Properties

Label 4003.2.a.c.1.6
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(0\)
Dimension: \(179\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.62123 q^{2} +2.13484 q^{3} +4.87085 q^{4} +4.03687 q^{5} -5.59591 q^{6} +2.86410 q^{7} -7.52515 q^{8} +1.55755 q^{9} +O(q^{10})\) \(q-2.62123 q^{2} +2.13484 q^{3} +4.87085 q^{4} +4.03687 q^{5} -5.59591 q^{6} +2.86410 q^{7} -7.52515 q^{8} +1.55755 q^{9} -10.5816 q^{10} +0.867170 q^{11} +10.3985 q^{12} -7.15978 q^{13} -7.50747 q^{14} +8.61809 q^{15} +9.98346 q^{16} +0.681304 q^{17} -4.08269 q^{18} +6.21847 q^{19} +19.6630 q^{20} +6.11440 q^{21} -2.27305 q^{22} -0.0962687 q^{23} -16.0650 q^{24} +11.2964 q^{25} +18.7674 q^{26} -3.07941 q^{27} +13.9506 q^{28} +0.607666 q^{29} -22.5900 q^{30} +5.46088 q^{31} -11.1186 q^{32} +1.85127 q^{33} -1.78585 q^{34} +11.5620 q^{35} +7.58657 q^{36} -6.27561 q^{37} -16.3000 q^{38} -15.2850 q^{39} -30.3781 q^{40} -7.97706 q^{41} -16.0273 q^{42} -3.42647 q^{43} +4.22385 q^{44} +6.28762 q^{45} +0.252343 q^{46} +8.34611 q^{47} +21.3131 q^{48} +1.20308 q^{49} -29.6104 q^{50} +1.45448 q^{51} -34.8742 q^{52} +9.41132 q^{53} +8.07184 q^{54} +3.50066 q^{55} -21.5528 q^{56} +13.2754 q^{57} -1.59283 q^{58} +2.34322 q^{59} +41.9774 q^{60} -4.64538 q^{61} -14.3142 q^{62} +4.46097 q^{63} +9.17758 q^{64} -28.9031 q^{65} -4.85261 q^{66} +12.6045 q^{67} +3.31853 q^{68} -0.205518 q^{69} -30.3067 q^{70} +3.23618 q^{71} -11.7208 q^{72} +14.8508 q^{73} +16.4498 q^{74} +24.1159 q^{75} +30.2892 q^{76} +2.48366 q^{77} +40.0655 q^{78} -5.38099 q^{79} +40.3020 q^{80} -11.2467 q^{81} +20.9097 q^{82} +11.5691 q^{83} +29.7823 q^{84} +2.75034 q^{85} +8.98158 q^{86} +1.29727 q^{87} -6.52559 q^{88} -0.0274887 q^{89} -16.4813 q^{90} -20.5063 q^{91} -0.468910 q^{92} +11.6581 q^{93} -21.8771 q^{94} +25.1032 q^{95} -23.7365 q^{96} -4.26065 q^{97} -3.15354 q^{98} +1.35066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62123 −1.85349 −0.926745 0.375692i \(-0.877405\pi\)
−0.926745 + 0.375692i \(0.877405\pi\)
\(3\) 2.13484 1.23255 0.616276 0.787531i \(-0.288641\pi\)
0.616276 + 0.787531i \(0.288641\pi\)
\(4\) 4.87085 2.43542
\(5\) 4.03687 1.80535 0.902673 0.430328i \(-0.141602\pi\)
0.902673 + 0.430328i \(0.141602\pi\)
\(6\) −5.59591 −2.28452
\(7\) 2.86410 1.08253 0.541264 0.840853i \(-0.317946\pi\)
0.541264 + 0.840853i \(0.317946\pi\)
\(8\) −7.52515 −2.66054
\(9\) 1.55755 0.519182
\(10\) −10.5816 −3.34619
\(11\) 0.867170 0.261462 0.130731 0.991418i \(-0.458268\pi\)
0.130731 + 0.991418i \(0.458268\pi\)
\(12\) 10.3985 3.00178
\(13\) −7.15978 −1.98576 −0.992882 0.119100i \(-0.961999\pi\)
−0.992882 + 0.119100i \(0.961999\pi\)
\(14\) −7.50747 −2.00646
\(15\) 8.61809 2.22518
\(16\) 9.98346 2.49586
\(17\) 0.681304 0.165240 0.0826202 0.996581i \(-0.473671\pi\)
0.0826202 + 0.996581i \(0.473671\pi\)
\(18\) −4.08269 −0.962299
\(19\) 6.21847 1.42661 0.713307 0.700851i \(-0.247196\pi\)
0.713307 + 0.700851i \(0.247196\pi\)
\(20\) 19.6630 4.39678
\(21\) 6.11440 1.33427
\(22\) −2.27305 −0.484617
\(23\) −0.0962687 −0.0200734 −0.0100367 0.999950i \(-0.503195\pi\)
−0.0100367 + 0.999950i \(0.503195\pi\)
\(24\) −16.0650 −3.27925
\(25\) 11.2964 2.25927
\(26\) 18.7674 3.68059
\(27\) −3.07941 −0.592633
\(28\) 13.9506 2.63642
\(29\) 0.607666 0.112841 0.0564204 0.998407i \(-0.482031\pi\)
0.0564204 + 0.998407i \(0.482031\pi\)
\(30\) −22.5900 −4.12435
\(31\) 5.46088 0.980803 0.490402 0.871497i \(-0.336850\pi\)
0.490402 + 0.871497i \(0.336850\pi\)
\(32\) −11.1186 −1.96552
\(33\) 1.85127 0.322265
\(34\) −1.78585 −0.306271
\(35\) 11.5620 1.95434
\(36\) 7.58657 1.26443
\(37\) −6.27561 −1.03170 −0.515852 0.856678i \(-0.672524\pi\)
−0.515852 + 0.856678i \(0.672524\pi\)
\(38\) −16.3000 −2.64422
\(39\) −15.2850 −2.44756
\(40\) −30.3781 −4.80320
\(41\) −7.97706 −1.24581 −0.622904 0.782299i \(-0.714047\pi\)
−0.622904 + 0.782299i \(0.714047\pi\)
\(42\) −16.0273 −2.47306
\(43\) −3.42647 −0.522532 −0.261266 0.965267i \(-0.584140\pi\)
−0.261266 + 0.965267i \(0.584140\pi\)
\(44\) 4.22385 0.636770
\(45\) 6.28762 0.937303
\(46\) 0.252343 0.0372059
\(47\) 8.34611 1.21740 0.608702 0.793399i \(-0.291690\pi\)
0.608702 + 0.793399i \(0.291690\pi\)
\(48\) 21.3131 3.07628
\(49\) 1.20308 0.171868
\(50\) −29.6104 −4.18754
\(51\) 1.45448 0.203667
\(52\) −34.8742 −4.83618
\(53\) 9.41132 1.29274 0.646372 0.763022i \(-0.276285\pi\)
0.646372 + 0.763022i \(0.276285\pi\)
\(54\) 8.07184 1.09844
\(55\) 3.50066 0.472029
\(56\) −21.5528 −2.88011
\(57\) 13.2754 1.75838
\(58\) −1.59283 −0.209149
\(59\) 2.34322 0.305062 0.152531 0.988299i \(-0.451258\pi\)
0.152531 + 0.988299i \(0.451258\pi\)
\(60\) 41.9774 5.41926
\(61\) −4.64538 −0.594781 −0.297390 0.954756i \(-0.596116\pi\)
−0.297390 + 0.954756i \(0.596116\pi\)
\(62\) −14.3142 −1.81791
\(63\) 4.46097 0.562030
\(64\) 9.17758 1.14720
\(65\) −28.9031 −3.58499
\(66\) −4.85261 −0.597315
\(67\) 12.6045 1.53988 0.769941 0.638115i \(-0.220286\pi\)
0.769941 + 0.638115i \(0.220286\pi\)
\(68\) 3.31853 0.402430
\(69\) −0.205518 −0.0247415
\(70\) −30.3067 −3.62234
