Properties

Label 6001.2.a.c.1.9
Level $6001$
Weight $2$
Character 6001.1
Self dual yes
Analytic conductor $47.918$
Analytic rank $0$
Dimension $121$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6001,2,Mod(1,6001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6001 = 17 \cdot 353 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6001.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: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 6001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.53200 q^{2} +0.341990 q^{3} +4.41103 q^{4} +2.95840 q^{5} -0.865919 q^{6} +4.74675 q^{7} -6.10474 q^{8} -2.88304 q^{9} +O(q^{10})\) \(q-2.53200 q^{2} +0.341990 q^{3} +4.41103 q^{4} +2.95840 q^{5} -0.865919 q^{6} +4.74675 q^{7} -6.10474 q^{8} -2.88304 q^{9} -7.49068 q^{10} -0.409857 q^{11} +1.50853 q^{12} -2.52058 q^{13} -12.0188 q^{14} +1.01174 q^{15} +6.63515 q^{16} -1.00000 q^{17} +7.29987 q^{18} +7.19313 q^{19} +13.0496 q^{20} +1.62334 q^{21} +1.03776 q^{22} +4.18683 q^{23} -2.08776 q^{24} +3.75215 q^{25} +6.38211 q^{26} -2.01194 q^{27} +20.9381 q^{28} +7.77491 q^{29} -2.56174 q^{30} +4.33420 q^{31} -4.59073 q^{32} -0.140167 q^{33} +2.53200 q^{34} +14.0428 q^{35} -12.7172 q^{36} -10.6364 q^{37} -18.2130 q^{38} -0.862012 q^{39} -18.0603 q^{40} +6.97135 q^{41} -4.11030 q^{42} -3.13226 q^{43} -1.80789 q^{44} -8.52920 q^{45} -10.6011 q^{46} -1.13711 q^{47} +2.26915 q^{48} +15.5316 q^{49} -9.50046 q^{50} -0.341990 q^{51} -11.1184 q^{52} +6.05777 q^{53} +5.09424 q^{54} -1.21252 q^{55} -28.9777 q^{56} +2.45998 q^{57} -19.6861 q^{58} -7.59327 q^{59} +4.46284 q^{60} -6.35868 q^{61} -10.9742 q^{62} -13.6851 q^{63} -1.64656 q^{64} -7.45689 q^{65} +0.354902 q^{66} -2.28847 q^{67} -4.41103 q^{68} +1.43185 q^{69} -35.5564 q^{70} +16.4609 q^{71} +17.6002 q^{72} +3.24981 q^{73} +26.9313 q^{74} +1.28320 q^{75} +31.7291 q^{76} -1.94549 q^{77} +2.18262 q^{78} -14.3364 q^{79} +19.6295 q^{80} +7.96107 q^{81} -17.6515 q^{82} -3.32716 q^{83} +7.16061 q^{84} -2.95840 q^{85} +7.93088 q^{86} +2.65894 q^{87} +2.50207 q^{88} +9.96866 q^{89} +21.5960 q^{90} -11.9646 q^{91} +18.4682 q^{92} +1.48225 q^{93} +2.87916 q^{94} +21.2802 q^{95} -1.56998 q^{96} -2.28126 q^{97} -39.3261 q^{98} +1.18163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53200 −1.79040 −0.895198 0.445669i \(-0.852966\pi\)
−0.895198 + 0.445669i \(0.852966\pi\)
\(3\) 0.341990 0.197448 0.0987239 0.995115i \(-0.468524\pi\)
0.0987239 + 0.995115i \(0.468524\pi\)
\(4\) 4.41103 2.20552
\(5\) 2.95840 1.32304 0.661519 0.749928i \(-0.269912\pi\)
0.661519 + 0.749928i \(0.269912\pi\)
\(6\) −0.865919 −0.353510
\(7\) 4.74675 1.79410 0.897051 0.441926i \(-0.145705\pi\)
0.897051 + 0.441926i \(0.145705\pi\)
\(8\) −6.10474 −2.15835
\(9\) −2.88304 −0.961014
\(10\) −7.49068 −2.36876
\(11\) −0.409857 −0.123576 −0.0617882 0.998089i \(-0.519680\pi\)
−0.0617882 + 0.998089i \(0.519680\pi\)
\(12\) 1.50853 0.435475
\(13\) −2.52058 −0.699083 −0.349541 0.936921i \(-0.613663\pi\)
−0.349541 + 0.936921i \(0.613663\pi\)
\(14\) −12.0188 −3.21215
\(15\) 1.01174 0.261231
\(16\) 6.63515 1.65879
\(17\) −1.00000 −0.242536
\(18\) 7.29987 1.72060
\(19\) 7.19313 1.65022 0.825109 0.564974i \(-0.191114\pi\)
0.825109 + 0.564974i \(0.191114\pi\)
\(20\) 13.0496 2.91798
\(21\) 1.62334 0.354242
\(22\) 1.03776 0.221251
\(23\) 4.18683 0.873014 0.436507 0.899701i \(-0.356215\pi\)
0.436507 + 0.899701i \(0.356215\pi\)
\(24\) −2.08776 −0.426162
\(25\) 3.75215 0.750430
\(26\) 6.38211 1.25163
\(27\) −2.01194 −0.387198
\(28\) 20.9381 3.95692
\(29\) 7.77491 1.44377 0.721883 0.692016i \(-0.243277\pi\)
0.721883 + 0.692016i \(0.243277\pi\)
\(30\) −2.56174 −0.467707
\(31\) 4.33420 0.778445 0.389222 0.921144i \(-0.372744\pi\)
0.389222 + 0.921144i \(0.372744\pi\)
\(32\) −4.59073 −0.811535
\(33\) −0.140167 −0.0243999
\(34\) 2.53200 0.434235
\(35\) 14.0428 2.37367
\(36\) −12.7172 −2.11953
\(37\) −10.6364 −1.74861 −0.874305 0.485376i \(-0.838683\pi\)
−0.874305 + 0.485376i \(0.838683\pi\)
\(38\) −18.2130 −2.95454
\(39\) −0.862012 −0.138032
\(40\) −18.0603 −2.85558
\(41\) 6.97135 1.08874 0.544371 0.838845i \(-0.316768\pi\)
0.544371 + 0.838845i \(0.316768\pi\)
\(42\) −4.11030 −0.634233
\(43\) −3.13226 −0.477665 −0.238832 0.971061i \(-0.576765\pi\)
−0.238832 + 0.971061i \(0.576765\pi\)
\(44\) −1.80789 −0.272550
\(45\) −8.52920 −1.27146
\(46\) −10.6011 −1.56304
\(47\) −1.13711 −0.165864 −0.0829321 0.996555i \(-0.526428\pi\)
−0.0829321 + 0.996555i \(0.526428\pi\)
\(48\) 2.26915 0.327524
\(49\) 15.5316 2.21880
\(50\) −9.50046 −1.34357
\(51\) −0.341990 −0.0478881
\(52\) −11.1184 −1.54184
\(53\) 6.05777 0.832099 0.416050 0.909342i \(-0.363414\pi\)
0.416050 + 0.909342i \(0.363414\pi\)
\(54\) 5.09424 0.693238
\(55\) −1.21252 −0.163496
\(56\) −28.9777 −3.87231
\(57\) 2.45998 0.325832
\(58\) −19.6861 −2.58491
\(59\) −7.59327 −0.988560 −0.494280 0.869303i \(-0.664568\pi\)
−0.494280 + 0.869303i \(0.664568\pi\)
\(60\) 4.46284 0.576150
\(61\) −6.35868 −0.814146 −0.407073 0.913396i \(-0.633451\pi\)
−0.407073 + 0.913396i \(0.633451\pi\)
\(62\) −10.9742 −1.39372
\(63\) −13.6851 −1.72416
