Properties

Label 8034.2.a.v.1.6
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $11$
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] = [8034,2,Mod(1,8034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8034, 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("8034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.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: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 5 x^{10} - 31 x^{9} + 168 x^{8} + 300 x^{7} - 1928 x^{6} - 736 x^{5} + 8532 x^{4} - 2065 x^{3} - 10494 x^{2} + 4024 x + 576 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.542814\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.542814 q^{5} +1.00000 q^{6} +3.05565 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.542814 q^{5} +1.00000 q^{6} +3.05565 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.542814 q^{10} +0.632985 q^{11} +1.00000 q^{12} +1.00000 q^{13} +3.05565 q^{14} +0.542814 q^{15} +1.00000 q^{16} +2.75403 q^{17} +1.00000 q^{18} +2.05565 q^{19} +0.542814 q^{20} +3.05565 q^{21} +0.632985 q^{22} +6.49267 q^{23} +1.00000 q^{24} -4.70535 q^{25} +1.00000 q^{26} +1.00000 q^{27} +3.05565 q^{28} -1.48269 q^{29} +0.542814 q^{30} -2.05565 q^{31} +1.00000 q^{32} +0.632985 q^{33} +2.75403 q^{34} +1.65865 q^{35} +1.00000 q^{36} -0.518334 q^{37} +2.05565 q^{38} +1.00000 q^{39} +0.542814 q^{40} +2.61666 q^{41} +3.05565 q^{42} +2.49072 q^{43} +0.632985 q^{44} +0.542814 q^{45} +6.49267 q^{46} +2.09567 q^{47} +1.00000 q^{48} +2.33697 q^{49} -4.70535 q^{50} +2.75403 q^{51} +1.00000 q^{52} -12.6644 q^{53} +1.00000 q^{54} +0.343593 q^{55} +3.05565 q^{56} +2.05565 q^{57} -1.48269 q^{58} +0.846439 q^{59} +0.542814 q^{60} -11.2974 q^{61} -2.05565 q^{62} +3.05565 q^{63} +1.00000 q^{64} +0.542814 q^{65} +0.632985 q^{66} +12.0004 q^{67} +2.75403 q^{68} +6.49267 q^{69} +1.65865 q^{70} +3.24887 q^{71} +1.00000 q^{72} +12.2886 q^{73} -0.518334 q^{74} -4.70535 q^{75} +2.05565 q^{76} +1.93418 q^{77} +1.00000 q^{78} +10.0724 q^{79} +0.542814 q^{80} +1.00000 q^{81} +2.61666 q^{82} +4.86110 q^{83} +3.05565 q^{84} +1.49493 q^{85} +2.49072 q^{86} -1.48269 q^{87} +0.632985 q^{88} -9.35113 q^{89} +0.542814 q^{90} +3.05565 q^{91} +6.49267 q^{92} -2.05565 q^{93} +2.09567 q^{94} +1.11583 q^{95} +1.00000 q^{96} -7.29369 q^{97} +2.33697 q^{98} +0.632985 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q + 11 q^{2} + 11 q^{3} + 11 q^{4} + 5 q^{5} + 11 q^{6} + 4 q^{7} + 11 q^{8} + 11 q^{9} + 5 q^{10} - 7 q^{11} + 11 q^{12} + 11 q^{13} + 4 q^{14} + 5 q^{15} + 11 q^{16} + 10 q^{17} + 11 q^{18} - 7 q^{19} + 5 q^{20} + 4 q^{21} - 7 q^{22} + 18 q^{23} + 11 q^{24} + 32 q^{25} + 11 q^{26} + 11 q^{27} + 4 q^{28} + 29 q^{29} + 5 q^{30} + 7 q^{31} + 11 q^{32} - 7 q^{33} + 10 q^{34} + 31 q^{35} + 11 q^{36} + 21 q^{37} - 7 q^{38} + 11 q^{39} + 5 q^{40} - 3 q^{41} + 4 q^{42} - 17 q^{43} - 7 q^{44} + 5 q^{45} + 18 q^{46} + 12 q^{47} + 11 q^{48} + 21 q^{49} + 32 q^{50} + 10 q^{51} + 11 q^{52} + 11 q^{53} + 11 q^{54} + 4 q^{55} + 4 q^{56} - 7 q^{57} + 29 q^{58} - 48 q^{59} + 5 q^{60} - q^{61} + 7 q^{62} + 4 q^{63} + 11 q^{64} + 5 q^{65} - 7 q^{66} - 9 q^{67} + 10 q^{68} + 18 q^{69} + 31 q^{70} + 17 q^{71} + 11 q^{72} - 23 q^{73} + 21 q^{74} + 32 q^{75} - 7 q^{76} + 26 q^{77} + 11 q^{78} + 41 q^{79} + 5 q^{80} + 11 q^{81} - 3 q^{82} + 19 q^{83} + 4 q^{84} + 17 q^{85} - 17 q^{86} + 29 q^{87} - 7 q^{88} + 32 q^{89} + 5 q^{90} + 4 q^{91} + 18 q^{92} + 7 q^{93} + 12 q^{94} + 26 q^{95} + 11 q^{96} - 16 q^{97} + 21 q^{98} - 7 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0.542814 0.242754 0.121377 0.992607i \(-0.461269\pi\)
0.121377 + 0.992607i \(0.461269\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.05565 1.15493 0.577463 0.816417i \(-0.304043\pi\)
0.577463 + 0.816417i \(0.304043\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0.542814 0.171653
\(11\) 0.632985 0.190852 0.0954261 0.995437i \(-0.469579\pi\)
0.0954261 + 0.995437i \(0.469579\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350
\(14\) 3.05565 0.816656
\(15\) 0.542814 0.140154
\(16\) 1.00000 0.250000
\(17\) 2.75403 0.667951 0.333976 0.942582i \(-0.391610\pi\)
0.333976 + 0.942582i \(0.391610\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.05565 0.471598 0.235799 0.971802i \(-0.424229\pi\)
0.235799 + 0.971802i \(0.424229\pi\)
\(20\) 0.542814 0.121377
\(21\) 3.05565 0.666797
\(22\) 0.632985 0.134953
\(23\) 6.49267 1.35382 0.676908 0.736068i \(-0.263320\pi\)
0.676908 + 0.736068i \(0.263320\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.70535 −0.941071
\(26\) 1.00000 0.196116
\(27\) 1.00000 0.192450
\(28\) 3.05565 0.577463
\(29\) −1.48269 −0.275329 −0.137665 0.990479i \(-0.543960\pi\)
−0.137665 + 0.990479i \(0.543960\pi\)
\(30\) 0.542814 0.0991037
\(31\) −2.05565 −0.369205 −0.184602 0.982813i \(-0.559100\pi\)
−0.184602 + 0.982813i \(0.559100\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.632985 0.110189
\(34\) 2.75403 0.472313
\(35\) 1.65865 0.280362
\(36\) 1.00000 0.166667
\(37\) −0.518334 −0.0852135 −0.0426068 0.999092i \(-0.513566\pi\)
−0.0426068 + 0.999092i \(0.513566\pi\)
\(38\) 2.05565 0.333470
\(39\) 1.00000 0.160128
\(40\) 0.542814 0.0858264
\(41\) 2.61666 0.408654 0.204327 0.978903i \(-0.434499\pi\)
0.204327 + 0.978903i \(0.434499\pi\)