\(71\) 3.23618 0.384064 0.192032 0.981389i \(-0.438492\pi\)
0.192032 + 0.981389i \(0.438492\pi\)
\(72\) −11.7208 −1.38131
\(73\) 14.8508 1.73815 0.869077 0.494676i \(-0.164713\pi\)
0.869077 + 0.494676i \(0.164713\pi\)
\(74\) 16.4498 1.91225
\(75\) 24.1159 2.78467
\(76\) 30.2892 3.47441
\(77\) 2.48366 0.283040
\(78\) 40.0655 4.53652
\(79\) −5.38099 −0.605408 −0.302704 0.953085i \(-0.597889\pi\)
−0.302704 + 0.953085i \(0.597889\pi\)
\(80\) 40.3020 4.50590
\(81\) −11.2467 −1.24963
\(82\) 20.9097 2.30909
\(83\) 11.5691 1.26988 0.634939 0.772563i \(-0.281025\pi\)
0.634939 + 0.772563i \(0.281025\pi\)
\(84\) 29.7823 3.24952
\(85\) 2.75034 0.298316
\(86\) 8.98158 0.968508
\(87\) 1.29727 0.139082
\(88\) −6.52559 −0.695630
\(89\) −0.0274887 −0.00291380 −0.00145690 0.999999i \(-0.500464\pi\)
−0.00145690 + 0.999999i \(0.500464\pi\)
\(90\) −16.4813 −1.73728
\(91\) −20.5063 −2.14965
\(92\) −0.468910 −0.0488873
\(93\) 11.6581 1.20889
\(94\) −21.8771 −2.25645
\(95\) 25.1032 2.57553
\(96\) −23.7365 −2.42260
\(97\) −4.26065 −0.432604 −0.216302 0.976327i \(-0.569400\pi\)
−0.216302 + 0.976327i \(0.569400\pi\)
\(98\) −3.15354 −0.318556
\(99\) 1.35066 0.135746
\(100\) 55.0228 5.50228
\(101\) −4.50233 −0.447999 −0.223999 0.974589i \(-0.571911\pi\)
−0.223999 + 0.974589i \(0.571911\pi\)
\(102\) −3.81251 −0.377495
\(103\) 11.2744 1.11090 0.555448 0.831551i \(-0.312547\pi\)
0.555448 + 0.831551i \(0.312547\pi\)
\(104\) 53.8784 5.28321
\(105\) 24.6831 2.40882
\(106\) −24.6692 −2.39609
\(107\) 14.4438 1.39633 0.698165 0.715937i \(-0.254000\pi\)
0.698165 + 0.715937i \(0.254000\pi\)
\(108\) −14.9993 −1.44331
\(109\) −20.4019 −1.95415 −0.977074 0.212901i \(-0.931709\pi\)
−0.977074 + 0.212901i \(0.931709\pi\)
\(110\) −9.17603 −0.874900
\(111\) −13.3974 −1.27163
\(112\) 28.5936 2.70184
\(113\) −0.626576 −0.0589433 −0.0294717 0.999566i \(-0.509382\pi\)
−0.0294717 + 0.999566i \(0.509382\pi\)
\(114\) −34.7980 −3.25913
\(115\) −0.388625 −0.0362395
\(116\) 2.95985 0.274815
\(117\) −11.1517 −1.03097
\(118\) −6.14213 −0.565429
\(119\) 1.95132 0.178878
\(120\) −64.8524 −5.92019
\(121\) −10.2480 −0.931638
\(122\) 12.1766 1.10242
\(123\) −17.0298 −1.53552
\(124\) 26.5991 2.38867
\(125\) 25.4176 2.27342
\(126\) −11.6932 −1.04172
\(127\) 2.69938 0.239531 0.119766 0.992802i \(-0.461786\pi\)
0.119766 + 0.992802i \(0.461786\pi\)
\(128\) −1.81929 −0.160804
\(129\) −7.31498 −0.644048
\(130\) 75.7617 6.64474
\(131\) −14.3672 −1.25527 −0.627633 0.778509i \(-0.715976\pi\)
−0.627633 + 0.778509i \(0.715976\pi\)
\(132\) 9.01726 0.784852
\(133\) 17.8103 1.54435
\(134\) −33.0392 −2.85415
\(135\) −12.4312 −1.06991
\(136\) −5.12691 −0.439629
\(137\) 13.0688 1.11655 0.558273 0.829658i \(-0.311464\pi\)
0.558273 + 0.829658i \(0.311464\pi\)
\(138\) 0.538711 0.0458581
\(139\) 22.5474 1.91245 0.956224 0.292636i \(-0.0945323\pi\)
0.956224 + 0.292636i \(0.0945323\pi\)
\(140\) 56.3168 4.75964
\(141\) 17.8176 1.50051
\(142\) −8.48278 −0.711859
\(143\) −6.20875 −0.519201
\(144\) 15.5497 1.29581
\(145\) 2.45307 0.203717
\(146\) −38.9274 −3.22165
\(147\) 2.56838 0.211836
\(148\) −30.5675 −2.51263
\(149\) 22.4243 1.83707 0.918534 0.395342i \(-0.129374\pi\)
0.918534 + 0.395342i \(0.129374\pi\)
\(150\) −63.2134 −5.16135
\(151\) 10.8379 0.881972 0.440986 0.897514i \(-0.354629\pi\)
0.440986 + 0.897514i \(0.354629\pi\)
\(152\) −46.7949 −3.79557
\(153\) 1.06116 0.0857899
\(154\) −6.51026 −0.524611
\(155\) 22.0449 1.77069
\(156\) −74.4508 −5.96084
\(157\) 0.780391 0.0622820 0.0311410 0.999515i \(-0.490086\pi\)
0.0311410 + 0.999515i \(0.490086\pi\)
\(158\) 14.1048 1.12212
\(159\) 20.0917 1.59337
\(160\) −44.8845 −3.54843
\(161\) −0.275723 −0.0217301
\(162\) 29.4802 2.31618
\(163\) −12.0256 −0.941916 −0.470958 0.882156i \(-0.656092\pi\)
−0.470958 + 0.882156i \(0.656092\pi\)
\(164\) −38.8550 −3.03407
\(165\) 7.47335 0.581799
\(166\) −30.3254 −2.35370
\(167\) 17.0674 1.32072 0.660358 0.750951i \(-0.270405\pi\)
0.660358 + 0.750951i \(0.270405\pi\)
\(168\) −46.0118 −3.54989
\(169\) 38.2624 2.94326
\(170\) −7.20927 −0.552926
\(171\) 9.68556 0.740673
\(172\) −16.6898 −1.27259
\(173\) 0.628992 0.0478214 0.0239107 0.999714i \(-0.492388\pi\)
0.0239107 + 0.999714i \(0.492388\pi\)
\(174\) −3.40045 −0.257787
\(175\) 32.3539 2.44573
\(176\) 8.65736 0.652573
\(177\) 5.00241 0.376004
\(178\) 0.0720542 0.00540069
\(179\) −17.7845 −1.32928 −0.664640 0.747164i \(-0.731415\pi\)
−0.664640 + 0.747164i \(0.731415\pi\)
\(180\) 30.6260 2.28273
\(181\) −16.5715 −1.23175 −0.615877 0.787843i \(-0.711198\pi\)
−0.615877 + 0.787843i \(0.711198\pi\)
\(182\) 53.7518 3.98435
\(183\) −9.91716 −0.733097
\(184\) 0.724437 0.0534062
\(185\) −25.3338 −1.86258
\(186\) −30.5586 −2.24067
\(187\) 0.590807 0.0432041
\(188\) 40.6526 2.96490
\(189\) −8.81974 −0.641542
\(190\) −65.8012 −4.77372
\(191\) −9.98762 −0.722679 −0.361339 0.932434i \(-0.617680\pi\)
−0.361339 + 0.932434i \(0.617680\pi\)
\(192\) 19.5927 1.41398
\(193\) −17.9641 −1.29308 −0.646541 0.762880i \(-0.723785\pi\)
−0.646541 + 0.762880i \(0.723785\pi\)
\(194\) 11.1682 0.801827
