Properties

Label 6017.2.a.f.1.19
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.19
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.22670 q^{2} +0.200688 q^{3} +2.95817 q^{4} +3.39958 q^{5} -0.446870 q^{6} -0.867591 q^{7} -2.13356 q^{8} -2.95972 q^{9} +O(q^{10})\) \(q-2.22670 q^{2} +0.200688 q^{3} +2.95817 q^{4} +3.39958 q^{5} -0.446870 q^{6} -0.867591 q^{7} -2.13356 q^{8} -2.95972 q^{9} -7.56983 q^{10} -1.00000 q^{11} +0.593668 q^{12} -5.52527 q^{13} +1.93186 q^{14} +0.682253 q^{15} -1.16556 q^{16} +3.54049 q^{17} +6.59040 q^{18} +0.206834 q^{19} +10.0565 q^{20} -0.174115 q^{21} +2.22670 q^{22} +6.80589 q^{23} -0.428178 q^{24} +6.55714 q^{25} +12.3031 q^{26} -1.19604 q^{27} -2.56648 q^{28} +3.50942 q^{29} -1.51917 q^{30} +3.97784 q^{31} +6.86247 q^{32} -0.200688 q^{33} -7.88359 q^{34} -2.94944 q^{35} -8.75537 q^{36} +5.88133 q^{37} -0.460555 q^{38} -1.10885 q^{39} -7.25320 q^{40} -0.545479 q^{41} +0.387700 q^{42} -9.67460 q^{43} -2.95817 q^{44} -10.0618 q^{45} -15.1546 q^{46} +12.1133 q^{47} -0.233914 q^{48} -6.24729 q^{49} -14.6008 q^{50} +0.710532 q^{51} -16.3447 q^{52} -4.89427 q^{53} +2.66322 q^{54} -3.39958 q^{55} +1.85105 q^{56} +0.0415089 q^{57} -7.81440 q^{58} +6.94782 q^{59} +2.01822 q^{60} +0.613662 q^{61} -8.85743 q^{62} +2.56783 q^{63} -12.9495 q^{64} -18.7836 q^{65} +0.446870 q^{66} -12.1450 q^{67} +10.4734 q^{68} +1.36586 q^{69} +6.56751 q^{70} +2.13501 q^{71} +6.31474 q^{72} -0.891895 q^{73} -13.0959 q^{74} +1.31594 q^{75} +0.611849 q^{76} +0.867591 q^{77} +2.46908 q^{78} -8.08839 q^{79} -3.96242 q^{80} +8.63914 q^{81} +1.21462 q^{82} -0.211727 q^{83} -0.515061 q^{84} +12.0362 q^{85} +21.5424 q^{86} +0.704296 q^{87} +2.13356 q^{88} -6.97044 q^{89} +22.4046 q^{90} +4.79367 q^{91} +20.1330 q^{92} +0.798302 q^{93} -26.9725 q^{94} +0.703147 q^{95} +1.37721 q^{96} -3.76158 q^{97} +13.9108 q^{98} +2.95972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22670 −1.57451 −0.787256 0.616627i \(-0.788499\pi\)
−0.787256 + 0.616627i \(0.788499\pi\)
\(3\) 0.200688 0.115867 0.0579335 0.998320i \(-0.481549\pi\)
0.0579335 + 0.998320i \(0.481549\pi\)
\(4\) 2.95817 1.47909
\(5\) 3.39958 1.52034 0.760169 0.649725i \(-0.225116\pi\)
0.760169 + 0.649725i \(0.225116\pi\)
\(6\) −0.446870 −0.182434
\(7\) −0.867591 −0.327918 −0.163959 0.986467i \(-0.552427\pi\)
−0.163959 + 0.986467i \(0.552427\pi\)
\(8\) −2.13356 −0.754326
\(9\) −2.95972 −0.986575
\(10\) −7.56983 −2.39379
\(11\) −1.00000 −0.301511
\(12\) 0.593668 0.171377
\(13\) −5.52527 −1.53243 −0.766217 0.642582i \(-0.777863\pi\)
−0.766217 + 0.642582i \(0.777863\pi\)
\(14\) 1.93186 0.516311
\(15\) 0.682253 0.176157
\(16\) −1.16556 −0.291391
\(17\) 3.54049 0.858695 0.429347 0.903139i \(-0.358744\pi\)
0.429347 + 0.903139i \(0.358744\pi\)
\(18\) 6.59040 1.55337
\(19\) 0.206834 0.0474509 0.0237254 0.999719i \(-0.492447\pi\)
0.0237254 + 0.999719i \(0.492447\pi\)
\(20\) 10.0565 2.24871
\(21\) −0.174115 −0.0379949
\(22\) 2.22670 0.474733
\(23\) 6.80589 1.41913 0.709563 0.704642i \(-0.248892\pi\)
0.709563 + 0.704642i \(0.248892\pi\)
\(24\) −0.428178 −0.0874016
\(25\) 6.55714 1.31143
\(26\) 12.3031 2.41283
\(27\) −1.19604 −0.230179
\(28\) −2.56648 −0.485020
\(29\) 3.50942 0.651682 0.325841 0.945425i \(-0.394353\pi\)
0.325841 + 0.945425i \(0.394353\pi\)
\(30\) −1.51917 −0.277361
\(31\) 3.97784 0.714441 0.357220 0.934020i \(-0.383725\pi\)
0.357220 + 0.934020i \(0.383725\pi\)
\(32\) 6.86247 1.21312
\(33\) −0.200688 −0.0349352
\(34\) −7.88359 −1.35202
\(35\) −2.94944 −0.498547
\(36\) −8.75537 −1.45923
\(37\) 5.88133 0.966885 0.483442 0.875376i \(-0.339386\pi\)
0.483442 + 0.875376i \(0.339386\pi\)
\(38\) −0.460555 −0.0747119
\(39\) −1.10885 −0.177559
\(40\) −7.25320 −1.14683
\(41\) −0.545479 −0.0851895 −0.0425948 0.999092i \(-0.513562\pi\)
−0.0425948 + 0.999092i \(0.513562\pi\)
\(42\) 0.387700 0.0598235
\(43\) −9.67460 −1.47536 −0.737682 0.675149i \(-0.764079\pi\)
−0.737682 + 0.675149i \(0.764079\pi\)
\(44\) −2.95817 −0.445961
\(45\) −10.0618 −1.49993
\(46\) −15.1546 −2.23443
\(47\) 12.1133 1.76690 0.883450 0.468526i \(-0.155215\pi\)
0.883450 + 0.468526i \(0.155215\pi\)
\(48\) −0.233914 −0.0337626
\(49\) −6.24729 −0.892470
\(50\) −14.6008 −2.06486
\(51\) 0.710532 0.0994944
\(52\) −16.3447 −2.26660
\(53\) −4.89427 −0.672280 −0.336140 0.941812i \(-0.609121\pi\)
−0.336140 + 0.941812i \(0.609121\pi\)
\(54\) 2.66322 0.362419
\(55\) −3.39958 −0.458399
\(56\) 1.85105 0.247358
\(57\) 0.0415089 0.00549799
\(58\) −7.81440 −1.02608
\(59\) 6.94782 0.904529 0.452264 0.891884i \(-0.350616\pi\)
0.452264 + 0.891884i \(0.350616\pi\)
\(60\) 2.01822 0.260551
\(61\) 0.613662 0.0785714 0.0392857 0.999228i \(-0.487492\pi\)
0.0392857 + 0.999228i \(0.487492\pi\)
\(62\) −8.85743 −1.12489
\(63\) 2.56783 0.323516
\(64\) −12.9495 −1.61869
\(65\) −18.7836 −2.32982
\(66\) 0.446870 0.0550059
\(67\) −12.1450 −1.48375 −0.741876 0.670537i \(-0.766064\pi\)
−0.741876 + 0.670537i \(0.766064\pi\)
\(68\) 10.4734 1.27008
\(69\) 1.36586 0.164430
\(70\) 6.56751 0.784968
\(71\) 2.13501 0.253378 0.126689 0.991942i \(-0.459565\pi\)
