Properties

Label 572.2.x.a.25.9
Level $572$
Weight $2$
Character 572.25
Analytic conductor $4.567$
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] = [572,2,Mod(25,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.x (of order \(10\), degree \(4\), 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: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 25.9
Character \(\chi\) \(=\) 572.25
Dual form 572.2.x.a.389.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.268029 + 0.824907i) q^{3} +(-0.0443935 + 0.0611023i) q^{5} +(2.23222 + 0.725291i) q^{7} +(1.81842 - 1.32116i) q^{9} +O(q^{10})\) \(q+(0.268029 + 0.824907i) q^{3} +(-0.0443935 + 0.0611023i) q^{5} +(2.23222 + 0.725291i) q^{7} +(1.81842 - 1.32116i) q^{9} +(0.201919 - 3.31047i) q^{11} +(-1.06077 - 3.44598i) q^{13} +(-0.0623025 - 0.0202433i) q^{15} +(5.53997 + 4.02503i) q^{17} +(-2.23156 + 0.725078i) q^{19} +2.03577i q^{21} -1.12468 q^{23} +(1.54332 + 4.74986i) q^{25} +(3.68235 + 2.67538i) q^{27} +(-0.0774921 + 0.238496i) q^{29} +(1.73805 + 2.39221i) q^{31} +(2.78495 - 0.720737i) q^{33} +(-0.143413 + 0.104195i) q^{35} +(-1.69257 - 0.549950i) q^{37} +(2.55829 - 1.79866i) q^{39} +(7.12738 - 2.31583i) q^{41} -1.30250 q^{43} +0.169760i q^{45} +(2.07499 - 0.674205i) q^{47} +(-1.20638 - 0.876487i) q^{49} +(-1.83540 + 5.64879i) q^{51} +(6.51307 - 4.73202i) q^{53} +(0.193314 + 0.159301i) q^{55} +(-1.19624 - 1.64649i) q^{57} +(-7.19999 - 2.33942i) q^{59} +(-4.04460 - 2.93857i) q^{61} +(5.01732 - 1.63023i) q^{63} +(0.257649 + 0.0881631i) q^{65} +10.2061i q^{67} +(-0.301447 - 0.927757i) q^{69} +(-7.14983 + 9.84089i) q^{71} +(-11.0405 - 3.58728i) q^{73} +(-3.50454 + 2.54620i) q^{75} +(2.85178 - 7.24324i) q^{77} +(-11.9485 + 8.68107i) q^{79} +(0.863755 - 2.65836i) q^{81} +(3.27816 - 4.51200i) q^{83} +(-0.491877 + 0.159821i) q^{85} -0.217507 q^{87} -5.61967i q^{89} +(0.131460 - 8.46153i) q^{91} +(-1.50751 + 2.07491i) q^{93} +(0.0547627 - 0.168542i) q^{95} +(8.37607 + 11.5287i) q^{97} +(-4.00648 - 6.28659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{4}{5}\right)\)

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
\(3\) 0.268029 + 0.824907i 0.154746 + 0.476261i 0.998135 0.0610434i \(-0.0194428\pi\)
−0.843389 + 0.537304i \(0.819443\pi\)
\(4\) 0 0
\(5\) −0.0443935 + 0.0611023i −0.0198534 + 0.0273258i −0.818828 0.574039i \(-0.805376\pi\)
0.798975 + 0.601364i \(0.205376\pi\)
\(6\) 0 0
\(7\) 2.23222 + 0.725291i 0.843698 + 0.274134i 0.698804 0.715313i \(-0.253716\pi\)
0.144894 + 0.989447i \(0.453716\pi\)
\(8\) 0 0
\(9\) 1.81842 1.32116i 0.606139 0.440386i
\(10\) 0 0
\(11\) 0.201919 3.31047i 0.0608808 0.998145i
\(12\) 0 0
\(13\) −1.06077 3.44598i −0.294206 0.955742i
\(14\) 0 0
\(15\) −0.0623025 0.0202433i −0.0160864 0.00522680i
\(16\) 0 0
\(17\) 5.53997 + 4.02503i 1.34364 + 0.976212i 0.999302 + 0.0373673i \(0.0118972\pi\)
0.344340 + 0.938845i \(0.388103\pi\)
\(18\) 0 0
\(19\) −2.23156 + 0.725078i −0.511955 + 0.166344i −0.553591 0.832789i \(-0.686743\pi\)
0.0416362 + 0.999133i \(0.486743\pi\)
\(20\) 0 0
\(21\) 2.03577i 0.444241i
\(22\) 0 0
\(23\) −1.12468 −0.234512 −0.117256 0.993102i \(-0.537410\pi\)
−0.117256 + 0.993102i \(0.537410\pi\)
\(24\) 0 0
\(25\) 1.54332 + 4.74986i 0.308664 + 0.949971i
\(26\) 0 0
\(27\) 3.68235 + 2.67538i 0.708668 + 0.514877i
\(28\) 0 0
\(29\) −0.0774921 + 0.238496i −0.0143899 + 0.0442876i −0.957994 0.286789i \(-0.907412\pi\)
0.943604 + 0.331077i \(0.107412\pi\)
\(30\) 0 0
\(31\) 1.73805 + 2.39221i 0.312162 + 0.429654i 0.936054 0.351856i \(-0.114449\pi\)
−0.623892 + 0.781511i \(0.714449\pi\)
\(32\) 0 0
\(33\) 2.78495 0.720737i 0.484798 0.125464i
\(34\) 0 0
\(35\) −0.143413 + 0.104195i −0.0242412 + 0.0176122i
\(36\) 0 0
\(37\) −1.69257 0.549950i −0.278257 0.0904113i 0.166564 0.986031i \(-0.446733\pi\)
−0.444821 + 0.895619i \(0.646733\pi\)
\(38\) 0 0
\(39\) 2.55829 1.79866i 0.409655 0.288016i
\(40\) 0 0
\(41\) 7.12738 2.31583i 1.11311 0.361671i 0.305975 0.952039i \(-0.401017\pi\)
0.807134 + 0.590368i \(0.201017\pi\)
\(42\) 0 0
\(43\) −1.30250 −0.198629 −0.0993144 0.995056i \(-0.531665\pi\)
−0.0993144 + 0.995056i \(0.531665\pi\)
\(44\) 0 0
\(45\) 0.169760i 0.0253064i
\(46\) 0 0
\(47\) 2.07499 0.674205i 0.302668 0.0983428i −0.153746 0.988110i \(-0.549134\pi\)
0.456414 + 0.889768i \(0.349134\pi\)
\(48\) 0 0
\(49\) −1.20638 0.876487i −0.172340 0.125212i
\(50\) 0 0
\(51\) −1.83540 + 5.64879i −0.257008 + 0.790989i
\(52\) 0 0
\(53\) 6.51307 4.73202i 0.894639 0.649993i −0.0424443 0.999099i \(-0.513515\pi\)
0.937083 + 0.349105i \(0.113515\pi\)
\(54\) 0 0
\(55\) 0.193314 + 0.159301i 0.0260664 + 0.0214801i
\(56\) 0 0
\(57\) −1.19624 1.64649i −0.158446 0.218083i
\(58\) 0 0
\(59\) −7.19999 2.33942i −0.937358 0.304566i −0.199790 0.979839i \(-0.564026\pi\)
−0.737568 + 0.675273i \(0.764026\pi\)
\(60\) 0 0
\(61\) −4.04460 2.93857i −0.517858 0.376246i 0.297938 0.954585i \(-0.403701\pi\)
−0.815796 + 0.578339i \(0.803701\pi\)
\(62\) 0 0
\(63\) 5.01732 1.63023i 0.632123 0.205389i
\(64\) 0 0
\(65\) 0.257649 + 0.0881631i 0.0319574 + 0.0109353i
\(66\) 0 0
\(67\) 10.2061i 1.24687i 0.781875 + 0.623436i \(0.214264\pi\)
−0.781875 + 0.623436i \(0.785736\pi\)
\(68\) 0 0
\(69\) −0.301447 0.927757i −0.0362899 0.111689i
\(70\) 0 0
\(71\) −7.14983 + 9.84089i −0.848528 + 1.16790i 0.135657 + 0.990756i \(0.456686\pi\)
−0.984185 + 0.177143i \(0.943314\pi\)
\(72\) 0 0
\(73\) −11.0405 3.58728i −1.29219 0.419859i −0.419334 0.907832i \(-0.637736\pi\)
