Properties

Label 504.2.j.a.323.6
Level $504$
Weight $2$
Character 504.323
Analytic conductor $4.024$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(323,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.323");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.j (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.6
Character \(\chi\) \(=\) 504.323
Dual form 504.2.j.a.323.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.937511 + 1.05881i) q^{2} +(-0.242146 - 1.98529i) q^{4} -4.34020 q^{5} +1.00000i q^{7} +(2.32905 + 1.60484i) q^{8} +O(q^{10})\) \(q+(-0.937511 + 1.05881i) q^{2} +(-0.242146 - 1.98529i) q^{4} -4.34020 q^{5} +1.00000i q^{7} +(2.32905 + 1.60484i) q^{8} +(4.06898 - 4.59543i) q^{10} +1.12627i q^{11} -0.491523i q^{13} +(-1.05881 - 0.937511i) q^{14} +(-3.88273 + 0.961458i) q^{16} -5.96280i q^{17} +2.34308 q^{19} +(1.05096 + 8.61654i) q^{20} +(-1.19251 - 1.05589i) q^{22} +6.68189 q^{23} +13.8373 q^{25} +(0.520429 + 0.460809i) q^{26} +(1.98529 - 0.242146i) q^{28} +4.70295 q^{29} -8.07383i q^{31} +(2.62210 - 5.01244i) q^{32} +(6.31346 + 5.59019i) q^{34} -4.34020i q^{35} +0.750286i q^{37} +(-2.19666 + 2.48087i) q^{38} +(-10.1085 - 6.96533i) q^{40} +3.41271i q^{41} -7.30336 q^{43} +(2.23598 - 0.272723i) q^{44} +(-6.26435 + 7.07484i) q^{46} +9.47430 q^{47} -1.00000 q^{49} +(-12.9726 + 14.6510i) q^{50} +(-0.975815 + 0.119020i) q^{52} -3.12323 q^{53} -4.88825i q^{55} +(-1.60484 + 2.32905i) q^{56} +(-4.40906 + 4.97951i) q^{58} -9.47430i q^{59} +1.64644i q^{61} +(8.54863 + 7.56931i) q^{62} +(2.84896 + 7.47552i) q^{64} +2.13331i q^{65} +9.48557 q^{67} +(-11.8379 + 1.44387i) q^{68} +(4.59543 + 4.06898i) q^{70} -9.14438 q^{71} +2.65767 q^{73} +(-0.794408 - 0.703401i) q^{74} +(-0.567367 - 4.65168i) q^{76} -1.12627 q^{77} +5.74652i q^{79} +(16.8518 - 4.17292i) q^{80} +(-3.61340 - 3.19946i) q^{82} -12.8786i q^{83} +25.8797i q^{85} +(6.84698 - 7.73285i) q^{86} +(-1.80749 + 2.62315i) q^{88} +12.9777i q^{89} +0.491523 q^{91} +(-1.61799 - 13.2655i) q^{92} +(-8.88226 + 10.0315i) q^{94} -10.1694 q^{95} -7.51246 q^{97} +(0.937511 - 1.05881i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 8 q^{4} + 24 q^{10} + 12 q^{16} + 32 q^{19} + 12 q^{22} + 24 q^{25} + 4 q^{28} - 8 q^{40} - 64 q^{43} - 12 q^{46} - 24 q^{49} - 16 q^{52} - 12 q^{58} + 16 q^{64} + 16 q^{67} + 24 q^{70} + 8 q^{76} + 24 q^{82} - 84 q^{88} - 72 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.937511 + 1.05881i −0.662920 + 0.748690i
\(3\) 0 0
\(4\) −0.242146 1.98529i −0.121073 0.992644i
\(5\) −4.34020 −1.94099 −0.970497 0.241112i \(-0.922488\pi\)
−0.970497 + 0.241112i \(0.922488\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 2.32905 + 1.60484i 0.823444 + 0.567398i
\(9\) 0 0
\(10\) 4.06898 4.59543i 1.28673 1.45320i
\(11\) 1.12627i 0.339584i 0.985480 + 0.169792i \(0.0543096\pi\)
−0.985480 + 0.169792i \(0.945690\pi\)
\(12\) 0 0
\(13\) 0.491523i 0.136324i −0.997674 0.0681620i \(-0.978287\pi\)
0.997674 0.0681620i \(-0.0217135\pi\)
\(14\) −1.05881 0.937511i −0.282978 0.250560i
\(15\) 0 0
\(16\) −3.88273 + 0.961458i −0.970683 + 0.240365i
\(17\) 5.96280i 1.44619i −0.690748 0.723096i \(-0.742719\pi\)
0.690748 0.723096i \(-0.257281\pi\)
\(18\) 0 0
\(19\) 2.34308 0.537539 0.268769 0.963205i \(-0.413383\pi\)
0.268769 + 0.963205i \(0.413383\pi\)
\(20\) 1.05096 + 8.61654i 0.235002 + 1.92672i
\(21\) 0 0
\(22\) −1.19251 1.05589i −0.254243 0.225117i
\(23\) 6.68189 1.39327 0.696636 0.717425i \(-0.254679\pi\)
0.696636 + 0.717425i \(0.254679\pi\)
\(24\) 0 0
\(25\) 13.8373 2.76746
\(26\) 0.520429 + 0.460809i 0.102064 + 0.0903720i
\(27\) 0 0
\(28\) 1.98529 0.242146i 0.375184 0.0457613i
\(29\) 4.70295 0.873315 0.436658 0.899628i \(-0.356162\pi\)
0.436658 + 0.899628i \(0.356162\pi\)
\(30\) 0 0
\(31\) 8.07383i 1.45010i −0.688694 0.725052i \(-0.741816\pi\)
0.688694 0.725052i \(-0.258184\pi\)
\(32\) 2.62210 5.01244i 0.463527 0.886083i
\(33\) 0 0
\(34\) 6.31346 + 5.59019i 1.08275 + 0.958710i
\(35\) 4.34020i 0.733627i
\(36\) 0 0
\(37\) 0.750286i 0.123346i 0.998096 + 0.0616731i \(0.0196436\pi\)
−0.998096 + 0.0616731i \(0.980356\pi\)
\(38\) −2.19666 + 2.48087i −0.356345 + 0.402450i
\(39\) 0 0
\(40\) −10.1085 6.96533i −1.59830 1.10132i
\(41\) 3.41271i 0.532976i 0.963838 + 0.266488i \(0.0858633\pi\)
−0.963838 + 0.266488i \(0.914137\pi\)
\(42\) 0 0
\(43\) −7.30336 −1.11375 −0.556876 0.830595i \(-0.688000\pi\)
−0.556876 + 0.830595i \(0.688000\pi\)
\(44\) 2.23598 0.272723i 0.337086 0.0411145i
\(45\) 0 0
\(46\) −6.26435 + 7.07484i −0.923628 + 1.04313i
\(47\) 9.47430 1.38197 0.690984 0.722870i \(-0.257177\pi\)
0.690984 + 0.722870i \(0.257177\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) −12.9726 + 14.6510i −1.83461 + 2.07197i
\(51\) 0 0
\(52\) −0.975815 + 0.119020i −0.135321 + 0.0165052i
\(53\) −3.12323 −0.429008 −0.214504 0.976723i \(-0.568814\pi\)
−0.214504 + 0.976723i \(0.568814\pi\)
\(54\) 0 0
\(55\) 4.88825i 0.659132i
\(56\) −1.60484 + 2.32905i −0.214456 + 0.311233i
\(57\) 0 0
\(58\) −4.40906 + 4.97951i −0.578938 + 0.653842i
\(59\) 9.47430i 1.23345i −0.787179 0.616724i \(-0.788459\pi\)
0.787179 0.616724i \(-0.211541\pi\)
\(60\) 0 0
\(61\) 1.64644i 0.210805i 0.994430 + 0.105403i \(0.0336131\pi\)
−0.994430 + 0.105403i \(0.966387\pi\)
\(62\) 8.54863 + 7.56931i 1.08568 + 0.961303i
\(63\) 0 0
\(64\) 2.84896 + 7.47552i 0.356120 + 0.934440i
\(65\) 2.13331i 0.264604i
\(66\) 0 0
\(67\) 9.48557 1.15885 0.579423 0.815027i \(-0.303278\pi\)
0.579423 + 0.815027i \(0.303278\pi\)
\(68\) −11.8379 + 1.44387i −1.43555 + 0.175095i
