Properties

Label 483.2.a.c.1.1
Level $483$
Weight $2$
Character 483.1
Self dual yes
Analytic conductor $3.857$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.85677441763\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 483.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} -3.61803 q^{5} -2.61803 q^{6} +1.00000 q^{7} -7.47214 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.61803 q^{2} +1.00000 q^{3} +4.85410 q^{4} -3.61803 q^{5} -2.61803 q^{6} +1.00000 q^{7} -7.47214 q^{8} +1.00000 q^{9} +9.47214 q^{10} +3.47214 q^{11} +4.85410 q^{12} -4.61803 q^{13} -2.61803 q^{14} -3.61803 q^{15} +9.85410 q^{16} -1.00000 q^{17} -2.61803 q^{18} -3.00000 q^{19} -17.5623 q^{20} +1.00000 q^{21} -9.09017 q^{22} -1.00000 q^{23} -7.47214 q^{24} +8.09017 q^{25} +12.0902 q^{26} +1.00000 q^{27} +4.85410 q^{28} +1.47214 q^{29} +9.47214 q^{30} -8.23607 q^{31} -10.8541 q^{32} +3.47214 q^{33} +2.61803 q^{34} -3.61803 q^{35} +4.85410 q^{36} -7.47214 q^{37} +7.85410 q^{38} -4.61803 q^{39} +27.0344 q^{40} +8.70820 q^{41} -2.61803 q^{42} -3.09017 q^{43} +16.8541 q^{44} -3.61803 q^{45} +2.61803 q^{46} -11.7082 q^{47} +9.85410 q^{48} +1.00000 q^{49} -21.1803 q^{50} -1.00000 q^{51} -22.4164 q^{52} -5.61803 q^{53} -2.61803 q^{54} -12.5623 q^{55} -7.47214 q^{56} -3.00000 q^{57} -3.85410 q^{58} -12.8541 q^{59} -17.5623 q^{60} -10.7984 q^{61} +21.5623 q^{62} +1.00000 q^{63} +8.70820 q^{64} +16.7082 q^{65} -9.09017 q^{66} +10.8541 q^{67} -4.85410 q^{68} -1.00000 q^{69} +9.47214 q^{70} -15.0902 q^{71} -7.47214 q^{72} -10.7082 q^{73} +19.5623 q^{74} +8.09017 q^{75} -14.5623 q^{76} +3.47214 q^{77} +12.0902 q^{78} +9.47214 q^{79} -35.6525 q^{80} +1.00000 q^{81} -22.7984 q^{82} -3.00000 q^{83} +4.85410 q^{84} +3.61803 q^{85} +8.09017 q^{86} +1.47214 q^{87} -25.9443 q^{88} +9.85410 q^{89} +9.47214 q^{90} -4.61803 q^{91} -4.85410 q^{92} -8.23607 q^{93} +30.6525 q^{94} +10.8541 q^{95} -10.8541 q^{96} +5.00000 q^{97} -2.61803 q^{98} +3.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - 3 q^{6} + 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - 3 q^{6} + 2 q^{7} - 6 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} - 7 q^{13} - 3 q^{14} - 5 q^{15} + 13 q^{16} - 2 q^{17} - 3 q^{18} - 6 q^{19} - 15 q^{20} + 2 q^{21} - 7 q^{22} - 2 q^{23} - 6 q^{24} + 5 q^{25} + 13 q^{26} + 2 q^{27} + 3 q^{28} - 6 q^{29} + 10 q^{30} - 12 q^{31} - 15 q^{32} - 2 q^{33} + 3 q^{34} - 5 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 7 q^{39} + 25 q^{40} + 4 q^{41} - 3 q^{42} + 5 q^{43} + 27 q^{44} - 5 q^{45} + 3 q^{46} - 10 q^{47} + 13 q^{48} + 2 q^{49} - 20 q^{50} - 2 q^{51} - 18 q^{52} - 9 q^{53} - 3 q^{54} - 5 q^{55} - 6 q^{56} - 6 q^{57} - q^{58} - 19 q^{59} - 15 q^{60} + 3 q^{61} + 23 q^{62} + 2 q^{63} + 4 q^{64} + 20 q^{65} - 7 q^{66} + 15 q^{67} - 3 q^{68} - 2 q^{69} + 10 q^{70} - 19 q^{71} - 6 q^{72} - 8 q^{73} + 19 q^{74} + 5 q^{75} - 9 q^{76} - 2 q^{77} + 13 q^{78} + 10 q^{79} - 40 q^{80} + 2 q^{81} - 21 q^{82} - 6 q^{83} + 3 q^{84} + 5 q^{85} + 5 q^{86} - 6 q^{87} - 34 q^{88} + 13 q^{89} + 10 q^{90} - 7 q^{91} - 3 q^{92} - 12 q^{93} + 30 q^{94} + 15 q^{95} - 15 q^{96} + 10 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61803 −1.85123 −0.925615 0.378467i \(-0.876451\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.85410 2.42705
\(5\) −3.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(6\) −2.61803 −1.06881
\(7\) 1.00000 0.377964
\(8\) −7.47214 −2.64180
\(9\) 1.00000 0.333333
\(10\) 9.47214 2.99535
\(11\) 3.47214 1.04689 0.523444 0.852060i \(-0.324647\pi\)
0.523444 + 0.852060i \(0.324647\pi\)
\(12\) 4.85410 1.40126
\(13\) −4.61803 −1.28081 −0.640406 0.768036i \(-0.721234\pi\)
−0.640406 + 0.768036i \(0.721234\pi\)
\(14\) −2.61803 −0.699699
\(15\) −3.61803 −0.934172
\(16\) 9.85410 2.46353
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) −2.61803 −0.617077
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) −17.5623 −3.92705
\(21\) 1.00000 0.218218
\(22\) −9.09017 −1.93803
\(23\) −1.00000 −0.208514
\(24\) −7.47214 −1.52524
\(25\) 8.09017 1.61803
\(26\) 12.0902 2.37108
\(27\) 1.00000 0.192450
\(28\) 4.85410 0.917339
\(29\) 1.47214 0.273369 0.136684 0.990615i \(-0.456355\pi\)
0.136684 + 0.990615i \(0.456355\pi\)
\(30\) 9.47214 1.72937
\(31\) −8.23607 −1.47924 −0.739621 0.673024i \(-0.764995\pi\)
−0.739621 + 0.673024i \(0.764995\pi\)
\(32\) −10.8541 −1.91875
\(33\) 3.47214 0.604421
\(34\) 2.61803 0.448989
\(35\) −3.61803 −0.611559
\(36\) 4.85410 0.809017
\(37\) −7.47214 −1.22841 −0.614206 0.789146i \(-0.710524\pi\)
−0.614206 + 0.789146i \(0.710524\pi\)
\(38\) 7.85410 1.27410
\(39\) −4.61803 −0.739477
\(40\) 27.0344 4.27452
\(41\) 8.70820 1.35999 0.679996 0.733215i \(-0.261981\pi\)
0.679996 + 0.733215i \(0.261981\pi\)
\(42\) −2.61803 −0.403971
\(43\) −3.09017 −0.471246 −0.235623 0.971844i \(-0.575713\pi\)
−0.235623 + 0.971844i \(0.575713\pi\)
\(44\) 16.8541 2.54085
\(45\) −3.61803 −0.539345
\(46\) 2.61803 0.386008
\(47\) −11.7082 −1.70782 −0.853909 0.520423i \(-0.825774\pi\)
−0.853909 + 0.520423i \(0.825774\pi\)
\(48\) 9.85410 1.42232
\(49\) 1.00000 0.142857
\(50\) −21.1803 −2.99535
\(51\) −1.00000 −0.140028
\(52\) −22.4164 −3.10860
