Properties

Label 2005.2.a.e.1.7
Level $2005$
Weight $2$
Character 2005.1
Self dual yes
Analytic conductor $16.010$
Analytic rank $1$
Dimension $29$
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] = [2005,2,Mod(1,2005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2005, 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("2005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.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: \(16.0100056053\)
Analytic rank: \(1\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 2005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.77645 q^{2} -3.27205 q^{3} +1.15578 q^{4} -1.00000 q^{5} +5.81263 q^{6} +2.00064 q^{7} +1.49972 q^{8} +7.70629 q^{9} +O(q^{10})\) \(q-1.77645 q^{2} -3.27205 q^{3} +1.15578 q^{4} -1.00000 q^{5} +5.81263 q^{6} +2.00064 q^{7} +1.49972 q^{8} +7.70629 q^{9} +1.77645 q^{10} -5.30313 q^{11} -3.78176 q^{12} +1.99088 q^{13} -3.55404 q^{14} +3.27205 q^{15} -4.97573 q^{16} -2.15638 q^{17} -13.6898 q^{18} -5.13856 q^{19} -1.15578 q^{20} -6.54620 q^{21} +9.42075 q^{22} +2.16945 q^{23} -4.90715 q^{24} +1.00000 q^{25} -3.53670 q^{26} -15.3992 q^{27} +2.31230 q^{28} -4.23544 q^{29} -5.81263 q^{30} +2.91445 q^{31} +5.83971 q^{32} +17.3521 q^{33} +3.83071 q^{34} -2.00064 q^{35} +8.90676 q^{36} +6.02644 q^{37} +9.12840 q^{38} -6.51424 q^{39} -1.49972 q^{40} +8.60000 q^{41} +11.6290 q^{42} +3.93746 q^{43} -6.12924 q^{44} -7.70629 q^{45} -3.85393 q^{46} +5.97785 q^{47} +16.2808 q^{48} -2.99743 q^{49} -1.77645 q^{50} +7.05579 q^{51} +2.30101 q^{52} +0.642395 q^{53} +27.3559 q^{54} +5.30313 q^{55} +3.00040 q^{56} +16.8136 q^{57} +7.52405 q^{58} -7.87937 q^{59} +3.78176 q^{60} +4.28306 q^{61} -5.17738 q^{62} +15.4175 q^{63} -0.422489 q^{64} -1.99088 q^{65} -30.8251 q^{66} +1.67698 q^{67} -2.49230 q^{68} -7.09856 q^{69} +3.55404 q^{70} -13.2242 q^{71} +11.5573 q^{72} +0.667843 q^{73} -10.7057 q^{74} -3.27205 q^{75} -5.93904 q^{76} -10.6097 q^{77} +11.5722 q^{78} +10.9897 q^{79} +4.97573 q^{80} +27.2680 q^{81} -15.2775 q^{82} +1.46499 q^{83} -7.56595 q^{84} +2.15638 q^{85} -6.99470 q^{86} +13.8586 q^{87} -7.95320 q^{88} +4.48277 q^{89} +13.6898 q^{90} +3.98303 q^{91} +2.50741 q^{92} -9.53622 q^{93} -10.6194 q^{94} +5.13856 q^{95} -19.1078 q^{96} +10.8071 q^{97} +5.32478 q^{98} -40.8674 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.77645 −1.25614 −0.628070 0.778157i \(-0.716155\pi\)
−0.628070 + 0.778157i \(0.716155\pi\)
\(3\) −3.27205 −1.88912 −0.944558 0.328343i \(-0.893510\pi\)
−0.944558 + 0.328343i \(0.893510\pi\)
\(4\) 1.15578 0.577889
\(5\) −1.00000 −0.447214
\(6\) 5.81263 2.37300
\(7\) 2.00064 0.756172 0.378086 0.925770i \(-0.376582\pi\)
0.378086 + 0.925770i \(0.376582\pi\)
\(8\) 1.49972 0.530231
\(9\) 7.70629 2.56876
\(10\) 1.77645 0.561763
\(11\) −5.30313 −1.59895 −0.799477 0.600697i \(-0.794890\pi\)
−0.799477 + 0.600697i \(0.794890\pi\)
\(12\) −3.78176 −1.09170
\(13\) 1.99088 0.552170 0.276085 0.961133i \(-0.410963\pi\)
0.276085 + 0.961133i \(0.410963\pi\)
\(14\) −3.55404 −0.949858
\(15\) 3.27205 0.844839
\(16\) −4.97573 −1.24393
\(17\) −2.15638 −0.523000 −0.261500 0.965203i \(-0.584217\pi\)
−0.261500 + 0.965203i \(0.584217\pi\)
\(18\) −13.6898 −3.22673
\(19\) −5.13856 −1.17887 −0.589433 0.807817i \(-0.700649\pi\)
−0.589433 + 0.807817i \(0.700649\pi\)
\(20\) −1.15578 −0.258440
\(21\) −6.54620 −1.42850
\(22\) 9.42075 2.00851
\(23\) 2.16945 0.452363 0.226181 0.974085i \(-0.427376\pi\)
0.226181 + 0.974085i \(0.427376\pi\)
\(24\) −4.90715 −1.00167
\(25\) 1.00000 0.200000
\(26\) −3.53670 −0.693603
\(27\) −15.3992 −2.96358
\(28\) 2.31230 0.436984
\(29\) −4.23544 −0.786501 −0.393251 0.919431i \(-0.628650\pi\)
−0.393251 + 0.919431i \(0.628650\pi\)
\(30\) −5.81263 −1.06124
\(31\) 2.91445 0.523451 0.261725 0.965142i \(-0.415709\pi\)
0.261725 + 0.965142i \(0.415709\pi\)
\(32\) 5.83971 1.03232
\(33\) 17.3521 3.02061
\(34\) 3.83071 0.656962
\(35\) −2.00064 −0.338170
\(36\) 8.90676 1.48446
\(37\) 6.02644 0.990740 0.495370 0.868682i \(-0.335032\pi\)
0.495370 + 0.868682i \(0.335032\pi\)
\(38\) 9.12840 1.48082
\(39\) −6.51424 −1.04311
\(40\) −1.49972 −0.237126
\(41\) 8.60000 1.34309 0.671547 0.740962i \(-0.265630\pi\)
0.671547 + 0.740962i \(0.265630\pi\)
\(42\) 11.6290 1.79439
\(43\) 3.93746 0.600456 0.300228 0.953867i \(-0.402937\pi\)
0.300228 + 0.953867i \(0.402937\pi\)
\(44\) −6.12924 −0.924018
\(45\) −7.70629 −1.14879
\(46\) −3.85393 −0.568231
\(47\) 5.97785 0.871959 0.435980 0.899957i \(-0.356402\pi\)
0.435980 + 0.899957i \(0.356402\pi\)
\(48\) 16.2808 2.34994
\(49\) −2.99743 −0.428204
\(50\) −1.77645 −0.251228
\(51\) 7.05579 0.988008
\(52\) 2.30101 0.319093
\(53\) 0.642395 0.0882397 0.0441199 0.999026i \(-0.485952\pi\)
0.0441199 + 0.999026i \(0.485952\pi\)
\(54\) 27.3559 3.72267
\(55\) 5.30313 0.715074
\(56\) 3.00040 0.400946
\(57\) 16.8136 2.22702
\(58\) 7.52405 0.987956
\(59\) −7.87937 −1.02581 −0.512903 0.858447i \(-0.671430\pi\)
−0.512903 + 0.858447i \(0.671430\pi\)
\(60\) 3.78176 0.488223
\(61\) 4.28306 0.548390 0.274195 0.961674i \(-0.411589\pi\)
0.274195 + 0.961674i \(0.411589\pi\)
