Properties

Label 6017.2.a.f.1.3
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73908 q^{2} +1.22981 q^{3} +5.50258 q^{4} -1.73351 q^{5} -3.36855 q^{6} -3.95971 q^{7} -9.59385 q^{8} -1.48757 q^{9} +O(q^{10})\) \(q-2.73908 q^{2} +1.22981 q^{3} +5.50258 q^{4} -1.73351 q^{5} -3.36855 q^{6} -3.95971 q^{7} -9.59385 q^{8} -1.48757 q^{9} +4.74824 q^{10} -1.00000 q^{11} +6.76711 q^{12} +4.72992 q^{13} +10.8460 q^{14} -2.13189 q^{15} +15.2732 q^{16} -1.93056 q^{17} +4.07459 q^{18} -2.39204 q^{19} -9.53879 q^{20} -4.86968 q^{21} +2.73908 q^{22} -7.13275 q^{23} -11.7986 q^{24} -1.99493 q^{25} -12.9557 q^{26} -5.51885 q^{27} -21.7886 q^{28} -8.01568 q^{29} +5.83942 q^{30} +2.04723 q^{31} -22.6469 q^{32} -1.22981 q^{33} +5.28796 q^{34} +6.86421 q^{35} -8.18549 q^{36} -2.64009 q^{37} +6.55199 q^{38} +5.81690 q^{39} +16.6311 q^{40} -9.10855 q^{41} +13.3385 q^{42} -1.45685 q^{43} -5.50258 q^{44} +2.57873 q^{45} +19.5372 q^{46} +6.96189 q^{47} +18.7831 q^{48} +8.67931 q^{49} +5.46429 q^{50} -2.37422 q^{51} +26.0268 q^{52} +0.782647 q^{53} +15.1166 q^{54} +1.73351 q^{55} +37.9889 q^{56} -2.94175 q^{57} +21.9556 q^{58} -4.13959 q^{59} -11.7309 q^{60} -9.39501 q^{61} -5.60752 q^{62} +5.89036 q^{63} +31.4853 q^{64} -8.19938 q^{65} +3.36855 q^{66} +4.47317 q^{67} -10.6230 q^{68} -8.77191 q^{69} -18.8016 q^{70} +0.839471 q^{71} +14.2716 q^{72} +6.96113 q^{73} +7.23142 q^{74} -2.45339 q^{75} -13.1624 q^{76} +3.95971 q^{77} -15.9330 q^{78} -13.0859 q^{79} -26.4763 q^{80} -2.32440 q^{81} +24.9491 q^{82} -0.279730 q^{83} -26.7958 q^{84} +3.34665 q^{85} +3.99043 q^{86} -9.85774 q^{87} +9.59385 q^{88} +6.42994 q^{89} -7.06335 q^{90} -18.7291 q^{91} -39.2485 q^{92} +2.51769 q^{93} -19.0692 q^{94} +4.14663 q^{95} -27.8513 q^{96} -3.44054 q^{97} -23.7734 q^{98} +1.48757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73908 −1.93682 −0.968412 0.249355i \(-0.919782\pi\)
−0.968412 + 0.249355i \(0.919782\pi\)
\(3\) 1.22981 0.710030 0.355015 0.934861i \(-0.384476\pi\)
0.355015 + 0.934861i \(0.384476\pi\)
\(4\) 5.50258 2.75129
\(5\) −1.73351 −0.775250 −0.387625 0.921817i \(-0.626705\pi\)
−0.387625 + 0.921817i \(0.626705\pi\)
\(6\) −3.36855 −1.37520
\(7\) −3.95971 −1.49663 −0.748315 0.663344i \(-0.769137\pi\)
−0.748315 + 0.663344i \(0.769137\pi\)
\(8\) −9.59385 −3.39194
\(9\) −1.48757 −0.495858
\(10\) 4.74824 1.50152
\(11\) −1.00000 −0.301511
\(12\) 6.76711 1.95350
\(13\) 4.72992 1.31184 0.655922 0.754828i \(-0.272280\pi\)
0.655922 + 0.754828i \(0.272280\pi\)
\(14\) 10.8460 2.89871
\(15\) −2.13189 −0.550451
\(16\) 15.2732 3.81830
\(17\) −1.93056 −0.468229 −0.234115 0.972209i \(-0.575219\pi\)
−0.234115 + 0.972209i \(0.575219\pi\)
\(18\) 4.07459 0.960390
\(19\) −2.39204 −0.548771 −0.274385 0.961620i \(-0.588474\pi\)
−0.274385 + 0.961620i \(0.588474\pi\)
\(20\) −9.53879 −2.13294
\(21\) −4.86968 −1.06265
\(22\) 2.73908 0.583975
\(23\) −7.13275 −1.48728 −0.743640 0.668580i \(-0.766902\pi\)
−0.743640 + 0.668580i \(0.766902\pi\)
\(24\) −11.7986 −2.40838
\(25\) −1.99493 −0.398987
\(26\) −12.9557 −2.54081
\(27\) −5.51885 −1.06210
\(28\) −21.7886 −4.11766
\(29\) −8.01568 −1.48847 −0.744237 0.667916i \(-0.767187\pi\)
−0.744237 + 0.667916i \(0.767187\pi\)
\(30\) 5.83942 1.06613
\(31\) 2.04723 0.367692 0.183846 0.982955i \(-0.441145\pi\)
0.183846 + 0.982955i \(0.441145\pi\)
\(32\) −22.6469 −4.00344
\(33\) −1.22981 −0.214082
\(34\) 5.28796 0.906878
\(35\) 6.86421 1.16026
\(36\) −8.18549 −1.36425
\(37\) −2.64009 −0.434028 −0.217014 0.976168i \(-0.569632\pi\)
−0.217014 + 0.976168i \(0.569632\pi\)
\(38\) 6.55199 1.06287
\(39\) 5.81690 0.931449
\(40\) 16.6311 2.62960
\(41\) −9.10855 −1.42252 −0.711258 0.702931i \(-0.751874\pi\)
−0.711258 + 0.702931i \(0.751874\pi\)
\(42\) 13.3385 2.05817
\(43\) −1.45685 −0.222167 −0.111084 0.993811i \(-0.535432\pi\)
−0.111084 + 0.993811i \(0.535432\pi\)
\(44\) −5.50258 −0.829545
\(45\) 2.57873 0.384414
\(46\) 19.5372 2.88060
\(47\) 6.96189 1.01550 0.507748 0.861506i \(-0.330478\pi\)
0.507748 + 0.861506i \(0.330478\pi\)
\(48\) 18.7831 2.71111
\(49\) 8.67931 1.23990
\(50\) 5.46429 0.772768
\(51\) −2.37422 −0.332457
\(52\) 26.0268 3.60926
\(53\) 0.782647 0.107505 0.0537524 0.998554i \(-0.482882\pi\)
0.0537524 + 0.998554i \(0.482882\pi\)
\(54\) 15.1166 2.05711
\(55\) 1.73351 0.233747
\(56\) 37.9889 5.07648
\(57\) −2.94175 −0.389644
\(58\) 21.9556 2.88291
\(59\) −4.13959 −0.538929 −0.269465 0.963010i \(-0.586847\pi\)
−0.269465 + 0.963010i \(0.586847\pi\)
\(60\) −11.7309 −1.51445
\(61\) −9.39501 −1.20291 −0.601454 0.798908i \(-0.705412\pi\)
−0.601454 + 0.798908i \(0.705412\pi\)
\(62\) −5.60752 −0.712156
\(63\) 5.89036 0.742116
\(64\) 31.4853 3.93566
\(65\) −8.19938 −1.01701
\(66\) 3.36855 0.414639
\(67\) 4.47317 0.546484 0.273242 0.961945i \(-0.411904\pi\)
0.273242 + 0.961945i \(0.411904\pi\)
\(68\) −10.6230 −1.28823
\(69\) −8.77191 −1.05601
\(70\) −18.8016 −2.24723
\(71\) 0.839471 0.0996268 0.0498134 0.998759i \(-0.484137\pi\)
0.0498134 + 0.998759i \(0.484137\pi\)
\(72\) 14.2716 1.68192
