Properties

Label 4001.2.a.b.1.10
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $0$
Dimension $184$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(31.9481458487\)
Analytic rank: \(0\)
Dimension: \(184\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.65266 q^{2} +3.05290 q^{3} +5.03661 q^{4} -1.94746 q^{5} -8.09830 q^{6} +2.48037 q^{7} -8.05510 q^{8} +6.32018 q^{9} +O(q^{10})\) \(q-2.65266 q^{2} +3.05290 q^{3} +5.03661 q^{4} -1.94746 q^{5} -8.09830 q^{6} +2.48037 q^{7} -8.05510 q^{8} +6.32018 q^{9} +5.16596 q^{10} -2.94497 q^{11} +15.3763 q^{12} +0.192789 q^{13} -6.57957 q^{14} -5.94540 q^{15} +11.2942 q^{16} +4.76794 q^{17} -16.7653 q^{18} -2.90135 q^{19} -9.80861 q^{20} +7.57230 q^{21} +7.81201 q^{22} -3.08821 q^{23} -24.5914 q^{24} -1.20739 q^{25} -0.511405 q^{26} +10.1362 q^{27} +12.4926 q^{28} +2.23235 q^{29} +15.7711 q^{30} -3.07974 q^{31} -13.8496 q^{32} -8.99069 q^{33} -12.6477 q^{34} -4.83042 q^{35} +31.8323 q^{36} +8.80848 q^{37} +7.69631 q^{38} +0.588566 q^{39} +15.6870 q^{40} -2.72877 q^{41} -20.0867 q^{42} +11.9799 q^{43} -14.8327 q^{44} -12.3083 q^{45} +8.19199 q^{46} -4.38663 q^{47} +34.4801 q^{48} -0.847785 q^{49} +3.20280 q^{50} +14.5560 q^{51} +0.971006 q^{52} +14.3594 q^{53} -26.8878 q^{54} +5.73522 q^{55} -19.9796 q^{56} -8.85753 q^{57} -5.92167 q^{58} -3.28792 q^{59} -29.9447 q^{60} +12.6102 q^{61} +8.16952 q^{62} +15.6764 q^{63} +14.1497 q^{64} -0.375450 q^{65} +23.8493 q^{66} +4.80775 q^{67} +24.0143 q^{68} -9.42800 q^{69} +12.8135 q^{70} +0.546449 q^{71} -50.9097 q^{72} +4.67236 q^{73} -23.3659 q^{74} -3.68604 q^{75} -14.6130 q^{76} -7.30461 q^{77} -1.56127 q^{78} -4.07327 q^{79} -21.9951 q^{80} +11.9841 q^{81} +7.23849 q^{82} -0.610918 q^{83} +38.1387 q^{84} -9.28538 q^{85} -31.7787 q^{86} +6.81513 q^{87} +23.7220 q^{88} +4.34903 q^{89} +32.6498 q^{90} +0.478188 q^{91} -15.5541 q^{92} -9.40214 q^{93} +11.6363 q^{94} +5.65028 q^{95} -42.2813 q^{96} +6.32560 q^{97} +2.24889 q^{98} -18.6127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65266 −1.87571 −0.937857 0.347021i \(-0.887193\pi\)
−0.937857 + 0.347021i \(0.887193\pi\)
\(3\) 3.05290 1.76259 0.881295 0.472566i \(-0.156672\pi\)
0.881295 + 0.472566i \(0.156672\pi\)
\(4\) 5.03661 2.51831
\(5\) −1.94746 −0.870932 −0.435466 0.900205i \(-0.643416\pi\)
−0.435466 + 0.900205i \(0.643416\pi\)
\(6\) −8.09830 −3.30612
\(7\) 2.48037 0.937490 0.468745 0.883333i \(-0.344706\pi\)
0.468745 + 0.883333i \(0.344706\pi\)
\(8\) −8.05510 −2.84791
\(9\) 6.32018 2.10673
\(10\) 5.16596 1.63362
\(11\) −2.94497 −0.887942 −0.443971 0.896041i \(-0.646431\pi\)
−0.443971 + 0.896041i \(0.646431\pi\)
\(12\) 15.3763 4.43874
\(13\) 0.192789 0.0534702 0.0267351 0.999643i \(-0.491489\pi\)
0.0267351 + 0.999643i \(0.491489\pi\)
\(14\) −6.57957 −1.75846
\(15\) −5.94540 −1.53510
\(16\) 11.2942 2.82356
\(17\) 4.76794 1.15640 0.578198 0.815897i \(-0.303756\pi\)
0.578198 + 0.815897i \(0.303756\pi\)
\(18\) −16.7653 −3.95162
\(19\) −2.90135 −0.665616 −0.332808 0.942995i \(-0.607996\pi\)
−0.332808 + 0.942995i \(0.607996\pi\)
\(20\) −9.80861 −2.19327
\(21\) 7.57230 1.65241
\(22\) 7.81201 1.66553
\(23\) −3.08821 −0.643937 −0.321969 0.946750i \(-0.604345\pi\)
−0.321969 + 0.946750i \(0.604345\pi\)
\(24\) −24.5914 −5.01970
\(25\) −1.20739 −0.241478
\(26\) −0.511405 −0.100295
\(27\) 10.1362 1.95070
\(28\) 12.4926 2.36089
\(29\) 2.23235 0.414537 0.207268 0.978284i \(-0.433543\pi\)
0.207268 + 0.978284i \(0.433543\pi\)
\(30\) 15.7711 2.87940
\(31\) −3.07974 −0.553138 −0.276569 0.960994i \(-0.589197\pi\)
−0.276569 + 0.960994i \(0.589197\pi\)
\(32\) −13.8496 −2.44828
\(33\) −8.99069 −1.56508
\(34\) −12.6477 −2.16907
\(35\) −4.83042 −0.816490
\(36\) 31.8323 5.30538
\(37\) 8.80848 1.44810 0.724052 0.689745i \(-0.242277\pi\)
0.724052 + 0.689745i \(0.242277\pi\)
\(38\) 7.69631 1.24851
\(39\) 0.588566 0.0942460
\(40\) 15.6870 2.48033
\(41\) −2.72877 −0.426162 −0.213081 0.977035i \(-0.568350\pi\)
−0.213081 + 0.977035i \(0.568350\pi\)
\(42\) −20.0867 −3.09945
\(43\) 11.9799 1.82692 0.913460 0.406929i \(-0.133400\pi\)
0.913460 + 0.406929i \(0.133400\pi\)
\(44\) −14.8327 −2.23611
\(45\) −12.3083 −1.83481
\(46\) 8.19199 1.20784
\(47\) −4.38663 −0.639856 −0.319928 0.947442i \(-0.603659\pi\)
−0.319928 + 0.947442i \(0.603659\pi\)
\(48\) 34.4801 4.97678
\(49\) −0.847785 −0.121112
\(50\) 3.20280 0.452944
\(51\) 14.5560 2.03825
\(52\) 0.971006 0.134654
\(53\) 14.3594 1.97242 0.986209 0.165504i \(-0.0529250\pi\)
0.986209 + 0.165504i \(0.0529250\pi\)
\(54\) −26.8878 −3.65896
\(55\) 5.73522 0.773337
\(56\) −19.9796 −2.66989
\(57\) −8.85753 −1.17321
\(58\) −5.92167 −0.777553
\(59\) −3.28792 −0.428050 −0.214025 0.976828i \(-0.568657\pi\)
−0.214025 + 0.976828i \(0.568657\pi\)
\(60\) −29.9447 −3.86584
\(61\) 12.6102 1.61458 0.807288 0.590158i \(-0.200935\pi\)
0.807288 + 0.590158i \(0.200935\pi\)
\(62\) 8.16952 1.03753
\(63\) 15.6764 1.97503
\(64\) 14.1497 1.76872
\(65\) −0.375450 −0.0465689
\(66\) 23.8493 2.93564
\(67\) 4.80775 0.587360 0.293680 0.955904i \(-0.405120\pi\)