\(53\) −5.61803 −0.771696 −0.385848 0.922562i \(-0.626091\pi\)
−0.385848 + 0.922562i \(0.626091\pi\)
\(54\) −2.61803 −0.356269
\(55\) −12.5623 −1.69390
\(56\) −7.47214 −0.998506
\(57\) −3.00000 −0.397360
\(58\) −3.85410 −0.506068
\(59\) −12.8541 −1.67346 −0.836731 0.547614i \(-0.815536\pi\)
−0.836731 + 0.547614i \(0.815536\pi\)
\(60\) −17.5623 −2.26728
\(61\) −10.7984 −1.38259 −0.691295 0.722573i \(-0.742960\pi\)
−0.691295 + 0.722573i \(0.742960\pi\)
\(62\) 21.5623 2.73842
\(63\) 1.00000 0.125988
\(64\) 8.70820 1.08853
\(65\) 16.7082 2.07240
\(66\) −9.09017 −1.11892
\(67\) 10.8541 1.32604 0.663020 0.748602i \(-0.269275\pi\)
0.663020 + 0.748602i \(0.269275\pi\)
\(68\) −4.85410 −0.588646
\(69\) −1.00000 −0.120386
\(70\) 9.47214 1.13214
\(71\) −15.0902 −1.79087 −0.895437 0.445189i \(-0.853137\pi\)
−0.895437 + 0.445189i \(0.853137\pi\)
\(72\) −7.47214 −0.880600
\(73\) −10.7082 −1.25330 −0.626650 0.779301i \(-0.715575\pi\)
−0.626650 + 0.779301i \(0.715575\pi\)
\(74\) 19.5623 2.27407
\(75\) 8.09017 0.934172
\(76\) −14.5623 −1.67041
\(77\) 3.47214 0.395687
\(78\) 12.0902 1.36894
\(79\) 9.47214 1.06570 0.532849 0.846210i \(-0.321121\pi\)
0.532849 + 0.846210i \(0.321121\pi\)
\(80\) −35.6525 −3.98607
\(81\) 1.00000 0.111111
\(82\) −22.7984 −2.51766
\(83\) −3.00000 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 4.85410 0.529626
\(85\) 3.61803 0.392431
\(86\) 8.09017 0.872385
\(87\) 1.47214 0.157830
\(88\) −25.9443 −2.76567
\(89\) 9.85410 1.04453 0.522266 0.852782i \(-0.325087\pi\)
0.522266 + 0.852782i \(0.325087\pi\)
\(90\) 9.47214 0.998451
\(91\) −4.61803 −0.484102
\(92\) −4.85410 −0.506075
\(93\) −8.23607 −0.854040
\(94\) 30.6525 3.16156
\(95\) 10.8541 1.11361
\(96\) −10.8541 −1.10779
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) −2.61803 −0.264461
\(99\) 3.47214 0.348963
\(100\) 39.2705 3.92705
\(101\) 4.85410 0.483001 0.241501 0.970401i \(-0.422360\pi\)
0.241501 + 0.970401i \(0.422360\pi\)
\(102\) 2.61803 0.259224
\(103\) 12.9443 1.27544 0.637719 0.770270i \(-0.279878\pi\)
0.637719 + 0.770270i \(0.279878\pi\)
\(104\) 34.5066 3.38365
\(105\) −3.61803 −0.353084
\(106\) 14.7082 1.42859
\(107\) −12.7984 −1.23727 −0.618633 0.785680i \(-0.712313\pi\)
−0.618633 + 0.785680i \(0.712313\pi\)
\(108\) 4.85410 0.467086
\(109\) 9.32624 0.893292 0.446646 0.894711i \(-0.352618\pi\)
0.446646 + 0.894711i \(0.352618\pi\)
\(110\) 32.8885 3.13580
\(111\) −7.47214 −0.709224
\(112\) 9.85410 0.931125
\(113\) −9.32624 −0.877339 −0.438669 0.898649i \(-0.644550\pi\)
−0.438669 + 0.898649i \(0.644550\pi\)
\(114\) 7.85410 0.735604
\(115\) 3.61803 0.337383
\(116\) 7.14590 0.663480
\(117\) −4.61803 −0.426937
\(118\) 33.6525 3.09796
\(119\) −1.00000 −0.0916698
\(120\) 27.0344 2.46790
\(121\) 1.05573 0.0959753
\(122\) 28.2705 2.55949
\(123\) 8.70820 0.785192
\(124\) −39.9787 −3.59019
\(125\) −11.1803 −1.00000
\(126\) −2.61803 −0.233233
\(127\) 12.1459 1.07777 0.538887 0.842378i \(-0.318845\pi\)
0.538887 + 0.842378i \(0.318845\pi\)
\(128\) −1.09017 −0.0963583
\(129\) −3.09017 −0.272074
\(130\) −43.7426 −3.83648
\(131\) −0.0557281 −0.00486899 −0.00243449 0.999997i \(-0.500775\pi\)
−0.00243449 + 0.999997i \(0.500775\pi\)
\(132\) 16.8541 1.46696
\(133\) −3.00000 −0.260133
\(134\) −28.4164 −2.45480
\(135\) −3.61803 −0.311391
\(136\) 7.47214 0.640730
\(137\) −13.1803 −1.12607 −0.563036 0.826432i \(-0.690367\pi\)
−0.563036 + 0.826432i \(0.690367\pi\)
\(138\) 2.61803 0.222862
\(139\) −0.673762 −0.0571478 −0.0285739 0.999592i \(-0.509097\pi\)
−0.0285739 + 0.999592i \(0.509097\pi\)
\(140\) −17.5623 −1.48429
\(141\) −11.7082 −0.986009
\(142\) 39.5066 3.31532
\(143\) −16.0344 −1.34087
\(144\) 9.85410 0.821175
\(145\) −5.32624 −0.442320
\(146\) 28.0344 2.32015
\(147\) 1.00000 0.0824786
\(148\) −36.2705 −2.98142
\(149\) 6.18034 0.506313 0.253157 0.967425i \(-0.418531\pi\)
0.253157 + 0.967425i \(0.418531\pi\)
\(150\) −21.1803 −1.72937
\(151\) 5.23607 0.426105 0.213053 0.977041i \(-0.431659\pi\)
0.213053 + 0.977041i \(0.431659\pi\)
\(152\) 22.4164 1.81821
\(153\) −1.00000 −0.0808452
\(154\) −9.09017 −0.732507
\(155\) 29.7984 2.39346
\(156\) −22.4164 −1.79475
\(157\) 10.6525 0.850160 0.425080 0.905156i \(-0.360246\pi\)
0.425080 + 0.905156i \(0.360246\pi\)
\(158\) −24.7984 −1.97285
\(159\) −5.61803 −0.445539
\(160\) 39.2705 3.10461
\(161\) −1.00000 −0.0788110
\(162\) −2.61803 −0.205692
\(163\) −21.7984 −1.70738 −0.853690 0.520781i \(-0.825641\pi\)
−0.853690 + 0.520781i \(0.825641\pi\)
\(164\) 42.2705 3.30077
\(165\) −12.5623 −0.977974
\(166\) 7.85410 0.609597
\(167\) 23.4721 1.81633 0.908164 0.418614i \(-0.137484\pi\)
0.908164 + 0.418614i \(0.137484\pi\)
\(168\) −7.47214 −0.576488
\(169\) 8.32624 0.640480
\(170\) −9.47214 −0.726480
\(171\) −3.00000 −0.229416
\(172\) −15.0000 −1.14374
\(173\) 13.1803 1.00208 0.501041 0.865423i \(-0.332950\pi\)
0.501041 + 0.865423i \(0.332950\pi\)
\(174\) −3.85410 −0.292179
\(175\) 8.09017 0.611559
\(176\) 34.2148 2.57904
\(177\) −12.8541 −0.966173
\(178\) −25.7984 −1.93367
\(179\) 1.14590 0.0856484 0.0428242 0.999083i \(-0.486364\pi\)
0.0428242 + 0.999083i \(0.486364\pi\)
\(180\) −17.5623 −1.30902
\(181\) −1.47214 −0.109423 −0.0547115 0.998502i \(-0.517424\pi\)