−0.872859 + 0.487973i \(0.837736\pi\)
\(74\) 0 0
\(75\) −3.50454 + 2.54620i −0.404669 + 0.294009i
\(76\) 0 0
\(77\) 2.85178 7.24324i 0.324991 0.825444i
\(78\) 0 0
\(79\) −11.9485 + 8.68107i −1.34431 + 0.976697i −0.345034 + 0.938590i \(0.612133\pi\)
−0.999274 + 0.0381070i \(0.987867\pi\)
\(80\) 0 0
\(81\) 0.863755 2.65836i 0.0959727 0.295374i
\(82\) 0 0
\(83\) 3.27816 4.51200i 0.359825 0.495256i −0.590275 0.807202i \(-0.700981\pi\)
0.950100 + 0.311946i \(0.100981\pi\)
\(84\) 0 0
\(85\) −0.491877 + 0.159821i −0.0533516 + 0.0173350i
\(86\) 0 0
\(87\) −0.217507 −0.0233192
\(88\) 0 0
\(89\) 5.61967i 0.595684i −0.954615 0.297842i \(-0.903733\pi\)
0.954615 0.297842i \(-0.0962669\pi\)
\(90\) 0 0
\(91\) 0.131460 8.46153i 0.0137807 0.887010i
\(92\) 0 0
\(93\) −1.50751 + 2.07491i −0.156321 + 0.215158i
\(94\) 0 0
\(95\) 0.0547627 0.168542i 0.00561853 0.0172921i
\(96\) 0 0
\(97\) 8.37607 + 11.5287i 0.850461 + 1.17056i 0.983761 + 0.179484i \(0.0574427\pi\)
−0.133300 + 0.991076i \(0.542557\pi\)
\(98\) 0 0
\(99\) −4.00648 6.28659i −0.402667 0.631826i
\(100\) 0 0
\(101\) 7.21145 5.23942i 0.717566 0.521342i −0.168040 0.985780i \(-0.553744\pi\)
0.885606 + 0.464438i \(0.153744\pi\)
\(102\) 0 0
\(103\) 0.0934082 0.287481i 0.00920378 0.0283263i −0.946349 0.323146i \(-0.895260\pi\)
0.955553 + 0.294820i \(0.0952595\pi\)
\(104\) 0 0
\(105\) −0.124390 0.0903748i −0.0121392 0.00881968i
\(106\) 0 0
\(107\) −1.29850 3.99637i −0.125531 0.386344i 0.868467 0.495748i \(-0.165106\pi\)
−0.993997 + 0.109404i \(0.965106\pi\)
\(108\) 0 0
\(109\) 8.18100i 0.783598i −0.920051 0.391799i \(-0.871853\pi\)
0.920051 0.391799i \(-0.128147\pi\)
\(110\) 0 0
\(111\) 1.54362i 0.146514i
\(112\) 0 0
\(113\) −1.72989 5.32405i −0.162734 0.500845i 0.836128 0.548535i \(-0.184814\pi\)
−0.998862 + 0.0476899i \(0.984814\pi\)
\(114\) 0 0
\(115\) 0.0499285 0.0687206i 0.00465585 0.00640823i
\(116\) 0 0
\(117\) −6.48161 4.86478i −0.599225 0.449749i
\(118\) 0 0
\(119\) 9.44710 + 13.0028i 0.866014 + 1.19197i
\(120\) 0 0
\(121\) −10.9185 1.33689i −0.992587 0.121536i
\(122\) 0 0
\(123\) 3.82068 + 5.25872i 0.344499 + 0.474163i
\(124\) 0 0
\(125\) −0.717891 0.233257i −0.0642102 0.0208631i
\(126\) 0 0
\(127\) −14.9405 10.8549i −1.32575 0.963215i −0.999841 0.0178150i \(-0.994329\pi\)
−0.325911 0.945400i \(-0.605671\pi\)
\(128\) 0 0
\(129\) −0.349106 1.07444i −0.0307371 0.0945991i
\(130\) 0 0
\(131\) −9.41882 −0.822926 −0.411463 0.911426i \(-0.634982\pi\)
−0.411463 + 0.911426i \(0.634982\pi\)
\(132\) 0 0
\(133\) −5.50721 −0.477536
\(134\) 0 0
\(135\) −0.326944 + 0.106231i −0.0281389 + 0.00914287i
\(136\) 0 0
\(137\) −8.50836 + 11.7108i −0.726918 + 1.00052i 0.272347 + 0.962199i \(0.412200\pi\)
−0.999266 + 0.0383182i \(0.987800\pi\)
\(138\) 0 0
\(139\) −0.814232 + 2.50595i −0.0690622 + 0.212552i −0.979631 0.200806i \(-0.935644\pi\)
0.910569 + 0.413357i \(0.135644\pi\)
\(140\) 0 0
\(141\) 1.11231 + 1.53097i 0.0936736 + 0.128931i
\(142\) 0 0
\(143\) −11.6220 + 2.81586i −0.971881 + 0.235474i
\(144\) 0 0
\(145\) −0.0111325 0.0153226i −0.000924507 0.00127247i
\(146\) 0 0
\(147\) 0.399676 1.23008i 0.0329647 0.101455i
\(148\) 0 0
\(149\) 0.674366 0.928186i 0.0552462 0.0760399i −0.780500 0.625156i \(-0.785035\pi\)
0.835746 + 0.549116i \(0.185035\pi\)
\(150\) 0 0
\(151\) −3.27215 + 1.06319i −0.266284 + 0.0865210i −0.439116 0.898430i \(-0.644708\pi\)
0.172832 + 0.984951i \(0.444708\pi\)
\(152\) 0 0
\(153\) 15.3917 1.24434
\(154\) 0 0
\(155\) −0.223328 −0.0179381
\(156\) 0 0
\(157\) −4.93333 15.1832i −0.393723 1.21175i −0.929952 0.367682i \(-0.880152\pi\)
0.536229 0.844073i \(-0.319848\pi\)
\(158\) 0 0
\(159\) 5.64917 + 4.10436i 0.448008 + 0.325497i
\(160\) 0 0
\(161\) −2.51053 0.815720i −0.197857 0.0642878i
\(162\) 0 0
\(163\) 8.84457 + 12.1735i 0.692760 + 0.953503i 0.999998 + 0.00186998i \(0.000595235\pi\)
−0.307238 + 0.951633i \(0.599405\pi\)
\(164\) 0 0
\(165\) −0.0795950 + 0.202163i −0.00619646 + 0.0157384i
\(166\) 0 0
\(167\) −11.8138 16.2604i −0.914183 1.25826i −0.965718 0.259593i \(-0.916411\pi\)
0.0515354 0.998671i \(-0.483589\pi\)
\(168\) 0 0
\(169\) −10.7495 + 7.31081i −0.826886 + 0.562370i
\(170\) 0 0
\(171\) −3.09997 + 4.26674i −0.237060 + 0.326286i
\(172\) 0 0
\(173\) −2.19978 6.77022i −0.167246 0.514731i 0.831949 0.554853i \(-0.187225\pi\)
−0.999195 + 0.0401220i \(0.987225\pi\)
\(174\) 0 0
\(175\) 11.7221i 0.886105i
\(176\) 0 0
\(177\) 6.56635i 0.493557i
\(178\) 0 0
\(179\) 6.25715 + 19.2575i 0.467682 + 1.43938i 0.855579 + 0.517673i \(0.173202\pi\)
−0.387897 + 0.921703i \(0.626798\pi\)
\(180\) 0 0
\(181\) −10.5449 7.66129i −0.783793 0.569459i 0.122322 0.992490i \(-0.460966\pi\)
−0.906115 + 0.423031i \(0.860966\pi\)
\(182\) 0 0
\(183\) 1.33998 4.12404i 0.0990544 0.304858i
\(184\) 0 0
\(185\) 0.108742 0.0790060i 0.00799490 0.00580864i
\(186\) 0 0
\(187\) 14.4434 17.5272i 1.05620 1.28172i
\(188\) 0 0
\(189\) 6.27936 + 8.64280i 0.456756 + 0.628671i
\(190\) 0 0
\(191\) −3.50888 + 10.7992i −0.253894 + 0.781404i 0.740152 + 0.672439i \(0.234753\pi\)
−0.994046 + 0.108964i \(0.965247\pi\)
\(192\) 0 0
\(193\) 12.7966 17.6130i 0.921118 1.26781i −0.0421073 0.999113i \(-0.513407\pi\)
0.963225 0.268696i \(-0.0865929\pi\)
\(194\) 0 0
\(195\) −0.00366912 + 0.236167i −0.000262751 + 0.0169122i
\(196\) 0 0
\(197\) 23.7957i 1.69537i 0.530500 + 0.847685i \(0.322004\pi\)
−0.530500 + 0.847685i \(0.677996\pi\)
\(198\) 0 0
