Properties

Label 5445.2.a.bd.1.3
Level $5445$
Weight $2$
Character 5445.1
Self dual yes
Analytic conductor $43.479$
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] = [5445,2,Mod(1,5445)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5445, 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("5445.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5445.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: \(43.4785439006\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.404.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 5x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 605)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.86620\) of defining polynomial
Character \(\chi\) \(=\) 5445.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.34889 q^{2} +3.51730 q^{4} +1.00000 q^{5} +3.38350 q^{7} +3.56399 q^{8} +O(q^{10})\) \(q+2.34889 q^{2} +3.51730 q^{4} +1.00000 q^{5} +3.38350 q^{7} +3.56399 q^{8} +2.34889 q^{10} -1.48270 q^{13} +7.94749 q^{14} +1.33682 q^{16} -3.73240 q^{17} +3.21509 q^{19} +3.51730 q^{20} +2.51730 q^{23} +1.00000 q^{25} -3.48270 q^{26} +11.9008 q^{28} +4.69779 q^{29} +9.21509 q^{31} -3.98793 q^{32} -8.76700 q^{34} +3.38350 q^{35} -2.69779 q^{37} +7.55191 q^{38} +3.56399 q^{40} +4.55191 q^{41} -5.38350 q^{43} +5.91288 q^{46} +10.5294 q^{47} +4.44809 q^{49} +2.34889 q^{50} -5.21509 q^{52} +2.51730 q^{53} +12.0588 q^{56} +11.0346 q^{58} -11.9129 q^{59} +13.6799 q^{61} +21.6453 q^{62} -12.0409 q^{64} -1.48270 q^{65} +7.83159 q^{67} -13.1280 q^{68} +7.94749 q^{70} -2.51730 q^{71} +2.96539 q^{73} -6.33682 q^{74} +11.3085 q^{76} -6.76700 q^{79} +1.33682 q^{80} +10.6920 q^{82} +7.55191 q^{83} -3.73240 q^{85} -12.6453 q^{86} -10.8016 q^{89} -5.01671 q^{91} +8.85412 q^{92} +24.7324 q^{94} +3.21509 q^{95} +11.0167 q^{97} +10.4481 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} + 9 q^{4} + 3 q^{5} + q^{7} - 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} + 9 q^{4} + 3 q^{5} + q^{7} - 9 q^{8} + q^{10} - 6 q^{13} - 5 q^{14} + 13 q^{16} + 4 q^{17} - 4 q^{19} + 9 q^{20} + 6 q^{23} + 3 q^{25} - 12 q^{26} + 25 q^{28} + 2 q^{29} + 14 q^{31} - 27 q^{32} - 8 q^{34} + q^{35} + 4 q^{37} + 18 q^{38} - 9 q^{40} + 9 q^{41} - 7 q^{43} - 8 q^{46} + 15 q^{47} + 18 q^{49} + q^{50} - 2 q^{52} + 6 q^{53} + 3 q^{56} + 30 q^{58} - 10 q^{59} - 3 q^{61} + 24 q^{62} + 29 q^{64} - 6 q^{65} + 19 q^{67} - 5 q^{70} - 6 q^{71} + 12 q^{73} - 28 q^{74} - 16 q^{76} - 2 q^{79} + 13 q^{80} - 27 q^{82} + 18 q^{83} + 4 q^{85} + 3 q^{86} - 11 q^{89} + 20 q^{91} + 34 q^{92} + 59 q^{94} - 4 q^{95} - 2 q^{97} + 36 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.34889 1.66092 0.830460 0.557079i \(-0.188078\pi\)
0.830460 + 0.557079i \(0.188078\pi\)
\(3\) 0 0
\(4\) 3.51730 1.75865
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 3.38350 1.27884 0.639422 0.768856i \(-0.279174\pi\)
0.639422 + 0.768856i \(0.279174\pi\)
\(8\) 3.56399 1.26006
\(9\) 0 0
\(10\) 2.34889 0.742786
\(11\) 0 0
\(12\) 0 0
\(13\) −1.48270 −0.411226 −0.205613 0.978633i \(-0.565919\pi\)
−0.205613 + 0.978633i \(0.565919\pi\)
\(14\) 7.94749 2.12406
\(15\) 0 0
\(16\) 1.33682 0.334205
\(17\) −3.73240 −0.905239 −0.452620 0.891704i \(-0.649510\pi\)
−0.452620 + 0.891704i \(0.649510\pi\)
\(18\) 0 0
\(19\) 3.21509 0.737593 0.368796 0.929510i \(-0.379770\pi\)
0.368796 + 0.929510i \(0.379770\pi\)
\(20\) 3.51730 0.786493
\(21\) 0 0
\(22\) 0 0
\(23\) 2.51730 0.524894 0.262447 0.964946i \(-0.415470\pi\)
0.262447 + 0.964946i \(0.415470\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −3.48270 −0.683013
\(27\) 0 0
\(28\) 11.9008 2.24904
\(29\) 4.69779 0.872357 0.436179 0.899860i \(-0.356332\pi\)
0.436179 + 0.899860i \(0.356332\pi\)
\(30\) 0 0
\(31\) 9.21509 1.65508 0.827540 0.561407i \(-0.189740\pi\)
0.827540 + 0.561407i \(0.189740\pi\)
\(32\) −3.98793 −0.704972
\(33\) 0 0
\(34\) −8.76700 −1.50353
\(35\) 3.38350 0.571916
\(36\) 0 0
\(37\) −2.69779 −0.443514 −0.221757 0.975102i \(-0.571179\pi\)
−0.221757 + 0.975102i \(0.571179\pi\)
\(38\) 7.55191 1.22508
\(39\) 0 0
\(40\) 3.56399 0.563516
\(41\) 4.55191 0.710889 0.355445 0.934697i \(-0.384329\pi\)
0.355445 + 0.934697i \(0.384329\pi\)
\(42\) 0 0
\(43\) −5.38350 −0.820976 −0.410488 0.911866i \(-0.634642\pi\)
−0.410488 + 0.911866i \(0.634642\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 5.91288 0.871807
\(47\) 10.5294 1.53587 0.767934 0.640529i \(-0.221285\pi\)
0.767934 + 0.640529i \(0.221285\pi\)
\(48\) 0 0
\(49\) 4.44809 0.635441
\(50\) 2.34889 0.332184
\(51\) 0 0
\(52\) −5.21509 −0.723203
\(53\) 2.51730 0.345778 0.172889 0.984941i \(-0.444690\pi\)
