Properties

Label 4006.2.a.g.1.8
Level 4006
Weight 2
Character 4006.1
Self dual yes
Analytic conductor 31.988
Analytic rank 1
Dimension 40
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4006.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9880710497\)
Analytic rank: \(1\)
Dimension: \(40\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4006.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.94007 q^{3} +1.00000 q^{4} -0.275091 q^{5} +1.94007 q^{6} -2.80268 q^{7} -1.00000 q^{8} +0.763873 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.94007 q^{3} +1.00000 q^{4} -0.275091 q^{5} +1.94007 q^{6} -2.80268 q^{7} -1.00000 q^{8} +0.763873 q^{9} +0.275091 q^{10} -2.43291 q^{11} -1.94007 q^{12} +1.63440 q^{13} +2.80268 q^{14} +0.533696 q^{15} +1.00000 q^{16} -1.12271 q^{17} -0.763873 q^{18} +6.24346 q^{19} -0.275091 q^{20} +5.43740 q^{21} +2.43291 q^{22} -5.13618 q^{23} +1.94007 q^{24} -4.92432 q^{25} -1.63440 q^{26} +4.33824 q^{27} -2.80268 q^{28} -3.36352 q^{29} -0.533696 q^{30} +7.35325 q^{31} -1.00000 q^{32} +4.72002 q^{33} +1.12271 q^{34} +0.770993 q^{35} +0.763873 q^{36} +10.5709 q^{37} -6.24346 q^{38} -3.17085 q^{39} +0.275091 q^{40} -8.26556 q^{41} -5.43740 q^{42} +11.1306 q^{43} -2.43291 q^{44} -0.210135 q^{45} +5.13618 q^{46} -1.86722 q^{47} -1.94007 q^{48} +0.855018 q^{49} +4.92432 q^{50} +2.17813 q^{51} +1.63440 q^{52} +6.50923 q^{53} -4.33824 q^{54} +0.669273 q^{55} +2.80268 q^{56} -12.1127 q^{57} +3.36352 q^{58} +6.17307 q^{59} +0.533696 q^{60} +2.40011 q^{61} -7.35325 q^{62} -2.14089 q^{63} +1.00000 q^{64} -0.449609 q^{65} -4.72002 q^{66} -3.85137 q^{67} -1.12271 q^{68} +9.96455 q^{69} -0.770993 q^{70} -4.38439 q^{71} -0.763873 q^{72} -0.249004 q^{73} -10.5709 q^{74} +9.55354 q^{75} +6.24346 q^{76} +6.81868 q^{77} +3.17085 q^{78} -12.4573 q^{79} -0.275091 q^{80} -10.7081 q^{81} +8.26556 q^{82} +16.6569 q^{83} +5.43740 q^{84} +0.308846 q^{85} -11.1306 q^{86} +6.52546 q^{87} +2.43291 q^{88} -8.22939 q^{89} +0.210135 q^{90} -4.58070 q^{91} -5.13618 q^{92} -14.2658 q^{93} +1.86722 q^{94} -1.71752 q^{95} +1.94007 q^{96} +1.29351 q^{97} -0.855018 q^{98} -1.85844 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + O(q^{10}) \) \( 40q - 40q^{2} - q^{3} + 40q^{4} - 23q^{5} + q^{6} + 12q^{7} - 40q^{8} + 29q^{9} + 23q^{10} - 28q^{11} - q^{12} - 12q^{13} - 12q^{14} - 14q^{15} + 40q^{16} - 10q^{17} - 29q^{18} + 3q^{19} - 23q^{20} - 40q^{21} + 28q^{22} - 10q^{23} + q^{24} + 43q^{25} + 12q^{26} - 7q^{27} + 12q^{28} - 37q^{29} + 14q^{30} - 16q^{31} - 40q^{32} - 11q^{33} + 10q^{34} - 24q^{35} + 29q^{36} - 17q^{37} - 3q^{38} - 10q^{39} + 23q^{40} - 58q^{41} + 40q^{42} + 37q^{43} - 28q^{44} - 66q^{45} + 10q^{46} - 34q^{47} - q^{48} + 28q^{49} - 43q^{50} - 7q^{51} - 12q^{52} - 43q^{53} + 7q^{54} + 28q^{55} - 12q^{56} - 25q^{57} + 37q^{58} - 92q^{59} - 14q^{60} - 37q^{61} + 16q^{62} + 14q^{63} + 40q^{64} - 54q^{65} + 11q^{66} - 10q^{67} - 10q^{68} - 49q^{69} + 24q^{70} - 87q^{71} - 29q^{72} + 12q^{73} + 17q^{74} - 31q^{75} + 3q^{76} - 53q^{77} + 10q^{78} + 14q^{79} - 23q^{80} - 4q^{81} + 58q^{82} - 42q^{83} - 40q^{84} - 24q^{85} - 37q^{86} + 24q^{87} + 28q^{88} - 118q^{89} + 66q^{90} - 35q^{91} - 10q^{92} - 22q^{93} + 34q^{94} - 18q^{95} + q^{96} + 2q^{97} - 28q^{98} - 48q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.94007 −1.12010 −0.560050 0.828459i \(-0.689218\pi\)
−0.560050 + 0.828459i \(0.689218\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.275091 −0.123025 −0.0615123 0.998106i \(-0.519592\pi\)
−0.0615123 + 0.998106i \(0.519592\pi\)
\(6\) 1.94007 0.792030
\(7\) −2.80268 −1.05931 −0.529657 0.848212i \(-0.677679\pi\)
−0.529657 + 0.848212i \(0.677679\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.763873 0.254624
\(10\) 0.275091 0.0869915
\(11\) −2.43291 −0.733551 −0.366776 0.930309i \(-0.619538\pi\)
−0.366776 + 0.930309i \(0.619538\pi\)
\(12\) −1.94007 −0.560050
\(13\) 1.63440 0.453301 0.226650 0.973976i \(-0.427223\pi\)
0.226650 + 0.973976i \(0.427223\pi\)
\(14\) 2.80268 0.749048
\(15\) 0.533696 0.137800
\(16\) 1.00000 0.250000
\(17\) −1.12271 −0.272296 −0.136148 0.990689i \(-0.543472\pi\)
−0.136148 + 0.990689i \(0.543472\pi\)
\(18\) −0.763873 −0.180047
\(19\) 6.24346 1.43235 0.716174 0.697922i \(-0.245892\pi\)
0.716174 + 0.697922i \(0.245892\pi\)
\(20\) −0.275091 −0.0615123
\(21\) 5.43740 1.18654
\(22\) 2.43291 0.518699
\(23\) −5.13618 −1.07097 −0.535484 0.844545i \(-0.679871\pi\)
−0.535484 + 0.844545i \(0.679871\pi\)
\(24\) 1.94007 0.396015
\(25\) −4.92432 −0.984865
\(26\) −1.63440 −0.320532
\(27\) 4.33824 0.834895
\(28\) −2.80268 −0.529657
\(29\) −3.36352 −0.624589 −0.312295 0.949985i \(-0.601098\pi\)
−0.312295 + 0.949985i \(0.601098\pi\)
\(30\) −0.533696 −0.0974391
\(31\) 7.35325 1.32068 0.660341 0.750966i \(-0.270412\pi\)
0.660341 + 0.750966i \(0.270412\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.72002 0.821651
\(34\) 1.12271 0.192542
\(35\) 0.770993 0.130322
\(36\) 0.763873 0.127312
\(37\) 10.5709 1.73785 0.868926 0.494942i \(-0.164811\pi\)
0.868926 + 0.494942i \(0.164811\pi\)
\(38\) −6.24346 −1.01282
\(39\) −3.17085 −0.507742
\(40\) 0.275091 0.0434957
\(41\) −8.26556 −1.29086 −0.645432 0.763818i \(-0.723323\pi\)
−0.645432 + 0.763818i \(0.723323\pi\)
\(42\) −5.43740 −0.839009
