Properties

Label 8003.2.a.b.1.3
Level 8003
Weight 2
Character 8003.1
Self dual yes
Analytic conductor 63.904
Analytic rank 1
Dimension 153
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.72579 q^{2} +2.89515 q^{3} +5.42994 q^{4} -2.27822 q^{5} -7.89157 q^{6} -3.84210 q^{7} -9.34930 q^{8} +5.38188 q^{9} +O(q^{10})\) \(q-2.72579 q^{2} +2.89515 q^{3} +5.42994 q^{4} -2.27822 q^{5} -7.89157 q^{6} -3.84210 q^{7} -9.34930 q^{8} +5.38188 q^{9} +6.20996 q^{10} +2.32327 q^{11} +15.7205 q^{12} +0.203934 q^{13} +10.4728 q^{14} -6.59579 q^{15} +14.6244 q^{16} +1.55678 q^{17} -14.6699 q^{18} -0.522326 q^{19} -12.3706 q^{20} -11.1235 q^{21} -6.33275 q^{22} -2.89946 q^{23} -27.0676 q^{24} +0.190298 q^{25} -0.555881 q^{26} +6.89591 q^{27} -20.8624 q^{28} +1.67183 q^{29} +17.9788 q^{30} -6.73048 q^{31} -21.1643 q^{32} +6.72621 q^{33} -4.24346 q^{34} +8.75317 q^{35} +29.2233 q^{36} +2.76054 q^{37} +1.42375 q^{38} +0.590418 q^{39} +21.2998 q^{40} +10.0381 q^{41} +30.3202 q^{42} +3.67885 q^{43} +12.6152 q^{44} -12.2611 q^{45} +7.90332 q^{46} -0.655415 q^{47} +42.3397 q^{48} +7.76177 q^{49} -0.518712 q^{50} +4.50711 q^{51} +1.10735 q^{52} -1.00000 q^{53} -18.7968 q^{54} -5.29293 q^{55} +35.9210 q^{56} -1.51221 q^{57} -4.55707 q^{58} -0.383772 q^{59} -35.8147 q^{60} +5.23951 q^{61} +18.3459 q^{62} -20.6778 q^{63} +28.4409 q^{64} -0.464606 q^{65} -18.3343 q^{66} -5.10346 q^{67} +8.45322 q^{68} -8.39437 q^{69} -23.8593 q^{70} -6.43413 q^{71} -50.3168 q^{72} +0.0435738 q^{73} -7.52465 q^{74} +0.550941 q^{75} -2.83620 q^{76} -8.92625 q^{77} -1.60936 q^{78} +6.92112 q^{79} -33.3175 q^{80} +3.81903 q^{81} -27.3619 q^{82} -3.05720 q^{83} -60.3997 q^{84} -3.54669 q^{85} -10.0278 q^{86} +4.84020 q^{87} -21.7209 q^{88} +15.0824 q^{89} +33.4213 q^{90} -0.783534 q^{91} -15.7439 q^{92} -19.4857 q^{93} +1.78653 q^{94} +1.18997 q^{95} -61.2739 q^{96} -7.18425 q^{97} -21.1570 q^{98} +12.5036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.72579 −1.92743 −0.963713 0.266941i \(-0.913987\pi\)
−0.963713 + 0.266941i \(0.913987\pi\)
\(3\) 2.89515 1.67151 0.835757 0.549099i \(-0.185029\pi\)
0.835757 + 0.549099i \(0.185029\pi\)
\(4\) 5.42994 2.71497
\(5\) −2.27822 −1.01885 −0.509426 0.860514i \(-0.670142\pi\)
−0.509426 + 0.860514i \(0.670142\pi\)
\(6\) −7.89157 −3.22172
\(7\) −3.84210 −1.45218 −0.726089 0.687600i \(-0.758664\pi\)
−0.726089 + 0.687600i \(0.758664\pi\)
\(8\) −9.34930 −3.30547
\(9\) 5.38188 1.79396
\(10\) 6.20996 1.96376
\(11\) 2.32327 0.700493 0.350246 0.936658i \(-0.386098\pi\)
0.350246 + 0.936658i \(0.386098\pi\)
\(12\) 15.7205 4.53811
\(13\) 0.203934 0.0565610 0.0282805 0.999600i \(-0.490997\pi\)
0.0282805 + 0.999600i \(0.490997\pi\)
\(14\) 10.4728 2.79897
\(15\) −6.59579 −1.70303
\(16\) 14.6244 3.65609
\(17\) 1.55678 0.377575 0.188787 0.982018i \(-0.439544\pi\)
0.188787 + 0.982018i \(0.439544\pi\)
\(18\) −14.6699 −3.45773
\(19\) −0.522326 −0.119830 −0.0599149 0.998203i \(-0.519083\pi\)
−0.0599149 + 0.998203i \(0.519083\pi\)
\(20\) −12.3706 −2.76615
\(21\) −11.1235 −2.42734
\(22\) −6.33275 −1.35015
\(23\) −2.89946 −0.604579 −0.302290 0.953216i \(-0.597751\pi\)
−0.302290 + 0.953216i \(0.597751\pi\)
\(24\) −27.0676 −5.52515
\(25\) 0.190298 0.0380596
\(26\) −0.555881 −0.109017
\(27\) 6.89591 1.32712
\(28\) −20.8624 −3.94262
\(29\) 1.67183 0.310452 0.155226 0.987879i \(-0.450389\pi\)
0.155226 + 0.987879i \(0.450389\pi\)
\(30\) 17.9788 3.28246
\(31\) −6.73048 −1.20883 −0.604415 0.796670i \(-0.706593\pi\)
−0.604415 + 0.796670i \(0.706593\pi\)
\(32\) −21.1643 −3.74136
\(33\) 6.72621 1.17088
\(34\) −4.24346 −0.727747
\(35\) 8.75317 1.47956
\(36\) 29.2233 4.87055
\(37\) 2.76054 0.453829 0.226915 0.973915i \(-0.427136\pi\)
0.226915 + 0.973915i \(0.427136\pi\)
\(38\) 1.42375 0.230963
\(39\) 0.590418 0.0945426
\(40\) 21.2998 3.36779
\(41\) 10.0381 1.56769 0.783846 0.620955i \(-0.213255\pi\)
0.783846 + 0.620955i \(0.213255\pi\)
\(42\) 30.3202 4.67851
\(43\) 3.67885 0.561020 0.280510 0.959851i \(-0.409496\pi\)
0.280510 + 0.959851i \(0.409496\pi\)
\(44\) 12.6152 1.90182
\(45\) −12.2611 −1.82778
\(46\) 7.90332 1.16528
\(47\) −0.655415 −0.0956022 −0.0478011 0.998857i \(-0.515221\pi\)
−0.0478011 + 0.998857i \(0.515221\pi\)
\(48\) 42.3397 6.11120
\(49\) 7.76177 1.10882
\(50\) −0.518712 −0.0733570
\(51\) 4.50711 0.631122
\(52\) 1.10735 0.153561
\(53\) −1.00000 −0.137361
\(54\) −18.7968 −2.55792
\(55\) −5.29293 −0.713698
\(56\) 35.9210 4.80014
\(57\) −1.51221 −0.200297
\(58\) −4.55707 −0.598372
\(59\) −0.383772 −0.0499629 −0.0249815 0.999688i \(-0.507953\pi\)
−0.0249815 + 0.999688i \(0.507953\pi\)
\(60\) −35.8147 −4.62366
\(61\) 5.23951 0.670850 0.335425 0.942067i \(-0.391120\pi\)
0.335425 + 0.942067i \(0.391120\pi\)
\(62\) 18.3459 2.32993
\(63\) −20.6778 −2.60515
\(64\) 28.4409 3.55511
\(65\) −0.464606 −0.0576273
\(66\) −18.3343 −2.25679
\(67\) −5.10346 −0.623487 −0.311744 0.950166i \(-0.600913\pi\)
−0.311744 + 0.950166i \(0.600913\pi\)
\(68\) 8.45322 1.02510
\(69\) −8.39437 −1.01056
\(70\) −23.8593 −2.85173
\(71\) −6.43413 −0.763591 −0.381795 0.924247i \(-0.624694\pi\)