\(195\) −61.7036 −4.41868
\(196\) 5.86001 0.418572
\(197\) −15.6061 −1.11189 −0.555944 0.831220i \(-0.687643\pi\)
−0.555944 + 0.831220i \(0.687643\pi\)
\(198\) −3.54039 −0.251604
\(199\) 4.87345 0.345469 0.172735 0.984968i \(-0.444740\pi\)
0.172735 + 0.984968i \(0.444740\pi\)
\(200\) −85.0068 −6.01089
\(201\) 26.9085 1.89798
\(202\) 11.8016 0.830361
\(203\) 1.74042 0.122153
\(204\) 7.08453 0.496016
\(205\) −32.2024 −2.24911
\(206\) −29.5527 −2.05903
\(207\) −0.149943 −0.0104218
\(208\) −71.4793 −4.95620
\(209\) 5.39247 0.373005
\(210\) −64.7000 −4.46473
\(211\) −19.7458 −1.35936 −0.679680 0.733509i \(-0.737881\pi\)
−0.679680 + 0.733509i \(0.737881\pi\)
\(212\) 45.8411 3.14838
\(213\) 6.90874 0.473379
\(214\) −37.8604 −2.58808
\(215\) −13.8322 −0.943352
\(216\) 23.1730 1.57672
\(217\) 15.6405 1.06175
\(218\) 53.4781 3.62199
\(219\) 31.7041 2.14236
\(220\) 17.0512 1.14959
\(221\) −4.87798 −0.328129
\(222\) 35.1177 2.35695
\(223\) 18.5978 1.24540 0.622701 0.782460i \(-0.286035\pi\)
0.622701 + 0.782460i \(0.286035\pi\)
\(224\) −31.8449 −2.12773
\(225\) 17.5946 1.17297
\(226\) 1.64240 0.109251
\(227\) −2.36186 −0.156762 −0.0783812 0.996923i \(-0.524975\pi\)
−0.0783812 + 0.996923i \(0.524975\pi\)
\(228\) 64.6627 4.28239
\(229\) 1.85623 0.122663 0.0613315 0.998117i \(-0.480465\pi\)
0.0613315 + 0.998117i \(0.480465\pi\)
\(230\) 1.01868 0.0671695
\(231\) 5.30223 0.348861
\(232\) −4.57278 −0.300218
\(233\) −5.30588 −0.347600 −0.173800 0.984781i \(-0.555605\pi\)
−0.173800 + 0.984781i \(0.555605\pi\)
\(234\) 29.2311 1.91090
\(235\) 33.6922 2.19784
\(236\) 11.4135 0.742955
\(237\) −11.4876 −0.746197
\(238\) −5.11487 −0.331548
\(239\) −3.84156 −0.248490 −0.124245 0.992252i \(-0.539651\pi\)
−0.124245 + 0.992252i \(0.539651\pi\)
\(240\) 86.0383 5.55375
\(241\) −26.1851 −1.68673 −0.843367 0.537339i \(-0.819430\pi\)
−0.843367 + 0.537339i \(0.819430\pi\)
\(242\) 26.8624 1.72678
\(243\) −14.7717 −0.947603
\(244\) −22.6270 −1.44854
\(245\) 4.85667 0.310281
\(246\) 44.6389 2.84607
\(247\) −44.5229 −2.83292
\(248\) −41.0940 −2.60947
\(249\) 24.6983 1.56519
\(250\) −66.6254 −4.21376
\(251\) 13.2411 0.835772 0.417886 0.908499i \(-0.362771\pi\)
0.417886 + 0.908499i \(0.362771\pi\)
\(252\) 21.7287 1.36878
\(253\) −0.0834814 −0.00524843
\(254\) −7.07570 −0.443969
\(255\) 5.87154 0.367690
\(256\) −13.5864 −0.849149
\(257\) −4.05989 −0.253249 −0.126625 0.991951i \(-0.540414\pi\)
−0.126625 + 0.991951i \(0.540414\pi\)
\(258\) 19.1742 1.19374
\(259\) −17.9740 −1.11685
\(260\) −140.783 −8.73097
\(261\) 0.946468 0.0585849
\(262\) 37.6597 2.32662
\(263\) −3.15494 −0.194542 −0.0972709 0.995258i \(-0.531011\pi\)
−0.0972709 + 0.995258i \(0.531011\pi\)
\(264\) −13.9311 −0.857400
\(265\) 37.9923 2.33385
\(266\) −46.6850 −2.86244
\(267\) −0.0586840 −0.00359140
\(268\) 61.3945 3.75026
\(269\) 0.264077 0.0161010 0.00805052 0.999968i \(-0.497437\pi\)
0.00805052 + 0.999968i \(0.497437\pi\)
\(270\) 32.5850 1.98306
\(271\) −4.27566 −0.259728 −0.129864 0.991532i \(-0.541454\pi\)
−0.129864 + 0.991532i \(0.541454\pi\)
\(272\) 6.80177 0.412418
\(273\) −43.7777 −2.64955
\(274\) −34.2564 −2.06951
\(275\) 9.79587 0.590713
\(276\) −1.00105 −0.0602561
\(277\) −7.65067 −0.459684 −0.229842 0.973228i \(-0.573821\pi\)
−0.229842 + 0.973228i \(0.573821\pi\)
\(278\) −59.1020 −3.54470
\(279\) 8.50558 0.509216
\(280\) −87.0059 −5.19960
\(281\) −11.2777 −0.672768 −0.336384 0.941725i \(-0.609204\pi\)
−0.336384 + 0.941725i \(0.609204\pi\)
\(282\) −46.7040 −2.78119
\(283\) 10.0415 0.596904 0.298452 0.954425i \(-0.403530\pi\)
0.298452 + 0.954425i \(0.403530\pi\)
\(284\) 15.7630 0.935359
\(285\) 53.5913 3.17448
\(286\) 16.2746 0.962334
\(287\) −22.8471 −1.34862
\(288\) −17.3178 −1.02046
\(289\) −16.5358 −0.972696
\(290\) −6.43007 −0.377587
\(291\) −9.09582 −0.533206
\(292\) 72.3360 4.23314
\(293\) 6.23243 0.364102 0.182051 0.983289i \(-0.441726\pi\)
0.182051 + 0.983289i \(0.441726\pi\)
\(294\) −6.73231 −0.392636
\(295\) 9.45930 0.550742
\(296\) 47.2249 2.74489
\(297\) −2.67037 −0.154951
\(298\) −58.7792 −3.40499
\(299\) 0.689263 0.0398611
\(300\) 117.465 6.78184
\(301\) −9.81377 −0.565656
\(302\) −28.4085 −1.63473
\(303\) −9.61176 −0.552181
\(304\) 62.0818 3.56064
\(305\) −18.7528 −1.07378
\(306\) −2.78155 −0.159011
\(307\) 4.56434 0.260501 0.130250 0.991481i \(-0.458422\pi\)
0.130250 + 0.991481i \(0.458422\pi\)
\(308\) 12.0975 0.689322
\(309\) 24.0690 1.36924
\(310\) −57.7847 −3.28195
\(311\) 22.7584 1.29051 0.645256 0.763966i \(-0.276751\pi\)
0.645256 + 0.763966i \(0.276751\pi\)
\(312\) 115.022 6.51183
\(313\) −22.0003 −1.24353 −0.621764 0.783205i \(-0.713584\pi\)
−0.621764 + 0.783205i \(0.713584\pi\)
\(314\) −2.04558 −0.115439
\(315\) 18.0084 1.01466
\(316\) −26.2100 −1.47443
\(317\) −11.1563 −0.626598 −0.313299 0.949655i \(-0.601434\pi\)
−0.313299 + 0.949655i \(0.601434\pi\)
\(318\) −52.6649 −2.95330
\(319\) 0.526950 0.0295035
\(320\) 37.0488 2.07109
\(321\) 30.8351 1.72105
\(322\) 0.722735 0.0402764
\(323\) 4.23667 0.235734
\(324\) −54.7809 −3.04338
\(325\) −80.8794 −4.48638