\(62\) −5.17738 −0.657528
\(63\) 15.4175 1.94243
\(64\) −0.422489 −0.0528111
\(65\) −1.99088 −0.246938
\(66\) −30.8251 −3.79431
\(67\) 1.67698 0.204876 0.102438 0.994739i \(-0.467336\pi\)
0.102438 + 0.994739i \(0.467336\pi\)
\(68\) −2.49230 −0.302236
\(69\) −7.09856 −0.854566
\(70\) 3.55404 0.424790
\(71\) −13.2242 −1.56943 −0.784713 0.619860i \(-0.787190\pi\)
−0.784713 + 0.619860i \(0.787190\pi\)
\(72\) 11.5573 1.36204
\(73\) 0.667843 0.0781651 0.0390826 0.999236i \(-0.487556\pi\)
0.0390826 + 0.999236i \(0.487556\pi\)
\(74\) −10.7057 −1.24451
\(75\) −3.27205 −0.377823
\(76\) −5.93904 −0.681254
\(77\) −10.6097 −1.20908
\(78\) 11.5722 1.31030
\(79\) 10.9897 1.23644 0.618221 0.786005i \(-0.287854\pi\)
0.618221 + 0.786005i \(0.287854\pi\)
\(80\) 4.97573 0.556304
\(81\) 27.2680 3.02978
\(82\) −15.2775 −1.68712
\(83\) 1.46499 0.160803 0.0804016 0.996763i \(-0.474380\pi\)
0.0804016 + 0.996763i \(0.474380\pi\)
\(84\) −7.56595 −0.825513
\(85\) 2.15638 0.233893
\(86\) −6.99470 −0.754258
\(87\) 13.8586 1.48579
\(88\) −7.95320 −0.847814
\(89\) 4.48277 0.475173 0.237586 0.971366i \(-0.423644\pi\)
0.237586 + 0.971366i \(0.423644\pi\)
\(90\) 13.6898 1.44304
\(91\) 3.98303 0.417535
\(92\) 2.50741 0.261415
\(93\) −9.53622 −0.988860
\(94\) −10.6194 −1.09530
\(95\) 5.13856 0.527205
\(96\) −19.1078 −1.95018
\(97\) 10.8071 1.09730 0.548648 0.836053i \(-0.315143\pi\)
0.548648 + 0.836053i \(0.315143\pi\)
\(98\) 5.32478 0.537884
\(99\) −40.8674 −4.10733
\(100\) 1.15578 0.115578
\(101\) −9.19515 −0.914952 −0.457476 0.889222i \(-0.651246\pi\)
−0.457476 + 0.889222i \(0.651246\pi\)
\(102\) −12.5343 −1.24108
\(103\) 4.41787 0.435306 0.217653 0.976026i \(-0.430160\pi\)
0.217653 + 0.976026i \(0.430160\pi\)
\(104\) 2.98576 0.292777
\(105\) 6.54620 0.638843
\(106\) −1.14118 −0.110842
\(107\) −13.3453 −1.29014 −0.645068 0.764126i \(-0.723171\pi\)
−0.645068 + 0.764126i \(0.723171\pi\)
\(108\) −17.7980 −1.71262
\(109\) 10.9998 1.05359 0.526795 0.849992i \(-0.323394\pi\)
0.526795 + 0.849992i \(0.323394\pi\)
\(110\) −9.42075 −0.898233
\(111\) −19.7188 −1.87162
\(112\) −9.95467 −0.940628
\(113\) −12.4778 −1.17381 −0.586906 0.809655i \(-0.699654\pi\)
−0.586906 + 0.809655i \(0.699654\pi\)
\(114\) −29.8686 −2.79745
\(115\) −2.16945 −0.202303
\(116\) −4.89523 −0.454510
\(117\) 15.3423 1.41839
\(118\) 13.9973 1.28856
\(119\) −4.31416 −0.395478
\(120\) 4.90715 0.447959
\(121\) 17.1232 1.55665
\(122\) −7.60865 −0.688855
\(123\) −28.1396 −2.53726
\(124\) 3.36846 0.302497
\(125\) −1.00000 −0.0894427
\(126\) −27.3885 −2.43996
\(127\) 1.98310 0.175972 0.0879858 0.996122i \(-0.471957\pi\)
0.0879858 + 0.996122i \(0.471957\pi\)
\(128\) −10.9289 −0.965986
\(129\) −12.8835 −1.13433
\(130\) 3.53670 0.310189
\(131\) 20.7594 1.81376 0.906881 0.421388i \(-0.138457\pi\)
0.906881 + 0.421388i \(0.138457\pi\)
\(132\) 20.0552 1.74558
\(133\) −10.2804 −0.891426
\(134\) −2.97908 −0.257353
\(135\) 15.3992 1.32535
\(136\) −3.23397 −0.277311
\(137\) 15.7003 1.34136 0.670682 0.741745i \(-0.266002\pi\)
0.670682 + 0.741745i \(0.266002\pi\)
\(138\) 12.6102 1.07345
\(139\) −16.8238 −1.42698 −0.713490 0.700665i \(-0.752887\pi\)
−0.713490 + 0.700665i \(0.752887\pi\)
\(140\) −2.31230 −0.195425
\(141\) −19.5598 −1.64723
\(142\) 23.4922 1.97142
\(143\) −10.5579 −0.882894
\(144\) −38.3444 −3.19537
\(145\) 4.23544 0.351734
\(146\) −1.18639 −0.0981864
\(147\) 9.80772 0.808927
\(148\) 6.96522 0.572538
\(149\) 10.9931 0.900587 0.450293 0.892881i \(-0.351319\pi\)
0.450293 + 0.892881i \(0.351319\pi\)
\(150\) 5.81263 0.474599
\(151\) −13.5460 −1.10236 −0.551179 0.834387i \(-0.685822\pi\)
−0.551179 + 0.834387i \(0.685822\pi\)
\(152\) −7.70640 −0.625071
\(153\) −16.6177 −1.34346
\(154\) 18.8476 1.51878
\(155\) −2.91445 −0.234094
\(156\) −7.52902 −0.602804
\(157\) 13.2825 1.06006 0.530029 0.847979i \(-0.322181\pi\)
0.530029 + 0.847979i \(0.322181\pi\)
\(158\) −19.5227 −1.55314
\(159\) −2.10195 −0.166695
\(160\) −5.83971 −0.461669
\(161\) 4.34030 0.342064
\(162\) −48.4403 −3.80583
\(163\) −16.5031 −1.29262 −0.646312 0.763073i \(-0.723689\pi\)
−0.646312 + 0.763073i \(0.723689\pi\)
\(164\) 9.93969 0.776160
\(165\) −17.3521 −1.35086
\(166\) −2.60248 −0.201991
\(167\) 2.97244 0.230014 0.115007 0.993365i \(-0.463311\pi\)
0.115007 + 0.993365i \(0.463311\pi\)
\(168\) −9.81746 −0.757433
\(169\) −9.03641 −0.695108
\(170\) −3.83071 −0.293802
\(171\) −39.5992 −3.02823
\(172\) 4.55083 0.346997
\(173\) 3.45083 0.262362 0.131181 0.991358i \(-0.458123\pi\)
0.131181 + 0.991358i \(0.458123\pi\)
\(174\) −24.6190 −1.86636
\(175\) 2.00064 0.151234
\(176\) 26.3870 1.98899
\(177\) 25.7817 1.93787
\(178\) −7.96342 −0.596884
\(179\) −17.5419 −1.31115 −0.655573 0.755132i \(-0.727573\pi\)
−0.655573 + 0.755132i \(0.727573\pi\)
\(180\) −8.90676 −0.663871
\(181\) −3.80660 −0.282942 −0.141471 0.989942i \(-0.545183\pi\)
−0.141471 + 0.989942i \(0.545183\pi\)
\(182\) −7.07567 −0.524483
\(183\) −14.0144 −1.03597
\(184\) 3.25357 0.239856
\(185\) −6.02644 −0.443073
\(186\) 16.9406 1.24215
\(187\) 11.4356 0.836253
\(188\) 6.90907 0.503896
\(189\) −30.8083 −2.24097