\(199\) −12.8012 −0.907451 −0.453725 0.891142i \(-0.649905\pi\)
−0.453725 + 0.891142i \(0.649905\pi\)
\(200\) 0 0
\(201\) −8.41907 + 2.73552i −0.593835 + 0.192949i
\(202\) 0 0
\(203\) −0.345958 + 0.476171i −0.0242815 + 0.0334206i
\(204\) 0 0
\(205\) −0.174907 + 0.538307i −0.0122160 + 0.0375970i
\(206\) 0 0
\(207\) −2.04514 + 1.48588i −0.142147 + 0.103276i
\(208\) 0 0
\(209\) 1.94976 + 7.53392i 0.134867 + 0.521132i
\(210\) 0 0
\(211\) −2.51595 + 1.82794i −0.173205 + 0.125841i −0.671010 0.741448i \(-0.734139\pi\)
0.497805 + 0.867289i \(0.334139\pi\)
\(212\) 0 0
\(213\) −10.0342 3.26030i −0.687531 0.223392i
\(214\) 0 0
\(215\) 0.0578223 0.0795856i 0.00394345 0.00542769i
\(216\) 0 0
\(217\) 2.14464 + 6.60053i 0.145588 + 0.448073i
\(218\) 0 0
\(219\) 10.0689i 0.680392i
\(220\) 0 0
\(221\) 7.99349 23.3603i 0.537700 1.57138i
\(222\) 0 0
\(223\) −10.9171 + 3.54717i −0.731061 + 0.237536i −0.650812 0.759239i \(-0.725572\pi\)
−0.0802490 + 0.996775i \(0.525572\pi\)
\(224\) 0 0
\(225\) 9.08172 + 6.59825i 0.605448 + 0.439884i
\(226\) 0 0
\(227\) −5.12105 1.66393i −0.339896 0.110439i 0.134095 0.990968i \(-0.457187\pi\)
−0.473991 + 0.880530i \(0.657187\pi\)
\(228\) 0 0
\(229\) 13.9307 + 19.1739i 0.920565 + 1.26705i 0.963428 + 0.267968i \(0.0863521\pi\)
−0.0428629 + 0.999081i \(0.513648\pi\)
\(230\) 0 0
\(231\) 6.73936 + 0.411060i 0.443417 + 0.0270458i
\(232\) 0 0
\(233\) 18.4259 13.3872i 1.20712 0.877025i 0.212155 0.977236i \(-0.431952\pi\)
0.994966 + 0.100211i \(0.0319519\pi\)
\(234\) 0 0
\(235\) −0.0509204 + 0.156717i −0.00332168 + 0.0102231i
\(236\) 0 0
\(237\) −10.3636 7.52961i −0.673189 0.489100i
\(238\) 0 0
\(239\) 19.1942 6.23657i 1.24157 0.403410i 0.386677 0.922215i \(-0.373623\pi\)
0.854893 + 0.518805i \(0.173623\pi\)
\(240\) 0 0
\(241\) 9.98765i 0.643361i 0.946848 + 0.321681i \(0.104248\pi\)
−0.946848 + 0.321681i \(0.895752\pi\)
\(242\) 0 0
\(243\) 16.0793 1.03149
\(244\) 0 0
\(245\) 0.107111 0.0348024i 0.00684306 0.00222344i
\(246\) 0 0
\(247\) 4.86578 + 6.92076i 0.309602 + 0.440357i
\(248\) 0 0
\(249\) 4.60062 + 1.49483i 0.291553 + 0.0947312i
\(250\) 0 0
\(251\) 20.4673 14.8704i 1.29188 0.938609i 0.292043 0.956405i \(-0.405665\pi\)
0.999842 + 0.0177963i \(0.00566502\pi\)
\(252\) 0 0
\(253\) −0.227094 + 3.72322i −0.0142773 + 0.234077i
\(254\) 0 0
\(255\) −0.263674 0.362917i −0.0165119 0.0227267i
\(256\) 0 0
\(257\) −2.92217 + 8.99351i −0.182280 + 0.561000i −0.999891 0.0147710i \(-0.995298\pi\)
0.817611 + 0.575771i \(0.195298\pi\)
\(258\) 0 0
\(259\) −3.37931 2.45521i −0.209980 0.152560i
\(260\) 0 0
\(261\) 0.174178 + 0.536065i 0.0107814 + 0.0331816i
\(262\) 0 0
\(263\) 12.2357 0.754484 0.377242 0.926115i \(-0.376873\pi\)
0.377242 + 0.926115i \(0.376873\pi\)
\(264\) 0 0
\(265\) 0.608035i 0.0373513i
\(266\) 0 0
\(267\) 4.63571 1.50623i 0.283701 0.0921800i
\(268\) 0 0
\(269\) −0.408835 0.297036i −0.0249271 0.0181106i 0.575252 0.817976i \(-0.304904\pi\)
−0.600179 + 0.799866i \(0.704904\pi\)
\(270\) 0 0
\(271\) −22.4486 7.29399i −1.36366 0.443079i −0.466394 0.884577i \(-0.654447\pi\)
−0.897262 + 0.441499i \(0.854447\pi\)
\(272\) 0 0
\(273\) 7.01522 2.15949i 0.424580 0.130698i
\(274\) 0 0
\(275\) 16.0359 4.15004i 0.967001 0.250257i
\(276\) 0 0
\(277\) −11.6800 + 8.48603i −0.701784 + 0.509876i −0.880513 0.474022i \(-0.842802\pi\)
0.178729 + 0.983898i \(0.442802\pi\)
\(278\) 0 0
\(279\) 6.32099 + 2.05381i 0.378428 + 0.122959i
\(280\) 0 0
\(281\) 12.7496 17.5483i 0.760576 1.04684i −0.236590 0.971610i \(-0.576030\pi\)
0.997166 0.0752337i \(-0.0239703\pi\)
\(282\) 0 0
\(283\) −1.79720 5.53121i −0.106832 0.328796i 0.883324 0.468763i \(-0.155300\pi\)
−0.990156 + 0.139967i \(0.955300\pi\)
\(284\) 0 0
\(285\) 0.153710 0.00910498
\(286\) 0 0
\(287\) 17.5895 1.03827
\(288\) 0 0
\(289\) 9.23719 + 28.4291i 0.543364 + 1.67230i
\(290\) 0 0
\(291\) −7.26506 + 9.99950i −0.425885 + 0.586181i
\(292\) 0 0
\(293\) −19.9971 6.49745i −1.16824 0.379585i −0.340256 0.940333i \(-0.610514\pi\)
−0.827987 + 0.560747i \(0.810514\pi\)
\(294\) 0 0
\(295\) 0.462576 0.336081i 0.0269322 0.0195674i
\(296\) 0 0
\(297\) 9.60031 11.6501i 0.557066 0.676007i
\(298\) 0 0
\(299\) 1.19303 + 3.87562i 0.0689948 + 0.224133i
\(300\) 0 0
\(301\) −2.90745 0.944688i −0.167583 0.0544509i
\(302\) 0 0
\(303\) 6.25491 + 4.54446i 0.359335 + 0.261072i
\(304\) 0 0
\(305\) 0.359108 0.116681i 0.0205624 0.00668114i
\(306\) 0 0
\(307\) 0.674788i 0.0385122i 0.999815 + 0.0192561i \(0.00612978\pi\)
−0.999815 + 0.0192561i \(0.993870\pi\)
\(308\) 0 0
\(309\) 0.262181 0.0149150
\(310\) 0 0
\(311\) −0.437944 1.34785i −0.0248335 0.0764297i 0.937872 0.346982i \(-0.112794\pi\)
−0.962705 + 0.270553i \(0.912794\pi\)
\(312\) 0 0
\(313\) 14.1220 + 10.2602i 0.798222 + 0.579942i 0.910392 0.413747i \(-0.135780\pi\)
−0.112170 + 0.993689i \(0.535780\pi\)
\(314\) 0 0
\(315\) −0.123126 + 0.378942i −0.00693734 + 0.0213509i
\(316\) 0 0
\(317\) −11.3426 15.6118i −0.637065 0.876845i 0.361389 0.932415i \(-0.382303\pi\)
−0.998455 + 0.0555697i \(0.982303\pi\)
\(318\) 0 0
\(319\) 0.773888 + 0.304692i 0.0433294 + 0.0170595i
\(320\) 0 0
\(321\) 2.94860 2.14228i 0.164575 0.119571i
\(322\) 0 0
\(323\) −15.2812 4.96518i −0.850271 0.276270i
\(324\) 0 0
\(325\) 14.7308 10.3568i 0.817117 0.574491i
\(326\) 0 0
\(327\) 6.74857 2.19274i 0.373197 0.121259i
\(328\) 0 0
\(329\) 5.12081 0.282320
\(330\) 0 0
\(331\) 23.9015i 1.31375i 0.754001 + 0.656873i \(0.228121\pi\)
−0.754001 + 0.656873i \(0.771879\pi\)
