Properties

Label 4017.2.a.g.1.11
Level $4017$
Weight $2$
Character 4017.1
Self dual yes
Analytic conductor $32.076$
Analytic rank $0$
Dimension $24$
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] = [4017,2,Mod(1,4017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4017, 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("4017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4017.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: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 4017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.389331 q^{2} -1.00000 q^{3} -1.84842 q^{4} +0.642702 q^{5} +0.389331 q^{6} -1.35418 q^{7} +1.49831 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.389331 q^{2} -1.00000 q^{3} -1.84842 q^{4} +0.642702 q^{5} +0.389331 q^{6} -1.35418 q^{7} +1.49831 q^{8} +1.00000 q^{9} -0.250224 q^{10} -3.00376 q^{11} +1.84842 q^{12} -1.00000 q^{13} +0.527226 q^{14} -0.642702 q^{15} +3.11350 q^{16} +3.71693 q^{17} -0.389331 q^{18} -2.28396 q^{19} -1.18798 q^{20} +1.35418 q^{21} +1.16946 q^{22} +1.06872 q^{23} -1.49831 q^{24} -4.58693 q^{25} +0.389331 q^{26} -1.00000 q^{27} +2.50310 q^{28} -5.70126 q^{29} +0.250224 q^{30} +7.17094 q^{31} -4.20881 q^{32} +3.00376 q^{33} -1.44712 q^{34} -0.870336 q^{35} -1.84842 q^{36} -0.297591 q^{37} +0.889218 q^{38} +1.00000 q^{39} +0.962967 q^{40} +2.02015 q^{41} -0.527226 q^{42} -2.05274 q^{43} +5.55222 q^{44} +0.642702 q^{45} -0.416088 q^{46} -10.0660 q^{47} -3.11350 q^{48} -5.16619 q^{49} +1.78584 q^{50} -3.71693 q^{51} +1.84842 q^{52} -10.1464 q^{53} +0.389331 q^{54} -1.93052 q^{55} -2.02899 q^{56} +2.28396 q^{57} +2.21968 q^{58} +9.99931 q^{59} +1.18798 q^{60} +3.25912 q^{61} -2.79187 q^{62} -1.35418 q^{63} -4.58839 q^{64} -0.642702 q^{65} -1.16946 q^{66} +1.23432 q^{67} -6.87046 q^{68} -1.06872 q^{69} +0.338849 q^{70} -1.30716 q^{71} +1.49831 q^{72} +10.2716 q^{73} +0.115861 q^{74} +4.58693 q^{75} +4.22173 q^{76} +4.06765 q^{77} -0.389331 q^{78} -1.65729 q^{79} +2.00105 q^{80} +1.00000 q^{81} -0.786507 q^{82} +12.8074 q^{83} -2.50310 q^{84} +2.38888 q^{85} +0.799197 q^{86} +5.70126 q^{87} -4.50057 q^{88} -11.2589 q^{89} -0.250224 q^{90} +1.35418 q^{91} -1.97545 q^{92} -7.17094 q^{93} +3.91902 q^{94} -1.46791 q^{95} +4.20881 q^{96} -4.32334 q^{97} +2.01136 q^{98} -3.00376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.389331 −0.275299 −0.137649 0.990481i \(-0.543955\pi\)
−0.137649 + 0.990481i \(0.543955\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.84842 −0.924211
\(5\) 0.642702 0.287425 0.143712 0.989619i \(-0.454096\pi\)
0.143712 + 0.989619i \(0.454096\pi\)
\(6\) 0.389331 0.158944
\(7\) −1.35418 −0.511833 −0.255917 0.966699i \(-0.582377\pi\)
−0.255917 + 0.966699i \(0.582377\pi\)
\(8\) 1.49831 0.529733
\(9\) 1.00000 0.333333
\(10\) −0.250224 −0.0791278
\(11\) −3.00376 −0.905669 −0.452835 0.891595i \(-0.649587\pi\)
−0.452835 + 0.891595i \(0.649587\pi\)
\(12\) 1.84842 0.533593
\(13\) −1.00000 −0.277350
\(14\) 0.527226 0.140907
\(15\) −0.642702 −0.165945
\(16\) 3.11350 0.778376
\(17\) 3.71693 0.901489 0.450745 0.892653i \(-0.351159\pi\)
0.450745 + 0.892653i \(0.351159\pi\)
\(18\) −0.389331 −0.0917663
\(19\) −2.28396 −0.523977 −0.261989 0.965071i \(-0.584378\pi\)
−0.261989 + 0.965071i \(0.584378\pi\)
\(20\) −1.18798 −0.265641
\(21\) 1.35418 0.295507
\(22\) 1.16946 0.249330
\(23\) 1.06872 0.222844 0.111422 0.993773i \(-0.464459\pi\)
0.111422 + 0.993773i \(0.464459\pi\)
\(24\) −1.49831 −0.305841
\(25\) −4.58693 −0.917387
\(26\) 0.389331 0.0763541
\(27\) −1.00000 −0.192450
\(28\) 2.50310 0.473042
\(29\) −5.70126 −1.05870 −0.529349 0.848404i \(-0.677564\pi\)
−0.529349 + 0.848404i \(0.677564\pi\)
\(30\) 0.250224 0.0456844
\(31\) 7.17094 1.28794 0.643969 0.765051i \(-0.277286\pi\)
0.643969 + 0.765051i \(0.277286\pi\)
\(32\) −4.20881 −0.744019
\(33\) 3.00376 0.522888
\(34\) −1.44712 −0.248179
\(35\) −0.870336 −0.147114
\(36\) −1.84842 −0.308070
\(37\) −0.297591 −0.0489236 −0.0244618 0.999701i \(-0.507787\pi\)
−0.0244618 + 0.999701i \(0.507787\pi\)
\(38\) 0.889218 0.144250
\(39\) 1.00000 0.160128
\(40\) 0.962967 0.152258
\(41\) 2.02015 0.315494 0.157747 0.987480i \(-0.449577\pi\)
0.157747 + 0.987480i \(0.449577\pi\)
\(42\) −0.527226 −0.0813528
\(43\) −2.05274 −0.313040 −0.156520 0.987675i \(-0.550028\pi\)
−0.156520 + 0.987675i \(0.550028\pi\)
\(44\) 5.55222 0.837029
\(45\) 0.642702 0.0958083
\(46\) −0.416088 −0.0613488
\(47\) −10.0660 −1.46828 −0.734140 0.678998i \(-0.762415\pi\)
−0.734140 + 0.678998i \(0.762415\pi\)
\(48\) −3.11350 −0.449395
\(49\) −5.16619 −0.738027
\(50\) 1.78584 0.252556
\(51\) −3.71693 −0.520475
\(52\) 1.84842 0.256330
\(53\) −10.1464 −1.39372 −0.696859 0.717208i \(-0.745420\pi\)
−0.696859 + 0.717208i \(0.745420\pi\)
\(54\) 0.389331 0.0529813
\(55\) −1.93052 −0.260312
\(56\) −2.02899 −0.271135
\(57\) 2.28396 0.302518
\(58\) 2.21968 0.291458
\(59\) 9.99931 1.30180 0.650900 0.759164i \(-0.274392\pi\)
0.650900 + 0.759164i \(0.274392\pi\)
\(60\) 1.18798 0.153368
\(61\) 3.25912 0.417287 0.208643 0.977992i \(-0.433095\pi\)
0.208643 + 0.977992i \(0.433095\pi\)
\(62\) −2.79187 −0.354568
\(63\) −1.35418 −0.170611
\(64\) −4.58839 −0.573548
