Properties

Label 483.2.a.h.1.1
Level $483$
Weight $2$
Character 483.1
Self dual yes
Analytic conductor $3.857$
Analytic rank $0$
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] = [483,2,Mod(1,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, 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("483.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.837.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 6x - 1 \) 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 1.1
Root \(-2.36147\) of defining polynomial
Character \(\chi\) \(=\) 483.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.36147 q^{2} +1.00000 q^{3} +3.57653 q^{4} +3.36147 q^{5} -2.36147 q^{6} -1.00000 q^{7} -3.72294 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.36147 q^{2} +1.00000 q^{3} +3.57653 q^{4} +3.36147 q^{5} -2.36147 q^{6} -1.00000 q^{7} -3.72294 q^{8} +1.00000 q^{9} -7.93800 q^{10} +5.93800 q^{11} +3.57653 q^{12} +1.42347 q^{13} +2.36147 q^{14} +3.36147 q^{15} +1.63853 q^{16} +2.78493 q^{17} -2.36147 q^{18} -5.93800 q^{19} +12.0224 q^{20} -1.00000 q^{21} -14.0224 q^{22} -1.00000 q^{23} -3.72294 q^{24} +6.29947 q^{25} -3.36147 q^{26} +1.00000 q^{27} -3.57653 q^{28} -6.66094 q^{29} -7.93800 q^{30} -9.93800 q^{31} +3.57653 q^{32} +5.93800 q^{33} -6.57653 q^{34} -3.36147 q^{35} +3.57653 q^{36} +10.6609 q^{37} +14.0224 q^{38} +1.42347 q^{39} -12.5145 q^{40} -9.09107 q^{41} +2.36147 q^{42} +3.29947 q^{43} +21.2375 q^{44} +3.36147 q^{45} +2.36147 q^{46} +9.15307 q^{47} +1.63853 q^{48} +1.00000 q^{49} -14.8760 q^{50} +2.78493 q^{51} +5.09107 q^{52} +3.36147 q^{53} -2.36147 q^{54} +19.9604 q^{55} +3.72294 q^{56} -5.93800 q^{57} +15.7296 q^{58} +0.208399 q^{59} +12.0224 q^{60} +5.29947 q^{61} +23.4683 q^{62} -1.00000 q^{63} -11.7229 q^{64} +4.78493 q^{65} -14.0224 q^{66} -10.9313 q^{67} +9.96041 q^{68} -1.00000 q^{69} +7.93800 q^{70} +3.00667 q^{71} -3.72294 q^{72} -1.50787 q^{73} -25.1755 q^{74} +6.29947 q^{75} -21.2375 q^{76} -5.93800 q^{77} -3.36147 q^{78} -4.66094 q^{79} +5.50787 q^{80} +1.00000 q^{81} +21.4683 q^{82} +4.78493 q^{83} -3.57653 q^{84} +9.36147 q^{85} -7.79160 q^{86} -6.66094 q^{87} -22.1068 q^{88} +6.57653 q^{89} -7.93800 q^{90} -1.42347 q^{91} -3.57653 q^{92} -9.93800 q^{93} -21.6147 q^{94} -19.9604 q^{95} +3.57653 q^{96} -9.50787 q^{97} -2.36147 q^{98} +5.93800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{3} + 6 q^{4} + 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{3} + 6 q^{4} + 3 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 12 q^{10} + 6 q^{11} + 6 q^{12} + 9 q^{13} + 3 q^{15} + 12 q^{16} + 6 q^{17} - 6 q^{19} + 3 q^{20} - 3 q^{21} - 9 q^{22} - 3 q^{23} + 3 q^{24} - 3 q^{26} + 3 q^{27} - 6 q^{28} + 6 q^{29} - 12 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 15 q^{34} - 3 q^{35} + 6 q^{36} + 6 q^{37} + 9 q^{38} + 9 q^{39} - 21 q^{40} - 6 q^{41} - 9 q^{43} + 33 q^{44} + 3 q^{45} + 18 q^{47} + 12 q^{48} + 3 q^{49} - 21 q^{50} + 6 q^{51} - 6 q^{52} + 3 q^{53} + 15 q^{55} - 3 q^{56} - 6 q^{57} + 33 q^{58} + 3 q^{59} + 3 q^{60} - 3 q^{61} + 9 q^{62} - 3 q^{63} - 21 q^{64} + 12 q^{65} - 9 q^{66} - 21 q^{67} - 15 q^{68} - 3 q^{69} + 12 q^{70} + 9 q^{71} + 3 q^{72} + 12 q^{73} - 33 q^{74} - 33 q^{76} - 6 q^{77} - 3 q^{78} + 12 q^{79} + 3 q^{81} + 3 q^{82} + 12 q^{83} - 6 q^{84} + 21 q^{85} - 21 q^{86} + 6 q^{87} - 12 q^{88} + 15 q^{89} - 12 q^{90} - 9 q^{91} - 6 q^{92} - 18 q^{93} + 6 q^{94} - 15 q^{95} + 6 q^{96} - 12 q^{97} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.36147 −1.66981 −0.834905 0.550394i \(-0.814478\pi\)
−0.834905 + 0.550394i \(0.814478\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.57653 1.78827
\(5\) 3.36147 1.50329 0.751647 0.659565i \(-0.229260\pi\)
0.751647 + 0.659565i \(0.229260\pi\)
\(6\) −2.36147 −0.964066
\(7\) −1.00000 −0.377964
\(8\) −3.72294 −1.31626
\(9\) 1.00000 0.333333
\(10\) −7.93800 −2.51022
\(11\) 5.93800 1.79038 0.895188 0.445689i \(-0.147041\pi\)
0.895188 + 0.445689i \(0.147041\pi\)
\(12\) 3.57653 1.03246
\(13\) 1.42347 0.394798 0.197399 0.980323i \(-0.436751\pi\)
0.197399 + 0.980323i \(0.436751\pi\)
\(14\) 2.36147 0.631129
\(15\) 3.36147 0.867928
\(16\) 1.63853 0.409633
\(17\) 2.78493 0.675446 0.337723 0.941246i \(-0.390343\pi\)
0.337723 + 0.941246i \(0.390343\pi\)
\(18\) −2.36147 −0.556604
\(19\) −5.93800 −1.36227 −0.681136 0.732157i \(-0.738514\pi\)
−0.681136 + 0.732157i \(0.738514\pi\)
\(20\) 12.0224 2.68829
\(21\) −1.00000 −0.218218
\(22\) −14.0224 −2.98959
\(23\) −1.00000 −0.208514
\(24\) −3.72294 −0.759941
\(25\) 6.29947 1.25989
\(26\) −3.36147 −0.659238
\(27\) 1.00000 0.192450
\(28\) −3.57653 −0.675902
\(29\) −6.66094 −1.23691 −0.618453 0.785822i \(-0.712240\pi\)
−0.618453 + 0.785822i \(0.712240\pi\)
\(30\) −7.93800 −1.44927
\(31\) −9.93800 −1.78492 −0.892459 0.451128i \(-0.851022\pi\)
−0.892459 + 0.451128i \(0.851022\pi\)
\(32\) 3.57653 0.632248
\(33\) 5.93800 1.03367
\(34\) −6.57653 −1.12787
\(35\) −3.36147 −0.568192
\(36\) 3.57653 0.596089
\(37\) 10.6609 1.75265 0.876324 0.481722i \(-0.159989\pi\)
0.876324 + 0.481722i \(0.159989\pi\)
\(38\) 14.0224 2.27474
\(39\) 1.42347 0.227937
\(40\) −12.5145 −1.97872
\(41\) −9.09107 −1.41979 −0.709894 0.704309i \(-0.751257\pi\)
−0.709894 + 0.704309i \(0.751257\pi\)