0.126689 + 0.991942i \(0.459565\pi\)
\(72\) 6.31474 0.744199
\(73\) −0.891895 −0.104388 −0.0521942 0.998637i \(-0.516621\pi\)
−0.0521942 + 0.998637i \(0.516621\pi\)
\(74\) −13.0959 −1.52237
\(75\) 1.31594 0.151951
\(76\) 0.611849 0.0701839
\(77\) 0.867591 0.0988711
\(78\) 2.46908 0.279568
\(79\) −8.08839 −0.910015 −0.455007 0.890488i \(-0.650363\pi\)
−0.455007 + 0.890488i \(0.650363\pi\)
\(80\) −3.96242 −0.443012
\(81\) 8.63914 0.959905
\(82\) 1.21462 0.134132
\(83\) −0.211727 −0.0232401 −0.0116200 0.999932i \(-0.503699\pi\)
−0.0116200 + 0.999932i \(0.503699\pi\)
\(84\) −0.515061 −0.0561978
\(85\) 12.0362 1.30551
\(86\) 21.5424 2.32298
\(87\) 0.704296 0.0755085
\(88\) 2.13356 0.227438
\(89\) −6.97044 −0.738865 −0.369432 0.929258i \(-0.620448\pi\)
−0.369432 + 0.929258i \(0.620448\pi\)
\(90\) 22.4046 2.36165
\(91\) 4.79367 0.502513
\(92\) 20.1330 2.09901
\(93\) 0.798302 0.0827801
\(94\) −26.9725 −2.78200
\(95\) 0.703147 0.0721414
\(96\) 1.37721 0.140561
\(97\) −3.76158 −0.381931 −0.190966 0.981597i \(-0.561162\pi\)
−0.190966 + 0.981597i \(0.561162\pi\)
\(98\) 13.9108 1.40520
\(99\) 2.95972 0.297464
\(100\) 19.3971 1.93971
\(101\) 12.6052 1.25426 0.627130 0.778915i \(-0.284229\pi\)
0.627130 + 0.778915i \(0.284229\pi\)
\(102\) −1.58214 −0.156655
\(103\) 5.51936 0.543838 0.271919 0.962320i \(-0.412342\pi\)
0.271919 + 0.962320i \(0.412342\pi\)
\(104\) 11.7885 1.15596
\(105\) −0.591917 −0.0577651
\(106\) 10.8980 1.05851
\(107\) −11.8705 −1.14756 −0.573780 0.819009i \(-0.694524\pi\)
−0.573780 + 0.819009i \(0.694524\pi\)
\(108\) −3.53810 −0.340454
\(109\) 6.29863 0.603299 0.301650 0.953419i \(-0.402463\pi\)
0.301650 + 0.953419i \(0.402463\pi\)
\(110\) 7.56983 0.721755
\(111\) 1.18031 0.112030
\(112\) 1.01123 0.0955523
\(113\) 0.891285 0.0838450 0.0419225 0.999121i \(-0.486652\pi\)
0.0419225 + 0.999121i \(0.486652\pi\)
\(114\) −0.0924277 −0.00865665
\(115\) 23.1372 2.15755
\(116\) 10.3815 0.963894
\(117\) 16.3533 1.51186
\(118\) −15.4707 −1.42419
\(119\) −3.07169 −0.281582
\(120\) −1.45563 −0.132880
\(121\) 1.00000 0.0909091
\(122\) −1.36644 −0.123712
\(123\) −0.109471 −0.00987066
\(124\) 11.7671 1.05672
\(125\) 5.29362 0.473476
\(126\) −5.71777 −0.509380
\(127\) −13.1468 −1.16659 −0.583296 0.812259i \(-0.698237\pi\)
−0.583296 + 0.812259i \(0.698237\pi\)
\(128\) 15.1097 1.33552
\(129\) −1.94157 −0.170946
\(130\) 41.8253 3.66832
\(131\) 9.90183 0.865127 0.432564 0.901603i \(-0.357609\pi\)
0.432564 + 0.901603i \(0.357609\pi\)
\(132\) −0.593668 −0.0516722
\(133\) −0.179447 −0.0155600
\(134\) 27.0433 2.33618
\(135\) −4.06604 −0.349949
\(136\) −7.55384 −0.647736
\(137\) 16.1414 1.37906 0.689528 0.724259i \(-0.257818\pi\)
0.689528 + 0.724259i \(0.257818\pi\)
\(138\) −3.04135 −0.258897
\(139\) 1.53194 0.129937 0.0649687 0.997887i \(-0.479305\pi\)
0.0649687 + 0.997887i \(0.479305\pi\)
\(140\) −8.72496 −0.737394
\(141\) 2.43098 0.204725
\(142\) −4.75401 −0.398947
\(143\) 5.52527 0.462046
\(144\) 3.44974 0.287479
\(145\) 11.9305 0.990777
\(146\) 1.98598 0.164361
\(147\) −1.25375 −0.103408
\(148\) 17.3980 1.43011
\(149\) 1.77842 0.145694 0.0728469 0.997343i \(-0.476792\pi\)
0.0728469 + 0.997343i \(0.476792\pi\)
\(150\) −2.93019 −0.239249
\(151\) −1.31045 −0.106643 −0.0533215 0.998577i \(-0.516981\pi\)
−0.0533215 + 0.998577i \(0.516981\pi\)
\(152\) −0.441291 −0.0357934
\(153\) −10.4789 −0.847166
\(154\) −1.93186 −0.155674
\(155\) 13.5230 1.08619
\(156\) −3.28018 −0.262624
\(157\) 4.29705 0.342942 0.171471 0.985189i \(-0.445148\pi\)
0.171471 + 0.985189i \(0.445148\pi\)
\(158\) 18.0104 1.43283
\(159\) −0.982219 −0.0778950
\(160\) 23.3295 1.84436
\(161\) −5.90473 −0.465358
\(162\) −19.2367 −1.51138
\(163\) −16.9369 −1.32660 −0.663298 0.748355i \(-0.730844\pi\)
−0.663298 + 0.748355i \(0.730844\pi\)
\(164\) −1.61362 −0.126003
\(165\) −0.682253 −0.0531134
\(166\) 0.471452 0.0365918
\(167\) −19.2890 −1.49263 −0.746315 0.665592i \(-0.768179\pi\)
−0.746315 + 0.665592i \(0.768179\pi\)
\(168\) 0.371484 0.0286606
\(169\) 17.5286 1.34835
\(170\) −26.8009 −2.05553
\(171\) −0.612170 −0.0468138
\(172\) −28.6191 −2.18219
\(173\) 7.62786 0.579936 0.289968 0.957036i \(-0.406355\pi\)
0.289968 + 0.957036i \(0.406355\pi\)
\(174\) −1.56825 −0.118889
\(175\) −5.68891 −0.430041
\(176\) 1.16556 0.0878575
\(177\) 1.39434 0.104805
\(178\) 15.5210 1.16335
\(179\) 24.1711 1.80663 0.903315 0.428978i \(-0.141126\pi\)
0.903315 + 0.428978i \(0.141126\pi\)
\(180\) −29.7646 −2.21852
\(181\) −0.0778879 −0.00578936 −0.00289468 0.999996i \(-0.500921\pi\)
−0.00289468 + 0.999996i \(0.500921\pi\)
\(182\) −10.6740 −0.791213
\(183\) 0.123154 0.00910384
\(184\) −14.5208 −1.07048
\(185\) 19.9941 1.46999
\(186\) −1.77758 −0.130338
\(187\) −3.54049 −0.258906
\(188\) 35.8331 2.61340
\(189\) 1.03768 0.0754798
\(190\) −1.56569 −0.113587
\(191\) 13.3915 0.968976 0.484488 0.874798i \(-0.339006\pi\)
0.484488 + 0.874798i \(0.339006\pi\)
\(192\) −2.59880 −0.187552
\(193\) 19.1370 1.37751 0.688754 0.724995i \(-0.258158\pi\)
0.688754 + 0.724995i \(0.258158\pi\)
\(194\) 8.37590 0.601355
\(195\) −3.76963 −0.269949
\(196\) −18.4805 −1.32004
