Properties

Label 289.2.a.d.1.3
Level $289$
Weight $2$
Character 289.1
Self dual yes
Analytic conductor $2.308$
Analytic rank $1$
Dimension $3$
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] = [289,2,Mod(1,289)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(289, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("289.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 289.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: \(2.30767661842\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{18})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 3x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.53209\) of defining polynomial
Character \(\chi\) \(=\) 289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.53209 q^{2} -1.34730 q^{3} +0.347296 q^{4} -3.53209 q^{5} -2.06418 q^{6} +0.347296 q^{7} -2.53209 q^{8} -1.18479 q^{9} +O(q^{10})\) \(q+1.53209 q^{2} -1.34730 q^{3} +0.347296 q^{4} -3.53209 q^{5} -2.06418 q^{6} +0.347296 q^{7} -2.53209 q^{8} -1.18479 q^{9} -5.41147 q^{10} +1.75877 q^{11} -0.467911 q^{12} -3.29086 q^{13} +0.532089 q^{14} +4.75877 q^{15} -4.57398 q^{16} -1.81521 q^{18} +1.53209 q^{19} -1.22668 q^{20} -0.467911 q^{21} +2.69459 q^{22} -2.81521 q^{23} +3.41147 q^{24} +7.47565 q^{25} -5.04189 q^{26} +5.63816 q^{27} +0.120615 q^{28} +1.18479 q^{29} +7.29086 q^{30} -7.10607 q^{31} -1.94356 q^{32} -2.36959 q^{33} -1.22668 q^{35} -0.411474 q^{36} +3.92127 q^{37} +2.34730 q^{38} +4.43376 q^{39} +8.94356 q^{40} -4.92127 q^{41} -0.716881 q^{42} +10.9855 q^{43} +0.610815 q^{44} +4.18479 q^{45} -4.31315 q^{46} -5.12061 q^{47} +6.16250 q^{48} -6.87939 q^{49} +11.4534 q^{50} -1.14290 q^{52} -8.36959 q^{53} +8.63816 q^{54} -6.21213 q^{55} -0.879385 q^{56} -2.06418 q^{57} +1.81521 q^{58} -10.8648 q^{59} +1.65270 q^{60} +4.41147 q^{61} -10.8871 q^{62} -0.411474 q^{63} +6.17024 q^{64} +11.6236 q^{65} -3.63041 q^{66} +8.07192 q^{67} +3.79292 q^{69} -1.87939 q^{70} -11.2490 q^{71} +3.00000 q^{72} -1.70233 q^{73} +6.00774 q^{74} -10.0719 q^{75} +0.532089 q^{76} +0.610815 q^{77} +6.79292 q^{78} -11.5817 q^{79} +16.1557 q^{80} -4.04189 q^{81} -7.53983 q^{82} -2.14796 q^{83} -0.162504 q^{84} +16.8307 q^{86} -1.59627 q^{87} -4.45336 q^{88} +6.41921 q^{89} +6.41147 q^{90} -1.14290 q^{91} -0.977711 q^{92} +9.57398 q^{93} -7.84524 q^{94} -5.41147 q^{95} +2.61856 q^{96} -4.08378 q^{97} -10.5398 q^{98} -2.08378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 3 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{18} + 3 q^{20} - 6 q^{21} + 6 q^{22} - 12 q^{23} + 3 q^{25} - 12 q^{26} + 6 q^{28} + 6 q^{30} - 9 q^{31} + 9 q^{32} + 3 q^{35} + 9 q^{36} + 3 q^{37} + 6 q^{38} - 3 q^{39} + 12 q^{40} - 6 q^{41} + 6 q^{42} + 15 q^{43} + 6 q^{44} + 9 q^{45} + 9 q^{46} - 21 q^{47} + 21 q^{48} - 15 q^{49} + 21 q^{50} - 3 q^{52} - 18 q^{53} + 9 q^{54} + 6 q^{55} + 3 q^{56} + 3 q^{57} + 9 q^{58} - 9 q^{59} + 6 q^{60} + 3 q^{61} - 3 q^{62} + 9 q^{63} - 3 q^{64} - 18 q^{66} - 9 q^{67} + 21 q^{69} - 21 q^{71} + 9 q^{72} + 21 q^{73} - 6 q^{74} + 3 q^{75} - 3 q^{76} + 6 q^{77} + 30 q^{78} - 3 q^{79} + 9 q^{80} - 9 q^{81} + 6 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{86} + 9 q^{87} - 15 q^{89} + 9 q^{90} - 3 q^{91} - 9 q^{92} + 21 q^{93} + 3 q^{94} - 6 q^{95} - 12 q^{96} - 6 q^{97} - 3 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.53209 1.08335 0.541675 0.840588i \(-0.317790\pi\)
0.541675 + 0.840588i \(0.317790\pi\)
\(3\) −1.34730 −0.777862 −0.388931 0.921267i \(-0.627156\pi\)
−0.388931 + 0.921267i \(0.627156\pi\)
\(4\) 0.347296 0.173648
\(5\) −3.53209 −1.57960 −0.789799 0.613366i \(-0.789815\pi\)
−0.789799 + 0.613366i \(0.789815\pi\)
\(6\) −2.06418 −0.842697
\(7\) 0.347296 0.131266 0.0656328 0.997844i \(-0.479093\pi\)
0.0656328 + 0.997844i \(0.479093\pi\)
\(8\) −2.53209 −0.895229
\(9\) −1.18479 −0.394931
\(10\) −5.41147 −1.71126
\(11\) 1.75877 0.530289 0.265145 0.964209i \(-0.414580\pi\)
0.265145 + 0.964209i \(0.414580\pi\)
\(12\) −0.467911 −0.135074
\(13\) −3.29086 −0.912720 −0.456360 0.889795i \(-0.650847\pi\)
−0.456360 + 0.889795i \(0.650847\pi\)
\(14\) 0.532089 0.142207
\(15\) 4.75877 1.22871
\(16\) −4.57398 −1.14349
\(17\) 0 0
\(18\) −1.81521 −0.427849
\(19\) 1.53209 0.351485 0.175743 0.984436i \(-0.443767\pi\)
0.175743 + 0.984436i \(0.443767\pi\)
\(20\) −1.22668 −0.274294
\(21\) −0.467911 −0.102107
\(22\) 2.69459 0.574489
\(23\) −2.81521 −0.587011 −0.293506 0.955957i \(-0.594822\pi\)
−0.293506 + 0.955957i \(0.594822\pi\)
\(24\) 3.41147 0.696364
\(25\) 7.47565 1.49513
\(26\) −5.04189 −0.988796
\(27\) 5.63816 1.08506
\(28\) 0.120615 0.0227940
\(29\) 1.18479 0.220010 0.110005 0.993931i \(-0.464913\pi\)
0.110005 + 0.993931i \(0.464913\pi\)
\(30\) 7.29086 1.33112
\(31\) −7.10607 −1.27629 −0.638144 0.769917i \(-0.720297\pi\)
−0.638144 + 0.769917i \(0.720297\pi\)
\(32\) −1.94356 −0.343577
\(33\) −2.36959 −0.412492
\(34\) 0 0
\(35\) −1.22668 −0.207347
\(36\) −0.411474 −0.0685790
\(37\) 3.92127 0.644654 0.322327 0.946628i \(-0.395535\pi\)
0.322327 + 0.946628i \(0.395535\pi\)
\(38\) 2.34730 0.380782
\(39\) 4.43376 0.709970
\(40\) 8.94356 1.41410
\(41\) −4.92127 −0.768574 −0.384287 0.923214i \(-0.625553\pi\)
−0.384287 + 0.923214i \(0.625553\pi\)
\(42\) −0.716881 −0.110617
\(43\) 10.9855 1.67527 0.837633 0.546234i \(-0.183939\pi\)
0.837633 + 0.546234i \(0.183939\pi\)
