Properties

Label 6017.2.a.f.1.20
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.10704 q^{2} -1.55624 q^{3} +2.43961 q^{4} -0.464512 q^{5} +3.27907 q^{6} -0.781558 q^{7} -0.926282 q^{8} -0.578102 q^{9} +O(q^{10})\) \(q-2.10704 q^{2} -1.55624 q^{3} +2.43961 q^{4} -0.464512 q^{5} +3.27907 q^{6} -0.781558 q^{7} -0.926282 q^{8} -0.578102 q^{9} +0.978744 q^{10} -1.00000 q^{11} -3.79664 q^{12} -6.89190 q^{13} +1.64677 q^{14} +0.722894 q^{15} -2.92751 q^{16} +4.41736 q^{17} +1.21808 q^{18} +6.82809 q^{19} -1.13323 q^{20} +1.21630 q^{21} +2.10704 q^{22} -0.0938169 q^{23} +1.44152 q^{24} -4.78423 q^{25} +14.5215 q^{26} +5.56840 q^{27} -1.90670 q^{28} +6.75883 q^{29} -1.52317 q^{30} -9.92986 q^{31} +8.02095 q^{32} +1.55624 q^{33} -9.30755 q^{34} +0.363043 q^{35} -1.41034 q^{36} +1.09753 q^{37} -14.3871 q^{38} +10.7255 q^{39} +0.430269 q^{40} -10.0398 q^{41} -2.56278 q^{42} +10.8534 q^{43} -2.43961 q^{44} +0.268535 q^{45} +0.197676 q^{46} -12.6125 q^{47} +4.55593 q^{48} -6.38917 q^{49} +10.0806 q^{50} -6.87450 q^{51} -16.8136 q^{52} +3.80944 q^{53} -11.7328 q^{54} +0.464512 q^{55} +0.723943 q^{56} -10.6262 q^{57} -14.2411 q^{58} -0.976632 q^{59} +1.76358 q^{60} -3.58002 q^{61} +20.9226 q^{62} +0.451820 q^{63} -11.0454 q^{64} +3.20137 q^{65} -3.27907 q^{66} -10.4523 q^{67} +10.7767 q^{68} +0.146002 q^{69} -0.764945 q^{70} -2.15531 q^{71} +0.535485 q^{72} +2.99520 q^{73} -2.31254 q^{74} +7.44543 q^{75} +16.6579 q^{76} +0.781558 q^{77} -22.5990 q^{78} +4.36567 q^{79} +1.35986 q^{80} -6.93149 q^{81} +21.1543 q^{82} -2.51149 q^{83} +2.96729 q^{84} -2.05192 q^{85} -22.8686 q^{86} -10.5184 q^{87} +0.926282 q^{88} +2.79207 q^{89} -0.565814 q^{90} +5.38642 q^{91} -0.228877 q^{92} +15.4533 q^{93} +26.5751 q^{94} -3.17173 q^{95} -12.4826 q^{96} -1.81420 q^{97} +13.4622 q^{98} +0.578102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.10704 −1.48990 −0.744951 0.667119i \(-0.767527\pi\)
−0.744951 + 0.667119i \(0.767527\pi\)
\(3\) −1.55624 −0.898498 −0.449249 0.893406i \(-0.648308\pi\)
−0.449249 + 0.893406i \(0.648308\pi\)
\(4\) 2.43961 1.21981
\(5\) −0.464512 −0.207736 −0.103868 0.994591i \(-0.533122\pi\)
−0.103868 + 0.994591i \(0.533122\pi\)
\(6\) 3.27907 1.33867
\(7\) −0.781558 −0.295401 −0.147701 0.989032i \(-0.547187\pi\)
−0.147701 + 0.989032i \(0.547187\pi\)
\(8\) −0.926282 −0.327490
\(9\) −0.578102 −0.192701
\(10\) 0.978744 0.309506
\(11\) −1.00000 −0.301511
\(12\) −3.79664 −1.09599
\(13\) −6.89190 −1.91147 −0.955735 0.294229i \(-0.904937\pi\)
−0.955735 + 0.294229i \(0.904937\pi\)
\(14\) 1.64677 0.440119
\(15\) 0.722894 0.186650
\(16\) −2.92751 −0.731879
\(17\) 4.41736 1.07137 0.535684 0.844419i \(-0.320054\pi\)
0.535684 + 0.844419i \(0.320054\pi\)
\(18\) 1.21808 0.287105
\(19\) 6.82809 1.56647 0.783236 0.621725i \(-0.213568\pi\)
0.783236 + 0.621725i \(0.213568\pi\)
\(20\) −1.13323 −0.253398
\(21\) 1.21630 0.265418
\(22\) 2.10704 0.449222
\(23\) −0.0938169 −0.0195622 −0.00978109 0.999952i \(-0.503113\pi\)
−0.00978109 + 0.999952i \(0.503113\pi\)
\(24\) 1.44152 0.294249
\(25\) −4.78423 −0.956846
\(26\) 14.5215 2.84790
\(27\) 5.56840 1.07164
\(28\) −1.90670 −0.360332
\(29\) 6.75883 1.25508 0.627541 0.778583i \(-0.284061\pi\)
0.627541 + 0.778583i \(0.284061\pi\)
\(30\) −1.52317 −0.278091
\(31\) −9.92986 −1.78345 −0.891727 0.452573i \(-0.850506\pi\)
−0.891727 + 0.452573i \(0.850506\pi\)
\(32\) 8.02095 1.41792
\(33\) 1.55624 0.270907
\(34\) −9.30755 −1.59623
\(35\) 0.363043 0.0613654
\(36\) −1.41034 −0.235057
\(37\) 1.09753 0.180433 0.0902165 0.995922i \(-0.471244\pi\)
0.0902165 + 0.995922i \(0.471244\pi\)
\(38\) −14.3871 −2.33389
\(39\) 10.7255 1.71745
\(40\) 0.430269 0.0680314
\(41\) −10.0398 −1.56796 −0.783980 0.620786i \(-0.786813\pi\)
−0.783980 + 0.620786i \(0.786813\pi\)
\(42\) −2.56278 −0.395446
\(43\) 10.8534 1.65513 0.827566 0.561368i \(-0.189725\pi\)
0.827566 + 0.561368i \(0.189725\pi\)
\(44\) −2.43961 −0.367786
\(45\) 0.268535 0.0400308
\(46\) 0.197676 0.0291457
\(47\) −12.6125 −1.83973 −0.919865 0.392236i \(-0.871702\pi\)
−0.919865 + 0.392236i \(0.871702\pi\)
\(48\) 4.55593 0.657592
\(49\) −6.38917 −0.912738
\(50\) 10.0806 1.42561
\(51\) −6.87450 −0.962622
\(52\) −16.8136 −2.33162
\(53\) 3.80944 0.523267 0.261634 0.965167i \(-0.415739\pi\)
0.261634 + 0.965167i \(0.415739\pi\)
\(54\) −11.7328 −1.59664
\(55\) 0.464512 0.0626347
\(56\) 0.723943 0.0967410
\(57\) −10.6262 −1.40747
\(58\) −14.2411 −1.86995
\(59\) −0.976632 −0.127147 −0.0635733 0.997977i \(-0.520250\pi\)
−0.0635733 + 0.997977i \(0.520250\pi\)
\(60\) 1.76358 0.227677
\(61\) −3.58002 −0.458374 −0.229187 0.973382i \(-0.573607\pi\)
−0.229187 + 0.973382i \(0.573607\pi\)
\(62\) 20.9226 2.65717
\(63\) 0.451820 0.0569240
\(64\) −11.0454 −1.38068
\(65\) 3.20137 0.397081
\(66\) −3.27907 −0.403625
\(67\) −10.4523 −1.27695 −0.638476 0.769641i \(-0.720435\pi\)
−0.638476 + 0.769641i \(0.720435\pi\)
\(68\) 10.7767 1.30686
\(69\) 0.146002 0.0175766
\(70\) −0.764945 −0.0914285
\(71\) −2.15531 −0.255789 −0.127894 0.991788i \(-0.540822\pi\)
−0.127894 + 0.991788i \(0.540822\pi\)