\(190\) −9.12840 −0.662244
\(191\) 4.66268 0.337379 0.168690 0.985669i \(-0.446046\pi\)
0.168690 + 0.985669i \(0.446046\pi\)
\(192\) 1.38240 0.0997664
\(193\) −27.1145 −1.95175 −0.975873 0.218337i \(-0.929937\pi\)
−0.975873 + 0.218337i \(0.929937\pi\)
\(194\) −19.1983 −1.37836
\(195\) 6.51424 0.466495
\(196\) −3.46436 −0.247454
\(197\) −7.56487 −0.538974 −0.269487 0.963004i \(-0.586854\pi\)
−0.269487 + 0.963004i \(0.586854\pi\)
\(198\) 72.5990 5.15939
\(199\) 13.8659 0.982929 0.491464 0.870898i \(-0.336462\pi\)
0.491464 + 0.870898i \(0.336462\pi\)
\(200\) 1.49972 0.106046
\(201\) −5.48717 −0.387035
\(202\) 16.3347 1.14931
\(203\) −8.47360 −0.594730
\(204\) 8.15493 0.570959
\(205\) −8.60000 −0.600650
\(206\) −7.84814 −0.546806
\(207\) 16.7184 1.16201
\(208\) −9.90607 −0.686863
\(209\) 27.2504 1.88495
\(210\) −11.6290 −0.802477
\(211\) 6.11062 0.420673 0.210336 0.977629i \(-0.432544\pi\)
0.210336 + 0.977629i \(0.432544\pi\)
\(212\) 0.742466 0.0509928
\(213\) 43.2702 2.96483
\(214\) 23.7072 1.62059
\(215\) −3.93746 −0.268532
\(216\) −23.0945 −1.57138
\(217\) 5.83078 0.395819
\(218\) −19.5406 −1.32346
\(219\) −2.18521 −0.147663
\(220\) 6.12924 0.413233
\(221\) −4.29310 −0.288785
\(222\) 35.0295 2.35102
\(223\) 6.53109 0.437354 0.218677 0.975797i \(-0.429826\pi\)
0.218677 + 0.975797i \(0.429826\pi\)
\(224\) 11.6832 0.780615
\(225\) 7.70629 0.513753
\(226\) 22.1662 1.47447
\(227\) 19.1455 1.27073 0.635366 0.772211i \(-0.280849\pi\)
0.635366 + 0.772211i \(0.280849\pi\)
\(228\) 19.4328 1.28697
\(229\) 19.0903 1.26153 0.630763 0.775976i \(-0.282742\pi\)
0.630763 + 0.775976i \(0.282742\pi\)
\(230\) 3.85393 0.254121
\(231\) 34.7153 2.28410
\(232\) −6.35197 −0.417027
\(233\) 18.5284 1.21383 0.606917 0.794765i \(-0.292406\pi\)
0.606917 + 0.794765i \(0.292406\pi\)
\(234\) −27.2548 −1.78170
\(235\) −5.97785 −0.389952
\(236\) −9.10680 −0.592802
\(237\) −35.9589 −2.33578
\(238\) 7.66389 0.496776
\(239\) −27.3329 −1.76802 −0.884008 0.467472i \(-0.845165\pi\)
−0.884008 + 0.467472i \(0.845165\pi\)
\(240\) −16.2808 −1.05092
\(241\) −7.61957 −0.490820 −0.245410 0.969419i \(-0.578923\pi\)
−0.245410 + 0.969419i \(0.578923\pi\)
\(242\) −30.4185 −1.95537
\(243\) −43.0246 −2.76003
\(244\) 4.95027 0.316909
\(245\) 2.99743 0.191499
\(246\) 49.9886 3.18716
\(247\) −10.2302 −0.650935
\(248\) 4.37086 0.277550
\(249\) −4.79351 −0.303776
\(250\) 1.77645 0.112353
\(251\) 25.2312 1.59258 0.796288 0.604918i \(-0.206794\pi\)
0.796288 + 0.604918i \(0.206794\pi\)
\(252\) 17.8192 1.12251
\(253\) −11.5049 −0.723307
\(254\) −3.52288 −0.221045
\(255\) −7.05579 −0.441851
\(256\) 20.2596 1.26623
\(257\) −25.9750 −1.62028 −0.810138 0.586240i \(-0.800608\pi\)
−0.810138 + 0.586240i \(0.800608\pi\)
\(258\) 22.8870 1.42488
\(259\) 12.0568 0.749170
\(260\) −2.30101 −0.142703
\(261\) −32.6395 −2.02033
\(262\) −36.8781 −2.27834
\(263\) −5.27279 −0.325134 −0.162567 0.986698i \(-0.551977\pi\)
−0.162567 + 0.986698i \(0.551977\pi\)
\(264\) 26.0232 1.60162
\(265\) −0.642395 −0.0394620
\(266\) 18.2627 1.11976
\(267\) −14.6678 −0.897657
\(268\) 1.93822 0.118396
\(269\) −17.4052 −1.06121 −0.530606 0.847618i \(-0.678036\pi\)
−0.530606 + 0.847618i \(0.678036\pi\)
\(270\) −27.3559 −1.66483
\(271\) −28.6279 −1.73902 −0.869511 0.493913i \(-0.835566\pi\)
−0.869511 + 0.493913i \(0.835566\pi\)
\(272\) 10.7296 0.650577
\(273\) −13.0327 −0.788773
\(274\) −27.8907 −1.68494
\(275\) −5.30313 −0.319791
\(276\) −8.20435 −0.493844
\(277\) 14.2130 0.853979 0.426990 0.904257i \(-0.359574\pi\)
0.426990 + 0.904257i \(0.359574\pi\)
\(278\) 29.8867 1.79249
\(279\) 22.4596 1.34462
\(280\) −3.00040 −0.179308
\(281\) −19.0089 −1.13398 −0.566989 0.823725i \(-0.691892\pi\)
−0.566989 + 0.823725i \(0.691892\pi\)
\(282\) 34.7470 2.06916
\(283\) 0.0513036 0.00304968 0.00152484 0.999999i \(-0.499515\pi\)
0.00152484 + 0.999999i \(0.499515\pi\)
\(284\) −15.2843 −0.906954
\(285\) −16.8136 −0.995952
\(286\) 18.7556 1.10904
\(287\) 17.2055 1.01561
\(288\) 45.0025 2.65180
\(289\) −12.3500 −0.726471
\(290\) −7.52405 −0.441827
\(291\) −35.3614 −2.07292
\(292\) 0.771878 0.0451708
\(293\) −11.8644 −0.693125 −0.346562 0.938027i \(-0.612651\pi\)
−0.346562 + 0.938027i \(0.612651\pi\)
\(294\) −17.4229 −1.01613
\(295\) 7.87937 0.458754
\(296\) 9.03796 0.525321
\(297\) 81.6639 4.73862
\(298\) −19.5286 −1.13126
\(299\) 4.31912 0.249781
\(300\) −3.78176 −0.218340
\(301\) 7.87745 0.454048
\(302\) 24.0638 1.38472
\(303\) 30.0870 1.72845
\(304\) 25.5681 1.46643
\(305\) −4.28306 −0.245248
\(306\) 29.5206 1.68758
\(307\) −22.1034 −1.26151 −0.630755 0.775982i \(-0.717255\pi\)
−0.630755 + 0.775982i \(0.717255\pi\)
\(308\) −12.2624 −0.698716
\(309\) −14.4555 −0.822344
\(310\) 5.17738 0.294055
\(311\) −26.3510 −1.49423 −0.747114 0.664696i \(-0.768561\pi\)
−0.747114 + 0.664696i \(0.768561\pi\)
\(312\) −9.76953 −0.553091
\(313\) −22.9371 −1.29648 −0.648241 0.761435i \(-0.724495\pi\)
−0.648241 + 0.761435i \(0.724495\pi\)
\(314\) −23.5957 −1.33158
\(315\) −15.4175 −0.868680
\(316\) 12.7017 0.714526
\(317\) 1.83582 0.103110 0.0515550 0.998670i \(-0.483582\pi\)