0.172889 + 0.984941i \(0.444690\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 12.0588 1.61142
\(57\) 0 0
\(58\) 11.0346 1.44892
\(59\) −11.9129 −1.55092 −0.775462 0.631394i \(-0.782483\pi\)
−0.775462 + 0.631394i \(0.782483\pi\)
\(60\) 0 0
\(61\) 13.6799 1.75153 0.875765 0.482738i \(-0.160358\pi\)
0.875765 + 0.482738i \(0.160358\pi\)
\(62\) 21.6453 2.74895
\(63\) 0 0
\(64\) −12.0409 −1.50511
\(65\) −1.48270 −0.183906
\(66\) 0 0
\(67\) 7.83159 0.956781 0.478391 0.878147i \(-0.341220\pi\)
0.478391 + 0.878147i \(0.341220\pi\)
\(68\) −13.1280 −1.59200
\(69\) 0 0
\(70\) 7.94749 0.949907
\(71\) −2.51730 −0.298749 −0.149375 0.988781i \(-0.547726\pi\)
−0.149375 + 0.988781i \(0.547726\pi\)
\(72\) 0 0
\(73\) 2.96539 0.347073 0.173536 0.984827i \(-0.444481\pi\)
0.173536 + 0.984827i \(0.444481\pi\)
\(74\) −6.33682 −0.736640
\(75\) 0 0
\(76\) 11.3085 1.29717
\(77\) 0 0
\(78\) 0 0
\(79\) −6.76700 −0.761348 −0.380674 0.924709i \(-0.624308\pi\)
−0.380674 + 0.924709i \(0.624308\pi\)
\(80\) 1.33682 0.149461
\(81\) 0 0
\(82\) 10.6920 1.18073
\(83\) 7.55191 0.828930 0.414465 0.910065i \(-0.363969\pi\)
0.414465 + 0.910065i \(0.363969\pi\)
\(84\) 0 0
\(85\) −3.73240 −0.404835
\(86\) −12.6453 −1.36358
\(87\) 0 0
\(88\) 0 0
\(89\) −10.8016 −1.14497 −0.572484 0.819916i \(-0.694020\pi\)
−0.572484 + 0.819916i \(0.694020\pi\)
\(90\) 0 0
\(91\) −5.01671 −0.525894
\(92\) 8.85412 0.923106
\(93\) 0 0
\(94\) 24.7324 2.55095
\(95\) 3.21509 0.329862
\(96\) 0 0
\(97\) 11.0167 1.11858 0.559288 0.828973i \(-0.311074\pi\)
0.559288 + 0.828973i \(0.311074\pi\)
\(98\) 10.4481 1.05542
\(99\) 0 0
\(100\) 3.51730 0.351730
\(101\) −12.7324 −1.26692 −0.633460 0.773775i \(-0.718366\pi\)
−0.633460 + 0.773775i \(0.718366\pi\)
\(102\) 0 0
\(103\) −18.3431 −1.80740 −0.903698 0.428170i \(-0.859158\pi\)
−0.903698 + 0.428170i \(0.859158\pi\)
\(104\) −5.28431 −0.518169
\(105\) 0 0
\(106\) 5.91288 0.574310
\(107\) 7.13380 0.689651 0.344825 0.938667i \(-0.387938\pi\)
0.344825 + 0.938667i \(0.387938\pi\)
\(108\) 0 0
\(109\) −4.14588 −0.397103 −0.198551 0.980090i \(-0.563624\pi\)
−0.198551 + 0.980090i \(0.563624\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 4.52313 0.427396
\(113\) −1.46479 −0.137796 −0.0688981 0.997624i \(-0.521948\pi\)
−0.0688981 + 0.997624i \(0.521948\pi\)
\(114\) 0 0
\(115\) 2.51730 0.234740
\(116\) 16.5236 1.53417
\(117\) 0 0
\(118\) −27.9821 −2.57596
\(119\) −12.6286 −1.15766
\(120\) 0 0
\(121\) 0 0
\(122\) 32.1326 2.90915
\(123\) 0 0
\(124\) 32.4123 2.91071
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −11.2964 −1.00239 −0.501196 0.865334i \(-0.667106\pi\)
−0.501196 + 0.865334i \(0.667106\pi\)
\(128\) −20.3068 −1.79489
\(129\) 0 0
\(130\) −3.48270 −0.305453
\(131\) −14.6799 −1.28259 −0.641294 0.767295i \(-0.721602\pi\)
−0.641294 + 0.767295i \(0.721602\pi\)
\(132\) 0 0
\(133\) 10.8783 0.943266
\(134\) 18.3956 1.58914
\(135\) 0 0
\(136\) −13.3022 −1.14066
\(137\) 15.6453 1.33667 0.668333 0.743862i \(-0.267008\pi\)
0.668333 + 0.743862i \(0.267008\pi\)
\(138\) 0 0
\(139\) −7.64528 −0.648464 −0.324232 0.945978i \(-0.605106\pi\)
−0.324232 + 0.945978i \(0.605106\pi\)
\(140\) 11.9008 1.00580
\(141\) 0 0
\(142\) −5.91288 −0.496198
\(143\) 0 0
\(144\) 0 0
\(145\) 4.69779 0.390130
\(146\) 6.96539 0.576460
\(147\) 0 0
\(148\) −9.48894 −0.779986
\(149\) 6.48270 0.531083 0.265542 0.964099i \(-0.414449\pi\)
0.265542 + 0.964099i \(0.414449\pi\)
\(150\) 0 0
\(151\) −10.8783 −0.885261 −0.442631 0.896704i \(-0.645955\pi\)
−0.442631 + 0.896704i \(0.645955\pi\)
\(152\) 11.4585 0.929411
\(153\) 0 0
\(154\) 0 0
\(155\) 9.21509 0.740174
\(156\) 0 0
\(157\) 10.4302 0.832419 0.416210 0.909269i \(-0.363358\pi\)
0.416210 + 0.909269i \(0.363358\pi\)
\(158\) −15.8950 −1.26454
\(159\) 0 0
\(160\) −3.98793 −0.315273
\(161\) 8.51730 0.671258
\(162\) 0 0
\(163\) −10.2439 −0.802362 −0.401181 0.915999i \(-0.631400\pi\)
−0.401181 + 0.915999i \(0.631400\pi\)
\(164\) 16.0105 1.25021
\(165\) 0 0
\(166\) 17.7386 1.37679
\(167\) −1.04668 −0.0809947 −0.0404974 0.999180i \(-0.512894\pi\)
−0.0404974 + 0.999180i \(0.512894\pi\)
\(168\) 0 0
\(169\) −10.8016 −0.830893
\(170\) −8.76700 −0.672399
\(171\) 0 0
\(172\) −18.9354 −1.44381
\(173\) 11.9129 0.905720 0.452860 0.891582i \(-0.350404\pi\)
0.452860 + 0.891582i \(0.350404\pi\)
\(174\) 0 0
\(175\) 3.38350 0.255769
\(176\) 0 0
\(177\) 0 0
\(178\) −25.3718 −1.90170
\(179\) 3.39558 0.253797 0.126899 0.991916i \(-0.459498\pi\)
0.126899 + 0.991916i \(0.459498\pi\)
\(180\) 0 0
\(181\) −5.69779 −0.423513 −0.211757 0.977322i \(-0.567918\pi\)
−0.211757 + 0.977322i \(0.567918\pi\)
