Properties

Label 624.2.cn.f.305.9
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
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] = [624,2,Mod(305,624)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(624, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("624.305");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not 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: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 305.9
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.386983 - 1.68827i) q^{3} +(1.56802 + 1.56802i) q^{5} +(0.418596 - 1.56222i) q^{7} +(-2.70049 - 1.30666i) q^{9} +O(q^{10})\) \(q+(0.386983 - 1.68827i) q^{3} +(1.56802 + 1.56802i) q^{5} +(0.418596 - 1.56222i) q^{7} +(-2.70049 - 1.30666i) q^{9} +(-0.781891 - 2.91806i) q^{11} +(-1.23090 - 3.38894i) q^{13} +(3.25403 - 2.04044i) q^{15} +(1.03846 + 1.79867i) q^{17} +(1.13167 + 0.303230i) q^{19} +(-2.47546 - 1.31126i) q^{21} +(2.51856 - 4.36228i) q^{23} -0.0826334i q^{25} +(-3.25104 + 4.05349i) q^{27} +(6.68935 + 3.86210i) q^{29} +(4.19633 - 4.19633i) q^{31} +(-5.22904 + 0.190802i) q^{33} +(3.10596 - 1.79323i) q^{35} +(1.42771 - 0.382554i) q^{37} +(-6.19776 + 0.766626i) q^{39} +(-1.36535 + 0.365846i) q^{41} +(-4.27542 + 2.46841i) q^{43} +(-2.18555 - 6.28329i) q^{45} +(-6.89160 + 6.89160i) q^{47} +(3.79686 + 2.19212i) q^{49} +(3.43850 - 1.05715i) q^{51} -9.85591i q^{53} +(3.34955 - 5.80159i) q^{55} +(0.949870 - 1.79321i) q^{57} +(-13.8606 - 3.71393i) q^{59} +(-5.63954 - 9.76798i) q^{61} +(-3.17171 + 3.67180i) q^{63} +(3.38384 - 7.24399i) q^{65} +(1.67035 + 6.23384i) q^{67} +(-6.39005 - 5.94013i) q^{69} +(-1.21689 + 4.54151i) q^{71} +(11.7107 + 11.7107i) q^{73} +(-0.139507 - 0.0319777i) q^{75} -4.88595 q^{77} +2.81772 q^{79} +(5.58527 + 7.05725i) q^{81} +(7.24736 + 7.24736i) q^{83} +(-1.19202 + 4.44868i) q^{85} +(9.10892 - 9.79884i) q^{87} +(1.86361 + 6.95510i) q^{89} +(-5.80952 + 0.504343i) q^{91} +(-5.46062 - 8.70843i) q^{93} +(1.29901 + 2.24995i) q^{95} +(10.6203 + 2.84569i) q^{97} +(-1.70142 + 8.90184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 4 q^{7} + 8 q^{13} + 8 q^{15} - 4 q^{19} + 16 q^{21} - 24 q^{27} + 36 q^{31} + 28 q^{33} + 20 q^{37} - 16 q^{39} + 84 q^{43} + 12 q^{45} - 12 q^{49} + 24 q^{55} - 36 q^{57} - 24 q^{61} + 12 q^{63} + 32 q^{67} - 36 q^{69} - 20 q^{73} + 60 q^{75} + 32 q^{79} - 88 q^{85} + 16 q^{87} - 28 q^{91} - 88 q^{93} - 36 q^{97} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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 0
\(3\) 0.386983 1.68827i 0.223425 0.974721i
\(4\) 0 0
\(5\) 1.56802 + 1.56802i 0.701239 + 0.701239i 0.964677 0.263437i \(-0.0848562\pi\)
−0.263437 + 0.964677i \(0.584856\pi\)
\(6\) 0 0
\(7\) 0.418596 1.56222i 0.158214 0.590464i −0.840594 0.541665i \(-0.817794\pi\)
0.998809 0.0487989i \(-0.0155394\pi\)
\(8\) 0 0
\(9\) −2.70049 1.30666i −0.900163 0.435554i
\(10\) 0 0
\(11\) −0.781891 2.91806i −0.235749 0.879827i −0.977810 0.209495i \(-0.932818\pi\)
0.742061 0.670332i \(-0.233849\pi\)
\(12\) 0 0
\(13\) −1.23090 3.38894i −0.341390 0.939922i
\(14\) 0 0
\(15\) 3.25403 2.04044i 0.840187 0.526839i
\(16\) 0 0
\(17\) 1.03846 + 1.79867i 0.251864 + 0.436242i 0.964039 0.265760i \(-0.0856230\pi\)
−0.712175 + 0.702002i \(0.752290\pi\)
\(18\) 0 0
\(19\) 1.13167 + 0.303230i 0.259623 + 0.0695657i 0.386283 0.922381i \(-0.373759\pi\)
−0.126660 + 0.991946i \(0.540426\pi\)
\(20\) 0 0
\(21\) −2.47546 1.31126i −0.540189 0.286139i
\(22\) 0 0
\(23\) 2.51856 4.36228i 0.525157 0.909598i −0.474414 0.880302i \(-0.657340\pi\)
0.999571 0.0292962i \(-0.00932662\pi\)
\(24\) 0 0
\(25\) 0.0826334i 0.0165267i
\(26\) 0 0
\(27\) −3.25104 + 4.05349i −0.625662 + 0.780094i
\(28\) 0 0
\(29\) 6.68935 + 3.86210i 1.24218 + 0.717174i 0.969538 0.244941i \(-0.0787688\pi\)
0.272643 + 0.962115i \(0.412102\pi\)
\(30\) 0 0
\(31\) 4.19633 4.19633i 0.753683 0.753683i −0.221481 0.975165i \(-0.571089\pi\)
0.975165 + 0.221481i \(0.0710892\pi\)
\(32\) 0 0
\(33\) −5.22904 + 0.190802i −0.910258 + 0.0332144i
\(34\) 0 0
\(35\) 3.10596 1.79323i 0.525003 0.303111i
\(36\) 0 0
\(37\) 1.42771 0.382554i 0.234714 0.0628915i −0.139545 0.990216i \(-0.544564\pi\)
0.374259 + 0.927324i \(0.377897\pi\)
\(38\) 0 0
\(39\) −6.19776 + 0.766626i −0.992437 + 0.122758i
\(40\) 0 0
\(41\) −1.36535 + 0.365846i −0.213232 + 0.0571355i −0.363854 0.931456i \(-0.618539\pi\)
0.150621 + 0.988592i \(0.451873\pi\)
\(42\) 0 0
\(43\) −4.27542 + 2.46841i −0.651995 + 0.376430i −0.789220 0.614110i \(-0.789515\pi\)
0.137225 + 0.990540i \(0.456182\pi\)
\(44\) 0 0
\(45\) −2.18555 6.28329i −0.325802 0.936657i
\(46\) 0 0
\(47\) −6.89160 + 6.89160i −1.00524 + 1.00524i −0.00525705 + 0.999986i \(0.501673\pi\)
−0.999986 + 0.00525705i \(0.998327\pi\)
\(48\) 0 0
\(49\) 3.79686 + 2.19212i 0.542409 + 0.313160i
\(50\) 0 0
\(51\) 3.43850 1.05715i 0.481487 0.148030i
\(52\) 0 0
\(53\) 9.85591i 1.35381i −0.736069 0.676907i \(-0.763320\pi\)
0.736069 0.676907i \(-0.236680\pi\)
\(54\) 0 0
\(55\) 3.34955 5.80159i 0.451653 0.782286i
\(56\) 0 0
\(57\) 0.949870 1.79321i 0.125813 0.237517i
\(58\) 0 0
\(59\) −13.8606 3.71393i −1.80449 0.483513i −0.809829 0.586666i \(-0.800440\pi\)
−0.994665 + 0.103154i \(0.967107\pi\)
\(60\) 0 0
\(61\) −5.63954 9.76798i −0.722070 1.25066i −0.960169 0.279420i \(-0.909858\pi\)
0.238099 0.971241i \(-0.423476\pi\)
\(62\) 0 0
\(63\) −3.17171 + 3.67180i −0.399598 + 0.462603i
\(64\) 0 0
\(65\) 3.38384 7.24399i 0.419714 0.898506i
\(66\) 0 0
\(67\) 1.67035 + 6.23384i 0.204066 + 0.761585i 0.989732 + 0.142934i \(0.0456538\pi\)