\(44\) 0.610815 0.0920838
\(45\) 4.18479 0.623832
\(46\) −4.31315 −0.635939
\(47\) −5.12061 −0.746918 −0.373459 0.927647i \(-0.621828\pi\)
−0.373459 + 0.927647i \(0.621828\pi\)
\(48\) 6.16250 0.889481
\(49\) −6.87939 −0.982769
\(50\) 11.4534 1.61975
\(51\) 0 0
\(52\) −1.14290 −0.158492
\(53\) −8.36959 −1.14965 −0.574825 0.818276i \(-0.694930\pi\)
−0.574825 + 0.818276i \(0.694930\pi\)
\(54\) 8.63816 1.17550
\(55\) −6.21213 −0.837644
\(56\) −0.879385 −0.117513
\(57\) −2.06418 −0.273407
\(58\) 1.81521 0.238348
\(59\) −10.8648 −1.41448 −0.707241 0.706973i \(-0.750060\pi\)
−0.707241 + 0.706973i \(0.750060\pi\)
\(60\) 1.65270 0.213363
\(61\) 4.41147 0.564831 0.282416 0.959292i \(-0.408864\pi\)
0.282416 + 0.959292i \(0.408864\pi\)
\(62\) −10.8871 −1.38267
\(63\) −0.411474 −0.0518409
\(64\) 6.17024 0.771281
\(65\) 11.6236 1.44173
\(66\) −3.63041 −0.446873
\(67\) 8.07192 0.986142 0.493071 0.869989i \(-0.335874\pi\)
0.493071 + 0.869989i \(0.335874\pi\)
\(68\) 0 0
\(69\) 3.79292 0.456614
\(70\) −1.87939 −0.224630
\(71\) −11.2490 −1.33501 −0.667504 0.744607i \(-0.732637\pi\)
−0.667504 + 0.744607i \(0.732637\pi\)
\(72\) 3.00000 0.353553
\(73\) −1.70233 −0.199243 −0.0996215 0.995025i \(-0.531763\pi\)
−0.0996215 + 0.995025i \(0.531763\pi\)
\(74\) 6.00774 0.698386
\(75\) −10.0719 −1.16300
\(76\) 0.532089 0.0610348
\(77\) 0.610815 0.0696088
\(78\) 6.79292 0.769147
\(79\) −11.5817 −1.30305 −0.651523 0.758629i \(-0.725869\pi\)
−0.651523 + 0.758629i \(0.725869\pi\)
\(80\) 16.1557 1.80626
\(81\) −4.04189 −0.449099
\(82\) −7.53983 −0.832635
\(83\) −2.14796 −0.235769 −0.117884 0.993027i \(-0.537611\pi\)
−0.117884 + 0.993027i \(0.537611\pi\)
\(84\) −0.162504 −0.0177306
\(85\) 0 0
\(86\) 16.8307 1.81490
\(87\) −1.59627 −0.171138
\(88\) −4.45336 −0.474730
\(89\) 6.41921 0.680435 0.340218 0.940347i \(-0.389499\pi\)
0.340218 + 0.940347i \(0.389499\pi\)
\(90\) 6.41147 0.675829
\(91\) −1.14290 −0.119809
\(92\) −0.977711 −0.101933
\(93\) 9.57398 0.992775
\(94\) −7.84524 −0.809174
\(95\) −5.41147 −0.555206
\(96\) 2.61856 0.267255
\(97\) −4.08378 −0.414645 −0.207322 0.978273i \(-0.566475\pi\)
−0.207322 + 0.978273i \(0.566475\pi\)
\(98\) −10.5398 −1.06468
\(99\) −2.08378 −0.209428
\(100\) 2.59627 0.259627
\(101\) 5.26857 0.524242 0.262121 0.965035i \(-0.415578\pi\)
0.262121 + 0.965035i \(0.415578\pi\)
\(102\) 0 0
\(103\) −18.4388 −1.81683 −0.908415 0.418069i \(-0.862707\pi\)
−0.908415 + 0.418069i \(0.862707\pi\)
\(104\) 8.33275 0.817093
\(105\) 1.65270 0.161287
\(106\) −12.8229 −1.24547
\(107\) −5.36184 −0.518349 −0.259175 0.965831i \(-0.583450\pi\)
−0.259175 + 0.965831i \(0.583450\pi\)
\(108\) 1.95811 0.188419
\(109\) 15.5175 1.48631 0.743155 0.669119i \(-0.233328\pi\)
0.743155 + 0.669119i \(0.233328\pi\)
\(110\) −9.51754 −0.907462
\(111\) −5.28312 −0.501451
\(112\) −1.58853 −0.150102
\(113\) 7.02734 0.661077 0.330538 0.943793i \(-0.392770\pi\)
0.330538 + 0.943793i \(0.392770\pi\)
\(114\) −3.16250 −0.296196
\(115\) 9.94356 0.927242
\(116\) 0.411474 0.0382044
\(117\) 3.89899 0.360461
\(118\) −16.6459 −1.53238
\(119\) 0 0
\(120\) −12.0496 −1.09998
\(121\) −7.90673 −0.718793
\(122\) 6.75877 0.611910
\(123\) 6.63041 0.597844
\(124\) −2.46791 −0.221625
\(125\) −8.74422 −0.782107
\(126\) −0.630415 −0.0561618
\(127\) 7.74422 0.687189 0.343594 0.939118i \(-0.388355\pi\)
0.343594 + 0.939118i \(0.388355\pi\)
\(128\) 13.3405 1.17914
\(129\) −14.8007 −1.30313
\(130\) 17.8084 1.56190
\(131\) −18.6186 −1.62671 −0.813355 0.581767i \(-0.802361\pi\)
−0.813355 + 0.581767i \(0.802361\pi\)
\(132\) −0.822948 −0.0716285
\(133\) 0.532089 0.0461380
\(134\) 12.3669 1.06834
\(135\) −19.9145 −1.71396
\(136\) 0 0
\(137\) 10.0719 0.860502 0.430251 0.902709i \(-0.358425\pi\)
0.430251 + 0.902709i \(0.358425\pi\)
\(138\) 5.81109 0.494673
\(139\) 8.55438 0.725573 0.362786 0.931872i \(-0.381825\pi\)
0.362786 + 0.931872i \(0.381825\pi\)
\(140\) −0.426022 −0.0360054
\(141\) 6.89899 0.580999
\(142\) −17.2344 −1.44628
\(143\) −5.78787 −0.484006
\(144\) 5.41921 0.451601
\(145\) −4.18479 −0.347528
\(146\) −2.60813 −0.215850
\(147\) 9.26857 0.764459
\(148\) 1.36184 0.111943
\(149\) 11.8794 0.973197 0.486599 0.873626i \(-0.338237\pi\)
0.486599 + 0.873626i \(0.338237\pi\)
\(150\) −15.4311 −1.25994
\(151\) 6.55943 0.533799 0.266899 0.963724i \(-0.414001\pi\)
0.266899 + 0.963724i \(0.414001\pi\)
\(152\) −3.87939 −0.314660
\(153\) 0 0
\(154\) 0.935822 0.0754107
\(155\) 25.0993 2.01602
\(156\) 1.53983 0.123285
\(157\) 8.88444 0.709055 0.354528 0.935046i \(-0.384642\pi\)
0.354528 + 0.935046i \(0.384642\pi\)
\(158\) −17.7442 −1.41165
\(159\) 11.2763 0.894270
\(160\) 6.86484 0.542713
\(161\) −0.977711 −0.0770544
\(162\) −6.19253 −0.486531
\(163\) 9.68004 0.758200 0.379100 0.925356i \(-0.376234\pi\)
0.379100 + 0.925356i \(0.376234\pi\)
\(164\) −1.70914 −0.133461
\(165\) 8.36959 0.651571
\(166\) −3.29086 −0.255420
\(167\) −1.83750 −0.142190 −0.0710949 0.997470i \(-0.522649\pi\)
−0.0710949 + 0.997470i \(0.522649\pi\)
\(168\) 1.18479 0.0914087
\(169\) −2.17024 −0.166942
\(170\) 0 0
\(171\) −1.81521 −0.138812
\(172\) 3.81521 0.290907
\(173\) −22.7597 −1.73039 −0.865194 0.501437i \(-0.832805\pi\)
−0.865194 + 0.501437i \(0.832805\pi\)
\(174\) −2.44562 −0.185402
\(175\) 2.59627 0.196259
\(176\) −8.04458 −0.606383
\(177\) 14.6382 1.10027