\(72\) 0.535485 0.0631075
\(73\) 2.99520 0.350562 0.175281 0.984518i \(-0.443917\pi\)
0.175281 + 0.984518i \(0.443917\pi\)
\(74\) −2.31254 −0.268827
\(75\) 7.44543 0.859724
\(76\) 16.6579 1.91079
\(77\) 0.781558 0.0890668
\(78\) −22.5990 −2.55884
\(79\) 4.36567 0.491176 0.245588 0.969374i \(-0.421019\pi\)
0.245588 + 0.969374i \(0.421019\pi\)
\(80\) 1.35986 0.152037
\(81\) −6.93149 −0.770166
\(82\) 21.1543 2.33611
\(83\) −2.51149 −0.275672 −0.137836 0.990455i \(-0.544015\pi\)
−0.137836 + 0.990455i \(0.544015\pi\)
\(84\) 2.96729 0.323758
\(85\) −2.05192 −0.222561
\(86\) −22.8686 −2.46598
\(87\) −10.5184 −1.12769
\(88\) 0.926282 0.0987420
\(89\) 2.79207 0.295959 0.147979 0.988990i \(-0.452723\pi\)
0.147979 + 0.988990i \(0.452723\pi\)
\(90\) −0.565814 −0.0596420
\(91\) 5.38642 0.564651
\(92\) −0.228877 −0.0238621
\(93\) 15.4533 1.60243
\(94\) 26.5751 2.74102
\(95\) −3.17173 −0.325412
\(96\) −12.4826 −1.27400
\(97\) −1.81420 −0.184204 −0.0921020 0.995750i \(-0.529359\pi\)
−0.0921020 + 0.995750i \(0.529359\pi\)
\(98\) 13.4622 1.35989
\(99\) 0.578102 0.0581014
\(100\) −11.6717 −1.16717
\(101\) 14.4043 1.43328 0.716642 0.697441i \(-0.245678\pi\)
0.716642 + 0.697441i \(0.245678\pi\)
\(102\) 14.4848 1.43421
\(103\) −1.45789 −0.143650 −0.0718249 0.997417i \(-0.522882\pi\)
−0.0718249 + 0.997417i \(0.522882\pi\)
\(104\) 6.38384 0.625987
\(105\) −0.564984 −0.0551367
\(106\) −8.02664 −0.779617
\(107\) −13.0371 −1.26035 −0.630173 0.776454i \(-0.717016\pi\)
−0.630173 + 0.776454i \(0.717016\pi\)
\(108\) 13.5847 1.30719
\(109\) 12.1611 1.16482 0.582410 0.812895i \(-0.302110\pi\)
0.582410 + 0.812895i \(0.302110\pi\)
\(110\) −0.978744 −0.0933196
\(111\) −1.70803 −0.162119
\(112\) 2.28802 0.216198
\(113\) 2.11125 0.198610 0.0993049 0.995057i \(-0.468338\pi\)
0.0993049 + 0.995057i \(0.468338\pi\)
\(114\) 22.3898 2.09700
\(115\) 0.0435790 0.00406377
\(116\) 16.4889 1.53096
\(117\) 3.98422 0.368341
\(118\) 2.05780 0.189436
\(119\) −3.45243 −0.316483
\(120\) −0.669603 −0.0611261
\(121\) 1.00000 0.0909091
\(122\) 7.54323 0.682932
\(123\) 15.6244 1.40881
\(124\) −24.2250 −2.17547
\(125\) 4.54489 0.406507
\(126\) −0.952003 −0.0848112
\(127\) −11.4929 −1.01983 −0.509915 0.860225i \(-0.670323\pi\)
−0.509915 + 0.860225i \(0.670323\pi\)
\(128\) 7.23124 0.639158
\(129\) −16.8906 −1.48713
\(130\) −6.74541 −0.591611
\(131\) −0.477214 −0.0416944 −0.0208472 0.999783i \(-0.506636\pi\)
−0.0208472 + 0.999783i \(0.506636\pi\)
\(132\) 3.79664 0.330455
\(133\) −5.33655 −0.462738
\(134\) 22.0234 1.90253
\(135\) −2.58659 −0.222618
\(136\) −4.09172 −0.350862
\(137\) −9.02273 −0.770864 −0.385432 0.922736i \(-0.625948\pi\)
−0.385432 + 0.922736i \(0.625948\pi\)
\(138\) −0.307632 −0.0261874
\(139\) −19.6593 −1.66748 −0.833742 0.552155i \(-0.813806\pi\)
−0.833742 + 0.552155i \(0.813806\pi\)
\(140\) 0.885684 0.0748540
\(141\) 19.6282 1.65299
\(142\) 4.54133 0.381100
\(143\) 6.89190 0.576330
\(144\) 1.69240 0.141033
\(145\) −3.13955 −0.260726
\(146\) −6.31101 −0.522303
\(147\) 9.94311 0.820094
\(148\) 2.67755 0.220093
\(149\) −19.0518 −1.56079 −0.780394 0.625288i \(-0.784981\pi\)
−0.780394 + 0.625288i \(0.784981\pi\)
\(150\) −15.6878 −1.28090
\(151\) −10.6080 −0.863266 −0.431633 0.902049i \(-0.642062\pi\)
−0.431633 + 0.902049i \(0.642062\pi\)
\(152\) −6.32474 −0.513004
\(153\) −2.55368 −0.206453
\(154\) −1.64677 −0.132701
\(155\) 4.61253 0.370488
\(156\) 26.1660 2.09496
\(157\) 16.8406 1.34403 0.672013 0.740539i \(-0.265430\pi\)
0.672013 + 0.740539i \(0.265430\pi\)
\(158\) −9.19863 −0.731804
\(159\) −5.92843 −0.470155
\(160\) −3.72582 −0.294552
\(161\) 0.0733234 0.00577869
\(162\) 14.6049 1.14747
\(163\) 13.6243 1.06714 0.533569 0.845757i \(-0.320851\pi\)
0.533569 + 0.845757i \(0.320851\pi\)
\(164\) −24.4933 −1.91261
\(165\) −0.722894 −0.0562772
\(166\) 5.29181 0.410724
\(167\) 6.31044 0.488317 0.244158 0.969735i \(-0.421488\pi\)
0.244158 + 0.969735i \(0.421488\pi\)
\(168\) −1.12663 −0.0869216
\(169\) 34.4983 2.65372
\(170\) 4.32347 0.331595
\(171\) −3.94733 −0.301860
\(172\) 26.4782 2.01894
\(173\) −17.0807 −1.29862 −0.649310 0.760524i \(-0.724942\pi\)
−0.649310 + 0.760524i \(0.724942\pi\)
\(174\) 22.1627 1.68015
\(175\) 3.73915 0.282653
\(176\) 2.92751 0.220670
\(177\) 1.51988 0.114241
\(178\) −5.88300 −0.440949
\(179\) −21.4178 −1.60084 −0.800421 0.599439i \(-0.795391\pi\)
−0.800421 + 0.599439i \(0.795391\pi\)
\(180\) 0.655121 0.0488299
\(181\) −14.1806 −1.05404 −0.527018 0.849854i \(-0.676690\pi\)
−0.527018 + 0.849854i \(0.676690\pi\)
\(182\) −11.3494 −0.841274
\(183\) 5.57138 0.411848
\(184\) 0.0869009 0.00640642
\(185\) −0.509816 −0.0374824
\(186\) −32.5607 −2.38746
\(187\) −4.41736 −0.323029
\(188\) −30.7697 −2.24411
\(189\) −4.35203 −0.316564
\(190\) 6.68295 0.484832
\(191\) −7.21785 −0.522265 −0.261133 0.965303i \(-0.584096\pi\)
−0.261133 + 0.965303i \(0.584096\pi\)
\(192\) 17.1894 1.24054
\(193\) −7.13565 −0.513635 −0.256818 0.966460i \(-0.582674\pi\)
−0.256818 + 0.966460i \(0.582674\pi\)
\(194\) 3.82259 0.274446
\(195\) −4.98211 −0.356776
\(196\) −15.5871 −1.11336