−0.785666 + 0.618651i \(0.787680\pi\)
\(68\) 0 0
\(69\) −6.39005 5.94013i −0.769271 0.715108i
\(70\) 0 0
\(71\) −1.21689 + 4.54151i −0.144419 + 0.538978i 0.855362 + 0.518031i \(0.173335\pi\)
−0.999781 + 0.0209472i \(0.993332\pi\)
\(72\) 0 0
\(73\) 11.7107 + 11.7107i 1.37063 + 1.37063i 0.859504 + 0.511130i \(0.170773\pi\)
0.511130 + 0.859504i \(0.329227\pi\)
\(74\) 0 0
\(75\) −0.139507 0.0319777i −0.0161089 0.00369247i
\(76\) 0 0
\(77\) −4.88595 −0.556805
\(78\) 0 0
\(79\) 2.81772 0.317018 0.158509 0.987358i \(-0.449331\pi\)
0.158509 + 0.987358i \(0.449331\pi\)
\(80\) 0 0
\(81\) 5.58527 + 7.05725i 0.620586 + 0.784138i
\(82\) 0 0
\(83\) 7.24736 + 7.24736i 0.795501 + 0.795501i 0.982382 0.186882i \(-0.0598381\pi\)
−0.186882 + 0.982382i \(0.559838\pi\)
\(84\) 0 0
\(85\) −1.19202 + 4.44868i −0.129293 + 0.482527i
\(86\) 0 0
\(87\) 9.10892 9.79884i 0.976578 1.05055i
\(88\) 0 0
\(89\) 1.86361 + 6.95510i 0.197543 + 0.737239i 0.991594 + 0.129388i \(0.0413014\pi\)
−0.794051 + 0.607851i \(0.792032\pi\)
\(90\) 0 0
\(91\) −5.80952 + 0.504343i −0.609003 + 0.0528695i
\(92\) 0 0
\(93\) −5.46062 8.70843i −0.566240 0.903023i
\(94\) 0 0
\(95\) 1.29901 + 2.24995i 0.133275 + 0.230840i
\(96\) 0 0
\(97\) 10.6203 + 2.84569i 1.07833 + 0.288936i 0.753910 0.656978i \(-0.228166\pi\)
0.324416 + 0.945915i \(0.394832\pi\)
\(98\) 0 0
\(99\) −1.70142 + 8.90184i −0.170999 + 0.894669i
\(100\) 0 0
\(101\) −4.73271 + 8.19730i −0.470923 + 0.815662i −0.999447 0.0332563i \(-0.989412\pi\)
0.528524 + 0.848918i \(0.322746\pi\)
\(102\) 0 0
\(103\) 14.2389i 1.40300i 0.712671 + 0.701498i \(0.247485\pi\)
−0.712671 + 0.701498i \(0.752515\pi\)
\(104\) 0 0
\(105\) −1.82549 5.93764i −0.178150 0.579454i
\(106\) 0 0
\(107\) 1.98557 + 1.14637i 0.191952 + 0.110824i 0.592896 0.805279i \(-0.297984\pi\)
−0.400944 + 0.916103i \(0.631318\pi\)
\(108\) 0 0
\(109\) 3.09877 3.09877i 0.296809 0.296809i −0.542954 0.839763i \(-0.682694\pi\)
0.839763 + 0.542954i \(0.182694\pi\)
\(110\) 0 0
\(111\) −0.0933533 2.55840i −0.00886070 0.242833i
\(112\) 0 0
\(113\) −15.6225 + 9.01967i −1.46964 + 0.848499i −0.999420 0.0340476i \(-0.989160\pi\)
−0.470224 + 0.882547i \(0.655827\pi\)
\(114\) 0 0
\(115\) 10.7893 2.89098i 1.00611 0.269585i
\(116\) 0 0
\(117\) −1.10416 + 10.7602i −0.102080 + 0.994776i
\(118\) 0 0
\(119\) 3.24462 0.869393i 0.297434 0.0796972i
\(120\) 0 0
\(121\) 1.62258 0.936798i 0.147507 0.0851634i
\(122\) 0 0
\(123\) 0.0892760 + 2.44666i 0.00804974 + 0.220608i
\(124\) 0 0
\(125\) 7.96967 7.96967i 0.712829 0.712829i
\(126\) 0 0
\(127\) 15.9524 + 9.21015i 1.41555 + 0.817268i 0.995904 0.0904193i \(-0.0288207\pi\)
0.419646 + 0.907688i \(0.362154\pi\)
\(128\) 0 0
\(129\) 2.51283 + 8.17328i 0.221242 + 0.719617i
\(130\) 0 0
\(131\) 10.6125i 0.927215i −0.886041 0.463608i \(-0.846555\pi\)
0.886041 0.463608i \(-0.153445\pi\)
\(132\) 0 0
\(133\) 0.947425 1.64099i 0.0821521 0.142292i
\(134\) 0 0
\(135\) −11.4536 + 1.25826i −0.985772 + 0.108294i
\(136\) 0 0
\(137\) 12.5864 + 3.37252i 1.07533 + 0.288134i 0.752682 0.658384i \(-0.228760\pi\)
0.322650 + 0.946519i \(0.395426\pi\)
\(138\) 0 0
\(139\) −5.10962 8.85012i −0.433392 0.750658i 0.563771 0.825931i \(-0.309350\pi\)
−0.997163 + 0.0752738i \(0.976017\pi\)
\(140\) 0 0
\(141\) 8.96793 + 14.3018i 0.755236 + 1.20443i
\(142\) 0 0
\(143\) −8.92668 + 6.24161i −0.746486 + 0.521950i
\(144\) 0 0
\(145\) 4.43319 + 16.5449i 0.368156 + 1.37398i
\(146\) 0 0
\(147\) 5.17020 5.56180i 0.426431 0.458730i
\(148\) 0 0
\(149\) −1.98820 + 7.42006i −0.162880 + 0.607875i 0.835422 + 0.549610i \(0.185224\pi\)
−0.998301 + 0.0582651i \(0.981443\pi\)
\(150\) 0 0
\(151\) 3.46798 + 3.46798i 0.282220 + 0.282220i 0.833994 0.551774i \(-0.186049\pi\)
−0.551774 + 0.833994i \(0.686049\pi\)
\(152\) 0 0
\(153\) −0.454105 6.21421i −0.0367122 0.502389i
\(154\) 0 0
\(155\) 13.1599 1.05702
\(156\) 0 0
\(157\) −3.70701 −0.295852 −0.147926 0.988998i \(-0.547260\pi\)
−0.147926 + 0.988998i \(0.547260\pi\)
\(158\) 0 0
\(159\) −16.6394 3.81407i −1.31959 0.302475i
\(160\) 0 0
\(161\) −5.76059 5.76059i −0.453998 0.453998i
\(162\) 0 0
\(163\) −3.50600 + 13.0846i −0.274611 + 1.02486i 0.681490 + 0.731827i \(0.261332\pi\)
−0.956101 + 0.293036i \(0.905334\pi\)
\(164\) 0 0
\(165\) −8.49841 7.90004i −0.661600 0.615018i
\(166\) 0 0
\(167\) −4.18631 15.6235i −0.323946 1.20898i −0.915367 0.402620i \(-0.868099\pi\)
0.591421 0.806363i \(-0.298567\pi\)
\(168\) 0 0
\(169\) −9.96977 + 8.34288i −0.766906 + 0.641760i
\(170\) 0 0
\(171\) −2.65984 2.29758i −0.203403 0.175700i
\(172\) 0 0
\(173\) −9.88581 17.1227i −0.751604 1.30182i −0.947045 0.321101i \(-0.895947\pi\)
0.195440 0.980716i \(-0.437386\pi\)
\(174\) 0 0
\(175\) −0.129092 0.0345900i −0.00975841 0.00261476i
\(176\) 0 0
\(177\) −11.6339 + 21.9631i −0.874459 + 1.65085i
\(178\) 0 0
\(179\) −1.41662 + 2.45366i −0.105883 + 0.183395i −0.914099 0.405492i \(-0.867100\pi\)
0.808216 + 0.588887i \(0.200434\pi\)
\(180\) 0 0
\(181\) 8.14854i 0.605676i 0.953042 + 0.302838i \(0.0979341\pi\)
−0.953042 + 0.302838i \(0.902066\pi\)
\(182\) 0 0
\(183\) −18.6734 + 5.74101i −1.38037 + 0.424388i
\(184\) 0 0
\(185\) 2.83853 + 1.63883i 0.208693 + 0.120489i
\(186\) 0 0
\(187\) 4.43666 4.43666i 0.324441 0.324441i
\(188\) 0 0
\(189\) 4.97158 + 6.77561i 0.361629 + 0.492853i
\(190\) 0 0
\(191\) 14.8793 8.59056i 1.07663 0.621591i 0.146643 0.989190i \(-0.453153\pi\)
0.929985 + 0.367598i \(0.119820\pi\)
\(192\) 0 0
\(193\) −8.63779 + 2.31449i −0.621762 + 0.166601i −0.555929 0.831230i \(-0.687637\pi\)
−0.0658334 + 0.997831i \(0.520971\pi\)