\(42\) 2.36147 0.364383
\(43\) 3.29947 0.503165 0.251582 0.967836i \(-0.419049\pi\)
0.251582 + 0.967836i \(0.419049\pi\)
\(44\) 21.2375 3.20167
\(45\) 3.36147 0.501098
\(46\) 2.36147 0.348180
\(47\) 9.15307 1.33511 0.667556 0.744559i \(-0.267340\pi\)
0.667556 + 0.744559i \(0.267340\pi\)
\(48\) 1.63853 0.236502
\(49\) 1.00000 0.142857
\(50\) −14.8760 −2.10379
\(51\) 2.78493 0.389969
\(52\) 5.09107 0.706005
\(53\) 3.36147 0.461733 0.230867 0.972985i \(-0.425844\pi\)
0.230867 + 0.972985i \(0.425844\pi\)
\(54\) −2.36147 −0.321355
\(55\) 19.9604 2.69146
\(56\) 3.72294 0.497498
\(57\) −5.93800 −0.786508
\(58\) 15.7296 2.06540
\(59\) 0.208399 0.0271313 0.0135656 0.999908i \(-0.495682\pi\)
0.0135656 + 0.999908i \(0.495682\pi\)
\(60\) 12.0224 1.55209
\(61\) 5.29947 0.678528 0.339264 0.940691i \(-0.389822\pi\)
0.339264 + 0.940691i \(0.389822\pi\)
\(62\) 23.4683 2.98048
\(63\) −1.00000 −0.125988
\(64\) −11.7229 −1.46537
\(65\) 4.78493 0.593498
\(66\) −14.0224 −1.72604
\(67\) −10.9313 −1.33548 −0.667738 0.744397i \(-0.732737\pi\)
−0.667738 + 0.744397i \(0.732737\pi\)
\(68\) 9.96041 1.20788
\(69\) −1.00000 −0.120386
\(70\) 7.93800 0.948773
\(71\) 3.00667 0.356826 0.178413 0.983956i \(-0.442904\pi\)
0.178413 + 0.983956i \(0.442904\pi\)
\(72\) −3.72294 −0.438752
\(73\) −1.50787 −0.176483 −0.0882415 0.996099i \(-0.528125\pi\)
−0.0882415 + 0.996099i \(0.528125\pi\)
\(74\) −25.1755 −2.92659
\(75\) 6.29947 0.727400
\(76\) −21.2375 −2.43611
\(77\) −5.93800 −0.676698
\(78\) −3.36147 −0.380611
\(79\) −4.66094 −0.524397 −0.262198 0.965014i \(-0.584447\pi\)
−0.262198 + 0.965014i \(0.584447\pi\)
\(80\) 5.50787 0.615799
\(81\) 1.00000 0.111111
\(82\) 21.4683 2.37078
\(83\) 4.78493 0.525215 0.262607 0.964903i \(-0.415418\pi\)
0.262607 + 0.964903i \(0.415418\pi\)
\(84\) −3.57653 −0.390232
\(85\) 9.36147 1.01539
\(86\) −7.79160 −0.840190
\(87\) −6.66094 −0.714128
\(88\) −22.1068 −2.35659
\(89\) 6.57653 0.697111 0.348556 0.937288i \(-0.386672\pi\)
0.348556 + 0.937288i \(0.386672\pi\)
\(90\) −7.93800 −0.836739
\(91\) −1.42347 −0.149220
\(92\) −3.57653 −0.372880
\(93\) −9.93800 −1.03052
\(94\) −21.6147 −2.22938
\(95\) −19.9604 −2.04790
\(96\) 3.57653 0.365029
\(97\) −9.50787 −0.965378 −0.482689 0.875792i \(-0.660340\pi\)
−0.482689 + 0.875792i \(0.660340\pi\)
\(98\) −2.36147 −0.238544
\(99\) 5.93800 0.596792
\(100\) 22.5303 2.25303
\(101\) 5.66761 0.563948 0.281974 0.959422i \(-0.409011\pi\)
0.281974 + 0.959422i \(0.409011\pi\)
\(102\) −6.57653 −0.651174
\(103\) 13.4459 1.32486 0.662431 0.749123i \(-0.269525\pi\)
0.662431 + 0.749123i \(0.269525\pi\)
\(104\) −5.29947 −0.519656
\(105\) −3.36147 −0.328046
\(106\) −7.93800 −0.771007
\(107\) −11.2995 −1.09236 −0.546181 0.837667i \(-0.683919\pi\)
−0.546181 + 0.837667i \(0.683919\pi\)
\(108\) 3.57653 0.344152
\(109\) 6.08441 0.582780 0.291390 0.956604i \(-0.405882\pi\)
0.291390 + 0.956604i \(0.405882\pi\)
\(110\) −47.1359 −4.49423
\(111\) 10.6609 1.01189
\(112\) −1.63853 −0.154827
\(113\) 3.06866 0.288676 0.144338 0.989528i \(-0.453895\pi\)
0.144338 + 0.989528i \(0.453895\pi\)
\(114\) 14.0224 1.31332
\(115\) −3.36147 −0.313459
\(116\) −23.8231 −2.21192
\(117\) 1.42347 0.131599
\(118\) −0.492128 −0.0453041
\(119\) −2.78493 −0.255294
\(120\) −12.5145 −1.14242
\(121\) 24.2599 2.20544
\(122\) −12.5145 −1.13301
\(123\) −9.09107 −0.819714
\(124\) −35.5436 −3.19191
\(125\) 4.36814 0.390698
\(126\) 2.36147 0.210376
\(127\) −21.8984 −1.94317 −0.971585 0.236690i \(-0.923937\pi\)
−0.971585 + 0.236690i \(0.923937\pi\)
\(128\) 20.5303 1.81464
\(129\) 3.29947 0.290502
\(130\) −11.2995 −0.991029
\(131\) −5.93800 −0.518806 −0.259403 0.965769i \(-0.583526\pi\)
−0.259403 + 0.965769i \(0.583526\pi\)
\(132\) 21.2375 1.84848
\(133\) 5.93800 0.514890
\(134\) 25.8140 2.22999
\(135\) 3.36147 0.289309
\(136\) −10.3681 −0.889060
\(137\) −1.33906 −0.114404 −0.0572018 0.998363i \(-0.518218\pi\)
−0.0572018 + 0.998363i \(0.518218\pi\)
\(138\) 2.36147 0.201022
\(139\) −17.3615 −1.47258 −0.736290 0.676666i \(-0.763424\pi\)
−0.736290 + 0.676666i \(0.763424\pi\)
\(140\) −12.0224 −1.01608
\(141\) 9.15307 0.770828
\(142\) −7.10015 −0.595831
\(143\) 8.45254 0.706837
\(144\) 1.63853 0.136544
\(145\) −22.3905 −1.85943
\(146\) 3.56079 0.294693
\(147\) 1.00000 0.0824786
\(148\) 38.1292 3.13420
\(149\) −7.02908 −0.575844 −0.287922 0.957654i \(-0.592964\pi\)
−0.287922 + 0.957654i \(0.592964\pi\)
\(150\) −14.8760 −1.21462
\(151\) 6.59894 0.537014 0.268507 0.963278i \(-0.413470\pi\)
0.268507 + 0.963278i \(0.413470\pi\)
\(152\) 22.1068 1.79310
\(153\) 2.78493 0.225149
\(154\) 14.0224 1.12996
\(155\) −33.4063 −2.68326
\(156\) 5.09107 0.407612
\(157\) −19.7387 −1.57532 −0.787659 0.616111i \(-0.788707\pi\)
−0.787659 + 0.616111i \(0.788707\pi\)
\(158\) 11.0067 0.875643
\(159\) 3.36147 0.266582
\(160\) 12.0224 0.950455
\(161\) 1.00000 0.0788110
\(162\) −2.36147 −0.185535
\(163\) 2.93134 0.229600 0.114800 0.993389i \(-0.463377\pi\)
0.114800 + 0.993389i \(0.463377\pi\)
\(164\) −32.5145 −2.53896
\(165\) 19.9604 1.55392
\(166\) −11.2995 −0.877009
\(167\) −11.2599 −0.871316 −0.435658 0.900112i \(-0.643484\pi\)
−0.435658 + 0.900112i \(0.643484\pi\)
\(168\) 3.72294 0.287231
\(169\) −10.9737 −0.844134
\(170\) −22.1068 −1.69552
\(171\) −5.93800 −0.454090
