Properties

Label 4003.2.a.c.1.8
Level 4003
Weight 2
Character 4003.1
Self dual yes
Analytic conductor 31.964
Analytic rank 0
Dimension 179
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61424 q^{2} -1.76762 q^{3} +4.83424 q^{4} +0.635426 q^{5} +4.62098 q^{6} +1.21621 q^{7} -7.40938 q^{8} +0.124480 q^{9} +O(q^{10})\) \(q-2.61424 q^{2} -1.76762 q^{3} +4.83424 q^{4} +0.635426 q^{5} +4.62098 q^{6} +1.21621 q^{7} -7.40938 q^{8} +0.124480 q^{9} -1.66116 q^{10} +2.32539 q^{11} -8.54510 q^{12} +0.569099 q^{13} -3.17948 q^{14} -1.12319 q^{15} +9.70141 q^{16} +4.78556 q^{17} -0.325419 q^{18} +2.29795 q^{19} +3.07180 q^{20} -2.14981 q^{21} -6.07911 q^{22} -0.558266 q^{23} +13.0970 q^{24} -4.59623 q^{25} -1.48776 q^{26} +5.08283 q^{27} +5.87948 q^{28} +2.51766 q^{29} +2.93629 q^{30} -3.75396 q^{31} -10.5430 q^{32} -4.11040 q^{33} -12.5106 q^{34} +0.772815 q^{35} +0.601764 q^{36} -3.73653 q^{37} -6.00739 q^{38} -1.00595 q^{39} -4.70812 q^{40} +6.36538 q^{41} +5.62010 q^{42} +10.3933 q^{43} +11.2415 q^{44} +0.0790976 q^{45} +1.45944 q^{46} +11.6980 q^{47} -17.1484 q^{48} -5.52082 q^{49} +12.0156 q^{50} -8.45906 q^{51} +2.75116 q^{52} -4.60740 q^{53} -13.2877 q^{54} +1.47761 q^{55} -9.01140 q^{56} -4.06190 q^{57} -6.58176 q^{58} +1.77970 q^{59} -5.42978 q^{60} -2.96059 q^{61} +9.81375 q^{62} +0.151394 q^{63} +8.15916 q^{64} +0.361620 q^{65} +10.7456 q^{66} +6.25986 q^{67} +23.1346 q^{68} +0.986802 q^{69} -2.02032 q^{70} -14.4807 q^{71} -0.922317 q^{72} +11.9693 q^{73} +9.76817 q^{74} +8.12439 q^{75} +11.1088 q^{76} +2.82817 q^{77} +2.62979 q^{78} -2.61737 q^{79} +6.16453 q^{80} -9.35794 q^{81} -16.6406 q^{82} -4.81954 q^{83} -10.3927 q^{84} +3.04087 q^{85} -27.1705 q^{86} -4.45026 q^{87} -17.2297 q^{88} +7.97919 q^{89} -0.206780 q^{90} +0.692146 q^{91} -2.69879 q^{92} +6.63558 q^{93} -30.5815 q^{94} +1.46018 q^{95} +18.6361 q^{96} +15.5490 q^{97} +14.4327 q^{98} +0.289463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + O(q^{10}) \) \( 179q + 22q^{2} + 16q^{3} + 196q^{4} + 61q^{5} + 7q^{6} + 21q^{7} + 60q^{8} + 221q^{9} + 9q^{10} + 46q^{11} + 33q^{12} + 47q^{13} + 22q^{14} + 36q^{15} + 222q^{16} + 103q^{17} + 43q^{18} + 12q^{19} + 102q^{20} + 50q^{21} + 39q^{22} + 121q^{23} - 3q^{24} + 246q^{25} + 52q^{26} + 49q^{27} + 41q^{28} + 138q^{29} + 28q^{30} + 5q^{31} + 137q^{32} + 63q^{33} + 2q^{34} + 72q^{35} + 279q^{36} + 118q^{37} + 123q^{38} + q^{39} + 9q^{40} + 50q^{41} + 48q^{42} + 48q^{43} + 108q^{44} + 158q^{45} + 13q^{46} + 85q^{47} + 50q^{48} + 230q^{49} + 78q^{50} + 15q^{51} + 41q^{52} + 399q^{53} - 5q^{54} + 24q^{55} + 53q^{56} + 45q^{57} + 27q^{58} + 48q^{59} + 66q^{60} + 46q^{61} + 81q^{62} + 78q^{63} + 252q^{64} + 153q^{65} + 6q^{66} + 70q^{67} + 240q^{68} + 120q^{69} - 31q^{70} + 86q^{71} + 89q^{72} + 45q^{73} + 68q^{74} + 17q^{75} - 13q^{76} + 362q^{77} + 69q^{78} + 31q^{79} + 169q^{80} + 303q^{81} + 25q^{82} + 106q^{83} + 13q^{84} + 115q^{85} + 95q^{86} + 32q^{87} + 83q^{88} + 105q^{89} - 38q^{90} + 3q^{91} + 310q^{92} + 298q^{93} - 17q^{94} + 102q^{95} - 82q^{96} + 34q^{97} + 81q^{98} + 58q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61424 −1.84855 −0.924273 0.381733i \(-0.875327\pi\)
−0.924273 + 0.381733i \(0.875327\pi\)
\(3\) −1.76762 −1.02054 −0.510268 0.860016i \(-0.670454\pi\)
−0.510268 + 0.860016i \(0.670454\pi\)
\(4\) 4.83424 2.41712
\(5\) 0.635426 0.284171 0.142086 0.989854i \(-0.454619\pi\)
0.142086 + 0.989854i \(0.454619\pi\)
\(6\) 4.62098 1.88651
\(7\) 1.21621 0.459686 0.229843 0.973228i \(-0.426179\pi\)
0.229843 + 0.973228i \(0.426179\pi\)
\(8\) −7.40938 −2.61961
\(9\) 0.124480 0.0414932
\(10\) −1.66116 −0.525304
\(11\) 2.32539 0.701130 0.350565 0.936538i \(-0.385989\pi\)
0.350565 + 0.936538i \(0.385989\pi\)
\(12\) −8.54510 −2.46676
\(13\) 0.569099 0.157840 0.0789198 0.996881i \(-0.474853\pi\)
0.0789198 + 0.996881i \(0.474853\pi\)
\(14\) −3.17948 −0.849751
\(15\) −1.12319 −0.290007
\(16\) 9.70141 2.42535
\(17\) 4.78556 1.16067 0.580335 0.814378i \(-0.302922\pi\)
0.580335 + 0.814378i \(0.302922\pi\)
\(18\) −0.325419 −0.0767021
\(19\) 2.29795 0.527186 0.263593 0.964634i \(-0.415092\pi\)
0.263593 + 0.964634i \(0.415092\pi\)
\(20\) 3.07180 0.686876
\(21\) −2.14981 −0.469126
\(22\) −6.07911 −1.29607
\(23\) −0.558266 −0.116406 −0.0582032 0.998305i \(-0.518537\pi\)
−0.0582032 + 0.998305i \(0.518537\pi\)
\(24\) 13.0970 2.67341
\(25\) −4.59623 −0.919247
\(26\) −1.48776 −0.291774
\(27\) 5.08283 0.978190
\(28\) 5.87948 1.11112
\(29\) 2.51766 0.467517 0.233759 0.972295i \(-0.424897\pi\)
0.233759 + 0.972295i \(0.424897\pi\)
\(30\) 2.93629 0.536091
\(31\) −3.75396 −0.674231 −0.337116 0.941463i \(-0.609451\pi\)
−0.337116 + 0.941463i \(0.609451\pi\)
\(32\) −10.5430 −1.86376
\(33\) −4.11040 −0.715529
\(34\) −12.5106 −2.14555
\(35\) 0.772815 0.130630
\(36\) 0.601764 0.100294
\(37\) −3.73653 −0.614281 −0.307141 0.951664i \(-0.599372\pi\)
−0.307141 + 0.951664i \(0.599372\pi\)
\(38\) −6.00739 −0.974527
\(39\) −1.00595 −0.161081
\(40\) −4.70812 −0.744419
\(41\) 6.36538 0.994105 0.497052 0.867720i \(-0.334416\pi\)
0.497052 + 0.867720i \(0.334416\pi\)
\(42\) 5.62010 0.867201
\(43\) 10.3933 1.58496 0.792480 0.609898i \(-0.208790\pi\)
0.792480 + 0.609898i \(0.208790\pi\)