−0.0547115 + 0.998502i \(0.517424\pi\)
\(182\) 12.0902 0.896183
\(183\) −10.7984 −0.798239
\(184\) 7.47214 0.550853
\(185\) 27.0344 1.98761
\(186\) 21.5623 1.58102
\(187\) −3.47214 −0.253908
\(188\) −56.8328 −4.14496
\(189\) 1.00000 0.0727393
\(190\) −28.4164 −2.06154
\(191\) 19.7082 1.42604 0.713018 0.701146i \(-0.247328\pi\)
0.713018 + 0.701146i \(0.247328\pi\)
\(192\) 8.70820 0.628460
\(193\) 8.18034 0.588834 0.294417 0.955677i \(-0.404875\pi\)
0.294417 + 0.955677i \(0.404875\pi\)
\(194\) −13.0902 −0.939819
\(195\) 16.7082 1.19650
\(196\) 4.85410 0.346722
\(197\) −6.14590 −0.437877 −0.218939 0.975739i \(-0.570259\pi\)
−0.218939 + 0.975739i \(0.570259\pi\)
\(198\) −9.09017 −0.646010
\(199\) 11.0344 0.782211 0.391105 0.920346i \(-0.372093\pi\)
0.391105 + 0.920346i \(0.372093\pi\)
\(200\) −60.4508 −4.27452
\(201\) 10.8541 0.765589
\(202\) −12.7082 −0.894146
\(203\) 1.47214 0.103324
\(204\) −4.85410 −0.339855
\(205\) −31.5066 −2.20051
\(206\) −33.8885 −2.36113
\(207\) −1.00000 −0.0695048
\(208\) −45.5066 −3.15531
\(209\) −10.4164 −0.720518
\(210\) 9.47214 0.653639
\(211\) −0.416408 −0.0286667 −0.0143333 0.999897i \(-0.504563\pi\)
−0.0143333 + 0.999897i \(0.504563\pi\)
\(212\) −27.2705 −1.87295
\(213\) −15.0902 −1.03396
\(214\) 33.5066 2.29046
\(215\) 11.1803 0.762493
\(216\) −7.47214 −0.508414
\(217\) −8.23607 −0.559101
\(218\) −24.4164 −1.65369
\(219\) −10.7082 −0.723593
\(220\) −60.9787 −4.11118
\(221\) 4.61803 0.310643
\(222\) 19.5623 1.31294
\(223\) −4.67376 −0.312978 −0.156489 0.987680i \(-0.550018\pi\)
−0.156489 + 0.987680i \(0.550018\pi\)
\(224\) −10.8541 −0.725220
\(225\) 8.09017 0.539345
\(226\) 24.4164 1.62416
\(227\) 15.7984 1.04857 0.524287 0.851541i \(-0.324332\pi\)
0.524287 + 0.851541i \(0.324332\pi\)
\(228\) −14.5623 −0.964412
\(229\) −1.43769 −0.0950055 −0.0475028 0.998871i \(-0.515126\pi\)
−0.0475028 + 0.998871i \(0.515126\pi\)
\(230\) −9.47214 −0.624574
\(231\) 3.47214 0.228450
\(232\) −11.0000 −0.722185
\(233\) −14.2705 −0.934892 −0.467446 0.884022i \(-0.654826\pi\)
−0.467446 + 0.884022i \(0.654826\pi\)
\(234\) 12.0902 0.790359
\(235\) 42.3607 2.76331
\(236\) −62.3951 −4.06158
\(237\) 9.47214 0.615281
\(238\) 2.61803 0.169702
\(239\) −11.1459 −0.720968 −0.360484 0.932765i \(-0.617388\pi\)
−0.360484 + 0.932765i \(0.617388\pi\)
\(240\) −35.6525 −2.30136
\(241\) 6.41641 0.413317 0.206659 0.978413i \(-0.433741\pi\)
0.206659 + 0.978413i \(0.433741\pi\)
\(242\) −2.76393 −0.177672
\(243\) 1.00000 0.0641500
\(244\) −52.4164 −3.35562
\(245\) −3.61803 −0.231148
\(246\) −22.7984 −1.45357
\(247\) 13.8541 0.881515
\(248\) 61.5410 3.90786
\(249\) −3.00000 −0.190117
\(250\) 29.2705 1.85123
\(251\) −3.23607 −0.204259 −0.102129 0.994771i \(-0.532566\pi\)
−0.102129 + 0.994771i \(0.532566\pi\)
\(252\) 4.85410 0.305780
\(253\) −3.47214 −0.218291
\(254\) −31.7984 −1.99521
\(255\) 3.61803 0.226570
\(256\) −14.5623 −0.910144
\(257\) 17.5967 1.09765 0.548827 0.835936i \(-0.315074\pi\)
0.548827 + 0.835936i \(0.315074\pi\)
\(258\) 8.09017 0.503672
\(259\) −7.47214 −0.464296
\(260\) 81.1033 5.02981
\(261\) 1.47214 0.0911229
\(262\) 0.145898 0.00901361
\(263\) −7.65248 −0.471872 −0.235936 0.971769i \(-0.575816\pi\)
−0.235936 + 0.971769i \(0.575816\pi\)
\(264\) −25.9443 −1.59676
\(265\) 20.3262 1.24863
\(266\) 7.85410 0.481566
\(267\) 9.85410 0.603061
\(268\) 52.6869 3.21837
\(269\) 19.2705 1.17494 0.587472 0.809245i \(-0.300123\pi\)
0.587472 + 0.809245i \(0.300123\pi\)
\(270\) 9.47214 0.576456
\(271\) −21.8328 −1.32625 −0.663125 0.748509i \(-0.730770\pi\)
−0.663125 + 0.748509i \(0.730770\pi\)
\(272\) −9.85410 −0.597493
\(273\) −4.61803 −0.279496
\(274\) 34.5066 2.08462
\(275\) 28.0902 1.69390
\(276\) −4.85410 −0.292183
\(277\) −25.8541 −1.55342 −0.776711 0.629857i \(-0.783114\pi\)
−0.776711 + 0.629857i \(0.783114\pi\)
\(278\) 1.76393 0.105794
\(279\) −8.23607 −0.493080
\(280\) 27.0344 1.61562
\(281\) 14.2918 0.852577 0.426289 0.904587i \(-0.359821\pi\)
0.426289 + 0.904587i \(0.359821\pi\)
\(282\) 30.6525 1.82533
\(283\) −15.9098 −0.945741 −0.472871 0.881132i \(-0.656782\pi\)
−0.472871 + 0.881132i \(0.656782\pi\)
\(284\) −73.2492 −4.34654
\(285\) 10.8541 0.642942
\(286\) 41.9787 2.48225
\(287\) 8.70820 0.514029
\(288\) −10.8541 −0.639584
\(289\) −16.0000 −0.941176
\(290\) 13.9443 0.818836
\(291\) 5.00000 0.293105
\(292\) −51.9787 −3.04182
\(293\) −23.4164 −1.36800 −0.684001 0.729481i \(-0.739761\pi\)
−0.684001 + 0.729481i \(0.739761\pi\)
\(294\) −2.61803 −0.152687
\(295\) 46.5066 2.70772
\(296\) 55.8328 3.24522
\(297\) 3.47214 0.201474
\(298\) −16.1803 −0.937302
\(299\) 4.61803 0.267068
\(300\) 39.2705 2.26728
\(301\) −3.09017 −0.178114
\(302\) −13.7082 −0.788818
\(303\) 4.85410 0.278861
\(304\) −29.5623 −1.69551
\(305\) 39.0689 2.23708
\(306\) 2.61803 0.149663
\(307\) −9.29180 −0.530311 −0.265155 0.964206i \(-0.585423\pi\)
−0.265155 + 0.964206i \(0.585423\pi\)
\(308\) 16.8541 0.960352
\(309\) 12.9443 0.736374
\(310\) −78.0132 −4.43085
\(311\) −16.5066 −0.936002 −0.468001 0.883728i \(-0.655026\pi\)
−0.468001 + 0.883728i \(0.655026\pi\)
\(312\) 34.5066 1.95355
\(313\) 6.47214 0.365827 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(314\) −27.8885 −1.57384