\(197\) −4.16251 −0.296566 −0.148283 0.988945i \(-0.547375\pi\)
−0.148283 + 0.988945i \(0.547375\pi\)
\(198\) −6.59040 −0.468360
\(199\) 18.2806 1.29588 0.647938 0.761693i \(-0.275632\pi\)
0.647938 + 0.761693i \(0.275632\pi\)
\(200\) −13.9900 −0.989245
\(201\) −2.43736 −0.171918
\(202\) −28.0678 −1.97485
\(203\) −3.04474 −0.213699
\(204\) 2.10188 0.147161
\(205\) −1.85440 −0.129517
\(206\) −12.2899 −0.856280
\(207\) −20.1436 −1.40007
\(208\) 6.44004 0.446537
\(209\) −0.206834 −0.0143070
\(210\) 1.31802 0.0909519
\(211\) 6.48189 0.446232 0.223116 0.974792i \(-0.428377\pi\)
0.223116 + 0.974792i \(0.428377\pi\)
\(212\) −14.4781 −0.994359
\(213\) 0.428469 0.0293582
\(214\) 26.4319 1.80685
\(215\) −32.8896 −2.24305
\(216\) 2.55183 0.173630
\(217\) −3.45113 −0.234278
\(218\) −14.0251 −0.949902
\(219\) −0.178992 −0.0120952
\(220\) −10.0565 −0.678012
\(221\) −19.5622 −1.31589
\(222\) −2.62819 −0.176393
\(223\) 2.33809 0.156570 0.0782849 0.996931i \(-0.475056\pi\)
0.0782849 + 0.996931i \(0.475056\pi\)
\(224\) −5.95381 −0.397806
\(225\) −19.4073 −1.29382
\(226\) −1.98462 −0.132015
\(227\) 14.5517 0.965833 0.482916 0.875666i \(-0.339577\pi\)
0.482916 + 0.875666i \(0.339577\pi\)
\(228\) 0.122791 0.00813200
\(229\) −10.6450 −0.703440 −0.351720 0.936105i \(-0.614403\pi\)
−0.351720 + 0.936105i \(0.614403\pi\)
\(230\) −51.5194 −3.39709
\(231\) 0.174115 0.0114559
\(232\) −7.48754 −0.491581
\(233\) 21.1216 1.38372 0.691861 0.722031i \(-0.256791\pi\)
0.691861 + 0.722031i \(0.256791\pi\)
\(234\) −36.4138 −2.38044
\(235\) 41.1800 2.68628
\(236\) 20.5528 1.33788
\(237\) −1.62324 −0.105441
\(238\) 6.83973 0.443354
\(239\) 11.7416 0.759503 0.379752 0.925088i \(-0.376009\pi\)
0.379752 + 0.925088i \(0.376009\pi\)
\(240\) −0.795209 −0.0513305
\(241\) −11.0347 −0.710807 −0.355404 0.934713i \(-0.615657\pi\)
−0.355404 + 0.934713i \(0.615657\pi\)
\(242\) −2.22670 −0.143137
\(243\) 5.32190 0.341400
\(244\) 1.81532 0.116214
\(245\) −21.2381 −1.35686
\(246\) 0.243758 0.0155415
\(247\) −1.14281 −0.0727153
\(248\) −8.48694 −0.538921
\(249\) −0.0424910 −0.00269276
\(250\) −11.7873 −0.745493
\(251\) −14.4514 −0.912163 −0.456081 0.889938i \(-0.650747\pi\)
−0.456081 + 0.889938i \(0.650747\pi\)
\(252\) 7.59608 0.478508
\(253\) −6.80589 −0.427883
\(254\) 29.2740 1.83681
\(255\) 2.41551 0.151265
\(256\) −7.74560 −0.484100
\(257\) 29.7081 1.85314 0.926570 0.376122i \(-0.122743\pi\)
0.926570 + 0.376122i \(0.122743\pi\)
\(258\) 4.32329 0.269156
\(259\) −5.10259 −0.317059
\(260\) −55.5651 −3.44600
\(261\) −10.3869 −0.642933
\(262\) −22.0484 −1.36215
\(263\) −5.13200 −0.316453 −0.158226 0.987403i \(-0.550578\pi\)
−0.158226 + 0.987403i \(0.550578\pi\)
\(264\) 0.428178 0.0263526
\(265\) −16.6385 −1.02209
\(266\) 0.399573 0.0244994
\(267\) −1.39888 −0.0856101
\(268\) −35.9271 −2.19460
\(269\) −1.71440 −0.104529 −0.0522643 0.998633i \(-0.516644\pi\)
−0.0522643 + 0.998633i \(0.516644\pi\)
\(270\) 9.05384 0.550999
\(271\) −6.55748 −0.398339 −0.199169 0.979965i \(-0.563824\pi\)
−0.199169 + 0.979965i \(0.563824\pi\)
\(272\) −4.12666 −0.250215
\(273\) 0.962030 0.0582247
\(274\) −35.9420 −2.17134
\(275\) −6.55714 −0.395410
\(276\) 4.04044 0.243206
\(277\) −4.60961 −0.276965 −0.138482 0.990365i \(-0.544222\pi\)
−0.138482 + 0.990365i \(0.544222\pi\)
\(278\) −3.41116 −0.204588
\(279\) −11.7733 −0.704849
\(280\) 6.29281 0.376067
\(281\) −0.333156 −0.0198744 −0.00993721 0.999951i \(-0.503163\pi\)
−0.00993721 + 0.999951i \(0.503163\pi\)
\(282\) −5.41305 −0.322342
\(283\) 30.9189 1.83794 0.918969 0.394330i \(-0.129023\pi\)
0.918969 + 0.394330i \(0.129023\pi\)
\(284\) 6.31571 0.374769
\(285\) 0.141113 0.00835880
\(286\) −12.3031 −0.727497
\(287\) 0.473252 0.0279352
\(288\) −20.3110 −1.19684
\(289\) −4.46494 −0.262644
\(290\) −26.5657 −1.55999
\(291\) −0.754903 −0.0442532
\(292\) −2.63838 −0.154399
\(293\) −15.5290 −0.907212 −0.453606 0.891202i \(-0.649863\pi\)
−0.453606 + 0.891202i \(0.649863\pi\)
\(294\) 2.79173 0.162817
\(295\) 23.6197 1.37519
\(296\) −12.5482 −0.729347
\(297\) 1.19604 0.0694014
\(298\) −3.96000 −0.229397
\(299\) −37.6044 −2.17472
\(300\) 3.89277 0.224749
\(301\) 8.39359 0.483799
\(302\) 2.91798 0.167911
\(303\) 2.52970 0.145327
\(304\) −0.241077 −0.0138267
\(305\) 2.08619 0.119455
\(306\) 23.3333 1.33387
\(307\) 24.1617 1.37898 0.689491 0.724294i \(-0.257834\pi\)
0.689491 + 0.724294i \(0.257834\pi\)
\(308\) 2.56648 0.146239
\(309\) 1.10767 0.0630129
\(310\) −30.1115 −1.71022
\(311\) 1.57570 0.0893498 0.0446749 0.999002i \(-0.485775\pi\)
0.0446749 + 0.999002i \(0.485775\pi\)
\(312\) 2.36580 0.133937
\(313\) 30.2000 1.70701 0.853504 0.521087i \(-0.174473\pi\)
0.853504 + 0.521087i \(0.174473\pi\)
\(314\) −9.56822 −0.539966
\(315\) 8.72954 0.491854
\(316\) −23.9268 −1.34599
\(317\) 18.1383 1.01875 0.509375 0.860545i \(-0.329877\pi\)
0.509375 + 0.860545i \(0.329877\pi\)
\(318\) 2.18710 0.122647
\(319\) −3.50942 −0.196490
\(320\) −44.0228 −2.46095
\(321\) −2.38225 −0.132964
\(322\) 13.1480 0.732711
\(323\) 0.732292 0.0407458
\(324\) 25.5561 1.41978
\(325\) −36.2300 −2.00968
\(326\) 37.7132 2.08874