\(73\) 6.96113 0.814738 0.407369 0.913264i \(-0.366446\pi\)
0.407369 + 0.913264i \(0.366446\pi\)
\(74\) 7.23142 0.840636
\(75\) −2.45339 −0.283293
\(76\) −13.1624 −1.50983
\(77\) 3.95971 0.451251
\(78\) −15.9330 −1.80405
\(79\) −13.0859 −1.47228 −0.736142 0.676827i \(-0.763354\pi\)
−0.736142 + 0.676827i \(0.763354\pi\)
\(80\) −26.4763 −2.96014
\(81\) −2.32440 −0.258267
\(82\) 24.9491 2.75516
\(83\) −0.279730 −0.0307044 −0.0153522 0.999882i \(-0.504887\pi\)
−0.0153522 + 0.999882i \(0.504887\pi\)
\(84\) −26.7958 −2.92366
\(85\) 3.34665 0.362995
\(86\) 3.99043 0.430299
\(87\) −9.85774 −1.05686
\(88\) 9.59385 1.02271
\(89\) 6.42994 0.681572 0.340786 0.940141i \(-0.389307\pi\)
0.340786 + 0.940141i \(0.389307\pi\)
\(90\) −7.06335 −0.744542
\(91\) −18.7291 −1.96335
\(92\) −39.2485 −4.09194
\(93\) 2.51769 0.261073
\(94\) −19.0692 −1.96684
\(95\) 4.14663 0.425435
\(96\) −27.8513 −2.84256
\(97\) −3.44054 −0.349334 −0.174667 0.984628i \(-0.555885\pi\)
−0.174667 + 0.984628i \(0.555885\pi\)
\(98\) −23.7734 −2.40147
\(99\) 1.48757 0.149507
\(100\) −10.9773 −1.09773
\(101\) 7.58996 0.755229 0.377615 0.925963i \(-0.376744\pi\)
0.377615 + 0.925963i \(0.376744\pi\)
\(102\) 6.50317 0.643910
\(103\) 7.74756 0.763390 0.381695 0.924288i \(-0.375340\pi\)
0.381695 + 0.924288i \(0.375340\pi\)
\(104\) −45.3782 −4.44970
\(105\) 8.44165 0.823821
\(106\) −2.14373 −0.208218
\(107\) −17.0194 −1.64532 −0.822661 0.568532i \(-0.807512\pi\)
−0.822661 + 0.568532i \(0.807512\pi\)
\(108\) −30.3679 −2.92215
\(109\) −6.43035 −0.615915 −0.307958 0.951400i \(-0.599646\pi\)
−0.307958 + 0.951400i \(0.599646\pi\)
\(110\) −4.74824 −0.452726
\(111\) −3.24680 −0.308173
\(112\) −60.4775 −5.71459
\(113\) −5.29614 −0.498219 −0.249110 0.968475i \(-0.580138\pi\)
−0.249110 + 0.968475i \(0.580138\pi\)
\(114\) 8.05769 0.754671
\(115\) 12.3647 1.15301
\(116\) −44.1069 −4.09522
\(117\) −7.03611 −0.650489
\(118\) 11.3387 1.04381
\(119\) 7.64445 0.700766
\(120\) 20.4530 1.86710
\(121\) 1.00000 0.0909091
\(122\) 25.7337 2.32982
\(123\) −11.2018 −1.01003
\(124\) 11.2650 1.01163
\(125\) 12.1258 1.08457
\(126\) −16.1342 −1.43735
\(127\) 10.3702 0.920208 0.460104 0.887865i \(-0.347812\pi\)
0.460104 + 0.887865i \(0.347812\pi\)
\(128\) −40.9471 −3.61924
\(129\) −1.79164 −0.157745
\(130\) 22.4588 1.96977
\(131\) −11.7083 −1.02296 −0.511481 0.859295i \(-0.670903\pi\)
−0.511481 + 0.859295i \(0.670903\pi\)
\(132\) −6.76711 −0.589001
\(133\) 9.47178 0.821307
\(134\) −12.2524 −1.05844
\(135\) 9.56700 0.823396
\(136\) 18.5215 1.58821
\(137\) 10.0482 0.858476 0.429238 0.903191i \(-0.358782\pi\)
0.429238 + 0.903191i \(0.358782\pi\)
\(138\) 24.0270 2.04531
\(139\) 5.91168 0.501422 0.250711 0.968062i \(-0.419336\pi\)
0.250711 + 0.968062i \(0.419336\pi\)
\(140\) 37.7708 3.19222
\(141\) 8.56179 0.721032
\(142\) −2.29938 −0.192960
\(143\) −4.72992 −0.395536
\(144\) −22.7200 −1.89333
\(145\) 13.8953 1.15394
\(146\) −19.0671 −1.57800
\(147\) 10.6739 0.880367
\(148\) −14.5273 −1.19414
\(149\) 17.9451 1.47012 0.735060 0.678002i \(-0.237154\pi\)
0.735060 + 0.678002i \(0.237154\pi\)
\(150\) 6.72003 0.548688
\(151\) −14.0846 −1.14619 −0.573094 0.819489i \(-0.694257\pi\)
−0.573094 + 0.819489i \(0.694257\pi\)
\(152\) 22.9489 1.86140
\(153\) 2.87185 0.232175
\(154\) −10.8460 −0.873994
\(155\) −3.54889 −0.285054
\(156\) 32.0079 2.56269
\(157\) −22.6019 −1.80383 −0.901914 0.431916i \(-0.857838\pi\)
−0.901914 + 0.431916i \(0.857838\pi\)
\(158\) 35.8435 2.85156
\(159\) 0.962505 0.0763316
\(160\) 39.2587 3.10367
\(161\) 28.2436 2.22591
\(162\) 6.36674 0.500218
\(163\) 11.3171 0.886427 0.443213 0.896416i \(-0.353838\pi\)
0.443213 + 0.896416i \(0.353838\pi\)
\(164\) −50.1205 −3.91375
\(165\) 2.13189 0.165967
\(166\) 0.766204 0.0594689
\(167\) −9.10587 −0.704633 −0.352317 0.935881i \(-0.614606\pi\)
−0.352317 + 0.935881i \(0.614606\pi\)
\(168\) 46.7190 3.60445
\(169\) 9.37218 0.720937
\(170\) −9.16675 −0.703057
\(171\) 3.55833 0.272112
\(172\) −8.01642 −0.611246
\(173\) −21.3921 −1.62641 −0.813205 0.581978i \(-0.802279\pi\)
−0.813205 + 0.581978i \(0.802279\pi\)
\(174\) 27.0012 2.04695
\(175\) 7.89936 0.597136
\(176\) −15.2732 −1.15126
\(177\) −5.09090 −0.382656
\(178\) −17.6121 −1.32009
\(179\) −20.6266 −1.54170 −0.770852 0.637015i \(-0.780169\pi\)
−0.770852 + 0.637015i \(0.780169\pi\)
\(180\) 14.1896 1.05763
\(181\) 0.126567 0.00940768 0.00470384 0.999989i \(-0.498503\pi\)
0.00470384 + 0.999989i \(0.498503\pi\)
\(182\) 51.3007 3.80266
\(183\) −11.5540 −0.854100
\(184\) 68.4305 5.04477
\(185\) 4.57663 0.336480
\(186\) −6.89617 −0.505652
\(187\) 1.93056 0.141176
\(188\) 38.3083 2.79392
\(189\) 21.8531 1.58958
\(190\) −11.3580 −0.823993
\(191\) −0.0198668 −0.00143751 −0.000718755 1.00000i \(-0.500229\pi\)
−0.000718755 1.00000i \(0.500229\pi\)
\(192\) 38.7208 2.79444
\(193\) 2.37822 0.171188 0.0855939 0.996330i \(-0.472721\pi\)
0.0855939 + 0.996330i \(0.472721\pi\)
\(194\) 9.42394 0.676599
\(195\) −10.0837 −0.722106
\(196\) 47.7586 3.41133
\(197\) −17.9498 −1.27887 −0.639435 0.768845i \(-0.720832\pi\)