\(64\) −1.64656 −0.205820
\(65\) −7.45689 −0.924913
\(66\) 0.354902 0.0436855
\(67\) −2.28847 −0.279581 −0.139790 0.990181i \(-0.544643\pi\)
−0.139790 + 0.990181i \(0.544643\pi\)
\(68\) −4.41103 −0.534916
\(69\) 1.43185 0.172375
\(70\) −35.5564 −4.24980
\(71\) 16.4609 1.95355 0.976777 0.214258i \(-0.0687332\pi\)
0.976777 + 0.214258i \(0.0687332\pi\)
\(72\) 17.6002 2.07421
\(73\) 3.24981 0.380362 0.190181 0.981749i \(-0.439093\pi\)
0.190181 + 0.981749i \(0.439093\pi\)
\(74\) 26.9313 3.13070
\(75\) 1.28320 0.148171
\(76\) 31.7291 3.63958
\(77\) −1.94549 −0.221709
\(78\) 2.18262 0.247133
\(79\) −14.3364 −1.61297 −0.806483 0.591257i \(-0.798632\pi\)
−0.806483 + 0.591257i \(0.798632\pi\)
\(80\) 19.6295 2.19464
\(81\) 7.96107 0.884563
\(82\) −17.6515 −1.94928
\(83\) −3.32716 −0.365203 −0.182602 0.983187i \(-0.558452\pi\)
−0.182602 + 0.983187i \(0.558452\pi\)
\(84\) 7.16061 0.781286
\(85\) −2.95840 −0.320884
\(86\) 7.93088 0.855209
\(87\) 2.65894 0.285068
\(88\) 2.50207 0.266721
\(89\) 9.96866 1.05668 0.528338 0.849034i \(-0.322815\pi\)
0.528338 + 0.849034i \(0.322815\pi\)
\(90\) 21.5960 2.27641
\(91\) −11.9646 −1.25423
\(92\) 18.4682 1.92545
\(93\) 1.48225 0.153702
\(94\) 2.87916 0.296962
\(95\) 21.2802 2.18330
\(96\) −1.56998 −0.160236
\(97\) −2.28126 −0.231626 −0.115813 0.993271i \(-0.536947\pi\)
−0.115813 + 0.993271i \(0.536947\pi\)
\(98\) −39.3261 −3.97254
\(99\) 1.18163 0.118759
\(100\) 16.5509 1.65509
\(101\) 4.26105 0.423990 0.211995 0.977271i \(-0.432004\pi\)
0.211995 + 0.977271i \(0.432004\pi\)
\(102\) 0.865919 0.0857387
\(103\) −14.4725 −1.42602 −0.713009 0.701155i \(-0.752668\pi\)
−0.713009 + 0.701155i \(0.752668\pi\)
\(104\) 15.3875 1.50887
\(105\) 4.80249 0.468675
\(106\) −15.3383 −1.48979
\(107\) 15.6412 1.51209 0.756045 0.654520i \(-0.227129\pi\)
0.756045 + 0.654520i \(0.227129\pi\)
\(108\) −8.87474 −0.853972
\(109\) 11.0554 1.05891 0.529457 0.848337i \(-0.322396\pi\)
0.529457 + 0.848337i \(0.322396\pi\)
\(110\) 3.07011 0.292723
\(111\) −3.63753 −0.345259
\(112\) 31.4954 2.97604
\(113\) −6.11056 −0.574833 −0.287416 0.957806i \(-0.592796\pi\)
−0.287416 + 0.957806i \(0.592796\pi\)
\(114\) −6.22867 −0.583368
\(115\) 12.3863 1.15503
\(116\) 34.2954 3.18425
\(117\) 7.26693 0.671828
\(118\) 19.2262 1.76991
\(119\) −4.74675 −0.435134
\(120\) −6.17643 −0.563829
\(121\) −10.8320 −0.984729
\(122\) 16.1002 1.45764
\(123\) 2.38413 0.214970
\(124\) 19.1183 1.71687
\(125\) −3.69164 −0.330190
\(126\) 34.6507 3.08693
\(127\) 16.8060 1.49129 0.745647 0.666341i \(-0.232140\pi\)
0.745647 + 0.666341i \(0.232140\pi\)
\(128\) 13.3506 1.18003
\(129\) −1.07120 −0.0943139
\(130\) 18.8809 1.65596
\(131\) −11.0365 −0.964261 −0.482131 0.876099i \(-0.660137\pi\)
−0.482131 + 0.876099i \(0.660137\pi\)
\(132\) −0.618280 −0.0538144
\(133\) 34.1440 2.96066
\(134\) 5.79440 0.500560
\(135\) −5.95213 −0.512278
\(136\) 6.10474 0.523477
\(137\) 12.2670 1.04804 0.524019 0.851707i \(-0.324432\pi\)
0.524019 + 0.851707i \(0.324432\pi\)
\(138\) −3.62545 −0.308619
\(139\) 2.27634 0.193076 0.0965381 0.995329i \(-0.469223\pi\)
0.0965381 + 0.995329i \(0.469223\pi\)
\(140\) 61.9433 5.23516
\(141\) −0.388879 −0.0327495
\(142\) −41.6791 −3.49764
\(143\) 1.03308 0.0863901
\(144\) −19.1294 −1.59412
\(145\) 23.0013 1.91016
\(146\) −8.22853 −0.680998
\(147\) 5.31166 0.438098
\(148\) −46.9174 −3.85659
\(149\) −6.31227 −0.517122 −0.258561 0.965995i \(-0.583248\pi\)
−0.258561 + 0.965995i \(0.583248\pi\)
\(150\) −3.24906 −0.265284
\(151\) 0.595975 0.0484997 0.0242499 0.999706i \(-0.492280\pi\)
0.0242499 + 0.999706i \(0.492280\pi\)
\(152\) −43.9122 −3.56175
\(153\) 2.88304 0.233080
\(154\) 4.92597 0.396946
\(155\) 12.8223 1.02991
\(156\) −3.80236 −0.304433
\(157\) 18.1956 1.45216 0.726082 0.687608i \(-0.241339\pi\)
0.726082 + 0.687608i \(0.241339\pi\)
\(158\) 36.2997 2.88785
\(159\) 2.07170 0.164296
\(160\) −13.5812 −1.07369
\(161\) 19.8738 1.56628
\(162\) −20.1574 −1.58372
\(163\) −12.0663 −0.945106 −0.472553 0.881302i \(-0.656667\pi\)
−0.472553 + 0.881302i \(0.656667\pi\)
\(164\) 30.7508 2.40124
\(165\) −0.414670 −0.0322820
\(166\) 8.42438 0.653858
\(167\) 14.4440 1.11771 0.558856 0.829265i \(-0.311240\pi\)
0.558856 + 0.829265i \(0.311240\pi\)
\(168\) −9.91007 −0.764579
\(169\) −6.64669 −0.511284
\(170\) 7.49068 0.574509
\(171\) −20.7381 −1.58588
\(172\) −13.8165 −1.05350
\(173\) 9.69087 0.736783 0.368391 0.929671i \(-0.379909\pi\)
0.368391 + 0.929671i \(0.379909\pi\)
\(174\) −6.73244 −0.510385
\(175\) 17.8105 1.34635
\(176\) −2.71946 −0.204987
\(177\) −2.59682 −0.195189
\(178\) −25.2407 −1.89187
\(179\) −12.2123 −0.912789 −0.456394 0.889778i \(-0.650859\pi\)
−0.456394 + 0.889778i \(0.650859\pi\)
\(180\) −37.6226 −2.80422
\(181\) −21.9847 −1.63411 −0.817055 0.576560i \(-0.804395\pi\)
−0.817055 + 0.576560i \(0.804395\pi\)
\(182\) 30.2943 2.24556
\(183\) −2.17460 −0.160751
\(184\) −25.5595 −1.88427
\(185\) −31.4667 −2.31348
\(186\) −3.75306 −0.275188
\(187\) 0.409857 0.0299717
\(188\) −5.01582 −0.365816
\(189\) −9.55018 −0.694673
\(190\) −53.8815 −3.90897
\(191\) 1.37577 0.0995476 0.0497738 0.998761i \(-0.484150\pi\)
