0.939526i \(0.388734\pi\)
\(282\) −0.148096 −0.00881898
\(283\) 6.49250 0.385939 0.192969 0.981205i \(-0.438188\pi\)
0.192969 + 0.981205i \(0.438188\pi\)
\(284\) −1.73838 −0.103154
\(285\) −0.251295 −0.0148854
\(286\) 43.0702 2.54680
\(287\) 1.71564 0.101271
\(288\) 1.15384 0.0679906
\(289\) 2.81985 0.165874
\(290\) −13.1975 −0.774983
\(291\) −0.135300 −0.00793145
\(292\) 35.2569 2.06325
\(293\) 0.948461 0.0554097 0.0277048 0.999616i \(-0.491180\pi\)
0.0277048 + 0.999616i \(0.491180\pi\)
\(294\) −0.477953 −0.0278748
\(295\) 12.0516 0.701671
\(296\) −11.4418 −0.665042
\(297\) −0.713294 −0.0413895
\(298\) −31.4900 −1.82416
\(299\) −1.91655 −0.110837
\(300\) 0.0354097 0.00204438
\(301\) 4.64988 0.268015
\(302\) −19.6640 −1.13154
\(303\) 0.310612 0.0178442
\(304\) 15.4374 0.885394
\(305\) 3.81249 0.218303
\(306\) −32.8107 −1.87566
\(307\) −29.0229 −1.65642 −0.828212 0.560415i \(-0.810642\pi\)
−0.828212 + 0.560415i \(0.810642\pi\)
\(308\) −58.8754 −3.35474
\(309\) −0.148053 −0.00842244
\(310\) 41.6839 2.36749
\(311\) 8.91374 0.505452 0.252726 0.967538i \(-0.418673\pi\)
0.252726 + 0.967538i \(0.418673\pi\)
\(312\) 0.662873 0.0375278
\(313\) −9.03011 −0.510412 −0.255206 0.966887i \(-0.582143\pi\)
−0.255206 + 0.966887i \(0.582143\pi\)
\(314\) 43.6814 2.46508
\(315\) −25.3434 −1.42794
\(316\) 10.7909 0.607037
\(317\) −15.8822 −0.892031 −0.446015 0.895025i \(-0.647157\pi\)
−0.446015 + 0.895025i \(0.647157\pi\)
\(318\) −0.285333 −0.0160007
\(319\) −9.26465 −0.518721
\(320\) 17.3066 0.967471
\(321\) 0.541321 0.0302136
\(322\) 3.91722 0.218298
\(323\) −16.2317 −0.903155
\(324\) 36.3163 2.01757
\(325\) −1.29239 −0.0716890
\(326\) 28.3433 1.56979
\(327\) 0.374928 0.0207336
\(328\) 2.34008 0.129209
\(329\) −7.38878 −0.407357
\(330\) 0.672191 0.0370029
\(331\) 12.5592 0.690314 0.345157 0.938545i \(-0.387826\pi\)
0.345157 + 0.938545i \(0.387826\pi\)
\(332\) −3.54958 −0.194808
\(333\) −6.84929 −0.375339
\(334\) 4.20988 0.230354
\(335\) −4.21462 −0.230269
\(336\) −0.465942 −0.0254192
\(337\) −13.9122 −0.757844 −0.378922 0.925429i \(-0.623705\pi\)
−0.378922 + 0.925429i \(0.623705\pi\)
\(338\) −15.9814 −0.869271
\(339\) 0.258036 0.0140146
\(340\) 41.3652 2.24334
\(341\) 29.2622 1.58464
\(342\) 26.8707 1.45300
\(343\) 1.86606 0.100758
\(344\) 6.34228 0.341953
\(345\) −0.0299114 −0.00161037
\(346\) −1.71055 −0.0919596
\(347\) −5.08480 −0.272966 −0.136483 0.990642i \(-0.543580\pi\)
−0.136483 + 0.990642i \(0.543580\pi\)
\(348\) −0.282464 −0.0151417
\(349\) 18.6250 0.996975 0.498488 0.866897i \(-0.333889\pi\)
0.498488 + 0.866897i \(0.333889\pi\)
\(350\) 2.64150 0.141194
\(351\) 0.793735 0.0423664
\(352\) −1.52687 −0.0813824
\(353\) −30.6953 −1.63375 −0.816873 0.576817i \(-0.804294\pi\)
−0.816873 + 0.576817i \(0.804294\pi\)
\(354\) 0.385671 0.0204982
\(355\) 0.990223 0.0525556
\(356\) 47.4276 2.51366
\(357\) 0.489916 0.0259291
\(358\) 62.8511 3.32178
\(359\) 35.1299 1.85408 0.927042 0.374957i \(-0.122342\pi\)
0.927042 + 0.374957i \(0.122342\pi\)
\(360\) −34.5676 −1.82187
\(361\) −5.70688 −0.300362
\(362\) −52.7405 −2.77198
\(363\) 0.142324 0.00747009
\(364\) 65.5151 3.43392
\(365\) −20.0832 −1.05120
\(366\) 0.122006 0.00637735
\(367\) 21.6804 1.13171 0.565854 0.824505i \(-0.308546\pi\)
0.565854 + 0.824505i \(0.308546\pi\)
\(368\) 1.83749 0.0957859
\(369\) 1.40081 0.0729234
\(370\) 12.9111 0.671218
\(371\) −14.2358 −0.739086
\(372\) 0.892156 0.0462562