\(332\) 0 0
\(333\) −3.80438 + 1.23612i −0.208479 + 0.0677388i
\(334\) 0 0
\(335\) −0.623615 0.453083i −0.0340718 0.0247546i
\(336\) 0 0
\(337\) −8.15890 + 25.1105i −0.444444 + 1.36786i 0.438649 + 0.898658i \(0.355457\pi\)
−0.883093 + 0.469198i \(0.844543\pi\)
\(338\) 0 0
\(339\) 3.92819 2.85400i 0.213350 0.155008i
\(340\) 0 0
\(341\) 8.27031 5.27072i 0.447862 0.285425i
\(342\) 0 0
\(343\) −11.7143 16.1233i −0.632512 0.870578i
\(344\) 0 0
\(345\) 0.0700704 + 0.0227673i 0.00377246 + 0.00122575i
\(346\) 0 0
\(347\) 18.3519 + 13.3335i 0.985183 + 0.715778i 0.958861 0.283876i \(-0.0916204\pi\)
0.0263223 + 0.999654i \(0.491620\pi\)
\(348\) 0 0
\(349\) 15.6882 5.09741i 0.839771 0.272858i 0.142616 0.989778i \(-0.454449\pi\)
0.697155 + 0.716920i \(0.254449\pi\)
\(350\) 0 0
\(351\) 5.31316 15.5273i 0.283596 0.828783i
\(352\) 0 0
\(353\) 21.8132i 1.16100i 0.814260 + 0.580500i \(0.197143\pi\)
−0.814260 + 0.580500i \(0.802857\pi\)
\(354\) 0 0
\(355\) −0.283896 0.873742i −0.0150676 0.0463734i
\(356\) 0 0
\(357\) −8.19403 + 11.2781i −0.433674 + 0.596901i
\(358\) 0 0
\(359\) −8.58451 2.78928i −0.453073 0.147212i 0.0735861 0.997289i \(-0.476556\pi\)
−0.526659 + 0.850076i \(0.676556\pi\)
\(360\) 0 0
\(361\) −10.9172 + 7.93181i −0.574590 + 0.417464i
\(362\) 0 0
\(363\) −1.82365 9.36504i −0.0957166 0.491537i
\(364\) 0 0
\(365\) 0.709317 0.515349i 0.0371273 0.0269746i
\(366\) 0 0
\(367\) 4.33767 13.3500i 0.226425 0.696863i −0.771719 0.635963i \(-0.780603\pi\)
0.998144 0.0608999i \(-0.0193971\pi\)
\(368\) 0 0
\(369\) 9.90098 13.6275i 0.515425 0.709421i
\(370\) 0 0
\(371\) 17.9707 5.83902i 0.932991 0.303147i
\(372\) 0 0
\(373\) −13.2291 −0.684979 −0.342489 0.939522i \(-0.611270\pi\)
−0.342489 + 0.939522i \(0.611270\pi\)
\(374\) 0 0
\(375\) 0.654714i 0.0338093i
\(376\) 0 0
\(377\) 0.904054 + 0.0140455i 0.0465612 + 0.000723381i
\(378\) 0 0
\(379\) −15.5410 + 21.3903i −0.798287 + 1.09875i 0.194739 + 0.980855i \(0.437614\pi\)
−0.993026 + 0.117893i \(0.962386\pi\)
\(380\) 0 0
\(381\) 4.94980 15.2339i 0.253586 0.780458i
\(382\) 0 0
\(383\) 21.2269 + 29.2163i 1.08464 + 1.49288i 0.854305 + 0.519772i \(0.173983\pi\)
0.230337 + 0.973111i \(0.426017\pi\)
\(384\) 0 0
\(385\) 0.315978 + 0.495803i 0.0161037 + 0.0252685i
\(386\) 0 0
\(387\) −2.36848 + 1.72080i −0.120397 + 0.0874734i
\(388\) 0 0
\(389\) −3.86122 + 11.8836i −0.195771 + 0.602523i 0.804195 + 0.594365i \(0.202597\pi\)
−0.999967 + 0.00815738i \(0.997403\pi\)
\(390\) 0 0
\(391\) −6.23070 4.52687i −0.315100 0.228934i
\(392\) 0 0
\(393\) −2.52451 7.76965i −0.127345 0.391927i
\(394\) 0 0
\(395\) 1.11546i 0.0561250i
\(396\) 0 0
\(397\) 4.26594i 0.214101i 0.994254 + 0.107051i \(0.0341407\pi\)
−0.994254 + 0.107051i \(0.965859\pi\)
\(398\) 0 0
\(399\) −1.47609 4.54294i −0.0738970 0.227432i
\(400\) 0 0
\(401\) 16.0228 22.0535i 0.800142 1.10130i −0.192628 0.981272i \(-0.561701\pi\)
0.992770 0.120030i \(-0.0382990\pi\)
\(402\) 0 0
\(403\) 6.39984 8.52686i 0.318799 0.424753i
\(404\) 0 0
\(405\) 0.124087 + 0.170791i 0.00616594 + 0.00848669i
\(406\) 0 0
\(407\) −2.16236 + 5.49217i −0.107184 + 0.272237i
\(408\) 0 0
\(409\) 19.4490 + 26.7693i 0.961694 + 1.32366i 0.946133 + 0.323779i \(0.104953\pi\)
0.0155607 + 0.999879i \(0.495047\pi\)
\(410\) 0 0
\(411\) −11.9408 3.87979i −0.588995 0.191376i
\(412\) 0 0
\(413\) −14.3752 10.4442i −0.707355 0.513924i
\(414\) 0 0
\(415\) 0.130165 + 0.400606i 0.00638955 + 0.0196650i
\(416\) 0 0
\(417\) −2.28541 −0.111917
\(418\) 0 0
\(419\) −26.0287 −1.27158 −0.635792 0.771861i \(-0.719326\pi\)
−0.635792 + 0.771861i \(0.719326\pi\)
\(420\) 0 0
\(421\) −26.9030 + 8.74132i −1.31117 + 0.426026i −0.879455 0.475982i \(-0.842093\pi\)
−0.431719 + 0.902008i \(0.642093\pi\)
\(422\) 0 0
\(423\) 2.88247 3.96737i 0.140150 0.192900i
\(424\) 0 0
\(425\) −10.5683 + 32.5260i −0.512640 + 1.57774i
\(426\) 0 0
\(427\) −6.89710 9.49304i −0.333774 0.459401i
\(428\) 0 0
\(429\) −5.43785 8.83235i −0.262542 0.426430i
\(430\) 0 0
\(431\) −4.33663 5.96886i −0.208888 0.287510i 0.691698 0.722186i \(-0.256863\pi\)
−0.900587 + 0.434676i \(0.856863\pi\)
\(432\) 0 0
\(433\) 1.41532 4.35590i 0.0680158 0.209331i −0.911272 0.411806i \(-0.864898\pi\)
0.979288 + 0.202474i \(0.0648983\pi\)
\(434\) 0 0
\(435\) 0.00965591 0.0132902i 0.000462965 0.000637217i
\(436\) 0 0
\(437\) 2.50979 0.815481i 0.120060 0.0390097i
\(438\) 0 0
\(439\) 2.42519 0.115748 0.0578740 0.998324i \(-0.481568\pi\)
0.0578740 + 0.998324i \(0.481568\pi\)
\(440\) 0 0
\(441\) −3.35168 −0.159604
\(442\) 0 0
\(443\) −2.27040 6.98757i −0.107870 0.331989i 0.882523 0.470269i \(-0.155843\pi\)
−0.990393 + 0.138279i \(0.955843\pi\)
\(444\) 0 0
\(445\) 0.343375 + 0.249477i 0.0162775 + 0.0118263i
\(446\) 0 0
\(447\) 0.946417 + 0.307509i 0.0447640 + 0.0145447i
\(448\) 0 0
\(449\) 6.57926 + 9.05558i 0.310495 + 0.427359i 0.935535 0.353233i \(-0.114918\pi\)
−0.625041 + 0.780592i \(0.714918\pi\)
\(450\) 0 0
\(451\) −6.22733 24.0626i −0.293233 1.13306i
\(452\) 0 0
\(453\) −1.75406 2.41426i −0.0824130 0.113432i
\(454\) 0 0
\(455\) 0.511184 + 0.383669i 0.0239647 + 0.0179867i
\(456\) 0 0
\(457\) −1.49129 + 2.05259i −0.0697598 + 0.0960161i −0.842471 0.538741i \(-0.818900\pi\)
0.772711 + 0.634757i \(0.218900\pi\)
\(458\) 0 0
\(459\) 9.63162 + 29.6431i 0.449566 + 1.38362i
\(460\) 0 0
\(461\) 33.0119i 1.53752i 0.639538 + 0.768760i \(0.279126\pi\)
−0.639538 + 0.768760i \(0.720874\pi\)
\(462\) 0 0