\(44\) 11.2415 1.69472
\(45\) 0.0790976 0.0117912
\(46\) 1.45944 0.215183
\(47\) 11.6980 1.70634 0.853168 0.521637i \(-0.174678\pi\)
0.853168 + 0.521637i \(0.174678\pi\)
\(48\) −17.1484 −2.47516
\(49\) −5.52082 −0.788689
\(50\) 12.0156 1.69927
\(51\) −8.45906 −1.18450
\(52\) 2.75116 0.381517
\(53\) −4.60740 −0.632875 −0.316438 0.948613i \(-0.602487\pi\)
−0.316438 + 0.948613i \(0.602487\pi\)
\(54\) −13.2877 −1.80823
\(55\) 1.47761 0.199241
\(56\) −9.01140 −1.20420
\(57\) −4.06190 −0.538012
\(58\) −6.58176 −0.864227
\(59\) 1.77970 0.231697 0.115848 0.993267i \(-0.463041\pi\)
0.115848 + 0.993267i \(0.463041\pi\)
\(60\) −5.42978 −0.700982
\(61\) −2.96059 −0.379065 −0.189532 0.981874i \(-0.560697\pi\)
−0.189532 + 0.981874i \(0.560697\pi\)
\(62\) 9.81375 1.24635
\(63\) 0.151394 0.0190738
\(64\) 8.15916 1.01989
\(65\) 0.361620 0.0448535
\(66\) 10.7456 1.32269
\(67\) 6.25986 0.764764 0.382382 0.924004i \(-0.375104\pi\)
0.382382 + 0.924004i \(0.375104\pi\)
\(68\) 23.1346 2.80548
\(69\) 0.986802 0.118797
\(70\) −2.02032 −0.241475
\(71\) −14.4807 −1.71855 −0.859274 0.511515i \(-0.829084\pi\)
−0.859274 + 0.511515i \(0.829084\pi\)
\(72\) −0.922317 −0.108696
\(73\) 11.9693 1.40090 0.700452 0.713699i \(-0.252982\pi\)
0.700452 + 0.713699i \(0.252982\pi\)
\(74\) 9.76817 1.13553
\(75\) 8.12439 0.938124
\(76\) 11.1088 1.27427
\(77\) 2.82817 0.322300
\(78\) 2.62979 0.297765
\(79\) −2.61737 −0.294477 −0.147239 0.989101i \(-0.547038\pi\)
−0.147239 + 0.989101i \(0.547038\pi\)
\(80\) 6.16453 0.689215
\(81\) −9.35794 −1.03977
\(82\) −16.6406 −1.83765
\(83\) −4.81954 −0.529014 −0.264507 0.964384i \(-0.585209\pi\)
−0.264507 + 0.964384i \(0.585209\pi\)
\(84\) −10.3927 −1.13393
\(85\) 3.04087 0.329829
\(86\) −27.1705 −2.92987
\(87\) −4.45026 −0.477118
\(88\) −17.2297 −1.83669
\(89\) 7.97919 0.845793 0.422896 0.906178i \(-0.361013\pi\)
0.422896 + 0.906178i \(0.361013\pi\)
\(90\) −0.206780 −0.0217965
\(91\) 0.692146 0.0725566
\(92\) −2.69879 −0.281369
\(93\) 6.63558 0.688077
\(94\) −30.5815 −3.15424
\(95\) 1.46018 0.149811
\(96\) 18.6361 1.90203
\(97\) 15.5490 1.57876 0.789380 0.613905i \(-0.210402\pi\)
0.789380 + 0.613905i \(0.210402\pi\)
\(98\) 14.4327 1.45793
\(99\) 0.289463 0.0290921
\(100\) −22.2193 −2.22193
\(101\) 13.9649 1.38956 0.694782 0.719221i \(-0.255501\pi\)
0.694782 + 0.719221i \(0.255501\pi\)
\(102\) 22.1140 2.18961
\(103\) 10.2346 1.00844 0.504221 0.863575i \(-0.331780\pi\)
0.504221 + 0.863575i \(0.331780\pi\)
\(104\) −4.21667 −0.413478
\(105\) −1.36604 −0.133312
\(106\) 12.0448 1.16990
\(107\) 17.7828 1.71913 0.859563 0.511030i \(-0.170736\pi\)
0.859563 + 0.511030i \(0.170736\pi\)
\(108\) 24.5716 2.36440
\(109\) −2.53870 −0.243163 −0.121581 0.992581i \(-0.538797\pi\)
−0.121581 + 0.992581i \(0.538797\pi\)
\(110\) −3.86283 −0.368306
\(111\) 6.60476 0.626896
\(112\) 11.7990 1.11490
\(113\) 9.84846 0.926466 0.463233 0.886237i \(-0.346689\pi\)
0.463233 + 0.886237i \(0.346689\pi\)
\(114\) 10.6188 0.994540
\(115\) −0.354737 −0.0330794
\(116\) 12.1710 1.13005
\(117\) 0.0708412 0.00654927
\(118\) −4.65255 −0.428302
\(119\) 5.82027 0.533544
\(120\) 8.32216 0.759706
\(121\) −5.59258 −0.508416
\(122\) 7.73969 0.700718
\(123\) −11.2516 −1.01452
\(124\) −18.1476 −1.62970
\(125\) −6.09770 −0.545395
\(126\) −0.395780 −0.0352589
\(127\) −11.3759 −1.00945 −0.504726 0.863280i \(-0.668407\pi\)
−0.504726 + 0.863280i \(0.668407\pi\)
\(128\) −0.243942 −0.0215617
\(129\) −18.3714 −1.61751
\(130\) −0.945361 −0.0829137
\(131\) −2.66845 −0.233144 −0.116572 0.993182i \(-0.537191\pi\)
−0.116572 + 0.993182i \(0.537191\pi\)
\(132\) −19.8707 −1.72952
\(133\) 2.79480 0.242340
\(134\) −16.3648 −1.41370
\(135\) 3.22976 0.277974
\(136\) −35.4581 −3.04050
\(137\) −12.9380 −1.10537 −0.552684 0.833391i \(-0.686397\pi\)
−0.552684 + 0.833391i \(0.686397\pi\)
\(138\) −2.57973 −0.219602
\(139\) −21.8624 −1.85435 −0.927174 0.374631i \(-0.877769\pi\)
−0.927174 + 0.374631i \(0.877769\pi\)
\(140\) 3.73597 0.315747
\(141\) −20.6777 −1.74138
\(142\) 37.8561 3.17681
\(143\) 1.32337 0.110666
\(144\) 1.20763 0.100636
\(145\) 1.59979 0.132855
\(146\) −31.2907 −2.58964
\(147\) 9.75871 0.804885
\(148\) −18.0633 −1.48479
\(149\) 22.1066 1.81104 0.905521 0.424301i \(-0.139480\pi\)
0.905521 + 0.424301i \(0.139480\pi\)
\(150\) −21.2391 −1.73417
\(151\) −18.1451 −1.47663 −0.738313 0.674458i \(-0.764377\pi\)
−0.738313 + 0.674458i \(0.764377\pi\)
\(152\) −17.0264 −1.38102
\(153\) 0.595705 0.0481599
\(154\) −7.39351 −0.595786
\(155\) −2.38537 −0.191597
\(156\) −4.86300 −0.389352
\(157\) −10.9297 −0.872287 −0.436143 0.899877i \(-0.643656\pi\)
−0.436143 + 0.899877i \(0.643656\pi\)
\(158\) 6.84243 0.544354
\(159\) 8.14413 0.645872
\(160\) −6.69931 −0.529627
\(161\) −0.678971 −0.0535104
\(162\) 24.4639 1.92206
\(163\) −19.6291 −1.53747 −0.768735 0.639567i \(-0.779114\pi\)
−0.768735 + 0.639567i \(0.779114\pi\)
\(164\) 30.7718 2.40287
\(165\) −2.61186 −0.203333
\(166\) 12.5994 0.977906
\(167\) 18.1017 1.40075 0.700377 0.713773i \(-0.253015\pi\)
0.700377 + 0.713773i \(0.253015\pi\)
\(168\) 15.9287 1.22893
\(169\) −12.6761 −0.975087
\(170\) −7.94957 −0.609704
\(171\) 0.286048 0.0218746
\(172\) 50.2436 3.83104
\(173\) −20.4973 −1.55838 −0.779192 0.626786i \(-0.784370\pi\)
