Properties

Label 8003.2.a.b.1.11
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 1.11
Character \(\chi\) \(=\) 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.49383 q^{2} -0.270355 q^{3} +4.21918 q^{4} -2.99495 q^{5} +0.674220 q^{6} -3.80387 q^{7} -5.53426 q^{8} -2.92691 q^{9} +O(q^{10})\) \(q-2.49383 q^{2} -0.270355 q^{3} +4.21918 q^{4} -2.99495 q^{5} +0.674220 q^{6} -3.80387 q^{7} -5.53426 q^{8} -2.92691 q^{9} +7.46890 q^{10} -5.91933 q^{11} -1.14068 q^{12} -0.710532 q^{13} +9.48621 q^{14} +0.809702 q^{15} +5.36314 q^{16} -1.35009 q^{17} +7.29921 q^{18} -5.05928 q^{19} -12.6363 q^{20} +1.02840 q^{21} +14.7618 q^{22} +6.13130 q^{23} +1.49622 q^{24} +3.96974 q^{25} +1.77195 q^{26} +1.60237 q^{27} -16.0492 q^{28} -0.793559 q^{29} -2.01926 q^{30} +1.55429 q^{31} -2.30622 q^{32} +1.60032 q^{33} +3.36690 q^{34} +11.3924 q^{35} -12.3492 q^{36} -11.1363 q^{37} +12.6170 q^{38} +0.192096 q^{39} +16.5748 q^{40} +7.91233 q^{41} -2.56465 q^{42} -11.5314 q^{43} -24.9747 q^{44} +8.76595 q^{45} -15.2904 q^{46} -3.68696 q^{47} -1.44995 q^{48} +7.46946 q^{49} -9.89985 q^{50} +0.365005 q^{51} -2.99786 q^{52} -1.00000 q^{53} -3.99604 q^{54} +17.7281 q^{55} +21.0516 q^{56} +1.36780 q^{57} +1.97900 q^{58} +1.22514 q^{59} +3.41628 q^{60} +1.94993 q^{61} -3.87613 q^{62} +11.1336 q^{63} -4.97495 q^{64} +2.12801 q^{65} -3.99093 q^{66} +6.11454 q^{67} -5.69629 q^{68} -1.65763 q^{69} -28.4108 q^{70} -13.2576 q^{71} +16.1983 q^{72} +5.38563 q^{73} +27.7720 q^{74} -1.07324 q^{75} -21.3460 q^{76} +22.5164 q^{77} -0.479055 q^{78} +10.0480 q^{79} -16.0623 q^{80} +8.34751 q^{81} -19.7320 q^{82} +13.3540 q^{83} +4.33900 q^{84} +4.04346 q^{85} +28.7574 q^{86} +0.214543 q^{87} +32.7591 q^{88} +7.27485 q^{89} -21.8608 q^{90} +2.70278 q^{91} +25.8691 q^{92} -0.420210 q^{93} +9.19464 q^{94} +15.1523 q^{95} +0.623500 q^{96} -12.8467 q^{97} -18.6276 q^{98} +17.3253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49383 −1.76340 −0.881702 0.471807i \(-0.843602\pi\)
−0.881702 + 0.471807i \(0.843602\pi\)
\(3\) −0.270355 −0.156090 −0.0780449 0.996950i \(-0.524868\pi\)
−0.0780449 + 0.996950i \(0.524868\pi\)
\(4\) 4.21918 2.10959
\(5\) −2.99495 −1.33938 −0.669692 0.742639i \(-0.733574\pi\)
−0.669692 + 0.742639i \(0.733574\pi\)
\(6\) 0.674220 0.275249
\(7\) −3.80387 −1.43773 −0.718865 0.695150i \(-0.755338\pi\)
−0.718865 + 0.695150i \(0.755338\pi\)
\(8\) −5.53426 −1.95666
\(9\) −2.92691 −0.975636
\(10\) 7.46890 2.36187
\(11\) −5.91933 −1.78475 −0.892373 0.451299i \(-0.850961\pi\)
−0.892373 + 0.451299i \(0.850961\pi\)
\(12\) −1.14068 −0.329286
\(13\) −0.710532 −0.197066 −0.0985331 0.995134i \(-0.531415\pi\)
−0.0985331 + 0.995134i \(0.531415\pi\)
\(14\) 9.48621 2.53530
\(15\) 0.809702 0.209064
\(16\) 5.36314 1.34078
\(17\) −1.35009 −0.327446 −0.163723 0.986506i \(-0.552350\pi\)
−0.163723 + 0.986506i \(0.552350\pi\)
\(18\) 7.29921 1.72044
\(19\) −5.05928 −1.16068 −0.580339 0.814375i \(-0.697080\pi\)
−0.580339 + 0.814375i \(0.697080\pi\)
\(20\) −12.6363 −2.82555
\(21\) 1.02840 0.224415
\(22\) 14.7618 3.14723
\(23\) 6.13130 1.27847 0.639233 0.769013i \(-0.279252\pi\)
0.639233 + 0.769013i \(0.279252\pi\)
\(24\) 1.49622 0.305414
\(25\) 3.96974 0.793948
\(26\) 1.77195 0.347507
\(27\) 1.60237 0.308377
\(28\) −16.0492 −3.03302
\(29\) −0.793559 −0.147360 −0.0736801 0.997282i \(-0.523474\pi\)
−0.0736801 + 0.997282i \(0.523474\pi\)
\(30\) −2.01926 −0.368664
\(31\) 1.55429 0.279158 0.139579 0.990211i \(-0.455425\pi\)
0.139579 + 0.990211i \(0.455425\pi\)
\(32\) −2.30622 −0.407686
\(33\) 1.60032 0.278581
\(34\) 3.36690 0.577419
\(35\) 11.3924 1.92567
\(36\) −12.3492 −2.05819
\(37\) −11.1363 −1.83080 −0.915399 0.402548i \(-0.868125\pi\)
−0.915399 + 0.402548i \(0.868125\pi\)
\(38\) 12.6170 2.04674
\(39\) 0.192096 0.0307600
\(40\) 16.5748 2.62071
\(41\) 7.91233 1.23570 0.617849 0.786297i \(-0.288004\pi\)
0.617849 + 0.786297i \(0.288004\pi\)
\(42\) −2.56465 −0.395734
\(43\) −11.5314 −1.75852 −0.879262 0.476339i \(-0.841963\pi\)
−0.879262 + 0.476339i \(0.841963\pi\)
\(44\) −24.9747 −3.76508
\(45\) 8.76595 1.30675
\(46\) −15.2904 −2.25445
\(47\) −3.68696 −0.537798 −0.268899 0.963168i \(-0.586660\pi\)
−0.268899 + 0.963168i \(0.586660\pi\)
\(48\) −1.44995 −0.209283
\(49\) 7.46946 1.06707
\(50\) −9.89985 −1.40005
\(51\) 0.365005 0.0511109
\(52\) −2.99786 −0.415729
\(53\) −1.00000 −0.137361
\(54\) −3.99604 −0.543792
\(55\) 17.7281 2.39046
\(56\) 21.0516 2.81314
\(57\) 1.36780 0.181170
\(58\) 1.97900 0.259855
\(59\) 1.22514 0.159499 0.0797496 0.996815i \(-0.474588\pi\)
0.0797496 + 0.996815i \(0.474588\pi\)
\(60\) 3.41628 0.441040
\(61\) 1.94993 0.249663 0.124831 0.992178i \(-0.460161\pi\)
0.124831 + 0.992178i \(0.460161\pi\)
\(62\) −3.87613 −0.492269
\(63\) 11.1336 1.40270
\(64\) −4.97495 −0.621869
\(65\) 2.12801 0.263947
\(66\) −3.99093 −0.491250
\(67\) 6.11454 0.747009 0.373505 0.927628i \(-0.378156\pi\)
0.373505 + 0.927628i \(0.378156\pi\)
\(68\) −5.69629 −0.690776
\(69\) −1.65763 −0.199555
\(70\) −28.4108 −3.39573
\(71\) −13.2576 −1.57339 −0.786694 0.617343i \(-0.788209\pi\)