\(373\) −5.22180 −0.270375 −0.135187 0.990820i \(-0.543164\pi\)
−0.135187 + 0.990820i \(0.543164\pi\)
\(374\) 43.4182 2.24510
\(375\) 0.324450 0.0167545
\(376\) −10.0780 −0.519735
\(377\) 10.3095 0.530964
\(378\) −1.62230 −0.0834423
\(379\) −24.6864 −1.26805 −0.634026 0.773311i \(-0.718599\pi\)
−0.634026 + 0.773311i \(0.718599\pi\)
\(380\) −33.8765 −1.73783
\(381\) −0.362992 −0.0185966
\(382\) −5.96580 −0.305237
\(383\) −0.438123 −0.0223870 −0.0111935 0.999937i \(-0.503563\pi\)
−0.0111935 + 0.999937i \(0.503563\pi\)
\(384\) 0.576893 0.0294394
\(385\) 33.5368 1.70920
\(386\) 41.9733 2.13639
\(387\) 3.79661 0.192992
\(388\) −18.2395 −0.925972
\(389\) −19.8622 −1.00705 −0.503526 0.863980i \(-0.667964\pi\)
−0.503526 + 0.863980i \(0.667964\pi\)
\(390\) −0.747996 −0.0378763
\(391\) −1.93204 −0.0977074
\(392\) −32.5250 −1.64276
\(393\) 0.00704790 0.000355520 0
\(394\) −59.8520 −3.01530
\(395\) −6.14676 −0.309277
\(396\) −48.0715 −2.41568
\(397\) 1.44135 0.0723392 0.0361696 0.999346i \(-0.488484\pi\)
0.0361696 + 0.999346i \(0.488484\pi\)
\(398\) 23.0622 1.15600
\(399\) −0.401223 −0.0200862
\(400\) 1.23908 0.0619540
\(401\) 24.0466 1.20083 0.600415 0.799688i \(-0.295002\pi\)
0.600415 + 0.799688i \(0.295002\pi\)
\(402\) −0.134875 −0.00672693
\(403\) −32.5622 −1.62204
\(404\) 41.8728 2.08325
\(405\) −20.6866 −1.02792
\(406\) −21.0714 −1.04575
\(407\) 9.06363 0.449267
\(408\) 0.668229 0.0330823
\(409\) 20.5156 1.01443 0.507216 0.861819i \(-0.330675\pi\)
0.507216 + 0.861819i \(0.330675\pi\)
\(410\) −2.64058 −0.130409
\(411\) −0.590491 −0.0291268
\(412\) −19.9587 −0.983294
\(413\) 19.2418 0.946828
\(414\) 3.19839 0.157192
\(415\) 2.02192 0.0992523
\(416\) 1.69906 0.0833033
\(417\) −0.258939 −0.0126803
\(418\) −35.5579 −1.73919
\(419\) 4.30722 0.210421 0.105211 0.994450i \(-0.466448\pi\)
0.105211 + 0.994450i \(0.466448\pi\)
\(420\) 1.02248 0.0498921
\(421\) −11.2581 −0.548688 −0.274344 0.961632i \(-0.588461\pi\)
−0.274344 + 0.961632i \(0.588461\pi\)
\(422\) 26.5714 1.29347
\(423\) −6.03290 −0.293330
\(424\) −19.4171 −0.942979
\(425\) −1.30284 −0.0631968
\(426\) 0.0316887 0.00153532
\(427\) 6.08710 0.294576
\(428\) 72.9742 3.52734
\(429\) −0.525094 −0.0253518
\(430\) −7.15673 −0.345128
\(431\) −22.5775 −1.08752 −0.543760 0.839241i \(-0.683000\pi\)
−0.543760 + 0.839241i \(0.683000\pi\)
\(432\) −0.760992 −0.0366133
\(433\) 0.589360 0.0283229 0.0141614 0.999900i \(-0.495492\pi\)
0.0141614 + 0.999900i \(0.495492\pi\)
\(434\) 66.5534 3.19467
\(435\) 0.160898 0.00771448
\(436\) 50.5431 2.42058
\(437\) 1.58227 0.0756900
\(438\) −0.642693 −0.0307091
\(439\) 7.28817 0.347845 0.173923 0.984759i \(-0.444356\pi\)
0.173923 + 0.984759i \(0.444356\pi\)
\(440\) 45.7431 2.18072
\(441\) −19.4701 −0.927147
\(442\) −48.3147 −2.29810
\(443\) 18.5904 0.883256 0.441628 0.897198i \(-0.354401\pi\)
0.441628 + 0.897198i \(0.354401\pi\)
\(444\) 0.276335 0.0131143
\(445\) −27.0158 −1.28067
\(446\) −21.5004 −1.01808
\(447\) 0.383912 0.0181584
\(448\) 27.6321 1.30550
\(449\) −2.96617 −0.139982 −0.0699911 0.997548i \(-0.522297\pi\)
−0.0699911 + 0.997548i \(0.522297\pi\)
\(450\) 2.15677 0.101671
\(451\) −1.85369 −0.0872868
\(452\) 34.7852 1.63616
\(453\) 0.239736 0.0112638
\(454\) −25.8984 −1.21547
\(455\) −37.3189 −1.74954
\(456\) −0.547254 −0.0256275
\(457\) −9.86488 −0.461460 −0.230730 0.973018i \(-0.574111\pi\)
−0.230730 + 0.973018i \(0.574111\pi\)
\(458\) 60.8340 2.84259
