Properties

Label 4015.2.a.e.1.4
Level $4015$
Weight $2$
Character 4015.1
Self dual yes
Analytic conductor $32.060$
Analytic rank $0$
Dimension $27$
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] = [4015,2,Mod(1,4015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4015.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: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 4015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.19462 q^{2} -2.47425 q^{3} +2.81638 q^{4} -1.00000 q^{5} +5.43004 q^{6} +3.64013 q^{7} -1.79164 q^{8} +3.12189 q^{9} +O(q^{10})\) \(q-2.19462 q^{2} -2.47425 q^{3} +2.81638 q^{4} -1.00000 q^{5} +5.43004 q^{6} +3.64013 q^{7} -1.79164 q^{8} +3.12189 q^{9} +2.19462 q^{10} +1.00000 q^{11} -6.96841 q^{12} -2.80642 q^{13} -7.98871 q^{14} +2.47425 q^{15} -1.70077 q^{16} +4.66302 q^{17} -6.85138 q^{18} -4.34117 q^{19} -2.81638 q^{20} -9.00657 q^{21} -2.19462 q^{22} -5.74058 q^{23} +4.43297 q^{24} +1.00000 q^{25} +6.15904 q^{26} -0.301589 q^{27} +10.2520 q^{28} +4.06241 q^{29} -5.43004 q^{30} -4.88222 q^{31} +7.31584 q^{32} -2.47425 q^{33} -10.2336 q^{34} -3.64013 q^{35} +8.79243 q^{36} +9.96750 q^{37} +9.52724 q^{38} +6.94378 q^{39} +1.79164 q^{40} -1.64330 q^{41} +19.7660 q^{42} +5.70250 q^{43} +2.81638 q^{44} -3.12189 q^{45} +12.5984 q^{46} +12.0297 q^{47} +4.20812 q^{48} +6.25052 q^{49} -2.19462 q^{50} -11.5375 q^{51} -7.90395 q^{52} -1.44311 q^{53} +0.661876 q^{54} -1.00000 q^{55} -6.52181 q^{56} +10.7411 q^{57} -8.91546 q^{58} +3.08475 q^{59} +6.96841 q^{60} -4.34581 q^{61} +10.7146 q^{62} +11.3641 q^{63} -12.6540 q^{64} +2.80642 q^{65} +5.43004 q^{66} -11.9606 q^{67} +13.1328 q^{68} +14.2036 q^{69} +7.98871 q^{70} +3.21937 q^{71} -5.59332 q^{72} -1.00000 q^{73} -21.8749 q^{74} -2.47425 q^{75} -12.2264 q^{76} +3.64013 q^{77} -15.2390 q^{78} -0.195611 q^{79} +1.70077 q^{80} -8.61947 q^{81} +3.60643 q^{82} -3.05395 q^{83} -25.3659 q^{84} -4.66302 q^{85} -12.5149 q^{86} -10.0514 q^{87} -1.79164 q^{88} +7.36450 q^{89} +6.85138 q^{90} -10.2157 q^{91} -16.1676 q^{92} +12.0798 q^{93} -26.4006 q^{94} +4.34117 q^{95} -18.1012 q^{96} +12.4554 q^{97} -13.7175 q^{98} +3.12189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9} - 6 q^{10} + 27 q^{11} + 28 q^{12} + 21 q^{13} + 11 q^{14} - 5 q^{15} + 12 q^{16} + 30 q^{17} + 10 q^{18} + 20 q^{19} - 22 q^{20} - 14 q^{21} + 6 q^{22} + 16 q^{23} + 23 q^{24} + 27 q^{25} + 13 q^{26} + 17 q^{27} + 6 q^{28} - 2 q^{29} - 7 q^{30} - 6 q^{31} + 41 q^{32} + 5 q^{33} + 8 q^{34} - 10 q^{35} + 13 q^{36} + 20 q^{37} + 11 q^{38} - 10 q^{39} - 15 q^{40} + 38 q^{41} - 33 q^{42} + 29 q^{43} + 22 q^{44} - 24 q^{45} + 23 q^{46} + 17 q^{47} + 37 q^{48} + 21 q^{49} + 6 q^{50} + 13 q^{51} + 29 q^{52} + 4 q^{53} + q^{54} - 27 q^{55} + 28 q^{56} + 51 q^{57} - 6 q^{58} + 35 q^{59} - 28 q^{60} - 13 q^{61} + 28 q^{62} + 41 q^{63} - 5 q^{64} - 21 q^{65} + 7 q^{66} + 10 q^{67} + 65 q^{68} - 12 q^{69} - 11 q^{70} + 22 q^{71} - 12 q^{72} - 27 q^{73} - 5 q^{74} + 5 q^{75} + 13 q^{76} + 10 q^{77} - 9 q^{78} - 18 q^{79} - 12 q^{80} + 39 q^{81} + 20 q^{82} + 54 q^{83} - 50 q^{84} - 30 q^{85} + 3 q^{86} + 15 q^{87} + 15 q^{88} + 89 q^{89} - 10 q^{90} - 18 q^{91} + 57 q^{92} + 20 q^{93} - 29 q^{94} - 20 q^{95} + 105 q^{96} + 35 q^{97} + 10 q^{98} + 24 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.19462 −1.55183 −0.775917 0.630835i \(-0.782712\pi\)
−0.775917 + 0.630835i \(0.782712\pi\)
\(3\) −2.47425 −1.42851 −0.714253 0.699887i \(-0.753233\pi\)
−0.714253 + 0.699887i \(0.753233\pi\)
\(4\) 2.81638 1.40819
\(5\) −1.00000 −0.447214
\(6\) 5.43004 2.21680
\(7\) 3.64013 1.37584 0.687919 0.725787i \(-0.258524\pi\)
0.687919 + 0.725787i \(0.258524\pi\)
\(8\) −1.79164 −0.633442
\(9\) 3.12189 1.04063
\(10\) 2.19462 0.694001
\(11\) 1.00000 0.301511
\(12\) −6.96841 −2.01161
\(13\) −2.80642 −0.778362 −0.389181 0.921161i \(-0.627242\pi\)
−0.389181 + 0.921161i \(0.627242\pi\)
\(14\) −7.98871 −2.13507
\(15\) 2.47425 0.638847
\(16\) −1.70077 −0.425193
\(17\) 4.66302 1.13095 0.565475 0.824766i \(-0.308693\pi\)
0.565475 + 0.824766i \(0.308693\pi\)
\(18\) −6.85138 −1.61489
\(19\) −4.34117 −0.995933 −0.497966 0.867196i \(-0.665920\pi\)
−0.497966 + 0.867196i \(0.665920\pi\)
\(20\) −2.81638 −0.629761
\(21\) −9.00657 −1.96539
\(22\) −2.19462 −0.467896
\(23\) −5.74058 −1.19699 −0.598497 0.801125i \(-0.704235\pi\)
−0.598497 + 0.801125i \(0.704235\pi\)
\(24\) 4.43297 0.904876
\(25\) 1.00000 0.200000
\(26\) 6.15904 1.20789
\(27\) −0.301589 −0.0580409
\(28\) 10.2520 1.93744
\(29\) 4.06241 0.754371 0.377185 0.926138i \(-0.376892\pi\)
0.377185 + 0.926138i \(0.376892\pi\)
\(30\) −5.43004 −0.991385
\(31\) −4.88222 −0.876872 −0.438436 0.898762i \(-0.644467\pi\)
−0.438436 + 0.898762i \(0.644467\pi\)
\(32\) 7.31584 1.29327
\(33\) −2.47425 −0.430711
\(34\) −10.2336 −1.75505
\(35\) −3.64013 −0.615294
\(36\) 8.79243 1.46540
\(37\) 9.96750 1.63865 0.819323 0.573332i \(-0.194349\pi\)
0.819323 + 0.573332i \(0.194349\pi\)
\(38\) 9.52724 1.54552
\(39\) 6.94378 1.11189
\(40\) 1.79164 0.283284
\(41\) −1.64330 −0.256641 −0.128320 0.991733i \(-0.540959\pi\)
−0.128320 + 0.991733i \(0.540959\pi\)
\(42\) 19.7660 3.04997
\(43\) 5.70250 0.869624 0.434812 0.900521i \(-0.356815\pi\)