\(178\) 9.83481 0.737150
\(179\) −17.5253 −1.30990 −0.654951 0.755672i \(-0.727311\pi\)
−0.654951 + 0.755672i \(0.727311\pi\)
\(180\) 1.45336 0.108327
\(181\) 4.56212 0.339100 0.169550 0.985522i \(-0.445769\pi\)
0.169550 + 0.985522i \(0.445769\pi\)
\(182\) −1.75103 −0.129795
\(183\) −5.94356 −0.439361
\(184\) 7.12836 0.525509
\(185\) −13.8503 −1.01829
\(186\) 14.6682 1.07552
\(187\) 0 0
\(188\) −1.77837 −0.129701
\(189\) 1.95811 0.142432
\(190\) −8.29086 −0.601482
\(191\) −9.72462 −0.703649 −0.351824 0.936066i \(-0.614439\pi\)
−0.351824 + 0.936066i \(0.614439\pi\)
\(192\) −8.31315 −0.599950
\(193\) 0.844303 0.0607743 0.0303871 0.999538i \(-0.490326\pi\)
0.0303871 + 0.999538i \(0.490326\pi\)
\(194\) −6.25671 −0.449206
\(195\) −15.6604 −1.12147
\(196\) −2.38919 −0.170656
\(197\) −17.0009 −1.21127 −0.605633 0.795744i \(-0.707080\pi\)
−0.605633 + 0.795744i \(0.707080\pi\)
\(198\) −3.19253 −0.226883
\(199\) 12.6955 0.899962 0.449981 0.893038i \(-0.351431\pi\)
0.449981 + 0.893038i \(0.351431\pi\)
\(200\) −18.9290 −1.33848
\(201\) −10.8753 −0.767082
\(202\) 8.07192 0.567938
\(203\) 0.411474 0.0288798
\(204\) 0 0
\(205\) 17.3824 1.21404
\(206\) −28.2499 −1.96826
\(207\) 3.33544 0.231829
\(208\) 15.0523 1.04369
\(209\) 2.69459 0.186389
\(210\) 2.53209 0.174731
\(211\) −23.5303 −1.61990 −0.809948 0.586502i \(-0.800504\pi\)
−0.809948 + 0.586502i \(0.800504\pi\)
\(212\) −2.90673 −0.199635
\(213\) 15.1557 1.03845
\(214\) −8.21482 −0.561554
\(215\) −38.8016 −2.64625
\(216\) −14.2763 −0.971380
\(217\) −2.46791 −0.167533
\(218\) 23.7743 1.61020
\(219\) 2.29355 0.154984
\(220\) −2.15745 −0.145455
\(221\) 0 0
\(222\) −8.09421 −0.543248
\(223\) 4.97090 0.332876 0.166438 0.986052i \(-0.446773\pi\)
0.166438 + 0.986052i \(0.446773\pi\)
\(224\) −0.674992 −0.0450998
\(225\) −8.85710 −0.590473
\(226\) 10.7665 0.716178
\(227\) 5.25671 0.348900 0.174450 0.984666i \(-0.444185\pi\)
0.174450 + 0.984666i \(0.444185\pi\)
\(228\) −0.716881 −0.0474766
\(229\) −24.2053 −1.59953 −0.799767 0.600311i \(-0.795043\pi\)
−0.799767 + 0.600311i \(0.795043\pi\)
\(230\) 15.2344 1.00453
\(231\) −0.822948 −0.0541460
\(232\) −3.00000 −0.196960
\(233\) 28.7219 1.88164 0.940818 0.338912i \(-0.110059\pi\)
0.940818 + 0.338912i \(0.110059\pi\)
\(234\) 5.97359 0.390506
\(235\) 18.0865 1.17983
\(236\) −3.77332 −0.245622
\(237\) 15.6040 1.01359
\(238\) 0 0
\(239\) −2.63310 −0.170321 −0.0851606 0.996367i \(-0.527140\pi\)
−0.0851606 + 0.996367i \(0.527140\pi\)
\(240\) −21.7665 −1.40502
\(241\) 25.3337 1.63189 0.815943 0.578132i \(-0.196218\pi\)
0.815943 + 0.578132i \(0.196218\pi\)
\(242\) −12.1138 −0.778705
\(243\) −11.4688 −0.735727
\(244\) 1.53209 0.0980819
\(245\) 24.2986 1.55238
\(246\) 10.1584 0.647675
\(247\) −5.04189 −0.320808
\(248\) 17.9932 1.14257
\(249\) 2.89393 0.183396
\(250\) −13.3969 −0.847296
\(251\) 10.6851 0.674437 0.337219 0.941426i \(-0.390514\pi\)
0.337219 + 0.941426i \(0.390514\pi\)
\(252\) −0.142903 −0.00900207
\(253\) −4.95130 −0.311286
\(254\) 11.8648 0.744466
\(255\) 0 0
\(256\) 8.09833 0.506145
\(257\) −3.73648 −0.233075 −0.116538 0.993186i \(-0.537180\pi\)
−0.116538 + 0.993186i \(0.537180\pi\)
\(258\) −22.6759 −1.41174
\(259\) 1.36184 0.0846209
\(260\) 4.03684 0.250354
\(261\) −1.40373 −0.0868889
\(262\) −28.5253 −1.76230
\(263\) 10.2094 0.629541 0.314771 0.949168i \(-0.398072\pi\)
0.314771 + 0.949168i \(0.398072\pi\)
\(264\) 6.00000 0.369274
\(265\) 29.5621 1.81599
\(266\) 0.815207 0.0499836
\(267\) −8.64858 −0.529285
\(268\) 2.80335 0.171242
\(269\) −11.7392 −0.715750 −0.357875 0.933770i \(-0.616499\pi\)
−0.357875 + 0.933770i \(0.616499\pi\)
\(270\) −30.5107 −1.85682
\(271\) 17.0000 1.03268 0.516338 0.856385i \(-0.327295\pi\)
0.516338 + 0.856385i \(0.327295\pi\)
\(272\) 0 0
\(273\) 1.53983 0.0931947
\(274\) 15.4311 0.932225
\(275\) 13.1480 0.792852
\(276\) 1.31727 0.0792901
\(277\) 24.3432 1.46264 0.731320 0.682035i \(-0.238905\pi\)
0.731320 + 0.682035i \(0.238905\pi\)
\(278\) 13.1061 0.786050
\(279\) 8.41921 0.504045
\(280\) 3.10607 0.185623
\(281\) −5.79385 −0.345632 −0.172816 0.984954i \(-0.555287\pi\)
−0.172816 + 0.984954i \(0.555287\pi\)
\(282\) 10.5699 0.629426
\(283\) 15.3200 0.910677 0.455338 0.890318i \(-0.349518\pi\)
0.455338 + 0.890318i \(0.349518\pi\)
\(284\) −3.90673 −0.231822
\(285\) 7.29086 0.431873
\(286\) −8.86753 −0.524348
\(287\) −1.70914 −0.100887
\(288\) 2.30272 0.135689
\(289\) 0 0
\(290\) −6.41147 −0.376495
\(291\) 5.50206 0.322536
\(292\) −0.591214 −0.0345982
\(293\) 2.98040 0.174117 0.0870584 0.996203i \(-0.472253\pi\)
0.0870584 + 0.996203i \(0.472253\pi\)
\(294\) 14.2003 0.828177
\(295\) 38.3756 2.23431
\(296\) −9.92902 −0.577112
\(297\) 9.91622 0.575398
\(298\) 18.2003 1.05431
\(299\) 9.26445 0.535777
\(300\) −3.49794 −0.201954
\(301\) 3.81521 0.219905
\(302\) 10.0496 0.578291
\(303\) −7.09833 −0.407788
\(304\) −7.00774 −0.401921
\(305\) −15.5817 −0.892207
\(306\) 0 0
\(307\) −3.26857 −0.186547 −0.0932736 0.995641i \(-0.529733\pi\)
−0.0932736 + 0.995641i \(0.529733\pi\)
\(308\) 0.212134 0.0120874
\(309\) 24.8425 1.41324
\(310\) 38.4543 2.18406
\(311\) −3.53209 −0.200286 −0.100143 0.994973i \(-0.531930\pi\)
−0.100143 + 0.994973i \(0.531930\pi\)
\(312\) −11.2267 −0.635586
\(313\) −1.48246 −0.0837935 −0.0418968 0.999122i \(-0.513340\pi\)
−0.0418968 + 0.999122i \(0.513340\pi\)