−0.786694 + 0.617343i \(0.788209\pi\)
\(72\) 16.1983 1.90898
\(73\) 5.38563 0.630340 0.315170 0.949035i \(-0.397938\pi\)
0.315170 + 0.949035i \(0.397938\pi\)
\(74\) 27.7720 3.22843
\(75\) −1.07324 −0.123927
\(76\) −21.3460 −2.44856
\(77\) 22.5164 2.56598
\(78\) −0.479055 −0.0542423
\(79\) 10.0480 1.13049 0.565247 0.824922i \(-0.308781\pi\)
0.565247 + 0.824922i \(0.308781\pi\)
\(80\) −16.0623 −1.79582
\(81\) 8.34751 0.927502
\(82\) −19.7320 −2.17903
\(83\) 13.3540 1.46579 0.732895 0.680342i \(-0.238169\pi\)
0.732895 + 0.680342i \(0.238169\pi\)
\(84\) 4.33900 0.473424
\(85\) 4.04346 0.438575
\(86\) 28.7574 3.10099
\(87\) 0.214543 0.0230014
\(88\) 32.7591 3.49213
\(89\) 7.27485 0.771132 0.385566 0.922680i \(-0.374006\pi\)
0.385566 + 0.922680i \(0.374006\pi\)
\(90\) −21.8608 −2.30433
\(91\) 2.70278 0.283328
\(92\) 25.8691 2.69704
\(93\) −0.420210 −0.0435738
\(94\) 9.19464 0.948355
\(95\) 15.1523 1.55459
\(96\) 0.623500 0.0636357
\(97\) −12.8467 −1.30438 −0.652190 0.758056i \(-0.726150\pi\)
−0.652190 + 0.758056i \(0.726150\pi\)
\(98\) −18.6276 −1.88167
\(99\) 17.3253 1.74126
\(100\) 16.7491 1.67491
\(101\) −12.7204 −1.26573 −0.632863 0.774264i \(-0.718120\pi\)
−0.632863 + 0.774264i \(0.718120\pi\)
\(102\) −0.910260 −0.0901292
\(103\) 6.80892 0.670903 0.335451 0.942058i \(-0.391111\pi\)
0.335451 + 0.942058i \(0.391111\pi\)
\(104\) 3.93227 0.385591
\(105\) −3.08000 −0.300578
\(106\) 2.49383 0.242222
\(107\) 7.22091 0.698071 0.349036 0.937109i \(-0.386509\pi\)
0.349036 + 0.937109i \(0.386509\pi\)
\(108\) 6.76070 0.650549
\(109\) −17.5619 −1.68212 −0.841061 0.540941i \(-0.818068\pi\)
−0.841061 + 0.540941i \(0.818068\pi\)
\(110\) −44.2109 −4.21534
\(111\) 3.01076 0.285769
\(112\) −20.4007 −1.92768
\(113\) −0.715990 −0.0673547 −0.0336773 0.999433i \(-0.510722\pi\)
−0.0336773 + 0.999433i \(0.510722\pi\)
\(114\) −3.41107 −0.319476
\(115\) −18.3630 −1.71236
\(116\) −3.34817 −0.310870
\(117\) 2.07966 0.192265
\(118\) −3.05528 −0.281261
\(119\) 5.13558 0.470778
\(120\) −4.48110 −0.409067
\(121\) 24.0385 2.18532
\(122\) −4.86279 −0.440256
\(123\) −2.13914 −0.192880
\(124\) 6.55782 0.588910
\(125\) 3.08558 0.275983
\(126\) −27.7653 −2.47353
\(127\) 5.75524 0.510695 0.255348 0.966849i \(-0.417810\pi\)
0.255348 + 0.966849i \(0.417810\pi\)
\(128\) 17.0191 1.50429
\(129\) 3.11758 0.274488
\(130\) −5.30689 −0.465445
\(131\) 4.95580 0.432991 0.216495 0.976284i \(-0.430537\pi\)
0.216495 + 0.976284i \(0.430537\pi\)
\(132\) 6.75206 0.587691
\(133\) 19.2449 1.66874
\(134\) −15.2486 −1.31728
\(135\) −4.79903 −0.413035
\(136\) 7.47177 0.640699
\(137\) 21.0949 1.80226 0.901128 0.433553i \(-0.142740\pi\)
0.901128 + 0.433553i \(0.142740\pi\)
\(138\) 4.13385 0.351897
\(139\) −12.6542 −1.07331 −0.536657 0.843801i \(-0.680313\pi\)
−0.536657 + 0.843801i \(0.680313\pi\)
\(140\) 48.0667 4.06238
\(141\) 0.996790 0.0839448
\(142\) 33.0622 2.77452
\(143\) 4.20587 0.351713
\(144\) −15.6974 −1.30812
\(145\) 2.37667 0.197372
\(146\) −13.4308 −1.11154
\(147\) −2.01941 −0.166558
\(148\) −46.9861 −3.86224
\(149\) 20.6126 1.68865 0.844326 0.535831i \(-0.180001\pi\)
0.844326 + 0.535831i \(0.180001\pi\)
\(150\) 2.67648 0.218534
\(151\) −1.00000 −0.0813788
\(152\) 27.9994 2.27105
\(153\) 3.95160 0.319468
\(154\) −56.1520 −4.52486
\(155\) −4.65502 −0.373900
\(156\) 0.810489 0.0648911
\(157\) 3.26944 0.260929 0.130465 0.991453i \(-0.458353\pi\)
0.130465 + 0.991453i \(0.458353\pi\)
\(158\) −25.0581 −1.99352
\(159\) 0.270355 0.0214406
\(160\) 6.90702 0.546048
\(161\) −23.3227 −1.83809
\(162\) −20.8173 −1.63556
\(163\) −4.61933 −0.361813 −0.180907 0.983500i \(-0.557903\pi\)
−0.180907 + 0.983500i \(0.557903\pi\)
\(164\) 33.3836 2.60682
\(165\) −4.79289 −0.373126
\(166\) −33.3025 −2.58478
\(167\) 13.8528 1.07196 0.535981 0.844230i \(-0.319942\pi\)
0.535981 + 0.844230i \(0.319942\pi\)
\(168\) −5.69143 −0.439103
\(169\) −12.4951 −0.961165
\(170\) −10.0837 −0.773385
\(171\) 14.8081 1.13240
\(172\) −48.6531 −3.70977
\(173\) −7.01099 −0.533036 −0.266518 0.963830i \(-0.585873\pi\)
−0.266518 + 0.963830i \(0.585873\pi\)
\(174\) −0.535033 −0.0405608
\(175\) −15.1004 −1.14148
\(176\) −31.7462 −2.39296
\(177\) −0.331222 −0.0248962
\(178\) −18.1422 −1.35982
\(179\) 18.7287 1.39985 0.699923 0.714218i \(-0.253218\pi\)
0.699923 + 0.714218i \(0.253218\pi\)
\(180\) 36.9851 2.75671
\(181\) 23.8184 1.77041 0.885205 0.465201i \(-0.154018\pi\)
0.885205 + 0.465201i \(0.154018\pi\)
\(182\) −6.74026 −0.499621
\(183\) −0.527174 −0.0389698
\(184\) −33.9322 −2.50152
\(185\) 33.3527 2.45214
\(186\) 1.04793 0.0768381
\(187\) 7.99164 0.584407
\(188\) −15.5560 −1.13453
\(189\) −6.09522 −0.443362
\(190\) −37.7873 −2.74138
\(191\) −2.16339 −0.156537 −0.0782687 0.996932i \(-0.524939\pi\)
−0.0782687 + 0.996932i \(0.524939\pi\)
\(192\) 1.34501 0.0970674
\(193\) −9.37160 −0.674582 −0.337291 0.941400i \(-0.609511\pi\)
−0.337291 + 0.941400i \(0.609511\pi\)
\(194\) 32.0373 2.30015
\(195\) −0.575319 −0.0411995
\(196\) 31.5150 2.25107
\(197\) −16.5235 −1.17725 −0.588627 0.808405i \(-0.700331\pi\)