\(315\) −3.61803 −0.203853
\(316\) 45.9787 2.58650
\(317\) −0.201626 −0.0113245 −0.00566223 0.999984i \(-0.501802\pi\)
−0.00566223 + 0.999984i \(0.501802\pi\)
\(318\) 14.7082 0.824795
\(319\) 5.11146 0.286187
\(320\) −31.5066 −1.76127
\(321\) −12.7984 −0.714336
\(322\) 2.61803 0.145897
\(323\) 3.00000 0.166924
\(324\) 4.85410 0.269672
\(325\) −37.3607 −2.07240
\(326\) 57.0689 3.16075
\(327\) 9.32624 0.515742
\(328\) −65.0689 −3.59283
\(329\) −11.7082 −0.645494
\(330\) 32.8885 1.81045
\(331\) 1.05573 0.0580281 0.0290140 0.999579i \(-0.490763\pi\)
0.0290140 + 0.999579i \(0.490763\pi\)
\(332\) −14.5623 −0.799210
\(333\) −7.47214 −0.409471
\(334\) −61.4508 −3.36244
\(335\) −39.2705 −2.14558
\(336\) 9.85410 0.537585
\(337\) 28.3262 1.54303 0.771514 0.636212i \(-0.219500\pi\)
0.771514 + 0.636212i \(0.219500\pi\)
\(338\) −21.7984 −1.18568
\(339\) −9.32624 −0.506532
\(340\) 17.5623 0.952450
\(341\) −28.5967 −1.54860
\(342\) 7.85410 0.424701
\(343\) 1.00000 0.0539949
\(344\) 23.0902 1.24494
\(345\) 3.61803 0.194788
\(346\) −34.5066 −1.85509
\(347\) 20.4164 1.09601 0.548005 0.836475i \(-0.315387\pi\)
0.548005 + 0.836475i \(0.315387\pi\)
\(348\) 7.14590 0.383060
\(349\) 15.2148 0.814429 0.407214 0.913333i \(-0.366500\pi\)
0.407214 + 0.913333i \(0.366500\pi\)
\(350\) −21.1803 −1.13214
\(351\) −4.61803 −0.246492
\(352\) −37.6869 −2.00872
\(353\) −19.6525 −1.04600 −0.522998 0.852334i \(-0.675186\pi\)
−0.522998 + 0.852334i \(0.675186\pi\)
\(354\) 33.6525 1.78861
\(355\) 54.5967 2.89769
\(356\) 47.8328 2.53513
\(357\) −1.00000 −0.0529256
\(358\) −3.00000 −0.158555
\(359\) 21.5066 1.13507 0.567537 0.823348i \(-0.307896\pi\)
0.567537 + 0.823348i \(0.307896\pi\)
\(360\) 27.0344 1.42484
\(361\) −10.0000 −0.526316
\(362\) 3.85410 0.202567
\(363\) 1.05573 0.0554114
\(364\) −22.4164 −1.17494
\(365\) 38.7426 2.02788
\(366\) 28.2705 1.47772
\(367\) 4.43769 0.231646 0.115823 0.993270i \(-0.463050\pi\)
0.115823 + 0.993270i \(0.463050\pi\)
\(368\) −9.85410 −0.513681
\(369\) 8.70820 0.453331
\(370\) −70.7771 −3.67953
\(371\) −5.61803 −0.291674
\(372\) −39.9787 −2.07280
\(373\) −29.9443 −1.55046 −0.775228 0.631682i \(-0.782365\pi\)
−0.775228 + 0.631682i \(0.782365\pi\)
\(374\) 9.09017 0.470041
\(375\) −11.1803 −0.577350
\(376\) 87.4853 4.51171
\(377\) −6.79837 −0.350134
\(378\) −2.61803 −0.134657
\(379\) −12.3607 −0.634925 −0.317463 0.948271i \(-0.602831\pi\)
−0.317463 + 0.948271i \(0.602831\pi\)
\(380\) 52.6869 2.70278
\(381\) 12.1459 0.622253
\(382\) −51.5967 −2.63992
\(383\) −18.5279 −0.946730 −0.473365 0.880866i \(-0.656961\pi\)
−0.473365 + 0.880866i \(0.656961\pi\)
\(384\) −1.09017 −0.0556325
\(385\) −12.5623 −0.640234
\(386\) −21.4164 −1.09007
\(387\) −3.09017 −0.157082
\(388\) 24.2705 1.23215
\(389\) −18.4164 −0.933749 −0.466874 0.884324i \(-0.654620\pi\)
−0.466874 + 0.884324i \(0.654620\pi\)
\(390\) −43.7426 −2.21499
\(391\) 1.00000 0.0505722
\(392\) −7.47214 −0.377400
\(393\) −0.0557281 −0.00281111
\(394\) 16.0902 0.810611
\(395\) −34.2705 −1.72434
\(396\) 16.8541 0.846950
\(397\) −16.2918 −0.817662 −0.408831 0.912610i \(-0.634063\pi\)
−0.408831 + 0.912610i \(0.634063\pi\)
\(398\) −28.8885 −1.44805
\(399\) −3.00000 −0.150188
\(400\) 79.7214 3.98607
\(401\) −32.4164 −1.61880 −0.809399 0.587259i \(-0.800207\pi\)
−0.809399 + 0.587259i \(0.800207\pi\)
\(402\) −28.4164 −1.41728
\(403\) 38.0344 1.89463
\(404\) 23.5623 1.17227
\(405\) −3.61803 −0.179782
\(406\) −3.85410 −0.191276
\(407\) −25.9443 −1.28601
\(408\) 7.47214 0.369926
\(409\) −4.41641 −0.218377 −0.109189 0.994021i \(-0.534825\pi\)
−0.109189 + 0.994021i \(0.534825\pi\)
\(410\) 82.4853 4.07366
\(411\) −13.1803 −0.650138
\(412\) 62.8328 3.09555
\(413\) −12.8541 −0.632509
\(414\) 2.61803 0.128669
\(415\) 10.8541 0.532807
\(416\) 50.1246 2.45756
\(417\) −0.673762 −0.0329943
\(418\) 27.2705 1.33384
\(419\) −18.2705 −0.892573 −0.446286 0.894890i \(-0.647254\pi\)
−0.446286 + 0.894890i \(0.647254\pi\)
\(420\) −17.5623 −0.856953
\(421\) −13.3820 −0.652197 −0.326099 0.945336i \(-0.605734\pi\)
−0.326099 + 0.945336i \(0.605734\pi\)
\(422\) 1.09017 0.0530686
\(423\) −11.7082 −0.569272
\(424\) 41.9787 2.03867
\(425\) −8.09017 −0.392431
\(426\) 39.5066 1.91410
\(427\) −10.7984 −0.522570
\(428\) −62.1246 −3.00291
\(429\) −16.0344 −0.774150
\(430\) −29.2705 −1.41155
\(431\) 37.1591 1.78989 0.894944 0.446178i \(-0.147215\pi\)
0.894944 + 0.446178i \(0.147215\pi\)
\(432\) 9.85410 0.474106
\(433\) 8.18034 0.393122 0.196561 0.980492i \(-0.437023\pi\)
0.196561 + 0.980492i \(0.437023\pi\)
\(434\) 21.5623 1.03502
\(435\) −5.32624 −0.255374
\(436\) 45.2705 2.16806
\(437\) 3.00000 0.143509
\(438\) 28.0344 1.33954
\(439\) 19.1803 0.915428 0.457714 0.889100i \(-0.348668\pi\)
0.457714 + 0.889100i \(0.348668\pi\)
\(440\) 93.8673 4.47495
\(441\) 1.00000 0.0476190
\(442\) −12.0902 −0.575071
\(443\) 31.4164 1.49264 0.746319 0.665588i \(-0.231819\pi\)
0.746319 + 0.665588i \(0.231819\pi\)
\(444\) −36.2705 −1.72132
\(445\) −35.6525 −1.69009
\(446\) 12.2361 0.579395
\(447\) 6.18034 0.292320
\(448\) 8.70820 0.411424
\(449\) −1.50658 −0.0710998 −0.0355499 0.999368i \(-0.511318\pi\)