0.293680 + 0.955904i \(0.405120\pi\)
\(68\) 24.0143 2.91216
\(69\) −9.42800 −1.13500
\(70\) 12.8135 1.53150
\(71\) 0.546449 0.0648516 0.0324258 0.999474i \(-0.489677\pi\)
0.0324258 + 0.999474i \(0.489677\pi\)
\(72\) −50.9097 −5.99976
\(73\) 4.67236 0.546858 0.273429 0.961892i \(-0.411842\pi\)
0.273429 + 0.961892i \(0.411842\pi\)
\(74\) −23.3659 −2.71623
\(75\) −3.68604 −0.425627
\(76\) −14.6130 −1.67622
\(77\) −7.30461 −0.832437
\(78\) −1.56127 −0.176779
\(79\) −4.07327 −0.458279 −0.229140 0.973394i \(-0.573591\pi\)
−0.229140 + 0.973394i \(0.573591\pi\)
\(80\) −21.9951 −2.45913
\(81\) 11.9841 1.33157
\(82\) 7.23849 0.799357
\(83\) −0.610918 −0.0670570 −0.0335285 0.999438i \(-0.510674\pi\)
−0.0335285 + 0.999438i \(0.510674\pi\)
\(84\) 38.1387 4.16128
\(85\) −9.28538 −1.00714
\(86\) −31.7787 −3.42678
\(87\) 6.81513 0.730659
\(88\) 23.7220 2.52878
\(89\) 4.34903 0.460996 0.230498 0.973073i \(-0.425965\pi\)
0.230498 + 0.973073i \(0.425965\pi\)
\(90\) 32.6498 3.44159
\(91\) 0.478188 0.0501278
\(92\) −15.5541 −1.62163
\(93\) −9.40214 −0.974956
\(94\) 11.6363 1.20019
\(95\) 5.65028 0.579706
\(96\) −42.2813 −4.31532
\(97\) 6.32560 0.642267 0.321134 0.947034i \(-0.395936\pi\)
0.321134 + 0.947034i \(0.395936\pi\)
\(98\) 2.24889 0.227172
\(99\) −18.6127 −1.87065
\(100\) −6.08115 −0.608115
\(101\) −4.28037 −0.425912 −0.212956 0.977062i \(-0.568309\pi\)
−0.212956 + 0.977062i \(0.568309\pi\)
\(102\) −38.6122 −3.82318
\(103\) −2.94064 −0.289750 −0.144875 0.989450i \(-0.546278\pi\)
−0.144875 + 0.989450i \(0.546278\pi\)
\(104\) −1.55294 −0.152278
\(105\) −14.7468 −1.43914
\(106\) −38.0907 −3.69969
\(107\) 2.21393 0.214028 0.107014 0.994257i \(-0.465871\pi\)
0.107014 + 0.994257i \(0.465871\pi\)
\(108\) 51.0519 4.91247
\(109\) 8.23984 0.789234 0.394617 0.918846i \(-0.370877\pi\)
0.394617 + 0.918846i \(0.370877\pi\)
\(110\) −15.2136 −1.45056
\(111\) 26.8914 2.55242
\(112\) 28.0138 2.64706
\(113\) 7.94211 0.747131 0.373566 0.927604i \(-0.378135\pi\)
0.373566 + 0.927604i \(0.378135\pi\)
\(114\) 23.4960 2.20060
\(115\) 6.01418 0.560825
\(116\) 11.2435 1.04393
\(117\) 1.21846 0.112647
\(118\) 8.72173 0.802900
\(119\) 11.8262 1.08411
\(120\) 47.8908 4.37181
\(121\) −2.32714 −0.211558
\(122\) −33.4507 −3.02848
\(123\) −8.33064 −0.751148
\(124\) −15.5115 −1.39297
\(125\) 12.0887 1.08124
\(126\) −41.5840 −3.70460
\(127\) 0.723073 0.0641623 0.0320812 0.999485i \(-0.489786\pi\)
0.0320812 + 0.999485i \(0.489786\pi\)
\(128\) −9.83535 −0.869330
\(129\) 36.5734 3.22011
\(130\) 0.995942 0.0873499
\(131\) −4.71928 −0.412325 −0.206163 0.978518i \(-0.566098\pi\)
−0.206163 + 0.978518i \(0.566098\pi\)
\(132\) −45.2826 −3.94135
\(133\) −7.19642 −0.624008
\(134\) −12.7533 −1.10172
\(135\) −19.7398 −1.69893
\(136\) −38.4062 −3.29331
\(137\) 8.90380 0.760703 0.380351 0.924842i \(-0.375803\pi\)
0.380351 + 0.924842i \(0.375803\pi\)
\(138\) 25.0093 2.12893
\(139\) 14.5272 1.23219 0.616093 0.787674i \(-0.288715\pi\)
0.616093 + 0.787674i \(0.288715\pi\)
\(140\) −24.3289 −2.05617
\(141\) −13.3919 −1.12780
\(142\) −1.44954 −0.121643
\(143\) −0.567760 −0.0474784
\(144\) 71.3815 5.94846
\(145\) −4.34742 −0.361033
\(146\) −12.3942 −1.02575
\(147\) −2.58820 −0.213471
\(148\) 44.3649 3.64677
\(149\) −8.73860 −0.715894 −0.357947 0.933742i \(-0.616523\pi\)
−0.357947 + 0.933742i \(0.616523\pi\)
\(150\) 9.77780 0.798354
\(151\) 17.6680 1.43781 0.718903 0.695111i \(-0.244645\pi\)
0.718903 + 0.695111i \(0.244645\pi\)
\(152\) 23.3707 1.89561
\(153\) 30.1342 2.43621
\(154\) 19.3767 1.56142
\(155\) 5.99769 0.481746
\(156\) 2.96438 0.237340
\(157\) 10.0397 0.801253 0.400627 0.916241i \(-0.368792\pi\)
0.400627 + 0.916241i \(0.368792\pi\)
\(158\) 10.8050 0.859601
\(159\) 43.8378 3.47657
\(160\) 26.9715 2.13229
\(161\) −7.65990 −0.603685
\(162\) −31.7898 −2.49764
\(163\) 13.5668 1.06263 0.531316 0.847174i \(-0.321698\pi\)
0.531316 + 0.847174i \(0.321698\pi\)
\(164\) −13.7437 −1.07321
\(165\) 17.5090 1.36308
\(166\) 1.62056 0.125780
\(167\) −10.5826 −0.818910 −0.409455 0.912330i \(-0.634281\pi\)
−0.409455 + 0.912330i \(0.634281\pi\)
\(168\) −60.9956 −4.70592
\(169\) −12.9628 −0.997141
\(170\) 24.6310 1.88911
\(171\) −18.3371 −1.40227
\(172\) 60.3382 4.60074
\(173\) −18.4685 −1.40414 −0.702068 0.712110i \(-0.747740\pi\)
−0.702068 + 0.712110i \(0.747740\pi\)
\(174\) −18.0782 −1.37051
\(175\) −2.99477 −0.226383
\(176\) −33.2612 −2.50716
\(177\) −10.0377 −0.754477
\(178\) −11.5365 −0.864697
\(179\) 22.2879 1.66588 0.832938 0.553366i \(-0.186657\pi\)
0.832938 + 0.553366i \(0.186657\pi\)
\(180\) −61.9922 −4.62062
\(181\) −7.48911 −0.556661 −0.278331 0.960485i \(-0.589781\pi\)
−0.278331 + 0.960485i \(0.589781\pi\)
\(182\) −1.26847 −0.0940254
\(183\) 38.4977 2.84584
\(184\) 24.8759 1.83387
\(185\) −17.1542 −1.26120
\(186\) 24.9407 1.82874
\(187\) −14.0414 −1.02681
\(188\) −22.0938 −1.61135
\(189\) 25.1414 1.82877
\(190\) −14.9883 −1.08736
\(191\) 22.8566 1.65385 0.826923 0.562315i \(-0.190089\pi\)
0.826923 + 0.562315i \(0.190089\pi\)
\(192\) 43.1977 3.11753
\(193\) 20.0189 1.44099 0.720496 0.693459i \(-0.243914\pi\)