\(65\) −0.642702 −0.0797173
\(66\) −1.16946 −0.143951
\(67\) 1.23432 0.150796 0.0753981 0.997154i \(-0.475977\pi\)
0.0753981 + 0.997154i \(0.475977\pi\)
\(68\) −6.87046 −0.833166
\(69\) −1.06872 −0.128659
\(70\) 0.338849 0.0405002
\(71\) −1.30716 −0.155131 −0.0775656 0.996987i \(-0.524715\pi\)
−0.0775656 + 0.996987i \(0.524715\pi\)
\(72\) 1.49831 0.176578
\(73\) 10.2716 1.20219 0.601097 0.799176i \(-0.294730\pi\)
0.601097 + 0.799176i \(0.294730\pi\)
\(74\) 0.115861 0.0134686
\(75\) 4.58693 0.529654
\(76\) 4.22173 0.484265
\(77\) 4.06765 0.463552
\(78\) −0.389331 −0.0440831
\(79\) −1.65729 −0.186460 −0.0932299 0.995645i \(-0.529719\pi\)
−0.0932299 + 0.995645i \(0.529719\pi\)
\(80\) 2.00105 0.223725
\(81\) 1.00000 0.111111
\(82\) −0.786507 −0.0868552
\(83\) 12.8074 1.40580 0.702900 0.711289i \(-0.251888\pi\)
0.702900 + 0.711289i \(0.251888\pi\)
\(84\) −2.50310 −0.273111
\(85\) 2.38888 0.259110
\(86\) 0.799197 0.0861796
\(87\) 5.70126 0.611239
\(88\) −4.50057 −0.479763
\(89\) −11.2589 −1.19344 −0.596720 0.802450i \(-0.703529\pi\)
−0.596720 + 0.802450i \(0.703529\pi\)
\(90\) −0.250224 −0.0263759
\(91\) 1.35418 0.141957
\(92\) −1.97545 −0.205955
\(93\) −7.17094 −0.743592
\(94\) 3.91902 0.404216
\(95\) −1.46791 −0.150604
\(96\) 4.20881 0.429559
\(97\) −4.32334 −0.438969 −0.219484 0.975616i \(-0.570437\pi\)
−0.219484 + 0.975616i \(0.570437\pi\)
\(98\) 2.01136 0.203178
\(99\) −3.00376 −0.301890
\(100\) 8.47859 0.847859
\(101\) −8.69672 −0.865356 −0.432678 0.901549i \(-0.642431\pi\)
−0.432678 + 0.901549i \(0.642431\pi\)
\(102\) 1.44712 0.143286
\(103\) 1.00000 0.0985329
\(104\) −1.49831 −0.146921
\(105\) 0.870336 0.0849361
\(106\) 3.95032 0.383689
\(107\) −0.866480 −0.0837658 −0.0418829 0.999123i \(-0.513336\pi\)
−0.0418829 + 0.999123i \(0.513336\pi\)
\(108\) 1.84842 0.177864
\(109\) −10.7007 −1.02495 −0.512473 0.858704i \(-0.671270\pi\)
−0.512473 + 0.858704i \(0.671270\pi\)
\(110\) 0.751614 0.0716636
\(111\) 0.297591 0.0282461
\(112\) −4.21626 −0.398399
\(113\) 8.80892 0.828674 0.414337 0.910124i \(-0.364014\pi\)
0.414337 + 0.910124i \(0.364014\pi\)
\(114\) −0.889218 −0.0832829
\(115\) 0.686871 0.0640510
\(116\) 10.5383 0.978459
\(117\) −1.00000 −0.0924500
\(118\) −3.89304 −0.358384
\(119\) −5.03341 −0.461412
\(120\) −0.962967 −0.0879065
\(121\) −1.97740 −0.179764
\(122\) −1.26888 −0.114879
\(123\) −2.02015 −0.182151
\(124\) −13.2549 −1.19033
\(125\) −6.16154 −0.551105
\(126\) 0.527226 0.0469690
\(127\) 15.7150 1.39449 0.697243 0.716835i \(-0.254410\pi\)
0.697243 + 0.716835i \(0.254410\pi\)
\(128\) 10.2040 0.901916
\(129\) 2.05274 0.180734
\(130\) 0.250224 0.0219461
\(131\) 11.2112 0.979523 0.489762 0.871856i \(-0.337084\pi\)
0.489762 + 0.871856i \(0.337084\pi\)
\(132\) −5.55222 −0.483259
\(133\) 3.09291 0.268189
\(134\) −0.480560 −0.0415140
\(135\) −0.642702 −0.0553150
\(136\) 5.56912 0.477548
\(137\) −13.9300 −1.19012 −0.595058 0.803682i \(-0.702871\pi\)
−0.595058 + 0.803682i \(0.702871\pi\)
\(138\) 0.416088 0.0354197
\(139\) 4.30921 0.365502 0.182751 0.983159i \(-0.441500\pi\)
0.182751 + 0.983159i \(0.441500\pi\)
\(140\) 1.60875 0.135964
\(141\) 10.0660 0.847712
\(142\) 0.508918 0.0427074
\(143\) 3.00376 0.251187
\(144\) 3.11350 0.259459
\(145\) −3.66421 −0.304296
\(146\) −3.99904 −0.330963
\(147\) 5.16619 0.426100
\(148\) 0.550073 0.0452157
\(149\) 20.3044 1.66340 0.831699 0.555227i \(-0.187369\pi\)
0.831699 + 0.555227i \(0.187369\pi\)
\(150\) −1.78584 −0.145813
\(151\) 14.1623 1.15251 0.576254 0.817270i \(-0.304514\pi\)
0.576254 + 0.817270i \(0.304514\pi\)
\(152\) −3.42209 −0.277568
\(153\) 3.71693 0.300496
\(154\) −1.58366 −0.127615
\(155\) 4.60877 0.370186
\(156\) −1.84842 −0.147992
\(157\) 19.3082 1.54096 0.770481 0.637462i \(-0.220016\pi\)
0.770481 + 0.637462i \(0.220016\pi\)
\(158\) 0.645235 0.0513322
\(159\) 10.1464 0.804664
\(160\) −2.70501 −0.213850
\(161\) −1.44725 −0.114059
\(162\) −0.389331 −0.0305888
\(163\) −6.41726 −0.502638 −0.251319 0.967904i \(-0.580864\pi\)
−0.251319 + 0.967904i \(0.580864\pi\)
\(164\) −3.73409 −0.291583
\(165\) 1.93052 0.150291
\(166\) −4.98634 −0.387015
\(167\) −0.717268 −0.0555039 −0.0277519 0.999615i \(-0.508835\pi\)
−0.0277519 + 0.999615i \(0.508835\pi\)
\(168\) 2.02899 0.156540
\(169\) 1.00000 0.0769231
\(170\) −0.930066 −0.0713328
\(171\) −2.28396 −0.174659
\(172\) 3.79433 0.289315
\(173\) 19.2602 1.46433 0.732164 0.681129i \(-0.238511\pi\)
0.732164 + 0.681129i \(0.238511\pi\)
\(174\) −2.21968 −0.168273
\(175\) 6.21155 0.469549
\(176\) −9.35223 −0.704951
\(177\) −9.99931 −0.751594
\(178\) 4.38343 0.328552
\(179\) 4.43432 0.331436 0.165718 0.986173i \(-0.447006\pi\)
0.165718 + 0.986173i \(0.447006\pi\)
\(180\) −1.18798 −0.0885471
\(181\) −9.60571 −0.713987 −0.356993 0.934107i \(-0.616198\pi\)
−0.356993 + 0.934107i \(0.616198\pi\)
\(182\) −0.527226 −0.0390806
\(183\) −3.25912 −0.240921
\(184\) 1.60128 0.118048
\(185\) −0.191262 −0.0140619
\(186\) 2.79187 0.204710
\(187\) −11.1648 −0.816451
\(188\) 18.6063 1.35700
\(189\) 1.35418 0.0985024
\(190\) 0.571502 0.0414611
\(191\) −0.0595551 −0.00430925 −0.00215463 0.999998i \(-0.500686\pi\)
−0.00215463 + 0.999998i \(0.500686\pi\)