\(43\) 11.1306 1.69741 0.848703 0.528869i \(-0.177384\pi\)
0.848703 + 0.528869i \(0.177384\pi\)
\(44\) −2.43291 −0.366776
\(45\) −0.210135 −0.0313250
\(46\) 5.13618 0.757288
\(47\) −1.86722 −0.272363 −0.136181 0.990684i \(-0.543483\pi\)
−0.136181 + 0.990684i \(0.543483\pi\)
\(48\) −1.94007 −0.280025
\(49\) 0.855018 0.122145
\(50\) 4.92432 0.696405
\(51\) 2.17813 0.304999
\(52\) 1.63440 0.226650
\(53\) 6.50923 0.894111 0.447056 0.894506i \(-0.352473\pi\)
0.447056 + 0.894506i \(0.352473\pi\)
\(54\) −4.33824 −0.590360
\(55\) 0.669273 0.0902448
\(56\) 2.80268 0.374524
\(57\) −12.1127 −1.60437
\(58\) 3.36352 0.441651
\(59\) 6.17307 0.803666 0.401833 0.915713i \(-0.368373\pi\)
0.401833 + 0.915713i \(0.368373\pi\)
\(60\) 0.533696 0.0688999
\(61\) 2.40011 0.307303 0.153651 0.988125i \(-0.450897\pi\)
0.153651 + 0.988125i \(0.450897\pi\)
\(62\) −7.35325 −0.933863
\(63\) −2.14089 −0.269727
\(64\) 1.00000 0.125000
\(65\) −0.449609 −0.0557671
\(66\) −4.72002 −0.580995
\(67\) −3.85137 −0.470520 −0.235260 0.971933i \(-0.575594\pi\)
−0.235260 + 0.971933i \(0.575594\pi\)
\(68\) −1.12271 −0.136148
\(69\) 9.96455 1.19959
\(70\) −0.770993 −0.0921512
\(71\) −4.38439 −0.520332 −0.260166 0.965564i \(-0.583777\pi\)
−0.260166 + 0.965564i \(0.583777\pi\)
\(72\) −0.763873 −0.0900233
\(73\) −0.249004 −0.0291437 −0.0145719 0.999894i \(-0.504639\pi\)
−0.0145719 + 0.999894i \(0.504639\pi\)
\(74\) −10.5709 −1.22885
\(75\) 9.55354 1.10315
\(76\) 6.24346 0.716174
\(77\) 6.81868 0.777061
\(78\) 3.17085 0.359028
\(79\) −12.4573 −1.40156 −0.700781 0.713377i \(-0.747165\pi\)
−0.700781 + 0.713377i \(0.747165\pi\)
\(80\) −0.275091 −0.0307561
\(81\) −10.7081 −1.18979
\(82\) 8.26556 0.912779
\(83\) 16.6569 1.82834 0.914168 0.405334i \(-0.132845\pi\)
0.914168 + 0.405334i \(0.132845\pi\)
\(84\) 5.43740 0.593269
\(85\) 0.308846 0.0334991
\(86\) −11.1306 −1.20025
\(87\) 6.52546 0.699602
\(88\) 2.43291 0.259350
\(89\) −8.22939 −0.872313 −0.436157 0.899871i \(-0.643661\pi\)
−0.436157 + 0.899871i \(0.643661\pi\)
\(90\) 0.210135 0.0221501
\(91\) −4.58070 −0.480187
\(92\) −5.13618 −0.535484
\(93\) −14.2658 −1.47930
\(94\) 1.86722 0.192589
\(95\) −1.71752 −0.176214
\(96\) 1.94007 0.198008
\(97\) 1.29351 0.131336 0.0656681 0.997842i \(-0.479082\pi\)
0.0656681 + 0.997842i \(0.479082\pi\)
\(98\) −0.855018 −0.0863699
\(99\) −1.85844 −0.186780
\(100\) −4.92432 −0.492432
\(101\) −0.460574 −0.0458288 −0.0229144 0.999737i \(-0.507295\pi\)
−0.0229144 + 0.999737i \(0.507295\pi\)
\(102\) −2.17813 −0.215667
\(103\) 5.21367 0.513718 0.256859 0.966449i \(-0.417312\pi\)
0.256859 + 0.966449i \(0.417312\pi\)
\(104\) −1.63440 −0.160266
\(105\) −1.49578 −0.145973
\(106\) −6.50923 −0.632232
\(107\) 3.51857 0.340153 0.170077 0.985431i \(-0.445598\pi\)
0.170077 + 0.985431i \(0.445598\pi\)
\(108\) 4.33824 0.417448
\(109\) 4.16929 0.399345 0.199673 0.979863i \(-0.436012\pi\)
0.199673 + 0.979863i \(0.436012\pi\)
\(110\) −0.669273 −0.0638127
\(111\) −20.5084 −1.94657
\(112\) −2.80268 −0.264828
\(113\) −5.75243 −0.541143 −0.270572 0.962700i \(-0.587213\pi\)
−0.270572 + 0.962700i \(0.587213\pi\)
\(114\) 12.1127 1.13446
\(115\) 1.41292 0.131755
\(116\) −3.36352 −0.312295
\(117\) 1.24847 0.115421
\(118\) −6.17307 −0.568278
\(119\) 3.14659 0.288447
\(120\) −0.533696 −0.0487196
\(121\) −5.08093 −0.461903
\(122\) −2.40011 −0.217296
\(123\) 16.0358 1.44590
\(124\) 7.35325 0.660341
\(125\) 2.73009 0.244187
\(126\) 2.14089 0.190726
\(127\) 16.7212 1.48376 0.741882 0.670531i \(-0.233934\pi\)
0.741882 + 0.670531i \(0.233934\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −21.5942 −1.90127
\(130\) 0.449609 0.0394333
\(131\) −6.26032 −0.546967 −0.273483 0.961877i \(-0.588176\pi\)
−0.273483 + 0.961877i \(0.588176\pi\)
\(132\) 4.72002 0.410825
\(133\) −17.4984 −1.51731
\(134\) 3.85137 0.332708
\(135\) −1.19341 −0.102713
\(136\) 1.12271 0.0962712
\(137\) 8.90358 0.760684 0.380342 0.924846i \(-0.375806\pi\)
0.380342 + 0.924846i \(0.375806\pi\)
\(138\) −9.96455 −0.848239
\(139\) 2.89358 0.245430 0.122715 0.992442i \(-0.460840\pi\)
0.122715 + 0.992442i \(0.460840\pi\)
\(140\) 0.770993 0.0651608
\(141\) 3.62255 0.305073
\(142\) 4.38439 0.367930
\(143\) −3.97635 −0.332519
\(144\) 0.763873 0.0636561
\(145\) 0.925273 0.0768398
\(146\) 0.249004 0.0206077
\(147\) −1.65880 −0.136815
\(148\) 10.5709 0.868926
\(149\) −10.3303 −0.846291 −0.423145 0.906062i \(-0.639074\pi\)
−0.423145 + 0.906062i \(0.639074\pi\)
\(150\) −9.55354 −0.780043
\(151\) −18.8141 −1.53107 −0.765536 0.643393i \(-0.777526\pi\)
−0.765536 + 0.643393i \(0.777526\pi\)
\(152\) −6.24346 −0.506411
\(153\) −0.857604 −0.0693332
\(154\) −6.81868 −0.549465
\(155\) −2.02281 −0.162476
\(156\) −3.17085 −0.253871
\(157\) −2.56362 −0.204599 −0.102300 0.994754i \(-0.532620\pi\)
−0.102300 + 0.994754i \(0.532620\pi\)
\(158\) 12.4573 0.991053
\(159\) −12.6284 −1.00149
\(160\) 0.275091 0.0217479
\(161\) 14.3951 1.13449
\(162\) 10.7081 0.841309
\(163\) −11.8007 −0.924302 −0.462151 0.886801i \(-0.652922\pi\)
−0.462151 + 0.886801i \(0.652922\pi\)
\(164\) −8.26556 −0.645432
\(165\) −1.29844 −0.101083
\(166\) −16.6569 −1.29283
\(167\) 7.22991 0.559468 0.279734 0.960078i \(-0.409754\pi\)
0.279734 + 0.960078i \(0.409754\pi\)
\(168\) −5.43740 −0.419504
\(169\) −10.3287 −0.794519
\(170\) −0.308846 −0.0236874