0.720496 + 0.693459i \(0.243914\pi\)
\(194\) −16.7797 −1.20471
\(195\) −1.14621 −0.0820819
\(196\) −4.26996 −0.304997
\(197\) −13.5736 −0.967079 −0.483540 0.875322i \(-0.660649\pi\)
−0.483540 + 0.875322i \(0.660649\pi\)
\(198\) 49.3733 3.50881
\(199\) 13.6861 0.970183 0.485091 0.874464i \(-0.338786\pi\)
0.485091 + 0.874464i \(0.338786\pi\)
\(200\) 9.72565 0.687707
\(201\) 14.6776 1.03528
\(202\) 11.3544 0.798890
\(203\) 5.53704 0.388624
\(204\) 73.3130 5.13294
\(205\) 5.31417 0.371158
\(206\) 7.80053 0.543489
\(207\) −19.5181 −1.35660
\(208\) 2.17741 0.150976
\(209\) 8.54440 0.591029
\(210\) 39.1182 2.69941
\(211\) −24.1510 −1.66262 −0.831312 0.555805i \(-0.812410\pi\)
−0.831312 + 0.555805i \(0.812410\pi\)
\(212\) 72.3228 4.96715
\(213\) 1.66825 0.114307
\(214\) −5.87280 −0.401456
\(215\) −23.3304 −1.59112
\(216\) −81.6477 −5.55543
\(217\) −7.63889 −0.518562
\(218\) −21.8575 −1.48038
\(219\) 14.2642 0.963887
\(220\) 28.8861 1.94750
\(221\) 0.919209 0.0618327
\(222\) −71.3337 −4.78760
\(223\) 19.6211 1.31393 0.656964 0.753922i \(-0.271840\pi\)
0.656964 + 0.753922i \(0.271840\pi\)
\(224\) −34.3520 −2.29524
\(225\) −7.63092 −0.508728
\(226\) −21.0677 −1.40141
\(227\) 17.1133 1.13585 0.567926 0.823080i \(-0.307746\pi\)
0.567926 + 0.823080i \(0.307746\pi\)
\(228\) −44.6119 −2.95450
\(229\) −19.4868 −1.28773 −0.643863 0.765141i \(-0.722669\pi\)
−0.643863 + 0.765141i \(0.722669\pi\)
\(230\) −15.9536 −1.05195
\(231\) −22.3002 −1.46725
\(232\) −17.9818 −1.18056
\(233\) −25.1005 −1.64439 −0.822196 0.569205i \(-0.807251\pi\)
−0.822196 + 0.569205i \(0.807251\pi\)
\(234\) −3.23217 −0.211294
\(235\) 8.54281 0.557271
\(236\) −16.5600 −1.07796
\(237\) −12.4353 −0.807758
\(238\) −31.3710 −2.03348
\(239\) 3.75871 0.243130 0.121565 0.992583i \(-0.461209\pi\)
0.121565 + 0.992583i \(0.461209\pi\)
\(240\) −67.1487 −4.33443
\(241\) −21.4799 −1.38364 −0.691820 0.722070i \(-0.743191\pi\)
−0.691820 + 0.722070i \(0.743191\pi\)
\(242\) 6.17311 0.396823
\(243\) 6.17775 0.396303
\(244\) 63.5129 4.06599
\(245\) 1.65103 0.105480
\(246\) 22.0984 1.40894
\(247\) −0.559350 −0.0355906
\(248\) 24.8076 1.57529
\(249\) −1.86507 −0.118194
\(250\) −32.0671 −2.02810
\(251\) 13.8248 0.872617 0.436308 0.899797i \(-0.356286\pi\)
0.436308 + 0.899797i \(0.356286\pi\)
\(252\) 78.9557 4.97374
\(253\) 9.09470 0.571779
\(254\) −1.91807 −0.120350
\(255\) −28.3473 −1.77518
\(256\) −2.20965 −0.138103
\(257\) −25.7785 −1.60802 −0.804010 0.594615i \(-0.797304\pi\)
−0.804010 + 0.594615i \(0.797304\pi\)
\(258\) −97.0169 −6.04001
\(259\) 21.8482 1.35758
\(260\) −1.89100 −0.117275
\(261\) 14.1088 0.873315
\(262\) 12.5187 0.773405
\(263\) −9.63979 −0.594415 −0.297208 0.954813i \(-0.596055\pi\)
−0.297208 + 0.954813i \(0.596055\pi\)
\(264\) 72.4210 4.45720
\(265\) −27.9644 −1.71784
\(266\) 19.0897 1.17046
\(267\) 13.2771 0.812547
\(268\) 24.2148 1.47915
\(269\) 3.78475 0.230760 0.115380 0.993321i \(-0.463191\pi\)
0.115380 + 0.993321i \(0.463191\pi\)
\(270\) 52.3630 3.18671
\(271\) 7.70490 0.468040 0.234020 0.972232i \(-0.424812\pi\)
0.234020 + 0.972232i \(0.424812\pi\)
\(272\) 53.8502 3.26515
\(273\) 1.45986 0.0883547
\(274\) −23.6188 −1.42686
\(275\) 3.55573 0.214419
\(276\) −47.4852 −2.85827
\(277\) −20.1388 −1.21003 −0.605013 0.796216i \(-0.706832\pi\)
−0.605013 + 0.796216i \(0.706832\pi\)
\(278\) −38.5359 −2.31123
\(279\) −19.4645 −1.16531
\(280\) 38.9095 2.32529
\(281\) −22.7383 −1.35645 −0.678225 0.734854i \(-0.737251\pi\)
−0.678225 + 0.734854i \(0.737251\pi\)
\(282\) 35.5243 2.11544
\(283\) 3.82502 0.227374 0.113687 0.993517i \(-0.463734\pi\)
0.113687 + 0.993517i \(0.463734\pi\)
\(284\) 2.75225 0.163316
\(285\) 17.2497 1.02178
\(286\) 1.50607 0.0890560
\(287\) −6.76834 −0.399522
\(288\) −87.5317 −5.15786
\(289\) 5.73325 0.337250
\(290\) 11.5322 0.677195
\(291\) 19.3114 1.13205
\(292\) 23.5329 1.37716
\(293\) −8.91049 −0.520556 −0.260278 0.965534i \(-0.583814\pi\)
−0.260278 + 0.965534i \(0.583814\pi\)
\(294\) 6.86562 0.400411
\(295\) 6.40309 0.372803
\(296\) −70.9532 −4.12407
\(297\) −29.8507 −1.73211
\(298\) 23.1805 1.34281
\(299\) −0.595375 −0.0344314
\(300\) −18.5651 −1.07186
\(301\) 29.7146 1.71272
\(302\) −46.8673 −2.69691
\(303\) −13.0675 −0.750709
\(304\) −32.7686 −1.87941
\(305\) −24.5580 −1.40618
\(306\) −79.9359 −4.56963
\(307\) −22.9425 −1.30940 −0.654698 0.755891i \(-0.727204\pi\)
−0.654698 + 0.755891i \(0.727204\pi\)
\(308\) −36.7905 −2.09633
\(309\) −8.97748 −0.510711
\(310\) −15.9098 −0.903618
\(311\) 13.8497 0.785346 0.392673 0.919678i \(-0.371550\pi\)
0.392673 + 0.919678i \(0.371550\pi\)
\(312\) −4.74096 −0.268404
\(313\) 18.9952 1.07367 0.536837 0.843686i \(-0.319619\pi\)
0.536837 + 0.843686i \(0.319619\pi\)
\(314\) −26.6319 −1.50292
\(315\) −30.5291 −1.72012
\(316\) −20.5155 −1.15409
\(317\) −8.11643 −0.455864 −0.227932 0.973677i \(-0.573196\pi\)
−0.227932 + 0.973677i \(0.573196\pi\)
\(318\) −116.287 −6.52105
\(319\) −6.57421 −0.368085
\(320\) −27.5561 −1.54043
\(321\) 6.75889 0.377244
\(322\) 20.3191 1.13234
\(323\) −13.8335 −0.769715