\(326\) 31.5218 1.74583
\(327\) −43.5548 −2.40859
\(328\) 60.0286 3.31452
\(329\) 23.9041 1.31788
\(330\) −19.5894 −1.07836
\(331\) −15.0550 −0.827497 −0.413749 0.910391i \(-0.635781\pi\)
−0.413749 + 0.910391i \(0.635781\pi\)
\(332\) 56.3515 3.09269
\(333\) −9.77455 −0.535642
\(334\) −44.7376 −2.44793
\(335\) 50.8827 2.78002
\(336\) 61.0429 3.33016
\(337\) −17.7475 −0.966767 −0.483384 0.875409i \(-0.660592\pi\)
−0.483384 + 0.875409i \(0.660592\pi\)
\(338\) −100.295 −5.45530
\(339\) −1.33764 −0.0726507
\(340\) 13.3965 0.726526
\(341\) 4.73552 0.256443
\(342\) −25.3881 −1.37283
\(343\) −16.6030 −0.896476
\(344\) 25.7847 1.39022
\(345\) −0.829652 −0.0446670
\(346\) −1.64873 −0.0886365
\(347\) 0.158237 0.00849461 0.00424731 0.999991i \(-0.498648\pi\)
0.00424731 + 0.999991i \(0.498648\pi\)
\(348\) 6.31881 0.338724
\(349\) −23.8725 −1.27786 −0.638931 0.769264i \(-0.720623\pi\)
−0.638931 + 0.769264i \(0.720623\pi\)
\(350\) −84.8071 −4.53313
\(351\) 22.0479 1.17683
\(352\) −9.64175 −0.513907
\(353\) 3.10640 0.165337 0.0826684 0.996577i \(-0.473656\pi\)
0.0826684 + 0.996577i \(0.473656\pi\)
\(354\) −13.1125 −0.696920
\(355\) 13.0641 0.693369
\(356\) −0.133893 −0.00709633
\(357\) 4.16577 0.220476
\(358\) 46.6174 2.46381
\(359\) −15.8827 −0.838255 −0.419128 0.907927i \(-0.637664\pi\)
−0.419128 + 0.907927i \(0.637664\pi\)
\(360\) −47.3153 −2.49373
\(361\) 19.6694 1.03523
\(362\) 43.4378 2.28304
\(363\) −21.8779 −1.14829
\(364\) −99.8832 −5.23530
\(365\) 59.9508 3.13797
\(366\) 25.9952 1.35879
\(367\) −25.5600 −1.33422 −0.667110 0.744960i \(-0.732469\pi\)
−0.667110 + 0.744960i \(0.732469\pi\)
\(368\) −0.961095 −0.0501005
\(369\) −12.4246 −0.646801
\(370\) 66.4058 3.45227
\(371\) 26.9550 1.39943
\(372\) 56.7849 2.94416
\(373\) −27.2007 −1.40840 −0.704198 0.710003i \(-0.748693\pi\)
−0.704198 + 0.710003i \(0.748693\pi\)
\(374\) −1.54864 −0.0800783
\(375\) 54.2626 2.80211
\(376\) −62.8057 −3.23896
\(377\) −4.35075 −0.224075
\(378\) 23.1186 1.18909
\(379\) 19.3268 0.992749 0.496374 0.868109i \(-0.334664\pi\)
0.496374 + 0.868109i \(0.334664\pi\)
\(380\) 122.274 6.27251
\(381\) 5.76275 0.295235
\(382\) 26.1799 1.33948
\(383\) 26.8329 1.37109 0.685547 0.728028i \(-0.259563\pi\)
0.685547 + 0.728028i \(0.259563\pi\)
\(384\) −3.88390 −0.198199
\(385\) 10.0262 0.510985
\(386\) 47.0879 2.39671
\(387\) −5.33689 −0.271290
\(388\) −20.7530 −1.05357
\(389\) 26.4315 1.34013 0.670066 0.742302i \(-0.266266\pi\)
0.670066 + 0.742302i \(0.266266\pi\)
\(390\) 161.739 8.18998
\(391\) −0.0655883 −0.00331694
\(392\) −9.05334 −0.457263
\(393\) −30.6717 −1.54718
\(394\) 40.9072 2.06087
\(395\) −21.7224 −1.09297
\(396\) 6.57885 0.330600
\(397\) 20.6008 1.03392 0.516962 0.856008i \(-0.327063\pi\)
0.516962 + 0.856008i \(0.327063\pi\)
\(398\) −12.7744 −0.640324
\(399\) 38.0222 1.90349
\(400\) 112.777 5.63883
\(401\) −14.1282 −0.705529 −0.352764 0.935712i \(-0.614758\pi\)
−0.352764 + 0.935712i \(0.614758\pi\)
\(402\) −70.5335 −3.51789
\(403\) −39.0987 −1.94764
\(404\) −21.9302 −1.09107
\(405\) −45.4015 −2.25602
\(406\) −4.56204 −0.226410
\(407\) −5.44202 −0.269751
\(408\) −10.9451 −0.541865
\(409\) −22.4868 −1.11190 −0.555951 0.831215i \(-0.687646\pi\)
−0.555951 + 0.831215i \(0.687646\pi\)
\(410\) 84.4099 4.16871
\(411\) 27.8999 1.37620
\(412\) 54.9157 2.70550
\(413\) 6.71123 0.330238
\(414\) 0.393035 0.0193166
\(415\) 46.7031 2.29257
\(416\) 79.6069 3.90305
\(417\) 48.1352 2.35719
\(418\) −14.1349 −0.691361
\(419\) −20.5411 −1.00350 −0.501748 0.865014i \(-0.667310\pi\)
−0.501748 + 0.865014i \(0.667310\pi\)
\(420\) 120.227 5.86650
\(421\) −28.3007 −1.37929 −0.689646 0.724147i \(-0.742234\pi\)
−0.689646 + 0.724147i \(0.742234\pi\)
\(422\) 51.7584 2.51956
\(423\) 12.9994 0.632055
\(424\) −70.8216 −3.43940
\(425\) 7.69625 0.373323
\(426\) −18.1094 −0.877403
\(427\) −13.3049 −0.643867
\(428\) 70.3533 3.40066
\(429\) −13.2547 −0.639942
\(430\) 36.2575 1.74849
\(431\) −0.241676 −0.0116411 −0.00582055 0.999983i \(-0.501853\pi\)
−0.00582055 + 0.999983i \(0.501853\pi\)
\(432\) −30.7431 −1.47913
\(433\) −21.8827 −1.05162 −0.525808 0.850603i \(-0.676237\pi\)
−0.525808 + 0.850603i \(0.676237\pi\)
\(434\) −40.9974 −1.96794
\(435\) 5.23692 0.251091
\(436\) −99.3745 −4.75918
\(437\) −0.598644 −0.0286370
\(438\) −83.1037 −3.97085
\(439\) −13.3774 −0.638471 −0.319235 0.947675i \(-0.603426\pi\)
−0.319235 + 0.947675i \(0.603426\pi\)
\(440\) −26.3430 −1.25585
\(441\) 1.87385 0.0892309
\(442\) 12.7863 0.608183
\(443\) 2.47915 0.117788 0.0588941 0.998264i \(-0.481243\pi\)
0.0588941 + 0.998264i \(0.481243\pi\)
\(444\) −65.2568 −3.09695
\(445\) −0.110968 −0.00526041
\(446\) −48.7491 −2.30834
\(447\) 47.8723 2.26428
\(448\) 26.2855 1.24187
\(449\) 2.98680 0.140956 0.0704780 0.997513i \(-0.477548\pi\)
0.0704780 + 0.997513i \(0.477548\pi\)
\(450\) −46.1195 −2.17409
\(451\) −6.91747 −0.325731
\(452\) −3.05196 −0.143552
\(453\) 23.1371 1.08708
\(454\) 6.19098 0.290557
\(455\) −82.7815 −3.88085
\(456\) −99.8997 −4.67823
\(457\) −38.4570 −1.79894 −0.899472 0.436979i \(-0.856048\pi\)
