Properties

Label 4033.2.a.f.1.12
Level 4033
Weight 2
Character 4033.1
Self dual yes
Analytic conductor 32.204
Analytic rank 0
Dimension 85
CM no
Inner twists 1

Related objects

Downloads

Learn more about

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 1.12
Character \(\chi\) = 4033.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.11247 q^{2} +2.70421 q^{3} +2.46253 q^{4} +2.42834 q^{5} -5.71257 q^{6} +1.36575 q^{7} -0.977087 q^{8} +4.31276 q^{9} +O(q^{10})\) \(q-2.11247 q^{2} +2.70421 q^{3} +2.46253 q^{4} +2.42834 q^{5} -5.71257 q^{6} +1.36575 q^{7} -0.977087 q^{8} +4.31276 q^{9} -5.12979 q^{10} -5.83835 q^{11} +6.65921 q^{12} +3.94237 q^{13} -2.88511 q^{14} +6.56674 q^{15} -2.86100 q^{16} -0.443864 q^{17} -9.11057 q^{18} +4.49035 q^{19} +5.97986 q^{20} +3.69328 q^{21} +12.3333 q^{22} +5.11497 q^{23} -2.64225 q^{24} +0.896826 q^{25} -8.32814 q^{26} +3.54997 q^{27} +3.36320 q^{28} +8.05928 q^{29} -13.8720 q^{30} -3.45560 q^{31} +7.99795 q^{32} -15.7881 q^{33} +0.937649 q^{34} +3.31650 q^{35} +10.6203 q^{36} +1.00000 q^{37} -9.48573 q^{38} +10.6610 q^{39} -2.37270 q^{40} -0.332675 q^{41} -7.80194 q^{42} -3.72912 q^{43} -14.3771 q^{44} +10.4728 q^{45} -10.8052 q^{46} +2.07687 q^{47} -7.73674 q^{48} -5.13473 q^{49} -1.89452 q^{50} -1.20030 q^{51} +9.70821 q^{52} +2.70802 q^{53} -7.49920 q^{54} -14.1775 q^{55} -1.33446 q^{56} +12.1428 q^{57} -17.0250 q^{58} +2.65523 q^{59} +16.1708 q^{60} -2.31531 q^{61} +7.29986 q^{62} +5.89015 q^{63} -11.1734 q^{64} +9.57340 q^{65} +33.3520 q^{66} +13.8635 q^{67} -1.09303 q^{68} +13.8319 q^{69} -7.00602 q^{70} +1.12509 q^{71} -4.21394 q^{72} -6.62746 q^{73} -2.11247 q^{74} +2.42521 q^{75} +11.0576 q^{76} -7.97373 q^{77} -22.5210 q^{78} -3.29503 q^{79} -6.94747 q^{80} -3.33841 q^{81} +0.702766 q^{82} -0.226071 q^{83} +9.09481 q^{84} -1.07785 q^{85} +7.87765 q^{86} +21.7940 q^{87} +5.70458 q^{88} +18.1623 q^{89} -22.1235 q^{90} +5.38429 q^{91} +12.5958 q^{92} -9.34468 q^{93} -4.38732 q^{94} +10.9041 q^{95} +21.6281 q^{96} -12.4517 q^{97} +10.8470 q^{98} -25.1794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + O(q^{10}) \) \( 85q + 11q^{2} + 21q^{3} + 93q^{4} + 12q^{5} + 4q^{6} + 17q^{7} + 30q^{8} + 98q^{9} + 9q^{10} + 37q^{11} + 44q^{12} + 14q^{13} + 26q^{14} + 27q^{15} + 85q^{16} + 34q^{17} + 3q^{18} + 15q^{19} + 15q^{20} + 17q^{21} + q^{22} + 72q^{23} + 15q^{24} + 85q^{25} + 33q^{26} + 69q^{27} + 7q^{28} + 19q^{29} - 9q^{30} + 23q^{31} + 51q^{32} + 32q^{33} + 49q^{34} + 40q^{35} + 121q^{36} + 85q^{37} + 84q^{38} + 39q^{39} + 22q^{40} + 55q^{41} - 28q^{42} + 78q^{44} + 28q^{45} + 17q^{46} + 184q^{47} + 97q^{48} + 88q^{49} + 26q^{50} + 27q^{51} + 73q^{52} + 64q^{53} + 31q^{54} + 39q^{55} + 68q^{56} - 33q^{57} + 28q^{58} + 60q^{59} - 22q^{60} + 7q^{61} + 70q^{62} + 28q^{63} + 102q^{64} + 17q^{65} - 15q^{66} + 82q^{67} + 92q^{68} + 22q^{69} - 41q^{70} + 113q^{71} - 19q^{73} + 11q^{74} + 45q^{75} + 34q^{76} + 64q^{77} + 29q^{78} + 23q^{79} + 54q^{80} + 149q^{81} + 4q^{82} + 100q^{83} - 49q^{84} - 5q^{85} - 24q^{86} + 65q^{87} + 14q^{88} + 84q^{89} - 21q^{90} + 32q^{91} + 95q^{92} + 19q^{93} - 47q^{94} + 102q^{95} + 29q^{96} + 7q^{97} + 26q^{98} + 107q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11247 −1.49374 −0.746871 0.664969i \(-0.768445\pi\)
−0.746871 + 0.664969i \(0.768445\pi\)
\(3\) 2.70421 1.56128 0.780638 0.624983i \(-0.214894\pi\)
0.780638 + 0.624983i \(0.214894\pi\)
\(4\) 2.46253 1.23127
\(5\) 2.42834 1.08599 0.542993 0.839737i \(-0.317291\pi\)
0.542993 + 0.839737i \(0.317291\pi\)
\(6\) −5.71257 −2.33215
\(7\) 1.36575 0.516205 0.258102 0.966118i \(-0.416903\pi\)
0.258102 + 0.966118i \(0.416903\pi\)
\(8\) −0.977087 −0.345453
\(9\) 4.31276 1.43759
\(10\) −5.12979 −1.62218
\(11\) −5.83835 −1.76033 −0.880164 0.474669i \(-0.842568\pi\)
−0.880164 + 0.474669i \(0.842568\pi\)
\(12\) 6.65921 1.92235
\(13\) 3.94237 1.09342 0.546708 0.837323i \(-0.315881\pi\)
0.546708 + 0.837323i \(0.315881\pi\)
\(14\) −2.88511 −0.771077
\(15\) 6.56674 1.69552
\(16\) −2.86100 −0.715249
\(17\) −0.443864 −0.107653 −0.0538264 0.998550i \(-0.517142\pi\)
−0.0538264 + 0.998550i \(0.517142\pi\)
\(18\) −9.11057 −2.14738
\(19\) 4.49035 1.03016 0.515078 0.857143i \(-0.327763\pi\)
0.515078 + 0.857143i \(0.327763\pi\)
\(20\) 5.97986 1.33714
\(21\) 3.69328 0.805939
\(22\) 12.3333 2.62948
\(23\) 5.11497 1.06654 0.533272 0.845944i \(-0.320962\pi\)
0.533272 + 0.845944i \(0.320962\pi\)
\(24\) −2.64225 −0.539347
\(25\) 0.896826 0.179365
\(26\) −8.32814 −1.63328
\(27\) 3.54997 0.683192
\(28\) 3.36320 0.635586
\(29\) 8.05928 1.49657 0.748286 0.663377i \(-0.230877\pi\)
0.748286 + 0.663377i \(0.230877\pi\)
\(30\) −13.8720 −2.53268
\(31\) −3.45560 −0.620645 −0.310322 0.950631i \(-0.600437\pi\)
−0.310322 + 0.950631i \(0.600437\pi\)
\(32\) 7.99795 1.41385
\(33\) −15.7881 −2.74836
\(34\) 0.937649 0.160806
\(35\) 3.31650 0.560591
\(36\) 10.6203 1.77005
\(37\) 1.00000 0.164399
\(38\) −9.48573 −1.53879
\(39\) 10.6610 1.70713
\(40\) −2.37270 −0.375157
\(41\) −0.332675 −0.0519551 −0.0259776 0.999663i \(-0.508270\pi\)
−0.0259776 + 0.999663i \(0.508270\pi\)
\(42\) −7.80194 −1.20387
\(43\) −3.72912 −0.568685 −0.284342 0.958723i \(-0.591775\pi\)
−0.284342 + 0.958723i \(0.591775\pi\)