\(42\) 3.05565 0.471496
\(43\) 2.49072 0.379831 0.189915 0.981800i \(-0.439179\pi\)
0.189915 + 0.981800i \(0.439179\pi\)
\(44\) 0.632985 0.0954261
\(45\) 0.542814 0.0809179
\(46\) 6.49267 0.957292
\(47\) 2.09567 0.305685 0.152843 0.988251i \(-0.451157\pi\)
0.152843 + 0.988251i \(0.451157\pi\)
\(48\) 1.00000 0.144338
\(49\) 2.33697 0.333853
\(50\) −4.70535 −0.665437
\(51\) 2.75403 0.385642
\(52\) 1.00000 0.138675
\(53\) −12.6644 −1.73959 −0.869795 0.493413i \(-0.835749\pi\)
−0.869795 + 0.493413i \(0.835749\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.343593 0.0463301
\(56\) 3.05565 0.408328
\(57\) 2.05565 0.272277
\(58\) −1.48269 −0.194687
\(59\) 0.846439 0.110197 0.0550985 0.998481i \(-0.482453\pi\)
0.0550985 + 0.998481i \(0.482453\pi\)
\(60\) 0.542814 0.0700769
\(61\) −11.2974 −1.44648 −0.723241 0.690596i \(-0.757348\pi\)
−0.723241 + 0.690596i \(0.757348\pi\)
\(62\) −2.05565 −0.261067
\(63\) 3.05565 0.384975
\(64\) 1.00000 0.125000
\(65\) 0.542814 0.0673277
\(66\) 0.632985 0.0779151
\(67\) 12.0004 1.46608 0.733039 0.680187i \(-0.238101\pi\)
0.733039 + 0.680187i \(0.238101\pi\)
\(68\) 2.75403 0.333976
\(69\) 6.49267 0.781626
\(70\) 1.65865 0.198246
\(71\) 3.24887 0.385570 0.192785 0.981241i \(-0.438248\pi\)
0.192785 + 0.981241i \(0.438248\pi\)
\(72\) 1.00000 0.117851
\(73\) 12.2886 1.43827 0.719136 0.694869i \(-0.244538\pi\)
0.719136 + 0.694869i \(0.244538\pi\)
\(74\) −0.518334 −0.0602551
\(75\) −4.70535 −0.543327
\(76\) 2.05565 0.235799
\(77\) 1.93418 0.220420
\(78\) 1.00000 0.113228
\(79\) 10.0724 1.13323 0.566615 0.823983i \(-0.308253\pi\)
0.566615 + 0.823983i \(0.308253\pi\)
\(80\) 0.542814 0.0606884
\(81\) 1.00000 0.111111
\(82\) 2.61666 0.288962
\(83\) 4.86110 0.533575 0.266787 0.963755i \(-0.414038\pi\)
0.266787 + 0.963755i \(0.414038\pi\)
\(84\) 3.05565 0.333398
\(85\) 1.49493 0.162148
\(86\) 2.49072 0.268581
\(87\) −1.48269 −0.158961
\(88\) 0.632985 0.0674765
\(89\) −9.35113 −0.991218 −0.495609 0.868546i \(-0.665055\pi\)
−0.495609 + 0.868546i \(0.665055\pi\)
\(90\) 0.542814 0.0572176
\(91\) 3.05565 0.320319
\(92\) 6.49267 0.676908
\(93\) −2.05565 −0.213161
\(94\) 2.09567 0.216152
\(95\) 1.11583 0.114482
\(96\) 1.00000 0.102062
\(97\) −7.29369 −0.740563 −0.370281 0.928920i \(-0.620739\pi\)
−0.370281 + 0.928920i \(0.620739\pi\)
\(98\) 2.33697 0.236070
\(99\) 0.632985 0.0636174
\(100\) −4.70535 −0.470535
\(101\) −15.2641 −1.51884 −0.759420 0.650601i \(-0.774517\pi\)
−0.759420 + 0.650601i \(0.774517\pi\)
\(102\) 2.75403 0.272690
\(103\) −1.00000 −0.0985329
\(104\) 1.00000 0.0980581
\(105\) 1.65865 0.161867
\(106\) −12.6644 −1.23008
\(107\) −17.5531 −1.69692 −0.848462 0.529256i \(-0.822471\pi\)
−0.848462 + 0.529256i \(0.822471\pi\)
\(108\) 1.00000 0.0962250
\(109\) −8.80317 −0.843191 −0.421596 0.906784i \(-0.638530\pi\)
−0.421596 + 0.906784i \(0.638530\pi\)
\(110\) 0.343593 0.0327603
\(111\) −0.518334 −0.0491980
\(112\) 3.05565 0.288731
\(113\) −1.00999 −0.0950122 −0.0475061 0.998871i \(-0.515127\pi\)
−0.0475061 + 0.998871i \(0.515127\pi\)
\(114\) 2.05565 0.192529
\(115\) 3.52431 0.328644
\(116\) −1.48269 −0.137665
\(117\) 1.00000 0.0924500
\(118\) 0.846439 0.0779211
\(119\) 8.41535 0.771434
\(120\) 0.542814 0.0495519
\(121\) −10.5993 −0.963575
\(122\) −11.2974 −1.02282
\(123\) 2.61666 0.235936
\(124\) −2.05565 −0.184602
\(125\) −5.26820 −0.471202
\(126\) 3.05565 0.272219
\(127\) −1.73086 −0.153589 −0.0767943 0.997047i \(-0.524468\pi\)
−0.0767943 + 0.997047i \(0.524468\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.49072 0.219296
\(130\) 0.542814 0.0476079
\(131\) 8.42898 0.736443 0.368222 0.929738i \(-0.379967\pi\)
0.368222 + 0.929738i \(0.379967\pi\)
\(132\) 0.632985 0.0550943
\(133\) 6.28133 0.544660
\(134\) 12.0004 1.03667
\(135\) 0.542814 0.0467180
\(136\) 2.75403 0.236157
\(137\) 8.45316 0.722202 0.361101 0.932527i \(-0.382401\pi\)
0.361101 + 0.932527i \(0.382401\pi\)
\(138\) 6.49267 0.552693
\(139\) −3.12795 −0.265310 −0.132655 0.991162i \(-0.542350\pi\)
−0.132655 + 0.991162i \(0.542350\pi\)
\(140\) 1.65865 0.140181
\(141\) 2.09567 0.176487
\(142\) 3.24887 0.272639
\(143\) 0.632985 0.0529329
\(144\) 1.00000 0.0833333
\(145\) −0.804826 −0.0668371
\(146\) 12.2886 1.01701
\(147\) 2.33697 0.192750
\(148\) −0.518334 −0.0426068
\(149\) 9.04546 0.741033 0.370517 0.928826i \(-0.379181\pi\)
0.370517 + 0.928826i \(0.379181\pi\)
\(150\) −4.70535 −0.384191
\(151\) −18.2754 −1.48723 −0.743617 0.668605i \(-0.766892\pi\)
−0.743617 + 0.668605i \(0.766892\pi\)
\(152\) 2.05565 0.166735
\(153\) 2.75403 0.222650
\(154\) 1.93418 0.155861
\(155\) −1.11583 −0.0896258
\(156\) 1.00000 0.0800641
\(157\) 15.5277 1.23925 0.619624 0.784899i \(-0.287285\pi\)
0.619624 + 0.784899i \(0.287285\pi\)
\(158\) 10.0724 0.801315
\(159\) −12.6644 −1.00435
\(160\) 0.542814 0.0429132
\(161\) 19.8393 1.56356
\(162\) 1.00000 0.0785674
\(163\) 15.4871 1.21305 0.606524 0.795066i \(-0.292564\pi\)
0.606524 + 0.795066i \(0.292564\pi\)
\(164\) 2.61666 0.204327
\(165\) 0.343593 0.0267487
\(166\) 4.86110 0.377294
\(167\) 8.73179 0.675686 0.337843 0.941202i \(-0.390303\pi\)
0.337843 + 0.941202i \(0.390303\pi\)
\(168\) 3.05565 0.235748
\(169\) 1.00000 0.0769231
\(170\) 1.49493 0.114656
\(171\) 2.05565 0.157199
\(172\) 2.49072 0.189915