0.0515550 + 0.998670i \(0.483582\pi\)
\(318\) 3.73400 0.209393
\(319\) 22.4611 1.25758
\(320\) 0.422489 0.0236179
\(321\) 43.6663 2.43722
\(322\) −7.71034 −0.429680
\(323\) 11.0807 0.616547
\(324\) 31.5158 1.75088
\(325\) 1.99088 0.110434
\(326\) 29.3170 1.62372
\(327\) −35.9919 −1.99035
\(328\) 12.8976 0.712150
\(329\) 11.9595 0.659351
\(330\) 30.8251 1.69687
\(331\) 8.69410 0.477871 0.238936 0.971035i \(-0.423202\pi\)
0.238936 + 0.971035i \(0.423202\pi\)
\(332\) 1.69320 0.0929264
\(333\) 46.4415 2.54498
\(334\) −5.28039 −0.288930
\(335\) −1.67698 −0.0916234
\(336\) 32.5721 1.77696
\(337\) 4.26203 0.232168 0.116084 0.993239i \(-0.462966\pi\)
0.116084 + 0.993239i \(0.462966\pi\)
\(338\) 16.0527 0.873154
\(339\) 40.8279 2.21747
\(340\) 2.49230 0.135164
\(341\) −15.4557 −0.836974
\(342\) 70.3461 3.80388
\(343\) −20.0013 −1.07997
\(344\) 5.90508 0.318380
\(345\) 7.09856 0.382173
\(346\) −6.13023 −0.329563
\(347\) −15.4188 −0.827724 −0.413862 0.910340i \(-0.635820\pi\)
−0.413862 + 0.910340i \(0.635820\pi\)
\(348\) 16.0174 0.858623
\(349\) −29.8920 −1.60008 −0.800041 0.599945i \(-0.795189\pi\)
−0.800041 + 0.599945i \(0.795189\pi\)
\(350\) −3.55404 −0.189972
\(351\) −30.6579 −1.63640
\(352\) −30.9687 −1.65064
\(353\) −18.8540 −1.00350 −0.501749 0.865013i \(-0.667310\pi\)
−0.501749 + 0.865013i \(0.667310\pi\)
\(354\) −45.7998 −2.43423
\(355\) 13.2242 0.701868
\(356\) 5.18109 0.274597
\(357\) 14.1161 0.747104
\(358\) 31.1624 1.64698
\(359\) −20.3588 −1.07450 −0.537249 0.843423i \(-0.680537\pi\)
−0.537249 + 0.843423i \(0.680537\pi\)
\(360\) −11.5573 −0.609121
\(361\) 7.40481 0.389727
\(362\) 6.76223 0.355415
\(363\) −56.0278 −2.94070
\(364\) 4.60350 0.241289
\(365\) −0.667843 −0.0349565
\(366\) 24.8959 1.30133
\(367\) 7.81716 0.408053 0.204026 0.978965i \(-0.434597\pi\)
0.204026 + 0.978965i \(0.434597\pi\)
\(368\) −10.7946 −0.562709
\(369\) 66.2741 3.45009
\(370\) 10.7057 0.556561
\(371\) 1.28520 0.0667244
\(372\) −11.0218 −0.571451
\(373\) −16.9545 −0.877871 −0.438936 0.898519i \(-0.644644\pi\)
−0.438936 + 0.898519i \(0.644644\pi\)
\(374\) −20.3148 −1.05045
\(375\) 3.27205 0.168968
\(376\) 8.96510 0.462339
\(377\) −8.43224 −0.434282
\(378\) 54.7294 2.81498
\(379\) 33.2628 1.70859 0.854297 0.519786i \(-0.173988\pi\)
0.854297 + 0.519786i \(0.173988\pi\)
\(380\) 5.93904 0.304666
\(381\) −6.48879 −0.332431
\(382\) −8.28301 −0.423796
\(383\) −17.5968 −0.899153 −0.449576 0.893242i \(-0.648425\pi\)
−0.449576 + 0.893242i \(0.648425\pi\)
\(384\) 35.7598 1.82486
\(385\) 10.6097 0.540719
\(386\) 48.1676 2.45167
\(387\) 30.3432 1.54243
\(388\) 12.4906 0.634115
\(389\) −24.3012 −1.23212 −0.616061 0.787698i \(-0.711273\pi\)
−0.616061 + 0.787698i \(0.711273\pi\)
\(390\) −11.5722 −0.585983
\(391\) −4.67818 −0.236586
\(392\) −4.49530 −0.227047
\(393\) −67.9259 −3.42641
\(394\) 13.4386 0.677028
\(395\) −10.9897 −0.552953
\(396\) −47.2337 −2.37358
\(397\) −6.84511 −0.343546 −0.171773 0.985137i \(-0.554950\pi\)
−0.171773 + 0.985137i \(0.554950\pi\)
\(398\) −24.6321 −1.23470
\(399\) 33.6380 1.68401
\(400\) −4.97573 −0.248787
\(401\) −1.00000 −0.0499376
\(402\) 9.74769 0.486171
\(403\) 5.80231 0.289034
\(404\) −10.6276 −0.528740
\(405\) −27.2680 −1.35496
\(406\) 15.0529 0.747065
\(407\) −31.9590 −1.58415
\(408\) 10.5817 0.523872
\(409\) −13.8179 −0.683253 −0.341626 0.939836i \(-0.610978\pi\)
−0.341626 + 0.939836i \(0.610978\pi\)
\(410\) 15.2775 0.754501
\(411\) −51.3720 −2.53399
\(412\) 5.10608 0.251559
\(413\) −15.7638 −0.775686
\(414\) −29.6995 −1.45965
\(415\) −1.46499 −0.0719134
\(416\) 11.6261 0.570018
\(417\) 55.0484 2.69573
\(418\) −48.4091 −2.36777
\(419\) 20.3903 0.996132 0.498066 0.867139i \(-0.334044\pi\)
0.498066 + 0.867139i \(0.334044\pi\)
\(420\) 7.56595 0.369181
\(421\) 21.0156 1.02424 0.512118 0.858915i \(-0.328861\pi\)
0.512118 + 0.858915i \(0.328861\pi\)
\(422\) −10.8552 −0.528424
\(423\) 46.0670 2.23986
\(424\) 0.963412 0.0467874
\(425\) −2.15638 −0.104600
\(426\) −76.8675 −3.72424
\(427\) 8.56888 0.414677
\(428\) −15.4242 −0.745555
\(429\) 34.5459 1.66789
\(430\) 6.99470 0.337314
\(431\) −28.6657 −1.38078 −0.690390 0.723438i \(-0.742561\pi\)
−0.690390 + 0.723438i \(0.742561\pi\)
\(432\) 76.6223 3.68649
\(433\) 36.1591 1.73770 0.868848 0.495078i \(-0.164861\pi\)
0.868848 + 0.495078i \(0.164861\pi\)
\(434\) −10.3581 −0.497204
\(435\) −13.8586 −0.664467
\(436\) 12.7133 0.608858
\(437\) −11.1479 −0.533275
\(438\) 3.88192 0.185486
\(439\) 37.4419 1.78700 0.893501 0.449061i \(-0.148241\pi\)
0.893501 + 0.449061i \(0.148241\pi\)
\(440\) 7.95320 0.379154
\(441\) −23.0990 −1.09995
\(442\) 7.62648 0.362755
\(443\) −20.5304 −0.975427 −0.487713 0.873004i \(-0.662169\pi\)
−0.487713 + 0.873004i \(0.662169\pi\)
\(444\) −22.7905 −1.08159
\(445\) −4.48277 −0.212504
\(446\) −11.6022 −0.549378
\(447\) −35.9698 −1.70131
\(448\) −0.845250 −0.0399343
\(449\) 0.797432 0.0376332 0.0188166 0.999823i \(-0.494010\pi\)
0.0188166 + 0.999823i \(0.494010\pi\)
\(450\) −13.6898 −0.645345
\(451\) −45.6069 −2.14755
\(452\) −14.4215 −0.678333
\(453\) 44.3231 2.08248
\(454\) −34.0110 −1.59622
\(455\) −3.98303 −0.186728