\(171\) 4.76921 0.364710
\(172\) 11.1306 0.848703
\(173\) 12.8262 0.975155 0.487577 0.873080i \(-0.337881\pi\)
0.487577 + 0.873080i \(0.337881\pi\)
\(174\) −6.52546 −0.494694
\(175\) 13.8013 1.04328
\(176\) −2.43291 −0.183388
\(177\) −11.9762 −0.900186
\(178\) 8.22939 0.616819
\(179\) 16.7297 1.25044 0.625218 0.780450i \(-0.285010\pi\)
0.625218 + 0.780450i \(0.285010\pi\)
\(180\) −0.210135 −0.0156625
\(181\) −11.0599 −0.822075 −0.411038 0.911618i \(-0.634833\pi\)
−0.411038 + 0.911618i \(0.634833\pi\)
\(182\) 4.58070 0.339544
\(183\) −4.65638 −0.344210
\(184\) 5.13618 0.378644
\(185\) −2.90797 −0.213798
\(186\) 14.2658 1.04602
\(187\) 2.73145 0.199743
\(188\) −1.86722 −0.136181
\(189\) −12.1587 −0.884416
\(190\) 1.71752 0.124602
\(191\) 16.5160 1.19505 0.597526 0.801849i \(-0.296150\pi\)
0.597526 + 0.801849i \(0.296150\pi\)
\(192\) −1.94007 −0.140013
\(193\) 8.13814 0.585796 0.292898 0.956144i \(-0.405380\pi\)
0.292898 + 0.956144i \(0.405380\pi\)
\(194\) −1.29351 −0.0928687
\(195\) 0.872272 0.0624647
\(196\) 0.855018 0.0610727
\(197\) −15.3167 −1.09127 −0.545633 0.838024i \(-0.683711\pi\)
−0.545633 + 0.838024i \(0.683711\pi\)
\(198\) 1.85844 0.132073
\(199\) 10.5399 0.747154 0.373577 0.927599i \(-0.378131\pi\)
0.373577 + 0.927599i \(0.378131\pi\)
\(200\) 4.92432 0.348202
\(201\) 7.47193 0.527029
\(202\) 0.460574 0.0324059
\(203\) 9.42686 0.661636
\(204\) 2.17813 0.152499
\(205\) 2.27378 0.158808
\(206\) −5.21367 −0.363253
\(207\) −3.92339 −0.272694
\(208\) 1.63440 0.113325
\(209\) −15.1898 −1.05070
\(210\) 1.49578 0.103219
\(211\) −15.7812 −1.08642 −0.543210 0.839597i \(-0.682791\pi\)
−0.543210 + 0.839597i \(0.682791\pi\)
\(212\) 6.50923 0.447056
\(213\) 8.50603 0.582824
\(214\) −3.51857 −0.240525
\(215\) −3.06194 −0.208823
\(216\) −4.33824 −0.295180
\(217\) −20.6088 −1.39902
\(218\) −4.16929 −0.282380
\(219\) 0.483085 0.0326439
\(220\) 0.669273 0.0451224
\(221\) −1.83495 −0.123432
\(222\) 20.5084 1.37643
\(223\) 19.7771 1.32437 0.662187 0.749339i \(-0.269629\pi\)
0.662187 + 0.749339i \(0.269629\pi\)
\(224\) 2.80268 0.187262
\(225\) −3.76156 −0.250770
\(226\) 5.75243 0.382646
\(227\) 2.17483 0.144349 0.0721744 0.997392i \(-0.477006\pi\)
0.0721744 + 0.997392i \(0.477006\pi\)
\(228\) −12.1127 −0.802186
\(229\) −16.7118 −1.10435 −0.552173 0.833730i \(-0.686201\pi\)
−0.552173 + 0.833730i \(0.686201\pi\)
\(230\) −1.41292 −0.0931650
\(231\) −13.2287 −0.870386
\(232\) 3.36352 0.220826
\(233\) −23.9078 −1.56625 −0.783127 0.621862i \(-0.786377\pi\)
−0.783127 + 0.621862i \(0.786377\pi\)
\(234\) −1.24847 −0.0816152
\(235\) 0.513657 0.0335073
\(236\) 6.17307 0.401833
\(237\) 24.1681 1.56989
\(238\) −3.14659 −0.203963
\(239\) −5.15820 −0.333656 −0.166828 0.985986i \(-0.553352\pi\)
−0.166828 + 0.985986i \(0.553352\pi\)
\(240\) 0.533696 0.0344499
\(241\) 13.3436 0.859539 0.429769 0.902939i \(-0.358595\pi\)
0.429769 + 0.902939i \(0.358595\pi\)
\(242\) 5.08093 0.326615
\(243\) 7.75977 0.497789
\(244\) 2.40011 0.153651
\(245\) −0.235208 −0.0150269
\(246\) −16.0358 −1.02240
\(247\) 10.2043 0.649284
\(248\) −7.35325 −0.466932
\(249\) −32.3156 −2.04792
\(250\) −2.73009 −0.172666
\(251\) 0.882907 0.0557286 0.0278643 0.999612i \(-0.491129\pi\)
0.0278643 + 0.999612i \(0.491129\pi\)
\(252\) −2.14089 −0.134863
\(253\) 12.4959 0.785610
\(254\) −16.7212 −1.04918
\(255\) −0.599184 −0.0375223
\(256\) 1.00000 0.0625000
\(257\) −15.9481 −0.994814 −0.497407 0.867517i \(-0.665714\pi\)
−0.497407 + 0.867517i \(0.665714\pi\)
\(258\) 21.5942 1.34440
\(259\) −29.6270 −1.84093
\(260\) −0.449609 −0.0278835
\(261\) −2.56930 −0.159036
\(262\) 6.26032 0.386764
\(263\) −29.6222 −1.82658 −0.913291 0.407307i \(-0.866468\pi\)
−0.913291 + 0.407307i \(0.866468\pi\)
\(264\) −4.72002 −0.290497
\(265\) −1.79063 −0.109998
\(266\) 17.4984 1.07290
\(267\) 15.9656 0.977078
\(268\) −3.85137 −0.235260
\(269\) 29.2664 1.78440 0.892201 0.451638i \(-0.149160\pi\)
0.892201 + 0.451638i \(0.149160\pi\)
\(270\) 1.19341 0.0726288
\(271\) −0.771400 −0.0468592 −0.0234296 0.999725i \(-0.507459\pi\)
−0.0234296 + 0.999725i \(0.507459\pi\)
\(272\) −1.12271 −0.0680740
\(273\) 8.88687 0.537858
\(274\) −8.90358 −0.537885
\(275\) 11.9805 0.722449
\(276\) 9.96455 0.599795
\(277\) −12.0783 −0.725712 −0.362856 0.931845i \(-0.618198\pi\)
−0.362856 + 0.931845i \(0.618198\pi\)
\(278\) −2.89358 −0.173545
\(279\) 5.61694 0.336278
\(280\) −0.770993 −0.0460756
\(281\) 8.91242 0.531671 0.265835 0.964018i \(-0.414352\pi\)
0.265835 + 0.964018i \(0.414352\pi\)
\(282\) −3.62255 −0.215719
\(283\) −2.71737 −0.161531 −0.0807656 0.996733i \(-0.525737\pi\)
−0.0807656 + 0.996733i \(0.525737\pi\)
\(284\) −4.38439 −0.260166
\(285\) 3.33211 0.197377
\(286\) 3.97635 0.235127
\(287\) 23.1657 1.36743
\(288\) −0.763873 −0.0450116
\(289\) −15.7395 −0.925855
\(290\) −0.925273 −0.0543339
\(291\) −2.50950 −0.147110
\(292\) −0.249004 −0.0145719
\(293\) −16.5724 −0.968169 −0.484085 0.875021i \(-0.660847\pi\)
−0.484085 + 0.875021i \(0.660847\pi\)
\(294\) 1.65880 0.0967429
\(295\) −1.69816 −0.0988706
\(296\) −10.5709 −0.614423
\(297\) −10.5546 −0.612439
\(298\) 10.3303 0.598418
\(299\) −8.39456 −0.485470
\(300\) 9.55354 0.551574
\(301\) −31.1956 −1.79809
\(302\) 18.8141 1.08263
\(303\) 0.893546 0.0513328
\(304\) 6.24346 0.358087
\(305\) −0.660249 −0.0378057