\(463\) 28.5889i 1.32864i −0.747448 0.664320i \(-0.768721\pi\)
0.747448 0.664320i \(-0.231279\pi\)
\(464\) 0 0
\(465\) −0.0598582 0.184225i −0.00277586 0.00854322i
\(466\) 0 0
\(467\) 2.37988 + 1.72908i 0.110127 + 0.0800123i 0.641486 0.767135i \(-0.278318\pi\)
−0.531358 + 0.847147i \(0.678318\pi\)
\(468\) 0 0
\(469\) −7.40237 + 22.7822i −0.341810 + 1.05198i
\(470\) 0 0
\(471\) 11.2025 8.13909i 0.516183 0.375029i
\(472\) 0 0
\(473\) −0.262999 + 4.31188i −0.0120927 + 0.198260i
\(474\) 0 0
\(475\) −6.88803 9.48056i −0.316045 0.434998i
\(476\) 0 0
\(477\) 5.59174 17.2096i 0.256028 0.787973i
\(478\) 0 0
\(479\) −0.551593 + 0.759203i −0.0252029 + 0.0346889i −0.821433 0.570306i \(-0.806825\pi\)
0.796230 + 0.604995i \(0.206825\pi\)
\(480\) 0 0
\(481\) −0.0996790 + 6.41594i −0.00454497 + 0.292542i
\(482\) 0 0
\(483\) 2.28959i 0.104180i
\(484\) 0 0
\(485\) −1.07627 −0.0488710
\(486\) 0 0
\(487\) 11.2585 3.65812i 0.510173 0.165765i −0.0426080 0.999092i \(-0.513567\pi\)
0.552781 + 0.833327i \(0.313567\pi\)
\(488\) 0 0
\(489\) −7.67142 + 10.5588i −0.346914 + 0.477485i
\(490\) 0 0
\(491\) 3.22310 9.91967i 0.145456 0.447669i −0.851613 0.524171i \(-0.824375\pi\)
0.997069 + 0.0765023i \(0.0243753\pi\)
\(492\) 0 0
\(493\) −1.38926 + 1.00936i −0.0625690 + 0.0454591i
\(494\) 0 0
\(495\) 0.561987 + 0.0342778i 0.0252594 + 0.00154067i
\(496\) 0 0
\(497\) −23.0975 + 16.7813i −1.03606 + 0.752743i
\(498\) 0 0
\(499\) −16.6248 5.40171i −0.744226 0.241814i −0.0877313 0.996144i \(-0.527962\pi\)
−0.656495 + 0.754330i \(0.727962\pi\)
\(500\) 0 0
\(501\) 10.2468 14.1036i 0.457795 0.630101i
\(502\) 0 0
\(503\) −11.8096 36.3462i −0.526564 1.62060i −0.761201 0.648516i \(-0.775390\pi\)
0.234637 0.972083i \(-0.424610\pi\)
\(504\) 0 0
\(505\) 0.673233i 0.0299585i
\(506\) 0 0
\(507\) −8.91192 6.90785i −0.395792 0.306788i
\(508\) 0 0
\(509\) −21.8035 + 7.08439i −0.966423 + 0.314010i −0.749371 0.662150i \(-0.769644\pi\)
−0.217052 + 0.976160i \(0.569644\pi\)
\(510\) 0 0
\(511\) −22.0430 16.0151i −0.975123 0.708468i
\(512\) 0 0
\(513\) −10.1572 3.30028i −0.448453 0.145711i
\(514\) 0 0
\(515\) 0.0134190 + 0.0184697i 0.000591314 + 0.000813873i
\(516\) 0 0
\(517\) −1.81296 7.00533i −0.0797337 0.308094i
\(518\) 0 0
\(519\) 4.99520 3.62923i 0.219265 0.159305i
\(520\) 0 0
\(521\) 0.436320 1.34286i 0.0191155 0.0588316i −0.941044 0.338285i \(-0.890153\pi\)
0.960159 + 0.279453i \(0.0901532\pi\)
\(522\) 0 0
\(523\) 7.65951 + 5.56496i 0.334927 + 0.243339i 0.742518 0.669826i \(-0.233631\pi\)
−0.407591 + 0.913164i \(0.633631\pi\)
\(524\) 0 0
\(525\) −9.66961 + 3.14185i −0.422017 + 0.137122i
\(526\) 0 0
\(527\) 20.2485i 0.882038i
\(528\) 0 0
\(529\) −21.7351 −0.945004
\(530\) 0 0
\(531\) −16.1833 + 5.25828i −0.702297 + 0.228190i
\(532\) 0 0
\(533\) −15.5408 22.1042i −0.673148 0.957440i
\(534\) 0 0
\(535\) 0.301833 + 0.0980714i 0.0130494 + 0.00424000i
\(536\) 0 0
\(537\) −14.2086 + 10.3231i −0.613146 + 0.445476i
\(538\) 0 0
\(539\) −3.14518 + 3.81671i −0.135472 + 0.164397i
\(540\) 0 0
\(541\) 24.8077 + 34.1448i 1.06657 + 1.46800i 0.873505 + 0.486815i \(0.161841\pi\)
0.193061 + 0.981187i \(0.438159\pi\)
\(542\) 0 0
\(543\) 3.49353 10.7520i 0.149922 0.461412i
\(544\) 0 0
\(545\) 0.499878 + 0.363183i 0.0214124 + 0.0155570i
\(546\) 0 0
\(547\) −10.4785 32.2495i −0.448029 1.37889i −0.879128 0.476586i \(-0.841874\pi\)
0.431099 0.902304i \(-0.358126\pi\)
\(548\) 0 0
\(549\) −11.2371 −0.479588
\(550\) 0 0
\(551\) 0.588406i 0.0250670i
\(552\) 0 0
\(553\) −32.9679 + 10.7119i −1.40194 + 0.455517i
\(554\) 0 0
\(555\) 0.0943187 + 0.0685266i 0.00400361 + 0.00290879i
\(556\) 0 0
\(557\) 3.44701 + 1.12000i 0.146055 + 0.0474561i 0.381132 0.924521i \(-0.375534\pi\)
−0.235077 + 0.971977i \(0.575534\pi\)
\(558\) 0 0
\(559\) 1.38165 + 4.48837i 0.0584377 + 0.189838i
\(560\) 0 0
\(561\) 18.3296 + 7.21665i 0.773875 + 0.304687i
\(562\) 0 0
\(563\) 10.3117 7.49186i 0.434584 0.315744i −0.348895 0.937162i \(-0.613443\pi\)
0.783479 + 0.621418i \(0.213443\pi\)
\(564\) 0 0
\(565\) 0.402108 + 0.130653i 0.0169168 + 0.00549660i
\(566\) 0 0
\(567\) 3.85617 5.30757i 0.161944 0.222897i
\(568\) 0 0
\(569\) 1.36757 + 4.20895i 0.0573316 + 0.176449i 0.975621 0.219460i \(-0.0704296\pi\)
−0.918290 + 0.395909i \(0.870430\pi\)
\(570\) 0 0
\(571\) 11.4355 0.478560 0.239280 0.970951i \(-0.423089\pi\)
0.239280 + 0.970951i \(0.423089\pi\)
\(572\) 0 0
\(573\) −9.84883 −0.411441
\(574\) 0 0
\(575\) −1.73574 5.34207i −0.0723856 0.222780i
\(576\) 0 0
\(577\) 11.8523 16.3133i 0.493417 0.679130i −0.487597 0.873069i \(-0.662126\pi\)
0.981014 + 0.193939i \(0.0621264\pi\)
\(578\) 0 0
\(579\) 17.9589 + 5.83521i 0.746347 + 0.242503i
\(580\) 0 0
\(581\) 10.5901 7.69414i 0.439350 0.319207i
\(582\) 0 0
\(583\) −14.3501 22.5168i −0.594321 0.932552i
\(584\) 0 0
\(585\) 0.584990 0.180077i 0.0241864 0.00744528i
\(586\) 0 0
\(587\) −25.9756 8.43997i −1.07213 0.348355i −0.280811 0.959763i \(-0.590603\pi\)
−0.791315 + 0.611408i \(0.790603\pi\)
\(588\) 0 0
\(589\) −5.61309 4.07815i −0.231284 0.168037i
\(590\) 0 0
\(591\) −19.6292 + 6.37792i −0.807438 + 0.262352i
\(592\) 0 0
\(593\) 11.2159i 0.460584i 0.973122 + 0.230292i \(0.0739681\pi\)
−0.973122 + 0.230292i \(0.926032\pi\)
\(594\) 0 0
\(595\) −1.21389 −0.0497647
\(596\) 0 0
\(597\) −3.43108 10.5598i −0.140425 0.432183i
\(598\) 0 0
\(599\) 22.1846 + 16.1180i 0.906437 + 0.658565i 0.940111 0.340868i \(-0.110721\pi\)
−0.0336742 + 0.999433i \(0.510721\pi\)
\(600\) 0 0