−0.899472 + 0.436979i \(0.856048\pi\)
\(458\) −4.86560 −0.227355
\(459\) −2.09801 −0.0979269
\(460\) −1.89293 −0.0882584
\(461\) 36.7175 1.71010 0.855051 0.518543i \(-0.173525\pi\)
0.855051 + 0.518543i \(0.173525\pi\)
\(462\) −13.8984 −0.646610
\(463\) 9.36886 0.435408 0.217704 0.976015i \(-0.430143\pi\)
0.217704 + 0.976015i \(0.430143\pi\)
\(464\) 6.06661 0.281635
\(465\) 47.0623 2.18246
\(466\) 13.9079 0.644272
\(467\) −22.4781 −1.04016 −0.520080 0.854117i \(-0.674098\pi\)
−0.520080 + 0.854117i \(0.674098\pi\)
\(468\) −54.3181 −2.51086
\(469\) 36.1005 1.66697
\(470\) −88.3150 −4.07367
\(471\) 1.66601 0.0767657
\(472\) −17.6331 −0.811630
\(473\) −2.97134 −0.136622
\(474\) 30.1115 1.38307
\(475\) 70.2461 3.22311
\(476\) 9.50460 0.435643
\(477\) 14.6586 0.671170
\(478\) 10.0696 0.460573
\(479\) 26.1358 1.19417 0.597087 0.802177i \(-0.296325\pi\)
0.597087 + 0.802177i \(0.296325\pi\)
\(480\) −95.8213 −4.37363
\(481\) 44.9319 2.04872
\(482\) 68.6373 3.12634
\(483\) −0.588626 −0.0267834
\(484\) −49.9165 −2.26893
\(485\) −17.1997 −0.780999
\(486\) 38.7199 1.75637
\(487\) −9.10139 −0.412423 −0.206212 0.978507i \(-0.566114\pi\)
−0.206212 + 0.978507i \(0.566114\pi\)
\(488\) 34.9572 1.58244
\(489\) −25.6727 −1.16096
\(490\) −12.7305 −0.575103
\(491\) 7.26704 0.327957 0.163978 0.986464i \(-0.447567\pi\)
0.163978 + 0.986464i \(0.447567\pi\)
\(492\) −82.9493 −3.73964
\(493\) 0.414005 0.0186459
\(494\) 116.705 5.25079
\(495\) 5.45244 0.245069
\(496\) 54.5185 2.44795
\(497\) 9.26876 0.415761
\(498\) −64.7398 −2.90106
\(499\) −22.0357 −0.986453 −0.493226 0.869901i \(-0.664183\pi\)
−0.493226 + 0.869901i \(0.664183\pi\)
\(500\) 123.805 5.53674
\(501\) 36.4362 1.62785
\(502\) −34.7080 −1.54910
\(503\) −25.1339 −1.12066 −0.560332 0.828268i \(-0.689326\pi\)
−0.560332 + 0.828268i \(0.689326\pi\)
\(504\) −33.5695 −1.49530
\(505\) −18.1754 −0.808793
\(506\) 0.218824 0.00972791
\(507\) 81.6841 3.62772
\(508\) 13.1483 0.583360
\(509\) −27.5299 −1.22024 −0.610121 0.792308i \(-0.708879\pi\)
−0.610121 + 0.792308i \(0.708879\pi\)
\(510\) −15.3906 −0.681509
\(511\) 42.5342 1.88160
\(512\) 39.2516 1.73469
\(513\) −19.1492 −0.845458
\(514\) 10.6419 0.469395
\(515\) 45.5132 2.00555
\(516\) −35.6301 −1.56853
\(517\) 7.23750 0.318305
\(518\) 47.1139 2.07007
\(519\) 1.34280 0.0589423
\(520\) 217.500 9.53802
\(521\) 26.8917 1.17815 0.589073 0.808080i \(-0.299493\pi\)
0.589073 + 0.808080i \(0.299493\pi\)
\(522\) −2.48091 −0.108587
\(523\) 5.77766 0.252639 0.126320 0.991990i \(-0.459683\pi\)
0.126320 + 0.991990i \(0.459683\pi\)
\(524\) −69.9804 −3.05711
\(525\) 69.0705 3.01448
\(526\) 8.26982 0.360581
\(527\) 3.72052 0.162068
\(528\) 18.4821 0.804329
\(529\) −22.9907 −0.999597
\(530\) −99.5866 −4.32577
\(531\) 3.64968 0.158383
\(532\) 86.7514 3.76115
\(533\) 57.1139 2.47388
\(534\) 0.153824 0.00665663
\(535\) 58.3076 2.52086
\(536\) −94.8505 −4.09692
\(537\) −37.9672 −1.63841
\(538\) −0.692206 −0.0298431
\(539\) 1.04327 0.0449370
\(540\) −60.5504 −2.60568
\(541\) −23.8804 −1.02670 −0.513349 0.858180i \(-0.671595\pi\)
−0.513349 + 0.858180i \(0.671595\pi\)
\(542\) 11.2075 0.481403
\(543\) −35.3776 −1.51820
\(544\) −7.57517 −0.324783
\(545\) −82.3599 −3.52791
\(546\) 114.752 4.91091
\(547\) −6.55675 −0.280346 −0.140173 0.990127i \(-0.544766\pi\)
−0.140173 + 0.990127i \(0.544766\pi\)
\(548\) 63.6563 2.71926
\(549\) −7.23540 −0.308799
\(550\) −25.6772 −1.09488
\(551\) 3.77875 0.160980
\(552\) 1.54656 0.0658259
\(553\) −15.4117 −0.655372
\(554\) 20.0542 0.852020
\(555\) −54.0837 −2.29573
\(556\) 109.825 4.65762
\(557\) −28.5175 −1.20833 −0.604163 0.796861i \(-0.706492\pi\)
−0.604163 + 0.796861i \(0.706492\pi\)
\(558\) −22.2951 −0.943826
\(559\) 24.5328 1.03763
\(560\) 115.429 4.87776
\(561\) 1.26128 0.0532512
\(562\) 29.5613 1.24697
\(563\) 34.7377 1.46402 0.732010 0.681294i \(-0.238582\pi\)
0.732010 + 0.681294i \(0.238582\pi\)
\(564\) 86.7868 3.65439
\(565\) −2.52941 −0.106413
\(566\) −26.3210 −1.10635
\(567\) −32.2117 −1.35276
\(568\) −24.3528 −1.02182
\(569\) −37.7861 −1.58407 −0.792037 0.610473i \(-0.790979\pi\)
−0.792037 + 0.610473i \(0.790979\pi\)
\(570\) −140.475 −5.88386
\(571\) −18.6846 −0.781928 −0.390964 0.920406i \(-0.627858\pi\)
−0.390964 + 0.920406i \(0.627858\pi\)
\(572\) −30.2419 −1.26448
\(573\) −21.3220 −0.890739
\(574\) 59.8875 2.49966
\(575\) −1.08749 −0.0453513
\(576\) 14.2945 0.595605
\(577\) 22.3072 0.928662 0.464331 0.885662i \(-0.346295\pi\)
0.464331 + 0.885662i \(0.346295\pi\)
\(578\) 43.3442 1.80288
\(579\) −38.3504 −1.59379
\(580\) 11.9485 0.496136
\(581\) 33.1352 1.37468
\(582\) 23.8422 0.988292
\(583\) 8.16122 0.338003
\(584\) −111.754 −4.62443
\(585\) −45.0179 −1.86126
\(586\) −16.3366 −0.674860
\(587\) 27.3264 1.12788 0.563941 0.825815i \(-0.309284\pi\)
0.563941 + 0.825815i \(0.309284\pi\)
\(588\) 12.5102 0.515911
\(589\) 33.9583 1.39923
\(590\) −24.7950 −1.02079
\(591\) −33.3165 −1.37046
\(592\) −62.6522 −2.57499
\(593\) 11.2956 0.463857 0.231928 0.972733i \(-0.425497\pi\)
0.231928 + 0.972733i \(0.425497\pi\)