\(173\) 21.1049 1.60457 0.802287 0.596939i \(-0.203616\pi\)
0.802287 + 0.596939i \(0.203616\pi\)
\(174\) −1.48269 −0.112403
\(175\) −14.3779 −1.08687
\(176\) 0.632985 0.0477131
\(177\) 0.846439 0.0636223
\(178\) −9.35113 −0.700897
\(179\) 8.18560 0.611820 0.305910 0.952060i \(-0.401039\pi\)
0.305910 + 0.952060i \(0.401039\pi\)
\(180\) 0.542814 0.0404589
\(181\) 6.24534 0.464212 0.232106 0.972690i \(-0.425438\pi\)
0.232106 + 0.972690i \(0.425438\pi\)
\(182\) 3.05565 0.226500
\(183\) −11.2974 −0.835126
\(184\) 6.49267 0.478646
\(185\) −0.281358 −0.0206859
\(186\) −2.05565 −0.150727
\(187\) 1.74326 0.127480
\(188\) 2.09567 0.152843
\(189\) 3.05565 0.222266
\(190\) 1.11583 0.0809510
\(191\) −21.2265 −1.53590 −0.767950 0.640510i \(-0.778723\pi\)
−0.767950 + 0.640510i \(0.778723\pi\)
\(192\) 1.00000 0.0721688
\(193\) −9.87884 −0.711094 −0.355547 0.934658i \(-0.615705\pi\)
−0.355547 + 0.934658i \(0.615705\pi\)
\(194\) −7.29369 −0.523657
\(195\) 0.542814 0.0388717
\(196\) 2.33697 0.166927
\(197\) −17.5032 −1.24705 −0.623526 0.781803i \(-0.714301\pi\)
−0.623526 + 0.781803i \(0.714301\pi\)
\(198\) 0.632985 0.0449843
\(199\) −26.7000 −1.89272 −0.946358 0.323120i \(-0.895268\pi\)
−0.946358 + 0.323120i \(0.895268\pi\)
\(200\) −4.70535 −0.332719
\(201\) 12.0004 0.846440
\(202\) −15.2641 −1.07398
\(203\) −4.53058 −0.317985
\(204\) 2.75403 0.192821
\(205\) 1.42036 0.0992022
\(206\) −1.00000 −0.0696733
\(207\) 6.49267 0.451272
\(208\) 1.00000 0.0693375
\(209\) 1.30119 0.0900054
\(210\) 1.65865 0.114457
\(211\) 14.8379 1.02148 0.510742 0.859734i \(-0.329371\pi\)
0.510742 + 0.859734i \(0.329371\pi\)
\(212\) −12.6644 −0.869795
\(213\) 3.24887 0.222609
\(214\) −17.5531 −1.19991
\(215\) 1.35200 0.0922053
\(216\) 1.00000 0.0680414
\(217\) −6.28133 −0.426404
\(218\) −8.80317 −0.596226
\(219\) 12.2886 0.830387
\(220\) 0.343593 0.0231650
\(221\) 2.75403 0.185256
\(222\) −0.518334 −0.0347883
\(223\) −14.8504 −0.994453 −0.497227 0.867621i \(-0.665648\pi\)
−0.497227 + 0.867621i \(0.665648\pi\)
\(224\) 3.05565 0.204164
\(225\) −4.70535 −0.313690
\(226\) −1.00999 −0.0671838
\(227\) 7.10596 0.471639 0.235820 0.971797i \(-0.424223\pi\)
0.235820 + 0.971797i \(0.424223\pi\)
\(228\) 2.05565 0.136138
\(229\) 2.94089 0.194340 0.0971698 0.995268i \(-0.469021\pi\)
0.0971698 + 0.995268i \(0.469021\pi\)
\(230\) 3.52431 0.232386
\(231\) 1.93418 0.127260
\(232\) −1.48269 −0.0973435
\(233\) 8.07222 0.528829 0.264414 0.964409i \(-0.414821\pi\)
0.264414 + 0.964409i \(0.414821\pi\)
\(234\) 1.00000 0.0653720
\(235\) 1.13756 0.0742062
\(236\) 0.846439 0.0550985
\(237\) 10.0724 0.654271
\(238\) 8.41535 0.545486
\(239\) 4.41447 0.285548 0.142774 0.989755i \(-0.454398\pi\)
0.142774 + 0.989755i \(0.454398\pi\)
\(240\) 0.542814 0.0350385
\(241\) −3.99479 −0.257327 −0.128664 0.991688i \(-0.541069\pi\)
−0.128664 + 0.991688i \(0.541069\pi\)
\(242\) −10.5993 −0.681351
\(243\) 1.00000 0.0641500
\(244\) −11.2974 −0.723241
\(245\) 1.26854 0.0810441
\(246\) 2.61666 0.166832
\(247\) 2.05565 0.130798
\(248\) −2.05565 −0.130534
\(249\) 4.86110 0.308060
\(250\) −5.26820 −0.333190
\(251\) −3.11912 −0.196877 −0.0984386 0.995143i \(-0.531385\pi\)
−0.0984386 + 0.995143i \(0.531385\pi\)
\(252\) 3.05565 0.192488
\(253\) 4.10977 0.258379
\(254\) −1.73086 −0.108604
\(255\) 1.49493 0.0936160
\(256\) 1.00000 0.0625000
\(257\) 0.0449774 0.00280561 0.00140281 0.999999i \(-0.499553\pi\)
0.00140281 + 0.999999i \(0.499553\pi\)
\(258\) 2.49072 0.155065
\(259\) −1.58384 −0.0984153
\(260\) 0.542814 0.0336639
\(261\) −1.48269 −0.0917764
\(262\) 8.42898 0.520744
\(263\) 28.7094 1.77030 0.885148 0.465309i \(-0.154057\pi\)
0.885148 + 0.465309i \(0.154057\pi\)
\(264\) 0.632985 0.0389576
\(265\) −6.87441 −0.422292
\(266\) 6.28133 0.385133
\(267\) −9.35113 −0.572280
\(268\) 12.0004 0.733039
\(269\) 13.4485 0.819971 0.409985 0.912092i \(-0.365534\pi\)
0.409985 + 0.912092i \(0.365534\pi\)
\(270\) 0.542814 0.0330346
\(271\) −8.93755 −0.542917 −0.271459 0.962450i \(-0.587506\pi\)
−0.271459 + 0.962450i \(0.587506\pi\)
\(272\) 2.75403 0.166988
\(273\) 3.05565 0.184936
\(274\) 8.45316 0.510674
\(275\) −2.97842 −0.179605
\(276\) 6.49267 0.390813
\(277\) 8.96300 0.538534 0.269267 0.963066i \(-0.413219\pi\)
0.269267 + 0.963066i \(0.413219\pi\)
\(278\) −3.12795 −0.187602
\(279\) −2.05565 −0.123068
\(280\) 1.65865 0.0991231
\(281\) 5.60492 0.334362 0.167181 0.985926i \(-0.446534\pi\)
0.167181 + 0.985926i \(0.446534\pi\)
\(282\) 2.09567 0.124796
\(283\) 13.6111 0.809096 0.404548 0.914517i \(-0.367429\pi\)
0.404548 + 0.914517i \(0.367429\pi\)
\(284\) 3.24887 0.192785
\(285\) 1.11583 0.0660962
\(286\) 0.632985 0.0374292
\(287\) 7.99559 0.471965
\(288\) 1.00000 0.0589256
\(289\) −9.41529 −0.553841
\(290\) −0.804826 −0.0472610
\(291\) −7.29369 −0.427564
\(292\) 12.2886 0.719136
\(293\) −17.7380 −1.03627 −0.518133 0.855300i \(-0.673373\pi\)
−0.518133 + 0.855300i \(0.673373\pi\)
\(294\) 2.33697 0.136295
\(295\) 0.459459 0.0267507
\(296\) −0.518334 −0.0301275
\(297\) 0.632985 0.0367295
\(298\) 9.04546 0.523990
\(299\) 6.49267 0.375481
\(300\) −4.70535 −0.271664
\(301\) 7.61075 0.438676
\(302\) −18.2754 −1.05163
\(303\) −15.2641 −0.876902
\(304\) 2.05565 0.117899
\(305\) −6.13237 −0.351138
\(306\) 2.75403 0.157438
\(307\) 6.26775 0.357719 0.178860 0.983875i \(-0.442759\pi\)
