Properties

Label 572.2.bc.a.241.5
Level $572$
Weight $2$
Character 572.241
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(197,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.197");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.bc (of order \(12\), 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 \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 241.5
Character \(\chi\) \(=\) 572.241
Dual form 572.2.bc.a.197.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.425370 + 0.736762i) q^{3} +(2.35532 + 2.35532i) q^{5} +(-0.337440 + 1.25934i) q^{7} +(1.13812 + 1.97128i) q^{9} +O(q^{10})\) \(q+(-0.425370 + 0.736762i) q^{3} +(2.35532 + 2.35532i) q^{5} +(-0.337440 + 1.25934i) q^{7} +(1.13812 + 1.97128i) q^{9} +(3.05160 - 1.29914i) q^{11} +(-3.56676 + 0.527479i) q^{13} +(-2.73719 + 0.733429i) q^{15} +(-1.12651 - 1.95118i) q^{17} +(-1.77011 - 0.474299i) q^{19} +(-0.784299 - 0.784299i) q^{21} +(-1.72379 - 0.995228i) q^{23} +6.09507i q^{25} -4.48871 q^{27} +(6.89826 + 3.98271i) q^{29} +(1.52216 + 1.52216i) q^{31} +(-0.340901 + 2.80091i) q^{33} +(-3.76093 + 2.17138i) q^{35} +(1.36555 + 5.09629i) q^{37} +(1.12856 - 2.85223i) q^{39} +(0.255426 + 0.953263i) q^{41} +(-5.50646 - 9.53747i) q^{43} +(-1.96237 + 7.32365i) q^{45} +(-0.190569 + 0.190569i) q^{47} +(4.59010 + 2.65010i) q^{49} +1.91674 q^{51} -1.82238 q^{53} +(10.2474 + 4.12760i) q^{55} +(1.10240 - 1.10240i) q^{57} +(1.64518 + 0.440824i) q^{59} +(-2.51005 + 1.44918i) q^{61} +(-2.86657 + 0.768095i) q^{63} +(-9.64324 - 7.15848i) q^{65} +(5.43944 - 1.45749i) q^{67} +(1.46649 - 0.846680i) q^{69} +(2.24519 - 8.37918i) q^{71} +(5.32332 + 5.32332i) q^{73} +(-4.49062 - 2.59266i) q^{75} +(0.606329 + 4.28139i) q^{77} +9.18416i q^{79} +(-1.50500 + 2.60674i) q^{81} +(1.51784 - 1.51784i) q^{83} +(1.94235 - 7.24895i) q^{85} +(-5.86862 + 3.38825i) q^{87} +(-2.08017 - 7.76328i) q^{89} +(0.539289 - 4.66976i) q^{91} +(-1.76895 + 0.473988i) q^{93} +(-3.05204 - 5.28630i) q^{95} +(2.47736 - 9.24563i) q^{97} +(6.03406 + 4.53699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(-1\)

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
\(3\) −0.425370 + 0.736762i −0.245587 + 0.425370i −0.962297 0.272002i \(-0.912314\pi\)
0.716709 + 0.697372i \(0.245647\pi\)
\(4\) 0 0
\(5\) 2.35532 + 2.35532i 1.05333 + 1.05333i 0.998495 + 0.0548361i \(0.0174636\pi\)
0.0548361 + 0.998495i \(0.482536\pi\)
\(6\) 0 0
\(7\) −0.337440 + 1.25934i −0.127540 + 0.475987i −0.999917 0.0128466i \(-0.995911\pi\)
0.872377 + 0.488833i \(0.162577\pi\)
\(8\) 0 0
\(9\) 1.13812 + 1.97128i 0.379374 + 0.657095i
\(10\) 0 0
\(11\) 3.05160 1.29914i 0.920091 0.391705i
\(12\) 0 0
\(13\) −3.56676 + 0.527479i −0.989241 + 0.146296i
\(14\) 0 0
\(15\) −2.73719 + 0.733429i −0.706740 + 0.189370i
\(16\) 0 0
\(17\) −1.12651 1.95118i −0.273219 0.473230i 0.696465 0.717591i \(-0.254755\pi\)
−0.969684 + 0.244361i \(0.921422\pi\)
\(18\) 0 0
\(19\) −1.77011 0.474299i −0.406091 0.108812i 0.0499909 0.998750i \(-0.484081\pi\)
−0.456081 + 0.889938i \(0.650747\pi\)
\(20\) 0 0
\(21\) −0.784299 0.784299i −0.171148 0.171148i
\(22\) 0 0