0.0497738 + 0.998761i \(0.484150\pi\)
\(192\) −0.563106 −0.0406387
\(193\) −0.410100 −0.0295197 −0.0147598 0.999891i \(-0.504698\pi\)
−0.0147598 + 0.999891i \(0.504698\pi\)
\(194\) 5.77614 0.414703
\(195\) −2.55018 −0.182622
\(196\) 68.5106 4.89361
\(197\) −21.6674 −1.54374 −0.771870 0.635780i \(-0.780679\pi\)
−0.771870 + 0.635780i \(0.780679\pi\)
\(198\) −2.99190 −0.212625
\(199\) −20.0987 −1.42476 −0.712381 0.701793i \(-0.752383\pi\)
−0.712381 + 0.701793i \(0.752383\pi\)
\(200\) −22.9059 −1.61969
\(201\) −0.782632 −0.0552026
\(202\) −10.7890 −0.759111
\(203\) 36.9056 2.59026
\(204\) −1.50853 −0.105618
\(205\) 20.6241 1.44045
\(206\) 36.6444 2.55314
\(207\) −12.0708 −0.838979
\(208\) −16.7244 −1.15963
\(209\) −2.94815 −0.203928
\(210\) −12.1599 −0.839114
\(211\) 14.9466 1.02897 0.514484 0.857500i \(-0.327983\pi\)
0.514484 + 0.857500i \(0.327983\pi\)
\(212\) 26.7210 1.83521
\(213\) 5.62947 0.385725
\(214\) −39.6035 −2.70724
\(215\) −9.26648 −0.631969
\(216\) 12.2824 0.835710
\(217\) 20.5734 1.39661
\(218\) −27.9922 −1.89587
\(219\) 1.11140 0.0751016
\(220\) −5.34847 −0.360594
\(221\) 2.52058 0.169552
\(222\) 9.21024 0.618151
\(223\) 8.23191 0.551250 0.275625 0.961265i \(-0.411115\pi\)
0.275625 + 0.961265i \(0.411115\pi\)
\(224\) −21.7911 −1.45598
\(225\) −10.8176 −0.721174
\(226\) 15.4719 1.02918
\(227\) −26.6748 −1.77047 −0.885235 0.465145i \(-0.846002\pi\)
−0.885235 + 0.465145i \(0.846002\pi\)
\(228\) 10.8510 0.718628
\(229\) 24.9900 1.65139 0.825694 0.564118i \(-0.190784\pi\)
0.825694 + 0.564118i \(0.190784\pi\)
\(230\) −31.3622 −2.06796
\(231\) −0.665336 −0.0437759
\(232\) −47.4638 −3.11615
\(233\) 13.9733 0.915421 0.457710 0.889101i \(-0.348670\pi\)
0.457710 + 0.889101i \(0.348670\pi\)
\(234\) −18.3999 −1.20284
\(235\) −3.36402 −0.219445
\(236\) −33.4942 −2.18029
\(237\) −4.90289 −0.318477
\(238\) 12.0188 0.779062
\(239\) 29.4534 1.90518 0.952590 0.304256i \(-0.0984078\pi\)
0.952590 + 0.304256i \(0.0984078\pi\)
\(240\) 6.71307 0.433327
\(241\) 6.60081 0.425195 0.212598 0.977140i \(-0.431808\pi\)
0.212598 + 0.977140i \(0.431808\pi\)
\(242\) 27.4267 1.76305
\(243\) 8.75842 0.561853
\(244\) −28.0484 −1.79561
\(245\) 45.9488 2.93556
\(246\) −6.03662 −0.384881
\(247\) −18.1308 −1.15364
\(248\) −26.4592 −1.68016
\(249\) −1.13785 −0.0721086
\(250\) 9.34724 0.591171
\(251\) 16.9869 1.07220 0.536101 0.844154i \(-0.319897\pi\)
0.536101 + 0.844154i \(0.319897\pi\)
\(252\) −60.3654 −3.80266
\(253\) −1.71600 −0.107884
\(254\) −42.5529 −2.67001
\(255\) −1.01174 −0.0633578
\(256\) −30.5105 −1.90691
\(257\) −3.78822 −0.236303 −0.118151 0.992996i \(-0.537697\pi\)
−0.118151 + 0.992996i \(0.537697\pi\)
\(258\) 2.71228 0.168859
\(259\) −50.4882 −3.13719
\(260\) −32.8926 −2.03991
\(261\) −22.4154 −1.38748
\(262\) 27.9444 1.72641
\(263\) −11.5568 −0.712624 −0.356312 0.934367i \(-0.615966\pi\)
−0.356312 + 0.934367i \(0.615966\pi\)
\(264\) 0.855682 0.0526636
\(265\) 17.9213 1.10090
\(266\) −86.4526 −5.30075
\(267\) 3.40918 0.208638
\(268\) −10.0945 −0.616620
\(269\) 22.4938 1.37147 0.685735 0.727851i \(-0.259481\pi\)
0.685735 + 0.727851i \(0.259481\pi\)
\(270\) 15.0708 0.917180
\(271\) 21.4222 1.30131 0.650653 0.759375i \(-0.274495\pi\)
0.650653 + 0.759375i \(0.274495\pi\)
\(272\) −6.63515 −0.402315
\(273\) −4.09175 −0.247644
\(274\) −31.0600 −1.87640
\(275\) −1.53784 −0.0927355
\(276\) 6.31595 0.380175
\(277\) 1.73374 0.104170 0.0520852 0.998643i \(-0.483413\pi\)
0.0520852 + 0.998643i \(0.483413\pi\)
\(278\) −5.76368 −0.345683
\(279\) −12.4957 −0.748097
\(280\) −85.7277 −5.12321
\(281\) −8.68295 −0.517981 −0.258991 0.965880i \(-0.583390\pi\)
−0.258991 + 0.965880i \(0.583390\pi\)
\(282\) 0.984642 0.0586346
\(283\) −20.9842 −1.24738 −0.623689 0.781672i \(-0.714367\pi\)
−0.623689 + 0.781672i \(0.714367\pi\)
\(284\) 72.6098 4.30860
\(285\) 7.27760 0.431088
\(286\) −2.61575 −0.154672
\(287\) 33.0912 1.95331
\(288\) 13.2353 0.779897
\(289\) 1.00000 0.0588235
\(290\) −58.2394 −3.41994
\(291\) −0.780166 −0.0457341
\(292\) 14.3350 0.838895
\(293\) 0.782898 0.0457374 0.0228687 0.999738i \(-0.492720\pi\)
0.0228687 + 0.999738i \(0.492720\pi\)
\(294\) −13.4491 −0.784369
\(295\) −22.4640 −1.30790
\(296\) 64.9324 3.77412
\(297\) 0.824607 0.0478485
\(298\) 15.9827 0.925852
\(299\) −10.5532 −0.610309
\(300\) 5.66023 0.326793
\(301\) −14.8680 −0.856980
\(302\) −1.50901 −0.0868337
\(303\) 1.45724 0.0837160
\(304\) 47.7275 2.73736
\(305\) −18.8116 −1.07715
\(306\) −7.29987 −0.417306
\(307\) −7.20908 −0.411444 −0.205722 0.978611i \(-0.565954\pi\)
−0.205722 + 0.978611i \(0.565954\pi\)
\(308\) −8.58161 −0.488982
\(309\) −4.94945 −0.281564
\(310\) −32.4661 −1.84395
\(311\) −12.0123 −0.681157 −0.340579 0.940216i \(-0.610623\pi\)
−0.340579 + 0.940216i \(0.610623\pi\)
\(312\) 5.26236 0.297922
\(313\) 32.9807 1.86418 0.932089 0.362231i \(-0.117985\pi\)
0.932089 + 0.362231i \(0.117985\pi\)
\(314\) −46.0712 −2.59995
\(315\) −40.4860 −2.28113
\(316\) −63.2381 −3.55742
\(317\) 18.6264 1.04616 0.523080 0.852283i \(-0.324783\pi\)
0.523080 + 0.852283i \(0.324783\pi\)