−0.639435 + 0.768845i \(0.720832\pi\)
\(198\) −4.07459 −0.289568
\(199\) 16.0847 1.14021 0.570107 0.821570i \(-0.306902\pi\)
0.570107 + 0.821570i \(0.306902\pi\)
\(200\) 19.1391 1.35334
\(201\) 5.50113 0.388020
\(202\) −20.7895 −1.46275
\(203\) 31.7398 2.22769
\(204\) −13.0643 −0.914684
\(205\) 15.7898 1.10281
\(206\) −21.2212 −1.47855
\(207\) 10.6105 0.737480
\(208\) 72.2411 5.00902
\(209\) 2.39204 0.165461
\(210\) −23.1224 −1.59560
\(211\) −20.1847 −1.38957 −0.694785 0.719217i \(-0.744501\pi\)
−0.694785 + 0.719217i \(0.744501\pi\)
\(212\) 4.30658 0.295777
\(213\) 1.03239 0.0707380
\(214\) 46.6174 3.18670
\(215\) 2.52546 0.172235
\(216\) 52.9471 3.60259
\(217\) −8.10642 −0.550300
\(218\) 17.6133 1.19292
\(219\) 8.56084 0.578488
\(220\) 9.53879 0.643105
\(221\) −9.13140 −0.614244
\(222\) 8.89326 0.596876
\(223\) 1.12254 0.0751706 0.0375853 0.999293i \(-0.488033\pi\)
0.0375853 + 0.999293i \(0.488033\pi\)
\(224\) 89.6751 5.99167
\(225\) 2.96761 0.197841
\(226\) 14.5066 0.964963
\(227\) 9.25146 0.614041 0.307021 0.951703i \(-0.400668\pi\)
0.307021 + 0.951703i \(0.400668\pi\)
\(228\) −16.1872 −1.07202
\(229\) −8.49724 −0.561513 −0.280757 0.959779i \(-0.590585\pi\)
−0.280757 + 0.959779i \(0.590585\pi\)
\(230\) −33.8680 −2.23319
\(231\) 4.86968 0.320402
\(232\) 76.9012 5.04881
\(233\) 12.7681 0.836469 0.418235 0.908339i \(-0.362649\pi\)
0.418235 + 0.908339i \(0.362649\pi\)
\(234\) 19.2725 1.25988
\(235\) −12.0685 −0.787264
\(236\) −22.7784 −1.48275
\(237\) −16.0932 −1.04537
\(238\) −20.9388 −1.35726
\(239\) −4.43309 −0.286753 −0.143376 0.989668i \(-0.545796\pi\)
−0.143376 + 0.989668i \(0.545796\pi\)
\(240\) −32.5607 −2.10179
\(241\) −14.4375 −0.930004 −0.465002 0.885310i \(-0.653946\pi\)
−0.465002 + 0.885310i \(0.653946\pi\)
\(242\) −2.73908 −0.176075
\(243\) 13.6980 0.878726
\(244\) −51.6968 −3.30955
\(245\) −15.0457 −0.961234
\(246\) 30.6826 1.95625
\(247\) −11.3142 −0.719902
\(248\) −19.6408 −1.24719
\(249\) −0.344014 −0.0218010
\(250\) −33.2136 −2.10061
\(251\) −3.72490 −0.235113 −0.117557 0.993066i \(-0.537506\pi\)
−0.117557 + 0.993066i \(0.537506\pi\)
\(252\) 32.4122 2.04177
\(253\) 7.13275 0.448432
\(254\) −28.4049 −1.78228
\(255\) 4.11573 0.257737
\(256\) 49.1869 3.07418
\(257\) 14.7880 0.922448 0.461224 0.887284i \(-0.347410\pi\)
0.461224 + 0.887284i \(0.347410\pi\)
\(258\) 4.90746 0.305525
\(259\) 10.4540 0.649579
\(260\) −45.1177 −2.79808
\(261\) 11.9239 0.738071
\(262\) 32.0701 1.98130
\(263\) 13.5386 0.834824 0.417412 0.908717i \(-0.362937\pi\)
0.417412 + 0.908717i \(0.362937\pi\)
\(264\) 11.7986 0.726153
\(265\) −1.35673 −0.0833431
\(266\) −25.9440 −1.59073
\(267\) 7.90759 0.483936
\(268\) 24.6139 1.50354
\(269\) −30.6150 −1.86663 −0.933315 0.359060i \(-0.883098\pi\)
−0.933315 + 0.359060i \(0.883098\pi\)
\(270\) −26.2048 −1.59477
\(271\) −10.5041 −0.638081 −0.319040 0.947741i \(-0.603361\pi\)
−0.319040 + 0.947741i \(0.603361\pi\)
\(272\) −29.4858 −1.78784
\(273\) −23.0332 −1.39403
\(274\) −27.5229 −1.66272
\(275\) 1.99493 0.120299
\(276\) −48.2681 −2.90540
\(277\) 13.6996 0.823130 0.411565 0.911380i \(-0.364982\pi\)
0.411565 + 0.911380i \(0.364982\pi\)
\(278\) −16.1926 −0.971167
\(279\) −3.04540 −0.182323
\(280\) −65.8542 −3.93554
\(281\) 14.3459 0.855806 0.427903 0.903825i \(-0.359253\pi\)
0.427903 + 0.903825i \(0.359253\pi\)
\(282\) −23.4514 −1.39651
\(283\) 20.5828 1.22352 0.611761 0.791042i \(-0.290461\pi\)
0.611761 + 0.791042i \(0.290461\pi\)
\(284\) 4.61925 0.274102
\(285\) 5.09955 0.302071
\(286\) 12.9557 0.766084
\(287\) 36.0672 2.12898
\(288\) 33.6889 1.98514
\(289\) −13.2729 −0.780761
\(290\) −38.0603 −2.23498
\(291\) −4.23121 −0.248038
\(292\) 38.3041 2.24158
\(293\) 4.81884 0.281519 0.140760 0.990044i \(-0.455045\pi\)
0.140760 + 0.990044i \(0.455045\pi\)
\(294\) −29.2366 −1.70512
\(295\) 7.17603 0.417805
\(296\) 25.3286 1.47220
\(297\) 5.51885 0.320236
\(298\) −49.1531 −2.84736
\(299\) −33.7374 −1.95108
\(300\) −13.4999 −0.779420
\(301\) 5.76870 0.332502
\(302\) 38.5789 2.21997
\(303\) 9.33419 0.536235
\(304\) −36.5341 −2.09537
\(305\) 16.2864 0.932554
\(306\) −7.86623 −0.449683
\(307\) 1.84524 0.105313 0.0526567 0.998613i \(-0.483231\pi\)
0.0526567 + 0.998613i \(0.483231\pi\)
\(308\) 21.7886 1.24152
\(309\) 9.52801 0.542030
\(310\) 9.72071 0.552099
\(311\) 13.1829 0.747533 0.373766 0.927523i \(-0.378066\pi\)
0.373766 + 0.927523i \(0.378066\pi\)
\(312\) −55.8065 −3.15942
\(313\) 25.7814 1.45725 0.728625 0.684913i \(-0.240160\pi\)
0.728625 + 0.684913i \(0.240160\pi\)
\(314\) 61.9085 3.49370
\(315\) −10.2110 −0.575325
\(316\) −72.0064 −4.05068
\(317\) −7.78098 −0.437023 −0.218512 0.975834i \(-0.570120\pi\)
−0.218512 + 0.975834i \(0.570120\pi\)
\(318\) −2.63638 −0.147841
\(319\) 8.01568 0.448792
\(320\) −54.5801 −3.05112
\(321\) −20.9305 −1.16823
\(322\) −77.3616 −4.31119
\(323\) 4.61797 0.256951
\(324\) −12.7902 −0.710568
\(325\) −9.43589 −0.523409
\(326\) −30.9986 −1.71685
\(327\) −7.90809 −0.437318
\(328\) 87.3861 4.82509