\(327\) 1.26406 0.0699025
\(328\) 1.16381 0.0642607
\(329\) −10.5093 −0.579399
\(330\) 1.51917 0.0836276
\(331\) 24.0653 1.32275 0.661374 0.750056i \(-0.269974\pi\)
0.661374 + 0.750056i \(0.269974\pi\)
\(332\) −0.626326 −0.0343741
\(333\) −17.4071 −0.953904
\(334\) 42.9508 2.35016
\(335\) −41.2880 −2.25580
\(336\) 0.202941 0.0110714
\(337\) 29.4864 1.60623 0.803113 0.595826i \(-0.203175\pi\)
0.803113 + 0.595826i \(0.203175\pi\)
\(338\) −39.0308 −2.12300
\(339\) 0.178870 0.00971487
\(340\) 35.6051 1.93096
\(341\) −3.97784 −0.215412
\(342\) 1.36312 0.0737089
\(343\) 11.4932 0.620576
\(344\) 20.6413 1.11291
\(345\) 4.64334 0.249989
\(346\) −16.9849 −0.913115
\(347\) 11.4900 0.616817 0.308408 0.951254i \(-0.400204\pi\)
0.308408 + 0.951254i \(0.400204\pi\)
\(348\) 2.08343 0.111684
\(349\) −34.6108 −1.85267 −0.926337 0.376695i \(-0.877060\pi\)
−0.926337 + 0.376695i \(0.877060\pi\)
\(350\) 12.6675 0.677105
\(351\) 6.60846 0.352733
\(352\) −6.86247 −0.365771
\(353\) 35.6310 1.89644 0.948222 0.317607i \(-0.102879\pi\)
0.948222 + 0.317607i \(0.102879\pi\)
\(354\) −3.10477 −0.165017
\(355\) 7.25812 0.385221
\(356\) −20.6198 −1.09284
\(357\) −0.616451 −0.0326260
\(358\) −53.8216 −2.84456
\(359\) 22.0620 1.16439 0.582193 0.813051i \(-0.302195\pi\)
0.582193 + 0.813051i \(0.302195\pi\)
\(360\) 21.4675 1.13143
\(361\) −18.9572 −0.997748
\(362\) 0.173433 0.00911541
\(363\) 0.200688 0.0105334
\(364\) 14.1805 0.743260
\(365\) −3.03207 −0.158706
\(366\) −0.274227 −0.0143341
\(367\) 21.1231 1.10262 0.551308 0.834302i \(-0.314129\pi\)
0.551308 + 0.834302i \(0.314129\pi\)
\(368\) −7.93269 −0.413520
\(369\) 1.61447 0.0840458
\(370\) −44.5207 −2.31452
\(371\) 4.24622 0.220453
\(372\) 2.36152 0.122439
\(373\) −2.33252 −0.120774 −0.0603868 0.998175i \(-0.519233\pi\)
−0.0603868 + 0.998175i \(0.519233\pi\)
\(374\) 7.88359 0.407651
\(375\) 1.06236 0.0548602
\(376\) −25.8443 −1.33282
\(377\) −19.3905 −0.998660
\(378\) −2.31059 −0.118844
\(379\) 29.0418 1.49178 0.745890 0.666070i \(-0.232025\pi\)
0.745890 + 0.666070i \(0.232025\pi\)
\(380\) 2.08003 0.106703
\(381\) −2.63841 −0.135170
\(382\) −29.8188 −1.52566
\(383\) −7.20579 −0.368199 −0.184099 0.982908i \(-0.558937\pi\)
−0.184099 + 0.982908i \(0.558937\pi\)
\(384\) 3.03232 0.154742
\(385\) 2.94944 0.150318
\(386\) −42.6122 −2.16890
\(387\) 28.6342 1.45556
\(388\) −11.1274 −0.564909
\(389\) −32.3934 −1.64241 −0.821205 0.570634i \(-0.806698\pi\)
−0.821205 + 0.570634i \(0.806698\pi\)
\(390\) 8.39383 0.425038
\(391\) 24.0962 1.21860
\(392\) 13.3289 0.673213
\(393\) 1.98718 0.100240
\(394\) 9.26863 0.466947
\(395\) −27.4971 −1.38353
\(396\) 8.75537 0.439974
\(397\) 2.63480 0.132237 0.0661184 0.997812i \(-0.478939\pi\)
0.0661184 + 0.997812i \(0.478939\pi\)
\(398\) −40.7053 −2.04037
\(399\) −0.0360127 −0.00180289
\(400\) −7.64275 −0.382138
\(401\) 5.89790 0.294527 0.147264 0.989097i \(-0.452953\pi\)
0.147264 + 0.989097i \(0.452953\pi\)
\(402\) 5.42725 0.270687
\(403\) −21.9786 −1.09483
\(404\) 37.2882 1.85516
\(405\) 29.3695 1.45938
\(406\) 6.77970 0.336471
\(407\) −5.88133 −0.291527
\(408\) −1.51596 −0.0750513
\(409\) −2.42631 −0.119973 −0.0599865 0.998199i \(-0.519106\pi\)
−0.0599865 + 0.998199i \(0.519106\pi\)
\(410\) 4.12918 0.203926
\(411\) 3.23938 0.159787
\(412\) 16.3272 0.804384
\(413\) −6.02786 −0.296612
\(414\) 44.8536 2.20443
\(415\) −0.719784 −0.0353328
\(416\) −37.9170 −1.85903
\(417\) 0.307441 0.0150555
\(418\) 0.460555 0.0225265
\(419\) −1.98956 −0.0971965 −0.0485982 0.998818i \(-0.515475\pi\)
−0.0485982 + 0.998818i \(0.515475\pi\)
\(420\) −1.75099 −0.0854396
\(421\) 5.05322 0.246279 0.123139 0.992389i \(-0.460704\pi\)
0.123139 + 0.992389i \(0.460704\pi\)
\(422\) −14.4332 −0.702597
\(423\) −35.8519 −1.74318
\(424\) 10.4422 0.507118
\(425\) 23.2155 1.12612
\(426\) −0.954070 −0.0462248
\(427\) −0.532408 −0.0257650
\(428\) −35.1149 −1.69734
\(429\) 1.10885 0.0535359
\(430\) 73.2351 3.53171
\(431\) 19.1611 0.922957 0.461479 0.887151i \(-0.347319\pi\)
0.461479 + 0.887151i \(0.347319\pi\)
\(432\) 1.39406 0.0670718
\(433\) −7.38041 −0.354680 −0.177340 0.984150i \(-0.556749\pi\)
−0.177340 + 0.984150i \(0.556749\pi\)
\(434\) 7.68462 0.368874
\(435\) 2.39431 0.114798
\(436\) 18.6324 0.892331
\(437\) 1.40769 0.0673388
\(438\) 0.398561 0.0190440
\(439\) −14.7902 −0.705900 −0.352950 0.935642i \(-0.614821\pi\)
−0.352950 + 0.935642i \(0.614821\pi\)
\(440\) 7.25320 0.345783
\(441\) 18.4902 0.880488
\(442\) 43.5590 2.07189
\(443\) 3.39973 0.161526 0.0807631 0.996733i \(-0.474264\pi\)
0.0807631 + 0.996733i \(0.474264\pi\)
\(444\) 3.49156 0.165702
\(445\) −23.6966 −1.12332
\(446\) −5.20621 −0.246521
\(447\) 0.356907 0.0168811
\(448\) 11.2349 0.530797
\(449\) −24.4752 −1.15506 −0.577529 0.816370i \(-0.695983\pi\)
−0.577529 + 0.816370i \(0.695983\pi\)
\(450\) 43.2142 2.03714
\(451\) 0.545479 0.0256856
\(452\) 2.63657 0.124014
\(453\) −0.262991 −0.0123564
\(454\) −32.4023 −1.52071
\(455\) 16.2965 0.763990
\(456\) −0.0885617 −0.00414728
\(457\) 31.2420 1.46144 0.730719 0.682678i \(-0.239185\pi\)
0.730719 + 0.682678i \(0.239185\pi\)
\(458\) 23.7031 1.10757