\(172\) 11.8007 0.899793
\(173\) 1.09107 0.0829527 0.0414764 0.999139i \(-0.486794\pi\)
0.0414764 + 0.999139i \(0.486794\pi\)
\(174\) 15.7296 1.19246
\(175\) −6.29947 −0.476195
\(176\) 9.72960 0.733397
\(177\) 0.208399 0.0156643
\(178\) −15.5303 −1.16404
\(179\) −13.2375 −0.989415 −0.494708 0.869059i \(-0.664725\pi\)
−0.494708 + 0.869059i \(0.664725\pi\)
\(180\) 12.0224 0.896098
\(181\) 18.2441 1.35608 0.678038 0.735027i \(-0.262830\pi\)
0.678038 + 0.735027i \(0.262830\pi\)
\(182\) 3.36147 0.249169
\(183\) 5.29947 0.391748
\(184\) 3.72294 0.274459
\(185\) 35.8364 2.63475
\(186\) 23.4683 1.72078
\(187\) 16.5369 1.20930
\(188\) 32.7363 2.38754
\(189\) −1.00000 −0.0727393
\(190\) 47.1359 3.41960
\(191\) 1.40106 0.101377 0.0506884 0.998715i \(-0.483858\pi\)
0.0506884 + 0.998715i \(0.483858\pi\)
\(192\) −11.7229 −0.846030
\(193\) 16.5989 1.19482 0.597409 0.801937i \(-0.296197\pi\)
0.597409 + 0.801937i \(0.296197\pi\)
\(194\) 22.4525 1.61200
\(195\) 4.78493 0.342656
\(196\) 3.57653 0.255467
\(197\) −2.86934 −0.204432 −0.102216 0.994762i \(-0.532593\pi\)
−0.102216 + 0.994762i \(0.532593\pi\)
\(198\) −14.0224 −0.996529
\(199\) 18.5594 1.31564 0.657819 0.753176i \(-0.271479\pi\)
0.657819 + 0.753176i \(0.271479\pi\)
\(200\) −23.4525 −1.65835
\(201\) −10.9313 −0.771037
\(202\) −13.3839 −0.941686
\(203\) 6.66094 0.467506
\(204\) 9.96041 0.697368
\(205\) −30.5594 −2.13436
\(206\) −31.7520 −2.21227
\(207\) −1.00000 −0.0695048
\(208\) 2.33239 0.161722
\(209\) −35.2599 −2.43898
\(210\) 7.93800 0.547774
\(211\) −9.81401 −0.675624 −0.337812 0.941214i \(-0.609687\pi\)
−0.337812 + 0.941214i \(0.609687\pi\)
\(212\) 12.0224 0.825702
\(213\) 3.00667 0.206013
\(214\) 26.6834 1.82404
\(215\) 11.0911 0.756405
\(216\) −3.72294 −0.253314
\(217\) 9.93800 0.674636
\(218\) −14.3681 −0.973133
\(219\) −1.50787 −0.101893
\(220\) 71.3891 4.81305
\(221\) 3.96426 0.266665
\(222\) −25.1755 −1.68967
\(223\) −15.6676 −1.04918 −0.524590 0.851355i \(-0.675781\pi\)
−0.524590 + 0.851355i \(0.675781\pi\)
\(224\) −3.57653 −0.238967
\(225\) 6.29947 0.419965
\(226\) −7.24655 −0.482033
\(227\) −7.96041 −0.528351 −0.264176 0.964475i \(-0.585100\pi\)
−0.264176 + 0.964475i \(0.585100\pi\)
\(228\) −21.2375 −1.40649
\(229\) −14.9447 −0.987572 −0.493786 0.869584i \(-0.664387\pi\)
−0.493786 + 0.869584i \(0.664387\pi\)
\(230\) 7.93800 0.523416
\(231\) −5.93800 −0.390692
\(232\) 24.7983 1.62809
\(233\) 9.83642 0.644405 0.322203 0.946671i \(-0.395577\pi\)
0.322203 + 0.946671i \(0.395577\pi\)
\(234\) −3.36147 −0.219746
\(235\) 30.7678 2.00707
\(236\) 0.745347 0.0485180
\(237\) −4.66094 −0.302761
\(238\) 6.57653 0.426293
\(239\) 18.8073 1.21655 0.608273 0.793728i \(-0.291863\pi\)
0.608273 + 0.793728i \(0.291863\pi\)
\(240\) 5.50787 0.355532
\(241\) −10.2441 −0.659883 −0.329942 0.944001i \(-0.607029\pi\)
−0.329942 + 0.944001i \(0.607029\pi\)
\(242\) −57.2890 −3.68267
\(243\) 1.00000 0.0641500
\(244\) 18.9537 1.21339
\(245\) 3.36147 0.214756
\(246\) 21.4683 1.36877
\(247\) −8.45254 −0.537822
\(248\) 36.9986 2.34941
\(249\) 4.78493 0.303233
\(250\) −10.3152 −0.652392
\(251\) −12.4168 −0.783741 −0.391871 0.920020i \(-0.628172\pi\)
−0.391871 + 0.920020i \(0.628172\pi\)
\(252\) −3.57653 −0.225301
\(253\) −5.93800 −0.373319
\(254\) 51.7124 3.24473
\(255\) 9.36147 0.586238
\(256\) −25.0357 −1.56473
\(257\) −5.58320 −0.348271 −0.174135 0.984722i \(-0.555713\pi\)
−0.174135 + 0.984722i \(0.555713\pi\)
\(258\) −7.79160 −0.485084
\(259\) −10.6609 −0.662439
\(260\) 17.1135 1.06133
\(261\) −6.66094 −0.412302
\(262\) 14.0224 0.866307
\(263\) 19.6767 1.21332 0.606658 0.794963i \(-0.292510\pi\)
0.606658 + 0.794963i \(0.292510\pi\)
\(264\) −22.1068 −1.36058
\(265\) 11.2995 0.694121
\(266\) −14.0224 −0.859769
\(267\) 6.57653 0.402477
\(268\) −39.0963 −2.38819
\(269\) −0.882674 −0.0538176 −0.0269088 0.999638i \(-0.508566\pi\)
−0.0269088 + 0.999638i \(0.508566\pi\)
\(270\) −7.93800 −0.483092
\(271\) −0.784934 −0.0476813 −0.0238407 0.999716i \(-0.507589\pi\)
−0.0238407 + 0.999716i \(0.507589\pi\)
\(272\) 4.56320 0.276685
\(273\) −1.42347 −0.0861520
\(274\) 3.16215 0.191032
\(275\) 37.4063 2.25568
\(276\) −3.57653 −0.215282
\(277\) −21.3443 −1.28245 −0.641227 0.767351i \(-0.721574\pi\)
−0.641227 + 0.767351i \(0.721574\pi\)
\(278\) 40.9986 2.45893
\(279\) −9.93800 −0.594973
\(280\) 12.5145 0.747887
\(281\) 21.4592 1.28015 0.640075 0.768313i \(-0.278903\pi\)
0.640075 + 0.768313i \(0.278903\pi\)
\(282\) −21.6147 −1.28714
\(283\) −13.6543 −0.811662 −0.405831 0.913948i \(-0.633018\pi\)
−0.405831 + 0.913948i \(0.633018\pi\)
\(284\) 10.7534 0.638100
\(285\) −19.9604 −1.18235
\(286\) −19.9604 −1.18028
\(287\) 9.09107 0.536629
\(288\) 3.57653 0.210749
\(289\) −9.24414 −0.543773
\(290\) 52.8746 3.10490
\(291\) −9.50787 −0.557361
\(292\) −5.39296 −0.315599
\(293\) −3.32188 −0.194066 −0.0970332 0.995281i \(-0.530935\pi\)
−0.0970332 + 0.995281i \(0.530935\pi\)
\(294\) −2.36147 −0.137724
\(295\) 0.700528 0.0407863
\(296\) −39.6900 −2.30694
\(297\) 5.93800 0.344558
\(298\) 16.5989 0.961551
\(299\) −1.42347 −0.0823211
\(300\) 22.5303 1.30079
\(301\) −3.29947 −0.190178
\(302\) −15.5832 −0.896712
\(303\) 5.66761 0.325596
\(304\) −9.72960 −0.558031
\(305\) 17.8140 1.02003
\(306\) −6.57653 −0.375955
