Properties

Label 8007.2.a.f.1.19
Level 8007
Weight 2
Character 8007.1
Self dual yes
Analytic conductor 63.936
Analytic rank 1
Dimension 48
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(48\)
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 \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.857233 q^{2} -1.00000 q^{3} -1.26515 q^{4} +0.241794 q^{5} +0.857233 q^{6} -3.40893 q^{7} +2.79900 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.857233 q^{2} -1.00000 q^{3} -1.26515 q^{4} +0.241794 q^{5} +0.857233 q^{6} -3.40893 q^{7} +2.79900 q^{8} +1.00000 q^{9} -0.207274 q^{10} +4.52587 q^{11} +1.26515 q^{12} -3.66863 q^{13} +2.92225 q^{14} -0.241794 q^{15} +0.130910 q^{16} -1.00000 q^{17} -0.857233 q^{18} +3.02291 q^{19} -0.305906 q^{20} +3.40893 q^{21} -3.87973 q^{22} -6.34192 q^{23} -2.79900 q^{24} -4.94154 q^{25} +3.14487 q^{26} -1.00000 q^{27} +4.31281 q^{28} +5.43257 q^{29} +0.207274 q^{30} +2.05869 q^{31} -5.71021 q^{32} -4.52587 q^{33} +0.857233 q^{34} -0.824258 q^{35} -1.26515 q^{36} +9.39150 q^{37} -2.59134 q^{38} +3.66863 q^{39} +0.676781 q^{40} +0.671979 q^{41} -2.92225 q^{42} -6.04121 q^{43} -5.72591 q^{44} +0.241794 q^{45} +5.43650 q^{46} -0.151884 q^{47} -0.130910 q^{48} +4.62079 q^{49} +4.23605 q^{50} +1.00000 q^{51} +4.64137 q^{52} -8.36573 q^{53} +0.857233 q^{54} +1.09433 q^{55} -9.54158 q^{56} -3.02291 q^{57} -4.65698 q^{58} +1.97010 q^{59} +0.305906 q^{60} +0.358392 q^{61} -1.76478 q^{62} -3.40893 q^{63} +4.63316 q^{64} -0.887052 q^{65} +3.87973 q^{66} +1.12443 q^{67} +1.26515 q^{68} +6.34192 q^{69} +0.706582 q^{70} -4.67774 q^{71} +2.79900 q^{72} +0.743140 q^{73} -8.05070 q^{74} +4.94154 q^{75} -3.82444 q^{76} -15.4284 q^{77} -3.14487 q^{78} +14.4989 q^{79} +0.0316532 q^{80} +1.00000 q^{81} -0.576043 q^{82} +4.57707 q^{83} -4.31281 q^{84} -0.241794 q^{85} +5.17872 q^{86} -5.43257 q^{87} +12.6679 q^{88} +1.89104 q^{89} -0.207274 q^{90} +12.5061 q^{91} +8.02349 q^{92} -2.05869 q^{93} +0.130200 q^{94} +0.730922 q^{95} +5.71021 q^{96} -1.97519 q^{97} -3.96110 q^{98} +4.52587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} + O(q^{10}) \) \( 48q - q^{2} - 48q^{3} + 45q^{4} + q^{5} + q^{6} - 13q^{7} - 6q^{8} + 48q^{9} - 20q^{10} + 5q^{11} - 45q^{12} - 8q^{13} + 4q^{14} - q^{15} + 39q^{16} - 48q^{17} - q^{18} - 6q^{19} + 6q^{20} + 13q^{21} - 35q^{22} - 8q^{23} + 6q^{24} + 13q^{25} + 17q^{26} - 48q^{27} - 38q^{28} + q^{29} + 20q^{30} - 21q^{31} - 3q^{32} - 5q^{33} + q^{34} + 19q^{35} + 45q^{36} - 58q^{37} - 14q^{38} + 8q^{39} - 54q^{40} - 3q^{41} - 4q^{42} - 33q^{43} + 2q^{44} + q^{45} - 26q^{46} + 9q^{47} - 39q^{48} + 11q^{49} + 4q^{50} + 48q^{51} - 31q^{52} - 33q^{53} + q^{54} - 21q^{55} + 6q^{57} - 55q^{58} + 77q^{59} - 6q^{60} - 29q^{61} - 46q^{62} - 13q^{63} + 24q^{64} - 49q^{65} + 35q^{66} - 44q^{67} - 45q^{68} + 8q^{69} + 4q^{70} + 22q^{71} - 6q^{72} - 63q^{73} - 16q^{74} - 13q^{75} - 46q^{76} - 30q^{77} - 17q^{78} - 46q^{79} - 14q^{80} + 48q^{81} - 75q^{82} + 11q^{83} + 38q^{84} - q^{85} + 8q^{86} - q^{87} - 116q^{88} + 10q^{89} - 20q^{90} - 67q^{91} - 64q^{92} + 21q^{93} - 16q^{94} - 8q^{95} + 3q^{96} - 96q^{97} - 46q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.857233 −0.606155 −0.303078 0.952966i \(-0.598014\pi\)
−0.303078 + 0.952966i \(0.598014\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.26515 −0.632576
\(5\) 0.241794 0.108134 0.0540668 0.998537i \(-0.482782\pi\)
0.0540668 + 0.998537i \(0.482782\pi\)
\(6\) 0.857233 0.349964
\(7\) −3.40893 −1.28845 −0.644227 0.764834i \(-0.722821\pi\)
−0.644227 + 0.764834i \(0.722821\pi\)
\(8\) 2.79900 0.989595
\(9\) 1.00000 0.333333
\(10\) −0.207274 −0.0655458
\(11\) 4.52587 1.36460 0.682301 0.731072i \(-0.260979\pi\)
0.682301 + 0.731072i \(0.260979\pi\)
\(12\) 1.26515 0.365218
\(13\) −3.66863 −1.01749 −0.508747 0.860916i \(-0.669891\pi\)
−0.508747 + 0.860916i \(0.669891\pi\)
\(14\) 2.92225 0.781003
\(15\) −0.241794 −0.0624309
\(16\) 0.130910 0.0327274
\(17\) −1.00000 −0.242536
\(18\) −0.857233 −0.202052
\(19\) 3.02291 0.693504 0.346752 0.937957i \(-0.387285\pi\)
0.346752 + 0.937957i \(0.387285\pi\)
\(20\) −0.305906 −0.0684027
\(21\) 3.40893 0.743889
\(22\) −3.87973 −0.827161
\(23\) −6.34192 −1.32238 −0.661191 0.750218i \(-0.729949\pi\)
−0.661191 + 0.750218i \(0.729949\pi\)
\(24\) −2.79900 −0.571343
\(25\) −4.94154 −0.988307
\(26\) 3.14487 0.616760
\(27\) −1.00000 −0.192450
\(28\) 4.31281 0.815044
\(29\) 5.43257 1.00880 0.504402 0.863469i \(-0.331713\pi\)
0.504402 + 0.863469i \(0.331713\pi\)
\(30\) 0.207274 0.0378429
\(31\) 2.05869 0.369752 0.184876 0.982762i \(-0.440812\pi\)
0.184876 + 0.982762i \(0.440812\pi\)
\(32\) −5.71021 −1.00943
\(33\) −4.52587 −0.787853
\(34\) 0.857233 0.147014
\(35\) −0.824258 −0.139325
\(36\) −1.26515 −0.210859
\(37\) 9.39150 1.54395 0.771976 0.635651i \(-0.219268\pi\)
0.771976 + 0.635651i \(0.219268\pi\)
\(38\) −2.59134 −0.420371
\(39\) 3.66863 0.587451
\(40\) 0.676781 0.107008
\(41\) 0.671979 0.104945 0.0524727 0.998622i \(-0.483290\pi\)
0.0524727 + 0.998622i \(0.483290\pi\)
\(42\) −2.92225 −0.450912
\(43\) −6.04121 −0.921275 −0.460638 0.887588i \(-0.652379\pi\)
−0.460638 + 0.887588i \(0.652379\pi\)
\(44\) −5.72591 −0.863214
\(45\) 0.241794 0.0360445
\(46\) 5.43650 0.801569
\(47\) −0.151884 −0.0221546 −0.0110773 0.999939i \(-0.503526\pi\)