\(197\) 0.844817 0.0601907 0.0300953 0.999547i \(-0.490419\pi\)
0.0300953 + 0.999547i \(0.490419\pi\)
\(198\) −1.21808 −0.0865654
\(199\) −11.9017 −0.843692 −0.421846 0.906668i \(-0.638618\pi\)
−0.421846 + 0.906668i \(0.638618\pi\)
\(200\) 4.43154 0.313358
\(201\) 16.2664 1.14734
\(202\) −30.3505 −2.13545
\(203\) −5.28242 −0.370753
\(204\) −16.7711 −1.17421
\(205\) 4.66362 0.325721
\(206\) 3.07182 0.214024
\(207\) 0.0542357 0.00376964
\(208\) 20.1761 1.39896
\(209\) −6.82809 −0.472309
\(210\) 1.19044 0.0821483
\(211\) −17.3963 −1.19761 −0.598804 0.800896i \(-0.704357\pi\)
−0.598804 + 0.800896i \(0.704357\pi\)
\(212\) 9.29357 0.638285
\(213\) 3.35420 0.229826
\(214\) 27.4697 1.87779
\(215\) −5.04154 −0.343830
\(216\) −5.15791 −0.350951
\(217\) 7.76076 0.526835
\(218\) −25.6238 −1.73547
\(219\) −4.66127 −0.314979
\(220\) 1.13323 0.0764022
\(221\) −30.4440 −2.04789
\(222\) 3.59888 0.241541
\(223\) 24.5414 1.64342 0.821708 0.569908i \(-0.193021\pi\)
0.821708 + 0.569908i \(0.193021\pi\)
\(224\) −6.26884 −0.418855
\(225\) 2.76577 0.184385
\(226\) −4.44849 −0.295909
\(227\) 6.45910 0.428706 0.214353 0.976756i \(-0.431236\pi\)
0.214353 + 0.976756i \(0.431236\pi\)
\(228\) −25.9238 −1.71684
\(229\) 21.5929 1.42690 0.713450 0.700706i \(-0.247132\pi\)
0.713450 + 0.700706i \(0.247132\pi\)
\(230\) −0.0918227 −0.00605461
\(231\) −1.21630 −0.0800264
\(232\) −6.26058 −0.411027
\(233\) −5.67337 −0.371675 −0.185837 0.982580i \(-0.559500\pi\)
−0.185837 + 0.982580i \(0.559500\pi\)
\(234\) −8.39491 −0.548792
\(235\) 5.85867 0.382178
\(236\) −2.38260 −0.155094
\(237\) −6.79405 −0.441321
\(238\) 7.27440 0.471529
\(239\) −20.4062 −1.31996 −0.659982 0.751281i \(-0.729436\pi\)
−0.659982 + 0.751281i \(0.729436\pi\)
\(240\) −2.11628 −0.136605
\(241\) −16.5604 −1.06675 −0.533374 0.845880i \(-0.679076\pi\)
−0.533374 + 0.845880i \(0.679076\pi\)
\(242\) −2.10704 −0.135446
\(243\) −5.91811 −0.379647
\(244\) −8.73385 −0.559128
\(245\) 2.96784 0.189608
\(246\) −32.9213 −2.09899
\(247\) −47.0585 −2.99426
\(248\) 9.19785 0.584064
\(249\) 3.90850 0.247691
\(250\) −9.57625 −0.605655
\(251\) −0.221098 −0.0139556 −0.00697780 0.999976i \(-0.502221\pi\)
−0.00697780 + 0.999976i \(0.502221\pi\)
\(252\) 1.10227 0.0694363
\(253\) 0.0938169 0.00589822
\(254\) 24.2160 1.51945
\(255\) 3.19328 0.199971
\(256\) 6.85434 0.428396
\(257\) 26.0049 1.62214 0.811070 0.584950i \(-0.198886\pi\)
0.811070 + 0.584950i \(0.198886\pi\)
\(258\) 35.5891 2.21568
\(259\) −0.857784 −0.0533001
\(260\) 7.81010 0.484362
\(261\) −3.90729 −0.241855
\(262\) 1.00551 0.0621205
\(263\) 17.1565 1.05791 0.528957 0.848648i \(-0.322583\pi\)
0.528957 + 0.848648i \(0.322583\pi\)
\(264\) −1.44152 −0.0887195
\(265\) −1.76953 −0.108701
\(266\) 11.2443 0.689434
\(267\) −4.34514 −0.265919
\(268\) −25.4996 −1.55764
\(269\) −16.5038 −1.00626 −0.503128 0.864212i \(-0.667818\pi\)
−0.503128 + 0.864212i \(0.667818\pi\)
\(270\) 5.45004 0.331679
\(271\) 25.7543 1.56446 0.782230 0.622989i \(-0.214082\pi\)
0.782230 + 0.622989i \(0.214082\pi\)
\(272\) −12.9319 −0.784111
\(273\) −8.38259 −0.507338
\(274\) 19.0112 1.14851
\(275\) 4.78423 0.288500
\(276\) 0.356189 0.0214400
\(277\) −22.2862 −1.33905 −0.669524 0.742791i \(-0.733502\pi\)
−0.669524 + 0.742791i \(0.733502\pi\)
\(278\) 41.4230 2.48439
\(279\) 5.74047 0.343673
\(280\) −0.336280 −0.0200966
\(281\) −1.63736 −0.0976765 −0.0488382 0.998807i \(-0.515552\pi\)
−0.0488382 + 0.998807i \(0.515552\pi\)
\(282\) −41.3574 −2.46280
\(283\) 12.1106 0.719899 0.359950 0.932972i \(-0.382794\pi\)
0.359950 + 0.932972i \(0.382794\pi\)
\(284\) −5.25813 −0.312013
\(285\) 4.93598 0.292382
\(286\) −14.5215 −0.858675
\(287\) 7.84672 0.463177
\(288\) −4.63693 −0.273233
\(289\) 2.51308 0.147828
\(290\) 6.61516 0.388456
\(291\) 2.82334 0.165507
\(292\) 7.30713 0.427618
\(293\) −10.8622 −0.634575 −0.317287 0.948329i \(-0.602772\pi\)
−0.317287 + 0.948329i \(0.602772\pi\)
\(294\) −20.9505 −1.22186
\(295\) 0.453657 0.0264129
\(296\) −1.01662 −0.0590900
\(297\) −5.56840 −0.323111
\(298\) 40.1430 2.32542
\(299\) 0.646577 0.0373925
\(300\) 18.1640 1.04870
\(301\) −8.48259 −0.488928
\(302\) 22.3515 1.28618
\(303\) −22.4167 −1.28780
\(304\) −19.9893 −1.14647
\(305\) 1.66296 0.0952207
\(306\) 5.38071 0.307595
\(307\) 29.5682 1.68755 0.843773 0.536701i \(-0.180330\pi\)
0.843773 + 0.536701i \(0.180330\pi\)
\(308\) 1.90670 0.108644
\(309\) 2.26883 0.129069
\(310\) −9.71879 −0.551990
\(311\) −30.3015 −1.71824 −0.859121 0.511773i \(-0.828989\pi\)
−0.859121 + 0.511773i \(0.828989\pi\)
\(312\) −9.93483 −0.562449
\(313\) −20.9506 −1.18420 −0.592099 0.805865i \(-0.701701\pi\)
−0.592099 + 0.805865i \(0.701701\pi\)
\(314\) −35.4838 −2.00247
\(315\) −0.209876 −0.0118252
\(316\) 10.6505 0.599139
\(317\) 0.351956 0.0197678 0.00988391 0.999951i \(-0.496854\pi\)
0.00988391 + 0.999951i \(0.496854\pi\)
\(318\) 12.4914 0.700484
\(319\) −6.75883 −0.378422
\(320\) 5.13073 0.286816
\(321\) 20.2890 1.13242
\(322\) −0.154495 −0.00860968
\(323\) 30.1622 1.67827
\(324\) −16.9102 −0.939453
\(325\) 32.9724 1.82898
\(326\) −28.7069 −1.58993
\(327\) −18.9256 −1.04659