\(324\) 60.3593 3.35329
\(325\) −0.232772 −0.0129119
\(326\) −35.9881 −1.99319
\(327\) 25.1554 1.39110
\(328\) 21.9805 1.21367
\(329\) −10.8805 −0.599859
\(330\) −46.4456 −2.55674
\(331\) −16.8979 −0.928792 −0.464396 0.885628i \(-0.653729\pi\)
−0.464396 + 0.885628i \(0.653729\pi\)
\(332\) −3.07696 −0.168870
\(333\) 55.6711 3.05076
\(334\) 28.0722 1.53604
\(335\) −9.36292 −0.511551
\(336\) 85.5233 4.66568
\(337\) −13.9713 −0.761068 −0.380534 0.924767i \(-0.624260\pi\)
−0.380534 + 0.924767i \(0.624260\pi\)
\(338\) 34.3860 1.87035
\(339\) 24.2465 1.31689
\(340\) −46.7669 −2.53629
\(341\) 9.06976 0.491155
\(342\) 48.6420 2.63026
\(343\) −19.4654 −1.05103
\(344\) −96.4994 −5.20290
\(345\) 18.3607 0.988505
\(346\) 48.9907 2.63376
\(347\) 7.97316 0.428022 0.214011 0.976831i \(-0.431347\pi\)
0.214011 + 0.976831i \(0.431347\pi\)
\(348\) 34.3252 1.84002
\(349\) −17.7457 −0.949908 −0.474954 0.880011i \(-0.657535\pi\)
−0.474954 + 0.880011i \(0.657535\pi\)
\(350\) 7.94411 0.424630
\(351\) 1.95414 0.104304
\(352\) 40.7866 2.17393
\(353\) −8.17292 −0.435001 −0.217500 0.976060i \(-0.569790\pi\)
−0.217500 + 0.976060i \(0.569790\pi\)
\(354\) 26.6265 1.41518
\(355\) −1.06419 −0.0564813
\(356\) 21.9044 1.16093
\(357\) 36.1043 1.91084
\(358\) −59.1223 −3.12471
\(359\) 11.1681 0.589427 0.294714 0.955586i \(-0.404776\pi\)
0.294714 + 0.955586i \(0.404776\pi\)
\(360\) 99.1447 5.22538
\(361\) −10.5822 −0.556955
\(362\) 19.8661 1.04414
\(363\) −7.10452 −0.372890
\(364\) 2.40845 0.126237
\(365\) −9.09925 −0.476276
\(366\) −102.121 −5.33798
\(367\) 31.1719 1.62716 0.813580 0.581453i \(-0.197516\pi\)
0.813580 + 0.581453i \(0.197516\pi\)
\(368\) −34.8790 −1.81819
\(369\) −17.2463 −0.897805
\(370\) 45.5042 2.36565
\(371\) 35.6166 1.84912
\(372\) −47.3549 −2.45524
\(373\) 20.2679 1.04943 0.524716 0.851277i \(-0.324172\pi\)
0.524716 + 0.851277i \(0.324172\pi\)
\(374\) 37.2472 1.92601
\(375\) 36.9054 1.90579
\(376\) 35.3348 1.82225
\(377\) 0.430373 0.0221654
\(378\) −66.6915 −3.43024
\(379\) −25.1834 −1.29358 −0.646792 0.762667i \(-0.723890\pi\)
−0.646792 + 0.762667i \(0.723890\pi\)
\(380\) 28.4582 1.45988
\(381\) 2.20747 0.113092
\(382\) −60.6309 −3.10214
\(383\) 12.7415 0.651059 0.325530 0.945532i \(-0.394457\pi\)
0.325530 + 0.945532i \(0.394457\pi\)
\(384\) −30.0263 −1.53227
\(385\) 14.2255 0.724996
\(386\) −53.1034 −2.70289
\(387\) 75.7152 3.84882
\(388\) 31.8596 1.61743
\(389\) 15.4663 0.784172 0.392086 0.919929i \(-0.371754\pi\)
0.392086 + 0.919929i \(0.371754\pi\)
\(390\) 3.04051 0.153962
\(391\) −14.7244 −0.744646
\(392\) 6.82899 0.344916
\(393\) −14.4075 −0.726761
\(394\) 36.0062 1.81396
\(395\) 7.93255 0.399130
\(396\) −93.7452 −4.71087
\(397\) −3.06504 −0.153830 −0.0769150 0.997038i \(-0.524507\pi\)
−0.0769150 + 0.997038i \(0.524507\pi\)
\(398\) −36.3046 −1.81979
\(399\) −21.9699 −1.09987
\(400\) −13.6365 −0.681827
\(401\) 0.0629464 0.00314339 0.00157170 0.999999i \(-0.499500\pi\)
0.00157170 + 0.999999i \(0.499500\pi\)
\(402\) −38.9346 −1.94188
\(403\) −0.593742 −0.0295764
\(404\) −21.5585 −1.07258
\(405\) −23.3386 −1.15970
\(406\) −14.6879 −0.728948
\(407\) −25.9407 −1.28583
\(408\) −117.250 −5.80475
\(409\) 2.35100 0.116250 0.0581248 0.998309i \(-0.481488\pi\)
0.0581248 + 0.998309i \(0.481488\pi\)
\(410\) −14.0967 −0.696186
\(411\) 27.1824 1.34081
\(412\) −14.8109 −0.729680
\(413\) −8.15524 −0.401293
\(414\) 51.7748 2.54459
\(415\) 1.18974 0.0584021
\(416\) −2.67005 −0.130910
\(417\) 44.3502 2.17184
\(418\) −22.6654 −1.10860
\(419\) 8.56477 0.418417 0.209208 0.977871i \(-0.432911\pi\)
0.209208 + 0.977871i \(0.432911\pi\)
\(420\) −74.2738 −3.62419
\(421\) 23.3286 1.13696 0.568482 0.822695i \(-0.307531\pi\)
0.568482 + 0.822695i \(0.307531\pi\)
\(422\) 64.0645 3.11861
\(423\) −27.7243 −1.34800
\(424\) −115.667 −5.61727
\(425\) −5.75676 −0.279244
\(426\) −4.42531 −0.214407
\(427\) 31.2780 1.51365
\(428\) 11.1507 0.538989
\(429\) −1.73331 −0.0836851
\(430\) 61.8877 2.98449
\(431\) 16.4071 0.790300 0.395150 0.918617i \(-0.370693\pi\)
0.395150 + 0.918617i \(0.370693\pi\)
\(432\) 114.480 5.50793
\(433\) 15.6613 0.752632 0.376316 0.926491i \(-0.377191\pi\)
0.376316 + 0.926491i \(0.377191\pi\)
\(434\) 20.2634 0.972674
\(435\) −13.2722 −0.636354
\(436\) 41.5009 1.98753
\(437\) 8.96000 0.428615
\(438\) −37.8382 −1.80798
\(439\) −33.3839 −1.59333 −0.796663 0.604424i \(-0.793404\pi\)
−0.796663 + 0.604424i \(0.793404\pi\)
\(440\) −46.1978 −2.20239
\(441\) −5.35815 −0.255150
\(442\) −2.43835 −0.115980
\(443\) 28.2026 1.33995 0.669973 0.742385i \(-0.266306\pi\)
0.669973 + 0.742385i \(0.266306\pi\)
\(444\) 135.441 6.42776
\(445\) −8.46957 −0.401496
\(446\) −52.0482 −2.46455
\(447\) −26.6780 −1.26183
\(448\) 35.0965 1.65816
\(449\) 31.4341 1.48347 0.741734 0.670694i \(-0.234004\pi\)
0.741734 + 0.670694i \(0.234004\pi\)
\(450\) 20.2422 0.954228
\(451\) 8.03614 0.378407
\(452\) 40.0013 1.88150
\(453\) 53.9387 2.53426
\(454\) −45.3958 −2.13053
\(455\) −0.931254 −0.0436579
\(456\) 71.3483 3.34119
\(457\) 14.4247 0.674760 0.337380 0.941369i \(-0.390459\pi\)