−0.0355499 + 0.999368i \(0.511318\pi\)
\(450\) −21.1803 −0.998451
\(451\) 30.2361 1.42376
\(452\) −45.2705 −2.12935
\(453\) 5.23607 0.246012
\(454\) −41.3607 −1.94115
\(455\) 16.7082 0.783293
\(456\) 22.4164 1.04974
\(457\) 30.0902 1.40756 0.703779 0.710419i \(-0.251494\pi\)
0.703779 + 0.710419i \(0.251494\pi\)
\(458\) 3.76393 0.175877
\(459\) −1.00000 −0.0466760
\(460\) 17.5623 0.818847
\(461\) −1.61803 −0.0753594 −0.0376797 0.999290i \(-0.511997\pi\)
−0.0376797 + 0.999290i \(0.511997\pi\)
\(462\) −9.09017 −0.422913
\(463\) 6.34752 0.294994 0.147497 0.989062i \(-0.452878\pi\)
0.147497 + 0.989062i \(0.452878\pi\)
\(464\) 14.5066 0.673451
\(465\) 29.7984 1.38187
\(466\) 37.3607 1.73070
\(467\) −32.7771 −1.51674 −0.758371 0.651823i \(-0.774005\pi\)
−0.758371 + 0.651823i \(0.774005\pi\)
\(468\) −22.4164 −1.03620
\(469\) 10.8541 0.501196
\(470\) −110.902 −5.11551
\(471\) 10.6525 0.490840
\(472\) 96.0476 4.42095
\(473\) −10.7295 −0.493342
\(474\) −24.7984 −1.13903
\(475\) −24.2705 −1.11361
\(476\) −4.85410 −0.222487
\(477\) −5.61803 −0.257232
\(478\) 29.1803 1.33468
\(479\) 13.7639 0.628890 0.314445 0.949276i \(-0.398182\pi\)
0.314445 + 0.949276i \(0.398182\pi\)
\(480\) 39.2705 1.79245
\(481\) 34.5066 1.57336
\(482\) −16.7984 −0.765145
\(483\) −1.00000 −0.0455016
\(484\) 5.12461 0.232937
\(485\) −18.0902 −0.821432
\(486\) −2.61803 −0.118756
\(487\) 0.708204 0.0320918 0.0160459 0.999871i \(-0.494892\pi\)
0.0160459 + 0.999871i \(0.494892\pi\)
\(488\) 80.6869 3.65253
\(489\) −21.7984 −0.985757
\(490\) 9.47214 0.427907
\(491\) −30.9787 −1.39805 −0.699025 0.715097i \(-0.746382\pi\)
−0.699025 + 0.715097i \(0.746382\pi\)
\(492\) 42.2705 1.90570
\(493\) −1.47214 −0.0663017
\(494\) −36.2705 −1.63189
\(495\) −12.5623 −0.564634
\(496\) −81.1591 −3.64415
\(497\) −15.0902 −0.676887
\(498\) 7.85410 0.351951
\(499\) 19.0344 0.852099 0.426049 0.904700i \(-0.359905\pi\)
0.426049 + 0.904700i \(0.359905\pi\)
\(500\) −54.2705 −2.42705
\(501\) 23.4721 1.04866
\(502\) 8.47214 0.378130
\(503\) 4.74265 0.211464 0.105732 0.994395i \(-0.466281\pi\)
0.105732 + 0.994395i \(0.466281\pi\)
\(504\) −7.47214 −0.332835
\(505\) −17.5623 −0.781512
\(506\) 9.09017 0.404107
\(507\) 8.32624 0.369781
\(508\) 58.9574 2.61581
\(509\) −14.1803 −0.628533 −0.314266 0.949335i \(-0.601758\pi\)
−0.314266 + 0.949335i \(0.601758\pi\)
\(510\) −9.47214 −0.419433
\(511\) −10.7082 −0.473703
\(512\) 40.3050 1.78124
\(513\) −3.00000 −0.132453
\(514\) −46.0689 −2.03201
\(515\) −46.8328 −2.06370
\(516\) −15.0000 −0.660338
\(517\) −40.6525 −1.78789
\(518\) 19.5623 0.859518
\(519\) 13.1803 0.578553
\(520\) −124.846 −5.47486
\(521\) 6.58359 0.288432 0.144216 0.989546i \(-0.453934\pi\)
0.144216 + 0.989546i \(0.453934\pi\)
\(522\) −3.85410 −0.168689
\(523\) 30.3607 1.32758 0.663790 0.747919i \(-0.268947\pi\)
0.663790 + 0.747919i \(0.268947\pi\)
\(524\) −0.270510 −0.0118173
\(525\) 8.09017 0.353084
\(526\) 20.0344 0.873543
\(527\) 8.23607 0.358769
\(528\) 34.2148 1.48901
\(529\) 1.00000 0.0434783
\(530\) −53.2148 −2.31150
\(531\) −12.8541 −0.557821
\(532\) −14.5623 −0.631356
\(533\) −40.2148 −1.74190
\(534\) −25.7984 −1.11640
\(535\) 46.3050 2.00194
\(536\) −81.1033 −3.50313
\(537\) 1.14590 0.0494492
\(538\) −50.4508 −2.17509
\(539\) 3.47214 0.149555
\(540\) −17.5623 −0.755761
\(541\) −7.34752 −0.315895 −0.157947 0.987448i \(-0.550488\pi\)
−0.157947 + 0.987448i \(0.550488\pi\)
\(542\) 57.1591 2.45519
\(543\) −1.47214 −0.0631754
\(544\) 10.8541 0.465366
\(545\) −33.7426 −1.44538
\(546\) 12.0902 0.517412
\(547\) −26.2705 −1.12325 −0.561623 0.827393i \(-0.689823\pi\)
−0.561623 + 0.827393i \(0.689823\pi\)
\(548\) −63.9787 −2.73304
\(549\) −10.7984 −0.460863
\(550\) −73.5410 −3.13580
\(551\) −4.41641 −0.188145
\(552\) 7.47214 0.318035
\(553\) 9.47214 0.402796
\(554\) 67.6869 2.87574
\(555\) 27.0344 1.14755
\(556\) −3.27051 −0.138701
\(557\) 14.2918 0.605563 0.302781 0.953060i \(-0.402085\pi\)
0.302781 + 0.953060i \(0.402085\pi\)
\(558\) 21.5623 0.912805
\(559\) 14.2705 0.603578
\(560\) −35.6525 −1.50659
\(561\) −3.47214 −0.146594
\(562\) −37.4164 −1.57832
\(563\) −9.74265 −0.410604 −0.205302 0.978699i \(-0.565818\pi\)
−0.205302 + 0.978699i \(0.565818\pi\)
\(564\) −56.8328 −2.39309
\(565\) 33.7426 1.41956
\(566\) 41.6525 1.75078
\(567\) 1.00000 0.0419961
\(568\) 112.756 4.73113
\(569\) 34.8328 1.46027 0.730134 0.683304i \(-0.239458\pi\)
0.730134 + 0.683304i \(0.239458\pi\)
\(570\) −28.4164 −1.19023
\(571\) 3.11146 0.130210 0.0651052 0.997878i \(-0.479262\pi\)
0.0651052 + 0.997878i \(0.479262\pi\)
\(572\) −77.8328 −3.25435
\(573\) 19.7082 0.823322
\(574\) −22.7984 −0.951586
\(575\) −8.09017 −0.337383
\(576\) 8.70820 0.362842
\(577\) −7.52786 −0.313389 −0.156695 0.987647i \(-0.550084\pi\)
−0.156695 + 0.987647i \(0.550084\pi\)
\(578\) 41.8885 1.74233
\(579\) 8.18034 0.339963
\(580\) −25.8541 −1.07353
\(581\) −3.00000 −0.124461
\(582\) −13.0902 −0.542605
\(583\) −19.5066 −0.807880
\(584\) 80.0132 3.31097
\(585\) 16.7082 0.690799
\(586\) 61.3050 2.53248
\(587\) 37.2705 1.53832 0.769159 0.639057i \(-0.220675\pi\)
0.769159 + 0.639057i \(0.220675\pi\)
\(588\) 4.85410 0.200180
\(589\) 24.7082 1.01808