\(192\) 4.58839 0.331138
\(193\) −18.3402 −1.32016 −0.660079 0.751196i \(-0.729477\pi\)
−0.660079 + 0.751196i \(0.729477\pi\)
\(194\) 1.68321 0.120848
\(195\) 0.642702 0.0460248
\(196\) 9.54929 0.682092
\(197\) −2.20431 −0.157051 −0.0785253 0.996912i \(-0.525021\pi\)
−0.0785253 + 0.996912i \(0.525021\pi\)
\(198\) 1.16946 0.0831099
\(199\) 23.4036 1.65904 0.829519 0.558478i \(-0.188615\pi\)
0.829519 + 0.558478i \(0.188615\pi\)
\(200\) −6.87265 −0.485970
\(201\) −1.23432 −0.0870623
\(202\) 3.38591 0.238231
\(203\) 7.72055 0.541877
\(204\) 6.87046 0.481028
\(205\) 1.29835 0.0906810
\(206\) −0.389331 −0.0271260
\(207\) 1.06872 0.0742814
\(208\) −3.11350 −0.215883
\(209\) 6.86049 0.474550
\(210\) −0.338849 −0.0233828
\(211\) −8.24603 −0.567680 −0.283840 0.958872i \(-0.591608\pi\)
−0.283840 + 0.958872i \(0.591608\pi\)
\(212\) 18.7549 1.28809
\(213\) 1.30716 0.0895650
\(214\) 0.337348 0.0230606
\(215\) −1.31930 −0.0899756
\(216\) −1.49831 −0.101947
\(217\) −9.71077 −0.659210
\(218\) 4.16613 0.282166
\(219\) −10.2716 −0.694087
\(220\) 3.56842 0.240583
\(221\) −3.71693 −0.250028
\(222\) −0.115861 −0.00777611
\(223\) 0.526175 0.0352353 0.0176177 0.999845i \(-0.494392\pi\)
0.0176177 + 0.999845i \(0.494392\pi\)
\(224\) 5.69950 0.380814
\(225\) −4.58693 −0.305796
\(226\) −3.42959 −0.228133
\(227\) 11.1873 0.742526 0.371263 0.928528i \(-0.378925\pi\)
0.371263 + 0.928528i \(0.378925\pi\)
\(228\) −4.22173 −0.279591
\(229\) −11.9515 −0.789780 −0.394890 0.918728i \(-0.629217\pi\)
−0.394890 + 0.918728i \(0.629217\pi\)
\(230\) −0.267420 −0.0176332
\(231\) −4.06765 −0.267632
\(232\) −8.54226 −0.560827
\(233\) −12.4646 −0.816582 −0.408291 0.912852i \(-0.633875\pi\)
−0.408291 + 0.912852i \(0.633875\pi\)
\(234\) 0.389331 0.0254514
\(235\) −6.46945 −0.422021
\(236\) −18.4829 −1.20314
\(237\) 1.65729 0.107653
\(238\) 1.95967 0.127026
\(239\) 14.8738 0.962109 0.481054 0.876691i \(-0.340254\pi\)
0.481054 + 0.876691i \(0.340254\pi\)
\(240\) −2.00105 −0.129167
\(241\) 21.4433 1.38128 0.690641 0.723198i \(-0.257329\pi\)
0.690641 + 0.723198i \(0.257329\pi\)
\(242\) 0.769863 0.0494887
\(243\) −1.00000 −0.0641500
\(244\) −6.02422 −0.385661
\(245\) −3.32032 −0.212127
\(246\) 0.786507 0.0501459
\(247\) 2.28396 0.145325
\(248\) 10.7443 0.682263
\(249\) −12.8074 −0.811639
\(250\) 2.39888 0.151719
\(251\) 19.2691 1.21625 0.608126 0.793840i \(-0.291921\pi\)
0.608126 + 0.793840i \(0.291921\pi\)
\(252\) 2.50310 0.157681
\(253\) −3.21019 −0.201823
\(254\) −6.11836 −0.383900
\(255\) −2.38888 −0.149598
\(256\) 5.20403 0.325252
\(257\) 10.4324 0.650758 0.325379 0.945584i \(-0.394508\pi\)
0.325379 + 0.945584i \(0.394508\pi\)
\(258\) −0.799197 −0.0497558
\(259\) 0.402993 0.0250408
\(260\) 1.18798 0.0736756
\(261\) −5.70126 −0.352899
\(262\) −4.36485 −0.269662
\(263\) −1.46328 −0.0902294 −0.0451147 0.998982i \(-0.514365\pi\)
−0.0451147 + 0.998982i \(0.514365\pi\)
\(264\) 4.50057 0.276991
\(265\) −6.52112 −0.400589
\(266\) −1.20417 −0.0738321
\(267\) 11.2589 0.689032
\(268\) −2.28154 −0.139367
\(269\) −3.88191 −0.236684 −0.118342 0.992973i \(-0.537758\pi\)
−0.118342 + 0.992973i \(0.537758\pi\)
\(270\) 0.250224 0.0152281
\(271\) 29.7812 1.80908 0.904541 0.426387i \(-0.140214\pi\)
0.904541 + 0.426387i \(0.140214\pi\)
\(272\) 11.5727 0.701697
\(273\) −1.35418 −0.0819589
\(274\) 5.42337 0.327638
\(275\) 13.7781 0.830849
\(276\) 1.97545 0.118908
\(277\) 6.18027 0.371336 0.185668 0.982613i \(-0.440555\pi\)
0.185668 + 0.982613i \(0.440555\pi\)
\(278\) −1.67771 −0.100622
\(279\) 7.17094 0.429313
\(280\) −1.30403 −0.0779310
\(281\) 16.3655 0.976286 0.488143 0.872764i \(-0.337674\pi\)
0.488143 + 0.872764i \(0.337674\pi\)
\(282\) −3.91902 −0.233374
\(283\) 1.26540 0.0752200 0.0376100 0.999292i \(-0.488026\pi\)
0.0376100 + 0.999292i \(0.488026\pi\)
\(284\) 2.41618 0.143374
\(285\) 1.46791 0.0869513
\(286\) −1.16946 −0.0691516
\(287\) −2.73565 −0.161481
\(288\) −4.20881 −0.248006
\(289\) −3.18440 −0.187317
\(290\) 1.42659 0.0837723
\(291\) 4.32334 0.253439
\(292\) −18.9862 −1.11108
\(293\) 22.0012 1.28532 0.642662 0.766150i \(-0.277830\pi\)
0.642662 + 0.766150i \(0.277830\pi\)
\(294\) −2.01136 −0.117305
\(295\) 6.42657 0.374170
\(296\) −0.445884 −0.0259165
\(297\) 3.00376 0.174296
\(298\) −7.90512 −0.457931
\(299\) −1.06872 −0.0618059
\(300\) −8.47859 −0.489511
\(301\) 2.77979 0.160224
\(302\) −5.51381 −0.317284
\(303\) 8.69672 0.499613
\(304\) −7.11113 −0.407851
\(305\) 2.09464 0.119939
\(306\) −1.44712 −0.0827263
\(307\) −6.06291 −0.346029 −0.173014 0.984919i \(-0.555351\pi\)
−0.173014 + 0.984919i \(0.555351\pi\)
\(308\) −7.51873 −0.428419
\(309\) −1.00000 −0.0568880
\(310\) −1.79434 −0.101912
\(311\) 21.4358 1.21551 0.607756 0.794123i \(-0.292070\pi\)
0.607756 + 0.794123i \(0.292070\pi\)
\(312\) 1.49831 0.0848251
\(313\) 22.0335 1.24541 0.622705 0.782457i \(-0.286034\pi\)
0.622705 + 0.782457i \(0.286034\pi\)
\(314\) −7.51729 −0.424225
\(315\) −0.870336 −0.0490379
\(316\) 3.06337 0.172328
\(317\) 5.82156 0.326971 0.163486 0.986546i \(-0.447726\pi\)
0.163486 + 0.986546i \(0.447726\pi\)
\(318\) −3.95032 −0.221523
\(319\) 17.1252 0.958829
\(320\) −2.94896 −0.164852
\(321\) 0.866480 0.0483622