−0.588627 + 0.808405i \(0.700331\pi\)
\(198\) −43.2064 −3.07055
\(199\) −0.932005 −0.0660681 −0.0330341 0.999454i \(-0.510517\pi\)
−0.0330341 + 0.999454i \(0.510517\pi\)
\(200\) −21.9696 −1.55348
\(201\) −1.65310 −0.116601
\(202\) 31.7225 2.23198
\(203\) 3.01860 0.211864
\(204\) 1.54002 0.107823
\(205\) −23.6970 −1.65507
\(206\) −16.9803 −1.18307
\(207\) −17.9458 −1.24732
\(208\) −3.81068 −0.264223
\(209\) 29.9476 2.07152
\(210\) 7.68100 0.530040
\(211\) 12.3506 0.850250 0.425125 0.905135i \(-0.360230\pi\)
0.425125 + 0.905135i \(0.360230\pi\)
\(212\) −4.21918 −0.289775
\(213\) 3.58427 0.245590
\(214\) −18.0077 −1.23098
\(215\) 34.5360 2.35534
\(216\) −8.86795 −0.603387
\(217\) −5.91232 −0.401354
\(218\) 43.7963 2.96626
\(219\) −1.45603 −0.0983897
\(220\) 74.7981 5.04289
\(221\) 0.959284 0.0645284
\(222\) −7.50833 −0.503926
\(223\) −26.4463 −1.77097 −0.885487 0.464665i \(-0.846175\pi\)
−0.885487 + 0.464665i \(0.846175\pi\)
\(224\) 8.77258 0.586142
\(225\) −11.6191 −0.774604
\(226\) 1.78556 0.118773
\(227\) −27.5481 −1.82843 −0.914217 0.405225i \(-0.867193\pi\)
−0.914217 + 0.405225i \(0.867193\pi\)
\(228\) 5.77102 0.382195
\(229\) 17.4888 1.15570 0.577848 0.816145i \(-0.303893\pi\)
0.577848 + 0.816145i \(0.303893\pi\)
\(230\) 45.7941 3.01957
\(231\) −6.08743 −0.400524
\(232\) 4.39176 0.288333
\(233\) 15.6435 1.02484 0.512421 0.858734i \(-0.328749\pi\)
0.512421 + 0.858734i \(0.328749\pi\)
\(234\) −5.18632 −0.339040
\(235\) 11.0423 0.720318
\(236\) 5.16908 0.336478
\(237\) −2.71654 −0.176458
\(238\) −12.8073 −0.830172
\(239\) 3.08331 0.199443 0.0997213 0.995015i \(-0.468205\pi\)
0.0997213 + 0.995015i \(0.468205\pi\)
\(240\) 4.34254 0.280310
\(241\) −13.8297 −0.890847 −0.445423 0.895320i \(-0.646947\pi\)
−0.445423 + 0.895320i \(0.646947\pi\)
\(242\) −59.9478 −3.85359
\(243\) −7.06391 −0.453150
\(244\) 8.22711 0.526687
\(245\) −22.3707 −1.42921
\(246\) 5.33465 0.340125
\(247\) 3.59478 0.228731
\(248\) −8.60184 −0.546217
\(249\) −3.61032 −0.228795
\(250\) −7.69491 −0.486669
\(251\) −12.5883 −0.794567 −0.397283 0.917696i \(-0.630047\pi\)
−0.397283 + 0.917696i \(0.630047\pi\)
\(252\) 46.9747 2.95913
\(253\) −36.2932 −2.28173
\(254\) −14.3526 −0.900562
\(255\) −1.09317 −0.0684571
\(256\) −32.4929 −2.03080
\(257\) −9.11094 −0.568325 −0.284162 0.958776i \(-0.591715\pi\)
−0.284162 + 0.958776i \(0.591715\pi\)
\(258\) −7.77471 −0.484032
\(259\) 42.3611 2.63219
\(260\) 8.97846 0.556821
\(261\) 2.32267 0.143770
\(262\) −12.3589 −0.763537
\(263\) −17.4088 −1.07347 −0.536737 0.843750i \(-0.680343\pi\)
−0.536737 + 0.843750i \(0.680343\pi\)
\(264\) −8.85661 −0.545087
\(265\) 2.99495 0.183978
\(266\) −47.9934 −2.94267
\(267\) −1.96679 −0.120366
\(268\) 25.7983 1.57588
\(269\) −12.0663 −0.735695 −0.367848 0.929886i \(-0.619905\pi\)
−0.367848 + 0.929886i \(0.619905\pi\)
\(270\) 11.9680 0.728347
\(271\) 17.1722 1.04314 0.521569 0.853209i \(-0.325347\pi\)
0.521569 + 0.853209i \(0.325347\pi\)
\(272\) −7.24073 −0.439034
\(273\) −0.730710 −0.0442246
\(274\) −52.6070 −3.17810
\(275\) −23.4982 −1.41699
\(276\) −6.99385 −0.420980
\(277\) 26.6336 1.60026 0.800129 0.599828i \(-0.204765\pi\)
0.800129 + 0.599828i \(0.204765\pi\)
\(278\) 31.5574 1.89268
\(279\) −4.54926 −0.272357
\(280\) −63.0487 −3.76788
\(281\) 1.20934 0.0721429 0.0360714 0.999349i \(-0.488516\pi\)
0.0360714 + 0.999349i \(0.488516\pi\)
\(282\) −2.48582 −0.148029
\(283\) −9.16240 −0.544648 −0.272324 0.962206i \(-0.587792\pi\)
−0.272324 + 0.962206i \(0.587792\pi\)
\(284\) −55.9363 −3.31921
\(285\) −4.09651 −0.242656
\(286\) −10.4887 −0.620212
\(287\) −30.0975 −1.77660
\(288\) 6.75010 0.397753
\(289\) −15.1772 −0.892779
\(290\) −5.92701 −0.348046
\(291\) 3.47316 0.203600
\(292\) 22.7229 1.32976
\(293\) −13.2386 −0.773408 −0.386704 0.922204i \(-0.626387\pi\)
−0.386704 + 0.922204i \(0.626387\pi\)
\(294\) 5.03606 0.293709
\(295\) −3.66923 −0.213631
\(296\) 61.6312 3.58224
\(297\) −9.48497 −0.550374
\(298\) −51.4043 −2.97777
\(299\) −4.35649 −0.251942
\(300\) −4.52820 −0.261436
\(301\) 43.8640 2.52828
\(302\) 2.49383 0.143504
\(303\) 3.43903 0.197567
\(304\) −27.1336 −1.55622
\(305\) −5.83995 −0.334394
\(306\) −9.85461 −0.563350
\(307\) −12.3148 −0.702843 −0.351421 0.936217i \(-0.614302\pi\)
−0.351421 + 0.936217i \(0.614302\pi\)
\(308\) 95.0008 5.41317
\(309\) −1.84083 −0.104721
\(310\) 11.6088 0.659337
\(311\) 17.8033 1.00953 0.504765 0.863257i \(-0.331579\pi\)
0.504765 + 0.863257i \(0.331579\pi\)
\(312\) −1.06311 −0.0601868
\(313\) 4.60176 0.260107 0.130054 0.991507i \(-0.458485\pi\)
0.130054 + 0.991507i \(0.458485\pi\)
\(314\) −8.15342 −0.460124
\(315\) −33.3446 −1.87875
\(316\) 42.3945 2.38488
\(317\) −26.0244 −1.46168 −0.730839 0.682550i \(-0.760871\pi\)
−0.730839 + 0.682550i \(0.760871\pi\)
\(318\) −0.674220 −0.0378084
\(319\) 4.69734 0.263000
\(320\) 14.8997 0.832921
\(321\) −1.95221 −0.108962
\(322\) 58.1629 3.24129
\(323\) 6.83050 0.380059
\(324\) 35.2197 1.95665
\(325\) −2.82063 −0.156460
\(326\) 11.5198 0.638023
\(327\) 4.74795 0.262562
\(328\) −43.7889 −2.41784