\(306\) 0.857604 0.0490260
\(307\) 19.8726 1.13419 0.567094 0.823653i \(-0.308068\pi\)
0.567094 + 0.823653i \(0.308068\pi\)
\(308\) 6.81868 0.388530
\(309\) −10.1149 −0.575415
\(310\) 2.02281 0.114888
\(311\) −20.3156 −1.15199 −0.575996 0.817452i \(-0.695386\pi\)
−0.575996 + 0.817452i \(0.695386\pi\)
\(312\) 3.17085 0.179514
\(313\) −32.1642 −1.81803 −0.909014 0.416766i \(-0.863164\pi\)
−0.909014 + 0.416766i \(0.863164\pi\)
\(314\) 2.56362 0.144673
\(315\) 0.588940 0.0331830
\(316\) −12.4573 −0.700781
\(317\) −25.1758 −1.41401 −0.707007 0.707207i \(-0.749955\pi\)
−0.707007 + 0.707207i \(0.749955\pi\)
\(318\) 12.6284 0.708163
\(319\) 8.18314 0.458168
\(320\) −0.275091 −0.0153781
\(321\) −6.82628 −0.381006
\(322\) −14.3951 −0.802206
\(323\) −7.00957 −0.390023
\(324\) −10.7081 −0.594895
\(325\) −8.04831 −0.446440
\(326\) 11.8007 0.653580
\(327\) −8.08871 −0.447307
\(328\) 8.26556 0.456389
\(329\) 5.23323 0.288517
\(330\) 1.29844 0.0714766
\(331\) −25.2843 −1.38975 −0.694876 0.719129i \(-0.744541\pi\)
−0.694876 + 0.719129i \(0.744541\pi\)
\(332\) 16.6569 0.914168
\(333\) 8.07485 0.442499
\(334\) −7.22991 −0.395603
\(335\) 1.05948 0.0578855
\(336\) 5.43740 0.296634
\(337\) −2.32522 −0.126663 −0.0633314 0.997993i \(-0.520173\pi\)
−0.0633314 + 0.997993i \(0.520173\pi\)
\(338\) 10.3287 0.561809
\(339\) 11.1601 0.606135
\(340\) 0.308846 0.0167495
\(341\) −17.8898 −0.968788
\(342\) −4.76921 −0.257889
\(343\) 17.2224 0.929923
\(344\) −11.1306 −0.600124
\(345\) −2.74116 −0.147579
\(346\) −12.8262 −0.689539
\(347\) −25.4324 −1.36528 −0.682640 0.730755i \(-0.739168\pi\)
−0.682640 + 0.730755i \(0.739168\pi\)
\(348\) 6.52546 0.349801
\(349\) −25.8002 −1.38105 −0.690527 0.723307i \(-0.742621\pi\)
−0.690527 + 0.723307i \(0.742621\pi\)
\(350\) −13.8013 −0.737711
\(351\) 7.09042 0.378459
\(352\) 2.43291 0.129675
\(353\) 5.96967 0.317734 0.158867 0.987300i \(-0.449216\pi\)
0.158867 + 0.987300i \(0.449216\pi\)
\(354\) 11.9762 0.636528
\(355\) 1.20611 0.0640136
\(356\) −8.22939 −0.436157
\(357\) −6.10460 −0.323089
\(358\) −16.7297 −0.884192
\(359\) −27.3006 −1.44087 −0.720435 0.693522i \(-0.756058\pi\)
−0.720435 + 0.693522i \(0.756058\pi\)
\(360\) 0.210135 0.0110751
\(361\) 19.9808 1.05162
\(362\) 11.0599 0.581295
\(363\) 9.85736 0.517377
\(364\) −4.58070 −0.240094
\(365\) 0.0684988 0.00358539
\(366\) 4.65638 0.243393
\(367\) −15.3449 −0.800999 −0.400499 0.916297i \(-0.631163\pi\)
−0.400499 + 0.916297i \(0.631163\pi\)
\(368\) −5.13618 −0.267742
\(369\) −6.31384 −0.328685
\(370\) 2.90797 0.151178
\(371\) −18.2433 −0.947144
\(372\) −14.2658 −0.739648
\(373\) 7.52956 0.389866 0.194933 0.980817i \(-0.437551\pi\)
0.194933 + 0.980817i \(0.437551\pi\)
\(374\) −2.73145 −0.141240
\(375\) −5.29657 −0.273514
\(376\) 1.86722 0.0962947
\(377\) −5.49732 −0.283127
\(378\) 12.1587 0.625377
\(379\) −32.0958 −1.64865 −0.824324 0.566118i \(-0.808445\pi\)
−0.824324 + 0.566118i \(0.808445\pi\)
\(380\) −1.71752 −0.0881069
\(381\) −32.4402 −1.66196
\(382\) −16.5160 −0.845030
\(383\) 17.1137 0.874468 0.437234 0.899348i \(-0.355958\pi\)
0.437234 + 0.899348i \(0.355958\pi\)
\(384\) 1.94007 0.0990038
\(385\) −1.87576 −0.0955975
\(386\) −8.13814 −0.414220
\(387\) 8.50239 0.432201
\(388\) 1.29351 0.0656681
\(389\) −21.6713 −1.09878 −0.549390 0.835566i \(-0.685140\pi\)
−0.549390 + 0.835566i \(0.685140\pi\)
\(390\) −0.872272 −0.0441692
\(391\) 5.76642 0.291620
\(392\) −0.855018 −0.0431849
\(393\) 12.1455 0.612658
\(394\) 15.3167 0.771642
\(395\) 3.42691 0.172426
\(396\) −1.85844 −0.0933899
\(397\) −22.8325 −1.14593 −0.572966 0.819579i \(-0.694207\pi\)
−0.572966 + 0.819579i \(0.694207\pi\)
\(398\) −10.5399 −0.528317
\(399\) 33.9482 1.69953
\(400\) −4.92432 −0.246216
\(401\) −18.5160 −0.924646 −0.462323 0.886712i \(-0.652984\pi\)
−0.462323 + 0.886712i \(0.652984\pi\)
\(402\) −7.47193 −0.372666
\(403\) 12.0181 0.598666
\(404\) −0.460574 −0.0229144
\(405\) 2.94571 0.146373
\(406\) −9.42686 −0.467847
\(407\) −25.7182 −1.27480
\(408\) −2.17813 −0.107833
\(409\) 4.45069 0.220072 0.110036 0.993928i \(-0.464903\pi\)
0.110036 + 0.993928i \(0.464903\pi\)
\(410\) −2.27378 −0.112294
\(411\) −17.2736 −0.852043
\(412\) 5.21367 0.256859
\(413\) −17.3012 −0.851334
\(414\) 3.92339 0.192824
\(415\) −4.58218 −0.224930
\(416\) −1.63440 −0.0801330
\(417\) −5.61374 −0.274906
\(418\) 15.1898 0.742957
\(419\) 15.6752 0.765785 0.382892 0.923793i \(-0.374928\pi\)
0.382892 + 0.923793i \(0.374928\pi\)
\(420\) −1.49578 −0.0729866
\(421\) 24.5106 1.19457 0.597287 0.802028i \(-0.296245\pi\)
0.597287 + 0.802028i \(0.296245\pi\)
\(422\) 15.7812 0.768216
\(423\) −1.42632 −0.0693501
\(424\) −6.50923 −0.316116
\(425\) 5.52857 0.268175
\(426\) −8.50603 −0.412119
\(427\) −6.72674 −0.325530
\(428\) 3.51857 0.170077
\(429\) 7.71440 0.372455
\(430\) 3.06194 0.147660
\(431\) 15.5408 0.748575 0.374287 0.927313i \(-0.377887\pi\)
0.374287 + 0.927313i \(0.377887\pi\)
\(432\) 4.33824 0.208724
\(433\) 34.5338 1.65959 0.829794 0.558071i \(-0.188458\pi\)
0.829794 + 0.558071i \(0.188458\pi\)
\(434\) 20.6088 0.989254
\(435\) −1.79510 −0.0860682
\(436\) 4.16929 0.199673
\(437\) −32.0675 −1.53400
\(438\) −0.483085 −0.0230827
\(439\) 13.1241 0.626379 0.313189 0.949691i \(-0.398603\pi\)
0.313189 + 0.949691i \(0.398603\pi\)
\(440\) −0.669273 −0.0319063