−0.0110773 + 0.999939i \(0.503526\pi\)
\(48\) −0.130910 −0.0188952
\(49\) 4.62079 0.660113
\(50\) 4.23605 0.599068
\(51\) 1.00000 0.140028
\(52\) 4.64137 0.643642
\(53\) −8.36573 −1.14912 −0.574561 0.818462i \(-0.694827\pi\)
−0.574561 + 0.818462i \(0.694827\pi\)
\(54\) 0.857233 0.116655
\(55\) 1.09433 0.147559
\(56\) −9.54158 −1.27505
\(57\) −3.02291 −0.400395
\(58\) −4.65698 −0.611492
\(59\) 1.97010 0.256486 0.128243 0.991743i \(-0.459066\pi\)
0.128243 + 0.991743i \(0.459066\pi\)
\(60\) 0.305906 0.0394923
\(61\) 0.358392 0.0458874 0.0229437 0.999737i \(-0.492696\pi\)
0.0229437 + 0.999737i \(0.492696\pi\)
\(62\) −1.76478 −0.224127
\(63\) −3.40893 −0.429485
\(64\) 4.63316 0.579146
\(65\) −0.887052 −0.110025
\(66\) 3.87973 0.477561
\(67\) 1.12443 0.137371 0.0686853 0.997638i \(-0.478120\pi\)
0.0686853 + 0.997638i \(0.478120\pi\)
\(68\) 1.26515 0.153422
\(69\) 6.34192 0.763477
\(70\) 0.706582 0.0844527
\(71\) −4.67774 −0.555145 −0.277573 0.960705i \(-0.589530\pi\)
−0.277573 + 0.960705i \(0.589530\pi\)
\(72\) 2.79900 0.329865
\(73\) 0.743140 0.0869779 0.0434890 0.999054i \(-0.486153\pi\)
0.0434890 + 0.999054i \(0.486153\pi\)
\(74\) −8.05070 −0.935875
\(75\) 4.94154 0.570599
\(76\) −3.82444 −0.438693
\(77\) −15.4284 −1.75823
\(78\) −3.14487 −0.356086
\(79\) 14.4989 1.63125 0.815624 0.578582i \(-0.196394\pi\)
0.815624 + 0.578582i \(0.196394\pi\)
\(80\) 0.0316532 0.00353893
\(81\) 1.00000 0.111111
\(82\) −0.576043 −0.0636133
\(83\) 4.57707 0.502399 0.251200 0.967935i \(-0.419175\pi\)
0.251200 + 0.967935i \(0.419175\pi\)
\(84\) −4.31281 −0.470566
\(85\) −0.241794 −0.0262262
\(86\) 5.17872 0.558436
\(87\) −5.43257 −0.582433
\(88\) 12.6679 1.35040
\(89\) 1.89104 0.200449 0.100225 0.994965i \(-0.468044\pi\)
0.100225 + 0.994965i \(0.468044\pi\)
\(90\) −0.207274 −0.0218486
\(91\) 12.5061 1.31099
\(92\) 8.02349 0.836506
\(93\) −2.05869 −0.213476
\(94\) 0.130200 0.0134291
\(95\) 0.730922 0.0749910
\(96\) 5.71021 0.582796
\(97\) −1.97519 −0.200550 −0.100275 0.994960i \(-0.531972\pi\)
−0.100275 + 0.994960i \(0.531972\pi\)
\(98\) −3.96110 −0.400131
\(99\) 4.52587 0.454867
\(100\) 6.25179 0.625179
\(101\) 5.48102 0.545381 0.272691 0.962102i \(-0.412086\pi\)
0.272691 + 0.962102i \(0.412086\pi\)
\(102\) −0.857233 −0.0848787
\(103\) 7.38351 0.727519 0.363760 0.931493i \(-0.381493\pi\)
0.363760 + 0.931493i \(0.381493\pi\)
\(104\) −10.2685 −1.00691
\(105\) 0.824258 0.0804394
\(106\) 7.17139 0.696547
\(107\) −14.7394 −1.42491 −0.712454 0.701719i \(-0.752416\pi\)
−0.712454 + 0.701719i \(0.752416\pi\)
\(108\) 1.26515 0.121739
\(109\) −1.57664 −0.151015 −0.0755073 0.997145i \(-0.524058\pi\)
−0.0755073 + 0.997145i \(0.524058\pi\)
\(110\) −0.938095 −0.0894438
\(111\) −9.39150 −0.891402
\(112\) −0.446262 −0.0421678
\(113\) 4.29677 0.404206 0.202103 0.979364i \(-0.435222\pi\)
0.202103 + 0.979364i \(0.435222\pi\)
\(114\) 2.59134 0.242701
\(115\) −1.53344 −0.142994
\(116\) −6.87303 −0.638145
\(117\) −3.66863 −0.339165
\(118\) −1.68884 −0.155470
\(119\) 3.40893 0.312496
\(120\) −0.676781 −0.0617813
\(121\) 9.48352 0.862138
\(122\) −0.307225 −0.0278149
\(123\) −0.671979 −0.0605903
\(124\) −2.60456 −0.233896
\(125\) −2.40380 −0.215003
\(126\) 2.92225 0.260334
\(127\) −15.9253 −1.41314 −0.706572 0.707641i \(-0.749760\pi\)
−0.706572 + 0.707641i \(0.749760\pi\)
\(128\) 7.44872 0.658380
\(129\) 6.04121 0.531899
\(130\) 0.760411 0.0666924
\(131\) −4.32209 −0.377623 −0.188812 0.982013i \(-0.560464\pi\)
−0.188812 + 0.982013i \(0.560464\pi\)
\(132\) 5.72591 0.498377
\(133\) −10.3049 −0.893547
\(134\) −0.963897 −0.0832680
\(135\) −0.241794 −0.0208103
\(136\) −2.79900 −0.240012
\(137\) 7.49284 0.640157 0.320078 0.947391i \(-0.396291\pi\)
0.320078 + 0.947391i \(0.396291\pi\)
\(138\) −5.43650 −0.462786
\(139\) 15.9522 1.35304 0.676522 0.736422i \(-0.263486\pi\)
0.676522 + 0.736422i \(0.263486\pi\)
\(140\) 1.04281 0.0881337
\(141\) 0.151884 0.0127910
\(142\) 4.00991 0.336504
\(143\) −16.6037 −1.38847
\(144\) 0.130910 0.0109091
\(145\) 1.31356 0.109086
\(146\) −0.637044 −0.0527221
\(147\) −4.62079 −0.381117
\(148\) −11.8817 −0.976667
\(149\) −4.20165 −0.344213 −0.172106 0.985078i \(-0.555057\pi\)
−0.172106 + 0.985078i \(0.555057\pi\)
\(150\) −4.23605 −0.345872
\(151\) 11.6665 0.949410 0.474705 0.880145i \(-0.342555\pi\)
0.474705 + 0.880145i \(0.342555\pi\)
\(152\) 8.46112 0.686287
\(153\) −1.00000 −0.0808452
\(154\) 13.2257 1.06576
\(155\) 0.497779 0.0399826
\(156\) −4.64137 −0.371607
\(157\) −1.00000 −0.0798087
\(158\) −12.4289 −0.988790
\(159\) 8.36573 0.663446
\(160\) −1.38070 −0.109154
\(161\) 21.6191 1.70383
\(162\) −0.857233 −0.0673506
\(163\) 17.3613 1.35984 0.679920 0.733286i \(-0.262015\pi\)
0.679920 + 0.733286i \(0.262015\pi\)
\(164\) −0.850155 −0.0663859
\(165\) −1.09433 −0.0851934
\(166\) −3.92362 −0.304532
\(167\) −3.28213 −0.253979 −0.126989 0.991904i \(-0.540531\pi\)
−0.126989 + 0.991904i \(0.540531\pi\)
\(168\) 9.54158 0.736149
\(169\) 0.458830 0.0352946
\(170\) 0.207274 0.0158972
\(171\) 3.02291 0.231168
\(172\) 7.64304 0.582776
\(173\) 19.1960 1.45945 0.729723 0.683743i \(-0.239649\pi\)
0.729723 + 0.683743i \(0.239649\pi\)
\(174\) 4.65698 0.353045
\(175\) 16.8453 1.27339
\(176\) 0.592480 0.0446599
\(177\) −1.97010 −0.148082