\(328\) 9.29972 0.513491
\(329\) 9.85744 0.543458
\(330\) 1.52317 0.0838475
\(331\) −24.3030 −1.33581 −0.667906 0.744246i \(-0.732809\pi\)
−0.667906 + 0.744246i \(0.732809\pi\)
\(332\) −6.12707 −0.336267
\(333\) −0.634484 −0.0347695
\(334\) −13.2964 −0.727544
\(335\) 4.85522 0.265269
\(336\) −3.56072 −0.194253
\(337\) −33.2534 −1.81143 −0.905715 0.423886i \(-0.860666\pi\)
−0.905715 + 0.423886i \(0.860666\pi\)
\(338\) −72.6893 −3.95378
\(339\) −3.28563 −0.178451
\(340\) −5.00588 −0.271482
\(341\) 9.92986 0.537732
\(342\) 8.31718 0.449742
\(343\) 10.4644 0.565025
\(344\) −10.0533 −0.542039
\(345\) −0.0678196 −0.00365129
\(346\) 35.9897 1.93482
\(347\) 33.3486 1.79025 0.895124 0.445817i \(-0.147087\pi\)
0.895124 + 0.445817i \(0.147087\pi\)
\(348\) −25.6608 −1.37556
\(349\) 30.1214 1.61236 0.806181 0.591670i \(-0.201531\pi\)
0.806181 + 0.591670i \(0.201531\pi\)
\(350\) −7.87854 −0.421126
\(351\) −38.3769 −2.04841
\(352\) −8.02095 −0.427518
\(353\) 5.82745 0.310164 0.155082 0.987902i \(-0.450436\pi\)
0.155082 + 0.987902i \(0.450436\pi\)
\(354\) −3.20244 −0.170208
\(355\) 1.00117 0.0531365
\(356\) 6.81157 0.361012
\(357\) 5.37282 0.284360
\(358\) 45.1281 2.38510
\(359\) −23.3824 −1.23408 −0.617038 0.786933i \(-0.711668\pi\)
−0.617038 + 0.786933i \(0.711668\pi\)
\(360\) −0.248739 −0.0131097
\(361\) 27.6228 1.45383
\(362\) 29.8791 1.57041
\(363\) −1.55624 −0.0816817
\(364\) 13.1408 0.688765
\(365\) −1.39131 −0.0728243
\(366\) −11.7391 −0.613613
\(367\) 8.32041 0.434322 0.217161 0.976136i \(-0.430320\pi\)
0.217161 + 0.976136i \(0.430320\pi\)
\(368\) 0.274650 0.0143171
\(369\) 5.80405 0.302147
\(370\) 1.07420 0.0558451
\(371\) −2.97730 −0.154574
\(372\) 37.7000 1.95466
\(373\) 32.5387 1.68479 0.842396 0.538860i \(-0.181145\pi\)
0.842396 + 0.538860i \(0.181145\pi\)
\(374\) 9.30755 0.481282
\(375\) −7.07296 −0.365246
\(376\) 11.6828 0.602493
\(377\) −46.5812 −2.39905
\(378\) 9.16990 0.471649
\(379\) 34.7857 1.78682 0.893411 0.449239i \(-0.148305\pi\)
0.893411 + 0.449239i \(0.148305\pi\)
\(380\) −7.73779 −0.396940
\(381\) 17.8858 0.916315
\(382\) 15.2083 0.778123
\(383\) 17.7180 0.905347 0.452673 0.891676i \(-0.350470\pi\)
0.452673 + 0.891676i \(0.350470\pi\)
\(384\) −11.2536 −0.574282
\(385\) −0.363043 −0.0185024
\(386\) 15.0351 0.765266
\(387\) −6.27439 −0.318945
\(388\) −4.42594 −0.224693
\(389\) −14.9057 −0.755749 −0.377875 0.925857i \(-0.623345\pi\)
−0.377875 + 0.925857i \(0.623345\pi\)
\(390\) 10.4975 0.531562
\(391\) −0.414423 −0.0209583
\(392\) 5.91817 0.298913
\(393\) 0.742661 0.0374623
\(394\) −1.78006 −0.0896782
\(395\) −2.02790 −0.102035
\(396\) 1.41034 0.0708725
\(397\) 9.74094 0.488884 0.244442 0.969664i \(-0.421395\pi\)
0.244442 + 0.969664i \(0.421395\pi\)
\(398\) 25.0774 1.25702
\(399\) 8.30498 0.415769
\(400\) 14.0059 0.700295
\(401\) −5.39741 −0.269534 −0.134767 0.990877i \(-0.543029\pi\)
−0.134767 + 0.990877i \(0.543029\pi\)
\(402\) −34.2738 −1.70942
\(403\) 68.4356 3.40902
\(404\) 35.1410 1.74833
\(405\) 3.21976 0.159991
\(406\) 11.1303 0.552385
\(407\) −1.09753 −0.0544026
\(408\) 6.36772 0.315249
\(409\) 12.9682 0.641235 0.320618 0.947209i \(-0.396110\pi\)
0.320618 + 0.947209i \(0.396110\pi\)
\(410\) −9.82643 −0.485293
\(411\) 14.0416 0.692620
\(412\) −3.55668 −0.175225
\(413\) 0.763295 0.0375593
\(414\) −0.114277 −0.00561640
\(415\) 1.16662 0.0572670
\(416\) −55.2796 −2.71031
\(417\) 30.5948 1.49823
\(418\) 14.3871 0.703694
\(419\) 38.7312 1.89214 0.946070 0.323961i \(-0.105015\pi\)
0.946070 + 0.323961i \(0.105015\pi\)
\(420\) −1.37834 −0.0672562
\(421\) −7.34889 −0.358163 −0.179081 0.983834i \(-0.557313\pi\)
−0.179081 + 0.983834i \(0.557313\pi\)
\(422\) 36.6546 1.78432
\(423\) 7.29134 0.354517
\(424\) −3.52862 −0.171365
\(425\) −21.1337 −1.02513
\(426\) −7.06742 −0.342418
\(427\) 2.79799 0.135404
\(428\) −31.8056 −1.53738
\(429\) −10.7255 −0.517831
\(430\) 10.6227 0.512273
\(431\) 27.3475 1.31728 0.658640 0.752458i \(-0.271132\pi\)
0.658640 + 0.752458i \(0.271132\pi\)
\(432\) −16.3016 −0.784310
\(433\) −8.25871 −0.396888 −0.198444 0.980112i \(-0.563589\pi\)
−0.198444 + 0.980112i \(0.563589\pi\)
\(434\) −16.3522 −0.784932
\(435\) 4.88591 0.234262
\(436\) 29.6683 1.42085
\(437\) −0.640590 −0.0306436
\(438\) 9.82147 0.469288
\(439\) −2.96070 −0.141307 −0.0706533 0.997501i \(-0.522508\pi\)
−0.0706533 + 0.997501i \(0.522508\pi\)
\(440\) −0.430269 −0.0205123
\(441\) 3.69359 0.175885
\(442\) 64.1467 3.05115
\(443\) 2.03486 0.0966791 0.0483395 0.998831i \(-0.484607\pi\)
0.0483395 + 0.998831i \(0.484607\pi\)
\(444\) −4.16692 −0.197753
\(445\) −1.29695 −0.0614813
\(446\) −51.7098 −2.44853
\(447\) 29.6493 1.40237
\(448\) 8.63264 0.407854
\(449\) 7.46400 0.352248 0.176124 0.984368i \(-0.443644\pi\)
0.176124 + 0.984368i \(0.443644\pi\)
\(450\) −5.82759 −0.274715
\(451\) 10.0398 0.472758
\(452\) 5.15064 0.242266
\(453\) 16.5086 0.775643
\(454\) −13.6096 −0.638729
\(455\) −2.50206 −0.117298
\(456\) 9.84284 0.460933
\(457\) −15.0131 −0.702284 −0.351142 0.936322i \(-0.614207\pi\)
−0.351142 + 0.936322i \(0.614207\pi\)
\(458\) −45.4971 −2.12594