\(459\) −4.23458 −0.197653
\(460\) 68.4437 3.19120
\(461\) 4.82516 0.224730 0.112365 0.993667i \(-0.464157\pi\)
0.112365 + 0.993667i \(0.464157\pi\)
\(462\) −0.387700 −0.0180375
\(463\) 39.9837 1.85820 0.929101 0.369826i \(-0.120583\pi\)
0.929101 + 0.369826i \(0.120583\pi\)
\(464\) −4.09044 −0.189894
\(465\) 2.71389 0.125854
\(466\) −47.0314 −2.17869
\(467\) 36.3976 1.68428 0.842141 0.539258i \(-0.181295\pi\)
0.842141 + 0.539258i \(0.181295\pi\)
\(468\) 48.3758 2.23617
\(469\) 10.5369 0.486550
\(470\) −91.6952 −4.22959
\(471\) 0.862364 0.0397357
\(472\) −14.8236 −0.682310
\(473\) 9.67460 0.444839
\(474\) 3.61446 0.166018
\(475\) 1.35624 0.0622284
\(476\) −9.08660 −0.416484
\(477\) 14.4857 0.663254
\(478\) −26.1450 −1.19585
\(479\) −13.8960 −0.634926 −0.317463 0.948271i \(-0.602831\pi\)
−0.317463 + 0.948271i \(0.602831\pi\)
\(480\) 4.68194 0.213700
\(481\) −32.4959 −1.48169
\(482\) 24.5709 1.11917
\(483\) −1.18501 −0.0539196
\(484\) 2.95817 0.134462
\(485\) −12.7878 −0.580664
\(486\) −11.8502 −0.537538
\(487\) 14.4811 0.656201 0.328101 0.944643i \(-0.393592\pi\)
0.328101 + 0.944643i \(0.393592\pi\)
\(488\) −1.30928 −0.0592685
\(489\) −3.39902 −0.153709
\(490\) 47.2909 2.13638
\(491\) 16.9051 0.762917 0.381458 0.924386i \(-0.375422\pi\)
0.381458 + 0.924386i \(0.375422\pi\)
\(492\) −0.323834 −0.0145995
\(493\) 12.4250 0.559596
\(494\) 2.54469 0.114491
\(495\) 10.0618 0.452245
\(496\) −4.63642 −0.208181
\(497\) −1.85231 −0.0830875
\(498\) 0.0946146 0.00423978
\(499\) −26.4697 −1.18495 −0.592474 0.805589i \(-0.701849\pi\)
−0.592474 + 0.805589i \(0.701849\pi\)
\(500\) 15.6594 0.700311
\(501\) −3.87107 −0.172947
\(502\) 32.1788 1.43621
\(503\) −8.81374 −0.392985 −0.196493 0.980505i \(-0.562955\pi\)
−0.196493 + 0.980505i \(0.562955\pi\)
\(504\) −5.47861 −0.244037
\(505\) 42.8522 1.90690
\(506\) 15.1546 0.673706
\(507\) 3.51777 0.156230
\(508\) −38.8906 −1.72549
\(509\) −19.9660 −0.884976 −0.442488 0.896774i \(-0.645904\pi\)
−0.442488 + 0.896774i \(0.645904\pi\)
\(510\) −5.37861 −0.238169
\(511\) 0.773800 0.0342309
\(512\) −12.9722 −0.573296
\(513\) −0.247382 −0.0109222
\(514\) −66.1509 −2.91779
\(515\) 18.7635 0.826818
\(516\) −5.74351 −0.252844
\(517\) −12.1133 −0.532740
\(518\) 11.3619 0.499214
\(519\) 1.53082 0.0671954
\(520\) 40.0759 1.75744
\(521\) 17.2473 0.755618 0.377809 0.925884i \(-0.376678\pi\)
0.377809 + 0.925884i \(0.376678\pi\)
\(522\) 23.1285 1.01231
\(523\) −4.71318 −0.206093 −0.103047 0.994677i \(-0.532859\pi\)
−0.103047 + 0.994677i \(0.532859\pi\)
\(524\) 29.2913 1.27960
\(525\) −1.14169 −0.0498276
\(526\) 11.4274 0.498259
\(527\) 14.0835 0.613486
\(528\) 0.233914 0.0101798
\(529\) 23.3201 1.01392
\(530\) 37.0488 1.60930
\(531\) −20.5636 −0.892386
\(532\) −0.530835 −0.0230146
\(533\) 3.01392 0.130547
\(534\) 3.11488 0.134794
\(535\) −40.3546 −1.74468
\(536\) 25.9121 1.11923
\(537\) 4.85083 0.209329
\(538\) 3.81744 0.164582
\(539\) 6.24729 0.269090
\(540\) −12.0281 −0.517605
\(541\) 1.86579 0.0802166 0.0401083 0.999195i \(-0.487230\pi\)
0.0401083 + 0.999195i \(0.487230\pi\)
\(542\) 14.6015 0.627189
\(543\) −0.0156311 −0.000670796 0
\(544\) 24.2965 1.04170
\(545\) 21.4127 0.917219
\(546\) −2.14215 −0.0916755
\(547\) 1.00000 0.0427569
\(548\) 47.7491 2.03974
\(549\) −1.81627 −0.0775166
\(550\) 14.6008 0.622578
\(551\) 0.725865 0.0309229
\(552\) −2.91414 −0.124034
\(553\) 7.01741 0.298411
\(554\) 10.2642 0.436084
\(555\) 4.01256 0.170324
\(556\) 4.53174 0.192189
\(557\) −20.8609 −0.883904 −0.441952 0.897039i \(-0.645714\pi\)
−0.441952 + 0.897039i \(0.645714\pi\)
\(558\) 26.2156 1.10979
\(559\) 53.4548 2.26090
\(560\) 3.43776 0.145272
\(561\) −0.710532 −0.0299987
\(562\) 0.741837 0.0312925
\(563\) −18.7401 −0.789801 −0.394901 0.918724i \(-0.629221\pi\)
−0.394901 + 0.918724i \(0.629221\pi\)
\(564\) 7.19126 0.302807
\(565\) 3.02999 0.127473
\(566\) −68.8470 −2.89385
\(567\) −7.49524 −0.314770
\(568\) −4.55516 −0.191130
\(569\) −17.2556 −0.723394 −0.361697 0.932296i \(-0.617803\pi\)
−0.361697 + 0.932296i \(0.617803\pi\)
\(570\) −0.314215 −0.0131610
\(571\) −7.22806 −0.302485 −0.151242 0.988497i \(-0.548327\pi\)
−0.151242 + 0.988497i \(0.548327\pi\)
\(572\) 16.3447 0.683406
\(573\) 2.68751 0.112272
\(574\) −1.05379 −0.0439843
\(575\) 44.6272 1.86108
\(576\) 38.3269 1.59696
\(577\) −6.06438 −0.252464 −0.126232 0.992001i \(-0.540288\pi\)
−0.126232 + 0.992001i \(0.540288\pi\)
\(578\) 9.94206 0.413535
\(579\) 3.84055 0.159608
\(580\) 35.2926 1.46544
\(581\) 0.183693 0.00762085
\(582\) 1.68094 0.0696772
\(583\) 4.89427 0.202700
\(584\) 1.90291 0.0787430
\(585\) 55.5943 2.29854
\(586\) 34.5783 1.42842
\(587\) −30.9404 −1.27705 −0.638524 0.769602i \(-0.720455\pi\)
−0.638524 + 0.769602i \(0.720455\pi\)
\(588\) −3.70882 −0.152949
\(589\) 0.822750 0.0339008
\(590\) −52.5938 −2.16525
\(591\) −0.835363 −0.0343622
\(592\) −6.85506 −0.281741
\(593\) 8.18850 0.336261 0.168131 0.985765i \(-0.446227\pi\)
0.168131 + 0.985765i \(0.446227\pi\)
\(594\) −2.66322 −0.109273
\(595\) −10.4425 −0.428100
\(596\) 5.26087 0.215494
\(597\) 3.66868 0.150149
\(598\) 83.7335 3.42412