\(178\) −1.62106 −0.121503
\(179\) −12.5693 −0.939470 −0.469735 0.882807i \(-0.655651\pi\)
−0.469735 + 0.882807i \(0.655651\pi\)
\(180\) −0.305906 −0.0228009
\(181\) 1.55001 0.115211 0.0576056 0.998339i \(-0.481653\pi\)
0.0576056 + 0.998339i \(0.481653\pi\)
\(182\) −10.7206 −0.794666
\(183\) −0.358392 −0.0264931
\(184\) −17.7510 −1.30862
\(185\) 2.27081 0.166953
\(186\) 1.76478 0.129400
\(187\) −4.52587 −0.330965
\(188\) 0.192156 0.0140144
\(189\) 3.40893 0.247963
\(190\) −0.626571 −0.0454562
\(191\) 24.8936 1.80123 0.900617 0.434613i \(-0.143115\pi\)
0.900617 + 0.434613i \(0.143115\pi\)
\(192\) −4.63316 −0.334370
\(193\) −0.656214 −0.0472353 −0.0236177 0.999721i \(-0.507518\pi\)
−0.0236177 + 0.999721i \(0.507518\pi\)
\(194\) 1.69320 0.121564
\(195\) 0.887052 0.0635231
\(196\) −5.84600 −0.417571
\(197\) 9.55795 0.680975 0.340488 0.940249i \(-0.389408\pi\)
0.340488 + 0.940249i \(0.389408\pi\)
\(198\) −3.87973 −0.275720
\(199\) 4.21395 0.298719 0.149359 0.988783i \(-0.452279\pi\)
0.149359 + 0.988783i \(0.452279\pi\)
\(200\) −13.8313 −0.978023
\(201\) −1.12443 −0.0793110
\(202\) −4.69851 −0.330586
\(203\) −18.5193 −1.29980
\(204\) −1.26515 −0.0885783
\(205\) 0.162480 0.0113481
\(206\) −6.32939 −0.440990
\(207\) −6.34192 −0.440794
\(208\) −0.480259 −0.0333000
\(209\) 13.6813 0.946356
\(210\) −0.706582 −0.0487588
\(211\) 14.7664 1.01656 0.508281 0.861191i \(-0.330281\pi\)
0.508281 + 0.861191i \(0.330281\pi\)
\(212\) 10.5839 0.726906
\(213\) 4.67774 0.320513
\(214\) 12.6351 0.863716
\(215\) −1.46073 −0.0996208
\(216\) −2.79900 −0.190448
\(217\) −7.01793 −0.476408
\(218\) 1.35155 0.0915383
\(219\) −0.743140 −0.0502167
\(220\) −1.38449 −0.0933424
\(221\) 3.66863 0.246779
\(222\) 8.05070 0.540328
\(223\) 6.48515 0.434277 0.217139 0.976141i \(-0.430328\pi\)
0.217139 + 0.976141i \(0.430328\pi\)
\(224\) 19.4657 1.30061
\(225\) −4.94154 −0.329436
\(226\) −3.68334 −0.245012
\(227\) 14.3079 0.949648 0.474824 0.880081i \(-0.342512\pi\)
0.474824 + 0.880081i \(0.342512\pi\)
\(228\) 3.82444 0.253280
\(229\) 11.7106 0.773861 0.386931 0.922109i \(-0.373535\pi\)
0.386931 + 0.922109i \(0.373535\pi\)
\(230\) 1.31451 0.0866765
\(231\) 15.4284 1.01511
\(232\) 15.2058 0.998307
\(233\) −25.2716 −1.65560 −0.827798 0.561026i \(-0.810407\pi\)
−0.827798 + 0.561026i \(0.810407\pi\)
\(234\) 3.14487 0.205587
\(235\) −0.0367247 −0.00239565
\(236\) −2.49248 −0.162247
\(237\) −14.4989 −0.941802
\(238\) −2.92225 −0.189421
\(239\) 10.0441 0.649698 0.324849 0.945766i \(-0.394687\pi\)
0.324849 + 0.945766i \(0.394687\pi\)
\(240\) −0.0316532 −0.00204320
\(241\) −17.3874 −1.12002 −0.560010 0.828486i \(-0.689203\pi\)
−0.560010 + 0.828486i \(0.689203\pi\)
\(242\) −8.12958 −0.522590
\(243\) −1.00000 −0.0641500
\(244\) −0.453420 −0.0290272
\(245\) 1.11728 0.0713804
\(246\) 0.576043 0.0367271
\(247\) −11.0899 −0.705636
\(248\) 5.76227 0.365905
\(249\) −4.57707 −0.290060
\(250\) 2.06062 0.130325
\(251\) −30.6012 −1.93153 −0.965765 0.259418i \(-0.916469\pi\)
−0.965765 + 0.259418i \(0.916469\pi\)
\(252\) 4.31281 0.271681
\(253\) −28.7027 −1.80452
\(254\) 13.6517 0.856585
\(255\) 0.241794 0.0151417
\(256\) −15.6516 −0.978226
\(257\) 1.86778 0.116509 0.0582544 0.998302i \(-0.481447\pi\)
0.0582544 + 0.998302i \(0.481447\pi\)
\(258\) −5.17872 −0.322413
\(259\) −32.0149 −1.98931
\(260\) 1.12226 0.0695993
\(261\) 5.43257 0.336268
\(262\) 3.70504 0.228898
\(263\) 2.20651 0.136059 0.0680296 0.997683i \(-0.478329\pi\)
0.0680296 + 0.997683i \(0.478329\pi\)
\(264\) −12.6679 −0.779655
\(265\) −2.02278 −0.124259
\(266\) 8.83370 0.541629
\(267\) −1.89104 −0.115729
\(268\) −1.42257 −0.0868973
\(269\) −4.73650 −0.288789 −0.144395 0.989520i \(-0.546123\pi\)
−0.144395 + 0.989520i \(0.546123\pi\)
\(270\) 0.207274 0.0126143
\(271\) −27.8344 −1.69082 −0.845408 0.534120i \(-0.820643\pi\)
−0.845408 + 0.534120i \(0.820643\pi\)
\(272\) −0.130910 −0.00793757
\(273\) −12.5061 −0.756903
\(274\) −6.42311 −0.388034
\(275\) −22.3648 −1.34865
\(276\) −8.02349 −0.482957
\(277\) 16.8515 1.01251 0.506253 0.862385i \(-0.331030\pi\)
0.506253 + 0.862385i \(0.331030\pi\)
\(278\) −13.6747 −0.820155
\(279\) 2.05869 0.123251
\(280\) −2.30710 −0.137875
\(281\) −7.80481 −0.465596 −0.232798 0.972525i \(-0.574788\pi\)
−0.232798 + 0.972525i \(0.574788\pi\)
\(282\) −0.130200 −0.00775330
\(283\) −6.52256 −0.387726 −0.193863 0.981029i \(-0.562102\pi\)
−0.193863 + 0.981029i \(0.562102\pi\)
\(284\) 5.91804 0.351171
\(285\) −0.730922 −0.0432961
\(286\) 14.2333 0.841631
\(287\) −2.29073 −0.135217
\(288\) −5.71021 −0.336477
\(289\) 1.00000 0.0588235
\(290\) −1.12603 −0.0661228
\(291\) 1.97519 0.115787
\(292\) −0.940184 −0.0550201
\(293\) −27.3131 −1.59565 −0.797825 0.602889i \(-0.794016\pi\)
−0.797825 + 0.602889i \(0.794016\pi\)
\(294\) 3.96110 0.231016
\(295\) 0.476360 0.0277347
\(296\) 26.2868 1.52789
\(297\) −4.52587 −0.262618
\(298\) 3.60180 0.208646
\(299\) 23.2661 1.34552
\(300\) −6.25179 −0.360947
\(301\) 20.5940 1.18702
\(302\) −10.0009 −0.575490
\(303\) −5.48102 −0.314876
\(304\) 0.395729 0.0226966
\(305\) 0.0866570 0.00496196
\(306\) 0.857233 0.0490048
\(307\) 9.25543 0.528235 0.264118 0.964490i \(-0.414919\pi\)
0.264118 + 0.964490i \(0.414919\pi\)
\(308\) 19.5192 1.11221
\(309\) −7.38351 −0.420033
\(310\) −0.426713 −0.0242357