\(44\) −14.3771 −2.16743
\(45\) 10.4728 1.56120
\(46\) −10.8052 −1.59314
\(47\) 2.07687 0.302942 0.151471 0.988462i \(-0.451599\pi\)
0.151471 + 0.988462i \(0.451599\pi\)
\(48\) −7.73674 −1.11670
\(49\) −5.13473 −0.733532
\(50\) −1.89452 −0.267925
\(51\) −1.20030 −0.168076
\(52\) 9.70821 1.34629
\(53\) 2.70802 0.371975 0.185987 0.982552i \(-0.440452\pi\)
0.185987 + 0.982552i \(0.440452\pi\)
\(54\) −7.49920 −1.02051
\(55\) −14.1775 −1.91169
\(56\) −1.33446 −0.178324
\(57\) 12.1428 1.60836
\(58\) −17.0250 −2.23549
\(59\) 2.65523 0.345682 0.172841 0.984950i \(-0.444705\pi\)
0.172841 + 0.984950i \(0.444705\pi\)
\(60\) 16.1708 2.08764
\(61\) −2.31531 −0.296445 −0.148222 0.988954i \(-0.547355\pi\)
−0.148222 + 0.988954i \(0.547355\pi\)
\(62\) 7.29986 0.927084
\(63\) 5.89015 0.742089
\(64\) −11.1734 −1.39668
\(65\) 9.57340 1.18743
\(66\) 33.3520 4.10534
\(67\) 13.8635 1.69370 0.846851 0.531830i \(-0.178496\pi\)
0.846851 + 0.531830i \(0.178496\pi\)
\(68\) −1.09303 −0.132549
\(69\) 13.8319 1.66517
\(70\) −7.00602 −0.837379
\(71\) 1.12509 0.133524 0.0667618 0.997769i \(-0.478733\pi\)
0.0667618 + 0.997769i \(0.478733\pi\)
\(72\) −4.21394 −0.496618
\(73\) −6.62746 −0.775686 −0.387843 0.921726i \(-0.626780\pi\)
−0.387843 + 0.921726i \(0.626780\pi\)
\(74\) −2.11247 −0.245570
\(75\) 2.42521 0.280039
\(76\) 11.0576 1.26840
\(77\) −7.97373 −0.908690
\(78\) −22.5210 −2.55001
\(79\) −3.29503 −0.370720 −0.185360 0.982671i \(-0.559345\pi\)
−0.185360 + 0.982671i \(0.559345\pi\)
\(80\) −6.94747 −0.776751
\(81\) −3.33841 −0.370934
\(82\) 0.702766 0.0776075
\(83\) −0.226071 −0.0248145 −0.0124073 0.999923i \(-0.503949\pi\)
−0.0124073 + 0.999923i \(0.503949\pi\)
\(84\) 9.09481 0.992325
\(85\) −1.07785 −0.116909
\(86\) 7.87765 0.849469
\(87\) 21.7940 2.33656
\(88\) 5.70458 0.608110
\(89\) 18.1623 1.92520 0.962599 0.270931i \(-0.0873315\pi\)
0.962599 + 0.270931i \(0.0873315\pi\)
\(90\) −22.1235 −2.33203
\(91\) 5.38429 0.564427
\(92\) 12.5958 1.31320
\(93\) −9.34468 −0.968998
\(94\) −4.38732 −0.452518
\(95\) 10.9041 1.11874
\(96\) 21.6281 2.20741
\(97\) −12.4517 −1.26428 −0.632139 0.774855i \(-0.717823\pi\)
−0.632139 + 0.774855i \(0.717823\pi\)
\(98\) 10.8470 1.09571
\(99\) −25.1794 −2.53062
\(100\) 2.20846 0.220846
\(101\) 8.02699 0.798715 0.399357 0.916795i \(-0.369233\pi\)
0.399357 + 0.916795i \(0.369233\pi\)
\(102\) 2.53560 0.251062
\(103\) −0.842268 −0.0829912 −0.0414956 0.999139i \(-0.513212\pi\)
−0.0414956 + 0.999139i \(0.513212\pi\)
\(104\) −3.85204 −0.377723
\(105\) 8.96852 0.875238
\(106\) −5.72061 −0.555635
\(107\) 11.8826 1.14874 0.574368 0.818597i \(-0.305248\pi\)
0.574368 + 0.818597i \(0.305248\pi\)
\(108\) 8.74191 0.841191
\(109\) −1.00000 −0.0957826
\(110\) 29.9495 2.85558
\(111\) 2.70421 0.256672
\(112\) −3.90741 −0.369215
\(113\) 9.90207 0.931508 0.465754 0.884914i \(-0.345783\pi\)
0.465754 + 0.884914i \(0.345783\pi\)
\(114\) −25.6514 −2.40247
\(115\) 12.4209 1.15825
\(116\) 19.8462 1.84268
\(117\) 17.0025 1.57188
\(118\) −5.60910 −0.516360
\(119\) −0.606207 −0.0555709
\(120\) −6.41628 −0.585723
\(121\) 23.0863 2.09876
\(122\) 4.89102 0.442812
\(123\) −0.899623 −0.0811163
\(124\) −8.50954 −0.764179
\(125\) −9.96389 −0.891198
\(126\) −12.4428 −1.10849
\(127\) −3.41427 −0.302967 −0.151484 0.988460i \(-0.548405\pi\)
−0.151484 + 0.988460i \(0.548405\pi\)
\(128\) 7.60766 0.672429
\(129\) −10.0843 −0.887875
\(130\) −20.2235 −1.77372
\(131\) 10.6662 0.931912 0.465956 0.884808i \(-0.345710\pi\)
0.465956 + 0.884808i \(0.345710\pi\)
\(132\) −38.8788 −3.38396
\(133\) 6.13269 0.531772
\(134\) −29.2863 −2.52995
\(135\) 8.62052 0.741936
\(136\) 0.433694 0.0371889
\(137\) −7.80770 −0.667057 −0.333529 0.942740i \(-0.608239\pi\)
−0.333529 + 0.942740i \(0.608239\pi\)
\(138\) −29.2196 −2.48734
\(139\) 0.780164 0.0661727 0.0330863 0.999452i \(-0.489466\pi\)
0.0330863 + 0.999452i \(0.489466\pi\)
\(140\) 8.16700 0.690237
\(141\) 5.61629 0.472977
\(142\) −2.37672 −0.199450
\(143\) −23.0169 −1.92477
\(144\) −12.3388 −1.02823
\(145\) 19.5707 1.62526
\(146\) 14.0003 1.15867
\(147\) −13.8854 −1.14525
\(148\) 2.46253 0.202419
\(149\) −2.89956 −0.237541 −0.118771 0.992922i \(-0.537895\pi\)
−0.118771 + 0.992922i \(0.537895\pi\)
\(150\) −5.12318 −0.418306
\(151\) −15.3926 −1.25263 −0.626315 0.779570i \(-0.715438\pi\)
−0.626315 + 0.779570i \(0.715438\pi\)
\(152\) −4.38746 −0.355870
\(153\) −1.91428 −0.154760
\(154\) 16.8443 1.35735
\(155\) −8.39138 −0.674012
\(156\) 26.2530 2.10193
\(157\) −0.359790 −0.0287144 −0.0143572 0.999897i \(-0.504570\pi\)
−0.0143572 + 0.999897i \(0.504570\pi\)
\(158\) 6.96065 0.553760
\(159\) 7.32305 0.580756
\(160\) 19.4217 1.53542
\(161\) 6.98576 0.550555
\(162\) 7.05228 0.554080
\(163\) 23.8185 1.86561 0.932805 0.360383i \(-0.117354\pi\)
0.932805 + 0.360383i \(0.117354\pi\)
\(164\) −0.819223 −0.0639706
\(165\) −38.3389 −2.98468
\(166\) 0.477568 0.0370665
\(167\) −6.54347 −0.506349 −0.253175 0.967421i \(-0.581475\pi\)
−0.253175 + 0.967421i \(0.581475\pi\)
\(168\) −3.60865 −0.278414
\(169\) 2.54226 0.195559
\(170\) 2.27693 0.174633
\(171\) 19.3658 1.48094
\(172\) −9.18307 −0.700203
\(173\) −19.2219 −1.46142 −0.730708 0.682691i \(-0.760810\pi\)
−0.730708 + 0.682691i \(0.760810\pi\)