\(194\) 0 0
\(195\) −10.9203 8.51613i −0.782019 0.609853i
\(196\) 0 0
\(197\) −9.64105 + 2.58331i −0.686897 + 0.184053i −0.585354 0.810778i \(-0.699044\pi\)
−0.101543 + 0.994831i \(0.532378\pi\)
\(198\) 0 0
\(199\) −2.76369 + 1.59562i −0.195913 + 0.113110i −0.594748 0.803912i \(-0.702748\pi\)
0.398835 + 0.917023i \(0.369415\pi\)
\(200\) 0 0
\(201\) 11.1708 0.407610i 0.787927 0.0287506i
\(202\) 0 0
\(203\) 8.83359 8.83359i 0.619997 0.619997i
\(204\) 0 0
\(205\) −2.71455 1.56725i −0.189593 0.109461i
\(206\) 0 0
\(207\) −12.5014 + 8.48938i −0.868905 + 0.590052i
\(208\) 0 0
\(209\) 3.53937i 0.244823i
\(210\) 0 0
\(211\) 1.83361 3.17591i 0.126231 0.218639i −0.795982 0.605320i \(-0.793045\pi\)
0.922214 + 0.386681i \(0.126379\pi\)
\(212\) 0 0
\(213\) 7.19637 + 3.81193i 0.493087 + 0.261189i
\(214\) 0 0
\(215\) −10.5745 2.83342i −0.721172 0.193237i
\(216\) 0 0
\(217\) −4.79903 8.31217i −0.325780 0.564267i
\(218\) 0 0
\(219\) 24.3026 15.2389i 1.64222 1.02975i
\(220\) 0 0
\(221\) 4.81734 5.73327i 0.324049 0.385661i
\(222\) 0 0
\(223\) 1.91856 + 7.16015i 0.128476 + 0.479479i 0.999940 0.0109811i \(-0.00349546\pi\)
−0.871464 + 0.490460i \(0.836829\pi\)
\(224\) 0 0
\(225\) −0.107974 + 0.223150i −0.00719825 + 0.0148767i
\(226\) 0 0
\(227\) −5.55618 + 20.7360i −0.368777 + 1.37629i 0.493451 + 0.869773i \(0.335735\pi\)
−0.862228 + 0.506520i \(0.830932\pi\)
\(228\) 0 0
\(229\) 0.0939698 + 0.0939698i 0.00620970 + 0.00620970i 0.710205 0.703995i \(-0.248602\pi\)
−0.703995 + 0.710205i \(0.748602\pi\)
\(230\) 0 0
\(231\) −1.89078 + 8.24878i −0.124404 + 0.542730i
\(232\) 0 0
\(233\) −28.0075 −1.83483 −0.917416 0.397929i \(-0.869729\pi\)
−0.917416 + 0.397929i \(0.869729\pi\)
\(234\) 0 0
\(235\) −21.6123 −1.40983
\(236\) 0 0
\(237\) 1.09041 4.75706i 0.0708297 0.309004i
\(238\) 0 0
\(239\) 5.71723 + 5.71723i 0.369817 + 0.369817i 0.867410 0.497594i \(-0.165783\pi\)
−0.497594 + 0.867410i \(0.665783\pi\)
\(240\) 0 0
\(241\) 3.57550 13.3439i 0.230318 0.859559i −0.749886 0.661568i \(-0.769891\pi\)
0.980204 0.197991i \(-0.0634418\pi\)
\(242\) 0 0
\(243\) 14.0759 6.69840i 0.902971 0.429702i
\(244\) 0 0
\(245\) 2.51627 + 9.39084i 0.160758 + 0.599959i
\(246\) 0 0
\(247\) −0.365345 4.20840i −0.0232463 0.267774i
\(248\) 0 0
\(249\) 15.0401 9.43087i 0.953126 0.597657i
\(250\) 0 0
\(251\) 11.7510 + 20.3533i 0.741716 + 1.28469i 0.951713 + 0.306988i \(0.0993211\pi\)
−0.209997 + 0.977702i \(0.567346\pi\)
\(252\) 0 0
\(253\) −14.6986 3.93848i −0.924094 0.247610i
\(254\) 0 0
\(255\) 7.04927 + 3.73401i 0.441442 + 0.233833i
\(256\) 0 0
\(257\) −1.32637 + 2.29733i −0.0827365 + 0.143304i −0.904424 0.426634i \(-0.859699\pi\)
0.821688 + 0.569938i \(0.193033\pi\)
\(258\) 0 0
\(259\) 2.39054i 0.148541i
\(260\) 0 0
\(261\) −13.0181 19.1703i −0.805798 1.18661i
\(262\) 0 0
\(263\) 17.6013 + 10.1621i 1.08534 + 0.626622i 0.932332 0.361603i \(-0.117770\pi\)
0.153009 + 0.988225i \(0.451104\pi\)
\(264\) 0 0
\(265\) 15.4543 15.4543i 0.949347 0.949347i
\(266\) 0 0
\(267\) 12.4632 0.454771i 0.762738 0.0278315i
\(268\) 0 0
\(269\) 21.7665 12.5669i 1.32712 0.766216i 0.342271 0.939601i \(-0.388804\pi\)
0.984854 + 0.173386i \(0.0554707\pi\)
\(270\) 0 0
\(271\) 9.61536 2.57643i 0.584092 0.156507i 0.0453401 0.998972i \(-0.485563\pi\)
0.538752 + 0.842465i \(0.318896\pi\)
\(272\) 0 0
\(273\) −1.39672 + 10.0032i −0.0845334 + 0.605421i
\(274\) 0 0
\(275\) −0.241129 + 0.0646103i −0.0145406 + 0.00389615i
\(276\) 0 0
\(277\) 11.9001 6.87054i 0.715009 0.412811i −0.0979039 0.995196i \(-0.531214\pi\)
0.812913 + 0.582385i \(0.197880\pi\)
\(278\) 0 0
\(279\) −16.8153 + 5.84896i −1.00671 + 0.350168i
\(280\) 0 0
\(281\) 3.32284 3.32284i 0.198224 0.198224i −0.601014 0.799238i \(-0.705237\pi\)
0.799238 + 0.601014i \(0.205237\pi\)
\(282\) 0 0
\(283\) −26.2042 15.1290i −1.55768 0.899326i −0.997478 0.0709694i \(-0.977391\pi\)
−0.560201 0.828357i \(-0.689276\pi\)
\(284\) 0 0
\(285\) 4.30121 1.32238i 0.254782 0.0783311i
\(286\) 0 0
\(287\) 2.28613i 0.134946i
\(288\) 0 0
\(289\) 6.34319 10.9867i 0.373129 0.646278i
\(290\) 0 0
\(291\) 8.91415 16.8286i 0.522557 0.986511i
\(292\) 0 0
\(293\) 15.2022 + 4.07340i 0.888119 + 0.237971i 0.673907 0.738816i \(-0.264615\pi\)
0.214212 + 0.976787i \(0.431282\pi\)
\(294\) 0 0
\(295\) −15.9101 27.5572i −0.926324 1.60444i
\(296\) 0 0
\(297\) 14.3703 + 6.31732i 0.833847 + 0.366568i
\(298\) 0 0
\(299\) −17.8836 3.16572i −1.03423 0.183078i
\(300\) 0 0
\(301\) 2.06654 + 7.71242i 0.119113 + 0.444537i
\(302\) 0 0
\(303\) 12.0077 + 11.1623i 0.689827 + 0.641257i
\(304\) 0 0
\(305\) 6.47346 24.1593i 0.370669 1.38336i
\(306\) 0 0
\(307\) 11.5169 + 11.5169i 0.657305 + 0.657305i 0.954742 0.297437i \(-0.0961318\pi\)
−0.297437 + 0.954742i \(0.596132\pi\)
\(308\) 0 0
\(309\) 24.0390 + 5.51020i 1.36753 + 0.313464i
\(310\) 0 0
\(311\) 7.59902 0.430901 0.215450 0.976515i \(-0.430878\pi\)
0.215450 + 0.976515i \(0.430878\pi\)
\(312\) 0 0
\(313\) −13.2916 −0.751284 −0.375642 0.926765i \(-0.622578\pi\)
−0.375642 + 0.926765i \(0.622578\pi\)
\(314\) 0 0
\(315\) −10.7307 + 0.784151i −0.604609 + 0.0441819i
\(316\) 0 0
\(317\) −8.03620 8.03620i −0.451358 0.451358i 0.444447 0.895805i \(-0.353400\pi\)
−0.895805 + 0.444447i \(0.853400\pi\)
\(318\) 0 0
\(319\) 6.03948 22.5396i 0.338146 1.26198i
\(320\) 0 0
\(321\) 2.70376 2.90855i 0.150909 0.162339i
\(322\) 0 0
\(323\) 0.629786 + 2.35039i 0.0350422 + 0.130779i
\(324\) 0 0
\(325\) −0.280039 + 0.101713i −0.0155338 + 0.00564204i
\(326\) 0 0
\(327\) −4.03238 6.43073i −0.222991 0.355620i
\(328\) 0 0