\(459\) 0.800149 0.0373477
\(460\) −4.03228 −0.188006
\(461\) 23.0718 1.07456 0.537280 0.843404i \(-0.319452\pi\)
0.537280 + 0.843404i \(0.319452\pi\)
\(462\) 1.07323 0.0499313
\(463\) 12.8543 0.597388 0.298694 0.954349i \(-0.403449\pi\)
0.298694 + 0.954349i \(0.403449\pi\)
\(464\) −9.88418 −0.458862
\(465\) −0.508193 −0.0235669
\(466\) −4.16422 −0.192904
\(467\) −41.5721 −1.92373 −0.961864 0.273529i \(-0.911809\pi\)
−0.961864 + 0.273529i \(0.911809\pi\)
\(468\) 53.4927 2.47270
\(469\) −6.72914 −0.310723
\(470\) 11.3722 0.524561
\(471\) −0.532545 −0.0245384
\(472\) 26.2452 1.20803
\(473\) −5.02403 −0.231005
\(474\) −0.196706 −0.00903502
\(475\) 1.06697 0.0489560
\(476\) 66.0445 3.02714
\(477\) −11.6235 −0.532201
\(478\) −1.18803 −0.0543391
\(479\) 7.58257 0.346457 0.173228 0.984882i \(-0.444580\pi\)
0.173228 + 0.984882i \(0.444580\pi\)
\(480\) 0.0265170 0.00121033
\(481\) −10.0858 −0.459871
\(482\) −8.52591 −0.388344
\(483\) −0.0477571 −0.00217302
\(484\) 19.1864 0.872109
\(485\) 10.3897 0.471770
\(486\) −1.98700 −0.0901323
\(487\) −9.30755 −0.421766 −0.210883 0.977511i \(-0.567634\pi\)
−0.210883 + 0.977511i \(0.567634\pi\)
\(488\) 8.30260 0.375841
\(489\) −0.345549 −0.0156263
\(490\) 36.7018 1.65802
\(491\) −39.7365 −1.79329 −0.896643 0.442755i \(-0.854001\pi\)
−0.896643 + 0.442755i \(0.854001\pi\)
\(492\) −0.0565160 −0.00254794
\(493\) 10.3928 0.468067
\(494\) 39.5679 1.78024
\(495\) 27.3827 1.23076
\(496\) 31.2190 1.40177
\(497\) 1.58101 0.0709179
\(498\) 0.0647048 0.00289949
\(499\) −40.8012 −1.82651 −0.913255 0.407387i \(-0.866440\pi\)
−0.913255 + 0.407387i \(0.866440\pi\)
\(500\) 43.7383 1.95604
\(501\) −0.0513251 −0.00229304
\(502\) −19.7793 −0.882793
\(503\) 10.5526 0.470516 0.235258 0.971933i \(-0.424406\pi\)
0.235258 + 0.971933i \(0.424406\pi\)
\(504\) −55.1912 −2.45841
\(505\) −23.8517 −1.06139
\(506\) −4.23241 −0.188154
\(507\) 0.194838 0.00865306
\(508\) −48.9341 −2.17110
\(509\) 14.2606 0.632091 0.316045 0.948744i \(-0.397645\pi\)
0.316045 + 0.948744i \(0.397645\pi\)
\(510\) −0.754041 −0.0333895
\(511\) −32.0651 −1.41848
\(512\) 40.7969 1.80299
\(513\) −0.655290 −0.0289318
\(514\) −43.3517 −1.91216
\(515\) 11.3689 0.500975
\(516\) −0.153175 −0.00674314
\(517\) 7.98331 0.351106
\(518\) 20.6142 0.905734
\(519\) 0.0208543 0.000915401 0
\(520\) −50.9017 −2.23219
\(521\) 21.8233 0.956098 0.478049 0.878333i \(-0.341344\pi\)
0.478049 + 0.878333i \(0.341344\pi\)
\(522\) −17.2047 −0.753028
\(523\) 29.5610 1.29261 0.646307 0.763078i \(-0.276313\pi\)
0.646307 + 0.763078i \(0.276313\pi\)
\(524\) 0.950111 0.0415058
\(525\) −0.0322041 −0.00140550
\(526\) −1.48328 −0.0646740
\(527\) −32.8253 −1.42989
\(528\) 0.503433 0.0219091
\(529\) −22.8117 −0.991812
\(530\) 21.9106 0.951736
\(531\) 15.7108 0.681793
\(532\) −54.0879 −2.34501
\(533\) 2.06274 0.0893471
\(534\) −0.864550 −0.0374128
\(535\) −41.5678 −1.79713
\(536\) −9.17832 −0.396443
\(537\) −0.766254 −0.0330663
\(538\) −30.5371 −1.31655
\(539\) 25.7647 1.10976
\(540\) 1.66996 0.0718635
\(541\) 5.60431 0.240948 0.120474 0.992716i \(-0.461559\pi\)
0.120474 + 0.992716i \(0.461559\pi\)
\(542\) 31.8507 1.36811
\(543\) 0.642990 0.0275933
\(544\) 1.71279 0.0734353
\(545\) −28.7906 −1.23325
\(546\) −1.19427 −0.0511098
\(547\) 22.6670 0.969172 0.484586 0.874744i \(-0.338970\pi\)
0.484586 + 0.874744i \(0.338970\pi\)
\(548\) −79.6027 −3.40046
\(549\) 4.97009 0.212118
\(550\) −2.85405 −0.121697