\(314\) 13.6117 0.768155
\(315\) 1.45336 0.0818877
\(316\) −4.02229 −0.226271
\(317\) 14.4638 0.812368 0.406184 0.913791i \(-0.366859\pi\)
0.406184 + 0.913791i \(0.366859\pi\)
\(318\) 17.2763 0.968807
\(319\) 2.08378 0.116669
\(320\) −21.7939 −1.21831
\(321\) 7.22399 0.403204
\(322\) −1.49794 −0.0834770
\(323\) 0 0
\(324\) −1.40373 −0.0779852
\(325\) −24.6013 −1.36464
\(326\) 14.8307 0.821396
\(327\) −20.9067 −1.15614
\(328\) 12.4611 0.688049
\(329\) −1.77837 −0.0980448
\(330\) 12.8229 0.705880
\(331\) −9.03508 −0.496613 −0.248307 0.968682i \(-0.579874\pi\)
−0.248307 + 0.968682i \(0.579874\pi\)
\(332\) −0.745977 −0.0409408
\(333\) −4.64590 −0.254594
\(334\) −2.81521 −0.154041
\(335\) −28.5107 −1.55771
\(336\) 2.14022 0.116758
\(337\) 17.9659 0.978662 0.489331 0.872098i \(-0.337241\pi\)
0.489331 + 0.872098i \(0.337241\pi\)
\(338\) −3.32501 −0.180857
\(339\) −9.46791 −0.514226
\(340\) 0 0
\(341\) −12.4979 −0.676801
\(342\) −2.78106 −0.150382
\(343\) −4.82026 −0.260270
\(344\) −27.8161 −1.49975
\(345\) −13.3969 −0.721266
\(346\) −34.8699 −1.87462
\(347\) 7.78375 0.417853 0.208927 0.977931i \(-0.433003\pi\)
0.208927 + 0.977931i \(0.433003\pi\)
\(348\) −0.554378 −0.0297178
\(349\) −6.65002 −0.355967 −0.177984 0.984033i \(-0.556957\pi\)
−0.177984 + 0.984033i \(0.556957\pi\)
\(350\) 3.97771 0.212618
\(351\) −18.5544 −0.990359
\(352\) −3.41828 −0.182195
\(353\) 4.14559 0.220648 0.110324 0.993896i \(-0.464811\pi\)
0.110324 + 0.993896i \(0.464811\pi\)
\(354\) 22.4270 1.19198
\(355\) 39.7324 2.10877
\(356\) 2.22937 0.118156
\(357\) 0 0
\(358\) −26.8503 −1.41908
\(359\) −17.0770 −0.901288 −0.450644 0.892704i \(-0.648806\pi\)
−0.450644 + 0.892704i \(0.648806\pi\)
\(360\) −10.5963 −0.558472
\(361\) −16.6527 −0.876458
\(362\) 6.98957 0.367364
\(363\) 10.6527 0.559122
\(364\) −0.396926 −0.0208046
\(365\) 6.01279 0.314724
\(366\) −9.10607 −0.475982
\(367\) −18.8307 −0.982954 −0.491477 0.870891i \(-0.663543\pi\)
−0.491477 + 0.870891i \(0.663543\pi\)
\(368\) 12.8767 0.671244
\(369\) 5.83069 0.303534
\(370\) −21.2199 −1.10317
\(371\) −2.90673 −0.150910
\(372\) 3.32501 0.172394
\(373\) −11.7314 −0.607430 −0.303715 0.952763i \(-0.598227\pi\)
−0.303715 + 0.952763i \(0.598227\pi\)
\(374\) 0 0
\(375\) 11.7811 0.608371
\(376\) 12.9659 0.668663
\(377\) −3.89899 −0.200808
\(378\) 3.00000 0.154303
\(379\) −8.16519 −0.419418 −0.209709 0.977764i \(-0.567252\pi\)
−0.209709 + 0.977764i \(0.567252\pi\)
\(380\) −1.87939 −0.0964104
\(381\) −10.4338 −0.534538
\(382\) −14.8990 −0.762298
\(383\) 16.2540 0.830542 0.415271 0.909698i \(-0.363687\pi\)
0.415271 + 0.909698i \(0.363687\pi\)
\(384\) −17.9736 −0.917211
\(385\) −2.15745 −0.109954
\(386\) 1.29355 0.0658398
\(387\) −13.0155 −0.661614
\(388\) −1.41828 −0.0720023
\(389\) −5.80747 −0.294450 −0.147225 0.989103i \(-0.547034\pi\)
−0.147225 + 0.989103i \(0.547034\pi\)
\(390\) −23.9932 −1.21494
\(391\) 0 0
\(392\) 17.4192 0.879803
\(393\) 25.0847 1.26536
\(394\) −26.0469 −1.31223
\(395\) 40.9077 2.05829
\(396\) −0.723689 −0.0363667
\(397\) −10.2517 −0.514516 −0.257258 0.966343i \(-0.582819\pi\)
−0.257258 + 0.966343i \(0.582819\pi\)
\(398\) 19.4507 0.974974
\(399\) −0.716881 −0.0358890
\(400\) −34.1935 −1.70967
\(401\) −30.5621 −1.52620 −0.763100 0.646281i \(-0.776323\pi\)
−0.763100 + 0.646281i \(0.776323\pi\)
\(402\) −16.6619 −0.831019
\(403\) 23.3851 1.16489
\(404\) 1.82976 0.0910337
\(405\) 14.2763 0.709396
\(406\) 0.630415 0.0312870
\(407\) 6.89662 0.341853
\(408\) 0 0
\(409\) 19.9736 0.987631 0.493815 0.869567i \(-0.335602\pi\)
0.493815 + 0.869567i \(0.335602\pi\)
\(410\) 26.6313 1.31523
\(411\) −13.5699 −0.669352
\(412\) −6.40373 −0.315489
\(413\) −3.77332 −0.185673
\(414\) 5.11019 0.251152
\(415\) 7.58677 0.372420
\(416\) 6.39599 0.313589
\(417\) −11.5253 −0.564395
\(418\) 4.12836 0.201924
\(419\) 16.9290 0.827037 0.413518 0.910496i \(-0.364300\pi\)
0.413518 + 0.910496i \(0.364300\pi\)
\(420\) 0.573978 0.0280073
\(421\) −23.7297 −1.15651 −0.578257 0.815855i \(-0.696267\pi\)
−0.578257 + 0.815855i \(0.696267\pi\)
\(422\) −36.0506 −1.75491
\(423\) 6.06687 0.294981
\(424\) 21.1925 1.02920
\(425\) 0 0
\(426\) 23.2199 1.12501
\(427\) 1.53209 0.0741430
\(428\) −1.86215 −0.0900104
\(429\) 7.79797 0.376490
\(430\) −59.4475 −2.86681
\(431\) −23.5921 −1.13639 −0.568197 0.822893i \(-0.692359\pi\)
−0.568197 + 0.822893i \(0.692359\pi\)
\(432\) −25.7888 −1.24076
\(433\) −12.6946 −0.610063 −0.305032 0.952342i \(-0.598667\pi\)
−0.305032 + 0.952342i \(0.598667\pi\)
\(434\) −3.78106 −0.181497
\(435\) 5.63816 0.270329
\(436\) 5.38919 0.258095
\(437\) −4.31315 −0.206326
\(438\) 3.51392 0.167902
\(439\) −23.4706 −1.12019 −0.560095 0.828428i \(-0.689235\pi\)
−0.560095 + 0.828428i \(0.689235\pi\)
\(440\) 15.7297 0.749883
\(441\) 8.15064 0.388126
\(442\) 0 0
\(443\) −19.4124 −0.922311 −0.461156 0.887319i \(-0.652565\pi\)
−0.461156 + 0.887319i \(0.652565\pi\)
\(444\) −1.83481 −0.0870761
\(445\) −22.6732 −1.07481
\(446\) 7.61587 0.360622
\(447\) −16.0051 −0.757013
\(448\) 2.14290 0.101243
\(449\) −17.6263 −0.831836 −0.415918 0.909402i \(-0.636540\pi\)
−0.415918 + 0.909402i \(0.636540\pi\)
\(450\) −13.5699 −0.639689
\(451\) −8.65539 −0.407566
\(452\) 2.44057 0.114795
\(453\) −8.83750 −0.415222
\(454\) 8.05375 0.377981
\(455\) 4.03684 0.189250
\(456\) 5.22668 0.244762