\(182\) −11.7837 −0.873467
\(183\) 0 0
\(184\) 8.97164 0.661398
\(185\) −2.69779 −0.198345
\(186\) 0 0
\(187\) 0 0
\(188\) 37.0350 2.70106
\(189\) 0 0
\(190\) 7.55191 0.547873
\(191\) 9.01671 0.652426 0.326213 0.945296i \(-0.394227\pi\)
0.326213 + 0.945296i \(0.394227\pi\)
\(192\) 0 0
\(193\) −26.2318 −1.88821 −0.944103 0.329650i \(-0.893069\pi\)
−0.944103 + 0.329650i \(0.893069\pi\)
\(194\) 25.8771 1.85787
\(195\) 0 0
\(196\) 15.6453 1.11752
\(197\) −16.6978 −1.18967 −0.594834 0.803849i \(-0.702782\pi\)
−0.594834 + 0.803849i \(0.702782\pi\)
\(198\) 0 0
\(199\) −16.7912 −1.19029 −0.595147 0.803617i \(-0.702906\pi\)
−0.595147 + 0.803617i \(0.702906\pi\)
\(200\) 3.56399 0.252012
\(201\) 0 0
\(202\) −29.9071 −2.10425
\(203\) 15.8950 1.11561
\(204\) 0 0
\(205\) 4.55191 0.317919
\(206\) −43.0859 −3.00194
\(207\) 0 0
\(208\) −1.98210 −0.137434
\(209\) 0 0
\(210\) 0 0
\(211\) −7.64528 −0.526323 −0.263161 0.964752i \(-0.584765\pi\)
−0.263161 + 0.964752i \(0.584765\pi\)
\(212\) 8.85412 0.608104
\(213\) 0 0
\(214\) 16.7565 1.14545
\(215\) −5.38350 −0.367152
\(216\) 0 0
\(217\) 31.1793 2.11659
\(218\) −9.73822 −0.659556
\(219\) 0 0
\(220\) 0 0
\(221\) 5.53401 0.372258
\(222\) 0 0
\(223\) −3.78954 −0.253766 −0.126883 0.991918i \(-0.540497\pi\)
−0.126883 + 0.991918i \(0.540497\pi\)
\(224\) −13.4932 −0.901549
\(225\) 0 0
\(226\) −3.44064 −0.228868
\(227\) −19.5461 −1.29732 −0.648660 0.761079i \(-0.724670\pi\)
−0.648660 + 0.761079i \(0.724670\pi\)
\(228\) 0 0
\(229\) 5.16258 0.341153 0.170576 0.985344i \(-0.445437\pi\)
0.170576 + 0.985344i \(0.445437\pi\)
\(230\) 5.91288 0.389884
\(231\) 0 0
\(232\) 16.7429 1.09922
\(233\) 6.24970 0.409431 0.204716 0.978821i \(-0.434373\pi\)
0.204716 + 0.978821i \(0.434373\pi\)
\(234\) 0 0
\(235\) 10.5294 0.686861
\(236\) −41.9012 −2.72754
\(237\) 0 0
\(238\) −29.6632 −1.92278
\(239\) 4.61067 0.298239 0.149120 0.988819i \(-0.452356\pi\)
0.149120 + 0.988819i \(0.452356\pi\)
\(240\) 0 0
\(241\) −7.87827 −0.507484 −0.253742 0.967272i \(-0.581661\pi\)
−0.253742 + 0.967272i \(0.581661\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 48.1163 3.08033
\(245\) 4.44809 0.284178
\(246\) 0 0
\(247\) −4.76700 −0.303317
\(248\) 32.8425 2.08550
\(249\) 0 0
\(250\) 2.34889 0.148557
\(251\) −10.6557 −0.672584 −0.336292 0.941758i \(-0.609173\pi\)
−0.336292 + 0.941758i \(0.609173\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −26.5340 −1.66489
\(255\) 0 0
\(256\) −23.6169 −1.47606
\(257\) −2.80906 −0.175224 −0.0876121 0.996155i \(-0.527924\pi\)
−0.0876121 + 0.996155i \(0.527924\pi\)
\(258\) 0 0
\(259\) −9.12797 −0.567185
\(260\) −5.21509 −0.323426
\(261\) 0 0
\(262\) −34.4815 −2.13027
\(263\) 27.6453 1.70468 0.852340 0.522987i \(-0.175183\pi\)
0.852340 + 0.522987i \(0.175183\pi\)
\(264\) 0 0
\(265\) 2.51730 0.154637
\(266\) 25.5519 1.56669
\(267\) 0 0
\(268\) 27.5461 1.68264
\(269\) 14.5761 0.888718 0.444359 0.895849i \(-0.353431\pi\)
0.444359 + 0.895849i \(0.353431\pi\)
\(270\) 0 0
\(271\) 2.16258 0.131367 0.0656837 0.997840i \(-0.479077\pi\)
0.0656837 + 0.997840i \(0.479077\pi\)
\(272\) −4.98954 −0.302535
\(273\) 0 0
\(274\) 36.7491 2.22009
\(275\) 0 0
\(276\) 0 0
\(277\) 15.3022 0.919421 0.459710 0.888069i \(-0.347953\pi\)
0.459710 + 0.888069i \(0.347953\pi\)
\(278\) −17.9579 −1.07705
\(279\) 0 0
\(280\) 12.0588 0.720649
\(281\) 2.13843 0.127568 0.0637841 0.997964i \(-0.479683\pi\)
0.0637841 + 0.997964i \(0.479683\pi\)
\(282\) 0 0
\(283\) −4.33099 −0.257451 −0.128725 0.991680i \(-0.541089\pi\)
−0.128725 + 0.991680i \(0.541089\pi\)
\(284\) −8.85412 −0.525396
\(285\) 0 0
\(286\) 0 0
\(287\) 15.4014 0.909116
\(288\) 0 0
\(289\) −3.06922 −0.180542
\(290\) 11.0346 0.647974
\(291\) 0 0
\(292\) 10.4302 0.610380
\(293\) −13.5068 −0.789078 −0.394539 0.918879i \(-0.629096\pi\)
−0.394539 + 0.918879i \(0.629096\pi\)
\(294\) 0 0
\(295\) −11.9129 −0.693595
\(296\) −9.61488 −0.558854
\(297\) 0 0
\(298\) 15.2272 0.882086
\(299\) −3.73240 −0.215850
\(300\) 0 0
\(301\) −18.2151 −1.04990
\(302\) −25.5519 −1.47035
\(303\) 0 0
\(304\) 4.29800 0.246507
\(305\) 13.6799 0.783308
\(306\) 0 0
\(307\) 2.37887 0.135769 0.0678847 0.997693i \(-0.478375\pi\)
0.0678847 + 0.997693i \(0.478375\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 21.6453 1.22937
\(311\) 22.1447 1.25571 0.627855 0.778331i \(-0.283933\pi\)
0.627855 + 0.778331i \(0.283933\pi\)
\(312\) 0 0
\(313\) −27.2843 −1.54220 −0.771100 0.636714i \(-0.780293\pi\)
−0.771100 + 0.636714i \(0.780293\pi\)
\(314\) 24.4994 1.38258
\(315\) 0 0
\(316\) −23.8016 −1.33895
\(317\) 15.3956 0.864702 0.432351 0.901705i \(-0.357684\pi\)