\(307\) −2.06200 −0.117684 −0.0588422 0.998267i \(-0.518741\pi\)
−0.0588422 + 0.998267i \(0.518741\pi\)
\(308\) −21.2375 −1.21012
\(309\) 13.4459 0.764909
\(310\) 78.8879 4.48053
\(311\) −8.45254 −0.479300 −0.239650 0.970859i \(-0.577033\pi\)
−0.239650 + 0.970859i \(0.577033\pi\)
\(312\) −5.29947 −0.300024
\(313\) 10.7363 0.606850 0.303425 0.952855i \(-0.401870\pi\)
0.303425 + 0.952855i \(0.401870\pi\)
\(314\) 46.6123 2.63048
\(315\) −3.36147 −0.189397
\(316\) −16.6700 −0.937762
\(317\) 16.8073 0.943994 0.471997 0.881600i \(-0.343533\pi\)
0.471997 + 0.881600i \(0.343533\pi\)
\(318\) −7.93800 −0.445141
\(319\) −39.5527 −2.21453
\(320\) −39.4063 −2.20288
\(321\) −11.2995 −0.630675
\(322\) −2.36147 −0.131600
\(323\) −16.5369 −0.920140
\(324\) 3.57653 0.198696
\(325\) 8.96708 0.497404
\(326\) −6.92226 −0.383389
\(327\) 6.08441 0.336468
\(328\) 33.8455 1.86880
\(329\) −9.15307 −0.504625
\(330\) −47.1359 −2.59475
\(331\) −21.5699 −1.18559 −0.592794 0.805354i \(-0.701975\pi\)
−0.592794 + 0.805354i \(0.701975\pi\)
\(332\) 17.1135 0.939224
\(333\) 10.6609 0.584216
\(334\) 26.5899 1.45493
\(335\) −36.7453 −2.00761
\(336\) −1.63853 −0.0893892
\(337\) 5.42347 0.295435 0.147717 0.989030i \(-0.452807\pi\)
0.147717 + 0.989030i \(0.452807\pi\)
\(338\) 25.9142 1.40954
\(339\) 3.06866 0.166667
\(340\) 33.4816 1.81580
\(341\) −59.0119 −3.19567
\(342\) 14.0224 0.758245
\(343\) −1.00000 −0.0539949
\(344\) −12.2837 −0.662294
\(345\) −3.36147 −0.180975
\(346\) −2.57653 −0.138515
\(347\) 25.9828 1.39483 0.697416 0.716667i \(-0.254333\pi\)
0.697416 + 0.716667i \(0.254333\pi\)
\(348\) −23.8231 −1.27705
\(349\) −2.50120 −0.133886 −0.0669432 0.997757i \(-0.521325\pi\)
−0.0669432 + 0.997757i \(0.521325\pi\)
\(350\) 14.8760 0.795156
\(351\) 1.42347 0.0759790
\(352\) 21.2375 1.13196
\(353\) 19.5212 1.03901 0.519504 0.854468i \(-0.326117\pi\)
0.519504 + 0.854468i \(0.326117\pi\)
\(354\) −0.492128 −0.0261563
\(355\) 10.1068 0.536414
\(356\) 23.5212 1.24662
\(357\) −2.78493 −0.147394
\(358\) 31.2599 1.65214
\(359\) −37.3615 −1.97186 −0.985931 0.167150i \(-0.946544\pi\)
−0.985931 + 0.167150i \(0.946544\pi\)
\(360\) −12.5145 −0.659574
\(361\) 16.2599 0.855783
\(362\) −43.0830 −2.26439
\(363\) 24.2599 1.27331
\(364\) −5.09107 −0.266845
\(365\) −5.06866 −0.265306
\(366\) −12.5145 −0.654145
\(367\) 0.452542 0.0236225 0.0118112 0.999930i \(-0.496240\pi\)
0.0118112 + 0.999930i \(0.496240\pi\)
\(368\) −1.63853 −0.0854143
\(369\) −9.09107 −0.473262
\(370\) −84.6266 −4.39953
\(371\) −3.36147 −0.174519
\(372\) −35.5436 −1.84285
\(373\) −13.0911 −0.677830 −0.338915 0.940817i \(-0.610060\pi\)
−0.338915 + 0.940817i \(0.610060\pi\)
\(374\) −39.0515 −2.01930
\(375\) 4.36814 0.225570
\(376\) −34.0763 −1.75735
\(377\) −9.48162 −0.488328
\(378\) 2.36147 0.121461
\(379\) 26.0315 1.33715 0.668574 0.743646i \(-0.266905\pi\)
0.668574 + 0.743646i \(0.266905\pi\)
\(380\) −71.3891 −3.66218
\(381\) −21.8984 −1.12189
\(382\) −3.30855 −0.169280
\(383\) −3.09107 −0.157946 −0.0789732 0.996877i \(-0.525164\pi\)
−0.0789732 + 0.996877i \(0.525164\pi\)
\(384\) 20.5303 1.04768
\(385\) −19.9604 −1.01728
\(386\) −39.1979 −1.99512
\(387\) 3.29947 0.167722
\(388\) −34.0052 −1.72635
\(389\) −4.77160 −0.241930 −0.120965 0.992657i \(-0.538599\pi\)
−0.120965 + 0.992657i \(0.538599\pi\)
\(390\) −11.2995 −0.572171
\(391\) −2.78493 −0.140840
\(392\) −3.72294 −0.188037
\(393\) −5.93800 −0.299533
\(394\) 6.77586 0.341363
\(395\) −15.6676 −0.788323
\(396\) 21.2375 1.06722
\(397\) −9.92083 −0.497912 −0.248956 0.968515i \(-0.580087\pi\)
−0.248956 + 0.968515i \(0.580087\pi\)
\(398\) −43.8273 −2.19687
\(399\) 5.93800 0.297272
\(400\) 10.3219 0.516094
\(401\) 16.5503 0.826482 0.413241 0.910622i \(-0.364397\pi\)
0.413241 + 0.910622i \(0.364397\pi\)
\(402\) 25.8140 1.28749
\(403\) −14.1464 −0.704683
\(404\) 20.2704 1.00849
\(405\) 3.36147 0.167033
\(406\) −15.7296 −0.780647
\(407\) 63.3047 3.13790
\(408\) −10.3681 −0.513299
\(409\) 12.3548 0.610906 0.305453 0.952207i \(-0.401192\pi\)
0.305453 + 0.952207i \(0.401192\pi\)
\(410\) 72.1650 3.56397
\(411\) −1.33906 −0.0660509
\(412\) 48.0896 2.36921
\(413\) −0.208399 −0.0102547
\(414\) 2.36147 0.116060
\(415\) 16.0844 0.789552
\(416\) 5.09107 0.249610
\(417\) −17.3615 −0.850195
\(418\) 83.2651 4.07263
\(419\) −37.8231 −1.84778 −0.923889 0.382660i \(-0.875008\pi\)
−0.923889 + 0.382660i \(0.875008\pi\)
\(420\) −12.0224 −0.586634
\(421\) 21.6189 1.05364 0.526821 0.849976i \(-0.323384\pi\)
0.526821 + 0.849976i \(0.323384\pi\)
\(422\) 23.1755 1.12816
\(423\) 9.15307 0.445037
\(424\) −12.5145 −0.607760
\(425\) 17.5436 0.850990
\(426\) −7.10015 −0.344003
\(427\) −5.29947 −0.256459
\(428\) −40.4130 −1.95343
\(429\) 8.45254 0.408093
\(430\) −26.1912 −1.26305
\(431\) 39.6371 1.90925 0.954626 0.297808i \(-0.0962554\pi\)
0.954626 + 0.297808i \(0.0962554\pi\)
\(432\) 1.63853 0.0788339
\(433\) −25.4592 −1.22349 −0.611746 0.791054i \(-0.709532\pi\)
−0.611746 + 0.791054i \(0.709532\pi\)
\(434\) −23.4683 −1.12651
\(435\) −22.3905 −1.07354
\(436\) 21.7611 1.04217
\(437\) 5.93800 0.284053
\(438\) 3.56079 0.170141
\(439\) −25.6900 −1.22612 −0.613059 0.790037i \(-0.710061\pi\)
−0.613059 + 0.790037i \(0.710061\pi\)
\(440\) −74.3114 −3.54266
\(441\) 1.00000 0.0476190