\(551\) −8.51127 −0.362592
\(552\) −0.0651390 −0.00277250
\(553\) −9.81404 −0.417335
\(554\) −31.9738 −1.35844
\(555\) −0.157407 −0.00668156
\(556\) −34.9069 −1.48038
\(557\) 4.19796 0.177873 0.0889366 0.996037i \(-0.471653\pi\)
0.0889366 + 0.996037i \(0.471653\pi\)
\(558\) 54.3405 2.30042
\(559\) 5.59061 0.236458
\(560\) 35.7795 1.51196
\(561\) −0.529337 −0.0223486
\(562\) −28.2157 −1.19021
\(563\) 16.9207 0.713122 0.356561 0.934272i \(-0.383949\pi\)
0.356561 + 0.934272i \(0.383949\pi\)
\(564\) 0.243398 0.0102489
\(565\) −19.8144 −0.833600
\(566\) −15.9546 −0.670622
\(567\) −33.0286 −1.38707
\(568\) 2.15644 0.0904823
\(569\) 6.46919 0.271203 0.135601 0.990763i \(-0.456703\pi\)
0.135601 + 0.990763i \(0.456703\pi\)
\(570\) 0.617530 0.0258655
\(571\) −17.0713 −0.714410 −0.357205 0.934026i \(-0.616270\pi\)
−0.357205 + 0.934026i \(0.616270\pi\)
\(572\) −70.7867 −2.95974
\(573\) 0.0727325 0.00303845
\(574\) −4.21600 −0.175972
\(575\) 0.127000 0.00529628
\(576\) 22.5615 0.940062
\(577\) −41.3855 −1.72290 −0.861450 0.507842i \(-0.830443\pi\)
−0.861450 + 0.507842i \(0.830443\pi\)
\(578\) −6.92948 −0.288228
\(579\) −0.511721 −0.0212664
\(580\) 21.6903 0.900641
\(581\) 3.22824 0.133930
\(582\) 0.332486 0.0137820
\(583\) 15.3813 0.637027
\(584\) −43.7357 −1.80980
\(585\) −30.4707 −1.25981
\(586\) −2.33074 −0.0962819
\(587\) −19.5429 −0.806623 −0.403312 0.915063i \(-0.632141\pi\)
−0.403312 + 0.915063i \(0.632141\pi\)
\(588\) 0.785524 0.0323944
\(589\) 26.8826 1.10768
\(590\) −29.6155 −1.21925
\(591\) 0.729691 0.0300155
\(592\) 9.66972 0.397423
\(593\) −31.0589 −1.27544 −0.637719 0.770269i \(-0.720122\pi\)
−0.637719 + 0.770269i \(0.720122\pi\)
\(594\) 1.75284 0.0719199
\(595\) −37.6205 −1.54229
\(596\) 51.7543 2.11994
\(597\) −0.281164 −0.0115073
\(598\) 4.70972 0.192595
\(599\) −13.4871 −0.551068 −0.275534 0.961291i \(-0.588855\pi\)
−0.275534 + 0.961291i \(0.588855\pi\)
\(600\) −0.0439253 −0.00179324
\(601\) 16.5412 0.674731 0.337365 0.941374i \(-0.390464\pi\)
0.337365 + 0.941374i \(0.390464\pi\)
\(602\) −11.4266 −0.465712
\(603\) −5.49431 −0.223746
\(604\) 32.3182 1.31501
\(605\) −10.9290 −0.444328
\(606\) −0.763294 −0.0310067
\(607\) 16.0877 0.652978 0.326489 0.945201i \(-0.394134\pi\)
0.326489 + 0.945201i \(0.394134\pi\)
\(608\) −1.40271 −0.0568873
\(609\) 0.256893 0.0104098
\(610\) −9.36878 −0.379331
\(611\) −8.88362 −0.359393
\(612\) 53.9250 2.17979
\(613\) −18.5499 −0.749223 −0.374611 0.927182i \(-0.622224\pi\)
−0.374611 + 0.927182i \(0.622224\pi\)
\(614\) 71.3206 2.87826
\(615\) 0.0321928 0.00129814
\(616\) 73.0343 2.94264
\(617\) −26.6845 −1.07428 −0.537138 0.843494i \(-0.680495\pi\)
−0.537138 + 0.843494i \(0.680495\pi\)
\(618\) 0.363824 0.0146351
\(619\) 2.85848 0.114892 0.0574461 0.998349i \(-0.481704\pi\)
0.0574461 + 0.998349i \(0.481704\pi\)
\(620\) −68.5083 −2.75136
\(621\) −0.0779985 −0.00312997
\(622\) −21.9045 −0.878292
\(623\) −43.1340 −1.72813
\(624\) −0.560208 −0.0224263
\(625\) −26.3776 −1.05510
\(626\) 22.1905 0.886911
\(627\) 0.433506 0.0173126
\(628\) −71.7911 −2.86478
\(629\) −10.1673 −0.405395
\(630\) 62.2787 2.48124
\(631\) 29.2552 1.16463 0.582315 0.812963i \(-0.302147\pi\)
0.582315 + 0.812963i \(0.302147\pi\)
\(632\) −13.3860 −0.532467
\(633\) −0.323947 −0.0128757
\(634\) 39.0287 1.55003
\(635\) 27.8740 1.10615
\(636\) 0.468950 0.0185951
\(637\) −28.6703 −1.13596
\(638\) 22.7668 0.901348