0.432351 + 0.901705i \(0.357684\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −12.0409 −0.673104
\(321\) 0 0
\(322\) 20.0062 1.11490
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) −1.48270 −0.0822452
\(326\) −24.0618 −1.33266
\(327\) 0 0
\(328\) 16.2230 0.895763
\(329\) 35.6262 1.96413
\(330\) 0 0
\(331\) 25.9129 1.42430 0.712150 0.702027i \(-0.247721\pi\)
0.712150 + 0.702027i \(0.247721\pi\)
\(332\) 26.5624 1.45780
\(333\) 0 0
\(334\) −2.45855 −0.134526
\(335\) 7.83159 0.427885
\(336\) 0 0
\(337\) −13.9821 −0.761653 −0.380827 0.924646i \(-0.624361\pi\)
−0.380827 + 0.924646i \(0.624361\pi\)
\(338\) −25.3718 −1.38005
\(339\) 0 0
\(340\) −13.1280 −0.711964
\(341\) 0 0
\(342\) 0 0
\(343\) −8.63440 −0.466214
\(344\) −19.1867 −1.03448
\(345\) 0 0
\(346\) 27.9821 1.50433
\(347\) −31.0467 −1.66667 −0.833337 0.552766i \(-0.813572\pi\)
−0.833337 + 0.552766i \(0.813572\pi\)
\(348\) 0 0
\(349\) −3.66318 −0.196086 −0.0980428 0.995182i \(-0.531258\pi\)
−0.0980428 + 0.995182i \(0.531258\pi\)
\(350\) 7.94749 0.424811
\(351\) 0 0
\(352\) 0 0
\(353\) −24.5749 −1.30799 −0.653994 0.756500i \(-0.726908\pi\)
−0.653994 + 0.756500i \(0.726908\pi\)
\(354\) 0 0
\(355\) −2.51730 −0.133605
\(356\) −37.9926 −2.01360
\(357\) 0 0
\(358\) 7.97585 0.421537
\(359\) −6.58652 −0.347623 −0.173812 0.984779i \(-0.555608\pi\)
−0.173812 + 0.984779i \(0.555608\pi\)
\(360\) 0 0
\(361\) −8.66318 −0.455957
\(362\) −13.3835 −0.703421
\(363\) 0 0
\(364\) −17.6453 −0.924864
\(365\) 2.96539 0.155216
\(366\) 0 0
\(367\) 8.16841 0.426388 0.213194 0.977010i \(-0.431613\pi\)
0.213194 + 0.977010i \(0.431613\pi\)
\(368\) 3.36518 0.175422
\(369\) 0 0
\(370\) −6.33682 −0.329436
\(371\) 8.51730 0.442196
\(372\) 0 0
\(373\) 27.0409 1.40012 0.700061 0.714083i \(-0.253156\pi\)
0.700061 + 0.714083i \(0.253156\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 37.5266 1.93528
\(377\) −6.96539 −0.358736
\(378\) 0 0
\(379\) 32.6620 1.67773 0.838867 0.544337i \(-0.183219\pi\)
0.838867 + 0.544337i \(0.183219\pi\)
\(380\) 11.3085 0.580112
\(381\) 0 0
\(382\) 21.1793 1.08363
\(383\) 2.64648 0.135229 0.0676143 0.997712i \(-0.478461\pi\)
0.0676143 + 0.997712i \(0.478461\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −61.6157 −3.13616
\(387\) 0 0
\(388\) 38.7491 1.96719
\(389\) 29.0513 1.47296 0.736480 0.676459i \(-0.236487\pi\)
0.736480 + 0.676459i \(0.236487\pi\)
\(390\) 0 0
\(391\) −9.39558 −0.475155
\(392\) 15.8529 0.800694
\(393\) 0 0
\(394\) −39.2213 −1.97594
\(395\) −6.76700 −0.340485
\(396\) 0 0
\(397\) −9.35977 −0.469753 −0.234877 0.972025i \(-0.575469\pi\)
−0.234877 + 0.972025i \(0.575469\pi\)
\(398\) −39.4406 −1.97698
\(399\) 0 0
\(400\) 1.33682 0.0668410
\(401\) −4.93078 −0.246232 −0.123116 0.992392i \(-0.539289\pi\)
−0.123116 + 0.992392i \(0.539289\pi\)
\(402\) 0 0
\(403\) −13.6632 −0.680611
\(404\) −44.7837 −2.22807
\(405\) 0 0
\(406\) 37.3356 1.85294
\(407\) 0 0
\(408\) 0 0
\(409\) 38.3085 1.89423 0.947116 0.320892i \(-0.103983\pi\)
0.947116 + 0.320892i \(0.103983\pi\)
\(410\) 10.6920 0.528038
\(411\) 0 0
\(412\) −64.5181 −3.17858
\(413\) −40.3073 −1.98339
\(414\) 0 0
\(415\) 7.55191 0.370709
\(416\) 5.91288 0.289903
\(417\) 0 0
\(418\) 0 0
\(419\) −37.3777 −1.82602 −0.913009 0.407938i \(-0.866248\pi\)
−0.913009 + 0.407938i \(0.866248\pi\)
\(420\) 0 0
\(421\) 29.4123 1.43347 0.716733 0.697347i \(-0.245636\pi\)
0.716733 + 0.697347i \(0.245636\pi\)
\(422\) −17.9579 −0.874179
\(423\) 0 0
\(424\) 8.97164 0.435701
\(425\) −3.73240 −0.181048
\(426\) 0 0
\(427\) 46.2859 2.23993
\(428\) 25.0917 1.21286
\(429\) 0 0
\(430\) −12.6453 −0.609809
\(431\) 1.76820 0.0851713 0.0425857 0.999093i \(-0.486440\pi\)
0.0425857 + 0.999093i \(0.486440\pi\)
\(432\) 0 0
\(433\) 10.0513 0.483035 0.241518 0.970396i \(-0.422355\pi\)
0.241518 + 0.970396i \(0.422355\pi\)
\(434\) 73.2368 3.51548
\(435\) 0 0
\(436\) −14.5823 −0.698366
\(437\) 8.09337 0.387158
\(438\) 0 0
\(439\) −39.1972 −1.87078 −0.935390 0.353618i \(-0.884951\pi\)
−0.935390 + 0.353618i \(0.884951\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.9988 0.618290
\(443\) 14.0121 0.665734 0.332867 0.942974i \(-0.391984\pi\)
0.332867 + 0.942974i \(0.391984\pi\)
\(444\) 0 0
\(445\) −10.8016 −0.512046
\(446\) −8.90122 −0.421485
\(447\) 0 0
\(448\) −40.7403 −1.92480
\(449\) −2.57606 −0.121572 −0.0607859 0.998151i \(-0.519361\pi\)
−0.0607859 + 0.998151i \(0.519361\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −5.15212 −0.242335
\(453\) 0 0
\(454\) −45.9117 −2.15474
\(455\) −5.01671 −0.235187
\(456\) 0 0
\(457\) −15.1217 −0.707365 −0.353682 0.935366i \(-0.615071\pi\)