\(311\) 10.6691 0.604991 0.302495 0.953151i \(-0.402180\pi\)
0.302495 + 0.953151i \(0.402180\pi\)
\(312\) 10.2685 0.581338
\(313\) −2.68328 −0.151668 −0.0758341 0.997120i \(-0.524162\pi\)
−0.0758341 + 0.997120i \(0.524162\pi\)
\(314\) 0.857233 0.0483765
\(315\) −0.824258 −0.0464417
\(316\) −18.3432 −1.03189
\(317\) 3.79941 0.213396 0.106698 0.994291i \(-0.465972\pi\)
0.106698 + 0.994291i \(0.465972\pi\)
\(318\) −7.17139 −0.402151
\(319\) 24.5871 1.37662
\(320\) 1.12027 0.0626251
\(321\) 14.7394 0.822671
\(322\) −18.5327 −1.03278
\(323\) −3.02291 −0.168199
\(324\) −1.26515 −0.0702862
\(325\) 18.1287 1.00560
\(326\) −14.8827 −0.824274
\(327\) 1.57664 0.0871883
\(328\) 1.88087 0.103853
\(329\) 0.517762 0.0285451
\(330\) 0.938095 0.0516404
\(331\) −23.4474 −1.28879 −0.644393 0.764694i \(-0.722890\pi\)
−0.644393 + 0.764694i \(0.722890\pi\)
\(332\) −5.79069 −0.317805
\(333\) 9.39150 0.514651
\(334\) 2.81355 0.153951
\(335\) 0.271880 0.0148544
\(336\) 0.446262 0.0243456
\(337\) −20.3377 −1.10786 −0.553932 0.832562i \(-0.686873\pi\)
−0.553932 + 0.832562i \(0.686873\pi\)
\(338\) −0.393324 −0.0213940
\(339\) −4.29677 −0.233369
\(340\) 0.305906 0.0165901
\(341\) 9.31738 0.504564
\(342\) −2.59134 −0.140124
\(343\) 8.11055 0.437928
\(344\) −16.9093 −0.911689
\(345\) 1.53344 0.0825575
\(346\) −16.4555 −0.884651
\(347\) 2.87697 0.154444 0.0772218 0.997014i \(-0.475395\pi\)
0.0772218 + 0.997014i \(0.475395\pi\)
\(348\) 6.87303 0.368433
\(349\) −19.2949 −1.03283 −0.516415 0.856338i \(-0.672734\pi\)
−0.516415 + 0.856338i \(0.672734\pi\)
\(350\) −14.4404 −0.771871
\(351\) 3.66863 0.195817
\(352\) −25.8437 −1.37747
\(353\) −31.2499 −1.66326 −0.831632 0.555327i \(-0.812593\pi\)
−0.831632 + 0.555327i \(0.812593\pi\)
\(354\) 1.68884 0.0897608
\(355\) −1.13105 −0.0600298
\(356\) −2.39245 −0.126799
\(357\) −3.40893 −0.180420
\(358\) 10.7748 0.569465
\(359\) 4.06561 0.214575 0.107287 0.994228i \(-0.465784\pi\)
0.107287 + 0.994228i \(0.465784\pi\)
\(360\) 0.676781 0.0356695
\(361\) −9.86200 −0.519053
\(362\) −1.32872 −0.0698359
\(363\) −9.48352 −0.497755
\(364\) −15.8221 −0.829303
\(365\) 0.179687 0.00940523
\(366\) 0.307225 0.0160589
\(367\) −34.9341 −1.82354 −0.911772 0.410696i \(-0.865286\pi\)
−0.911772 + 0.410696i \(0.865286\pi\)
\(368\) −0.830219 −0.0432781
\(369\) 0.671979 0.0349818
\(370\) −1.94661 −0.101200
\(371\) 28.5182 1.48059
\(372\) 2.60456 0.135040
\(373\) −25.7863 −1.33516 −0.667581 0.744537i \(-0.732670\pi\)
−0.667581 + 0.744537i \(0.732670\pi\)
\(374\) 3.87973 0.200616
\(375\) 2.40380 0.124132
\(376\) −0.425123 −0.0219240
\(377\) −19.9301 −1.02645
\(378\) −2.92225 −0.150304
\(379\) −15.7885 −0.811002 −0.405501 0.914095i \(-0.632903\pi\)
−0.405501 + 0.914095i \(0.632903\pi\)
\(380\) −0.924727 −0.0474375
\(381\) 15.9253 0.815880
\(382\) −21.3396 −1.09183
\(383\) 29.7876 1.52208 0.761038 0.648707i \(-0.224690\pi\)
0.761038 + 0.648707i \(0.224690\pi\)
\(384\) −7.44872 −0.380116
\(385\) −3.73049 −0.190123
\(386\) 0.562528 0.0286319
\(387\) −6.04121 −0.307092
\(388\) 2.49891 0.126863
\(389\) −8.45717 −0.428796 −0.214398 0.976746i \(-0.568779\pi\)
−0.214398 + 0.976746i \(0.568779\pi\)
\(390\) −0.760411 −0.0385049
\(391\) 6.34192 0.320725
\(392\) 12.9336 0.653244
\(393\) 4.32209 0.218021
\(394\) −8.19339 −0.412777
\(395\) 3.50574 0.176393
\(396\) −5.72591 −0.287738
\(397\) −29.7287 −1.49204 −0.746020 0.665924i \(-0.768038\pi\)
−0.746020 + 0.665924i \(0.768038\pi\)
\(398\) −3.61234 −0.181070
\(399\) 10.3049 0.515890
\(400\) −0.646895 −0.0323447
\(401\) −15.9131 −0.794663 −0.397332 0.917675i \(-0.630064\pi\)
−0.397332 + 0.917675i \(0.630064\pi\)
\(402\) 0.963897 0.0480748
\(403\) −7.55257 −0.376221
\(404\) −6.93431 −0.344995
\(405\) 0.241794 0.0120148
\(406\) 15.8753 0.787879
\(407\) 42.5047 2.10688
\(408\) 2.79900 0.138571
\(409\) 0.0427216 0.00211245 0.00105622 0.999999i \(-0.499664\pi\)
0.00105622 + 0.999999i \(0.499664\pi\)
\(410\) −0.139284 −0.00687873
\(411\) −7.49284 −0.369595
\(412\) −9.34126 −0.460211
\(413\) −6.71595 −0.330470
\(414\) 5.43650 0.267190
\(415\) 1.10671 0.0543262
\(416\) 20.9486 1.02709
\(417\) −15.9522 −0.781181
\(418\) −11.7281 −0.573639
\(419\) 13.9571 0.681851 0.340926 0.940090i \(-0.389260\pi\)
0.340926 + 0.940090i \(0.389260\pi\)
\(420\) −1.04281 −0.0508840
\(421\) 25.2133 1.22882 0.614411 0.788986i \(-0.289394\pi\)
0.614411 + 0.788986i \(0.289394\pi\)
\(422\) −12.6583 −0.616195
\(423\) −0.151884 −0.00738486
\(424\) −23.4157 −1.13716
\(425\) 4.94154 0.239700
\(426\) −4.00991 −0.194281
\(427\) −1.22173 −0.0591237
\(428\) 18.6475 0.901362
\(429\) 16.6037 0.801636
\(430\) 1.25218 0.0603857
\(431\) −26.5718 −1.27992 −0.639959 0.768409i \(-0.721049\pi\)
−0.639959 + 0.768409i \(0.721049\pi\)
\(432\) −0.130910 −0.00629840
\(433\) −15.8640 −0.762378 −0.381189 0.924497i \(-0.624485\pi\)
−0.381189 + 0.924497i \(0.624485\pi\)
\(434\) 6.01601 0.288778
\(435\) −1.31356 −0.0629806
\(436\) 1.99469 0.0955281
\(437\) −19.1711 −0.917077
\(438\) 0.637044 0.0304391
\(439\) −11.6157 −0.554389 −0.277194 0.960814i \(-0.589405\pi\)
−0.277194 + 0.960814i \(0.589405\pi\)
\(440\) 3.06302 0.146024
\(441\) 4.62079 0.220038
\(442\) −3.14487 −0.149586
\(443\) 7.59717 0.360952 0.180476 0.983579i \(-0.442236\pi\)
0.180476 + 0.983579i \(0.442236\pi\)
\(444\) 11.8817 0.563879