−0.381795 + 0.924247i \(0.624694\pi\)
\(72\) −50.3168 −5.92990
\(73\) 0.0435738 0.00509993 0.00254996 0.999997i \(-0.499188\pi\)
0.00254996 + 0.999997i \(0.499188\pi\)
\(74\) −7.52465 −0.874722
\(75\) 0.550941 0.0636172
\(76\) −2.83620 −0.325334
\(77\) −8.92625 −1.01724
\(78\) −1.60936 −0.182224
\(79\) 6.92112 0.778687 0.389343 0.921093i \(-0.372702\pi\)
0.389343 + 0.921093i \(0.372702\pi\)
\(80\) −33.3175 −3.72501
\(81\) 3.81903 0.424337
\(82\) −27.3619 −3.02161
\(83\) −3.05720 −0.335571 −0.167786 0.985824i \(-0.553662\pi\)
−0.167786 + 0.985824i \(0.553662\pi\)
\(84\) −60.3997 −6.59015
\(85\) −3.54669 −0.384693
\(86\) −10.0278 −1.08132
\(87\) 4.84020 0.518924
\(88\) −21.7209 −2.31546
\(89\) 15.0824 1.59873 0.799366 0.600845i \(-0.205169\pi\)
0.799366 + 0.600845i \(0.205169\pi\)
\(90\) 33.4213 3.52291
\(91\) −0.783534 −0.0821367
\(92\) −15.7439 −1.64141
\(93\) −19.4857 −2.02058
\(94\) 1.78653 0.184266
\(95\) 1.18997 0.122089
\(96\) −61.2739 −6.25374
\(97\) −7.18425 −0.729450 −0.364725 0.931115i \(-0.618837\pi\)
−0.364725 + 0.931115i \(0.618837\pi\)
\(98\) −21.1570 −2.13718
\(99\) 12.5036 1.25666
\(100\) 1.03331 0.103331
\(101\) 6.26842 0.623731 0.311866 0.950126i \(-0.399046\pi\)
0.311866 + 0.950126i \(0.399046\pi\)
\(102\) −12.2854 −1.21644
\(103\) −13.2590 −1.30645 −0.653226 0.757163i \(-0.726585\pi\)
−0.653226 + 0.757163i \(0.726585\pi\)
\(104\) −1.90664 −0.186961
\(105\) 25.3417 2.47310
\(106\) 2.72579 0.264752
\(107\) 7.75951 0.750140 0.375070 0.926996i \(-0.377619\pi\)
0.375070 + 0.926996i \(0.377619\pi\)
\(108\) 37.4444 3.60309
\(109\) −17.7031 −1.69565 −0.847824 0.530278i \(-0.822088\pi\)
−0.847824 + 0.530278i \(0.822088\pi\)
\(110\) 14.4274 1.37560
\(111\) 7.99216 0.758582
\(112\) −56.1883 −5.30929
\(113\) −4.72616 −0.444599 −0.222300 0.974978i \(-0.571356\pi\)
−0.222300 + 0.974978i \(0.571356\pi\)
\(114\) 4.12197 0.386058
\(115\) 6.60562 0.615977
\(116\) 9.07795 0.842866
\(117\) 1.09755 0.101468
\(118\) 1.04608 0.0962998
\(119\) −5.98131 −0.548306
\(120\) 61.6660 5.62931
\(121\) −5.60241 −0.509310
\(122\) −14.2818 −1.29301
\(123\) 29.0619 2.62042
\(124\) −36.5461 −3.28194
\(125\) 10.9576 0.980075
\(126\) 56.3633 5.02124
\(127\) 3.57719 0.317424 0.158712 0.987325i \(-0.449266\pi\)
0.158712 + 0.987325i \(0.449266\pi\)
\(128\) −35.1952 −3.11084
\(129\) 10.6508 0.937752
\(130\) 1.26642 0.111072
\(131\) 17.8001 1.55520 0.777602 0.628756i \(-0.216436\pi\)
0.777602 + 0.628756i \(0.216436\pi\)
\(132\) 36.5229 3.17891
\(133\) 2.00683 0.174014
\(134\) 13.9110 1.20172
\(135\) −15.7104 −1.35214
\(136\) −14.5548 −1.24806
\(137\) −10.9461 −0.935185 −0.467592 0.883944i \(-0.654878\pi\)
−0.467592 + 0.883944i \(0.654878\pi\)
\(138\) 22.8813 1.94779
\(139\) −14.9371 −1.26695 −0.633473 0.773765i \(-0.718371\pi\)
−0.633473 + 0.773765i \(0.718371\pi\)
\(140\) 47.5292 4.01695
\(141\) −1.89753 −0.159800
\(142\) 17.5381 1.47176
\(143\) 0.473793 0.0396206
\(144\) 78.7066 6.55888
\(145\) −3.80881 −0.316304
\(146\) −0.118773 −0.00982973
\(147\) 22.4715 1.85342
\(148\) 14.9895 1.23213
\(149\) −7.65613 −0.627215 −0.313607 0.949553i \(-0.601538\pi\)
−0.313607 + 0.949553i \(0.601538\pi\)
\(150\) −1.50175 −0.122617
\(151\) −1.00000 −0.0813788
\(152\) 4.88338 0.396094
\(153\) 8.37841 0.677354
\(154\) 24.3311 1.96066
\(155\) 15.3335 1.23162
\(156\) 3.20593 0.256680
\(157\) −18.0028 −1.43678 −0.718391 0.695639i \(-0.755121\pi\)
−0.718391 + 0.695639i \(0.755121\pi\)
\(158\) −18.8655 −1.50086
\(159\) −2.89515 −0.229600
\(160\) 48.2171 3.81189
\(161\) 11.1400 0.877957
\(162\) −10.4099 −0.817877
\(163\) −4.85204 −0.380041 −0.190021 0.981780i \(-0.560855\pi\)
−0.190021 + 0.981780i \(0.560855\pi\)
\(164\) 54.5064 4.25624
\(165\) −15.3238 −1.19296
\(166\) 8.33328 0.646788
\(167\) 0.117714 0.00910897 0.00455448 0.999990i \(-0.498550\pi\)
0.00455448 + 0.999990i \(0.498550\pi\)
\(168\) 103.997 8.02351
\(169\) −12.9584 −0.996801
\(170\) 9.66754 0.741466
\(171\) −2.81110 −0.214970
\(172\) 19.9759 1.52315
\(173\) −1.68091 −0.127797 −0.0638985 0.997956i \(-0.520353\pi\)
−0.0638985 + 0.997956i \(0.520353\pi\)
\(174\) −13.1934 −1.00019
\(175\) −0.731145 −0.0552693
\(176\) 33.9763 2.56106
\(177\) −1.11108 −0.0835137
\(178\) −41.1115 −3.08144
\(179\) −9.90153 −0.740075 −0.370038 0.929017i \(-0.620655\pi\)
−0.370038 + 0.929017i \(0.620655\pi\)
\(180\) −66.5772 −4.96237
\(181\) 19.2260 1.42906 0.714530 0.699605i \(-0.246640\pi\)
0.714530 + 0.699605i \(0.246640\pi\)
\(182\) 2.13575 0.158312
\(183\) 15.1691 1.12134
\(184\) 27.1079 1.99842
\(185\) −6.28912 −0.462385
\(186\) 53.1141 3.89451
\(187\) 3.61682 0.264488
\(188\) −3.55887 −0.259557
\(189\) −26.4948 −1.92721
\(190\) −3.24362 −0.235317
\(191\) 8.67772 0.627898 0.313949 0.949440i \(-0.398348\pi\)
0.313949 + 0.949440i \(0.398348\pi\)
\(192\) 82.3405 5.94242
\(193\) 6.44883 0.464197 0.232099 0.972692i \(-0.425441\pi\)
0.232099 + 0.972692i \(0.425441\pi\)
\(194\) 19.5828 1.40596
\(195\) −1.34510 −0.0963249
\(196\) 42.1459 3.01042
\(197\) −11.4335 −0.814605 −0.407303 0.913293i \(-0.633531\pi\)