\(69\) 0 0
\(70\) 4.59543 + 4.06898i 0.549259 + 0.486336i
\(71\) −9.14438 −1.08524 −0.542619 0.839979i \(-0.682567\pi\)
−0.542619 + 0.839979i \(0.682567\pi\)
\(72\) 0 0
\(73\) 2.65767 0.311057 0.155529 0.987831i \(-0.450292\pi\)
0.155529 + 0.987831i \(0.450292\pi\)
\(74\) −0.794408 0.703401i −0.0923480 0.0817687i
\(75\) 0 0
\(76\) −0.567367 4.65168i −0.0650814 0.533585i
\(77\) −1.12627 −0.128351
\(78\) 0 0
\(79\) 5.74652i 0.646534i 0.946308 + 0.323267i \(0.104781\pi\)
−0.946308 + 0.323267i \(0.895219\pi\)
\(80\) 16.8518 4.17292i 1.88409 0.466546i
\(81\) 0 0
\(82\) −3.61340 3.19946i −0.399034 0.353321i
\(83\) 12.8786i 1.41361i −0.707408 0.706805i \(-0.750136\pi\)
0.707408 0.706805i \(-0.249864\pi\)
\(84\) 0 0
\(85\) 25.8797i 2.80705i
\(86\) 6.84698 7.73285i 0.738329 0.833855i
\(87\) 0 0
\(88\) −1.80749 + 2.62315i −0.192679 + 0.279629i
\(89\) 12.9777i 1.37563i 0.725884 + 0.687817i \(0.241431\pi\)
−0.725884 + 0.687817i \(0.758569\pi\)
\(90\) 0 0
\(91\) 0.491523 0.0515257
\(92\) −1.61799 13.2655i −0.168687 1.38302i
\(93\) 0 0
\(94\) −8.88226 + 10.0315i −0.916135 + 1.03467i
\(95\) −10.1694 −1.04336
\(96\) 0 0
\(97\) −7.51246 −0.762775 −0.381387 0.924415i \(-0.624554\pi\)
−0.381387 + 0.924415i \(0.624554\pi\)
\(98\) 0.937511 1.05881i 0.0947029 0.106956i
\(99\) 0 0
\(100\) −3.35065 27.4710i −0.335065 2.74710i
\(101\) 12.2496 1.21888 0.609440 0.792832i \(-0.291394\pi\)
0.609440 + 0.792832i \(0.291394\pi\)
\(102\) 0 0
\(103\) 4.29883i 0.423577i −0.977316 0.211788i \(-0.932071\pi\)
0.977316 0.211788i \(-0.0679288\pi\)
\(104\) 0.788818 1.14478i 0.0773500 0.112255i
\(105\) 0 0
\(106\) 2.92806 3.30690i 0.284398 0.321194i
\(107\) 18.4871i 1.78721i −0.448853 0.893606i \(-0.648167\pi\)
0.448853 0.893606i \(-0.351833\pi\)
\(108\) 0 0
\(109\) 8.41691i 0.806194i 0.915157 + 0.403097i \(0.132066\pi\)
−0.915157 + 0.403097i \(0.867934\pi\)
\(110\) 5.17572 + 4.58279i 0.493485 + 0.436952i
\(111\) 0 0
\(112\) −0.961458 3.88273i −0.0908493 0.366884i
\(113\) 14.1717i 1.33317i −0.745431 0.666583i \(-0.767756\pi\)
0.745431 0.666583i \(-0.232244\pi\)
\(114\) 0 0
\(115\) −29.0007 −2.70433
\(116\) −1.13880 9.33670i −0.105735 0.866891i
\(117\) 0 0
\(118\) 10.0315 + 8.88226i 0.923470 + 0.817678i
\(119\) 5.96280 0.546609
\(120\) 0 0
\(121\) 9.73151 0.884682
\(122\) −1.74326 1.54356i −0.157828 0.139747i
\(123\) 0 0
\(124\) −16.0289 + 1.95505i −1.43944 + 0.175568i
\(125\) −38.3556 −3.43063
\(126\) 0 0
\(127\) 17.0394i 1.51200i −0.654570 0.756001i \(-0.727150\pi\)
0.654570 0.756001i \(-0.272850\pi\)
\(128\) −10.5861 3.99189i −0.935685 0.352836i
\(129\) 0 0
\(130\) −2.25876 2.00000i −0.198107 0.175412i
\(131\) 4.87851i 0.426237i 0.977026 + 0.213119i \(0.0683621\pi\)
−0.977026 + 0.213119i \(0.931638\pi\)
\(132\) 0 0
\(133\) 2.34308i 0.203171i
\(134\) −8.89283 + 10.0434i −0.768223 + 0.867617i
\(135\) 0 0
\(136\) 9.56936 13.8877i 0.820566 1.19086i
\(137\) 10.0039i 0.854692i 0.904088 + 0.427346i \(0.140551\pi\)
−0.904088 + 0.427346i \(0.859449\pi\)
\(138\) 0 0
\(139\) 3.60637 0.305888 0.152944 0.988235i \(-0.451125\pi\)
0.152944 + 0.988235i \(0.451125\pi\)
\(140\) −8.61654 + 1.05096i −0.728230 + 0.0888224i
\(141\) 0 0
\(142\) 8.57295 9.68213i 0.719426 0.812507i
\(143\) 0.553590 0.0462935
\(144\) 0 0
\(145\) −20.4117 −1.69510
\(146\) −2.49160 + 2.81396i −0.206206 + 0.232885i
\(147\) 0 0
\(148\) 1.48953 0.181679i 0.122439 0.0149339i
\(149\) 8.87078 0.726722 0.363361 0.931648i \(-0.381629\pi\)
0.363361 + 0.931648i \(0.381629\pi\)
\(150\) 0 0
\(151\) 0.393631i 0.0320333i 0.999872 + 0.0160166i \(0.00509847\pi\)
−0.999872 + 0.0160166i \(0.994902\pi\)
\(152\) 5.45715 + 3.76027i 0.442633 + 0.304998i
\(153\) 0 0
\(154\) 1.05589 1.19251i 0.0850864 0.0960950i
\(155\) 35.0420i 2.81464i
\(156\) 0 0
\(157\) 12.8320i 1.02411i −0.858954 0.512054i \(-0.828885\pi\)
0.858954 0.512054i \(-0.171115\pi\)
\(158\) −6.08445 5.38742i −0.484053 0.428600i
\(159\) 0 0
\(160\) −11.3804 + 21.7550i −0.899703 + 1.71988i
\(161\) 6.68189i 0.526607i
\(162\) 0 0
\(163\) −7.51948 −0.588971 −0.294485 0.955656i \(-0.595148\pi\)
−0.294485 + 0.955656i \(0.595148\pi\)
\(164\) 6.77521 0.826374i 0.529055 0.0645290i
\(165\) 0 0
\(166\) 13.6360 + 12.0738i 1.05836 + 0.937111i
\(167\) −4.30627 −0.333229 −0.166615 0.986022i \(-0.553284\pi\)
−0.166615 + 0.986022i \(0.553284\pi\)
\(168\) 0 0
\(169\) 12.7584 0.981416
\(170\) −27.4016 24.2625i −2.10161 1.86085i
\(171\) 0 0
\(172\) 1.76848 + 14.4993i 0.134845 + 1.10556i
\(173\) −8.33156 −0.633437 −0.316718 0.948520i \(-0.602581\pi\)
−0.316718 + 0.948520i \(0.602581\pi\)
\(174\) 0 0
\(175\) 13.8373i 1.04600i
\(176\) −1.08287 4.37302i −0.0816240 0.329629i
\(177\) 0 0
\(178\) −13.7409 12.1667i −1.02992 0.911936i
\(179\) 4.40770i 0.329447i −0.986340 0.164723i \(-0.947327\pi\)
0.986340 0.164723i \(-0.0526731\pi\)
\(180\) 0 0
\(181\) 14.3110i 1.06373i −0.846830 0.531864i \(-0.821492\pi\)
0.846830 0.531864i \(-0.178508\pi\)
\(182\) −0.460809 + 0.520429i −0.0341574 + 0.0385767i
\(183\) 0 0
\(184\) 15.5625 + 10.7234i 1.14728 + 0.790539i
\(185\) 3.25639i 0.239414i
\(186\) 0 0
\(187\) 6.71575 0.491104
\(188\) −2.29416 18.8092i −0.167319 1.37180i
\(189\) 0 0
\(190\) 9.53394 10.7675i 0.691665 0.781153i
\(191\) 11.5050 0.832471 0.416236 0.909257i \(-0.363349\pi\)
0.416236 + 0.909257i \(0.363349\pi\)
\(192\) 0 0
\(193\) 0.0619465 0.00445901 0.00222950 0.999998i \(-0.499290\pi\)
0.00222950 + 0.999998i \(0.499290\pi\)
\(194\) 7.04301 7.95425i 0.505659 0.571082i
\(195\) 0 0
\(196\) 0.242146 + 1.98529i 0.0172961 + 0.141806i