\(322\) 0.563459 0.0314004
\(323\) −8.48934 −0.472360
\(324\) −1.84842 −0.102690
\(325\) 4.58693 0.254437
\(326\) 2.49844 0.138376
\(327\) 10.7007 0.591752
\(328\) 3.02681 0.167128
\(329\) 13.6313 0.751515
\(330\) −0.751614 −0.0413750
\(331\) −9.74349 −0.535551 −0.267775 0.963481i \(-0.586289\pi\)
−0.267775 + 0.963481i \(0.586289\pi\)
\(332\) −23.6736 −1.29925
\(333\) −0.297591 −0.0163079
\(334\) 0.279255 0.0152802
\(335\) 0.793300 0.0433426
\(336\) 4.21626 0.230016
\(337\) 31.4773 1.71468 0.857339 0.514752i \(-0.172116\pi\)
0.857339 + 0.514752i \(0.172116\pi\)
\(338\) −0.389331 −0.0211768
\(339\) −8.80892 −0.478435
\(340\) −4.41566 −0.239473
\(341\) −21.5398 −1.16645
\(342\) 0.889218 0.0480834
\(343\) 16.4753 0.889580
\(344\) −3.07565 −0.165828
\(345\) −0.686871 −0.0369799
\(346\) −7.49860 −0.403127
\(347\) 4.48252 0.240634 0.120317 0.992736i \(-0.461609\pi\)
0.120317 + 0.992736i \(0.461609\pi\)
\(348\) −10.5383 −0.564914
\(349\) 11.1704 0.597935 0.298968 0.954263i \(-0.403358\pi\)
0.298968 + 0.954263i \(0.403358\pi\)
\(350\) −2.41835 −0.129266
\(351\) 1.00000 0.0533761
\(352\) 12.6423 0.673835
\(353\) 28.2802 1.50520 0.752602 0.658476i \(-0.228798\pi\)
0.752602 + 0.658476i \(0.228798\pi\)
\(354\) 3.89304 0.206913
\(355\) −0.840113 −0.0445886
\(356\) 20.8112 1.10299
\(357\) 5.03341 0.266396
\(358\) −1.72642 −0.0912441
\(359\) 12.2438 0.646201 0.323100 0.946365i \(-0.395275\pi\)
0.323100 + 0.946365i \(0.395275\pi\)
\(360\) 0.962967 0.0507528
\(361\) −13.7835 −0.725448
\(362\) 3.73980 0.196560
\(363\) 1.97740 0.103787
\(364\) −2.50310 −0.131198
\(365\) 6.60155 0.345541
\(366\) 1.26888 0.0663252
\(367\) −2.60849 −0.136162 −0.0680811 0.997680i \(-0.521688\pi\)
−0.0680811 + 0.997680i \(0.521688\pi\)
\(368\) 3.32748 0.173457
\(369\) 2.02015 0.105165
\(370\) 0.0744644 0.00387122
\(371\) 13.7401 0.713352
\(372\) 13.2549 0.687235
\(373\) −13.4756 −0.697740 −0.348870 0.937171i \(-0.613435\pi\)
−0.348870 + 0.937171i \(0.613435\pi\)
\(374\) 4.34680 0.224768
\(375\) 6.16154 0.318181
\(376\) −15.0820 −0.777797
\(377\) 5.70126 0.293630
\(378\) −0.527226 −0.0271176
\(379\) −22.3063 −1.14580 −0.572899 0.819626i \(-0.694181\pi\)
−0.572899 + 0.819626i \(0.694181\pi\)
\(380\) 2.71331 0.139190
\(381\) −15.7150 −0.805106
\(382\) 0.0231866 0.00118633
\(383\) 33.1365 1.69320 0.846599 0.532232i \(-0.178647\pi\)
0.846599 + 0.532232i \(0.178647\pi\)
\(384\) −10.2040 −0.520721
\(385\) 2.61429 0.133236
\(386\) 7.14042 0.363438
\(387\) −2.05274 −0.104347
\(388\) 7.99135 0.405699
\(389\) −1.12469 −0.0570242 −0.0285121 0.999593i \(-0.509077\pi\)
−0.0285121 + 0.999593i \(0.509077\pi\)
\(390\) −0.250224 −0.0126706
\(391\) 3.97238 0.200892
\(392\) −7.74055 −0.390957
\(393\) −11.2112 −0.565528
\(394\) 0.858207 0.0432358
\(395\) −1.06514 −0.0535932
\(396\) 5.55222 0.279010
\(397\) −23.8859 −1.19880 −0.599401 0.800449i \(-0.704594\pi\)
−0.599401 + 0.800449i \(0.704594\pi\)
\(398\) −9.11176 −0.456731
\(399\) −3.09291 −0.154839
\(400\) −14.2814 −0.714072
\(401\) −23.3086 −1.16398 −0.581988 0.813197i \(-0.697725\pi\)
−0.581988 + 0.813197i \(0.697725\pi\)
\(402\) 0.480560 0.0239681
\(403\) −7.17094 −0.357210
\(404\) 16.0752 0.799771
\(405\) 0.642702 0.0319361
\(406\) −3.00585 −0.149178
\(407\) 0.893893 0.0443086
\(408\) −5.56912 −0.275713
\(409\) 21.1034 1.04350 0.521748 0.853100i \(-0.325280\pi\)
0.521748 + 0.853100i \(0.325280\pi\)
\(410\) −0.505490 −0.0249644
\(411\) 13.9300 0.687114
\(412\) −1.84842 −0.0910652
\(413\) −13.5409 −0.666304
\(414\) −0.416088 −0.0204496
\(415\) 8.23137 0.404062
\(416\) 4.20881 0.206354
\(417\) −4.30921 −0.211023
\(418\) −2.67100 −0.130643
\(419\) −10.1892 −0.497774 −0.248887 0.968532i \(-0.580065\pi\)
−0.248887 + 0.968532i \(0.580065\pi\)
\(420\) −1.60875 −0.0784989
\(421\) 12.4669 0.607598 0.303799 0.952736i \(-0.401745\pi\)
0.303799 + 0.952736i \(0.401745\pi\)
\(422\) 3.21044 0.156282
\(423\) −10.0660 −0.489427
\(424\) −15.2025 −0.738298
\(425\) −17.0493 −0.827014
\(426\) −0.508918 −0.0246571
\(427\) −4.41344 −0.213581
\(428\) 1.60162 0.0774172
\(429\) −3.00376 −0.145023
\(430\) 0.513645 0.0247702
\(431\) 14.2559 0.686682 0.343341 0.939211i \(-0.388441\pi\)
0.343341 + 0.939211i \(0.388441\pi\)
\(432\) −3.11350 −0.149798
\(433\) −7.41028 −0.356116 −0.178058 0.984020i \(-0.556981\pi\)
−0.178058 + 0.984020i \(0.556981\pi\)
\(434\) 3.78071 0.181480
\(435\) 3.66421 0.175685
\(436\) 19.7795 0.947265
\(437\) −2.44093 −0.116765
\(438\) 3.99904 0.191081
\(439\) 5.97218 0.285036 0.142518 0.989792i \(-0.454480\pi\)
0.142518 + 0.989792i \(0.454480\pi\)
\(440\) −2.89253 −0.137896
\(441\) −5.16619 −0.246009
\(442\) 1.44712 0.0688324
\(443\) 0.244976 0.0116391 0.00581957 0.999983i \(-0.498148\pi\)
0.00581957 + 0.999983i \(0.498148\pi\)
\(444\) −0.550073 −0.0261053
\(445\) −7.23610 −0.343024
\(446\) −0.204856 −0.00970024
\(447\) −20.3044 −0.960363
\(448\) 6.21352 0.293561
\(449\) 4.69213 0.221435 0.110718 0.993852i \(-0.464685\pi\)
0.110718 + 0.993852i \(0.464685\pi\)
\(450\) 1.78584 0.0841852
\(451\) −6.06805 −0.285733
\(452\) −16.2826 −0.765869
\(453\) −14.1623 −0.665401
\(454\) −4.35556 −0.204417
\(455\) 0.870336 0.0408020
\(456\) 3.42209 0.160254