0.337380 + 0.941369i \(0.390459\pi\)
\(458\) 51.6919 2.41541
\(459\) 48.3286 2.25578
\(460\) 30.2911 1.41233
\(461\) 23.2219 1.08155 0.540775 0.841167i \(-0.318131\pi\)
0.540775 + 0.841167i \(0.318131\pi\)
\(462\) 59.1549 2.75214
\(463\) −26.5874 −1.23562 −0.617811 0.786327i \(-0.711980\pi\)
−0.617811 + 0.786327i \(0.711980\pi\)
\(464\) 25.2127 1.17047
\(465\) 18.3103 0.849120
\(466\) 66.5832 3.08441
\(467\) 5.02961 0.232743 0.116371 0.993206i \(-0.462874\pi\)
0.116371 + 0.993206i \(0.462874\pi\)
\(468\) 6.13693 0.283680
\(469\) 11.9250 0.550645
\(470\) −22.6612 −1.04528
\(471\) 30.6501 1.41228
\(472\) 26.4845 1.21905
\(473\) −35.2805 −1.62220
\(474\) 32.9866 1.51512
\(475\) 3.50306 0.160732
\(476\) 59.5642 2.73012
\(477\) 90.7541 4.15534
\(478\) −9.97057 −0.456043
\(479\) 19.0655 0.871126 0.435563 0.900158i \(-0.356549\pi\)
0.435563 + 0.900158i \(0.356549\pi\)
\(480\) 82.3412 3.75835
\(481\) 1.69818 0.0774304
\(482\) 56.9788 2.59532
\(483\) −23.3849 −1.06405
\(484\) −11.7209 −0.532768
\(485\) −12.3189 −0.559371
\(486\) −16.3875 −0.743351
\(487\) 10.5597 0.478504 0.239252 0.970957i \(-0.423098\pi\)
0.239252 + 0.970957i \(0.423098\pi\)
\(488\) −101.577 −4.59816
\(489\) 41.4180 1.87299
\(490\) −4.37962 −0.197851
\(491\) −19.7303 −0.890416 −0.445208 0.895427i \(-0.646870\pi\)
−0.445208 + 0.895427i \(0.646870\pi\)
\(492\) −41.9582 −1.89162
\(493\) 10.6437 0.479368
\(494\) 1.48377 0.0667578
\(495\) 36.2476 1.62921
\(496\) −34.7833 −1.56182
\(497\) 1.35539 0.0607977
\(498\) 4.94740 0.221698
\(499\) −36.7245 −1.64401 −0.822007 0.569477i \(-0.807146\pi\)
−0.822007 + 0.569477i \(0.807146\pi\)
\(500\) 60.8859 2.72290
\(501\) −32.3077 −1.44340
\(502\) −36.6726 −1.63678
\(503\) 17.0151 0.758664 0.379332 0.925261i \(-0.376154\pi\)
0.379332 + 0.925261i \(0.376154\pi\)
\(504\) −126.275 −5.62472
\(505\) 8.33585 0.370941
\(506\) −24.1252 −1.07249
\(507\) −39.5742 −1.75755
\(508\) 3.64184 0.161580
\(509\) 23.0865 1.02329 0.511647 0.859196i \(-0.329036\pi\)
0.511647 + 0.859196i \(0.329036\pi\)
\(510\) 75.1958 3.32973
\(511\) 11.5892 0.512674
\(512\) 25.5321 1.12837
\(513\) −29.4086 −1.29842
\(514\) 68.3817 3.01619
\(515\) 5.72679 0.252353
\(516\) 184.206 8.10922
\(517\) 12.9185 0.568156
\(518\) −57.9560 −2.54644
\(519\) −56.3825 −2.47492
\(520\) 3.02429 0.132624
\(521\) 10.9621 0.480260 0.240130 0.970741i \(-0.422810\pi\)
0.240130 + 0.970741i \(0.422810\pi\)
\(522\) −37.4260 −1.63809
\(523\) 9.53969 0.417141 0.208571 0.978007i \(-0.433119\pi\)
0.208571 + 0.978007i \(0.433119\pi\)
\(524\) −23.7692 −1.03836
\(525\) −9.14272 −0.399021
\(526\) 25.5711 1.11495
\(527\) −14.6840 −0.639647
\(528\) −101.543 −4.41909
\(529\) −13.4629 −0.585345
\(530\) 74.1802 3.22218
\(531\) −20.7802 −0.901784
\(532\) −36.2456 −1.57144
\(533\) −0.526077 −0.0227869
\(534\) −35.2197 −1.52411
\(535\) −4.31154 −0.186404
\(536\) −38.7269 −1.67275
\(537\) 68.0427 2.93626
\(538\) −10.0397 −0.432841
\(539\) 2.49670 0.107541
\(540\) −99.4216 −4.27842
\(541\) −42.0727 −1.80885 −0.904423 0.426637i \(-0.859698\pi\)
−0.904423 + 0.426637i \(0.859698\pi\)
\(542\) −20.4385 −0.877909
\(543\) −22.8635 −0.981166
\(544\) −66.0339 −2.83118
\(545\) −16.0468 −0.687369
\(546\) −3.87251 −0.165728
\(547\) −14.8311 −0.634132 −0.317066 0.948403i \(-0.602698\pi\)
−0.317066 + 0.948403i \(0.602698\pi\)
\(548\) 44.8450 1.91568
\(549\) 79.6989 3.40147
\(550\) −9.43214 −0.402188
\(551\) −6.47683 −0.275922
\(552\) 75.9435 3.23237
\(553\) −10.1032 −0.429632
\(554\) 53.4215 2.26966
\(555\) −52.3699 −2.22298
\(556\) 73.1681 3.10302
\(557\) 1.04920 0.0444562 0.0222281 0.999753i \(-0.492924\pi\)
0.0222281 + 0.999753i \(0.492924\pi\)
\(558\) 51.6328 2.18579
\(559\) 2.30960 0.0976857
\(560\) −54.5559 −2.30541
\(561\) −42.8671 −1.80985
\(562\) 60.3169 2.54431
\(563\) −30.8680 −1.30093 −0.650465 0.759536i \(-0.725426\pi\)
−0.650465 + 0.759536i \(0.725426\pi\)
\(564\) −67.4500 −2.84016
\(565\) −15.4670 −0.650700
\(566\) −10.1465 −0.426488
\(567\) 29.7250 1.24833
\(568\) −4.40170 −0.184691
\(569\) −40.4706 −1.69662 −0.848308 0.529502i \(-0.822379\pi\)
−0.848308 + 0.529502i \(0.822379\pi\)
\(570\) −45.7576 −1.91658
\(571\) 0.232265 0.00971999 0.00485999 0.999988i \(-0.498453\pi\)
0.00485999 + 0.999988i \(0.498453\pi\)
\(572\) −2.85958 −0.119565
\(573\) 69.7789 2.91505
\(574\) 17.9541 0.749390
\(575\) 3.72868 0.155497
\(576\) 89.4289 3.72620
\(577\) −6.15819 −0.256369 −0.128184 0.991750i \(-0.540915\pi\)
−0.128184 + 0.991750i \(0.540915\pi\)
\(578\) −15.2084 −0.632585
\(579\) 61.1156 2.53988
\(580\) −21.8962 −0.909192
\(581\) −1.51530 −0.0628653
\(582\) −51.2266 −2.12341
\(583\) −42.2881 −1.75139
\(584\) −37.6363 −1.55740
\(585\) −2.37291 −0.0981078
\(586\) 23.6365 0.976415
\(587\) 36.2164 1.49481 0.747405 0.664368i \(-0.231299\pi\)
0.747405 + 0.664368i \(0.231299\pi\)
\(588\) −13.0358 −0.537585
\(589\) 8.93542 0.368178
\(590\) −16.9852 −0.699271
\(591\) −41.4388 −1.70456
\(592\) 99.4850 4.08881
\(593\) −46.6241 −1.91462 −0.957312 0.289058i \(-0.906658\pi\)
−0.957312 + 0.289058i \(0.906658\pi\)