\(445\) 0.457241 0.0216753
\(446\) −5.55928 −0.263240
\(447\) 4.20165 0.198731
\(448\) −15.7941 −0.746202
\(449\) 6.98900 0.329831 0.164916 0.986308i \(-0.447265\pi\)
0.164916 + 0.986308i \(0.447265\pi\)
\(450\) 4.23605 0.199689
\(451\) 3.04129 0.143209
\(452\) −5.43607 −0.255691
\(453\) −11.6665 −0.548142
\(454\) −12.2652 −0.575635
\(455\) 3.02390 0.141763
\(456\) −8.46112 −0.396228
\(457\) 32.2045 1.50647 0.753233 0.657754i \(-0.228493\pi\)
0.753233 + 0.657754i \(0.228493\pi\)
\(458\) −10.0388 −0.469080
\(459\) 1.00000 0.0466760
\(460\) 1.94003 0.0904544
\(461\) 1.95480 0.0910443 0.0455221 0.998963i \(-0.485505\pi\)
0.0455221 + 0.998963i \(0.485505\pi\)
\(462\) −13.2257 −0.615316
\(463\) −1.49937 −0.0696814 −0.0348407 0.999393i \(-0.511092\pi\)
−0.0348407 + 0.999393i \(0.511092\pi\)
\(464\) 0.711177 0.0330155
\(465\) −0.497779 −0.0230840
\(466\) 21.6636 1.00355
\(467\) −17.9307 −0.829733 −0.414867 0.909882i \(-0.636172\pi\)
−0.414867 + 0.909882i \(0.636172\pi\)
\(468\) 4.64137 0.214547
\(469\) −3.83309 −0.176996
\(470\) 0.0314816 0.00145214
\(471\) 1.00000 0.0460776
\(472\) 5.51432 0.253817
\(473\) −27.3417 −1.25717
\(474\) 12.4289 0.570878
\(475\) −14.9378 −0.685395
\(476\) −4.31281 −0.197677
\(477\) −8.36573 −0.383041
\(478\) −8.61012 −0.393818
\(479\) −2.97262 −0.135823 −0.0679113 0.997691i \(-0.521633\pi\)
−0.0679113 + 0.997691i \(0.521633\pi\)
\(480\) 1.38070 0.0630198
\(481\) −34.4539 −1.57096
\(482\) 14.9051 0.678907
\(483\) −21.6191 −0.983705
\(484\) −11.9981 −0.545367
\(485\) −0.477588 −0.0216862
\(486\) 0.857233 0.0388849
\(487\) −16.6735 −0.755548 −0.377774 0.925898i \(-0.623310\pi\)
−0.377774 + 0.925898i \(0.623310\pi\)
\(488\) 1.00314 0.0454099
\(489\) −17.3613 −0.785104
\(490\) −0.957770 −0.0432676
\(491\) −34.2413 −1.54529 −0.772645 0.634839i \(-0.781067\pi\)
−0.772645 + 0.634839i \(0.781067\pi\)
\(492\) 0.850155 0.0383279
\(493\) −5.43257 −0.244671
\(494\) 9.50667 0.427725
\(495\) 1.09433 0.0491864
\(496\) 0.269503 0.0121010
\(497\) 15.9461 0.715279
\(498\) 3.92362 0.175822
\(499\) −17.4042 −0.779118 −0.389559 0.921001i \(-0.627373\pi\)
−0.389559 + 0.921001i \(0.627373\pi\)
\(500\) 3.04118 0.136005
\(501\) 3.28213 0.146635
\(502\) 26.2324 1.17081
\(503\) −9.10033 −0.405764 −0.202882 0.979203i \(-0.565031\pi\)
−0.202882 + 0.979203i \(0.565031\pi\)
\(504\) −9.54158 −0.425016
\(505\) 1.32528 0.0589740
\(506\) 24.6049 1.09382
\(507\) −0.458830 −0.0203774
\(508\) 20.1480 0.893921
\(509\) 31.7793 1.40859 0.704296 0.709906i \(-0.251263\pi\)
0.704296 + 0.709906i \(0.251263\pi\)
\(510\) −0.207274 −0.00917824
\(511\) −2.53331 −0.112067
\(512\) −1.48035 −0.0654230
\(513\) −3.02291 −0.133465
\(514\) −1.60112 −0.0706224
\(515\) 1.78529 0.0786693
\(516\) −7.64304 −0.336466
\(517\) −0.687408 −0.0302322
\(518\) 27.4443 1.20583
\(519\) −19.1960 −0.842612
\(520\) −2.48286 −0.108880
\(521\) 9.90072 0.433758 0.216879 0.976198i \(-0.430412\pi\)
0.216879 + 0.976198i \(0.430412\pi\)
\(522\) −4.65698 −0.203831
\(523\) −42.1632 −1.84367 −0.921834 0.387584i \(-0.873310\pi\)
−0.921834 + 0.387584i \(0.873310\pi\)
\(524\) 5.46810 0.238875
\(525\) −16.8453 −0.735191
\(526\) −1.89149 −0.0824731
\(527\) −2.05869 −0.0896780
\(528\) −0.592480 −0.0257844
\(529\) 17.2199 0.748693
\(530\) 1.73400 0.0753201
\(531\) 1.97010 0.0854953
\(532\) 13.0372 0.565236
\(533\) −2.46524 −0.106781
\(534\) 1.62106 0.0701501
\(535\) −3.56389 −0.154080
\(536\) 3.14727 0.135941
\(537\) 12.5693 0.542403
\(538\) 4.06028 0.175051
\(539\) 20.9131 0.900792
\(540\) 0.305906 0.0131641
\(541\) −24.3145 −1.04536 −0.522682 0.852528i \(-0.675068\pi\)
−0.522682 + 0.852528i \(0.675068\pi\)
\(542\) 23.8605 1.02490
\(543\) −1.55001 −0.0665173
\(544\) 5.71021 0.244823
\(545\) −0.381222 −0.0163297
\(546\) 10.7206 0.458801
\(547\) 31.7220 1.35634 0.678168 0.734907i \(-0.262774\pi\)
0.678168 + 0.734907i \(0.262774\pi\)
\(548\) −9.47958 −0.404947
\(549\) 0.358392 0.0152958
\(550\) 19.1718 0.817489
\(551\) 16.4222 0.699609
\(552\) 17.7510 0.755533
\(553\) −49.4256 −2.10179
\(554\) −14.4456 −0.613736
\(555\) −2.27081 −0.0963904
\(556\) −20.1819 −0.855903
\(557\) −10.6754 −0.452330 −0.226165 0.974089i \(-0.572619\pi\)
−0.226165 + 0.974089i \(0.572619\pi\)
\(558\) −1.76478 −0.0747091
\(559\) 22.1629 0.937392
\(560\) −0.107903 −0.00455975
\(561\) 4.52587 0.191082
\(562\) 6.69054 0.282224
\(563\) 12.3621 0.521000 0.260500 0.965474i \(-0.416113\pi\)
0.260500 + 0.965474i \(0.416113\pi\)
\(564\) −0.192156 −0.00809124
\(565\) 1.03893 0.0437083
\(566\) 5.59136 0.235022
\(567\) −3.40893 −0.143162
\(568\) −13.0930 −0.549369
\(569\) 0.563472 0.0236220 0.0118110 0.999930i \(-0.496240\pi\)
0.0118110 + 0.999930i \(0.496240\pi\)
\(570\) 0.626571 0.0262442
\(571\) 0.335604 0.0140446 0.00702230 0.999975i \(-0.497765\pi\)
0.00702230 + 0.999975i \(0.497765\pi\)
\(572\) 21.0062 0.878315
\(573\) −24.8936 −1.03994
\(574\) 1.96369 0.0819627
\(575\) 31.3388 1.30692
\(576\) 4.63316 0.193049
\(577\) 18.9547 0.789093 0.394547 0.918876i \(-0.370902\pi\)
0.394547 + 0.918876i \(0.370902\pi\)
\(578\) −0.857233 −0.0356562
\(579\) 0.656214 0.0272713
\(580\) −1.66186 −0.0690048
\(581\) −15.6029 −0.647318
\(582\) −1.69320 −0.0701852
\(583\) −37.8622 −1.56809
\(584\) 2.08004 0.0860729
\(585\) −0.887052 −0.0366751