\(329\) −27.5671 −1.51982
\(330\) −5.83942 −0.321449
\(331\) 9.43119 0.518385 0.259193 0.965826i \(-0.416544\pi\)
0.259193 + 0.965826i \(0.416544\pi\)
\(332\) −1.53924 −0.0844766
\(333\) 3.92733 0.215216
\(334\) 24.9417 1.36475
\(335\) −7.75429 −0.423662
\(336\) −74.3757 −4.05753
\(337\) −26.7505 −1.45719 −0.728595 0.684944i \(-0.759826\pi\)
−0.728595 + 0.684944i \(0.759826\pi\)
\(338\) −25.6712 −1.39633
\(339\) −6.51324 −0.353750
\(340\) 18.4152 0.998704
\(341\) −2.04723 −0.110863
\(342\) −9.74657 −0.527034
\(343\) −6.64958 −0.359044
\(344\) 13.9768 0.753578
\(345\) 15.2062 0.818675
\(346\) 58.5947 3.15007
\(347\) 7.77330 0.417292 0.208646 0.977991i \(-0.433094\pi\)
0.208646 + 0.977991i \(0.433094\pi\)
\(348\) −54.2430 −2.90773
\(349\) 21.1507 1.13217 0.566085 0.824347i \(-0.308457\pi\)
0.566085 + 0.824347i \(0.308457\pi\)
\(350\) −21.6370 −1.15655
\(351\) −26.1038 −1.39332
\(352\) 22.6469 1.20708
\(353\) 26.4425 1.40739 0.703696 0.710501i \(-0.251532\pi\)
0.703696 + 0.710501i \(0.251532\pi\)
\(354\) 13.9444 0.741137
\(355\) −1.45523 −0.0772357
\(356\) 35.3812 1.87520
\(357\) 9.40121 0.497565
\(358\) 56.4979 2.98601
\(359\) −27.4097 −1.44663 −0.723315 0.690518i \(-0.757382\pi\)
−0.723315 + 0.690518i \(0.757382\pi\)
\(360\) −24.7399 −1.30391
\(361\) −13.2782 −0.698850
\(362\) −0.346679 −0.0182210
\(363\) 1.22981 0.0645482
\(364\) −103.059 −5.40173
\(365\) −12.0672 −0.631626
\(366\) 31.6475 1.65424
\(367\) 20.3637 1.06298 0.531488 0.847066i \(-0.321633\pi\)
0.531488 + 0.847066i \(0.321633\pi\)
\(368\) −108.940 −5.67889
\(369\) 13.5496 0.705366
\(370\) −12.5358 −0.651703
\(371\) −3.09906 −0.160895
\(372\) 13.8538 0.718286
\(373\) −2.86738 −0.148467 −0.0742337 0.997241i \(-0.523651\pi\)
−0.0742337 + 0.997241i \(0.523651\pi\)
\(374\) −5.28796 −0.273434
\(375\) 14.9124 0.770073
\(376\) −66.7914 −3.44450
\(377\) −37.9135 −1.95265
\(378\) −59.8573 −3.07873
\(379\) 37.6791 1.93545 0.967724 0.252014i \(-0.0810929\pi\)
0.967724 + 0.252014i \(0.0810929\pi\)
\(380\) 22.8171 1.17049
\(381\) 12.7534 0.653375
\(382\) 0.0544168 0.00278421
\(383\) −0.690341 −0.0352748 −0.0176374 0.999844i \(-0.505614\pi\)
−0.0176374 + 0.999844i \(0.505614\pi\)
\(384\) −50.3570 −2.56977
\(385\) −6.86421 −0.349832
\(386\) −6.51413 −0.331561
\(387\) 2.16717 0.110163
\(388\) −18.9319 −0.961120
\(389\) 2.77315 0.140604 0.0703021 0.997526i \(-0.477604\pi\)
0.0703021 + 0.997526i \(0.477604\pi\)
\(390\) 27.6200 1.39859
\(391\) 13.7702 0.696388
\(392\) −83.2680 −4.20567
\(393\) −14.3990 −0.726333
\(394\) 49.1660 2.47695
\(395\) 22.6847 1.14139
\(396\) 8.18549 0.411336
\(397\) −3.06928 −0.154043 −0.0770213 0.997029i \(-0.524541\pi\)
−0.0770213 + 0.997029i \(0.524541\pi\)
\(398\) −44.0573 −2.20839
\(399\) 11.6485 0.583152
\(400\) −30.4690 −1.52345
\(401\) 6.29501 0.314358 0.157179 0.987570i \(-0.449760\pi\)
0.157179 + 0.987570i \(0.449760\pi\)
\(402\) −15.0681 −0.751527
\(403\) 9.68322 0.482356
\(404\) 41.7643 2.07785
\(405\) 4.02938 0.200222
\(406\) −86.9378 −4.31465
\(407\) 2.64009 0.130864
\(408\) 22.7779 1.12767
\(409\) 9.62339 0.475846 0.237923 0.971284i \(-0.423533\pi\)
0.237923 + 0.971284i \(0.423533\pi\)
\(410\) −43.2495 −2.13594
\(411\) 12.3574 0.609544
\(412\) 42.6316 2.10031
\(413\) 16.3916 0.806577
\(414\) −29.0630 −1.42837
\(415\) 0.484915 0.0238036
\(416\) −107.118 −5.25189
\(417\) 7.27023 0.356025
\(418\) −6.55199 −0.320468
\(419\) −34.0693 −1.66439 −0.832197 0.554480i \(-0.812917\pi\)
−0.832197 + 0.554480i \(0.812917\pi\)
\(420\) 46.4509 2.26657
\(421\) 25.2422 1.23023 0.615114 0.788438i \(-0.289110\pi\)
0.615114 + 0.788438i \(0.289110\pi\)
\(422\) 55.2875 2.69135
\(423\) −10.3563 −0.503542
\(424\) −7.50860 −0.364650
\(425\) 3.85134 0.186817
\(426\) −2.82780 −0.137007
\(427\) 37.2015 1.80031
\(428\) −93.6503 −4.52676
\(429\) −5.81690 −0.280842
\(430\) −6.91746 −0.333589
\(431\) 36.9030 1.77755 0.888777 0.458341i \(-0.151556\pi\)
0.888777 + 0.458341i \(0.151556\pi\)
\(432\) −84.2906 −4.05543
\(433\) −37.9997 −1.82615 −0.913074 0.407795i \(-0.866298\pi\)
−0.913074 + 0.407795i \(0.866298\pi\)
\(434\) 22.2042 1.06583
\(435\) 17.0885 0.819332
\(436\) −35.3835 −1.69456
\(437\) 17.0618 0.816176
\(438\) −23.4489 −1.12043
\(439\) −1.37700 −0.0657205 −0.0328603 0.999460i \(-0.510462\pi\)
−0.0328603 + 0.999460i \(0.510462\pi\)
\(440\) −16.6311 −0.792855
\(441\) −12.9111 −0.614815
\(442\) 25.0117 1.18968
\(443\) 39.2297 1.86386 0.931929 0.362642i \(-0.118125\pi\)
0.931929 + 0.362642i \(0.118125\pi\)
\(444\) −17.8658 −0.847872
\(445\) −11.1464 −0.528389
\(446\) −3.07472 −0.145592
\(447\) 22.0690 1.04383
\(448\) −124.673 −5.89023
\(449\) −5.96218 −0.281372 −0.140686 0.990054i \(-0.544931\pi\)
−0.140686 + 0.990054i \(0.544931\pi\)
\(450\) −8.12854 −0.383183
\(451\) 9.10855 0.428905
\(452\) −29.1424 −1.37075
\(453\) −17.3214 −0.813828
\(454\) −25.3405 −1.18929
\(455\) 32.4672 1.52209
\(456\) 28.2227 1.32165
\(457\) −3.67345 −0.171837 −0.0859184 0.996302i \(-0.527382\pi\)
−0.0859184 + 0.996302i \(0.527382\pi\)