−0.407303 + 0.913293i \(0.633531\pi\)
\(198\) −34.0821 −2.42211
\(199\) −12.3363 −0.874498 −0.437249 0.899340i \(-0.644047\pi\)
−0.437249 + 0.899340i \(0.644047\pi\)
\(200\) −1.77915 −0.125805
\(201\) −14.7753 −1.04217
\(202\) −17.0864 −1.20220
\(203\) −6.42336 −0.450831
\(204\) 24.4733 1.71348
\(205\) −22.8691 −1.59725
\(206\) 36.1414 2.51809
\(207\) −15.6046 −1.08459
\(208\) 2.98240 0.206792
\(209\) −1.21350 −0.0839398
\(210\) −69.0762 −4.76671
\(211\) −17.0729 −1.17535 −0.587674 0.809097i \(-0.699956\pi\)
−0.587674 + 0.809097i \(0.699956\pi\)
\(212\) −5.42994 −0.372930
\(213\) −18.6278 −1.27635
\(214\) −21.1508 −1.44584
\(215\) −8.38124 −0.571596
\(216\) −64.4719 −4.38676
\(217\) 25.8592 1.75544
\(218\) 48.2549 3.26823
\(219\) 0.126153 0.00852461
\(220\) −28.7403 −1.93767
\(221\) 0.317480 0.0213560
\(222\) −21.7850 −1.46211
\(223\) 25.9887 1.74033 0.870167 0.492756i \(-0.164011\pi\)
0.870167 + 0.492756i \(0.164011\pi\)
\(224\) 81.3156 5.43313
\(225\) 1.02416 0.0682774
\(226\) 12.8825 0.856932
\(227\) −9.63109 −0.639238 −0.319619 0.947546i \(-0.603555\pi\)
−0.319619 + 0.947546i \(0.603555\pi\)
\(228\) −8.21121 −0.543801
\(229\) −1.92835 −0.127429 −0.0637144 0.997968i \(-0.520295\pi\)
−0.0637144 + 0.997968i \(0.520295\pi\)
\(230\) −18.0055 −1.18725
\(231\) −25.8428 −1.70033
\(232\) −15.6305 −1.02619
\(233\) −28.5746 −1.87199 −0.935993 0.352020i \(-0.885495\pi\)
−0.935993 + 0.352020i \(0.885495\pi\)
\(234\) −2.99169 −0.195573
\(235\) 1.49318 0.0974045
\(236\) −2.08386 −0.135648
\(237\) 20.0377 1.30159
\(238\) 16.3038 1.05682
\(239\) −11.0854 −0.717054 −0.358527 0.933519i \(-0.616721\pi\)
−0.358527 + 0.933519i \(0.616721\pi\)
\(240\) −96.4592 −6.22641
\(241\) 3.11433 0.200611 0.100306 0.994957i \(-0.468018\pi\)
0.100306 + 0.994957i \(0.468018\pi\)
\(242\) 15.2710 0.981657
\(243\) −9.63107 −0.617834
\(244\) 28.4502 1.82134
\(245\) −17.6830 −1.12973
\(246\) −79.2166 −5.05067
\(247\) −0.106520 −0.00677769
\(248\) 62.9253 3.99576
\(249\) −8.85104 −0.560912
\(250\) −29.8681 −1.88902
\(251\) 9.29619 0.586770 0.293385 0.955994i \(-0.405218\pi\)
0.293385 + 0.955994i \(0.405218\pi\)
\(252\) −112.279 −7.07291
\(253\) −6.73623 −0.423503
\(254\) −9.75066 −0.611811
\(255\) −10.2682 −0.643020
\(256\) 39.0530 2.44081
\(257\) −9.16503 −0.571699 −0.285849 0.958275i \(-0.592276\pi\)
−0.285849 + 0.958275i \(0.592276\pi\)
\(258\) −29.0319 −1.80745
\(259\) −10.6063 −0.659041
\(260\) −2.52278 −0.156456
\(261\) 8.99761 0.556938
\(262\) −48.5194 −2.99754
\(263\) 3.19827 0.197214 0.0986068 0.995126i \(-0.468561\pi\)
0.0986068 + 0.995126i \(0.468561\pi\)
\(264\) −62.8854 −3.87033
\(265\) 2.27822 0.139950
\(266\) −5.47020 −0.335399
\(267\) 43.6658 2.67230
\(268\) −27.7115 −1.69275
\(269\) 16.7559 1.02162 0.510812 0.859692i \(-0.329345\pi\)
0.510812 + 0.859692i \(0.329345\pi\)
\(270\) 42.8233 2.60614
\(271\) −17.7458 −1.07798 −0.538990 0.842312i \(-0.681194\pi\)
−0.538990 + 0.842312i \(0.681194\pi\)
\(272\) 22.7669 1.38045
\(273\) −2.26845 −0.137293
\(274\) 29.8367 1.80250
\(275\) 0.442114 0.0266605
\(276\) −45.5809 −2.74365
\(277\) 13.9595 0.838748 0.419374 0.907814i \(-0.362250\pi\)
0.419374 + 0.907814i \(0.362250\pi\)
\(278\) 40.7153 2.44194
\(279\) −36.2227 −2.16859
\(280\) −81.8360 −4.89063
\(281\) 3.39667 0.202628 0.101314 0.994854i \(-0.467695\pi\)
0.101314 + 0.994854i \(0.467695\pi\)
\(282\) 5.17226 0.308003
\(283\) 23.8686 1.41884 0.709420 0.704786i \(-0.248957\pi\)
0.709420 + 0.704786i \(0.248957\pi\)
\(284\) −34.9369 −2.07313
\(285\) 3.44515 0.204073
\(286\) −1.29146 −0.0763657
\(287\) −38.5676 −2.27657
\(288\) −113.904 −6.71186
\(289\) −14.5764 −0.857437
\(290\) 10.3820 0.609653
\(291\) −20.7995 −1.21929
\(292\) 0.236603 0.0138461
\(293\) −4.81108 −0.281066 −0.140533 0.990076i \(-0.544882\pi\)
−0.140533 + 0.990076i \(0.544882\pi\)
\(294\) −61.2525 −3.57232
\(295\) 0.874319 0.0509048
\(296\) −25.8091 −1.50012
\(297\) 16.0211 0.929637
\(298\) 20.8690 1.20891
\(299\) −0.591298 −0.0341956
\(300\) 2.99157 0.172719
\(301\) −14.1345 −0.814701
\(302\) 2.72579 0.156852
\(303\) 18.1480 1.04258
\(304\) −7.63867 −0.438108
\(305\) −11.9368 −0.683497
\(306\) −22.8378 −1.30555
\(307\) 2.90468 0.165779 0.0828893 0.996559i \(-0.473585\pi\)
0.0828893 + 0.996559i \(0.473585\pi\)
\(308\) −48.4690 −2.76178
\(309\) −38.3869 −2.18375
\(310\) −41.7960 −2.37385
\(311\) 16.7201 0.948111 0.474055 0.880495i \(-0.342790\pi\)
0.474055 + 0.880495i \(0.342790\pi\)
\(312\) −5.51999 −0.312508
\(313\) −16.6733 −0.942432 −0.471216 0.882018i \(-0.656185\pi\)
−0.471216 + 0.882018i \(0.656185\pi\)
\(314\) 49.0720 2.76929
\(315\) 47.1085 2.65427
\(316\) 37.5812 2.11411
\(317\) −24.1799 −1.35808 −0.679041 0.734101i \(-0.737604\pi\)
−0.679041 + 0.734101i \(0.737604\pi\)
\(318\) 7.89157 0.442537
\(319\) 3.88412 0.217469
\(320\) −64.7946 −3.62213
\(321\) 22.4649 1.25387
\(322\) −30.3654 −1.69220
\(323\) −0.813146 −0.0452447
\(324\) 20.7371 1.15206
\(325\) 0.0388082 0.00215269
\(326\) 13.2257 0.732501
\(327\) −51.2530 −2.83430
\(328\) −93.8495 −5.18197