\(457\) −37.1215 −1.73647 −0.868236 0.496151i \(-0.834746\pi\)
−0.868236 + 0.496151i \(0.834746\pi\)
\(458\) −37.0847 −1.73285
\(459\) 0 0
\(460\) 3.45336 0.161014
\(461\) 29.4074 1.36964 0.684819 0.728714i \(-0.259881\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(462\) −1.26083 −0.0586591
\(463\) −9.72462 −0.451942 −0.225971 0.974134i \(-0.572555\pi\)
−0.225971 + 0.974134i \(0.572555\pi\)
\(464\) −5.41921 −0.251581
\(465\) −33.8161 −1.56819
\(466\) 44.0046 2.03847
\(467\) −4.62267 −0.213912 −0.106956 0.994264i \(-0.534110\pi\)
−0.106956 + 0.994264i \(0.534110\pi\)
\(468\) 1.35410 0.0625935
\(469\) 2.80335 0.129447
\(470\) 27.7101 1.27817
\(471\) −11.9700 −0.551547
\(472\) 27.5107 1.26628
\(473\) 19.3209 0.888375
\(474\) 23.9067 1.09807
\(475\) 11.4534 0.525516
\(476\) 0 0
\(477\) 9.91622 0.454033
\(478\) −4.03415 −0.184518
\(479\) −6.83656 −0.312371 −0.156185 0.987728i \(-0.549920\pi\)
−0.156185 + 0.987728i \(0.549920\pi\)
\(480\) −9.24897 −0.422156
\(481\) −12.9044 −0.588388
\(482\) 38.8135 1.76790
\(483\) 1.31727 0.0599377
\(484\) −2.74598 −0.124817
\(485\) 14.4243 0.654972
\(486\) −17.5713 −0.797050
\(487\) 7.66281 0.347235 0.173617 0.984813i \(-0.444454\pi\)
0.173617 + 0.984813i \(0.444454\pi\)
\(488\) −11.1702 −0.505653
\(489\) −13.0419 −0.589775
\(490\) 37.2276 1.68177
\(491\) 9.02465 0.407277 0.203638 0.979046i \(-0.434723\pi\)
0.203638 + 0.979046i \(0.434723\pi\)
\(492\) 2.30272 0.103815
\(493\) 0 0
\(494\) −7.72462 −0.347547
\(495\) 7.36009 0.330811
\(496\) 32.5030 1.45943
\(497\) −3.90673 −0.175241
\(498\) 4.43376 0.198682
\(499\) −26.6928 −1.19494 −0.597468 0.801893i \(-0.703826\pi\)
−0.597468 + 0.801893i \(0.703826\pi\)
\(500\) −3.03684 −0.135811
\(501\) 2.47565 0.110604
\(502\) 16.3705 0.730652
\(503\) −12.9267 −0.576371 −0.288185 0.957575i \(-0.593052\pi\)
−0.288185 + 0.957575i \(0.593052\pi\)
\(504\) 1.04189 0.0464094
\(505\) −18.6091 −0.828092
\(506\) −7.58584 −0.337232
\(507\) 2.92396 0.129858
\(508\) 2.68954 0.119329
\(509\) −27.8753 −1.23555 −0.617775 0.786355i \(-0.711966\pi\)
−0.617775 + 0.786355i \(0.711966\pi\)
\(510\) 0 0
\(511\) −0.591214 −0.0261538
\(512\) −14.2736 −0.630811
\(513\) 8.63816 0.381384
\(514\) −5.72462 −0.252502
\(515\) 65.1275 2.86986
\(516\) −5.14022 −0.226285
\(517\) −9.00599 −0.396083
\(518\) 2.08647 0.0916741
\(519\) 30.6641 1.34600
\(520\) −29.4320 −1.29068
\(521\) −5.11886 −0.224261 −0.112131 0.993693i \(-0.535768\pi\)
−0.112131 + 0.993693i \(0.535768\pi\)
\(522\) −2.15064 −0.0941311
\(523\) 15.3182 0.669818 0.334909 0.942250i \(-0.391294\pi\)
0.334909 + 0.942250i \(0.391294\pi\)
\(524\) −6.46616 −0.282475
\(525\) −3.49794 −0.152663
\(526\) 15.6418 0.682014
\(527\) 0 0
\(528\) 10.8384 0.471682
\(529\) −15.0746 −0.655418
\(530\) 45.2918 1.96735
\(531\) 12.8726 0.558622
\(532\) 0.184793 0.00801177
\(533\) 16.1952 0.701493
\(534\) −13.2504 −0.573401
\(535\) 18.9385 0.818783
\(536\) −20.4388 −0.882822
\(537\) 23.6117 1.01892
\(538\) −17.9855 −0.775408
\(539\) −12.0993 −0.521152
\(540\) −6.91622 −0.297627
\(541\) −37.4466 −1.60995 −0.804977 0.593307i \(-0.797822\pi\)
−0.804977 + 0.593307i \(0.797822\pi\)
\(542\) 26.0455 1.11875
\(543\) −6.14653 −0.263773
\(544\) 0 0
\(545\) −54.8093 −2.34777
\(546\) 2.35916 0.100963
\(547\) −27.3928 −1.17123 −0.585616 0.810589i \(-0.699147\pi\)
−0.585616 + 0.810589i \(0.699147\pi\)
\(548\) 3.49794 0.149425
\(549\) −5.22668 −0.223069
\(550\) 20.1438 0.858936
\(551\) 1.81521 0.0773304
\(552\) −9.60401 −0.408774
\(553\) −4.02229 −0.171045
\(554\) 37.2959 1.58455
\(555\) 18.6604 0.792092
\(556\) 2.97090 0.125994
\(557\) 9.07604 0.384564 0.192282 0.981340i \(-0.438411\pi\)
0.192282 + 0.981340i \(0.438411\pi\)
\(558\) 12.8990 0.546058
\(559\) −36.1516 −1.52905
\(560\) 5.61081 0.237100
\(561\) 0 0
\(562\) −8.87670 −0.374441
\(563\) −38.4894 −1.62213 −0.811067 0.584953i \(-0.801113\pi\)
−0.811067 + 0.584953i \(0.801113\pi\)
\(564\) 2.39599 0.100889
\(565\) −24.8212 −1.04424
\(566\) 23.4715 0.986582
\(567\) −1.40373 −0.0589513
\(568\) 28.4834 1.19514
\(569\) 45.1830 1.89417 0.947086 0.320981i \(-0.104012\pi\)
0.947086 + 0.320981i \(0.104012\pi\)
\(570\) 11.1702 0.467870
\(571\) 30.4570 1.27459 0.637293 0.770622i \(-0.280054\pi\)
0.637293 + 0.770622i \(0.280054\pi\)
\(572\) −2.01010 −0.0840467
\(573\) 13.1019 0.547342
\(574\) −2.61856 −0.109296
\(575\) −21.0455 −0.877658
\(576\) −7.31046 −0.304602
\(577\) −9.90167 −0.412212 −0.206106 0.978530i \(-0.566079\pi\)
−0.206106 + 0.978530i \(0.566079\pi\)
\(578\) 0 0
\(579\) −1.13753 −0.0472740
\(580\) −1.45336 −0.0603476
\(581\) −0.745977 −0.0309484
\(582\) 8.42964 0.349420
\(583\) −14.7202 −0.609648
\(584\) 4.31046 0.178368
\(585\) −13.7716 −0.569384
\(586\) 4.56624 0.188630
\(587\) −36.1343 −1.49142 −0.745712 0.666268i \(-0.767890\pi\)
−0.745712 + 0.666268i \(0.767890\pi\)
\(588\) 3.21894 0.132747
\(589\) −10.8871 −0.448596
\(590\) 58.7948 2.42054
\(591\) 22.9053 0.942198
\(592\) −17.9358 −0.737158
\(593\) −7.41653 −0.304560 −0.152280 0.988337i \(-0.548662\pi\)
−0.152280 + 0.988337i \(0.548662\pi\)
\(594\) 15.1925 0.623357
\(595\) 0 0
\(596\) 4.12567 0.168994
\(597\) −17.1046 −0.700046
\(598\) 14.1940 0.580434
\(599\) 7.61350 0.311079 0.155540 0.987830i \(-0.450288\pi\)
0.155540 + 0.987830i \(0.450288\pi\)
\(600\) 25.5030 1.04116
\(601\) 32.5732 1.32869 0.664343 0.747427i \(-0.268711\pi\)