\(456\) 25.2157 1.18083
\(457\) 37.8312 1.76967 0.884834 0.465906i \(-0.154272\pi\)
0.884834 + 0.465906i \(0.154272\pi\)
\(458\) −33.9131 −1.58465
\(459\) 33.2066 1.54995
\(460\) −2.50741 −0.116908
\(461\) 4.50255 0.209705 0.104852 0.994488i \(-0.466563\pi\)
0.104852 + 0.994488i \(0.466563\pi\)
\(462\) −61.6701 −2.86915
\(463\) −18.2279 −0.847120 −0.423560 0.905868i \(-0.639220\pi\)
−0.423560 + 0.905868i \(0.639220\pi\)
\(464\) 21.0744 0.978355
\(465\) 9.53622 0.442232
\(466\) −32.9148 −1.52475
\(467\) 11.6686 0.539958 0.269979 0.962866i \(-0.412983\pi\)
0.269979 + 0.962866i \(0.412983\pi\)
\(468\) 17.7323 0.819674
\(469\) 3.35505 0.154922
\(470\) 10.6194 0.489834
\(471\) −43.4609 −2.00257
\(472\) −11.8168 −0.543914
\(473\) −20.8808 −0.960102
\(474\) 63.8792 2.93407
\(475\) −5.13856 −0.235773
\(476\) −4.98621 −0.228542
\(477\) 4.95048 0.226667
\(478\) 48.5555 2.22088
\(479\) −0.846587 −0.0386815 −0.0193408 0.999813i \(-0.506157\pi\)
−0.0193408 + 0.999813i \(0.506157\pi\)
\(480\) 19.1078 0.872148
\(481\) 11.9979 0.547057
\(482\) 13.5358 0.616539
\(483\) −14.2017 −0.646199
\(484\) 19.7906 0.899572
\(485\) −10.8071 −0.490726
\(486\) 76.4311 3.46699
\(487\) −23.0455 −1.04429 −0.522145 0.852857i \(-0.674868\pi\)
−0.522145 + 0.852857i \(0.674868\pi\)
\(488\) 6.42339 0.290773
\(489\) 53.9989 2.44192
\(490\) −5.32478 −0.240549
\(491\) −24.9565 −1.12627 −0.563136 0.826364i \(-0.690405\pi\)
−0.563136 + 0.826364i \(0.690405\pi\)
\(492\) −32.5231 −1.46626
\(493\) 9.13324 0.411340
\(494\) 18.1735 0.817666
\(495\) 40.8674 1.83685
\(496\) −14.5015 −0.651138
\(497\) −26.4569 −1.18676
\(498\) 8.51543 0.381585
\(499\) −10.7280 −0.480252 −0.240126 0.970742i \(-0.577189\pi\)
−0.240126 + 0.970742i \(0.577189\pi\)
\(500\) −1.15578 −0.0516880
\(501\) −9.72595 −0.434524
\(502\) −44.8219 −2.00050
\(503\) −7.61939 −0.339732 −0.169866 0.985467i \(-0.554333\pi\)
−0.169866 + 0.985467i \(0.554333\pi\)
\(504\) 23.1220 1.02993
\(505\) 9.19515 0.409179
\(506\) 20.4379 0.908575
\(507\) 29.5675 1.31314
\(508\) 2.29202 0.101692
\(509\) 19.0995 0.846570 0.423285 0.905997i \(-0.360877\pi\)
0.423285 + 0.905997i \(0.360877\pi\)
\(510\) 12.5343 0.555027
\(511\) 1.33612 0.0591063
\(512\) −14.1324 −0.624571
\(513\) 79.1297 3.49366
\(514\) 46.1433 2.03529
\(515\) −4.41787 −0.194675
\(516\) −14.8905 −0.655518
\(517\) −31.7013 −1.39422
\(518\) −21.4182 −0.941063
\(519\) −11.2913 −0.495632
\(520\) −2.98576 −0.130934
\(521\) 30.7586 1.34756 0.673779 0.738933i \(-0.264670\pi\)
0.673779 + 0.738933i \(0.264670\pi\)
\(522\) 57.9825 2.53782
\(523\) −12.7016 −0.555402 −0.277701 0.960668i \(-0.589573\pi\)
−0.277701 + 0.960668i \(0.589573\pi\)
\(524\) 23.9933 1.04815
\(525\) −6.54620 −0.285699
\(526\) 9.36684 0.408414
\(527\) −6.28468 −0.273765
\(528\) −86.3393 −3.75744
\(529\) −18.2935 −0.795368
\(530\) 1.14118 0.0495698
\(531\) −60.7207 −2.63505
\(532\) −11.8819 −0.515145
\(533\) 17.1215 0.741616
\(534\) 26.0567 1.12758
\(535\) 13.3453 0.576966
\(536\) 2.51500 0.108632
\(537\) 57.3980 2.47691
\(538\) 30.9194 1.33303
\(539\) 15.8957 0.684678
\(540\) 17.7980 0.765906
\(541\) 31.3673 1.34858 0.674292 0.738465i \(-0.264449\pi\)
0.674292 + 0.738465i \(0.264449\pi\)
\(542\) 50.8561 2.18446
\(543\) 12.4554 0.534511
\(544\) −12.5927 −0.539906
\(545\) −10.9998 −0.471180
\(546\) 23.1519 0.990810
\(547\) 39.1222 1.67275 0.836373 0.548161i \(-0.184672\pi\)
0.836373 + 0.548161i \(0.184672\pi\)
\(548\) 18.1460 0.775159
\(549\) 33.0065 1.40868
\(550\) 9.42075 0.401702
\(551\) 21.7641 0.927180
\(552\) −10.6458 −0.453117
\(553\) 21.9865 0.934962
\(554\) −25.2488 −1.07272
\(555\) 19.7188 0.837016
\(556\) −19.4446 −0.824636
\(557\) 33.2541 1.40902 0.704512 0.709692i \(-0.251166\pi\)
0.704512 + 0.709692i \(0.251166\pi\)
\(558\) −39.8984 −1.68903
\(559\) 7.83899 0.331554
\(560\) 9.95467 0.420661
\(561\) −37.4178 −1.57978
\(562\) 33.7684 1.42444
\(563\) 13.6925 0.577071 0.288536 0.957469i \(-0.406832\pi\)
0.288536 + 0.957469i \(0.406832\pi\)
\(564\) −22.6068 −0.951918
\(565\) 12.4778 0.524944
\(566\) −0.0911384 −0.00383083
\(567\) 54.5536 2.29103
\(568\) −19.8326 −0.832158
\(569\) −30.4598 −1.27694 −0.638471 0.769646i \(-0.720433\pi\)
−0.638471 + 0.769646i \(0.720433\pi\)
\(570\) 29.8686 1.25106
\(571\) −37.1882 −1.55628 −0.778140 0.628091i \(-0.783836\pi\)
−0.778140 + 0.628091i \(0.783836\pi\)
\(572\) −12.2026 −0.510215
\(573\) −15.2565 −0.637349
\(574\) −30.5648 −1.27575
\(575\) 2.16945 0.0904725
\(576\) −3.25582 −0.135659
\(577\) −28.1409 −1.17152 −0.585761 0.810484i \(-0.699204\pi\)
−0.585761 + 0.810484i \(0.699204\pi\)
\(578\) 21.9392 0.912549
\(579\) 88.7200 3.68708
\(580\) 4.89523 0.203263
\(581\) 2.93092 0.121595
\(582\) 62.8178 2.60388
\(583\) −3.40670 −0.141091
\(584\) 1.00158 0.0414455
\(585\) −15.3423 −0.634325
\(586\) 21.0765 0.870662
\(587\) 4.28532 0.176874 0.0884371 0.996082i \(-0.471813\pi\)
0.0884371 + 0.996082i \(0.471813\pi\)
\(588\) 11.3355 0.467470
\(589\) −14.9761 −0.617079
\(590\) −13.9973 −0.576260
\(591\) 24.7526 1.01819
\(592\) −29.9859 −1.23241
\(593\) 9.97721 0.409715 0.204857 0.978792i \(-0.434327\pi\)