\(590\) −121.756 −5.01261
\(591\) −6.14590 −0.252808
\(592\) −73.6312 −3.02622
\(593\) −21.1246 −0.867484 −0.433742 0.901037i \(-0.642807\pi\)
−0.433742 + 0.901037i \(0.642807\pi\)
\(594\) −9.09017 −0.372974
\(595\) 3.61803 0.148325
\(596\) 30.0000 1.22885
\(597\) 11.0344 0.451610
\(598\) −12.0902 −0.494404
\(599\) 2.90983 0.118892 0.0594462 0.998232i \(-0.481067\pi\)
0.0594462 + 0.998232i \(0.481067\pi\)
\(600\) −60.4508 −2.46790
\(601\) −31.3262 −1.27782 −0.638912 0.769280i \(-0.720615\pi\)
−0.638912 + 0.769280i \(0.720615\pi\)
\(602\) 8.09017 0.329731
\(603\) 10.8541 0.442013
\(604\) 25.4164 1.03418
\(605\) −3.81966 −0.155291
\(606\) −12.7082 −0.516235
\(607\) 8.90983 0.361639 0.180819 0.983516i \(-0.442125\pi\)
0.180819 + 0.983516i \(0.442125\pi\)
\(608\) 32.5623 1.32058
\(609\) 1.47214 0.0596540
\(610\) −102.284 −4.14134
\(611\) 54.0689 2.18739
\(612\) −4.85410 −0.196215
\(613\) 29.6525 1.19765 0.598826 0.800879i \(-0.295634\pi\)
0.598826 + 0.800879i \(0.295634\pi\)
\(614\) 24.3262 0.981727
\(615\) −31.5066 −1.27047
\(616\) −25.9443 −1.04532
\(617\) 40.3951 1.62625 0.813123 0.582092i \(-0.197766\pi\)
0.813123 + 0.582092i \(0.197766\pi\)
\(618\) −33.8885 −1.36320
\(619\) 41.3820 1.66328 0.831641 0.555314i \(-0.187402\pi\)
0.831641 + 0.555314i \(0.187402\pi\)
\(620\) 144.644 5.80906
\(621\) −1.00000 −0.0401286
\(622\) 43.2148 1.73275
\(623\) 9.85410 0.394796
\(624\) −45.5066 −1.82172
\(625\) 0 0
\(626\) −16.9443 −0.677229
\(627\) −10.4164 −0.415991
\(628\) 51.7082 2.06338
\(629\) 7.47214 0.297934
\(630\) 9.47214 0.377379
\(631\) −7.29180 −0.290282 −0.145141 0.989411i \(-0.546364\pi\)
−0.145141 + 0.989411i \(0.546364\pi\)
\(632\) −70.7771 −2.81536
\(633\) −0.416408 −0.0165507
\(634\) 0.527864 0.0209642
\(635\) −43.9443 −1.74388
\(636\) −27.2705 −1.08135
\(637\) −4.61803 −0.182973
\(638\) −13.3820 −0.529797
\(639\) −15.0902 −0.596958
\(640\) 3.94427 0.155911
\(641\) −24.2148 −0.956426 −0.478213 0.878244i \(-0.658715\pi\)
−0.478213 + 0.878244i \(0.658715\pi\)
\(642\) 33.5066 1.32240
\(643\) 11.8541 0.467480 0.233740 0.972299i \(-0.424904\pi\)
0.233740 + 0.972299i \(0.424904\pi\)
\(644\) −4.85410 −0.191278
\(645\) 11.1803 0.440225
\(646\) −7.85410 −0.309016
\(647\) 2.67376 0.105116 0.0525582 0.998618i \(-0.483262\pi\)
0.0525582 + 0.998618i \(0.483262\pi\)
\(648\) −7.47214 −0.293533
\(649\) −44.6312 −1.75193
\(650\) 97.8115 3.83648
\(651\) −8.23607 −0.322797
\(652\) −105.812 −4.14390
\(653\) −19.4377 −0.760656 −0.380328 0.924852i \(-0.624189\pi\)
−0.380328 + 0.924852i \(0.624189\pi\)
\(654\) −24.4164 −0.954757
\(655\) 0.201626 0.00787818
\(656\) 85.8115 3.35038
\(657\) −10.7082 −0.417767
\(658\) 30.6525 1.19496
\(659\) −20.5279 −0.799652 −0.399826 0.916591i \(-0.630929\pi\)
−0.399826 + 0.916591i \(0.630929\pi\)
\(660\) −60.9787 −2.37359
\(661\) −38.7771 −1.50825 −0.754127 0.656729i \(-0.771940\pi\)
−0.754127 + 0.656729i \(0.771940\pi\)
\(662\) −2.76393 −0.107423
\(663\) 4.61803 0.179350
\(664\) 22.4164 0.869925
\(665\) 10.8541 0.420904
\(666\) 19.5623 0.758024
\(667\) −1.47214 −0.0570013
\(668\) 113.936 4.40832
\(669\) −4.67376 −0.180698
\(670\) 102.812 3.97196
\(671\) −37.4934 −1.44742
\(672\) −10.8541 −0.418706
\(673\) 2.88854 0.111345 0.0556726 0.998449i \(-0.482270\pi\)
0.0556726 + 0.998449i \(0.482270\pi\)
\(674\) −74.1591 −2.85650
\(675\) 8.09017 0.311391
\(676\) 40.4164 1.55448
\(677\) −1.38197 −0.0531133 −0.0265566 0.999647i \(-0.508454\pi\)
−0.0265566 + 0.999647i \(0.508454\pi\)
\(678\) 24.4164 0.937706
\(679\) 5.00000 0.191882
\(680\) −27.0344 −1.03672
\(681\) 15.7984 0.605395
\(682\) 74.8673 2.86682
\(683\) 0.888544 0.0339992 0.0169996 0.999855i \(-0.494589\pi\)
0.0169996 + 0.999855i \(0.494589\pi\)
\(684\) −14.5623 −0.556804
\(685\) 47.6869 1.82202
\(686\) −2.61803 −0.0999570
\(687\) −1.43769 −0.0548515
\(688\) −30.4508 −1.16093
\(689\) 25.9443 0.988398
\(690\) −9.47214 −0.360598
\(691\) 28.0344 1.06648 0.533240 0.845964i \(-0.320974\pi\)
0.533240 + 0.845964i \(0.320974\pi\)
\(692\) 63.9787 2.43211
\(693\) 3.47214 0.131896
\(694\) −53.4508 −2.02897
\(695\) 2.43769 0.0924670
\(696\) −11.0000 −0.416954
\(697\) −8.70820 −0.329847
\(698\) −39.8328 −1.50769
\(699\) −14.2705 −0.539760
\(700\) 39.2705 1.48429
\(701\) 9.03444 0.341226 0.170613 0.985338i \(-0.445425\pi\)
0.170613 + 0.985338i \(0.445425\pi\)
\(702\) 12.0902 0.456314
\(703\) 22.4164 0.845451
\(704\) 30.2361 1.13956
\(705\) 42.3607 1.59540
\(706\) 51.4508 1.93638
\(707\) 4.85410 0.182557
\(708\) −62.3951 −2.34495
\(709\) −33.9230 −1.27400 −0.637002 0.770862i \(-0.719826\pi\)
−0.637002 + 0.770862i \(0.719826\pi\)
\(710\) −142.936 −5.36430
\(711\) 9.47214 0.355233
\(712\) −73.6312 −2.75945
\(713\) 8.23607 0.308443
\(714\) 2.61803 0.0979775
\(715\) 58.0132 2.16957
\(716\) 5.56231 0.207873
\(717\) −11.1459 −0.416251
\(718\) −56.3050 −2.10128
\(719\) −15.2918 −0.570288 −0.285144 0.958485i \(-0.592041\pi\)
−0.285144 + 0.958485i \(0.592041\pi\)
\(720\) −35.6525 −1.32869
\(721\) 12.9443 0.482070
\(722\) 26.1803 0.974331
\(723\) 6.41641 0.238629
\(724\) −7.14590 −0.265575
\(725\) 11.9098 0.442320
\(726\) −2.76393 −0.102579
\(727\) −41.3607 −1.53398 −0.766991 0.641657i \(-0.778247\pi\)