\(457\) −21.8979 −1.02434 −0.512169 0.858885i \(-0.671158\pi\)
−0.512169 + 0.858885i \(0.671158\pi\)
\(458\) 4.65311 0.217425
\(459\) −3.71693 −0.173492
\(460\) −1.26963 −0.0591966
\(461\) 13.7694 0.641306 0.320653 0.947197i \(-0.396098\pi\)
0.320653 + 0.947197i \(0.396098\pi\)
\(462\) 1.58366 0.0736787
\(463\) −34.9696 −1.62517 −0.812587 0.582840i \(-0.801942\pi\)
−0.812587 + 0.582840i \(0.801942\pi\)
\(464\) −17.7509 −0.824064
\(465\) −4.60877 −0.213727
\(466\) 4.85286 0.224804
\(467\) −16.0893 −0.744524 −0.372262 0.928128i \(-0.621418\pi\)
−0.372262 + 0.928128i \(0.621418\pi\)
\(468\) 1.84842 0.0854433
\(469\) −1.67150 −0.0771826
\(470\) 2.51876 0.116182
\(471\) −19.3082 −0.889675
\(472\) 14.9821 0.689606
\(473\) 6.16595 0.283511
\(474\) −0.645235 −0.0296366
\(475\) 10.4764 0.480690
\(476\) 9.30387 0.426442
\(477\) −10.1464 −0.464573
\(478\) −5.79085 −0.264867
\(479\) 21.0086 0.959906 0.479953 0.877294i \(-0.340654\pi\)
0.479953 + 0.877294i \(0.340654\pi\)
\(480\) 2.70501 0.123466
\(481\) 0.297591 0.0135690
\(482\) −8.34853 −0.380265
\(483\) 1.44725 0.0658521
\(484\) 3.65507 0.166139
\(485\) −2.77862 −0.126171
\(486\) 0.389331 0.0176604
\(487\) −14.5423 −0.658973 −0.329486 0.944160i \(-0.606876\pi\)
−0.329486 + 0.944160i \(0.606876\pi\)
\(488\) 4.88317 0.221051
\(489\) 6.41726 0.290198
\(490\) 1.29270 0.0583984
\(491\) 34.1591 1.54158 0.770789 0.637090i \(-0.219862\pi\)
0.770789 + 0.637090i \(0.219862\pi\)
\(492\) 3.73409 0.168346
\(493\) −21.1912 −0.954404
\(494\) −0.889218 −0.0400078
\(495\) −1.93052 −0.0867706
\(496\) 22.3267 1.00250
\(497\) 1.77013 0.0794013
\(498\) 4.98634 0.223443
\(499\) −5.80677 −0.259947 −0.129973 0.991517i \(-0.541489\pi\)
−0.129973 + 0.991517i \(0.541489\pi\)
\(500\) 11.3891 0.509337
\(501\) 0.717268 0.0320452
\(502\) −7.50205 −0.334833
\(503\) 24.7511 1.10360 0.551798 0.833978i \(-0.313942\pi\)
0.551798 + 0.833978i \(0.313942\pi\)
\(504\) −2.02899 −0.0903783
\(505\) −5.58940 −0.248725
\(506\) 1.24983 0.0555617
\(507\) −1.00000 −0.0444116
\(508\) −29.0480 −1.28880
\(509\) −29.9406 −1.32709 −0.663547 0.748135i \(-0.730950\pi\)
−0.663547 + 0.748135i \(0.730950\pi\)
\(510\) 0.930066 0.0411840
\(511\) −13.9096 −0.615323
\(512\) −22.4341 −0.991457
\(513\) 2.28396 0.100839
\(514\) −4.06168 −0.179153
\(515\) 0.642702 0.0283208
\(516\) −3.79433 −0.167036
\(517\) 30.2360 1.32978
\(518\) −0.156898 −0.00689369
\(519\) −19.2602 −0.845430
\(520\) −0.962967 −0.0422289
\(521\) 40.3306 1.76692 0.883458 0.468509i \(-0.155209\pi\)
0.883458 + 0.468509i \(0.155209\pi\)
\(522\) 2.21968 0.0971527
\(523\) −22.7558 −0.995041 −0.497521 0.867452i \(-0.665756\pi\)
−0.497521 + 0.867452i \(0.665756\pi\)
\(524\) −20.7229 −0.905286
\(525\) −6.21155 −0.271094
\(526\) 0.569699 0.0248401
\(527\) 26.6539 1.16106
\(528\) 9.35223 0.407004
\(529\) −21.8578 −0.950340
\(530\) 2.53888 0.110282
\(531\) 9.99931 0.433933
\(532\) −5.71699 −0.247863
\(533\) −2.02015 −0.0875024
\(534\) −4.38343 −0.189690
\(535\) −0.556888 −0.0240764
\(536\) 1.84940 0.0798817
\(537\) −4.43432 −0.191355
\(538\) 1.51135 0.0651589
\(539\) 15.5180 0.668408
\(540\) 1.18798 0.0511227
\(541\) −14.0755 −0.605153 −0.302576 0.953125i \(-0.597847\pi\)
−0.302576 + 0.953125i \(0.597847\pi\)
\(542\) −11.5948 −0.498038
\(543\) 9.60571 0.412220
\(544\) −15.6439 −0.670725
\(545\) −6.87739 −0.294595
\(546\) 0.527226 0.0225632
\(547\) 12.1714 0.520410 0.260205 0.965553i \(-0.416210\pi\)
0.260205 + 0.965553i \(0.416210\pi\)
\(548\) 25.7484 1.09992
\(549\) 3.25912 0.139096
\(550\) −5.36423 −0.228732
\(551\) 13.0215 0.554733
\(552\) −1.60128 −0.0681550
\(553\) 2.24428 0.0954364
\(554\) −2.40617 −0.102228
\(555\) 0.191262 0.00811863
\(556\) −7.96523 −0.337801
\(557\) −34.6179 −1.46681 −0.733403 0.679794i \(-0.762069\pi\)
−0.733403 + 0.679794i \(0.762069\pi\)
\(558\) −2.79187 −0.118189
\(559\) 2.05274 0.0868217
\(560\) −2.70980 −0.114510
\(561\) 11.1648 0.471378
\(562\) −6.37161 −0.268770
\(563\) 10.5183 0.443292 0.221646 0.975127i \(-0.428857\pi\)
0.221646 + 0.975127i \(0.428857\pi\)
\(564\) −18.6063 −0.783465
\(565\) 5.66151 0.238182
\(566\) −0.492659 −0.0207080
\(567\) −1.35418 −0.0568704
\(568\) −1.95853 −0.0821781
\(569\) −8.84536 −0.370817 −0.185408 0.982662i \(-0.559361\pi\)
−0.185408 + 0.982662i \(0.559361\pi\)
\(570\) −0.571502 −0.0239376
\(571\) −11.9955 −0.501996 −0.250998 0.967988i \(-0.580759\pi\)
−0.250998 + 0.967988i \(0.580759\pi\)
\(572\) −5.55222 −0.232150
\(573\) 0.0595551 0.00248795
\(574\) 1.06508 0.0444554
\(575\) −4.90217 −0.204434
\(576\) −4.58839 −0.191183
\(577\) −33.7368 −1.40448 −0.702242 0.711939i \(-0.747817\pi\)
−0.702242 + 0.711939i \(0.747817\pi\)
\(578\) 1.23979 0.0515683
\(579\) 18.3402 0.762194
\(580\) 6.77300 0.281234
\(581\) −17.3436 −0.719535
\(582\) −1.68321 −0.0697714
\(583\) 30.4775 1.26225
\(584\) 15.3900 0.636842
\(585\) −0.642702 −0.0265724
\(586\) −8.56576 −0.353848
\(587\) −2.66128 −0.109843 −0.0549213 0.998491i \(-0.517491\pi\)
−0.0549213 + 0.998491i \(0.517491\pi\)
\(588\) −9.54929 −0.393806
\(589\) −16.3782 −0.674850
\(590\) −2.50207 −0.103008
\(591\) 2.20431 0.0906732
\(592\) −0.926550 −0.0380810