0.434812 + 0.900521i \(0.356815\pi\)
\(44\) 2.81638 0.424585
\(45\) −3.12189 −0.465384
\(46\) 12.5984 1.85754
\(47\) 12.0297 1.75471 0.877353 0.479845i \(-0.159307\pi\)
0.877353 + 0.479845i \(0.159307\pi\)
\(48\) 4.20812 0.607390
\(49\) 6.25052 0.892932
\(50\) −2.19462 −0.310367
\(51\) −11.5375 −1.61557
\(52\) −7.90395 −1.09608
\(53\) −1.44311 −0.198227 −0.0991134 0.995076i \(-0.531601\pi\)
−0.0991134 + 0.995076i \(0.531601\pi\)
\(54\) 0.661876 0.0900699
\(55\) −1.00000 −0.134840
\(56\) −6.52181 −0.871514
\(57\) 10.7411 1.42270
\(58\) −8.91546 −1.17066
\(59\) 3.08475 0.401600 0.200800 0.979632i \(-0.435646\pi\)
0.200800 + 0.979632i \(0.435646\pi\)
\(60\) 6.96841 0.899618
\(61\) −4.34581 −0.556424 −0.278212 0.960520i \(-0.589742\pi\)
−0.278212 + 0.960520i \(0.589742\pi\)
\(62\) 10.7146 1.36076
\(63\) 11.3641 1.43174
\(64\) −12.6540 −1.58175
\(65\) 2.80642 0.348094
\(66\) 5.43004 0.668392
\(67\) −11.9606 −1.46122 −0.730609 0.682796i \(-0.760764\pi\)
−0.730609 + 0.682796i \(0.760764\pi\)
\(68\) 13.1328 1.59259
\(69\) 14.2036 1.70991
\(70\) 7.98871 0.954834
\(71\) 3.21937 0.382069 0.191035 0.981583i \(-0.438816\pi\)
0.191035 + 0.981583i \(0.438816\pi\)
\(72\) −5.59332 −0.659179
\(73\) −1.00000 −0.117041
\(74\) −21.8749 −2.54291
\(75\) −2.47425 −0.285701
\(76\) −12.2264 −1.40246
\(77\) 3.64013 0.414831
\(78\) −15.2390 −1.72548
\(79\) −0.195611 −0.0220080 −0.0110040 0.999939i \(-0.503503\pi\)
−0.0110040 + 0.999939i \(0.503503\pi\)
\(80\) 1.70077 0.190152
\(81\) −8.61947 −0.957719
\(82\) 3.60643 0.398264
\(83\) −3.05395 −0.335214 −0.167607 0.985854i \(-0.553604\pi\)
−0.167607 + 0.985854i \(0.553604\pi\)
\(84\) −25.3659 −2.76765
\(85\) −4.66302 −0.505776
\(86\) −12.5149 −1.34951
\(87\) −10.0514 −1.07762
\(88\) −1.79164 −0.190990
\(89\) 7.36450 0.780636 0.390318 0.920680i \(-0.372365\pi\)
0.390318 + 0.920680i \(0.372365\pi\)
\(90\) 6.85138 0.722199
\(91\) −10.2157 −1.07090
\(92\) −16.1676 −1.68559
\(93\) 12.0798 1.25262
\(94\) −26.4006 −2.72301
\(95\) 4.34117 0.445395
\(96\) −18.1012 −1.84744
\(97\) 12.4554 1.26466 0.632329 0.774700i \(-0.282099\pi\)
0.632329 + 0.774700i \(0.282099\pi\)
\(98\) −13.7175 −1.38568
\(99\) 3.12189 0.313762
\(100\) 2.81638 0.281638
\(101\) −1.09557 −0.109013 −0.0545066 0.998513i \(-0.517359\pi\)
−0.0545066 + 0.998513i \(0.517359\pi\)
\(102\) 25.3204 2.50709
\(103\) −0.294190 −0.0289874 −0.0144937 0.999895i \(-0.504614\pi\)
−0.0144937 + 0.999895i \(0.504614\pi\)
\(104\) 5.02811 0.493047
\(105\) 9.00657 0.878951
\(106\) 3.16709 0.307615
\(107\) −9.35533 −0.904414 −0.452207 0.891913i \(-0.649363\pi\)
−0.452207 + 0.891913i \(0.649363\pi\)
\(108\) −0.849390 −0.0817326
\(109\) −9.39473 −0.899852 −0.449926 0.893066i \(-0.648550\pi\)
−0.449926 + 0.893066i \(0.648550\pi\)
\(110\) 2.19462 0.209249
\(111\) −24.6620 −2.34082
\(112\) −6.19102 −0.584996
\(113\) 5.74075 0.540044 0.270022 0.962854i \(-0.412969\pi\)
0.270022 + 0.962854i \(0.412969\pi\)
\(114\) −23.5727 −2.20779
\(115\) 5.74058 0.535312
\(116\) 11.4413 1.06230
\(117\) −8.76135 −0.809987
\(118\) −6.76987 −0.623217
\(119\) 16.9740 1.55600
\(120\) −4.43297 −0.404673
\(121\) 1.00000 0.0909091
\(122\) 9.53742 0.863477
\(123\) 4.06593 0.366613
\(124\) −13.7502 −1.23480
\(125\) −1.00000 −0.0894427
\(126\) −24.9399 −2.22182
\(127\) 14.7636 1.31006 0.655030 0.755603i \(-0.272656\pi\)
0.655030 + 0.755603i \(0.272656\pi\)
\(128\) 13.1391 1.16134
\(129\) −14.1094 −1.24226
\(130\) −6.15904 −0.540184
\(131\) −4.12655 −0.360539 −0.180269 0.983617i \(-0.557697\pi\)
−0.180269 + 0.983617i \(0.557697\pi\)
\(132\) −6.96841 −0.606522
\(133\) −15.8024 −1.37024
\(134\) 26.2490 2.26757
\(135\) 0.301589 0.0259567
\(136\) −8.35448 −0.716391
\(137\) 0.921093 0.0786943 0.0393472 0.999226i \(-0.487472\pi\)
0.0393472 + 0.999226i \(0.487472\pi\)
\(138\) −31.1716 −2.65350
\(139\) −6.81597 −0.578123 −0.289061 0.957311i \(-0.593343\pi\)
−0.289061 + 0.957311i \(0.593343\pi\)
\(140\) −10.2520 −0.866450
\(141\) −29.7643 −2.50661
\(142\) −7.06532 −0.592908
\(143\) −2.80642 −0.234685
\(144\) −5.30962 −0.442468
\(145\) −4.06241 −0.337365
\(146\) 2.19462 0.181628
\(147\) −15.4653 −1.27556
\(148\) 28.0722 2.30752
\(149\) −3.85111 −0.315495 −0.157748 0.987479i \(-0.550423\pi\)
−0.157748 + 0.987479i \(0.550423\pi\)
\(150\) 5.43004 0.443361
\(151\) −2.47794 −0.201652 −0.100826 0.994904i \(-0.532149\pi\)
−0.100826 + 0.994904i \(0.532149\pi\)
\(152\) 7.77783 0.630866
\(153\) 14.5575 1.17690
\(154\) −7.98871 −0.643749
\(155\) 4.88222 0.392149
\(156\) 19.5563 1.56576
\(157\) −17.7582 −1.41726 −0.708629 0.705581i \(-0.750686\pi\)
−0.708629 + 0.705581i \(0.750686\pi\)
\(158\) 0.429293 0.0341527
\(159\) 3.57061 0.283168
\(160\) −7.31584 −0.578368
\(161\) −20.8964 −1.64687
\(162\) 18.9165 1.48622
\(163\) −6.72566 −0.526795 −0.263397 0.964687i \(-0.584843\pi\)
−0.263397 + 0.964687i \(0.584843\pi\)
\(164\) −4.62816 −0.361399
\(165\) 2.47425 0.192620
\(166\) 6.70227 0.520197
\(167\) 11.4657 0.887239 0.443620 0.896215i \(-0.353694\pi\)
0.443620 + 0.896215i \(0.353694\pi\)
\(168\) 16.1366 1.24496
\(169\) −5.12399 −0.394153
\(170\) 10.2336 0.784880
\(171\) −13.5527 −1.03640
\(172\) 16.0604 1.22459
\(173\) 21.0607 1.60122 0.800608 0.599188i \(-0.204510\pi\)