\(329\) 7.88141 + 13.6510i 0.434516 + 0.752604i
\(330\) 0 0
\(331\) −22.5940 6.05406i −1.24188 0.332761i −0.422686 0.906276i \(-0.638913\pi\)
−0.819195 + 0.573515i \(0.805579\pi\)
\(332\) 0 0
\(333\) −4.35539 0.832452i −0.238674 0.0456181i
\(334\) 0 0
\(335\) −7.15564 + 12.3939i −0.390954 + 0.677153i
\(336\) 0 0
\(337\) 3.48612i 0.189901i −0.995482 0.0949505i \(-0.969731\pi\)
0.995482 0.0949505i \(-0.0302693\pi\)
\(338\) 0 0
\(339\) 9.18196 + 29.8655i 0.498696 + 1.62207i
\(340\) 0 0
\(341\) −15.5262 8.96406i −0.840791 0.485431i
\(342\) 0 0
\(343\) 13.0193 13.0193i 0.702977 0.702977i
\(344\) 0 0
\(345\) −0.705476 19.3340i −0.0379815 1.04091i
\(346\) 0 0
\(347\) −6.26164 + 3.61516i −0.336142 + 0.194072i −0.658565 0.752524i \(-0.728836\pi\)
0.322422 + 0.946596i \(0.395503\pi\)
\(348\) 0 0
\(349\) 9.00361 2.41251i 0.481952 0.129139i −0.00965939 0.999953i \(-0.503075\pi\)
0.491611 + 0.870815i \(0.336408\pi\)
\(350\) 0 0
\(351\) 17.7387 + 6.02811i 0.946822 + 0.321757i
\(352\) 0 0
\(353\) −3.97036 + 1.06385i −0.211321 + 0.0566233i −0.362926 0.931818i \(-0.618222\pi\)
0.151605 + 0.988441i \(0.451556\pi\)
\(354\) 0 0
\(355\) −9.02929 + 5.21306i −0.479225 + 0.276681i
\(356\) 0 0
\(357\) −0.212155 5.81423i −0.0112284 0.307721i
\(358\) 0 0
\(359\) −0.612655 + 0.612655i −0.0323347 + 0.0323347i −0.723089 0.690755i \(-0.757278\pi\)
0.690755 + 0.723089i \(0.257278\pi\)
\(360\) 0 0
\(361\) −15.2658 8.81369i −0.803461 0.463878i
\(362\) 0 0
\(363\) −0.953653 3.10187i −0.0500538 0.162806i
\(364\) 0 0
\(365\) 36.7252i 1.92228i
\(366\) 0 0
\(367\) 6.17281 10.6916i 0.322218 0.558098i −0.658727 0.752382i \(-0.728905\pi\)
0.980945 + 0.194284i \(0.0622382\pi\)
\(368\) 0 0
\(369\) 4.16516 + 0.796093i 0.216829 + 0.0414430i
\(370\) 0 0
\(371\) −15.3971 4.12565i −0.799379 0.214193i
\(372\) 0 0
\(373\) −16.8205 29.1340i −0.870934 1.50850i −0.861032 0.508551i \(-0.830181\pi\)
−0.00990208 0.999951i \(-0.503152\pi\)
\(374\) 0 0
\(375\) −10.3708 16.5390i −0.535546 0.854073i
\(376\) 0 0
\(377\) 4.85449 27.4236i 0.250019 1.41239i
\(378\) 0 0
\(379\) 6.81176 + 25.4219i 0.349897 + 1.30583i 0.886786 + 0.462180i \(0.152933\pi\)
−0.536889 + 0.843653i \(0.680401\pi\)
\(380\) 0 0
\(381\) 21.7225 23.3678i 1.11288 1.19717i
\(382\) 0 0
\(383\) 9.04647 33.7619i 0.462253 1.72515i −0.203587 0.979057i \(-0.565260\pi\)
0.665840 0.746094i \(-0.268073\pi\)
\(384\) 0 0
\(385\) −7.66126 7.66126i −0.390454 0.390454i
\(386\) 0 0
\(387\) 14.7711 1.07940i 0.750857 0.0548690i
\(388\) 0 0
\(389\) −4.41992 −0.224099 −0.112049 0.993703i \(-0.535741\pi\)
−0.112049 + 0.993703i \(0.535741\pi\)
\(390\) 0 0
\(391\) 10.4617 0.529073
\(392\) 0 0
\(393\) −17.9167 4.10684i −0.903776 0.207163i
\(394\) 0 0
\(395\) 4.41824 + 4.41824i 0.222306 + 0.222306i
\(396\) 0 0
\(397\) −9.03870 + 33.7329i −0.453639 + 1.69300i 0.238419 + 0.971162i \(0.423371\pi\)
−0.692058 + 0.721842i \(0.743296\pi\)
\(398\) 0 0
\(399\) −2.40379 2.23454i −0.120340 0.111867i
\(400\) 0 0
\(401\) 2.67186 + 9.97150i 0.133426 + 0.497953i 0.999999 0.00109677i \(-0.000349113\pi\)
−0.866573 + 0.499050i \(0.833682\pi\)
\(402\) 0 0
\(403\) −19.3864 9.05584i −0.965703 0.451103i
\(404\) 0 0
\(405\) −2.30808 + 19.8237i −0.114689 + 0.985048i
\(406\) 0 0
\(407\) −2.23263 3.86703i −0.110667 0.191681i
\(408\) 0 0
\(409\) −27.8715 7.46816i −1.37816 0.369277i −0.507707 0.861530i \(-0.669507\pi\)
−0.870452 + 0.492253i \(0.836173\pi\)
\(410\) 0 0
\(411\) 10.5645 19.9441i 0.521106 0.983772i
\(412\) 0 0
\(413\) −11.6040 + 20.0987i −0.570994 + 0.988991i
\(414\) 0 0
\(415\) 22.7280i 1.11567i
\(416\) 0 0
\(417\) −16.9187 + 5.20156i −0.828512 + 0.254721i
\(418\) 0 0
\(419\) −10.1249 5.84561i −0.494633 0.285577i 0.231861 0.972749i \(-0.425518\pi\)
−0.726494 + 0.687172i \(0.758852\pi\)
\(420\) 0 0
\(421\) 13.5303 13.5303i 0.659424 0.659424i −0.295820 0.955244i \(-0.595593\pi\)
0.955244 + 0.295820i \(0.0955928\pi\)
\(422\) 0 0
\(423\) 27.6157 9.60570i 1.34272 0.467045i
\(424\) 0 0
\(425\) 0.148630 0.0858117i 0.00720963 0.00416248i
\(426\) 0 0
\(427\) −17.6204 + 4.72138i −0.852713 + 0.228484i
\(428\) 0 0
\(429\) 7.08303 + 17.4860i 0.341972 + 0.844232i
\(430\) 0 0
\(431\) −4.33330 + 1.16110i −0.208728 + 0.0559284i −0.361668 0.932307i \(-0.617793\pi\)
0.152940 + 0.988235i \(0.451126\pi\)
\(432\) 0 0
\(433\) −20.2735 + 11.7049i −0.974280 + 0.562501i −0.900538 0.434776i \(-0.856827\pi\)
−0.0737418 + 0.997277i \(0.523494\pi\)
\(434\) 0 0
\(435\) 29.6477 1.08181i 1.42150 0.0518690i
\(436\) 0 0
\(437\) 4.17295 4.17295i 0.199619 0.199619i
\(438\) 0 0
\(439\) −12.1163 6.99536i −0.578281 0.333870i 0.182169 0.983267i \(-0.441688\pi\)
−0.760450 + 0.649397i \(0.775021\pi\)
\(440\) 0 0
\(441\) −7.38903 10.8810i −0.351858 0.518143i
\(442\) 0 0
\(443\) 26.3319i 1.25107i −0.780198 0.625533i \(-0.784882\pi\)
0.780198 0.625533i \(-0.215118\pi\)
\(444\) 0 0
\(445\) −7.98354 + 13.8279i −0.378456 + 0.655505i
\(446\) 0 0
\(447\) 11.7576 + 6.22804i 0.556117 + 0.294576i
\(448\) 0 0
\(449\) 27.1589 + 7.27720i 1.28171 + 0.343432i 0.834505 0.551001i \(-0.185754\pi\)
0.447202 + 0.894433i \(0.352421\pi\)
\(450\) 0 0
\(451\) 2.13512 + 3.69813i 0.100539 + 0.174138i
\(452\) 0 0
\(453\) 7.19692 4.51282i 0.338141 0.212031i
\(454\) 0 0
\(455\) −9.90026 8.31862i −0.464131 0.389983i
\(456\) 0 0
\(457\) 3.28100 + 12.2448i 0.153478 + 0.572790i 0.999231 + 0.0392139i \(0.0124854\pi\)
−0.845752 + 0.533576i \(0.820848\pi\)
\(458\) 0 0
\(459\) −10.6670 1.63814i −0.497892 0.0764620i
\(460\) 0 0
\(461\) −0.145136 + 0.541655i −0.00675966 + 0.0252274i −0.969223 0.246183i \(-0.920823\pi\)