\(318\) −5.24554 −0.294155
\(319\) −3.18660 −0.178415
\(320\) −4.87118 −0.272307
\(321\) 5.34912 0.298559
\(322\) −50.3206 −2.80426
\(323\) −7.19313 −0.400236
\(324\) 35.1165 1.95092
\(325\) −9.45759 −0.524613
\(326\) 30.5519 1.69211
\(327\) 3.78083 0.209080
\(328\) −42.5583 −2.34989
\(329\) −5.39756 −0.297577
\(330\) 1.04994 0.0577975
\(331\) −17.4541 −0.959364 −0.479682 0.877442i \(-0.659248\pi\)
−0.479682 + 0.877442i \(0.659248\pi\)
\(332\) −14.6762 −0.805462
\(333\) 30.6651 1.68044
\(334\) −36.5723 −2.00115
\(335\) −6.77020 −0.369896
\(336\) 10.7711 0.587612
\(337\) −14.1556 −0.771103 −0.385551 0.922686i \(-0.625989\pi\)
−0.385551 + 0.922686i \(0.625989\pi\)
\(338\) 16.8294 0.915400
\(339\) −2.08975 −0.113500
\(340\) −13.0496 −0.707715
\(341\) −1.77640 −0.0961974
\(342\) 52.5089 2.83936
\(343\) 40.4975 2.18666
\(344\) 19.1216 1.03097
\(345\) 4.23600 0.228058
\(346\) −24.5373 −1.31913
\(347\) −25.8478 −1.38758 −0.693792 0.720176i \(-0.744061\pi\)
−0.693792 + 0.720176i \(0.744061\pi\)
\(348\) 11.7287 0.628723
\(349\) 6.77753 0.362793 0.181396 0.983410i \(-0.441938\pi\)
0.181396 + 0.983410i \(0.441938\pi\)
\(350\) −45.0963 −2.41050
\(351\) 5.07125 0.270683
\(352\) 1.88154 0.100287
\(353\) 1.00000 0.0532246
\(354\) 6.57516 0.349466
\(355\) 48.6981 2.58463
\(356\) 43.9721 2.33052
\(357\) −1.62334 −0.0859162
\(358\) 30.9215 1.63425
\(359\) −12.7456 −0.672687 −0.336343 0.941739i \(-0.609190\pi\)
−0.336343 + 0.941739i \(0.609190\pi\)
\(360\) 52.0686 2.74426
\(361\) 32.7411 1.72322
\(362\) 55.6653 2.92570
\(363\) −3.70444 −0.194433
\(364\) −52.7760 −2.76622
\(365\) 9.61426 0.503233
\(366\) 5.50610 0.287809
\(367\) 4.22149 0.220360 0.110180 0.993912i \(-0.464857\pi\)
0.110180 + 0.993912i \(0.464857\pi\)
\(368\) 27.7802 1.44815
\(369\) −20.0987 −1.04630
\(370\) 79.6738 4.14204
\(371\) 28.7547 1.49287
\(372\) 6.53826 0.338993
\(373\) 27.8829 1.44372 0.721861 0.692038i \(-0.243287\pi\)
0.721861 + 0.692038i \(0.243287\pi\)
\(374\) −1.03776 −0.0536612
\(375\) −1.26250 −0.0651953
\(376\) 6.94175 0.357993
\(377\) −19.5973 −1.00931
\(378\) 24.1811 1.24374
\(379\) 14.0382 0.721094 0.360547 0.932741i \(-0.382590\pi\)
0.360547 + 0.932741i \(0.382590\pi\)
\(380\) 93.8676 4.81531
\(381\) 5.74749 0.294453
\(382\) −3.48346 −0.178230
\(383\) 33.3653 1.70489 0.852443 0.522820i \(-0.175120\pi\)
0.852443 + 0.522820i \(0.175120\pi\)
\(384\) 4.56575 0.232995
\(385\) −5.75553 −0.293329
\(386\) 1.03837 0.0528519
\(387\) 9.03043 0.459043
\(388\) −10.0627 −0.510856
\(389\) −19.3089 −0.978999 −0.489499 0.872004i \(-0.662820\pi\)
−0.489499 + 0.872004i \(0.662820\pi\)
\(390\) 6.45706 0.326966
\(391\) −4.18683 −0.211737
\(392\) −94.8166 −4.78896
\(393\) −3.77436 −0.190391
\(394\) 54.8620 2.76391
\(395\) −42.4127 −2.13402
\(396\) 5.21223 0.261924
\(397\) −36.6621 −1.84002 −0.920008 0.391899i \(-0.871818\pi\)
−0.920008 + 0.391899i \(0.871818\pi\)
\(398\) 50.8901 2.55089
\(399\) 11.6769 0.584576
\(400\) 24.8961 1.24480
\(401\) −20.1902 −1.00825 −0.504124 0.863631i \(-0.668185\pi\)
−0.504124 + 0.863631i \(0.668185\pi\)
\(402\) 1.98162 0.0988345
\(403\) −10.9247 −0.544197
\(404\) 18.7956 0.935118
\(405\) 23.5520 1.17031
\(406\) −93.4450 −4.63760
\(407\) 4.35939 0.216087
\(408\) 2.08776 0.103359
\(409\) 16.0783 0.795021 0.397511 0.917598i \(-0.369874\pi\)
0.397511 + 0.917598i \(0.369874\pi\)
\(410\) −52.2202 −2.57897
\(411\) 4.19517 0.206933
\(412\) −63.8387 −3.14511
\(413\) −36.0434 −1.77358
\(414\) 30.5633 1.50210
\(415\) −9.84308 −0.483178
\(416\) 11.5713 0.567330
\(417\) 0.778483 0.0381225
\(418\) 7.46472 0.365112
\(419\) 23.9982 1.17239 0.586194 0.810170i \(-0.300626\pi\)
0.586194 + 0.810170i \(0.300626\pi\)
\(420\) 21.1840 1.03367
\(421\) −26.2973 −1.28165 −0.640827 0.767685i \(-0.721408\pi\)
−0.640827 + 0.767685i \(0.721408\pi\)
\(422\) −37.8449 −1.84226
\(423\) 3.27833 0.159398
\(424\) −36.9812 −1.79596
\(425\) −3.75215 −0.182006
\(426\) −14.2538 −0.690601
\(427\) −30.1831 −1.46066
\(428\) 68.9938 3.33494
\(429\) 0.353301 0.0170575
\(430\) 23.4628 1.13147
\(431\) 0.426122 0.0205256 0.0102628 0.999947i \(-0.496733\pi\)
0.0102628 + 0.999947i \(0.496733\pi\)
\(432\) −13.3495 −0.642280
\(433\) 28.9559 1.39153 0.695765 0.718269i \(-0.255065\pi\)
0.695765 + 0.718269i \(0.255065\pi\)
\(434\) −52.0918 −2.50048
\(435\) 7.86622 0.377156
\(436\) 48.7656 2.33545
\(437\) 30.1164 1.44066
\(438\) −2.81407 −0.134462
\(439\) 5.15871 0.246212 0.123106 0.992394i \(-0.460714\pi\)
0.123106 + 0.992394i \(0.460714\pi\)
\(440\) 7.40213 0.352883
\(441\) −44.7784 −2.13230
\(442\) −6.38211 −0.303566
\(443\) −11.7649 −0.558966 −0.279483 0.960151i \(-0.590163\pi\)
−0.279483 + 0.960151i \(0.590163\pi\)
\(444\) −16.0453 −0.761475
\(445\) 29.4913 1.39802
\(446\) −20.8432 −0.986955
\(447\) −2.15873 −0.102105
\(448\) −7.81580 −0.369262
\(449\) 27.3016 1.28844 0.644222 0.764839i \(-0.277181\pi\)
0.644222 + 0.764839i \(0.277181\pi\)
\(450\) 27.3902 1.29119
\(451\) −2.85725 −0.134543
\(452\) −26.9539 −1.26780
\(453\) 0.203817 0.00957617
\(454\) 67.5407 3.16984
\(455\) −35.3960 −1.65939
\(456\) −15.0175 −0.703260