0.800608 + 0.599188i \(0.204510\pi\)
\(174\) 22.0591 1.67229
\(175\) 3.64013 0.275168
\(176\) −1.70077 −0.128200
\(177\) −7.63243 −0.573688
\(178\) −16.1623 −1.21142
\(179\) −8.24694 −0.616406 −0.308203 0.951321i \(-0.599728\pi\)
−0.308203 + 0.951321i \(0.599728\pi\)
\(180\) −8.79243 −0.655349
\(181\) 20.1422 1.49716 0.748580 0.663044i \(-0.230736\pi\)
0.748580 + 0.663044i \(0.230736\pi\)
\(182\) 22.4197 1.66186
\(183\) 10.7526 0.794855
\(184\) 10.2851 0.758226
\(185\) −9.96750 −0.732825
\(186\) −26.5106 −1.94385
\(187\) 4.66302 0.340994
\(188\) 33.8801 2.47096
\(189\) −1.09782 −0.0798549
\(190\) −9.52724 −0.691179
\(191\) 10.0721 0.728792 0.364396 0.931244i \(-0.381275\pi\)
0.364396 + 0.931244i \(0.381275\pi\)
\(192\) 31.3091 2.25954
\(193\) −18.6235 −1.34055 −0.670275 0.742113i \(-0.733824\pi\)
−0.670275 + 0.742113i \(0.733824\pi\)
\(194\) −27.3350 −1.96254
\(195\) −6.94378 −0.497254
\(196\) 17.6038 1.25742
\(197\) −4.27797 −0.304793 −0.152396 0.988319i \(-0.548699\pi\)
−0.152396 + 0.988319i \(0.548699\pi\)
\(198\) −6.85138 −0.486906
\(199\) 6.41209 0.454541 0.227270 0.973832i \(-0.427020\pi\)
0.227270 + 0.973832i \(0.427020\pi\)
\(200\) −1.79164 −0.126688
\(201\) 29.5934 2.08736
\(202\) 2.40436 0.169170
\(203\) 14.7877 1.03789
\(204\) −32.4939 −2.27503
\(205\) 1.64330 0.114773
\(206\) 0.645636 0.0449836
\(207\) −17.9215 −1.24563
\(208\) 4.77308 0.330954
\(209\) −4.34117 −0.300285
\(210\) −19.7660 −1.36399
\(211\) −13.7589 −0.947201 −0.473600 0.880740i \(-0.657046\pi\)
−0.473600 + 0.880740i \(0.657046\pi\)
\(212\) −4.06435 −0.279141
\(213\) −7.96552 −0.545788
\(214\) 20.5314 1.40350
\(215\) −5.70250 −0.388908
\(216\) 0.540341 0.0367655
\(217\) −17.7719 −1.20643
\(218\) 20.6179 1.39642
\(219\) 2.47425 0.167194
\(220\) −2.81638 −0.189880
\(221\) −13.0864 −0.880288
\(222\) 54.1239 3.63256
\(223\) 1.61027 0.107831 0.0539157 0.998545i \(-0.482830\pi\)
0.0539157 + 0.998545i \(0.482830\pi\)
\(224\) 26.6306 1.77933
\(225\) 3.12189 0.208126
\(226\) −12.5988 −0.838059
\(227\) 10.6625 0.707697 0.353848 0.935303i \(-0.384873\pi\)
0.353848 + 0.935303i \(0.384873\pi\)
\(228\) 30.2511 2.00343
\(229\) −14.1419 −0.934523 −0.467262 0.884119i \(-0.654759\pi\)
−0.467262 + 0.884119i \(0.654759\pi\)
\(230\) −12.5984 −0.830715
\(231\) −9.00657 −0.592589
\(232\) −7.27839 −0.477850
\(233\) −10.0006 −0.655160 −0.327580 0.944824i \(-0.606233\pi\)
−0.327580 + 0.944824i \(0.606233\pi\)
\(234\) 19.2279 1.25697
\(235\) −12.0297 −0.784729
\(236\) 8.68782 0.565529
\(237\) 0.483990 0.0314385
\(238\) −37.2516 −2.41466
\(239\) −15.9358 −1.03080 −0.515401 0.856949i \(-0.672357\pi\)
−0.515401 + 0.856949i \(0.672357\pi\)
\(240\) −4.20812 −0.271633
\(241\) −9.68288 −0.623729 −0.311865 0.950127i \(-0.600954\pi\)
−0.311865 + 0.950127i \(0.600954\pi\)
\(242\) −2.19462 −0.141076
\(243\) 22.2314 1.42615
\(244\) −12.2394 −0.783550
\(245\) −6.25052 −0.399331
\(246\) −8.92320 −0.568922
\(247\) 12.1832 0.775196
\(248\) 8.74719 0.555447
\(249\) 7.55621 0.478856
\(250\) 2.19462 0.138800
\(251\) 20.1970 1.27483 0.637413 0.770523i \(-0.280005\pi\)
0.637413 + 0.770523i \(0.280005\pi\)
\(252\) 32.0055 2.01616
\(253\) −5.74058 −0.360907
\(254\) −32.4006 −2.03300
\(255\) 11.5375 0.722504
\(256\) −3.52736 −0.220460
\(257\) 17.1357 1.06890 0.534448 0.845201i \(-0.320519\pi\)
0.534448 + 0.845201i \(0.320519\pi\)
\(258\) 30.9648 1.92779
\(259\) 36.2829 2.25451
\(260\) 7.90395 0.490182
\(261\) 12.6824 0.785021
\(262\) 9.05624 0.559496
\(263\) 27.0099 1.66550 0.832752 0.553647i \(-0.186764\pi\)
0.832752 + 0.553647i \(0.186764\pi\)
\(264\) 4.43297 0.272830
\(265\) 1.44311 0.0886497
\(266\) 34.6804 2.12639
\(267\) −18.2216 −1.11514
\(268\) −33.6855 −2.05767
\(269\) 9.73801 0.593737 0.296868 0.954918i \(-0.404058\pi\)
0.296868 + 0.954918i \(0.404058\pi\)
\(270\) −0.661876 −0.0402805
\(271\) 6.01256 0.365237 0.182619 0.983184i \(-0.441543\pi\)
0.182619 + 0.983184i \(0.441543\pi\)
\(272\) −7.93073 −0.480871
\(273\) 25.2762 1.52979
\(274\) −2.02145 −0.122121
\(275\) 1.00000 0.0603023
\(276\) 40.0027 2.40788
\(277\) −15.5173 −0.932344 −0.466172 0.884694i \(-0.654367\pi\)
−0.466172 + 0.884694i \(0.654367\pi\)
\(278\) 14.9585 0.897151
\(279\) −15.2417 −0.912499
\(280\) 6.52181 0.389753
\(281\) 20.5454 1.22563 0.612817 0.790225i \(-0.290036\pi\)
0.612817 + 0.790225i \(0.290036\pi\)
\(282\) 65.3216 3.88984
\(283\) −7.51200 −0.446542 −0.223271 0.974756i \(-0.571674\pi\)
−0.223271 + 0.974756i \(0.571674\pi\)
\(284\) 9.06697 0.538026
\(285\) −10.7411 −0.636249
\(286\) 6.15904 0.364192
\(287\) −5.98183 −0.353096
\(288\) 22.8393 1.34582
\(289\) 4.74380 0.279047
\(290\) 8.91546 0.523534
\(291\) −30.8178 −1.80657
\(292\) −2.81638 −0.164816
\(293\) 0.356672 0.0208370 0.0104185 0.999946i \(-0.496684\pi\)
0.0104185 + 0.999946i \(0.496684\pi\)
\(294\) 33.9406 1.97946
\(295\) −3.08475 −0.179601
\(296\) −17.8582 −1.03799
\(297\) −0.301589 −0.0175000
\(298\) 8.45174 0.489596
\(299\) 16.1105 0.931694
\(300\) −6.96841 −0.402321
\(301\) 20.7578 1.19646
\(302\) 5.43815 0.312930
\(303\) 2.71071 0.155726
\(304\) 7.38334 0.423463
\(305\) 4.34581 0.248840
\(306\) −31.9482 −1.82635
\(307\) −8.18397 −0.467084 −0.233542 0.972347i \(-0.575032\pi\)
−0.233542 + 0.972347i \(0.575032\pi\)