0.962464 + 0.271411i \(0.0874902\pi\)
\(462\) 0 0
\(463\) 13.7097 + 13.7097i 0.637143 + 0.637143i 0.949850 0.312707i \(-0.101236\pi\)
−0.312707 + 0.949850i \(0.601236\pi\)
\(464\) 0 0
\(465\) 5.09264 22.2173i 0.236165 1.03030i
\(466\) 0 0
\(467\) −4.97267 −0.230108 −0.115054 0.993359i \(-0.536704\pi\)
−0.115054 + 0.993359i \(0.536704\pi\)
\(468\) 0 0
\(469\) 10.4379 0.481975
\(470\) 0 0
\(471\) −1.43455 + 6.25843i −0.0661006 + 0.288373i
\(472\) 0 0
\(473\) 10.5459 + 10.5459i 0.484900 + 0.484900i
\(474\) 0 0
\(475\) 0.0250569 0.0935137i 0.00114969 0.00429070i
\(476\) 0 0
\(477\) −12.8783 + 26.6158i −0.589658 + 1.21865i
\(478\) 0 0
\(479\) −1.36129 5.08042i −0.0621991 0.232130i 0.927828 0.373009i \(-0.121674\pi\)
−0.990027 + 0.140879i \(0.955007\pi\)
\(480\) 0 0
\(481\) −3.05382 4.36754i −0.139242 0.199143i
\(482\) 0 0
\(483\) −11.9547 + 7.49616i −0.543956 + 0.341087i
\(484\) 0 0
\(485\) 12.1907 + 21.1149i 0.553551 + 0.958778i
\(486\) 0 0
\(487\) −29.0847 7.79321i −1.31795 0.353144i −0.469741 0.882804i \(-0.655653\pi\)
−0.848210 + 0.529660i \(0.822320\pi\)
\(488\) 0 0
\(489\) 20.7335 + 10.9826i 0.937601 + 0.496649i
\(490\) 0 0
\(491\) 16.1436 27.9615i 0.728549 1.26188i −0.228948 0.973439i \(-0.573529\pi\)
0.957497 0.288444i \(-0.0931380\pi\)
\(492\) 0 0
\(493\) 16.0426i 0.722522i
\(494\) 0 0
\(495\) −16.6261 + 11.2904i −0.747289 + 0.507465i
\(496\) 0 0
\(497\) 6.58546 + 3.80212i 0.295398 + 0.170548i
\(498\) 0 0
\(499\) 15.8520 15.8520i 0.709634 0.709634i −0.256824 0.966458i \(-0.582676\pi\)
0.966458 + 0.256824i \(0.0826761\pi\)
\(500\) 0 0
\(501\) −27.9967 + 1.02157i −1.25080 + 0.0456403i
\(502\) 0 0
\(503\) −18.7253 + 10.8111i −0.834921 + 0.482042i −0.855535 0.517745i \(-0.826771\pi\)
0.0206133 + 0.999788i \(0.493438\pi\)
\(504\) 0 0
\(505\) −20.2745 + 5.43254i −0.902204 + 0.241745i
\(506\) 0 0
\(507\) 10.2269 + 20.0602i 0.454191 + 0.890904i
\(508\) 0 0
\(509\) −20.7682 + 5.56482i −0.920534 + 0.246656i −0.687814 0.725887i \(-0.741429\pi\)
−0.232721 + 0.972544i \(0.574763\pi\)
\(510\) 0 0
\(511\) 23.1968 13.3927i 1.02616 0.592456i
\(512\) 0 0
\(513\) −4.90824 + 3.60140i −0.216704 + 0.159006i
\(514\) 0 0
\(515\) −22.3268 + 22.3268i −0.983837 + 0.983837i
\(516\) 0 0
\(517\) 25.4986 + 14.7216i 1.12143 + 0.647455i
\(518\) 0 0
\(519\) −32.7334 + 10.0637i −1.43684 + 0.441747i
\(520\) 0 0
\(521\) 28.4493i 1.24638i 0.782069 + 0.623192i \(0.214165\pi\)
−0.782069 + 0.623192i \(0.785835\pi\)
\(522\) 0 0
\(523\) −22.4493 + 38.8833i −0.981639 + 1.70025i −0.325628 + 0.945498i \(0.605576\pi\)
−0.656011 + 0.754751i \(0.727758\pi\)
\(524\) 0 0
\(525\) −0.108353 + 0.204555i −0.00472893 + 0.00892753i
\(526\) 0 0
\(527\) 11.9056 + 3.19008i 0.518614 + 0.138962i
\(528\) 0 0
\(529\) −1.18632 2.05476i −0.0515791 0.0893376i
\(530\) 0 0
\(531\) 32.5775 + 28.1405i 1.41374 + 1.22119i
\(532\) 0 0
\(533\) 2.92044 + 4.17678i 0.126498 + 0.180916i
\(534\) 0 0
\(535\) 1.31588 + 4.91094i 0.0568906 + 0.212318i
\(536\) 0 0
\(537\) 3.59422 + 3.34116i 0.155102 + 0.144182i
\(538\) 0 0
\(539\) 3.42800 12.7935i 0.147654 0.551053i
\(540\) 0 0
\(541\) 10.3303 + 10.3303i 0.444135 + 0.444135i 0.893399 0.449264i \(-0.148314\pi\)
−0.449264 + 0.893399i \(0.648314\pi\)
\(542\) 0 0
\(543\) 13.7569 + 3.15334i 0.590365 + 0.135323i
\(544\) 0 0
\(545\) 9.71787 0.416268
\(546\) 0 0
\(547\) 4.88585 0.208904 0.104452 0.994530i \(-0.466691\pi\)
0.104452 + 0.994530i \(0.466691\pi\)
\(548\) 0 0
\(549\) 2.46609 + 33.7473i 0.105250 + 1.44030i
\(550\) 0 0
\(551\) 6.39903 + 6.39903i 0.272608 + 0.272608i
\(552\) 0 0
\(553\) 1.17949 4.40190i 0.0501568 0.187188i
\(554\) 0 0
\(555\) 3.86524 4.15800i 0.164070 0.176497i
\(556\) 0 0
\(557\) −8.70865 32.5011i −0.368997 1.37712i −0.861920 0.507044i \(-0.830738\pi\)
0.492923 0.870073i \(-0.335929\pi\)
\(558\) 0 0
\(559\) 13.6279 + 11.4508i 0.576399 + 0.484315i
\(560\) 0 0
\(561\) −5.77335 9.20718i −0.243751 0.388727i
\(562\) 0 0
\(563\) −12.3927 21.4647i −0.522288 0.904630i −0.999664 0.0259303i \(-0.991745\pi\)
0.477376 0.878699i \(-0.341588\pi\)
\(564\) 0 0
\(565\) −38.6394 10.3534i −1.62557 0.435571i
\(566\) 0 0
\(567\) 13.3630 5.77130i 0.561191 0.242372i
\(568\) 0 0
\(569\) 3.35537 5.81167i 0.140664 0.243638i −0.787083 0.616848i \(-0.788409\pi\)
0.927747 + 0.373210i \(0.121743\pi\)
\(570\) 0 0
\(571\) 26.7992i 1.12151i −0.827982 0.560755i \(-0.810511\pi\)
0.827982 0.560755i \(-0.189489\pi\)
\(572\) 0 0
\(573\) −8.74513 28.4446i −0.365333 1.18829i
\(574\) 0 0
\(575\) −0.360470 0.208117i −0.0150326 0.00867909i
\(576\) 0 0
\(577\) 30.5894 30.5894i 1.27345 1.27345i 0.329189 0.944264i \(-0.393225\pi\)
0.944264 0.329189i \(-0.106775\pi\)
\(578\) 0 0
\(579\) 0.564797 + 15.4786i 0.0234721 + 0.643267i
\(580\) 0 0
\(581\) 14.3557 8.28826i 0.595575 0.343855i
\(582\) 0 0
\(583\) −28.7601 + 7.70625i −1.19112 + 0.319160i
\(584\) 0 0
\(585\) −18.6035 + 15.1408i −0.769159 + 0.625994i
\(586\) 0 0
\(587\) −21.5900 + 5.78501i −0.891113 + 0.238773i −0.675196 0.737639i \(-0.735941\pi\)
−0.215918 + 0.976412i \(0.569274\pi\)
\(588\) 0 0
\(589\) 6.02131 3.47641i 0.248104 0.143243i
\(590\) 0 0
\(591\) 0.630396 + 17.2764i 0.0259310 + 0.710655i
\(592\) 0 0
\(593\) 8.05590 8.05590i 0.330816 0.330816i −0.522080 0.852896i \(-0.674844\pi\)
0.852896 + 0.522080i \(0.174844\pi\)
\(594\) 0 0
\(595\) 6.45085 + 3.72440i 0.264459 + 0.152686i
\(596\) 0 0
\(597\) 1.62433 + 5.28332i 0.0664792 + 0.216232i
\(598\) 0 0
\(599\) 25.2313i 1.03092i −0.856913 0.515461i \(-0.827621\pi\)
0.856913 0.515461i \(-0.172379\pi\)
\(600\) 0 0