\(599\) 32.1275 1.31270 0.656348 0.754458i \(-0.272100\pi\)
0.656348 + 0.754458i \(0.272100\pi\)
\(600\) −2.80763 −0.114621
\(601\) −23.1252 −0.943297 −0.471648 0.881787i \(-0.656341\pi\)
−0.471648 + 0.881787i \(0.656341\pi\)
\(602\) −18.6900 −0.761747
\(603\) 35.9459 1.46383
\(604\) −3.87654 −0.157734
\(605\) 3.39958 0.138213
\(606\) −5.63287 −0.228820
\(607\) 18.9949 0.770981 0.385491 0.922712i \(-0.374032\pi\)
0.385491 + 0.922712i \(0.374032\pi\)
\(608\) 1.41939 0.0575638
\(609\) −0.611041 −0.0247606
\(610\) −4.64532 −0.188083
\(611\) −66.9290 −2.70766
\(612\) −30.9983 −1.25303
\(613\) 9.30281 0.375737 0.187869 0.982194i \(-0.439842\pi\)
0.187869 + 0.982194i \(0.439842\pi\)
\(614\) −53.8008 −2.17122
\(615\) −0.372155 −0.0150067
\(616\) −1.85105 −0.0745811
\(617\) 18.9104 0.761302 0.380651 0.924719i \(-0.375700\pi\)
0.380651 + 0.924719i \(0.375700\pi\)
\(618\) −2.46644 −0.0992146
\(619\) 26.4456 1.06294 0.531470 0.847077i \(-0.321640\pi\)
0.531470 + 0.847077i \(0.321640\pi\)
\(620\) 40.0033 1.60657
\(621\) −8.14013 −0.326652
\(622\) −3.50861 −0.140682
\(623\) 6.04749 0.242287
\(624\) 1.29244 0.0517389
\(625\) −14.7896 −0.591585
\(626\) −67.2463 −2.68770
\(627\) −0.0415089 −0.00165771
\(628\) 12.7114 0.507241
\(629\) 20.8228 0.830259
\(630\) −19.4380 −0.774429
\(631\) 3.72567 0.148317 0.0741583 0.997246i \(-0.476373\pi\)
0.0741583 + 0.997246i \(0.476373\pi\)
\(632\) 17.2570 0.686448
\(633\) 1.30084 0.0517036
\(634\) −40.3885 −1.60403
\(635\) −44.6937 −1.77362
\(636\) −2.90557 −0.115213
\(637\) 34.5179 1.36765
\(638\) 7.81440 0.309375
\(639\) −6.31903 −0.249977
\(640\) 51.3665 2.03044
\(641\) −32.3257 −1.27679 −0.638394 0.769710i \(-0.720401\pi\)
−0.638394 + 0.769710i \(0.720401\pi\)
\(642\) 5.30455 0.209354
\(643\) 14.9790 0.590713 0.295357 0.955387i \(-0.404562\pi\)
0.295357 + 0.955387i \(0.404562\pi\)
\(644\) −17.4672 −0.688304
\(645\) −6.60053 −0.259896
\(646\) −1.63059 −0.0641547
\(647\) 39.0331 1.53455 0.767275 0.641318i \(-0.221612\pi\)
0.767275 + 0.641318i \(0.221612\pi\)
\(648\) −18.4321 −0.724081
\(649\) −6.94782 −0.272726
\(650\) 80.6731 3.16426
\(651\) −0.692600 −0.0271451
\(652\) −50.1021 −1.96215
\(653\) 23.0434 0.901756 0.450878 0.892586i \(-0.351111\pi\)
0.450878 + 0.892586i \(0.351111\pi\)
\(654\) −2.81467 −0.110062
\(655\) 33.6621 1.31529
\(656\) 0.635790 0.0248234
\(657\) 2.63976 0.102987
\(658\) 23.4011 0.912270
\(659\) 35.5500 1.38483 0.692415 0.721499i \(-0.256547\pi\)
0.692415 + 0.721499i \(0.256547\pi\)
\(660\) −2.01822 −0.0785592
\(661\) −21.5004 −0.836267 −0.418133 0.908386i \(-0.637316\pi\)
−0.418133 + 0.908386i \(0.637316\pi\)
\(662\) −53.5861 −2.08268
\(663\) −3.92588 −0.152469
\(664\) 0.451732 0.0175306
\(665\) −0.610044 −0.0236565
\(666\) 38.7603 1.50193
\(667\) 23.8847 0.924819
\(668\) −57.0603 −2.20773
\(669\) 0.469225 0.0181413
\(670\) 91.9358 3.55179
\(671\) −0.613662 −0.0236902
\(672\) −1.19486 −0.0460926
\(673\) −0.0598608 −0.00230746 −0.00115373 0.999999i \(-0.500367\pi\)
−0.00115373 + 0.999999i \(0.500367\pi\)
\(674\) −65.6572 −2.52902
\(675\) −7.84262 −0.301863
\(676\) 51.8526 1.99433
\(677\) −2.11168 −0.0811584 −0.0405792 0.999176i \(-0.512920\pi\)
−0.0405792 + 0.999176i \(0.512920\pi\)
\(678\) −0.398288 −0.0152962
\(679\) 3.26352 0.125242
\(680\) −25.6799 −0.984778
\(681\) 2.92035 0.111908
\(682\) 8.85743 0.339169
\(683\) 31.7498 1.21487 0.607435 0.794369i \(-0.292198\pi\)
0.607435 + 0.794369i \(0.292198\pi\)
\(684\) −1.81090 −0.0692417
\(685\) 54.8741 2.09663
\(686\) −25.5919 −0.977103
\(687\) −2.13631 −0.0815055
\(688\) 11.2764 0.429907
\(689\) 27.0422 1.03022
\(690\) −10.3393 −0.393611
\(691\) −3.00187 −0.114197 −0.0570983 0.998369i \(-0.518185\pi\)
−0.0570983 + 0.998369i \(0.518185\pi\)
\(692\) 22.5645 0.857775
\(693\) −2.56783 −0.0975438
\(694\) −25.5848 −0.971185
\(695\) 5.20795 0.197549
\(696\) −1.50266 −0.0569580
\(697\) −1.93126 −0.0731518
\(698\) 77.0677 2.91706
\(699\) 4.23884 0.160328
\(700\) −16.8288 −0.636068
\(701\) 21.8108 0.823783 0.411892 0.911233i \(-0.364868\pi\)
0.411892 + 0.911233i \(0.364868\pi\)
\(702\) −14.7150 −0.555383
\(703\) 1.21646 0.0458795
\(704\) 12.9495 0.488053
\(705\) 8.26431 0.311252
\(706\) −79.3393 −2.98597
\(707\) −10.9361 −0.411295
\(708\) 4.12470 0.155016
\(709\) 2.83035 0.106296 0.0531480 0.998587i \(-0.483075\pi\)
0.0531480 + 0.998587i \(0.483075\pi\)
\(710\) −16.1616 −0.606535
\(711\) 23.9394 0.897798
\(712\) 14.8718 0.557345
\(713\) 27.0727 1.01388
\(714\) 1.37265 0.0513701
\(715\) 18.7836 0.702466
\(716\) 71.5022 2.67216
\(717\) 2.35640 0.0880014
\(718\) −49.1253 −1.83334
\(719\) 4.48456 0.167246 0.0836230 0.996497i \(-0.473351\pi\)
0.0836230 + 0.996497i \(0.473351\pi\)
\(720\) 11.7277 0.437065
\(721\) −4.78854 −0.178335
\(722\) 42.2120 1.57097
\(723\) −2.21453 −0.0823591
\(724\) −0.230406 −0.00856296
\(725\) 23.0117 0.854634
\(726\) −0.446870 −0.0165849
\(727\) −5.59601 −0.207545 −0.103772 0.994601i \(-0.533091\pi\)
−0.103772 + 0.994601i \(0.533091\pi\)
\(728\) −10.2276 −0.379059
\(729\) −24.8494 −0.920348
\(730\) 6.75149 0.249884
\(731\) −34.2528 −1.26689
