Properties

Label 4033.2.a.f.1.6
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4033 = 37 \cdot 109 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4033.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
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 \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.42751 q^{2} +0.768452 q^{3} +3.89281 q^{4} -1.80408 q^{5} -1.86543 q^{6} -1.49541 q^{7} -4.59481 q^{8} -2.40948 q^{9} +O(q^{10})\) \(q-2.42751 q^{2} +0.768452 q^{3} +3.89281 q^{4} -1.80408 q^{5} -1.86543 q^{6} -1.49541 q^{7} -4.59481 q^{8} -2.40948 q^{9} +4.37943 q^{10} +2.97086 q^{11} +2.99144 q^{12} -1.84647 q^{13} +3.63013 q^{14} -1.38635 q^{15} +3.36833 q^{16} -6.82756 q^{17} +5.84904 q^{18} -5.71406 q^{19} -7.02294 q^{20} -1.14915 q^{21} -7.21179 q^{22} -5.61717 q^{23} -3.53089 q^{24} -1.74529 q^{25} +4.48233 q^{26} -4.15693 q^{27} -5.82136 q^{28} -3.47630 q^{29} +3.36538 q^{30} -5.39445 q^{31} +1.01295 q^{32} +2.28296 q^{33} +16.5740 q^{34} +2.69785 q^{35} -9.37964 q^{36} +1.00000 q^{37} +13.8709 q^{38} -1.41893 q^{39} +8.28942 q^{40} +3.17793 q^{41} +2.78958 q^{42} +7.12496 q^{43} +11.5650 q^{44} +4.34690 q^{45} +13.6357 q^{46} +9.94586 q^{47} +2.58841 q^{48} -4.76374 q^{49} +4.23670 q^{50} -5.24666 q^{51} -7.18796 q^{52} -2.03347 q^{53} +10.0910 q^{54} -5.35967 q^{55} +6.87114 q^{56} -4.39098 q^{57} +8.43875 q^{58} -0.552160 q^{59} -5.39680 q^{60} -1.33903 q^{61} +13.0951 q^{62} +3.60317 q^{63} -9.19562 q^{64} +3.33119 q^{65} -5.54192 q^{66} -13.5490 q^{67} -26.5784 q^{68} -4.31652 q^{69} -6.54906 q^{70} +3.11420 q^{71} +11.0711 q^{72} +5.87331 q^{73} -2.42751 q^{74} -1.34117 q^{75} -22.2437 q^{76} -4.44266 q^{77} +3.44446 q^{78} -3.44403 q^{79} -6.07675 q^{80} +4.03404 q^{81} -7.71445 q^{82} +10.5073 q^{83} -4.47344 q^{84} +12.3175 q^{85} -17.2959 q^{86} -2.67137 q^{87} -13.6505 q^{88} -7.22436 q^{89} -10.5521 q^{90} +2.76124 q^{91} -21.8665 q^{92} -4.14538 q^{93} -24.1437 q^{94} +10.3086 q^{95} +0.778405 q^{96} +7.20542 q^{97} +11.5640 q^{98} -7.15822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42751 −1.71651 −0.858255 0.513224i \(-0.828451\pi\)
−0.858255 + 0.513224i \(0.828451\pi\)
\(3\) 0.768452 0.443666 0.221833 0.975085i \(-0.428796\pi\)
0.221833 + 0.975085i \(0.428796\pi\)
\(4\) 3.89281 1.94640
\(5\) −1.80408 −0.806810 −0.403405 0.915022i \(-0.632173\pi\)
−0.403405 + 0.915022i \(0.632173\pi\)
\(6\) −1.86543 −0.761557
\(7\) −1.49541 −0.565213 −0.282607 0.959236i \(-0.591199\pi\)
−0.282607 + 0.959236i \(0.591199\pi\)
\(8\) −4.59481 −1.62451
\(9\) −2.40948 −0.803160
\(10\) 4.37943 1.38490
\(11\) 2.97086 0.895747 0.447874 0.894097i \(-0.352181\pi\)
0.447874 + 0.894097i \(0.352181\pi\)
\(12\) 2.99144 0.863554
\(13\) −1.84647 −0.512119 −0.256060 0.966661i \(-0.582424\pi\)
−0.256060 + 0.966661i \(0.582424\pi\)
\(14\) 3.63013 0.970194
\(15\) −1.38635 −0.357954
\(16\) 3.36833 0.842084
\(17\) −6.82756 −1.65593 −0.827963 0.560782i \(-0.810501\pi\)
−0.827963 + 0.560782i \(0.810501\pi\)
\(18\) 5.84904 1.37863
\(19\) −5.71406 −1.31090 −0.655448 0.755240i \(-0.727520\pi\)
−0.655448 + 0.755240i \(0.727520\pi\)
\(20\) −7.02294 −1.57038
\(21\) −1.14915 −0.250766
\(22\) −7.21179 −1.53756
\(23\) −5.61717 −1.17126 −0.585630 0.810578i \(-0.699153\pi\)
−0.585630 + 0.810578i \(0.699153\pi\)
\(24\) −3.53089 −0.720740
\(25\) −1.74529 −0.349057
\(26\) 4.48233 0.879057
\(27\) −4.15693 −0.800001
\(28\) −5.82136 −1.10013
\(29\) −3.47630 −0.645532 −0.322766 0.946479i \(-0.604613\pi\)
−0.322766 + 0.946479i \(0.604613\pi\)
\(30\) 3.36538 0.614432
\(31\) −5.39445 −0.968873 −0.484436 0.874827i \(-0.660975\pi\)
−0.484436 + 0.874827i \(0.660975\pi\)
\(32\) 1.01295 0.179066
\(33\) 2.28296 0.397413
\(34\) 16.5740 2.84241
\(35\) 2.69785 0.456020
\(36\) −9.37964 −1.56327
\(37\) 1.00000 0.164399
\(38\) 13.8709 2.25016
\(39\) −1.41893 −0.227210
\(40\) 8.28942 1.31067
\(41\) 3.17793 0.496309 0.248154 0.968720i \(-0.420176\pi\)
0.248154 + 0.968720i \(0.420176\pi\)
\(42\) 2.78958 0.430442
\(43\) 7.12496 1.08655 0.543273 0.839556i \(-0.317185\pi\)
0.543273 + 0.839556i \(0.317185\pi\)
\(44\) 11.5650 1.74349
\(45\) 4.34690 0.647998
\(46\) 13.6357 2.01048
\(47\) 9.94586 1.45075 0.725376 0.688352i \(-0.241666\pi\)
0.725376 + 0.688352i \(0.241666\pi\)
\(48\) 2.58841 0.373604
\(49\) −4.76374 −0.680534
\(50\) 4.23670 0.599160
\(51\) −5.24666 −0.734679
\(52\) −7.18796 −0.996791
\(53\) −2.03347 −0.279319 −0.139659 0.990200i \(-0.544601\pi\)
−0.139659 + 0.990200i \(0.544601\pi\)
\(54\) 10.0910 1.37321
\(55\) −5.35967 −0.722698
\(56\) 6.87114 0.918195
\(57\) −4.39098 −0.581600
\(58\) 8.43875 1.10806
\(59\) −0.552160 −0.0718852 −0.0359426 0.999354i \(-0.511443\pi\)
−0.0359426 + 0.999354i \(0.511443\pi\)
\(60\) −5.39680 −0.696724
\(61\) −1.33903 −0.171445 −0.0857225 0.996319i \(-0.527320\pi\)
−0.0857225 + 0.996319i \(0.527320\pi\)
\(62\) 13.0951 1.66308
\(63\) 3.60317 0.453957
\(64\) −9.19562 −1.14945
\(65\) 3.33119 0.413183
\(66\) −5.54192 −0.682163
\(67\) −13.5490 −1.65528 −0.827639 0.561260i \(-0.810317\pi\)
−0.827639 + 0.561260i \(0.810317\pi\)