\(586\) 23.4137 0.967212
\(587\) −11.9679 −0.493967 −0.246984 0.969020i \(-0.579439\pi\)
−0.246984 + 0.969020i \(0.579439\pi\)
\(588\) 5.84600 0.241085
\(589\) 6.22325 0.256424
\(590\) −0.408351 −0.0168116
\(591\) −9.55795 −0.393161
\(592\) 1.22944 0.0505296
\(593\) −6.06945 −0.249242 −0.124621 0.992204i \(-0.539772\pi\)
−0.124621 + 0.992204i \(0.539772\pi\)
\(594\) 3.87973 0.159187
\(595\) 0.824258 0.0337913
\(596\) 5.31573 0.217741
\(597\) −4.21395 −0.172465
\(598\) −19.9445 −0.815592
\(599\) 2.80080 0.114438 0.0572188 0.998362i \(-0.481777\pi\)
0.0572188 + 0.998362i \(0.481777\pi\)
\(600\) 13.8313 0.564662
\(601\) −1.92608 −0.0785665 −0.0392833 0.999228i \(-0.512507\pi\)
−0.0392833 + 0.999228i \(0.512507\pi\)
\(602\) −17.6539 −0.719519
\(603\) 1.12443 0.0457902
\(604\) −14.7599 −0.600573
\(605\) 2.29306 0.0932260
\(606\) 4.69851 0.190864
\(607\) −20.5281 −0.833210 −0.416605 0.909088i \(-0.636780\pi\)
−0.416605 + 0.909088i \(0.636780\pi\)
\(608\) −17.2615 −0.700045
\(609\) 18.5193 0.750438
\(610\) −0.0742852 −0.00300772
\(611\) 0.557206 0.0225422
\(612\) 1.26515 0.0511407
\(613\) 11.7315 0.473833 0.236916 0.971530i \(-0.423863\pi\)
0.236916 + 0.971530i \(0.423863\pi\)
\(614\) −7.93406 −0.320193
\(615\) −0.162480 −0.00655184
\(616\) −43.1840 −1.73993
\(617\) 25.9547 1.04490 0.522448 0.852671i \(-0.325019\pi\)
0.522448 + 0.852671i \(0.325019\pi\)
\(618\) 6.32939 0.254606
\(619\) −20.4435 −0.821694 −0.410847 0.911704i \(-0.634767\pi\)
−0.410847 + 0.911704i \(0.634767\pi\)
\(620\) −0.629766 −0.0252920
\(621\) 6.34192 0.254492
\(622\) −9.14593 −0.366718
\(623\) −6.44640 −0.258270
\(624\) 0.480259 0.0192257
\(625\) 24.1265 0.965058
\(626\) 2.30020 0.0919345
\(627\) −13.6813 −0.546379
\(628\) 1.26515 0.0504850
\(629\) −9.39150 −0.374464
\(630\) 0.706582 0.0281509
\(631\) 9.03129 0.359530 0.179765 0.983710i \(-0.442466\pi\)
0.179765 + 0.983710i \(0.442466\pi\)
\(632\) 40.5822 1.61427
\(633\) −14.7664 −0.586912
\(634\) −3.25698 −0.129351
\(635\) −3.85065 −0.152808
\(636\) −10.5839 −0.419680
\(637\) −16.9520 −0.671661
\(638\) −21.0769 −0.834443
\(639\) −4.67774 −0.185048
\(640\) 1.80106 0.0711930
\(641\) 10.3769 0.409863 0.204931 0.978776i \(-0.434303\pi\)
0.204931 + 0.978776i \(0.434303\pi\)
\(642\) −12.6351 −0.498667
\(643\) −1.03564 −0.0408416 −0.0204208 0.999791i \(-0.506501\pi\)
−0.0204208 + 0.999791i \(0.506501\pi\)
\(644\) −27.3515 −1.07780
\(645\) 1.46073 0.0575161
\(646\) 2.59134 0.101955
\(647\) 7.27403 0.285972 0.142986 0.989725i \(-0.454330\pi\)
0.142986 + 0.989725i \(0.454330\pi\)
\(648\) 2.79900 0.109955
\(649\) 8.91644 0.350001
\(650\) −15.5405 −0.609548
\(651\) 7.01793 0.275054
\(652\) −21.9646 −0.860202
\(653\) −25.1804 −0.985386 −0.492693 0.870203i \(-0.663987\pi\)
−0.492693 + 0.870203i \(0.663987\pi\)
\(654\) −1.35155 −0.0528496
\(655\) −1.04506 −0.0408337
\(656\) 0.0879685 0.00343459
\(657\) 0.743140 0.0289926
\(658\) −0.443843 −0.0173028
\(659\) 14.0170 0.546023 0.273012 0.962011i \(-0.411980\pi\)
0.273012 + 0.962011i \(0.411980\pi\)
\(660\) 1.38449 0.0538912
\(661\) −16.6106 −0.646076 −0.323038 0.946386i \(-0.604704\pi\)
−0.323038 + 0.946386i \(0.604704\pi\)
\(662\) 20.0999 0.781205
\(663\) −3.66863 −0.142478
\(664\) 12.8112 0.497171
\(665\) −2.49166 −0.0966225
\(666\) −8.05070 −0.311958
\(667\) −34.4529 −1.33402
\(668\) 4.15239 0.160661
\(669\) −6.48515 −0.250730
\(670\) −0.233064 −0.00900406
\(671\) 1.62204 0.0626180
\(672\) −19.4657 −0.750906
\(673\) 41.8185 1.61198 0.805992 0.591926i \(-0.201632\pi\)
0.805992 + 0.591926i \(0.201632\pi\)
\(674\) 17.4341 0.671538
\(675\) 4.94154 0.190200
\(676\) −0.580489 −0.0223265
\(677\) −34.9775 −1.34429 −0.672147 0.740417i \(-0.734628\pi\)
−0.672147 + 0.740417i \(0.734628\pi\)
\(678\) 3.68334 0.141458
\(679\) 6.73327 0.258399
\(680\) −0.676781 −0.0259533
\(681\) −14.3079 −0.548280
\(682\) −7.98716 −0.305844
\(683\) 30.8653 1.18103 0.590514 0.807028i \(-0.298925\pi\)
0.590514 + 0.807028i \(0.298925\pi\)
\(684\) −3.82444 −0.146231
\(685\) 1.81172 0.0692224
\(686\) −6.95263 −0.265453
\(687\) −11.7106 −0.446789
\(688\) −0.790852 −0.0301510
\(689\) 30.6908 1.16923
\(690\) −1.31451 −0.0500427
\(691\) −7.18879 −0.273475 −0.136737 0.990607i \(-0.543662\pi\)
−0.136737 + 0.990607i \(0.543662\pi\)
\(692\) −24.2859 −0.923210
\(693\) −15.4284 −0.586075
\(694\) −2.46623 −0.0936169
\(695\) 3.85714 0.146310
\(696\) −15.2058 −0.576373
\(697\) −0.671979 −0.0254530
\(698\) 16.5402 0.626056
\(699\) 25.2716 0.955859
\(700\) −21.3119 −0.805514
\(701\) −35.6772 −1.34751 −0.673755 0.738955i \(-0.735320\pi\)
−0.673755 + 0.738955i \(0.735320\pi\)
\(702\) −3.14487 −0.118695
\(703\) 28.3897 1.07074
\(704\) 20.9691 0.790303
\(705\) 0.0367247 0.00138313
\(706\) 26.7885 1.00820
\(707\) −18.6844 −0.702699
\(708\) 2.49248 0.0936731
\(709\) −3.61747 −0.135857 −0.0679285 0.997690i \(-0.521639\pi\)
−0.0679285 + 0.997690i \(0.521639\pi\)
\(710\) 0.969572 0.0363874
\(711\) 14.4989 0.543749
\(712\) 5.29300 0.198364
\(713\) −13.0561 −0.488953
\(714\) 2.92225 0.109362
\(715\) −4.01468 −0.150141
\(716\) 15.9020 0.594286
\(717\) −10.0441 −0.375103
\(718\) −3.48517 −0.130066
\(719\) 16.7119 0.623250 0.311625 0.950205i \(-0.399127\pi\)
0.311625 + 0.950205i \(0.399127\pi\)
\(720\) 0.0316532 0.00117964
\(721\) −25.1699 −0.937375