\(308\) 10.2520 0.584160
\(309\) 0.727898 0.0414086
\(310\) −10.7146 −0.608550
\(311\) −0.203576 −0.0115438 −0.00577188 0.999983i \(-0.501837\pi\)
−0.00577188 + 0.999983i \(0.501837\pi\)
\(312\) −12.4408 −0.704320
\(313\) −10.2880 −0.581514 −0.290757 0.956797i \(-0.593907\pi\)
−0.290757 + 0.956797i \(0.593907\pi\)
\(314\) 38.9726 2.19935
\(315\) −11.3641 −0.640293
\(316\) −0.550915 −0.0309914
\(317\) 22.4822 1.26273 0.631363 0.775487i \(-0.282496\pi\)
0.631363 + 0.775487i \(0.282496\pi\)
\(318\) −7.83616 −0.439430
\(319\) 4.06241 0.227451
\(320\) 12.6540 0.707379
\(321\) 23.1474 1.29196
\(322\) 45.8598 2.55567
\(323\) −20.2430 −1.12635
\(324\) −24.2757 −1.34865
\(325\) −2.80642 −0.155672
\(326\) 14.7603 0.817498
\(327\) 23.2449 1.28544
\(328\) 2.94421 0.162567
\(329\) 43.7895 2.41419
\(330\) −5.43004 −0.298914
\(331\) −7.78673 −0.427997 −0.213999 0.976834i \(-0.568649\pi\)
−0.213999 + 0.976834i \(0.568649\pi\)
\(332\) −8.60107 −0.472045
\(333\) 31.1174 1.70523
\(334\) −25.1628 −1.37685
\(335\) 11.9606 0.653476
\(336\) 15.3181 0.835671
\(337\) 17.8175 0.970580 0.485290 0.874353i \(-0.338714\pi\)
0.485290 + 0.874353i \(0.338714\pi\)
\(338\) 11.2452 0.611660
\(339\) −14.2040 −0.771457
\(340\) −13.1328 −0.712228
\(341\) −4.88222 −0.264387
\(342\) 29.7430 1.60832
\(343\) −2.72820 −0.147309
\(344\) −10.2169 −0.550856
\(345\) −14.2036 −0.764696
\(346\) −46.2204 −2.48482
\(347\) −17.3513 −0.931465 −0.465732 0.884926i \(-0.654209\pi\)
−0.465732 + 0.884926i \(0.654209\pi\)
\(348\) −28.3085 −1.51750
\(349\) −2.02662 −0.108483 −0.0542413 0.998528i \(-0.517274\pi\)
−0.0542413 + 0.998528i \(0.517274\pi\)
\(350\) −7.98871 −0.427015
\(351\) 0.846387 0.0451768
\(352\) 7.31584 0.389936
\(353\) −9.44223 −0.502559 −0.251280 0.967915i \(-0.580851\pi\)
−0.251280 + 0.967915i \(0.580851\pi\)
\(354\) 16.7503 0.890269
\(355\) −3.21937 −0.170867
\(356\) 20.7412 1.09928
\(357\) −41.9978 −2.22276
\(358\) 18.0989 0.956559
\(359\) −13.5248 −0.713813 −0.356907 0.934140i \(-0.616169\pi\)
−0.356907 + 0.934140i \(0.616169\pi\)
\(360\) 5.59332 0.294794
\(361\) −0.154232 −0.00811746
\(362\) −44.2047 −2.32334
\(363\) −2.47425 −0.129864
\(364\) −28.7714 −1.50803
\(365\) 1.00000 0.0523424
\(366\) −23.5979 −1.23348
\(367\) −18.8315 −0.982999 −0.491499 0.870878i \(-0.663551\pi\)
−0.491499 + 0.870878i \(0.663551\pi\)
\(368\) 9.76341 0.508953
\(369\) −5.13021 −0.267068
\(370\) 21.8749 1.13722
\(371\) −5.25311 −0.272728
\(372\) 34.0213 1.76392
\(373\) 32.9971 1.70852 0.854262 0.519842i \(-0.174009\pi\)
0.854262 + 0.519842i \(0.174009\pi\)
\(374\) −10.2336 −0.529166
\(375\) 2.47425 0.127769
\(376\) −21.5529 −1.11150
\(377\) −11.4008 −0.587173
\(378\) 2.40931 0.123922
\(379\) 27.7488 1.42536 0.712680 0.701489i \(-0.247481\pi\)
0.712680 + 0.701489i \(0.247481\pi\)
\(380\) 12.2264 0.627200
\(381\) −36.5289 −1.87143
\(382\) −22.1045 −1.13096
\(383\) −4.45851 −0.227819 −0.113910 0.993491i \(-0.536337\pi\)
−0.113910 + 0.993491i \(0.536337\pi\)
\(384\) −32.5093 −1.65898
\(385\) −3.64013 −0.185518
\(386\) 40.8716 2.08031
\(387\) 17.8026 0.904957
\(388\) 35.0792 1.78088
\(389\) −29.5097 −1.49620 −0.748101 0.663584i \(-0.769034\pi\)
−0.748101 + 0.663584i \(0.769034\pi\)
\(390\) 15.2390 0.771656
\(391\) −26.7685 −1.35374
\(392\) −11.1987 −0.565620
\(393\) 10.2101 0.515032
\(394\) 9.38854 0.472988
\(395\) 0.195611 0.00984226
\(396\) 8.79243 0.441836
\(397\) 1.85205 0.0929517 0.0464759 0.998919i \(-0.485201\pi\)
0.0464759 + 0.998919i \(0.485201\pi\)
\(398\) −14.0721 −0.705372
\(399\) 39.0991 1.95740
\(400\) −1.70077 −0.0850385
\(401\) 23.0963 1.15338 0.576688 0.816965i \(-0.304345\pi\)
0.576688 + 0.816965i \(0.304345\pi\)
\(402\) −64.9464 −3.23923
\(403\) 13.7016 0.682523
\(404\) −3.08554 −0.153511
\(405\) 8.61947 0.428305
\(406\) −32.4534 −1.61064
\(407\) 9.96750 0.494070
\(408\) 20.6710 1.02337
\(409\) 4.35359 0.215271 0.107635 0.994190i \(-0.465672\pi\)
0.107635 + 0.994190i \(0.465672\pi\)
\(410\) −3.60643 −0.178109
\(411\) −2.27901 −0.112415
\(412\) −0.828550 −0.0408197
\(413\) 11.2289 0.552537
\(414\) 39.3309 1.93301
\(415\) 3.05395 0.149912
\(416\) −20.5313 −1.00663
\(417\) 16.8644 0.825852
\(418\) 9.52724 0.465993
\(419\) −8.52259 −0.416356 −0.208178 0.978091i \(-0.566753\pi\)
−0.208178 + 0.978091i \(0.566753\pi\)
\(420\) 25.3659 1.23773
\(421\) 27.5755 1.34395 0.671974 0.740575i \(-0.265447\pi\)
0.671974 + 0.740575i \(0.265447\pi\)
\(422\) 30.1956 1.46990
\(423\) 37.5553 1.82600
\(424\) 2.58554 0.125565
\(425\) 4.66302 0.226190
\(426\) 17.4813 0.846973
\(427\) −15.8193 −0.765549
\(428\) −26.3481 −1.27359
\(429\) 6.94378 0.335249
\(430\) 12.5149 0.603520
\(431\) −4.24124 −0.204293 −0.102147 0.994769i \(-0.532571\pi\)
−0.102147 + 0.994769i \(0.532571\pi\)
\(432\) 0.512934 0.0246786
\(433\) 20.8649 1.00270 0.501351 0.865244i \(-0.332836\pi\)
0.501351 + 0.865244i \(0.332836\pi\)
\(434\) 39.0026 1.87219
\(435\) 10.0514 0.481928
\(436\) −26.4591 −1.26716
\(437\) 24.9208 1.19213
\(438\) −5.43004 −0.259457
\(439\) 40.6450 1.93988 0.969940 0.243343i \(-0.0782441\pi\)
0.969940 + 0.243343i \(0.0782441\pi\)
\(440\) 1.79164 0.0854133
\(441\) 19.5134 0.929212
\(442\) 28.7198 1.36606
\(443\) 17.3800 0.825750 0.412875 0.910788i \(-0.364525\pi\)