\(68\) −26.5784 −3.22310
\(69\) −4.31652 −0.519649
\(70\) −6.54906 −0.782762
\(71\) 3.11420 0.369588 0.184794 0.982777i \(-0.440838\pi\)
0.184794 + 0.982777i \(0.440838\pi\)
\(72\) 11.0711 1.30474
\(73\) 5.87331 0.687419 0.343710 0.939076i \(-0.388316\pi\)
0.343710 + 0.939076i \(0.388316\pi\)
\(74\) −2.42751 −0.282192
\(75\) −1.34117 −0.154865
\(76\) −22.2437 −2.55153
\(77\) −4.44266 −0.506288
\(78\) 3.44446 0.390008
\(79\) −3.44403 −0.387484 −0.193742 0.981053i \(-0.562062\pi\)
−0.193742 + 0.981053i \(0.562062\pi\)
\(80\) −6.07675 −0.679402
\(81\) 4.03404 0.448227
\(82\) −7.71445 −0.851919
\(83\) 10.5073 1.15332 0.576662 0.816983i \(-0.304355\pi\)
0.576662 + 0.816983i \(0.304355\pi\)
\(84\) −4.47344 −0.488092
\(85\) 12.3175 1.33602
\(86\) −17.2959 −1.86507
\(87\) −2.67137 −0.286401
\(88\) −13.6505 −1.45515
\(89\) −7.22436 −0.765781 −0.382890 0.923794i \(-0.625071\pi\)
−0.382890 + 0.923794i \(0.625071\pi\)
\(90\) −10.5521 −1.11229
\(91\) 2.76124 0.289456
\(92\) −21.8665 −2.27974
\(93\) −4.14538 −0.429856
\(94\) −24.1437 −2.49023
\(95\) 10.3086 1.05764
\(96\) 0.778405 0.0794457
\(97\) 7.20542 0.731600 0.365800 0.930694i \(-0.380795\pi\)
0.365800 + 0.930694i \(0.380795\pi\)
\(98\) 11.5640 1.16814
\(99\) −7.15822 −0.719429
\(100\) −6.79407 −0.679407
\(101\) 8.44211 0.840021 0.420011 0.907519i \(-0.362026\pi\)
0.420011 + 0.907519i \(0.362026\pi\)
\(102\) 12.7363 1.26108
\(103\) −9.22361 −0.908829 −0.454414 0.890790i \(-0.650151\pi\)
−0.454414 + 0.890790i \(0.650151\pi\)
\(104\) 8.48419 0.831943
\(105\) 2.07317 0.202321
\(106\) 4.93627 0.479453
\(107\) 15.7803 1.52554 0.762770 0.646670i \(-0.223839\pi\)
0.762770 + 0.646670i \(0.223839\pi\)
\(108\) −16.1821 −1.55713
\(109\) −1.00000 −0.0957826
\(110\) 13.0107 1.24052
\(111\) 0.768452 0.0729383
\(112\) −5.03705 −0.475957
\(113\) 6.58148 0.619134 0.309567 0.950878i \(-0.399816\pi\)
0.309567 + 0.950878i \(0.399816\pi\)
\(114\) 10.6592 0.998322
\(115\) 10.1338 0.944984
\(116\) −13.5326 −1.25647
\(117\) 4.44904 0.411314
\(118\) 1.34038 0.123392
\(119\) 10.2100 0.935952
\(120\) 6.37002 0.581501
\(121\) −2.17401 −0.197637
\(122\) 3.25051 0.294287
\(123\) 2.44209 0.220195
\(124\) −20.9996 −1.88582
\(125\) 12.1691 1.08843
\(126\) −8.74673 −0.779221
\(127\) 2.62821 0.233216 0.116608 0.993178i \(-0.462798\pi\)
0.116608 + 0.993178i \(0.462798\pi\)
\(128\) 20.2966 1.79398
\(129\) 5.47519 0.482064
\(130\) −8.08649 −0.709232
\(131\) −16.6664 −1.45615 −0.728075 0.685497i \(-0.759585\pi\)
−0.728075 + 0.685497i \(0.759585\pi\)
\(132\) 8.88713 0.773526
\(133\) 8.54489 0.740936
\(134\) 32.8904 2.84130
\(135\) 7.49944 0.645449
\(136\) 31.3713 2.69007
\(137\) −10.3835 −0.887120 −0.443560 0.896245i \(-0.646285\pi\)
−0.443560 + 0.896245i \(0.646285\pi\)
\(138\) 10.4784 0.891981
\(139\) −15.7388 −1.33495 −0.667473 0.744634i \(-0.732624\pi\)
−0.667473 + 0.744634i \(0.732624\pi\)
\(140\) 10.5022 0.887598
\(141\) 7.64292 0.643650
\(142\) −7.55975 −0.634400
\(143\) −5.48561 −0.458729
\(144\) −8.11594 −0.676328
\(145\) 6.27152 0.520822
\(146\) −14.2575 −1.17996
\(147\) −3.66071 −0.301930
\(148\) 3.89281 0.319987
\(149\) −13.3812 −1.09623 −0.548116 0.836402i \(-0.684655\pi\)
−0.548116 + 0.836402i \(0.684655\pi\)
\(150\) 3.25570 0.265827
\(151\) −5.21263 −0.424198 −0.212099 0.977248i \(-0.568030\pi\)
−0.212099 + 0.977248i \(0.568030\pi\)
\(152\) 26.2550 2.12956
\(153\) 16.4509 1.32997
\(154\) 10.7846 0.869048
\(155\) 9.73204 0.781696
\(156\) −5.52361 −0.442242
\(157\) 21.6289 1.72617 0.863085 0.505058i \(-0.168529\pi\)
0.863085 + 0.505058i \(0.168529\pi\)
\(158\) 8.36042 0.665120
\(159\) −1.56262 −0.123924
\(160\) −1.82745 −0.144472
\(161\) 8.39999 0.662012
\(162\) −9.79268 −0.769385
\(163\) 4.61421 0.361413 0.180706 0.983537i \(-0.442162\pi\)
0.180706 + 0.983537i \(0.442162\pi\)
\(164\) 12.3711 0.966017
\(165\) −4.11865 −0.320637
\(166\) −25.5065 −1.97969
\(167\) 7.92133 0.612971 0.306486 0.951875i \(-0.400847\pi\)
0.306486 + 0.951875i \(0.400847\pi\)
\(168\) 5.28014 0.407372
\(169\) −9.59054 −0.737734
\(170\) −29.9008 −2.29329
\(171\) 13.7679 1.05286
\(172\) 27.7361 2.11486
\(173\) 2.80971 0.213618 0.106809 0.994280i \(-0.465937\pi\)
0.106809 + 0.994280i \(0.465937\pi\)
\(174\) 6.48477 0.491609
\(175\) 2.60993 0.197292
\(176\) 10.0068 0.754294
\(177\) −0.424309 −0.0318930
\(178\) 17.5372 1.31447
\(179\) 23.4144 1.75008 0.875038 0.484055i \(-0.160837\pi\)
0.875038 + 0.484055i \(0.160837\pi\)
\(180\) 16.9217 1.26127
\(181\) −1.29466 −0.0962316 −0.0481158 0.998842i \(-0.515322\pi\)
−0.0481158 + 0.998842i \(0.515322\pi\)
\(182\) −6.70294 −0.496855
\(183\) −1.02898 −0.0760644
\(184\) 25.8098 1.90272
\(185\) −1.80408 −0.132639
\(186\) 10.0630 0.737852
\(187\) −20.2837 −1.48329
\(188\) 38.7173 2.82375
\(189\) 6.21633 0.452171
\(190\) −25.0243 −1.81546
\(191\) −10.4978 −0.759594 −0.379797 0.925070i \(-0.624006\pi\)
−0.379797 + 0.925070i \(0.624006\pi\)
\(192\) −7.06640 −0.509973
\(193\) −17.2135 −1.23906 −0.619528 0.784974i \(-0.712676\pi\)
−0.619528 + 0.784974i \(0.712676\pi\)
\(194\) −17.4912 −1.25580