0.204857 + 0.978792i \(0.434327\pi\)
\(594\) −145.072 −5.95237
\(595\) 4.31416 0.176863
\(596\) 12.7055 0.520439
\(597\) −45.3699 −1.85687
\(598\) −7.67270 −0.313760
\(599\) −40.6145 −1.65946 −0.829732 0.558162i \(-0.811507\pi\)
−0.829732 + 0.558162i \(0.811507\pi\)
\(600\) −4.90715 −0.200334
\(601\) −7.67886 −0.313227 −0.156614 0.987660i \(-0.550058\pi\)
−0.156614 + 0.987660i \(0.550058\pi\)
\(602\) −13.9939 −0.570349
\(603\) 12.9233 0.526278
\(604\) −15.6562 −0.637041
\(605\) −17.1232 −0.696156
\(606\) −53.4480 −2.17118
\(607\) 25.2126 1.02335 0.511675 0.859179i \(-0.329025\pi\)
0.511675 + 0.859179i \(0.329025\pi\)
\(608\) −30.0077 −1.21697
\(609\) 27.7260 1.12351
\(610\) 7.60865 0.308065
\(611\) 11.9012 0.481470
\(612\) −19.2064 −0.776373
\(613\) −46.8372 −1.89174 −0.945868 0.324553i \(-0.894786\pi\)
−0.945868 + 0.324553i \(0.894786\pi\)
\(614\) 39.2657 1.58463
\(615\) 28.1396 1.13470
\(616\) −15.9115 −0.641093
\(617\) −15.3288 −0.617113 −0.308557 0.951206i \(-0.599846\pi\)
−0.308557 + 0.951206i \(0.599846\pi\)
\(618\) 25.6795 1.03298
\(619\) −18.0418 −0.725161 −0.362581 0.931952i \(-0.618104\pi\)
−0.362581 + 0.931952i \(0.618104\pi\)
\(620\) −3.36846 −0.135281
\(621\) −33.4078 −1.34061
\(622\) 46.8112 1.87696
\(623\) 8.96843 0.359312
\(624\) 32.4131 1.29756
\(625\) 1.00000 0.0400000
\(626\) 40.7467 1.62856
\(627\) −89.1647 −3.56090
\(628\) 15.3516 0.612596
\(629\) −12.9953 −0.518157
\(630\) 27.3885 1.09118
\(631\) 10.2808 0.409272 0.204636 0.978838i \(-0.434399\pi\)
0.204636 + 0.978838i \(0.434399\pi\)
\(632\) 16.4815 0.655599
\(633\) −19.9942 −0.794700
\(634\) −3.26125 −0.129521
\(635\) −1.98310 −0.0786969
\(636\) −2.42938 −0.0963313
\(637\) −5.96751 −0.236441
\(638\) −39.9010 −1.57970
\(639\) −101.910 −4.03148
\(640\) 10.9289 0.432002
\(641\) 47.3547 1.87040 0.935199 0.354123i \(-0.115221\pi\)
0.935199 + 0.354123i \(0.115221\pi\)
\(642\) −77.5711 −3.06149
\(643\) −27.0838 −1.06808 −0.534040 0.845459i \(-0.679327\pi\)
−0.534040 + 0.845459i \(0.679327\pi\)
\(644\) 5.01643 0.197675
\(645\) 12.8835 0.507289
\(646\) −19.6843 −0.774470
\(647\) −1.69051 −0.0664609 −0.0332304 0.999448i \(-0.510580\pi\)
−0.0332304 + 0.999448i \(0.510580\pi\)
\(648\) 40.8943 1.60648
\(649\) 41.7853 1.64022
\(650\) −3.53670 −0.138721
\(651\) −19.0786 −0.747748
\(652\) −19.0739 −0.746993
\(653\) −19.3044 −0.755440 −0.377720 0.925920i \(-0.623292\pi\)
−0.377720 + 0.925920i \(0.623292\pi\)
\(654\) 63.9378 2.50016
\(655\) −20.7594 −0.811139
\(656\) −42.7913 −1.67072
\(657\) 5.14659 0.200788
\(658\) −21.2455 −0.828238
\(659\) −15.3639 −0.598494 −0.299247 0.954176i \(-0.596735\pi\)
−0.299247 + 0.954176i \(0.596735\pi\)
\(660\) −20.0552 −0.780646
\(661\) −22.5171 −0.875815 −0.437908 0.899020i \(-0.644280\pi\)
−0.437908 + 0.899020i \(0.644280\pi\)
\(662\) −15.4446 −0.600273
\(663\) 14.0472 0.545549
\(664\) 2.19707 0.0852628
\(665\) 10.2804 0.398658
\(666\) −82.5010 −3.19685
\(667\) −9.18859 −0.355784
\(668\) 3.43548 0.132923
\(669\) −21.3700 −0.826212
\(670\) 2.97908 0.115092
\(671\) −22.7136 −0.876850
\(672\) −38.2279 −1.47467
\(673\) 33.7034 1.29917 0.649585 0.760289i \(-0.274943\pi\)
0.649585 + 0.760289i \(0.274943\pi\)
\(674\) −7.57129 −0.291635
\(675\) −15.3992 −0.592715
\(676\) −10.4441 −0.401695
\(677\) −4.38534 −0.168542 −0.0842711 0.996443i \(-0.526856\pi\)
−0.0842711 + 0.996443i \(0.526856\pi\)
\(678\) −72.5287 −2.78545
\(679\) 21.6212 0.829745
\(680\) 3.23397 0.124017
\(681\) −62.6450 −2.40056
\(682\) 27.4563 1.05136
\(683\) 27.9445 1.06927 0.534633 0.845084i \(-0.320450\pi\)
0.534633 + 0.845084i \(0.320450\pi\)
\(684\) −45.7679 −1.74998
\(685\) −15.7003 −0.599876
\(686\) 35.5313 1.35659
\(687\) −62.4645 −2.38317
\(688\) −19.5917 −0.746928
\(689\) 1.27893 0.0487233
\(690\) −12.6102 −0.480063
\(691\) −5.41290 −0.205916 −0.102958 0.994686i \(-0.532831\pi\)
−0.102958 + 0.994686i \(0.532831\pi\)
\(692\) 3.98840 0.151616
\(693\) −81.7612 −3.10585
\(694\) 27.3907 1.03974
\(695\) 16.8238 0.638165
\(696\) 20.7839 0.787813
\(697\) −18.5449 −0.702439
\(698\) 53.1017 2.00993
\(699\) −60.6257 −2.29308
\(700\) 2.31230 0.0873967
\(701\) −8.97974 −0.339160 −0.169580 0.985516i \(-0.554241\pi\)
−0.169580 + 0.985516i \(0.554241\pi\)
\(702\) 54.4623 2.05555
\(703\) −30.9672 −1.16795
\(704\) 2.24051 0.0844425
\(705\) 19.5598 0.736665
\(706\) 33.4932 1.26053
\(707\) −18.3962 −0.691861
\(708\) 29.7979 1.11987
\(709\) −22.4010 −0.841286 −0.420643 0.907226i \(-0.638196\pi\)
−0.420643 + 0.907226i \(0.638196\pi\)
\(710\) −23.4922 −0.881645
\(711\) 84.6900 3.17612
\(712\) 6.72290 0.251951
\(713\) 6.32277 0.236790
\(714\) −25.0766 −0.938468
\(715\) 10.5579 0.394842
\(716\) −20.2746 −0.757697
\(717\) 89.4344 3.33999
\(718\) 36.1665 1.34972
\(719\) 29.8562 1.11345 0.556724 0.830697i \(-0.312058\pi\)
0.556724 + 0.830697i \(0.312058\pi\)
\(720\) 38.3444 1.42901
\(721\) 8.83859 0.329166
\(722\) −13.1543 −0.489551
\(723\) 24.9316 0.927216
\(724\) −4.39958 −0.163509
\(725\) −4.23544 −0.157300
\(726\) 99.5307 3.69393
\(727\) −8.59321 −0.318705 −0.159352 0.987222i \(-0.550941\pi\)