\(458\) 23.2746 1.08755
\(459\) 10.6545 0.497308
\(460\) 68.0378 3.17228
\(461\) −29.0994 −1.35529 −0.677646 0.735388i \(-0.737000\pi\)
−0.677646 + 0.735388i \(0.737000\pi\)
\(462\) −13.3385 −0.620562
\(463\) 29.4331 1.36787 0.683936 0.729542i \(-0.260267\pi\)
0.683936 + 0.729542i \(0.260267\pi\)
\(464\) −122.425 −5.68344
\(465\) −4.36445 −0.202397
\(466\) −34.9730 −1.62009
\(467\) 23.9806 1.10969 0.554845 0.831954i \(-0.312778\pi\)
0.554845 + 0.831954i \(0.312778\pi\)
\(468\) −38.7167 −1.78968
\(469\) −17.7124 −0.817885
\(470\) 33.0567 1.52479
\(471\) −27.7960 −1.28077
\(472\) 39.7146 1.82801
\(473\) 1.45685 0.0669859
\(474\) 44.0806 2.02469
\(475\) 4.77196 0.218952
\(476\) 42.0642 1.92801
\(477\) −1.16424 −0.0533071
\(478\) 12.1426 0.555390
\(479\) 26.9887 1.23314 0.616572 0.787298i \(-0.288521\pi\)
0.616572 + 0.787298i \(0.288521\pi\)
\(480\) 48.2806 2.20370
\(481\) −12.4874 −0.569377
\(482\) 39.5456 1.80125
\(483\) 34.7342 1.58046
\(484\) 5.50258 0.250117
\(485\) 5.96423 0.270822
\(486\) −37.5199 −1.70194
\(487\) −25.4736 −1.15432 −0.577159 0.816631i \(-0.695839\pi\)
−0.577159 + 0.816631i \(0.695839\pi\)
\(488\) 90.1343 4.08019
\(489\) 13.9179 0.629389
\(490\) 41.2114 1.86174
\(491\) 7.69386 0.347219 0.173610 0.984815i \(-0.444457\pi\)
0.173610 + 0.984815i \(0.444457\pi\)
\(492\) −61.6386 −2.77888
\(493\) 15.4747 0.696947
\(494\) 30.9904 1.39432
\(495\) −2.57873 −0.115905
\(496\) 31.2677 1.40396
\(497\) −3.32406 −0.149105
\(498\) 0.942283 0.0422247
\(499\) 2.76216 0.123651 0.0618256 0.998087i \(-0.480308\pi\)
0.0618256 + 0.998087i \(0.480308\pi\)
\(500\) 66.7232 2.98395
\(501\) −11.1985 −0.500310
\(502\) 10.2028 0.455374
\(503\) 21.0811 0.939958 0.469979 0.882677i \(-0.344261\pi\)
0.469979 + 0.882677i \(0.344261\pi\)
\(504\) −56.5113 −2.51721
\(505\) −13.1573 −0.585492
\(506\) −19.5372 −0.868534
\(507\) 11.5260 0.511887
\(508\) 57.0629 2.53176
\(509\) 13.8856 0.615468 0.307734 0.951472i \(-0.400429\pi\)
0.307734 + 0.951472i \(0.400429\pi\)
\(510\) −11.2733 −0.499192
\(511\) −27.5640 −1.21936
\(512\) −52.8328 −2.33490
\(513\) 13.2013 0.582852
\(514\) −40.5055 −1.78662
\(515\) −13.4305 −0.591818
\(516\) −9.85865 −0.434003
\(517\) −6.96189 −0.306184
\(518\) −28.6343 −1.25812
\(519\) −26.3081 −1.15480
\(520\) 78.6637 3.44963
\(521\) −34.6247 −1.51693 −0.758467 0.651712i \(-0.774051\pi\)
−0.758467 + 0.651712i \(0.774051\pi\)
\(522\) −32.6606 −1.42951
\(523\) −29.8221 −1.30403 −0.652016 0.758205i \(-0.726076\pi\)
−0.652016 + 0.758205i \(0.726076\pi\)
\(524\) −64.4260 −2.81446
\(525\) 9.71470 0.423984
\(526\) −37.0833 −1.61691
\(527\) −3.95229 −0.172164
\(528\) −18.7831 −0.817430
\(529\) 27.8761 1.21200
\(530\) 3.71619 0.161421
\(531\) 6.15795 0.267232
\(532\) 52.1192 2.25965
\(533\) −43.0827 −1.86612
\(534\) −21.6595 −0.937300
\(535\) 29.5033 1.27554
\(536\) −42.9149 −1.85364
\(537\) −25.3667 −1.09466
\(538\) 83.8570 3.61533
\(539\) −8.67931 −0.373844
\(540\) 52.6432 2.26540
\(541\) 28.2080 1.21276 0.606378 0.795177i \(-0.292622\pi\)
0.606378 + 0.795177i \(0.292622\pi\)
\(542\) 28.7717 1.23585
\(543\) 0.155654 0.00667973
\(544\) 43.7211 1.87453
\(545\) 11.1471 0.477489
\(546\) 63.0899 2.70000
\(547\) 1.00000 0.0427569
\(548\) 55.2911 2.36192
\(549\) 13.9758 0.596471
\(550\) −5.46429 −0.232998
\(551\) 19.1738 0.816831
\(552\) 84.1564 3.58193
\(553\) 51.8166 2.20346
\(554\) −37.5244 −1.59426
\(555\) 5.62837 0.238911
\(556\) 32.5295 1.37956
\(557\) −27.9957 −1.18622 −0.593108 0.805123i \(-0.702099\pi\)
−0.593108 + 0.805123i \(0.702099\pi\)
\(558\) 8.34160 0.353128
\(559\) −6.89078 −0.291449
\(560\) 104.838 4.43023
\(561\) 2.37422 0.100239
\(562\) −39.2947 −1.65755
\(563\) 2.65084 0.111720 0.0558599 0.998439i \(-0.482210\pi\)
0.0558599 + 0.998439i \(0.482210\pi\)
\(564\) 47.1119 1.98377
\(565\) 9.18093 0.386245
\(566\) −56.3781 −2.36975
\(567\) 9.20397 0.386530
\(568\) −8.05376 −0.337928
\(569\) 37.6515 1.57843 0.789216 0.614116i \(-0.210487\pi\)
0.789216 + 0.614116i \(0.210487\pi\)
\(570\) −13.9681 −0.585059
\(571\) 29.0869 1.21725 0.608624 0.793459i \(-0.291722\pi\)
0.608624 + 0.793459i \(0.291722\pi\)
\(572\) −26.0268 −1.08823
\(573\) −0.0244323 −0.00102068
\(574\) −98.7911 −4.12346
\(575\) 14.2294 0.593405
\(576\) −46.8367 −1.95153
\(577\) −8.66197 −0.360603 −0.180301 0.983611i \(-0.557707\pi\)
−0.180301 + 0.983611i \(0.557707\pi\)
\(578\) 36.3557 1.51220
\(579\) 2.92475 0.121548
\(580\) 76.4598 3.17482
\(581\) 1.10765 0.0459531
\(582\) 11.5896 0.480406
\(583\) −0.782647 −0.0324139
\(584\) −66.7840 −2.76354
\(585\) 12.1972 0.504292
\(586\) −13.1992 −0.545254
\(587\) −4.84942 −0.200157 −0.100079 0.994980i \(-0.531909\pi\)
−0.100079 + 0.994980i \(0.531909\pi\)
\(588\) 58.7339 2.42214
\(589\) −4.89704 −0.201779
\(590\) −19.6558 −0.809215
\(591\) −22.0748 −0.908036
\(592\) −40.3226 −1.65725
\(593\) −1.01068 −0.0415036 −0.0207518 0.999785i \(-0.506606\pi\)
−0.0207518 + 0.999785i \(0.506606\pi\)
\(594\) −15.1166 −0.620241
\(595\) −13.2518 −0.543269
\(596\) 98.7443 4.04473
\(597\) 19.7811 0.809586