\(594\) 6.99966 0.287200
\(595\) 7.87725 0.322936
\(596\) 109.225 4.47404
\(597\) 10.4040 0.425809
\(598\) −1.80672 −0.0738821
\(599\) 13.8204 0.564686 0.282343 0.959313i \(-0.408888\pi\)
0.282343 + 0.959313i \(0.408888\pi\)
\(600\) −181.476 −7.40873
\(601\) −17.7634 −0.724584 −0.362292 0.932065i \(-0.618006\pi\)
−0.362292 + 0.932065i \(0.618006\pi\)
\(602\) 25.7242 1.04844
\(603\) 19.6321 0.799479
\(604\) 52.7895 2.14798
\(605\) −41.3700 −1.68193
\(606\) 25.1946 1.02346
\(607\) −25.1984 −1.02277 −0.511386 0.859351i \(-0.670868\pi\)
−0.511386 + 0.859351i \(0.670868\pi\)
\(608\) −69.1409 −2.80403
\(609\) 3.71552 0.150560
\(610\) 49.1555 1.99025
\(611\) −59.7562 −2.41748
\(612\) 5.16876 0.208935
\(613\) 12.0627 0.487207 0.243603 0.969875i \(-0.421670\pi\)
0.243603 + 0.969875i \(0.421670\pi\)
\(614\) −11.9642 −0.482835
\(615\) −68.7470 −2.77215
\(616\) −18.6899 −0.753039
\(617\) −4.95127 −0.199331 −0.0996654 0.995021i \(-0.531777\pi\)
−0.0996654 + 0.995021i \(0.531777\pi\)
\(618\) −63.0903 −2.53786
\(619\) −5.65952 −0.227475 −0.113738 0.993511i \(-0.536282\pi\)
−0.113738 + 0.993511i \(0.536282\pi\)
\(620\) 107.377 4.31238
\(621\) 0.296451 0.0118962
\(622\) −59.6551 −2.39195
\(623\) −0.0787304 −0.00315427
\(624\) −152.597 −6.10877
\(625\) 46.1259 1.84504
\(626\) 57.6677 2.30487
\(627\) 11.5121 0.459748
\(628\) 3.80117 0.151683
\(629\) −4.27560 −0.170479
\(630\) −47.2041 −1.88066
\(631\) 31.0986 1.23802 0.619009 0.785384i \(-0.287535\pi\)
0.619009 + 0.785384i \(0.287535\pi\)
\(632\) 40.4927 1.61071
\(633\) −42.1542 −1.67548
\(634\) 29.2431 1.16139
\(635\) 10.8971 0.432437
\(636\) 97.8635 3.88054
\(637\) −8.61377 −0.341290
\(638\) −1.38126 −0.0546845
\(639\) 5.04051 0.199399
\(640\) −7.34425 −0.290307
\(641\) −19.6792 −0.777284 −0.388642 0.921389i \(-0.627056\pi\)
−0.388642 + 0.921389i \(0.627056\pi\)
\(642\) −80.8260 −3.18995
\(643\) 27.6655 1.09102 0.545511 0.838104i \(-0.316336\pi\)
0.545511 + 0.838104i \(0.316336\pi\)
\(644\) −1.34301 −0.0529219
\(645\) −29.5297 −1.16273
\(646\) −11.1053 −0.436931
\(647\) −29.8399 −1.17313 −0.586564 0.809903i \(-0.699520\pi\)
−0.586564 + 0.809903i \(0.699520\pi\)
\(648\) 84.6330 3.32470
\(649\) 2.03197 0.0797620
\(650\) 212.003 8.31546
\(651\) 33.3900 1.30866
\(652\) −58.5747 −2.29396
\(653\) −21.2356 −0.831014 −0.415507 0.909590i \(-0.636396\pi\)
−0.415507 + 0.909590i \(0.636396\pi\)
\(654\) 114.167 4.46429
\(655\) −57.9985 −2.26619
\(656\) −79.6386 −3.10936
\(657\) 23.1308 0.902419
\(658\) −62.6581 −2.44267
\(659\) −16.9360 −0.659733 −0.329867 0.944028i \(-0.607004\pi\)
−0.329867 + 0.944028i \(0.607004\pi\)
\(660\) 36.4015 1.41693
\(661\) −12.5334 −0.487492 −0.243746 0.969839i \(-0.578376\pi\)
−0.243746 + 0.969839i \(0.578376\pi\)
\(662\) 39.4626 1.53376
\(663\) −10.4137 −0.404435
\(664\) −87.0595 −3.37856
\(665\) 71.8981 2.78809
\(666\) 25.6213 0.992807
\(667\) −0.0584993 −0.00226510
\(668\) 83.1328 3.21650
\(669\) 39.7034 1.53502
\(670\) −133.375 −5.15273
\(671\) −4.02834 −0.155512
\(672\) −67.9838 −2.62253
\(673\) 50.8267 1.95923 0.979613 0.200896i \(-0.0643853\pi\)
0.979613 + 0.200896i \(0.0643853\pi\)
\(674\) 46.5202 1.79189
\(675\) −34.7861 −1.33892
\(676\) 186.370 7.16809
\(677\) 25.2997 0.972347 0.486173 0.873862i \(-0.338392\pi\)
0.486173 + 0.873862i \(0.338392\pi\)
\(678\) 3.50626 0.134657
\(679\) −12.2029 −0.468306
\(680\) −20.6967 −0.793683
\(681\) −5.04220 −0.193218
\(682\) −12.4129 −0.475314
\(683\) −33.8433 −1.29498 −0.647489 0.762075i \(-0.724181\pi\)
−0.647489 + 0.762075i \(0.724181\pi\)
\(684\) 47.1769 1.80385
\(685\) 52.7572 2.01575
\(686\) 43.5202 1.66161
\(687\) 3.96275 0.151189
\(688\) −34.2081 −1.30417
\(689\) −67.3830 −2.56709
\(690\) 2.17471 0.0827898
\(691\) 7.72893 0.294023 0.147011 0.989135i \(-0.453035\pi\)
0.147011 + 0.989135i \(0.453035\pi\)
\(692\) 3.06373 0.116465
\(693\) 3.86842 0.146949
\(694\) −0.414776 −0.0157447
\(695\) 91.0212 3.45263
\(696\) −9.76216 −0.370034
\(697\) −5.43480 −0.205858
\(698\) 62.5752 2.36851
\(699\) −11.3272 −0.428434
\(700\) 157.591 5.95638
\(701\) 6.24698 0.235945 0.117973 0.993017i \(-0.462361\pi\)
0.117973 + 0.993017i \(0.462361\pi\)
\(702\) −57.7926 −2.18124
\(703\) −39.0247 −1.47184
\(704\) 7.95853 0.299948
\(705\) 71.9275 2.70894
\(706\) −8.14258 −0.306450
\(707\) −12.8951 −0.484972
\(708\) 24.3660 0.915729
\(709\) 20.4179 0.766811 0.383406 0.923580i \(-0.374751\pi\)
0.383406 + 0.923580i \(0.374751\pi\)
\(710\) −34.2439 −1.28515
\(711\) −8.38114 −0.314317
\(712\) 0.206857 0.00775228
\(713\) −0.525712 −0.0196881
\(714\) −10.9194 −0.408649
\(715\) −25.0639 −0.937338
\(716\) −86.6258 −3.23736
\(717\) −8.20111 −0.306276
\(718\) 41.6321 1.55370
\(719\) −35.1464 −1.31074 −0.655369 0.755309i \(-0.727487\pi\)
−0.655369 + 0.755309i \(0.727487\pi\)
\(720\) 62.7722 2.33938
\(721\) 32.2909 1.20258
\(722\) −51.5579 −1.91879
\(723\) −55.9011 −2.07898
\(724\) −80.7175 −2.99984
\(725\) 6.86442 0.254938
\(726\) 57.3470 2.12835
\(727\) 12.8903 0.478073 0.239037 0.971011i \(-0.423168\pi\)
0.239037 + 0.971011i \(0.423168\pi\)
\(728\) 154.313 5.71923