\(174\) −46.0392 −3.49022
\(175\) 1.22484 0.0925892
\(176\) 16.7035 1.25907
\(177\) 7.18031 0.539705
\(178\) −38.3673 −2.87575
\(179\) 14.4784 1.08217 0.541084 0.840968i \(-0.318014\pi\)
0.541084 + 0.840968i \(0.318014\pi\)
\(180\) 25.7897 1.92225
\(181\) −9.97548 −0.741471 −0.370736 0.928738i \(-0.620894\pi\)
−0.370736 + 0.928738i \(0.620894\pi\)
\(182\) −11.3742 −0.843108
\(183\) −6.26107 −0.462832
\(184\) −4.99777 −0.368440
\(185\) 2.42834 0.178535
\(186\) 19.7404 1.44743
\(187\) 2.59143 0.189504
\(188\) 5.11436 0.373003
\(189\) 4.84837 0.352667
\(190\) −23.0346 −1.67110
\(191\) −3.05153 −0.220801 −0.110400 0.993887i \(-0.535213\pi\)
−0.110400 + 0.993887i \(0.535213\pi\)
\(192\) −30.2153 −2.18060
\(193\) −3.79710 −0.273321 −0.136661 0.990618i \(-0.543637\pi\)
−0.136661 + 0.990618i \(0.543637\pi\)
\(194\) 26.3039 1.88851
\(195\) 25.8885 1.85391
\(196\) −12.6444 −0.903174
\(197\) 24.8818 1.77276 0.886378 0.462962i \(-0.153213\pi\)
0.886378 + 0.462962i \(0.153213\pi\)
\(198\) 53.1907 3.78010
\(199\) 7.27834 0.515948 0.257974 0.966152i \(-0.416945\pi\)
0.257974 + 0.966152i \(0.416945\pi\)
\(200\) −0.876277 −0.0619622
\(201\) 37.4900 2.64434
\(202\) −16.9568 −1.19307
\(203\) 11.0070 0.772537
\(204\) −2.95578 −0.206946
\(205\) −0.807847 −0.0564225
\(206\) 1.77927 0.123967
\(207\) 22.0596 1.53325
\(208\) −11.2791 −0.782065
\(209\) −26.2162 −1.81341
\(210\) −18.9457 −1.30738
\(211\) 24.5592 1.69072 0.845362 0.534194i \(-0.179385\pi\)
0.845362 + 0.534194i \(0.179385\pi\)
\(212\) 6.66858 0.458000
\(213\) 3.04248 0.208467
\(214\) −25.1017 −1.71592
\(215\) −9.05556 −0.617584
\(216\) −3.46863 −0.236010
\(217\) −4.71949 −0.320380
\(218\) 2.11247 0.143075
\(219\) −17.9220 −1.21106
\(220\) −34.9125 −2.35380
\(221\) −1.74987 −0.117709
\(222\) −5.71257 −0.383402
\(223\) −8.11629 −0.543507 −0.271753 0.962367i \(-0.587604\pi\)
−0.271753 + 0.962367i \(0.587604\pi\)
\(224\) 10.9232 0.729837
\(225\) 3.86779 0.257853
\(226\) −20.9178 −1.39143
\(227\) −16.5920 −1.10125 −0.550623 0.834754i \(-0.685610\pi\)
−0.550623 + 0.834754i \(0.685610\pi\)
\(228\) 29.9022 1.98032
\(229\) 8.05774 0.532470 0.266235 0.963908i \(-0.414220\pi\)
0.266235 + 0.963908i \(0.414220\pi\)
\(230\) −26.2387 −1.73013
\(231\) −21.5626 −1.41872
\(232\) −7.87462 −0.516994
\(233\) −2.42793 −0.159059 −0.0795295 0.996833i \(-0.525342\pi\)
−0.0795295 + 0.996833i \(0.525342\pi\)
\(234\) −35.9172 −2.34798
\(235\) 5.04334 0.328991
\(236\) 6.53860 0.425626
\(237\) −8.91046 −0.578796
\(238\) 1.28059 0.0830086
\(239\) −11.8038 −0.763525 −0.381762 0.924261i \(-0.624683\pi\)
−0.381762 + 0.924261i \(0.624683\pi\)
\(240\) −18.7874 −1.21272
\(241\) 10.7099 0.689886 0.344943 0.938624i \(-0.387898\pi\)
0.344943 + 0.938624i \(0.387898\pi\)
\(242\) −48.7692 −3.13500
\(243\) −19.6777 −1.26232
\(244\) −5.70152 −0.365002
\(245\) −12.4689 −0.796606
\(246\) 1.90043 0.121167
\(247\) 17.7026 1.12639
\(248\) 3.37643 0.214403
\(249\) −0.611343 −0.0387423
\(250\) 21.0484 1.33122
\(251\) −7.15304 −0.451496 −0.225748 0.974186i \(-0.572483\pi\)
−0.225748 + 0.974186i \(0.572483\pi\)
\(252\) 14.5047 0.913709
\(253\) −29.8630 −1.87747
\(254\) 7.21254 0.452555
\(255\) −2.91474 −0.182528
\(256\) 6.27591 0.392244
\(257\) −20.0109 −1.24824 −0.624121 0.781327i \(-0.714543\pi\)
−0.624121 + 0.781327i \(0.714543\pi\)
\(258\) 21.3028 1.32626
\(259\) 1.36575 0.0848636
\(260\) 23.5748 1.46205
\(261\) 34.7577 2.15145
\(262\) −22.5321 −1.39204
\(263\) −7.90913 −0.487698 −0.243849 0.969813i \(-0.578410\pi\)
−0.243849 + 0.969813i \(0.578410\pi\)
\(264\) 15.4264 0.949428
\(265\) 6.57598 0.403959
\(266\) −12.9551 −0.794330
\(267\) 49.1146 3.00577
\(268\) 34.1394 2.08540
\(269\) 8.60657 0.524752 0.262376 0.964966i \(-0.415494\pi\)
0.262376 + 0.964966i \(0.415494\pi\)
\(270\) −18.2106 −1.10826
\(271\) −0.196579 −0.0119413 −0.00597067 0.999982i \(-0.501901\pi\)
−0.00597067 + 0.999982i \(0.501901\pi\)
\(272\) 1.26989 0.0769986
\(273\) 14.5603 0.881226
\(274\) 16.4935 0.996412
\(275\) −5.23598 −0.315742
\(276\) 34.0616 2.05027
\(277\) −19.8252 −1.19118 −0.595589 0.803289i \(-0.703081\pi\)
−0.595589 + 0.803289i \(0.703081\pi\)
\(278\) −1.64807 −0.0988449
\(279\) −14.9032 −0.892230
\(280\) −3.24051 −0.193658
\(281\) −15.6115 −0.931307 −0.465653 0.884967i \(-0.654181\pi\)
−0.465653 + 0.884967i \(0.654181\pi\)
\(282\) −11.8642 −0.706506
\(283\) −14.1811 −0.842976 −0.421488 0.906834i \(-0.638492\pi\)
−0.421488 + 0.906834i \(0.638492\pi\)
\(284\) 2.77057 0.164403
\(285\) 29.4869 1.74666
\(286\) 48.6226 2.87511
\(287\) −0.454351 −0.0268195
\(288\) 34.4932 2.03253
\(289\) −16.8030 −0.988411
\(290\) −41.3425 −2.42771
\(291\) −33.6720 −1.97389
\(292\) −16.3203 −0.955076
\(293\) −9.36224 −0.546948 −0.273474 0.961879i \(-0.588173\pi\)
−0.273474 + 0.961879i \(0.588173\pi\)
\(294\) 29.3325 1.71070
\(295\) 6.44780 0.375406
\(296\) −0.977087 −0.0567921
\(297\) −20.7260 −1.20264
\(298\) 6.12524 0.354825
\(299\) 20.1651 1.16618
\(300\) 5.97215 0.344802
\(301\) −5.09304 −0.293558
\(302\) 32.5164 1.87111
\(303\) 21.7067 1.24701
\(304\) −12.8469 −0.736819
\(305\) −5.62235 −0.321935
\(306\) 4.04385 0.231172
\(307\) 7.92978 0.452576 0.226288 0.974060i \(-0.427341\pi\)