\(329\) 14.0247 0.773208
\(330\) 11.9527 0.657972
\(331\) −34.8481 −1.91542 −0.957712 0.287727i \(-0.907100\pi\)
−0.957712 + 0.287727i \(0.907100\pi\)
\(332\) 56.3429 3.09222
\(333\) 32.5949 1.78619
\(334\) −34.5465 −1.89030
\(335\) −18.3127 −1.00053
\(336\) 5.51544 0.300892
\(337\) −19.4476 −1.05938 −0.529688 0.848193i \(-0.677691\pi\)
−0.529688 + 0.848193i \(0.677691\pi\)
\(338\) 31.1608 1.69492
\(339\) 0.193572 0.0105134
\(340\) 17.0601 0.925214
\(341\) −9.20034 −0.498227
\(342\) −36.9287 −1.99688
\(343\) −1.78578 −0.0964231
\(344\) 63.8178 3.44083
\(345\) 4.96453 0.267281
\(346\) 17.4842 0.939957
\(347\) −1.99030 −0.106845 −0.0534224 0.998572i \(-0.517013\pi\)
−0.0534224 + 0.998572i \(0.517013\pi\)
\(348\) 0.905196 0.0485236
\(349\) −28.4979 −1.52546 −0.762728 0.646719i \(-0.776141\pi\)
−0.762728 + 0.646719i \(0.776141\pi\)
\(350\) 37.6578 2.01289
\(351\) −1.13854 −0.0607706
\(352\) 13.6513 0.727616
\(353\) −12.3755 −0.658681 −0.329340 0.944211i \(-0.606826\pi\)
−0.329340 + 0.944211i \(0.606826\pi\)
\(354\) 0.826012 0.0439021
\(355\) 39.7059 2.10737
\(356\) 30.6939 1.62677
\(357\) −1.38843 −0.0734837
\(358\) −46.7061 −2.46849
\(359\) 18.6661 0.985160 0.492580 0.870267i \(-0.336054\pi\)
0.492580 + 0.870267i \(0.336054\pi\)
\(360\) −48.5131 −2.55686
\(361\) 6.59633 0.347175
\(362\) −59.3991 −3.12195
\(363\) −6.49893 −0.341106
\(364\) 11.4035 0.597706
\(365\) −16.1297 −0.844267
\(366\) 1.31468 0.0687195
\(367\) 20.6907 1.08004 0.540022 0.841651i \(-0.318416\pi\)
0.540022 + 0.841651i \(0.318416\pi\)
\(368\) 32.8830 1.71415
\(369\) −23.1587 −1.20559
\(370\) −83.1760 −4.32411
\(371\) 3.80387 0.197487
\(372\) −1.77294 −0.0919229
\(373\) 31.1248 1.61158 0.805791 0.592200i \(-0.201741\pi\)
0.805791 + 0.592200i \(0.201741\pi\)
\(374\) −19.9298 −1.03055
\(375\) −0.834204 −0.0430781
\(376\) 20.4046 1.05229
\(377\) 0.563849 0.0290397
\(378\) 15.2004 0.781826
\(379\) 25.2642 1.29774 0.648868 0.760901i \(-0.275243\pi\)
0.648868 + 0.760901i \(0.275243\pi\)
\(380\) 63.9303 3.27956
\(381\) −1.55596 −0.0797143
\(382\) 5.39512 0.276039
\(383\) 33.1576 1.69427 0.847136 0.531376i \(-0.178325\pi\)
0.847136 + 0.531376i \(0.178325\pi\)
\(384\) −4.60121 −0.234805
\(385\) −67.4355 −3.43683
\(386\) 23.3712 1.18956
\(387\) 33.7514 1.71568
\(388\) −54.2024 −2.75171
\(389\) −2.79210 −0.141565 −0.0707827 0.997492i \(-0.522550\pi\)
−0.0707827 + 0.997492i \(0.522550\pi\)
\(390\) 1.43475 0.0726513
\(391\) −8.27783 −0.418628
\(392\) −41.3380 −2.08788
\(393\) −1.33983 −0.0675854
\(394\) 41.2069 2.07597
\(395\) −30.0934 −1.51416
\(396\) 73.0988 3.67335
\(397\) −25.0948 −1.25947 −0.629735 0.776810i \(-0.716837\pi\)
−0.629735 + 0.776810i \(0.716837\pi\)
\(398\) 2.32426 0.116505
\(399\) −5.20296 −0.260474
\(400\) 21.2903 1.06451
\(401\) 18.6521 0.931442 0.465721 0.884932i \(-0.345795\pi\)
0.465721 + 0.884932i \(0.345795\pi\)
\(402\) 4.12254 0.205614
\(403\) −1.10437 −0.0550127
\(404\) −53.6696 −2.67016
\(405\) −25.0004 −1.24228
\(406\) −7.52787 −0.373602
\(407\) 65.9195 3.26751
\(408\) −2.02003 −0.100007
\(409\) 16.0222 0.792248 0.396124 0.918197i \(-0.370355\pi\)
0.396124 + 0.918197i \(0.370355\pi\)
\(410\) 59.0964 2.91856
\(411\) −5.70311 −0.281314
\(412\) 28.7281 1.41533
\(413\) −4.66027 −0.229317
\(414\) 44.7537 2.19952
\(415\) −39.9945 −1.96325
\(416\) 1.63864 0.0803411
\(417\) 3.42113 0.167533
\(418\) −74.6841 −3.65292
\(419\) 32.2329 1.57468 0.787340 0.616520i \(-0.211458\pi\)
0.787340 + 0.616520i \(0.211458\pi\)
\(420\) −12.9951 −0.634096
\(421\) −3.91209 −0.190663 −0.0953317 0.995446i \(-0.530391\pi\)
−0.0953317 + 0.995446i \(0.530391\pi\)
\(422\) −30.8003 −1.49933
\(423\) 10.7914 0.524695
\(424\) 5.53426 0.268767
\(425\) −5.35952 −0.259975
\(426\) −8.93855 −0.433074
\(427\) −7.41729 −0.358948
\(428\) 30.4663 1.47265
\(429\) −1.13708 −0.0548988
\(430\) −86.1269 −4.15341
\(431\) 18.8524 0.908090 0.454045 0.890979i \(-0.349981\pi\)
0.454045 + 0.890979i \(0.349981\pi\)
\(432\) 8.59374 0.413467
\(433\) −27.0571 −1.30028 −0.650140 0.759815i \(-0.725290\pi\)
−0.650140 + 0.759815i \(0.725290\pi\)
\(434\) 14.7443 0.707749
\(435\) −0.642546 −0.0308077
\(436\) −74.0967 −3.54859
\(437\) −31.0200 −1.48389
\(438\) 3.63110 0.173501
\(439\) 18.9505 0.904458 0.452229 0.891902i \(-0.350629\pi\)
0.452229 + 0.891902i \(0.350629\pi\)
\(440\) −98.1120 −4.67731
\(441\) −21.8624 −1.04107
\(442\) −2.39229 −0.113790
\(443\) −34.4655 −1.63750 −0.818752 0.574148i \(-0.805333\pi\)
−0.818752 + 0.574148i \(0.805333\pi\)
\(444\) 12.7030 0.602856
\(445\) −21.7878 −1.03284
\(446\) 65.9525 3.12294
\(447\) −5.57273 −0.263581
\(448\) 18.9241 0.894079
\(449\) 5.47937 0.258588 0.129294 0.991606i \(-0.458729\pi\)
0.129294 + 0.991606i \(0.458729\pi\)
\(450\) 28.9759 1.36594
\(451\) −46.8357 −2.20541
\(452\) −3.02089 −0.142091
\(453\) 0.270355 0.0127024
\(454\) 68.7003 3.22427
\(455\) −8.09468 −0.379485
\(456\) −7.56979 −0.354488
\(457\) 3.31085 0.154875 0.0774374 0.996997i \(-0.475326\pi\)
0.0774374 + 0.996997i \(0.475326\pi\)
\(458\) −43.6142 −2.03796
\(459\) −2.16335 −0.100977