\(601\) 8.37064 25.7622i 0.341446 1.05086i −0.622014 0.783006i \(-0.713685\pi\)
0.963459 0.267855i \(-0.0863148\pi\)
\(602\) 0 0
\(603\) 13.4838 + 18.5589i 0.549105 + 0.755778i
\(604\) 0 0
\(605\) 0.566395 0.607794i 0.0230272 0.0247103i
\(606\) 0 0
\(607\) 10.3888 7.54789i 0.421668 0.306360i −0.356641 0.934242i \(-0.616078\pi\)
0.778308 + 0.627882i \(0.216078\pi\)
\(608\) 0 0
\(609\) −0.485523 0.157756i −0.0196744 0.00639260i
\(610\) 0 0
\(611\) −4.52439 6.43518i −0.183037 0.260340i
\(612\) 0 0
\(613\) 9.99288 3.24688i 0.403609 0.131140i −0.100176 0.994970i \(-0.531941\pi\)
0.503785 + 0.863829i \(0.331941\pi\)
\(614\) 0 0
\(615\) −0.490933 −0.0197963
\(616\) 0 0
\(617\) 33.2428i 1.33831i −0.743125 0.669153i \(-0.766657\pi\)
0.743125 0.669153i \(-0.233343\pi\)
\(618\) 0 0
\(619\) 27.0278 8.78187i 1.08634 0.352973i 0.289509 0.957175i \(-0.406508\pi\)
0.796831 + 0.604202i \(0.206508\pi\)
\(620\) 0 0
\(621\) −4.14146 3.00895i −0.166191 0.120745i
\(622\) 0 0
\(623\) 4.07590 12.5443i 0.163297 0.502577i
\(624\) 0 0
\(625\) −20.1562 + 14.6444i −0.806249 + 0.585774i
\(626\) 0 0
\(627\) −5.69220 + 3.62768i −0.227325 + 0.144875i
\(628\) 0 0
\(629\) −7.16325 9.85936i −0.285617 0.393119i
\(630\) 0 0
\(631\) 24.1416 + 7.84408i 0.961061 + 0.312268i 0.747202 0.664597i \(-0.231397\pi\)
0.213859 + 0.976865i \(0.431397\pi\)
\(632\) 0 0
\(633\) −2.18223 1.58548i −0.0867358 0.0630172i
\(634\) 0 0
\(635\) 1.32652 0.431012i 0.0526413 0.0171042i
\(636\) 0 0
\(637\) −1.74066 + 5.08692i −0.0689673 + 0.201551i
\(638\) 0 0
\(639\) 27.3409i 1.08159i
\(640\) 0 0
\(641\) 10.2735 + 31.6185i 0.405777 + 1.24885i 0.920244 + 0.391344i \(0.127990\pi\)
−0.514467 + 0.857510i \(0.672010\pi\)
\(642\) 0 0
\(643\) −1.35518 + 1.86525i −0.0534431 + 0.0735581i −0.834902 0.550398i \(-0.814476\pi\)
0.781459 + 0.623957i \(0.214476\pi\)
\(644\) 0 0
\(645\) 0.0811488 + 0.0263668i 0.00319523 + 0.00103819i
\(646\) 0 0
\(647\) 19.3140 14.0324i 0.759310 0.551671i −0.139388 0.990238i \(-0.544514\pi\)
0.898699 + 0.438567i \(0.144514\pi\)
\(648\) 0 0
\(649\) −9.19839 + 23.3630i −0.361068 + 0.917077i
\(650\) 0 0
\(651\) −4.87000 + 3.53826i −0.190870 + 0.138675i
\(652\) 0 0
\(653\) 4.37626 13.4687i 0.171256 0.527073i −0.828186 0.560453i \(-0.810627\pi\)
0.999443 + 0.0333800i \(0.0106272\pi\)
\(654\) 0 0
\(655\) 0.418134 0.575512i 0.0163378 0.0224871i
\(656\) 0 0
\(657\) −24.8156 + 8.06308i −0.968149 + 0.314571i
\(658\) 0 0
\(659\) −24.7568 −0.964388 −0.482194 0.876065i \(-0.660160\pi\)
−0.482194 + 0.876065i \(0.660160\pi\)
\(660\) 0 0
\(661\) 16.9087i 0.657670i −0.944387 0.328835i \(-0.893344\pi\)
0.944387 0.328835i \(-0.106656\pi\)
\(662\) 0 0
\(663\) 21.4125 + 0.332668i 0.831594 + 0.0129198i
\(664\) 0 0
\(665\) 0.244484 0.336504i 0.00948069 0.0130491i
\(666\) 0 0
\(667\) 0.0871539 0.268232i 0.00337461 0.0103860i
\(668\) 0 0
\(669\) −5.85218 8.05483i −0.226258 0.311418i
\(670\) 0 0
\(671\) −10.5448 + 12.7962i −0.407076 + 0.493991i
\(672\) 0 0
\(673\) −1.72281 + 1.25170i −0.0664096 + 0.0482494i −0.620495 0.784211i \(-0.713068\pi\)
0.554085 + 0.832460i \(0.313068\pi\)
\(674\) 0 0
\(675\) −7.02463 + 21.6196i −0.270378 + 0.832138i
\(676\) 0 0
\(677\) −34.0942 24.7709i −1.31035 0.952022i −0.999999 0.00139885i \(-0.999555\pi\)
−0.310347 0.950623i \(-0.600445\pi\)
\(678\) 0 0
\(679\) 10.3356 + 31.8096i 0.396642 + 1.22074i
\(680\) 0 0
\(681\) 4.67037i 0.178969i
\(682\) 0 0
\(683\) 8.17932i 0.312973i 0.987680 + 0.156486i \(0.0500167\pi\)
−0.987680 + 0.156486i \(0.949983\pi\)
\(684\) 0 0
\(685\) −0.337839 1.03976i −0.0129082 0.0397273i
\(686\) 0 0
\(687\) −12.0829 + 16.6307i −0.460991 + 0.634500i
\(688\) 0 0
\(689\) −23.2153 17.4243i −0.884434 0.663812i
\(690\) 0 0
\(691\) −13.9708 19.2292i −0.531475 0.731513i 0.455879 0.890042i \(-0.349325\pi\)
−0.987354 + 0.158529i \(0.949325\pi\)
\(692\) 0 0
\(693\) −4.38373 16.9389i −0.166524 0.643455i
\(694\) 0 0
\(695\) −0.116973 0.160999i −0.00443703 0.00610704i
\(696\) 0 0
\(697\) 48.8068 + 15.8583i 1.84869 + 0.600675i
\(698\) 0 0
\(699\) 15.9819 + 11.6115i 0.604490 + 0.439188i
\(700\) 0 0
\(701\) −2.60555 8.01907i −0.0984104 0.302876i 0.889717 0.456512i \(-0.150902\pi\)
−0.988127 + 0.153636i \(0.950902\pi\)
\(702\) 0 0
\(703\) 4.17583 0.157495
\(704\) 0 0
\(705\) −0.142925 −0.00538287
\(706\) 0 0
\(707\) 19.8976 6.46513i 0.748327 0.243146i
\(708\) 0 0
\(709\) −1.50015 + 2.06478i −0.0563393 + 0.0775444i −0.836257 0.548338i \(-0.815261\pi\)
0.779918 + 0.625882i \(0.215261\pi\)
\(710\) 0 0
\(711\) −10.2582 + 31.5716i −0.384714 + 1.18403i
\(712\) 0 0
\(713\) −1.95475 2.69048i −0.0732058 0.100759i
\(714\) 0 0
\(715\) 0.343886 0.835137i 0.0128606 0.0312324i
\(716\) 0 0
\(717\) 10.2892 + 14.1619i 0.384257 + 0.528884i
\(718\) 0 0
\(719\) −9.06468 + 27.8982i −0.338055 + 1.04043i 0.627142 + 0.778905i \(0.284225\pi\)
−0.965197 + 0.261523i \(0.915775\pi\)
\(720\) 0 0
\(721\) 0.417014 0.573971i 0.0155304 0.0213758i
\(722\) 0 0
\(723\) −8.23889 + 2.67698i −0.306407 + 0.0995578i
\(724\) 0 0
\(725\) −1.25242 −0.0465137
\(726\) 0 0
\(727\) 52.3565 1.94180 0.970898 0.239493i \(-0.0769812\pi\)
0.970898 + 0.239493i \(0.0769812\pi\)
\(728\) 0 0
\(729\) 1.71845 + 5.28885i 0.0636463 + 0.195883i
\(730\) 0 0
\(731\) −7.21580 5.24258i −0.266886 0.193904i
\(732\) 0 0
\(733\) −22.9239 7.44841i −0.846712 0.275113i −0.146644 0.989189i \(-0.546847\pi\)
−0.700068 + 0.714076i \(0.746847\pi\)
\(734\) 0 0