\(441\) 0.653125 0.0311012
\(442\) 1.83495 0.0872796
\(443\) −18.1521 −0.862430 −0.431215 0.902249i \(-0.641915\pi\)
−0.431215 + 0.902249i \(0.641915\pi\)
\(444\) −20.5084 −0.973284
\(445\) 2.26383 0.107316
\(446\) −19.7771 −0.936473
\(447\) 20.0415 0.947930
\(448\) −2.80268 −0.132414
\(449\) −2.68659 −0.126788 −0.0633941 0.997989i \(-0.520192\pi\)
−0.0633941 + 0.997989i \(0.520192\pi\)
\(450\) 3.76156 0.177321
\(451\) 20.1094 0.946915
\(452\) −5.75243 −0.270572
\(453\) 36.5007 1.71495
\(454\) −2.17483 −0.102070
\(455\) 1.26011 0.0590748
\(456\) 12.1127 0.567231
\(457\) 27.5313 1.28786 0.643930 0.765085i \(-0.277303\pi\)
0.643930 + 0.765085i \(0.277303\pi\)
\(458\) 16.7118 0.780891
\(459\) −4.87057 −0.227339
\(460\) 1.41292 0.0658776
\(461\) −3.54762 −0.165229 −0.0826146 0.996582i \(-0.526327\pi\)
−0.0826146 + 0.996582i \(0.526327\pi\)
\(462\) 13.2287 0.615456
\(463\) −19.5632 −0.909180 −0.454590 0.890701i \(-0.650214\pi\)
−0.454590 + 0.890701i \(0.650214\pi\)
\(464\) −3.36352 −0.156147
\(465\) 3.92440 0.181990
\(466\) 23.9078 1.10751
\(467\) 9.56141 0.442449 0.221225 0.975223i \(-0.428995\pi\)
0.221225 + 0.975223i \(0.428995\pi\)
\(468\) 1.24847 0.0577106
\(469\) 10.7942 0.498428
\(470\) −0.513657 −0.0236932
\(471\) 4.97360 0.229171
\(472\) −6.17307 −0.284139
\(473\) −27.0799 −1.24513
\(474\) −24.1681 −1.11008
\(475\) −30.7448 −1.41067
\(476\) 3.14659 0.144223
\(477\) 4.97222 0.227662
\(478\) 5.15820 0.235930
\(479\) −18.8832 −0.862796 −0.431398 0.902162i \(-0.641980\pi\)
−0.431398 + 0.902162i \(0.641980\pi\)
\(480\) −0.533696 −0.0243598
\(481\) 17.2771 0.787769
\(482\) −13.3436 −0.607786
\(483\) −27.9275 −1.27074
\(484\) −5.08093 −0.230951
\(485\) −0.355834 −0.0161576
\(486\) −7.75977 −0.351990
\(487\) 11.2812 0.511202 0.255601 0.966782i \(-0.417727\pi\)
0.255601 + 0.966782i \(0.417727\pi\)
\(488\) −2.40011 −0.108648
\(489\) 22.8942 1.03531
\(490\) 0.235208 0.0106256
\(491\) 2.40116 0.108363 0.0541814 0.998531i \(-0.482745\pi\)
0.0541814 + 0.998531i \(0.482745\pi\)
\(492\) 16.0358 0.722949
\(493\) 3.77624 0.170073
\(494\) −10.2043 −0.459113
\(495\) 0.511239 0.0229785
\(496\) 7.35325 0.330171
\(497\) 12.2881 0.551195
\(498\) 32.3156 1.44810
\(499\) 27.1221 1.21415 0.607075 0.794644i \(-0.292343\pi\)
0.607075 + 0.794644i \(0.292343\pi\)
\(500\) 2.73009 0.122094
\(501\) −14.0265 −0.626660
\(502\) −0.882907 −0.0394061
\(503\) −2.05143 −0.0914686 −0.0457343 0.998954i \(-0.514563\pi\)
−0.0457343 + 0.998954i \(0.514563\pi\)
\(504\) 2.14089 0.0953629
\(505\) 0.126700 0.00563807
\(506\) −12.4959 −0.555510
\(507\) 20.0385 0.889940
\(508\) 16.7212 0.741882
\(509\) 6.34162 0.281088 0.140544 0.990074i \(-0.455115\pi\)
0.140544 + 0.990074i \(0.455115\pi\)
\(510\) 0.599184 0.0265323
\(511\) 0.697878 0.0308723
\(512\) −1.00000 −0.0441942
\(513\) 27.0856 1.19586
\(514\) 15.9481 0.703440
\(515\) −1.43423 −0.0631999
\(516\) −21.5942 −0.950633
\(517\) 4.54280 0.199792
\(518\) 29.6270 1.30173
\(519\) −24.8837 −1.09227
\(520\) 0.449609 0.0197166
\(521\) −20.7037 −0.907048 −0.453524 0.891244i \(-0.649833\pi\)
−0.453524 + 0.891244i \(0.649833\pi\)
\(522\) 2.56930 0.112455
\(523\) 1.39716 0.0610934 0.0305467 0.999533i \(-0.490275\pi\)
0.0305467 + 0.999533i \(0.490275\pi\)
\(524\) −6.26032 −0.273483
\(525\) −26.7755 −1.16858
\(526\) 29.6222 1.29159
\(527\) −8.25553 −0.359617
\(528\) 4.72002 0.205413
\(529\) 3.38035 0.146972
\(530\) 1.79063 0.0777801
\(531\) 4.71544 0.204633
\(532\) −17.4984 −0.758653
\(533\) −13.5092 −0.585150
\(534\) −15.9656 −0.690898
\(535\) −0.967928 −0.0418472
\(536\) 3.85137 0.166354
\(537\) −32.4568 −1.40061
\(538\) −29.2664 −1.26176
\(539\) −2.08019 −0.0895999
\(540\) −1.19341 −0.0513563
\(541\) −23.8933 −1.02725 −0.513626 0.858014i \(-0.671698\pi\)
−0.513626 + 0.858014i \(0.671698\pi\)
\(542\) 0.771400 0.0331345
\(543\) 21.4570 0.920806
\(544\) 1.12271 0.0481356
\(545\) −1.14693 −0.0491292
\(546\) −8.88687 −0.380323
\(547\) 7.15810 0.306058 0.153029 0.988222i \(-0.451097\pi\)
0.153029 + 0.988222i \(0.451097\pi\)
\(548\) 8.90358 0.380342
\(549\) 1.83338 0.0782467
\(550\) −11.9805 −0.510848
\(551\) −21.0000 −0.894629
\(552\) −9.96455 −0.424119
\(553\) 34.9140 1.48469
\(554\) 12.0783 0.513156
\(555\) 5.64167 0.239476
\(556\) 2.89358 0.122715
\(557\) 1.21106 0.0513143 0.0256572 0.999671i \(-0.491832\pi\)
0.0256572 + 0.999671i \(0.491832\pi\)
\(558\) −5.61694 −0.237784
\(559\) 18.1919 0.769435
\(560\) 0.770993 0.0325804
\(561\) −5.29920 −0.223732
\(562\) −8.91242 −0.375948
\(563\) −19.2792 −0.812521 −0.406261 0.913757i \(-0.633167\pi\)
−0.406261 + 0.913757i \(0.633167\pi\)
\(564\) 3.62255 0.152537
\(565\) 1.58244 0.0665739
\(566\) 2.71737 0.114220
\(567\) 30.0114 1.26036
\(568\) 4.38439 0.183965
\(569\) 6.01657 0.252228 0.126114 0.992016i \(-0.459750\pi\)
0.126114 + 0.992016i \(0.459750\pi\)
\(570\) −3.33211 −0.139567
\(571\) 16.9092 0.707626 0.353813 0.935316i \(-0.384885\pi\)
0.353813 + 0.935316i \(0.384885\pi\)
\(572\) −3.97635 −0.166260
\(573\) −32.0421 −1.33858
\(574\) −23.1657 −0.966919
\(575\) 25.2922 1.05476
\(576\) 0.763873 0.0318280
\(577\) −12.5210 −0.521257 −0.260628 0.965439i \(-0.583930\pi\)
−0.260628 + 0.965439i \(0.583930\pi\)
\(578\) 15.7395 0.654678
\(579\) −15.7886 −0.656150
\(580\) 0.925273 0.0384199