\(195\) 2.55986 0.183315
\(196\) −18.5443 −1.32459
\(197\) −25.9580 −1.84943 −0.924715 0.380659i \(-0.875697\pi\)
−0.924715 + 0.380659i \(0.875697\pi\)
\(198\) 17.3767 1.23491
\(199\) −11.2636 −0.798453 −0.399227 0.916852i \(-0.630721\pi\)
−0.399227 + 0.916852i \(0.630721\pi\)
\(200\) 8.01926 0.567048
\(201\) −10.4118 −0.734391
\(202\) −20.4933 −1.44190
\(203\) 5.19850 0.364863
\(204\) −20.4242 −1.42998
\(205\) −5.73324 −0.400427
\(206\) 22.3904 1.56001
\(207\) 13.5345 0.940710
\(208\) −6.21954 −0.431247
\(209\) −16.9757 −1.17423
\(210\) −5.03264 −0.347285
\(211\) 13.5970 0.936059 0.468029 0.883713i \(-0.344964\pi\)
0.468029 + 0.883713i \(0.344964\pi\)
\(212\) −7.91591 −0.543667
\(213\) 2.39311 0.163974
\(214\) −38.3069 −2.61860
\(215\) −12.8540 −0.876636
\(216\) 19.1003 1.29961
\(217\) 8.06694 0.547619
\(218\) 2.42751 0.164412
\(219\) 4.51336 0.304985
\(220\) −20.8642 −1.40666
\(221\) 12.6069 0.848032
\(222\) −1.86543 −0.125199
\(223\) −4.64712 −0.311194 −0.155597 0.987821i \(-0.549730\pi\)
−0.155597 + 0.987821i \(0.549730\pi\)
\(224\) −1.51478 −0.101211
\(225\) 4.20524 0.280349
\(226\) −15.9766 −1.06275
\(227\) −1.34031 −0.0889596 −0.0444798 0.999010i \(-0.514163\pi\)
−0.0444798 + 0.999010i \(0.514163\pi\)
\(228\) −17.0933 −1.13203
\(229\) 16.5231 1.09187 0.545937 0.837826i \(-0.316174\pi\)
0.545937 + 0.837826i \(0.316174\pi\)
\(230\) −24.6000 −1.62207
\(231\) −3.41397 −0.224623
\(232\) 15.9729 1.04867
\(233\) 26.1575 1.71364 0.856818 0.515618i \(-0.172438\pi\)
0.856818 + 0.515618i \(0.172438\pi\)
\(234\) −10.8001 −0.706024
\(235\) −17.9431 −1.17048
\(236\) −2.14945 −0.139918
\(237\) −2.64657 −0.171913
\(238\) −24.7849 −1.60657
\(239\) −3.63978 −0.235438 −0.117719 0.993047i \(-0.537558\pi\)
−0.117719 + 0.993047i \(0.537558\pi\)
\(240\) −4.66970 −0.301428
\(241\) 28.8732 1.85989 0.929943 0.367704i \(-0.119856\pi\)
0.929943 + 0.367704i \(0.119856\pi\)
\(242\) 5.27742 0.339245
\(243\) 15.5708 0.998864
\(244\) −5.21258 −0.333701
\(245\) 8.59418 0.549062
\(246\) −5.92819 −0.377968
\(247\) 10.5509 0.671335
\(248\) 24.7865 1.57394
\(249\) 8.07435 0.511691
\(250\) −29.5405 −1.86831
\(251\) −9.68954 −0.611598 −0.305799 0.952096i \(-0.598924\pi\)
−0.305799 + 0.952096i \(0.598924\pi\)
\(252\) 14.0264 0.883583
\(253\) −16.6878 −1.04915
\(254\) −6.38001 −0.400317
\(255\) 9.46540 0.592746
\(256\) −30.8789 −1.92993
\(257\) −14.8035 −0.923416 −0.461708 0.887032i \(-0.652763\pi\)
−0.461708 + 0.887032i \(0.652763\pi\)
\(258\) −13.2911 −0.827467
\(259\) −1.49541 −0.0929205
\(260\) 12.9677 0.804221
\(261\) 8.37607 0.518466
\(262\) 40.4579 2.49950
\(263\) −6.50204 −0.400933 −0.200467 0.979701i \(-0.564246\pi\)
−0.200467 + 0.979701i \(0.564246\pi\)
\(264\) −10.4898 −0.645601
\(265\) 3.66855 0.225357
\(266\) −20.7428 −1.27182
\(267\) −5.55158 −0.339751
\(268\) −52.7438 −3.22184
\(269\) 3.12058 0.190265 0.0951326 0.995465i \(-0.469672\pi\)
0.0951326 + 0.995465i \(0.469672\pi\)
\(270\) −18.2050 −1.10792
\(271\) −26.9663 −1.63809 −0.819043 0.573732i \(-0.805495\pi\)
−0.819043 + 0.573732i \(0.805495\pi\)
\(272\) −22.9975 −1.39443
\(273\) 2.12188 0.128422
\(274\) 25.2060 1.52275
\(275\) −5.18500 −0.312667
\(276\) −16.8034 −1.01145
\(277\) 20.3106 1.22034 0.610172 0.792269i \(-0.291100\pi\)
0.610172 + 0.792269i \(0.291100\pi\)
\(278\) 38.2061 2.29145
\(279\) 12.9978 0.778160
\(280\) −12.3961 −0.740809
\(281\) −26.7524 −1.59591 −0.797956 0.602716i \(-0.794085\pi\)
−0.797956 + 0.602716i \(0.794085\pi\)
\(282\) −18.5533 −1.10483
\(283\) −13.2987 −0.790524 −0.395262 0.918568i \(-0.629346\pi\)
−0.395262 + 0.918568i \(0.629346\pi\)
\(284\) 12.1230 0.719367
\(285\) 7.92170 0.469241
\(286\) 13.3164 0.787413
\(287\) −4.75232 −0.280520
\(288\) −2.44069 −0.143819
\(289\) 29.6156 1.74209
\(290\) −15.2242 −0.893995
\(291\) 5.53702 0.324586
\(292\) 22.8637 1.33800
\(293\) 9.15156 0.534640 0.267320 0.963608i \(-0.413862\pi\)
0.267320 + 0.963608i \(0.413862\pi\)
\(294\) 8.88640 0.518266
\(295\) 0.996143 0.0579977
\(296\) −4.59481 −0.267068
\(297\) −12.3496 −0.716599
\(298\) 32.4830 1.88169
\(299\) 10.3719 0.599825
\(300\) −5.22092 −0.301430
\(301\) −10.6548 −0.614130
\(302\) 12.6537 0.728139
\(303\) 6.48736 0.372689
\(304\) −19.2469 −1.10388
\(305\) 2.41572 0.138324
\(306\) −39.9347 −2.28291
\(307\) −26.3195 −1.50214 −0.751068 0.660225i \(-0.770461\pi\)
−0.751068 + 0.660225i \(0.770461\pi\)
\(308\) −17.2944 −0.985441
\(309\) −7.08790 −0.403217
\(310\) −23.6246 −1.34179
\(311\) 31.0047 1.75812 0.879058 0.476715i \(-0.158173\pi\)
0.879058 + 0.476715i \(0.158173\pi\)
\(312\) 6.51969 0.369105
\(313\) −1.40460 −0.0793925 −0.0396963 0.999212i \(-0.512639\pi\)
−0.0396963 + 0.999212i \(0.512639\pi\)
\(314\) −52.5043 −2.96299
\(315\) −6.50041 −0.366257
\(316\) −13.4070 −0.754200
\(317\) 29.3446 1.64816 0.824079 0.566475i \(-0.191693\pi\)
0.824079 + 0.566475i \(0.191693\pi\)
\(318\) 3.79329 0.212717
\(319\) −10.3276 −0.578234
\(320\) 16.5897 0.927390
\(321\) 12.1264 0.676831
\(322\) −20.3911 −1.13635
\(323\) 39.0131 2.17075
\(324\) 15.7037 0.872430