\(732\) 0.364312 0.0134654
\(733\) −11.6629 −0.430780 −0.215390 0.976528i \(-0.569102\pi\)
−0.215390 + 0.976528i \(0.569102\pi\)
\(734\) −47.0347 −1.73608
\(735\) −4.26223 −0.157215
\(736\) 46.7052 1.72158
\(737\) 12.1450 0.447368
\(738\) −3.59493 −0.132331
\(739\) −39.1508 −1.44019 −0.720094 0.693877i \(-0.755901\pi\)
−0.720094 + 0.693877i \(0.755901\pi\)
\(740\) 59.1458 2.17424
\(741\) −0.229348 −0.00842531
\(742\) −9.45504 −0.347106
\(743\) −32.7690 −1.20218 −0.601090 0.799181i \(-0.705267\pi\)
−0.601090 + 0.799181i \(0.705267\pi\)
\(744\) −1.70322 −0.0624432
\(745\) 6.04588 0.221504
\(746\) 5.19382 0.190159
\(747\) 0.626654 0.0229281
\(748\) −10.4734 −0.382944
\(749\) 10.2987 0.376306
\(750\) −2.36556 −0.0863781
\(751\) 18.1478 0.662223 0.331111 0.943592i \(-0.392576\pi\)
0.331111 + 0.943592i \(0.392576\pi\)
\(752\) −14.1187 −0.514858
\(753\) −2.90021 −0.105690
\(754\) 43.1767 1.57240
\(755\) −4.45498 −0.162133
\(756\) 3.06962 0.111641
\(757\) −17.9111 −0.650989 −0.325494 0.945544i \(-0.605531\pi\)
−0.325494 + 0.945544i \(0.605531\pi\)
\(758\) −64.6673 −2.34882
\(759\) −1.36586 −0.0495775
\(760\) −1.50020 −0.0544181
\(761\) 24.5640 0.890443 0.445222 0.895420i \(-0.353125\pi\)
0.445222 + 0.895420i \(0.353125\pi\)
\(762\) 5.87493 0.212826
\(763\) −5.46463 −0.197833
\(764\) 39.6144 1.43320
\(765\) −35.6238 −1.28798
\(766\) 16.0451 0.579733
\(767\) −38.3886 −1.38613
\(768\) −1.55445 −0.0560912
\(769\) −3.14368 −0.113364 −0.0566820 0.998392i \(-0.518052\pi\)
−0.0566820 + 0.998392i \(0.518052\pi\)
\(770\) −6.56751 −0.236677
\(771\) 5.96205 0.214718
\(772\) 56.6104 2.03745
\(773\) −30.8113 −1.10821 −0.554103 0.832448i \(-0.686939\pi\)
−0.554103 + 0.832448i \(0.686939\pi\)
\(774\) −63.7595 −2.29179
\(775\) 26.0832 0.936937
\(776\) 8.02556 0.288101
\(777\) −1.02403 −0.0367367
\(778\) 72.1302 2.58599
\(779\) −0.112823 −0.00404232
\(780\) −11.1512 −0.399278
\(781\) −2.13501 −0.0763965
\(782\) −53.6548 −1.91869
\(783\) −4.19741 −0.150003
\(784\) 7.28160 0.260057
\(785\) 14.6082 0.521388
\(786\) −4.42483 −0.157829
\(787\) 30.7840 1.09733 0.548665 0.836042i \(-0.315136\pi\)
0.548665 + 0.836042i \(0.315136\pi\)
\(788\) −12.3134 −0.438647
\(789\) −1.02993 −0.0366664
\(790\) 61.2277 2.17838
\(791\) −0.773270 −0.0274943
\(792\) −6.31474 −0.224385
\(793\) −3.39065 −0.120406
\(794\) −5.86689 −0.208208
\(795\) −3.33913 −0.118427
\(796\) 54.0771 1.91671
\(797\) 14.3420 0.508019 0.254009 0.967202i \(-0.418251\pi\)
0.254009 + 0.967202i \(0.418251\pi\)
\(798\) 0.0801894 0.00283867
\(799\) 42.8868 1.51723
\(800\) 44.9982 1.59092
\(801\) 20.6306 0.728945
\(802\) −13.1328 −0.463737
\(803\) 0.891895 0.0314743
\(804\) −7.21012 −0.254281
\(805\) −20.0736 −0.707501
\(806\) 48.9397 1.72383
\(807\) −0.344058 −0.0121114
\(808\) −26.8938 −0.946122
\(809\) 16.1758 0.568711 0.284355 0.958719i \(-0.408220\pi\)
0.284355 + 0.958719i \(0.408220\pi\)
\(810\) −65.3968 −2.29781
\(811\) −41.2489 −1.44844 −0.724222 0.689567i \(-0.757801\pi\)
−0.724222 + 0.689567i \(0.757801\pi\)
\(812\) −9.00685 −0.316079
\(813\) −1.31601 −0.0461543
\(814\) 13.0959 0.459012
\(815\) −57.5782 −2.01688
\(816\) −0.828169 −0.0289917
\(817\) −2.00103 −0.0700073
\(818\) 5.40264 0.188899
\(819\) −14.1879 −0.495767
\(820\) −5.48563 −0.191567
\(821\) 16.5848 0.578812 0.289406 0.957206i \(-0.406542\pi\)
0.289406 + 0.957206i \(0.406542\pi\)
\(822\) −7.21312 −0.251587
\(823\) 37.2624 1.29889 0.649443 0.760410i \(-0.275002\pi\)
0.649443 + 0.760410i \(0.275002\pi\)
\(824\) −11.7759 −0.410232
\(825\) −1.31594 −0.0458150
\(826\) 13.4222 0.467019
\(827\) −40.3798 −1.40414 −0.702071 0.712107i \(-0.747741\pi\)
−0.702071 + 0.712107i \(0.747741\pi\)
\(828\) −59.5881 −2.07083
\(829\) −40.7782 −1.41628 −0.708142 0.706070i \(-0.750466\pi\)
−0.708142 + 0.706070i \(0.750466\pi\)
\(830\) 1.60274 0.0556319
\(831\) −0.925092 −0.0320911
\(832\) 71.5495 2.48053
\(833\) −22.1184 −0.766359
\(834\) −0.684578 −0.0237050
\(835\) −65.5746 −2.26930
\(836\) −0.611849 −0.0211612
\(837\) −4.75766 −0.164449
\(838\) 4.43015 0.153037
\(839\) 55.0965 1.90214 0.951072 0.308971i \(-0.0999845\pi\)
0.951072 + 0.308971i \(0.0999845\pi\)
\(840\) 1.26289 0.0435738
\(841\) −16.6840 −0.575310
\(842\) −11.2520 −0.387769
\(843\) −0.0668603 −0.00230279
\(844\) 19.1746 0.660015
\(845\) 59.5899 2.04995
\(846\) 79.8312 2.74465
\(847\) −0.867591 −0.0298108
\(848\) 5.70457 0.195896
\(849\) 6.20504 0.212956
\(850\) −51.6938 −1.77308
\(851\) 40.0277 1.37213
\(852\) 1.26749 0.0434233
\(853\) −35.5855 −1.21842 −0.609211 0.793008i \(-0.708514\pi\)
−0.609211 + 0.793008i \(0.708514\pi\)
\(854\) 1.18551 0.0405673
\(855\) −2.08112 −0.0711728
\(856\) 25.3263 0.865635
\(857\) 23.4393 0.800672 0.400336 0.916368i \(-0.368893\pi\)
0.400336 + 0.916368i \(0.368893\pi\)
\(858\) −2.46908 −0.0842929
\(859\) −5.29623 −0.180705 −0.0903525 0.995910i \(-0.528799\pi\)
−0.0903525 + 0.995910i \(0.528799\pi\)
\(860\) −97.2930 −3.31767
\(861\) 0.0949759 0.00323677
\(862\) −42.6659 −1.45321
\(863\) −4.16711 −0.141850 −0.0709250 0.997482i \(-0.522595\pi\)
−0.0709250 + 0.997482i \(0.522595\pi\)