\(329\) 2.51817 0.138831
\(330\) 41.7695 2.29934
\(331\) 1.51180 0.0830959 0.0415480 0.999137i \(-0.486771\pi\)
0.0415480 + 0.999137i \(0.486771\pi\)
\(332\) −16.6004 −0.911065
\(333\) 14.8569 0.814152
\(334\) −0.320863 −0.0175569
\(335\) 11.6268 0.635241
\(336\) −162.673 −8.87456
\(337\) −5.85763 −0.319085 −0.159543 0.987191i \(-0.551002\pi\)
−0.159543 + 0.987191i \(0.551002\pi\)
\(338\) 35.3219 1.92126
\(339\) −13.6829 −0.743155
\(340\) −19.2583 −1.04443
\(341\) −15.6367 −0.846776
\(342\) 7.66246 0.414339
\(343\) −2.92679 −0.158032
\(344\) −34.3947 −1.85444
\(345\) 19.1242 1.02961
\(346\) 4.58180 0.246319
\(347\) 13.8115 0.741438 0.370719 0.928745i \(-0.379111\pi\)
0.370719 + 0.928745i \(0.379111\pi\)
\(348\) 26.2820 1.40886
\(349\) −26.2982 −1.40771 −0.703855 0.710343i \(-0.748540\pi\)
−0.703855 + 0.710343i \(0.748540\pi\)
\(350\) 1.99295 0.106528
\(351\) 1.40631 0.0750632
\(352\) −49.1705 −2.62080
\(353\) 12.5272 0.666754 0.333377 0.942794i \(-0.391812\pi\)
0.333377 + 0.942794i \(0.391812\pi\)
\(354\) 3.02857 0.160966
\(355\) 14.6584 0.777986
\(356\) 81.8965 4.34051
\(357\) −17.3168 −0.916501
\(358\) 26.9895 1.42644
\(359\) −15.1845 −0.801407 −0.400704 0.916208i \(-0.631234\pi\)
−0.400704 + 0.916208i \(0.631234\pi\)
\(360\) 114.633 6.04169
\(361\) −18.7272 −0.985641
\(362\) −52.4062 −2.75441
\(363\) −16.2198 −0.851319
\(364\) −4.25454 −0.222999
\(365\) −0.0992708 −0.00519607
\(366\) −41.3479 −2.16129
\(367\) −10.9649 −0.572364 −0.286182 0.958175i \(-0.592386\pi\)
−0.286182 + 0.958175i \(0.592386\pi\)
\(368\) −42.4027 −2.21039
\(369\) 54.0241 2.81238
\(370\) 17.1428 0.891213
\(371\) 3.84210 0.199472
\(372\) −105.806 −5.48580
\(373\) −16.3216 −0.845100 −0.422550 0.906340i \(-0.638865\pi\)
−0.422550 + 0.906340i \(0.638865\pi\)
\(374\) −9.85870 −0.509781
\(375\) 31.7238 1.63821
\(376\) 6.12767 0.316011
\(377\) 0.340943 0.0175595
\(378\) 72.2193 3.71456
\(379\) −1.64087 −0.0842861 −0.0421430 0.999112i \(-0.513419\pi\)
−0.0421430 + 0.999112i \(0.513419\pi\)
\(380\) 6.46149 0.331467
\(381\) 10.3565 0.530579
\(382\) −23.6537 −1.21023
\(383\) −18.4499 −0.942745 −0.471372 0.881934i \(-0.656241\pi\)
−0.471372 + 0.881934i \(0.656241\pi\)
\(384\) −101.895 −5.19982
\(385\) 20.3360 1.03642
\(386\) −17.5782 −0.894705
\(387\) 19.7992 1.00645
\(388\) −39.0100 −1.98043
\(389\) 5.00166 0.253594 0.126797 0.991929i \(-0.459530\pi\)
0.126797 + 0.991929i \(0.459530\pi\)
\(390\) 3.66647 0.185659
\(391\) −4.51382 −0.228274
\(392\) −72.5670 −3.66519
\(393\) 51.5340 2.59955
\(394\) 31.1654 1.57009
\(395\) −15.7678 −0.793366
\(396\) 67.8936 3.41178
\(397\) −34.0309 −1.70796 −0.853980 0.520306i \(-0.825818\pi\)
−0.853980 + 0.520306i \(0.825818\pi\)
\(398\) 33.6262 1.68553
\(399\) 5.81007 0.290867
\(400\) 2.78298 0.139149
\(401\) −8.42042 −0.420496 −0.210248 0.977648i \(-0.567427\pi\)
−0.210248 + 0.977648i \(0.567427\pi\)
\(402\) 40.2743 2.00870
\(403\) −1.37257 −0.0683727
\(404\) 34.0371 1.69341
\(405\) −8.70060 −0.432336
\(406\) 17.5087 0.868944
\(407\) 6.41347 0.317904
\(408\) −42.1383 −2.08616
\(409\) 29.2362 1.44564 0.722818 0.691039i \(-0.242847\pi\)
0.722818 + 0.691039i \(0.242847\pi\)
\(410\) 62.3364 3.07858
\(411\) −31.6905 −1.56318
\(412\) −71.9958 −3.54698
\(413\) 1.47449 0.0725551
\(414\) 42.5348 2.09047
\(415\) 6.96498 0.341897
\(416\) −4.31612 −0.211615
\(417\) −43.2450 −2.11772
\(418\) 3.30776 0.161788
\(419\) 15.1511 0.740181 0.370091 0.928996i \(-0.379327\pi\)
0.370091 + 0.928996i \(0.379327\pi\)
\(420\) 137.604 6.71439
\(421\) −31.8504 −1.55229 −0.776146 0.630553i \(-0.782828\pi\)
−0.776146 + 0.630553i \(0.782828\pi\)
\(422\) 46.5372 2.26540
\(423\) −3.52737 −0.171507
\(424\) 9.34930 0.454042
\(425\) 0.296252 0.0143703
\(426\) 50.7754 2.46008
\(427\) −20.1307 −0.974194
\(428\) 42.1337 2.03661
\(429\) 1.37170 0.0662264
\(430\) 22.8455 1.10171
\(431\) −8.11994 −0.391124 −0.195562 0.980691i \(-0.562653\pi\)
−0.195562 + 0.980691i \(0.562653\pi\)
\(432\) 100.848 4.85206
\(433\) −4.30676 −0.206970 −0.103485 0.994631i \(-0.532999\pi\)
−0.103485 + 0.994631i \(0.532999\pi\)
\(434\) −70.4868 −3.38348
\(435\) −11.0271 −0.528707
\(436\) −96.1266 −4.60363
\(437\) 1.51446 0.0724466
\(438\) −0.343866 −0.0164305
\(439\) 19.7306 0.941690 0.470845 0.882216i \(-0.343949\pi\)
0.470845 + 0.882216i \(0.343949\pi\)
\(440\) 49.4851 2.35911
\(441\) 41.7729 1.98919
\(442\) −0.865384 −0.0411621
\(443\) −3.01218 −0.143113 −0.0715565 0.997437i \(-0.522797\pi\)
−0.0715565 + 0.997437i \(0.522797\pi\)
\(444\) 43.3969 2.05953
\(445\) −34.3611 −1.62887
\(446\) −70.8399 −3.35437
\(447\) −22.1656 −1.04840
\(448\) −109.273 −5.16265
\(449\) −1.05075 −0.0495878 −0.0247939 0.999693i \(-0.507893\pi\)
−0.0247939 + 0.999693i \(0.507893\pi\)
\(450\) −2.79165 −0.131600
\(451\) 23.3213 1.09816
\(452\) −25.6627 −1.20707
\(453\) −2.89515 −0.136026
\(454\) 26.2523 1.23208
\(455\) 1.78507 0.0836852
\(456\) 14.1381 0.662077
\(457\) −10.4105 −0.486981 −0.243490 0.969903i \(-0.578292\pi\)
−0.243490 + 0.969903i \(0.578292\pi\)
\(458\) 5.25627 0.245609
\(459\) 10.7354 0.501086