\(197\) 15.0637 1.07324 0.536620 0.843824i \(-0.319701\pi\)
0.536620 + 0.843824i \(0.319701\pi\)
\(198\) 0 0
\(199\) 9.80891i 0.695335i −0.937618 0.347667i \(-0.886974\pi\)
0.937618 0.347667i \(-0.113026\pi\)
\(200\) 32.2278 + 22.2067i 2.27885 + 1.57025i
\(201\) 0 0
\(202\) −11.4841 + 12.9700i −0.808021 + 0.912564i
\(203\) 4.70295i 0.330082i
\(204\) 0 0
\(205\) 14.8118i 1.03450i
\(206\) 4.55164 + 4.03021i 0.317128 + 0.280798i
\(207\) 0 0
\(208\) 0.472579 + 1.90845i 0.0327675 + 0.132327i
\(209\) 2.63895i 0.182540i
\(210\) 0 0
\(211\) 7.17510 0.493954 0.246977 0.969021i \(-0.420563\pi\)
0.246977 + 0.969021i \(0.420563\pi\)
\(212\) 0.756277 + 6.20050i 0.0519413 + 0.425852i
\(213\) 0 0
\(214\) 19.5742 + 17.3318i 1.33807 + 1.18478i
\(215\) 31.6980 2.16179
\(216\) 0 0
\(217\) 8.07383 0.548088
\(218\) −8.91189 7.89095i −0.603589 0.534442i
\(219\) 0 0
\(220\) −9.70458 + 1.18367i −0.654283 + 0.0798030i
\(221\) −2.93086 −0.197151
\(222\) 0 0
\(223\) 2.06283i 0.138138i 0.997612 + 0.0690688i \(0.0220028\pi\)
−0.997612 + 0.0690688i \(0.977997\pi\)
\(224\) 5.01244 + 2.62210i 0.334908 + 0.175197i
\(225\) 0 0
\(226\) 15.0051 + 13.2862i 0.998127 + 0.883783i
\(227\) 20.5663i 1.36504i 0.730869 + 0.682518i \(0.239115\pi\)
−0.730869 + 0.682518i \(0.760885\pi\)
\(228\) 0 0
\(229\) 14.9296i 0.986577i 0.869866 + 0.493289i \(0.164205\pi\)
−0.869866 + 0.493289i \(0.835795\pi\)
\(230\) 27.1885 30.7062i 1.79276 2.02471i
\(231\) 0 0
\(232\) 10.9534 + 7.54749i 0.719126 + 0.495517i
\(233\) 14.3687i 0.941324i 0.882314 + 0.470662i \(0.155985\pi\)
−0.882314 + 0.470662i \(0.844015\pi\)
\(234\) 0 0
\(235\) −41.1203 −2.68239
\(236\) −18.8092 + 2.29416i −1.22437 + 0.149337i
\(237\) 0 0
\(238\) −5.59019 + 6.31346i −0.362358 + 0.409241i
\(239\) 16.3432 1.05715 0.528577 0.848885i \(-0.322726\pi\)
0.528577 + 0.848885i \(0.322726\pi\)
\(240\) 0 0
\(241\) 0.456020 0.0293748 0.0146874 0.999892i \(-0.495325\pi\)
0.0146874 + 0.999892i \(0.495325\pi\)
\(242\) −9.12340 + 10.3038i −0.586474 + 0.662353i
\(243\) 0 0
\(244\) 3.26866 0.398679i 0.209254 0.0255228i
\(245\) 4.34020 0.277285
\(246\) 0 0
\(247\) 1.15168i 0.0732795i
\(248\) 12.9572 18.8044i 0.822785 1.19408i
\(249\) 0 0
\(250\) 35.9588 40.6112i 2.27424 2.56848i
\(251\) 21.9739i 1.38698i 0.720465 + 0.693491i \(0.243928\pi\)
−0.720465 + 0.693491i \(0.756072\pi\)
\(252\) 0 0
\(253\) 7.52564i 0.473133i
\(254\) 18.0414 + 15.9746i 1.13202 + 1.00234i
\(255\) 0 0
\(256\) 14.1512 7.46617i 0.884450 0.466635i
\(257\) 13.7264i 0.856230i −0.903724 0.428115i \(-0.859178\pi\)
0.903724 0.428115i \(-0.140822\pi\)
\(258\) 0 0
\(259\) −0.750286 −0.0466205
\(260\) 4.23523 0.516572i 0.262658 0.0320364i
\(261\) 0 0
\(262\) −5.16540 4.57365i −0.319119 0.282561i
\(263\) −28.3093 −1.74563 −0.872813 0.488055i \(-0.837707\pi\)
−0.872813 + 0.488055i \(0.837707\pi\)
\(264\) 0 0
\(265\) 13.5554 0.832703
\(266\) −2.48087 2.19666i −0.152112 0.134686i
\(267\) 0 0
\(268\) −2.29689 18.8316i −0.140305 1.15032i
\(269\) −6.38645 −0.389389 −0.194694 0.980864i \(-0.562372\pi\)
−0.194694 + 0.980864i \(0.562372\pi\)
\(270\) 0 0
\(271\) 4.63869i 0.281780i −0.990025 0.140890i \(-0.955004\pi\)
0.990025 0.140890i \(-0.0449965\pi\)
\(272\) 5.73298 + 23.1519i 0.347613 + 1.40379i
\(273\) 0 0
\(274\) −10.5922 9.37878i −0.639899 0.566593i
\(275\) 15.5846i 0.939786i
\(276\) 0 0
\(277\) 22.9701i 1.38014i −0.723744 0.690069i \(-0.757580\pi\)
0.723744 0.690069i \(-0.242420\pi\)
\(278\) −3.38101 + 3.81845i −0.202780 + 0.229015i
\(279\) 0 0
\(280\) 6.96533 10.1085i 0.416258 0.604101i
\(281\) 13.1528i 0.784630i 0.919831 + 0.392315i \(0.128326\pi\)
−0.919831 + 0.392315i \(0.871674\pi\)
\(282\) 0 0
\(283\) 29.1290 1.73154 0.865769 0.500443i \(-0.166830\pi\)
0.865769 + 0.500443i \(0.166830\pi\)
\(284\) 2.21427 + 18.1542i 0.131393 + 1.07725i
\(285\) 0 0
\(286\) −0.518997 + 0.586145i −0.0306889 + 0.0346595i
\(287\) −3.41271 −0.201446
\(288\) 0 0
\(289\) −18.5550 −1.09147
\(290\) 19.1362 21.6121i 1.12372 1.26910i
\(291\) 0 0
\(292\) −0.643545 5.27624i −0.0376606 0.308769i
\(293\) −0.874951 −0.0511152 −0.0255576 0.999673i \(-0.508136\pi\)
−0.0255576 + 0.999673i \(0.508136\pi\)
\(294\) 0 0
\(295\) 41.1203i 2.39412i
\(296\) −1.20409 + 1.74745i −0.0699863 + 0.101569i
\(297\) 0 0
\(298\) −8.31645 + 9.39244i −0.481759 + 0.544090i
\(299\) 3.28431i 0.189936i
\(300\) 0 0
\(301\) 7.30336i 0.420959i
\(302\) −0.416780 0.369034i −0.0239830 0.0212355i
\(303\) 0 0
\(304\) −9.09754 + 2.25277i −0.521780 + 0.129205i
\(305\) 7.14588i 0.409172i
\(306\) 0 0
\(307\) 17.0895 0.975350 0.487675 0.873025i \(-0.337845\pi\)
0.487675 + 0.873025i \(0.337845\pi\)
\(308\) 0.272723 + 2.23598i 0.0155398 + 0.127407i
\(309\) 0 0
\(310\) −37.1028 32.8523i −2.10729 1.86588i
\(311\) −20.9397 −1.18738 −0.593692 0.804692i \(-0.702330\pi\)
−0.593692 + 0.804692i \(0.702330\pi\)
\(312\) 0 0
\(313\) −26.3947 −1.49191 −0.745957 0.665994i \(-0.768008\pi\)
−0.745957 + 0.665994i \(0.768008\pi\)
\(314\) 13.5866 + 12.0302i 0.766739 + 0.678902i
\(315\) 0 0
\(316\) 11.4085 1.39150i 0.641778 0.0782777i
\(317\) 23.9039 1.34258 0.671288 0.741197i \(-0.265741\pi\)
0.671288 + 0.741197i \(0.265741\pi\)
\(318\) 0 0
\(319\) 5.29681i 0.296564i
\(320\) −12.3650 32.4452i −0.691227 1.81374i
\(321\) 0 0
\(322\) −7.07484 6.26435i −0.394265 0.349099i
\(323\) 13.9713i 0.777384i
\(324\) 0 0
\(325\) 6.80136i 0.377272i
\(326\) 7.04959 7.96168i 0.390441 0.440957i
\(327\) 0 0
\(328\) −5.47687 + 7.94838i −0.302409 + 0.438876i
\(329\) 9.47430i 0.522335i
\(330\) 0 0