−0.766991 + 0.641657i \(0.778247\pi\)
\(728\) 34.5066 1.27890
\(729\) 1.00000 0.0370370
\(730\) −101.430 −3.75408
\(731\) 3.09017 0.114294
\(732\) −52.4164 −1.93737
\(733\) −20.1803 −0.745378 −0.372689 0.927956i \(-0.621564\pi\)
−0.372689 + 0.927956i \(0.621564\pi\)
\(734\) −11.6180 −0.428829
\(735\) −3.61803 −0.133453
\(736\) 10.8541 0.400088
\(737\) 37.6869 1.38822
\(738\) −22.7984 −0.839220
\(739\) −30.8885 −1.13625 −0.568127 0.822941i \(-0.692332\pi\)
−0.568127 + 0.822941i \(0.692332\pi\)
\(740\) 131.228 4.82403
\(741\) 13.8541 0.508943
\(742\) 14.7082 0.539955
\(743\) 7.03444 0.258069 0.129034 0.991640i \(-0.458812\pi\)
0.129034 + 0.991640i \(0.458812\pi\)
\(744\) 61.5410 2.25620
\(745\) −22.3607 −0.819232
\(746\) 78.3951 2.87025
\(747\) −3.00000 −0.109764
\(748\) −16.8541 −0.616247
\(749\) −12.7984 −0.467642
\(750\) 29.2705 1.06881
\(751\) 29.3951 1.07264 0.536322 0.844014i \(-0.319813\pi\)
0.536322 + 0.844014i \(0.319813\pi\)
\(752\) −115.374 −4.20725
\(753\) −3.23607 −0.117929
\(754\) 17.7984 0.648179
\(755\) −18.9443 −0.689453
\(756\) 4.85410 0.176542
\(757\) 38.8885 1.41343 0.706714 0.707499i \(-0.250177\pi\)
0.706714 + 0.707499i \(0.250177\pi\)
\(758\) 32.3607 1.17539
\(759\) −3.47214 −0.126031
\(760\) −81.1033 −2.94193
\(761\) −49.3050 −1.78730 −0.893652 0.448762i \(-0.851865\pi\)
−0.893652 + 0.448762i \(0.851865\pi\)
\(762\) −31.7984 −1.15193
\(763\) 9.32624 0.337632
\(764\) 95.6656 3.46106
\(765\) 3.61803 0.130810
\(766\) 48.5066 1.75261
\(767\) 59.3607 2.14339
\(768\) −14.5623 −0.525472
\(769\) 31.5967 1.13941 0.569704 0.821850i \(-0.307058\pi\)
0.569704 + 0.821850i \(0.307058\pi\)
\(770\) 32.8885 1.18522
\(771\) 17.5967 0.633731
\(772\) 39.7082 1.42913
\(773\) 36.0132 1.29530 0.647652 0.761937i \(-0.275751\pi\)
0.647652 + 0.761937i \(0.275751\pi\)
\(774\) 8.09017 0.290795
\(775\) −66.6312 −2.39346
\(776\) −37.3607 −1.34117
\(777\) −7.47214 −0.268061
\(778\) 48.2148 1.72858
\(779\) −26.1246 −0.936011
\(780\) 81.1033 2.90396
\(781\) −52.3951 −1.87484
\(782\) −2.61803 −0.0936207
\(783\) 1.47214 0.0526098
\(784\) 9.85410 0.351932
\(785\) −38.5410 −1.37559
\(786\) 0.145898 0.00520401
\(787\) −0.965558 −0.0344184 −0.0172092 0.999852i \(-0.505478\pi\)
−0.0172092 + 0.999852i \(0.505478\pi\)
\(788\) −29.8328 −1.06275
\(789\) −7.65248 −0.272435
\(790\) 89.7214 3.19214
\(791\) −9.32624 −0.331603
\(792\) −25.9443 −0.921890
\(793\) 49.8673 1.77084
\(794\) 42.6525 1.51368
\(795\) 20.3262 0.720897
\(796\) 53.5623 1.89847
\(797\) 13.5967 0.481622 0.240811 0.970572i \(-0.422587\pi\)
0.240811 + 0.970572i \(0.422587\pi\)
\(798\) 7.85410 0.278032
\(799\) 11.7082 0.414206
\(800\) −87.8115 −3.10461
\(801\) 9.85410 0.348178
\(802\) 84.8673 2.99677
\(803\) −37.1803 −1.31207
\(804\) 52.6869 1.85812
\(805\) 3.61803 0.127519
\(806\) −99.5755 −3.50740
\(807\) 19.2705 0.678354
\(808\) −36.2705 −1.27599
\(809\) 30.0344 1.05595 0.527977 0.849258i \(-0.322951\pi\)
0.527977 + 0.849258i \(0.322951\pi\)
\(810\) 9.47214 0.332817
\(811\) −19.4721 −0.683759 −0.341880 0.939744i \(-0.611064\pi\)
−0.341880 + 0.939744i \(0.611064\pi\)
\(812\) 7.14590 0.250772
\(813\) −21.8328 −0.765710
\(814\) 67.9230 2.38070
\(815\) 78.8673 2.76260
\(816\) −9.85410 −0.344963
\(817\) 9.27051 0.324334
\(818\) 11.5623 0.404267
\(819\) −4.61803 −0.161367
\(820\) −152.936 −5.34076
\(821\) −2.18034 −0.0760944 −0.0380472 0.999276i \(-0.512114\pi\)
−0.0380472 + 0.999276i \(0.512114\pi\)
\(822\) 34.5066 1.20356
\(823\) −40.5623 −1.41391 −0.706957 0.707257i \(-0.749932\pi\)
−0.706957 + 0.707257i \(0.749932\pi\)
\(824\) −96.7214 −3.36945
\(825\) 28.0902 0.977974
\(826\) 33.6525 1.17092
\(827\) −13.4377 −0.467274 −0.233637 0.972324i \(-0.575063\pi\)
−0.233637 + 0.972324i \(0.575063\pi\)
\(828\) −4.85410 −0.168692
\(829\) −47.9443 −1.66517 −0.832587 0.553895i \(-0.813141\pi\)
−0.832587 + 0.553895i \(0.813141\pi\)
\(830\) −28.4164 −0.986348
\(831\) −25.8541 −0.896869
\(832\) −40.2148 −1.39420
\(833\) −1.00000 −0.0346479
\(834\) 1.76393 0.0610800
\(835\) −84.9230 −2.93888
\(836\) −50.5623 −1.74873
\(837\) −8.23607 −0.284680
\(838\) 47.8328 1.65236
\(839\) −21.8541 −0.754487 −0.377244 0.926114i \(-0.623128\pi\)
−0.377244 + 0.926114i \(0.623128\pi\)
\(840\) 27.0344 0.932777
\(841\) −26.8328 −0.925270
\(842\) 35.0344 1.20737
\(843\) 14.2918 0.492236
\(844\) −2.02129 −0.0695755
\(845\) −30.1246 −1.03632
\(846\) 30.6525 1.05385
\(847\) 1.05573 0.0362752
\(848\) −55.3607 −1.90109
\(849\) −15.9098 −0.546024
\(850\) 21.1803 0.726480
\(851\) 7.47214 0.256142
\(852\) −73.2492 −2.50948
\(853\) 42.6525 1.46039 0.730196 0.683237i \(-0.239429\pi\)
0.730196 + 0.683237i \(0.239429\pi\)
\(854\) 28.2705 0.967397
\(855\) 10.8541 0.371202
\(856\) 95.6312 3.26861
\(857\) −13.1246 −0.448328 −0.224164 0.974551i \(-0.571965\pi\)
−0.224164 + 0.974551i \(0.571965\pi\)
\(858\) 41.9787 1.43313
\(859\) −36.8328 −1.25672 −0.628360 0.777923i \(-0.716273\pi\)
−0.628360 + 0.777923i \(0.716273\pi\)
\(860\) 54.2705 1.85061
\(861\) 8.70820 0.296775
\(862\) −97.2837 −3.31349
\(863\) −8.18034 −0.278462 −0.139231 0.990260i \(-0.544463\pi\)
−0.139231 + 0.990260i \(0.544463\pi\)
\(864\) −10.8541 −0.369264