0.226288 + 0.974060i \(0.427341\pi\)
\(308\) −19.6356 −1.11884
\(309\) −2.27767 −0.129572
\(310\) 17.7265 1.00680
\(311\) 1.38182 0.0783558 0.0391779 0.999232i \(-0.487526\pi\)
0.0391779 + 0.999232i \(0.487526\pi\)
\(312\) −10.4167 −0.589731
\(313\) 4.57223 0.258438 0.129219 0.991616i \(-0.458753\pi\)
0.129219 + 0.991616i \(0.458753\pi\)
\(314\) 0.760046 0.0428919
\(315\) 14.3033 0.805898
\(316\) −8.11412 −0.456455
\(317\) −7.52627 −0.422717 −0.211359 0.977409i \(-0.567789\pi\)
−0.211359 + 0.977409i \(0.567789\pi\)
\(318\) −15.4697 −0.867500
\(319\) −47.0529 −2.63446
\(320\) −27.1329 −1.51677
\(321\) 32.1331 1.79350
\(322\) −14.7572 −0.822388
\(323\) −1.99310 −0.110899
\(324\) −8.22093 −0.456719
\(325\) 3.53562 0.196121
\(326\) −50.3159 −2.78674
\(327\) −2.70421 −0.149543
\(328\) 0.325053 0.0179480
\(329\) 2.83648 0.156380
\(330\) 80.9898 4.45834
\(331\) −11.6500 −0.640340 −0.320170 0.947360i \(-0.603740\pi\)
−0.320170 + 0.947360i \(0.603740\pi\)
\(332\) −0.556707 −0.0305533
\(333\) 4.31276 0.236338
\(334\) 13.8229 0.756355
\(335\) 33.6654 1.83934
\(336\) −10.5665 −0.576447
\(337\) −26.6134 −1.44972 −0.724862 0.688894i \(-0.758096\pi\)
−0.724862 + 0.688894i \(0.758096\pi\)
\(338\) −5.37046 −0.292114
\(339\) 26.7773 1.45434
\(340\) −2.65425 −0.143947
\(341\) 20.1750 1.09254
\(342\) −40.9096 −2.21214
\(343\) −16.5730 −0.894858
\(344\) 3.64367 0.196454
\(345\) 33.5886 1.80835
\(346\) 40.6057 2.18298
\(347\) 22.5875 1.21256 0.606279 0.795252i \(-0.292661\pi\)
0.606279 + 0.795252i \(0.292661\pi\)
\(348\) 53.6684 2.87693
\(349\) −18.0850 −0.968065 −0.484033 0.875050i \(-0.660828\pi\)
−0.484033 + 0.875050i \(0.660828\pi\)
\(350\) −2.58744 −0.138304
\(351\) 13.9953 0.747013
\(352\) −46.6948 −2.48884
\(353\) −26.1218 −1.39032 −0.695162 0.718854i \(-0.744667\pi\)
−0.695162 + 0.718854i \(0.744667\pi\)
\(354\) −15.1682 −0.806180
\(355\) 2.73210 0.145005
\(356\) 44.7252 2.37043
\(357\) −1.63931 −0.0867616
\(358\) −30.5853 −1.61648
\(359\) 16.1626 0.853030 0.426515 0.904481i \(-0.359741\pi\)
0.426515 + 0.904481i \(0.359741\pi\)
\(360\) −10.2329 −0.539320
\(361\) 1.16323 0.0612226
\(362\) 21.0729 1.10757
\(363\) 62.4303 3.27674
\(364\) 13.2590 0.694960
\(365\) −16.0937 −0.842384
\(366\) 13.2263 0.691352
\(367\) 19.1446 0.999340 0.499670 0.866216i \(-0.333455\pi\)
0.499670 + 0.866216i \(0.333455\pi\)
\(368\) −14.6339 −0.762845
\(369\) −1.43475 −0.0746899
\(370\) −5.12979 −0.266685
\(371\) 3.69848 0.192015
\(372\) −23.0116 −1.19310
\(373\) −31.1180 −1.61123 −0.805614 0.592441i \(-0.798164\pi\)
−0.805614 + 0.592441i \(0.798164\pi\)
\(374\) −5.47433 −0.283071
\(375\) −26.9445 −1.39141
\(376\) −2.02928 −0.104652
\(377\) 31.7727 1.63637
\(378\) −10.2420 −0.526794
\(379\) −3.60303 −0.185075 −0.0925377 0.995709i \(-0.529498\pi\)
−0.0925377 + 0.995709i \(0.529498\pi\)
\(380\) 26.8517 1.37746
\(381\) −9.23290 −0.473016
\(382\) 6.44626 0.329819
\(383\) 1.22529 0.0626095 0.0313048 0.999510i \(-0.490034\pi\)
0.0313048 + 0.999510i \(0.490034\pi\)
\(384\) 20.5727 1.04985
\(385\) −19.3629 −0.986825
\(386\) 8.02126 0.408272
\(387\) −16.0828 −0.817533
\(388\) −30.6627 −1.55666
\(389\) −2.93083 −0.148599 −0.0742995 0.997236i \(-0.523672\pi\)
−0.0742995 + 0.997236i \(0.523672\pi\)
\(390\) −54.6887 −2.76927
\(391\) −2.27035 −0.114816
\(392\) 5.01708 0.253401
\(393\) 28.8437 1.45497
\(394\) −52.5621 −2.64804
\(395\) −8.00145 −0.402596
\(396\) −62.0050 −3.11587
\(397\) 11.8536 0.594916 0.297458 0.954735i \(-0.403861\pi\)
0.297458 + 0.954735i \(0.403861\pi\)
\(398\) −15.3753 −0.770693
\(399\) 16.5841 0.830243
\(400\) −2.56582 −0.128291
\(401\) 5.00202 0.249789 0.124894 0.992170i \(-0.460141\pi\)
0.124894 + 0.992170i \(0.460141\pi\)
\(402\) −79.1964 −3.94996
\(403\) −13.6233 −0.678623
\(404\) 19.7667 0.983431
\(405\) −8.10678 −0.402829
\(406\) −23.2519 −1.15397
\(407\) −5.83835 −0.289396
\(408\) 1.17280 0.0580622
\(409\) −15.9656 −0.789448 −0.394724 0.918800i \(-0.629160\pi\)
−0.394724 + 0.918800i \(0.629160\pi\)
\(410\) 1.70655 0.0842807
\(411\) −21.1137 −1.04146
\(412\) −2.07411 −0.102184
\(413\) 3.62638 0.178443
\(414\) −46.6003 −2.29028
\(415\) −0.548977 −0.0269482
\(416\) 31.5309 1.54593
\(417\) 2.10973 0.103314
\(418\) 55.3810 2.70877
\(419\) 32.7296 1.59894 0.799472 0.600703i \(-0.205113\pi\)
0.799472 + 0.600703i \(0.205113\pi\)
\(420\) 22.0853 1.07765
\(421\) 11.0666 0.539355 0.269677 0.962951i \(-0.413083\pi\)
0.269677 + 0.962951i \(0.413083\pi\)
\(422\) −51.8806 −2.52551
\(423\) 8.95702 0.435505
\(424\) −2.64597 −0.128500
\(425\) −0.398069 −0.0193092
\(426\) −6.42715 −0.311396
\(427\) −3.16213 −0.153026
\(428\) 29.2613 1.41440
\(429\) −62.2426 −3.00510
\(430\) 19.1296 0.922511
\(431\) −28.1460 −1.35574 −0.677871 0.735180i \(-0.737097\pi\)
−0.677871 + 0.735180i \(0.737097\pi\)
\(432\) −10.1564 −0.488652
\(433\) 0.131642 0.00632632 0.00316316 0.999995i \(-0.498993\pi\)
0.00316316 + 0.999995i \(0.498993\pi\)
\(434\) 9.96979 0.478565
\(435\) 52.9232 2.53747
\(436\) −2.46253 −0.117934
\(437\) 22.9680 1.09871
\(438\) 37.8598 1.80901
\(439\) 29.4863 1.40730 0.703651 0.710546i \(-0.251552\pi\)
0.703651 + 0.710546i \(0.251552\pi\)
\(440\) 13.8526 0.660399
\(441\) −22.1448 −1.05452
\(442\) 3.69656 0.175827