\(457\) −7.11366 −0.332763 −0.166382 0.986061i \(-0.553208\pi\)
−0.166382 + 0.986061i \(0.553208\pi\)
\(458\) −63.2748 −2.95664
\(459\) 2.01194 0.0939093
\(460\) 54.6365 2.54744
\(461\) 8.72953 0.406575 0.203287 0.979119i \(-0.434837\pi\)
0.203287 + 0.979119i \(0.434837\pi\)
\(462\) 1.68463 0.0783762
\(463\) −6.66026 −0.309528 −0.154764 0.987951i \(-0.549462\pi\)
−0.154764 + 0.987951i \(0.549462\pi\)
\(464\) 51.5877 2.39490
\(465\) 4.38510 0.203354
\(466\) −35.3804 −1.63897
\(467\) −6.84422 −0.316713 −0.158356 0.987382i \(-0.550619\pi\)
−0.158356 + 0.987382i \(0.550619\pi\)
\(468\) 32.0547 1.48173
\(469\) −10.8628 −0.501596
\(470\) 8.51771 0.392893
\(471\) 6.22270 0.286727
\(472\) 46.3550 2.13366
\(473\) 1.28378 0.0590281
\(474\) 12.4141 0.570199
\(475\) 26.9897 1.23837
\(476\) −20.9381 −0.959695
\(477\) −17.4648 −0.799659
\(478\) −74.5760 −3.41103
\(479\) −6.21841 −0.284126 −0.142063 0.989858i \(-0.545374\pi\)
−0.142063 + 0.989858i \(0.545374\pi\)
\(480\) −4.64465 −0.211998
\(481\) 26.8098 1.22242
\(482\) −16.7133 −0.761268
\(483\) 6.79664 0.309258
\(484\) −47.7804 −2.17184
\(485\) −6.74888 −0.306451
\(486\) −22.1763 −1.00594
\(487\) −10.1103 −0.458140 −0.229070 0.973410i \(-0.573568\pi\)
−0.229070 + 0.973410i \(0.573568\pi\)
\(488\) 38.8181 1.75721
\(489\) −4.12655 −0.186609
\(490\) −116.343 −5.25582
\(491\) −23.1841 −1.04628 −0.523142 0.852246i \(-0.675240\pi\)
−0.523142 + 0.852246i \(0.675240\pi\)
\(492\) 10.5165 0.474119
\(493\) −7.77491 −0.350164
\(494\) 45.9073 2.06547
\(495\) 3.49575 0.157122
\(496\) 28.7581 1.29128
\(497\) 78.1360 3.50488
\(498\) 2.88105 0.129103
\(499\) −8.02004 −0.359026 −0.179513 0.983756i \(-0.557452\pi\)
−0.179513 + 0.983756i \(0.557452\pi\)
\(500\) −16.2839 −0.728240
\(501\) 4.93971 0.220690
\(502\) −43.0108 −1.91967
\(503\) −40.2426 −1.79433 −0.897164 0.441697i \(-0.854377\pi\)
−0.897164 + 0.441697i \(0.854377\pi\)
\(504\) 83.5439 3.72134
\(505\) 12.6059 0.560956
\(506\) 4.34491 0.193155
\(507\) −2.27310 −0.100952
\(508\) 74.1320 3.28908
\(509\) −36.6408 −1.62408 −0.812038 0.583604i \(-0.801642\pi\)
−0.812038 + 0.583604i \(0.801642\pi\)
\(510\) 2.56174 0.113436
\(511\) 15.4260 0.682408
\(512\) 50.5516 2.23409
\(513\) −14.4721 −0.638961
\(514\) 9.59179 0.423076
\(515\) −42.8155 −1.88668
\(516\) −4.72510 −0.208011
\(517\) 0.466051 0.0204969
\(518\) 127.836 5.61681
\(519\) 3.31418 0.145476
\(520\) 45.5224 1.99629
\(521\) 6.10851 0.267619 0.133809 0.991007i \(-0.457279\pi\)
0.133809 + 0.991007i \(0.457279\pi\)
\(522\) 56.7559 2.48414
\(523\) −2.29166 −0.100207 −0.0501036 0.998744i \(-0.515955\pi\)
−0.0501036 + 0.998744i \(0.515955\pi\)
\(524\) −48.6823 −2.12669
\(525\) 6.09102 0.265834
\(526\) 29.2619 1.27588
\(527\) −4.33420 −0.188801
\(528\) −0.930028 −0.0404743
\(529\) −5.47046 −0.237846
\(530\) −45.3769 −1.97105
\(531\) 21.8917 0.950020
\(532\) 150.610 6.52978
\(533\) −17.5718 −0.761120
\(534\) −8.63205 −0.373545
\(535\) 46.2729 2.00055
\(536\) 13.9705 0.603433
\(537\) −4.17647 −0.180228
\(538\) −56.9543 −2.45548
\(539\) −6.36574 −0.274192
\(540\) −26.2551 −1.12984
\(541\) 19.3560 0.832179 0.416090 0.909324i \(-0.363400\pi\)
0.416090 + 0.909324i \(0.363400\pi\)
\(542\) −54.2411 −2.32985
\(543\) −7.51854 −0.322652
\(544\) 4.59073 0.196826
\(545\) 32.7063 1.40098
\(546\) 10.3603 0.443381
\(547\) −1.50650 −0.0644134 −0.0322067 0.999481i \(-0.510253\pi\)
−0.0322067 + 0.999481i \(0.510253\pi\)
\(548\) 54.1100 2.31146
\(549\) 18.3324 0.782406
\(550\) 3.89382 0.166033
\(551\) 55.9260 2.38253
\(552\) −8.74109 −0.372046
\(553\) −68.0511 −2.89383
\(554\) −4.38983 −0.186506
\(555\) −10.7613 −0.456791
\(556\) 10.0410 0.425833
\(557\) −25.6913 −1.08857 −0.544287 0.838899i \(-0.683200\pi\)
−0.544287 + 0.838899i \(0.683200\pi\)
\(558\) 31.6391 1.33939
\(559\) 7.89510 0.333927
\(560\) 93.1761 3.93741
\(561\) 0.140167 0.00591784
\(562\) 21.9852 0.927391
\(563\) 39.1193 1.64868 0.824341 0.566094i \(-0.191546\pi\)
0.824341 + 0.566094i \(0.191546\pi\)
\(564\) −1.71536 −0.0722296
\(565\) −18.0775 −0.760526
\(566\) 53.1319 2.23330
\(567\) 37.7892 1.58700
\(568\) −100.490 −4.21646
\(569\) 2.67575 0.112173 0.0560867 0.998426i \(-0.482138\pi\)
0.0560867 + 0.998426i \(0.482138\pi\)
\(570\) −18.4269 −0.771818
\(571\) 20.2454 0.847246 0.423623 0.905839i \(-0.360758\pi\)
0.423623 + 0.905839i \(0.360758\pi\)
\(572\) 4.55693 0.190535
\(573\) 0.470501 0.0196555
\(574\) −83.7871 −3.49720
\(575\) 15.7096 0.655136
\(576\) 4.74710 0.197796
\(577\) −6.21131 −0.258580 −0.129290 0.991607i \(-0.541270\pi\)
−0.129290 + 0.991607i \(0.541270\pi\)
\(578\) −2.53200 −0.105317
\(579\) −0.140250 −0.00582859
\(580\) 101.460 4.21288
\(581\) −15.7932 −0.655212
\(582\) 1.97538 0.0818822
\(583\) −2.48282 −0.102828
\(584\) −19.8393 −0.820955
\(585\) 21.4985 0.888855
\(586\) −1.98230 −0.0818880
\(587\) 2.46999 0.101948 0.0509738 0.998700i \(-0.483768\pi\)
0.0509738 + 0.998700i \(0.483768\pi\)
\(588\) 23.4299 0.966233
\(589\) 31.1764 1.28460
\(590\) 56.8788 2.34166
\(591\) −7.41004 −0.304808
\(592\) −70.5740 −2.90057
\(593\) −6.64938 −0.273057 −0.136529 0.990636i \(-0.543595\pi\)