\(331\) −15.8718 −0.872394 −0.436197 0.899851i \(-0.643675\pi\)
−0.436197 + 0.899851i \(0.643675\pi\)
\(332\) −25.5677 + 3.11850i −1.40321 + 0.171150i
\(333\) 0 0
\(334\) 4.03718 4.55951i 0.220904 0.249485i
\(335\) −41.1692 −2.24932
\(336\) 0 0
\(337\) −8.80926 −0.479871 −0.239936 0.970789i \(-0.577126\pi\)
−0.239936 + 0.970789i \(0.577126\pi\)
\(338\) −11.9611 + 13.5087i −0.650601 + 0.734776i
\(339\) 0 0
\(340\) 51.3787 6.26667i 2.78640 0.339858i
\(341\) 9.09335 0.492432
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −17.0099 11.7208i −0.917113 0.631941i
\(345\) 0 0
\(346\) 7.81093 8.82152i 0.419918 0.474248i
\(347\) 18.5105i 0.993697i −0.867837 0.496849i \(-0.834490\pi\)
0.867837 0.496849i \(-0.165510\pi\)
\(348\) 0 0
\(349\) 3.03971i 0.162712i −0.996685 0.0813561i \(-0.974075\pi\)
0.996685 0.0813561i \(-0.0259251\pi\)
\(350\) −14.6510 12.9726i −0.783131 0.693416i
\(351\) 0 0
\(352\) 5.64538 + 2.95321i 0.300900 + 0.157407i
\(353\) 17.0150i 0.905616i 0.891608 + 0.452808i \(0.149578\pi\)
−0.891608 + 0.452808i \(0.850422\pi\)
\(354\) 0 0
\(355\) 39.6884 2.10644
\(356\) 25.7645 3.14250i 1.36551 0.166552i
\(357\) 0 0
\(358\) 4.66690 + 4.13227i 0.246653 + 0.218397i
\(359\) 10.7746 0.568661 0.284331 0.958726i \(-0.408229\pi\)
0.284331 + 0.958726i \(0.408229\pi\)
\(360\) 0 0
\(361\) −13.5100 −0.711052
\(362\) 15.1526 + 13.4167i 0.796402 + 0.705167i
\(363\) 0 0
\(364\) −0.119020 0.975815i −0.00623836 0.0511466i
\(365\) −11.5348 −0.603760
\(366\) 0 0
\(367\) 6.78051i 0.353940i −0.984216 0.176970i \(-0.943370\pi\)
0.984216 0.176970i \(-0.0566295\pi\)
\(368\) −25.9440 + 6.42436i −1.35242 + 0.334893i
\(369\) 0 0
\(370\) 3.44789 + 3.05290i 0.179247 + 0.158713i
\(371\) 3.12323i 0.162150i
\(372\) 0 0
\(373\) 18.6952i 0.968001i 0.875068 + 0.484001i \(0.160817\pi\)
−0.875068 + 0.484001i \(0.839183\pi\)
\(374\) −6.29609 + 7.11068i −0.325563 + 0.367685i
\(375\) 0 0
\(376\) 22.0661 + 15.2048i 1.13797 + 0.784126i
\(377\) 2.31161i 0.119054i
\(378\) 0 0
\(379\) 28.5414 1.46607 0.733036 0.680190i \(-0.238103\pi\)
0.733036 + 0.680190i \(0.238103\pi\)
\(380\) 2.46248 + 20.1892i 0.126323 + 1.03568i
\(381\) 0 0
\(382\) −10.7861 + 12.1816i −0.551862 + 0.623263i
\(383\) −9.88924 −0.505317 −0.252658 0.967556i \(-0.581305\pi\)
−0.252658 + 0.967556i \(0.581305\pi\)
\(384\) 0 0
\(385\) 4.88825 0.249128
\(386\) −0.0580756 + 0.0655895i −0.00295597 + 0.00333842i
\(387\) 0 0
\(388\) 1.81911 + 14.9144i 0.0923514 + 0.757163i
\(389\) 10.5873 0.536798 0.268399 0.963308i \(-0.413505\pi\)
0.268399 + 0.963308i \(0.413505\pi\)
\(390\) 0 0
\(391\) 39.8428i 2.01494i
\(392\) −2.32905 1.60484i −0.117635 0.0810568i
\(393\) 0 0
\(394\) −14.1223 + 15.9495i −0.711473 + 0.803524i
\(395\) 24.9410i 1.25492i
\(396\) 0 0
\(397\) 11.8639i 0.595432i 0.954654 + 0.297716i \(0.0962249\pi\)
−0.954654 + 0.297716i \(0.903775\pi\)
\(398\) 10.3857 + 9.19596i 0.520590 + 0.460952i
\(399\) 0 0
\(400\) −53.7265 + 13.3040i −2.68633 + 0.665199i
\(401\) 12.2757i 0.613017i 0.951868 + 0.306509i \(0.0991608\pi\)
−0.951868 + 0.306509i \(0.900839\pi\)
\(402\) 0 0
\(403\) −3.96848 −0.197684
\(404\) −2.96619 24.3190i −0.147573 1.20991i
\(405\) 0 0
\(406\) −4.97951 4.40906i −0.247129 0.218818i
\(407\) −0.845027 −0.0418864
\(408\) 0 0
\(409\) 1.87041 0.0924858 0.0462429 0.998930i \(-0.485275\pi\)
0.0462429 + 0.998930i \(0.485275\pi\)
\(410\) 15.6829 + 13.8863i 0.774522 + 0.685794i
\(411\) 0 0
\(412\) −8.53442 + 1.04095i −0.420461 + 0.0512837i
\(413\) 9.47430 0.466200
\(414\) 0 0
\(415\) 55.8957i 2.74381i
\(416\) −2.46373 1.28883i −0.120794 0.0631899i
\(417\) 0 0
\(418\) −2.79414 2.47404i −0.136666 0.121009i
\(419\) 4.70969i 0.230083i 0.993361 + 0.115042i \(0.0367001\pi\)
−0.993361 + 0.115042i \(0.963300\pi\)
\(420\) 0 0
\(421\) 3.21062i 0.156476i 0.996935 + 0.0782381i \(0.0249294\pi\)
−0.996935 + 0.0782381i \(0.975071\pi\)
\(422\) −6.72674 + 7.59705i −0.327452 + 0.369819i
\(423\) 0 0
\(424\) −7.27416 5.01229i −0.353264 0.243418i
\(425\) 82.5091i 4.00228i
\(426\) 0 0
\(427\) −1.64644 −0.0796769
\(428\) −36.7021 + 4.47656i −1.77406 + 0.216383i
\(429\) 0 0
\(430\) −29.7173 + 33.5621i −1.43309 + 1.61851i
\(431\) −0.126718 −0.00610381 −0.00305190 0.999995i \(-0.500971\pi\)
−0.00305190 + 0.999995i \(0.500971\pi\)
\(432\) 0 0
\(433\) −1.28232 −0.0616245 −0.0308123 0.999525i \(-0.509809\pi\)
−0.0308123 + 0.999525i \(0.509809\pi\)
\(434\) −7.56931 + 8.54863i −0.363338 + 0.410348i
\(435\) 0 0
\(436\) 16.7100 2.03812i 0.800263 0.0976083i
\(437\) 15.6562 0.748937
\(438\) 0 0
\(439\) 27.9888i 1.33583i −0.744236 0.667917i \(-0.767186\pi\)
0.744236 0.667917i \(-0.232814\pi\)
\(440\) 7.84487 11.3850i 0.373990 0.542758i
\(441\) 0 0
\(442\) 2.74771 3.10321i 0.130695 0.147605i
\(443\) 3.08184i 0.146422i −0.997316 0.0732112i \(-0.976675\pi\)
0.997316 0.0732112i \(-0.0233247\pi\)
\(444\) 0 0
\(445\) 56.3258i 2.67010i
\(446\) −2.18414 1.93393i −0.103422 0.0915742i
\(447\) 0 0
\(448\) −7.47552 + 2.84896i −0.353185 + 0.134601i
\(449\) 9.63488i 0.454698i −0.973813 0.227349i \(-0.926994\pi\)
0.973813 0.227349i \(-0.0730058\pi\)
\(450\) 0 0
\(451\) −3.84365 −0.180990
\(452\) −28.1350 + 3.43163i −1.32336 + 0.161410i
\(453\) 0 0
\(454\) −21.7758 19.2812i −1.02199 0.904910i
\(455\) −2.13331 −0.100011
\(456\) 0 0
\(457\) −8.42000 −0.393871 −0.196936 0.980416i \(-0.563099\pi\)
−0.196936 + 0.980416i \(0.563099\pi\)
\(458\) −15.8076 13.9967i −0.738640 0.654022i
\(459\) 0 0
\(460\) 7.02241 + 57.5748i 0.327421 + 2.68444i
\(461\) −1.69743 −0.0790570 −0.0395285 0.999218i \(-0.512586\pi\)