\(601\) 5.19058 8.99035i 0.211728 0.366724i −0.740527 0.672026i \(-0.765424\pi\)
0.952255 + 0.305302i \(0.0987575\pi\)
\(602\) 0 0
\(603\) 3.63475 19.0170i 0.148018 0.774432i
\(604\) 0 0
\(605\) 4.01315 + 1.07532i 0.163158 + 0.0437180i
\(606\) 0 0
\(607\) 11.5164 + 19.9470i 0.467437 + 0.809624i 0.999308 0.0372012i \(-0.0118442\pi\)
−0.531871 + 0.846825i \(0.678511\pi\)
\(608\) 0 0
\(609\) −11.4950 18.3319i −0.465801 0.742846i
\(610\) 0 0
\(611\) 31.8381 + 14.8723i 1.28803 + 0.601670i
\(612\) 0 0
\(613\) 8.72938 + 32.5785i 0.352576 + 1.31583i 0.883507 + 0.468418i \(0.155176\pi\)
−0.530931 + 0.847415i \(0.678158\pi\)
\(614\) 0 0
\(615\) −3.69642 + 3.97639i −0.149054 + 0.160344i
\(616\) 0 0
\(617\) −2.65220 + 9.89815i −0.106774 + 0.398485i −0.998540 0.0540108i \(-0.982799\pi\)
0.891767 + 0.452495i \(0.149466\pi\)
\(618\) 0 0
\(619\) −11.5373 11.5373i −0.463723 0.463723i 0.436151 0.899874i \(-0.356341\pi\)
−0.899874 + 0.436151i \(0.856341\pi\)
\(620\) 0 0
\(621\) 9.49451 + 24.3909i 0.381002 + 0.978773i
\(622\) 0 0
\(623\) 11.6455 0.466567
\(624\) 0 0
\(625\) 24.5800 0.983200
\(626\) 0 0
\(627\) −5.97540 1.36968i −0.238634 0.0546996i
\(628\) 0 0
\(629\) 2.17072 + 2.17072i 0.0865521 + 0.0865521i
\(630\) 0 0
\(631\) −7.07557 + 26.4064i −0.281674 + 1.05122i 0.669562 + 0.742756i \(0.266482\pi\)
−0.951236 + 0.308465i \(0.900185\pi\)
\(632\) 0 0
\(633\) −4.65221 4.32465i −0.184909 0.171889i
\(634\) 0 0
\(635\) 10.5720 + 39.4554i 0.419539 + 1.56574i
\(636\) 0 0
\(637\) 2.75540 15.5656i 0.109173 0.616732i
\(638\) 0 0
\(639\) 9.22043 10.6742i 0.364754 0.422266i
\(640\) 0 0
\(641\) −11.6077 20.1051i −0.458476 0.794103i 0.540405 0.841405i \(-0.318271\pi\)
−0.998881 + 0.0473020i \(0.984938\pi\)
\(642\) 0 0
\(643\) −9.86387 2.64302i −0.388993 0.104230i 0.0590213 0.998257i \(-0.481202\pi\)
−0.448014 + 0.894026i \(0.647869\pi\)
\(644\) 0 0
\(645\) −8.87570 + 16.7560i −0.349480 + 0.659768i
\(646\) 0 0
\(647\) −12.8120 + 22.1911i −0.503692 + 0.872420i 0.496299 + 0.868152i \(0.334692\pi\)
−0.999991 + 0.00426847i \(0.998641\pi\)
\(648\) 0 0
\(649\) 43.3498i 1.70163i
\(650\) 0 0
\(651\) −15.8903 + 4.88538i −0.622790 + 0.191473i
\(652\) 0 0
\(653\) −20.3016 11.7212i −0.794465 0.458685i 0.0470671 0.998892i \(-0.485013\pi\)
−0.841532 + 0.540207i \(0.818346\pi\)
\(654\) 0 0
\(655\) 16.6405 16.6405i 0.650200 0.650200i
\(656\) 0 0
\(657\) −16.3227 46.9265i −0.636809 1.83078i
\(658\) 0 0
\(659\) −4.19864 + 2.42408i −0.163556 + 0.0944289i −0.579544 0.814941i \(-0.696769\pi\)
0.415988 + 0.909370i \(0.363436\pi\)
\(660\) 0 0
\(661\) 35.3299 9.46662i 1.37417 0.368209i 0.505173 0.863018i \(-0.331429\pi\)
0.869002 + 0.494809i \(0.164762\pi\)
\(662\) 0 0
\(663\) −7.81506 10.3516i −0.303512 0.402024i
\(664\) 0 0
\(665\) 4.05868 1.08752i 0.157389 0.0421722i
\(666\) 0 0
\(667\) 33.6951 19.4539i 1.30468 0.753257i
\(668\) 0 0
\(669\) 12.8307 0.468178i 0.496063 0.0181008i
\(670\) 0 0
\(671\) −24.0940 + 24.0940i −0.930138 + 0.930138i
\(672\) 0 0
\(673\) −43.5065 25.1185i −1.67705 0.968248i −0.963524 0.267623i \(-0.913762\pi\)
−0.713530 0.700624i \(-0.752905\pi\)
\(674\) 0 0
\(675\) 0.334953 + 0.268644i 0.0128924 + 0.0103401i
\(676\) 0 0
\(677\) 21.2309i 0.815970i −0.912989 0.407985i \(-0.866232\pi\)
0.912989 0.407985i \(-0.133768\pi\)
\(678\) 0 0
\(679\) 8.89121 15.4000i 0.341213 0.590999i
\(680\) 0 0
\(681\) 32.8577 + 17.4048i 1.25911 + 0.666953i
\(682\) 0 0
\(683\) 13.3137 + 3.56740i 0.509435 + 0.136503i 0.504375 0.863484i \(-0.331723\pi\)
0.00505974 + 0.999987i \(0.498389\pi\)
\(684\) 0 0
\(685\) 14.4476 + 25.0239i 0.552014 + 0.956116i
\(686\) 0 0
\(687\) 0.195011 0.122281i 0.00744013 0.00466533i
\(688\) 0 0
\(689\) −33.4010 + 12.1316i −1.27248 + 0.462178i
\(690\) 0 0
\(691\) 12.6969 + 47.3855i 0.483013 + 1.80263i 0.588847 + 0.808245i \(0.299582\pi\)
−0.105834 + 0.994384i \(0.533751\pi\)
\(692\) 0 0
\(693\) 13.1944 + 6.38428i 0.501215 + 0.242519i
\(694\) 0 0
\(695\) 5.86518 21.8891i 0.222479 0.830302i
\(696\) 0 0
\(697\) −2.07591 2.07591i −0.0786306 0.0786306i
\(698\) 0 0
\(699\) −10.8384 + 47.2841i −0.409947 + 1.78845i
\(700\) 0 0
\(701\) 22.4699 0.848677 0.424338 0.905504i \(-0.360507\pi\)
0.424338 + 0.905504i \(0.360507\pi\)
\(702\) 0 0
\(703\) 1.73170 0.0653123
\(704\) 0 0
\(705\) −8.36360 + 36.4874i −0.314991 + 1.37419i
\(706\) 0 0
\(707\) 10.8249 + 10.8249i 0.407113 + 0.407113i
\(708\) 0 0
\(709\) 2.76758 10.3287i 0.103939 0.387904i −0.894284 0.447500i \(-0.852315\pi\)
0.998223 + 0.0595959i \(0.0189812\pi\)
\(710\) 0 0
\(711\) −7.60921 3.68180i −0.285368 0.138078i
\(712\) 0 0
\(713\) −7.73684 28.8743i −0.289747 1.08135i
\(714\) 0 0
\(715\) −23.7842 4.21023i −0.889477 0.157454i
\(716\) 0 0
\(717\) 11.8647 7.43974i 0.443094 0.277842i
\(718\) 0 0
\(719\) −7.22594 12.5157i −0.269482 0.466757i 0.699246 0.714881i \(-0.253519\pi\)
−0.968728 + 0.248124i \(0.920186\pi\)
\(720\) 0 0
\(721\) 22.2443 + 5.96033i 0.828420 + 0.221974i
\(722\) 0 0
\(723\) −21.1445 11.2003i −0.786372 0.416543i
\(724\) 0 0
\(725\) 0.319138 0.552764i 0.0118525 0.0205291i
\(726\) 0 0
\(727\) 14.7369i 0.546560i 0.961935 + 0.273280i \(0.0881085\pi\)
−0.961935 + 0.273280i \(0.911892\pi\)
\(728\) 0 0
\(729\) −5.86154 26.3561i −0.217094 0.976151i
\(730\) 0 0
\(731\) −8.87973 5.12672i −0.328429 0.189618i
\(732\) 0 0
\(733\) −26.4060 + 26.4060i −0.975328 + 0.975328i −0.999703 0.0243745i \(-0.992241\pi\)
0.0243745 + 0.999703i \(0.492241\pi\)
\(734\) 0 0
\(735\) 16.8280 0.614036i 0.620710 0.0226490i
\(736\) 0 0
\(737\) 16.8847 9.74837i 0.621955 0.359086i
\(738\) 0 0