−0.136529 + 0.990636i \(0.543595\pi\)
\(594\) −2.08791 −0.0856678
\(595\) −14.0428 −0.575699
\(596\) −27.8436 −1.14052
\(597\) −6.87356 −0.281316
\(598\) 26.7208 1.09269
\(599\) 32.4310 1.32509 0.662547 0.749020i \(-0.269475\pi\)
0.662547 + 0.749020i \(0.269475\pi\)
\(600\) −7.83359 −0.319805
\(601\) 14.6369 0.597053 0.298527 0.954401i \(-0.403505\pi\)
0.298527 + 0.954401i \(0.403505\pi\)
\(602\) 37.6459 1.53433
\(603\) 6.59774 0.268681
\(604\) 2.62887 0.106967
\(605\) −32.0455 −1.30283
\(606\) −3.68972 −0.149885
\(607\) −5.94197 −0.241177 −0.120589 0.992703i \(-0.538478\pi\)
−0.120589 + 0.992703i \(0.538478\pi\)
\(608\) −33.0217 −1.33921
\(609\) 12.6213 0.511442
\(610\) 47.6309 1.92852
\(611\) 2.86617 0.115953
\(612\) 12.7172 0.514062
\(613\) −23.6245 −0.954183 −0.477091 0.878854i \(-0.658309\pi\)
−0.477091 + 0.878854i \(0.658309\pi\)
\(614\) 18.2534 0.736647
\(615\) 7.05322 0.284413
\(616\) 11.8767 0.478526
\(617\) −31.6910 −1.27583 −0.637915 0.770106i \(-0.720203\pi\)
−0.637915 + 0.770106i \(0.720203\pi\)
\(618\) 12.5320 0.504112
\(619\) −6.63221 −0.266571 −0.133286 0.991078i \(-0.542553\pi\)
−0.133286 + 0.991078i \(0.542553\pi\)
\(620\) 56.5596 2.27149
\(621\) −8.42365 −0.338029
\(622\) 30.4153 1.21954
\(623\) 47.3187 1.89579
\(624\) −5.71958 −0.228966
\(625\) −29.6821 −1.18728
\(626\) −83.5071 −3.33761
\(627\) −1.00824 −0.0402651
\(628\) 80.2612 3.20277
\(629\) 10.6364 0.424100
\(630\) 102.511 4.08412
\(631\) 41.9770 1.67108 0.835538 0.549432i \(-0.185156\pi\)
0.835538 + 0.549432i \(0.185156\pi\)
\(632\) 87.5198 3.48135
\(633\) 5.11160 0.203168
\(634\) −47.1620 −1.87304
\(635\) 49.7190 1.97304
\(636\) 9.13832 0.362358
\(637\) −39.1487 −1.55113
\(638\) 8.06847 0.319434
\(639\) −47.4576 −1.87739
\(640\) 39.4963 1.56123
\(641\) 34.5377 1.36416 0.682078 0.731279i \(-0.261076\pi\)
0.682078 + 0.731279i \(0.261076\pi\)
\(642\) −13.5440 −0.534539
\(643\) −33.6910 −1.32864 −0.664322 0.747447i \(-0.731280\pi\)
−0.664322 + 0.747447i \(0.731280\pi\)
\(644\) 87.6641 3.45445
\(645\) −3.16904 −0.124781
\(646\) 18.2130 0.716582
\(647\) −39.8177 −1.56540 −0.782698 0.622402i \(-0.786157\pi\)
−0.782698 + 0.622402i \(0.786157\pi\)
\(648\) −48.6003 −1.90920
\(649\) 3.11215 0.122163
\(650\) 23.9466 0.939265
\(651\) 7.03587 0.275758
\(652\) −53.2249 −2.08445
\(653\) −36.9263 −1.44504 −0.722519 0.691351i \(-0.757016\pi\)
−0.722519 + 0.691351i \(0.757016\pi\)
\(654\) −9.57306 −0.374336
\(655\) −32.6503 −1.27575
\(656\) 46.2559 1.80599
\(657\) −9.36935 −0.365533
\(658\) 13.6666 0.532781
\(659\) 30.0812 1.17180 0.585898 0.810385i \(-0.300742\pi\)
0.585898 + 0.810385i \(0.300742\pi\)
\(660\) −1.82912 −0.0711985
\(661\) −3.32441 −0.129305 −0.0646524 0.997908i \(-0.520594\pi\)
−0.0646524 + 0.997908i \(0.520594\pi\)
\(662\) 44.1938 1.71764
\(663\) 0.862012 0.0334778
\(664\) 20.3115 0.788237
\(665\) 101.012 3.91707
\(666\) −77.6442 −3.00865
\(667\) 32.5522 1.26043
\(668\) 63.7131 2.46513
\(669\) 2.81523 0.108843
\(670\) 17.1422 0.662260
\(671\) 2.60615 0.100609
\(672\) −7.45232 −0.287479
\(673\) 0.727099 0.0280276 0.0140138 0.999902i \(-0.495539\pi\)
0.0140138 + 0.999902i \(0.495539\pi\)
\(674\) 35.8419 1.38058
\(675\) −7.54911 −0.290565
\(676\) −29.3188 −1.12764
\(677\) 47.3716 1.82064 0.910319 0.413908i \(-0.135837\pi\)
0.910319 + 0.413908i \(0.135837\pi\)
\(678\) 5.29124 0.203209
\(679\) −10.8286 −0.415562
\(680\) 18.0603 0.692581
\(681\) −9.12251 −0.349575
\(682\) 4.49785 0.172231
\(683\) −12.6897 −0.485558 −0.242779 0.970082i \(-0.578059\pi\)
−0.242779 + 0.970082i \(0.578059\pi\)
\(684\) −91.4765 −3.49769
\(685\) 36.2906 1.38659
\(686\) −102.540 −3.91499
\(687\) 8.54633 0.326063
\(688\) −20.7830 −0.792345
\(689\) −15.2691 −0.581706
\(690\) −10.7256 −0.408315
\(691\) −37.5014 −1.42662 −0.713310 0.700848i \(-0.752805\pi\)
−0.713310 + 0.700848i \(0.752805\pi\)
\(692\) 42.7467 1.62499
\(693\) 5.60892 0.213065
\(694\) 65.4467 2.48432
\(695\) 6.73432 0.255447
\(696\) −16.2321 −0.615278
\(697\) −6.97135 −0.264059
\(698\) −17.1607 −0.649543
\(699\) 4.77872 0.180748
\(700\) 78.5628 2.96940
\(701\) 30.9827 1.17020 0.585100 0.810961i \(-0.301055\pi\)
0.585100 + 0.810961i \(0.301055\pi\)
\(702\) −12.8404 −0.484630
\(703\) −76.5089 −2.88559
\(704\) 0.674852 0.0254345
\(705\) −1.15046 −0.0433289
\(706\) −2.53200 −0.0952932
\(707\) 20.2261 0.760682
\(708\) −11.4547 −0.430493
\(709\) 26.2119 0.984409 0.492204 0.870480i \(-0.336191\pi\)
0.492204 + 0.870480i \(0.336191\pi\)
\(710\) −123.304 −4.62751
\(711\) 41.3323 1.55008
\(712\) −60.8561 −2.28068
\(713\) 18.1465 0.679593
\(714\) 4.11030 0.153824
\(715\) 3.05625 0.114297
\(716\) −53.8688 −2.01317
\(717\) 10.0728 0.376174
\(718\) 32.2719 1.20438
\(719\) −10.3708 −0.386766 −0.193383 0.981123i \(-0.561946\pi\)
−0.193383 + 0.981123i \(0.561946\pi\)
\(720\) −56.5926 −2.10908
\(721\) −68.6974 −2.55842
\(722\) −82.9006 −3.08524
\(723\) 2.25741 0.0839539
\(724\) −96.9753 −3.60406
\(725\) 29.1727 1.08345
\(726\) 9.37965 0.348111
\(727\) −5.97667 −0.221663 −0.110831 0.993839i \(-0.535351\pi\)
−0.110831 + 0.993839i \(0.535351\pi\)