−0.779192 + 0.626786i \(0.784370\pi\)
\(174\) 11.6340 0.881974
\(175\) −5.59001 −0.422565
\(176\) 22.5595 1.70049
\(177\) −3.14583 −0.236455
\(178\) −20.8595 −1.56349
\(179\) −17.4580 −1.30487 −0.652436 0.757844i \(-0.726253\pi\)
−0.652436 + 0.757844i \(0.726253\pi\)
\(180\) 0.382377 0.0285007
\(181\) −15.9102 −1.18260 −0.591298 0.806453i \(-0.701384\pi\)
−0.591298 + 0.806453i \(0.701384\pi\)
\(182\) −1.80944 −0.134124
\(183\) 5.23320 0.386849
\(184\) 4.13640 0.304940
\(185\) −2.37429 −0.174561
\(186\) −17.3470 −1.27194
\(187\) 11.1283 0.813781
\(188\) 56.5512 4.12442
\(189\) 6.18181 0.449661
\(190\) −3.81725 −0.276933
\(191\) 6.98269 0.505250 0.252625 0.967564i \(-0.418706\pi\)
0.252625 + 0.967564i \(0.418706\pi\)
\(192\) −14.4223 −1.04084
\(193\) −16.1536 −1.16276 −0.581379 0.813633i \(-0.697487\pi\)
−0.581379 + 0.813633i \(0.697487\pi\)
\(194\) −40.6487 −2.91841
\(195\) −0.639207 −0.0457746
\(196\) −26.6890 −1.90636
\(197\) −18.2648 −1.30131 −0.650656 0.759373i \(-0.725506\pi\)
−0.650656 + 0.759373i \(0.725506\pi\)
\(198\) −0.756726 −0.0537782
\(199\) 18.8995 1.33975 0.669874 0.742474i \(-0.266348\pi\)
0.669874 + 0.742474i \(0.266348\pi\)
\(200\) 34.0552 2.40807
\(201\) −11.0651 −0.780469
\(202\) −36.5077 −2.56867
\(203\) 3.06201 0.214911
\(204\) −40.8931 −2.86309
\(205\) 4.04473 0.282496
\(206\) −26.7556 −1.86415
\(207\) −0.0694927 −0.00483008
\(208\) 5.52106 0.382816
\(209\) 5.34362 0.369626
\(210\) 3.57116 0.246434
\(211\) −3.25580 −0.224138 −0.112069 0.993700i \(-0.535748\pi\)
−0.112069 + 0.993700i \(0.535748\pi\)
\(212\) −22.2733 −1.52974
\(213\) 25.5965 1.75384
\(214\) −46.4884 −3.17788
\(215\) 6.60416 0.450400
\(216\) −37.6606 −2.56248
\(217\) −4.56562 −0.309935
\(218\) 6.63675 0.449498
\(219\) −21.1572 −1.42967
\(220\) 7.14313 0.481590
\(221\) 2.72346 0.183200
\(222\) −17.2664 −1.15885
\(223\) −17.8718 −1.19678 −0.598391 0.801204i \(-0.704193\pi\)
−0.598391 + 0.801204i \(0.704193\pi\)
\(224\) −12.8226 −0.856745
\(225\) −0.572137 −0.0381425
\(226\) −25.7462 −1.71261
\(227\) −6.77533 −0.449694 −0.224847 0.974394i \(-0.572188\pi\)
−0.224847 + 0.974394i \(0.572188\pi\)
\(228\) −19.6362 −1.30044
\(229\) 15.6402 1.03353 0.516767 0.856126i \(-0.327135\pi\)
0.516767 + 0.856126i \(0.327135\pi\)
\(230\) 0.927367 0.0611487
\(231\) −4.99913 −0.328919
\(232\) −18.6543 −1.22471
\(233\) 23.6859 1.55171 0.775856 0.630910i \(-0.217318\pi\)
0.775856 + 0.630910i \(0.217318\pi\)
\(234\) −0.185196 −0.0121066
\(235\) 7.43325 0.484891
\(236\) 8.60348 0.560039
\(237\) 4.62651 0.300524
\(238\) −15.2156 −0.986280
\(239\) 17.2769 1.11755 0.558775 0.829319i \(-0.311271\pi\)
0.558775 + 0.829319i \(0.311271\pi\)
\(240\) −10.8965 −0.703369
\(241\) 15.4529 0.995411 0.497705 0.867346i \(-0.334176\pi\)
0.497705 + 0.867346i \(0.334176\pi\)
\(242\) 14.6203 0.939830
\(243\) 1.29281 0.0829335
\(244\) −14.3122 −0.916245
\(245\) −3.50808 −0.224123
\(246\) 29.4143 1.87539
\(247\) 1.30776 0.0832108
\(248\) 27.8145 1.76622
\(249\) 8.51912 0.539877
\(250\) 15.9408 1.00819
\(251\) −23.9145 −1.50947 −0.754734 0.656031i \(-0.772234\pi\)
−0.754734 + 0.656031i \(0.772234\pi\)
\(252\) 0.731875 0.0461038
\(253\) −1.29818 −0.0816161
\(254\) 29.7394 1.86602
\(255\) −5.37511 −0.336602
\(256\) −15.6806 −0.980037
\(257\) −15.4765 −0.965400 −0.482700 0.875786i \(-0.660344\pi\)
−0.482700 + 0.875786i \(0.660344\pi\)
\(258\) 48.0271 2.99004
\(259\) −4.54442 −0.282377
\(260\) 1.74816 0.108416
\(261\) 0.313397 0.0193988
\(262\) 6.97598 0.430977
\(263\) 23.0987 1.42433 0.712163 0.702014i \(-0.247716\pi\)
0.712163 + 0.702014i \(0.247716\pi\)
\(264\) 30.4555 1.87441
\(265\) −2.92766 −0.179845
\(266\) −7.30628 −0.447977
\(267\) −14.1042 −0.863162
\(268\) 30.2617 1.84853
\(269\) 10.9497 0.667614 0.333807 0.942641i \(-0.391667\pi\)
0.333807 + 0.942641i \(0.391667\pi\)
\(270\) −8.44337 −0.513847
\(271\) 27.8489 1.69170 0.845852 0.533418i \(-0.179093\pi\)
0.845852 + 0.533418i \(0.179093\pi\)
\(272\) 46.4267 2.81503
\(273\) −1.22345 −0.0740466
\(274\) 33.8230 2.04332
\(275\) −10.6880 −0.644512
\(276\) 4.77044 0.287147
\(277\) 16.1475 0.970210 0.485105 0.874456i \(-0.338781\pi\)
0.485105 + 0.874456i \(0.338781\pi\)
\(278\) 57.1536 3.42785
\(279\) −0.467292 −0.0279760
\(280\) −5.72608 −0.342199
\(281\) 20.3570 1.21439 0.607197 0.794551i \(-0.292294\pi\)
0.607197 + 0.794551i \(0.292294\pi\)
\(282\) 54.0564 3.21901
\(283\) 1.90046 0.112971 0.0564853 0.998403i \(-0.482011\pi\)
0.0564853 + 0.998403i \(0.482011\pi\)
\(284\) −70.0034 −4.15394
\(285\) −2.58104 −0.152888
\(286\) −3.45962 −0.204571
\(287\) 7.74167 0.456976
\(288\) −1.31239 −0.0773334
\(289\) 5.90161 0.347154
\(290\) −4.18222 −0.245588
\(291\) −27.4847 −1.61118
\(292\) 57.8627 3.38616
\(293\) 26.2495 1.53351 0.766757 0.641938i \(-0.221869\pi\)
0.766757 + 0.641938i \(0.221869\pi\)
\(294\) −25.5116 −1.48787
\(295\) 1.13087 0.0658416
\(296\) 27.6854 1.60918
\(297\) 11.8195 0.685839
\(298\) −57.7919 −3.34779
\(299\) −0.317708 −0.0183735
\(300\) 39.2753 2.26756
\(301\) 12.6405 0.728584
\(302\) 47.4356 2.72961
\(303\) −24.6847 −1.41810
\(304\) 22.2933 1.27861
\(305\) −1.88124 −0.107719
\(306\) −1.55731 −0.0890257
\(307\) −15.1314 −0.863594 −0.431797 0.901971i \(-0.642120\pi\)