0.178860 + 0.983875i \(0.442759\pi\)
\(308\) 1.93418 0.110210
\(309\) −1.00000 −0.0568880
\(310\) −1.11583 −0.0633750
\(311\) 24.8115 1.40693 0.703466 0.710729i \(-0.251635\pi\)
0.703466 + 0.710729i \(0.251635\pi\)
\(312\) 1.00000 0.0566139
\(313\) −26.4684 −1.49608 −0.748040 0.663653i \(-0.769005\pi\)
−0.748040 + 0.663653i \(0.769005\pi\)
\(314\) 15.5277 0.876281
\(315\) 1.65865 0.0934541
\(316\) 10.0724 0.566615
\(317\) 24.8381 1.39505 0.697524 0.716561i \(-0.254285\pi\)
0.697524 + 0.716561i \(0.254285\pi\)
\(318\) −12.6644 −0.710185
\(319\) −0.938523 −0.0525472
\(320\) 0.542814 0.0303442
\(321\) −17.5531 −0.979720
\(322\) 19.8393 1.10560
\(323\) 5.66132 0.315004
\(324\) 1.00000 0.0555556
\(325\) −4.70535 −0.261006
\(326\) 15.4871 0.857754
\(327\) −8.80317 −0.486817
\(328\) 2.61666 0.144481
\(329\) 6.40363 0.353044
\(330\) 0.343593 0.0189142
\(331\) 24.3920 1.34071 0.670354 0.742041i \(-0.266142\pi\)
0.670354 + 0.742041i \(0.266142\pi\)
\(332\) 4.86110 0.266787
\(333\) −0.518334 −0.0284045
\(334\) 8.73179 0.477782
\(335\) 6.51396 0.355896
\(336\) 3.05565 0.166699
\(337\) −28.4373 −1.54908 −0.774539 0.632527i \(-0.782018\pi\)
−0.774539 + 0.632527i \(0.782018\pi\)
\(338\) 1.00000 0.0543928
\(339\) −1.00999 −0.0548553
\(340\) 1.49493 0.0810738
\(341\) −1.30119 −0.0704636
\(342\) 2.05565 0.111157
\(343\) −14.2486 −0.769350
\(344\) 2.49072 0.134291
\(345\) 3.52431 0.189743
\(346\) 21.1049 1.13461
\(347\) 3.72720 0.200087 0.100043 0.994983i \(-0.468102\pi\)
0.100043 + 0.994983i \(0.468102\pi\)
\(348\) −1.48269 −0.0794807
\(349\) −18.4589 −0.988081 −0.494040 0.869439i \(-0.664481\pi\)
−0.494040 + 0.869439i \(0.664481\pi\)
\(350\) −14.3779 −0.768531
\(351\) 1.00000 0.0533761
\(352\) 0.632985 0.0337382
\(353\) −10.9773 −0.584262 −0.292131 0.956378i \(-0.594364\pi\)
−0.292131 + 0.956378i \(0.594364\pi\)
\(354\) 0.846439 0.0449877
\(355\) 1.76353 0.0935985
\(356\) −9.35113 −0.495609
\(357\) 8.41535 0.445388
\(358\) 8.18560 0.432622
\(359\) 17.8262 0.940829 0.470415 0.882446i \(-0.344104\pi\)
0.470415 + 0.882446i \(0.344104\pi\)
\(360\) 0.542814 0.0286088
\(361\) −14.7743 −0.777596
\(362\) 6.24534 0.328248
\(363\) −10.5993 −0.556321
\(364\) 3.05565 0.160159
\(365\) 6.67042 0.349146
\(366\) −11.2974 −0.590523
\(367\) 3.69689 0.192976 0.0964880 0.995334i \(-0.469239\pi\)
0.0964880 + 0.995334i \(0.469239\pi\)
\(368\) 6.49267 0.338454
\(369\) 2.61666 0.136218
\(370\) −0.281358 −0.0146271
\(371\) −38.6979 −2.00910
\(372\) −2.05565 −0.106580
\(373\) 17.8883 0.926222 0.463111 0.886300i \(-0.346733\pi\)
0.463111 + 0.886300i \(0.346733\pi\)
\(374\) 1.74326 0.0901420
\(375\) −5.26820 −0.272049
\(376\) 2.09567 0.108076
\(377\) −1.48269 −0.0763626
\(378\) 3.05565 0.157165
\(379\) −29.0777 −1.49362 −0.746812 0.665035i \(-0.768416\pi\)
−0.746812 + 0.665035i \(0.768416\pi\)
\(380\) 1.11583 0.0572410
\(381\) −1.73086 −0.0886744
\(382\) −21.2265 −1.08604
\(383\) 9.42500 0.481595 0.240797 0.970575i \(-0.422591\pi\)
0.240797 + 0.970575i \(0.422591\pi\)
\(384\) 1.00000 0.0510310
\(385\) 1.04990 0.0535078
\(386\) −9.87884 −0.502820
\(387\) 2.49072 0.126610
\(388\) −7.29369 −0.370281
\(389\) −23.4042 −1.18664 −0.593319 0.804967i \(-0.702183\pi\)
−0.593319 + 0.804967i \(0.702183\pi\)
\(390\) 0.542814 0.0274864
\(391\) 17.8810 0.904283
\(392\) 2.33697 0.118035
\(393\) 8.42898 0.425186
\(394\) −17.5032 −0.881799
\(395\) 5.46742 0.275096
\(396\) 0.632985 0.0318087
\(397\) −10.8257 −0.543325 −0.271663 0.962393i \(-0.587573\pi\)
−0.271663 + 0.962393i \(0.587573\pi\)
\(398\) −26.7000 −1.33835
\(399\) 6.28133 0.314460
\(400\) −4.70535 −0.235268
\(401\) −2.98820 −0.149223 −0.0746117 0.997213i \(-0.523772\pi\)
−0.0746117 + 0.997213i \(0.523772\pi\)
\(402\) 12.0004 0.598524
\(403\) −2.05565 −0.102399
\(404\) −15.2641 −0.759420
\(405\) 0.542814 0.0269726
\(406\) −4.53058 −0.224849
\(407\) −0.328098 −0.0162632
\(408\) 2.75403 0.136345
\(409\) −25.2550 −1.24878 −0.624391 0.781112i \(-0.714653\pi\)
−0.624391 + 0.781112i \(0.714653\pi\)
\(410\) 1.42036 0.0701466
\(411\) 8.45316 0.416964
\(412\) −1.00000 −0.0492665
\(413\) 2.58642 0.127269
\(414\) 6.49267 0.319097
\(415\) 2.63867 0.129527
\(416\) 1.00000 0.0490290
\(417\) −3.12795 −0.153177
\(418\) 1.30119 0.0636435
\(419\) −1.20744 −0.0589873 −0.0294937 0.999565i \(-0.509389\pi\)
−0.0294937 + 0.999565i \(0.509389\pi\)
\(420\) 1.65865 0.0809336
\(421\) 13.8740 0.676179 0.338089 0.941114i \(-0.390219\pi\)
0.338089 + 0.941114i \(0.390219\pi\)
\(422\) 14.8379 0.722298
\(423\) 2.09567 0.101895
\(424\) −12.6644 −0.615038
\(425\) −12.9587 −0.628590
\(426\) 3.24887 0.157408
\(427\) −34.5208 −1.67058
\(428\) −17.5531 −0.848462
\(429\) 0.632985 0.0305608
\(430\) 1.35200 0.0651990
\(431\) −11.8762 −0.572055 −0.286027 0.958221i \(-0.592335\pi\)
−0.286027 + 0.958221i \(0.592335\pi\)
\(432\) 1.00000 0.0481125
\(433\) 39.6312 1.90455 0.952277 0.305234i \(-0.0987346\pi\)
0.952277 + 0.305234i \(0.0987346\pi\)
\(434\) −6.28133 −0.301513
\(435\) −0.804826 −0.0385884
\(436\) −8.80317 −0.421596
\(437\) 13.3466 0.638456
\(438\) 12.2886 0.587172
\(439\) −18.7402 −0.894421 −0.447210 0.894429i \(-0.647582\pi\)
−0.447210 + 0.894429i \(0.647582\pi\)
\(440\) 0.343593 0.0163802
\(441\) 2.33697 0.111284
\(442\) 2.75403 0.130996