\(459\) 24.5976 1.14812
\(460\) 0.106316 0.00495701
\(461\) −1.46451 −0.0682089 −0.0341044 0.999418i \(-0.510858\pi\)
−0.0341044 + 0.999418i \(0.510858\pi\)
\(462\) 2.56278 0.119231
\(463\) 11.5876 0.538522 0.269261 0.963067i \(-0.413221\pi\)
0.269261 + 0.963067i \(0.413221\pi\)
\(464\) −19.7866 −0.918568
\(465\) −7.17823 −0.332882
\(466\) 11.9540 0.553759
\(467\) −35.7088 −1.65241 −0.826204 0.563372i \(-0.809504\pi\)
−0.826204 + 0.563372i \(0.809504\pi\)
\(468\) 9.71996 0.449305
\(469\) 8.16909 0.377213
\(470\) −12.3445 −0.569407
\(471\) −26.2081 −1.20761
\(472\) 0.904636 0.0416393
\(473\) −10.8534 −0.499041
\(474\) 14.3153 0.657524
\(475\) −32.6672 −1.49887
\(476\) −8.42258 −0.386048
\(477\) −2.20225 −0.100834
\(478\) 42.9966 1.96662
\(479\) 21.5204 0.983291 0.491646 0.870795i \(-0.336396\pi\)
0.491646 + 0.870795i \(0.336396\pi\)
\(480\) 5.79829 0.264655
\(481\) −7.56407 −0.344892
\(482\) 34.8933 1.58935
\(483\) −0.114109 −0.00519215
\(484\) 2.43961 0.110892
\(485\) 0.842716 0.0382658
\(486\) 12.4697 0.565636
\(487\) 26.6710 1.20858 0.604289 0.796766i \(-0.293457\pi\)
0.604289 + 0.796766i \(0.293457\pi\)
\(488\) 3.31610 0.150113
\(489\) −21.2027 −0.958821
\(490\) −6.25336 −0.282498
\(491\) −12.2152 −0.551266 −0.275633 0.961263i \(-0.588888\pi\)
−0.275633 + 0.961263i \(0.588888\pi\)
\(492\) 38.1176 1.71847
\(493\) 29.8562 1.34465
\(494\) 99.1542 4.46116
\(495\) −0.268535 −0.0120697
\(496\) 29.0698 1.30527
\(497\) 1.68450 0.0755603
\(498\) −8.23536 −0.369035
\(499\) 29.7420 1.33144 0.665718 0.746203i \(-0.268125\pi\)
0.665718 + 0.746203i \(0.268125\pi\)
\(500\) 11.0878 0.495860
\(501\) −9.82060 −0.438752
\(502\) 0.465863 0.0207925
\(503\) 24.2720 1.08224 0.541119 0.840946i \(-0.318001\pi\)
0.541119 + 0.840946i \(0.318001\pi\)
\(504\) −0.418513 −0.0186420
\(505\) −6.69097 −0.297744
\(506\) −0.197676 −0.00878776
\(507\) −53.6878 −2.38436
\(508\) −28.0382 −1.24399
\(509\) 5.90079 0.261548 0.130774 0.991412i \(-0.458254\pi\)
0.130774 + 0.991412i \(0.458254\pi\)
\(510\) −6.72837 −0.297937
\(511\) −2.34093 −0.103556
\(512\) −28.9049 −1.27743
\(513\) 38.0216 1.67869
\(514\) −54.7933 −2.41683
\(515\) 0.677205 0.0298412
\(516\) −41.2065 −1.81402
\(517\) 12.6125 0.554699
\(518\) 1.80738 0.0794119
\(519\) 26.5817 1.16681
\(520\) −2.96537 −0.130040
\(521\) −39.2608 −1.72005 −0.860024 0.510253i \(-0.829552\pi\)
−0.860024 + 0.510253i \(0.829552\pi\)
\(522\) 8.23281 0.360340
\(523\) 40.9889 1.79232 0.896160 0.443731i \(-0.146345\pi\)
0.896160 + 0.443731i \(0.146345\pi\)
\(524\) −1.16422 −0.0508590
\(525\) −5.81904 −0.253964
\(526\) −36.1494 −1.57619
\(527\) −43.8638 −1.91074
\(528\) −4.55593 −0.198271
\(529\) −22.9912 −0.999617
\(530\) 3.72847 0.161954
\(531\) 0.564593 0.0245012
\(532\) −13.0191 −0.564451
\(533\) 69.1936 2.99711
\(534\) 9.15539 0.396192
\(535\) 6.05590 0.261819
\(536\) 9.68179 0.418189
\(537\) 33.3313 1.43835
\(538\) 34.7742 1.49922
\(539\) 6.38917 0.275201
\(540\) −6.31027 −0.271551
\(541\) 31.8812 1.37068 0.685340 0.728224i \(-0.259654\pi\)
0.685340 + 0.728224i \(0.259654\pi\)
\(542\) −54.2652 −2.33089
\(543\) 22.0685 0.947050
\(544\) 35.4314 1.51911
\(545\) −5.64896 −0.241975
\(546\) 17.6625 0.755883
\(547\) 1.00000 0.0427569
\(548\) −22.0120 −0.940305
\(549\) 2.06961 0.0883290
\(550\) −10.0806 −0.429836
\(551\) 46.1499 1.96605
\(552\) −0.135239 −0.00575616
\(553\) −3.41202 −0.145094
\(554\) 46.9579 1.99505
\(555\) 0.793398 0.0336779
\(556\) −47.9612 −2.03401
\(557\) −23.6530 −1.00221 −0.501104 0.865387i \(-0.667073\pi\)
−0.501104 + 0.865387i \(0.667073\pi\)
\(558\) −12.0954 −0.512039
\(559\) −74.8008 −3.16373
\(560\) −1.06281 −0.0449120
\(561\) 6.87450 0.290241
\(562\) 3.44997 0.145528
\(563\) −20.9677 −0.883681 −0.441841 0.897094i \(-0.645674\pi\)
−0.441841 + 0.897094i \(0.645674\pi\)
\(564\) 47.8853 2.01633
\(565\) −0.980701 −0.0412584
\(566\) −25.5175 −1.07258
\(567\) 5.41737 0.227508
\(568\) 1.99643 0.0837683
\(569\) −27.5476 −1.15485 −0.577427 0.816442i \(-0.695943\pi\)
−0.577427 + 0.816442i \(0.695943\pi\)
\(570\) −10.4003 −0.435621
\(571\) −29.0532 −1.21584 −0.607920 0.793999i \(-0.707996\pi\)
−0.607920 + 0.793999i \(0.707996\pi\)
\(572\) 16.8136 0.703011
\(573\) 11.2327 0.469254
\(574\) −16.5333 −0.690088
\(575\) 0.448842 0.0187180
\(576\) 6.38538 0.266058
\(577\) 12.7582 0.531131 0.265565 0.964093i \(-0.414441\pi\)
0.265565 + 0.964093i \(0.414441\pi\)
\(578\) −5.29517 −0.220250
\(579\) 11.1048 0.461501
\(580\) −7.65929 −0.318035
\(581\) 1.96288 0.0814339
\(582\) −5.94888 −0.246589
\(583\) −3.80944 −0.157771
\(584\) −2.77440 −0.114806
\(585\) −1.85072 −0.0765177
\(586\) 22.8870 0.945454
\(587\) 2.22645 0.0918954 0.0459477 0.998944i \(-0.485369\pi\)
0.0459477 + 0.998944i \(0.485369\pi\)
\(588\) 24.2573 1.00036
\(589\) −67.8020 −2.79373
\(590\) −0.955872 −0.0393526
\(591\) −1.31474 −0.0540812
\(592\) −3.21304 −0.132055
\(593\) −28.6928 −1.17827 −0.589136 0.808034i \(-0.700532\pi\)
−0.589136 + 0.808034i \(0.700532\pi\)
\(594\) 11.7328 0.481404
\(595\) 1.60369 0.0657449
\(596\) −46.4791 −1.90386
\(597\) 18.5220 0.758056