−0.431797 + 0.901971i \(0.642120\pi\)
\(308\) 13.6721 0.779038
\(309\) −18.0908 −1.02915
\(310\) 6.23591 0.354176
\(311\) 21.5502 1.22200 0.610999 0.791632i \(-0.290768\pi\)
0.610999 + 0.791632i \(0.290768\pi\)
\(312\) 7.45347 0.421969
\(313\) 22.2632 1.25839 0.629194 0.777248i \(-0.283385\pi\)
0.629194 + 0.777248i \(0.283385\pi\)
\(314\) 28.5729 1.61246
\(315\) 0.0961997 0.00542024
\(316\) −12.6530 −0.711787
\(317\) −24.0174 −1.34895 −0.674476 0.738297i \(-0.735630\pi\)
−0.674476 + 0.738297i \(0.735630\pi\)
\(318\) −21.2907 −1.19392
\(319\) 5.85453 0.327791
\(320\) 5.18455 0.289825
\(321\) −31.4332 −1.75443
\(322\) 1.77499 0.0989165
\(323\) 10.9970 0.611889
\(324\) −45.2386 −2.51325
\(325\) −2.61571 −0.145093
\(326\) 51.3152 2.84209
\(327\) 4.48745 0.248156
\(328\) −47.1635 −2.60417
\(329\) 14.2273 0.784378
\(330\) 6.82801 0.375870
\(331\) −24.9804 −1.37305 −0.686523 0.727109i \(-0.740864\pi\)
−0.686523 + 0.727109i \(0.740864\pi\)
\(332\) −23.2988 −1.27869
\(333\) −0.465121 −0.0254885
\(334\) −47.3223 −2.58936
\(335\) 3.97768 0.217324
\(336\) −20.8561 −1.13780
\(337\) −3.22461 −0.175656 −0.0878278 0.996136i \(-0.527993\pi\)
−0.0878278 + 0.996136i \(0.527993\pi\)
\(338\) 33.1384 1.80249
\(339\) −17.4083 −0.945491
\(340\) 14.7003 0.797236
\(341\) −8.72941 −0.472724
\(342\) −0.747797 −0.0404363
\(343\) −15.2280 −0.822235
\(344\) −77.0077 −4.15198
\(345\) 0.627040 0.0337587
\(346\) 53.5849 2.88074
\(347\) 11.6525 0.625540 0.312770 0.949829i \(-0.398743\pi\)
0.312770 + 0.949829i \(0.398743\pi\)
\(348\) −21.5136 −1.15325
\(349\) 20.8462 1.11587 0.557936 0.829884i \(-0.311594\pi\)
0.557936 + 0.829884i \(0.311594\pi\)
\(350\) 14.6136 0.781130
\(351\) 2.89263 0.154397
\(352\) −24.5166 −1.30674
\(353\) 20.9571 1.11543 0.557717 0.830031i \(-0.311678\pi\)
0.557717 + 0.830031i \(0.311678\pi\)
\(354\) 8.22394 0.437097
\(355\) −9.20145 −0.488362
\(356\) 38.5733 2.04438
\(357\) −10.2880 −0.544500
\(358\) 45.6394 2.41212
\(359\) −28.9982 −1.53047 −0.765233 0.643753i \(-0.777376\pi\)
−0.765233 + 0.643753i \(0.777376\pi\)
\(360\) −0.586064 −0.0308883
\(361\) −13.7194 −0.722075
\(362\) 41.5931 2.18608
\(363\) 9.88555 0.518857
\(364\) 3.34600 0.175378
\(365\) 7.60563 0.398097
\(366\) −13.6808 −0.715108
\(367\) 20.0389 1.04602 0.523012 0.852326i \(-0.324808\pi\)
0.523012 + 0.852326i \(0.324808\pi\)
\(368\) −5.41596 −0.282327
\(369\) 0.792360 0.0412486
\(370\) 6.20696 0.322684
\(371\) −5.60359 −0.290924
\(372\) 32.0780 1.66317
\(373\) 22.2545 1.15229 0.576147 0.817346i \(-0.304556\pi\)
0.576147 + 0.817346i \(0.304556\pi\)
\(374\) −29.0920 −1.50431
\(375\) 10.7784 0.556595
\(376\) −86.6753 −4.46994
\(377\) 1.43280 0.0737927
\(378\) −16.1607 −0.831218
\(379\) −0.974799 −0.0500721 −0.0250360 0.999687i \(-0.507970\pi\)
−0.0250360 + 0.999687i \(0.507970\pi\)
\(380\) 7.05885 0.362112
\(381\) 20.1084 1.03018
\(382\) −18.2544 −0.933977
\(383\) −10.1599 −0.519149 −0.259574 0.965723i \(-0.583582\pi\)
−0.259574 + 0.965723i \(0.583582\pi\)
\(384\) 0.431198 0.0220045
\(385\) 1.79709 0.0915884
\(386\) 42.2292 2.14941
\(387\) 1.29375 0.0657650
\(388\) 75.1675 3.81605
\(389\) 11.5605 0.586140 0.293070 0.956091i \(-0.405323\pi\)
0.293070 + 0.956091i \(0.405323\pi\)
\(390\) 1.67104 0.0846164
\(391\) −2.67162 −0.135109
\(392\) 40.9059 2.06606
\(393\) 4.71681 0.237932
\(394\) 47.7485 2.40553
\(395\) −1.66315 −0.0836819
\(396\) 1.39933 0.0703192
\(397\) 24.7766 1.24350 0.621752 0.783214i \(-0.286421\pi\)
0.621752 + 0.783214i \(0.286421\pi\)
\(398\) −49.4078 −2.47659
\(399\) −4.94015 −0.247317
\(400\) −44.5899 −2.22950
\(401\) −1.71878 −0.0858317 −0.0429159 0.999079i \(-0.513665\pi\)
−0.0429159 + 0.999079i \(0.513665\pi\)
\(402\) 28.9267 1.44273
\(403\) −2.13637 −0.106420
\(404\) 67.5099 3.35874
\(405\) −5.94628 −0.295473
\(406\) −8.00483 −0.397273
\(407\) −8.68887 −0.430691
\(408\) 62.6764 3.10294
\(409\) 33.0250 1.63298 0.816491 0.577357i \(-0.195916\pi\)
0.816491 + 0.577357i \(0.195916\pi\)
\(410\) −10.5739 −0.522207
\(411\) 22.8695 1.12807
\(412\) 49.4764 2.43753
\(413\) 2.16449 0.106508
\(414\) 0.181670 0.00892862
\(415\) −3.06247 −0.150331
\(416\) −6.00002 −0.294175
\(417\) 38.6445 1.89243
\(418\) −13.9695 −0.683271
\(419\) 16.8697 0.824137 0.412069 0.911153i \(-0.364806\pi\)
0.412069 + 0.911153i \(0.364806\pi\)
\(420\) −6.60378 −0.322232
\(421\) 34.8891 1.70039 0.850195 0.526467i \(-0.176484\pi\)
0.850195 + 0.526467i \(0.176484\pi\)
\(422\) 8.51143 0.414330
\(423\) 1.45617 0.0708013
\(424\) 34.1380 1.65789
\(425\) −21.9956 −1.06694
\(426\) −66.9152 −3.24205
\(427\) −3.60071 −0.174251
\(428\) 85.9662 4.15533
\(429\) −2.33922 −0.112939
\(430\) −17.2648 −0.832585
\(431\) −7.55076 −0.363707 −0.181854 0.983326i \(-0.558210\pi\)
−0.181854 + 0.983326i \(0.558210\pi\)
\(432\) 49.3106 2.37246
\(433\) −6.37306 −0.306270 −0.153135 0.988205i \(-0.548937\pi\)
−0.153135 + 0.988205i \(0.548937\pi\)
\(434\) 11.9356 0.572928
\(435\) −2.82781 −0.135583
\(436\) −12.2727 −0.587754
\(437\) −1.28287 −0.0613679
\(438\) 55.3101 2.64282
\(439\) 10.0360 0.478990 0.239495 0.970898i \(-0.423018\pi\)
0.239495 + 0.970898i \(0.423018\pi\)
\(440\) −10.9482 −0.521935
\(441\) −0.687230 −0.0327252
\(442\) −7.11977 −0.338653