\(735\) 0.0574175 + 0.0790285i 0.00211788 + 0.00291501i
\(736\) 0 0
\(737\) 33.7869 + 2.06080i 1.24456 + 0.0759105i
\(738\) 0 0
\(739\) −6.99522 9.62810i −0.257323 0.354175i 0.660736 0.750619i \(-0.270244\pi\)
−0.918059 + 0.396443i \(0.870244\pi\)
\(740\) 0 0
\(741\) −4.40482 + 5.86878i −0.161815 + 0.215595i
\(742\) 0 0
\(743\) −13.1643 + 18.1190i −0.482950 + 0.664723i −0.979068 0.203532i \(-0.934758\pi\)
0.496119 + 0.868255i \(0.334758\pi\)
\(744\) 0 0
\(745\) 0.0267769 + 0.0824107i 0.000981029 + 0.00301930i
\(746\) 0 0
\(747\) 12.5357i 0.458656i
\(748\) 0 0
\(749\) 9.86255i 0.360370i
\(750\) 0 0
\(751\) −9.74442 29.9902i −0.355579 1.09436i −0.955673 0.294430i \(-0.904870\pi\)
0.600094 0.799929i \(-0.295130\pi\)
\(752\) 0 0
\(753\) 17.7525 + 12.8979i 0.646937 + 0.470027i
\(754\) 0 0
\(755\) 0.0802990 0.247135i 0.00292238 0.00899416i
\(756\) 0 0
\(757\) 22.0931 16.0515i 0.802986 0.583403i −0.108803 0.994063i \(-0.534702\pi\)
0.911789 + 0.410660i \(0.134702\pi\)
\(758\) 0 0
\(759\) −3.13218 + 0.810599i −0.113691 + 0.0294229i
\(760\) 0 0
\(761\) 3.97599 + 5.47247i 0.144129 + 0.198377i 0.874978 0.484162i \(-0.160876\pi\)
−0.730849 + 0.682539i \(0.760876\pi\)
\(762\) 0 0
\(763\) 5.93360 18.2618i 0.214811 0.661120i
\(764\) 0 0
\(765\) −0.683290 + 0.940468i −0.0247044 + 0.0340027i
\(766\) 0 0
\(767\) −0.424021 + 27.2926i −0.0153105 + 0.985478i
\(768\) 0 0
\(769\) 21.8891i 0.789341i −0.918823 0.394671i \(-0.870859\pi\)
0.918823 0.394671i \(-0.129141\pi\)
\(770\) 0 0
\(771\) −8.20204 −0.295389
\(772\) 0 0
\(773\) 21.2402 6.90135i 0.763956 0.248224i 0.0989802 0.995089i \(-0.468442\pi\)
0.664976 + 0.746865i \(0.268442\pi\)
\(774\) 0 0
\(775\) −8.68031 + 11.9474i −0.311806 + 0.429164i
\(776\) 0 0
\(777\) 1.11957 3.44569i 0.0401644 0.123613i
\(778\) 0 0
\(779\) −14.2260 + 10.3358i −0.509700 + 0.370319i
\(780\) 0 0
\(781\) 31.1343 + 25.6564i 1.11407 + 0.918057i
\(782\) 0 0
\(783\) −0.923421 + 0.670905i −0.0330004 + 0.0239762i
\(784\) 0 0
\(785\) 1.14674 + 0.372598i 0.0409289 + 0.0132986i
\(786\) 0 0
\(787\) −12.7507 + 17.5498i −0.454512 + 0.625583i −0.973359 0.229285i \(-0.926361\pi\)
0.518847 + 0.854867i \(0.326361\pi\)
\(788\) 0 0
\(789\) 3.27951 + 10.0933i 0.116754 + 0.359331i
\(790\) 0 0
\(791\) 13.1391i 0.467173i
\(792\) 0 0
\(793\) −5.83585 + 17.0548i −0.207237 + 0.605633i
\(794\) 0 0
\(795\) −0.501572 + 0.162971i −0.0177889 + 0.00577998i
\(796\) 0 0
\(797\) −15.5708 11.3129i −0.551547 0.400723i 0.276808 0.960925i \(-0.410723\pi\)
−0.828356 + 0.560203i \(0.810723\pi\)
\(798\) 0 0
\(799\) 14.2091 + 4.61681i 0.502681 + 0.163331i
\(800\) 0 0
\(801\) −7.42448 10.2189i −0.262331 0.361068i
\(802\) 0 0
\(803\) −14.1049 + 35.8249i −0.497750 + 1.26423i
\(804\) 0 0
\(805\) 0.161294 0.117187i 0.00568485 0.00413028i
\(806\) 0 0
\(807\) 0.135448 0.416865i 0.00476798 0.0146743i
\(808\) 0 0
\(809\) 28.4469 + 20.6679i 1.00014 + 0.726645i 0.962118 0.272632i \(-0.0878940\pi\)
0.0380228 + 0.999277i \(0.487894\pi\)
\(810\) 0 0
\(811\) 33.7636 10.9704i 1.18560 0.385224i 0.351155 0.936317i \(-0.385789\pi\)
0.834444 + 0.551093i \(0.185789\pi\)
\(812\) 0 0
\(813\) 20.4730i 0.718020i
\(814\) 0 0
\(815\) −1.13647 −0.0398088
\(816\) 0 0
\(817\) 2.90660 0.944411i 0.101689 0.0330408i
\(818\) 0 0
\(819\) −10.9400 15.5603i −0.382274 0.543720i
\(820\) 0 0
\(821\) 8.84316 + 2.87332i 0.308628 + 0.100279i 0.459236 0.888314i \(-0.348123\pi\)
−0.150608 + 0.988594i \(0.548123\pi\)
\(822\) 0 0
\(823\) 20.6324 14.9903i 0.719200 0.522530i −0.166928 0.985969i \(-0.553385\pi\)
0.886129 + 0.463439i \(0.153385\pi\)
\(824\) 0 0
\(825\) 7.72148 + 12.1158i 0.268827 + 0.421818i
\(826\) 0 0
\(827\) −26.3965 36.3317i −0.917897 1.26338i −0.964397 0.264458i \(-0.914807\pi\)
0.0465006 0.998918i \(-0.485193\pi\)
\(828\) 0 0
\(829\) −8.00607 + 24.6401i −0.278062 + 0.855787i 0.710331 + 0.703868i \(0.248545\pi\)
−0.988393 + 0.151919i \(0.951455\pi\)
\(830\) 0 0
\(831\) −10.1308 7.36043i −0.351432 0.255331i
\(832\) 0 0
\(833\) −3.15544 9.71143i −0.109329 0.336481i
\(834\) 0 0
\(835\) 1.51800 0.0525327
\(836\) 0 0
\(837\) 13.4589i 0.465207i
\(838\) 0 0
\(839\) 37.8892 12.3110i 1.30808 0.425021i 0.429695 0.902974i \(-0.358621\pi\)
0.878386 + 0.477953i \(0.158621\pi\)
\(840\) 0 0
\(841\) 23.4106 + 17.0088i 0.807263 + 0.586511i
\(842\) 0 0
\(843\) 17.8930 + 5.81378i 0.616267 + 0.200237i
\(844\) 0 0
\(845\) 0.0305008 0.981373i 0.00104926 0.0337602i
\(846\) 0 0
\(847\) −23.4027 10.9033i −0.804127 0.374641i
\(848\) 0 0
\(849\) 4.08103 2.96505i 0.140061 0.101760i
\(850\) 0 0
\(851\) 1.90360 + 0.618519i 0.0652547 + 0.0212025i
\(852\) 0 0
\(853\) 3.41150 4.69553i 0.116808 0.160772i −0.746610 0.665262i \(-0.768320\pi\)
0.863417 + 0.504490i \(0.168320\pi\)
\(854\) 0 0
\(855\) −0.123089 0.378830i −0.00420957 0.0129557i
\(856\) 0 0
\(857\) −17.4010 −0.594406 −0.297203 0.954814i \(-0.596054\pi\)
−0.297203 + 0.954814i \(0.596054\pi\)
\(858\) 0 0
\(859\) 54.0169 1.84303 0.921516 0.388341i \(-0.126952\pi\)
0.921516 + 0.388341i \(0.126952\pi\)
\(860\) 0 0
\(861\) 4.71449 + 14.5097i 0.160669 + 0.494489i
\(862\) 0 0
\(863\) 14.9778 20.6152i 0.509851 0.701750i −0.474043 0.880502i \(-0.657206\pi\)
0.983894 + 0.178752i \(0.0572060\pi\)
\(864\) 0 0
\(865\) 0.511332 + 0.166142i 0.0173858 + 0.00564900i
\(866\) 0 0
\(867\) −20.9756 + 15.2396i −0.712368 + 0.517566i
\(868\) 0 0
\(869\) 26.3258 + 41.3080i 0.893043 + 1.40128i
\(870\) 0 0
\(871\) 35.1699 10.8263i 1.19169 0.366837i
\(872\) 0 0