0.412875 + 0.910788i \(0.364525\pi\)
\(444\) −69.4576 −3.29631
\(445\) −7.36450 −0.349111
\(446\) −3.53393 −0.167337
\(447\) 9.52859 0.450687
\(448\) −46.0621 −2.17623
\(449\) −4.04946 −0.191106 −0.0955530 0.995424i \(-0.530462\pi\)
−0.0955530 + 0.995424i \(0.530462\pi\)
\(450\) −6.85138 −0.322977
\(451\) −1.64330 −0.0773801
\(452\) 16.1681 0.760485
\(453\) 6.13103 0.288061
\(454\) −23.4002 −1.09823
\(455\) 10.2157 0.478921
\(456\) −19.2443 −0.901195
\(457\) 1.55809 0.0728842 0.0364421 0.999336i \(-0.488398\pi\)
0.0364421 + 0.999336i \(0.488398\pi\)
\(458\) 31.0362 1.45023
\(459\) −1.40632 −0.0656413
\(460\) 16.1676 0.753820
\(461\) 36.6604 1.70745 0.853723 0.520728i \(-0.174339\pi\)
0.853723 + 0.520728i \(0.174339\pi\)
\(462\) 19.7660 0.919599
\(463\) −33.4585 −1.55495 −0.777474 0.628915i \(-0.783500\pi\)
−0.777474 + 0.628915i \(0.783500\pi\)
\(464\) −6.90923 −0.320753
\(465\) −12.0798 −0.560187
\(466\) 21.9475 1.01670
\(467\) −24.1951 −1.11962 −0.559809 0.828622i \(-0.689125\pi\)
−0.559809 + 0.828622i \(0.689125\pi\)
\(468\) −24.6753 −1.14061
\(469\) −43.5380 −2.01040
\(470\) 26.4006 1.21777
\(471\) 43.9382 2.02456
\(472\) −5.52677 −0.254390
\(473\) 5.70250 0.262201
\(474\) −1.06218 −0.0487874
\(475\) −4.34117 −0.199187
\(476\) 47.8052 2.19115
\(477\) −4.50524 −0.206281
\(478\) 34.9731 1.59963
\(479\) 23.6600 1.08105 0.540527 0.841326i \(-0.318225\pi\)
0.540527 + 0.841326i \(0.318225\pi\)
\(480\) 18.1012 0.826202
\(481\) −27.9730 −1.27546
\(482\) 21.2503 0.967924
\(483\) 51.7029 2.35256
\(484\) 2.81638 0.128017
\(485\) −12.4554 −0.565572
\(486\) −48.7897 −2.21315
\(487\) 18.7526 0.849763 0.424881 0.905249i \(-0.360316\pi\)
0.424881 + 0.905249i \(0.360316\pi\)
\(488\) 7.78614 0.352462
\(489\) 16.6409 0.752530
\(490\) 13.7175 0.619696
\(491\) −22.0103 −0.993311 −0.496656 0.867948i \(-0.665439\pi\)
−0.496656 + 0.867948i \(0.665439\pi\)
\(492\) 11.4512 0.516260
\(493\) 18.9431 0.853155
\(494\) −26.7375 −1.20298
\(495\) −3.12189 −0.140319
\(496\) 8.30353 0.372839
\(497\) 11.7189 0.525666
\(498\) −16.5831 −0.743104
\(499\) −31.3218 −1.40216 −0.701078 0.713085i \(-0.747297\pi\)
−0.701078 + 0.713085i \(0.747297\pi\)
\(500\) −2.81638 −0.125952
\(501\) −28.3689 −1.26743
\(502\) −44.3249 −1.97832
\(503\) 29.9817 1.33682 0.668409 0.743794i \(-0.266975\pi\)
0.668409 + 0.743794i \(0.266975\pi\)
\(504\) −20.3604 −0.906924
\(505\) 1.09557 0.0487522
\(506\) 12.5984 0.560068
\(507\) 12.6780 0.563050
\(508\) 41.5800 1.84481
\(509\) 37.8795 1.67898 0.839491 0.543374i \(-0.182854\pi\)
0.839491 + 0.543374i \(0.182854\pi\)
\(510\) −25.3204 −1.12121
\(511\) −3.64013 −0.161030
\(512\) −18.5369 −0.819224
\(513\) 1.30925 0.0578049
\(514\) −37.6065 −1.65875
\(515\) 0.294190 0.0129635
\(516\) −39.7374 −1.74934
\(517\) 12.0297 0.529064
\(518\) −79.6275 −3.49863
\(519\) −52.1094 −2.28735
\(520\) −5.02811 −0.220497
\(521\) 23.3971 1.02505 0.512524 0.858673i \(-0.328711\pi\)
0.512524 + 0.858673i \(0.328711\pi\)
\(522\) −27.8331 −1.21822
\(523\) −16.3607 −0.715404 −0.357702 0.933836i \(-0.616440\pi\)
−0.357702 + 0.933836i \(0.616440\pi\)
\(524\) −11.6219 −0.507707
\(525\) −9.00657 −0.393079
\(526\) −59.2767 −2.58459
\(527\) −22.7659 −0.991698
\(528\) 4.20812 0.183135
\(529\) 9.95424 0.432793
\(530\) −3.16709 −0.137570
\(531\) 9.63025 0.417917
\(532\) −44.5056 −1.92956
\(533\) 4.61180 0.199759
\(534\) 39.9895 1.73052
\(535\) 9.35533 0.404466
\(536\) 21.4291 0.925596
\(537\) 20.4050 0.880539
\(538\) −21.3713 −0.921381
\(539\) 6.25052 0.269229
\(540\) 0.849390 0.0365519
\(541\) 6.15317 0.264545 0.132273 0.991213i \(-0.457773\pi\)
0.132273 + 0.991213i \(0.457773\pi\)
\(542\) −13.1953 −0.566788
\(543\) −49.8368 −2.13870
\(544\) 34.1139 1.46262
\(545\) 9.39473 0.402426
\(546\) −55.4719 −2.37398
\(547\) 3.83976 0.164176 0.0820881 0.996625i \(-0.473841\pi\)
0.0820881 + 0.996625i \(0.473841\pi\)
\(548\) 2.59415 0.110816
\(549\) −13.5671 −0.579031
\(550\) −2.19462 −0.0935791
\(551\) −17.6356 −0.751302
\(552\) −25.4478 −1.08313
\(553\) −0.712049 −0.0302794
\(554\) 34.0546 1.44684
\(555\) 24.6620 1.04685
\(556\) −19.1963 −0.814106
\(557\) −1.40081 −0.0593542 −0.0296771 0.999560i \(-0.509448\pi\)
−0.0296771 + 0.999560i \(0.509448\pi\)
\(558\) 33.4499 1.41605
\(559\) −16.0036 −0.676882
\(560\) 6.19102 0.261618
\(561\) −11.5375 −0.487112
\(562\) −45.0894 −1.90198
\(563\) 24.9166 1.05011 0.525056 0.851068i \(-0.324045\pi\)
0.525056 + 0.851068i \(0.324045\pi\)
\(564\) −83.8276 −3.52978
\(565\) −5.74075 −0.241515
\(566\) 16.4860 0.692960
\(567\) −31.3760 −1.31767
\(568\) −5.76797 −0.242019
\(569\) −21.3975 −0.897031 −0.448516 0.893775i \(-0.648047\pi\)
−0.448516 + 0.893775i \(0.648047\pi\)
\(570\) 23.5727 0.987353
\(571\) 30.2271 1.26496 0.632482 0.774575i \(-0.282036\pi\)
0.632482 + 0.774575i \(0.282036\pi\)
\(572\) −7.90395 −0.330481
\(573\) −24.9209 −1.04108
\(574\) 13.1279 0.547947
\(575\) −5.74058 −0.239399
\(576\) −39.5044 −1.64602
\(577\) 29.9408 1.24645 0.623226 0.782042i \(-0.285822\pi\)
0.623226 + 0.782042i \(0.285822\pi\)
\(578\) −10.4109 −0.433034
\(579\) 46.0792 1.91498
\(580\) −11.4413 −0.475073
\(581\) −11.1167 −0.461200
\(582\) 67.6335 2.80350
\(583\) −1.44311 −0.0597676