\(325\) 3.22262 0.178759
\(326\) −11.2010 −0.620368
\(327\) −0.768452 −0.0424955
\(328\) −14.6020 −0.806259
\(329\) −14.8732 −0.819984
\(330\) 9.99807 0.550376
\(331\) −7.92208 −0.435437 −0.217719 0.976012i \(-0.569861\pi\)
−0.217719 + 0.976012i \(0.569861\pi\)
\(332\) 40.9028 2.24483
\(333\) −2.40948 −0.132039
\(334\) −19.2291 −1.05217
\(335\) 24.4436 1.33550
\(336\) −3.87074 −0.211166
\(337\) −30.1705 −1.64349 −0.821746 0.569853i \(-0.807000\pi\)
−0.821746 + 0.569853i \(0.807000\pi\)
\(338\) 23.2811 1.26633
\(339\) 5.05755 0.274689
\(340\) 47.9496 2.60043
\(341\) −16.0262 −0.867865
\(342\) −33.4218 −1.80724
\(343\) 17.5917 0.949860
\(344\) −32.7378 −1.76511
\(345\) 7.78737 0.419258
\(346\) −6.82059 −0.366677
\(347\) 11.0403 0.592677 0.296338 0.955083i \(-0.404234\pi\)
0.296338 + 0.955083i \(0.404234\pi\)
\(348\) −10.3991 −0.557451
\(349\) −7.66309 −0.410196 −0.205098 0.978741i \(-0.565751\pi\)
−0.205098 + 0.978741i \(0.565751\pi\)
\(350\) −6.33562 −0.338653
\(351\) 7.67565 0.409696
\(352\) 3.00934 0.160398
\(353\) 30.9741 1.64858 0.824291 0.566166i \(-0.191574\pi\)
0.824291 + 0.566166i \(0.191574\pi\)
\(354\) 1.03001 0.0547447
\(355\) −5.61827 −0.298187
\(356\) −28.1230 −1.49052
\(357\) 7.84592 0.415250
\(358\) −56.8387 −3.00402
\(359\) −16.3775 −0.864370 −0.432185 0.901785i \(-0.642257\pi\)
−0.432185 + 0.901785i \(0.642257\pi\)
\(360\) −19.9732 −1.05268
\(361\) 13.6505 0.718448
\(362\) 3.14281 0.165182
\(363\) −1.67062 −0.0876848
\(364\) 10.7490 0.563399
\(365\) −10.5959 −0.554617
\(366\) 2.49786 0.130565
\(367\) 6.75363 0.352537 0.176268 0.984342i \(-0.443597\pi\)
0.176268 + 0.984342i \(0.443597\pi\)
\(368\) −18.9205 −0.986299
\(369\) −7.65716 −0.398616
\(370\) 4.37943 0.227676
\(371\) 3.04088 0.157875
\(372\) −16.1372 −0.836673
\(373\) 7.94066 0.411152 0.205576 0.978641i \(-0.434093\pi\)
0.205576 + 0.978641i \(0.434093\pi\)
\(374\) 49.2389 2.54608
\(375\) 9.35134 0.482901
\(376\) −45.6993 −2.35676
\(377\) 6.41888 0.330589
\(378\) −15.0902 −0.776156
\(379\) −7.92977 −0.407325 −0.203663 0.979041i \(-0.565285\pi\)
−0.203663 + 0.979041i \(0.565285\pi\)
\(380\) 40.1295 2.05860
\(381\) 2.01965 0.103470
\(382\) 25.4835 1.30385
\(383\) 4.61879 0.236009 0.118004 0.993013i \(-0.462350\pi\)
0.118004 + 0.993013i \(0.462350\pi\)
\(384\) 15.5969 0.795928
\(385\) 8.01492 0.408478
\(386\) 41.7860 2.12685
\(387\) −17.1674 −0.872670
\(388\) 28.0493 1.42399
\(389\) −14.7434 −0.747521 −0.373760 0.927525i \(-0.621932\pi\)
−0.373760 + 0.927525i \(0.621932\pi\)
\(390\) −6.21408 −0.314662
\(391\) 38.3515 1.93952
\(392\) 21.8885 1.10553
\(393\) −12.8073 −0.646045
\(394\) 63.0133 3.17457
\(395\) 6.21332 0.312626
\(396\) −27.8656 −1.40030
\(397\) −10.5883 −0.531412 −0.265706 0.964054i \(-0.585605\pi\)
−0.265706 + 0.964054i \(0.585605\pi\)
\(398\) 27.3424 1.37055
\(399\) 6.56634 0.328728
\(400\) −5.87871 −0.293936
\(401\) 32.2288 1.60943 0.804715 0.593662i \(-0.202318\pi\)
0.804715 + 0.593662i \(0.202318\pi\)
\(402\) 25.2747 1.26059
\(403\) 9.96071 0.496178
\(404\) 32.8635 1.63502
\(405\) −7.27774 −0.361634
\(406\) −12.6194 −0.626291
\(407\) 2.97086 0.147260
\(408\) 24.1074 1.19349
\(409\) −0.719509 −0.0355775 −0.0177887 0.999842i \(-0.505663\pi\)
−0.0177887 + 0.999842i \(0.505663\pi\)
\(410\) 13.9175 0.687337
\(411\) −7.97921 −0.393585
\(412\) −35.9057 −1.76895
\(413\) 0.825708 0.0406304
\(414\) −32.8550 −1.61474
\(415\) −18.9560 −0.930514
\(416\) −1.87039 −0.0917033
\(417\) −12.0945 −0.592271
\(418\) 41.2086 2.01558
\(419\) −24.0515 −1.17499 −0.587496 0.809227i \(-0.699886\pi\)
−0.587496 + 0.809227i \(0.699886\pi\)
\(420\) 8.07045 0.393797
\(421\) −1.84902 −0.0901159 −0.0450579 0.998984i \(-0.514347\pi\)
−0.0450579 + 0.998984i \(0.514347\pi\)
\(422\) −33.0069 −1.60675
\(423\) −23.9644 −1.16519
\(424\) 9.34341 0.453756
\(425\) 11.9161 0.578014
\(426\) −5.80931 −0.281462
\(427\) 2.00240 0.0969030
\(428\) 61.4297 2.96932
\(429\) −4.21543 −0.203523
\(430\) 31.2032 1.50475
\(431\) −4.55937 −0.219617 −0.109809 0.993953i \(-0.535024\pi\)
−0.109809 + 0.993953i \(0.535024\pi\)
\(432\) −14.0019 −0.673668
\(433\) −2.12948 −0.102336 −0.0511681 0.998690i \(-0.516294\pi\)
−0.0511681 + 0.998690i \(0.516294\pi\)
\(434\) −19.5826 −0.939994
\(435\) 4.81937 0.231071
\(436\) −3.89281 −0.186432
\(437\) 32.0968 1.53540
\(438\) −10.9562 −0.523509
\(439\) −6.17343 −0.294642 −0.147321 0.989089i \(-0.547065\pi\)
−0.147321 + 0.989089i \(0.547065\pi\)
\(440\) 24.6267 1.17403
\(441\) 11.4781 0.546578
\(442\) −30.6034 −1.45565
\(443\) −36.6404 −1.74084 −0.870419 0.492312i \(-0.836152\pi\)
−0.870419 + 0.492312i \(0.836152\pi\)
\(444\) 2.99144 0.141967
\(445\) 13.0333 0.617840
\(446\) 11.2809 0.534167
\(447\) −10.2828 −0.486361
\(448\) 13.7513 0.649686
\(449\) −13.2742 −0.626450 −0.313225 0.949679i \(-0.601409\pi\)
−0.313225 + 0.949679i \(0.601409\pi\)
\(450\) −10.2083 −0.481222
\(451\) 9.44117 0.444567
\(452\) 25.6204 1.20508
\(453\) −4.00566 −0.188202
\(454\) 3.25362 0.152700
\(455\) −4.98150 −0.233536
\(456\) 20.1757 0.944816
\(457\) 9.93558 0.464767 0.232383 0.972624i \(-0.425348\pi\)