\(581\) −46.6841 −1.93678
\(582\) 2.50950 0.104022
\(583\) −15.8364 −0.655876
\(584\) 0.249004 0.0103039
\(585\) −0.343444 −0.0141996
\(586\) 16.5724 0.684599
\(587\) −22.3235 −0.921389 −0.460694 0.887559i \(-0.652400\pi\)
−0.460694 + 0.887559i \(0.652400\pi\)
\(588\) −1.65880 −0.0684076
\(589\) 45.9097 1.89168
\(590\) 1.69816 0.0699121
\(591\) 29.7154 1.22233
\(592\) 10.5709 0.434463
\(593\) 20.7240 0.851033 0.425517 0.904951i \(-0.360092\pi\)
0.425517 + 0.904951i \(0.360092\pi\)
\(594\) 10.5546 0.433059
\(595\) −0.865598 −0.0354860
\(596\) −10.3303 −0.423145
\(597\) −20.4481 −0.836887
\(598\) 8.39456 0.343279
\(599\) −8.81251 −0.360069 −0.180035 0.983660i \(-0.557621\pi\)
−0.180035 + 0.983660i \(0.557621\pi\)
\(600\) −9.55354 −0.390021
\(601\) 1.45283 0.0592623 0.0296311 0.999561i \(-0.490567\pi\)
0.0296311 + 0.999561i \(0.490567\pi\)
\(602\) 31.1956 1.27144
\(603\) −2.94196 −0.119806
\(604\) −18.8141 −0.765536
\(605\) 1.39772 0.0568253
\(606\) −0.893546 −0.0362978
\(607\) −26.1434 −1.06113 −0.530564 0.847645i \(-0.678020\pi\)
−0.530564 + 0.847645i \(0.678020\pi\)
\(608\) −6.24346 −0.253206
\(609\) −18.2888 −0.741098
\(610\) 0.660249 0.0267327
\(611\) −3.05179 −0.123462
\(612\) −0.857604 −0.0346666
\(613\) −12.2985 −0.496730 −0.248365 0.968667i \(-0.579893\pi\)
−0.248365 + 0.968667i \(0.579893\pi\)
\(614\) −19.8726 −0.801992
\(615\) −4.41130 −0.177881
\(616\) −6.81868 −0.274732
\(617\) 28.0317 1.12851 0.564257 0.825599i \(-0.309163\pi\)
0.564257 + 0.825599i \(0.309163\pi\)
\(618\) 10.1149 0.406880
\(619\) −25.9021 −1.04109 −0.520547 0.853833i \(-0.674272\pi\)
−0.520547 + 0.853833i \(0.674272\pi\)
\(620\) −2.02281 −0.0812381
\(621\) −22.2820 −0.894146
\(622\) 20.3156 0.814582
\(623\) 23.0643 0.924053
\(624\) −3.17085 −0.126935
\(625\) 23.8706 0.954824
\(626\) 32.1642 1.28554
\(627\) 29.4693 1.17689
\(628\) −2.56362 −0.102300
\(629\) −11.8681 −0.473210
\(630\) −0.588940 −0.0234639
\(631\) 22.4846 0.895100 0.447550 0.894259i \(-0.352297\pi\)
0.447550 + 0.894259i \(0.352297\pi\)
\(632\) 12.4573 0.495527
\(633\) 30.6166 1.21690
\(634\) 25.1758 0.999858
\(635\) −4.59984 −0.182539
\(636\) −12.6284 −0.500747
\(637\) 1.39744 0.0553686
\(638\) −8.18314 −0.323974
\(639\) −3.34912 −0.132489
\(640\) 0.275091 0.0108739
\(641\) −30.0448 −1.18670 −0.593349 0.804945i \(-0.702195\pi\)
−0.593349 + 0.804945i \(0.702195\pi\)
\(642\) 6.82628 0.269412
\(643\) −15.0181 −0.592257 −0.296129 0.955148i \(-0.595696\pi\)
−0.296129 + 0.955148i \(0.595696\pi\)
\(644\) 14.3951 0.567245
\(645\) 5.94038 0.233902
\(646\) 7.00957 0.275788
\(647\) −48.2366 −1.89638 −0.948188 0.317711i \(-0.897086\pi\)
−0.948188 + 0.317711i \(0.897086\pi\)
\(648\) 10.7081 0.420655
\(649\) −15.0186 −0.589530
\(650\) 8.04831 0.315681
\(651\) 39.9825 1.56704
\(652\) −11.8007 −0.462151
\(653\) −2.97201 −0.116304 −0.0581518 0.998308i \(-0.518521\pi\)
−0.0581518 + 0.998308i \(0.518521\pi\)
\(654\) 8.08871 0.316294
\(655\) 1.72216 0.0672903
\(656\) −8.26556 −0.322716
\(657\) −0.190207 −0.00742069
\(658\) −5.23323 −0.204013
\(659\) 23.1266 0.900885 0.450442 0.892806i \(-0.351266\pi\)
0.450442 + 0.892806i \(0.351266\pi\)
\(660\) −1.29844 −0.0505416
\(661\) 23.8625 0.928145 0.464072 0.885797i \(-0.346388\pi\)
0.464072 + 0.885797i \(0.346388\pi\)
\(662\) 25.2843 0.982704
\(663\) 3.55993 0.138256
\(664\) −16.6569 −0.646415
\(665\) 4.81366 0.186666
\(666\) −8.07485 −0.312894
\(667\) 17.2756 0.668915
\(668\) 7.22991 0.279734
\(669\) −38.3690 −1.48343
\(670\) −1.05948 −0.0409312
\(671\) −5.83926 −0.225422
\(672\) −5.43740 −0.209752
\(673\) −37.6477 −1.45121 −0.725606 0.688110i \(-0.758441\pi\)
−0.725606 + 0.688110i \(0.758441\pi\)
\(674\) 2.32522 0.0895641
\(675\) −21.3629 −0.822259
\(676\) −10.3287 −0.397259
\(677\) 24.2085 0.930407 0.465204 0.885204i \(-0.345981\pi\)
0.465204 + 0.885204i \(0.345981\pi\)
\(678\) −11.1601 −0.428602
\(679\) −3.62530 −0.139126
\(680\) −0.308846 −0.0118437
\(681\) −4.21933 −0.161685
\(682\) 17.8898 0.685037
\(683\) −0.966306 −0.0369747 −0.0184873 0.999829i \(-0.505885\pi\)
−0.0184873 + 0.999829i \(0.505885\pi\)
\(684\) 4.76921 0.182355
\(685\) −2.44930 −0.0935828
\(686\) −17.2224 −0.657555
\(687\) 32.4220 1.23698
\(688\) 11.1306 0.424352
\(689\) 10.6387 0.405301
\(690\) 2.74116 0.104354
\(691\) 16.2000 0.616275 0.308138 0.951342i \(-0.400294\pi\)
0.308138 + 0.951342i \(0.400294\pi\)
\(692\) 12.8262 0.487577
\(693\) 5.20860 0.197858
\(694\) 25.4324 0.965399
\(695\) −0.795998 −0.0301939
\(696\) −6.52546 −0.247347
\(697\) 9.27980 0.351497
\(698\) 25.8002 0.976552
\(699\) 46.3829 1.75436
\(700\) 13.8013 0.521640
\(701\) −0.649950 −0.0245483 −0.0122741 0.999925i \(-0.503907\pi\)
−0.0122741 + 0.999925i \(0.503907\pi\)
\(702\) −7.09042 −0.267611
\(703\) 65.9992 2.48921
\(704\) −2.43291 −0.0916939
\(705\) −0.996530 −0.0375315
\(706\) −5.96967 −0.224672
\(707\) 1.29084 0.0485471
\(708\) −11.9762 −0.450093
\(709\) 41.2234 1.54818 0.774089 0.633077i \(-0.218208\pi\)
0.774089 + 0.633077i \(0.218208\pi\)
\(710\) −1.20611 −0.0452644
\(711\) −9.51583 −0.356871
\(712\) 8.22939 0.308409
\(713\) −37.7676 −1.41441
\(714\) 6.10460 0.228459
\(715\) 1.09386 0.0409080
\(716\) 16.7297 0.625218
\(717\) 10.0073 0.373728
\(718\) 27.3006 1.01885
\(719\) 33.0929 1.23416 0.617078 0.786902i \(-0.288316\pi\)