\(639\) 1.29089 0.0510667
\(640\) −44.2994 −1.75109
\(641\) −9.48262 −0.374541 −0.187270 0.982308i \(-0.559964\pi\)
−0.187270 + 0.982308i \(0.559964\pi\)
\(642\) −1.33024 −0.0525003
\(643\) −39.0757 −1.54100 −0.770498 0.637442i \(-0.779992\pi\)
−0.770498 + 0.637442i \(0.779992\pi\)
\(644\) −6.43801 −0.253693
\(645\) 0.0872519 0.00343554
\(646\) 39.8876 1.56936
\(647\) 31.2789 1.22970 0.614850 0.788644i \(-0.289217\pi\)
0.614850 + 0.788644i \(0.289217\pi\)
\(648\) −45.0499 −1.76973
\(649\) −20.7901 −0.816082
\(650\) 3.17591 0.124569
\(651\) −0.811391 −0.0318009
\(652\) −46.5827 −1.82432
\(653\) 8.63237 0.337811 0.168905 0.985632i \(-0.445977\pi\)
0.168905 + 0.985632i \(0.445977\pi\)
\(654\) −0.921344 −0.0360274
\(655\) −0.541205 −0.0211466
\(656\) −1.97765 −0.0772141
\(657\) −26.1810 −1.02142
\(658\) 18.1571 0.707838
\(659\) −43.9965 −1.71386 −0.856930 0.515432i \(-0.827631\pi\)
−0.856930 + 0.515432i \(0.827631\pi\)
\(660\) −1.10476 −0.0430026
\(661\) −16.7583 −0.651822 −0.325911 0.945400i \(-0.605671\pi\)
−0.325911 + 0.945400i \(0.605671\pi\)
\(662\) −30.8628 −1.19952
\(663\) 0.589033 0.0228761
\(664\) 4.40321 0.170878
\(665\) 30.8097 1.19475
\(666\) 16.8314 0.652202
\(667\) −1.01309 −0.0392269
\(668\) −6.91901 −0.267705
\(669\) 0.262124 0.0101343
\(670\) 10.3570 0.400124
\(671\) −6.57689 −0.253898
\(672\) 0.0423375 0.00163321
\(673\) 1.14402 0.0440988 0.0220494 0.999757i \(-0.492981\pi\)
0.0220494 + 0.999757i \(0.492981\pi\)
\(674\) 34.1876 1.31686
\(675\) −0.0525968 −0.00202445
\(676\) 26.2657 1.01022
\(677\) 0.318243 0.0122311 0.00611554 0.999981i \(-0.498053\pi\)
0.00611554 + 0.999981i \(0.498053\pi\)
\(678\) −0.634094 −0.0243522
\(679\) 16.5883 0.636602
\(680\) −51.3130 −1.96776
\(681\) 0.315742 0.0120993
\(682\) −71.9085 −2.75352
\(683\) −3.70899 −0.141921 −0.0709603 0.997479i \(-0.522606\pi\)
−0.0709603 + 0.997479i \(0.522606\pi\)
\(684\) −44.1625 −1.68859
\(685\) 45.3436 1.73249
\(686\) −4.58563 −0.175080
\(687\) −0.741663 −0.0282962
\(688\) −5.35999 −0.204348
\(689\) −17.1159 −0.652063
\(690\) 0.0735039 0.00279824
\(691\) −6.31761 −0.240333 −0.120167 0.992754i \(-0.538343\pi\)
−0.120167 + 0.992754i \(0.538343\pi\)
\(692\) 2.81132 0.106870
\(693\) 43.7197 1.66077
\(694\) 12.4953 0.474316
\(695\) 19.8838 0.754235
\(696\) 0.350393 0.0132816
\(697\) 2.07940 0.0787631
\(698\) −45.7690 −1.73238
\(699\) 0.0507685 0.00192024
\(700\) −4.34136 −0.164088
\(701\) −41.8377 −1.58019 −0.790095 0.612985i \(-0.789969\pi\)
−0.790095 + 0.612985i \(0.789969\pi\)
\(702\) −1.95052 −0.0736175
\(703\) 8.32660 0.314044
\(704\) −29.8555 −1.12522
\(705\) −0.138645 −0.00522169
\(706\) 75.4303 2.83886
\(707\) −38.0822 −1.43223
\(708\) −0.633857 −0.0238218
\(709\) −5.26296 −0.197655 −0.0988273 0.995105i \(-0.531509\pi\)
−0.0988273 + 0.995105i \(0.531509\pi\)
\(710\) −2.43336 −0.0913225
\(711\) −8.01311 −0.300515
\(712\) −58.8333 −2.20487
\(713\) 3.19981 0.119834
\(714\) −1.20392 −0.0450554
\(715\) 40.3218 1.50795
\(716\) −103.297 −3.86038
\(717\) 0.0144839 0.000540913 0
\(718\) −86.3278 −3.22173
\(719\) 12.2664 0.457459 0.228730 0.973490i \(-0.426543\pi\)
0.228730 + 0.973490i \(0.426543\pi\)
\(720\) 29.2138 1.08873
\(721\) 18.1519 0.676010
\(722\) 14.0240 0.521920
\(723\) 0.103944 0.00386573
\(724\) 86.6799 3.22143
\(725\) −0.683156 −0.0253718
\(726\) −0.349746 −0.0129803
\(727\) −37.6878 −1.39776 −0.698882 0.715237i \(-0.746319\pi\)
−0.698882 + 0.715237i \(0.746319\pi\)