\(739\) 0.773003 0.207126i 0.0284354 0.00761924i −0.244573 0.969631i \(-0.578648\pi\)
0.273009 + 0.962012i \(0.411981\pi\)
\(740\) 0 0
\(741\) −7.24628 1.01178i −0.266199 0.0371687i
\(742\) 0 0
\(743\) 8.82884 2.36568i 0.323899 0.0867885i −0.0932059 0.995647i \(-0.529711\pi\)
0.417105 + 0.908858i \(0.363045\pi\)
\(744\) 0 0
\(745\) −14.7523 + 8.51726i −0.540483 + 0.312048i
\(746\) 0 0
\(747\) −10.1016 29.0412i −0.369597 1.06256i
\(748\) 0 0
\(749\) 2.62203 2.62203i 0.0958071 0.0958071i
\(750\) 0 0
\(751\) 16.1851 + 9.34448i 0.590603 + 0.340985i 0.765336 0.643631i \(-0.222573\pi\)
−0.174733 + 0.984616i \(0.555906\pi\)
\(752\) 0 0
\(753\) 38.9093 11.9624i 1.41793 0.435935i
\(754\) 0 0
\(755\) 10.8757i 0.395808i
\(756\) 0 0
\(757\) −5.18418 + 8.97927i −0.188422 + 0.326357i −0.944724 0.327866i \(-0.893671\pi\)
0.756302 + 0.654223i \(0.227004\pi\)
\(758\) 0 0
\(759\) −12.3373 + 23.2911i −0.447816 + 0.845412i
\(760\) 0 0
\(761\) −19.8250 5.31209i −0.718655 0.192563i −0.119083 0.992884i \(-0.537996\pi\)
−0.599571 + 0.800321i \(0.704662\pi\)
\(762\) 0 0
\(763\) −3.54384 6.13811i −0.128296 0.222214i
\(764\) 0 0
\(765\) 9.03196 10.4560i 0.326551 0.378039i
\(766\) 0 0
\(767\) 4.47471 + 51.5441i 0.161572 + 1.86115i
\(768\) 0 0
\(769\) −6.30665 23.5367i −0.227424 0.848756i −0.981419 0.191877i \(-0.938543\pi\)
0.753995 0.656880i \(-0.228124\pi\)
\(770\) 0 0
\(771\) 3.36523 + 3.12829i 0.121196 + 0.112663i
\(772\) 0 0
\(773\) −2.24882 + 8.39271i −0.0808844 + 0.301865i −0.994503 0.104707i \(-0.966609\pi\)
0.913619 + 0.406572i \(0.133276\pi\)
\(774\) 0 0
\(775\) −0.346757 0.346757i −0.0124559 0.0124559i
\(776\) 0 0
\(777\) −4.03586 0.925097i −0.144786 0.0331877i
\(778\) 0 0
\(779\) −1.65606 −0.0593347
\(780\) 0 0
\(781\) 14.2039 0.508254
\(782\) 0 0
\(783\) −37.4023 + 14.5594i −1.33665 + 0.520310i
\(784\) 0 0
\(785\) −5.81267 5.81267i −0.207463 0.207463i
\(786\) 0 0
\(787\) 1.02627 3.83008i 0.0365824 0.136528i −0.945219 0.326436i \(-0.894152\pi\)
0.981802 + 0.189908i \(0.0608190\pi\)
\(788\) 0 0
\(789\) 23.9677 25.7831i 0.853274 0.917902i
\(790\) 0 0
\(791\) 7.55120 + 28.1815i 0.268490 + 1.00202i
\(792\) 0 0
\(793\) −26.1613 + 31.1355i −0.929016 + 1.10565i
\(794\) 0 0
\(795\) −20.1104 32.0714i −0.713241 1.13746i
\(796\) 0 0
\(797\) 24.6204 + 42.6438i 0.872100 + 1.51052i 0.859820 + 0.510597i \(0.170576\pi\)
0.0122797 + 0.999925i \(0.496091\pi\)
\(798\) 0 0
\(799\) −19.5524 5.23905i −0.691714 0.185344i
\(800\) 0 0
\(801\) 4.05529 21.2173i 0.143287 0.749675i
\(802\) 0 0
\(803\) 25.0160 43.3290i 0.882795 1.52905i
\(804\) 0 0
\(805\) 18.0654i 0.636722i
\(806\) 0 0
\(807\) −12.7930 41.6108i −0.450334 1.46477i
\(808\) 0 0
\(809\) −25.2106 14.5553i −0.886357 0.511739i −0.0136080 0.999907i \(-0.504332\pi\)
−0.872749 + 0.488169i \(0.837665\pi\)
\(810\) 0 0
\(811\) −11.4094 + 11.4094i −0.400639 + 0.400639i −0.878458 0.477819i \(-0.841427\pi\)
0.477819 + 0.878458i \(0.341427\pi\)
\(812\) 0 0
\(813\) −0.628716 17.2303i −0.0220500 0.604294i
\(814\) 0 0
\(815\) −26.0143 + 15.0194i −0.911243 + 0.526106i
\(816\) 0 0
\(817\) −5.58686 + 1.49699i −0.195459 + 0.0523732i
\(818\) 0 0
\(819\) 16.3475 + 6.22910i 0.571229 + 0.217662i
\(820\) 0 0
\(821\) 0.492396 0.131937i 0.0171847 0.00460464i −0.250216 0.968190i \(-0.580502\pi\)
0.267401 + 0.963585i \(0.413835\pi\)
\(822\) 0 0
\(823\) −16.2968 + 9.40898i −0.568072 + 0.327976i −0.756379 0.654134i \(-0.773033\pi\)
0.188307 + 0.982110i \(0.439700\pi\)
\(824\) 0 0
\(825\) 0.0157666 + 0.432093i 0.000548923 + 0.0150435i
\(826\) 0 0
\(827\) 13.7947 13.7947i 0.479688 0.479688i −0.425344 0.905032i \(-0.639847\pi\)
0.905032 + 0.425344i \(0.139847\pi\)
\(828\) 0 0
\(829\) 11.0322 + 6.36943i 0.383163 + 0.221219i 0.679194 0.733959i \(-0.262330\pi\)
−0.296030 + 0.955179i \(0.595663\pi\)
\(830\) 0 0
\(831\) −6.99416 22.7494i −0.242625 0.789167i
\(832\) 0 0
\(833\) 9.10575i 0.315495i
\(834\) 0 0
\(835\) 17.9337 31.0622i 0.620623 1.07495i
\(836\) 0 0
\(837\) 3.36736 + 30.6522i 0.116393 + 1.05950i
\(838\) 0 0
\(839\) −20.6957 5.54539i −0.714494 0.191448i −0.116780 0.993158i \(-0.537257\pi\)
−0.597714 + 0.801710i \(0.703924\pi\)
\(840\) 0 0
\(841\) 15.3316 + 26.5551i 0.528676 + 0.915694i
\(842\) 0 0
\(843\) −4.32395 6.89571i −0.148925 0.237501i
\(844\) 0 0
\(845\) −28.7146 2.55100i −0.987812 0.0877571i
\(846\) 0 0
\(847\) −0.784280 2.92697i −0.0269482 0.100572i
\(848\) 0 0
\(849\) −35.6824 + 38.3850i −1.22462 + 1.31737i
\(850\) 0 0
\(851\) 1.92697 7.19156i 0.0660558 0.246524i
\(852\) 0 0
\(853\) 7.24525 + 7.24525i 0.248073 + 0.248073i 0.820179 0.572107i \(-0.193874\pi\)
−0.572107 + 0.820179i \(0.693874\pi\)
\(854\) 0 0
\(855\) −0.568037 7.77333i −0.0194265 0.265842i
\(856\) 0 0
\(857\) −6.48368 −0.221478 −0.110739 0.993850i \(-0.535322\pi\)
−0.110739 + 0.993850i \(0.535322\pi\)
\(858\) 0 0
\(859\) 31.3981 1.07129 0.535644 0.844444i \(-0.320069\pi\)
0.535644 + 0.844444i \(0.320069\pi\)
\(860\) 0 0
\(861\) 3.85959 + 0.884692i 0.131535 + 0.0301502i
\(862\) 0 0
\(863\) −24.0869 24.0869i −0.819927 0.819927i 0.166170 0.986097i \(-0.446860\pi\)
−0.986097 + 0.166170i \(0.946860\pi\)
\(864\) 0 0
\(865\) 11.3476 42.3499i 0.385831 1.43994i
\(866\) 0 0
\(867\) −16.0938 14.9607i −0.546574 0.508091i
\(868\) 0 0
\(869\) −2.20315 8.22226i −0.0747367 0.278921i
\(870\) 0 0
\(871\) 19.0701 13.3340i 0.646164 0.451804i
\(872\) 0 0
\(873\) −24.9616 21.5619i −0.844821 0.729758i
\(874\) 0 0
\(875\) −9.11431 15.7865i −0.308120 0.533680i
\(876\) 0 0
\(877\) −23.7637 6.36747i −0.802444 0.215014i −0.165787 0.986162i \(-0.553016\pi\)