0.617078 + 0.786902i \(0.288316\pi\)
\(720\) −0.210135 −0.00783125
\(721\) −14.6122 −0.544188
\(722\) −19.9808 −0.743607
\(723\) −25.8876 −0.962769
\(724\) −11.0599 −0.411038
\(725\) 16.5630 0.615136
\(726\) −9.85736 −0.365841
\(727\) 2.56353 0.0950762 0.0475381 0.998869i \(-0.484862\pi\)
0.0475381 + 0.998869i \(0.484862\pi\)
\(728\) 4.58070 0.169772
\(729\) 17.0699 0.632217
\(730\) −0.0684988 −0.00253525
\(731\) −12.4964 −0.462197
\(732\) −4.65638 −0.172105
\(733\) −10.6829 −0.394582 −0.197291 0.980345i \(-0.563214\pi\)
−0.197291 + 0.980345i \(0.563214\pi\)
\(734\) 15.3449 0.566391
\(735\) 0.456320 0.0168316
\(736\) 5.13618 0.189322
\(737\) 9.37005 0.345150
\(738\) 6.31384 0.232416
\(739\) 16.6718 0.613281 0.306640 0.951825i \(-0.400795\pi\)
0.306640 + 0.951825i \(0.400795\pi\)
\(740\) −2.90797 −0.106899
\(741\) −19.7971 −0.727263
\(742\) 18.2433 0.669732
\(743\) 42.6923 1.56623 0.783115 0.621877i \(-0.213630\pi\)
0.783115 + 0.621877i \(0.213630\pi\)
\(744\) 14.2658 0.523010
\(745\) 2.84177 0.104115
\(746\) −7.52956 −0.275677
\(747\) 12.7238 0.465539
\(748\) 2.73145 0.0998716
\(749\) −9.86143 −0.360329
\(750\) 5.29657 0.193404
\(751\) −29.6088 −1.08044 −0.540220 0.841524i \(-0.681659\pi\)
−0.540220 + 0.841524i \(0.681659\pi\)
\(752\) −1.86722 −0.0680907
\(753\) −1.71290 −0.0624216
\(754\) 5.49732 0.200201
\(755\) 5.17560 0.188359
\(756\) −12.1587 −0.442208
\(757\) 46.2049 1.67935 0.839673 0.543092i \(-0.182746\pi\)
0.839673 + 0.543092i \(0.182746\pi\)
\(758\) 32.0958 1.16577
\(759\) −24.2429 −0.879961
\(760\) 1.71752 0.0623010
\(761\) −19.5516 −0.708746 −0.354373 0.935104i \(-0.615306\pi\)
−0.354373 + 0.935104i \(0.615306\pi\)
\(762\) 32.4402 1.17519
\(763\) −11.6852 −0.423032
\(764\) 16.5160 0.597526
\(765\) 0.235919 0.00852968
\(766\) −17.1137 −0.618342
\(767\) 10.0893 0.364302
\(768\) −1.94007 −0.0700063
\(769\) 9.21475 0.332292 0.166146 0.986101i \(-0.446868\pi\)
0.166146 + 0.986101i \(0.446868\pi\)
\(770\) 1.87576 0.0675977
\(771\) 30.9404 1.11429
\(772\) 8.13814 0.292898
\(773\) 30.9269 1.11236 0.556181 0.831061i \(-0.312266\pi\)
0.556181 + 0.831061i \(0.312266\pi\)
\(774\) −8.50239 −0.305612
\(775\) −36.2098 −1.30069
\(776\) −1.29351 −0.0464344
\(777\) 57.4784 2.06203
\(778\) 21.6713 0.776954
\(779\) −51.6057 −1.84897
\(780\) 0.872272 0.0312324
\(781\) 10.6669 0.381690
\(782\) −5.76642 −0.206207
\(783\) −14.5918 −0.521467
\(784\) 0.855018 0.0305364
\(785\) 0.705229 0.0251707
\(786\) −12.1455 −0.433214
\(787\) 18.2309 0.649861 0.324930 0.945738i \(-0.394659\pi\)
0.324930 + 0.945738i \(0.394659\pi\)
\(788\) −15.3167 −0.545633
\(789\) 57.4691 2.04596
\(790\) −3.42691 −0.121924
\(791\) 16.1222 0.573241
\(792\) 1.85844 0.0660367
\(793\) 3.92274 0.139300
\(794\) 22.8325 0.810296
\(795\) 3.47395 0.123208
\(796\) 10.5399 0.373577
\(797\) 0.247791 0.00877722 0.00438861 0.999990i \(-0.498603\pi\)
0.00438861 + 0.999990i \(0.498603\pi\)
\(798\) −33.9482 −1.20175
\(799\) 2.09634 0.0741633
\(800\) 4.92432 0.174101
\(801\) −6.28620 −0.222112
\(802\) 18.5160 0.653824
\(803\) 0.605805 0.0213784
\(804\) 7.47193 0.263515
\(805\) −3.95996 −0.139570
\(806\) −12.0181 −0.423321
\(807\) −56.7788 −1.99871
\(808\) 0.460574 0.0162029
\(809\) 3.85660 0.135591 0.0677954 0.997699i \(-0.478403\pi\)
0.0677954 + 0.997699i \(0.478403\pi\)
\(810\) −2.94571 −0.103502
\(811\) 18.6514 0.654939 0.327470 0.944862i \(-0.393804\pi\)
0.327470 + 0.944862i \(0.393804\pi\)
\(812\) 9.42686 0.330818
\(813\) 1.49657 0.0524870
\(814\) 25.7182 0.901422
\(815\) 3.24627 0.113712
\(816\) 2.17813 0.0762497
\(817\) 69.4937 2.43128
\(818\) −4.45069 −0.155615
\(819\) −3.49907 −0.122267
\(820\) 2.27378 0.0794040
\(821\) −2.35684 −0.0822544 −0.0411272 0.999154i \(-0.513095\pi\)
−0.0411272 + 0.999154i \(0.513095\pi\)
\(822\) 17.2736 0.602485
\(823\) −32.0784 −1.11818 −0.559092 0.829106i \(-0.688850\pi\)
−0.559092 + 0.829106i \(0.688850\pi\)
\(824\) −5.21367 −0.181627
\(825\) −23.2429 −0.809215
\(826\) 17.3012 0.601984
\(827\) 33.3082 1.15824 0.579120 0.815242i \(-0.303396\pi\)
0.579120 + 0.815242i \(0.303396\pi\)
\(828\) −3.92339 −0.136347
\(829\) 37.8284 1.31383 0.656917 0.753963i \(-0.271860\pi\)
0.656917 + 0.753963i \(0.271860\pi\)
\(830\) 4.58218 0.159050
\(831\) 23.4327 0.812871
\(832\) 1.63440 0.0566626
\(833\) −0.959934 −0.0332597
\(834\) 5.61374 0.194388
\(835\) −1.98889 −0.0688282
\(836\) −15.1898 −0.525350
\(837\) 31.9002 1.10263
\(838\) −15.6752 −0.541491
\(839\) 25.2002 0.870008 0.435004 0.900429i \(-0.356747\pi\)
0.435004 + 0.900429i \(0.356747\pi\)
\(840\) 1.49578 0.0516093
\(841\) −17.6868 −0.609888
\(842\) −24.5106 −0.844691
\(843\) −17.2907 −0.595524
\(844\) −15.7812 −0.543210
\(845\) 2.84135 0.0977453
\(846\) 1.42632 0.0490379
\(847\) 14.2402 0.489300
\(848\) 6.50923 0.223528
\(849\) 5.27190 0.180931
\(850\) −5.52857 −0.189628
\(851\) −54.2943 −1.86118
\(852\) 8.50603 0.291412
\(853\) −17.9826 −0.615714 −0.307857 0.951433i \(-0.599612\pi\)
−0.307857 + 0.951433i \(0.599612\pi\)
\(854\) 6.72674 0.230184
\(855\) −1.31197 −0.0448683
\(856\) −3.51857 −0.120262
\(857\) 12.0180 0.410526 0.205263 0.978707i \(-0.434195\pi\)
0.205263 + 0.978707i \(0.434195\pi\)
\(858\) −7.71440 −0.263365
\(859\) 10.9243 0.372734 0.186367 0.982480i \(-0.440329\pi\)
0.186367 + 0.982480i \(0.440329\pi\)