\(873\) 30.4624 + 9.89783i 1.03100 + 0.334991i
\(874\) 0 0
\(875\) −1.43331 1.04136i −0.0484547 0.0352044i
\(876\) 0 0
\(877\) 7.29502 2.37030i 0.246335 0.0800392i −0.183247 0.983067i \(-0.558661\pi\)
0.429582 + 0.903028i \(0.358661\pi\)
\(878\) 0 0
\(879\) 18.2373i 0.615128i
\(880\) 0 0
\(881\) 28.9326 0.974763 0.487382 0.873189i \(-0.337952\pi\)
0.487382 + 0.873189i \(0.337952\pi\)
\(882\) 0 0
\(883\) −9.42741 29.0146i −0.317258 0.976419i −0.974815 0.223014i \(-0.928410\pi\)
0.657557 0.753404i \(-0.271590\pi\)
\(884\) 0 0
\(885\) 0.401220 + 0.291503i 0.0134868 + 0.00979877i
\(886\) 0 0
\(887\) 0.856686 2.63661i 0.0287647 0.0885287i −0.935644 0.352946i \(-0.885180\pi\)
0.964408 + 0.264418i \(0.0851798\pi\)
\(888\) 0 0
\(889\) −25.4774 35.0666i −0.854484 1.17610i
\(890\) 0 0
\(891\) −8.62603 3.39621i −0.288983 0.113777i
\(892\) 0 0
\(893\) −4.14161 + 3.00906i −0.138594 + 0.100694i
\(894\) 0 0
\(895\) −1.45446 0.472582i −0.0486171 0.0157967i
\(896\) 0 0
\(897\) −2.87726 + 2.02292i −0.0960691 + 0.0675433i
\(898\) 0 0
\(899\) −0.705219 + 0.229140i −0.0235204 + 0.00764223i
\(900\) 0 0
\(901\) 55.1288 1.83661
\(902\) 0 0
\(903\) 2.65158i 0.0882391i
\(904\) 0 0
\(905\) 0.936245 0.304205i 0.0311219 0.0101121i
\(906\) 0 0
\(907\) 40.8306 + 29.6652i 1.35576 + 0.985016i 0.998702 + 0.0509337i \(0.0162197\pi\)
0.357057 + 0.934083i \(0.383780\pi\)
\(908\) 0 0
\(909\) 6.19132 19.0549i 0.205353 0.632012i
\(910\) 0 0
\(911\) −48.6301 + 35.3319i −1.61119 + 1.17060i −0.751582 + 0.659639i \(0.770709\pi\)
−0.859606 + 0.510958i \(0.829291\pi\)
\(912\) 0 0
\(913\) −14.2749 11.7633i −0.472431 0.389309i
\(914\) 0 0
\(915\) 0.192502 + 0.264957i 0.00636393 + 0.00875920i
\(916\) 0 0
\(917\) −21.0248 6.83138i −0.694301 0.225592i
\(918\) 0 0
\(919\) 33.3766 + 24.2496i 1.10099 + 0.799919i 0.981222 0.192883i \(-0.0617836\pi\)
0.119772 + 0.992801i \(0.461784\pi\)
\(920\) 0 0
\(921\) −0.556637 + 0.180862i −0.0183418 + 0.00595962i
\(922\) 0 0
\(923\) 41.4958 + 14.1992i 1.36585 + 0.467372i
\(924\) 0 0
\(925\) 8.88823i 0.292243i
\(926\) 0 0
\(927\) −0.209953 0.646167i −0.00689575 0.0212229i
\(928\) 0 0
\(929\) 18.8488 25.9432i 0.618410 0.851169i −0.378826 0.925468i \(-0.623672\pi\)
0.997236 + 0.0742992i \(0.0236720\pi\)
\(930\) 0 0
\(931\) 3.32763 + 1.08121i 0.109059 + 0.0354353i
\(932\) 0 0
\(933\) 0.994471 0.722526i 0.0325575 0.0236544i
\(934\) 0 0
\(935\) 0.429762 + 1.66062i 0.0140547 + 0.0543080i
\(936\) 0 0
\(937\) 35.6472 25.8992i 1.16454 0.846090i 0.174197 0.984711i \(-0.444267\pi\)
0.990345 + 0.138621i \(0.0442670\pi\)
\(938\) 0 0
\(939\) −4.67864 + 14.3994i −0.152682 + 0.469906i
\(940\) 0 0
\(941\) −31.9988 + 44.0426i −1.04313 + 1.43575i −0.148518 + 0.988910i \(0.547450\pi\)
−0.894614 + 0.446839i \(0.852550\pi\)
\(942\) 0 0
\(943\) −8.01603 + 2.60456i −0.261038 + 0.0848163i
\(944\) 0 0
\(945\) −0.806858 −0.0262471
\(946\) 0 0
\(947\) 25.0466i 0.813906i 0.913449 + 0.406953i \(0.133409\pi\)
−0.913449 + 0.406953i \(0.866591\pi\)
\(948\) 0 0
\(949\) −0.650197 + 41.8506i −0.0211063 + 1.35853i
\(950\) 0 0
\(951\) 9.83813 13.5410i 0.319023 0.439098i
\(952\) 0 0
\(953\) 13.3012 40.9367i 0.430867 1.32607i −0.466397 0.884576i \(-0.654448\pi\)
0.897263 0.441496i \(-0.145552\pi\)
\(954\) 0 0
\(955\) −0.504086 0.693815i −0.0163118 0.0224513i
\(956\) 0 0
\(957\) −0.0439189 + 0.720052i −0.00141969 + 0.0232760i
\(958\) 0 0
\(959\) −27.4862 + 19.9699i −0.887575 + 0.644861i
\(960\) 0 0
\(961\) 6.87764 21.1672i 0.221859 0.682813i
\(962\) 0 0
\(963\) −7.64106 5.55155i −0.246230 0.178896i
\(964\) 0 0
\(965\) 0.508110 + 1.56380i 0.0163566 + 0.0503405i
\(966\) 0 0
\(967\) 0.982271i 0.0315877i 0.999875 + 0.0157939i \(0.00502755\pi\)
−0.999875 + 0.0157939i \(0.994972\pi\)
\(968\) 0 0
\(969\) 13.9364i 0.447702i
\(970\) 0 0
\(971\) −1.67895 5.16727i −0.0538800 0.165826i 0.920495 0.390753i \(-0.127785\pi\)
−0.974375 + 0.224928i \(0.927785\pi\)
\(972\) 0 0
\(973\) −3.63508 + 5.00326i −0.116535 + 0.160397i
\(974\) 0 0
\(975\) 12.4917 + 9.37562i 0.400053 + 0.300260i
\(976\) 0 0
\(977\) 3.58555 + 4.93508i 0.114712 + 0.157887i 0.862512 0.506037i \(-0.168890\pi\)
−0.747800 + 0.663924i \(0.768890\pi\)
\(978\) 0 0
\(979\) −18.6038 1.13472i −0.594579 0.0362657i
\(980\) 0 0
\(981\) −10.8084 14.8765i −0.345085 0.474969i
\(982\) 0 0
\(983\) −45.9123 14.9178i −1.46438 0.475805i −0.534972 0.844870i \(-0.679678\pi\)
−0.929404 + 0.369065i \(0.879678\pi\)
\(984\) 0 0
\(985\) −1.45397 1.05637i −0.0463273 0.0336588i
\(986\) 0 0
\(987\) 1.37252 + 4.22420i 0.0436880 + 0.134458i
\(988\) 0 0
\(989\) 1.46489 0.0465809
\(990\) 0 0
\(991\) −23.0289 −0.731538 −0.365769 0.930706i \(-0.619194\pi\)
−0.365769 + 0.930706i \(0.619194\pi\)
\(992\) 0 0
\(993\) −19.7165 + 6.40629i −0.625685 + 0.203297i
\(994\) 0 0
\(995\) 0.568288 0.782181i 0.0180159 0.0247968i
\(996\) 0 0
\(997\) −5.68333 + 17.4915i −0.179993 + 0.553961i −0.999826 0.0186412i \(-0.994066\pi\)
0.819833 + 0.572602i \(0.194066\pi\)
\(998\) 0 0
\(999\) −4.76131 6.55338i −0.150641 0.207340i
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 572.2.x.a.25.9 56
11.4 even 5 inner 572.2.x.a.389.10 yes 56
13.12 even 2 inner 572.2.x.a.25.10 yes 56
143.103 even 10 inner 572.2.x.a.389.9 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.x.a.25.9 56 1.1 even 1 trivial
572.2.x.a.25.10 yes 56 13.12 even 2 inner
572.2.x.a.389.9 yes 56 143.103 even 10 inner
572.2.x.a.389.10 yes 56 11.4 even 5 inner