\(443\) −1.45204 −0.0689887 −0.0344943 0.999405i \(-0.510982\pi\)
−0.0344943 + 0.999405i \(0.510982\pi\)
\(444\) −0.518334 −0.0245990
\(445\) −5.07592 −0.240622
\(446\) −14.8504 −0.703185
\(447\) 9.04546 0.427836
\(448\) 3.05565 0.144366
\(449\) −31.2014 −1.47249 −0.736243 0.676717i \(-0.763402\pi\)
−0.736243 + 0.676717i \(0.763402\pi\)
\(450\) −4.70535 −0.221812
\(451\) 1.65631 0.0779925
\(452\) −1.00999 −0.0475061
\(453\) −18.2754 −0.858655
\(454\) 7.10596 0.333499
\(455\) 1.65865 0.0777585
\(456\) 2.05565 0.0962644
\(457\) −4.40435 −0.206027 −0.103013 0.994680i \(-0.532848\pi\)
−0.103013 + 0.994680i \(0.532848\pi\)
\(458\) 2.94089 0.137419
\(459\) 2.75403 0.128547
\(460\) 3.52431 0.164322
\(461\) 18.3876 0.856394 0.428197 0.903685i \(-0.359149\pi\)
0.428197 + 0.903685i \(0.359149\pi\)
\(462\) 1.93418 0.0899861
\(463\) −10.6320 −0.494110 −0.247055 0.969001i \(-0.579463\pi\)
−0.247055 + 0.969001i \(0.579463\pi\)
\(464\) −1.48269 −0.0688323
\(465\) −1.11583 −0.0517455
\(466\) 8.07222 0.373938
\(467\) 6.28660 0.290909 0.145455 0.989365i \(-0.453536\pi\)
0.145455 + 0.989365i \(0.453536\pi\)
\(468\) 1.00000 0.0462250
\(469\) 36.6689 1.69321
\(470\) 1.13756 0.0524717
\(471\) 15.5277 0.715480
\(472\) 0.846439 0.0389605
\(473\) 1.57659 0.0724916
\(474\) 10.0724 0.462639
\(475\) −9.67254 −0.443807
\(476\) 8.41535 0.385717
\(477\) −12.6644 −0.579863
\(478\) 4.41447 0.201913
\(479\) 1.22227 0.0558471 0.0279236 0.999610i \(-0.491110\pi\)
0.0279236 + 0.999610i \(0.491110\pi\)
\(480\) 0.542814 0.0247759
\(481\) −0.518334 −0.0236340
\(482\) −3.99479 −0.181958
\(483\) 19.8393 0.902720
\(484\) −10.5993 −0.481788
\(485\) −3.95912 −0.179774
\(486\) 1.00000 0.0453609
\(487\) 1.80937 0.0819903 0.0409951 0.999159i \(-0.486947\pi\)
0.0409951 + 0.999159i \(0.486947\pi\)
\(488\) −11.2974 −0.511408
\(489\) 15.4871 0.700353
\(490\) 1.26854 0.0573068
\(491\) −20.4058 −0.920902 −0.460451 0.887685i \(-0.652312\pi\)
−0.460451 + 0.887685i \(0.652312\pi\)
\(492\) 2.61666 0.117968
\(493\) −4.08339 −0.183907
\(494\) 2.05565 0.0924879
\(495\) 0.343593 0.0154434
\(496\) −2.05565 −0.0923012
\(497\) 9.92740 0.445305
\(498\) 4.86110 0.217831
\(499\) 25.4883 1.14101 0.570506 0.821293i \(-0.306747\pi\)
0.570506 + 0.821293i \(0.306747\pi\)
\(500\) −5.26820 −0.235601
\(501\) 8.73179 0.390107
\(502\) −3.11912 −0.139213
\(503\) −10.1064 −0.450623 −0.225311 0.974287i \(-0.572340\pi\)
−0.225311 + 0.974287i \(0.572340\pi\)
\(504\) 3.05565 0.136109
\(505\) −8.28558 −0.368704
\(506\) 4.10977 0.182701
\(507\) 1.00000 0.0444116
\(508\) −1.73086 −0.0767943
\(509\) 24.7866 1.09865 0.549323 0.835610i \(-0.314886\pi\)
0.549323 + 0.835610i \(0.314886\pi\)
\(510\) 1.49493 0.0661965
\(511\) 37.5496 1.66110
\(512\) 1.00000 0.0441942
\(513\) 2.05565 0.0907590
\(514\) 0.0449774 0.00198387
\(515\) −0.542814 −0.0239192
\(516\) 2.49072 0.109648
\(517\) 1.32653 0.0583407
\(518\) −1.58384 −0.0695901
\(519\) 21.1049 0.926401
\(520\) 0.542814 0.0238039
\(521\) −7.43893 −0.325905 −0.162953 0.986634i \(-0.552102\pi\)
−0.162953 + 0.986634i \(0.552102\pi\)
\(522\) −1.48269 −0.0648957
\(523\) −39.1467 −1.71177 −0.855883 0.517169i \(-0.826986\pi\)
−0.855883 + 0.517169i \(0.826986\pi\)
\(524\) 8.42898 0.368222
\(525\) −14.3779 −0.627503
\(526\) 28.7094 1.25179
\(527\) −5.66132 −0.246611
\(528\) 0.632985 0.0275471
\(529\) 19.1548 0.832817
\(530\) −6.87441 −0.298605
\(531\) 0.846439 0.0367323
\(532\) 6.28133 0.272330
\(533\) 2.61666 0.113340
\(534\) −9.35113 −0.404663
\(535\) −9.52807 −0.411934
\(536\) 12.0004 0.518337
\(537\) 8.18560 0.353235
\(538\) 13.4485 0.579807
\(539\) 1.47927 0.0637166
\(540\) 0.542814 0.0233590
\(541\) −18.0899 −0.777746 −0.388873 0.921291i \(-0.627135\pi\)
−0.388873 + 0.921291i \(0.627135\pi\)
\(542\) −8.93755 −0.383901
\(543\) 6.24534 0.268013
\(544\) 2.75403 0.118078
\(545\) −4.77848 −0.204688
\(546\) 3.05565 0.130770
\(547\) 16.3919 0.700867 0.350434 0.936588i \(-0.386034\pi\)
0.350434 + 0.936588i \(0.386034\pi\)
\(548\) 8.45316 0.361101
\(549\) −11.2974 −0.482160
\(550\) −2.97842 −0.127000
\(551\) −3.04789 −0.129845
\(552\) 6.49267 0.276347
\(553\) 30.7776 1.30880
\(554\) 8.96300 0.380801
\(555\) −0.281358 −0.0119430
\(556\) −3.12795 −0.132655
\(557\) −5.32319 −0.225551 −0.112775 0.993621i \(-0.535974\pi\)
−0.112775 + 0.993621i \(0.535974\pi\)
\(558\) −2.05565 −0.0870224
\(559\) 2.49072 0.105346
\(560\) 1.65865 0.0700906
\(561\) 1.74326 0.0736006
\(562\) 5.60492 0.236429
\(563\) −9.15521 −0.385846 −0.192923 0.981214i \(-0.561797\pi\)
−0.192923 + 0.981214i \(0.561797\pi\)
\(564\) 2.09567 0.0882437
\(565\) −0.548238 −0.0230645
\(566\) 13.6111 0.572117
\(567\) 3.05565 0.128325
\(568\) 3.24887 0.136320
\(569\) 13.9289 0.583929 0.291964 0.956429i \(-0.405691\pi\)
0.291964 + 0.956429i \(0.405691\pi\)
\(570\) 1.11583 0.0467371
\(571\) −37.2016 −1.55684 −0.778420 0.627744i \(-0.783978\pi\)
−0.778420 + 0.627744i \(0.783978\pi\)
\(572\) 0.632985 0.0264664
\(573\) −21.2265 −0.886752
\(574\) 7.99559 0.333730
\(575\) −30.5503 −1.27404
\(576\) 1.00000 0.0416667
\(577\) −3.84309 −0.159990 −0.0799950 0.996795i \(-0.525490\pi\)
−0.0799950 + 0.996795i \(0.525490\pi\)
\(578\) −9.41529 −0.391625
\(579\) −9.87884 −0.410551
\(580\) −0.804826 −0.0334186
\(581\) 14.8538 0.616239
\(582\) −7.29369 −0.302333