\(593\) −1.55005 −0.0636531 −0.0318266 0.999493i \(-0.510132\pi\)
−0.0318266 + 0.999493i \(0.510132\pi\)
\(594\) −1.16946 −0.0479835
\(595\) −3.23498 −0.132621
\(596\) −37.5310 −1.53733
\(597\) −23.4036 −0.957846
\(598\) 0.416088 0.0170151
\(599\) 13.4015 0.547571 0.273786 0.961791i \(-0.411724\pi\)
0.273786 + 0.961791i \(0.411724\pi\)
\(600\) 6.87265 0.280575
\(601\) −44.7777 −1.82652 −0.913259 0.407378i \(-0.866443\pi\)
−0.913259 + 0.407378i \(0.866443\pi\)
\(602\) −1.08226 −0.0441096
\(603\) 1.23432 0.0502654
\(604\) −26.1778 −1.06516
\(605\) −1.27088 −0.0516685
\(606\) −3.38591 −0.137543
\(607\) −38.2141 −1.55106 −0.775531 0.631309i \(-0.782518\pi\)
−0.775531 + 0.631309i \(0.782518\pi\)
\(608\) 9.61276 0.389849
\(609\) −7.72055 −0.312853
\(610\) −0.815509 −0.0330190
\(611\) 10.0660 0.407228
\(612\) −6.87046 −0.277722
\(613\) −21.8566 −0.882779 −0.441389 0.897316i \(-0.645514\pi\)
−0.441389 + 0.897316i \(0.645514\pi\)
\(614\) 2.36048 0.0952612
\(615\) −1.29835 −0.0523547
\(616\) 6.09460 0.245559
\(617\) 32.7065 1.31671 0.658357 0.752706i \(-0.271252\pi\)
0.658357 + 0.752706i \(0.271252\pi\)
\(618\) 0.389331 0.0156612
\(619\) −24.2386 −0.974233 −0.487117 0.873337i \(-0.661951\pi\)
−0.487117 + 0.873337i \(0.661951\pi\)
\(620\) −8.51896 −0.342130
\(621\) −1.06872 −0.0428864
\(622\) −8.34563 −0.334629
\(623\) 15.2466 0.610842
\(624\) 3.11350 0.124640
\(625\) 18.9746 0.758986
\(626\) −8.57835 −0.342860
\(627\) −6.86049 −0.273981
\(628\) −35.6897 −1.42417
\(629\) −1.10613 −0.0441041
\(630\) 0.338849 0.0135001
\(631\) −7.96732 −0.317174 −0.158587 0.987345i \(-0.550694\pi\)
−0.158587 + 0.987345i \(0.550694\pi\)
\(632\) −2.48314 −0.0987739
\(633\) 8.24603 0.327750
\(634\) −2.26651 −0.0900148
\(635\) 10.1001 0.400810
\(636\) −18.7549 −0.743679
\(637\) 5.16619 0.204692
\(638\) −6.66739 −0.263965
\(639\) −1.30716 −0.0517104
\(640\) 6.55814 0.259233
\(641\) 33.0630 1.30591 0.652955 0.757397i \(-0.273529\pi\)
0.652955 + 0.757397i \(0.273529\pi\)
\(642\) −0.337348 −0.0133141
\(643\) 3.82237 0.150739 0.0753697 0.997156i \(-0.475986\pi\)
0.0753697 + 0.997156i \(0.475986\pi\)
\(644\) 2.67513 0.105415
\(645\) 1.31930 0.0519474
\(646\) 3.30517 0.130040
\(647\) 6.43456 0.252969 0.126484 0.991969i \(-0.459631\pi\)
0.126484 + 0.991969i \(0.459631\pi\)
\(648\) 1.49831 0.0588592
\(649\) −30.0356 −1.17900
\(650\) −1.78584 −0.0700463
\(651\) 9.71077 0.380595
\(652\) 11.8618 0.464544
\(653\) −14.9742 −0.585986 −0.292993 0.956115i \(-0.594651\pi\)
−0.292993 + 0.956115i \(0.594651\pi\)
\(654\) −4.16613 −0.162909
\(655\) 7.20543 0.281539
\(656\) 6.28974 0.245573
\(657\) 10.2716 0.400731
\(658\) −5.30707 −0.206891
\(659\) 32.1155 1.25104 0.625522 0.780207i \(-0.284886\pi\)
0.625522 + 0.780207i \(0.284886\pi\)
\(660\) −3.56842 −0.138901
\(661\) −49.4261 −1.92245 −0.961226 0.275760i \(-0.911070\pi\)
−0.961226 + 0.275760i \(0.911070\pi\)
\(662\) 3.79345 0.147436
\(663\) 3.71693 0.144354
\(664\) 19.1895 0.744698
\(665\) 1.98782 0.0770842
\(666\) 0.115861 0.00448954
\(667\) −6.09307 −0.235925
\(668\) 1.32581 0.0512973
\(669\) −0.526175 −0.0203431
\(670\) −0.308857 −0.0119322
\(671\) −9.78961 −0.377924
\(672\) −5.69950 −0.219863
\(673\) 23.2243 0.895232 0.447616 0.894226i \(-0.352273\pi\)
0.447616 + 0.894226i \(0.352273\pi\)
\(674\) −12.2551 −0.472049
\(675\) 4.58693 0.176551
\(676\) −1.84842 −0.0710931
\(677\) −14.1618 −0.544282 −0.272141 0.962257i \(-0.587732\pi\)
−0.272141 + 0.962257i \(0.587732\pi\)
\(678\) 3.42959 0.131713
\(679\) 5.85460 0.224679
\(680\) 3.57929 0.137259
\(681\) −11.1873 −0.428698
\(682\) 8.38612 0.321121
\(683\) 14.3440 0.548858 0.274429 0.961607i \(-0.411511\pi\)
0.274429 + 0.961607i \(0.411511\pi\)
\(684\) 4.22173 0.161422
\(685\) −8.95281 −0.342069
\(686\) −6.41433 −0.244900
\(687\) 11.9515 0.455980
\(688\) −6.39122 −0.243663
\(689\) 10.1464 0.386548
\(690\) 0.267420 0.0101805
\(691\) 25.9061 0.985515 0.492758 0.870167i \(-0.335989\pi\)
0.492758 + 0.870167i \(0.335989\pi\)
\(692\) −35.6010 −1.35335
\(693\) 4.06765 0.154517
\(694\) −1.74519 −0.0662464
\(695\) 2.76954 0.105054
\(696\) 8.54226 0.323793
\(697\) 7.50876 0.284415
\(698\) −4.34897 −0.164611
\(699\) 12.4646 0.471454
\(700\) −11.4816 −0.433962
\(701\) 9.97933 0.376914 0.188457 0.982081i \(-0.439651\pi\)
0.188457 + 0.982081i \(0.439651\pi\)
\(702\) −0.389331 −0.0146944
\(703\) 0.679687 0.0256349
\(704\) 13.7824 0.519445
\(705\) 6.46945 0.243654
\(706\) −11.0104 −0.414381
\(707\) 11.7770 0.442918
\(708\) 18.4829 0.694631
\(709\) 12.0282 0.451728 0.225864 0.974159i \(-0.427480\pi\)
0.225864 + 0.974159i \(0.427480\pi\)
\(710\) 0.327082 0.0122752
\(711\) −1.65729 −0.0621533
\(712\) −16.8693 −0.632204
\(713\) 7.66375 0.287010
\(714\) −1.95967 −0.0733386
\(715\) 1.93052 0.0721975
\(716\) −8.19649 −0.306317
\(717\) −14.8738 −0.555474
\(718\) −4.76688 −0.177898
\(719\) −16.6861 −0.622288 −0.311144 0.950363i \(-0.600712\pi\)
−0.311144 + 0.950363i \(0.600712\pi\)
\(720\) 2.00105 0.0745749
\(721\) −1.35418 −0.0504324
\(722\) 5.36635 0.199715
\(723\) −21.4433 −0.797483
\(724\) 17.7554 0.659874
\(725\) 26.1513 0.971235
\(726\) −0.769863 −0.0285723
\(727\) 36.2715 1.34523 0.672617 0.739991i \(-0.265170\pi\)