\(460\) 35.8681 1.67236
\(461\) 26.0201 1.21188 0.605938 0.795512i \(-0.292798\pi\)
0.605938 + 0.795512i \(0.292798\pi\)
\(462\) 70.4421 3.27726
\(463\) 16.6583 0.774177 0.387089 0.922043i \(-0.373481\pi\)
0.387089 + 0.922043i \(0.373481\pi\)
\(464\) 24.4495 1.13504
\(465\) 44.3929 2.05867
\(466\) 77.8884 3.60811
\(467\) 30.8844 1.42916 0.714580 0.699554i \(-0.246618\pi\)
0.714580 + 0.699554i \(0.246618\pi\)
\(468\) 5.95962 0.275483
\(469\) 19.6080 0.905415
\(470\) −4.07010 −0.187740
\(471\) −52.1209 −2.40160
\(472\) 3.58800 0.165151
\(473\) 8.54697 0.392990
\(474\) −54.6185 −2.50871
\(475\) −0.0993975 −0.00456067
\(476\) −32.4782 −1.48863
\(477\) −5.38188 −0.246420
\(478\) 30.2164 1.38207
\(479\) −3.25271 −0.148620 −0.0743099 0.997235i \(-0.523675\pi\)
−0.0743099 + 0.997235i \(0.523675\pi\)
\(480\) 139.596 6.37164
\(481\) 0.562966 0.0256691
\(482\) −8.48900 −0.386664
\(483\) 32.2520 1.46752
\(484\) −30.4207 −1.38276
\(485\) 16.3673 0.743202
\(486\) 26.2523 1.19083
\(487\) −7.91375 −0.358606 −0.179303 0.983794i \(-0.557384\pi\)
−0.179303 + 0.983794i \(0.557384\pi\)
\(488\) −48.9857 −2.21748
\(489\) −14.0474 −0.635245
\(490\) 48.2003 2.17747
\(491\) −38.7922 −1.75067 −0.875333 0.483521i \(-0.839358\pi\)
−0.875333 + 0.483521i \(0.839358\pi\)
\(492\) 157.804 7.11436
\(493\) 2.60268 0.117219
\(494\) 0.290351 0.0130635
\(495\) −28.4859 −1.28035
\(496\) −98.4289 −4.41959
\(497\) 24.7206 1.10887
\(498\) 24.1261 1.08112
\(499\) 21.1361 0.946184 0.473092 0.881013i \(-0.343138\pi\)
0.473092 + 0.881013i \(0.343138\pi\)
\(500\) 59.4989 2.66087
\(501\) 0.340799 0.0152258
\(502\) −25.3395 −1.13096
\(503\) −12.2665 −0.546937 −0.273469 0.961881i \(-0.588171\pi\)
−0.273469 + 0.961881i \(0.588171\pi\)
\(504\) 193.323 8.61127
\(505\) −14.2809 −0.635490
\(506\) 18.3616 0.816271
\(507\) −37.5165 −1.66617
\(508\) 19.4239 0.861796
\(509\) 3.97730 0.176291 0.0881453 0.996108i \(-0.471906\pi\)
0.0881453 + 0.996108i \(0.471906\pi\)
\(510\) 27.9890 1.23937
\(511\) −0.167415 −0.00740601
\(512\) −36.0600 −1.59364
\(513\) −3.60191 −0.159028
\(514\) 24.9819 1.10191
\(515\) 30.2071 1.33108
\(516\) 57.8333 2.54597
\(517\) −1.52271 −0.0669686
\(518\) 28.9105 1.27025
\(519\) −4.86648 −0.213615
\(520\) 4.34374 0.190486
\(521\) −31.6494 −1.38659 −0.693293 0.720656i \(-0.743841\pi\)
−0.693293 + 0.720656i \(0.743841\pi\)
\(522\) −24.5256 −1.07346
\(523\) −40.7785 −1.78312 −0.891559 0.452904i \(-0.850388\pi\)
−0.891559 + 0.452904i \(0.850388\pi\)
\(524\) 96.6536 4.22233
\(525\) −2.11677 −0.0923835
\(526\) −8.71780 −0.380114
\(527\) −10.4779 −0.456424
\(528\) 98.3665 4.28085
\(529\) −14.5931 −0.634484
\(530\) −6.20996 −0.269743
\(531\) −2.06542 −0.0896315
\(532\) 10.8970 0.472443
\(533\) 2.04711 0.0886703
\(534\) −119.024 −5.15067
\(535\) −17.6779 −0.764282
\(536\) 47.7138 2.06092
\(537\) −28.6664 −1.23705
\(538\) −45.6730 −1.96910
\(539\) 18.0327 0.776723
\(540\) −85.3066 −3.67101
\(541\) −40.8766 −1.75742 −0.878711 0.477355i \(-0.841596\pi\)
−0.878711 + 0.477355i \(0.841596\pi\)
\(542\) 48.3713 2.07773
\(543\) 55.6623 2.38870
\(544\) −32.9482 −1.41264
\(545\) 40.3316 1.72761
\(546\) 6.18332 0.264622
\(547\) −13.2169 −0.565114 −0.282557 0.959250i \(-0.591183\pi\)
−0.282557 + 0.959250i \(0.591183\pi\)
\(548\) −59.4364 −2.53900
\(549\) 28.1984 1.20348
\(550\) −1.20511 −0.0513860
\(551\) −0.873241 −0.0372013
\(552\) 78.4814 3.34039
\(553\) −26.5917 −1.13079
\(554\) −38.0508 −1.61662
\(555\) −18.2079 −0.772883
\(556\) −81.1073 −3.43972
\(557\) −40.9754 −1.73618 −0.868091 0.496405i \(-0.834653\pi\)
−0.868091 + 0.496405i \(0.834653\pi\)
\(558\) 98.7354 4.17980
\(559\) 0.750242 0.0317318
\(560\) 128.009 5.40938
\(561\) 10.4712 0.442096
\(562\) −9.25862 −0.390551
\(563\) 44.7913 1.88773 0.943863 0.330336i \(-0.107162\pi\)
0.943863 + 0.330336i \(0.107162\pi\)
\(564\) −10.3034 −0.433853
\(565\) 10.7672 0.452981
\(566\) −65.0608 −2.73471
\(567\) −14.6731 −0.616213
\(568\) 60.1546 2.52403
\(569\) 43.7045 1.83219 0.916093 0.400966i \(-0.131325\pi\)
0.916093 + 0.400966i \(0.131325\pi\)
\(570\) −9.39076 −0.393336
\(571\) 6.86801 0.287417 0.143709 0.989620i \(-0.454097\pi\)
0.143709 + 0.989620i \(0.454097\pi\)
\(572\) 2.57267 0.107569
\(573\) 25.1233 1.04954
\(574\) 105.127 4.38792
\(575\) −0.551761 −0.0230100
\(576\) 153.065 6.37773
\(577\) −8.72931 −0.363406 −0.181703 0.983353i \(-0.558161\pi\)
−0.181703 + 0.983353i \(0.558161\pi\)
\(578\) 39.7323 1.65265
\(579\) 18.6703 0.775912
\(580\) −20.6816 −0.858756
\(581\) 11.7461 0.487309
\(582\) 56.6950 2.35008
\(583\) −2.32327 −0.0962201
\(584\) −0.407384 −0.0168577
\(585\) −2.50046 −0.103381
\(586\) 13.1140 0.541735
\(587\) −22.2323 −0.917627 −0.458813 0.888533i \(-0.651725\pi\)
−0.458813 + 0.888533i \(0.651725\pi\)
\(588\) 122.019 5.03196
\(589\) 3.51550 0.144854
\(590\) −2.38321 −0.0981152
\(591\) −33.1018 −1.36162
\(592\) 40.3711 1.65924
\(593\) 33.1822 1.36263 0.681315 0.731990i \(-0.261408\pi\)
0.681315 + 0.731990i \(0.261408\pi\)
\(594\) −43.6701 −1.79181
\(595\) 13.6268 0.558643
\(596\) −41.5723 −1.70287
\(597\) −35.7155 −1.46174