\(728\) −81.2707 −3.01209
\(729\) −26.9515 −0.998205
\(730\) 49.3521 1.82660
\(731\) 5.63579 0.208447
\(732\) −0.200519 −0.00741139
\(733\) −28.0391 −1.03565 −0.517825 0.855487i \(-0.673258\pi\)
−0.517825 + 0.855487i \(0.673258\pi\)
\(734\) −53.2772 −1.96650
\(735\) −0.447453 −0.0165045
\(736\) −0.166963 −0.00615433
\(737\) 7.27059 0.267816
\(738\) −3.44234 −0.126714
\(739\) 9.92055 0.364933 0.182467 0.983212i \(-0.441592\pi\)
0.182467 + 0.983212i \(0.441592\pi\)
\(740\) −21.2197 −0.780051
\(741\) −0.482395 −0.0177212
\(742\) 34.9829 1.28426
\(743\) −13.0878 −0.480145 −0.240072 0.970755i \(-0.577171\pi\)
−0.240072 + 0.970755i \(0.577171\pi\)
\(744\) −1.10671 −0.0405739
\(745\) −29.4805 −1.08008
\(746\) 12.8320 0.469813
\(747\) 2.63584 0.0964405
\(748\) −71.3587 −2.60913
\(749\) −66.3680 −2.42503
\(750\) −0.797300 −0.0291133
\(751\) −3.70319 −0.135131 −0.0675656 0.997715i \(-0.521523\pi\)
−0.0675656 + 0.997715i \(0.521523\pi\)
\(752\) 8.51716 0.310589
\(753\) 0.241141 0.00878766
\(754\) −25.3344 −0.922623
\(755\) −18.4092 −0.669980
\(756\) 2.66629 0.0969719
\(757\) −12.1679 −0.442250 −0.221125 0.975245i \(-0.570973\pi\)
−0.221125 + 0.975245i \(0.570973\pi\)
\(758\) 60.6640 2.20342
\(759\) 0.0515998 0.00187295
\(760\) 42.0234 1.52435
\(761\) 37.9926 1.37723 0.688616 0.725126i \(-0.258219\pi\)
0.688616 + 0.725126i \(0.258219\pi\)
\(762\) 0.892013 0.0323142
\(763\) −45.9676 −1.66414
\(764\) 9.80490 0.354729
\(765\) −30.7169 −1.11057
\(766\) 1.07664 0.0389005
\(767\) 23.1347 0.835345
\(768\) −0.966896 −0.0348898
\(769\) 5.12991 0.184989 0.0924946 0.995713i \(-0.470516\pi\)
0.0924946 + 0.995713i \(0.470516\pi\)
\(770\) −82.4131 −2.96996
\(771\) 0.528525 0.0190344
\(772\) −68.9839 −2.48279
\(773\) −4.63926 −0.166863 −0.0834313 0.996514i \(-0.526588\pi\)
−0.0834313 + 0.996514i \(0.526588\pi\)
\(774\) −9.32974 −0.335351
\(775\) 2.15773 0.0775081
\(776\) 22.6259 0.812223
\(777\) −0.251319 −0.00901603
\(778\) 48.8091 1.74989
\(779\) −1.70295 −0.0610146
\(780\) 1.22935 0.0440176
\(781\) −1.70822 −0.0611250
\(782\) 4.74777 0.169780
\(783\) 0.419567 0.0149941
\(784\) 27.4876 0.981699
\(785\) 40.8939 1.45957
\(786\) −0.0173194 −0.000617764 0
\(787\) 15.6019 0.556149 0.278075 0.960559i \(-0.410304\pi\)
0.278075 + 0.960559i \(0.410304\pi\)
\(788\) 98.3679 3.50421
\(789\) 0.0180835 0.000643790 0
\(790\) 15.1050 0.537411
\(791\) −31.6361 −1.12485
\(792\) 59.6321 2.11894
\(793\) 7.31860 0.259891
\(794\) −3.54195 −0.125699
\(795\) −0.267125 −0.00947394
\(796\) −37.9031 −1.34344
\(797\) −23.4170 −0.829473 −0.414736 0.909942i \(-0.636126\pi\)
−0.414736 + 0.909942i \(0.636126\pi\)
\(798\) 0.985960 0.0349026
\(799\) −8.95540 −0.316819
\(800\) −0.112588 −0.00398060
\(801\) −35.2187 −1.24439
\(802\) −59.0919 −2.08661
\(803\) 34.6452 1.22260
\(804\) 0.221669 0.00781765
\(805\) 3.66724 0.129253
\(806\) 80.0180 2.81851
\(807\) 0.372296 0.0131054
\(808\) −51.9427 −1.82734
\(809\) −29.0478 −1.02126 −0.510632 0.859799i \(-0.670589\pi\)
−0.510632 + 0.859799i \(0.670589\pi\)
\(810\) 50.8350 1.78616
\(811\) 14.0219 0.492377 0.246188 0.969222i \(-0.420822\pi\)
0.246188 + 0.969222i \(0.420822\pi\)
\(812\) 34.6312 1.21532
\(813\) −0.388311 −0.0136186
\(814\) −22.2729 −0.780663
\(815\) 26.5346 0.929466
\(816\) −0.564734 −0.0197697
\(817\) −4.61549 −0.161476
\(818\) −50.4149 −1.76271
\(819\) −48.6501 −1.69997
\(820\) 4.33984 0.151554