−0.0395285 + 0.999218i \(0.512586\pi\)
\(462\) 0 0
\(463\) 26.7887i 1.24498i −0.782628 0.622489i \(-0.786121\pi\)
0.782628 0.622489i \(-0.213879\pi\)
\(464\) −18.2603 + 4.52169i −0.847712 + 0.209914i
\(465\) 0 0
\(466\) −15.2137 13.4708i −0.704760 0.624023i
\(467\) 13.5366i 0.626400i 0.949687 + 0.313200i \(0.101401\pi\)
−0.949687 + 0.313200i \(0.898599\pi\)
\(468\) 0 0
\(469\) 9.48557i 0.438003i
\(470\) 38.5507 43.5385i 1.77821 2.00828i
\(471\) 0 0
\(472\) 15.2048 22.0661i 0.699856 1.01568i
\(473\) 8.22559i 0.378213i
\(474\) 0 0
\(475\) 32.4219 1.48762
\(476\) −1.44387 11.8379i −0.0661795 0.542588i
\(477\) 0 0
\(478\) −15.3219 + 17.3043i −0.700809 + 0.791481i
\(479\) −2.91420 −0.133153 −0.0665765 0.997781i \(-0.521208\pi\)
−0.0665765 + 0.997781i \(0.521208\pi\)
\(480\) 0 0
\(481\) 0.368783 0.0168151
\(482\) −0.427524 + 0.482837i −0.0194732 + 0.0219926i
\(483\) 0 0
\(484\) −2.35644 19.3198i −0.107111 0.878174i
\(485\) 32.6055 1.48054
\(486\) 0 0
\(487\) 29.7819i 1.34955i 0.738025 + 0.674774i \(0.235759\pi\)
−0.738025 + 0.674774i \(0.764241\pi\)
\(488\) −2.64228 + 3.83465i −0.119610 + 0.173586i
\(489\) 0 0
\(490\) −4.06898 + 4.59543i −0.183818 + 0.207600i
\(491\) 19.8773i 0.897050i −0.893770 0.448525i \(-0.851950\pi\)
0.893770 0.448525i \(-0.148050\pi\)
\(492\) 0 0
\(493\) 28.0427i 1.26298i
\(494\) 1.21940 + 1.07971i 0.0548636 + 0.0485785i
\(495\) 0 0
\(496\) 7.76265 + 31.3485i 0.348553 + 1.40759i
\(497\) 9.14438i 0.410181i
\(498\) 0 0
\(499\) −29.3452 −1.31367 −0.656837 0.754033i \(-0.728106\pi\)
−0.656837 + 0.754033i \(0.728106\pi\)
\(500\) 9.28766 + 76.1470i 0.415357 + 3.40540i
\(501\) 0 0
\(502\) −23.2662 20.6008i −1.03842 0.919459i
\(503\) −1.44916 −0.0646150 −0.0323075 0.999478i \(-0.510286\pi\)
−0.0323075 + 0.999478i \(0.510286\pi\)
\(504\) 0 0
\(505\) −53.1657 −2.36584
\(506\) −7.96821 7.05537i −0.354230 0.313650i
\(507\) 0 0
\(508\) −33.8281 + 4.12602i −1.50088 + 0.183063i
\(509\) −1.87334 −0.0830342 −0.0415171 0.999138i \(-0.513219\pi\)
−0.0415171 + 0.999138i \(0.513219\pi\)
\(510\) 0 0
\(511\) 2.65767i 0.117569i
\(512\) −5.36167 + 21.9830i −0.236955 + 0.971521i
\(513\) 0 0
\(514\) 14.5336 + 12.8687i 0.641050 + 0.567612i
\(515\) 18.6578i 0.822160i
\(516\) 0 0
\(517\) 10.6707i 0.469295i
\(518\) 0.703401 0.794408i 0.0309057 0.0349043i
\(519\) 0 0
\(520\) −3.42362 + 4.96858i −0.150136 + 0.217887i
\(521\) 21.9333i 0.960917i 0.877017 + 0.480459i \(0.159530\pi\)
−0.877017 + 0.480459i \(0.840470\pi\)
\(522\) 0 0
\(523\) −3.06684 −0.134104 −0.0670518 0.997749i \(-0.521359\pi\)
−0.0670518 + 0.997749i \(0.521359\pi\)
\(524\) 9.68524 1.18131i 0.423102 0.0516058i
\(525\) 0 0
\(526\) 26.5403 29.9741i 1.15721 1.30693i
\(527\) −48.1427 −2.09713
\(528\) 0 0
\(529\) 21.6477 0.941205
\(530\) −12.7084 + 14.3526i −0.552016 + 0.623436i
\(531\) 0 0
\(532\) 4.65168 0.567367i 0.201676 0.0245985i
\(533\) 1.67743 0.0726575
\(534\) 0 0
\(535\) 80.2375i 3.46897i
\(536\) 22.0924 + 15.2229i 0.954245 + 0.657527i
\(537\) 0 0
\(538\) 5.98737 6.76202i 0.258134 0.291532i
\(539\) 1.12627i 0.0485121i
\(540\) 0 0
\(541\) 21.5872i 0.928106i −0.885807 0.464053i \(-0.846395\pi\)
0.885807 0.464053i \(-0.153605\pi\)
\(542\) 4.91148 + 4.34882i 0.210966 + 0.186798i
\(543\) 0 0
\(544\) −29.8882 15.6351i −1.28145 0.670349i
\(545\) 36.5310i 1.56482i
\(546\) 0 0
\(547\) 31.1736 1.33289 0.666443 0.745556i \(-0.267816\pi\)
0.666443 + 0.745556i \(0.267816\pi\)
\(548\) 19.8606 2.42241i 0.848404 0.103480i
\(549\) 0 0
\(550\) −16.5011 14.6107i −0.703609 0.623004i
\(551\) 11.0194 0.469441
\(552\) 0 0
\(553\) −5.74652 −0.244367
\(554\) 24.3209 + 21.5347i 1.03329 + 0.914921i
\(555\) 0 0
\(556\) −0.873267 7.15968i −0.0370348 0.303638i
\(557\) −38.7541 −1.64206 −0.821032 0.570882i \(-0.806602\pi\)
−0.821032 + 0.570882i \(0.806602\pi\)
\(558\) 0 0
\(559\) 3.58977i 0.151831i
\(560\) 4.17292 + 16.8518i 0.176338 + 0.712119i
\(561\) 0 0
\(562\) −13.9263 12.3309i −0.587444 0.520147i
\(563\) 26.4152i 1.11327i −0.830758 0.556634i \(-0.812092\pi\)
0.830758 0.556634i \(-0.187908\pi\)
\(564\) 0 0
\(565\) 61.5081i 2.58767i
\(566\) −27.3088 + 30.8420i −1.14787 + 1.29639i
\(567\) 0 0
\(568\) −21.2977 14.6753i −0.893632 0.615761i
\(569\) 37.6248i 1.57731i −0.614833 0.788657i \(-0.710777\pi\)
0.614833 0.788657i \(-0.289223\pi\)
\(570\) 0 0
\(571\) 21.7106 0.908559 0.454280 0.890859i \(-0.349897\pi\)
0.454280 + 0.890859i \(0.349897\pi\)
\(572\) −0.134050 1.09904i −0.00560489 0.0459530i
\(573\) 0 0
\(574\) 3.19946 3.61340i 0.133543 0.150821i
\(575\) 92.4594 3.85582
\(576\) 0 0
\(577\) 31.1816 1.29811 0.649054 0.760742i \(-0.275165\pi\)
0.649054 + 0.760742i \(0.275165\pi\)
\(578\) 17.3955 19.6461i 0.723557 0.817172i
\(579\) 0 0
\(580\) 4.94261 + 40.5231i 0.205231 + 1.68263i
\(581\) 12.8786 0.534295
\(582\) 0 0
\(583\) 3.51761i 0.145685i
\(584\) 6.18986 + 4.26515i 0.256138 + 0.176493i
\(585\) 0 0
\(586\) 0.820276 0.926405i 0.0338853 0.0382694i
\(587\) 5.00948i 0.206763i −0.994642 0.103382i \(-0.967034\pi\)
0.994642 0.103382i \(-0.0329663\pi\)
\(588\) 0 0
\(589\) 18.9176i 0.779487i
\(590\) −43.5385 38.5507i −1.79245 1.58711i
\(591\) 0 0
\(592\) −0.721368 2.91316i −0.0296481 0.119730i
\(593\) 1.48006i 0.0607789i 0.999538 + 0.0303895i \(0.00967476\pi\)
−0.999538 + 0.0303895i \(0.990325\pi\)
\(594\) 0 0
\(595\) −25.8797 −1.06097
\(596\) −2.14802 17.6110i −0.0879864 0.721376i
\(597\) 0 0
\(598\) 3.47745 + 3.07907i 0.142203 + 0.125913i
\(599\) 9.72452 0.397333 0.198667 0.980067i \(-0.436339\pi\)
0.198667 + 0.980067i \(0.436339\pi\)
\(600\) 0 0