\(598\) 1.61175 0.0659095
\(599\) −18.6892 −0.763622 −0.381811 0.924241i \(-0.624699\pi\)
−0.381811 + 0.924241i \(0.624699\pi\)
\(600\) −5.15091 −0.210285
\(601\) −1.58501 −0.0646540 −0.0323270 0.999477i \(-0.510292\pi\)
−0.0323270 + 0.999477i \(0.510292\pi\)
\(602\) 38.5278 1.57027
\(603\) −27.4662 −1.11851
\(604\) −5.42994 −0.220941
\(605\) 12.7635 0.518912
\(606\) −49.4677 −2.00949
\(607\) −37.1175 −1.50655 −0.753277 0.657704i \(-0.771528\pi\)
−0.753277 + 0.657704i \(0.771528\pi\)
\(608\) 11.0547 0.448326
\(609\) −18.5966 −0.753571
\(610\) 32.5371 1.31739
\(611\) −0.133661 −0.00540736
\(612\) 45.4943 1.83900
\(613\) −6.02541 −0.243364 −0.121682 0.992569i \(-0.538829\pi\)
−0.121682 + 0.992569i \(0.538829\pi\)
\(614\) −7.91754 −0.319526
\(615\) −66.2094 −2.66982
\(616\) 83.4541 3.36246
\(617\) −47.4335 −1.90960 −0.954801 0.297245i \(-0.903932\pi\)
−0.954801 + 0.297245i \(0.903932\pi\)
\(618\) 104.635 4.20902
\(619\) 3.47340 0.139608 0.0698039 0.997561i \(-0.477763\pi\)
0.0698039 + 0.997561i \(0.477763\pi\)
\(620\) 83.2601 3.34381
\(621\) −19.9944 −0.802348
\(622\) −45.5755 −1.82741
\(623\) −57.9482 −2.32164
\(624\) 8.63448 0.345656
\(625\) −25.9153 −1.03661
\(626\) 45.4480 1.81647
\(627\) −3.51327 −0.140307
\(628\) −97.7542 −3.90082
\(629\) 4.29755 0.171354
\(630\) −128.408 −5.11590
\(631\) −6.94325 −0.276407 −0.138203 0.990404i \(-0.544133\pi\)
−0.138203 + 0.990404i \(0.544133\pi\)
\(632\) −64.7076 −2.57393
\(633\) −49.4287 −1.96461
\(634\) 65.9095 2.61760
\(635\) −8.14963 −0.323408
\(636\) −15.7205 −0.623357
\(637\) 1.58289 0.0627162
\(638\) −10.5873 −0.419155
\(639\) −34.6277 −1.36985
\(640\) 80.1825 3.16949
\(641\) −1.81266 −0.0715956 −0.0357978 0.999359i \(-0.511397\pi\)
−0.0357978 + 0.999359i \(0.511397\pi\)
\(642\) −61.2347 −2.41674
\(643\) 36.4934 1.43916 0.719580 0.694409i \(-0.244334\pi\)
0.719580 + 0.694409i \(0.244334\pi\)
\(644\) 60.4897 2.38363
\(645\) −24.2649 −0.955431
\(646\) 2.21647 0.0872057
\(647\) 32.8803 1.29266 0.646329 0.763059i \(-0.276303\pi\)
0.646329 + 0.763059i \(0.276303\pi\)
\(648\) −35.7052 −1.40263
\(649\) −0.891607 −0.0349986
\(650\) −0.105783 −0.00414915
\(651\) 74.8663 2.93424
\(652\) −26.3463 −1.03180
\(653\) −5.76635 −0.225655 −0.112827 0.993615i \(-0.535991\pi\)
−0.112827 + 0.993615i \(0.535991\pi\)
\(654\) 139.705 5.46290
\(655\) −40.5527 −1.58452
\(656\) 146.801 5.73162
\(657\) 0.234509 0.00914908
\(658\) −6.86402 −0.267587
\(659\) 44.4810 1.73273 0.866366 0.499410i \(-0.166450\pi\)
0.866366 + 0.499410i \(0.166450\pi\)
\(660\) −83.2074 −3.23884
\(661\) 11.2993 0.439493 0.219746 0.975557i \(-0.429477\pi\)
0.219746 + 0.975557i \(0.429477\pi\)
\(662\) −4.12085 −0.160161
\(663\) 0.919151 0.0356969
\(664\) 28.5826 1.10922
\(665\) −4.57200 −0.177295
\(666\) −40.4968 −1.56922
\(667\) −4.84741 −0.187693
\(668\) 0.639179 0.0247306
\(669\) 75.2413 2.90899
\(670\) −31.6923 −1.22438
\(671\) 12.1728 0.469926
\(672\) 235.421 9.08155
\(673\) 13.8835 0.535169 0.267584 0.963534i \(-0.413775\pi\)
0.267584 + 0.963534i \(0.413775\pi\)
\(674\) 15.9667 0.615013
\(675\) 1.31228 0.0505096
\(676\) −70.3634 −2.70628
\(677\) −16.4266 −0.631325 −0.315663 0.948871i \(-0.602227\pi\)
−0.315663 + 0.948871i \(0.602227\pi\)
\(678\) 37.2968 1.43237
\(679\) 27.6026 1.05929
\(680\) 33.1591 1.27159
\(681\) −27.8834 −1.06850
\(682\) 42.6225 1.63210
\(683\) 21.7647 0.832802 0.416401 0.909181i \(-0.363291\pi\)
0.416401 + 0.909181i \(0.363291\pi\)
\(684\) −15.2641 −0.583637
\(685\) 24.9376 0.952815
\(686\) 7.97781 0.304594
\(687\) −5.58285 −0.212999
\(688\) 53.8008 2.05114
\(689\) −0.203934 −0.00776925
\(690\) −52.1287 −1.98450
\(691\) 2.54294 0.0967378 0.0483689 0.998830i \(-0.484598\pi\)
0.0483689 + 0.998830i \(0.484598\pi\)
\(692\) −9.12722 −0.346965
\(693\) −48.0400 −1.82489
\(694\) −37.6472 −1.42907
\(695\) 34.0300 1.29083
\(696\) −45.2525 −1.71529
\(697\) 15.6272 0.591921
\(698\) 71.6834 2.71326
\(699\) −82.7277 −3.12905
\(700\) −3.97007 −0.150055
\(701\) 5.17645 0.195512 0.0977560 0.995210i \(-0.468834\pi\)
0.0977560 + 0.995210i \(0.468834\pi\)
\(702\) −3.83330 −0.144679
\(703\) −1.44190 −0.0543822
\(704\) 66.0758 2.49033
\(705\) 4.32298 0.162813
\(706\) −34.1465 −1.28512
\(707\) −24.0839 −0.905769
\(708\) −6.03308 −0.226737
\(709\) −27.5605 −1.03506 −0.517529 0.855666i \(-0.673148\pi\)
−0.517529 + 0.855666i \(0.673148\pi\)
\(710\) −39.9557 −1.49951
\(711\) 37.2487 1.39693
\(712\) −141.010 −5.28457
\(713\) 19.5148 0.730834
\(714\) 47.2019 1.76649
\(715\) −1.07941 −0.0403675
\(716\) −53.7647 −2.00928
\(717\) −32.0938 −1.19857
\(718\) 41.3898 1.54465
\(719\) −28.1653 −1.05039 −0.525194 0.850982i \(-0.676007\pi\)
−0.525194 + 0.850982i \(0.676007\pi\)
\(720\) −179.311 −6.68253
\(721\) 50.9426 1.89720
\(722\) 51.0464 1.89975
\(723\) 9.01644 0.335325
\(724\) 104.396 3.87986
\(725\) 0.318146 0.0118157
\(726\) 44.2118 1.64085
\(727\) 7.65975 0.284085 0.142042 0.989861i \(-0.454633\pi\)
0.142042 + 0.989861i \(0.454633\pi\)
\(728\) 7.32550 0.271501
\(729\) −39.3405 −1.45705
\(730\) 0.270592 0.0100150