0.664343 + 0.747427i \(0.268711\pi\)
\(602\) 5.84524 0.238234
\(603\) −9.56355 −0.389458
\(604\) 2.27807 0.0926932
\(605\) 27.9273 1.13540
\(606\) −10.8753 −0.441778
\(607\) 3.01455 0.122357 0.0611784 0.998127i \(-0.480514\pi\)
0.0611784 + 0.998127i \(0.480514\pi\)
\(608\) −2.97771 −0.120762
\(609\) −0.554378 −0.0224645
\(610\) −23.8726 −0.966572
\(611\) 16.8512 0.681728
\(612\) 0 0
\(613\) 7.26857 0.293575 0.146787 0.989168i \(-0.453107\pi\)
0.146787 + 0.989168i \(0.453107\pi\)
\(614\) −5.00774 −0.202096
\(615\) −23.4192 −0.944354
\(616\) −1.54664 −0.0623158
\(617\) 34.2449 1.37865 0.689323 0.724454i \(-0.257908\pi\)
0.689323 + 0.724454i \(0.257908\pi\)
\(618\) 38.0610 1.53104
\(619\) −20.4296 −0.821137 −0.410568 0.911830i \(-0.634670\pi\)
−0.410568 + 0.911830i \(0.634670\pi\)
\(620\) 8.71688 0.350078
\(621\) −15.8726 −0.636945
\(622\) −5.41147 −0.216980
\(623\) 2.22937 0.0893178
\(624\) −20.2799 −0.811847
\(625\) −6.49289 −0.259716
\(626\) −2.27126 −0.0907778
\(627\) −3.63041 −0.144985
\(628\) 3.08553 0.123126
\(629\) 0 0
\(630\) 2.22668 0.0887131
\(631\) 15.5080 0.617366 0.308683 0.951165i \(-0.400112\pi\)
0.308683 + 0.951165i \(0.400112\pi\)
\(632\) 29.3259 1.16652
\(633\) 31.7023 1.26005
\(634\) 22.1598 0.880079
\(635\) −27.3533 −1.08548
\(636\) 3.91622 0.155288
\(637\) 22.6391 0.896993
\(638\) 3.19253 0.126394
\(639\) 13.3277 0.527236
\(640\) −47.1198 −1.86257
\(641\) −32.5945 −1.28741 −0.643703 0.765275i \(-0.722603\pi\)
−0.643703 + 0.765275i \(0.722603\pi\)
\(642\) 11.0678 0.436811
\(643\) 41.2080 1.62509 0.812543 0.582902i \(-0.198083\pi\)
0.812543 + 0.582902i \(0.198083\pi\)
\(644\) −0.339556 −0.0133804
\(645\) 52.2772 2.05841
\(646\) 0 0
\(647\) 26.5131 1.04234 0.521169 0.853454i \(-0.325496\pi\)
0.521169 + 0.853454i \(0.325496\pi\)
\(648\) 10.2344 0.402046
\(649\) −19.1088 −0.750084
\(650\) −37.6914 −1.47838
\(651\) 3.32501 0.130317
\(652\) 3.36184 0.131660
\(653\) −14.1875 −0.555199 −0.277600 0.960697i \(-0.589539\pi\)
−0.277600 + 0.960697i \(0.589539\pi\)
\(654\) −32.0310 −1.25251
\(655\) 65.7624 2.56955
\(656\) 22.5098 0.878860
\(657\) 2.01691 0.0786872
\(658\) −2.72462 −0.106217
\(659\) −28.3628 −1.10486 −0.552428 0.833560i \(-0.686299\pi\)
−0.552428 + 0.833560i \(0.686299\pi\)
\(660\) 2.90673 0.113144
\(661\) 29.1661 1.13443 0.567215 0.823569i \(-0.308021\pi\)
0.567215 + 0.823569i \(0.308021\pi\)
\(662\) −13.8425 −0.538006
\(663\) 0 0
\(664\) 5.43882 0.211067
\(665\) −1.87939 −0.0728794
\(666\) −7.11793 −0.275814
\(667\) −3.33544 −0.129149
\(668\) −0.638156 −0.0246910
\(669\) −6.69728 −0.258932
\(670\) −43.6810 −1.68754
\(671\) 7.75877 0.299524
\(672\) 0.909415 0.0350814
\(673\) −29.3678 −1.13205 −0.566023 0.824389i \(-0.691519\pi\)
−0.566023 + 0.824389i \(0.691519\pi\)
\(674\) 27.5253 1.06023
\(675\) 42.1489 1.62231
\(676\) −0.753718 −0.0289892
\(677\) 39.3783 1.51343 0.756715 0.653745i \(-0.226803\pi\)
0.756715 + 0.653745i \(0.226803\pi\)
\(678\) −14.5057 −0.557087
\(679\) −1.41828 −0.0544286
\(680\) 0 0
\(681\) −7.08235 −0.271396
\(682\) −19.1480 −0.733213
\(683\) 27.1634 1.03938 0.519690 0.854355i \(-0.326047\pi\)
0.519690 + 0.854355i \(0.326047\pi\)
\(684\) −0.630415 −0.0241045
\(685\) −35.5749 −1.35925
\(686\) −7.38507 −0.281963
\(687\) 32.6117 1.24422
\(688\) −50.2472 −1.91566
\(689\) 27.5431 1.04931
\(690\) −20.5253 −0.781384
\(691\) −33.8503 −1.28773 −0.643863 0.765141i \(-0.722669\pi\)
−0.643863 + 0.765141i \(0.722669\pi\)
\(692\) −7.90436 −0.300479
\(693\) −0.723689 −0.0274907
\(694\) 11.9254 0.452682
\(695\) −30.2148 −1.14611
\(696\) 4.04189 0.153207
\(697\) 0 0
\(698\) −10.1884 −0.385637
\(699\) −38.6970 −1.46365
\(700\) 0.901674 0.0340801
\(701\) 20.9540 0.791421 0.395711 0.918375i \(-0.370498\pi\)
0.395711 + 0.918375i \(0.370498\pi\)
\(702\) −28.4270 −1.07291
\(703\) 6.00774 0.226586
\(704\) 10.8520 0.409002
\(705\) −24.3678 −0.917746
\(706\) 6.35142 0.239039
\(707\) 1.82976 0.0688150
\(708\) 5.08378 0.191060
\(709\) −31.3236 −1.17638 −0.588191 0.808722i \(-0.700160\pi\)
−0.588191 + 0.808722i \(0.700160\pi\)
\(710\) 60.8735 2.28454
\(711\) 13.7219 0.514613
\(712\) −16.2540 −0.609145
\(713\) 20.0051 0.749195
\(714\) 0 0
\(715\) 20.4433 0.764535
\(716\) −6.08647 −0.227462
\(717\) 3.54757 0.132486
\(718\) −26.1634 −0.976411
\(719\) −44.4097 −1.65620 −0.828102 0.560578i \(-0.810579\pi\)
−0.828102 + 0.560578i \(0.810579\pi\)
\(720\) −19.1411 −0.713348
\(721\) −6.40373 −0.238487
\(722\) −25.5134 −0.949511
\(723\) −34.1320 −1.26938
\(724\) 1.58441 0.0588840
\(725\) 8.85710 0.328944
\(726\) 16.3209 0.605725
\(727\) −39.5354 −1.46629 −0.733143 0.680074i \(-0.761947\pi\)
−0.733143 + 0.680074i \(0.761947\pi\)
\(728\) 2.89393 0.107256
\(729\) 27.5776 1.02139
\(730\) 9.21213 0.340956
\(731\) 0 0
\(732\) −2.06418 −0.0762942
\(733\) 13.8990 0.513371 0.256685 0.966495i \(-0.417370\pi\)
0.256685 + 0.966495i \(0.417370\pi\)
\(734\) −28.8503 −1.06488
\(735\) −32.7374 −1.20754
\(736\) 5.47153 0.201683
\(737\) 14.1967 0.522940
\(738\) 8.93313 0.328833
\(739\) 11.4037 0.419493 0.209747 0.977756i \(-0.432736\pi\)
0.209747 + 0.977756i \(0.432736\pi\)
\(740\) −4.81016 −0.176825
\(741\) 6.79292 0.249544
\(742\) −4.45336 −0.163488
\(743\) −14.6209 −0.536390 −0.268195 0.963365i \(-0.586427\pi\)
−0.268195 + 0.963365i \(0.586427\pi\)