\(443\) 9.77181 0.464273 0.232136 0.972683i \(-0.425428\pi\)
0.232136 + 0.972683i \(0.425428\pi\)
\(444\) 6.65921 0.316032
\(445\) 44.1042 2.09074
\(446\) 17.1454 0.811859
\(447\) −7.84102 −0.370868
\(448\) −15.2601 −0.720973
\(449\) 26.7623 1.26299 0.631495 0.775380i \(-0.282442\pi\)
0.631495 + 0.775380i \(0.282442\pi\)
\(450\) −8.17060 −0.385166
\(451\) 1.94227 0.0914580
\(452\) 24.3842 1.14693
\(453\) −41.6248 −1.95570
\(454\) 35.0500 1.64498
\(455\) 13.0749 0.612960
\(456\) −11.8646 −0.555612
\(457\) −8.53641 −0.399317 −0.199658 0.979866i \(-0.563983\pi\)
−0.199658 + 0.979866i \(0.563983\pi\)
\(458\) −17.0217 −0.795373
\(459\) −1.57570 −0.0735475
\(460\) 30.5868 1.42612
\(461\) 16.4917 0.768096 0.384048 0.923313i \(-0.374530\pi\)
0.384048 + 0.923313i \(0.374530\pi\)
\(462\) 45.5504 2.11920
\(463\) 8.19071 0.380654 0.190327 0.981721i \(-0.439045\pi\)
0.190327 + 0.981721i \(0.439045\pi\)
\(464\) −23.0576 −1.07042
\(465\) −22.6920 −1.05232
\(466\) 5.12893 0.237593
\(467\) 34.2606 1.58539 0.792695 0.609618i \(-0.208677\pi\)
0.792695 + 0.609618i \(0.208677\pi\)
\(468\) 41.8691 1.93540
\(469\) 18.9341 0.874297
\(470\) −10.6539 −0.491428
\(471\) −0.972948 −0.0448311
\(472\) −2.59439 −0.119417
\(473\) 21.7719 1.00107
\(474\) 18.8231 0.864573
\(475\) 4.02706 0.184774
\(476\) −1.49280 −0.0684226
\(477\) 11.6790 0.534746
\(478\) 24.9352 1.14051
\(479\) −29.1701 −1.33282 −0.666409 0.745586i \(-0.732170\pi\)
−0.666409 + 0.745586i \(0.732170\pi\)
\(480\) 52.5204 2.39722
\(481\) 3.94237 0.179756
\(482\) −22.6244 −1.03051
\(483\) 18.8910 0.859569
\(484\) 56.8508 2.58413
\(485\) −30.2369 −1.37299
\(486\) 41.5685 1.88558
\(487\) −13.8088 −0.625736 −0.312868 0.949797i \(-0.601290\pi\)
−0.312868 + 0.949797i \(0.601290\pi\)
\(488\) 2.26226 0.102408
\(489\) 64.4102 2.91273
\(490\) 26.3401 1.18992
\(491\) 1.05407 0.0475694 0.0237847 0.999717i \(-0.492428\pi\)
0.0237847 + 0.999717i \(0.492428\pi\)
\(492\) −2.21535 −0.0998758
\(493\) −3.57722 −0.161110
\(494\) −37.3962 −1.68254
\(495\) −61.1440 −2.74822
\(496\) 9.88648 0.443916
\(497\) 1.53659 0.0689255
\(498\) 1.29145 0.0578710
\(499\) 32.4643 1.45330 0.726650 0.687008i \(-0.241076\pi\)
0.726650 + 0.687008i \(0.241076\pi\)
\(500\) −24.5364 −1.09730
\(501\) −17.6949 −0.790551
\(502\) 15.1106 0.674418
\(503\) −10.4898 −0.467717 −0.233858 0.972271i \(-0.575135\pi\)
−0.233858 + 0.972271i \(0.575135\pi\)
\(504\) −5.75519 −0.256356
\(505\) 19.4922 0.867393
\(506\) 63.0846 2.80445
\(507\) 6.87482 0.305321
\(508\) −8.40775 −0.373034
\(509\) 37.5494 1.66435 0.832174 0.554515i \(-0.187096\pi\)
0.832174 + 0.554515i \(0.187096\pi\)
\(510\) 6.15730 0.272650
\(511\) −9.05145 −0.400413
\(512\) −28.4730 −1.25834
\(513\) 15.9406 0.703794
\(514\) 42.2723 1.86455
\(515\) −2.04531 −0.0901272
\(516\) −24.8330 −1.09321
\(517\) −12.1255 −0.533278
\(518\) −2.88511 −0.126764
\(519\) −51.9801 −2.28167
\(520\) −9.35405 −0.410202
\(521\) 30.9278 1.35497 0.677486 0.735535i \(-0.263069\pi\)
0.677486 + 0.735535i \(0.263069\pi\)
\(522\) −73.4247 −3.21371
\(523\) 2.02784 0.0886711 0.0443355 0.999017i \(-0.485883\pi\)
0.0443355 + 0.999017i \(0.485883\pi\)
\(524\) 26.2659 1.14743
\(525\) 3.31223 0.144557
\(526\) 16.7078 0.728495
\(527\) 1.53382 0.0668142
\(528\) 45.1698 1.96576
\(529\) 3.16288 0.137516
\(530\) −13.8916 −0.603411
\(531\) 11.4514 0.496947
\(532\) 15.1020 0.654753
\(533\) −1.31153 −0.0568085
\(534\) −103.753 −4.48984
\(535\) 28.8550 1.24751
\(536\) −13.5459 −0.585094
\(537\) 39.1527 1.68957
\(538\) −18.1811 −0.783844
\(539\) 29.9783 1.29126
\(540\) 21.2283 0.913521
\(541\) −15.6952 −0.674789 −0.337394 0.941363i \(-0.609546\pi\)
−0.337394 + 0.941363i \(0.609546\pi\)
\(542\) 0.415268 0.0178373
\(543\) −26.9758 −1.15764
\(544\) −3.55000 −0.152205
\(545\) −2.42834 −0.104019
\(546\) −30.7581 −1.31633
\(547\) −31.8968 −1.36381 −0.681904 0.731441i \(-0.738848\pi\)
−0.681904 + 0.731441i \(0.738848\pi\)
\(548\) −19.2267 −0.821325
\(549\) −9.98535 −0.426164
\(550\) 11.0609 0.471637
\(551\) 36.1890 1.54170
\(552\) −13.5150 −0.575237
\(553\) −4.50019 −0.191367
\(554\) 41.8801 1.77931
\(555\) 6.56674 0.278743
\(556\) 1.92118 0.0814762
\(557\) 14.2168 0.602386 0.301193 0.953563i \(-0.402615\pi\)
0.301193 + 0.953563i \(0.402615\pi\)
\(558\) 31.4825 1.33276
\(559\) −14.7015 −0.621809
\(560\) −9.48851 −0.400963
\(561\) 7.00778 0.295869
\(562\) 32.9789 1.39113
\(563\) 16.2007 0.682778 0.341389 0.939922i \(-0.389103\pi\)
0.341389 + 0.939922i \(0.389103\pi\)
\(564\) 13.8303 0.582360
\(565\) 24.0456 1.01160
\(566\) 29.9571 1.25919
\(567\) −4.55943 −0.191478
\(568\) −1.09931 −0.0461260
\(569\) −44.2465 −1.85491 −0.927454 0.373937i \(-0.878007\pi\)
−0.927454 + 0.373937i \(0.878007\pi\)
\(570\) −62.2903 −2.60905
\(571\) 46.5263 1.94707 0.973533 0.228546i \(-0.0733972\pi\)
0.973533 + 0.228546i \(0.0733972\pi\)
\(572\) −56.6799 −2.36991
\(573\) −8.25197 −0.344731
\(574\) 0.959803 0.0400614
\(575\) 4.58723 0.191301
\(576\) −48.1883 −2.00785
\(577\) −8.25627 −0.343713 −0.171857 0.985122i \(-0.554977\pi\)
−0.171857 + 0.985122i \(0.554977\pi\)
\(578\) 35.4958 1.47643
\(579\) −10.2682 −0.426730
\(580\) 48.1934 2.00112
\(581\) −0.308756 −0.0128094
\(582\) 71.1312 2.94848
\(583\) −15.8104 −0.654798