\(442\) −9.36147 −0.445280
\(443\) 1.44588 0.0686956 0.0343478 0.999410i \(-0.489065\pi\)
0.0343478 + 0.999410i \(0.489065\pi\)
\(444\) 38.1292 1.80953
\(445\) 22.1068 1.04796
\(446\) 36.9986 1.75193
\(447\) −7.02908 −0.332464
\(448\) 11.7229 0.553857
\(449\) 10.2532 0.483879 0.241940 0.970291i \(-0.422216\pi\)
0.241940 + 0.970291i \(0.422216\pi\)
\(450\) −14.8760 −0.701262
\(451\) −53.9828 −2.54195
\(452\) 10.9752 0.516229
\(453\) 6.59894 0.310045
\(454\) 18.7983 0.882246
\(455\) −4.78493 −0.224321
\(456\) 22.1068 1.03525
\(457\) −35.5303 −1.66204 −0.831018 0.556245i \(-0.812242\pi\)
−0.831018 + 0.556245i \(0.812242\pi\)
\(458\) 35.2914 1.64906
\(459\) 2.78493 0.129990
\(460\) −12.0224 −0.560548
\(461\) 19.9471 0.929028 0.464514 0.885566i \(-0.346229\pi\)
0.464514 + 0.885566i \(0.346229\pi\)
\(462\) 14.0224 0.652382
\(463\) 3.92467 0.182395 0.0911974 0.995833i \(-0.470931\pi\)
0.0911974 + 0.995833i \(0.470931\pi\)
\(464\) −10.9142 −0.506677
\(465\) −33.4063 −1.54918
\(466\) −23.2284 −1.07603
\(467\) −15.0911 −0.698332 −0.349166 0.937061i \(-0.613535\pi\)
−0.349166 + 0.937061i \(0.613535\pi\)
\(468\) 5.09107 0.235335
\(469\) 10.9313 0.504762
\(470\) −72.6571 −3.35142
\(471\) −19.7387 −0.909510
\(472\) −0.775858 −0.0357117
\(473\) 19.5923 0.900854
\(474\) 11.0067 0.505553
\(475\) −37.4063 −1.71632
\(476\) −9.96041 −0.456535
\(477\) 3.36147 0.153911
\(478\) −44.4130 −2.03140
\(479\) 16.1201 0.736548 0.368274 0.929717i \(-0.379949\pi\)
0.368274 + 0.929717i \(0.379949\pi\)
\(480\) 12.0224 0.548745
\(481\) 15.1755 0.691942
\(482\) 24.1912 1.10188
\(483\) 1.00000 0.0455016
\(484\) 86.7663 3.94392
\(485\) −31.9604 −1.45125
\(486\) −2.36147 −0.107118
\(487\) 15.8007 0.715997 0.357999 0.933722i \(-0.383459\pi\)
0.357999 + 0.933722i \(0.383459\pi\)
\(488\) −19.7296 −0.893117
\(489\) 2.93134 0.132560
\(490\) −7.93800 −0.358602
\(491\) −1.97759 −0.0892474 −0.0446237 0.999004i \(-0.514209\pi\)
−0.0446237 + 0.999004i \(0.514209\pi\)
\(492\) −32.5145 −1.46587
\(493\) −18.5503 −0.835463
\(494\) 19.9604 0.898061
\(495\) 19.9604 0.897154
\(496\) −16.2837 −0.731161
\(497\) −3.00667 −0.134867
\(498\) −11.2995 −0.506341
\(499\) 20.5012 0.917760 0.458880 0.888498i \(-0.348251\pi\)
0.458880 + 0.888498i \(0.348251\pi\)
\(500\) 15.6228 0.698672
\(501\) −11.2599 −0.503055
\(502\) 29.3219 1.30870
\(503\) 20.1292 0.897518 0.448759 0.893653i \(-0.351866\pi\)
0.448759 + 0.893653i \(0.351866\pi\)
\(504\) 3.72294 0.165833
\(505\) 19.0515 0.847780
\(506\) 14.0224 0.623372
\(507\) −10.9737 −0.487361
\(508\) −78.3204 −3.47491
\(509\) 2.44347 0.108305 0.0541523 0.998533i \(-0.482754\pi\)
0.0541523 + 0.998533i \(0.482754\pi\)
\(510\) −22.1068 −0.978906
\(511\) 1.50787 0.0667043
\(512\) 18.0606 0.798172
\(513\) −5.93800 −0.262169
\(514\) 13.1846 0.581546
\(515\) 45.1979 1.99166
\(516\) 11.8007 0.519496
\(517\) 54.3510 2.39035
\(518\) 25.1755 1.10615
\(519\) 1.09107 0.0478928
\(520\) −17.8140 −0.781196
\(521\) −5.16640 −0.226344 −0.113172 0.993575i \(-0.536101\pi\)
−0.113172 + 0.993575i \(0.536101\pi\)
\(522\) 15.7296 0.688466
\(523\) 34.5198 1.50944 0.754722 0.656045i \(-0.227772\pi\)
0.754722 + 0.656045i \(0.227772\pi\)
\(524\) −21.2375 −0.927763
\(525\) −6.29947 −0.274932
\(526\) −46.4659 −2.02601
\(527\) −27.6767 −1.20562
\(528\) 9.72960 0.423427
\(529\) 1.00000 0.0434783
\(530\) −26.6834 −1.15905
\(531\) 0.208399 0.00904376
\(532\) 21.2375 0.920761
\(533\) −12.9408 −0.560529
\(534\) −15.5303 −0.672061
\(535\) −37.9828 −1.64214
\(536\) 40.6967 1.75783
\(537\) −13.2375 −0.571239
\(538\) 2.08441 0.0898651
\(539\) 5.93800 0.255768
\(540\) 12.0224 0.517362
\(541\) 43.3667 1.86448 0.932240 0.361840i \(-0.117851\pi\)
0.932240 + 0.361840i \(0.117851\pi\)
\(542\) 1.85360 0.0796188
\(543\) 18.2441 0.782931
\(544\) 9.96041 0.427049
\(545\) 20.4525 0.876091
\(546\) 3.36147 0.143858
\(547\) 16.5279 0.706681 0.353340 0.935495i \(-0.385046\pi\)
0.353340 + 0.935495i \(0.385046\pi\)
\(548\) −4.78919 −0.204584
\(549\) 5.29947 0.226176
\(550\) −88.3338 −3.76657
\(551\) 39.5527 1.68500
\(552\) 3.72294 0.158459
\(553\) 4.66094 0.198203
\(554\) 50.4039 2.14146
\(555\) 35.8364 1.52117
\(556\) −62.0939 −2.63337
\(557\) 20.3510 0.862298 0.431149 0.902281i \(-0.358108\pi\)
0.431149 + 0.902281i \(0.358108\pi\)
\(558\) 23.4683 0.993492
\(559\) 4.69668 0.198649
\(560\) −5.50787 −0.232750
\(561\) 16.5369 0.698190
\(562\) −50.6753 −2.13761
\(563\) −29.1888 −1.23016 −0.615081 0.788464i \(-0.710877\pi\)
−0.615081 + 0.788464i \(0.710877\pi\)
\(564\) 32.7363 1.37845
\(565\) 10.3152 0.433964
\(566\) 32.2441 1.35532
\(567\) −1.00000 −0.0419961
\(568\) −11.1936 −0.469674
\(569\) 16.1821 0.678391 0.339195 0.940716i \(-0.389845\pi\)
0.339195 + 0.940716i \(0.389845\pi\)
\(570\) 47.1359 1.97431
\(571\) −37.1226 −1.55353 −0.776765 0.629790i \(-0.783141\pi\)
−0.776765 + 0.629790i \(0.783141\pi\)
\(572\) 30.2308 1.26401
\(573\) 1.40106 0.0585299
\(574\) −21.4683 −0.896069
\(575\) −6.29947 −0.262706
\(576\) −11.7229 −0.488456
\(577\) 41.7520 1.73816 0.869080 0.494672i \(-0.164712\pi\)
0.869080 + 0.494672i \(0.164712\pi\)
\(578\) 21.8298 0.907998
\(579\) 16.5989 0.689829
\(580\) −80.0806 −3.32516
\(581\) −4.78493 −0.198513
\(582\) 22.4525 0.930688
\(583\) 19.9604 0.826676