\(443\) −37.9851 −1.80473 −0.902363 0.430976i \(-0.858169\pi\)
−0.902363 + 0.430976i \(0.858169\pi\)
\(444\) 31.9290 1.51528
\(445\) 5.07019 0.240350
\(446\) 46.7210 2.21231
\(447\) −39.0760 −1.84823
\(448\) 9.92329 0.468832
\(449\) −1.17432 −0.0554195 −0.0277097 0.999616i \(-0.508821\pi\)
−0.0277097 + 0.999616i \(0.508821\pi\)
\(450\) 1.49570 0.0705081
\(451\) 14.8020 0.696997
\(452\) 47.6099 2.23938
\(453\) 32.0736 1.50695
\(454\) 17.7123 0.831280
\(455\) 0.439808 0.0206185
\(456\) 30.0962 1.40938
\(457\) 9.46386 0.442701 0.221350 0.975194i \(-0.428954\pi\)
0.221350 + 0.975194i \(0.428954\pi\)
\(458\) −40.8872 −1.91054
\(459\) 24.3242 1.13536
\(460\) −1.71488 −0.0799569
\(461\) −16.6067 −0.773449 −0.386725 0.922195i \(-0.626394\pi\)
−0.386725 + 0.922195i \(0.626394\pi\)
\(462\) 13.0689 0.608021
\(463\) −29.5498 −1.37330 −0.686648 0.726991i \(-0.740918\pi\)
−0.686648 + 0.726991i \(0.740918\pi\)
\(464\) 24.4248 1.13389
\(465\) 4.21642 0.195532
\(466\) −61.9205 −2.86841
\(467\) 28.2613 1.30778 0.653888 0.756591i \(-0.273137\pi\)
0.653888 + 0.756591i \(0.273137\pi\)
\(468\) 0.342463 0.0158304
\(469\) 7.61334 0.351551
\(470\) −19.4323 −0.896344
\(471\) 19.3196 0.890200
\(472\) −13.1864 −0.606955
\(473\) 24.1684 1.11126
\(474\) −12.0948 −0.555533
\(475\) −10.5619 −0.484614
\(476\) 28.1366 1.28964
\(477\) −0.573527 −0.0262600
\(478\) −45.1660 −2.06584
\(479\) 10.7974 0.493348 0.246674 0.969099i \(-0.420662\pi\)
0.246674 + 0.969099i \(0.420662\pi\)
\(480\) 11.8418 0.540504
\(481\) −2.12645 −0.0969579
\(482\) −40.3977 −1.84006
\(483\) 1.20016 0.0546093
\(484\) −27.0359 −1.22890
\(485\) 9.88023 0.448638
\(486\) −3.37970 −0.153306
\(487\) −18.5032 −0.838462 −0.419231 0.907880i \(-0.637700\pi\)
−0.419231 + 0.907880i \(0.637700\pi\)
\(488\) 21.9361 0.993002
\(489\) 34.6968 1.56904
\(490\) 9.17094 0.414301
\(491\) 8.86501 0.400072 0.200036 0.979789i \(-0.435894\pi\)
0.200036 + 0.979789i \(0.435894\pi\)
\(492\) −54.3928 −2.45222
\(493\) 12.0484 0.542633
\(494\) −3.41880 −0.153819
\(495\) 0.183933 0.00826715
\(496\) −36.4187 −1.63525
\(497\) −17.6117 −0.789993
\(498\) −22.2710 −0.997988
\(499\) 30.8547 1.38124 0.690622 0.723216i \(-0.257337\pi\)
0.690622 + 0.723216i \(0.257337\pi\)
\(500\) −29.4778 −1.31829
\(501\) −31.9970 −1.42952
\(502\) 62.5181 2.79032
\(503\) −23.8974 −1.06553 −0.532765 0.846263i \(-0.678847\pi\)
−0.532765 + 0.846263i \(0.678847\pi\)
\(504\) −1.12174 −0.0499661
\(505\) 8.87369 0.394874
\(506\) 3.39376 0.150871
\(507\) 22.4066 0.995111
\(508\) −54.9941 −2.43997
\(509\) −12.7857 −0.566715 −0.283357 0.959014i \(-0.591448\pi\)
−0.283357 + 0.959014i \(0.591448\pi\)
\(510\) 14.0518 0.622225
\(511\) 14.5573 0.643976
\(512\) 41.4807 1.83321
\(513\) 11.6801 0.515688
\(514\) 40.4594 1.78459
\(515\) 6.50332 0.286570
\(516\) −88.8116 −3.90971
\(517\) 27.2025 1.19636
\(518\) 11.8802 0.521986
\(519\) 36.2315 1.59039
\(520\) −2.67938 −0.117499
\(521\) −11.5015 −0.503891 −0.251945 0.967741i \(-0.581070\pi\)
−0.251945 + 0.967741i \(0.581070\pi\)
\(522\) −0.819294 −0.0358595
\(523\) 20.0814 0.878099 0.439049 0.898463i \(-0.355315\pi\)
0.439049 + 0.898463i \(0.355315\pi\)
\(524\) −12.9000 −0.563537
\(525\) 9.88101 0.431243
\(526\) −60.3855 −2.63293
\(527\) −17.9648 −0.782560
\(528\) −39.8767 −1.73541
\(529\) −22.6883 −0.986450
\(530\) 7.65361 0.332452
\(531\) 0.221536 0.00961384
\(532\) 13.5107 0.585765
\(533\) 3.62253 0.156909
\(534\) 36.8717 1.59559
\(535\) 11.2996 0.488526
\(536\) −46.3817 −2.00338
\(537\) 30.8591 1.33167
\(538\) −28.6251 −1.23411
\(539\) −12.8380 −0.552974
\(540\) 15.6134 0.671896
\(541\) 6.25326 0.268849 0.134424 0.990924i \(-0.457081\pi\)
0.134424 + 0.990924i \(0.457081\pi\)
\(542\) −72.8038 −3.12719
\(543\) 28.1232 1.20688
\(544\) −50.4543 −2.16321
\(545\) −1.61315 −0.0690999
\(546\) 3.19839 0.136879
\(547\) 31.0365 1.32702 0.663512 0.748166i \(-0.269065\pi\)
0.663512 + 0.748166i \(0.269065\pi\)
\(548\) −62.5455 −2.67181
\(549\) −0.368533 −0.0157286
\(550\) 27.9410 1.19141
\(551\) 5.78545 0.246468
\(552\) −7.31159 −0.311202
\(553\) −3.18328 −0.135367
\(554\) −42.2134 −1.79348
\(555\) 4.19684 0.178146
\(556\) −105.688 −4.48218
\(557\) 39.3710 1.66820 0.834102 0.551610i \(-0.185986\pi\)
0.834102 + 0.551610i \(0.185986\pi\)
\(558\) 1.22161 0.0517149
\(559\) 5.91480 0.250169
\(560\) 7.49739 0.316823
\(561\) −19.6706 −0.830492
\(562\) −53.2179 −2.24486
\(563\) −22.9380 −0.966722 −0.483361 0.875421i \(-0.660584\pi\)
−0.483361 + 0.875421i \(0.660584\pi\)
\(564\) −99.9610 −4.20912
\(565\) 6.25797 0.263275
\(566\) −4.96825 −0.208831
\(567\) −11.3813 −0.477968
\(568\) 107.293 4.50193
\(569\) −8.76379 −0.367397 −0.183699 0.982983i \(-0.558807\pi\)
−0.183699 + 0.982983i \(0.558807\pi\)
\(570\) 6.74745 0.282620
\(571\) 32.5623 1.36269 0.681344 0.731963i \(-0.261396\pi\)
0.681344 + 0.731963i \(0.261396\pi\)
\(572\) 6.39751 0.267493
\(573\) −12.3427 −0.515625
\(574\) −20.2386 −0.844741
\(575\) 2.56592 0.107006
\(576\) 1.01565 0.0423187
\(577\) 40.2664 1.67631 0.838156 0.545431i \(-0.183634\pi\)
0.838156 + 0.545431i \(0.183634\pi\)
\(578\) −15.4282 −0.641729
\(579\) 28.5533 1.18664
\(580\) 7.73375 0.321126
\(581\) −5.86160 −0.243180
\(582\) 71.8515 2.97834
\(583\) −10.7140 −0.443728
\(584\) −88.6854 −3.66983