\(601\) −22.1582 −0.903853 −0.451926 0.892055i \(-0.649263\pi\)
−0.451926 + 0.892055i \(0.649263\pi\)
\(602\) 7.73285 + 6.84698i 0.315168 + 0.279062i
\(603\) 0 0
\(604\) 0.781471 0.0953162i 0.0317976 0.00387836i
\(605\) −42.2367 −1.71716
\(606\) 0 0
\(607\) 32.4508i 1.31714i 0.752522 + 0.658568i \(0.228837\pi\)
−0.752522 + 0.658568i \(0.771163\pi\)
\(608\) 6.14379 11.7445i 0.249164 0.476304i
\(609\) 0 0
\(610\) 7.56611 + 6.69934i 0.306343 + 0.271248i
\(611\) 4.65684i 0.188396i
\(612\) 0 0
\(613\) 18.5345i 0.748603i 0.927307 + 0.374302i \(0.122118\pi\)
−0.927307 + 0.374302i \(0.877882\pi\)
\(614\) −16.0216 + 18.0945i −0.646579 + 0.730234i
\(615\) 0 0
\(616\) −2.62315 1.80749i −0.105690 0.0728260i
\(617\) 25.8856i 1.04212i −0.853522 0.521058i \(-0.825538\pi\)
0.853522 0.521058i \(-0.174462\pi\)
\(618\) 0 0
\(619\) −21.0528 −0.846183 −0.423091 0.906087i \(-0.639055\pi\)
−0.423091 + 0.906087i \(0.639055\pi\)
\(620\) 69.5685 8.48528i 2.79394 0.340777i
\(621\) 0 0
\(622\) 19.6312 22.1712i 0.787141 0.888982i
\(623\) −12.9777 −0.519941
\(624\) 0 0
\(625\) 97.2845 3.89138
\(626\) 24.7453 27.9469i 0.989021 1.11698i
\(627\) 0 0
\(628\) −25.4753 + 3.10722i −1.01657 + 0.123992i
\(629\) 4.47380 0.178382
\(630\) 0 0
\(631\) 35.5468i 1.41510i 0.706666 + 0.707548i \(0.250199\pi\)
−0.706666 + 0.707548i \(0.749801\pi\)
\(632\) −9.22226 + 13.3839i −0.366842 + 0.532384i
\(633\) 0 0
\(634\) −22.4102 + 25.3096i −0.890021 + 1.00517i
\(635\) 73.9543i 2.93479i
\(636\) 0 0
\(637\) 0.491523i 0.0194749i
\(638\) −5.60830 4.96581i −0.222035 0.196598i
\(639\) 0 0
\(640\) 45.9456 + 17.3256i 1.81616 + 0.684854i
\(641\) 44.8131i 1.77001i 0.465581 + 0.885005i \(0.345845\pi\)
−0.465581 + 0.885005i \(0.654155\pi\)
\(642\) 0 0
\(643\) −35.5002 −1.39999 −0.699995 0.714148i \(-0.746814\pi\)
−0.699995 + 0.714148i \(0.746814\pi\)
\(644\) 13.2655 1.61799i 0.522733 0.0637579i
\(645\) 0 0
\(646\) 14.7929 + 13.0983i 0.582020 + 0.515344i
\(647\) −8.53449 −0.335525 −0.167763 0.985827i \(-0.553654\pi\)
−0.167763 + 0.985827i \(0.553654\pi\)
\(648\) 0 0
\(649\) 10.6707 0.418860
\(650\) 7.20133 + 6.37635i 0.282459 + 0.250101i
\(651\) 0 0
\(652\) 1.82081 + 14.9283i 0.0713084 + 0.584638i
\(653\) −18.0406 −0.705984 −0.352992 0.935626i \(-0.614836\pi\)
−0.352992 + 0.935626i \(0.614836\pi\)
\(654\) 0 0
\(655\) 21.1737i 0.827324i
\(656\) −3.28118 13.2506i −0.128109 0.517351i
\(657\) 0 0
\(658\) −10.0315 8.88226i −0.391067 0.346267i
\(659\) 11.6857i 0.455212i −0.973753 0.227606i \(-0.926910\pi\)
0.973753 0.227606i \(-0.0730897\pi\)
\(660\) 0 0
\(661\) 3.24527i 0.126227i −0.998006 0.0631133i \(-0.979897\pi\)
0.998006 0.0631133i \(-0.0201029\pi\)
\(662\) 14.8800 16.8052i 0.578328 0.653152i
\(663\) 0 0
\(664\) 20.6681 29.9949i 0.802079 1.16403i
\(665\) 10.1694i 0.394353i
\(666\) 0 0
\(667\) 31.4246 1.21676
\(668\) 1.04275 + 8.54918i 0.0403450 + 0.330778i
\(669\) 0 0
\(670\) 38.5966 43.5903i 1.49112 1.68404i
\(671\) −1.85434 −0.0715861
\(672\) 0 0
\(673\) −30.3154 −1.16857 −0.584287 0.811547i \(-0.698626\pi\)
−0.584287 + 0.811547i \(0.698626\pi\)
\(674\) 8.25878 9.32731i 0.318116 0.359275i
\(675\) 0 0
\(676\) −3.08939 25.3291i −0.118823 0.974196i
\(677\) 25.5344 0.981368 0.490684 0.871338i \(-0.336747\pi\)
0.490684 + 0.871338i \(0.336747\pi\)
\(678\) 0 0
\(679\) 7.51246i 0.288302i
\(680\) −41.5329 + 60.2752i −1.59271 + 2.31145i
\(681\) 0 0
\(682\) −8.52512 + 9.62810i −0.326444 + 0.368679i
\(683\) 42.9534i 1.64357i −0.569799 0.821784i \(-0.692979\pi\)
0.569799 0.821784i \(-0.307021\pi\)
\(684\) 0 0
\(685\) 43.4189i 1.65895i
\(686\) 1.05881 + 0.937511i 0.0404255 + 0.0357943i
\(687\) 0 0
\(688\) 28.3570 7.02188i 1.08110 0.267707i
\(689\) 1.53514i 0.0584842i
\(690\) 0 0
\(691\) 30.2219 1.14970 0.574848 0.818260i \(-0.305061\pi\)
0.574848 + 0.818260i \(0.305061\pi\)
\(692\) 2.01745 + 16.5405i 0.0766921 + 0.628777i
\(693\) 0 0
\(694\) 19.5991 + 17.3538i 0.743971 + 0.658742i
\(695\) −15.6523 −0.593727
\(696\) 0 0
\(697\) 20.3493 0.770785
\(698\) 3.21847 + 2.84977i 0.121821 + 0.107865i
\(699\) 0 0
\(700\) 27.4710 3.35065i 1.03831 0.126643i
\(701\) −47.5750 −1.79688 −0.898441 0.439094i \(-0.855300\pi\)
−0.898441 + 0.439094i \(0.855300\pi\)
\(702\) 0 0
\(703\) 1.75798i 0.0663034i
\(704\) −8.41949 + 3.20871i −0.317321 + 0.120933i
\(705\) 0 0
\(706\) −18.0156 15.9517i −0.678026 0.600351i
\(707\) 12.2496i 0.460694i
\(708\) 0 0
\(709\) 5.97537i 0.224410i −0.993685 0.112205i \(-0.964209\pi\)
0.993685 0.112205i \(-0.0357913\pi\)
\(710\) −37.2083 + 42.0224i −1.39640 + 1.57707i
\(711\) 0 0
\(712\) −20.8272 + 30.2257i −0.780531 + 1.13276i
\(713\) 53.9485i 2.02039i
\(714\) 0 0
\(715\) −2.40269 −0.0898555
\(716\) −8.75055 + 1.06731i −0.327023 + 0.0398871i
\(717\) 0 0
\(718\) −10.1013 + 11.4082i −0.376977 + 0.425751i
\(719\) −15.5907 −0.581434 −0.290717 0.956809i \(-0.593894\pi\)
−0.290717 + 0.956809i \(0.593894\pi\)
\(720\) 0 0
\(721\) 4.29883 0.160097
\(722\) 12.6658 14.3045i 0.471371 0.532357i
\(723\) 0 0
\(724\) −28.4114 + 3.46535i −1.05590 + 0.128789i
\(725\) 65.0761 2.41687
\(726\) 0 0
\(727\) 37.3382i 1.38480i −0.721515 0.692399i \(-0.756554\pi\)
0.721515 0.692399i \(-0.243446\pi\)
\(728\) 1.14478 + 0.788818i 0.0424285 + 0.0292355i
\(729\) 0 0
\(730\) 10.8140 12.2132i 0.400245 0.452029i
\(731\) 43.5485i 1.61070i
\(732\) 0 0
\(733\) 2.18169i 0.0805825i −0.999188 0.0402912i \(-0.987171\pi\)
0.999188 0.0402912i \(-0.0128286\pi\)
\(734\) 7.17925 + 6.35680i 0.264991 + 0.234634i
\(735\) 0 0
\(736\) 17.5206 33.4926i 0.645819 1.23455i