\(584\) 1.79164 0.0741387
\(585\) 8.76135 0.362237
\(586\) −0.782762 −0.0323356
\(587\) −2.46650 −0.101803 −0.0509017 0.998704i \(-0.516210\pi\)
−0.0509017 + 0.998704i \(0.516210\pi\)
\(588\) −43.5562 −1.79623
\(589\) 21.1945 0.873305
\(590\) 6.76987 0.278711
\(591\) 10.5847 0.435398
\(592\) −16.9524 −0.696740
\(593\) 20.8216 0.855041 0.427520 0.904006i \(-0.359387\pi\)
0.427520 + 0.904006i \(0.359387\pi\)
\(594\) 0.661876 0.0271571
\(595\) −16.9740 −0.695866
\(596\) −10.8462 −0.444277
\(597\) −15.8651 −0.649315
\(598\) −35.3565 −1.44583
\(599\) −28.8207 −1.17758 −0.588792 0.808285i \(-0.700396\pi\)
−0.588792 + 0.808285i \(0.700396\pi\)
\(600\) 4.43297 0.180975
\(601\) 3.36972 0.137454 0.0687269 0.997636i \(-0.478106\pi\)
0.0687269 + 0.997636i \(0.478106\pi\)
\(602\) −45.5557 −1.85671
\(603\) −37.3396 −1.52059
\(604\) −6.97881 −0.283964
\(605\) −1.00000 −0.0406558
\(606\) −5.94899 −0.241661
\(607\) 10.7172 0.434998 0.217499 0.976061i \(-0.430210\pi\)
0.217499 + 0.976061i \(0.430210\pi\)
\(608\) −31.7593 −1.28801
\(609\) −36.5884 −1.48264
\(610\) −9.53742 −0.386159
\(611\) −33.7603 −1.36580
\(612\) 40.9993 1.65730
\(613\) −26.2977 −1.06215 −0.531077 0.847324i \(-0.678212\pi\)
−0.531077 + 0.847324i \(0.678212\pi\)
\(614\) 17.9608 0.724837
\(615\) −4.06593 −0.163954
\(616\) −6.52181 −0.262771
\(617\) 10.4666 0.421368 0.210684 0.977554i \(-0.432431\pi\)
0.210684 + 0.977554i \(0.432431\pi\)
\(618\) −1.59746 −0.0642594
\(619\) 20.3956 0.819770 0.409885 0.912137i \(-0.365569\pi\)
0.409885 + 0.912137i \(0.365569\pi\)
\(620\) 13.7502 0.552220
\(621\) 1.73130 0.0694746
\(622\) 0.446774 0.0179140
\(623\) 26.8077 1.07403
\(624\) −11.8098 −0.472769
\(625\) 1.00000 0.0400000
\(626\) 22.5784 0.902414
\(627\) 10.7411 0.428959
\(628\) −50.0138 −1.99577
\(629\) 46.4787 1.85323
\(630\) 24.9399 0.993629
\(631\) 25.1243 1.00018 0.500090 0.865973i \(-0.333300\pi\)
0.500090 + 0.865973i \(0.333300\pi\)
\(632\) 0.350465 0.0139408
\(633\) 34.0429 1.35308
\(634\) −49.3400 −1.95954
\(635\) −14.7636 −0.585877
\(636\) 10.0562 0.398754
\(637\) −17.5416 −0.695024
\(638\) −8.91546 −0.352967
\(639\) 10.0505 0.397593
\(640\) −13.1391 −0.519367
\(641\) −35.2324 −1.39160 −0.695799 0.718237i \(-0.744949\pi\)
−0.695799 + 0.718237i \(0.744949\pi\)
\(642\) −50.7998 −2.00491
\(643\) −26.6067 −1.04927 −0.524634 0.851328i \(-0.675798\pi\)
−0.524634 + 0.851328i \(0.675798\pi\)
\(644\) −58.8523 −2.31910
\(645\) 14.1094 0.555557
\(646\) 44.4258 1.74791
\(647\) 35.9696 1.41411 0.707055 0.707158i \(-0.250023\pi\)
0.707055 + 0.707158i \(0.250023\pi\)
\(648\) 15.4430 0.606659
\(649\) 3.08475 0.121087
\(650\) 6.15904 0.241578
\(651\) 43.9720 1.72340
\(652\) −18.9420 −0.741826
\(653\) 43.3096 1.69484 0.847418 0.530926i \(-0.178156\pi\)
0.847418 + 0.530926i \(0.178156\pi\)
\(654\) −51.0137 −1.99480
\(655\) 4.12655 0.161238
\(656\) 2.79488 0.109122
\(657\) −3.12189 −0.121797
\(658\) −96.1015 −3.74643
\(659\) 25.4710 0.992209 0.496105 0.868263i \(-0.334763\pi\)
0.496105 + 0.868263i \(0.334763\pi\)
\(660\) 6.96841 0.271245
\(661\) 45.1553 1.75634 0.878169 0.478350i \(-0.158765\pi\)
0.878169 + 0.478350i \(0.158765\pi\)
\(662\) 17.0889 0.664181
\(663\) 32.3790 1.25750
\(664\) 5.47158 0.212339
\(665\) 15.8024 0.612791
\(666\) −68.2911 −2.64623
\(667\) −23.3206 −0.902977
\(668\) 32.2916 1.24940
\(669\) −3.98420 −0.154038
\(670\) −26.2490 −1.01409
\(671\) −4.34581 −0.167768
\(672\) −65.8906 −2.54179
\(673\) 42.2888 1.63011 0.815057 0.579381i \(-0.196706\pi\)
0.815057 + 0.579381i \(0.196706\pi\)
\(674\) −39.1027 −1.50618
\(675\) −0.301589 −0.0116082
\(676\) −14.4311 −0.555042
\(677\) −43.8186 −1.68409 −0.842043 0.539411i \(-0.818647\pi\)
−0.842043 + 0.539411i \(0.818647\pi\)
\(678\) 31.1725 1.19717
\(679\) 45.3393 1.73996
\(680\) 8.35448 0.320380
\(681\) −26.3817 −1.01095
\(682\) 10.7146 0.410284
\(683\) 22.4666 0.859662 0.429831 0.902909i \(-0.358573\pi\)
0.429831 + 0.902909i \(0.358573\pi\)
\(684\) −38.1694 −1.45944
\(685\) −0.921093 −0.0351932
\(686\) 5.98737 0.228599
\(687\) 34.9905 1.33497
\(688\) −9.69865 −0.369758
\(689\) 4.04998 0.154292
\(690\) 31.1716 1.18668
\(691\) 6.92332 0.263376 0.131688 0.991291i \(-0.457960\pi\)
0.131688 + 0.991291i \(0.457960\pi\)
\(692\) 59.3149 2.25482
\(693\) 11.3641 0.431686
\(694\) 38.0795 1.44548
\(695\) 6.81597 0.258544
\(696\) 18.0085 0.682611
\(697\) −7.66276 −0.290248
\(698\) 4.44768 0.168347
\(699\) 24.7439 0.935900
\(700\) 10.2520 0.387488
\(701\) 18.3795 0.694183 0.347092 0.937831i \(-0.387169\pi\)
0.347092 + 0.937831i \(0.387169\pi\)
\(702\) −1.85750 −0.0701069
\(703\) −43.2706 −1.63198
\(704\) −12.6540 −0.476915
\(705\) 29.7643 1.12099
\(706\) 20.7222 0.779889
\(707\) −3.98801 −0.149985
\(708\) −21.4958 −0.807862
\(709\) 3.37053 0.126583 0.0632915 0.997995i \(-0.479840\pi\)
0.0632915 + 0.997995i \(0.479840\pi\)
\(710\) 7.06532 0.265157
\(711\) −0.610676 −0.0229022
\(712\) −13.1946 −0.494487
\(713\) 28.0267 1.04961
\(714\) 92.1695 3.44936
\(715\) 2.80642 0.104954
\(716\) −23.2265 −0.868016
\(717\) 39.4291 1.47251
\(718\) 29.6819 1.10772
\(719\) −27.3627 −1.02045 −0.510227 0.860039i \(-0.670439\pi\)
−0.510227 + 0.860039i \(0.670439\pi\)
\(720\) 5.30962 0.197878
\(721\) −1.07089 −0.0398819