\(583\) −8.01638 −0.332005
\(584\) 12.2886 0.508506
\(585\) 0.542814 0.0224426
\(586\) −17.7380 −0.732751
\(587\) 38.2646 1.57935 0.789675 0.613526i \(-0.210249\pi\)
0.789675 + 0.613526i \(0.210249\pi\)
\(588\) 2.33697 0.0963751
\(589\) −4.22568 −0.174116
\(590\) 0.459459 0.0189156
\(591\) −17.5032 −0.719986
\(592\) −0.518334 −0.0213034
\(593\) 34.1185 1.40108 0.700539 0.713614i \(-0.252943\pi\)
0.700539 + 0.713614i \(0.252943\pi\)
\(594\) 0.632985 0.0259717
\(595\) 4.56797 0.187268
\(596\) 9.04546 0.370517
\(597\) −26.7000 −1.09276
\(598\) 6.49267 0.265505
\(599\) −16.2920 −0.665671 −0.332836 0.942985i \(-0.608005\pi\)
−0.332836 + 0.942985i \(0.608005\pi\)
\(600\) −4.70535 −0.192095
\(601\) 25.1192 1.02463 0.512317 0.858796i \(-0.328787\pi\)
0.512317 + 0.858796i \(0.328787\pi\)
\(602\) 7.61075 0.310191
\(603\) 12.0004 0.488692
\(604\) −18.2754 −0.743617
\(605\) −5.75346 −0.233911
\(606\) −15.2641 −0.620063
\(607\) 13.5665 0.550646 0.275323 0.961352i \(-0.411215\pi\)
0.275323 + 0.961352i \(0.411215\pi\)
\(608\) 2.05565 0.0833675
\(609\) −4.53058 −0.183589
\(610\) −6.13237 −0.248292
\(611\) 2.09567 0.0847818
\(612\) 2.75403 0.111325
\(613\) −10.3604 −0.418452 −0.209226 0.977867i \(-0.567095\pi\)
−0.209226 + 0.977867i \(0.567095\pi\)
\(614\) 6.26775 0.252946
\(615\) 1.42036 0.0572744
\(616\) 1.93418 0.0779303
\(617\) 4.53975 0.182763 0.0913817 0.995816i \(-0.470872\pi\)
0.0913817 + 0.995816i \(0.470872\pi\)
\(618\) −1.00000 −0.0402259
\(619\) −14.5122 −0.583293 −0.291647 0.956526i \(-0.594203\pi\)
−0.291647 + 0.956526i \(0.594203\pi\)
\(620\) −1.11583 −0.0448129
\(621\) 6.49267 0.260542
\(622\) 24.8115 0.994851
\(623\) −28.5737 −1.14478
\(624\) 1.00000 0.0400320
\(625\) 20.6671 0.826685
\(626\) −26.4684 −1.05789
\(627\) 1.30119 0.0519647
\(628\) 15.5277 0.619624
\(629\) −1.42751 −0.0569185
\(630\) 1.65865 0.0660820
\(631\) 9.81313 0.390654 0.195327 0.980738i \(-0.437423\pi\)
0.195327 + 0.980738i \(0.437423\pi\)
\(632\) 10.0724 0.400657
\(633\) 14.8379 0.589754
\(634\) 24.8381 0.986449
\(635\) −0.939532 −0.0372842
\(636\) −12.6644 −0.502176
\(637\) 2.33697 0.0925942
\(638\) −0.938523 −0.0371565
\(639\) 3.24887 0.128523
\(640\) 0.542814 0.0214566
\(641\) 8.38545 0.331205 0.165603 0.986193i \(-0.447043\pi\)
0.165603 + 0.986193i \(0.447043\pi\)
\(642\) −17.5531 −0.692766
\(643\) 3.02004 0.119099 0.0595495 0.998225i \(-0.481034\pi\)
0.0595495 + 0.998225i \(0.481034\pi\)
\(644\) 19.8393 0.781778
\(645\) 1.35200 0.0532348
\(646\) 5.66132 0.222742
\(647\) 4.43260 0.174264 0.0871318 0.996197i \(-0.472230\pi\)
0.0871318 + 0.996197i \(0.472230\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0.535784 0.0210313
\(650\) −4.70535 −0.184559
\(651\) −6.28133 −0.246185
\(652\) 15.4871 0.606524
\(653\) −0.274241 −0.0107319 −0.00536595 0.999986i \(-0.501708\pi\)
−0.00536595 + 0.999986i \(0.501708\pi\)
\(654\) −8.80317 −0.344231
\(655\) 4.57536 0.178774
\(656\) 2.61666 0.102163
\(657\) 12.2886 0.479424
\(658\) 6.40363 0.249640
\(659\) 47.4429 1.84811 0.924057 0.382256i \(-0.124853\pi\)
0.924057 + 0.382256i \(0.124853\pi\)
\(660\) 0.343593 0.0133743
\(661\) −33.6301 −1.30806 −0.654029 0.756469i \(-0.726923\pi\)
−0.654029 + 0.756469i \(0.726923\pi\)
\(662\) 24.3920 0.948024
\(663\) 2.75403 0.106958
\(664\) 4.86110 0.188647
\(665\) 3.40959 0.132218
\(666\) −0.518334 −0.0200850
\(667\) −9.62664 −0.372745
\(668\) 8.73179 0.337843
\(669\) −14.8504 −0.574148
\(670\) 6.51396 0.251656
\(671\) −7.15107 −0.276064
\(672\) 3.05565 0.117874
\(673\) −30.9360 −1.19249 −0.596247 0.802801i \(-0.703342\pi\)
−0.596247 + 0.802801i \(0.703342\pi\)
\(674\) −28.4373 −1.09536
\(675\) −4.70535 −0.181109
\(676\) 1.00000 0.0384615
\(677\) 7.31704 0.281217 0.140608 0.990065i \(-0.455094\pi\)
0.140608 + 0.990065i \(0.455094\pi\)
\(678\) −1.00999 −0.0387886
\(679\) −22.2869 −0.855295
\(680\) 1.49493 0.0573278
\(681\) 7.10596 0.272301
\(682\) −1.30119 −0.0498253
\(683\) 43.4758 1.66356 0.831778 0.555108i \(-0.187323\pi\)
0.831778 + 0.555108i \(0.187323\pi\)
\(684\) 2.05565 0.0785996
\(685\) 4.58849 0.175317
\(686\) −14.2486 −0.544013
\(687\) 2.94089 0.112202
\(688\) 2.49072 0.0949577
\(689\) −12.6644 −0.482475
\(690\) 3.52431 0.134168
\(691\) 0.441434 0.0167929 0.00839646 0.999965i \(-0.497327\pi\)
0.00839646 + 0.999965i \(0.497327\pi\)
\(692\) 21.1049 0.802287
\(693\) 1.93418 0.0734734
\(694\) 3.72720 0.141483
\(695\) −1.69790 −0.0644049
\(696\) −1.48269 −0.0562013
\(697\) 7.20638 0.272961
\(698\) −18.4589 −0.698679
\(699\) 8.07222 0.305319
\(700\) −14.3779 −0.543433
\(701\) −25.8603 −0.976731 −0.488365 0.872639i \(-0.662407\pi\)
−0.488365 + 0.872639i \(0.662407\pi\)
\(702\) 1.00000 0.0377426
\(703\) −1.06551 −0.0401865
\(704\) 0.632985 0.0238565
\(705\) 1.13756 0.0428430
\(706\) −10.9773 −0.413136
\(707\) −46.6418 −1.75415
\(708\) 0.846439 0.0318111
\(709\) −17.9601 −0.674507 −0.337254 0.941414i \(-0.609498\pi\)
−0.337254 + 0.941414i \(0.609498\pi\)
\(710\) 1.76353 0.0661841
\(711\) 10.0724 0.377743
\(712\) −9.35113 −0.350448
\(713\) −13.3466 −0.499835
\(714\) 8.41535 0.314937
\(715\) 0.343593 0.0128496
\(716\) 8.18560 0.305910
\(717\) 4.41447 0.164861
\(718\) 17.8262 0.665267
\(719\) −38.0909 −1.42055 −0.710276 0.703924i \(-0.751430\pi\)
−0.710276 + 0.703924i \(0.751430\pi\)