0.232383 + 0.972624i \(0.425348\pi\)
\(458\) −40.1099 −1.87421
\(459\) 28.3817 1.32474
\(460\) 39.4490 1.83932
\(461\) 18.0982 0.842917 0.421459 0.906848i \(-0.361518\pi\)
0.421459 + 0.906848i \(0.361518\pi\)
\(462\) 8.28746 0.385567
\(463\) 15.5171 0.721139 0.360569 0.932732i \(-0.382582\pi\)
0.360569 + 0.932732i \(0.382582\pi\)
\(464\) −11.7093 −0.543592
\(465\) 7.47861 0.346812
\(466\) −63.4977 −2.94147
\(467\) 28.8867 1.33672 0.668358 0.743840i \(-0.266997\pi\)
0.668358 + 0.743840i \(0.266997\pi\)
\(468\) 17.3193 0.800583
\(469\) 20.2614 0.935585
\(470\) 43.5572 2.00914
\(471\) 16.6207 0.765843
\(472\) 2.53707 0.116778
\(473\) 21.1672 0.973270
\(474\) 6.42459 0.295091
\(475\) 9.97268 0.457578
\(476\) 39.7457 1.82174
\(477\) 4.89961 0.224338
\(478\) 8.83560 0.404131
\(479\) −15.7258 −0.718528 −0.359264 0.933236i \(-0.616972\pi\)
−0.359264 + 0.933236i \(0.616972\pi\)
\(480\) −1.40431 −0.0640976
\(481\) −1.84647 −0.0841919
\(482\) −70.0900 −3.19251
\(483\) 6.45499 0.293712
\(484\) −8.46298 −0.384681
\(485\) −12.9992 −0.590262
\(486\) −37.7982 −1.71456
\(487\) 9.75574 0.442075 0.221037 0.975265i \(-0.429056\pi\)
0.221037 + 0.975265i \(0.429056\pi\)
\(488\) 6.15258 0.278514
\(489\) 3.54580 0.160347
\(490\) −20.8625 −0.942470
\(491\) 26.7865 1.20886 0.604430 0.796658i \(-0.293401\pi\)
0.604430 + 0.796658i \(0.293401\pi\)
\(492\) 9.50657 0.428589
\(493\) 23.7346 1.06895
\(494\) −25.6123 −1.15235
\(495\) 12.9140 0.580442
\(496\) −18.1703 −0.815872
\(497\) −4.65702 −0.208896
\(498\) −19.6006 −0.878322
\(499\) 22.6275 1.01295 0.506473 0.862256i \(-0.330949\pi\)
0.506473 + 0.862256i \(0.330949\pi\)
\(500\) 47.3718 2.11853
\(501\) 6.08717 0.271955
\(502\) 23.5215 1.04981
\(503\) −26.0984 −1.16367 −0.581834 0.813307i \(-0.697665\pi\)
−0.581834 + 0.813307i \(0.697665\pi\)
\(504\) −16.5559 −0.737458
\(505\) −15.2303 −0.677738
\(506\) 40.5098 1.80088
\(507\) −7.36987 −0.327308
\(508\) 10.2311 0.453932
\(509\) 24.6889 1.09431 0.547157 0.837030i \(-0.315710\pi\)
0.547157 + 0.837030i \(0.315710\pi\)
\(510\) −22.9774 −1.01745
\(511\) −8.78303 −0.388538
\(512\) 34.3657 1.51876
\(513\) 23.7529 1.04872
\(514\) 35.9356 1.58505
\(515\) 16.6401 0.733252
\(516\) 21.3139 0.938291
\(517\) 29.5477 1.29951
\(518\) 3.63013 0.159499
\(519\) 2.15913 0.0947751
\(520\) −15.3062 −0.671220
\(521\) 38.3615 1.68065 0.840324 0.542084i \(-0.182364\pi\)
0.840324 + 0.542084i \(0.182364\pi\)
\(522\) −20.3330 −0.889951
\(523\) −32.4665 −1.41966 −0.709830 0.704373i \(-0.751228\pi\)
−0.709830 + 0.704373i \(0.751228\pi\)
\(524\) −64.8791 −2.83426
\(525\) 2.00560 0.0875317
\(526\) 15.7838 0.688206
\(527\) 36.8310 1.60438
\(528\) 7.68978 0.334655
\(529\) 8.55255 0.371850
\(530\) −8.90544 −0.386827
\(531\) 1.33042 0.0577353
\(532\) 33.2636 1.44216
\(533\) −5.86795 −0.254169
\(534\) 13.4765 0.583186
\(535\) −28.4690 −1.23082
\(536\) 62.2553 2.68902
\(537\) 17.9929 0.776449
\(538\) −7.57524 −0.326592
\(539\) −14.1524 −0.609587
\(540\) 29.1939 1.25630
\(541\) 43.3814 1.86511 0.932555 0.361027i \(-0.117574\pi\)
0.932555 + 0.361027i \(0.117574\pi\)
\(542\) 65.4610 2.81179
\(543\) −0.994887 −0.0426947
\(544\) −6.91599 −0.296521
\(545\) 1.80408 0.0772784
\(546\) −5.15089 −0.220438
\(547\) 9.07706 0.388107 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(548\) −40.4209 −1.72669
\(549\) 3.22636 0.137698
\(550\) 12.5866 0.536696
\(551\) 19.8638 0.846225
\(552\) 19.8336 0.844175
\(553\) 5.15025 0.219011
\(554\) −49.3041 −2.09473
\(555\) −1.38635 −0.0588473
\(556\) −61.2681 −2.59834
\(557\) 13.2666 0.562122 0.281061 0.959690i \(-0.409314\pi\)
0.281061 + 0.959690i \(0.409314\pi\)
\(558\) −31.5524 −1.33572
\(559\) −13.1560 −0.556441
\(560\) 9.08726 0.384007
\(561\) −15.5871 −0.658087
\(562\) 64.9416 2.73940
\(563\) 16.3421 0.688738 0.344369 0.938834i \(-0.388093\pi\)
0.344369 + 0.938834i \(0.388093\pi\)
\(564\) 29.7524 1.25280
\(565\) −11.8735 −0.499523
\(566\) 32.2827 1.35694
\(567\) −6.03256 −0.253344
\(568\) −14.3092 −0.600399
\(569\) −19.1386 −0.802332 −0.401166 0.916005i \(-0.631395\pi\)
−0.401166 + 0.916005i \(0.631395\pi\)
\(570\) −19.2300 −0.805456
\(571\) −29.1169 −1.21850 −0.609251 0.792977i \(-0.708530\pi\)
−0.609251 + 0.792977i \(0.708530\pi\)
\(572\) −21.3544 −0.892873
\(573\) −8.06705 −0.337006
\(574\) 11.5363 0.481516
\(575\) 9.80357 0.408837
\(576\) 22.1567 0.923195
\(577\) 16.9472 0.705521 0.352760 0.935714i \(-0.385243\pi\)
0.352760 + 0.935714i \(0.385243\pi\)
\(578\) −71.8922 −2.99032
\(579\) −13.2278 −0.549727
\(580\) 24.4138 1.01373
\(581\) −15.7127 −0.651874
\(582\) −13.4412 −0.557155
\(583\) −6.04115 −0.250199
\(584\) −26.9867 −1.11672
\(585\) −8.02643 −0.331852
\(586\) −22.2155 −0.917714
\(587\) 7.67418 0.316747 0.158374 0.987379i \(-0.449375\pi\)
0.158374 + 0.987379i \(0.449375\pi\)
\(588\) −14.2504 −0.587678
\(589\) 30.8242 1.27009
\(590\) −2.41815 −0.0995535
\(591\) −19.9475 −0.820530
\(592\) 3.36833 0.138438
\(593\) −35.0815 −1.44063 −0.720313 0.693649i \(-0.756002\pi\)
−0.720313 + 0.693649i \(0.756002\pi\)
\(594\) 29.9789 1.23005