\(584\) 5.61371 0.232297
\(585\) 4.78493 0.197833
\(586\) 7.84452 0.324054
\(587\) −43.4683 −1.79413 −0.897064 0.441901i \(-0.854304\pi\)
−0.897064 + 0.441901i \(0.854304\pi\)
\(588\) 3.57653 0.147494
\(589\) 59.0119 2.43154
\(590\) −1.65427 −0.0681054
\(591\) −2.86934 −0.118029
\(592\) 17.4683 0.717942
\(593\) −4.84693 −0.199040 −0.0995198 0.995036i \(-0.531731\pi\)
−0.0995198 + 0.995036i \(0.531731\pi\)
\(594\) −14.0224 −0.575346
\(595\) −9.36147 −0.383783
\(596\) −25.1397 −1.02976
\(597\) 18.5594 0.759584
\(598\) 3.36147 0.137461
\(599\) 2.27040 0.0927659 0.0463829 0.998924i \(-0.485231\pi\)
0.0463829 + 0.998924i \(0.485231\pi\)
\(600\) −23.4525 −0.957446
\(601\) −34.7940 −1.41928 −0.709639 0.704566i \(-0.751142\pi\)
−0.709639 + 0.704566i \(0.751142\pi\)
\(602\) 7.79160 0.317562
\(603\) −10.9313 −0.445158
\(604\) 23.6014 0.960325
\(605\) 81.5488 3.31543
\(606\) −13.3839 −0.543683
\(607\) 18.1912 0.738359 0.369179 0.929358i \(-0.379639\pi\)
0.369179 + 0.929358i \(0.379639\pi\)
\(608\) −21.2375 −0.861293
\(609\) 6.66094 0.269915
\(610\) −42.0672 −1.70325
\(611\) 13.0291 0.527100
\(612\) 9.96041 0.402626
\(613\) 22.2175 0.897355 0.448678 0.893694i \(-0.351895\pi\)
0.448678 + 0.893694i \(0.351895\pi\)
\(614\) 4.86934 0.196511
\(615\) −30.5594 −1.23227
\(616\) 22.1068 0.890709
\(617\) −19.5789 −0.788219 −0.394109 0.919064i \(-0.628947\pi\)
−0.394109 + 0.919064i \(0.628947\pi\)
\(618\) −31.7520 −1.27725
\(619\) 28.4525 1.14360 0.571802 0.820392i \(-0.306245\pi\)
0.571802 + 0.820392i \(0.306245\pi\)
\(620\) −119.479 −4.79838
\(621\) −1.00000 −0.0401286
\(622\) 19.9604 0.800340
\(623\) −6.57653 −0.263483
\(624\) 2.33239 0.0933704
\(625\) −16.8140 −0.672560
\(626\) −25.3534 −1.01332
\(627\) −35.2599 −1.40814
\(628\) −70.5961 −2.81709
\(629\) 29.6900 1.18382
\(630\) 7.93800 0.316258
\(631\) −42.0276 −1.67309 −0.836547 0.547895i \(-0.815429\pi\)
−0.836547 + 0.547895i \(0.815429\pi\)
\(632\) 17.3524 0.690241
\(633\) −9.81401 −0.390072
\(634\) −39.6900 −1.57629
\(635\) −73.6108 −2.92116
\(636\) 12.0224 0.476720
\(637\) 1.42347 0.0563997
\(638\) 93.4024 3.69784
\(639\) 3.00667 0.118942
\(640\) 69.0119 2.72793
\(641\) 4.85601 0.191801 0.0959004 0.995391i \(-0.469427\pi\)
0.0959004 + 0.995391i \(0.469427\pi\)
\(642\) 26.6834 1.05311
\(643\) −37.6056 −1.48302 −0.741510 0.670942i \(-0.765890\pi\)
−0.741510 + 0.670942i \(0.765890\pi\)
\(644\) 3.57653 0.140935
\(645\) 11.0911 0.436711
\(646\) 39.0515 1.53646
\(647\) −33.7258 −1.32590 −0.662948 0.748665i \(-0.730695\pi\)
−0.662948 + 0.748665i \(0.730695\pi\)
\(648\) −3.72294 −0.146251
\(649\) 1.23748 0.0485752
\(650\) −21.1755 −0.830571
\(651\) 9.93800 0.389501
\(652\) 10.4840 0.410586
\(653\) 30.6700 1.20021 0.600105 0.799921i \(-0.295125\pi\)
0.600105 + 0.799921i \(0.295125\pi\)
\(654\) −14.3681 −0.561839
\(655\) −19.9604 −0.779918
\(656\) −14.8960 −0.581591
\(657\) −1.50787 −0.0588277
\(658\) 21.6147 0.842628
\(659\) −7.50787 −0.292465 −0.146233 0.989250i \(-0.546715\pi\)
−0.146233 + 0.989250i \(0.546715\pi\)
\(660\) 71.3891 2.77882
\(661\) 7.35239 0.285975 0.142987 0.989725i \(-0.454329\pi\)
0.142987 + 0.989725i \(0.454329\pi\)
\(662\) 50.9366 1.97971
\(663\) 3.96426 0.153959
\(664\) −17.8140 −0.691318
\(665\) 19.9604 0.774032
\(666\) −25.1755 −0.975530
\(667\) 6.66094 0.257913
\(668\) −40.2714 −1.55815
\(669\) −15.6676 −0.605745
\(670\) 86.7730 3.35233
\(671\) 31.4683 1.21482
\(672\) −3.57653 −0.137968
\(673\) −25.0119 −0.964138 −0.482069 0.876133i \(-0.660115\pi\)
−0.482069 + 0.876133i \(0.660115\pi\)
\(674\) −12.8073 −0.493320
\(675\) 6.29947 0.242467
\(676\) −39.2480 −1.50954
\(677\) 10.1597 0.390470 0.195235 0.980756i \(-0.437453\pi\)
0.195235 + 0.980756i \(0.437453\pi\)
\(678\) −7.24655 −0.278302
\(679\) 9.50787 0.364879
\(680\) −34.8522 −1.33652
\(681\) −7.96041 −0.305044
\(682\) 139.355 5.33617
\(683\) −17.9828 −0.688094 −0.344047 0.938953i \(-0.611798\pi\)
−0.344047 + 0.938953i \(0.611798\pi\)
\(684\) −21.2375 −0.812035
\(685\) −4.50120 −0.171982
\(686\) 2.36147 0.0901613
\(687\) −14.9447 −0.570175
\(688\) 5.40629 0.206113
\(689\) 4.78493 0.182291
\(690\) 7.93800 0.302195
\(691\) 26.7320 1.01693 0.508467 0.861082i \(-0.330212\pi\)
0.508467 + 0.861082i \(0.330212\pi\)
\(692\) 3.90226 0.148342
\(693\) −5.93800 −0.225566
\(694\) −61.3576 −2.32910
\(695\) −58.3600 −2.21372
\(696\) 24.7983 0.939976
\(697\) −25.3180 −0.958989
\(698\) 5.90652 0.223565
\(699\) 9.83642 0.372048
\(700\) −22.5303 −0.851565
\(701\) −41.7572 −1.57715 −0.788575 0.614939i \(-0.789181\pi\)
−0.788575 + 0.614939i \(0.789181\pi\)
\(702\) −3.36147 −0.126870
\(703\) −63.3047 −2.38758
\(704\) −69.6108 −2.62356
\(705\) 30.7678 1.15878
\(706\) −46.0987 −1.73495
\(707\) −5.66761 −0.213152
\(708\) 0.745347 0.0280119
\(709\) −31.1621 −1.17032 −0.585159 0.810918i \(-0.698968\pi\)
−0.585159 + 0.810918i \(0.698968\pi\)
\(710\) −23.8669 −0.895710
\(711\) −4.66094 −0.174799
\(712\) −24.4840 −0.917578
\(713\) 9.93800 0.372181
\(714\) 6.57653 0.246121
\(715\) 28.4130 1.06258
\(716\) −47.3443 −1.76934
\(717\) 18.8073 0.702373
\(718\) 88.2279 3.29264
\(719\) −36.1650 −1.34873 −0.674363 0.738400i \(-0.735582\pi\)
−0.674363 + 0.738400i \(0.735582\pi\)
\(720\) 5.50787 0.205266
\(721\) −13.4459 −0.500751
\(722\) −38.3972 −1.42900