\(598\) −1.36236 −0.0557112
\(599\) 19.1236 0.781371 0.390685 0.920524i \(-0.372238\pi\)
0.390685 + 0.920524i \(0.372238\pi\)
\(600\) −6.89657 −0.281551
\(601\) 15.6066 0.636607 0.318303 0.947989i \(-0.396887\pi\)
0.318303 + 0.947989i \(0.396887\pi\)
\(602\) 17.8731 0.728455
\(603\) 6.04250 0.246070
\(604\) −25.8794 −1.05302
\(605\) −0.464512 −0.0188851
\(606\) 47.2328 1.91870
\(607\) 36.9665 1.50042 0.750212 0.661197i \(-0.229951\pi\)
0.750212 + 0.661197i \(0.229951\pi\)
\(608\) 54.7678 2.22113
\(609\) 8.22074 0.333121
\(610\) −3.50392 −0.141870
\(611\) 86.9245 3.51659
\(612\) −6.23000 −0.251833
\(613\) −8.44792 −0.341208 −0.170604 0.985340i \(-0.554572\pi\)
−0.170604 + 0.985340i \(0.554572\pi\)
\(614\) −62.3013 −2.51428
\(615\) −7.25774 −0.292660
\(616\) −0.723943 −0.0291685
\(617\) −19.2430 −0.774694 −0.387347 0.921934i \(-0.626609\pi\)
−0.387347 + 0.921934i \(0.626609\pi\)
\(618\) −4.78051 −0.192300
\(619\) −21.6280 −0.869302 −0.434651 0.900599i \(-0.643128\pi\)
−0.434651 + 0.900599i \(0.643128\pi\)
\(620\) 11.2528 0.451923
\(621\) −0.522410 −0.0209636
\(622\) 63.8465 2.56001
\(623\) −2.18217 −0.0874266
\(624\) −31.3990 −1.25697
\(625\) 21.8100 0.872400
\(626\) 44.1438 1.76434
\(627\) 10.6262 0.424369
\(628\) 41.0846 1.63945
\(629\) 4.84819 0.193310
\(630\) 0.442216 0.0176183
\(631\) 32.1437 1.27962 0.639810 0.768533i \(-0.279013\pi\)
0.639810 + 0.768533i \(0.279013\pi\)
\(632\) −4.04384 −0.160855
\(633\) 27.0728 1.07605
\(634\) −0.741585 −0.0294521
\(635\) 5.33858 0.211855
\(636\) −14.4631 −0.573498
\(637\) 44.0335 1.74467
\(638\) 14.2411 0.563811
\(639\) 1.24599 0.0492906
\(640\) −3.35900 −0.132776
\(641\) 21.9280 0.866105 0.433052 0.901369i \(-0.357437\pi\)
0.433052 + 0.901369i \(0.357437\pi\)
\(642\) −42.7496 −1.68719
\(643\) 27.2923 1.07630 0.538151 0.842848i \(-0.319123\pi\)
0.538151 + 0.842848i \(0.319123\pi\)
\(644\) 0.178881 0.00704889
\(645\) 7.84587 0.308931
\(646\) −63.5528 −2.50045
\(647\) 30.0400 1.18099 0.590497 0.807040i \(-0.298932\pi\)
0.590497 + 0.807040i \(0.298932\pi\)
\(648\) 6.42052 0.252222
\(649\) 0.976632 0.0383362
\(650\) −69.4742 −2.72500
\(651\) −12.0776 −0.473360
\(652\) 33.2380 1.30170
\(653\) −18.4555 −0.722219 −0.361109 0.932523i \(-0.617602\pi\)
−0.361109 + 0.932523i \(0.617602\pi\)
\(654\) 39.8770 1.55931
\(655\) 0.221671 0.00866141
\(656\) 29.3918 1.14756
\(657\) −1.73153 −0.0675535
\(658\) −20.7700 −0.809700
\(659\) 11.9488 0.465461 0.232730 0.972541i \(-0.425234\pi\)
0.232730 + 0.972541i \(0.425234\pi\)
\(660\) −1.76358 −0.0686473
\(661\) 23.3109 0.906688 0.453344 0.891336i \(-0.350231\pi\)
0.453344 + 0.891336i \(0.350231\pi\)
\(662\) 51.2073 1.99023
\(663\) 47.3784 1.84002
\(664\) 2.32635 0.0902799
\(665\) 2.47889 0.0961272
\(666\) 1.33688 0.0518032
\(667\) −0.634092 −0.0245521
\(668\) 15.3950 0.595652
\(669\) −38.1925 −1.47661
\(670\) −10.2301 −0.395225
\(671\) 3.58002 0.138205
\(672\) 9.75585 0.376340
\(673\) −23.8973 −0.921173 −0.460586 0.887615i \(-0.652361\pi\)
−0.460586 + 0.887615i \(0.652361\pi\)
\(674\) 70.0663 2.69885
\(675\) −26.6405 −1.02539
\(676\) 84.1625 3.23702
\(677\) −16.1862 −0.622084 −0.311042 0.950396i \(-0.600678\pi\)
−0.311042 + 0.950396i \(0.600678\pi\)
\(678\) 6.92294 0.265874
\(679\) 1.41790 0.0544141
\(680\) 1.90065 0.0728867
\(681\) −10.0519 −0.385191
\(682\) −20.9226 −0.801168
\(683\) −20.6285 −0.789328 −0.394664 0.918826i \(-0.629139\pi\)
−0.394664 + 0.918826i \(0.629139\pi\)
\(684\) −9.62996 −0.368211
\(685\) 4.19116 0.160136
\(686\) −22.0489 −0.841832
\(687\) −33.6038 −1.28207
\(688\) −31.7736 −1.21136
\(689\) −26.2543 −1.00021
\(690\) 0.142899 0.00544006
\(691\) −21.6319 −0.822915 −0.411457 0.911429i \(-0.634980\pi\)
−0.411457 + 0.911429i \(0.634980\pi\)
\(692\) −41.6703 −1.58407
\(693\) −0.451820 −0.0171632
\(694\) −70.2669 −2.66729
\(695\) 9.13199 0.346396
\(696\) 9.74299 0.369307
\(697\) −44.3496 −1.67986
\(698\) −63.4669 −2.40226
\(699\) 8.82916 0.333949
\(700\) 9.12209 0.344783
\(701\) 6.73632 0.254427 0.127214 0.991875i \(-0.459397\pi\)
0.127214 + 0.991875i \(0.459397\pi\)
\(702\) 80.8616 3.05192
\(703\) 7.49404 0.282643
\(704\) 11.0454 0.416290
\(705\) −9.11753 −0.343386
\(706\) −12.2787 −0.462113
\(707\) −11.2578 −0.423394
\(708\) 3.70792 0.139352
\(709\) 2.95332 0.110914 0.0554571 0.998461i \(-0.482338\pi\)
0.0554571 + 0.998461i \(0.482338\pi\)
\(710\) −2.10950 −0.0791681
\(711\) −2.52380 −0.0946499
\(712\) −2.58624 −0.0969236
\(713\) 0.931588 0.0348883
\(714\) −11.3207 −0.423668
\(715\) −3.20137 −0.119724
\(716\) −52.2511 −1.95272
\(717\) 31.7570 1.18599
\(718\) 49.2677 1.83865
\(719\) −4.80117 −0.179053 −0.0895267 0.995984i \(-0.528535\pi\)
−0.0895267 + 0.995984i \(0.528535\pi\)
\(720\) −0.786140 −0.0292977
\(721\) 1.13942 0.0424343
\(722\) −58.2024 −2.16607
\(723\) 25.7720 0.958471
\(724\) −34.5952 −1.28572
\(725\) −32.3358 −1.20092
\(726\) 3.27907 0.121698
\(727\) 35.2737 1.30823 0.654115 0.756395i \(-0.273041\pi\)
0.654115 + 0.756395i \(0.273041\pi\)
\(728\) −4.98935 −0.184917
\(729\) 30.0045 1.11128
\(730\) 2.93154 0.108501