\(729\) 2.20491 0.0816632
\(730\) −157.145 −5.81619
\(731\) −2.33447 −0.0863435
\(732\) −48.3050 −1.78540
\(733\) 27.8011 1.02686 0.513429 0.858132i \(-0.328375\pi\)
0.513429 + 0.858132i \(0.328375\pi\)
\(734\) 66.9985 2.47296
\(735\) 10.3682 0.382438
\(736\) 1.07038 0.0394546
\(737\) 10.9302 0.402620
\(738\) 32.5678 1.19884
\(739\) −31.9088 −1.17378 −0.586892 0.809665i \(-0.699649\pi\)
−0.586892 + 0.809665i \(0.699649\pi\)
\(740\) −123.397 −4.53617
\(741\) −95.0492 −3.49172
\(742\) −70.6552 −2.59383
\(743\) −11.9823 −0.439590 −0.219795 0.975546i \(-0.570539\pi\)
−0.219795 + 0.975546i \(0.570539\pi\)
\(744\) −87.7291 −3.21630
\(745\) 90.5240 3.31654
\(746\) 71.2992 2.61045
\(747\) 18.0195 0.659298
\(748\) 2.87773 0.105220
\(749\) 41.3684 1.51157
\(750\) −142.235 −5.19367
\(751\) −52.5543 −1.91773 −0.958867 0.283856i \(-0.908386\pi\)
−0.958867 + 0.283856i \(0.908386\pi\)
\(752\) 83.3230 3.03848
\(753\) 28.2677 1.03013
\(754\) 11.4043 0.415321
\(755\) 43.7511 1.59226
\(756\) −42.9596 −1.56243
\(757\) −19.7075 −0.716280 −0.358140 0.933668i \(-0.616589\pi\)
−0.358140 + 0.933668i \(0.616589\pi\)
\(758\) −50.6599 −1.84005
\(759\) −0.178220 −0.00646896
\(760\) −188.905 −6.85231
\(761\) −34.1110 −1.23652 −0.618261 0.785973i \(-0.712162\pi\)
−0.618261 + 0.785973i \(0.712162\pi\)
\(762\) −15.1055 −0.547214
\(763\) −58.4331 −2.11542
\(764\) −48.6482 −1.76003
\(765\) 4.28378 0.154880
\(766\) −70.3351 −2.54131
\(767\) −16.7770 −0.605781
\(768\) −29.0048 −1.04662
\(769\) 11.3929 0.410840 0.205420 0.978674i \(-0.434144\pi\)
0.205420 + 0.978674i \(0.434144\pi\)
\(770\) −26.2811 −0.947105
\(771\) −8.66722 −0.312142
\(772\) −87.5002 −3.14920
\(773\) −11.0854 −0.398715 −0.199357 0.979927i \(-0.563885\pi\)
−0.199357 + 0.979927i \(0.563885\pi\)
\(774\) 13.9892 0.502832
\(775\) 61.6881 2.21590
\(776\) 32.0621 1.15096
\(777\) −38.3716 −1.37657
\(778\) −69.2831 −2.48392
\(779\) −49.6051 −1.77729
\(780\) −300.549 −10.7614
\(781\) 2.80632 0.100418
\(782\) 0.171922 0.00614792
\(783\) −1.87125 −0.0668731
\(784\) 12.0109 0.428960
\(785\) 3.15034 0.112440
\(786\) 80.3975 2.86768
\(787\) 41.9647 1.49588 0.747940 0.663766i \(-0.231043\pi\)
0.747940 + 0.663766i \(0.231043\pi\)
\(788\) −76.0149 −2.70792
\(789\) −6.73529 −0.239783
\(790\) 56.9393 2.02581
\(791\) −1.79458 −0.0638078
\(792\) −10.1639 −0.361159
\(793\) 33.2599 1.18109
\(794\) −53.9994 −1.91637
\(795\) 81.1076 2.87659
\(796\) 23.7378 0.841364
\(797\) −13.2168 −0.468163 −0.234082 0.972217i \(-0.575208\pi\)
−0.234082 + 0.972217i \(0.575208\pi\)
\(798\) −99.6650 −3.52810
\(799\) 5.68623 0.201164
\(800\) −125.600 −4.44063
\(801\) −0.0428149 −0.00151279
\(802\) 37.0333 1.30769
\(803\) 12.8782 0.454461
\(804\) 131.067 4.62239
\(805\) −1.11306 −0.0392302
\(806\) 102.487 3.60994
\(807\) 0.563762 0.0198454
\(808\) 33.8807 1.19192
\(809\) −19.8043 −0.696284 −0.348142 0.937442i \(-0.613187\pi\)
−0.348142 + 0.937442i \(0.613187\pi\)
\(810\) 119.008 4.18150
\(811\) 44.1877 1.55164 0.775820 0.630954i \(-0.217336\pi\)
0.775820 + 0.630954i \(0.217336\pi\)
\(812\) 8.47731 0.297495
\(813\) −9.12785 −0.320128
\(814\) 14.2648 0.499981
\(815\) −48.5457 −1.70048
\(816\) 14.5207 0.508326
\(817\) −21.3074 −0.745453
\(818\) 58.9431 2.06090
\(819\) −31.9396 −1.11606
\(820\) −156.853 −5.47754
\(821\) 25.4472 0.888112 0.444056 0.895999i \(-0.353539\pi\)
0.444056 + 0.895999i \(0.353539\pi\)
\(822\) −73.1320 −2.55077
\(823\) 6.00165 0.209204 0.104602 0.994514i \(-0.466643\pi\)
0.104602 + 0.994514i \(0.466643\pi\)
\(824\) −84.8413 −2.95559
\(825\) 20.9126 0.728084
\(826\) −17.5917 −0.612093
\(827\) 32.3286 1.12418 0.562088 0.827077i \(-0.309998\pi\)
0.562088 + 0.827077i \(0.309998\pi\)
\(828\) −0.730350 −0.0253814
\(829\) 43.0539 1.49532 0.747662 0.664080i \(-0.231176\pi\)
0.747662 + 0.664080i \(0.231176\pi\)
\(830\) −122.420 −4.24925
\(831\) −16.3330 −0.566585
\(832\) −65.7094 −2.27806
\(833\) 0.819661 0.0283996
\(834\) −126.173 −4.36903
\(835\) 68.8990 2.38435
\(836\) 26.2659 0.908426
\(837\) −16.8163 −0.581256
\(838\) 53.8428 1.85997
\(839\) −30.5027 −1.05307 −0.526536 0.850153i \(-0.676509\pi\)
−0.526536 + 0.850153i \(0.676509\pi\)
\(840\) −185.744 −6.40877
\(841\) −28.6307 −0.987267
\(842\) 74.1826 2.55650
\(843\) −24.0760 −0.829221
\(844\) −96.1789 −3.31062
\(845\) 154.460 5.31360
\(846\) −34.0745 −1.17151
\(847\) −29.3514 −1.00852
\(848\) 93.9575 3.22651
\(849\) 21.4369 0.735714
\(850\) −20.1736 −0.691950
\(851\) 0.604145 0.0207098
\(852\) 33.6514 1.15288
\(853\) −6.93424 −0.237424 −0.118712 0.992929i \(-0.537877\pi\)
−0.118712 + 0.992929i \(0.537877\pi\)
\(854\) 34.8751 1.19340
\(855\) 39.0994 1.33717
\(856\) −108.691 −3.71500
\(857\) −51.7599 −1.76808 −0.884042 0.467408i \(-0.845188\pi\)
−0.884042 + 0.467408i \(0.845188\pi\)
\(858\) 34.7436 1.18613
\(859\) −26.2800 −0.896662 −0.448331 0.893868i \(-0.647981\pi\)
−0.448331 + 0.893868i \(0.647981\pi\)
\(860\) −67.3748 −2.29746
\(861\) −48.7749 −1.66225
\(862\) 0.633487 0.0215767
\(863\) −8.76982 −0.298528 −0.149264 0.988797i \(-0.547690\pi\)