\(723\) −10.2441 −0.380984
\(724\) 65.2508 2.42503
\(725\) −41.9604 −1.55837
\(726\) −57.2890 −2.12619
\(727\) 44.3338 1.64425 0.822124 0.569308i \(-0.192789\pi\)
0.822124 + 0.569308i \(0.192789\pi\)
\(728\) 5.29947 0.196412
\(729\) 1.00000 0.0370370
\(730\) 11.9695 0.443011
\(731\) 9.18881 0.339861
\(732\) 18.9537 0.700551
\(733\) −16.5989 −0.613096 −0.306548 0.951855i \(-0.599174\pi\)
−0.306548 + 0.951855i \(0.599174\pi\)
\(734\) −1.06866 −0.0394451
\(735\) 3.36147 0.123990
\(736\) −3.57653 −0.131833
\(737\) −64.9103 −2.39100
\(738\) 21.4683 0.790258
\(739\) 21.6900 0.797880 0.398940 0.916977i \(-0.369378\pi\)
0.398940 + 0.916977i \(0.369378\pi\)
\(740\) 128.170 4.71163
\(741\) −8.45254 −0.310512
\(742\) 7.93800 0.291413
\(743\) −13.1135 −0.481087 −0.240544 0.970638i \(-0.577326\pi\)
−0.240544 + 0.970638i \(0.577326\pi\)
\(744\) 36.9986 1.35643
\(745\) −23.6280 −0.865664
\(746\) 30.9142 1.13185
\(747\) 4.78493 0.175072
\(748\) 59.1450 2.16255
\(749\) 11.2995 0.412874
\(750\) −10.3152 −0.376658
\(751\) −48.6700 −1.77599 −0.887997 0.459849i \(-0.847904\pi\)
−0.887997 + 0.459849i \(0.847904\pi\)
\(752\) 14.9976 0.546906
\(753\) −12.4168 −0.452493
\(754\) 22.3905 0.815416
\(755\) 22.1821 0.807291
\(756\) −3.57653 −0.130077
\(757\) 28.2308 1.02607 0.513033 0.858369i \(-0.328522\pi\)
0.513033 + 0.858369i \(0.328522\pi\)
\(758\) −61.4725 −2.23278
\(759\) −5.93800 −0.215536
\(760\) 74.3114 2.69556
\(761\) 25.6014 0.928048 0.464024 0.885823i \(-0.346405\pi\)
0.464024 + 0.885823i \(0.346405\pi\)
\(762\) 51.7124 1.87334
\(763\) −6.08441 −0.220270
\(764\) 5.01092 0.181289
\(765\) 9.36147 0.338465
\(766\) 7.29947 0.263741
\(767\) 0.296649 0.0107114
\(768\) −25.0357 −0.903400
\(769\) −18.8784 −0.680773 −0.340387 0.940286i \(-0.610558\pi\)
−0.340387 + 0.940286i \(0.610558\pi\)
\(770\) 47.1359 1.69866
\(771\) −5.58320 −0.201074
\(772\) 59.3667 2.13665
\(773\) 29.6319 1.06578 0.532892 0.846183i \(-0.321105\pi\)
0.532892 + 0.846183i \(0.321105\pi\)
\(774\) −7.79160 −0.280063
\(775\) −62.6042 −2.24881
\(776\) 35.3972 1.27069
\(777\) −10.6609 −0.382459
\(778\) 11.2680 0.403977
\(779\) 53.9828 1.93414
\(780\) 17.1135 0.612761
\(781\) 17.8536 0.638852
\(782\) 6.57653 0.235176
\(783\) −6.66094 −0.238043
\(784\) 1.63853 0.0585190
\(785\) −66.3510 −2.36817
\(786\) 14.0224 0.500163
\(787\) −12.3324 −0.439602 −0.219801 0.975545i \(-0.570541\pi\)
−0.219801 + 0.975545i \(0.570541\pi\)
\(788\) −10.2623 −0.365579
\(789\) 19.6767 0.700509
\(790\) 36.9986 1.31635
\(791\) −3.06866 −0.109109
\(792\) −22.1068 −0.785532
\(793\) 7.54361 0.267882
\(794\) 23.4277 0.831419
\(795\) 11.2995 0.400751
\(796\) 66.3782 2.35271
\(797\) 9.55653 0.338510 0.169255 0.985572i \(-0.445864\pi\)
0.169255 + 0.985572i \(0.445864\pi\)
\(798\) −14.0224 −0.496388
\(799\) 25.4907 0.901796
\(800\) 22.5303 0.796566
\(801\) 6.57653 0.232370
\(802\) −39.0830 −1.38007
\(803\) −8.95375 −0.315971
\(804\) −39.0963 −1.37882
\(805\) 3.36147 0.118476
\(806\) 33.4063 1.17669
\(807\) −0.882674 −0.0310716
\(808\) −21.1001 −0.742301
\(809\) −40.7587 −1.43300 −0.716499 0.697588i \(-0.754257\pi\)
−0.716499 + 0.697588i \(0.754257\pi\)
\(810\) −7.93800 −0.278913
\(811\) −6.35480 −0.223147 −0.111574 0.993756i \(-0.535589\pi\)
−0.111574 + 0.993756i \(0.535589\pi\)
\(812\) 23.8231 0.836026
\(813\) −0.784934 −0.0275288
\(814\) −149.492 −5.23969
\(815\) 9.85360 0.345156
\(816\) 4.56320 0.159744
\(817\) −19.5923 −0.685447
\(818\) −29.1755 −1.02010
\(819\) −1.42347 −0.0497399
\(820\) −109.297 −3.81680
\(821\) 32.2270 1.12473 0.562364 0.826890i \(-0.309892\pi\)
0.562364 + 0.826890i \(0.309892\pi\)
\(822\) 3.16215 0.110293
\(823\) 5.19266 0.181005 0.0905023 0.995896i \(-0.471153\pi\)
0.0905023 + 0.995896i \(0.471153\pi\)
\(824\) −50.0582 −1.74386
\(825\) 37.4063 1.30232
\(826\) 0.492128 0.0171233
\(827\) 39.1268 1.36057 0.680286 0.732946i \(-0.261855\pi\)
0.680286 + 0.732946i \(0.261855\pi\)
\(828\) −3.57653 −0.124293
\(829\) −11.2732 −0.391535 −0.195768 0.980650i \(-0.562720\pi\)
−0.195768 + 0.980650i \(0.562720\pi\)
\(830\) −37.9828 −1.31840
\(831\) −21.3443 −0.740425
\(832\) −16.6872 −0.578524
\(833\) 2.78493 0.0964922
\(834\) 40.9986 1.41966
\(835\) −37.8498 −1.30984
\(836\) −126.108 −4.36154
\(837\) −9.93800 −0.343508
\(838\) 89.3180 3.08544
\(839\) 26.1912 0.904221 0.452111 0.891962i \(-0.350671\pi\)
0.452111 + 0.891962i \(0.350671\pi\)
\(840\) 12.5145 0.431793
\(841\) 15.3681 0.529936
\(842\) −51.0525 −1.75938
\(843\) 21.4592 0.739094
\(844\) −35.1001 −1.20820
\(845\) −36.8879 −1.26898
\(846\) −21.6147 −0.743128
\(847\) −24.2599 −0.833580
\(848\) 5.50787 0.189141
\(849\) −13.6543 −0.468613
\(850\) −41.4287 −1.42099
\(851\) −10.6609 −0.365452
\(852\) 10.7534 0.368407
\(853\) 39.7387 1.36063 0.680313 0.732921i \(-0.261844\pi\)
0.680313 + 0.732921i \(0.261844\pi\)
\(854\) 12.5145 0.428239
\(855\) −19.9604 −0.682632
\(856\) 42.0672 1.43783
\(857\) −36.9366 −1.26173 −0.630865 0.775893i \(-0.717300\pi\)
−0.630865 + 0.775893i \(0.717300\pi\)
\(858\) −19.9604 −0.681437
\(859\) 9.59653 0.327430 0.163715 0.986508i \(-0.447652\pi\)
0.163715 + 0.986508i \(0.447652\pi\)
\(860\) 39.6676 1.35265
\(861\) 9.09107 0.309823
\(862\) −93.6018 −3.18809
\(863\) 26.2270 0.892776 0.446388 0.894839i \(-0.352710\pi\)