−0.353682 + 0.935366i \(0.615071\pi\)
\(458\) 12.1264 0.566627
\(459\) 0 0
\(460\) 8.85412 0.412826
\(461\) 9.83622 0.458118 0.229059 0.973412i \(-0.426435\pi\)
0.229059 + 0.973412i \(0.426435\pi\)
\(462\) 0 0
\(463\) 21.2093 0.985678 0.492839 0.870120i \(-0.335959\pi\)
0.492839 + 0.870120i \(0.335959\pi\)
\(464\) 6.28010 0.291546
\(465\) 0 0
\(466\) 14.6799 0.680033
\(467\) 9.56399 0.442569 0.221284 0.975209i \(-0.428975\pi\)
0.221284 + 0.975209i \(0.428975\pi\)
\(468\) 0 0
\(469\) 26.4982 1.22357
\(470\) 24.7324 1.14082
\(471\) 0 0
\(472\) −42.4573 −1.95426
\(473\) 0 0
\(474\) 0 0
\(475\) 3.21509 0.147519
\(476\) −44.4185 −2.03592
\(477\) 0 0
\(478\) 10.8300 0.495352
\(479\) −17.1972 −0.785760 −0.392880 0.919590i \(-0.628521\pi\)
−0.392880 + 0.919590i \(0.628521\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) −18.5052 −0.842890
\(483\) 0 0
\(484\) 0 0
\(485\) 11.0167 0.500243
\(486\) 0 0
\(487\) 15.5519 0.704724 0.352362 0.935864i \(-0.385379\pi\)
0.352362 + 0.935864i \(0.385379\pi\)
\(488\) 48.7549 2.20703
\(489\) 0 0
\(490\) 10.4481 0.471996
\(491\) −9.05876 −0.408816 −0.204408 0.978886i \(-0.565527\pi\)
−0.204408 + 0.978886i \(0.565527\pi\)
\(492\) 0 0
\(493\) −17.5340 −0.789692
\(494\) −11.1972 −0.503785
\(495\) 0 0
\(496\) 12.3189 0.553136
\(497\) −8.51730 −0.382053
\(498\) 0 0
\(499\) 24.5686 1.09984 0.549921 0.835217i \(-0.314658\pi\)
0.549921 + 0.835217i \(0.314658\pi\)
\(500\) 3.51730 0.157299
\(501\) 0 0
\(502\) −25.0292 −1.11711
\(503\) −11.3322 −0.505277 −0.252639 0.967561i \(-0.581298\pi\)
−0.252639 + 0.967561i \(0.581298\pi\)
\(504\) 0 0
\(505\) −12.7324 −0.566584
\(506\) 0 0
\(507\) 0 0
\(508\) −39.7328 −1.76286
\(509\) 26.4889 1.17410 0.587051 0.809550i \(-0.300289\pi\)
0.587051 + 0.809550i \(0.300289\pi\)
\(510\) 0 0
\(511\) 10.0334 0.443852
\(512\) −14.8600 −0.656723
\(513\) 0 0
\(514\) −6.59818 −0.291033
\(515\) −18.3431 −0.808292
\(516\) 0 0
\(517\) 0 0
\(518\) −21.4406 −0.942048
\(519\) 0 0
\(520\) −5.28431 −0.231732
\(521\) −26.6966 −1.16960 −0.584799 0.811178i \(-0.698827\pi\)
−0.584799 + 0.811178i \(0.698827\pi\)
\(522\) 0 0
\(523\) 4.85412 0.212256 0.106128 0.994352i \(-0.466155\pi\)
0.106128 + 0.994352i \(0.466155\pi\)
\(524\) −51.6336 −2.25563
\(525\) 0 0
\(526\) 64.9358 2.83134
\(527\) −34.3944 −1.49824
\(528\) 0 0
\(529\) −16.6632 −0.724486
\(530\) 5.91288 0.256839
\(531\) 0 0
\(532\) 38.2622 1.65888
\(533\) −6.74910 −0.292336
\(534\) 0 0
\(535\) 7.13380 0.308421
\(536\) 27.9117 1.20560
\(537\) 0 0
\(538\) 34.2376 1.47609
\(539\) 0 0
\(540\) 0 0
\(541\) −19.8246 −0.852325 −0.426162 0.904647i \(-0.640135\pi\)
−0.426162 + 0.904647i \(0.640135\pi\)
\(542\) 5.07968 0.218191
\(543\) 0 0
\(544\) 14.8845 0.638168
\(545\) −4.14588 −0.177590
\(546\) 0 0
\(547\) −14.6557 −0.626634 −0.313317 0.949649i \(-0.601440\pi\)
−0.313317 + 0.949649i \(0.601440\pi\)
\(548\) 55.0292 2.35073
\(549\) 0 0
\(550\) 0 0
\(551\) 15.1038 0.643445
\(552\) 0 0
\(553\) −22.8962 −0.973644
\(554\) 35.9433 1.52708
\(555\) 0 0
\(556\) −26.8908 −1.14042
\(557\) 5.83742 0.247339 0.123670 0.992323i \(-0.460534\pi\)
0.123670 + 0.992323i \(0.460534\pi\)
\(558\) 0 0
\(559\) 7.98210 0.337607
\(560\) 4.52313 0.191137
\(561\) 0 0
\(562\) 5.02295 0.211880
\(563\) −39.3026 −1.65641 −0.828204 0.560426i \(-0.810637\pi\)
−0.828204 + 0.560426i \(0.810637\pi\)
\(564\) 0 0
\(565\) −1.46479 −0.0616243
\(566\) −10.1730 −0.427605
\(567\) 0 0
\(568\) −8.97164 −0.376442
\(569\) −8.11007 −0.339992 −0.169996 0.985445i \(-0.554375\pi\)
−0.169996 + 0.985445i \(0.554375\pi\)
\(570\) 0 0
\(571\) −35.6274 −1.49096 −0.745480 0.666528i \(-0.767780\pi\)
−0.745480 + 0.666528i \(0.767780\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 36.1763 1.50997
\(575\) 2.51730 0.104979
\(576\) 0 0
\(577\) −31.8529 −1.32605 −0.663027 0.748595i \(-0.730729\pi\)
−0.663027 + 0.748595i \(0.730729\pi\)
\(578\) −7.20926 −0.299866
\(579\) 0 0
\(580\) 16.5236 0.686103
\(581\) 25.5519 1.06007
\(582\) 0 0
\(583\) 0 0
\(584\) 10.5686 0.437332
\(585\) 0 0
\(586\) −31.7262 −1.31060
\(587\) 44.3823 1.83185 0.915927 0.401345i \(-0.131457\pi\)
0.915927 + 0.401345i \(0.131457\pi\)
\(588\) 0 0
\(589\) 29.6274 1.22077
\(590\) −27.9821 −1.15200
\(591\) 0 0
\(592\) −3.60646 −0.148224
\(593\) −41.9463 −1.72253 −0.861264 0.508158i \(-0.830327\pi\)
−0.861264 + 0.508158i \(0.830327\pi\)
\(594\) 0 0
\(595\) −12.6286 −0.517721
\(596\) 22.8016 0.933990
\(597\) 0 0
\(598\) −8.76700 −0.358509
\(599\) −16.6107 −0.678694 −0.339347 0.940661i \(-0.610206\pi\)
−0.339347 + 0.940661i \(0.610206\pi\)
\(600\) 0 0