\(864\) −8.20780 −0.279235
\(865\) 25.9315 0.881698
\(866\) 16.4339 0.558447
\(867\) −0.896058 −0.0304317
\(868\) −10.2090 −0.346518
\(869\) 8.08839 0.274380
\(870\) −5.33140 −0.180751
\(871\) 67.1046 2.27375
\(872\) −13.4385 −0.455085
\(873\) 11.1333 0.376804
\(874\) −3.13449 −0.106026
\(875\) −4.59270 −0.155261
\(876\) −0.529490 −0.0178898
\(877\) −39.1819 −1.32308 −0.661539 0.749911i \(-0.730096\pi\)
−0.661539 + 0.749911i \(0.730096\pi\)
\(878\) 32.9334 1.11145
\(879\) −3.11647 −0.105116
\(880\) 3.96242 0.133573
\(881\) −35.5080 −1.19630 −0.598148 0.801386i \(-0.704096\pi\)
−0.598148 + 0.801386i \(0.704096\pi\)
\(882\) −41.1721 −1.38634
\(883\) 28.5051 0.959273 0.479637 0.877467i \(-0.340768\pi\)
0.479637 + 0.877467i \(0.340768\pi\)
\(884\) −57.8682 −1.94632
\(885\) 4.74017 0.159339
\(886\) −7.57017 −0.254325
\(887\) −17.9442 −0.602507 −0.301253 0.953544i \(-0.597405\pi\)
−0.301253 + 0.953544i \(0.597405\pi\)
\(888\) −2.51826 −0.0845072
\(889\) 11.4061 0.382547
\(890\) 52.7650 1.76869
\(891\) −8.63914 −0.289422
\(892\) 6.91646 0.231580
\(893\) 2.50543 0.0838409
\(894\) −0.794723 −0.0265795
\(895\) 82.1715 2.74669
\(896\) −13.1090 −0.437941
\(897\) −7.54673 −0.251978
\(898\) 54.4989 1.81865
\(899\) 13.9599 0.465588
\(900\) −57.4102 −1.91367
\(901\) −17.3281 −0.577283
\(902\) −1.21462 −0.0404423
\(903\) 1.68449 0.0560563
\(904\) −1.90161 −0.0632465
\(905\) −0.264786 −0.00880178
\(906\) 0.585601 0.0194553
\(907\) 12.0757 0.400966 0.200483 0.979697i \(-0.435749\pi\)
0.200483 + 0.979697i \(0.435749\pi\)
\(908\) 43.0465 1.42855
\(909\) −37.3078 −1.23742
\(910\) −36.2873 −1.20291
\(911\) −7.33155 −0.242905 −0.121452 0.992597i \(-0.538755\pi\)
−0.121452 + 0.992597i \(0.538755\pi\)
\(912\) −0.0483812 −0.00160206
\(913\) 0.211727 0.00700715
\(914\) −69.5664 −2.30105
\(915\) 0.418673 0.0138409
\(916\) −31.4897 −1.04045
\(917\) −8.59074 −0.283691
\(918\) 9.42911 0.311207
\(919\) 2.59188 0.0854982 0.0427491 0.999086i \(-0.486388\pi\)
0.0427491 + 0.999086i \(0.486388\pi\)
\(920\) −49.3645 −1.62750
\(921\) 4.84896 0.159779
\(922\) −10.7442 −0.353840
\(923\) −11.7965 −0.388286
\(924\) 0.515061 0.0169443
\(925\) 38.5647 1.26800
\(926\) −89.0316 −2.92576
\(927\) −16.3358 −0.536537
\(928\) 24.0832 0.790571
\(929\) −40.7807 −1.33797 −0.668986 0.743275i \(-0.733271\pi\)
−0.668986 + 0.743275i \(0.733271\pi\)
\(930\) −6.04301 −0.198158
\(931\) −1.29215 −0.0423484
\(932\) 62.4813 2.04664
\(933\) 0.316224 0.0103527
\(934\) −81.0464 −2.65192
\(935\) −12.0362 −0.393625
\(936\) −34.8906 −1.14044
\(937\) 44.0812 1.44007 0.720034 0.693938i \(-0.244126\pi\)
0.720034 + 0.693938i \(0.244126\pi\)
\(938\) −23.4625 −0.766078
\(939\) 6.06077 0.197786
\(940\) 121.817 3.97325
\(941\) −16.7531 −0.546134 −0.273067 0.961995i \(-0.588038\pi\)
−0.273067 + 0.961995i \(0.588038\pi\)
\(942\) −1.92022 −0.0625642
\(943\) −3.71247 −0.120895
\(944\) −8.09811 −0.263571
\(945\) 3.52766 0.114755
\(946\) −21.5424 −0.700404
\(947\) −49.5329 −1.60960 −0.804802 0.593543i \(-0.797729\pi\)
−0.804802 + 0.593543i \(0.797729\pi\)
\(948\) −4.80182 −0.155956
\(949\) 4.92796 0.159968
\(950\) −3.01993 −0.0979793
\(951\) 3.64014 0.118040
\(952\) 6.55364 0.212405
\(953\) −47.2104 −1.52930 −0.764648 0.644448i \(-0.777087\pi\)
−0.764648 + 0.644448i \(0.777087\pi\)
\(954\) −32.2552 −1.04430
\(955\) 45.5255 1.47317
\(956\) 34.7338 1.12337
\(957\) −0.704296 −0.0227667
\(958\) 30.9423 0.999699
\(959\) −14.0042 −0.452218
\(960\) −8.83484 −0.285143
\(961\) −15.1768 −0.489575
\(962\) 72.3585 2.33293
\(963\) 35.1333 1.13215
\(964\) −32.6425 −1.05134
\(965\) 65.0576 2.09428
\(966\) 2.63865 0.0848970
\(967\) −30.6831 −0.986701 −0.493350 0.869831i \(-0.664228\pi\)
−0.493350 + 0.869831i \(0.664228\pi\)
\(968\) −2.13356 −0.0685751
\(969\) 0.146962 0.00472110
\(970\) 28.4745 0.914263
\(971\) −56.1396 −1.80161 −0.900803 0.434229i \(-0.857021\pi\)
−0.900803 + 0.434229i \(0.857021\pi\)
\(972\) 15.7431 0.504960
\(973\) −1.32910 −0.0426089
\(974\) −32.2450 −1.03320
\(975\) −7.27090 −0.232855
\(976\) −0.715262 −0.0228950
\(977\) 24.5356 0.784964 0.392482 0.919760i \(-0.371617\pi\)
0.392482 + 0.919760i \(0.371617\pi\)
\(978\) 7.56857 0.242016
\(979\) 6.97044 0.222776
\(980\) −62.8261 −2.00691
\(981\) −18.6422 −0.595200
\(982\) −37.6425 −1.20122
\(983\) 7.15067 0.228071 0.114035 0.993477i \(-0.463622\pi\)
0.114035 + 0.993477i \(0.463622\pi\)
\(984\) 0.233562 0.00744570
\(985\) −14.1508 −0.450881
\(986\) −27.6668 −0.881090
\(987\) −2.10910 −0.0671332
\(988\) −3.38063 −0.107552
\(989\) −65.8443 −2.09373
\(990\) −22.4046 −0.712065
\(991\) −49.6523 −1.57726 −0.788628 0.614870i \(-0.789208\pi\)
−0.788628 + 0.614870i \(0.789208\pi\)
\(992\) 27.2978 0.866705
\(993\) 4.82960 0.153263
\(994\) 4.12453 0.130822
\(995\) 62.1462 1.97017
\(996\) −0.125696 −0.00398282
\(997\) −10.3325 −0.327232 −0.163616 0.986524i \(-0.552316\pi\)
−0.163616 + 0.986524i \(0.552316\pi\)
\(998\) 58.9401 1.86572
\(999\) −7.03432 −0.222556
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.1.19 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.19 121 1.1 even 1 trivial