\(460\) −77.4767 −3.61237
\(461\) 3.79258 0.176638 0.0883189 0.996092i \(-0.471851\pi\)
0.0883189 + 0.996092i \(0.471851\pi\)
\(462\) 15.1810 0.706285
\(463\) −20.1484 −0.936376 −0.468188 0.883629i \(-0.655093\pi\)
−0.468188 + 0.883629i \(0.655093\pi\)
\(464\) −4.25596 −0.197578
\(465\) 1.25851 0.0583620
\(466\) −39.0123 −1.80721
\(467\) 27.3475 1.26549 0.632746 0.774359i \(-0.281928\pi\)
0.632746 + 0.774359i \(0.281928\pi\)
\(468\) 8.77447 0.405600
\(469\) −23.2589 −1.07400
\(470\) −27.5375 −1.27021
\(471\) −0.883910 −0.0407284
\(472\) −6.78023 −0.312085
\(473\) 68.2582 3.13852
\(474\) 6.77459 0.311167
\(475\) −20.0840 −0.921518
\(476\) 21.6680 0.993149
\(477\) 2.92691 0.134014
\(478\) −7.68924 −0.351698
\(479\) 30.7768 1.40623 0.703114 0.711078i \(-0.251793\pi\)
0.703114 + 0.711078i \(0.251793\pi\)
\(480\) −1.86735 −0.0852325
\(481\) 7.91271 0.360788
\(482\) 34.4888 1.57092
\(483\) 6.30542 0.286907
\(484\) 101.423 4.61012
\(485\) 38.4751 1.74706
\(486\) 17.6162 0.799087
\(487\) −3.29348 −0.149242 −0.0746209 0.997212i \(-0.523775\pi\)
−0.0746209 + 0.997212i \(0.523775\pi\)
\(488\) −10.7914 −0.488505
\(489\) 1.24886 0.0564754
\(490\) 55.7887 2.52028
\(491\) −7.82130 −0.352970 −0.176485 0.984303i \(-0.556473\pi\)
−0.176485 + 0.984303i \(0.556473\pi\)
\(492\) −9.02543 −0.406898
\(493\) 1.07138 0.0482524
\(494\) −8.96477 −0.403344
\(495\) −51.8886 −2.33222
\(496\) 8.33586 0.374291
\(497\) 50.4303 2.26211
\(498\) 9.00353 0.403458
\(499\) 26.3426 1.17926 0.589629 0.807674i \(-0.299274\pi\)
0.589629 + 0.807674i \(0.299274\pi\)
\(500\) 13.0186 0.582211
\(501\) −3.74518 −0.167322
\(502\) 31.3931 1.40114
\(503\) 39.4518 1.75907 0.879534 0.475836i \(-0.157854\pi\)
0.879534 + 0.475836i \(0.157854\pi\)
\(504\) −61.6162 −2.74460
\(505\) 38.0969 1.69529
\(506\) 90.5091 4.02362
\(507\) 3.37813 0.150028
\(508\) 24.2824 1.07736
\(509\) −13.5318 −0.599788 −0.299894 0.953973i \(-0.596951\pi\)
−0.299894 + 0.953973i \(0.596951\pi\)
\(510\) 2.72619 0.120718
\(511\) −20.4863 −0.906258
\(512\) 46.9934 2.07684
\(513\) −8.10685 −0.357926
\(514\) 22.7211 1.00219
\(515\) −20.3924 −0.898596
\(516\) 13.1536 0.579057
\(517\) 21.8243 0.959833
\(518\) −105.641 −4.64162
\(519\) 1.89546 0.0832014
\(520\) −11.7770 −0.516454
\(521\) 30.1322 1.32012 0.660058 0.751215i \(-0.270532\pi\)
0.660058 + 0.751215i \(0.270532\pi\)
\(522\) −5.79235 −0.253524
\(523\) 20.9590 0.916472 0.458236 0.888831i \(-0.348482\pi\)
0.458236 + 0.888831i \(0.348482\pi\)
\(524\) 20.9094 0.913433
\(525\) 4.08247 0.178174
\(526\) 43.4146 1.89297
\(527\) −2.09843 −0.0914092
\(528\) 8.58275 0.373516
\(529\) 14.5929 0.634473
\(530\) −7.46890 −0.324428
\(531\) −3.58586 −0.155613
\(532\) 81.1976 3.52036
\(533\) −5.62196 −0.243514
\(534\) 4.90485 0.212254
\(535\) −21.6263 −0.934985
\(536\) −33.8394 −1.46164
\(537\) −5.06340 −0.218502
\(538\) 30.0913 1.29733
\(539\) −44.2142 −1.90444
\(540\) −20.2480 −0.871334
\(541\) 11.7712 0.506082 0.253041 0.967456i \(-0.418569\pi\)
0.253041 + 0.967456i \(0.418569\pi\)
\(542\) −42.8245 −1.83947
\(543\) −6.43944 −0.276343
\(544\) 3.11361 0.133495
\(545\) 52.5969 2.25301
\(546\) 1.82227 0.0779858
\(547\) −38.8657 −1.66178 −0.830888 0.556440i \(-0.812167\pi\)
−0.830888 + 0.556440i \(0.812167\pi\)
\(548\) 89.0031 3.80202
\(549\) −5.70726 −0.243580
\(550\) 58.6005 2.49873
\(551\) 4.01484 0.171038
\(552\) 9.17377 0.390461
\(553\) −38.2215 −1.62534
\(554\) −66.4196 −2.82190
\(555\) −9.01709 −0.382754
\(556\) −53.3903 −2.26425
\(557\) −9.30813 −0.394398 −0.197199 0.980363i \(-0.563185\pi\)
−0.197199 + 0.980363i \(0.563185\pi\)
\(558\) 11.3451 0.480275
\(559\) 8.19344 0.346545
\(560\) 61.0991 2.58191
\(561\) −2.16059 −0.0912200
\(562\) −3.01587 −0.127217
\(563\) −46.8765 −1.97561 −0.987804 0.155705i \(-0.950235\pi\)
−0.987804 + 0.155705i \(0.950235\pi\)
\(564\) 4.20564 0.177089
\(565\) 2.14436 0.0902137
\(566\) 22.8495 0.960435
\(567\) −31.7529 −1.33350
\(568\) 73.3711 3.07858
\(569\) 4.50586 0.188895 0.0944477 0.995530i \(-0.469891\pi\)
0.0944477 + 0.995530i \(0.469891\pi\)
\(570\) 10.2160 0.427901
\(571\) 19.3350 0.809144 0.404572 0.914506i \(-0.367421\pi\)
0.404572 + 0.914506i \(0.367421\pi\)
\(572\) 17.7454 0.741971
\(573\) 0.584884 0.0244339
\(574\) 75.0580 3.13286
\(575\) 24.3397 1.01503
\(576\) 14.5612 0.606718
\(577\) 11.9494 0.497461 0.248731 0.968573i \(-0.419987\pi\)
0.248731 + 0.968573i \(0.419987\pi\)
\(578\) 37.8495 1.57433
\(579\) 2.53366 0.105295
\(580\) 10.0276 0.416374
\(581\) −50.7969 −2.10741
\(582\) −8.66147 −0.359030
\(583\) 5.91933 0.245154
\(584\) −29.8055 −1.23336
\(585\) −6.22849 −0.257516
\(586\) 33.0148 1.36383
\(587\) −44.6268 −1.84195 −0.920973 0.389626i \(-0.872604\pi\)
−0.920973 + 0.389626i \(0.872604\pi\)
\(588\) −8.52026 −0.351370
\(589\) −7.86358 −0.324013
\(590\) 9.15042 0.376717
\(591\) 4.46723 0.183757
\(592\) −59.7255 −2.45470
\(593\) 33.5780 1.37888 0.689442 0.724341i \(-0.257856\pi\)
0.689442 + 0.724341i \(0.257856\pi\)
\(594\) 23.6539 0.970531
\(595\) −15.3808 −0.630552
\(596\) 86.9684 3.56236