\(601\) 13.1972 0.538325 0.269162 0.963095i \(-0.413253\pi\)
0.269162 + 0.963095i \(0.413253\pi\)
\(602\) −42.7853 −1.74380
\(603\) 0 0
\(604\) −38.2622 −1.55687
\(605\) 0 0
\(606\) 0 0
\(607\) 9.04085 0.366957 0.183478 0.983024i \(-0.441264\pi\)
0.183478 + 0.983024i \(0.441264\pi\)
\(608\) −12.8215 −0.519982
\(609\) 0 0
\(610\) 32.1326 1.30101
\(611\) −15.6119 −0.631589
\(612\) 0 0
\(613\) 7.66318 0.309513 0.154756 0.987953i \(-0.450541\pi\)
0.154756 + 0.987953i \(0.450541\pi\)
\(614\) 5.58772 0.225502
\(615\) 0 0
\(616\) 0 0
\(617\) 2.67989 0.107888 0.0539441 0.998544i \(-0.482821\pi\)
0.0539441 + 0.998544i \(0.482821\pi\)
\(618\) 0 0
\(619\) 8.17424 0.328550 0.164275 0.986415i \(-0.447471\pi\)
0.164275 + 0.986415i \(0.447471\pi\)
\(620\) 32.4123 1.30171
\(621\) 0 0
\(622\) 52.0155 2.08563
\(623\) −36.5473 −1.46424
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −64.0880 −2.56147
\(627\) 0 0
\(628\) 36.6861 1.46394
\(629\) 10.0692 0.401486
\(630\) 0 0
\(631\) 5.56982 0.221731 0.110865 0.993835i \(-0.464638\pi\)
0.110865 + 0.993835i \(0.464638\pi\)
\(632\) −24.1175 −0.959343
\(633\) 0 0
\(634\) 36.1626 1.43620
\(635\) −11.2964 −0.448283
\(636\) 0 0
\(637\) −6.59516 −0.261310
\(638\) 0 0
\(639\) 0 0
\(640\) −20.3068 −0.802698
\(641\) 13.2906 0.524945 0.262473 0.964939i \(-0.415462\pi\)
0.262473 + 0.964939i \(0.415462\pi\)
\(642\) 0 0
\(643\) 17.8137 0.702503 0.351252 0.936281i \(-0.385756\pi\)
0.351252 + 0.936281i \(0.385756\pi\)
\(644\) 29.9579 1.18051
\(645\) 0 0
\(646\) −28.1867 −1.10899
\(647\) 25.8829 1.01756 0.508781 0.860896i \(-0.330096\pi\)
0.508781 + 0.860896i \(0.330096\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −3.48270 −0.136603
\(651\) 0 0
\(652\) −36.0308 −1.41108
\(653\) −13.3356 −0.521863 −0.260932 0.965357i \(-0.584030\pi\)
−0.260932 + 0.965357i \(0.584030\pi\)
\(654\) 0 0
\(655\) −14.6799 −0.573591
\(656\) 6.08509 0.237583
\(657\) 0 0
\(658\) 83.6821 3.26227
\(659\) −24.4877 −0.953907 −0.476954 0.878929i \(-0.658259\pi\)
−0.476954 + 0.878929i \(0.658259\pi\)
\(660\) 0 0
\(661\) −23.2738 −0.905248 −0.452624 0.891702i \(-0.649512\pi\)
−0.452624 + 0.891702i \(0.649512\pi\)
\(662\) 60.8666 2.36565
\(663\) 0 0
\(664\) 26.9149 1.04450
\(665\) 10.8783 0.421841
\(666\) 0 0
\(667\) 11.8258 0.457895
\(668\) −3.68150 −0.142442
\(669\) 0 0
\(670\) 18.3956 0.710683
\(671\) 0 0
\(672\) 0 0
\(673\) −11.3443 −0.437289 −0.218645 0.975805i \(-0.570164\pi\)
−0.218645 + 0.975805i \(0.570164\pi\)
\(674\) −32.8425 −1.26504
\(675\) 0 0
\(676\) −37.9926 −1.46125
\(677\) −21.3956 −0.822299 −0.411149 0.911568i \(-0.634873\pi\)
−0.411149 + 0.911568i \(0.634873\pi\)
\(678\) 0 0
\(679\) 37.2750 1.43049
\(680\) −13.3022 −0.510117
\(681\) 0 0
\(682\) 0 0
\(683\) 5.11590 0.195754 0.0978772 0.995198i \(-0.468795\pi\)
0.0978772 + 0.995198i \(0.468795\pi\)
\(684\) 0 0
\(685\) 15.6453 0.597775
\(686\) −20.2813 −0.774343
\(687\) 0 0
\(688\) −7.19677 −0.274374
\(689\) −3.73240 −0.142193
\(690\) 0 0
\(691\) −22.9117 −0.871602 −0.435801 0.900043i \(-0.643535\pi\)
−0.435801 + 0.900043i \(0.643535\pi\)
\(692\) 41.9012 1.59285
\(693\) 0 0
\(694\) −72.9254 −2.76821
\(695\) −7.64528 −0.290002
\(696\) 0 0
\(697\) −16.9895 −0.643525
\(698\) −8.60442 −0.325682
\(699\) 0 0
\(700\) 11.9008 0.449808
\(701\) −37.9191 −1.43219 −0.716093 0.698005i \(-0.754071\pi\)
−0.716093 + 0.698005i \(0.754071\pi\)
\(702\) 0 0
\(703\) −8.67364 −0.327133
\(704\) 0 0
\(705\) 0 0
\(706\) −57.7238 −2.17246
\(707\) −43.0801 −1.62019
\(708\) 0 0
\(709\) −5.27686 −0.198177 −0.0990884 0.995079i \(-0.531593\pi\)
−0.0990884 + 0.995079i \(0.531593\pi\)
\(710\) −5.91288 −0.221906
\(711\) 0 0
\(712\) −38.4968 −1.44273
\(713\) 23.1972 0.868742
\(714\) 0 0
\(715\) 0 0
\(716\) 11.9433 0.446341
\(717\) 0 0
\(718\) −15.4710 −0.577374
\(719\) −30.9117 −1.15281 −0.576406 0.817164i \(-0.695545\pi\)
−0.576406 + 0.817164i \(0.695545\pi\)
\(720\) 0 0
\(721\) −62.0638 −2.31138
\(722\) −20.3489 −0.757307
\(723\) 0 0
\(724\) −20.0409 −0.744812
\(725\) 4.69779 0.174471
\(726\) 0 0
\(727\) 8.24387 0.305748 0.152874 0.988246i \(-0.451147\pi\)
0.152874 + 0.988246i \(0.451147\pi\)
\(728\) −17.8795 −0.662657
\(729\) 0 0
\(730\) 6.96539 0.257801
\(731\) 20.0934 0.743180
\(732\) 0 0
\(733\) −43.3839 −1.60242 −0.801211 0.598382i \(-0.795810\pi\)
−0.801211 + 0.598382i \(0.795810\pi\)
\(734\) 19.1867 0.708195
\(735\) 0 0
\(736\) −10.0388 −0.370036
\(737\) 0 0
\(738\) 0 0
\(739\) −0.301014 −0.0110730 −0.00553649 0.999985i \(-0.501762\pi\)
−0.00553649 + 0.999985i \(0.501762\pi\)
\(740\) −9.48894 −0.348820
\(741\) 0 0
\(742\) 20.0062 0.734452