\(594\) 79.1838 3.24895
\(595\) −23.0312 −0.944185
\(596\) −44.0129 −1.80284
\(597\) 41.7823 1.71003
\(598\) 1.57933 0.0645836
\(599\) 16.5338 0.675551 0.337776 0.941227i \(-0.390326\pi\)
0.337776 + 0.941227i \(0.390326\pi\)
\(600\) 29.6914 1.21215
\(601\) 22.3970 0.913593 0.456797 0.889571i \(-0.348997\pi\)
0.456797 + 0.889571i \(0.348997\pi\)
\(602\) −78.8227 −3.21257
\(603\) 30.3858 1.23741
\(604\) 88.9871 3.62083
\(605\) 4.53202 0.184253
\(606\) 34.6637 1.40812
\(607\) 2.43468 0.0988205 0.0494103 0.998779i \(-0.484266\pi\)
0.0494103 + 0.998779i \(0.484266\pi\)
\(608\) 40.1825 1.62961
\(609\) 16.9040 0.684985
\(610\) 65.1440 2.63760
\(611\) −0.845697 −0.0342132
\(612\) 151.774 6.13511
\(613\) −12.1857 −0.492177 −0.246089 0.969247i \(-0.579145\pi\)
−0.246089 + 0.969247i \(0.579145\pi\)
\(614\) 60.8586 2.45605
\(615\) 16.2236 0.654199
\(616\) 58.8394 2.37071
\(617\) 5.63392 0.226813 0.113407 0.993549i \(-0.463824\pi\)
0.113407 + 0.993549i \(0.463824\pi\)
\(618\) 23.8142 0.957948
\(619\) −17.8395 −0.717028 −0.358514 0.933524i \(-0.616716\pi\)
−0.358514 + 0.933524i \(0.616716\pi\)
\(620\) 30.2080 1.21318
\(621\) −31.3026 −1.25613
\(622\) −36.7387 −1.47309
\(623\) 10.7872 0.432179
\(624\) 6.64740 0.266109
\(625\) −17.5053 −0.700210
\(626\) −50.3879 −2.01391
\(627\) 26.0852 1.04174
\(628\) 50.5659 2.01780
\(629\) 41.9983 1.67458
\(630\) 80.9834 3.22645
\(631\) −13.0005 −0.517544 −0.258772 0.965938i \(-0.583318\pi\)
−0.258772 + 0.965938i \(0.583318\pi\)
\(632\) 32.8106 1.30514
\(633\) −73.7306 −2.93053
\(634\) 21.5301 0.855071
\(635\) −1.40816 −0.0558810
\(636\) 220.794 8.75506
\(637\) −0.163444 −0.00647589
\(638\) 17.4391 0.690422
\(639\) 3.45366 0.136625
\(640\) 19.1540 0.757127
\(641\) 29.2012 1.15338 0.576690 0.816963i \(-0.304344\pi\)
0.576690 + 0.816963i \(0.304344\pi\)
\(642\) −17.9290 −0.707603
\(643\) 25.6030 1.00968 0.504841 0.863212i \(-0.331551\pi\)
0.504841 + 0.863212i \(0.331551\pi\)
\(644\) −38.5799 −1.52026
\(645\) −71.2254 −2.80450
\(646\) 36.6955 1.44377
\(647\) 31.7663 1.24886 0.624432 0.781080i \(-0.285331\pi\)
0.624432 + 0.781080i \(0.285331\pi\)
\(648\) −96.5331 −3.79218
\(649\) 9.68282 0.380084
\(650\) 0.617465 0.0242190
\(651\) −23.3207 −0.914012
\(652\) 68.3306 2.67603
\(653\) 0.771188 0.0301789 0.0150895 0.999886i \(-0.495197\pi\)
0.0150895 + 0.999886i \(0.495197\pi\)
\(654\) −66.7287 −2.60930
\(655\) 9.19062 0.359107
\(656\) −30.8193 −1.20329
\(657\) 29.5301 1.15208
\(658\) 28.8622 1.12516
\(659\) −35.1877 −1.37072 −0.685359 0.728205i \(-0.740355\pi\)
−0.685359 + 0.728205i \(0.740355\pi\)
\(660\) 88.1862 3.43264
\(661\) −11.3851 −0.442829 −0.221415 0.975180i \(-0.571067\pi\)
−0.221415 + 0.975180i \(0.571067\pi\)
\(662\) 44.8244 1.74215
\(663\) 2.80625 0.108986
\(664\) 4.92101 0.190972
\(665\) 14.0148 0.543469
\(666\) −147.677 −5.72235
\(667\) −6.89397 −0.266936
\(668\) −53.3007 −2.06227
\(669\) 59.9013 2.31592
\(670\) 24.8366 0.959523
\(671\) −37.1368 −1.43365
\(672\) −104.873 −4.04557
\(673\) −33.2938 −1.28338 −0.641690 0.766964i \(-0.721766\pi\)
−0.641690 + 0.766964i \(0.721766\pi\)
\(674\) 37.0613 1.42755
\(675\) −12.2383 −0.471052
\(676\) −65.2887 −2.51111
\(677\) 47.7487 1.83513 0.917566 0.397583i \(-0.130151\pi\)
0.917566 + 0.397583i \(0.130151\pi\)
\(678\) −64.3176 −2.47010
\(679\) 15.6898 0.602119
\(680\) 74.7947 2.86825
\(681\) 52.2452 2.00204
\(682\) −24.0590 −0.921267
\(683\) −18.2576 −0.698608 −0.349304 0.937010i \(-0.613582\pi\)
−0.349304 + 0.937010i \(0.613582\pi\)
\(684\) −92.3567 −3.53134
\(685\) −17.3398 −0.662520
\(686\) 51.6351 1.97144
\(687\) −59.4912 −2.26973
\(688\) 135.304 5.15841
\(689\) 2.76835 0.105466
\(690\) −48.7046 −1.85415
\(691\) 26.2426 0.998317 0.499159 0.866511i \(-0.333643\pi\)
0.499159 + 0.866511i \(0.333643\pi\)
\(692\) −93.0188 −3.53604
\(693\) −46.1664 −1.75372
\(694\) −21.1501 −0.802846
\(695\) −28.2913 −1.07315
\(696\) −54.8966 −2.08085
\(697\) −13.0106 −0.492811
\(698\) 47.0734 1.78176
\(699\) −76.6293 −2.89839
\(700\) −15.0835 −0.570102
\(701\) 25.3670 0.958100 0.479050 0.877788i \(-0.340981\pi\)
0.479050 + 0.877788i \(0.340981\pi\)
\(702\) −5.18368 −0.195645
\(703\) −25.5565 −0.963881
\(704\) −41.6706 −1.57052
\(705\) 26.0803 0.982241
\(706\) 21.6800 0.815937
\(707\) −10.6169 −0.399289
\(708\) −50.5558 −1.90000
\(709\) −10.6978 −0.401764 −0.200882 0.979615i \(-0.564381\pi\)
−0.200882 + 0.979615i \(0.564381\pi\)
\(710\) 2.82293 0.105943
\(711\) −25.7438 −0.965468
\(712\) −35.0318 −1.31287
\(713\) 9.51091 0.356186
\(714\) −95.7724 −3.58419
\(715\) 1.10569 0.0413505
\(716\) 112.256 4.19519
\(717\) 11.4749 0.428539
\(718\) −29.6251 −1.10560
\(719\) 15.7594 0.587726 0.293863 0.955848i \(-0.405059\pi\)
0.293863 + 0.955848i \(0.405059\pi\)
\(720\) −139.013 −5.18070
\(721\) −7.29387 −0.271638
\(722\) 28.0709 1.04469
\(723\) −65.5759 −2.43879
\(724\) −37.7197 −1.40184
\(725\) −2.69532 −0.100101
\(726\) 18.8459 0.699436
\(727\) −28.4397 −1.05477 −0.527386 0.849626i \(-0.676828\pi\)
−0.527386 + 0.849626i \(0.676828\pi\)
\(728\) −3.85186 −0.142759