\(865\) −47.6869 −1.62140
\(866\) −21.4164 −0.727759
\(867\) −16.0000 −0.543388
\(868\) −39.9787 −1.35697
\(869\) 32.8885 1.11567
\(870\) 13.9443 0.472755
\(871\) −50.1246 −1.69841
\(872\) −69.6869 −2.35990
\(873\) 5.00000 0.169224
\(874\) −7.85410 −0.265669
\(875\) −11.1803 −0.377964
\(876\) −51.9787 −1.75620
\(877\) 11.4164 0.385505 0.192752 0.981247i \(-0.438259\pi\)
0.192752 + 0.981247i \(0.438259\pi\)
\(878\) −50.2148 −1.69467
\(879\) −23.4164 −0.789816
\(880\) −123.790 −4.17297
\(881\) 37.4853 1.26291 0.631456 0.775412i \(-0.282458\pi\)
0.631456 + 0.775412i \(0.282458\pi\)
\(882\) −2.61803 −0.0881538
\(883\) −30.5066 −1.02663 −0.513314 0.858201i \(-0.671582\pi\)
−0.513314 + 0.858201i \(0.671582\pi\)
\(884\) 22.4164 0.753945
\(885\) 46.5066 1.56330
\(886\) −82.2492 −2.76322
\(887\) 43.8541 1.47248 0.736238 0.676722i \(-0.236600\pi\)
0.736238 + 0.676722i \(0.236600\pi\)
\(888\) 55.8328 1.87363
\(889\) 12.1459 0.407360
\(890\) 93.3394 3.12874
\(891\) 3.47214 0.116321
\(892\) −22.6869 −0.759614
\(893\) 35.1246 1.17540
\(894\) −16.1803 −0.541152
\(895\) −4.14590 −0.138582
\(896\) −1.09017 −0.0364200
\(897\) 4.61803 0.154192
\(898\) 3.94427 0.131622
\(899\) −12.1246 −0.404378
\(900\) 39.2705 1.30902
\(901\) 5.61803 0.187164
\(902\) −79.1591 −2.63571
\(903\) −3.09017 −0.102834
\(904\) 69.6869 2.31775
\(905\) 5.32624 0.177050
\(906\) −13.7082 −0.455425
\(907\) 53.0344 1.76098 0.880490 0.474065i \(-0.157214\pi\)
0.880490 + 0.474065i \(0.157214\pi\)
\(908\) 76.6869 2.54494
\(909\) 4.85410 0.161000
\(910\) −43.7426 −1.45005
\(911\) −13.8197 −0.457866 −0.228933 0.973442i \(-0.573524\pi\)
−0.228933 + 0.973442i \(0.573524\pi\)
\(912\) −29.5623 −0.978906
\(913\) −10.4164 −0.344733
\(914\) −78.7771 −2.60571
\(915\) 39.0689 1.29158
\(916\) −6.97871 −0.230583
\(917\) −0.0557281 −0.00184030
\(918\) 2.61803 0.0864080
\(919\) −43.0689 −1.42071 −0.710356 0.703843i \(-0.751466\pi\)
−0.710356 + 0.703843i \(0.751466\pi\)
\(920\) −27.0344 −0.891299
\(921\) −9.29180 −0.306175
\(922\) 4.23607 0.139507
\(923\) 69.6869 2.29377
\(924\) 16.8541 0.554459
\(925\) −60.4508 −1.98761
\(926\) −16.6180 −0.546102
\(927\) 12.9443 0.425146
\(928\) −15.9787 −0.524527
\(929\) −52.3820 −1.71860 −0.859298 0.511475i \(-0.829099\pi\)
−0.859298 + 0.511475i \(0.829099\pi\)
\(930\) −78.0132 −2.55815
\(931\) −3.00000 −0.0983210
\(932\) −69.2705 −2.26903
\(933\) −16.5066 −0.540401
\(934\) 85.8115 2.80784
\(935\) 12.5623 0.410831
\(936\) 34.5066 1.12788
\(937\) 3.87539 0.126603 0.0633017 0.997994i \(-0.479837\pi\)
0.0633017 + 0.997994i \(0.479837\pi\)
\(938\) −28.4164 −0.927829
\(939\) 6.47214 0.211210
\(940\) 205.623 6.70668
\(941\) −26.8328 −0.874725 −0.437362 0.899285i \(-0.644087\pi\)
−0.437362 + 0.899285i \(0.644087\pi\)
\(942\) −27.8885 −0.908658
\(943\) −8.70820 −0.283578
\(944\) −126.666 −4.12262
\(945\) −3.61803 −0.117695
\(946\) 28.0902 0.913290
\(947\) −18.5836 −0.603886 −0.301943 0.953326i \(-0.597635\pi\)
−0.301943 + 0.953326i \(0.597635\pi\)
\(948\) 45.9787 1.49332
\(949\) 49.4508 1.60524
\(950\) 63.5410 2.06154
\(951\) −0.201626 −0.00653818
\(952\) 7.47214 0.242173
\(953\) −0.686918 −0.0222514 −0.0111257 0.999938i \(-0.503542\pi\)
−0.0111257 + 0.999938i \(0.503542\pi\)
\(954\) 14.7082 0.476196
\(955\) −71.3050 −2.30737
\(956\) −54.1033 −1.74983
\(957\) 5.11146 0.165230
\(958\) −36.0344 −1.16422
\(959\) −13.1803 −0.425615
\(960\) −31.5066 −1.01687
\(961\) 36.8328 1.18816
\(962\) −90.3394 −2.91266
\(963\) −12.7984 −0.412422
\(964\) 31.1459 1.00314
\(965\) −29.5967 −0.952753
\(966\) 2.61803 0.0842339
\(967\) 49.7771 1.60072 0.800362 0.599518i \(-0.204641\pi\)
0.800362 + 0.599518i \(0.204641\pi\)
\(968\) −7.88854 −0.253547
\(969\) 3.00000 0.0963739
\(970\) 47.3607 1.52066
\(971\) −10.9787 −0.352324 −0.176162 0.984361i \(-0.556368\pi\)
−0.176162 + 0.984361i \(0.556368\pi\)
\(972\) 4.85410 0.155695
\(973\) −0.673762 −0.0215998
\(974\) −1.85410 −0.0594093
\(975\) −37.3607 −1.19650
\(976\) −106.408 −3.40605
\(977\) −48.7984 −1.56120 −0.780599 0.625032i \(-0.785086\pi\)
−0.780599 + 0.625032i \(0.785086\pi\)
\(978\) 57.0689 1.82486
\(979\) 34.2148 1.09351
\(980\) −17.5623 −0.561007
\(981\) 9.32624 0.297764
\(982\) 81.1033 2.58811
\(983\) 11.3607 0.362349 0.181175 0.983451i \(-0.442010\pi\)
0.181175 + 0.983451i \(0.442010\pi\)
\(984\) −65.0689 −2.07432
\(985\) 22.2361 0.708500
\(986\) 3.85410 0.122740
\(987\) −11.7082 −0.372676
\(988\) 67.2492 2.13948
\(989\) 3.09017 0.0982617
\(990\) 32.8885 1.04527
\(991\) 2.90983 0.0924338 0.0462169 0.998931i \(-0.485283\pi\)
0.0462169 + 0.998931i \(0.485283\pi\)
\(992\) 89.3951 2.83830
\(993\) 1.05573 0.0335025
\(994\) 39.5066 1.25307
\(995\) −39.9230 −1.26564
\(996\) −14.5623 −0.461424
\(997\) −5.11146 −0.161881 −0.0809407 0.996719i \(-0.525792\pi\)
−0.0809407 + 0.996719i \(0.525792\pi\)
\(998\) −49.8328 −1.57743
\(999\) −7.47214 −0.236408
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 483.2.a.c.1.1 2
3.2 odd 2 1449.2.a.k.1.2 2
4.3 odd 2 7728.2.a.v.1.1 2
7.6 odd 2 3381.2.a.n.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.a.c.1.1 2 1.1 even 1 trivial
1449.2.a.k.1.2 2 3.2 odd 2
3381.2.a.n.1.1 2 7.6 odd 2
7728.2.a.v.1.1 2 4.3 odd 2