−0.159352 + 0.987222i \(0.550941\pi\)
\(728\) 5.97343 0.221390
\(729\) 58.9745 2.18424
\(730\) 1.18639 0.0439103
\(731\) −8.49067 −0.314039
\(732\) −16.1975 −0.598677
\(733\) −52.2592 −1.93024 −0.965119 0.261812i \(-0.915680\pi\)
−0.965119 + 0.261812i \(0.915680\pi\)
\(734\) −13.8868 −0.512572
\(735\) −9.80772 −0.361763
\(736\) 12.6690 0.466985
\(737\) −8.89326 −0.327588
\(738\) −117.733 −4.33380
\(739\) −51.3512 −1.88898 −0.944492 0.328534i \(-0.893445\pi\)
−0.944492 + 0.328534i \(0.893445\pi\)
\(740\) −6.96522 −0.256047
\(741\) 33.4738 1.22969
\(742\) −2.28310 −0.0838153
\(743\) −13.9480 −0.511704 −0.255852 0.966716i \(-0.582356\pi\)
−0.255852 + 0.966716i \(0.582356\pi\)
\(744\) −14.3016 −0.524324
\(745\) −10.9931 −0.402755
\(746\) 30.1188 1.10273
\(747\) 11.2896 0.413065
\(748\) 13.2170 0.483261
\(749\) −26.6991 −0.975564
\(750\) −5.81263 −0.212247
\(751\) 11.9693 0.436764 0.218382 0.975863i \(-0.429922\pi\)
0.218382 + 0.975863i \(0.429922\pi\)
\(752\) −29.7442 −1.08466
\(753\) −82.5575 −3.00856
\(754\) 14.9795 0.545520
\(755\) 13.5460 0.492990
\(756\) −35.6075 −1.29503
\(757\) 14.6995 0.534262 0.267131 0.963660i \(-0.413924\pi\)
0.267131 + 0.963660i \(0.413924\pi\)
\(758\) −59.0897 −2.14623
\(759\) 37.6446 1.36641
\(760\) 7.70640 0.279540
\(761\) 47.6939 1.72890 0.864452 0.502716i \(-0.167666\pi\)
0.864452 + 0.502716i \(0.167666\pi\)
\(762\) 11.5270 0.417580
\(763\) 22.0067 0.796695
\(764\) 5.38902 0.194968
\(765\) 16.6177 0.600815
\(766\) 31.2598 1.12946
\(767\) −15.6869 −0.566419
\(768\) −66.2904 −2.39205
\(769\) −5.49025 −0.197984 −0.0989918 0.995088i \(-0.531562\pi\)
−0.0989918 + 0.995088i \(0.531562\pi\)
\(770\) −18.8476 −0.679219
\(771\) 84.9914 3.06089
\(772\) −31.3384 −1.12789
\(773\) −7.29402 −0.262348 −0.131174 0.991359i \(-0.541875\pi\)
−0.131174 + 0.991359i \(0.541875\pi\)
\(774\) −53.9032 −1.93751
\(775\) 2.91445 0.104690
\(776\) 16.2076 0.581820
\(777\) −39.4503 −1.41527
\(778\) 43.1700 1.54772
\(779\) −44.1916 −1.58333
\(780\) 7.52902 0.269582
\(781\) 70.1297 2.50944
\(782\) 8.31056 0.297185
\(783\) 65.2223 2.33086
\(784\) 14.9144 0.532657
\(785\) −13.2825 −0.474072
\(786\) 120.667 4.30405
\(787\) 54.5469 1.94439 0.972194 0.234178i \(-0.0752397\pi\)
0.972194 + 0.234178i \(0.0752397\pi\)
\(788\) −8.74331 −0.311467
\(789\) 17.2528 0.614216
\(790\) 19.5227 0.694587
\(791\) −24.9636 −0.887603
\(792\) −61.2897 −2.17783
\(793\) 8.52705 0.302805
\(794\) 12.1600 0.431542
\(795\) 2.10195 0.0745483
\(796\) 16.0259 0.568024
\(797\) −36.7033 −1.30010 −0.650049 0.759893i \(-0.725252\pi\)
−0.650049 + 0.759893i \(0.725252\pi\)
\(798\) −59.7563 −2.11535
\(799\) −12.8905 −0.456035
\(800\) 5.83971 0.206465
\(801\) 34.5455 1.22061
\(802\) 1.77645 0.0627287
\(803\) −3.54166 −0.124982
\(804\) −6.34195 −0.223663
\(805\) −4.34030 −0.152976
\(806\) −10.3075 −0.363067
\(807\) 56.9506 2.00475
\(808\) −13.7901 −0.485135
\(809\) −6.11934 −0.215144 −0.107572 0.994197i \(-0.534308\pi\)
−0.107572 + 0.994197i \(0.534308\pi\)
\(810\) 48.4403 1.70202
\(811\) −8.53782 −0.299803 −0.149902 0.988701i \(-0.547896\pi\)
−0.149902 + 0.988701i \(0.547896\pi\)
\(812\) −9.79360 −0.343688
\(813\) 93.6719 3.28522
\(814\) 56.7735 1.98991
\(815\) 16.5031 0.578079
\(816\) −35.1077 −1.22902
\(817\) −20.2329 −0.707858
\(818\) 24.5469 0.858262
\(819\) 30.6944 1.07255
\(820\) −9.93969 −0.347109
\(821\) −12.9579 −0.452233 −0.226117 0.974100i \(-0.572603\pi\)
−0.226117 + 0.974100i \(0.572603\pi\)
\(822\) 91.2598 3.18305
\(823\) −43.5865 −1.51933 −0.759665 0.650315i \(-0.774637\pi\)
−0.759665 + 0.650315i \(0.774637\pi\)
\(824\) 6.62557 0.230813
\(825\) 17.3521 0.604122
\(826\) 28.0036 0.974371
\(827\) −23.7283 −0.825115 −0.412557 0.910932i \(-0.635364\pi\)
−0.412557 + 0.910932i \(0.635364\pi\)
\(828\) 19.3228 0.671514
\(829\) −45.9721 −1.59668 −0.798338 0.602209i \(-0.794287\pi\)
−0.798338 + 0.602209i \(0.794287\pi\)
\(830\) 2.60248 0.0903333
\(831\) −46.5057 −1.61327
\(832\) −0.841124 −0.0291607
\(833\) 6.46361 0.223951
\(834\) −97.7908 −3.38622
\(835\) −2.97244 −0.102865
\(836\) 31.4955 1.08929
\(837\) −44.8802 −1.55129
\(838\) −36.2224 −1.25128
\(839\) −40.4736 −1.39730 −0.698652 0.715462i \(-0.746216\pi\)
−0.698652 + 0.715462i \(0.746216\pi\)
\(840\) 9.81746 0.338734
\(841\) −11.0611 −0.381416
\(842\) −37.3331 −1.28658
\(843\) 62.1981 2.14222
\(844\) 7.06252 0.243102
\(845\) 9.03641 0.310862
\(846\) −81.8358 −2.81357
\(847\) 34.2574 1.17710
\(848\) −3.19639 −0.109764
\(849\) −0.167868 −0.00576121
\(850\) 3.83071 0.131392
\(851\) 13.0741 0.448174
\(852\) 50.0108 1.71334
\(853\) 47.1795 1.61539 0.807697 0.589597i \(-0.200714\pi\)
0.807697 + 0.589597i \(0.200714\pi\)
\(854\) −15.2222 −0.520893
\(855\) 39.5992 1.35427
\(856\) −20.0141 −0.684069
\(857\) −25.4135 −0.868110 −0.434055 0.900886i \(-0.642918\pi\)
−0.434055 + 0.900886i \(0.642918\pi\)
\(858\) −61.3690 −2.09510
\(859\) −28.2965 −0.965464 −0.482732 0.875768i \(-0.660356\pi\)
−0.482732 + 0.875768i \(0.660356\pi\)
\(860\) −4.55083 −0.155182
\(861\) −56.2973 −1.91861
\(862\) 50.9233 1.73445
\(863\) 31.1687 1.06100 0.530498 0.847686i \(-0.322005\pi\)