\(597\) 0.251973 0.0103126
\(598\) 10.8643 0.444276
\(599\) −7.11680 −0.290784 −0.145392 0.989374i \(-0.546444\pi\)
−0.145392 + 0.989374i \(0.546444\pi\)
\(600\) 5.93960 0.242483
\(601\) −8.78356 −0.358289 −0.179144 0.983823i \(-0.557333\pi\)
−0.179144 + 0.983823i \(0.557333\pi\)
\(602\) −109.389 −4.45838
\(603\) −17.8967 −0.728809
\(604\) −4.21918 −0.171676
\(605\) −71.9941 −2.92698
\(606\) −8.57634 −0.348390
\(607\) 19.7804 0.802862 0.401431 0.915889i \(-0.368513\pi\)
0.401431 + 0.915889i \(0.368513\pi\)
\(608\) 11.6678 0.473193
\(609\) −0.816094 −0.0330698
\(610\) 14.5638 0.589672
\(611\) 2.61970 0.105982
\(612\) 16.6725 0.673946
\(613\) −37.0598 −1.49683 −0.748415 0.663231i \(-0.769185\pi\)
−0.748415 + 0.663231i \(0.769185\pi\)
\(614\) 30.7110 1.23940
\(615\) 6.40663 0.258340
\(616\) −124.612 −5.02074
\(617\) 0.629611 0.0253472 0.0126736 0.999920i \(-0.495966\pi\)
0.0126736 + 0.999920i \(0.495966\pi\)
\(618\) 4.59071 0.184666
\(619\) −13.4695 −0.541385 −0.270692 0.962666i \(-0.587253\pi\)
−0.270692 + 0.962666i \(0.587253\pi\)
\(620\) −19.6404 −0.788776
\(621\) 9.82463 0.394249
\(622\) −44.3983 −1.78021
\(623\) −27.6726 −1.10868
\(624\) 1.03024 0.0412425
\(625\) −29.0899 −1.16359
\(626\) −11.4760 −0.458674
\(627\) −8.09649 −0.323343
\(628\) 13.7944 0.550455
\(629\) 15.0350 0.599487
\(630\) 83.1557 3.31300
\(631\) −17.0508 −0.678781 −0.339390 0.940646i \(-0.610221\pi\)
−0.339390 + 0.940646i \(0.610221\pi\)
\(632\) −55.6085 −2.21199
\(633\) −3.33905 −0.132715
\(634\) 64.9005 2.57753
\(635\) −17.2367 −0.684017
\(636\) 1.14068 0.0452309
\(637\) −5.30729 −0.210283
\(638\) −11.7144 −0.463776
\(639\) 38.8038 1.53505
\(640\) −50.9715 −2.01482
\(641\) −25.8251 −1.02003 −0.510015 0.860165i \(-0.670360\pi\)
−0.510015 + 0.860165i \(0.670360\pi\)
\(642\) 4.86848 0.192144
\(643\) −9.98445 −0.393748 −0.196874 0.980429i \(-0.563079\pi\)
−0.196874 + 0.980429i \(0.563079\pi\)
\(644\) −98.4028 −3.87761
\(645\) −9.33700 −0.367644
\(646\) −17.0341 −0.670197
\(647\) −28.3035 −1.11273 −0.556363 0.830939i \(-0.687804\pi\)
−0.556363 + 0.830939i \(0.687804\pi\)
\(648\) −46.1973 −1.81480
\(649\) −7.25199 −0.284666
\(650\) 7.03416 0.275903
\(651\) 1.59843 0.0626473
\(652\) −19.4898 −0.763279
\(653\) 6.16685 0.241327 0.120664 0.992693i \(-0.461498\pi\)
0.120664 + 0.992693i \(0.461498\pi\)
\(654\) −11.8406 −0.463003
\(655\) −14.8424 −0.579940
\(656\) 42.4349 1.65680
\(657\) −15.7632 −0.614982
\(658\) −34.9753 −1.36348
\(659\) 7.71567 0.300560 0.150280 0.988643i \(-0.451983\pi\)
0.150280 + 0.988643i \(0.451983\pi\)
\(660\) −20.2221 −0.787144
\(661\) 6.20728 0.241435 0.120718 0.992687i \(-0.461480\pi\)
0.120718 + 0.992687i \(0.461480\pi\)
\(662\) 86.9052 3.37767
\(663\) −0.259348 −0.0100722
\(664\) −73.9044 −2.86805
\(665\) −57.6375 −2.23509
\(666\) −81.2862 −3.14978
\(667\) −4.86555 −0.188395
\(668\) 58.4475 2.26140
\(669\) 7.14989 0.276431
\(670\) 45.6688 1.76434
\(671\) −11.5423 −0.445585
\(672\) −2.37171 −0.0914909
\(673\) 1.45038 0.0559082 0.0279541 0.999609i \(-0.491101\pi\)
0.0279541 + 0.999609i \(0.491101\pi\)
\(674\) 48.4989 1.86811
\(675\) 6.36100 0.244835
\(676\) −52.7193 −2.02767
\(677\) 7.96736 0.306210 0.153105 0.988210i \(-0.451073\pi\)
0.153105 + 0.988210i \(0.451073\pi\)
\(678\) −0.482735 −0.0185393
\(679\) 48.8671 1.87535
\(680\) −22.3776 −0.858141
\(681\) 7.44779 0.285400
\(682\) 22.9441 0.878574
\(683\) −12.7448 −0.487667 −0.243833 0.969817i \(-0.578405\pi\)
−0.243833 + 0.969817i \(0.578405\pi\)
\(684\) 62.4779 2.38890
\(685\) −63.1781 −2.41391
\(686\) 4.45343 0.170033
\(687\) −4.72821 −0.180392
\(688\) −61.8445 −2.35780
\(689\) 0.710532 0.0270691
\(690\) −12.3807 −0.471325
\(691\) 10.4885 0.399002 0.199501 0.979898i \(-0.436068\pi\)
0.199501 + 0.979898i \(0.436068\pi\)
\(692\) −29.5806 −1.12449
\(693\) −65.9034 −2.50346
\(694\) 4.96346 0.188411
\(695\) 37.8987 1.43758
\(696\) −1.18734 −0.0450059
\(697\) −10.6824 −0.404624
\(698\) 71.0689 2.69000
\(699\) −4.22932 −0.159967
\(700\) −63.7113 −2.40806
\(701\) −8.51378 −0.321561 −0.160781 0.986990i \(-0.551401\pi\)
−0.160781 + 0.986990i \(0.551401\pi\)
\(702\) 2.83932 0.107163
\(703\) 56.3417 2.12497
\(704\) 29.4484 1.10988
\(705\) −2.98534 −0.112434
\(706\) 30.8624 1.16152
\(707\) 48.3867 1.81977
\(708\) −1.39749 −0.0525208
\(709\) 12.5248 0.470378 0.235189 0.971950i \(-0.424429\pi\)
0.235189 + 0.971950i \(0.424429\pi\)
\(710\) −99.0197 −3.71614
\(711\) −29.4097 −1.10295
\(712\) −40.2609 −1.50884
\(713\) 9.52981 0.356894
\(714\) 3.46251 0.129581
\(715\) −12.5964 −0.471078
\(716\) 79.0197 2.95310
\(717\) −0.833589 −0.0311310
\(718\) −46.5501 −1.73723
\(719\) 15.4011 0.574366 0.287183 0.957876i \(-0.407281\pi\)
0.287183 + 0.957876i \(0.407281\pi\)
\(720\) 47.0130 1.75207
\(721\) −25.9003 −0.964577
\(722\) −16.4501 −0.612210
\(723\) 3.73892 0.139052
\(724\) 100.494 3.73484
\(725\) −3.15022 −0.116996
\(726\) 16.2072 0.601507
\(727\) 28.9939 1.07532 0.537662 0.843161i \(-0.319308\pi\)
0.537662 + 0.843161i \(0.319308\pi\)
\(728\) −14.9579 −0.554375
\(729\) −23.1328 −0.856769