\(598\) 92.4094 3.77890
\(599\) −30.9901 −1.26622 −0.633110 0.774062i \(-0.718222\pi\)
−0.633110 + 0.774062i \(0.718222\pi\)
\(600\) 23.5374 0.960911
\(601\) −7.02055 −0.286374 −0.143187 0.989696i \(-0.545735\pi\)
−0.143187 + 0.989696i \(0.545735\pi\)
\(602\) −15.8009 −0.643998
\(603\) −6.65416 −0.270979
\(604\) −77.5016 −3.15350
\(605\) −1.73351 −0.0704773
\(606\) −25.5671 −1.03859
\(607\) 35.5691 1.44370 0.721852 0.692048i \(-0.243291\pi\)
0.721852 + 0.692048i \(0.243291\pi\)
\(608\) 54.1722 2.19697
\(609\) 39.0338 1.58173
\(610\) −44.6097 −1.80619
\(611\) 32.9292 1.33217
\(612\) 15.8026 0.638781
\(613\) −13.5252 −0.546276 −0.273138 0.961975i \(-0.588062\pi\)
−0.273138 + 0.961975i \(0.588062\pi\)
\(614\) −5.05427 −0.203974
\(615\) 19.4184 0.783025
\(616\) −37.9889 −1.53062
\(617\) 32.6767 1.31551 0.657756 0.753231i \(-0.271506\pi\)
0.657756 + 0.753231i \(0.271506\pi\)
\(618\) −26.0980 −1.04982
\(619\) 8.38613 0.337067 0.168534 0.985696i \(-0.446097\pi\)
0.168534 + 0.985696i \(0.446097\pi\)
\(620\) −19.5280 −0.784265
\(621\) 39.3646 1.57965
\(622\) −36.1090 −1.44784
\(623\) −25.4607 −1.02006
\(624\) 88.8427 3.55655
\(625\) −11.0456 −0.441823
\(626\) −70.6174 −2.82244
\(627\) 2.94175 0.117482
\(628\) −124.369 −4.96285
\(629\) 5.09685 0.203225
\(630\) 27.9688 1.11430
\(631\) −21.0747 −0.838971 −0.419485 0.907762i \(-0.637789\pi\)
−0.419485 + 0.907762i \(0.637789\pi\)
\(632\) 125.545 4.99390
\(633\) −24.8233 −0.986636
\(634\) 21.3127 0.846437
\(635\) −17.9769 −0.713391
\(636\) 5.29626 0.210010
\(637\) 41.0525 1.62656
\(638\) −21.9556 −0.869231
\(639\) −1.24877 −0.0494008
\(640\) 70.9823 2.80582
\(641\) −19.9611 −0.788417 −0.394208 0.919021i \(-0.628981\pi\)
−0.394208 + 0.919021i \(0.628981\pi\)
\(642\) 57.3305 2.26265
\(643\) −35.7651 −1.41044 −0.705219 0.708989i \(-0.749151\pi\)
−0.705219 + 0.708989i \(0.749151\pi\)
\(644\) 155.413 6.12412
\(645\) 3.10583 0.122292
\(646\) −12.6490 −0.497668
\(647\) −38.0146 −1.49451 −0.747254 0.664539i \(-0.768628\pi\)
−0.747254 + 0.664539i \(0.768628\pi\)
\(648\) 22.3000 0.876027
\(649\) 4.13959 0.162493
\(650\) 25.8457 1.01375
\(651\) −9.96934 −0.390729
\(652\) 62.2734 2.43882
\(653\) 33.7737 1.32167 0.660833 0.750533i \(-0.270203\pi\)
0.660833 + 0.750533i \(0.270203\pi\)
\(654\) 21.6609 0.847009
\(655\) 20.2965 0.793051
\(656\) −139.117 −5.43160
\(657\) −10.3552 −0.403994
\(658\) 75.5085 2.94363
\(659\) −23.9907 −0.934543 −0.467272 0.884114i \(-0.654763\pi\)
−0.467272 + 0.884114i \(0.654763\pi\)
\(660\) 11.7309 0.456624
\(661\) −9.09448 −0.353734 −0.176867 0.984235i \(-0.556596\pi\)
−0.176867 + 0.984235i \(0.556596\pi\)
\(662\) −25.8328 −1.00402
\(663\) −11.2299 −0.436132
\(664\) 2.68369 0.104147
\(665\) −16.4194 −0.636719
\(666\) −10.7573 −0.416836
\(667\) 57.1738 2.21378
\(668\) −50.1057 −1.93865
\(669\) 1.38050 0.0533733
\(670\) 21.2396 0.820559
\(671\) 9.39501 0.362690
\(672\) 110.283 4.25426
\(673\) 35.2531 1.35891 0.679454 0.733718i \(-0.262217\pi\)
0.679454 + 0.733718i \(0.262217\pi\)
\(674\) 73.2718 2.82232
\(675\) 11.0097 0.423765
\(676\) 51.5712 1.98351
\(677\) 6.73720 0.258932 0.129466 0.991584i \(-0.458674\pi\)
0.129466 + 0.991584i \(0.458674\pi\)
\(678\) 17.8403 0.685153
\(679\) 13.6236 0.522824
\(680\) −32.1072 −1.23126
\(681\) 11.3775 0.435988
\(682\) 5.60752 0.214723
\(683\) −38.5469 −1.47496 −0.737479 0.675370i \(-0.763984\pi\)
−0.737479 + 0.675370i \(0.763984\pi\)
\(684\) 19.5800 0.748660
\(685\) −17.4187 −0.665534
\(686\) 18.2138 0.695404
\(687\) −10.4500 −0.398691
\(688\) −22.2507 −0.848302
\(689\) 3.70186 0.141030
\(690\) −41.6511 −1.58563
\(691\) 18.6359 0.708945 0.354472 0.935066i \(-0.384660\pi\)
0.354472 + 0.935066i \(0.384660\pi\)
\(692\) −117.712 −4.47472
\(693\) −5.89036 −0.223756
\(694\) −21.2917 −0.808222
\(695\) −10.2480 −0.388728
\(696\) 94.5737 3.58481
\(697\) 17.5846 0.666064
\(698\) −57.9335 −2.19282
\(699\) 15.7024 0.593918
\(700\) 43.4669 1.64289
\(701\) −44.4192 −1.67769 −0.838844 0.544371i \(-0.816768\pi\)
−0.838844 + 0.544371i \(0.816768\pi\)
\(702\) 71.5004 2.69861
\(703\) 6.31519 0.238182
\(704\) −31.4853 −1.18665
\(705\) −14.8420 −0.558981
\(706\) −72.4282 −2.72587
\(707\) −30.0540 −1.13030
\(708\) −28.0131 −1.05280
\(709\) 3.92951 0.147576 0.0737880 0.997274i \(-0.476491\pi\)
0.0737880 + 0.997274i \(0.476491\pi\)
\(710\) 3.98600 0.149592
\(711\) 19.4663 0.730044
\(712\) −61.6879 −2.31185
\(713\) −14.6023 −0.546862
\(714\) −25.7507 −0.963695
\(715\) 8.19938 0.306640
\(716\) −113.499 −4.24167
\(717\) −5.45185 −0.203603
\(718\) 75.0775 2.80187
\(719\) 16.2377 0.605563 0.302782 0.953060i \(-0.402085\pi\)
0.302782 + 0.953060i \(0.402085\pi\)
\(720\) 39.3854 1.46781
\(721\) −30.6781 −1.14251
\(722\) 36.3700 1.35355
\(723\) −17.7554 −0.660330
\(724\) 0.696447 0.0258833
\(725\) 15.9907 0.593881
\(726\) −3.36855 −0.125018
\(727\) 17.7454 0.658142 0.329071 0.944305i \(-0.393264\pi\)
0.329071 + 0.944305i \(0.393264\pi\)
\(728\) 179.685 6.65955
\(729\) 23.8191 0.882189
\(730\) 33.0531 1.22335