0.672617 + 0.739991i \(0.265170\pi\)
\(728\) 2.02899 0.0751993
\(729\) 1.00000 0.0370370
\(730\) −2.57019 −0.0951269
\(731\) −7.62991 −0.282202
\(732\) 6.02422 0.222661
\(733\) 28.1998 1.04158 0.520792 0.853684i \(-0.325637\pi\)
0.520792 + 0.853684i \(0.325637\pi\)
\(734\) 1.01557 0.0374853
\(735\) 3.32032 0.122472
\(736\) −4.49805 −0.165800
\(737\) −3.70761 −0.136572
\(738\) −0.786507 −0.0289517
\(739\) 8.08229 0.297312 0.148656 0.988889i \(-0.452505\pi\)
0.148656 + 0.988889i \(0.452505\pi\)
\(740\) 0.353533 0.0129961
\(741\) −2.28396 −0.0839035
\(742\) −5.34946 −0.196385
\(743\) −47.3255 −1.73620 −0.868101 0.496387i \(-0.834660\pi\)
−0.868101 + 0.496387i \(0.834660\pi\)
\(744\) −10.7443 −0.393905
\(745\) 13.0496 0.478102
\(746\) 5.24647 0.192087
\(747\) 12.8074 0.468600
\(748\) 20.6372 0.754572
\(749\) 1.17337 0.0428741
\(750\) −2.39888 −0.0875947
\(751\) 16.3887 0.598033 0.299016 0.954248i \(-0.403341\pi\)
0.299016 + 0.954248i \(0.403341\pi\)
\(752\) −31.3406 −1.14287
\(753\) −19.2691 −0.702204
\(754\) −2.21968 −0.0808359
\(755\) 9.10211 0.331260
\(756\) −2.50310 −0.0910370
\(757\) 33.2828 1.20968 0.604842 0.796345i \(-0.293236\pi\)
0.604842 + 0.796345i \(0.293236\pi\)
\(758\) 8.68454 0.315437
\(759\) 3.21019 0.116523
\(760\) −2.19938 −0.0797799
\(761\) −22.2884 −0.807953 −0.403976 0.914769i \(-0.632372\pi\)
−0.403976 + 0.914769i \(0.632372\pi\)
\(762\) 6.11836 0.221645
\(763\) 14.4908 0.524601
\(764\) 0.110083 0.00398266
\(765\) 2.38888 0.0863702
\(766\) −12.9011 −0.466135
\(767\) −9.99931 −0.361054
\(768\) −5.20403 −0.187784
\(769\) 14.8200 0.534423 0.267212 0.963638i \(-0.413898\pi\)
0.267212 + 0.963638i \(0.413898\pi\)
\(770\) −1.01782 −0.0366798
\(771\) −10.4324 −0.375715
\(772\) 33.9005 1.22010
\(773\) −21.0194 −0.756016 −0.378008 0.925802i \(-0.623391\pi\)
−0.378008 + 0.925802i \(0.623391\pi\)
\(774\) 0.799197 0.0287265
\(775\) −32.8926 −1.18154
\(776\) −6.47771 −0.232536
\(777\) −0.402993 −0.0144573
\(778\) 0.437878 0.0156987
\(779\) −4.61395 −0.165312
\(780\) −1.18798 −0.0425366
\(781\) 3.92640 0.140498
\(782\) −1.54657 −0.0553053
\(783\) 5.70126 0.203746
\(784\) −16.0849 −0.574462
\(785\) 12.4094 0.442911
\(786\) 4.36485 0.155689
\(787\) −29.1852 −1.04034 −0.520169 0.854063i \(-0.674131\pi\)
−0.520169 + 0.854063i \(0.674131\pi\)
\(788\) 4.07449 0.145148
\(789\) 1.46328 0.0520940
\(790\) 0.414694 0.0147541
\(791\) −11.9289 −0.424143
\(792\) −4.50057 −0.159921
\(793\) −3.25912 −0.115735
\(794\) 9.29955 0.330029
\(795\) 6.52112 0.231280
\(796\) −43.2597 −1.53330
\(797\) 12.4917 0.442479 0.221240 0.975219i \(-0.428990\pi\)
0.221240 + 0.975219i \(0.428990\pi\)
\(798\) 1.20417 0.0426270
\(799\) −37.4148 −1.32364
\(800\) 19.3055 0.682553
\(801\) −11.2589 −0.397813
\(802\) 9.07477 0.320441
\(803\) −30.8533 −1.08879
\(804\) 2.28154 0.0804639
\(805\) −0.930149 −0.0327835
\(806\) 2.79187 0.0983394
\(807\) 3.88191 0.136650
\(808\) −13.0304 −0.458407
\(809\) 23.0780 0.811378 0.405689 0.914011i \(-0.367032\pi\)
0.405689 + 0.914011i \(0.367032\pi\)
\(810\) −0.250224 −0.00879197
\(811\) −34.4387 −1.20930 −0.604652 0.796490i \(-0.706688\pi\)
−0.604652 + 0.796490i \(0.706688\pi\)
\(812\) −14.2708 −0.500808
\(813\) −29.7812 −1.04447
\(814\) −0.348020 −0.0121981
\(815\) −4.12438 −0.144471
\(816\) −11.5727 −0.405125
\(817\) 4.68839 0.164026
\(818\) −8.21622 −0.287273
\(819\) 1.35418 0.0473190
\(820\) −2.39990 −0.0838083
\(821\) −38.8773 −1.35683 −0.678413 0.734681i \(-0.737332\pi\)
−0.678413 + 0.734681i \(0.737332\pi\)
\(822\) −5.42337 −0.189162
\(823\) −40.3817 −1.40762 −0.703809 0.710389i \(-0.748519\pi\)
−0.703809 + 0.710389i \(0.748519\pi\)
\(824\) 1.49831 0.0521961
\(825\) −13.7781 −0.479691
\(826\) 5.27190 0.183433
\(827\) −3.88693 −0.135162 −0.0675810 0.997714i \(-0.521528\pi\)
−0.0675810 + 0.997714i \(0.521528\pi\)
\(828\) −1.97545 −0.0686517
\(829\) 31.2107 1.08399 0.541996 0.840381i \(-0.317669\pi\)
0.541996 + 0.840381i \(0.317669\pi\)
\(830\) −3.20473 −0.111238
\(831\) −6.18027 −0.214391
\(832\) 4.58839 0.159074
\(833\) −19.2024 −0.665323
\(834\) 1.67771 0.0580943
\(835\) −0.460990 −0.0159532
\(836\) −12.6811 −0.438584
\(837\) −7.17094 −0.247864
\(838\) 3.96697 0.137037
\(839\) 55.0313 1.89989 0.949945 0.312417i \(-0.101139\pi\)
0.949945 + 0.312417i \(0.101139\pi\)
\(840\) 1.30403 0.0449935
\(841\) 3.50435 0.120840
\(842\) −4.85374 −0.167271
\(843\) −16.3655 −0.563659
\(844\) 15.2421 0.524656
\(845\) 0.642702 0.0221096
\(846\) 3.91902 0.134739
\(847\) 2.67776 0.0920090
\(848\) −31.5909 −1.08484
\(849\) −1.26540 −0.0434283
\(850\) 6.63784 0.227676
\(851\) −0.318042 −0.0109024
\(852\) −2.41618 −0.0827769
\(853\) −7.78015 −0.266387 −0.133194 0.991090i \(-0.542523\pi\)
−0.133194 + 0.991090i \(0.542523\pi\)
\(854\) 1.71829 0.0587987
\(855\) −1.46791 −0.0502014
\(856\) −1.29826 −0.0443735
\(857\) −2.27773 −0.0778057 −0.0389029 0.999243i \(-0.512386\pi\)
−0.0389029 + 0.999243i \(0.512386\pi\)
\(858\) 1.16946 0.0399247
\(859\) −1.10615 −0.0377413 −0.0188707 0.999822i \(-0.506007\pi\)
−0.0188707 + 0.999822i \(0.506007\pi\)
\(860\) 2.43862 0.0831564
\(861\) 2.73565 0.0932309
\(862\) −5.55027 −0.189043
\(863\) 32.7298 1.11414 0.557068 0.830467i \(-0.311926\pi\)