\(730\) 40.2247 1.48878
\(731\) 15.5685 0.575821
\(732\) −2.22424 −0.0822104
\(733\) 12.5287 0.462758 0.231379 0.972864i \(-0.425676\pi\)
0.231379 + 0.972864i \(0.425676\pi\)
\(734\) −51.5990 −1.90455
\(735\) 6.04804 0.223085
\(736\) −14.1401 −0.521213
\(737\) −36.1940 −1.33322
\(738\) 57.7537 2.12594
\(739\) 34.7636 1.27880 0.639400 0.768874i \(-0.279183\pi\)
0.639400 + 0.768874i \(0.279183\pi\)
\(740\) 140.721 5.17301
\(741\) −0.971869 −0.0357025
\(742\) −9.48621 −0.348250
\(743\) −17.8328 −0.654223 −0.327112 0.944986i \(-0.606075\pi\)
−0.327112 + 0.944986i \(0.606075\pi\)
\(744\) 2.32555 0.0852589
\(745\) −61.7338 −2.26175
\(746\) −77.6199 −2.84187
\(747\) −39.0859 −1.43008
\(748\) 33.7182 1.23286
\(749\) −27.4674 −1.00364
\(750\) 2.08036 0.0759641
\(751\) −32.8177 −1.19753 −0.598767 0.800923i \(-0.704343\pi\)
−0.598767 + 0.800923i \(0.704343\pi\)
\(752\) −19.7737 −0.721071
\(753\) 3.40332 0.124024
\(754\) −1.40614 −0.0512087
\(755\) 2.99495 0.108997
\(756\) −25.7169 −0.935313
\(757\) 19.2850 0.700925 0.350463 0.936577i \(-0.386024\pi\)
0.350463 + 0.936577i \(0.386024\pi\)
\(758\) −63.0047 −2.28843
\(759\) 9.81207 0.356156
\(760\) −83.8568 −3.04181
\(761\) −9.65993 −0.350172 −0.175086 0.984553i \(-0.556020\pi\)
−0.175086 + 0.984553i \(0.556020\pi\)
\(762\) 3.88030 0.140569
\(763\) 66.8031 2.41844
\(764\) −9.12774 −0.330230
\(765\) −11.8348 −0.427890
\(766\) −82.6893 −2.98769
\(767\) −0.870499 −0.0314319
\(768\) 8.78463 0.316988
\(769\) 5.82885 0.210194 0.105097 0.994462i \(-0.466485\pi\)
0.105097 + 0.994462i \(0.466485\pi\)
\(770\) 168.173 6.06052
\(771\) 2.46319 0.0887097
\(772\) −39.5405 −1.42309
\(773\) 8.60045 0.309337 0.154668 0.987966i \(-0.450569\pi\)
0.154668 + 0.987966i \(0.450569\pi\)
\(774\) −84.1701 −3.02543
\(775\) 6.17012 0.221637
\(776\) 71.0967 2.55222
\(777\) −11.4526 −0.410858
\(778\) 6.96303 0.249637
\(779\) −40.0307 −1.43425
\(780\) −2.42738 −0.0869140
\(781\) 78.4761 2.80810
\(782\) 20.6435 0.738210
\(783\) −1.27158 −0.0454424
\(784\) 40.0598 1.43071
\(785\) −9.79181 −0.349485
\(786\) 3.34130 0.119180
\(787\) 21.7986 0.777037 0.388518 0.921441i \(-0.372987\pi\)
0.388518 + 0.921441i \(0.372987\pi\)
\(788\) −69.7159 −2.48352
\(789\) 4.70657 0.167558
\(790\) 75.0478 2.67008
\(791\) 2.72354 0.0968378
\(792\) −95.8829 −3.40705
\(793\) −1.38549 −0.0492001
\(794\) 62.5821 2.22095
\(795\) −0.809702 −0.0287172
\(796\) −3.93230 −0.139377
\(797\) −45.0899 −1.59717 −0.798584 0.601883i \(-0.794417\pi\)
−0.798584 + 0.601883i \(0.794417\pi\)
\(798\) 12.9753 0.459320
\(799\) 4.97774 0.176100
\(800\) −9.15510 −0.323682
\(801\) −21.2928 −0.752344
\(802\) −46.5152 −1.64251
\(803\) −31.8793 −1.12500
\(804\) −6.97472 −0.245980
\(805\) 69.8504 2.46190
\(806\) 2.75411 0.0970095
\(807\) 3.26219 0.114835
\(808\) 70.3979 2.47659
\(809\) 10.5838 0.372107 0.186054 0.982540i \(-0.440430\pi\)
0.186054 + 0.982540i \(0.440430\pi\)
\(810\) 62.3467 2.19064
\(811\) 49.0823 1.72351 0.861756 0.507323i \(-0.169365\pi\)
0.861756 + 0.507323i \(0.169365\pi\)
\(812\) 12.7360 0.446946
\(813\) −4.64260 −0.162823
\(814\) −164.392 −5.76193
\(815\) 13.8347 0.484607
\(816\) 1.95757 0.0685287
\(817\) 58.3406 2.04108
\(818\) −39.9567 −1.39705
\(819\) −7.91077 −0.276425
\(820\) −99.9821 −3.49153
\(821\) −45.1254 −1.57489 −0.787443 0.616387i \(-0.788596\pi\)
−0.787443 + 0.616387i \(0.788596\pi\)
\(822\) 14.2226 0.496070
\(823\) −24.2784 −0.846291 −0.423146 0.906062i \(-0.639074\pi\)
−0.423146 + 0.906062i \(0.639074\pi\)
\(824\) −37.6823 −1.31273
\(825\) 6.35287 0.221178
\(826\) 11.6219 0.404378
\(827\) −40.3463 −1.40298 −0.701489 0.712680i \(-0.747481\pi\)
−0.701489 + 0.712680i \(0.747481\pi\)
\(828\) −75.7164 −2.63133
\(829\) 55.2221 1.91794 0.958971 0.283504i \(-0.0914969\pi\)
0.958971 + 0.283504i \(0.0914969\pi\)
\(830\) 99.7395 3.46201
\(831\) −7.20054 −0.249784
\(832\) 3.53486 0.122549
\(833\) −10.0845 −0.349406
\(834\) −8.53171 −0.295429
\(835\) −41.4885 −1.43577
\(836\) 126.354 4.37005
\(837\) 2.49055 0.0860859
\(838\) −80.3833 −2.77679
\(839\) −18.1392 −0.626233 −0.313117 0.949715i \(-0.601373\pi\)
−0.313117 + 0.949715i \(0.601373\pi\)
\(840\) 17.0455 0.588127
\(841\) −28.3703 −0.978285
\(842\) 9.75607 0.336217
\(843\) −0.326950 −0.0112608
\(844\) 52.1094 1.79368
\(845\) 37.4224 1.28737
\(846\) −26.9119 −0.925249
\(847\) −91.4394 −3.14189
\(848\) −5.36314 −0.184171
\(849\) 2.47711 0.0850140
\(850\) 13.3657 0.458440
\(851\) −68.2801 −2.34061
\(852\) 15.1227 0.518094
\(853\) −1.67034 −0.0571914 −0.0285957 0.999591i \(-0.509104\pi\)
−0.0285957 + 0.999591i \(0.509104\pi\)
\(854\) 18.4974 0.632970
\(855\) −44.3494 −1.51672
\(856\) −39.9624 −1.36589
\(857\) 9.03369 0.308585 0.154292 0.988025i \(-0.450690\pi\)
0.154292 + 0.988025i \(0.450690\pi\)
\(858\) 2.83569 0.0968087
\(859\) −36.1729 −1.23420 −0.617101 0.786884i \(-0.711693\pi\)
−0.617101 + 0.786884i \(0.711693\pi\)
\(860\) 145.714 4.96880
\(861\) 8.13703 0.277309
\(862\) −47.0147 −1.60133
\(863\) −40.4673 −1.37752 −0.688761 0.724989i \(-0.741845\pi\)
−0.688761 + 0.724989i \(0.741845\pi\)