\(729\) −17.0923 −0.633047
\(730\) 24.1372 0.893359
\(731\) 57.1195 2.11264
\(732\) 193.898 7.16668
\(733\) 12.5454 0.463377 0.231688 0.972790i \(-0.425575\pi\)
0.231688 + 0.972790i \(0.425575\pi\)
\(734\) −82.6885 −3.05209
\(735\) 5.04042 0.185919
\(736\) 42.7704 1.57654
\(737\) −14.1587 −0.521542
\(738\) 45.7485 1.68403
\(739\) 27.6264 1.01625 0.508126 0.861282i \(-0.330338\pi\)
0.508126 + 0.861282i \(0.330338\pi\)
\(740\) −86.3989 −3.17609
\(741\) −1.70764 −0.0627317
\(742\) −94.4788 −3.46843
\(743\) 36.1684 1.32689 0.663444 0.748226i \(-0.269094\pi\)
0.663444 + 0.748226i \(0.269094\pi\)
\(744\) 75.7352 2.77659
\(745\) 17.0181 0.623495
\(746\) −53.7639 −1.96843
\(747\) −3.86111 −0.141271
\(748\) −70.7213 −2.58583
\(749\) 5.49135 0.200649
\(750\) −97.8976 −3.57471
\(751\) −35.1141 −1.28133 −0.640667 0.767819i \(-0.721342\pi\)
−0.640667 + 0.767819i \(0.721342\pi\)
\(752\) −49.5437 −1.80667
\(753\) 42.2058 1.53807
\(754\) −1.14163 −0.0415759
\(755\) −34.4079 −1.25223
\(756\) 126.627 4.60539
\(757\) −33.3690 −1.21282 −0.606409 0.795153i \(-0.707391\pi\)
−0.606409 + 0.795153i \(0.707391\pi\)
\(758\) 66.8030 2.42639
\(759\) 27.7652 1.00781
\(760\) −45.5135 −1.65095
\(761\) 8.83761 0.320363 0.160182 0.987088i \(-0.448792\pi\)
0.160182 + 0.987088i \(0.448792\pi\)
\(762\) −5.85566 −0.212128
\(763\) 20.4378 0.739899
\(764\) 115.120 4.16489
\(765\) −58.6853 −2.12177
\(766\) −33.7988 −1.22120
\(767\) −0.633876 −0.0228879
\(768\) −6.74582 −0.243419
\(769\) −6.33489 −0.228442 −0.114221 0.993455i \(-0.536437\pi\)
−0.114221 + 0.993455i \(0.536437\pi\)
\(770\) −37.7353 −1.35989
\(771\) −78.6992 −2.83428
\(772\) 100.827 3.62886
\(773\) −36.3218 −1.30641 −0.653203 0.757183i \(-0.726575\pi\)
−0.653203 + 0.757183i \(0.726575\pi\)
\(774\) −200.847 −7.21928
\(775\) 3.71845 0.133571
\(776\) −50.9533 −1.82912
\(777\) 66.7004 2.39286
\(778\) −41.0268 −1.47088
\(779\) 7.91711 0.283660
\(780\) −5.77302 −0.206707
\(781\) −1.60928 −0.0575845
\(782\) 39.0589 1.39674
\(783\) 22.6274 0.808639
\(784\) −9.57508 −0.341967
\(785\) −19.5519 −0.697837
\(786\) 38.2182 1.36320
\(787\) −12.2804 −0.437750 −0.218875 0.975753i \(-0.570239\pi\)
−0.218875 + 0.975753i \(0.570239\pi\)
\(788\) −68.3650 −2.43540
\(789\) −29.4293 −1.04771
\(790\) −21.0424 −0.748654
\(791\) 19.6993 0.700428
\(792\) 149.928 5.32744
\(793\) 2.43112 0.0863316
\(794\) 8.13052 0.288541
\(795\) −85.3725 −3.02785
\(796\) 68.9316 2.44322
\(797\) 7.89371 0.279610 0.139805 0.990179i \(-0.455352\pi\)
0.139805 + 0.990179i \(0.455352\pi\)
\(798\) 58.2787 2.06305
\(799\) −20.9152 −0.739927
\(800\) 16.7218 0.591206
\(801\) 27.4866 0.971192
\(802\) −0.166975 −0.00589611
\(803\) −13.7600 −0.485579
\(804\) 73.9252 2.60714
\(805\) 14.9174 0.525768
\(806\) 1.57500 0.0554769
\(807\) 11.5545 0.406736
\(808\) 34.4788 1.21296
\(809\) 36.9078 1.29761 0.648804 0.760956i \(-0.275269\pi\)
0.648804 + 0.760956i \(0.275269\pi\)
\(810\) 61.9094 2.17527
\(811\) 0.639212 0.0224458 0.0112229 0.999937i \(-0.496428\pi\)
0.0112229 + 0.999937i \(0.496428\pi\)
\(812\) 27.8879 0.978674
\(813\) 23.5223 0.824962
\(814\) 68.8119 2.41186
\(815\) −26.4208 −0.925480
\(816\) 164.399 5.75512
\(817\) −34.7580 −1.21603
\(818\) −6.23642 −0.218051
\(819\) 3.02224 0.105605
\(820\) 26.7654 0.934688
\(821\) 11.7143 0.408833 0.204416 0.978884i \(-0.434470\pi\)
0.204416 + 0.978884i \(0.434470\pi\)
\(822\) −72.1056 −2.51497
\(823\) −27.2835 −0.951044 −0.475522 0.879704i \(-0.657741\pi\)
−0.475522 + 0.879704i \(0.657741\pi\)
\(824\) 23.6872 0.825182
\(825\) 10.8553 0.377932
\(826\) 21.6331 0.752711
\(827\) −44.5108 −1.54779 −0.773895 0.633314i \(-0.781694\pi\)
−0.773895 + 0.633314i \(0.781694\pi\)
\(828\) −98.3049 −3.41633
\(829\) −35.5248 −1.23383 −0.616913 0.787031i \(-0.711617\pi\)
−0.616913 + 0.787031i \(0.711617\pi\)
\(830\) −3.15598 −0.109546
\(831\) −61.4818 −2.13278
\(832\) 2.72792 0.0945737
\(833\) −4.04219 −0.140053
\(834\) −117.646 −4.07375
\(835\) 20.6093 0.713215
\(836\) 43.0348 1.48839
\(837\) −31.2168 −1.07901
\(838\) −22.7194 −0.784830
\(839\) 27.0186 0.932784 0.466392 0.884578i \(-0.345554\pi\)
0.466392 + 0.884578i \(0.345554\pi\)
\(840\) 118.787 4.09853
\(841\) −24.0166 −0.828159
\(842\) −61.8828 −2.13262
\(843\) −69.4175 −2.39087
\(844\) −121.639 −4.18700
\(845\) 25.2446 0.868442
\(846\) 73.5432 2.52847
\(847\) −5.77216 −0.198334
\(848\) 162.179 5.56924
\(849\) 11.6774 0.400766
\(850\) 15.2707 0.523782
\(851\) −27.2025 −0.932488
\(852\) 8.40234 0.287860
\(853\) 37.9312 1.29874 0.649369 0.760474i \(-0.275033\pi\)
0.649369 + 0.760474i \(0.275033\pi\)
\(854\) −82.9699 −2.83917
\(855\) 35.7107 1.22128
\(856\) −17.8334 −0.609533
\(857\) −31.0229 −1.05972 −0.529862 0.848084i \(-0.677756\pi\)
−0.529862 + 0.848084i \(0.677756\pi\)
\(858\) 4.59789 0.156969
\(859\) 25.8123 0.880703 0.440351 0.897826i \(-0.354854\pi\)
0.440351 + 0.897826i \(0.354854\pi\)
\(860\) −117.506 −4.00693
\(861\) −20.6630 −0.704194
\(862\) −43.5224 −1.48238
\(863\) −7.14893 −0.243352 −0.121676 0.992570i \(-0.538827\pi\)