\(743\) 31.5040 1.15577 0.577885 0.816118i \(-0.303878\pi\)
0.577885 + 0.816118i \(0.303878\pi\)
\(744\) 0 0
\(745\) 6.48270 0.237508
\(746\) 63.5161 2.32549
\(747\) 0 0
\(748\) 0 0
\(749\) 24.1372 0.881955
\(750\) 0 0
\(751\) 33.2906 1.21479 0.607395 0.794400i \(-0.292215\pi\)
0.607395 + 0.794400i \(0.292215\pi\)
\(752\) 14.0759 0.513295
\(753\) 0 0
\(754\) −16.3610 −0.595831
\(755\) −10.8783 −0.395901
\(756\) 0 0
\(757\) 15.5068 0.563606 0.281803 0.959472i \(-0.409068\pi\)
0.281803 + 0.959472i \(0.409068\pi\)
\(758\) 76.7195 2.78658
\(759\) 0 0
\(760\) 11.4585 0.415645
\(761\) −52.3944 −1.89929 −0.949647 0.313321i \(-0.898559\pi\)
−0.949647 + 0.313321i \(0.898559\pi\)
\(762\) 0 0
\(763\) −14.0276 −0.507833
\(764\) 31.7145 1.14739
\(765\) 0 0
\(766\) 6.21629 0.224604
\(767\) 17.6632 0.637780
\(768\) 0 0
\(769\) −44.2652 −1.59624 −0.798122 0.602496i \(-0.794173\pi\)
−0.798122 + 0.602496i \(0.794173\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −92.2652 −3.32070
\(773\) 35.3177 1.27029 0.635145 0.772393i \(-0.280940\pi\)
0.635145 + 0.772393i \(0.280940\pi\)
\(774\) 0 0
\(775\) 9.21509 0.331016
\(776\) 39.2634 1.40947
\(777\) 0 0
\(778\) 68.2385 2.44647
\(779\) 14.6348 0.524347
\(780\) 0 0
\(781\) 0 0
\(782\) −22.0692 −0.789194
\(783\) 0 0
\(784\) 5.94629 0.212368
\(785\) 10.4302 0.372269
\(786\) 0 0
\(787\) 36.6920 1.30793 0.653964 0.756526i \(-0.273105\pi\)
0.653964 + 0.756526i \(0.273105\pi\)
\(788\) −58.7312 −2.09221
\(789\) 0 0
\(790\) −15.8950 −0.565518
\(791\) −4.95613 −0.176220
\(792\) 0 0
\(793\) −20.2831 −0.720274
\(794\) −21.9851 −0.780222
\(795\) 0 0
\(796\) −59.0596 −2.09331
\(797\) 2.85412 0.101098 0.0505491 0.998722i \(-0.483903\pi\)
0.0505491 + 0.998722i \(0.483903\pi\)
\(798\) 0 0
\(799\) −39.2998 −1.39033
\(800\) −3.98793 −0.140994
\(801\) 0 0
\(802\) −11.5819 −0.408971
\(803\) 0 0
\(804\) 0 0
\(805\) 8.51730 0.300196
\(806\) −32.0934 −1.13044
\(807\) 0 0
\(808\) −45.3781 −1.59640
\(809\) −26.0934 −0.917394 −0.458697 0.888593i \(-0.651684\pi\)
−0.458697 + 0.888593i \(0.651684\pi\)
\(810\) 0 0
\(811\) −19.6453 −0.689839 −0.344919 0.938632i \(-0.612094\pi\)
−0.344919 + 0.938632i \(0.612094\pi\)
\(812\) 55.9075 1.96197
\(813\) 0 0
\(814\) 0 0
\(815\) −10.2439 −0.358827
\(816\) 0 0
\(817\) −17.3085 −0.605546
\(818\) 89.9825 3.14616
\(819\) 0 0
\(820\) 16.0105 0.559109
\(821\) 51.9117 1.81173 0.905865 0.423566i \(-0.139222\pi\)
0.905865 + 0.423566i \(0.139222\pi\)
\(822\) 0 0
\(823\) 15.9250 0.555109 0.277555 0.960710i \(-0.410476\pi\)
0.277555 + 0.960710i \(0.410476\pi\)
\(824\) −65.3744 −2.27743
\(825\) 0 0
\(826\) −94.6775 −3.29425
\(827\) −9.77164 −0.339793 −0.169897 0.985462i \(-0.554343\pi\)
−0.169897 + 0.985462i \(0.554343\pi\)
\(828\) 0 0
\(829\) 1.01790 0.0353532 0.0176766 0.999844i \(-0.494373\pi\)
0.0176766 + 0.999844i \(0.494373\pi\)
\(830\) 17.7386 0.615717
\(831\) 0 0
\(832\) 17.8529 0.618939
\(833\) −16.6020 −0.575226
\(834\) 0 0
\(835\) −1.04668 −0.0362219
\(836\) 0 0
\(837\) 0 0
\(838\) −87.7962 −3.03287
\(839\) −13.7900 −0.476082 −0.238041 0.971255i \(-0.576505\pi\)
−0.238041 + 0.971255i \(0.576505\pi\)
\(840\) 0 0
\(841\) −6.93078 −0.238993
\(842\) 69.0863 2.38087
\(843\) 0 0
\(844\) −26.8908 −0.925618
\(845\) −10.8016 −0.371587
\(846\) 0 0
\(847\) 0 0
\(848\) 3.36518 0.115561
\(849\) 0 0
\(850\) −8.76700 −0.300706
\(851\) −6.79115 −0.232798
\(852\) 0 0
\(853\) −27.3264 −0.935637 −0.467818 0.883825i \(-0.654960\pi\)
−0.467818 + 0.883825i \(0.654960\pi\)
\(854\) 108.721 3.72035
\(855\) 0 0
\(856\) 25.4248 0.869001
\(857\) 22.2318 0.759424 0.379712 0.925105i \(-0.376023\pi\)
0.379712 + 0.925105i \(0.376023\pi\)
\(858\) 0 0
\(859\) 28.5173 0.972998 0.486499 0.873681i \(-0.338274\pi\)
0.486499 + 0.873681i \(0.338274\pi\)
\(860\) −18.9354 −0.645692
\(861\) 0 0
\(862\) 4.15332 0.141463
\(863\) −52.2594 −1.77893 −0.889465 0.457003i \(-0.848923\pi\)
−0.889465 + 0.457003i \(0.848923\pi\)
\(864\) 0 0
\(865\) 11.9129 0.405050
\(866\) 23.6095 0.802283
\(867\) 0 0
\(868\) 109.667 3.72234
\(869\) 0 0
\(870\) 0 0
\(871\) −11.6119 −0.393453
\(872\) −14.7758 −0.500373
\(873\) 0 0
\(874\) 19.0105 0.643038
\(875\) 3.38350 0.114383
\(876\) 0 0
\(877\) 21.0074 0.709371 0.354685 0.934986i \(-0.384588\pi\)
0.354685 + 0.934986i \(0.384588\pi\)
\(878\) −92.0701 −3.10721
\(879\) 0 0
\(880\) 0 0
\(881\) −46.0743 −1.55228 −0.776141 0.630560i \(-0.782825\pi\)
−0.776141 + 0.630560i \(0.782825\pi\)
\(882\) 0 0
\(883\) 0.622326 0.0209429 0.0104715 0.999945i \(-0.496667\pi\)
0.0104715 + 0.999945i \(0.496667\pi\)
\(884\) 19.4648 0.654672
\(885\) 0 0