\(722\) 0.338481 0.0125970
\(723\) 23.9578 0.891001
\(724\) 56.7282 2.10829
\(725\) 4.06241 0.150874
\(726\) 5.43004 0.201528
\(727\) −18.6057 −0.690048 −0.345024 0.938594i \(-0.612129\pi\)
−0.345024 + 0.938594i \(0.612129\pi\)
\(728\) 18.3030 0.678353
\(729\) −29.1477 −1.07954
\(730\) −2.19462 −0.0812267
\(731\) 26.5909 0.983501
\(732\) 30.2834 1.11931
\(733\) 23.0238 0.850405 0.425203 0.905098i \(-0.360203\pi\)
0.425203 + 0.905098i \(0.360203\pi\)
\(734\) 41.3282 1.52545
\(735\) 15.4653 0.570447
\(736\) −41.9972 −1.54804
\(737\) −11.9606 −0.440574
\(738\) 11.2589 0.414445
\(739\) 44.1029 1.62235 0.811175 0.584804i \(-0.198828\pi\)
0.811175 + 0.584804i \(0.198828\pi\)
\(740\) −28.0722 −1.03196
\(741\) −30.1441 −1.10737
\(742\) 11.5286 0.423229
\(743\) −21.4811 −0.788067 −0.394033 0.919096i \(-0.628921\pi\)
−0.394033 + 0.919096i \(0.628921\pi\)
\(744\) −21.6427 −0.793460
\(745\) 3.85111 0.141094
\(746\) −72.4162 −2.65135
\(747\) −9.53409 −0.348834
\(748\) 13.1328 0.480184
\(749\) −34.0546 −1.24433
\(750\) −5.43004 −0.198277
\(751\) −32.4913 −1.18563 −0.592813 0.805340i \(-0.701983\pi\)
−0.592813 + 0.805340i \(0.701983\pi\)
\(752\) −20.4597 −0.746088
\(753\) −49.9724 −1.82110
\(754\) 25.0206 0.911195
\(755\) 2.47794 0.0901814
\(756\) −3.09189 −0.112451
\(757\) −10.0855 −0.366563 −0.183282 0.983060i \(-0.558672\pi\)
−0.183282 + 0.983060i \(0.558672\pi\)
\(758\) −60.8982 −2.21192
\(759\) 14.2036 0.515558
\(760\) −7.77783 −0.282132
\(761\) 2.99779 0.108670 0.0543349 0.998523i \(-0.482696\pi\)
0.0543349 + 0.998523i \(0.482696\pi\)
\(762\) 80.1671 2.90415
\(763\) −34.1980 −1.23805
\(764\) 28.3669 1.02628
\(765\) −14.5575 −0.526326
\(766\) 9.78475 0.353537
\(767\) −8.65711 −0.312590
\(768\) 8.72754 0.314928
\(769\) 28.2696 1.01943 0.509714 0.860344i \(-0.329751\pi\)
0.509714 + 0.860344i \(0.329751\pi\)
\(770\) 7.98871 0.287893
\(771\) −42.3980 −1.52693
\(772\) −52.4509 −1.88775
\(773\) −44.3826 −1.59633 −0.798166 0.602437i \(-0.794196\pi\)
−0.798166 + 0.602437i \(0.794196\pi\)
\(774\) −39.0700 −1.40434
\(775\) −4.88222 −0.175374
\(776\) −22.3157 −0.801087
\(777\) −89.7729 −3.22059
\(778\) 64.7628 2.32186
\(779\) 7.13386 0.255597
\(780\) −19.5563 −0.700228
\(781\) 3.21937 0.115198
\(782\) 58.7467 2.10078
\(783\) −1.22518 −0.0437844
\(784\) −10.6307 −0.379668
\(785\) 17.7582 0.633817
\(786\) −22.4074 −0.799244
\(787\) 50.1514 1.78770 0.893852 0.448362i \(-0.147992\pi\)
0.893852 + 0.448362i \(0.147992\pi\)
\(788\) −12.0484 −0.429206
\(789\) −66.8292 −2.37918
\(790\) −0.429293 −0.0152736
\(791\) 20.8971 0.743014
\(792\) −5.59332 −0.198750
\(793\) 12.1962 0.433099
\(794\) −4.06456 −0.144246
\(795\) −3.57061 −0.126637
\(796\) 18.0589 0.640080
\(797\) −20.1489 −0.713711 −0.356855 0.934160i \(-0.616151\pi\)
−0.356855 + 0.934160i \(0.616151\pi\)
\(798\) −85.8077 −3.03756
\(799\) 56.0946 1.98448
\(800\) 7.31584 0.258654
\(801\) 22.9912 0.812353
\(802\) −50.6878 −1.78985
\(803\) −1.00000 −0.0352892
\(804\) 83.3462 2.93940
\(805\) 20.8964 0.736502
\(806\) −30.0698 −1.05916
\(807\) −24.0942 −0.848157
\(808\) 1.96287 0.0690535
\(809\) 53.8212 1.89225 0.946126 0.323798i \(-0.104960\pi\)
0.946126 + 0.323798i \(0.104960\pi\)
\(810\) −18.9165 −0.664658
\(811\) −28.4447 −0.998830 −0.499415 0.866363i \(-0.666452\pi\)
−0.499415 + 0.866363i \(0.666452\pi\)
\(812\) 41.6477 1.46155
\(813\) −14.8766 −0.521744
\(814\) −21.8749 −0.766715
\(815\) 6.72566 0.235590
\(816\) 19.6226 0.686928
\(817\) −24.7555 −0.866087
\(818\) −9.55449 −0.334065
\(819\) −31.8924 −1.11441
\(820\) 4.62816 0.161622
\(821\) −47.5293 −1.65878 −0.829391 0.558668i \(-0.811313\pi\)
−0.829391 + 0.558668i \(0.811313\pi\)
\(822\) 5.00158 0.174450
\(823\) 40.4250 1.40913 0.704564 0.709640i \(-0.251143\pi\)
0.704564 + 0.709640i \(0.251143\pi\)
\(824\) 0.527083 0.0183618
\(825\) −2.47425 −0.0861422
\(826\) −24.6432 −0.857446
\(827\) 42.4552 1.47631 0.738156 0.674630i \(-0.235697\pi\)
0.738156 + 0.674630i \(0.235697\pi\)
\(828\) −50.4736 −1.75408
\(829\) 47.8975 1.66355 0.831774 0.555114i \(-0.187325\pi\)
0.831774 + 0.555114i \(0.187325\pi\)
\(830\) −6.70227 −0.232639
\(831\) 38.3936 1.33186
\(832\) 35.5124 1.23117
\(833\) 29.1463 1.00986
\(834\) −37.0110 −1.28159
\(835\) −11.4657 −0.396785
\(836\) −12.2264 −0.422858
\(837\) 1.47242 0.0508944
\(838\) 18.7039 0.646115
\(839\) 2.59083 0.0894453 0.0447227 0.998999i \(-0.485760\pi\)
0.0447227 + 0.998999i \(0.485760\pi\)
\(840\) −16.1366 −0.556764
\(841\) −12.4968 −0.430925
\(842\) −60.5179 −2.08558
\(843\) −50.8343 −1.75083
\(844\) −38.7502 −1.33384
\(845\) 5.12399 0.176271
\(846\) −82.4198 −2.83365
\(847\) 3.64013 0.125076
\(848\) 2.45440 0.0842845
\(849\) 18.5865 0.637889
\(850\) −10.2336 −0.351009
\(851\) −57.2192 −1.96145
\(852\) −22.4339 −0.768573
\(853\) 48.1761 1.64952 0.824760 0.565483i \(-0.191310\pi\)
0.824760 + 0.565483i \(0.191310\pi\)
\(854\) 34.7174 1.18801
\(855\) 13.5527 0.463491
\(856\) 16.7614 0.572893
\(857\) 41.9844 1.43416 0.717080 0.696991i \(-0.245478\pi\)
0.717080 + 0.696991i \(0.245478\pi\)
\(858\) −15.2390 −0.520251
\(859\) 42.2777 1.44250 0.721248 0.692677i \(-0.243569\pi\)
0.721248 + 0.692677i \(0.243569\pi\)
\(860\) −16.0604 −0.547655
\(861\) 14.8005 0.504400