\(584\) 6.47561 0.267963
\(585\) 41.2877 1.70704
\(586\) 19.7775 0.816999
\(587\) −5.27724 −0.217815 −0.108908 0.994052i \(-0.534735\pi\)
−0.108908 + 0.994052i \(0.534735\pi\)
\(588\) −34.1932 −1.41010
\(589\) −15.5169 −0.639361
\(590\) −13.6208 −0.560759
\(591\) 67.2857 2.76776
\(592\) −2.86100 −0.117586
\(593\) −37.1400 −1.52516 −0.762578 0.646896i \(-0.776067\pi\)
−0.762578 + 0.646896i \(0.776067\pi\)
\(594\) 43.7830 1.79644
\(595\) −1.47208 −0.0603492
\(596\) −7.14026 −0.292477
\(597\) 19.6822 0.805537
\(598\) −42.5981 −1.74197
\(599\) 26.9329 1.10045 0.550223 0.835018i \(-0.314543\pi\)
0.550223 + 0.835018i \(0.314543\pi\)
\(600\) −2.36964 −0.0967401
\(601\) −37.0207 −1.51011 −0.755053 0.655664i \(-0.772389\pi\)
−0.755053 + 0.655664i \(0.772389\pi\)
\(602\) 10.7589 0.438500
\(603\) 59.7901 2.43484
\(604\) −37.9047 −1.54232
\(605\) 56.0614 2.27922
\(606\) −45.8547 −1.86272
\(607\) 25.2568 1.02514 0.512571 0.858645i \(-0.328693\pi\)
0.512571 + 0.858645i \(0.328693\pi\)
\(608\) 35.9136 1.45649
\(609\) 29.7652 1.20614
\(610\) 11.8770 0.480887
\(611\) 8.18778 0.331242
\(612\) −4.71397 −0.190551
\(613\) −11.4573 −0.462757 −0.231379 0.972864i \(-0.574324\pi\)
−0.231379 + 0.972864i \(0.574324\pi\)
\(614\) −16.7514 −0.676033
\(615\) −2.18459 −0.0880911
\(616\) 7.79103 0.313909
\(617\) −25.9319 −1.04398 −0.521990 0.852952i \(-0.674810\pi\)
−0.521990 + 0.852952i \(0.674810\pi\)
\(618\) 4.81151 0.193547
\(619\) 12.0225 0.483225 0.241612 0.970373i \(-0.422324\pi\)
0.241612 + 0.970373i \(0.422324\pi\)
\(620\) −20.6640 −0.829888
\(621\) 18.1580 0.728654
\(622\) −2.91905 −0.117043
\(623\) 24.8051 0.993797
\(624\) −30.5011 −1.22102
\(625\) −28.6798 −1.14719
\(626\) −9.65870 −0.386039
\(627\) −70.8942 −2.83124
\(628\) −0.885995 −0.0353551
\(629\) −0.443864 −0.0176980
\(630\) −30.2152 −1.20380
\(631\) 13.5994 0.541385 0.270693 0.962666i \(-0.412747\pi\)
0.270693 + 0.962666i \(0.412747\pi\)
\(632\) 3.21953 0.128066
\(633\) 66.4132 2.63969
\(634\) 15.8990 0.631431
\(635\) −8.29100 −0.329018
\(636\) 18.0333 0.715065
\(637\) −20.2430 −0.802056
\(638\) 99.3979 3.93520
\(639\) 4.85223 0.191951
\(640\) 18.4740 0.730248
\(641\) 10.5029 0.414840 0.207420 0.978252i \(-0.433493\pi\)
0.207420 + 0.978252i \(0.433493\pi\)
\(642\) −67.8803 −2.67902
\(643\) 8.59087 0.338791 0.169395 0.985548i \(-0.445818\pi\)
0.169395 + 0.985548i \(0.445818\pi\)
\(644\) 17.2027 0.677880
\(645\) −24.4881 −0.964219
\(646\) 4.21037 0.165655
\(647\) −22.9431 −0.901986 −0.450993 0.892527i \(-0.648930\pi\)
−0.450993 + 0.892527i \(0.648930\pi\)
\(648\) 3.26191 0.128140
\(649\) −15.5022 −0.608514
\(650\) −7.46889 −0.292954
\(651\) −12.7625 −0.500202
\(652\) 58.6538 2.29706
\(653\) 6.90598 0.270252 0.135126 0.990828i \(-0.456856\pi\)
0.135126 + 0.990828i \(0.456856\pi\)
\(654\) 5.71257 0.223379
\(655\) 25.9012 1.01204
\(656\) 0.951782 0.0371609
\(657\) −28.5826 −1.11511
\(658\) −5.99199 −0.233592
\(659\) 38.3691 1.49465 0.747324 0.664460i \(-0.231338\pi\)
0.747324 + 0.664460i \(0.231338\pi\)
\(660\) −94.4108 −3.67494
\(661\) −18.0755 −0.703055 −0.351527 0.936178i \(-0.614338\pi\)
−0.351527 + 0.936178i \(0.614338\pi\)
\(662\) 24.6102 0.956503
\(663\) −4.73203 −0.183777
\(664\) 0.220891 0.00857224
\(665\) 14.8923 0.577497
\(666\) −9.11057 −0.353027
\(667\) 41.2230 1.59616
\(668\) −16.1135 −0.623451
\(669\) −21.9482 −0.848565
\(670\) −71.1171 −2.74749
\(671\) 13.5176 0.521840
\(672\) 29.5386 1.13948
\(673\) −34.5285 −1.33098 −0.665488 0.746408i \(-0.731777\pi\)
−0.665488 + 0.746408i \(0.731777\pi\)
\(674\) 56.2200 2.16551
\(675\) 3.18370 0.122541
\(676\) 6.26041 0.240785
\(677\) 21.9742 0.844536 0.422268 0.906471i \(-0.361234\pi\)
0.422268 + 0.906471i \(0.361234\pi\)
\(678\) −56.5662 −2.17241
\(679\) −17.0059 −0.652627
\(680\) 1.05316 0.0403867
\(681\) −44.8681 −1.71935
\(682\) −42.6192 −1.63197
\(683\) −29.6177 −1.13329 −0.566645 0.823962i \(-0.691759\pi\)
−0.566645 + 0.823962i \(0.691759\pi\)
\(684\) 47.6889 1.82343
\(685\) −18.9597 −0.724415
\(686\) 35.0100 1.33669
\(687\) 21.7898 0.831333
\(688\) 10.6690 0.406752
\(689\) 10.6760 0.406723
\(690\) −70.9550 −2.70121
\(691\) 15.0498 0.572521 0.286261 0.958152i \(-0.407588\pi\)
0.286261 + 0.958152i \(0.407588\pi\)
\(692\) −47.3346 −1.79939
\(693\) −34.3887 −1.30632
\(694\) −47.7154 −1.81125
\(695\) 1.89450 0.0718626
\(696\) −21.2946 −0.807171
\(697\) 0.147662 0.00559311
\(698\) 38.2039 1.44604
\(699\) −6.56564 −0.248335
\(700\) 3.01621 0.114002
\(701\) −1.80541 −0.0681896 −0.0340948 0.999419i \(-0.510855\pi\)
−0.0340948 + 0.999419i \(0.510855\pi\)
\(702\) −29.5646 −1.11584
\(703\) 4.49035 0.169357
\(704\) 65.2344 2.45862
\(705\) 13.6382 0.513646
\(706\) 55.1815 2.07678
\(707\) 10.9629 0.412301
\(708\) 17.6817 0.664521
\(709\) −0.439093 −0.0164905 −0.00824524 0.999966i \(-0.502625\pi\)
−0.00824524 + 0.999966i \(0.502625\pi\)
\(710\) −5.77148 −0.216600
\(711\) −14.2107 −0.532941
\(712\) −17.7461 −0.665064
\(713\) −17.6753 −0.661945
\(714\) 3.46300 0.129599
\(715\) −55.8929 −2.09027
\(716\) 35.6536 1.33244
\(717\) −31.9200 −1.19207
\(718\) −34.1430 −1.27421
\(719\) −18.9968 −0.708462 −0.354231 0.935158i \(-0.615257\pi\)
−0.354231 + 0.935158i \(0.615257\pi\)
\(720\) −29.9627 −1.11665