\(821\) 2.90389 0.101346 0.0506732 0.998715i \(-0.483863\pi\)
0.0506732 + 0.998715i \(0.483863\pi\)
\(822\) 1.45107 0.0506118
\(823\) −35.2812 −1.22982 −0.614912 0.788595i \(-0.710809\pi\)
−0.614912 + 0.788595i \(0.710809\pi\)
\(824\) 24.7585 0.862503
\(825\) 0.0347954 0.00121142
\(826\) −47.2846 −1.64524
\(827\) 23.6924 0.823866 0.411933 0.911214i \(-0.364854\pi\)
0.411933 + 0.911214i \(0.364854\pi\)
\(828\) −5.25661 −0.182680
\(829\) 23.5014 0.816236 0.408118 0.912929i \(-0.366185\pi\)
0.408118 + 0.912929i \(0.366185\pi\)
\(830\) −4.96865 −0.172464
\(831\) 0.389811 0.0135224
\(832\) 33.2224 1.15178
\(833\) −28.9019 −1.00139
\(834\) 0.636313 0.0220337
\(835\) 3.94123 0.136392
\(836\) 58.4400 2.02119
\(837\) −1.32519 −0.0458053
\(838\) −10.5845 −0.365636
\(839\) −17.8511 −0.616290 −0.308145 0.951339i \(-0.599708\pi\)
−0.308145 + 0.951339i \(0.599708\pi\)
\(840\) −1.26838 −0.0437632
\(841\) −23.5504 −0.812084
\(842\) 27.6656 0.953421
\(843\) 0.343994 0.0118478
\(844\) −43.6706 −1.50320
\(845\) −14.9615 −0.514692
\(846\) 14.8252 0.509701
\(847\) −17.4495 −0.599571
\(848\) 16.4098 0.563516
\(849\) 0.194512 0.00667563
\(850\) 3.20157 0.109813
\(851\) 0.991105 0.0339746
\(852\) −0.0520810 −0.00178427
\(853\) −15.8929 −0.544163 −0.272081 0.962274i \(-0.587712\pi\)
−0.272081 + 0.962274i \(0.587712\pi\)
\(854\) −14.9584 −0.511865
\(855\) 25.1560 0.860316
\(856\) −90.5236 −3.09403
\(857\) 30.3569 1.03697 0.518487 0.855086i \(-0.326496\pi\)
0.518487 + 0.855086i \(0.326496\pi\)
\(858\) 1.29036 0.0440522
\(859\) −32.0070 −1.09207 −0.546033 0.837764i \(-0.683863\pi\)
−0.546033 + 0.837764i \(0.683863\pi\)
\(860\) 11.7622 0.401088
\(861\) 0.0513997 0.00175170
\(862\) 55.4817 1.88971
\(863\) 19.4936 0.663569 0.331785 0.943355i \(-0.392349\pi\)
0.331785 + 0.943355i \(0.392349\pi\)
\(864\) 0.0691471 0.00235243
\(865\) −1.60139 −0.0544489
\(866\) −1.44829 −0.0492148
\(867\) 0.0844813 0.00286914
\(868\) −109.382 −3.71266
\(869\) 10.6037 0.359706
\(870\) −0.395390 −0.0134050
\(871\) −8.09053 −0.274137
\(872\) −62.6981 −2.12323
\(873\) 13.5443 0.458405
\(874\) −3.88824 −0.131522
\(875\) −39.7787 −1.34477
\(876\) 1.05628 0.0356883
\(877\) −19.1594 −0.646969 −0.323484 0.946234i \(-0.604854\pi\)
−0.323484 + 0.946234i \(0.604854\pi\)
\(878\) −17.9099 −0.604429
\(879\) 0.0284154 0.000958427 0
\(880\) −38.6584 −1.30318
\(881\) 42.9793 1.44801 0.724005 0.689795i \(-0.242299\pi\)
0.724005 + 0.689795i \(0.242299\pi\)
\(882\) 47.8456 1.61105
\(883\) 57.0739 1.92069 0.960344 0.278817i \(-0.0899421\pi\)
0.960344 + 0.278817i \(0.0899421\pi\)
\(884\) 79.4061 2.67072
\(885\) 0.361060 0.0121369
\(886\) −45.6838 −1.53478
\(887\) 38.7172 1.30000 0.649998 0.759935i \(-0.274770\pi\)
0.649998 + 0.759935i \(0.274770\pi\)
\(888\) −0.342791 −0.0115033
\(889\) 44.5042 1.49262
\(890\) 66.3885 2.22535
\(891\) 35.6862 1.19553
\(892\) 35.3364 1.18315
\(893\) 7.33413 0.245427
\(894\) −0.943422 −0.0315528
\(895\) 58.8403 1.96681
\(896\) −70.7292 −2.36290
\(897\) −0.0574189 −0.00191716
\(898\) 7.28904 0.243238
\(899\) −17.2123 −0.574063
\(900\) −3.54470 −0.118157
\(901\) −17.2542 −0.574820
\(902\) 4.55524 0.151673
\(903\) 0.139308 0.00463588
\(904\) −43.1506 −1.43517
\(905\) −49.3749 −1.64128
\(906\) −0.589124 −0.0195723
\(907\) 42.2984 1.40449 0.702247 0.711933i \(-0.252180\pi\)
0.702247 + 0.711933i \(0.252180\pi\)
\(908\) 42.5645 1.41255
\(909\) −31.0939 −1.03132
\(910\) 91.7071 3.04006