0.557068 + 0.830467i \(0.311926\pi\)
\(864\) 4.20881 0.143186
\(865\) 12.3786 0.420884
\(866\) 2.88506 0.0980382
\(867\) 3.18440 0.108148
\(868\) 17.9496 0.609249
\(869\) 4.97811 0.168871
\(870\) −1.42659 −0.0483660
\(871\) −1.23432 −0.0418234
\(872\) −16.0330 −0.542947
\(873\) −4.32334 −0.146323
\(874\) 0.950329 0.0321454
\(875\) 8.34386 0.282074
\(876\) 18.9862 0.641483
\(877\) 35.4220 1.19611 0.598057 0.801453i \(-0.295939\pi\)
0.598057 + 0.801453i \(0.295939\pi\)
\(878\) −2.32516 −0.0784702
\(879\) −22.0012 −0.742083
\(880\) −6.01069 −0.202620
\(881\) −16.0042 −0.539195 −0.269598 0.962973i \(-0.586891\pi\)
−0.269598 + 0.962973i \(0.586891\pi\)
\(882\) 2.01136 0.0677259
\(883\) 39.1782 1.31845 0.659226 0.751945i \(-0.270884\pi\)
0.659226 + 0.751945i \(0.270884\pi\)
\(884\) 6.87046 0.231079
\(885\) −6.42657 −0.216027
\(886\) −0.0953767 −0.00320424
\(887\) −23.8804 −0.801824 −0.400912 0.916116i \(-0.631307\pi\)
−0.400912 + 0.916116i \(0.631307\pi\)
\(888\) 0.445884 0.0149629
\(889\) −21.2811 −0.713744
\(890\) 2.81724 0.0944341
\(891\) −3.00376 −0.100630
\(892\) −0.972593 −0.0325648
\(893\) 22.9904 0.769345
\(894\) 7.90512 0.264387
\(895\) 2.84994 0.0952631
\(896\) −13.8181 −0.461631
\(897\) 1.06872 0.0356837
\(898\) −1.82679 −0.0609608
\(899\) −40.8834 −1.36354
\(900\) 8.47859 0.282620
\(901\) −37.7136 −1.25642
\(902\) 2.36248 0.0786621
\(903\) −2.77979 −0.0925056
\(904\) 13.1985 0.438976
\(905\) −6.17360 −0.205218
\(906\) 5.51381 0.183184
\(907\) 33.0754 1.09825 0.549125 0.835740i \(-0.314961\pi\)
0.549125 + 0.835740i \(0.314961\pi\)
\(908\) −20.6788 −0.686251
\(909\) −8.69672 −0.288452
\(910\) −0.338849 −0.0112327
\(911\) −48.6164 −1.61073 −0.805366 0.592777i \(-0.798031\pi\)
−0.805366 + 0.592777i \(0.798031\pi\)
\(912\) 7.11113 0.235473
\(913\) −38.4705 −1.27319
\(914\) 8.52552 0.281999
\(915\) −2.09464 −0.0692466
\(916\) 22.0915 0.729923
\(917\) −15.1820 −0.501353
\(918\) 1.44712 0.0477620
\(919\) −54.9938 −1.81408 −0.907040 0.421045i \(-0.861663\pi\)
−0.907040 + 0.421045i \(0.861663\pi\)
\(920\) 1.02915 0.0339299
\(921\) 6.06291 0.199780
\(922\) −5.36086 −0.176551
\(923\) 1.30716 0.0430256
\(924\) 7.51873 0.247348
\(925\) 1.36503 0.0448819
\(926\) 13.6148 0.447409
\(927\) 1.00000 0.0328443
\(928\) 23.9955 0.787691
\(929\) 20.6765 0.678375 0.339187 0.940719i \(-0.389848\pi\)
0.339187 + 0.940719i \(0.389848\pi\)
\(930\) 1.79434 0.0588387
\(931\) 11.7994 0.386709
\(932\) 23.0398 0.754694
\(933\) −21.4358 −0.701777
\(934\) 6.26407 0.204967
\(935\) −7.17563 −0.234668
\(936\) −1.49831 −0.0489738
\(937\) 36.4697 1.19141 0.595706 0.803202i \(-0.296872\pi\)
0.595706 + 0.803202i \(0.296872\pi\)
\(938\) 0.650766 0.0212483
\(939\) −22.0335 −0.719037
\(940\) 11.9583 0.390036
\(941\) −37.1490 −1.21102 −0.605512 0.795836i \(-0.707032\pi\)
−0.605512 + 0.795836i \(0.707032\pi\)
\(942\) 7.51729 0.244927
\(943\) 2.15898 0.0703061
\(944\) 31.1329 1.01329
\(945\) 0.870336 0.0283120
\(946\) −2.40060 −0.0780502
\(947\) 18.1906 0.591116 0.295558 0.955325i \(-0.404494\pi\)
0.295558 + 0.955325i \(0.404494\pi\)
\(948\) −3.06337 −0.0994937
\(949\) −10.2716 −0.333429
\(950\) −4.07879 −0.132333
\(951\) −5.82156 −0.188777
\(952\) −7.54162 −0.244425
\(953\) 52.7833 1.70982 0.854909 0.518778i \(-0.173613\pi\)
0.854909 + 0.518778i \(0.173613\pi\)
\(954\) 3.95032 0.127896
\(955\) −0.0382761 −0.00123859
\(956\) −27.4931 −0.889191
\(957\) −17.1252 −0.553580
\(958\) −8.17929 −0.264261
\(959\) 18.8637 0.609142
\(960\) 2.94896 0.0951774
\(961\) 20.4223 0.658785
\(962\) −0.115861 −0.00373552
\(963\) −0.866480 −0.0279219
\(964\) −39.6362 −1.27659
\(965\) −11.7873 −0.379446
\(966\) −0.563459 −0.0181290
\(967\) 28.3632 0.912100 0.456050 0.889954i \(-0.349264\pi\)
0.456050 + 0.889954i \(0.349264\pi\)
\(968\) −2.96276 −0.0952267
\(969\) 8.48934 0.272717
\(970\) 1.08180 0.0347346
\(971\) 54.2490 1.74093 0.870467 0.492226i \(-0.163817\pi\)
0.870467 + 0.492226i \(0.163817\pi\)
\(972\) 1.84842 0.0592881
\(973\) −5.83546 −0.187076
\(974\) 5.66176 0.181414
\(975\) −4.58693 −0.146899
\(976\) 10.1473 0.324806
\(977\) 6.90212 0.220818 0.110409 0.993886i \(-0.464784\pi\)
0.110409 + 0.993886i \(0.464784\pi\)
\(978\) −2.49844 −0.0798912
\(979\) 33.8190 1.08086
\(980\) 6.13734 0.196050
\(981\) −10.7007 −0.341648
\(982\) −13.2992 −0.424395
\(983\) 1.20088 0.0383023 0.0191511 0.999817i \(-0.493904\pi\)
0.0191511 + 0.999817i \(0.493904\pi\)
\(984\) −3.02681 −0.0964912
\(985\) −1.41671 −0.0451403
\(986\) 8.25040 0.262746
\(987\) −13.6313 −0.433888
\(988\) −4.22173 −0.134311
\(989\) −2.19381 −0.0697592
\(990\) 0.751614 0.0238879
\(991\) −27.6817 −0.879339 −0.439669 0.898160i \(-0.644904\pi\)
−0.439669 + 0.898160i \(0.644904\pi\)
\(992\) −30.1811 −0.958250
\(993\) 9.74349 0.309200
\(994\) −0.689168 −0.0218591
\(995\) 15.0415 0.476849
\(996\) 23.6736 0.750125
\(997\) −17.3294 −0.548829 −0.274415 0.961611i \(-0.588484\pi\)
−0.274415 + 0.961611i \(0.588484\pi\)
\(998\) 2.26076 0.0715630
\(999\) 0.297591 0.00941536
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 4017.2.a.g.1.11 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4017.2.a.g.1.11 24 1.1 even 1 trivial