\(722\) 8.45403 0.314627
\(723\) 17.3874 0.646644
\(724\) −1.96100 −0.0728798
\(725\) −26.8453 −0.997008
\(726\) 8.12958 0.301717
\(727\) −36.7966 −1.36471 −0.682356 0.731020i \(-0.739044\pi\)
−0.682356 + 0.731020i \(0.739044\pi\)
\(728\) 35.0045 1.29735
\(729\) 1.00000 0.0370370
\(730\) −0.154033 −0.00570103
\(731\) 6.04121 0.223442
\(732\) 0.453420 0.0167589
\(733\) −2.92572 −0.108064 −0.0540320 0.998539i \(-0.517207\pi\)
−0.0540320 + 0.998539i \(0.517207\pi\)
\(734\) 29.9467 1.10535
\(735\) −1.11728 −0.0412115
\(736\) 36.2137 1.33485
\(737\) 5.08901 0.187456
\(738\) −0.576043 −0.0212044
\(739\) −10.9595 −0.403151 −0.201575 0.979473i \(-0.564606\pi\)
−0.201575 + 0.979473i \(0.564606\pi\)
\(740\) −2.87292 −0.105610
\(741\) 11.0899 0.407399
\(742\) −24.4467 −0.897468
\(743\) 22.6789 0.832008 0.416004 0.909363i \(-0.363430\pi\)
0.416004 + 0.909363i \(0.363430\pi\)
\(744\) −5.76227 −0.211255
\(745\) −1.01593 −0.0372210
\(746\) 22.1048 0.809316
\(747\) 4.57707 0.167466
\(748\) 5.72591 0.209360
\(749\) 50.2455 1.83593
\(750\) −2.06062 −0.0752432
\(751\) −7.56336 −0.275991 −0.137995 0.990433i \(-0.544066\pi\)
−0.137995 + 0.990433i \(0.544066\pi\)
\(752\) −0.0198831 −0.000725062 0
\(753\) 30.6012 1.11517
\(754\) 17.0847 0.622189
\(755\) 2.82090 0.102663
\(756\) −4.31281 −0.156855
\(757\) −40.5615 −1.47423 −0.737116 0.675766i \(-0.763813\pi\)
−0.737116 + 0.675766i \(0.763813\pi\)
\(758\) 13.5345 0.491593
\(759\) 28.7027 1.04184
\(760\) 2.04585 0.0742107
\(761\) 3.32068 0.120374 0.0601872 0.998187i \(-0.480830\pi\)
0.0601872 + 0.998187i \(0.480830\pi\)
\(762\) −13.6517 −0.494550
\(763\) 5.37465 0.194575
\(764\) −31.4941 −1.13942
\(765\) −0.241794 −0.00874208
\(766\) −25.5349 −0.922615
\(767\) −7.22758 −0.260973
\(768\) 15.6516 0.564779
\(769\) −17.8214 −0.642657 −0.321329 0.946968i \(-0.604129\pi\)
−0.321329 + 0.946968i \(0.604129\pi\)
\(770\) 3.19790 0.115244
\(771\) −1.86778 −0.0672664
\(772\) 0.830210 0.0298799
\(773\) −12.8445 −0.461985 −0.230992 0.972956i \(-0.574197\pi\)
−0.230992 + 0.972956i \(0.574197\pi\)
\(774\) 5.17872 0.186145
\(775\) −10.1731 −0.365429
\(776\) −5.52854 −0.198463
\(777\) 32.0149 1.14853
\(778\) 7.24977 0.259917
\(779\) 2.03133 0.0727801
\(780\) −1.12226 −0.0401832
\(781\) −21.1708 −0.757552
\(782\) −5.43650 −0.194409
\(783\) −5.43257 −0.194144
\(784\) 0.604906 0.0216038
\(785\) −0.241794 −0.00863000
\(786\) −3.70504 −0.132154
\(787\) −39.9600 −1.42442 −0.712210 0.701966i \(-0.752306\pi\)
−0.712210 + 0.701966i \(0.752306\pi\)
\(788\) −12.0922 −0.430768
\(789\) −2.20651 −0.0785539
\(790\) −3.00523 −0.106921
\(791\) −14.6474 −0.520801
\(792\) 12.6679 0.450134
\(793\) −1.31481 −0.0466901
\(794\) 25.4844 0.904408
\(795\) 2.02278 0.0717408
\(796\) −5.33128 −0.188962
\(797\) −15.5761 −0.551733 −0.275866 0.961196i \(-0.588965\pi\)
−0.275866 + 0.961196i \(0.588965\pi\)
\(798\) −8.83370 −0.312709
\(799\) 0.151884 0.00537327
\(800\) 28.2172 0.997629
\(801\) 1.89104 0.0668165
\(802\) 13.6413 0.481690
\(803\) 3.36335 0.118690
\(804\) 1.42257 0.0501702
\(805\) 5.22738 0.184241
\(806\) 6.47432 0.228048
\(807\) 4.73650 0.166733
\(808\) 15.3413 0.539707
\(809\) 3.58732 0.126124 0.0630618 0.998010i \(-0.479913\pi\)
0.0630618 + 0.998010i \(0.479913\pi\)
\(810\) −0.207274 −0.00728286
\(811\) 0.477963 0.0167836 0.00839178 0.999965i \(-0.497329\pi\)
0.00839178 + 0.999965i \(0.497329\pi\)
\(812\) 23.4297 0.822220
\(813\) 27.8344 0.976194
\(814\) −36.4365 −1.27710
\(815\) 4.19785 0.147044
\(816\) 0.130910 0.00458276
\(817\) −18.2620 −0.638908
\(818\) −0.0366224 −0.00128047
\(819\) 12.5061 0.436998
\(820\) −0.205562 −0.00717855
\(821\) −50.6974 −1.76935 −0.884675 0.466207i \(-0.845620\pi\)
−0.884675 + 0.466207i \(0.845620\pi\)
\(822\) 6.42311 0.224032
\(823\) −26.6583 −0.929250 −0.464625 0.885508i \(-0.653811\pi\)
−0.464625 + 0.885508i \(0.653811\pi\)
\(824\) 20.6664 0.719949
\(825\) 22.3648 0.778641
\(826\) 5.75713 0.200316
\(827\) −48.6942 −1.69326 −0.846632 0.532179i \(-0.821373\pi\)
−0.846632 + 0.532179i \(0.821373\pi\)
\(828\) 8.02349 0.278835
\(829\) 20.6776 0.718164 0.359082 0.933306i \(-0.383090\pi\)
0.359082 + 0.933306i \(0.383090\pi\)
\(830\) −0.948708 −0.0329301
\(831\) −16.8515 −0.584571
\(832\) −16.9974 −0.589277
\(833\) −4.62079 −0.160101
\(834\) 13.6747 0.473517
\(835\) −0.793600 −0.0274637
\(836\) −17.3089 −0.598642
\(837\) −2.05869 −0.0711588
\(838\) −11.9645 −0.413308
\(839\) −1.97127 −0.0680558 −0.0340279 0.999421i \(-0.510834\pi\)
−0.0340279 + 0.999421i \(0.510834\pi\)
\(840\) 2.30710 0.0796024
\(841\) 0.512862 0.0176849
\(842\) −21.6137 −0.744857
\(843\) 7.80481 0.268812
\(844\) −18.6817 −0.643052
\(845\) 0.110942 0.00381653
\(846\) 0.130200 0.00447637
\(847\) −32.3286 −1.11082
\(848\) −1.09516 −0.0376078
\(849\) 6.52256 0.223854
\(850\) −4.23605 −0.145295
\(851\) −59.5601 −2.04169
\(852\) −5.91804 −0.202749
\(853\) −24.2132 −0.829046 −0.414523 0.910039i \(-0.636051\pi\)
−0.414523 + 0.910039i \(0.636051\pi\)
\(854\) 1.04731 0.0358382
\(855\) 0.730922 0.0249970
\(856\) −41.2554 −1.41008
\(857\) 9.75325 0.333165 0.166582 0.986028i \(-0.446727\pi\)
0.166582 + 0.986028i \(0.446727\pi\)
\(858\) −14.2333 −0.485916
\(859\) −8.41048 −0.286962 −0.143481 0.989653i \(-0.545830\pi\)
−0.143481 + 0.989653i \(0.545830\pi\)