\(862\) 9.30792 0.317029
\(863\) −6.26259 −0.213181 −0.106591 0.994303i \(-0.533993\pi\)
−0.106591 + 0.994303i \(0.533993\pi\)
\(864\) −2.20638 −0.0750626
\(865\) −21.0607 −0.716086
\(866\) −45.7906 −1.55603
\(867\) −11.7373 −0.398620
\(868\) −50.0523 −1.69889
\(869\) −0.195611 −0.00663565
\(870\) −22.0591 −0.747872
\(871\) 33.5664 1.13736
\(872\) 16.8320 0.570004
\(873\) 38.8845 1.31604
\(874\) −54.6919 −1.84998
\(875\) −3.64013 −0.123059
\(876\) 6.96841 0.235441
\(877\) −12.6290 −0.426450 −0.213225 0.977003i \(-0.568397\pi\)
−0.213225 + 0.977003i \(0.568397\pi\)
\(878\) −89.2005 −3.01037
\(879\) −0.882495 −0.0297658
\(880\) 1.70077 0.0573330
\(881\) 23.0629 0.777009 0.388505 0.921447i \(-0.372992\pi\)
0.388505 + 0.921447i \(0.372992\pi\)
\(882\) −42.8247 −1.44198
\(883\) 47.0786 1.58432 0.792161 0.610312i \(-0.208956\pi\)
0.792161 + 0.610312i \(0.208956\pi\)
\(884\) −36.8563 −1.23961
\(885\) 7.63243 0.256561
\(886\) −38.1427 −1.28143
\(887\) −25.6178 −0.860161 −0.430081 0.902791i \(-0.641515\pi\)
−0.430081 + 0.902791i \(0.641515\pi\)
\(888\) 44.1856 1.48277
\(889\) 53.7415 1.80243
\(890\) 16.1623 0.541762
\(891\) −8.61947 −0.288763
\(892\) 4.53512 0.151847
\(893\) −52.2228 −1.74757
\(894\) −20.9117 −0.699391
\(895\) 8.24694 0.275665
\(896\) 47.8279 1.59782
\(897\) −39.8613 −1.33093
\(898\) 8.88705 0.296565
\(899\) −19.8336 −0.661486
\(900\) 8.79243 0.293081
\(901\) −6.72927 −0.224184
\(902\) 3.60643 0.120081
\(903\) −51.3600 −1.70915
\(904\) −10.2854 −0.342087
\(905\) −20.1422 −0.669551
\(906\) −13.4553 −0.447023
\(907\) −40.7122 −1.35183 −0.675914 0.736981i \(-0.736251\pi\)
−0.675914 + 0.736981i \(0.736251\pi\)
\(908\) 30.0297 0.996571
\(909\) −3.42025 −0.113442
\(910\) −22.4197 −0.743206
\(911\) −2.66730 −0.0883717 −0.0441859 0.999023i \(-0.514069\pi\)
−0.0441859 + 0.999023i \(0.514069\pi\)
\(912\) −18.2682 −0.604920
\(913\) −3.05395 −0.101071
\(914\) −3.41941 −0.113104
\(915\) −10.7526 −0.355470
\(916\) −39.8289 −1.31599
\(917\) −15.0212 −0.496043
\(918\) 3.08634 0.101864
\(919\) −12.8028 −0.422326 −0.211163 0.977451i \(-0.567725\pi\)
−0.211163 + 0.977451i \(0.567725\pi\)
\(920\) −10.2851 −0.339089
\(921\) 20.2492 0.667233
\(922\) −80.4559 −2.64967
\(923\) −9.03492 −0.297388
\(924\) −25.3659 −0.834477
\(925\) 9.96750 0.327729
\(926\) 73.4289 2.41302
\(927\) −0.918428 −0.0301651
\(928\) 29.7199 0.975605
\(929\) −35.2716 −1.15722 −0.578612 0.815603i \(-0.696405\pi\)
−0.578612 + 0.815603i \(0.696405\pi\)
\(930\) 26.5106 0.869318
\(931\) −27.1346 −0.889300
\(932\) −28.1654 −0.922588
\(933\) 0.503698 0.0164903
\(934\) 53.0992 1.73746
\(935\) −4.66302 −0.152497
\(936\) 15.6972 0.513079
\(937\) 26.5731 0.868106 0.434053 0.900887i \(-0.357083\pi\)
0.434053 + 0.900887i \(0.357083\pi\)
\(938\) 95.5496 3.11981
\(939\) 25.4551 0.830697
\(940\) −33.8801 −1.10505
\(941\) 28.2273 0.920183 0.460092 0.887871i \(-0.347817\pi\)
0.460092 + 0.887871i \(0.347817\pi\)
\(942\) −96.4278 −3.14179
\(943\) 9.43351 0.307197
\(944\) −5.24645 −0.170757
\(945\) 1.09782 0.0357122
\(946\) −12.5149 −0.406893
\(947\) −24.8105 −0.806234 −0.403117 0.915148i \(-0.632073\pi\)
−0.403117 + 0.915148i \(0.632073\pi\)
\(948\) 1.36310 0.0442714
\(949\) 2.80642 0.0911003
\(950\) 9.52724 0.309105
\(951\) −55.6265 −1.80381
\(952\) −30.4114 −0.985638
\(953\) −0.650393 −0.0210683 −0.0105341 0.999945i \(-0.503353\pi\)
−0.0105341 + 0.999945i \(0.503353\pi\)
\(954\) 9.88731 0.320114
\(955\) −10.0721 −0.325926
\(956\) −44.8813 −1.45156
\(957\) −10.0514 −0.324916
\(958\) −51.9249 −1.67762
\(959\) 3.35290 0.108271
\(960\) −31.3091 −1.01050
\(961\) −7.16398 −0.231096
\(962\) 61.3903 1.97930
\(963\) −29.2063 −0.941160
\(964\) −27.2706 −0.878328
\(965\) 18.6235 0.599512
\(966\) −113.468 −3.65079
\(967\) −43.1429 −1.38738 −0.693691 0.720273i \(-0.744017\pi\)
−0.693691 + 0.720273i \(0.744017\pi\)
\(968\) −1.79164 −0.0575856
\(969\) 50.0861 1.60900
\(970\) 27.3350 0.877674
\(971\) −55.2874 −1.77426 −0.887129 0.461521i \(-0.847304\pi\)
−0.887129 + 0.461521i \(0.847304\pi\)
\(972\) 62.6122 2.00829
\(973\) −24.8110 −0.795404
\(974\) −41.1550 −1.31869
\(975\) 6.94378 0.222379
\(976\) 7.39122 0.236587
\(977\) 3.59426 0.114991 0.0574954 0.998346i \(-0.481689\pi\)
0.0574954 + 0.998346i \(0.481689\pi\)
\(978\) −36.5206 −1.16780
\(979\) 7.36450 0.235371
\(980\) −17.6038 −0.562334
\(981\) −29.3293 −0.936413
\(982\) 48.3044 1.54145
\(983\) −26.7667 −0.853725 −0.426863 0.904317i \(-0.640381\pi\)
−0.426863 + 0.904317i \(0.640381\pi\)
\(984\) −7.28471 −0.232228
\(985\) 4.27797 0.136307
\(986\) −41.5730 −1.32396
\(987\) −108.346 −3.44869
\(988\) 34.3124 1.09162
\(989\) −32.7357 −1.04093
\(990\) 6.85138 0.217751
\(991\) −47.1497 −1.49776 −0.748881 0.662705i \(-0.769408\pi\)
−0.748881 + 0.662705i \(0.769408\pi\)
\(992\) −35.7175 −1.13403
\(993\) 19.2663 0.611397
\(994\) −25.7186 −0.815746
\(995\) −6.41209 −0.203277
\(996\) 21.2812 0.674319
\(997\) −43.3273 −1.37219 −0.686094 0.727513i \(-0.740676\pi\)
−0.686094 + 0.727513i \(0.740676\pi\)
\(998\) 68.7395 2.17591
\(999\) −3.00609 −0.0951085
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 4015.2.a.e.1.4 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4015.2.a.e.1.4 27 1.1 even 1 trivial