\(731\) 2.81253 0.104025
\(732\) −63.5771 −2.34988
\(733\) 39.3367 1.45293 0.726466 0.687202i \(-0.241161\pi\)
0.726466 + 0.687202i \(0.241161\pi\)
\(734\) −55.7779 −2.05880
\(735\) −18.5033 −0.682505
\(736\) 161.535 5.95424
\(737\) −4.47317 −0.164771
\(738\) −37.1136 −1.36617
\(739\) 14.6809 0.540044 0.270022 0.962854i \(-0.412969\pi\)
0.270022 + 0.962854i \(0.412969\pi\)
\(740\) 25.1832 0.925755
\(741\) −13.9142 −0.511152
\(742\) 8.48857 0.311625
\(743\) 8.58571 0.314979 0.157490 0.987521i \(-0.449660\pi\)
0.157490 + 0.987521i \(0.449660\pi\)
\(744\) −24.1544 −0.885542
\(745\) −31.1081 −1.13971
\(746\) 7.85399 0.287555
\(747\) 0.416119 0.0152250
\(748\) 10.6230 0.388417
\(749\) 67.3917 2.46244
\(750\) −40.8463 −1.49150
\(751\) 23.8377 0.869851 0.434925 0.900466i \(-0.356775\pi\)
0.434925 + 0.900466i \(0.356775\pi\)
\(752\) 106.330 3.87747
\(753\) −4.58091 −0.166938
\(754\) 103.848 3.78193
\(755\) 24.4158 0.888583
\(756\) 120.248 4.37338
\(757\) −24.4379 −0.888210 −0.444105 0.895975i \(-0.646478\pi\)
−0.444105 + 0.895975i \(0.646478\pi\)
\(758\) −103.206 −3.74862
\(759\) 8.77191 0.318400
\(760\) −39.7821 −1.44305
\(761\) −48.9521 −1.77451 −0.887257 0.461276i \(-0.847392\pi\)
−0.887257 + 0.461276i \(0.847392\pi\)
\(762\) −34.9325 −1.26547
\(763\) 25.4623 0.921797
\(764\) −0.109319 −0.00395501
\(765\) −4.97838 −0.179994
\(766\) 1.89090 0.0683210
\(767\) −19.5800 −0.706991
\(768\) 60.4904 2.18276
\(769\) −47.0547 −1.69684 −0.848418 0.529327i \(-0.822445\pi\)
−0.848418 + 0.529327i \(0.822445\pi\)
\(770\) 18.8016 0.677564
\(771\) 18.1864 0.654965
\(772\) 13.0863 0.470987
\(773\) 17.8356 0.641504 0.320752 0.947163i \(-0.396064\pi\)
0.320752 + 0.947163i \(0.396064\pi\)
\(774\) −5.93605 −0.213367
\(775\) −4.08408 −0.146704
\(776\) 33.0081 1.18492
\(777\) 12.8564 0.461221
\(778\) −7.59588 −0.272326
\(779\) 21.7880 0.780636
\(780\) −55.4861 −1.98672
\(781\) −0.839471 −0.0300386
\(782\) −37.7177 −1.34878
\(783\) 44.2373 1.58091
\(784\) 132.561 4.73432
\(785\) 39.1807 1.39842
\(786\) 39.4400 1.40678
\(787\) −9.06857 −0.323260 −0.161630 0.986851i \(-0.551675\pi\)
−0.161630 + 0.986851i \(0.551675\pi\)
\(788\) −98.7702 −3.51854
\(789\) 16.6498 0.592750
\(790\) −62.1352 −2.21067
\(791\) 20.9712 0.745650
\(792\) −14.2716 −0.507118
\(793\) −44.4377 −1.57803
\(794\) 8.40700 0.298353
\(795\) −1.66851 −0.0591761
\(796\) 88.5073 3.13706
\(797\) −24.3483 −0.862460 −0.431230 0.902242i \(-0.641920\pi\)
−0.431230 + 0.902242i \(0.641920\pi\)
\(798\) −31.9061 −1.12946
\(799\) −13.4403 −0.475485
\(800\) 45.1790 1.59732
\(801\) −9.56501 −0.337963
\(802\) −17.2426 −0.608856
\(803\) −6.96113 −0.245653
\(804\) 30.2704 1.06756
\(805\) −48.9607 −1.72564
\(806\) −26.5231 −0.934238
\(807\) −37.6506 −1.32536
\(808\) −72.8169 −2.56169
\(809\) 26.2578 0.923174 0.461587 0.887095i \(-0.347280\pi\)
0.461587 + 0.887095i \(0.347280\pi\)
\(810\) −11.0368 −0.387794
\(811\) −49.5592 −1.74026 −0.870129 0.492825i \(-0.835964\pi\)
−0.870129 + 0.492825i \(0.835964\pi\)
\(812\) 174.650 6.12903
\(813\) −12.9181 −0.453056
\(814\) −7.23142 −0.253461
\(815\) −19.6184 −0.687202
\(816\) −36.2619 −1.26942
\(817\) 3.48483 0.121919
\(818\) −26.3593 −0.921630
\(819\) 27.8610 0.973541
\(820\) 86.8845 3.03414
\(821\) 43.9245 1.53298 0.766488 0.642259i \(-0.222003\pi\)
0.766488 + 0.642259i \(0.222003\pi\)
\(822\) −33.8478 −1.18058
\(823\) 7.87402 0.274471 0.137236 0.990538i \(-0.456178\pi\)
0.137236 + 0.990538i \(0.456178\pi\)
\(824\) −74.3290 −2.58937
\(825\) 2.45339 0.0854159
\(826\) −44.8979 −1.56220
\(827\) 30.3212 1.05437 0.527185 0.849750i \(-0.323247\pi\)
0.527185 + 0.849750i \(0.323247\pi\)
\(828\) 58.3850 2.02902
\(829\) 10.7679 0.373984 0.186992 0.982361i \(-0.440126\pi\)
0.186992 + 0.982361i \(0.440126\pi\)
\(830\) −1.32822 −0.0461033
\(831\) 16.8479 0.584447
\(832\) 148.923 5.16298
\(833\) −16.7559 −0.580558
\(834\) −19.9138 −0.689557
\(835\) 15.7851 0.546267
\(836\) 13.1624 0.455230
\(837\) −11.2983 −0.390527
\(838\) 93.3186 3.22364
\(839\) −40.3893 −1.39439 −0.697196 0.716880i \(-0.745569\pi\)
−0.697196 + 0.716880i \(0.745569\pi\)
\(840\) −80.9880 −2.79435
\(841\) 35.2511 1.21555
\(842\) −69.1404 −2.38274
\(843\) 17.6427 0.607648
\(844\) −111.068 −3.82311
\(845\) −16.2468 −0.558907
\(846\) 28.3668 0.975272
\(847\) −3.95971 −0.136057
\(848\) 11.9535 0.410486
\(849\) 25.3129 0.868738
\(850\) −10.5491 −0.361832
\(851\) 18.8311 0.645521
\(852\) 5.68079 0.194621
\(853\) 0.938688 0.0321401 0.0160700 0.999871i \(-0.494885\pi\)
0.0160700 + 0.999871i \(0.494885\pi\)
\(854\) −101.898 −3.48688
\(855\) −6.16841 −0.210955
\(856\) 163.281 5.58084
\(857\) 47.4657 1.62140 0.810698 0.585464i \(-0.199088\pi\)
0.810698 + 0.585464i \(0.199088\pi\)
\(858\) 15.9330 0.543942
\(859\) 15.9173 0.543090 0.271545 0.962426i \(-0.412465\pi\)
0.271545 + 0.962426i \(0.412465\pi\)
\(860\) 13.8966 0.473869
\(861\) 44.3557 1.51164
\(862\) −101.080 −3.44281
\(863\) 50.9735 1.73516 0.867579 0.497299i \(-0.165675\pi\)
0.867579 + 0.497299i \(0.165675\pi\)