\(744\) −24.2422 −0.888761
\(745\) −41.9590 −1.53726
\(746\) −17.9736 −0.658060
\(747\) 2.54488 0.0931124
\(748\) 0 0
\(749\) −1.86215 −0.0680414
\(750\) 18.0496 0.659079
\(751\) 28.0196 1.02245 0.511225 0.859447i \(-0.329192\pi\)
0.511225 + 0.859447i \(0.329192\pi\)
\(752\) 23.4216 0.854097
\(753\) −14.3960 −0.524619
\(754\) −5.97359 −0.217545
\(755\) −23.1685 −0.843188
\(756\) 0.680045 0.0247330
\(757\) 15.6186 0.567666 0.283833 0.958874i \(-0.408394\pi\)
0.283833 + 0.958874i \(0.408394\pi\)
\(758\) −12.5098 −0.454376
\(759\) 6.67087 0.242137
\(760\) 13.7023 0.497036
\(761\) 20.5868 0.746270 0.373135 0.927777i \(-0.378283\pi\)
0.373135 + 0.927777i \(0.378283\pi\)
\(762\) −15.9855 −0.579092
\(763\) 5.38919 0.195102
\(764\) −3.37733 −0.122187
\(765\) 0 0
\(766\) 24.9026 0.899768
\(767\) 35.7547 1.29103
\(768\) −10.9108 −0.393711
\(769\) 22.2249 0.801451 0.400726 0.916198i \(-0.368758\pi\)
0.400726 + 0.916198i \(0.368758\pi\)
\(770\) −3.30541 −0.119119
\(771\) 5.03415 0.181300
\(772\) 0.293223 0.0105533
\(773\) −27.0087 −0.971434 −0.485717 0.874116i \(-0.661442\pi\)
−0.485717 + 0.874116i \(0.661442\pi\)
\(774\) −19.9409 −0.716760
\(775\) −53.1225 −1.90822
\(776\) 10.3405 0.371202
\(777\) −1.83481 −0.0658234
\(778\) −8.89756 −0.318993
\(779\) −7.53983 −0.270142
\(780\) −5.43882 −0.194741
\(781\) −19.7844 −0.707940
\(782\) 0 0
\(783\) 6.68004 0.238725
\(784\) 31.4662 1.12379
\(785\) −31.3806 −1.12002
\(786\) 38.4320 1.37082
\(787\) 20.9810 0.747892 0.373946 0.927450i \(-0.378004\pi\)
0.373946 + 0.927450i \(0.378004\pi\)
\(788\) −5.90436 −0.210334
\(789\) −13.7551 −0.489696
\(790\) 62.6742 2.22985
\(791\) 2.44057 0.0867767
\(792\) 5.27631 0.187486
\(793\) −14.5175 −0.515533
\(794\) −15.7065 −0.557401
\(795\) −39.8289 −1.41259
\(796\) 4.40911 0.156277
\(797\) 34.4347 1.21974 0.609870 0.792502i \(-0.291222\pi\)
0.609870 + 0.792502i \(0.291222\pi\)
\(798\) −1.09833 −0.0388803
\(799\) 0 0
\(800\) −14.5294 −0.513692
\(801\) −7.60544 −0.268725
\(802\) −46.8239 −1.65341
\(803\) −2.99401 −0.105656
\(804\) −3.77694 −0.133202
\(805\) 3.45336 0.121715
\(806\) 35.8280 1.26199
\(807\) 15.8161 0.556755
\(808\) −13.3405 −0.469317
\(809\) 28.9246 1.01693 0.508467 0.861082i \(-0.330212\pi\)
0.508467 + 0.861082i \(0.330212\pi\)
\(810\) 21.8726 0.768524
\(811\) 38.6236 1.35626 0.678129 0.734943i \(-0.262791\pi\)
0.678129 + 0.734943i \(0.262791\pi\)
\(812\) 0.142903 0.00501493
\(813\) −22.9040 −0.803280
\(814\) 10.5662 0.370346
\(815\) −34.1908 −1.19765
\(816\) 0 0
\(817\) 16.8307 0.588831
\(818\) 30.6013 1.06995
\(819\) 1.35410 0.0473162
\(820\) 6.03684 0.210815
\(821\) 5.39599 0.188321 0.0941607 0.995557i \(-0.469983\pi\)
0.0941607 + 0.995557i \(0.469983\pi\)
\(822\) −20.7902 −0.725143
\(823\) 30.6878 1.06971 0.534854 0.844944i \(-0.320366\pi\)
0.534854 + 0.844944i \(0.320366\pi\)
\(824\) 46.6887 1.62648
\(825\) −17.7142 −0.616729
\(826\) −5.78106 −0.201149
\(827\) 35.5381 1.23578 0.617890 0.786265i \(-0.287988\pi\)
0.617890 + 0.786265i \(0.287988\pi\)
\(828\) 1.15839 0.0402567
\(829\) 3.17200 0.110168 0.0550840 0.998482i \(-0.482457\pi\)
0.0550840 + 0.998482i \(0.482457\pi\)
\(830\) 11.6236 0.403461
\(831\) −32.7975 −1.13773
\(832\) −20.3054 −0.703963
\(833\) 0 0
\(834\) −17.6578 −0.611438
\(835\) 6.49020 0.224603
\(836\) 0.935822 0.0323661
\(837\) −40.0651 −1.38485
\(838\) 25.9368 0.895970
\(839\) −36.8152 −1.27100 −0.635501 0.772100i \(-0.719206\pi\)
−0.635501 + 0.772100i \(0.719206\pi\)
\(840\) −4.18479 −0.144389
\(841\) −27.5963 −0.951595
\(842\) −36.3560 −1.25291
\(843\) 7.80604 0.268854
\(844\) −8.17200 −0.281292
\(845\) 7.66550 0.263701
\(846\) 9.29498 0.319568
\(847\) −2.74598 −0.0943529
\(848\) 38.2823 1.31462
\(849\) −20.6405 −0.708381
\(850\) 0 0
\(851\) −11.0392 −0.378419
\(852\) 5.26352 0.180325
\(853\) 20.0651 0.687016 0.343508 0.939150i \(-0.388385\pi\)
0.343508 + 0.939150i \(0.388385\pi\)
\(854\) 2.34730 0.0803228
\(855\) 6.41147 0.219268
\(856\) 13.5767 0.464041
\(857\) 19.9299 0.680794 0.340397 0.940282i \(-0.389439\pi\)
0.340397 + 0.940282i \(0.389439\pi\)
\(858\) 11.9472 0.407870
\(859\) −23.3527 −0.796783 −0.398391 0.917215i \(-0.630431\pi\)
−0.398391 + 0.917215i \(0.630431\pi\)
\(860\) −13.4757 −0.459516
\(861\) 2.30272 0.0784765
\(862\) −36.1453 −1.23111
\(863\) 44.3878 1.51098 0.755488 0.655162i \(-0.227400\pi\)
0.755488 + 0.655162i \(0.227400\pi\)
\(864\) −10.9581 −0.372803
\(865\) 80.3893 2.73332
\(866\) −19.4492 −0.660912
\(867\) 0 0
\(868\) −0.857097 −0.0290918
\(869\) −20.3696 −0.690991
\(870\) 8.63816 0.292861
\(871\) −26.5635 −0.900072
\(872\) −39.2918 −1.33059
\(873\) 4.83843 0.163756
\(874\) −6.60813 −0.223523
\(875\) −3.03684 −0.102664
\(876\) 0.796541 0.0269126
\(877\) −9.14971 −0.308964 −0.154482 0.987996i \(-0.549371\pi\)
−0.154482 + 0.987996i \(0.549371\pi\)
\(878\) −35.9590 −1.21356
\(879\) −4.01548 −0.135439
\(880\) 28.4142 0.957841
\(881\) −6.76794 −0.228018 −0.114009 0.993480i \(-0.536369\pi\)
−0.114009 + 0.993480i \(0.536369\pi\)
\(882\) 12.4875 0.420476
\(883\) −47.9760 −1.61452 −0.807260 0.590196i \(-0.799050\pi\)
−0.807260 + 0.590196i \(0.799050\pi\)
\(884\) 0 0
\(885\) −51.7033 −1.73799
\(886\) −29.7415 −0.999186
\(887\) 41.6982 1.40009 0.700045 0.714099i \(-0.253163\pi\)
0.700045 + 0.714099i \(0.253163\pi\)
\(888\) 13.3773 0.448914
\(889\) 2.68954 0.0902043