\(728\) 73.0405 2.70706
\(729\) −20.8879 −0.773626
\(730\) −24.3433 −0.900987
\(731\) 3.13226 0.115851
\(732\) −9.59226 −0.354540
\(733\) 8.67316 0.320350 0.160175 0.987089i \(-0.448794\pi\)
0.160175 + 0.987089i \(0.448794\pi\)
\(734\) −10.6888 −0.394532
\(735\) 15.7140 0.579621
\(736\) −19.2206 −0.708481
\(737\) 0.937943 0.0345496
\(738\) 50.8899 1.87328
\(739\) −20.3093 −0.747091 −0.373546 0.927612i \(-0.621858\pi\)
−0.373546 + 0.927612i \(0.621858\pi\)
\(740\) −138.801 −5.10242
\(741\) −6.20056 −0.227783
\(742\) −72.8071 −2.67283
\(743\) −16.6153 −0.609557 −0.304778 0.952423i \(-0.598582\pi\)
−0.304778 + 0.952423i \(0.598582\pi\)
\(744\) −9.04876 −0.331744
\(745\) −18.6743 −0.684172
\(746\) −70.5996 −2.58484
\(747\) 9.59234 0.350966
\(748\) 1.80789 0.0661030
\(749\) 74.2448 2.71284
\(750\) 3.19666 0.116725
\(751\) 30.1638 1.10069 0.550347 0.834936i \(-0.314495\pi\)
0.550347 + 0.834936i \(0.314495\pi\)
\(752\) −7.54488 −0.275133
\(753\) 5.80934 0.211704
\(754\) 49.6203 1.80707
\(755\) 1.76313 0.0641670
\(756\) −42.1262 −1.53211
\(757\) 9.90884 0.360143 0.180071 0.983654i \(-0.442367\pi\)
0.180071 + 0.983654i \(0.442367\pi\)
\(758\) −35.5447 −1.29104
\(759\) −0.586854 −0.0213015
\(760\) −129.910 −4.71233
\(761\) 1.65148 0.0598660 0.0299330 0.999552i \(-0.490471\pi\)
0.0299330 + 0.999552i \(0.490471\pi\)
\(762\) −14.5527 −0.527187
\(763\) 52.4771 1.89980
\(764\) 6.06859 0.219554
\(765\) 8.52920 0.308374
\(766\) −84.4809 −3.05242
\(767\) 19.1394 0.691085
\(768\) −10.4343 −0.376515
\(769\) −40.4713 −1.45943 −0.729717 0.683750i \(-0.760348\pi\)
−0.729717 + 0.683750i \(0.760348\pi\)
\(770\) 14.5730 0.525175
\(771\) −1.29553 −0.0466575
\(772\) −1.80897 −0.0651061
\(773\) 6.38055 0.229492 0.114746 0.993395i \(-0.463395\pi\)
0.114746 + 0.993395i \(0.463395\pi\)
\(774\) −22.8651 −0.821868
\(775\) 16.2626 0.584169
\(776\) 13.9265 0.499932
\(777\) −17.2665 −0.619431
\(778\) 48.8901 1.75280
\(779\) 50.1458 1.79666
\(780\) −11.2489 −0.402776
\(781\) −6.74662 −0.241413
\(782\) 10.6011 0.379093
\(783\) −15.6427 −0.559023
\(784\) 103.055 3.68053
\(785\) 53.8298 1.92127
\(786\) 9.55669 0.340876
\(787\) −32.1561 −1.14624 −0.573120 0.819471i \(-0.694267\pi\)
−0.573120 + 0.819471i \(0.694267\pi\)
\(788\) −95.5758 −3.40475
\(789\) −3.95231 −0.140706
\(790\) 107.389 3.82073
\(791\) −29.0053 −1.03131
\(792\) −7.21357 −0.256323
\(793\) 16.0276 0.569155
\(794\) 92.8284 3.29436
\(795\) 6.12891 0.217370
\(796\) −88.6563 −3.14234
\(797\) 27.3217 0.967786 0.483893 0.875127i \(-0.339222\pi\)
0.483893 + 0.875127i \(0.339222\pi\)
\(798\) −29.5659 −1.04662
\(799\) 1.13711 0.0402280
\(800\) −17.2251 −0.609000
\(801\) −28.7401 −1.01548
\(802\) 51.1215 1.80516
\(803\) −1.33196 −0.0470037
\(804\) −3.45221 −0.121750
\(805\) 58.7948 2.07224
\(806\) 27.6613 0.974328
\(807\) 7.69265 0.270794
\(808\) −26.0126 −0.915121
\(809\) 36.3355 1.27749 0.638744 0.769419i \(-0.279454\pi\)
0.638744 + 0.769419i \(0.279454\pi\)
\(810\) −59.6338 −2.09532
\(811\) −5.01312 −0.176034 −0.0880171 0.996119i \(-0.528053\pi\)
−0.0880171 + 0.996119i \(0.528053\pi\)
\(812\) 162.792 5.71287
\(813\) 7.32618 0.256940
\(814\) −11.0380 −0.386881
\(815\) −35.6970 −1.25041
\(816\) −2.26915 −0.0794363
\(817\) −22.5307 −0.788251
\(818\) −40.7103 −1.42340
\(819\) 34.4943 1.20533
\(820\) 90.9734 3.17693
\(821\) −29.5605 −1.03167 −0.515835 0.856688i \(-0.672518\pi\)
−0.515835 + 0.856688i \(0.672518\pi\)
\(822\) −10.6222 −0.370491
\(823\) −8.83593 −0.308001 −0.154001 0.988071i \(-0.549216\pi\)
−0.154001 + 0.988071i \(0.549216\pi\)
\(824\) 88.3509 3.07785
\(825\) −0.525927 −0.0183104
\(826\) 91.2619 3.17541
\(827\) −0.669650 −0.0232860 −0.0116430 0.999932i \(-0.503706\pi\)
−0.0116430 + 0.999932i \(0.503706\pi\)
\(828\) −53.2447 −1.85038
\(829\) −17.0754 −0.593052 −0.296526 0.955025i \(-0.595828\pi\)
−0.296526 + 0.955025i \(0.595828\pi\)
\(830\) 24.9227 0.865080
\(831\) 0.592921 0.0205682
\(832\) 4.15028 0.143885
\(833\) −15.5316 −0.538139
\(834\) −1.97112 −0.0682543
\(835\) 42.7313 1.47878
\(836\) −13.0044 −0.449766
\(837\) −8.72015 −0.301412
\(838\) −60.7635 −2.09904
\(839\) 26.8408 0.926647 0.463324 0.886189i \(-0.346657\pi\)
0.463324 + 0.886189i \(0.346657\pi\)
\(840\) −29.3180 −1.01157
\(841\) 31.4493 1.08446
\(842\) 66.5849 2.29467
\(843\) −2.96948 −0.102274
\(844\) 65.9301 2.26941
\(845\) −19.6636 −0.676448
\(846\) −8.30073 −0.285385
\(847\) −51.4169 −1.76670
\(848\) 40.1943 1.38028
\(849\) −7.17636 −0.246292
\(850\) 9.50046 0.325863
\(851\) −44.5327 −1.52656
\(852\) 24.8318 0.850723
\(853\) −19.2153 −0.657921 −0.328960 0.944344i \(-0.606698\pi\)
−0.328960 + 0.944344i \(0.606698\pi\)
\(854\) 76.4236 2.61516
\(855\) −61.3517 −2.09818
\(856\) −95.4854 −3.26362
\(857\) −0.0237696 −0.000811952 0 −0.000405976 1.00000i \(-0.500129\pi\)
−0.000405976 1.00000i \(0.500129\pi\)
\(858\) −0.894559 −0.0305397
\(859\) 26.7019 0.911057 0.455529 0.890221i \(-0.349450\pi\)
0.455529 + 0.890221i \(0.349450\pi\)
\(860\) −40.8748 −1.39382
\(861\) 11.3169 0.385678
\(862\) −1.07894 −0.0367489
\(863\) 19.5962 0.667061 0.333531 0.942739i \(-0.391760\pi\)