\(737\) 10.6834i 0.393526i
\(738\) 0 0
\(739\) −9.14831 −0.336526 −0.168263 0.985742i \(-0.553816\pi\)
−0.168263 + 0.985742i \(0.553816\pi\)
\(740\) −6.46486 + 0.788521i −0.237653 + 0.0289866i
\(741\) 0 0
\(742\) 3.30690 + 2.92806i 0.121400 + 0.107493i
\(743\) −19.6022 −0.719134 −0.359567 0.933119i \(-0.617076\pi\)
−0.359567 + 0.933119i \(0.617076\pi\)
\(744\) 0 0
\(745\) −38.5009 −1.41056
\(746\) −19.7946 17.5270i −0.724733 0.641708i
\(747\) 0 0
\(748\) −1.62619 13.3327i −0.0594594 0.487491i
\(749\) 18.4871 0.675502
\(750\) 0 0
\(751\) 27.9656i 1.02048i −0.860032 0.510240i \(-0.829556\pi\)
0.860032 0.510240i \(-0.170444\pi\)
\(752\) −36.7861 + 9.10914i −1.34145 + 0.332176i
\(753\) 0 0
\(754\) 2.44755 + 2.16716i 0.0891344 + 0.0789232i
\(755\) 1.70844i 0.0621764i
\(756\) 0 0
\(757\) 34.1370i 1.24073i −0.784312 0.620366i \(-0.786984\pi\)
0.784312 0.620366i \(-0.213016\pi\)
\(758\) −26.7579 + 30.2198i −0.971889 + 1.09763i
\(759\) 0 0
\(760\) −23.6851 16.3203i −0.859149 0.592000i
\(761\) 49.4689i 1.79325i 0.442795 + 0.896623i \(0.353987\pi\)
−0.442795 + 0.896623i \(0.646013\pi\)
\(762\) 0 0
\(763\) −8.41691 −0.304713
\(764\) −2.78588 22.8407i −0.100790 0.826347i
\(765\) 0 0
\(766\) 9.27127 10.4708i 0.334985 0.378325i
\(767\) −4.65684 −0.168149
\(768\) 0 0
\(769\) 3.30479 0.119174 0.0595868 0.998223i \(-0.481022\pi\)
0.0595868 + 0.998223i \(0.481022\pi\)
\(770\) −4.58279 + 5.17572i −0.165152 + 0.186520i
\(771\) 0 0
\(772\) −0.0150001 0.122982i −0.000539865 0.00442621i
\(773\) −20.4350 −0.734995 −0.367498 0.930024i \(-0.619785\pi\)
−0.367498 + 0.930024i \(0.619785\pi\)
\(774\) 0 0
\(775\) 111.720i 4.01310i
\(776\) −17.4969 12.0563i −0.628102 0.432797i
\(777\) 0 0
\(778\) −9.92572 + 11.2099i −0.355854 + 0.401895i
\(779\) 7.99625i 0.286495i
\(780\) 0 0
\(781\) 10.2991i 0.368530i
\(782\) 42.1858 + 37.3531i 1.50856 + 1.33574i
\(783\) 0 0
\(784\) 3.88273 0.961458i 0.138669 0.0343378i
\(785\) 55.6935i 1.98779i
\(786\) 0 0
\(787\) 38.8368 1.38438 0.692192 0.721713i \(-0.256645\pi\)
0.692192 + 0.721713i \(0.256645\pi\)
\(788\) −3.64760 29.9057i −0.129940 1.06535i
\(789\) 0 0
\(790\) 26.4077 + 23.3825i 0.939545 + 0.831911i
\(791\) 14.1717 0.503889
\(792\) 0 0
\(793\) 0.809264 0.0287378
\(794\) −12.5616 11.1225i −0.445794 0.394724i
\(795\) 0 0
\(796\) −19.4735 + 2.37519i −0.690220 + 0.0841862i
\(797\) 20.3591 0.721157 0.360578 0.932729i \(-0.382579\pi\)
0.360578 + 0.932729i \(0.382579\pi\)
\(798\) 0 0
\(799\) 56.4933i 1.99859i
\(800\) 36.2829 69.3587i 1.28279 2.45220i
\(801\) 0 0
\(802\) −12.9976 11.5086i −0.458960 0.406382i
\(803\) 2.99327i 0.105630i
\(804\) 0 0
\(805\) 29.0007i 1.02214i
\(806\) 3.72049 4.20185i 0.131049 0.148004i
\(807\) 0 0
\(808\) 28.5299 + 19.6587i 1.00368 + 0.691590i
\(809\) 51.7428i 1.81918i 0.415505 + 0.909591i \(0.363605\pi\)
−0.415505 + 0.909591i \(0.636395\pi\)
\(810\) 0 0
\(811\) −53.4436 −1.87666 −0.938329 0.345744i \(-0.887627\pi\)
−0.938329 + 0.345744i \(0.887627\pi\)
\(812\) 9.33670 1.13880i 0.327654 0.0399640i
\(813\) 0 0
\(814\) 0.792222 0.894721i 0.0277674 0.0313600i
\(815\) 32.6360 1.14319
\(816\) 0 0
\(817\) −17.1123 −0.598685
\(818\) −1.75353 + 1.98040i −0.0613108 + 0.0692432i
\(819\) 0 0
\(820\) −29.4058 + 3.58663i −1.02689 + 0.125250i
\(821\) 24.1628 0.843289 0.421644 0.906761i \(-0.361453\pi\)
0.421644 + 0.906761i \(0.361453\pi\)
\(822\) 0 0
\(823\) 23.3024i 0.812270i 0.913813 + 0.406135i \(0.133124\pi\)
−0.913813 + 0.406135i \(0.866876\pi\)
\(824\) 6.89895 10.0122i 0.240336 0.348792i
\(825\) 0 0
\(826\) −8.88226 + 10.0315i −0.309053 + 0.349039i
\(827\) 24.6097i 0.855764i −0.903835 0.427882i \(-0.859260\pi\)
0.903835 0.427882i \(-0.140740\pi\)
\(828\) 0 0
\(829\) 50.5634i 1.75614i 0.478534 + 0.878069i \(0.341168\pi\)
−0.478534 + 0.878069i \(0.658832\pi\)
\(830\) −59.1827 52.4028i −2.05426 1.81893i
\(831\) 0 0
\(832\) 3.67439 1.40033i 0.127387 0.0485477i
\(833\) 5.96280i 0.206599i
\(834\) 0 0
\(835\) 18.6901 0.646796
\(836\) 5.23907 0.639010i 0.181197 0.0221006i
\(837\) 0 0
\(838\) −4.98665 4.41538i −0.172261 0.152527i
\(839\) 10.4578 0.361042 0.180521 0.983571i \(-0.442222\pi\)
0.180521 + 0.983571i \(0.442222\pi\)
\(840\) 0 0
\(841\) −6.88230 −0.237321
\(842\) −3.39943 3.01000i −0.117152 0.103731i
\(843\) 0 0
\(844\) −1.73742 14.2446i −0.0598045 0.490321i
\(845\) −55.3740 −1.90492
\(846\) 0 0
\(847\) 9.73151i 0.334379i
\(848\) 12.1267 3.00285i 0.416431 0.103118i
\(849\) 0 0
\(850\) 87.3612 + 77.3532i 2.99646 + 2.65319i
\(851\) 5.01333i 0.171855i
\(852\) 0 0
\(853\) 48.5133i 1.66106i 0.556971 + 0.830532i \(0.311963\pi\)
−0.556971 + 0.830532i \(0.688037\pi\)
\(854\) 1.54356 1.74326i 0.0528194 0.0596533i
\(855\) 0 0
\(856\) 29.6688 43.0573i 1.01406 1.47167i
\(857\) 26.0672i 0.890437i −0.895422 0.445219i \(-0.853126\pi\)
0.895422 0.445219i \(-0.146874\pi\)
\(858\) 0 0
\(859\) 20.1390 0.687133 0.343567 0.939128i \(-0.388365\pi\)
0.343567 + 0.939128i \(0.388365\pi\)
\(860\) −7.67555 62.9297i −0.261734 2.14588i
\(861\) 0 0
\(862\) 0.118800 0.134170i 0.00404634 0.00456986i
\(863\) 12.6122 0.429323 0.214662 0.976689i \(-0.431135\pi\)
0.214662 + 0.976689i \(0.431135\pi\)
\(864\) 0 0
\(865\) 36.1606 1.22950
\(866\) 1.20219 1.35773i 0.0408522 0.0461377i
\(867\) 0 0
\(868\) −1.95505 16.0289i −0.0663586 0.544056i
\(869\) −6.47215 −0.219553
\(870\) 0 0
\(871\) 4.66238i 0.157979i
\(872\) −13.5078 + 19.6034i −0.457433 + 0.663855i
\(873\) 0 0
\(874\) −14.6779 + 16.5769i −0.496486 + 0.560722i
\(875\) 38.3556i 1.29666i
\(876\) 0 0
\(877\) 44.9111i 1.51654i 0.651940 + 0.758270i \(0.273955\pi\)