\(595\) −18.4197 −0.755135
\(596\) −52.0905 −2.13371
\(597\) −8.65552 −0.354247
\(598\) −25.1780 −1.02960
\(599\) 22.3188 0.911922 0.455961 0.890000i \(-0.349296\pi\)
0.455961 + 0.890000i \(0.349296\pi\)
\(600\) 6.16242 0.251580
\(601\) −32.0374 −1.30683 −0.653417 0.756998i \(-0.726665\pi\)
−0.653417 + 0.756998i \(0.726665\pi\)
\(602\) 25.8645 1.05416
\(603\) 32.6462 1.32945
\(604\) −20.2918 −0.825660
\(605\) 3.92208 0.159455
\(606\) −15.7481 −0.639724
\(607\) −25.8635 −1.04977 −0.524884 0.851174i \(-0.675891\pi\)
−0.524884 + 0.851174i \(0.675891\pi\)
\(608\) −5.78807 −0.234737
\(609\) 3.99480 0.161877
\(610\) −5.86418 −0.237434
\(611\) −18.3648 −0.742958
\(612\) 64.0401 2.58867
\(613\) 22.5697 0.911580 0.455790 0.890087i \(-0.349357\pi\)
0.455790 + 0.890087i \(0.349357\pi\)
\(614\) 63.8909 2.57843
\(615\) −4.40572 −0.177656
\(616\) 20.4132 0.822470
\(617\) 5.70917 0.229842 0.114921 0.993375i \(-0.463338\pi\)
0.114921 + 0.993375i \(0.463338\pi\)
\(618\) 17.2060 0.692125
\(619\) −14.4862 −0.582248 −0.291124 0.956685i \(-0.594029\pi\)
−0.291124 + 0.956685i \(0.594029\pi\)
\(620\) 37.8850 1.52150
\(621\) 23.3502 0.937010
\(622\) −75.2643 −3.01782
\(623\) 10.8034 0.432829
\(624\) −4.77942 −0.191330
\(625\) −13.2275 −0.529101
\(626\) 3.40968 0.136278
\(627\) −13.0450 −0.520967
\(628\) 84.1970 3.35982
\(629\) −6.82756 −0.272233
\(630\) 15.7798 0.628683
\(631\) −11.3676 −0.452536 −0.226268 0.974065i \(-0.572653\pi\)
−0.226268 + 0.974065i \(0.572653\pi\)
\(632\) 15.8247 0.629472
\(633\) 10.4487 0.415298
\(634\) −71.2343 −2.82908
\(635\) −4.74151 −0.188161
\(636\) −6.08300 −0.241207
\(637\) 8.79611 0.348515
\(638\) 25.0703 0.992543
\(639\) −7.50361 −0.296838
\(640\) −36.6167 −1.44740
\(641\) 43.9382 1.73546 0.867728 0.497040i \(-0.165580\pi\)
0.867728 + 0.497040i \(0.165580\pi\)
\(642\) −29.4370 −1.16179
\(643\) 35.6279 1.40503 0.702513 0.711671i \(-0.252061\pi\)
0.702513 + 0.711671i \(0.252061\pi\)
\(644\) 32.6995 1.28854
\(645\) −9.87769 −0.388934
\(646\) −94.7047 −3.72611
\(647\) −28.8264 −1.13328 −0.566641 0.823965i \(-0.691757\pi\)
−0.566641 + 0.823965i \(0.691757\pi\)
\(648\) −18.5356 −0.728149
\(649\) −1.64039 −0.0643909
\(650\) −7.82295 −0.306841
\(651\) 6.19906 0.242960
\(652\) 17.9622 0.703455
\(653\) −39.1269 −1.53115 −0.765576 0.643345i \(-0.777546\pi\)
−0.765576 + 0.643345i \(0.777546\pi\)
\(654\) 1.86543 0.0729439
\(655\) 30.0676 1.17484
\(656\) 10.7043 0.417934
\(657\) −14.1516 −0.552108
\(658\) 36.1048 1.40751
\(659\) 46.7538 1.82127 0.910635 0.413212i \(-0.135593\pi\)
0.910635 + 0.413212i \(0.135593\pi\)
\(660\) −16.0331 −0.624088
\(661\) −21.2214 −0.825417 −0.412709 0.910863i \(-0.635417\pi\)
−0.412709 + 0.910863i \(0.635417\pi\)
\(662\) 19.2309 0.747432
\(663\) 9.68780 0.376243
\(664\) −48.2790 −1.87359
\(665\) −15.4157 −0.597794
\(666\) 5.84904 0.226646
\(667\) 19.5269 0.756086
\(668\) 30.8362 1.19309
\(669\) −3.57109 −0.138066
\(670\) −59.3371 −2.29239
\(671\) −3.97806 −0.153571
\(672\) −1.16404 −0.0449037
\(673\) −42.5169 −1.63891 −0.819453 0.573146i \(-0.805723\pi\)
−0.819453 + 0.573146i \(0.805723\pi\)
\(674\) 73.2393 2.82107
\(675\) 7.25503 0.279246
\(676\) −37.3341 −1.43593
\(677\) 25.9938 0.999023 0.499512 0.866307i \(-0.333513\pi\)
0.499512 + 0.866307i \(0.333513\pi\)
\(678\) −12.2773 −0.471506
\(679\) −10.7751 −0.413510
\(680\) −56.5965 −2.17038
\(681\) −1.02997 −0.0394684
\(682\) 38.9037 1.48970
\(683\) 8.52276 0.326114 0.163057 0.986617i \(-0.447865\pi\)
0.163057 + 0.986617i \(0.447865\pi\)
\(684\) 53.5959 2.04929
\(685\) 18.7326 0.715738
\(686\) −42.7039 −1.63044
\(687\) 12.6972 0.484428
\(688\) 23.9992 0.914963
\(689\) 3.75475 0.143044
\(690\) −18.9039 −0.719660
\(691\) −11.4557 −0.435796 −0.217898 0.975972i \(-0.569920\pi\)
−0.217898 + 0.975972i \(0.569920\pi\)
\(692\) 10.9376 0.415787
\(693\) 10.7045 0.406631
\(694\) −26.8006 −1.01734
\(695\) 28.3941 1.07705
\(696\) 12.2744 0.465261
\(697\) −21.6975 −0.821851
\(698\) 18.6022 0.704105
\(699\) 20.1008 0.760283
\(700\) 10.1599 0.384010
\(701\) 31.6903 1.19693 0.598464 0.801150i \(-0.295778\pi\)
0.598464 + 0.801150i \(0.295778\pi\)
\(702\) −18.6327 −0.703247
\(703\) −5.71406 −0.215510
\(704\) −27.3189 −1.02962
\(705\) −13.7885 −0.519303
\(706\) −75.1898 −2.82981
\(707\) −12.6244 −0.474791
\(708\) −1.65175 −0.0620767
\(709\) −9.43588 −0.354372 −0.177186 0.984177i \(-0.556699\pi\)
−0.177186 + 0.984177i \(0.556699\pi\)
\(710\) 13.6384 0.511841
\(711\) 8.29833 0.311212
\(712\) 33.1946 1.24402
\(713\) 30.3015 1.13480
\(714\) −19.0461 −0.712781
\(715\) 9.89648 0.370107
\(716\) 91.1478 3.40635
\(717\) −2.79700 −0.104456
\(718\) 39.7565 1.48370
\(719\) 32.5271 1.21305 0.606527 0.795063i \(-0.292562\pi\)
0.606527 + 0.795063i \(0.292562\pi\)
\(720\) 14.6418 0.545668
\(721\) 13.7931 0.513682
\(722\) −33.1367 −1.23322
\(723\) 22.1877 0.825169
\(724\) −5.03988 −0.187306
\(725\) 6.06713 0.225328
\(726\) 4.05545 0.150512
\(727\) 19.4193 0.720222 0.360111 0.932909i \(-0.382739\pi\)
0.360111 + 0.932909i \(0.382739\pi\)
\(728\) −12.6874 −0.470225
\(729\) −0.136737 −0.00506435