0.446388 + 0.894839i \(0.352710\pi\)
\(864\) 3.57653 0.121676
\(865\) 3.66761 0.124702
\(866\) 60.1211 2.04300
\(867\) −9.24414 −0.313948
\(868\) 35.5436 1.20643
\(869\) −27.6767 −0.938867
\(870\) 52.8746 1.79262
\(871\) −15.5604 −0.527243
\(872\) −22.6519 −0.767089
\(873\) −9.50787 −0.321793
\(874\) −14.0224 −0.474315
\(875\) −4.36814 −0.147670
\(876\) −5.39296 −0.182211
\(877\) 26.1240 0.882145 0.441072 0.897472i \(-0.354598\pi\)
0.441072 + 0.897472i \(0.354598\pi\)
\(878\) 60.6662 2.04738
\(879\) −3.32188 −0.112044
\(880\) 32.7058 1.10251
\(881\) −20.8469 −0.702351 −0.351175 0.936310i \(-0.614218\pi\)
−0.351175 + 0.936310i \(0.614218\pi\)
\(882\) −2.36147 −0.0795148
\(883\) 58.6347 1.97321 0.986607 0.163114i \(-0.0521539\pi\)
0.986607 + 0.163114i \(0.0521539\pi\)
\(884\) 14.1783 0.476868
\(885\) 0.700528 0.0235480
\(886\) −3.41439 −0.114709
\(887\) 28.1597 0.945511 0.472756 0.881194i \(-0.343259\pi\)
0.472756 + 0.881194i \(0.343259\pi\)
\(888\) −39.6900 −1.33191
\(889\) 21.8984 0.734449
\(890\) −52.2046 −1.74990
\(891\) 5.93800 0.198931
\(892\) −56.0357 −1.87622
\(893\) −54.3510 −1.81879
\(894\) 16.5989 0.555152
\(895\) −44.4974 −1.48738
\(896\) −20.5303 −0.685869
\(897\) −1.42347 −0.0475281
\(898\) −24.2127 −0.807987
\(899\) 66.1965 2.20778
\(900\) 22.5303 0.751009
\(901\) 9.36147 0.311876
\(902\) 127.479 4.24458
\(903\) −3.29947 −0.109800
\(904\) −11.4244 −0.379971
\(905\) 61.3271 2.03858
\(906\) −15.5832 −0.517717
\(907\) −11.5884 −0.384788 −0.192394 0.981318i \(-0.561625\pi\)
−0.192394 + 0.981318i \(0.561625\pi\)
\(908\) −28.4707 −0.944833
\(909\) 5.66761 0.187983
\(910\) 11.2995 0.374574
\(911\) 14.5989 0.483685 0.241842 0.970316i \(-0.422248\pi\)
0.241842 + 0.970316i \(0.422248\pi\)
\(912\) −9.72960 −0.322179
\(913\) 28.4130 0.940332
\(914\) 83.9036 2.77529
\(915\) 17.8140 0.588913
\(916\) −53.4501 −1.76604
\(917\) 5.93800 0.196090
\(918\) −6.57653 −0.217058
\(919\) −33.9380 −1.11951 −0.559756 0.828658i \(-0.689105\pi\)
−0.559756 + 0.828658i \(0.689105\pi\)
\(920\) 12.5145 0.412592
\(921\) −2.06200 −0.0679451
\(922\) −47.1044 −1.55130
\(923\) 4.27989 0.140874
\(924\) −21.2375 −0.698662
\(925\) 67.1583 2.20815
\(926\) −9.26799 −0.304565
\(927\) 13.4459 0.441620
\(928\) −23.8231 −0.782031
\(929\) −5.17932 −0.169928 −0.0849640 0.996384i \(-0.527078\pi\)
−0.0849640 + 0.996384i \(0.527078\pi\)
\(930\) 78.8879 2.58684
\(931\) −5.93800 −0.194610
\(932\) 35.1803 1.15237
\(933\) −8.45254 −0.276724
\(934\) 35.6371 1.16608
\(935\) 55.5884 1.81794
\(936\) −5.29947 −0.173219
\(937\) 28.6924 0.937341 0.468670 0.883373i \(-0.344733\pi\)
0.468670 + 0.883373i \(0.344733\pi\)
\(938\) −25.8140 −0.842857
\(939\) 10.7363 0.350365
\(940\) 110.042 3.58917
\(941\) −31.9342 −1.04102 −0.520512 0.853854i \(-0.674259\pi\)
−0.520512 + 0.853854i \(0.674259\pi\)
\(942\) 46.6123 1.51871
\(943\) 9.09107 0.296046
\(944\) 0.341469 0.0111139
\(945\) −3.36147 −0.109349
\(946\) −46.2666 −1.50426
\(947\) −8.46162 −0.274966 −0.137483 0.990504i \(-0.543901\pi\)
−0.137483 + 0.990504i \(0.543901\pi\)
\(948\) −16.6700 −0.541417
\(949\) −2.14640 −0.0696752
\(950\) 88.3338 2.86593
\(951\) 16.8073 0.545015
\(952\) 10.3681 0.336033
\(953\) −21.5475 −0.697991 −0.348995 0.937124i \(-0.613477\pi\)
−0.348995 + 0.937124i \(0.613477\pi\)
\(954\) −7.93800 −0.257002
\(955\) 4.70960 0.152399
\(956\) 67.2651 2.17551
\(957\) −39.5527 −1.27856
\(958\) −38.0672 −1.22990
\(959\) 1.33906 0.0432405
\(960\) −39.4063 −1.27183
\(961\) 67.7639 2.18593
\(962\) −35.8364 −1.15541
\(963\) −11.2995 −0.364120
\(964\) −36.6385 −1.18005
\(965\) 55.7968 1.79616
\(966\) −2.36147 −0.0759790
\(967\) 32.4883 1.04475 0.522376 0.852715i \(-0.325046\pi\)
0.522376 + 0.852715i \(0.325046\pi\)
\(968\) −90.3180 −2.90293
\(969\) −16.5369 −0.531243
\(970\) 75.4735 2.42331
\(971\) 17.1621 0.550759 0.275380 0.961336i \(-0.411196\pi\)
0.275380 + 0.961336i \(0.411196\pi\)
\(972\) 3.57653 0.114717
\(973\) 17.3615 0.556583
\(974\) −37.3128 −1.19558
\(975\) 8.96708 0.287176
\(976\) 8.68335 0.277947
\(977\) 22.3285 0.714354 0.357177 0.934037i \(-0.383739\pi\)
0.357177 + 0.934037i \(0.383739\pi\)
\(978\) −6.92226 −0.221349
\(979\) 39.0515 1.24809
\(980\) 12.0224 0.384042
\(981\) 6.08441 0.194260
\(982\) 4.67002 0.149026
\(983\) 39.2151 1.25077 0.625383 0.780318i \(-0.284943\pi\)
0.625383 + 0.780318i \(0.284943\pi\)
\(984\) 33.8455 1.07896
\(985\) −9.64520 −0.307322
\(986\) 43.8059 1.39506
\(987\) −9.15307 −0.291345
\(988\) −30.2308 −0.961770
\(989\) −3.29947 −0.104917
\(990\) −47.1359 −1.49808
\(991\) −36.4974 −1.15938 −0.579688 0.814838i \(-0.696826\pi\)
−0.579688 + 0.814838i \(0.696826\pi\)
\(992\) −35.5436 −1.12851
\(993\) −21.5699 −0.684499
\(994\) 7.10015 0.225203
\(995\) 62.3867 1.97779
\(996\) 17.1135 0.542261
\(997\) 29.0644 0.920479 0.460239 0.887795i \(-0.347764\pi\)
0.460239 + 0.887795i \(0.347764\pi\)
\(998\) −48.4130 −1.53249
\(999\) 10.6609 0.337297
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 483.2.a.h.1.1 3
3.2 odd 2 1449.2.a.l.1.3 3
4.3 odd 2 7728.2.a.bt.1.3 3
7.6 odd 2 3381.2.a.v.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
483.2.a.h.1.1 3 1.1 even 1 trivial
1449.2.a.l.1.3 3 3.2 odd 2
3381.2.a.v.1.1 3 7.6 odd 2
7728.2.a.bt.1.3 3 4.3 odd 2