0.333531 + 0.942739i \(0.391760\pi\)
\(864\) 9.23628 0.314225
\(865\) 28.6695 0.974792
\(866\) −73.3163 −2.49139
\(867\) 0.341990 0.0116146
\(868\) 90.7498 3.08025
\(869\) 5.87585 0.199324
\(870\) −19.9173 −0.675259
\(871\) 5.76826 0.195450
\(872\) −67.4902 −2.28551
\(873\) 6.57696 0.222596
\(874\) −76.2548 −2.57936
\(875\) −17.5233 −0.592395
\(876\) 4.90243 0.165638
\(877\) −51.5392 −1.74035 −0.870177 0.492739i \(-0.835996\pi\)
−0.870177 + 0.492739i \(0.835996\pi\)
\(878\) −13.0619 −0.440817
\(879\) 0.267743 0.00903075
\(880\) −8.04526 −0.271206
\(881\) 14.8020 0.498693 0.249347 0.968414i \(-0.419784\pi\)
0.249347 + 0.968414i \(0.419784\pi\)
\(882\) 113.379 3.81767
\(883\) 53.7521 1.80890 0.904452 0.426576i \(-0.140280\pi\)
0.904452 + 0.426576i \(0.140280\pi\)
\(884\) 11.1184 0.373951
\(885\) −7.68245 −0.258243
\(886\) 29.7887 1.00077
\(887\) −43.9478 −1.47562 −0.737811 0.675007i \(-0.764140\pi\)
−0.737811 + 0.675007i \(0.764140\pi\)
\(888\) 22.2062 0.745191
\(889\) 79.7741 2.67554
\(890\) −74.6721 −2.50301
\(891\) −3.26289 −0.109311
\(892\) 36.3112 1.21579
\(893\) −8.17936 −0.273712
\(894\) 5.46591 0.182808
\(895\) −36.1289 −1.20765
\(896\) 63.3717 2.11710
\(897\) −3.60910 −0.120504
\(898\) −69.1278 −2.30682
\(899\) 33.6980 1.12389
\(900\) −47.7169 −1.59056
\(901\) −6.05777 −0.201814
\(902\) 7.23457 0.240885
\(903\) −5.08472 −0.169209
\(904\) 37.3034 1.24069
\(905\) −65.0396 −2.16199
\(906\) −0.516066 −0.0171451
\(907\) 54.1901 1.79935 0.899677 0.436556i \(-0.143802\pi\)
0.899677 + 0.436556i \(0.143802\pi\)
\(908\) −117.664 −3.90480
\(909\) −12.2848 −0.407461
\(910\) 89.6227 2.97096
\(911\) −35.4911 −1.17587 −0.587936 0.808907i \(-0.700059\pi\)
−0.587936 + 0.808907i \(0.700059\pi\)
\(912\) 16.3223 0.540486
\(913\) 1.36366 0.0451305
\(914\) 18.0118 0.595778
\(915\) −6.43336 −0.212680
\(916\) 110.232 3.64216
\(917\) −52.3874 −1.72998
\(918\) −5.09424 −0.168135
\(919\) 48.0560 1.58522 0.792610 0.609728i \(-0.208721\pi\)
0.792610 + 0.609728i \(0.208721\pi\)
\(920\) −75.6154 −2.49296
\(921\) −2.46543 −0.0812387
\(922\) −22.1032 −0.727930
\(923\) −41.4911 −1.36570
\(924\) −2.93482 −0.0965485
\(925\) −39.9093 −1.31221
\(926\) 16.8638 0.554178
\(927\) 41.7249 1.37042
\(928\) −35.6926 −1.17167
\(929\) 37.3467 1.22531 0.612653 0.790352i \(-0.290102\pi\)
0.612653 + 0.790352i \(0.290102\pi\)
\(930\) −11.1031 −0.364084
\(931\) 111.721 3.66151
\(932\) 61.6367 2.01898
\(933\) −4.10810 −0.134493
\(934\) 17.3296 0.567041
\(935\) 1.21252 0.0396537
\(936\) −44.3628 −1.45004
\(937\) 22.5737 0.737451 0.368725 0.929538i \(-0.379794\pi\)
0.368725 + 0.929538i \(0.379794\pi\)
\(938\) 27.5046 0.898056
\(939\) 11.2790 0.368078
\(940\) −14.8388 −0.483989
\(941\) −18.6755 −0.608804 −0.304402 0.952544i \(-0.598457\pi\)
−0.304402 + 0.952544i \(0.598457\pi\)
\(942\) −15.7559 −0.513354
\(943\) 29.1878 0.950487
\(944\) −50.3825 −1.63981
\(945\) −28.2533 −0.919079
\(946\) −3.25052 −0.105684
\(947\) 30.4023 0.987942 0.493971 0.869478i \(-0.335545\pi\)
0.493971 + 0.869478i \(0.335545\pi\)
\(948\) −21.6268 −0.702406
\(949\) −8.19141 −0.265904
\(950\) −68.3380 −2.21718
\(951\) 6.37002 0.206562
\(952\) 28.9777 0.939172
\(953\) −4.08548 −0.132342 −0.0661708 0.997808i \(-0.521078\pi\)
−0.0661708 + 0.997808i \(0.521078\pi\)
\(954\) 44.2210 1.43171
\(955\) 4.07010 0.131705
\(956\) 129.920 4.20191
\(957\) −1.08978 −0.0352277
\(958\) 15.7450 0.508699
\(959\) 58.2282 1.88029
\(960\) −1.66589 −0.0537665
\(961\) −12.2147 −0.394024
\(962\) −67.8826 −2.18862
\(963\) −45.0942 −1.45314
\(964\) 29.1164 0.937776
\(965\) −1.21324 −0.0390556
\(966\) −17.2091 −0.553694
\(967\) −54.3561 −1.74797 −0.873987 0.485950i \(-0.838474\pi\)
−0.873987 + 0.485950i \(0.838474\pi\)
\(968\) 66.1267 2.12539
\(969\) −2.45998 −0.0790258
\(970\) 17.0882 0.548668
\(971\) 4.53285 0.145466 0.0727330 0.997351i \(-0.476828\pi\)
0.0727330 + 0.997351i \(0.476828\pi\)
\(972\) 38.6337 1.23918
\(973\) 10.8052 0.346399
\(974\) 25.5992 0.820252
\(975\) −3.23440 −0.103584
\(976\) −42.1908 −1.35050
\(977\) −0.939849 −0.0300684 −0.0150342 0.999887i \(-0.504786\pi\)
−0.0150342 + 0.999887i \(0.504786\pi\)
\(978\) 10.4484 0.334104
\(979\) −4.08572 −0.130580
\(980\) 202.682 6.47443
\(981\) −31.8731 −1.01763
\(982\) 58.7022 1.87326
\(983\) 47.6806 1.52077 0.760387 0.649470i \(-0.225009\pi\)
0.760387 + 0.649470i \(0.225009\pi\)
\(984\) −14.5545 −0.463980
\(985\) −64.1010 −2.04243
\(986\) 19.6861 0.626933
\(987\) −1.84591 −0.0587560
\(988\) −79.9758 −2.54437
\(989\) −13.1142 −0.417008
\(990\) −8.85125 −0.281311
\(991\) 58.6709 1.86374 0.931871 0.362791i \(-0.118176\pi\)
0.931871 + 0.362791i \(0.118176\pi\)
\(992\) −19.8971 −0.631735
\(993\) −5.96912 −0.189424
\(994\) −197.840 −6.27512
\(995\) −59.4602 −1.88502
\(996\) −5.01911 −0.159037
\(997\) 13.7179 0.434450 0.217225 0.976122i \(-0.430299\pi\)
0.217225 + 0.976122i \(0.430299\pi\)
\(998\) 20.3068 0.642799
\(999\) 21.3998 0.677059
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 6001.2.a.c.1.9 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.c.1.9 121 1.1 even 1 trivial