\(911\) 5.18769 0.171876 0.0859379 0.996300i \(-0.472611\pi\)
0.0859379 + 0.996300i \(0.472611\pi\)
\(912\) 0.462495 0.0153148
\(913\) −3.48800 −0.115436
\(914\) 24.2419 0.801850
\(915\) 0.114220 0.00377601
\(916\) −99.9818 −3.30349
\(917\) −0.864099 −0.0285351
\(918\) −1.96628 −0.0648968
\(919\) −22.7782 −0.751385 −0.375692 0.926744i \(-0.622595\pi\)
−0.375692 + 0.926744i \(0.622595\pi\)
\(920\) 5.00199 0.164911
\(921\) −0.869510 −0.0286513
\(922\) −56.6963 −1.86719
\(923\) 1.90087 0.0625678
\(924\) −1.76388 −0.0580273
\(925\) 0.668333 0.0219747
\(926\) −31.5879 −1.03804
\(927\) 14.8209 0.486782
\(928\) 0.898121 0.0294823
\(929\) −32.2505 −1.05811 −0.529053 0.848589i \(-0.677453\pi\)
−0.529053 + 0.848589i \(0.677453\pi\)
\(930\) 1.24883 0.0409507
\(931\) 23.6696 0.775738
\(932\) 6.84397 0.224182
\(933\) 0.267051 0.00874285
\(934\) 102.159 3.34274
\(935\) 40.6476 1.32932
\(936\) −66.3571 −2.16895
\(937\) 23.0020 0.751441 0.375721 0.926733i \(-0.377395\pi\)
0.375721 + 0.926733i \(0.377395\pi\)
\(938\) 16.5361 0.539924
\(939\) −0.270537 −0.00882865
\(940\) −18.6905 −0.609615
\(941\) −44.0625 −1.43640 −0.718198 0.695839i \(-0.755033\pi\)
−0.718198 + 0.695839i \(0.755033\pi\)
\(942\) 1.30867 0.0426388
\(943\) −0.202700 −0.00660083
\(944\) −22.1803 −0.721909
\(945\) −1.51878 −0.0494059
\(946\) 12.3460 0.401403
\(947\) 27.2627 0.885918 0.442959 0.896542i \(-0.353929\pi\)
0.442959 + 0.896542i \(0.353929\pi\)
\(948\) 0.323290 0.0105000
\(949\) −38.5523 −1.25146
\(950\) −2.62196 −0.0850678
\(951\) −0.475821 −0.0154296
\(952\) −81.9274 −2.65528
\(953\) 5.41403 0.175378 0.0876888 0.996148i \(-0.472052\pi\)
0.0876888 + 0.996148i \(0.472052\pi\)
\(954\) 28.5634 0.924773
\(955\) −5.58510 −0.180730
\(956\) 1.95255 0.0631498
\(957\) −0.277564 −0.00897237
\(958\) −18.6333 −0.602016
\(959\) 72.3964 2.33780
\(960\) 0.518498 0.0167344
\(961\) 23.3647 0.753700
\(962\) 24.7847 0.799090
\(963\) −54.1891 −1.74622
\(964\) 14.0125 0.451312
\(965\) 39.2949 1.26495
\(966\) 0.117358 0.00377592
\(967\) 0.766053 0.0246346 0.0123173 0.999924i \(-0.496079\pi\)
0.0123173 + 0.999924i \(0.496079\pi\)
\(968\) −23.8005 −0.764977
\(969\) −0.486293 −0.0156220
\(970\) −25.5314 −0.819765
\(971\) −42.5788 −1.36642 −0.683209 0.730223i \(-0.739416\pi\)
−0.683209 + 0.730223i \(0.739416\pi\)
\(972\) 3.26568 0.104747
\(973\) 31.7468 1.01776
\(974\) 22.8723 0.732875
\(975\) −0.0387194 −0.00124001
\(976\) −7.01670 −0.224599
\(977\) −15.5492 −0.497461 −0.248731 0.968573i \(-0.580013\pi\)
−0.248731 + 0.968573i \(0.580013\pi\)
\(978\) 0.849149 0.0271528
\(979\) 46.6048 1.48949
\(980\) −60.3200 −1.92685
\(981\) −37.5323 −1.19831
\(982\) 97.6482 3.11608
\(983\) −30.8689 −0.984566 −0.492283 0.870435i \(-0.663838\pi\)
−0.492283 + 0.870435i \(0.663838\pi\)
\(984\) 0.0701074 0.00223494
\(985\) −56.0326 −1.78535
\(986\) −25.5391 −0.813330
\(987\) −0.221364 −0.00704609
\(988\) −65.0305 −2.06890
\(989\) −0.549376 −0.0174692
\(990\) −67.2899 −2.13861
\(991\) 34.5400 1.09720 0.548600 0.836085i \(-0.315161\pi\)
0.548600 + 0.836085i \(0.315161\pi\)
\(992\) −2.83669 −0.0900651
\(993\) 0.376266 0.0119404
\(994\) −3.88516 −0.123230
\(995\) 21.5905 0.684464
\(996\) −0.106344 −0.00336962
\(997\) −53.6381 −1.69873 −0.849367 0.527802i \(-0.823016\pi\)
−0.849367 + 0.527802i \(0.823016\pi\)
\(998\) 100.264 3.17381
\(999\) −0.410463 −0.0129865
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 \(a_p\))