\(730\) 25.7217 0.952005
\(731\) −48.6461 −1.79924
\(732\) −4.00562 −0.148052
\(733\) 37.7826 1.39553 0.697765 0.716326i \(-0.254178\pi\)
0.697765 + 0.716326i \(0.254178\pi\)
\(734\) −16.3945 −0.605133
\(735\) 6.60422 0.243600
\(736\) −5.68992 −0.209733
\(737\) −40.2523 −1.48271
\(738\) 18.5878 0.684227
\(739\) 23.5061 0.864686 0.432343 0.901709i \(-0.357687\pi\)
0.432343 + 0.901709i \(0.357687\pi\)
\(740\) −7.02294 −0.258169
\(741\) 8.10783 0.297849
\(742\) −7.38176 −0.270993
\(743\) −22.1057 −0.810979 −0.405489 0.914100i \(-0.632899\pi\)
−0.405489 + 0.914100i \(0.632899\pi\)
\(744\) 19.0472 0.698306
\(745\) 24.1408 0.884451
\(746\) −19.2760 −0.705746
\(747\) −25.3171 −0.926304
\(748\) −78.9606 −2.88709
\(749\) −23.5981 −0.862255
\(750\) −22.7005 −0.828904
\(751\) 16.1621 0.589764 0.294882 0.955534i \(-0.404720\pi\)
0.294882 + 0.955534i \(0.404720\pi\)
\(752\) 33.5010 1.22166
\(753\) −7.44595 −0.271346
\(754\) −15.5819 −0.567460
\(755\) 9.40401 0.342247
\(756\) 24.1990 0.880108
\(757\) −9.69500 −0.352371 −0.176185 0.984357i \(-0.556376\pi\)
−0.176185 + 0.984357i \(0.556376\pi\)
\(758\) 19.2496 0.699177
\(759\) −12.8238 −0.465474
\(760\) −47.3662 −1.71815
\(761\) −42.1444 −1.52773 −0.763867 0.645374i \(-0.776702\pi\)
−0.763867 + 0.645374i \(0.776702\pi\)
\(762\) −4.90273 −0.177607
\(763\) 1.49541 0.0541376
\(764\) −40.8659 −1.47848
\(765\) −29.6787 −1.07304
\(766\) −11.2122 −0.405112
\(767\) 1.01955 0.0368138
\(768\) −23.7289 −0.856245
\(769\) −41.3788 −1.49216 −0.746080 0.665857i \(-0.768066\pi\)
−0.746080 + 0.665857i \(0.768066\pi\)
\(770\) −19.4563 −0.701157
\(771\) −11.3758 −0.409688
\(772\) −67.0089 −2.41170
\(773\) 3.21809 0.115747 0.0578733 0.998324i \(-0.481568\pi\)
0.0578733 + 0.998324i \(0.481568\pi\)
\(774\) 41.6742 1.49795
\(775\) 9.41487 0.338192
\(776\) −33.1075 −1.18849
\(777\) −1.14915 −0.0412257
\(778\) 35.7898 1.28313
\(779\) −18.1589 −0.650609
\(780\) 9.96504 0.356806
\(781\) 9.25185 0.331057
\(782\) −93.0988 −3.32921
\(783\) 14.4507 0.516426
\(784\) −16.0459 −0.573067
\(785\) −39.0202 −1.39269
\(786\) 31.0899 1.10894
\(787\) 17.2217 0.613886 0.306943 0.951728i \(-0.400694\pi\)
0.306943 + 0.951728i \(0.400694\pi\)
\(788\) −101.049 −3.59974
\(789\) −4.99651 −0.177881
\(790\) −15.0829 −0.536625
\(791\) −9.84203 −0.349942
\(792\) 32.8907 1.16872
\(793\) 2.47248 0.0878003
\(794\) 25.7032 0.912173
\(795\) 2.81910 0.0999833
\(796\) −43.8469 −1.55411
\(797\) 11.8976 0.421435 0.210718 0.977547i \(-0.432420\pi\)
0.210718 + 0.977547i \(0.432420\pi\)
\(798\) −15.9399 −0.564265
\(799\) −67.9060 −2.40234
\(800\) −1.76789 −0.0625044
\(801\) 17.4070 0.615045
\(802\) −78.2358 −2.76260
\(803\) 17.4488 0.615754
\(804\) −40.5311 −1.42942
\(805\) −15.1543 −0.534118
\(806\) −24.1797 −0.851694
\(807\) 2.39802 0.0844142
\(808\) −38.7899 −1.36462
\(809\) −47.0706 −1.65491 −0.827457 0.561530i \(-0.810213\pi\)
−0.827457 + 0.561530i \(0.810213\pi\)
\(810\) 17.6668 0.620748
\(811\) 0.533781 0.0187436 0.00937179 0.999956i \(-0.497017\pi\)
0.00937179 + 0.999956i \(0.497017\pi\)
\(812\) 20.2368 0.710171
\(813\) −20.7223 −0.726764
\(814\) −7.21179 −0.252773
\(815\) −8.32441 −0.291591
\(816\) −17.6725 −0.618661
\(817\) −40.7124 −1.42435
\(818\) 1.74662 0.0610690
\(819\) −6.65315 −0.232480
\(820\) −22.3184 −0.779393
\(821\) 22.7810 0.795062 0.397531 0.917589i \(-0.369867\pi\)
0.397531 + 0.917589i \(0.369867\pi\)
\(822\) 19.3696 0.675593
\(823\) 15.3633 0.535532 0.267766 0.963484i \(-0.413715\pi\)
0.267766 + 0.963484i \(0.413715\pi\)
\(824\) 42.3807 1.47640
\(825\) −3.98443 −0.138720
\(826\) −2.00441 −0.0697425
\(827\) −47.0424 −1.63582 −0.817912 0.575343i \(-0.804869\pi\)
−0.817912 + 0.575343i \(0.804869\pi\)
\(828\) 52.6870 1.83100
\(829\) −2.02486 −0.0703262 −0.0351631 0.999382i \(-0.511195\pi\)
−0.0351631 + 0.999382i \(0.511195\pi\)
\(830\) 46.0159 1.59724
\(831\) 15.6077 0.541425
\(832\) 16.9795 0.588657
\(833\) 32.5247 1.12691
\(834\) 29.3595 1.01664
\(835\) −14.2907 −0.494551
\(836\) −66.0830 −2.28553
\(837\) 22.4244 0.775099
\(838\) 58.3853 2.01689
\(839\) −27.3951 −0.945784 −0.472892 0.881120i \(-0.656790\pi\)
−0.472892 + 0.881120i \(0.656790\pi\)
\(840\) −9.52582 −0.328672
\(841\) −16.9154 −0.583288
\(842\) 4.48852 0.154685
\(843\) −20.5579 −0.708052
\(844\) 52.9306 1.82195
\(845\) 17.3021 0.595211
\(846\) 58.1737 2.00005
\(847\) 3.25104 0.111707
\(848\) −6.84941 −0.235210
\(849\) −10.2194 −0.350729
\(850\) −28.9264 −0.992166
\(851\) −5.61717 −0.192554
\(852\) 9.31594 0.319159
\(853\) −18.8910 −0.646815 −0.323407 0.946260i \(-0.604828\pi\)
−0.323407 + 0.946260i \(0.604828\pi\)
\(854\) −4.86085 −0.166335
\(855\) −24.8385 −0.849458
\(856\) −72.5075 −2.47826
\(857\) −18.3001 −0.625119 −0.312559 0.949898i \(-0.601186\pi\)
−0.312559 + 0.949898i \(0.601186\pi\)
\(858\) 10.2330 0.349349
\(859\) 13.9083 0.474546 0.237273 0.971443i \(-0.423746\pi\)
0.237273 + 0.971443i \(0.423746\pi\)
\(860\) −50.0382 −1.70629
\(861\) −3.65193 −0.124457
\(862\) 11.0679 0.376975
\(863\) −43.9533 −1.49619 −0.748093 0.663594i \(-0.769030\pi\)