\(731\) 47.9435 1.77325
\(732\) 13.5920 0.502375
\(733\) 32.5383 1.20183 0.600915 0.799313i \(-0.294803\pi\)
0.600915 + 0.799313i \(0.294803\pi\)
\(734\) −17.5314 −0.647097
\(735\) −4.61869 −0.170363
\(736\) −0.752501 −0.0277375
\(737\) 10.4523 0.385016
\(738\) −12.2294 −0.450169
\(739\) −23.1591 −0.851922 −0.425961 0.904741i \(-0.640064\pi\)
−0.425961 + 0.904741i \(0.640064\pi\)
\(740\) −1.24375 −0.0457213
\(741\) 73.2346 2.69034
\(742\) 6.27329 0.230300
\(743\) 48.0380 1.76235 0.881173 0.472795i \(-0.156755\pi\)
0.881173 + 0.472795i \(0.156755\pi\)
\(744\) −14.3141 −0.524780
\(745\) 8.84980 0.324232
\(746\) −68.5603 −2.51017
\(747\) 1.45190 0.0531222
\(748\) −10.7767 −0.394033
\(749\) 10.1893 0.372308
\(750\) 14.9030 0.544180
\(751\) −26.7033 −0.974416 −0.487208 0.873286i \(-0.661985\pi\)
−0.487208 + 0.873286i \(0.661985\pi\)
\(752\) 36.9234 1.34646
\(753\) 0.344083 0.0125391
\(754\) 98.1483 3.57435
\(755\) 4.92754 0.179331
\(756\) −10.6173 −0.386146
\(757\) 19.3461 0.703145 0.351573 0.936161i \(-0.385647\pi\)
0.351573 + 0.936161i \(0.385647\pi\)
\(758\) −73.2949 −2.66219
\(759\) −0.146002 −0.00529954
\(760\) 2.93791 0.106569
\(761\) 3.47525 0.125978 0.0629888 0.998014i \(-0.479937\pi\)
0.0629888 + 0.998014i \(0.479937\pi\)
\(762\) −37.6860 −1.36522
\(763\) −9.50458 −0.344089
\(764\) −17.6088 −0.637062
\(765\) 1.18622 0.0428877
\(766\) −37.3325 −1.34888
\(767\) 6.73085 0.243037
\(768\) −10.6670 −0.384913
\(769\) −14.3148 −0.516207 −0.258103 0.966117i \(-0.583097\pi\)
−0.258103 + 0.966117i \(0.583097\pi\)
\(770\) 0.764945 0.0275667
\(771\) −40.4699 −1.45749
\(772\) −17.4082 −0.626536
\(773\) 35.2376 1.26741 0.633705 0.773575i \(-0.281533\pi\)
0.633705 + 0.773575i \(0.281533\pi\)
\(774\) 13.2204 0.475197
\(775\) 47.5067 1.70649
\(776\) 1.68046 0.0603250
\(777\) 1.33492 0.0478901
\(778\) 31.4069 1.12599
\(779\) −68.5529 −2.45616
\(780\) −12.1544 −0.435198
\(781\) 2.15531 0.0771232
\(782\) 0.873206 0.0312258
\(783\) 37.6359 1.34500
\(784\) 18.7044 0.668013
\(785\) −7.82266 −0.279203
\(786\) −1.56482 −0.0558151
\(787\) 22.2012 0.791386 0.395693 0.918383i \(-0.370505\pi\)
0.395693 + 0.918383i \(0.370505\pi\)
\(788\) 2.06103 0.0734210
\(789\) −26.6997 −0.950534
\(790\) 4.27287 0.152022
\(791\) −1.65007 −0.0586696
\(792\) −0.535485 −0.0190276
\(793\) 24.6731 0.876168
\(794\) −20.5245 −0.728389
\(795\) 2.75382 0.0976680
\(796\) −29.0356 −1.02914
\(797\) 16.1029 0.570395 0.285197 0.958469i \(-0.407941\pi\)
0.285197 + 0.958469i \(0.407941\pi\)
\(798\) −17.4989 −0.619455
\(799\) −55.7142 −1.97103
\(800\) −38.3741 −1.35673
\(801\) −1.61410 −0.0570314
\(802\) 11.3726 0.401579
\(803\) −2.99520 −0.105698
\(804\) 39.6836 1.39953
\(805\) −0.0340596 −0.00120044
\(806\) −144.196 −5.07910
\(807\) 25.6840 0.904120
\(808\) −13.3425 −0.469386
\(809\) 14.6650 0.515593 0.257796 0.966199i \(-0.417004\pi\)
0.257796 + 0.966199i \(0.417004\pi\)
\(810\) −6.78416 −0.238371
\(811\) −16.3449 −0.573948 −0.286974 0.957938i \(-0.592649\pi\)
−0.286974 + 0.957938i \(0.592649\pi\)
\(812\) −12.8871 −0.452247
\(813\) −40.0800 −1.40567
\(814\) 2.31254 0.0810545
\(815\) −6.32864 −0.221683
\(816\) 20.1252 0.704522
\(817\) 74.1082 2.59272
\(818\) −27.3245 −0.955377
\(819\) −3.11390 −0.108809
\(820\) 11.3774 0.397317
\(821\) 26.5610 0.926986 0.463493 0.886101i \(-0.346596\pi\)
0.463493 + 0.886101i \(0.346596\pi\)
\(822\) −29.5861 −1.03194
\(823\) −9.25481 −0.322602 −0.161301 0.986905i \(-0.551569\pi\)
−0.161301 + 0.986905i \(0.551569\pi\)
\(824\) 1.35041 0.0470439
\(825\) −7.44543 −0.259217
\(826\) −1.60829 −0.0559596
\(827\) 28.1400 0.978524 0.489262 0.872137i \(-0.337266\pi\)
0.489262 + 0.872137i \(0.337266\pi\)
\(828\) 0.132314 0.00459824
\(829\) 46.1754 1.60374 0.801868 0.597501i \(-0.203839\pi\)
0.801868 + 0.597501i \(0.203839\pi\)
\(830\) −2.45811 −0.0853222
\(831\) 34.6828 1.20313
\(832\) 76.1240 2.63912
\(833\) −28.2233 −0.977878
\(834\) −64.4643 −2.23222
\(835\) −2.93127 −0.101441
\(836\) −16.6579 −0.576126
\(837\) −55.2934 −1.91122
\(838\) −81.6081 −2.81910
\(839\) −16.3322 −0.563850 −0.281925 0.959436i \(-0.590973\pi\)
−0.281925 + 0.959436i \(0.590973\pi\)
\(840\) 0.523334 0.0180567
\(841\) 16.6817 0.575232
\(842\) 15.4844 0.533627
\(843\) 2.54813 0.0877622
\(844\) −42.4401 −1.46085
\(845\) −16.0249 −0.551272
\(846\) −15.3631 −0.528195
\(847\) −0.781558 −0.0268547
\(848\) −11.1522 −0.382968
\(849\) −18.8470 −0.646828
\(850\) 44.5295 1.52735
\(851\) −0.102967 −0.00352966
\(852\) 8.18294 0.280343
\(853\) −38.3110 −1.31174 −0.655872 0.754872i \(-0.727699\pi\)
−0.655872 + 0.754872i \(0.727699\pi\)
\(854\) −5.89548 −0.201739
\(855\) 1.83358 0.0627072
\(856\) 12.0761 0.412751
\(857\) 8.80332 0.300716 0.150358 0.988632i \(-0.451957\pi\)
0.150358 + 0.988632i \(0.451957\pi\)
\(858\) 22.5990 0.771518
\(859\) 39.2768 1.34011 0.670053 0.742313i \(-0.266271\pi\)
0.670053 + 0.742313i \(0.266271\pi\)
\(860\) −12.2994 −0.419406
\(861\) −12.2114 −0.416164
\(862\) −57.6221 −1.96262
\(863\) 25.6138 0.871905 0.435952 0.899970i \(-0.356412\pi\)
0.435952 + 0.899970i \(0.356412\pi\)