\(890\) −34.7374 −1.16440
\(891\) −7.10876 −0.238152
\(892\) 1.72638 0.0578034
\(893\) −7.84524 −0.262531
\(894\) −24.5212 −0.820110
\(895\) 61.9009 2.06912
\(896\) 4.63310 0.154781
\(897\) −12.4820 −0.416761
\(898\) −27.0051 −0.901170
\(899\) −8.41921 −0.280797
\(900\) −3.07604 −0.102535
\(901\) 0 0
\(902\) −13.2608 −0.441537
\(903\) −5.14022 −0.171056
\(904\) −17.7939 −0.591815
\(905\) −16.1138 −0.535641
\(906\) −13.5398 −0.449831
\(907\) −32.9350 −1.09359 −0.546794 0.837267i \(-0.684152\pi\)
−0.546794 + 0.837267i \(0.684152\pi\)
\(908\) 1.82564 0.0605859
\(909\) −6.24216 −0.207039
\(910\) 6.18479 0.205024
\(911\) −18.4926 −0.612686 −0.306343 0.951921i \(-0.599105\pi\)
−0.306343 + 0.951921i \(0.599105\pi\)
\(912\) 9.44150 0.312639
\(913\) −3.77776 −0.125026
\(914\) −56.8735 −1.88121
\(915\) 20.9932 0.694014
\(916\) −8.40642 −0.277756
\(917\) −6.46616 −0.213531
\(918\) 0 0
\(919\) −13.3909 −0.441726 −0.220863 0.975305i \(-0.570887\pi\)
−0.220863 + 0.975305i \(0.570887\pi\)
\(920\) −25.1780 −0.830094
\(921\) 4.40373 0.145108
\(922\) 45.0547 1.48380
\(923\) 37.0188 1.21849
\(924\) −0.285807 −0.00940236
\(925\) 29.3141 0.963841
\(926\) −14.8990 −0.489611
\(927\) 21.8462 0.717522
\(928\) −2.30272 −0.0755905
\(929\) −5.33956 −0.175185 −0.0875926 0.996156i \(-0.527917\pi\)
−0.0875926 + 0.996156i \(0.527917\pi\)
\(930\) −51.8093 −1.69889
\(931\) −10.5398 −0.345429
\(932\) 9.97502 0.326743
\(933\) 4.75877 0.155795
\(934\) −7.08235 −0.231741
\(935\) 0 0
\(936\) −9.87258 −0.322695
\(937\) 41.4361 1.35366 0.676830 0.736140i \(-0.263353\pi\)
0.676830 + 0.736140i \(0.263353\pi\)
\(938\) 4.29498 0.140236
\(939\) 1.99731 0.0651798
\(940\) 6.28136 0.204876
\(941\) 42.0601 1.37112 0.685559 0.728017i \(-0.259558\pi\)
0.685559 + 0.728017i \(0.259558\pi\)
\(942\) −18.3391 −0.597519
\(943\) 13.8544 0.451162
\(944\) 49.6955 1.61745
\(945\) −6.91622 −0.224985
\(946\) 29.6013 0.962422
\(947\) 41.4270 1.34620 0.673098 0.739554i \(-0.264963\pi\)
0.673098 + 0.739554i \(0.264963\pi\)
\(948\) 5.41921 0.176008
\(949\) 5.60214 0.181853
\(950\) 17.5476 0.569318
\(951\) −19.4870 −0.631910
\(952\) 0 0
\(953\) 27.0719 0.876945 0.438473 0.898744i \(-0.355520\pi\)
0.438473 + 0.898744i \(0.355520\pi\)
\(954\) 15.1925 0.491876
\(955\) 34.3482 1.11148
\(956\) −0.914467 −0.0295760
\(957\) −2.80747 −0.0907525
\(958\) −10.4742 −0.338407
\(959\) 3.49794 0.112954
\(960\) 29.3628 0.947680
\(961\) 19.4962 0.628909
\(962\) −19.7706 −0.637431
\(963\) 6.35267 0.204712
\(964\) 8.79830 0.283374
\(965\) −2.98215 −0.0959989
\(966\) 2.01817 0.0649336
\(967\) −43.3637 −1.39448 −0.697241 0.716836i \(-0.745589\pi\)
−0.697241 + 0.716836i \(0.745589\pi\)
\(968\) 20.0205 0.643484
\(969\) 0 0
\(970\) 22.0993 0.709564
\(971\) −1.27126 −0.0407966 −0.0203983 0.999792i \(-0.506493\pi\)
−0.0203983 + 0.999792i \(0.506493\pi\)
\(972\) −3.98309 −0.127758
\(973\) 2.97090 0.0952428
\(974\) 11.7401 0.376177
\(975\) 33.1453 1.06150
\(976\) −20.1780 −0.645882
\(977\) −24.7641 −0.792275 −0.396138 0.918191i \(-0.629650\pi\)
−0.396138 + 0.918191i \(0.629650\pi\)
\(978\) −19.9813 −0.638933
\(979\) 11.2899 0.360828
\(980\) 8.43882 0.269568
\(981\) −18.3851 −0.586990
\(982\) 13.8266 0.441224
\(983\) −39.6144 −1.26350 −0.631752 0.775170i \(-0.717664\pi\)
−0.631752 + 0.775170i \(0.717664\pi\)
\(984\) −16.7888 −0.535207
\(985\) 60.0488 1.91331
\(986\) 0 0
\(987\) 2.39599 0.0762653
\(988\) −1.75103 −0.0557077
\(989\) −30.9263 −0.983400
\(990\) 11.2763 0.358385
\(991\) −33.3138 −1.05825 −0.529123 0.848545i \(-0.677479\pi\)
−0.529123 + 0.848545i \(0.677479\pi\)
\(992\) 13.8111 0.438503
\(993\) 12.1729 0.386296
\(994\) −5.98545 −0.189847
\(995\) −44.8417 −1.42158
\(996\) 1.00505 0.0318463
\(997\) −25.8958 −0.820128 −0.410064 0.912057i \(-0.634494\pi\)
−0.410064 + 0.912057i \(0.634494\pi\)
\(998\) −40.8958 −1.29453
\(999\) 22.1088 0.699490
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 289.2.a.d.1.3 3
3.2 odd 2 2601.2.a.x.1.1 3
4.3 odd 2 4624.2.a.bg.1.2 3
5.4 even 2 7225.2.a.t.1.1 3
17.2 even 8 289.2.c.d.38.5 12
17.3 odd 16 289.2.d.f.179.5 24
17.4 even 4 289.2.b.d.288.2 6
17.5 odd 16 289.2.d.f.110.2 24
17.6 odd 16 289.2.d.f.155.5 24
17.7 odd 16 289.2.d.f.134.2 24
17.8 even 8 289.2.c.d.251.2 12
17.9 even 8 289.2.c.d.251.1 12
17.10 odd 16 289.2.d.f.134.1 24
17.11 odd 16 289.2.d.f.155.6 24
17.12 odd 16 289.2.d.f.110.1 24
17.13 even 4 289.2.b.d.288.1 6
17.14 odd 16 289.2.d.f.179.6 24
17.15 even 8 289.2.c.d.38.6 12
17.16 even 2 289.2.a.e.1.3 yes 3
51.50 odd 2 2601.2.a.w.1.1 3
68.67 odd 2 4624.2.a.bd.1.2 3
85.84 even 2 7225.2.a.s.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.2.a.d.1.3 3 1.1 even 1 trivial
289.2.a.e.1.3 yes 3 17.16 even 2
289.2.b.d.288.1 6 17.13 even 4
289.2.b.d.288.2 6 17.4 even 4
289.2.c.d.38.5 12 17.2 even 8
289.2.c.d.38.6 12 17.15 even 8
289.2.c.d.251.1 12 17.9 even 8
289.2.c.d.251.2 12 17.8 even 8
289.2.d.f.110.1 24 17.12 odd 16
289.2.d.f.110.2 24 17.5 odd 16
289.2.d.f.134.1 24 17.10 odd 16
289.2.d.f.134.2 24 17.7 odd 16
289.2.d.f.155.5 24 17.6 odd 16
289.2.d.f.155.6 24 17.11 odd 16
289.2.d.f.179.5 24 17.3 odd 16
289.2.d.f.179.6 24 17.14 odd 16
2601.2.a.w.1.1 3 51.50 odd 2
2601.2.a.x.1.1 3 3.2 odd 2
4624.2.a.bd.1.2 3 68.67 odd 2
4624.2.a.bg.1.2 3 4.3 odd 2
7225.2.a.s.1.1 3 85.84 even 2
7225.2.a.t.1.1 3 5.4 even 2