\(720\) 0.542814 0.0202295
\(721\) −3.05565 −0.113798
\(722\) −14.7743 −0.549843
\(723\) −3.99479 −0.148568
\(724\) 6.24534 0.232106
\(725\) 6.97659 0.259104
\(726\) −10.5993 −0.393378
\(727\) −11.9914 −0.444736 −0.222368 0.974963i \(-0.571379\pi\)
−0.222368 + 0.974963i \(0.571379\pi\)
\(728\) 3.05565 0.113250
\(729\) 1.00000 0.0370370
\(730\) 6.67042 0.246883
\(731\) 6.85952 0.253709
\(732\) −11.2974 −0.417563
\(733\) −19.4540 −0.718550 −0.359275 0.933232i \(-0.616976\pi\)
−0.359275 + 0.933232i \(0.616976\pi\)
\(734\) 3.69689 0.136455
\(735\) 1.26854 0.0467908
\(736\) 6.49267 0.239323
\(737\) 7.59605 0.279804
\(738\) 2.61666 0.0963207
\(739\) −25.2685 −0.929515 −0.464758 0.885438i \(-0.653859\pi\)
−0.464758 + 0.885438i \(0.653859\pi\)
\(740\) −0.281358 −0.0103429
\(741\) 2.05565 0.0755160
\(742\) −38.6979 −1.42065
\(743\) −7.19524 −0.263968 −0.131984 0.991252i \(-0.542135\pi\)
−0.131984 + 0.991252i \(0.542135\pi\)
\(744\) −2.05565 −0.0753636
\(745\) 4.91000 0.179888
\(746\) 17.8883 0.654938
\(747\) 4.86110 0.177858
\(748\) 1.74326 0.0637400
\(749\) −53.6361 −1.95982
\(750\) −5.26820 −0.192367
\(751\) 30.5362 1.11428 0.557140 0.830418i \(-0.311899\pi\)
0.557140 + 0.830418i \(0.311899\pi\)
\(752\) 2.09567 0.0764213
\(753\) −3.11912 −0.113667
\(754\) −1.48269 −0.0539965
\(755\) −9.92016 −0.361032
\(756\) 3.05565 0.111133
\(757\) 3.23081 0.117426 0.0587129 0.998275i \(-0.481300\pi\)
0.0587129 + 0.998275i \(0.481300\pi\)
\(758\) −29.0777 −1.05615
\(759\) 4.10977 0.149175
\(760\) 1.11583 0.0404755
\(761\) −28.5912 −1.03643 −0.518214 0.855251i \(-0.673403\pi\)
−0.518214 + 0.855251i \(0.673403\pi\)
\(762\) −1.73086 −0.0627023
\(763\) −26.8994 −0.973823
\(764\) −21.2265 −0.767950
\(765\) 1.49493 0.0540492
\(766\) 9.42500 0.340539
\(767\) 0.846439 0.0305632
\(768\) 1.00000 0.0360844
\(769\) 49.1119 1.77102 0.885511 0.464619i \(-0.153809\pi\)
0.885511 + 0.464619i \(0.153809\pi\)
\(770\) 1.04990 0.0378357
\(771\) 0.0449774 0.00161982
\(772\) −9.87884 −0.355547
\(773\) 31.4008 1.12941 0.564704 0.825294i \(-0.308990\pi\)
0.564704 + 0.825294i \(0.308990\pi\)
\(774\) 2.49072 0.0895270
\(775\) 9.67254 0.347448
\(776\) −7.29369 −0.261828
\(777\) −1.58384 −0.0568201
\(778\) −23.4042 −0.839080
\(779\) 5.37893 0.192720
\(780\) 0.542814 0.0194358
\(781\) 2.05649 0.0735869
\(782\) 17.8810 0.639425
\(783\) −1.48269 −0.0529871
\(784\) 2.33697 0.0834633
\(785\) 8.42867 0.300832
\(786\) 8.42898 0.300652
\(787\) 35.2321 1.25589 0.627944 0.778259i \(-0.283897\pi\)
0.627944 + 0.778259i \(0.283897\pi\)
\(788\) −17.5032 −0.623526
\(789\) 28.7094 1.02208
\(790\) 5.46742 0.194522
\(791\) −3.08618 −0.109732
\(792\) 0.632985 0.0224922
\(793\) −11.2974 −0.401182
\(794\) −10.8257 −0.384189
\(795\) −6.87441 −0.243810
\(796\) −26.7000 −0.946358
\(797\) 3.39691 0.120325 0.0601623 0.998189i \(-0.480838\pi\)
0.0601623 + 0.998189i \(0.480838\pi\)
\(798\) 6.28133 0.222357
\(799\) 5.77156 0.204183
\(800\) −4.70535 −0.166359
\(801\) −9.35113 −0.330406
\(802\) −2.98820 −0.105517
\(803\) 7.77851 0.274498
\(804\) 12.0004 0.423220
\(805\) 10.7690 0.379559
\(806\) −2.05565 −0.0724070
\(807\) 13.4485 0.473410
\(808\) −15.2641 −0.536991
\(809\) −13.9946 −0.492023 −0.246011 0.969267i \(-0.579120\pi\)
−0.246011 + 0.969267i \(0.579120\pi\)
\(810\) 0.542814 0.0190725
\(811\) −43.2608 −1.51909 −0.759546 0.650453i \(-0.774579\pi\)
−0.759546 + 0.650453i \(0.774579\pi\)
\(812\) −4.53058 −0.158992
\(813\) −8.93755 −0.313453
\(814\) −0.328098 −0.0114998
\(815\) 8.40663 0.294472
\(816\) 2.75403 0.0964105
\(817\) 5.12003 0.179127
\(818\) −25.2550 −0.883022
\(819\) 3.05565 0.106773
\(820\) 1.42036 0.0496011
\(821\) 42.8319 1.49485 0.747423 0.664349i \(-0.231291\pi\)
0.747423 + 0.664349i \(0.231291\pi\)
\(822\) 8.45316 0.294838
\(823\) 20.1546 0.702545 0.351273 0.936273i \(-0.385749\pi\)
0.351273 + 0.936273i \(0.385749\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −2.97842 −0.103695
\(826\) 2.58642 0.0899930
\(827\) 30.2332 1.05131 0.525656 0.850697i \(-0.323820\pi\)
0.525656 + 0.850697i \(0.323820\pi\)
\(828\) 6.49267 0.225636
\(829\) −13.4789 −0.468140 −0.234070 0.972220i \(-0.575204\pi\)
−0.234070 + 0.972220i \(0.575204\pi\)
\(830\) 2.63867 0.0915896
\(831\) 8.96300 0.310923
\(832\) 1.00000 0.0346688
\(833\) 6.43610 0.222998
\(834\) −3.12795 −0.108312
\(835\) 4.73973 0.164025
\(836\) 1.30119 0.0450027
\(837\) −2.05565 −0.0710535
\(838\) −1.20744 −0.0417103
\(839\) 23.6608 0.816861 0.408430 0.912790i \(-0.366076\pi\)
0.408430 + 0.912790i \(0.366076\pi\)
\(840\) 1.65865 0.0572287
\(841\) −26.8016 −0.924194
\(842\) 13.8740 0.478130
\(843\) 5.60492 0.193044
\(844\) 14.8379 0.510742
\(845\) 0.542814 0.0186734
\(846\) 2.09567 0.0720507
\(847\) −32.3878 −1.11286
\(848\) −12.6644 −0.434898
\(849\) 13.6111 0.467132
\(850\) −12.9587 −0.444480
\(851\) −3.36537 −0.115363
\(852\) 3.24887 0.111304
\(853\) 42.1021 1.44155 0.720774 0.693170i \(-0.243787\pi\)
0.720774 + 0.693170i \(0.243787\pi\)
\(854\) −34.5208 −1.18128
\(855\) 1.11583 0.0381607
\(856\) −17.5531 −0.599953
\(857\) −4.41287 −0.150741 −0.0753704 0.997156i \(-0.524014\pi\)
−0.0753704 + 0.997156i \(0.524014\pi\)
\(858\) 0.632985 0.0216098
\(859\) −11.8602 −0.404665 −0.202333 0.979317i \(-0.564852\pi\)
−0.202333 + 0.979317i \(0.564852\pi\)