\(864\) −3.69542 −0.125721
\(865\) 20.9976 0.713939
\(866\) 67.4757 2.29292
\(867\) 4.10325 0.139354
\(868\) −24.9451 −0.846693
\(869\) −59.4777 −2.01764
\(870\) 1.60240 0.0543264
\(871\) −4.34457 −0.147210
\(872\) 97.1919 3.29133
\(873\) 37.6010 1.27260
\(874\) 77.3585 2.61669
\(875\) −11.7372 −0.396789
\(876\) −6.14327 −0.207562
\(877\) −38.4110 −1.29705 −0.648524 0.761194i \(-0.724614\pi\)
−0.648524 + 0.761194i \(0.724614\pi\)
\(878\) −47.2593 −1.59492
\(879\) 3.57913 0.120721
\(880\) 95.0783 3.20509
\(881\) −7.06338 −0.237971 −0.118986 0.992896i \(-0.537964\pi\)
−0.118986 + 0.992896i \(0.537964\pi\)
\(882\) 54.5212 1.83582
\(883\) 7.98840 0.268831 0.134416 0.990925i \(-0.457084\pi\)
0.134416 + 0.990925i \(0.457084\pi\)
\(884\) 4.04740 0.136129
\(885\) 0.991995 0.0333456
\(886\) 85.9509 2.88758
\(887\) 29.8603 1.00261 0.501305 0.865270i \(-0.332853\pi\)
0.501305 + 0.865270i \(0.332853\pi\)
\(888\) −16.6623 −0.559152
\(889\) −21.8922 −0.734242
\(890\) 54.3351 1.82132
\(891\) −49.4117 −1.65535
\(892\) −111.582 −3.73603
\(893\) 18.6534 0.624211
\(894\) 13.8974 0.464800
\(895\) −56.0915 −1.87493
\(896\) −64.7386 −2.16277
\(897\) 1.17780 0.0393256
\(898\) −13.6646 −0.455994
\(899\) −1.23342 −0.0411368
\(900\) −49.0229 −1.63410
\(901\) 1.35009 0.0449781
\(902\) 116.800 3.88902
\(903\) −11.8589 −0.394639
\(904\) 3.96248 0.131790
\(905\) −71.3351 −2.37126
\(906\) −0.674220 −0.0223995
\(907\) 30.3325 1.00717 0.503587 0.863944i \(-0.332013\pi\)
0.503587 + 0.863944i \(0.332013\pi\)
\(908\) −116.231 −3.85725
\(909\) 37.2314 1.23489
\(910\) 20.1868 0.669184
\(911\) −20.5698 −0.681507 −0.340753 0.940153i \(-0.610682\pi\)
−0.340753 + 0.940153i \(0.610682\pi\)
\(912\) 7.33572 0.242910
\(913\) −79.0466 −2.61606
\(914\) −8.25669 −0.273107
\(915\) 1.57886 0.0521956
\(916\) 73.7886 2.43804
\(917\) −18.8513 −0.622523
\(918\) 5.39503 0.178062
\(919\) −10.0515 −0.331569 −0.165784 0.986162i \(-0.553016\pi\)
−0.165784 + 0.986162i \(0.553016\pi\)
\(920\) 101.625 3.35049
\(921\) 3.32937 0.109707
\(922\) −9.45804 −0.311484
\(923\) 9.41995 0.310062
\(924\) −25.6840 −0.844941
\(925\) −44.2082 −1.45356
\(926\) 50.2467 1.65121
\(927\) −19.9291 −0.654557
\(928\) 1.83012 0.0600767
\(929\) 38.7601 1.27168 0.635839 0.771822i \(-0.280654\pi\)
0.635839 + 0.771822i \(0.280654\pi\)
\(930\) −3.13851 −0.102916
\(931\) −37.7901 −1.23852
\(932\) 66.0029 2.16200
\(933\) −4.81321 −0.157577
\(934\) −68.2000 −2.23157
\(935\) −23.9346 −0.782745
\(936\) −11.5094 −0.376196
\(937\) 28.0589 0.916645 0.458323 0.888786i \(-0.348450\pi\)
0.458323 + 0.888786i \(0.348450\pi\)
\(938\) 58.0038 1.89389
\(939\) −1.24411 −0.0406001
\(940\) 46.5893 1.51958
\(941\) −0.0441714 −0.00143995 −0.000719974 1.00000i \(-0.500229\pi\)
−0.000719974 1.00000i \(0.500229\pi\)
\(942\) 2.20432 0.0718207
\(943\) 48.5129 1.57980
\(944\) 6.57058 0.213854
\(945\) 18.2549 0.593832
\(946\) −170.224 −5.53447
\(947\) 28.2800 0.918975 0.459488 0.888184i \(-0.348033\pi\)
0.459488 + 0.888184i \(0.348033\pi\)
\(948\) −11.4616 −0.372255
\(949\) −3.82666 −0.124219
\(950\) 50.0861 1.62501
\(951\) 7.03585 0.228153
\(952\) −28.4217 −0.921151
\(953\) −26.8106 −0.868481 −0.434240 0.900797i \(-0.642983\pi\)
−0.434240 + 0.900797i \(0.642983\pi\)
\(954\) −7.29921 −0.236321
\(955\) 6.47925 0.209664
\(956\) 13.0090 0.420742
\(957\) −1.26995 −0.0410517
\(958\) −76.7520 −2.47975
\(959\) −80.2422 −2.59116
\(960\) −4.02823 −0.130010
\(961\) −28.5842 −0.922071
\(962\) −19.7329 −0.636215
\(963\) −21.1349 −0.681064
\(964\) −58.3498 −1.87932
\(965\) 28.0675 0.903525
\(966\) −15.7246 −0.505932
\(967\) −28.5787 −0.919028 −0.459514 0.888171i \(-0.651976\pi\)
−0.459514 + 0.888171i \(0.651976\pi\)
\(968\) −133.035 −4.27591
\(969\) −1.84666 −0.0593234
\(970\) −95.9503 −3.08078
\(971\) −6.40099 −0.205417 −0.102709 0.994711i \(-0.532751\pi\)
−0.102709 + 0.994711i \(0.532751\pi\)
\(972\) −29.8039 −0.955962
\(973\) 48.1349 1.54313
\(974\) 8.21337 0.263173
\(975\) 0.762572 0.0244219
\(976\) 10.4577 0.334744
\(977\) 15.9966 0.511775 0.255887 0.966707i \(-0.417632\pi\)
0.255887 + 0.966707i \(0.417632\pi\)
\(978\) −3.11444 −0.0995889
\(979\) −43.0622 −1.37627
\(980\) −94.3860 −3.01505
\(981\) 51.4020 1.64114
\(982\) 19.5050 0.622429
\(983\) 46.7269 1.49036 0.745178 0.666866i \(-0.232364\pi\)
0.745178 + 0.666866i \(0.232364\pi\)
\(984\) 11.8386 0.377400
\(985\) 49.4872 1.57679
\(986\) −2.67183 −0.0850885
\(987\) −3.79166 −0.120690
\(988\) 15.1670 0.482528
\(989\) −70.7026 −2.24821
\(990\) 129.401 4.11264
\(991\) −11.5653 −0.367383 −0.183691 0.982984i \(-0.558805\pi\)
−0.183691 + 0.982984i \(0.558805\pi\)
\(992\) −3.58453 −0.113809
\(993\) 9.42138 0.298978
\(994\) −125.764 −3.98901
\(995\) 2.79131 0.0884905
\(996\) −15.2326 −0.482664
\(997\) 8.85376 0.280401 0.140201 0.990123i \(-0.455225\pi\)
0.140201 + 0.990123i \(0.455225\pi\)
\(998\) −65.6940 −2.07951
\(999\) −17.8445 −0.564575
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.1.11 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.b.1.11 153 1.1 even 1 trivial