\(731\) 5.72716 0.211827
\(732\) 82.3675 3.04439
\(733\) −34.7970 −1.28526 −0.642629 0.766178i \(-0.722156\pi\)
−0.642629 + 0.766178i \(0.722156\pi\)
\(734\) 29.8881 1.10319
\(735\) −51.1950 −1.88836
\(736\) 61.3652 2.26195
\(737\) −11.8567 −0.436748
\(738\) −147.258 −5.42065
\(739\) 19.1345 0.703874 0.351937 0.936024i \(-0.385523\pi\)
0.351937 + 0.936024i \(0.385523\pi\)
\(740\) −34.1495 −1.25536
\(741\) −0.308391 −0.0113290
\(742\) −10.4728 −0.384468
\(743\) −36.9082 −1.35403 −0.677016 0.735968i \(-0.736727\pi\)
−0.677016 + 0.735968i \(0.736727\pi\)
\(744\) 182.178 6.67897
\(745\) 17.4424 0.639039
\(746\) 44.4893 1.62887
\(747\) −16.4535 −0.602002
\(748\) 19.6391 0.718077
\(749\) −29.8129 −1.08934
\(750\) −86.4724 −3.15753
\(751\) −15.4281 −0.562978 −0.281489 0.959564i \(-0.590828\pi\)
−0.281489 + 0.959564i \(0.590828\pi\)
\(752\) −9.58503 −0.349530
\(753\) 26.9138 0.980795
\(754\) −0.929340 −0.0338446
\(755\) 2.27822 0.0829130
\(756\) −143.865 −5.23232
\(757\) −17.1093 −0.621849 −0.310925 0.950435i \(-0.600639\pi\)
−0.310925 + 0.950435i \(0.600639\pi\)
\(758\) 4.47268 0.162455
\(759\) −19.5024 −0.707892
\(760\) −11.1254 −0.403561
\(761\) 54.0508 1.95934 0.979669 0.200619i \(-0.0642953\pi\)
0.979669 + 0.200619i \(0.0642953\pi\)
\(762\) −28.2296 −1.02265
\(763\) 68.0171 2.46238
\(764\) 47.1195 1.70472
\(765\) −19.0879 −0.690124
\(766\) 50.2905 1.81707
\(767\) −0.0782641 −0.00282595
\(768\) 113.064 4.07985
\(769\) −16.8159 −0.606396 −0.303198 0.952928i \(-0.598054\pi\)
−0.303198 + 0.952928i \(0.598054\pi\)
\(770\) −55.4316 −1.99762
\(771\) −26.5341 −0.955603
\(772\) 35.0168 1.26028
\(773\) −39.3482 −1.41526 −0.707628 0.706585i \(-0.750235\pi\)
−0.707628 + 0.706585i \(0.750235\pi\)
\(774\) −53.9684 −1.93985
\(775\) −1.28080 −0.0460076
\(776\) 67.1677 2.41118
\(777\) −30.7067 −1.10160
\(778\) −13.6335 −0.488784
\(779\) −5.24317 −0.187856
\(780\) −7.30383 −0.261519
\(781\) −14.9482 −0.534890
\(782\) 12.3037 0.439981
\(783\) 11.5288 0.412006
\(784\) 113.511 4.05396
\(785\) 41.0145 1.46387
\(786\) −140.471 −5.01043
\(787\) 0.00184276 6.56873e−5 0 3.28437e−5 1.00000i \(-0.499990\pi\)
3.28437e−5 1.00000i \(0.499990\pi\)
\(788\) −62.0834 −2.21163
\(789\) 9.25945 0.329645
\(790\) 42.9799 1.52915
\(791\) 18.1584 0.645638
\(792\) −116.900 −4.15385
\(793\) 1.06851 0.0379440
\(794\) 92.7610 3.29197
\(795\) 6.59579 0.233929
\(796\) −66.9854 −2.37424
\(797\) −34.7510 −1.23094 −0.615472 0.788159i \(-0.711035\pi\)
−0.615472 + 0.788159i \(0.711035\pi\)
\(798\) −15.8370 −0.560625
\(799\) −1.02034 −0.0360970
\(800\) −4.02753 −0.142395
\(801\) 81.1717 2.86806
\(802\) 22.9523 0.810474
\(803\) 0.101234 0.00357246
\(804\) −80.2289 −2.82945
\(805\) −25.3795 −0.894509
\(806\) 3.74134 0.131783
\(807\) 48.5108 1.70766
\(808\) −58.6053 −2.06173
\(809\) −9.01460 −0.316936 −0.158468 0.987364i \(-0.550656\pi\)
−0.158468 + 0.987364i \(0.550656\pi\)
\(810\) 23.7160 0.833296
\(811\) −9.05066 −0.317812 −0.158906 0.987294i \(-0.550797\pi\)
−0.158906 + 0.987294i \(0.550797\pi\)
\(812\) −34.8784 −1.22399
\(813\) −51.3767 −1.80186
\(814\) −17.4818 −0.612736
\(815\) 11.0540 0.387206
\(816\) 65.9135 2.30744
\(817\) −1.92156 −0.0672268
\(818\) −79.6917 −2.78635
\(819\) −4.21689 −0.147350
\(820\) −124.178 −4.33648
\(821\) −6.82623 −0.238237 −0.119119 0.992880i \(-0.538007\pi\)
−0.119119 + 0.992880i \(0.538007\pi\)
\(822\) 86.3816 3.01290
\(823\) 12.2202 0.425969 0.212984 0.977056i \(-0.431682\pi\)
0.212984 + 0.977056i \(0.431682\pi\)
\(824\) 123.963 4.31845
\(825\) 1.27998 0.0445634
\(826\) −4.01916 −0.139844
\(827\) 19.4915 0.677785 0.338893 0.940825i \(-0.389948\pi\)
0.338893 + 0.940825i \(0.389948\pi\)
\(828\) −84.7318 −2.94463
\(829\) −43.3048 −1.50404 −0.752019 0.659141i \(-0.770920\pi\)
−0.752019 + 0.659141i \(0.770920\pi\)
\(830\) −18.9851 −0.658982
\(831\) 40.4150 1.40198
\(832\) 5.80005 0.201081
\(833\) 12.0834 0.418664
\(834\) 117.877 4.08174
\(835\) −0.268178 −0.00928069
\(836\) −6.58925 −0.227894
\(837\) −46.4128 −1.60426
\(838\) −41.2988 −1.42664
\(839\) −15.4619 −0.533805 −0.266902 0.963724i \(-0.586000\pi\)
−0.266902 + 0.963724i \(0.586000\pi\)
\(840\) −236.927 −8.17477
\(841\) −26.2050 −0.903620
\(842\) 86.8174 2.99193
\(843\) 9.83387 0.338697
\(844\) −92.7049 −3.19104
\(845\) 29.5221 1.01559
\(846\) 9.61488 0.330566
\(847\) 21.5251 0.739610
\(848\) −14.6244 −0.502202
\(849\) 69.1031 2.37161
\(850\) −0.807521 −0.0276978
\(851\) −8.00406 −0.274376
\(852\) −101.148 −3.46526
\(853\) −5.46365 −0.187072 −0.0935358 0.995616i \(-0.529817\pi\)
−0.0935358 + 0.995616i \(0.529817\pi\)
\(854\) 54.8722 1.87769
\(855\) 6.40430 0.219023
\(856\) −72.5460 −2.47957
\(857\) −15.1580 −0.517789 −0.258894 0.965906i \(-0.583358\pi\)
−0.258894 + 0.965906i \(0.583358\pi\)
\(858\) −3.73897 −0.127646
\(859\) 35.7423 1.21951 0.609755 0.792590i \(-0.291268\pi\)
0.609755 + 0.792590i \(0.291268\pi\)
\(860\) −45.5096 −1.55187
\(861\) −111.659 −3.80532
\(862\) 22.1332 0.753861
\(863\) −54.6459 −1.86017 −0.930084 0.367348i \(-0.880266\pi\)
−0.930084 + 0.367348i \(0.880266\pi\)