\(860\) 1.35200 0.0461027
\(861\) 7.99559 0.272489
\(862\) −11.8762 −0.404504
\(863\) 21.0952 0.718088 0.359044 0.933321i \(-0.383103\pi\)
0.359044 + 0.933321i \(0.383103\pi\)
\(864\) 1.00000 0.0340207
\(865\) 11.4560 0.389516
\(866\) 39.6312 1.34672
\(867\) −9.41529 −0.319760
\(868\) −6.28133 −0.213202
\(869\) 6.37566 0.216279
\(870\) −0.804826 −0.0272861
\(871\) 12.0004 0.406617
\(872\) −8.80317 −0.298113
\(873\) −7.29369 −0.246854
\(874\) 13.3466 0.451457
\(875\) −16.0977 −0.544203
\(876\) 12.2886 0.415194
\(877\) −15.0715 −0.508927 −0.254464 0.967082i \(-0.581899\pi\)
−0.254464 + 0.967082i \(0.581899\pi\)
\(878\) −18.7402 −0.632451
\(879\) −17.7380 −0.598289
\(880\) 0.343593 0.0115825
\(881\) −20.9867 −0.707061 −0.353530 0.935423i \(-0.615019\pi\)
−0.353530 + 0.935423i \(0.615019\pi\)
\(882\) 2.33697 0.0786900
\(883\) 42.6118 1.43400 0.717000 0.697073i \(-0.245515\pi\)
0.717000 + 0.697073i \(0.245515\pi\)
\(884\) 2.75403 0.0926282
\(885\) 0.459459 0.0154445
\(886\) −1.45204 −0.0487824
\(887\) 11.4372 0.384023 0.192011 0.981393i \(-0.438499\pi\)
0.192011 + 0.981393i \(0.438499\pi\)
\(888\) −0.518334 −0.0173941
\(889\) −5.28888 −0.177383
\(890\) −5.07592 −0.170145
\(891\) 0.632985 0.0212058
\(892\) −14.8504 −0.497227
\(893\) 4.30796 0.144160
\(894\) 9.04546 0.302526
\(895\) 4.44325 0.148522
\(896\) 3.05565 0.102082
\(897\) 6.49267 0.216784
\(898\) −31.2014 −1.04121
\(899\) 3.04789 0.101653
\(900\) −4.70535 −0.156845
\(901\) −34.8782 −1.16196
\(902\) 1.65631 0.0551490
\(903\) 7.61075 0.253270
\(904\) −1.00999 −0.0335919
\(905\) 3.39006 0.112689
\(906\) −18.2754 −0.607161
\(907\) −57.8074 −1.91946 −0.959732 0.280919i \(-0.909361\pi\)
−0.959732 + 0.280919i \(0.909361\pi\)
\(908\) 7.10596 0.235820
\(909\) −15.2641 −0.506280
\(910\) 1.65865 0.0549836
\(911\) 40.3706 1.33754 0.668769 0.743471i \(-0.266822\pi\)
0.668769 + 0.743471i \(0.266822\pi\)
\(912\) 2.05565 0.0680692
\(913\) 3.07700 0.101834
\(914\) −4.40435 −0.145683
\(915\) −6.13237 −0.202730
\(916\) 2.94089 0.0971698
\(917\) 25.7560 0.850537
\(918\) 2.75403 0.0908967
\(919\) −6.88287 −0.227045 −0.113522 0.993535i \(-0.536213\pi\)
−0.113522 + 0.993535i \(0.536213\pi\)
\(920\) 3.52431 0.116193
\(921\) 6.26775 0.206529
\(922\) 18.3876 0.605562
\(923\) 3.24887 0.106938
\(924\) 1.93418 0.0636298
\(925\) 2.43894 0.0801919
\(926\) −10.6320 −0.349389
\(927\) −1.00000 −0.0328443
\(928\) −1.48269 −0.0486718
\(929\) −53.6348 −1.75970 −0.879850 0.475252i \(-0.842357\pi\)
−0.879850 + 0.475252i \(0.842357\pi\)
\(930\) −1.11583 −0.0365896
\(931\) 4.80399 0.157444
\(932\) 8.07222 0.264414
\(933\) 24.8115 0.812292
\(934\) 6.28660 0.205704
\(935\) 0.946267 0.0309462
\(936\) 1.00000 0.0326860
\(937\) −47.5909 −1.55473 −0.777364 0.629051i \(-0.783444\pi\)
−0.777364 + 0.629051i \(0.783444\pi\)
\(938\) 36.6689 1.19728
\(939\) −26.4684 −0.863763
\(940\) 1.13756 0.0371031
\(941\) −59.9987 −1.95590 −0.977952 0.208831i \(-0.933034\pi\)
−0.977952 + 0.208831i \(0.933034\pi\)
\(942\) 15.5277 0.505921
\(943\) 16.9891 0.553242
\(944\) 0.846439 0.0275493
\(945\) 1.65865 0.0539558
\(946\) 1.57659 0.0512593
\(947\) −29.0066 −0.942587 −0.471293 0.881976i \(-0.656213\pi\)
−0.471293 + 0.881976i \(0.656213\pi\)
\(948\) 10.0724 0.327135
\(949\) 12.2886 0.398905
\(950\) −9.67254 −0.313819
\(951\) 24.8381 0.805432
\(952\) 8.41535 0.272743
\(953\) −0.708339 −0.0229454 −0.0114727 0.999934i \(-0.503652\pi\)
−0.0114727 + 0.999934i \(0.503652\pi\)
\(954\) −12.6644 −0.410025
\(955\) −11.5221 −0.372845
\(956\) 4.41447 0.142774
\(957\) −0.938523 −0.0303381
\(958\) 1.22227 0.0394899
\(959\) 25.8299 0.834090
\(960\) 0.542814 0.0175192
\(961\) −26.7743 −0.863688
\(962\) −0.518334 −0.0167117
\(963\) −17.5531 −0.565641
\(964\) −3.99479 −0.128664
\(965\) −5.36237 −0.172621
\(966\) 19.8393 0.638319
\(967\) 27.6094 0.887859 0.443929 0.896062i \(-0.353584\pi\)
0.443929 + 0.896062i \(0.353584\pi\)
\(968\) −10.5993 −0.340675
\(969\) 5.66132 0.181868
\(970\) −3.95912 −0.127120
\(971\) −0.295774 −0.00949185 −0.00474592 0.999989i \(-0.501511\pi\)
−0.00474592 + 0.999989i \(0.501511\pi\)
\(972\) 1.00000 0.0320750
\(973\) −9.55792 −0.306413
\(974\) 1.80937 0.0579759
\(975\) −4.70535 −0.150692
\(976\) −11.2974 −0.361620
\(977\) −42.2062 −1.35030 −0.675148 0.737683i \(-0.735920\pi\)
−0.675148 + 0.737683i \(0.735920\pi\)
\(978\) 15.4871 0.495224
\(979\) −5.91913 −0.189176
\(980\) 1.26854 0.0405220
\(981\) −8.80317 −0.281064
\(982\) −20.4058 −0.651176
\(983\) 38.8764 1.23996 0.619982 0.784616i \(-0.287140\pi\)
0.619982 + 0.784616i \(0.287140\pi\)
\(984\) 2.61666 0.0834161
\(985\) −9.50098 −0.302726
\(986\) −4.08339 −0.130042
\(987\) 6.40363 0.203830
\(988\) 2.05565 0.0653988
\(989\) 16.1714 0.514221
\(990\) 0.343593 0.0109201
\(991\) −22.1102 −0.702353 −0.351177 0.936309i \(-0.614218\pi\)
−0.351177 + 0.936309i \(0.614218\pi\)
\(992\) −2.05565 −0.0652668
\(993\) 24.3920 0.774058
\(994\) 9.92740 0.314878
\(995\) −14.4931 −0.459464
\(996\) 4.86110 0.154030
\(997\) −17.8364 −0.564885 −0.282442 0.959284i \(-0.591145\pi\)
−0.282442 + 0.959284i \(0.591145\pi\)
\(998\) 25.4883 0.806818
\(999\) −0.518334 −0.0163993
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 8034.2.a.v.1.6 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.v.1.6 11 1.1 even 1 trivial