\(860\) −3.06194 −0.104411
\(861\) −44.9432 −1.53166
\(862\) −15.5408 −0.529322
\(863\) 19.5829 0.666611 0.333305 0.942819i \(-0.391836\pi\)
0.333305 + 0.942819i \(0.391836\pi\)
\(864\) −4.33824 −0.147590
\(865\) −3.52836 −0.119968
\(866\) −34.5338 −1.17351
\(867\) 30.5358 1.03705
\(868\) −20.6088 −0.699508
\(869\) 30.3077 1.02812
\(870\) 1.79510 0.0608594
\(871\) −6.29467 −0.213287
\(872\) −4.16929 −0.141190
\(873\) 0.988078 0.0334414
\(874\) 32.0675 1.08470
\(875\) −7.65158 −0.258671
\(876\) 0.483085 0.0163219
\(877\) −10.5926 −0.357686 −0.178843 0.983878i \(-0.557235\pi\)
−0.178843 + 0.983878i \(0.557235\pi\)
\(878\) −13.1241 −0.442917
\(879\) 32.1516 1.08445
\(880\) 0.669273 0.0225612
\(881\) 0.183373 0.00617799 0.00308899 0.999995i \(-0.499017\pi\)
0.00308899 + 0.999995i \(0.499017\pi\)
\(882\) −0.653125 −0.0219919
\(883\) −16.4433 −0.553363 −0.276681 0.960962i \(-0.589235\pi\)
−0.276681 + 0.960962i \(0.589235\pi\)
\(884\) −1.83495 −0.0617160
\(885\) 3.29455 0.110745
\(886\) 18.1521 0.609830
\(887\) −9.45852 −0.317586 −0.158793 0.987312i \(-0.550760\pi\)
−0.158793 + 0.987312i \(0.550760\pi\)
\(888\) 20.5084 0.688216
\(889\) −46.8641 −1.57177
\(890\) −2.26383 −0.0758838
\(891\) 26.0519 0.872772
\(892\) 19.7771 0.662187
\(893\) −11.6579 −0.390118
\(894\) −20.0415 −0.670288
\(895\) −4.60219 −0.153834
\(896\) 2.80268 0.0936310
\(897\) 16.2860 0.543775
\(898\) 2.68659 0.0896528
\(899\) −24.7328 −0.824884
\(900\) −3.76156 −0.125385
\(901\) −7.30795 −0.243463
\(902\) −20.1094 −0.669570
\(903\) 60.5217 2.01404
\(904\) 5.75243 0.191323
\(905\) 3.04248 0.101135
\(906\) −36.5007 −1.21266
\(907\) −12.8173 −0.425591 −0.212796 0.977097i \(-0.568257\pi\)
−0.212796 + 0.977097i \(0.568257\pi\)
\(908\) 2.17483 0.0721744
\(909\) −0.351820 −0.0116691
\(910\) −1.26011 −0.0417722
\(911\) 20.2926 0.672323 0.336161 0.941804i \(-0.390871\pi\)
0.336161 + 0.941804i \(0.390871\pi\)
\(912\) −12.1127 −0.401093
\(913\) −40.5249 −1.34118
\(914\) −27.5313 −0.910654
\(915\) 1.28093 0.0423462
\(916\) −16.7118 −0.552173
\(917\) 17.5457 0.579410
\(918\) 4.87057 0.160753
\(919\) −9.33957 −0.308084 −0.154042 0.988064i \(-0.549229\pi\)
−0.154042 + 0.988064i \(0.549229\pi\)
\(920\) −1.41292 −0.0465825
\(921\) −38.5542 −1.27040
\(922\) 3.54762 0.116835
\(923\) −7.16585 −0.235867
\(924\) −13.2287 −0.435193
\(925\) −52.0547 −1.71155
\(926\) 19.5632 0.642887
\(927\) 3.98258 0.130805
\(928\) 3.36352 0.110413
\(929\) −23.9109 −0.784491 −0.392245 0.919861i \(-0.628302\pi\)
−0.392245 + 0.919861i \(0.628302\pi\)
\(930\) −3.92440 −0.128686
\(931\) 5.33827 0.174955
\(932\) −23.9078 −0.783127
\(933\) 39.4137 1.29035
\(934\) −9.56141 −0.312859
\(935\) −0.751397 −0.0245733
\(936\) −1.24847 −0.0408076
\(937\) −12.1991 −0.398527 −0.199264 0.979946i \(-0.563855\pi\)
−0.199264 + 0.979946i \(0.563855\pi\)
\(938\) −10.7942 −0.352442
\(939\) 62.4008 2.03637
\(940\) 0.513657 0.0167536
\(941\) 40.0558 1.30578 0.652891 0.757452i \(-0.273556\pi\)
0.652891 + 0.757452i \(0.273556\pi\)
\(942\) −4.97360 −0.162049
\(943\) 42.4534 1.38247
\(944\) 6.17307 0.200916
\(945\) 3.34475 0.108805
\(946\) 27.0799 0.880443
\(947\) 48.3544 1.57131 0.785653 0.618667i \(-0.212327\pi\)
0.785653 + 0.618667i \(0.212327\pi\)
\(948\) 24.1681 0.784944
\(949\) −0.406972 −0.0132109
\(950\) 30.7448 0.997494
\(951\) 48.8428 1.58384
\(952\) −3.14659 −0.101981
\(953\) 2.27188 0.0735933 0.0367967 0.999323i \(-0.488285\pi\)
0.0367967 + 0.999323i \(0.488285\pi\)
\(954\) −4.97222 −0.160982
\(955\) −4.54339 −0.147021
\(956\) −5.15820 −0.166828
\(957\) −15.8759 −0.513194
\(958\) 18.8832 0.610089
\(959\) −24.9539 −0.805803
\(960\) 0.533696 0.0172250
\(961\) 23.0703 0.744202
\(962\) −17.2771 −0.557037
\(963\) 2.68774 0.0866112
\(964\) 13.3436 0.429769
\(965\) −2.23873 −0.0720672
\(966\) 27.9275 0.898551
\(967\) −20.4777 −0.658519 −0.329260 0.944239i \(-0.606799\pi\)
−0.329260 + 0.944239i \(0.606799\pi\)
\(968\) 5.08093 0.163307
\(969\) 13.5990 0.436864
\(970\) 0.355834 0.0114251
\(971\) −16.7850 −0.538656 −0.269328 0.963049i \(-0.586802\pi\)
−0.269328 + 0.963049i \(0.586802\pi\)
\(972\) 7.75977 0.248895
\(973\) −8.10977 −0.259987
\(974\) −11.2812 −0.361474
\(975\) 15.6143 0.500057
\(976\) 2.40011 0.0768256
\(977\) 35.9953 1.15159 0.575796 0.817594i \(-0.304692\pi\)
0.575796 + 0.817594i \(0.304692\pi\)
\(978\) −22.8942 −0.732075
\(979\) 20.0214 0.639886
\(980\) −0.235208 −0.00751344
\(981\) 3.18480 0.101683
\(982\) −2.40116 −0.0766240
\(983\) −23.3866 −0.745915 −0.372958 0.927848i \(-0.621656\pi\)
−0.372958 + 0.927848i \(0.621656\pi\)
\(984\) −16.0358 −0.511202
\(985\) 4.21348 0.134253
\(986\) −3.77624 −0.120260
\(987\) −10.1528 −0.323168
\(988\) 10.2043 0.324642
\(989\) −57.1690 −1.81787
\(990\) −0.511239 −0.0162483
\(991\) 4.45132 0.141401 0.0707004 0.997498i \(-0.477477\pi\)
0.0707004 + 0.997498i \(0.477477\pi\)
\(992\) −7.35325 −0.233466
\(993\) 49.0534 1.55666
\(994\) −12.2881 −0.389753
\(995\) −2.89943 −0.0919182
\(996\) −32.3156 −1.02396
\(997\) −36.5925 −1.15890 −0.579448 0.815009i \(-0.696732\pi\)
−0.579448 + 0.815009i \(0.696732\pi\)
\(998\) −27.1221 −0.858534
\(999\) 45.8593 1.45092
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 4006.2.a.g.1.8 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.g.1.8 40 1.1 even 1 trivial