\(860\) 1.84804 0.0630177
\(861\) 2.29073 0.0780678
\(862\) 22.7782 0.775829
\(863\) 17.9550 0.611195 0.305598 0.952161i \(-0.401144\pi\)
0.305598 + 0.952161i \(0.401144\pi\)
\(864\) 5.71021 0.194265
\(865\) 4.64148 0.157815
\(866\) 13.5992 0.462119
\(867\) −1.00000 −0.0339618
\(868\) 8.87875 0.301364
\(869\) 65.6200 2.22600
\(870\) 1.12603 0.0381760
\(871\) −4.12511 −0.139774
\(872\) −4.41300 −0.149443
\(873\) −1.97519 −0.0668499
\(874\) 16.4341 0.555891
\(875\) 8.19439 0.277021
\(876\) 0.940184 0.0317659
\(877\) 1.70283 0.0575004 0.0287502 0.999587i \(-0.490847\pi\)
0.0287502 + 0.999587i \(0.490847\pi\)
\(878\) 9.95739 0.336046
\(879\) 27.3131 0.921249
\(880\) 0.143258 0.00482923
\(881\) −33.1265 −1.11606 −0.558031 0.829820i \(-0.688443\pi\)
−0.558031 + 0.829820i \(0.688443\pi\)
\(882\) −3.96110 −0.133377
\(883\) 33.4640 1.12615 0.563077 0.826405i \(-0.309618\pi\)
0.563077 + 0.826405i \(0.309618\pi\)
\(884\) −4.64137 −0.156106
\(885\) −0.476360 −0.0160126
\(886\) −6.51255 −0.218793
\(887\) 13.1954 0.443059 0.221530 0.975154i \(-0.428895\pi\)
0.221530 + 0.975154i \(0.428895\pi\)
\(888\) −26.2868 −0.882126
\(889\) 54.2883 1.82077
\(890\) −0.391962 −0.0131386
\(891\) 4.52587 0.151622
\(892\) −8.20469 −0.274713
\(893\) −0.459132 −0.0153643
\(894\) −3.60180 −0.120462
\(895\) −3.03917 −0.101588
\(896\) −25.3922 −0.848293
\(897\) −23.2661 −0.776834
\(898\) −5.99120 −0.199929
\(899\) 11.1840 0.373007
\(900\) 6.25179 0.208393
\(901\) 8.36573 0.278703
\(902\) −2.60709 −0.0868068
\(903\) −20.5940 −0.685327
\(904\) 12.0267 0.400000
\(905\) 0.374783 0.0124582
\(906\) 10.0009 0.332259
\(907\) −51.5280 −1.71096 −0.855480 0.517836i \(-0.826738\pi\)
−0.855480 + 0.517836i \(0.826738\pi\)
\(908\) −18.1017 −0.600724
\(909\) 5.48102 0.181794
\(910\) −2.59219 −0.0859301
\(911\) −7.85423 −0.260222 −0.130111 0.991499i \(-0.541533\pi\)
−0.130111 + 0.991499i \(0.541533\pi\)
\(912\) −0.395729 −0.0131039
\(913\) 20.7152 0.685575
\(914\) −27.6068 −0.913152
\(915\) −0.0866570 −0.00286479
\(916\) −14.8157 −0.489526
\(917\) 14.7337 0.486550
\(918\) −0.857233 −0.0282929
\(919\) 27.1275 0.894853 0.447427 0.894321i \(-0.352341\pi\)
0.447427 + 0.894321i \(0.352341\pi\)
\(920\) −4.29209 −0.141506
\(921\) −9.25543 −0.304977
\(922\) −1.67572 −0.0551870
\(923\) 17.1609 0.564857
\(924\) −19.5192 −0.642135
\(925\) −46.4084 −1.52590
\(926\) 1.28531 0.0422378
\(927\) 7.38351 0.242506
\(928\) −31.0212 −1.01832
\(929\) 11.8559 0.388979 0.194489 0.980905i \(-0.437695\pi\)
0.194489 + 0.980905i \(0.437695\pi\)
\(930\) 0.426713 0.0139925
\(931\) 13.9683 0.457791
\(932\) 31.9724 1.04729
\(933\) −10.6691 −0.349291
\(934\) 15.3708 0.502947
\(935\) −1.09433 −0.0357884
\(936\) −10.2685 −0.335636
\(937\) 41.9932 1.37186 0.685929 0.727669i \(-0.259396\pi\)
0.685929 + 0.727669i \(0.259396\pi\)
\(938\) 3.28585 0.107287
\(939\) 2.68328 0.0875657
\(940\) 0.0464623 0.00151543
\(941\) 8.05144 0.262470 0.131235 0.991351i \(-0.458106\pi\)
0.131235 + 0.991351i \(0.458106\pi\)
\(942\) −0.857233 −0.0279302
\(943\) −4.26163 −0.138778
\(944\) 0.257906 0.00839412
\(945\) 0.824258 0.0268131
\(946\) 23.4382 0.762043
\(947\) −11.8260 −0.384292 −0.192146 0.981366i \(-0.561545\pi\)
−0.192146 + 0.981366i \(0.561545\pi\)
\(948\) 18.3432 0.595761
\(949\) −2.72630 −0.0884995
\(950\) 12.8052 0.415456
\(951\) −3.79941 −0.123204
\(952\) 9.54158 0.309244
\(953\) 15.0486 0.487472 0.243736 0.969842i \(-0.421627\pi\)
0.243736 + 0.969842i \(0.421627\pi\)
\(954\) 7.17139 0.232182
\(955\) 6.01911 0.194774
\(956\) −12.7073 −0.410983
\(957\) −24.5871 −0.794789
\(958\) 2.54823 0.0823296
\(959\) −25.5426 −0.824812
\(960\) −1.12027 −0.0361566
\(961\) −26.7618 −0.863283
\(962\) 29.5350 0.952248
\(963\) −14.7394 −0.474970
\(964\) 21.9977 0.708498
\(965\) −0.158669 −0.00510772
\(966\) 18.5327 0.596278
\(967\) 36.3070 1.16755 0.583777 0.811914i \(-0.301574\pi\)
0.583777 + 0.811914i \(0.301574\pi\)
\(968\) 26.5443 0.853167
\(969\) 3.02291 0.0971099
\(970\) 0.409405 0.0131452
\(971\) 11.0138 0.353451 0.176726 0.984260i \(-0.443449\pi\)
0.176726 + 0.984260i \(0.443449\pi\)
\(972\) 1.26515 0.0405797
\(973\) −54.3798 −1.74334
\(974\) 14.2931 0.457980
\(975\) −18.1287 −0.580582
\(976\) 0.0469169 0.00150177
\(977\) −40.6258 −1.29973 −0.649867 0.760048i \(-0.725176\pi\)
−0.649867 + 0.760048i \(0.725176\pi\)
\(978\) 14.8827 0.475895
\(979\) 8.55858 0.273534
\(980\) −1.41353 −0.0451535
\(981\) −1.57664 −0.0503382
\(982\) 29.3528 0.936686
\(983\) −35.9967 −1.14812 −0.574059 0.818814i \(-0.694632\pi\)
−0.574059 + 0.818814i \(0.694632\pi\)
\(984\) −1.88087 −0.0599598
\(985\) 2.31105 0.0736363
\(986\) 4.65698 0.148309
\(987\) −0.517762 −0.0164805
\(988\) 14.0305 0.446368
\(989\) 38.3128 1.21828
\(990\) −0.938095 −0.0298146
\(991\) −12.1862 −0.387107 −0.193554 0.981090i \(-0.562001\pi\)
−0.193554 + 0.981090i \(0.562001\pi\)
\(992\) −11.7556 −0.373240
\(993\) 23.4474 0.744081
\(994\) −13.6695 −0.433570
\(995\) 1.01891 0.0323015
\(996\) 5.79069 0.183485
\(997\) 46.9573 1.48715 0.743576 0.668651i \(-0.233128\pi\)
0.743576 + 0.668651i \(0.233128\pi\)
\(998\) 14.9194 0.472267
\(999\) −9.39150 −0.297134
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 8007.2.a.f.1.19 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.f.1.19 48 1.1 even 1 trivial