\(721\) −1.15033 −0.0428405
\(722\) −2.45729 −0.0914507
\(723\) 28.9619 1.07710
\(724\) −24.5649 −0.912949
\(725\) 7.22777 0.268433
\(726\) −131.882 −4.89461
\(727\) 16.6450 0.617328 0.308664 0.951171i \(-0.400118\pi\)
0.308664 + 0.951171i \(0.400118\pi\)
\(728\) −5.26092 −0.194983
\(729\) −43.1973 −1.59990
\(730\) 33.9975 1.25830
\(731\) 1.65522 0.0612205
\(732\) −15.4181 −0.569869
\(733\) −46.7273 −1.72591 −0.862955 0.505280i \(-0.831389\pi\)
−0.862955 + 0.505280i \(0.831389\pi\)
\(734\) −40.4424 −1.49276
\(735\) −33.7184 −1.24372
\(736\) 40.9092 1.50793
\(737\) −80.9402 −2.98147
\(738\) 3.03086 0.111567
\(739\) −52.9090 −1.94629 −0.973144 0.230196i \(-0.926063\pi\)
−0.973144 + 0.230196i \(0.926063\pi\)
\(740\) 5.97986 0.219824
\(741\) 47.8716 1.75861
\(742\) −7.81292 −0.286821
\(743\) −12.5736 −0.461281 −0.230640 0.973039i \(-0.574082\pi\)
−0.230640 + 0.973039i \(0.574082\pi\)
\(744\) 9.13057 0.334743
\(745\) −7.04111 −0.257966
\(746\) 65.7358 2.40676
\(747\) −0.974989 −0.0356730
\(748\) 6.38149 0.233330
\(749\) 16.2287 0.592983
\(750\) 56.9194 2.07840
\(751\) −34.4844 −1.25835 −0.629177 0.777262i \(-0.716608\pi\)
−0.629177 + 0.777262i \(0.716608\pi\)
\(752\) −5.94191 −0.216679
\(753\) −19.3433 −0.704910
\(754\) −67.1188 −2.44432
\(755\) −37.3784 −1.36034
\(756\) 11.9393 0.434227
\(757\) 27.7134 1.00726 0.503630 0.863920i \(-0.331998\pi\)
0.503630 + 0.863920i \(0.331998\pi\)
\(758\) 7.61130 0.276455
\(759\) −80.7557 −2.93125
\(760\) −10.6542 −0.386470
\(761\) −45.3965 −1.64562 −0.822811 0.568315i \(-0.807595\pi\)
−0.822811 + 0.568315i \(0.807595\pi\)
\(762\) 19.5042 0.706564
\(763\) −1.36575 −0.0494435
\(764\) −7.51449 −0.271865
\(765\) −4.64851 −0.168067
\(766\) −2.58839 −0.0935225
\(767\) 10.4679 0.377974
\(768\) 16.9714 0.612402
\(769\) 9.03554 0.325830 0.162915 0.986640i \(-0.447910\pi\)
0.162915 + 0.986640i \(0.447910\pi\)
\(770\) 40.9036 1.47406
\(771\) −54.1136 −1.94885
\(772\) −9.35049 −0.336531
\(773\) 33.0170 1.18754 0.593770 0.804635i \(-0.297639\pi\)
0.593770 + 0.804635i \(0.297639\pi\)
\(774\) 33.9744 1.22118
\(775\) −3.09908 −0.111322
\(776\) 12.1664 0.436748
\(777\) 3.69328 0.132496
\(778\) 6.19130 0.221969
\(779\) −1.49383 −0.0535219
\(780\) 63.7513 2.28266
\(781\) −6.56866 −0.235045
\(782\) 4.79605 0.171506
\(783\) 28.6102 1.02244
\(784\) 14.6904 0.524659
\(785\) −0.873692 −0.0311834
\(786\) −60.9315 −2.17336
\(787\) −30.3462 −1.08172 −0.540862 0.841111i \(-0.681902\pi\)
−0.540862 + 0.841111i \(0.681902\pi\)
\(788\) 61.2723 2.18274
\(789\) −21.3879 −0.761431
\(790\) 16.9028 0.601375
\(791\) 13.5237 0.480849
\(792\) 24.6024 0.874210
\(793\) −9.12779 −0.324137
\(794\) −25.0404 −0.888651
\(795\) 17.7828 0.630693
\(796\) 17.9232 0.635269
\(797\) −32.3344 −1.14534 −0.572672 0.819785i \(-0.694093\pi\)
−0.572672 + 0.819785i \(0.694093\pi\)
\(798\) −35.0334 −1.24017
\(799\) −0.921847 −0.0326126
\(800\) 7.17277 0.253596
\(801\) 78.3295 2.76764
\(802\) −10.5666 −0.373120
\(803\) 38.6934 1.36546
\(804\) 92.3202 3.25588
\(805\) 16.9638 0.597895
\(806\) 28.7787 1.01369
\(807\) 23.2740 0.819283
\(808\) −7.84307 −0.275918
\(809\) 18.0109 0.633228 0.316614 0.948554i \(-0.397454\pi\)
0.316614 + 0.948554i \(0.397454\pi\)
\(810\) 17.1253 0.601723
\(811\) −28.0217 −0.983976 −0.491988 0.870602i \(-0.663730\pi\)
−0.491988 + 0.870602i \(0.663730\pi\)
\(812\) 27.1050 0.951199
\(813\) −0.531592 −0.0186437
\(814\) 12.3333 0.432283
\(815\) 57.8394 2.02602
\(816\) 3.43406 0.120216
\(817\) −16.7450 −0.585835
\(818\) 33.7269 1.17923
\(819\) 23.2211 0.811412
\(820\) −1.98935 −0.0694711
\(821\) −21.5825 −0.753234 −0.376617 0.926369i \(-0.622913\pi\)
−0.376617 + 0.926369i \(0.622913\pi\)
\(822\) 44.6020 1.55567
\(823\) 24.1561 0.842028 0.421014 0.907054i \(-0.361674\pi\)
0.421014 + 0.907054i \(0.361674\pi\)
\(824\) 0.822970 0.0286695
\(825\) −14.1592 −0.492960
\(826\) −7.66063 −0.266547
\(827\) 19.6118 0.681969 0.340984 0.940069i \(-0.389240\pi\)
0.340984 + 0.940069i \(0.389240\pi\)
\(828\) 54.3225 1.88784
\(829\) −40.4379 −1.40447 −0.702234 0.711946i \(-0.747814\pi\)
−0.702234 + 0.711946i \(0.747814\pi\)
\(830\) 1.15970 0.0402537
\(831\) −53.6114 −1.85976
\(832\) −44.0498 −1.52715
\(833\) 2.27912 0.0789668
\(834\) −4.45674 −0.154324
\(835\) −15.8898 −0.549888
\(836\) −64.5583 −2.23280
\(837\) −12.2673 −0.424019
\(838\) −69.1403 −2.38841
\(839\) −21.4299 −0.739844 −0.369922 0.929063i \(-0.620616\pi\)
−0.369922 + 0.929063i \(0.620616\pi\)
\(840\) −8.76303 −0.302353
\(841\) 35.9520 1.23973
\(842\) −23.3779 −0.805657
\(843\) −42.2169 −1.45403
\(844\) 60.4778 2.08173
\(845\) 6.17347 0.212374
\(846\) −18.9215 −0.650533
\(847\) 31.5301 1.08339
\(848\) −7.74763 −0.266055
\(849\) −38.3486 −1.31612
\(850\) 0.840908 0.0288429
\(851\) 5.11497 0.175339
\(852\) 7.49220 0.256679
\(853\) 45.5361 1.55913 0.779563 0.626323i \(-0.215441\pi\)
0.779563 + 0.626323i \(0.215441\pi\)
\(854\) 6.67991 0.228582
\(855\) 47.0267 1.60828
\(856\) −11.6104 −0.396834
\(857\) −11.2757 −0.385171 −0.192586 0.981280i \(-0.561687\pi\)
−0.192586 + 0.981280i \(0.561687\pi\)
\(858\) 131.486 4.48885
\(859\) −1.68851 −0.0576112 −0.0288056 0.999585i \(-0.509170\pi\)
−0.0288056 + 0.999585i \(0.509170\pi\)
\(860\) −22.2996 −0.760410