0.530498 + 0.847686i \(0.322005\pi\)
\(864\) −89.9268 −3.05937
\(865\) −3.45083 −0.117332
\(866\) −64.2349 −2.18279
\(867\) 40.4098 1.37239
\(868\) 6.73908 0.228739
\(869\) −58.2799 −1.97701
\(870\) 24.6190 0.834664
\(871\) 3.33867 0.113126
\(872\) 16.4966 0.558646
\(873\) 83.2827 2.81869
\(874\) 19.8037 0.669868
\(875\) −2.00064 −0.0676341
\(876\) −2.52562 −0.0853328
\(877\) 6.10598 0.206184 0.103092 0.994672i \(-0.467126\pi\)
0.103092 + 0.994672i \(0.467126\pi\)
\(878\) −66.5136 −2.24473
\(879\) 38.8208 1.30939
\(880\) −26.3870 −0.889504
\(881\) 48.6591 1.63937 0.819684 0.572816i \(-0.194149\pi\)
0.819684 + 0.572816i \(0.194149\pi\)
\(882\) 41.0343 1.38170
\(883\) 50.2633 1.69149 0.845747 0.533584i \(-0.179155\pi\)
0.845747 + 0.533584i \(0.179155\pi\)
\(884\) −4.96187 −0.166886
\(885\) −25.7817 −0.866641
\(886\) 36.4712 1.22527
\(887\) −6.15197 −0.206563 −0.103281 0.994652i \(-0.532934\pi\)
−0.103281 + 0.994652i \(0.532934\pi\)
\(888\) −29.5726 −0.992393
\(889\) 3.96747 0.133065
\(890\) 7.96342 0.266935
\(891\) −144.606 −4.84448
\(892\) 7.54849 0.252742
\(893\) −30.7175 −1.02792
\(894\) 63.8986 2.13709
\(895\) 17.5419 0.586362
\(896\) −21.8648 −0.730452
\(897\) −14.1324 −0.471865
\(898\) −1.41660 −0.0472725
\(899\) −12.3440 −0.411695
\(900\) 8.90676 0.296892
\(901\) −1.38525 −0.0461494
\(902\) 81.0184 2.69762
\(903\) −25.7754 −0.857751
\(904\) −18.7132 −0.622391
\(905\) 3.80660 0.126536
\(906\) −78.7379 −2.61589
\(907\) −33.7824 −1.12173 −0.560863 0.827908i \(-0.689531\pi\)
−0.560863 + 0.827908i \(0.689531\pi\)
\(908\) 22.1280 0.734342
\(909\) −70.8605 −2.35029
\(910\) 7.07567 0.234556
\(911\) −22.4517 −0.743859 −0.371930 0.928261i \(-0.621304\pi\)
−0.371930 + 0.928261i \(0.621304\pi\)
\(912\) −83.6600 −2.77026
\(913\) −7.76901 −0.257117
\(914\) −67.2052 −2.22295
\(915\) 14.0144 0.463301
\(916\) 22.0642 0.729022
\(917\) 41.5322 1.37152
\(918\) −58.9899 −1.94696
\(919\) −40.9486 −1.35077 −0.675385 0.737466i \(-0.736022\pi\)
−0.675385 + 0.737466i \(0.736022\pi\)
\(920\) −3.25357 −0.107267
\(921\) 72.3235 2.38314
\(922\) −7.99856 −0.263419
\(923\) −26.3278 −0.866590
\(924\) 40.1232 1.31996
\(925\) 6.02644 0.198148
\(926\) 32.3809 1.06410
\(927\) 34.0454 1.11820
\(928\) −24.7337 −0.811924
\(929\) −25.1507 −0.825167 −0.412583 0.910920i \(-0.635373\pi\)
−0.412583 + 0.910920i \(0.635373\pi\)
\(930\) −16.9406 −0.555505
\(931\) 15.4025 0.504795
\(932\) 21.4147 0.701462
\(933\) 86.2216 2.82277
\(934\) −20.7287 −0.678263
\(935\) −11.4356 −0.373984
\(936\) 23.0091 0.752076
\(937\) 11.6143 0.379422 0.189711 0.981840i \(-0.439245\pi\)
0.189711 + 0.981840i \(0.439245\pi\)
\(938\) −5.96008 −0.194603
\(939\) 75.0513 2.44921
\(940\) −6.90907 −0.225349
\(941\) −9.80807 −0.319734 −0.159867 0.987139i \(-0.551107\pi\)
−0.159867 + 0.987139i \(0.551107\pi\)
\(942\) 77.2062 2.51551
\(943\) 18.6573 0.607566
\(944\) 39.2056 1.27603
\(945\) 30.8083 1.00219
\(946\) 37.0938 1.20602
\(947\) 26.9200 0.874783 0.437391 0.899271i \(-0.355902\pi\)
0.437391 + 0.899271i \(0.355902\pi\)
\(948\) −41.5605 −1.34982
\(949\) 1.32959 0.0431604
\(950\) 9.12840 0.296164
\(951\) −6.00690 −0.194787
\(952\) −6.47002 −0.209695
\(953\) −10.8377 −0.351067 −0.175534 0.984473i \(-0.556165\pi\)
−0.175534 + 0.984473i \(0.556165\pi\)
\(954\) −8.79429 −0.284726
\(955\) −4.66268 −0.150881
\(956\) −31.5907 −1.02172
\(957\) −73.4937 −2.37571
\(958\) 1.50392 0.0485894
\(959\) 31.4106 1.01430
\(960\) −1.38240 −0.0446169
\(961\) −22.5060 −0.725999
\(962\) −21.3137 −0.687180
\(963\) −102.842 −3.31405
\(964\) −8.80653 −0.283639
\(965\) 27.1145 0.872848
\(966\) 25.2286 0.811716
\(967\) 47.0076 1.51166 0.755831 0.654767i \(-0.227233\pi\)
0.755831 + 0.654767i \(0.227233\pi\)
\(968\) 25.6799 0.825385
\(969\) −36.2566 −1.16473
\(970\) 19.1983 0.616421
\(971\) 1.85484 0.0595247 0.0297623 0.999557i \(-0.490525\pi\)
0.0297623 + 0.999557i \(0.490525\pi\)
\(972\) −49.7269 −1.59499
\(973\) −33.6585 −1.07904
\(974\) 40.9392 1.31178
\(975\) −6.51424 −0.208623
\(976\) −21.3114 −0.682161
\(977\) 26.1144 0.835473 0.417736 0.908568i \(-0.362824\pi\)
0.417736 + 0.908568i \(0.362824\pi\)
\(978\) −95.9265 −3.06739
\(979\) −23.7727 −0.759779
\(980\) 3.46436 0.110665
\(981\) 84.7676 2.70642
\(982\) 44.3340 1.41476
\(983\) 24.7248 0.788599 0.394300 0.918982i \(-0.370987\pi\)
0.394300 + 0.918982i \(0.370987\pi\)
\(984\) −42.2015 −1.34533
\(985\) 7.56487 0.241037
\(986\) −16.2247 −0.516701
\(987\) −39.1322 −1.24559
\(988\) −11.8239 −0.376168
\(989\) 8.54213 0.271624
\(990\) −72.5990 −2.30735
\(991\) −47.3321 −1.50355 −0.751777 0.659418i \(-0.770803\pi\)
−0.751777 + 0.659418i \(0.770803\pi\)
\(992\) 17.0195 0.540371
\(993\) −28.4475 −0.902754
\(994\) 46.9995 1.49073
\(995\) −13.8659 −0.439579
\(996\) −5.54023 −0.175549
\(997\) −44.5922 −1.41225 −0.706124 0.708088i \(-0.749558\pi\)
−0.706124 + 0.708088i \(0.749558\pi\)
\(998\) 19.0578 0.603264
\(999\) −92.8023 −2.93613
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 2005.2.a.e.1.7 29
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2005.2.a.e.1.7 29 1.1 even 1 trivial