\(864\) 44.6639 1.51950
\(865\) 7.93418 0.269770
\(866\) 17.4014 0.591325
\(867\) −3.91097 −0.132824
\(868\) 18.9333 0.642637
\(869\) −4.36567 −0.148095
\(870\) −10.2948 −0.349027
\(871\) 72.0363 2.44086
\(872\) −11.2646 −0.381467
\(873\) 1.04879 0.0354962
\(874\) 1.34975 0.0456559
\(875\) −3.55209 −0.120083
\(876\) −11.3717 −0.384214
\(877\) −10.1716 −0.343470 −0.171735 0.985143i \(-0.554937\pi\)
−0.171735 + 0.985143i \(0.554937\pi\)
\(878\) 6.23832 0.210533
\(879\) 16.9042 0.570165
\(880\) −1.35986 −0.0458410
\(881\) −37.9802 −1.27959 −0.639793 0.768547i \(-0.720980\pi\)
−0.639793 + 0.768547i \(0.720980\pi\)
\(882\) −7.78254 −0.262052
\(883\) −4.78415 −0.160999 −0.0804997 0.996755i \(-0.525652\pi\)
−0.0804997 + 0.996755i \(0.525652\pi\)
\(884\) −74.2716 −2.49803
\(885\) −0.706001 −0.0237320
\(886\) −4.28753 −0.144042
\(887\) 40.6272 1.36413 0.682064 0.731293i \(-0.261083\pi\)
0.682064 + 0.731293i \(0.261083\pi\)
\(888\) 1.58211 0.0530923
\(889\) 8.98236 0.301259
\(890\) 2.73272 0.0916010
\(891\) 6.93149 0.232214
\(892\) 59.8716 2.00465
\(893\) −86.1196 −2.88188
\(894\) −62.4723 −2.08939
\(895\) 9.94881 0.332552
\(896\) −5.65164 −0.188808
\(897\) −1.00623 −0.0335971
\(898\) −15.7269 −0.524815
\(899\) −67.1142 −2.23838
\(900\) 6.74741 0.224914
\(901\) 16.8277 0.560611
\(902\) −21.1543 −0.704362
\(903\) 13.2010 0.439301
\(904\) −1.95561 −0.0650428
\(905\) 6.58705 0.218961
\(906\) −34.7843 −1.15563
\(907\) −0.368797 −0.0122457 −0.00612285 0.999981i \(-0.501949\pi\)
−0.00612285 + 0.999981i \(0.501949\pi\)
\(908\) 15.7577 0.522938
\(909\) −8.32717 −0.276195
\(910\) 5.27193 0.174763
\(911\) 13.6707 0.452931 0.226466 0.974019i \(-0.427283\pi\)
0.226466 + 0.974019i \(0.427283\pi\)
\(912\) 31.1083 1.03010
\(913\) 2.51149 0.0831183
\(914\) 31.6332 1.04633
\(915\) −2.58797 −0.0855557
\(916\) 52.6783 1.74054
\(917\) 0.372970 0.0123166
\(918\) −51.8282 −1.71059
\(919\) 10.9742 0.362006 0.181003 0.983483i \(-0.442066\pi\)
0.181003 + 0.983483i \(0.442066\pi\)
\(920\) −0.0403665 −0.00133084
\(921\) −46.0153 −1.51626
\(922\) 3.08577 0.101624
\(923\) 14.8542 0.488932
\(924\) −2.96729 −0.0976167
\(925\) −5.25084 −0.172646
\(926\) −24.4155 −0.802344
\(927\) 0.842807 0.0276814
\(928\) 54.2122 1.77960
\(929\) −3.09566 −0.101565 −0.0507827 0.998710i \(-0.516172\pi\)
−0.0507827 + 0.998710i \(0.516172\pi\)
\(930\) 15.1248 0.495962
\(931\) −43.6258 −1.42978
\(932\) −13.8408 −0.453372
\(933\) 47.1566 1.54384
\(934\) 75.2399 2.46192
\(935\) 2.05192 0.0671048
\(936\) −3.69051 −0.120628
\(937\) −5.44538 −0.177893 −0.0889463 0.996036i \(-0.528350\pi\)
−0.0889463 + 0.996036i \(0.528350\pi\)
\(938\) −17.2126 −0.562011
\(939\) 32.6043 1.06400
\(940\) 14.2929 0.466183
\(941\) −3.08325 −0.100511 −0.0502556 0.998736i \(-0.516004\pi\)
−0.0502556 + 0.998736i \(0.516004\pi\)
\(942\) 55.2215 1.79921
\(943\) 0.941907 0.0306727
\(944\) 2.85910 0.0930559
\(945\) 2.02157 0.0657616
\(946\) 22.8686 0.743522
\(947\) −7.41852 −0.241070 −0.120535 0.992709i \(-0.538461\pi\)
−0.120535 + 0.992709i \(0.538461\pi\)
\(948\) −16.5748 −0.538326
\(949\) −20.6426 −0.670088
\(950\) 68.8310 2.23317
\(951\) −0.547730 −0.0177614
\(952\) 3.19792 0.103645
\(953\) 33.8231 1.09564 0.547819 0.836597i \(-0.315458\pi\)
0.547819 + 0.836597i \(0.315458\pi\)
\(954\) 4.64022 0.150233
\(955\) 3.35277 0.108493
\(956\) −49.7831 −1.61010
\(957\) 10.5184 0.340011
\(958\) −45.3443 −1.46501
\(959\) 7.05179 0.227714
\(960\) −7.98467 −0.257704
\(961\) 67.6020 2.18071
\(962\) 15.9378 0.513855
\(963\) 7.53679 0.242870
\(964\) −40.4009 −1.30123
\(965\) 3.31459 0.106700
\(966\) 0.240432 0.00773579
\(967\) 48.6831 1.56554 0.782771 0.622310i \(-0.213806\pi\)
0.782771 + 0.622310i \(0.213806\pi\)
\(968\) −0.926282 −0.0297718
\(969\) −46.9397 −1.50792
\(970\) −1.77564 −0.0570122
\(971\) −13.0405 −0.418488 −0.209244 0.977863i \(-0.567100\pi\)
−0.209244 + 0.977863i \(0.567100\pi\)
\(972\) −14.4379 −0.463096
\(973\) 15.3649 0.492577
\(974\) −56.1968 −1.80066
\(975\) −51.3132 −1.64334
\(976\) 10.4805 0.335474
\(977\) 17.1476 0.548599 0.274299 0.961644i \(-0.411554\pi\)
0.274299 + 0.961644i \(0.411554\pi\)
\(978\) 44.6750 1.42855
\(979\) −2.79207 −0.0892349
\(980\) 7.24038 0.231286
\(981\) −7.03034 −0.224461
\(982\) 25.7380 0.821333
\(983\) 51.9784 1.65785 0.828926 0.559358i \(-0.188952\pi\)
0.828926 + 0.559358i \(0.188952\pi\)
\(984\) −14.4726 −0.461371
\(985\) −0.392427 −0.0125038
\(986\) −62.9081 −2.00340
\(987\) −15.3406 −0.488297
\(988\) −114.805 −3.65242
\(989\) −1.01823 −0.0323780
\(990\) 0.565814 0.0179827
\(991\) −7.57921 −0.240761 −0.120381 0.992728i \(-0.538412\pi\)
−0.120381 + 0.992728i \(0.538412\pi\)
\(992\) −79.6469 −2.52879
\(993\) 37.8214 1.20022
\(994\) −3.54931 −0.112577
\(995\) 5.52849 0.175265
\(996\) 9.53522 0.302135
\(997\) −14.3053 −0.453053 −0.226526 0.974005i \(-0.572737\pi\)
−0.226526 + 0.974005i \(0.572737\pi\)
\(998\) −62.6677 −1.98371
\(999\) 6.11149 0.193359
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 6017.2.a.f.1.20 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.20 121 1.1 even 1 trivial