\(886\) 32.9129 1.10573
\(887\) 11.4077 0.383031 0.191516 0.981490i \(-0.438660\pi\)
0.191516 + 0.981490i \(0.438660\pi\)
\(888\) 0 0
\(889\) −38.2213 −1.28190
\(890\) −25.3718 −0.850466
\(891\) 0 0
\(892\) −13.3290 −0.446287
\(893\) 33.8529 1.13284
\(894\) 0 0
\(895\) 3.39558 0.113502
\(896\) −68.7082 −2.29538
\(897\) 0 0
\(898\) −6.05090 −0.201921
\(899\) 43.2906 1.44382
\(900\) 0 0
\(901\) −9.39558 −0.313012
\(902\) 0 0
\(903\) 0 0
\(904\) −5.22050 −0.173631
\(905\) −5.69779 −0.189401
\(906\) 0 0
\(907\) 38.9175 1.29223 0.646117 0.763238i \(-0.276392\pi\)
0.646117 + 0.763238i \(0.276392\pi\)
\(908\) −68.7495 −2.28153
\(909\) 0 0
\(910\) −11.7837 −0.390626
\(911\) −38.0934 −1.26209 −0.631045 0.775746i \(-0.717374\pi\)
−0.631045 + 0.775746i \(0.717374\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −35.5193 −1.17488
\(915\) 0 0
\(916\) 18.1584 0.599969
\(917\) −49.6694 −1.64023
\(918\) 0 0
\(919\) 19.2727 0.635746 0.317873 0.948133i \(-0.397031\pi\)
0.317873 + 0.948133i \(0.397031\pi\)
\(920\) 8.97164 0.295786
\(921\) 0 0
\(922\) 23.1042 0.760898
\(923\) 3.73240 0.122853
\(924\) 0 0
\(925\) −2.69779 −0.0887027
\(926\) 49.8183 1.63713
\(927\) 0 0
\(928\) −18.7344 −0.614988
\(929\) −31.1730 −1.02275 −0.511377 0.859356i \(-0.670864\pi\)
−0.511377 + 0.859356i \(0.670864\pi\)
\(930\) 0 0
\(931\) 14.3010 0.468697
\(932\) 21.9821 0.720048
\(933\) 0 0
\(934\) 22.4648 0.735070
\(935\) 0 0
\(936\) 0 0
\(937\) 25.8708 0.845163 0.422582 0.906325i \(-0.361124\pi\)
0.422582 + 0.906325i \(0.361124\pi\)
\(938\) 62.2415 2.03226
\(939\) 0 0
\(940\) 37.0350 1.20795
\(941\) −29.4636 −0.960486 −0.480243 0.877136i \(-0.659451\pi\)
−0.480243 + 0.877136i \(0.659451\pi\)
\(942\) 0 0
\(943\) 11.4585 0.373142
\(944\) −15.9254 −0.518327
\(945\) 0 0
\(946\) 0 0
\(947\) 14.3881 0.467551 0.233776 0.972291i \(-0.424892\pi\)
0.233776 + 0.972291i \(0.424892\pi\)
\(948\) 0 0
\(949\) −4.39677 −0.142725
\(950\) 7.55191 0.245016
\(951\) 0 0
\(952\) −45.0081 −1.45872
\(953\) 31.9191 1.03396 0.516981 0.855997i \(-0.327056\pi\)
0.516981 + 0.855997i \(0.327056\pi\)
\(954\) 0 0
\(955\) 9.01671 0.291774
\(956\) 16.2171 0.524499
\(957\) 0 0
\(958\) −40.3944 −1.30508
\(959\) 52.9358 1.70939
\(960\) 0 0
\(961\) 53.9179 1.73929
\(962\) 9.39558 0.302926
\(963\) 0 0
\(964\) −27.7103 −0.892488
\(965\) −26.2318 −0.844431
\(966\) 0 0
\(967\) 46.8425 1.50635 0.753176 0.657819i \(-0.228521\pi\)
0.753176 + 0.657819i \(0.228521\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 25.8771 0.830863
\(971\) 6.66198 0.213793 0.106897 0.994270i \(-0.465909\pi\)
0.106897 + 0.994270i \(0.465909\pi\)
\(972\) 0 0
\(973\) −25.8678 −0.829284
\(974\) 36.5298 1.17049
\(975\) 0 0
\(976\) 18.2875 0.585370
\(977\) 24.1960 0.774098 0.387049 0.922059i \(-0.373494\pi\)
0.387049 + 0.922059i \(0.373494\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 15.6453 0.499770
\(981\) 0 0
\(982\) −21.2781 −0.679010
\(983\) 27.7716 0.885778 0.442889 0.896577i \(-0.353954\pi\)
0.442889 + 0.896577i \(0.353954\pi\)
\(984\) 0 0
\(985\) −16.6978 −0.532036
\(986\) −41.1855 −1.31161
\(987\) 0 0
\(988\) −16.7670 −0.533429
\(989\) −13.5519 −0.430926
\(990\) 0 0
\(991\) 45.4227 1.44290 0.721450 0.692466i \(-0.243476\pi\)
0.721450 + 0.692466i \(0.243476\pi\)
\(992\) −36.7491 −1.16679
\(993\) 0 0
\(994\) −20.0062 −0.634560
\(995\) −16.7912 −0.532315
\(996\) 0 0
\(997\) 50.7491 1.60724 0.803620 0.595143i \(-0.202904\pi\)
0.803620 + 0.595143i \(0.202904\pi\)
\(998\) 57.7091 1.82675
\(999\) 0 0
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 5445.2.a.bd.1.3 3
3.2 odd 2 605.2.a.g.1.1 3
11.10 odd 2 5445.2.a.bb.1.1 3
12.11 even 2 9680.2.a.bz.1.1 3
15.14 odd 2 3025.2.a.u.1.3 3
33.2 even 10 605.2.g.o.81.1 12
33.5 odd 10 605.2.g.p.366.3 12
33.8 even 10 605.2.g.o.251.3 12
33.14 odd 10 605.2.g.p.251.1 12
33.17 even 10 605.2.g.o.366.1 12
33.20 odd 10 605.2.g.p.81.3 12
33.26 odd 10 605.2.g.p.511.1 12
33.29 even 10 605.2.g.o.511.3 12
33.32 even 2 605.2.a.h.1.3 yes 3
132.131 odd 2 9680.2.a.cb.1.1 3
165.164 even 2 3025.2.a.p.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.a.g.1.1 3 3.2 odd 2
605.2.a.h.1.3 yes 3 33.32 even 2
605.2.g.o.81.1 12 33.2 even 10
605.2.g.o.251.3 12 33.8 even 10
605.2.g.o.366.1 12 33.17 even 10
605.2.g.o.511.3 12 33.29 even 10
605.2.g.p.81.3 12 33.20 odd 10
605.2.g.p.251.1 12 33.14 odd 10
605.2.g.p.366.3 12 33.5 odd 10
605.2.g.p.511.1 12 33.26 odd 10
3025.2.a.p.1.1 3 165.164 even 2
3025.2.a.u.1.3 3 15.14 odd 2
5445.2.a.bb.1.1 3 11.10 odd 2
5445.2.a.bd.1.3 3 1.1 even 1 trivial
9680.2.a.bz.1.1 3 12.11 even 2
9680.2.a.cb.1.1 3 132.131 odd 2