−0.748093 + 0.663594i \(0.769030\pi\)
\(864\) −4.21077 −0.143253
\(865\) −5.06894 −0.172349
\(866\) 5.16933 0.175661
\(867\) 22.7582 0.772908
\(868\) 31.4030 1.06589
\(869\) −10.2317 −0.347088
\(870\) −11.6991 −0.396636
\(871\) 25.0179 0.847700
\(872\) 4.59481 0.155600
\(873\) −17.3613 −0.587592
\(874\) −77.9154 −2.63553
\(875\) −18.1978 −0.615197
\(876\) 17.5696 0.593623
\(877\) −27.7996 −0.938727 −0.469363 0.883005i \(-0.655517\pi\)
−0.469363 + 0.883005i \(0.655517\pi\)
\(878\) 14.9861 0.505756
\(879\) 7.03254 0.237202
\(880\) −18.0532 −0.608572
\(881\) 12.5856 0.424020 0.212010 0.977268i \(-0.431999\pi\)
0.212010 + 0.977268i \(0.431999\pi\)
\(882\) −27.8633 −0.938206
\(883\) −1.66946 −0.0561820 −0.0280910 0.999605i \(-0.508943\pi\)
−0.0280910 + 0.999605i \(0.508943\pi\)
\(884\) 49.0762 1.65061
\(885\) 0.765488 0.0257316
\(886\) 88.9449 2.98816
\(887\) 35.6071 1.19557 0.597785 0.801656i \(-0.296048\pi\)
0.597785 + 0.801656i \(0.296048\pi\)
\(888\) −3.53089 −0.118489
\(889\) −3.93026 −0.131817
\(890\) −31.6386 −1.06053
\(891\) 11.9846 0.401498
\(892\) −18.0903 −0.605709
\(893\) −56.8313 −1.90179
\(894\) 24.9617 0.834843
\(895\) −42.2415 −1.41198
\(896\) −30.3518 −1.01398
\(897\) 7.97034 0.266122
\(898\) 32.2234 1.07531
\(899\) 18.7527 0.625438
\(900\) 16.3702 0.545672
\(901\) 13.8836 0.462531
\(902\) −22.9185 −0.763104
\(903\) −8.18767 −0.272469
\(904\) −30.2406 −1.00579
\(905\) 2.33568 0.0776406
\(906\) 9.72378 0.323051
\(907\) 18.0801 0.600339 0.300169 0.953886i \(-0.402957\pi\)
0.300169 + 0.953886i \(0.402957\pi\)
\(908\) −5.21758 −0.173151
\(909\) −20.3411 −0.674672
\(910\) 12.0926 0.400867
\(911\) −10.4180 −0.345164 −0.172582 0.984995i \(-0.555211\pi\)
−0.172582 + 0.984995i \(0.555211\pi\)
\(912\) −14.7903 −0.489756
\(913\) 31.2156 1.03309
\(914\) −24.1187 −0.797776
\(915\) 1.85636 0.0613695
\(916\) 64.3211 2.12523
\(917\) 24.9232 0.823035
\(918\) −68.8968 −2.27393
\(919\) −47.8241 −1.57757 −0.788786 0.614667i \(-0.789290\pi\)
−0.788786 + 0.614667i \(0.789290\pi\)
\(920\) −46.5630 −1.53514
\(921\) −20.2253 −0.666447
\(922\) −43.9336 −1.44688
\(923\) −5.75028 −0.189273
\(924\) −13.2899 −0.437207
\(925\) −1.74529 −0.0573847
\(926\) −37.6678 −1.23784
\(927\) 22.2241 0.729935
\(928\) −3.52132 −0.115593
\(929\) 27.2410 0.893748 0.446874 0.894597i \(-0.352537\pi\)
0.446874 + 0.894597i \(0.352537\pi\)
\(930\) −18.1544 −0.595306
\(931\) 27.2203 0.892109
\(932\) 101.826 3.33543
\(933\) 23.8256 0.780017
\(934\) −70.1227 −2.29449
\(935\) 36.5935 1.19674
\(936\) −20.4425 −0.668184
\(937\) 21.6530 0.707371 0.353686 0.935364i \(-0.384928\pi\)
0.353686 + 0.935364i \(0.384928\pi\)
\(938\) −49.1848 −1.60594
\(939\) −1.07937 −0.0352238
\(940\) −69.8492 −2.27823
\(941\) −20.5011 −0.668318 −0.334159 0.942517i \(-0.608452\pi\)
−0.334159 + 0.942517i \(0.608452\pi\)
\(942\) −40.3470 −1.31458
\(943\) −17.8509 −0.581307
\(944\) −1.85986 −0.0605333
\(945\) −11.2148 −0.364816
\(946\) −51.3837 −1.67063
\(947\) −0.779229 −0.0253215 −0.0126608 0.999920i \(-0.504030\pi\)
−0.0126608 + 0.999920i \(0.504030\pi\)
\(948\) −10.3026 −0.334613
\(949\) −10.8449 −0.352040
\(950\) −24.2088 −0.785437
\(951\) 22.5499 0.731232
\(952\) −46.9131 −1.52046
\(953\) 19.7057 0.638329 0.319164 0.947699i \(-0.396598\pi\)
0.319164 + 0.947699i \(0.396598\pi\)
\(954\) −11.8938 −0.385078
\(955\) 18.9389 0.612848
\(956\) −14.1690 −0.458257
\(957\) −7.93625 −0.256543
\(958\) 38.1744 1.23336
\(959\) 15.5276 0.501412
\(960\) 12.7484 0.411452
\(961\) −1.89986 −0.0612860
\(962\) 4.48233 0.144516
\(963\) −38.0224 −1.22525
\(964\) 112.398 3.62009
\(965\) 31.0546 0.999683
\(966\) −15.6696 −0.504160
\(967\) −10.7340 −0.345181 −0.172590 0.984994i \(-0.555214\pi\)
−0.172590 + 0.984994i \(0.555214\pi\)
\(968\) 9.98914 0.321063
\(969\) 29.9797 0.963087
\(970\) 31.5556 1.01319
\(971\) −41.1901 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(972\) 60.6139 1.94419
\(973\) 23.5360 0.754529
\(974\) −23.6822 −0.758825
\(975\) 2.47643 0.0793093
\(976\) −4.51030 −0.144371
\(977\) −18.9453 −0.606114 −0.303057 0.952972i \(-0.598007\pi\)
−0.303057 + 0.952972i \(0.598007\pi\)
\(978\) −8.60747 −0.275236
\(979\) −21.4625 −0.685946
\(980\) 33.4555 1.06870
\(981\) 2.40948 0.0769288
\(982\) −65.0246 −2.07502
\(983\) 42.5920 1.35847 0.679236 0.733920i \(-0.262311\pi\)
0.679236 + 0.733920i \(0.262311\pi\)
\(984\) −11.2209 −0.357710
\(985\) 46.8304 1.49214
\(986\) −57.6161 −1.83487
\(987\) −11.4293 −0.363799
\(988\) 41.0724 1.30669
\(989\) −40.0221 −1.27263
\(990\) −31.3489 −0.996335
\(991\) 23.2385 0.738196 0.369098 0.929391i \(-0.379667\pi\)
0.369098 + 0.929391i \(0.379667\pi\)
\(992\) −5.46432 −0.173492
\(993\) −6.08774 −0.193189
\(994\) 11.3050 0.358571
\(995\) 20.3204 0.644200
\(996\) 31.4319 0.995957
\(997\) 38.5164 1.21983 0.609914 0.792468i \(-0.291204\pi\)
0.609914 + 0.792468i \(0.291204\pi\)
\(998\) −54.9284 −1.73873
\(999\) −4.15693 −0.131519
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 4033.2.a.f.1.6 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.6 85 1.1 even 1 trivial