−0.121676 + 0.992570i \(0.538827\pi\)
\(864\) −140.381 −4.77587
\(865\) 35.9668 1.22291
\(866\) −41.5440 −1.41172
\(867\) 17.5030 0.594434
\(868\) −38.4741 −1.30590
\(869\) 11.9957 0.406925
\(870\) 35.2067 1.19362
\(871\) 0.926884 0.0314063
\(872\) −66.3728 −2.24767
\(873\) 39.9789 1.35308
\(874\) −23.7678 −0.803959
\(875\) 29.9843 1.01365
\(876\) 71.8434 2.42736
\(877\) −12.0065 −0.405431 −0.202716 0.979238i \(-0.564977\pi\)
−0.202716 + 0.979238i \(0.564977\pi\)
\(878\) 88.5562 2.98863
\(879\) −27.2028 −0.917528
\(880\) 64.7749 2.18356
\(881\) −32.1303 −1.08250 −0.541249 0.840862i \(-0.682049\pi\)
−0.541249 + 0.840862i \(0.682049\pi\)
\(882\) 14.2134 0.478589
\(883\) −19.6821 −0.662356 −0.331178 0.943568i \(-0.607446\pi\)
−0.331178 + 0.943568i \(0.607446\pi\)
\(884\) 4.62970 0.155714
\(885\) 19.5480 0.657098
\(886\) −74.8120 −2.51336
\(887\) −1.13995 −0.0382759 −0.0191379 0.999817i \(-0.506092\pi\)
−0.0191379 + 0.999817i \(0.506092\pi\)
\(888\) −216.613 −7.26904
\(889\) 1.79349 0.0601516
\(890\) 22.4669 0.753092
\(891\) −35.2928 −1.18235
\(892\) 98.8240 3.30887
\(893\) 12.7272 0.425899
\(894\) 70.7678 2.36683
\(895\) −43.4049 −1.45086
\(896\) −24.3953 −0.814988
\(897\) −1.81762 −0.0606885
\(898\) −83.3841 −2.78256
\(899\) −6.87506 −0.229296
\(900\) −38.4340 −1.28113
\(901\) 68.4649 2.28090
\(902\) −21.3172 −0.709783
\(903\) 90.7155 3.01882
\(904\) −63.9745 −2.12776
\(905\) 14.5848 0.484814
\(906\) −143.081 −4.75355
\(907\) −36.9999 −1.22856 −0.614281 0.789088i \(-0.710554\pi\)
−0.614281 + 0.789088i \(0.710554\pi\)
\(908\) 86.1932 2.86042
\(909\) −27.0527 −0.897280
\(910\) 2.47030 0.0818897
\(911\) 49.1117 1.62714 0.813572 0.581465i \(-0.197520\pi\)
0.813572 + 0.581465i \(0.197520\pi\)
\(912\) −100.039 −3.31262
\(913\) 1.79914 0.0595428
\(914\) −38.2639 −1.26566
\(915\) −74.9729 −2.47853
\(916\) −98.1475 −3.24289
\(917\) −11.7055 −0.386551
\(918\) −128.199 −4.23121
\(919\) 36.1027 1.19092 0.595459 0.803386i \(-0.296970\pi\)
0.595459 + 0.803386i \(0.296970\pi\)
\(920\) −48.4448 −1.59718
\(921\) −70.0410 −2.30793
\(922\) −61.5997 −2.02868
\(923\) 0.105350 0.00346763
\(924\) −112.318 −3.69497
\(925\) −10.6353 −0.349685
\(926\) 70.5274 2.31767
\(927\) −18.5854 −0.610424
\(928\) −30.9171 −1.01490
\(929\) 35.9924 1.18087 0.590436 0.807084i \(-0.298956\pi\)
0.590436 + 0.807084i \(0.298956\pi\)
\(930\) −48.5711 −1.59271
\(931\) 2.45972 0.0806142
\(932\) −126.422 −4.14108
\(933\) 42.2818 1.38424
\(934\) −13.3419 −0.436559
\(935\) 27.3452 0.894284
\(936\) −9.81485 −0.320808
\(937\) 0.368168 0.0120275 0.00601377 0.999982i \(-0.498086\pi\)
0.00601377 + 0.999982i \(0.498086\pi\)
\(938\) −31.6329 −1.03285
\(939\) 57.9904 1.89245
\(940\) 43.0268 1.40338
\(941\) 10.1487 0.330837 0.165418 0.986223i \(-0.447103\pi\)
0.165418 + 0.986223i \(0.447103\pi\)
\(942\) −81.3043 −2.64904
\(943\) 8.42701 0.274421
\(944\) −37.1345 −1.20862
\(945\) −48.9619 −1.59273
\(946\) 93.5872 3.04278
\(947\) 5.78211 0.187893 0.0939467 0.995577i \(-0.470052\pi\)
0.0939467 + 0.995577i \(0.470052\pi\)
\(948\) −62.6317 −2.03418
\(949\) 0.900782 0.0292406
\(950\) −9.29244 −0.301487
\(951\) −24.7786 −0.803502
\(952\) −95.2615 −3.08744
\(953\) 35.5792 1.15252 0.576262 0.817265i \(-0.304511\pi\)
0.576262 + 0.817265i \(0.304511\pi\)
\(954\) −240.740 −7.79424
\(955\) −44.5124 −1.44039
\(956\) 18.9311 0.612277
\(957\) −20.0704 −0.648783
\(958\) −50.5744 −1.63398
\(959\) 22.0847 0.713151
\(960\) −84.1259 −2.71515
\(961\) −21.5152 −0.694038
\(962\) −4.50470 −0.145237
\(963\) 13.9924 0.450899
\(964\) −108.186 −3.48443
\(965\) −38.9861 −1.25501
\(966\) 62.0322 1.99585
\(967\) 54.9249 1.76626 0.883132 0.469124i \(-0.155430\pi\)
0.883132 + 0.469124i \(0.155430\pi\)
\(968\) 18.7453 0.602498
\(969\) −42.2322 −1.35669
\(970\) 32.6778 1.04922
\(971\) −24.6072 −0.789682 −0.394841 0.918749i \(-0.629200\pi\)
−0.394841 + 0.918749i \(0.629200\pi\)
\(972\) 31.1149 0.998012
\(973\) 36.0329 1.15516
\(974\) −28.0112 −0.897537
\(975\) −0.710629 −0.0227583
\(976\) 142.423 4.55885
\(977\) 39.1338 1.25200 0.626001 0.779822i \(-0.284691\pi\)
0.626001 + 0.779822i \(0.284691\pi\)
\(978\) −109.868 −3.51319
\(979\) −12.8078 −0.409338
\(980\) 8.31559 0.265632
\(981\) 52.0773 1.66270
\(982\) 52.3378 1.67017
\(983\) −5.02643 −0.160318 −0.0801591 0.996782i \(-0.525543\pi\)
−0.0801591 + 0.996782i \(0.525543\pi\)
\(984\) 67.1041 2.13920
\(985\) 26.4341 0.842260
\(986\) −28.2341 −0.899158
\(987\) −33.2169 −1.05731
\(988\) −2.81723 −0.0896280
\(989\) −36.9965 −1.17642
\(990\) −96.1527 −3.05593
\(991\) 12.3304 0.391688 0.195844 0.980635i \(-0.437255\pi\)
0.195844 + 0.980635i \(0.437255\pi\)
\(992\) 42.6531 1.35424
\(993\) −51.5875 −1.63708
\(994\) −3.59540 −0.114039
\(995\) −26.6532 −0.844963
\(996\) −9.39364 −0.297649
\(997\) −51.5304 −1.63198 −0.815991 0.578064i \(-0.803808\pi\)
−0.815991 + 0.578064i \(0.803808\pi\)
\(998\) 97.4176 3.08370
\(999\) 89.2841 2.82482
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 4001.2.a.b.1.10 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.10 184 1.1 even 1 trivial