\(864\) 124.985 4.25207
\(865\) 37.0834 1.26087
\(866\) 104.084 3.53693
\(867\) −16.3232 −0.554364
\(868\) −44.6062 −1.51403
\(869\) 13.0859 0.443910
\(870\) −46.8069 −1.58690
\(871\) 21.1577 0.716903
\(872\) 61.6918 2.08915
\(873\) 5.11806 0.173220
\(874\) −46.7337 −1.58079
\(875\) −48.0147 −1.62319
\(876\) 47.1067 1.59159
\(877\) −16.6641 −0.562708 −0.281354 0.959604i \(-0.590783\pi\)
−0.281354 + 0.959604i \(0.590783\pi\)
\(878\) 3.77171 0.127289
\(879\) 5.92624 0.199887
\(880\) 26.4763 0.892516
\(881\) −47.4762 −1.59951 −0.799757 0.600323i \(-0.795039\pi\)
−0.799757 + 0.600323i \(0.795039\pi\)
\(882\) 35.3646 1.19079
\(883\) −23.3789 −0.786764 −0.393382 0.919375i \(-0.628695\pi\)
−0.393382 + 0.919375i \(0.628695\pi\)
\(884\) −50.2462 −1.68996
\(885\) 8.82514 0.296654
\(886\) −107.453 −3.60996
\(887\) 6.01617 0.202003 0.101002 0.994886i \(-0.467795\pi\)
0.101002 + 0.994886i \(0.467795\pi\)
\(888\) 31.1493 1.04530
\(889\) −41.0631 −1.37721
\(890\) 30.5309 1.02340
\(891\) 2.32440 0.0778705
\(892\) 6.17684 0.206816
\(893\) −16.6531 −0.557275
\(894\) −60.4489 −2.02171
\(895\) 35.7564 1.19521
\(896\) 162.139 5.41667
\(897\) −41.4905 −1.38533
\(898\) 16.3309 0.544969
\(899\) −16.4099 −0.547301
\(900\) 16.3295 0.544317
\(901\) −1.51095 −0.0503369
\(902\) −24.9491 −0.830713
\(903\) 7.09439 0.236086
\(904\) 50.8104 1.68993
\(905\) −0.219406 −0.00729331
\(906\) 47.4446 1.57624
\(907\) 13.5416 0.449641 0.224821 0.974400i \(-0.427820\pi\)
0.224821 + 0.974400i \(0.427820\pi\)
\(908\) 50.9069 1.68941
\(909\) −11.2906 −0.374486
\(910\) −88.9303 −2.94801
\(911\) 15.6109 0.517213 0.258607 0.965983i \(-0.416737\pi\)
0.258607 + 0.965983i \(0.416737\pi\)
\(912\) −44.9299 −1.48778
\(913\) 0.279730 0.00925771
\(914\) 10.0619 0.332818
\(915\) 20.0291 0.662141
\(916\) −46.7567 −1.54489
\(917\) 46.3616 1.53099
\(918\) −29.1835 −0.963198
\(919\) 7.44490 0.245585 0.122792 0.992432i \(-0.460815\pi\)
0.122792 + 0.992432i \(0.460815\pi\)
\(920\) −118.625 −3.91096
\(921\) 2.26929 0.0747757
\(922\) 79.7056 2.62496
\(923\) 3.97063 0.130695
\(924\) 26.7958 0.881517
\(925\) 5.26680 0.173171
\(926\) −80.6198 −2.64933
\(927\) −11.5251 −0.378533
\(928\) 181.530 5.95902
\(929\) 49.4252 1.62159 0.810794 0.585332i \(-0.199036\pi\)
0.810794 + 0.585332i \(0.199036\pi\)
\(930\) 11.9546 0.392007
\(931\) −20.7612 −0.680422
\(932\) 70.2577 2.30137
\(933\) 16.2124 0.530770
\(934\) −65.6848 −2.14927
\(935\) −3.34665 −0.109447
\(936\) 67.5034 2.20642
\(937\) −22.8820 −0.747523 −0.373761 0.927525i \(-0.621932\pi\)
−0.373761 + 0.927525i \(0.621932\pi\)
\(938\) 48.5159 1.58410
\(939\) 31.7061 1.03469
\(940\) −66.4080 −2.16599
\(941\) −40.0881 −1.30683 −0.653417 0.756998i \(-0.726665\pi\)
−0.653417 + 0.756998i \(0.726665\pi\)
\(942\) 76.1355 2.48063
\(943\) 64.9690 2.11568
\(944\) −63.2249 −2.05779
\(945\) −37.8825 −1.23232
\(946\) −3.99043 −0.129740
\(947\) −56.2411 −1.82759 −0.913794 0.406177i \(-0.866862\pi\)
−0.913794 + 0.406177i \(0.866862\pi\)
\(948\) −88.5541 −2.87610
\(949\) 32.9256 1.06881
\(950\) −13.0708 −0.424072
\(951\) −9.56911 −0.310299
\(952\) −73.3398 −2.37696
\(953\) −4.69397 −0.152053 −0.0760263 0.997106i \(-0.524223\pi\)
−0.0760263 + 0.997106i \(0.524223\pi\)
\(954\) 3.18896 0.103246
\(955\) 0.0344393 0.00111443
\(956\) −24.3934 −0.788940
\(957\) 9.85774 0.318655
\(958\) −73.9243 −2.38838
\(959\) −39.7880 −1.28482
\(960\) −67.1231 −2.16639
\(961\) −26.8089 −0.864802
\(962\) 34.2041 1.10278
\(963\) 25.3175 0.815846
\(964\) −79.4437 −2.55871
\(965\) −4.12267 −0.132713
\(966\) −95.1399 −3.06108
\(967\) −38.9428 −1.25232 −0.626159 0.779696i \(-0.715374\pi\)
−0.626159 + 0.779696i \(0.715374\pi\)
\(968\) −9.59385 −0.308358
\(969\) 5.67921 0.182443
\(970\) −16.3365 −0.524534
\(971\) −38.9759 −1.25080 −0.625399 0.780305i \(-0.715064\pi\)
−0.625399 + 0.780305i \(0.715064\pi\)
\(972\) 75.3742 2.41763
\(973\) −23.4085 −0.750444
\(974\) 69.7743 2.23571
\(975\) −11.6043 −0.371636
\(976\) −143.492 −4.59306
\(977\) −24.4860 −0.783376 −0.391688 0.920098i \(-0.628109\pi\)
−0.391688 + 0.920098i \(0.628109\pi\)
\(978\) −38.1223 −1.21902
\(979\) −6.42994 −0.205502
\(980\) −82.7901 −2.64463
\(981\) 9.56561 0.305406
\(982\) −21.0741 −0.672503
\(983\) −13.2378 −0.422219 −0.211109 0.977462i \(-0.567708\pi\)
−0.211109 + 0.977462i \(0.567708\pi\)
\(984\) 107.468 3.42596
\(985\) 31.1162 0.991445
\(986\) −42.3866 −1.34986
\(987\) −33.9022 −1.07912
\(988\) −62.2570 −1.98066
\(989\) 10.3913 0.330425
\(990\) 7.06335 0.224488
\(991\) −27.7822 −0.882531 −0.441265 0.897377i \(-0.645470\pi\)
−0.441265 + 0.897377i \(0.645470\pi\)
\(992\) −46.3633 −1.47204
\(993\) 11.5985 0.368069
\(994\) 9.10488 0.288789
\(995\) −27.8830 −0.883952
\(996\) −1.89296 −0.0599809
\(997\) 32.4575 1.02794 0.513969 0.857809i \(-0.328175\pi\)
0.513969 + 0.857809i \(0.328175\pi\)
\(998\) −7.56578 −0.239491
\(999\) 14.5703 0.460983
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 6017.2.a.f.1.3 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.3 121 1.1 even 1 trivial