\(585\) 0.0450143 0.00186111
\(586\) −68.6225 −2.83477
\(587\) 20.2642 0.836395 0.418197 0.908356i \(-0.362662\pi\)
0.418197 + 0.908356i \(0.362662\pi\)
\(588\) 47.1760 1.94550
\(589\) −8.62642 −0.355445
\(590\) −2.95635 −0.121711
\(591\) 32.2852 1.32804
\(592\) −36.2496 −1.48985
\(593\) 8.40970 0.345345 0.172673 0.984979i \(-0.444760\pi\)
0.172673 + 0.984979i \(0.444760\pi\)
\(594\) −30.8991 −1.26780
\(595\) 3.69836 0.151618
\(596\) 106.869 4.37751
\(597\) −33.4071 −1.36726
\(598\) 0.830565 0.0339643
\(599\) 15.8064 0.645834 0.322917 0.946427i \(-0.395337\pi\)
0.322917 + 0.946427i \(0.395337\pi\)
\(600\) −60.1967 −2.45752
\(601\) −32.9172 −1.34272 −0.671359 0.741132i \(-0.734289\pi\)
−0.671359 + 0.741132i \(0.734289\pi\)
\(602\) −33.0452 −1.34682
\(603\) 0.779225 0.0317325
\(604\) −87.7177 −3.56918
\(605\) −3.55367 −0.144477
\(606\) 64.5317 2.62142
\(607\) −16.5774 −0.672857 −0.336428 0.941709i \(-0.609219\pi\)
−0.336428 + 0.941709i \(0.609219\pi\)
\(608\) −24.2273 −0.982548
\(609\) −5.41247 −0.219324
\(610\) 4.91800 0.199124
\(611\) 6.65734 0.269327
\(612\) 2.87978 0.116408
\(613\) 41.4845 1.67554 0.837772 0.546020i \(-0.183858\pi\)
0.837772 + 0.546020i \(0.183858\pi\)
\(614\) 39.5570 1.59639
\(615\) −7.14954 −0.288297
\(616\) −20.9550 −0.844301
\(617\) −43.5895 −1.75485 −0.877423 0.479718i \(-0.840739\pi\)
−0.877423 + 0.479718i \(0.840739\pi\)
\(618\) 47.2937 1.90243
\(619\) 13.5986 0.546572 0.273286 0.961933i \(-0.411889\pi\)
0.273286 + 0.961933i \(0.411889\pi\)
\(620\) −11.5314 −0.463114
\(621\) −2.83757 −0.113868
\(622\) −56.3373 −2.25892
\(623\) 9.70442 0.388799
\(624\) −9.75913 −0.390678
\(625\) 19.1065 0.764261
\(626\) −58.2012 −2.32619
\(627\) −9.44549 −0.377217
\(628\) −52.8369 −2.10842
\(629\) −17.8814 −0.712978
\(630\) −0.251489 −0.0100196
\(631\) 1.43274 0.0570365 0.0285183 0.999593i \(-0.490921\pi\)
0.0285183 + 0.999593i \(0.490921\pi\)
\(632\) 19.3931 0.771416
\(633\) 5.75502 0.228741
\(634\) 62.7872 2.49360
\(635\) −7.22858 −0.286857
\(636\) 39.3707 1.56115
\(637\) −3.14189 −0.124486
\(638\) −15.3051 −0.605936
\(639\) −1.80256 −0.0713081
\(640\) −0.155007 −0.00612721
\(641\) −9.10492 −0.359623 −0.179811 0.983701i \(-0.557549\pi\)
−0.179811 + 0.983701i \(0.557549\pi\)
\(642\) 82.1738 3.24314
\(643\) −15.6431 −0.616905 −0.308452 0.951240i \(-0.599811\pi\)
−0.308452 + 0.951240i \(0.599811\pi\)
\(644\) −3.28231 −0.129341
\(645\) −11.6736 −0.459649
\(646\) −28.7487 −1.13110
\(647\) −13.1595 −0.517353 −0.258677 0.965964i \(-0.583286\pi\)
−0.258677 + 0.965964i \(0.583286\pi\)
\(648\) 69.3366 2.72380
\(649\) 4.13848 0.162450
\(650\) 6.83809 0.268212
\(651\) 8.07029 0.316299
\(652\) −94.8919 −3.71625
\(653\) −2.05167 −0.0802882 −0.0401441 0.999194i \(-0.512782\pi\)
−0.0401441 + 0.999194i \(0.512782\pi\)
\(654\) −11.7313 −0.458728
\(655\) −1.69561 −0.0662528
\(656\) 61.7531 2.41105
\(657\) 1.48994 0.0581280
\(658\) −37.1936 −1.44996
\(659\) 0.884049 0.0344377 0.0172188 0.999852i \(-0.494519\pi\)
0.0172188 + 0.999852i \(0.494519\pi\)
\(660\) −12.6263 −0.491480
\(661\) −0.984166 −0.0382796 −0.0191398 0.999817i \(-0.506093\pi\)
−0.0191398 + 0.999817i \(0.506093\pi\)
\(662\) 65.3046 2.53814
\(663\) −4.81404 −0.186962
\(664\) 35.7098 1.38581
\(665\) 1.77589 0.0688661
\(666\) 1.21594 0.0471167
\(667\) −1.40552 −0.0544220
\(668\) 87.5082 3.38579
\(669\) 31.5905 1.22136
\(670\) −10.3986 −0.401733
\(671\) −6.88451 −0.265774
\(672\) 22.6654 0.874339
\(673\) −28.7172 −1.10697 −0.553484 0.832860i \(-0.686702\pi\)
−0.553484 + 0.832860i \(0.686702\pi\)
\(674\) 8.42989 0.324707
\(675\) −23.3619 −0.899198
\(676\) −61.2795 −2.35690
\(677\) 20.5258 0.788871 0.394436 0.918924i \(-0.370940\pi\)
0.394436 + 0.918924i \(0.370940\pi\)
\(678\) 45.5095 1.74778
\(679\) 18.9109 0.725734
\(680\) −22.5310 −0.864024
\(681\) 11.9762 0.458929
\(682\) 22.8208 0.873852
\(683\) 14.4392 0.552500 0.276250 0.961086i \(-0.410908\pi\)
0.276250 + 0.961086i \(0.410908\pi\)
\(684\) 1.38282 0.0528736
\(685\) −8.22115 −0.314114
\(686\) 39.8096 1.51994
\(687\) −27.6460 −1.05476
\(688\) 100.829 3.84408
\(689\) −2.62207 −0.0998927
\(690\) −1.63923 −0.0624045
\(691\) −36.2435 −1.37877 −0.689383 0.724397i \(-0.742118\pi\)
−0.689383 + 0.724397i \(0.742118\pi\)
\(692\) −99.0891 −3.76680
\(693\) 0.352049 0.0133733
\(694\) −30.4625 −1.15634
\(695\) −13.8920 −0.526953
\(696\) 32.9737 1.24986
\(697\) 30.4619 1.15383
\(698\) −54.4969 −2.06274
\(699\) −41.8676 −1.58358
\(700\) −27.0234 −1.02139
\(701\) 26.8016 1.01228 0.506142 0.862450i \(-0.331071\pi\)
0.506142 + 0.862450i \(0.331071\pi\)
\(702\) −7.56202 −0.285410
\(703\) −8.58636 −0.323841
\(704\) 18.9732 0.715079
\(705\) −13.1392 −0.494849
\(706\) −54.7868 −2.06193
\(707\) 16.9844 0.638763
\(708\) −15.2077 −0.571540
\(709\) 4.03134 0.151400 0.0757001 0.997131i \(-0.475881\pi\)
0.0757001 + 0.997131i \(0.475881\pi\)
\(710\) 24.0548 0.902760
\(711\) −0.325809 −0.0122188
\(712\) −59.1209 −2.21565
\(713\) 2.09571 0.0784849
\(714\) 26.8954 1.00653
\(715\) 0.840907 0.0314481
\(716\) −84.3962 −3.15403
\(717\) −30.5390 −1.14050
\(718\) 75.8082 2.82914
\(719\) 45.4399 1.69462 0.847310 0.531098i \(-0.178220\pi\)
0.847310 + 0.531098i \(0.178220\pi\)
\(720\) 0.767358 0.0285977