−0.149264 + 0.988797i \(0.547690\pi\)
\(864\) 34.2388 1.16483
\(865\) 2.53916 0.0863341
\(866\) 57.3596 1.94916
\(867\) −35.3014 −1.19890
\(868\) 76.1826 2.58580
\(869\) −4.66623 −0.158291
\(870\) −13.7272 −0.465395
\(871\) −90.2452 −3.05784
\(872\) 153.527 5.19909
\(873\) −6.63617 −0.224600
\(874\) 1.56918 0.0530785
\(875\) 72.7986 2.46104
\(876\) 154.426 5.21756
\(877\) −37.7607 −1.27509 −0.637545 0.770413i \(-0.720050\pi\)
−0.637545 + 0.770413i \(0.720050\pi\)
\(878\) 35.0654 1.18340
\(879\) 13.3052 0.448775
\(880\) 34.9487 1.17812
\(881\) 31.9723 1.07717 0.538587 0.842570i \(-0.318958\pi\)
0.538587 + 0.842570i \(0.318958\pi\)
\(882\) −4.91179 −0.165389
\(883\) −28.4875 −0.958680 −0.479340 0.877629i \(-0.659124\pi\)
−0.479340 + 0.877629i \(0.659124\pi\)
\(884\) −23.7599 −0.799132
\(885\) 20.1941 0.678817
\(886\) −6.49843 −0.218319
\(887\) 10.5495 0.354218 0.177109 0.984191i \(-0.443325\pi\)
0.177109 + 0.984191i \(0.443325\pi\)
\(888\) 100.818 3.38322
\(889\) 7.73130 0.259300
\(890\) 0.290874 0.00975011
\(891\) −9.75280 −0.326731
\(892\) 90.5871 3.03308
\(893\) 51.9000 1.73677
\(894\) −125.484 −4.19682
\(895\) −71.7940 −2.39981
\(896\) −5.21063 −0.174075
\(897\) 1.47147 0.0491308
\(898\) −7.82910 −0.261260
\(899\) 3.31839 0.110675
\(900\) 85.7006 2.85669
\(901\) 6.41197 0.213614
\(902\) 18.1323 0.603739
\(903\) −20.9508 −0.697200
\(904\) 4.71508 0.156821
\(905\) −66.8973 −2.22374
\(906\) −60.6477 −2.01488
\(907\) 35.9151 1.19254 0.596271 0.802783i \(-0.296648\pi\)
0.596271 + 0.802783i \(0.296648\pi\)
\(908\) −11.5043 −0.381783
\(909\) −7.01259 −0.232593
\(910\) 216.989 7.19312
\(911\) 28.4962 0.944122 0.472061 0.881566i \(-0.343510\pi\)
0.472061 + 0.881566i \(0.343510\pi\)
\(912\) 132.535 4.38867
\(913\) 10.0324 0.332024
\(914\) 100.805 3.33432
\(915\) −40.0343 −1.32349
\(916\) 9.04141 0.298737
\(917\) −41.1491 −1.35886
\(918\) 5.49938 0.181506
\(919\) −18.8041 −0.620291 −0.310146 0.950689i \(-0.600378\pi\)
−0.310146 + 0.950689i \(0.600378\pi\)
\(920\) 2.92446 0.0964166
\(921\) 9.74414 0.321080
\(922\) −96.2449 −3.16966
\(923\) −23.1703 −0.762661
\(924\) 25.8263 0.849624
\(925\) −70.8915 −2.33090
\(926\) −24.5579 −0.807024
\(927\) 17.5603 0.576757
\(928\) −6.75642 −0.221790
\(929\) −35.3920 −1.16117 −0.580586 0.814199i \(-0.697177\pi\)
−0.580586 + 0.814199i \(0.697177\pi\)
\(930\) −123.361 −4.04517
\(931\) 7.48130 0.245190
\(932\) −25.8441 −0.846552
\(933\) 48.5856 1.59062
\(934\) 58.9202 1.92793
\(935\) 2.38501 0.0779982
\(936\) 83.9181 2.74295
\(937\) 12.4380 0.406332 0.203166 0.979144i \(-0.434877\pi\)
0.203166 + 0.979144i \(0.434877\pi\)
\(938\) −94.6277 −3.08970
\(939\) −46.9670 −1.53271
\(940\) 164.109 5.35266
\(941\) 48.4868 1.58062 0.790312 0.612704i \(-0.209918\pi\)
0.790312 + 0.612704i \(0.209918\pi\)
\(942\) −4.36700 −0.142284
\(943\) 0.767941 0.0250076
\(944\) 23.3935 0.761393
\(945\) −35.6042 −1.15820
\(946\) 7.78856 0.253228
\(947\) −31.2476 −1.01541 −0.507705 0.861531i \(-0.669506\pi\)
−0.507705 + 0.861531i \(0.669506\pi\)
\(948\) −55.9541 −1.81730
\(949\) −106.328 −3.45157
\(950\) −184.131 −5.97400
\(951\) −23.8168 −0.772314
\(952\) −14.6840 −0.475911
\(953\) 61.0696 1.97824 0.989119 0.147119i \(-0.0470001\pi\)
0.989119 + 0.147119i \(0.0470001\pi\)
\(954\) −38.4235 −1.24401
\(955\) −40.3188 −1.30469
\(956\) −18.7116 −0.605177
\(957\) 1.12495 0.0363646
\(958\) −68.5079 −2.21339
\(959\) 37.4305 1.20869
\(960\) 79.0932 2.55272
\(961\) −1.17877 −0.0380250
\(962\) −117.777 −3.79728
\(963\) 22.4968 0.724950
\(964\) −127.544 −4.10791
\(965\) −72.5186 −2.33446
\(966\) 1.54292 0.0496428
\(967\) −22.7600 −0.731913 −0.365956 0.930632i \(-0.619258\pi\)
−0.365956 + 0.930632i \(0.619258\pi\)
\(968\) 77.1179 2.47866
\(969\) 9.04461 0.290555
\(970\) 45.0844 1.44757
\(971\) 21.2709 0.682616 0.341308 0.939951i \(-0.389130\pi\)
0.341308 + 0.939951i \(0.389130\pi\)
\(972\) −71.9505 −2.30781
\(973\) 64.5781 2.07028
\(974\) 23.8568 0.764422
\(975\) −172.665 −5.52969
\(976\) −46.3770 −1.48449
\(977\) 35.5602 1.13767 0.568836 0.822451i \(-0.307394\pi\)
0.568836 + 0.822451i \(0.307394\pi\)
\(978\) 67.2940 2.15183
\(979\) −0.0238374 −0.000761846 0
\(980\) 23.6561 0.755667
\(981\) −31.7769 −1.01456
\(982\) −19.0486 −0.607865
\(983\) −21.8961 −0.698377 −0.349189 0.937052i \(-0.613543\pi\)
−0.349189 + 0.937052i \(0.613543\pi\)
\(984\) 128.151 4.08532
\(985\) −62.9999 −2.00734
\(986\) −1.08520 −0.0345599
\(987\) 51.0314 1.62435
\(988\) −216.864 −6.89936
\(989\) 0.329862 0.0104890
\(990\) −14.2921 −0.454233
\(991\) 32.9145 1.04556 0.522782 0.852466i \(-0.324894\pi\)
0.522782 + 0.852466i \(0.324894\pi\)
\(992\) −60.7175 −1.92778
\(993\) −32.1400 −1.01993
\(994\) −24.2955 −0.770608
\(995\) 19.6735 0.623692
\(996\) 120.301 3.81190
\(997\) 28.7641 0.910969 0.455485 0.890244i \(-0.349466\pi\)
0.455485 + 0.890244i \(0.349466\pi\)
\(998\) 57.7606 1.82838
\(999\) 19.3252 0.611421
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 4003.2.a.c.1.6 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.6 179 1.1 even 1 trivial