−0.651940 + 0.758270i \(0.726045\pi\)
\(878\) 29.6348 + 26.2398i 1.00012 + 0.885551i
\(879\) 0 0
\(880\) 4.69985 + 18.9798i 0.158432 + 0.639808i
\(881\) 46.5834i 1.56943i 0.619854 + 0.784717i \(0.287192\pi\)
−0.619854 + 0.784717i \(0.712808\pi\)
\(882\) 0 0
\(883\) −29.5508 −0.994463 −0.497232 0.867618i \(-0.665650\pi\)
−0.497232 + 0.867618i \(0.665650\pi\)
\(884\) 0.709695 + 5.81859i 0.0238696 + 0.195700i
\(885\) 0 0
\(886\) 3.26307 + 2.88926i 0.109625 + 0.0970664i
\(887\) 22.8412 0.766932 0.383466 0.923555i \(-0.374730\pi\)
0.383466 + 0.923555i \(0.374730\pi\)
\(888\) 0 0
\(889\) 17.0394 0.571483
\(890\) 59.6382 + 52.8060i 1.99908 + 1.77006i
\(891\) 0 0
\(892\) 4.09532 0.499507i 0.137121 0.0167247i
\(893\) 22.1990 0.742862
\(894\) 0 0
\(895\) 19.1303i 0.639454i
\(896\) 3.99189 10.5861i 0.133360 0.353656i
\(897\) 0 0
\(898\) 10.2015 + 9.03281i 0.340428 + 0.301429i
\(899\) 37.9708i 1.26640i
\(900\) 0 0
\(901\) 18.6232i 0.620428i
\(902\) 3.60346 4.06968i 0.119982 0.135506i
\(903\) 0 0
\(904\) 22.7434 33.0067i 0.756435 1.09779i
\(905\) 62.1125i 2.06469i
\(906\) 0 0
\(907\) 24.9022 0.826864 0.413432 0.910535i \(-0.364330\pi\)
0.413432 + 0.910535i \(0.364330\pi\)
\(908\) 40.8301 4.98005i 1.35499 0.165269i
\(909\) 0 0
\(910\) 2.00000 2.25876i 0.0662994 0.0748772i
\(911\) 12.2059 0.404401 0.202200 0.979344i \(-0.435191\pi\)
0.202200 + 0.979344i \(0.435191\pi\)
\(912\) 0 0
\(913\) 14.5048 0.480040
\(914\) 7.89384 8.91516i 0.261105 0.294887i
\(915\) 0 0
\(916\) 29.6396 3.61515i 0.979319 0.119448i
\(917\) −4.87851 −0.161103
\(918\) 0 0
\(919\) 29.0260i 0.957480i 0.877957 + 0.478740i \(0.158906\pi\)
−0.877957 + 0.478740i \(0.841094\pi\)
\(920\) −67.5442 46.5416i −2.22687 1.53443i
\(921\) 0 0
\(922\) 1.59136 1.79725i 0.0524085 0.0591892i
\(923\) 4.49467i 0.147944i
\(924\) 0 0
\(925\) 10.3819i 0.341356i
\(926\) 28.3641 + 25.1147i 0.932103 + 0.825322i
\(927\) 0 0
\(928\) 12.3316 23.5732i 0.404805 0.773830i
\(929\) 0.717723i 0.0235477i 0.999931 + 0.0117739i \(0.00374782\pi\)
−0.999931 + 0.0117739i \(0.996252\pi\)
\(930\) 0 0
\(931\) −2.34308 −0.0767913
\(932\) 28.5260 3.47932i 0.934399 0.113969i
\(933\) 0 0
\(934\) −14.3327 12.6907i −0.468979 0.415253i
\(935\) −29.1477 −0.953230
\(936\) 0 0
\(937\) −36.3608 −1.18785 −0.593927 0.804519i \(-0.702423\pi\)
−0.593927 + 0.804519i \(0.702423\pi\)
\(938\) −10.0434 8.89283i −0.327928 0.290361i
\(939\) 0 0
\(940\) 9.95711 + 81.6356i 0.324765 + 2.66266i
\(941\) 22.6783 0.739290 0.369645 0.929173i \(-0.379479\pi\)
0.369645 + 0.929173i \(0.379479\pi\)
\(942\) 0 0
\(943\) 22.8034i 0.742580i
\(944\) 9.10914 + 36.7861i 0.296477 + 1.19729i
\(945\) 0 0
\(946\) 8.70931 + 7.71158i 0.283164 + 0.250725i
\(947\) 14.8231i 0.481685i −0.970564 0.240842i \(-0.922576\pi\)
0.970564 0.240842i \(-0.0774237\pi\)
\(948\) 0 0
\(949\) 1.30631i 0.0424046i
\(950\) −30.3959 + 34.3285i −0.986172 + 1.11376i
\(951\) 0 0
\(952\) 13.8877 + 9.56936i 0.450102 + 0.310145i
\(953\) 3.80423i 0.123231i 0.998100 + 0.0616155i \(0.0196253\pi\)
−0.998100 + 0.0616155i \(0.980375\pi\)
\(954\) 0 0
\(955\) −49.9339 −1.61582
\(956\) −3.95744 32.4460i −0.127993 1.04938i
\(957\) 0 0
\(958\) 2.73209 3.08557i 0.0882699 0.0996904i
\(959\) −10.0039 −0.323043
\(960\) 0 0
\(961\) −34.1868 −1.10280
\(962\) −0.345738 + 0.390470i −0.0111470 + 0.0125893i
\(963\) 0 0
\(964\) −0.110423 0.905330i −0.00355649 0.0291587i
\(965\) −0.268860 −0.00865491
\(966\) 0 0
\(967\) 11.2095i 0.360474i 0.983623 + 0.180237i \(0.0576865\pi\)
−0.983623 + 0.180237i \(0.942313\pi\)
\(968\) 22.6652 + 15.6175i 0.728486 + 0.501967i
\(969\) 0 0
\(970\) −30.5681 + 34.5230i −0.981481 + 1.10847i
\(971\) 50.7626i 1.62905i 0.580129 + 0.814525i \(0.303002\pi\)
−0.580129 + 0.814525i \(0.696998\pi\)
\(972\) 0 0
\(973\) 3.60637i 0.115615i
\(974\) −31.5333 27.9209i −1.01039 0.894642i
\(975\) 0 0
\(976\) −1.58298 6.39269i −0.0506701 0.204625i
\(977\) 28.4952i 0.911644i −0.890071 0.455822i \(-0.849345\pi\)
0.890071 0.455822i \(-0.150655\pi\)
\(978\) 0 0
\(979\) −14.6164 −0.467144
\(980\) −1.05096 8.61654i −0.0335717 0.275245i
\(981\) 0 0
\(982\) 21.0462 + 18.6352i 0.671612 + 0.594673i
\(983\) −19.8866 −0.634283 −0.317142 0.948378i \(-0.602723\pi\)
−0.317142 + 0.948378i \(0.602723\pi\)
\(984\) 0 0
\(985\) −65.3792 −2.08315
\(986\) 29.6918 + 26.2904i 0.945581 + 0.837256i
\(987\) 0 0
\(988\) −2.28641 + 0.278874i −0.0727404 + 0.00887216i
\(989\) −48.8003 −1.55176
\(990\) 0 0
\(991\) 14.1816i 0.450493i −0.974302 0.225246i \(-0.927681\pi\)
0.974302 0.225246i \(-0.0723187\pi\)
\(992\) −40.4696 21.1704i −1.28491 0.672162i
\(993\) 0 0
\(994\) 9.68213 + 8.57295i 0.307099 + 0.271918i
\(995\) 42.5726i 1.34964i
\(996\) 0 0
\(997\) 26.5442i 0.840663i 0.907371 + 0.420331i \(0.138086\pi\)
−0.907371 + 0.420331i \(0.861914\pi\)
\(998\) 27.5115 31.0709i 0.870861 0.983534i
\(999\) 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 504.2.j.a.323.6 yes 24
3.2 odd 2 inner 504.2.j.a.323.19 yes 24
4.3 odd 2 2016.2.j.a.1583.2 24
8.3 odd 2 inner 504.2.j.a.323.20 yes 24
8.5 even 2 2016.2.j.a.1583.24 24
12.11 even 2 2016.2.j.a.1583.23 24
24.5 odd 2 2016.2.j.a.1583.1 24
24.11 even 2 inner 504.2.j.a.323.5 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.j.a.323.5 24 24.11 even 2 inner
504.2.j.a.323.6 yes 24 1.1 even 1 trivial
504.2.j.a.323.19 yes 24 3.2 odd 2 inner
504.2.j.a.323.20 yes 24 8.3 odd 2 inner
2016.2.j.a.1583.1 24 24.5 odd 2
2016.2.j.a.1583.2 24 4.3 odd 2
2016.2.j.a.1583.23 24 12.11 even 2
2016.2.j.a.1583.24 24 8.5 even 2