\(721\) 12.4474 0.463567
\(722\) 35.8658 1.33479
\(723\) −27.3149 −1.01585
\(724\) −76.9138 −2.85848
\(725\) −11.5717 −0.429764
\(726\) −25.8432 −0.959130
\(727\) −17.8773 −0.663033 −0.331517 0.943449i \(-0.607560\pi\)
−0.331517 + 0.943449i \(0.607560\pi\)
\(728\) −5.12838 −0.190070
\(729\) 25.7886 0.955135
\(730\) −19.8829 −0.735900
\(731\) 49.7377 1.83961
\(732\) 25.2985 0.935061
\(733\) 19.4001 0.716560 0.358280 0.933614i \(-0.383363\pi\)
0.358280 + 0.933614i \(0.383363\pi\)
\(734\) −52.3865 −1.93362
\(735\) 6.20094 0.228725
\(736\) 5.88581 0.216954
\(737\) 14.5566 0.536199
\(738\) −2.07142 −0.0762499
\(739\) −2.25640 −0.0830029 −0.0415014 0.999138i \(-0.513214\pi\)
−0.0415014 + 0.999138i \(0.513214\pi\)
\(740\) −11.4779 −0.421935
\(741\) −2.31162 −0.0849196
\(742\) 14.6491 0.537786
\(743\) 8.03870 0.294911 0.147456 0.989069i \(-0.452892\pi\)
0.147456 + 0.989069i \(0.452892\pi\)
\(744\) −49.1655 −1.80250
\(745\) 14.0471 0.514646
\(746\) −58.1785 −2.13007
\(747\) −0.599935 −0.0219505
\(748\) 53.7968 1.96701
\(749\) 21.6277 0.790258
\(750\) −28.1773 −1.02889
\(751\) −25.0536 −0.914219 −0.457110 0.889410i \(-0.651115\pi\)
−0.457110 + 0.889410i \(0.651115\pi\)
\(752\) 113.487 4.13846
\(753\) 42.2717 1.54047
\(754\) −3.74567 −0.136409
\(755\) −11.5299 −0.419615
\(756\) 29.8844 1.08688
\(757\) 31.6208 1.14928 0.574639 0.818407i \(-0.305142\pi\)
0.574639 + 0.818407i \(0.305142\pi\)
\(758\) 2.54836 0.0925605
\(759\) 2.29470 0.0832922
\(760\) −10.8190 −0.392447
\(761\) 18.3459 0.665037 0.332519 0.943097i \(-0.392102\pi\)
0.332519 + 0.943097i \(0.392102\pi\)
\(762\) −52.5680 −1.90434
\(763\) −3.08760 −0.111779
\(764\) 33.7560 1.22125
\(765\) 0.378527 0.0136857
\(766\) 26.5605 0.959670
\(767\) 1.01282 0.0365709
\(768\) 27.7173 1.00016
\(769\) −16.2301 −0.585271 −0.292635 0.956224i \(-0.594532\pi\)
−0.292635 + 0.956224i \(0.594532\pi\)
\(770\) −4.69803 −0.169305
\(771\) 27.3567 0.985226
\(772\) −78.0902 −2.81053
\(773\) 32.6118 1.17296 0.586482 0.809962i \(-0.300513\pi\)
0.586482 + 0.809962i \(0.300513\pi\)
\(774\) −3.38217 −0.121570
\(775\) 17.2541 0.619785
\(776\) −115.208 −4.13574
\(777\) 8.03281 0.288175
\(778\) −30.2219 −1.08351
\(779\) 14.6273 0.524078
\(780\) −3.09008 −0.110643
\(781\) −33.6733 −1.20493
\(782\) 6.98424 0.249756
\(783\) 12.7968 0.457321
\(784\) −53.5597 −1.91285
\(785\) −6.94504 −0.247879
\(786\) −12.3309 −0.439828
\(787\) 8.55390 0.304914 0.152457 0.988310i \(-0.451281\pi\)
0.152457 + 0.988310i \(0.451281\pi\)
\(788\) −88.2964 −3.14543
\(789\) −40.8297 −1.45358
\(790\) 4.34786 0.154690
\(791\) 11.9778 0.425883
\(792\) −2.14474 −0.0762101
\(793\) −1.68487 −0.0598314
\(794\) −64.7720 −2.29867
\(795\) 5.17500 0.183538
\(796\) 91.3647 3.23833
\(797\) −7.27866 −0.257823 −0.128912 0.991656i \(-0.541148\pi\)
−0.128912 + 0.991656i \(0.541148\pi\)
\(798\) 12.9147 0.457176
\(799\) 55.9817 1.98049
\(800\) 48.4582 1.71326
\(801\) 0.993247 0.0350947
\(802\) 4.49330 0.158664
\(803\) 27.8333 0.982217
\(804\) −53.4911 −1.88649
\(805\) −0.431436 −0.0152061
\(806\) 5.58499 0.196723
\(807\) −19.3549 −0.681324
\(808\) −103.472 −3.64012
\(809\) 29.7966 1.04759 0.523797 0.851843i \(-0.324515\pi\)
0.523797 + 0.851843i \(0.324515\pi\)
\(810\) 15.5450 0.546196
\(811\) −51.0519 −1.79268 −0.896338 0.443371i \(-0.853782\pi\)
−0.896338 + 0.443371i \(0.853782\pi\)
\(812\) 14.8025 0.519466
\(813\) −49.2263 −1.72644
\(814\) 22.7148 0.796153
\(815\) −12.4729 −0.436905
\(816\) −82.0647 −2.87284
\(817\) 23.8832 0.835568
\(818\) −86.3353 −3.01864
\(819\) 0.0861581 0.00301061
\(820\) 19.5532 0.682827
\(821\) 22.6256 0.789640 0.394820 0.918758i \(-0.370807\pi\)
0.394820 + 0.918758i \(0.370807\pi\)
\(822\) −59.7863 −2.08529
\(823\) −19.2625 −0.671450 −0.335725 0.941960i \(-0.608981\pi\)
−0.335725 + 0.941960i \(0.608981\pi\)
\(824\) −75.8319 −2.64173
\(825\) 18.8924 0.657747
\(826\) −5.65850 −0.196884
\(827\) −3.69779 −0.128585 −0.0642924 0.997931i \(-0.520479\pi\)
−0.0642924 + 0.997931i \(0.520479\pi\)
\(828\) −0.335945 −0.0116749
\(829\) −4.98917 −0.173281 −0.0866404 0.996240i \(-0.527613\pi\)
−0.0866404 + 0.996240i \(0.527613\pi\)
\(830\) 8.00601 0.277893
\(831\) −28.5427 −0.990134
\(832\) 4.64337 0.160980
\(833\) −26.4202 −0.915407
\(834\) −101.026 −3.49824
\(835\) 11.5023 0.398054
\(836\) 25.8324 0.893431
\(837\) −19.0807 −0.659527
\(838\) −44.1013 −1.52346
\(839\) 11.3927 0.393319 0.196660 0.980472i \(-0.436991\pi\)
0.196660 + 0.980472i \(0.436991\pi\)
\(840\) 10.1215 0.349226
\(841\) −22.6614 −0.781428
\(842\) −91.2084 −3.14325
\(843\) −35.9834 −1.23933
\(844\) −15.7393 −0.541770
\(845\) −8.05475 −0.277092
\(846\) −3.80677 −0.130879
\(847\) −6.80178 −0.233712
\(848\) −44.6983 −1.53494
\(849\) −3.35929 −0.115290
\(850\) 57.5016 1.97229
\(851\) 2.08598 0.0715063
\(852\) 123.739 4.23924
\(853\) 29.5432 1.01154 0.505769 0.862669i \(-0.331209\pi\)
0.505769 + 0.862669i \(0.331209\pi\)
\(854\) 9.41312 0.322110
\(855\) 0.181762 0.00621614
\(856\) −131.759 −4.50344
\(857\) −10.1137 −0.345479 −0.172739 0.984968i \(-0.555262\pi\)
−0.172739 + 0.984968i \(0.555262\pi\)
\(858\) 6.11528 0.208772
\(859\) 1.95689 0.0667683 0.0333842 0.999443i \(-0.489372\pi\)
0.0333842 + 0.999443i \(0.489372\pi\)
\(860\) 31.9261 1.08867