−0.636657 + 0.771147i \(0.719683\pi\)
\(878\) 0 0
\(879\) 12.7600 24.0889i 0.430383 0.812500i
\(880\) 0 0
\(881\) −0.578074 + 1.00125i −0.0194758 + 0.0337331i −0.875599 0.483039i \(-0.839533\pi\)
0.856123 + 0.516772i \(0.172866\pi\)
\(882\) 0 0
\(883\) 3.10113i 0.104361i 0.998638 + 0.0521806i \(0.0166171\pi\)
−0.998638 + 0.0521806i \(0.983383\pi\)
\(884\) 0 0
\(885\) −52.6808 + 16.1964i −1.77085 + 0.544436i
\(886\) 0 0
\(887\) 39.2130 + 22.6396i 1.31664 + 0.760165i 0.983187 0.182600i \(-0.0584514\pi\)
0.333457 + 0.942765i \(0.391785\pi\)
\(888\) 0 0
\(889\) 21.0659 21.0659i 0.706528 0.706528i
\(890\) 0 0
\(891\) 16.2264 21.8161i 0.543604 0.730868i
\(892\) 0 0
\(893\) −9.88875 + 5.70927i −0.330914 + 0.191054i
\(894\) 0 0
\(895\) −6.06867 + 1.62610i −0.202853 + 0.0543544i
\(896\) 0 0
\(897\) −12.2652 + 28.9672i −0.409524 + 0.967186i
\(898\) 0 0
\(899\) 44.2774 11.8641i 1.47673 0.395689i
\(900\) 0 0
\(901\) 17.7275 10.2350i 0.590590 0.340977i
\(902\) 0 0
\(903\) 13.8203 0.504290i 0.459912 0.0167817i
\(904\) 0 0
\(905\) −12.7771 + 12.7771i −0.424724 + 0.424724i
\(906\) 0 0
\(907\) −7.35502 4.24642i −0.244219 0.141000i 0.372895 0.927873i \(-0.378365\pi\)
−0.617114 + 0.786873i \(0.711698\pi\)
\(908\) 0 0
\(909\) 23.4917 15.9527i 0.779172 0.529116i
\(910\) 0 0
\(911\) 29.1375i 0.965367i −0.875795 0.482684i \(-0.839662\pi\)
0.875795 0.482684i \(-0.160338\pi\)
\(912\) 0 0
\(913\) 15.4816 26.8148i 0.512365 0.887442i
\(914\) 0 0
\(915\) −38.2822 20.2782i −1.26557 0.670375i
\(916\) 0 0
\(917\) −16.5790 4.44233i −0.547487 0.146699i
\(918\) 0 0
\(919\) −11.9109 20.6303i −0.392904 0.680530i 0.599927 0.800055i \(-0.295196\pi\)
−0.992831 + 0.119525i \(0.961863\pi\)
\(920\) 0 0
\(921\) 23.9005 14.9868i 0.787547 0.493831i
\(922\) 0 0
\(923\) 16.8888 1.46617i 0.555901 0.0482595i
\(924\) 0 0
\(925\) −0.0316117 0.117977i −0.00103939 0.00387905i
\(926\) 0 0
\(927\) 18.6054 38.4519i 0.611080 1.26293i
\(928\) 0 0
\(929\) −12.2567 + 45.7426i −0.402129 + 1.50077i 0.407160 + 0.913357i \(0.366519\pi\)
−0.809290 + 0.587410i \(0.800148\pi\)
\(930\) 0 0
\(931\) 3.63208 + 3.63208i 0.119037 + 0.119037i
\(932\) 0 0
\(933\) 2.94069 12.8292i 0.0962739 0.420008i
\(934\) 0 0
\(935\) 13.9135 0.455021
\(936\) 0 0
\(937\) 18.5181 0.604961 0.302480 0.953156i \(-0.402185\pi\)
0.302480 + 0.953156i \(0.402185\pi\)
\(938\) 0 0
\(939\) −5.14362 + 22.4397i −0.167856 + 0.732293i
\(940\) 0 0
\(941\) −7.71712 7.71712i −0.251571 0.251571i 0.570044 0.821614i \(-0.306926\pi\)
−0.821614 + 0.570044i \(0.806926\pi\)
\(942\) 0 0
\(943\) −1.84281 + 6.87746i −0.0600101 + 0.223961i
\(944\) 0 0
\(945\) −2.82876 + 18.4198i −0.0920196 + 0.599197i
\(946\) 0 0
\(947\) 2.41686 + 9.01986i 0.0785375 + 0.293106i 0.994012 0.109270i \(-0.0348512\pi\)
−0.915475 + 0.402376i \(0.868185\pi\)
\(948\) 0 0
\(949\) 25.2721 54.1015i 0.820367 1.75621i
\(950\) 0 0
\(951\) −16.6771 + 10.4574i −0.540792 + 0.339103i
\(952\) 0 0
\(953\) −5.24649 9.08718i −0.169950 0.294363i 0.768452 0.639908i \(-0.221027\pi\)
−0.938402 + 0.345545i \(0.887694\pi\)
\(954\) 0 0
\(955\) 36.8012 + 9.86084i 1.19086 + 0.319089i
\(956\) 0 0
\(957\) −35.7157 18.9187i −1.15453 0.611555i
\(958\) 0 0
\(959\) 10.5373 18.2511i 0.340266 0.589358i
\(960\) 0 0
\(961\) 4.21839i 0.136077i
\(962\) 0 0
\(963\) −3.86409 5.69022i −0.124519 0.183365i
\(964\) 0 0
\(965\) −17.1734 9.91506i −0.552831 0.319177i
\(966\) 0 0
\(967\) 13.3894 13.3894i 0.430575 0.430575i −0.458249 0.888824i \(-0.651523\pi\)
0.888824 + 0.458249i \(0.151523\pi\)
\(968\) 0 0
\(969\) 4.21181 0.153684i 0.135303 0.00493706i
\(970\) 0 0
\(971\) −36.1983 + 20.8991i −1.16166 + 0.670684i −0.951701 0.307026i \(-0.900666\pi\)
−0.209958 + 0.977710i \(0.567333\pi\)
\(972\) 0 0
\(973\) −15.9647 + 4.27773i −0.511806 + 0.137138i
\(974\) 0 0
\(975\) 0.0633489 + 0.512142i 0.00202879 + 0.0164017i
\(976\) 0 0
\(977\) 51.8326 13.8885i 1.65827 0.444332i 0.696360 0.717693i \(-0.254802\pi\)
0.961912 + 0.273360i \(0.0881352\pi\)
\(978\) 0 0
\(979\) 18.8382 10.8763i 0.602072 0.347607i
\(980\) 0 0
\(981\) −12.4172 + 4.31916i −0.396452 + 0.137900i
\(982\) 0 0
\(983\) −3.22088 + 3.22088i −0.102730 + 0.102730i −0.756604 0.653874i \(-0.773143\pi\)
0.653874 + 0.756604i \(0.273143\pi\)
\(984\) 0 0
\(985\) −19.1680 11.0667i −0.610745 0.352614i
\(986\) 0 0
\(987\) 26.0965 8.02322i 0.830661 0.255382i
\(988\) 0 0
\(989\) 24.8674i 0.790738i
\(990\) 0 0
\(991\) −0.213053 + 0.369019i −0.00676785 + 0.0117223i −0.869389 0.494127i \(-0.835488\pi\)
0.862622 + 0.505850i \(0.168821\pi\)
\(992\) 0 0
\(993\) −18.9644 + 35.8020i −0.601816 + 1.13614i
\(994\) 0 0
\(995\) −6.83548 1.83156i −0.216699 0.0580644i
\(996\) 0 0
\(997\) −20.9763 36.3321i −0.664327 1.15065i −0.979467 0.201603i \(-0.935385\pi\)
0.315140 0.949045i \(-0.397948\pi\)
\(998\) 0 0
\(999\) −3.09086 + 7.03091i −0.0977905 + 0.222448i
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 624.2.cn.f.305.9 56
3.2 odd 2 inner 624.2.cn.f.305.11 56
4.3 odd 2 312.2.bp.a.305.6 yes 56
12.11 even 2 312.2.bp.a.305.4 yes 56
13.11 odd 12 inner 624.2.cn.f.401.11 56
39.11 even 12 inner 624.2.cn.f.401.9 56
52.11 even 12 312.2.bp.a.89.4 56
156.11 odd 12 312.2.bp.a.89.6 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
312.2.bp.a.89.4 56 52.11 even 12
312.2.bp.a.89.6 yes 56 156.11 odd 12
312.2.bp.a.305.4 yes 56 12.11 even 2
312.2.bp.a.305.6 yes 56 4.3 odd 2
624.2.cn.f.305.9 56 1.1 even 1 trivial
624.2.cn.f.305.11 56 3.2 odd 2 inner
624.2.cn.f.401.9 56 39.11 even 12 inner
624.2.cn.f.401.11 56 13.11 odd 12 inner