\(864\) −145.947 −4.96523
\(865\) 3.82948 0.130206
\(866\) 11.7393 0.398919
\(867\) −42.2009 −1.43322
\(868\) 140.414 4.76596
\(869\) 16.0796 0.545464
\(870\) 30.0575 1.01904
\(871\) −1.04077 −0.0352651
\(872\) 165.511 5.60492
\(873\) −38.6648 −1.30861
\(874\) −4.12811 −0.139635
\(875\) −42.1001 −1.42324
\(876\) 0.685001 0.0231440
\(877\) 44.0614 1.48785 0.743924 0.668265i \(-0.232963\pi\)
0.743924 + 0.668265i \(0.232963\pi\)
\(878\) −53.7815 −1.81504
\(879\) −13.9288 −0.469807
\(880\) −77.4056 −2.60934
\(881\) −38.2241 −1.28780 −0.643901 0.765109i \(-0.722685\pi\)
−0.643901 + 0.765109i \(0.722685\pi\)
\(882\) −113.864 −3.83401
\(883\) −5.84288 −0.196629 −0.0983143 0.995155i \(-0.531345\pi\)
−0.0983143 + 0.995155i \(0.531345\pi\)
\(884\) 1.72390 0.0579809
\(885\) 2.53128 0.0850881
\(886\) 8.21057 0.275840
\(887\) 25.0989 0.842737 0.421369 0.906889i \(-0.361550\pi\)
0.421369 + 0.906889i \(0.361550\pi\)
\(888\) −74.7211 −2.50748
\(889\) −13.7439 −0.460956
\(890\) 93.6611 3.13953
\(891\) 8.87264 0.297245
\(892\) 141.117 4.72495
\(893\) 0.342340 0.0114560
\(894\) 60.4189 2.02071
\(895\) 22.5579 0.754027
\(896\) 135.224 4.51750
\(897\) −1.71189 −0.0571585
\(898\) 2.86411 0.0955767
\(899\) −11.2522 −0.375283
\(900\) 5.56113 0.185371
\(901\) −1.55678 −0.0518639
\(902\) −63.5690 −2.11662
\(903\) −40.9216 −1.36178
\(904\) 44.1862 1.46961
\(905\) −43.8012 −1.45600
\(906\) 7.89157 0.262180
\(907\) −17.8735 −0.593480 −0.296740 0.954958i \(-0.595899\pi\)
−0.296740 + 0.954958i \(0.595899\pi\)
\(908\) −52.2962 −1.73551
\(909\) 33.7359 1.11895
\(910\) −4.86572 −0.161297
\(911\) 28.7282 0.951807 0.475904 0.879497i \(-0.342121\pi\)
0.475904 + 0.879497i \(0.342121\pi\)
\(912\) −22.1151 −0.732304
\(913\) −7.10270 −0.235065
\(914\) 28.3767 0.938619
\(915\) −34.5587 −1.14248
\(916\) −10.4708 −0.345965
\(917\) −68.3900 −2.25844
\(918\) −29.2625 −0.965806
\(919\) 23.8901 0.788062 0.394031 0.919097i \(-0.371080\pi\)
0.394031 + 0.919097i \(0.371080\pi\)
\(920\) −61.7578 −2.03610
\(921\) 8.40947 0.277101
\(922\) −70.9254 −2.33580
\(923\) −1.31214 −0.0431895
\(924\) −140.325 −4.61635
\(925\) 0.525324 0.0172726
\(926\) −45.4071 −1.49217
\(927\) −71.3587 −2.34373
\(928\) −35.3832 −1.16151
\(929\) −19.1197 −0.627297 −0.313648 0.949539i \(-0.601551\pi\)
−0.313648 + 0.949539i \(0.601551\pi\)
\(930\) −121.006 −3.96793
\(931\) −4.05417 −0.132870
\(932\) −155.158 −5.08238
\(933\) 48.4072 1.58478
\(934\) −84.1845 −2.75460
\(935\) −8.23993 −0.269474
\(936\) −10.2613 −0.335401
\(937\) 28.4572 0.929655 0.464827 0.885401i \(-0.346116\pi\)
0.464827 + 0.885401i \(0.346116\pi\)
\(938\) −53.4474 −1.74512
\(939\) −48.2718 −1.57529
\(940\) 8.10789 0.264450
\(941\) −1.55702 −0.0507573 −0.0253787 0.999678i \(-0.508079\pi\)
−0.0253787 + 0.999678i \(0.508079\pi\)
\(942\) 142.071 4.62891
\(943\) −29.1052 −0.947795
\(944\) −5.61242 −0.182669
\(945\) 60.3611 1.96355
\(946\) −23.2973 −0.757459
\(947\) −58.2130 −1.89167 −0.945834 0.324649i \(-0.894754\pi\)
−0.945834 + 0.324649i \(0.894754\pi\)
\(948\) 108.803 3.53377
\(949\) 0.00888617 0.000288457 0
\(950\) 0.270937 0.00879035
\(951\) −70.0045 −2.27005
\(952\) 55.9210 1.81241
\(953\) −43.2609 −1.40136 −0.700678 0.713477i \(-0.747119\pi\)
−0.700678 + 0.713477i \(0.747119\pi\)
\(954\) 14.6699 0.474955
\(955\) −19.7698 −0.639735
\(956\) −60.1930 −1.94678
\(957\) 11.2451 0.363503
\(958\) 8.86620 0.286454
\(959\) 42.0559 1.35806
\(960\) −187.590 −6.05444
\(961\) 14.2994 0.461270
\(962\) −1.53453 −0.0494752
\(963\) 41.7608 1.34572
\(964\) 16.9106 0.544654
\(965\) −14.6919 −0.472948
\(966\) −87.9123 −2.82853
\(967\) 6.90444 0.222032 0.111016 0.993819i \(-0.464590\pi\)
0.111016 + 0.993819i \(0.464590\pi\)
\(968\) 52.3786 1.68351
\(969\) −2.35418 −0.0756271
\(970\) −44.6139 −1.43247
\(971\) 2.38279 0.0764672 0.0382336 0.999269i \(-0.487827\pi\)
0.0382336 + 0.999269i \(0.487827\pi\)
\(972\) −52.2961 −1.67740
\(973\) 57.3898 1.83983
\(974\) 21.5712 0.691186
\(975\) 0.112355 0.00359825
\(976\) 76.6244 2.45269
\(977\) −4.46821 −0.142951 −0.0714754 0.997442i \(-0.522771\pi\)
−0.0714754 + 0.997442i \(0.522771\pi\)
\(978\) 38.2902 1.22439
\(979\) 35.0405 1.11990
\(980\) −96.0178 −3.06717
\(981\) −95.2759 −3.04193
\(982\) 105.739 3.37428
\(983\) 9.87718 0.315033 0.157517 0.987516i \(-0.449651\pi\)
0.157517 + 0.987516i \(0.449651\pi\)
\(984\) −271.708 −8.66174
\(985\) 26.0481 0.829962
\(986\) −7.09435 −0.225930
\(987\) 7.29049 0.232059
\(988\) −0.578396 −0.0184012
\(989\) −10.6667 −0.339181
\(990\) 77.6467 2.46777
\(991\) 60.2048 1.91247 0.956234 0.292604i \(-0.0945218\pi\)
0.956234 + 0.292604i \(0.0945218\pi\)
\(992\) 142.446 4.52267
\(993\) 4.37688 0.138896
\(994\) −67.3832 −2.13727
\(995\) 28.1049 0.890984
\(996\) −48.0606 −1.52286
\(997\) −27.8113 −0.880792 −0.440396 0.897804i \(-0.645162\pi\)
−0.440396 + 0.897804i \(0.645162\pi\)
\(998\) −57.6127 −1.82370
\(999\) 19.0364 0.602285
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 8003.2.a.b.1.3 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.3 153 1.1 even 1 trivial