\(861\) −13.6843 −0.466361
\(862\) 19.7395 0.672330
\(863\) 40.6127 1.38247 0.691237 0.722629i \(-0.257066\pi\)
0.691237 + 0.722629i \(0.257066\pi\)
\(864\) −53.5884 −1.82311
\(865\) −13.0245 −0.442848
\(866\) 16.6607 0.566154
\(867\) −10.4318 −0.354283
\(868\) −22.0713 −0.749150
\(869\) −6.08640 −0.206467
\(870\) 7.39258 0.250632
\(871\) 3.56248 0.120710
\(872\) 18.8102 0.636992
\(873\) 1.93553 0.0655078
\(874\) 3.35372 0.113441
\(875\) −7.41611 −0.250710
\(876\) −102.279 −3.45569
\(877\) 35.3103 1.19235 0.596173 0.802856i \(-0.296687\pi\)
0.596173 + 0.802856i \(0.296687\pi\)
\(878\) −26.2364 −0.885435
\(879\) −46.3992 −1.56501
\(880\) 14.3349 0.483230
\(881\) −32.5461 −1.09651 −0.548253 0.836312i \(-0.684707\pi\)
−0.548253 + 0.836312i \(0.684707\pi\)
\(882\) 1.79658 0.0604941
\(883\) 51.3315 1.72744 0.863721 0.503970i \(-0.168128\pi\)
0.863721 + 0.503970i \(0.168128\pi\)
\(884\) 13.1658 0.442815
\(885\) −1.99894 −0.0671937
\(886\) 99.3021 3.33612
\(887\) 41.0965 1.37988 0.689942 0.723864i \(-0.257636\pi\)
0.689942 + 0.723864i \(0.257636\pi\)
\(888\) −48.9372 −1.64222
\(889\) −13.8356 −0.464031
\(890\) −13.2547 −0.444298
\(891\) −21.7608 −0.729015
\(892\) −86.3964 −2.89277
\(893\) 26.8815 0.899556
\(894\) 102.154 3.41654
\(895\) −11.0933 −0.370807
\(896\) −0.296687 −0.00991160
\(897\) 0.561588 0.0187509
\(898\) 3.06995 0.102445
\(899\) −9.45119 −0.315215
\(900\) −2.76585 −0.0921950
\(901\) −22.0490 −0.734559
\(902\) −38.6959 −1.28843
\(903\) −22.3435 −0.743546
\(904\) −72.9710 −2.42698
\(905\) −10.1098 −0.336060
\(906\) −83.8480 −2.78566
\(907\) 18.4224 0.611705 0.305852 0.952079i \(-0.401059\pi\)
0.305852 + 0.952079i \(0.401059\pi\)
\(908\) −32.7536 −1.08697
\(909\) 1.73835 0.0576574
\(910\) −1.14976 −0.0381143
\(911\) 17.9016 0.593106 0.296553 0.955016i \(-0.404163\pi\)
0.296553 + 0.955016i \(0.404163\pi\)
\(912\) −39.4062 −1.30487
\(913\) −11.2073 −0.370908
\(914\) −24.7408 −0.818352
\(915\) 3.32531 0.109931
\(916\) 75.6086 2.49818
\(917\) −3.24541 −0.107173
\(918\) −63.5892 −2.09876
\(919\) −46.5329 −1.53498 −0.767490 0.641061i \(-0.778494\pi\)
−0.767490 + 0.641061i \(0.778494\pi\)
\(920\) 2.62838 0.0866551
\(921\) 26.7465 0.881328
\(922\) 43.4138 1.42976
\(923\) −8.24097 −0.271255
\(924\) −24.1670 −0.795036
\(925\) 17.1740 0.564676
\(926\) 77.2502 2.53860
\(927\) 1.27400 0.0418435
\(928\) −26.5437 −0.871340
\(929\) 11.6709 0.382911 0.191455 0.981501i \(-0.438679\pi\)
0.191455 + 0.981501i \(0.438679\pi\)
\(930\) −11.0227 −0.361449
\(931\) −12.6866 −0.415786
\(932\) 114.503 3.75068
\(933\) −38.0925 −1.24709
\(934\) −73.8817 −2.41748
\(935\) 7.07121 0.231253
\(936\) −0.524889 −0.0171565
\(937\) 29.9619 0.978812 0.489406 0.872056i \(-0.337214\pi\)
0.489406 + 0.872056i \(0.337214\pi\)
\(938\) −19.9031 −0.649859
\(939\) −39.3528 −1.28423
\(940\) 35.9341 1.17204
\(941\) 47.1043 1.53556 0.767778 0.640715i \(-0.221362\pi\)
0.767778 + 0.640715i \(0.221362\pi\)
\(942\) −50.5060 −1.64558
\(943\) −3.55357 −0.115720
\(944\) 17.2656 0.561946
\(945\) 3.92808 0.127781
\(946\) −63.1819 −2.05422
\(947\) −0.464077 −0.0150805 −0.00754023 0.999972i \(-0.502400\pi\)
−0.00754023 + 0.999972i \(0.502400\pi\)
\(948\) 22.3657 0.726404
\(949\) 6.81173 0.221118
\(950\) 27.6114 0.895831
\(951\) 42.4537 1.37665
\(952\) −43.1246 −1.39768
\(953\) 28.0049 0.907168 0.453584 0.891214i \(-0.350145\pi\)
0.453584 + 0.891214i \(0.350145\pi\)
\(954\) 1.49934 0.0485428
\(955\) 4.43698 0.143577
\(956\) 83.5208 2.70126
\(957\) −10.3486 −0.334522
\(958\) −28.2271 −0.911975
\(959\) −15.7354 −0.508123
\(960\) −9.16430 −0.295777
\(961\) −16.9078 −0.545412
\(962\) 5.55905 0.179231
\(963\) 2.21359 0.0713320
\(964\) 74.7032 2.40603
\(965\) −10.2644 −0.330422
\(966\) −3.13751 −0.100948
\(967\) −39.5032 −1.27034 −0.635169 0.772373i \(-0.719069\pi\)
−0.635169 + 0.772373i \(0.719069\pi\)
\(968\) 41.4375 1.33185
\(969\) −19.4385 −0.624454
\(970\) −25.8293 −0.829328
\(971\) −30.0799 −0.965311 −0.482656 0.875810i \(-0.660328\pi\)
−0.482656 + 0.875810i \(0.660328\pi\)
\(972\) 6.24974 0.200460
\(973\) −26.5894 −0.852418
\(974\) 48.3719 1.54993
\(975\) 4.62358 0.148073
\(976\) −28.7219 −0.919365
\(977\) −41.0253 −1.31252 −0.656258 0.754536i \(-0.727862\pi\)
−0.656258 + 0.754536i \(0.727862\pi\)
\(978\) −90.7057 −2.90045
\(979\) 18.5547 0.593011
\(980\) −16.9589 −0.541732
\(981\) −0.316016 −0.0100896
\(982\) −23.1753 −0.739552
\(983\) −34.4956 −1.10024 −0.550119 0.835086i \(-0.685418\pi\)
−0.550119 + 0.835086i \(0.685418\pi\)
\(984\) 83.3672 2.65765
\(985\) −11.6059 −0.369795
\(986\) −31.4974 −1.00308
\(987\) −25.1485 −0.800486
\(988\) 6.32203 0.201131
\(989\) −5.80221 −0.184500
\(990\) −0.480843 −0.0152822
\(991\) −5.26566 −0.167269 −0.0836345 0.996496i \(-0.526653\pi\)
−0.0836345 + 0.996496i \(0.526653\pi\)
\(992\) 39.5781 1.25661
\(993\) 44.1558 1.40124
\(994\) 46.0412 1.46034
\(995\) 12.0092 0.380718
\(996\) 41.1835 1.30495
\(997\) 34.1314 1.08095 0.540476 0.841359i \(-0.318244\pi\)
0.540476 + 0.841359i \(0.318244\pi\)
\(998\) −80.6614 −2.55329
\(999\) −18.9921 −0.600884
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4003.2.a.c.1.8 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4003.2.a.c.1.8 179 1.1 even 1 trivial