\(861\) −1.22866 −0.0418726
\(862\) 59.4575 2.02513
\(863\) −5.22137 −0.177738 −0.0888688 0.996043i \(-0.528325\pi\)
−0.0888688 + 0.996043i \(0.528325\pi\)
\(864\) 28.3925 0.965931
\(865\) −46.6773 −1.58708
\(866\) −0.278090 −0.00944989
\(867\) −45.4388 −1.54318
\(868\) −11.6219 −0.394473
\(869\) 19.2375 0.652589
\(870\) −111.799 −3.79033
\(871\) 54.6552 1.85192
\(872\) 0.977087 0.0330884
\(873\) −53.7012 −1.81751
\(874\) −48.5192 −1.64119
\(875\) −13.6082 −0.460041
\(876\) −44.1336 −1.49114
\(877\) 27.1859 0.918002 0.459001 0.888436i \(-0.348207\pi\)
0.459001 + 0.888436i \(0.348207\pi\)
\(878\) −62.2889 −2.10215
\(879\) −25.3175 −0.853937
\(880\) 40.5617 1.36734
\(881\) −6.43419 −0.216773 −0.108387 0.994109i \(-0.534568\pi\)
−0.108387 + 0.994109i \(0.534568\pi\)
\(882\) 46.7803 1.57517
\(883\) 34.9601 1.17650 0.588251 0.808678i \(-0.299817\pi\)
0.588251 + 0.808678i \(0.299817\pi\)
\(884\) −4.30912 −0.144932
\(885\) 17.4362 0.586112
\(886\) −20.6427 −0.693504
\(887\) 56.0114 1.88068 0.940340 0.340237i \(-0.110507\pi\)
0.940340 + 0.340237i \(0.110507\pi\)
\(888\) −2.64225 −0.0886681
\(889\) −4.66304 −0.156393
\(890\) −93.1687 −3.12302
\(891\) 19.4908 0.652966
\(892\) −19.9866 −0.669202
\(893\) 9.32586 0.312078
\(894\) 16.5639 0.553981
\(895\) 35.1585 1.17522
\(896\) 10.3902 0.347111
\(897\) 54.5306 1.82072
\(898\) −56.5345 −1.88658
\(899\) −27.8497 −0.928839
\(900\) 9.52456 0.317485
\(901\) −1.20199 −0.0400441
\(902\) −4.10299 −0.136615
\(903\) −13.7727 −0.458325
\(904\) −9.67518 −0.321792
\(905\) −24.2238 −0.805227
\(906\) 87.9311 2.92131
\(907\) 0.730391 0.0242522 0.0121261 0.999926i \(-0.496140\pi\)
0.0121261 + 0.999926i \(0.496140\pi\)
\(908\) −40.8582 −1.35593
\(909\) 34.6184 1.14822
\(910\) −27.6203 −0.915604
\(911\) −20.9578 −0.694364 −0.347182 0.937798i \(-0.612861\pi\)
−0.347182 + 0.937798i \(0.612861\pi\)
\(912\) −34.7407 −1.15038
\(913\) 1.31988 0.0436817
\(914\) 18.0329 0.596476
\(915\) −15.2040 −0.502629
\(916\) 19.8424 0.655613
\(917\) 14.5674 0.481058
\(918\) 3.32863 0.109861
\(919\) −27.1161 −0.894478 −0.447239 0.894414i \(-0.647593\pi\)
−0.447239 + 0.894414i \(0.647593\pi\)
\(920\) −12.1363 −0.400121
\(921\) 21.4438 0.706597
\(922\) −34.8383 −1.14734
\(923\) 4.43552 0.145997
\(924\) −53.0987 −1.74682
\(925\) 0.896826 0.0294875
\(926\) −17.3026 −0.568600
\(927\) −3.63250 −0.119307
\(928\) 64.4577 2.11593
\(929\) 33.1168 1.08653 0.543264 0.839562i \(-0.317188\pi\)
0.543264 + 0.839562i \(0.317188\pi\)
\(930\) 47.9363 1.57189
\(931\) −23.0567 −0.755653
\(932\) −5.97886 −0.195844
\(933\) 3.73673 0.122335
\(934\) −72.3745 −2.36816
\(935\) 6.29287 0.205799
\(936\) −16.6129 −0.543010
\(937\) 39.9188 1.30409 0.652045 0.758180i \(-0.273911\pi\)
0.652045 + 0.758180i \(0.273911\pi\)
\(938\) −39.9978 −1.30597
\(939\) 12.3643 0.403493
\(940\) 12.4194 0.405076
\(941\) −7.20902 −0.235007 −0.117504 0.993072i \(-0.537489\pi\)
−0.117504 + 0.993072i \(0.537489\pi\)
\(942\) 2.05532 0.0669661
\(943\) −1.70162 −0.0554124
\(944\) −7.59661 −0.247249
\(945\) 11.7735 0.382991
\(946\) −45.9925 −1.49534
\(947\) −13.6196 −0.442576 −0.221288 0.975208i \(-0.571026\pi\)
−0.221288 + 0.975208i \(0.571026\pi\)
\(948\) −21.9423 −0.712652
\(949\) −26.1279 −0.848147
\(950\) −8.50705 −0.276005
\(951\) −20.3526 −0.659979
\(952\) 0.592317 0.0191971
\(953\) 44.5830 1.44419 0.722093 0.691796i \(-0.243180\pi\)
0.722093 + 0.691796i \(0.243180\pi\)
\(954\) −24.6716 −0.798772
\(955\) −7.41014 −0.239787
\(956\) −29.0673 −0.940102
\(957\) −127.241 −4.11312
\(958\) 61.6211 1.99089
\(959\) −10.6634 −0.344338
\(960\) −73.3730 −2.36810
\(961\) −19.0588 −0.614800
\(962\) −8.32814 −0.268510
\(963\) 51.2468 1.65141
\(964\) 26.3735 0.849434
\(965\) −9.22064 −0.296823
\(966\) −39.9066 −1.28398
\(967\) −35.9540 −1.15620 −0.578101 0.815965i \(-0.696206\pi\)
−0.578101 + 0.815965i \(0.696206\pi\)
\(968\) −22.5574 −0.725021
\(969\) −5.38977 −0.173144
\(970\) 63.8747 2.05089
\(971\) −50.5357 −1.62177 −0.810884 0.585206i \(-0.801013\pi\)
−0.810884 + 0.585206i \(0.801013\pi\)
\(972\) −48.4569 −1.55426
\(973\) 1.06551 0.0341587
\(974\) 29.1707 0.934688
\(975\) 9.56105 0.306199
\(976\) 6.62408 0.212032
\(977\) −40.4478 −1.29404 −0.647020 0.762473i \(-0.723985\pi\)
−0.647020 + 0.762473i \(0.723985\pi\)
\(978\) −136.065 −4.35087
\(979\) −106.038 −3.38898
\(980\) −30.7050 −0.980834
\(981\) −4.31276 −0.137696
\(982\) −2.22669 −0.0710564
\(983\) 42.8009 1.36514 0.682569 0.730822i \(-0.260863\pi\)
0.682569 + 0.730822i \(0.260863\pi\)
\(984\) 0.879011 0.0280218
\(985\) 60.4215 1.92519
\(986\) 7.55678 0.240657
\(987\) 7.67045 0.244153
\(988\) 43.5932 1.38689
\(989\) −19.0743 −0.606528
\(990\) 129.165 4.10513
\(991\) −51.5768 −1.63839 −0.819196 0.573514i \(-0.805580\pi\)
−0.819196 + 0.573514i \(0.805580\pi\)
\(992\) −27.6377 −0.877499
\(993\) −31.5040 −0.999748
\(994\) −3.24600 −0.102957
\(995\) 17.6743 0.560312
\(996\) −1.50545 −0.0477021
\(997\) 26.3663 0.835030 0.417515 0.908670i \(-0.362901\pi\)
0.417515 + 0.908670i \(0.362901\pi\)
\(998\) −68.5798 −2.17086
\(999\) 3.54997 0.112316
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.1.12 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.12 85 1.1 even 1 trivial