\(23\) −1.72379 0.995228i −0.359434 0.207519i 0.309398 0.950932i \(-0.399872\pi\)
−0.668832 + 0.743413i \(0.733206\pi\)
\(24\) 0 0
\(25\) 6.09507i 1.21901i
\(26\) 0 0
\(27\) −4.48871 −0.863852
\(28\) 0 0
\(29\) 6.89826 + 3.98271i 1.28097 + 0.739571i 0.977027 0.213117i \(-0.0683617\pi\)
0.303948 + 0.952689i \(0.401695\pi\)
\(30\) 0 0
\(31\) 1.52216 + 1.52216i 0.273388 + 0.273388i 0.830462 0.557075i \(-0.188076\pi\)
−0.557075 + 0.830462i \(0.688076\pi\)
\(32\) 0 0
\(33\) −0.340901 + 2.80091i −0.0593433 + 0.487577i
\(34\) 0 0
\(35\) −3.76093 + 2.17138i −0.635714 + 0.367030i
\(36\) 0 0
\(37\) 1.36555 + 5.09629i 0.224494 + 0.837824i 0.982606 + 0.185700i \(0.0594553\pi\)
−0.758112 + 0.652124i \(0.773878\pi\)
\(38\) 0 0
\(39\) 1.12856 2.85223i 0.180715 0.456722i
\(40\) 0 0
\(41\) 0.255426 + 0.953263i 0.0398908 + 0.148875i 0.982999 0.183612i \(-0.0587790\pi\)
−0.943108 + 0.332487i \(0.892112\pi\)
\(42\) 0 0
\(43\) −5.50646 9.53747i −0.839728 1.45445i −0.890122 0.455722i \(-0.849381\pi\)
0.0503947 0.998729i \(-0.483952\pi\)
\(44\) 0 0
\(45\) −1.96237 + 7.32365i −0.292532 + 1.09174i
\(46\) 0 0
\(47\) −0.190569 + 0.190569i −0.0277974 + 0.0277974i −0.720869 0.693071i \(-0.756257\pi\)
0.693071 + 0.720869i \(0.256257\pi\)
\(48\) 0 0
\(49\) 4.59010 + 2.65010i 0.655729 + 0.378585i
\(50\) 0 0
\(51\) 1.91674 0.268397
\(52\) 0 0
\(53\) −1.82238 −0.250323 −0.125162 0.992136i \(-0.539945\pi\)
−0.125162 + 0.992136i \(0.539945\pi\)
\(54\) 0 0
\(55\) 10.2474 + 4.12760i 1.38176 + 0.556566i
\(56\) 0 0
\(57\) 1.10240 1.10240i 0.146016 0.146016i
\(58\) 0 0
\(59\) 1.64518 + 0.440824i 0.214184 + 0.0573905i 0.364315 0.931276i \(-0.381303\pi\)
−0.150131 + 0.988666i \(0.547970\pi\)
\(60\) 0 0
\(61\) −2.51005 + 1.44918i −0.321379 + 0.185548i −0.652007 0.758213i \(-0.726073\pi\)
0.330628 + 0.943761i \(0.392739\pi\)
\(62\) 0 0
\(63\) −2.86657 + 0.768095i −0.361154 + 0.0967708i
\(64\) 0 0
\(65\) −9.64324 7.15848i −1.19610 0.887900i
\(66\) 0 0
\(67\) 5.43944 1.45749i 0.664533 0.178061i 0.0892424 0.996010i \(-0.471555\pi\)
0.575291 + 0.817949i \(0.304889\pi\)
\(68\) 0 0
\(69\) 1.46649 0.846680i 0.176545 0.101928i
\(70\) 0 0
\(71\) 2.24519 8.37918i 0.266456 0.994426i −0.694898 0.719108i \(-0.744550\pi\)
0.961353 0.275317i \(-0.0887829\pi\)
\(72\) 0 0
\(73\) 5.32332 + 5.32332i 0.623048 + 0.623048i 0.946310 0.323262i \(-0.104779\pi\)
−0.323262 + 0.946310i \(0.604779\pi\)
\(74\) 0 0
\(75\) −4.49062 2.59266i −0.518532 0.299374i
\(76\) 0 0
\(77\) 0.606329 + 4.28139i 0.0690977 + 0.487909i
\(78\) 0 0
\(79\) 9.18416i 1.03330i 0.856197 + 0.516649i \(0.172821\pi\)
−0.856197 + 0.516649i \(0.827179\pi\)
\(80\) 0 0
\(81\) −1.50500 + 2.60674i −0.167223 + 0.289638i
\(82\) 0 0
\(83\) 1.51784 1.51784i 0.166604 0.166604i −0.618881 0.785485i \(-0.712414\pi\)
0.785485 + 0.618881i \(0.212414\pi\)
\(84\) 0 0
\(85\) 1.94235 7.24895i 0.210677 0.786259i
\(86\) 0 0
\(87\) −5.86862 + 3.38825i −0.629182 + 0.363259i
\(88\) 0 0
\(89\) −2.08017 7.76328i −0.220497 0.822906i −0.984159 0.177290i \(-0.943267\pi\)
0.763662 0.645617i \(-0.223400\pi\)
\(90\) 0 0
\(91\) 0.539289 4.66976i 0.0565329 0.489524i
\(92\) 0 0
\(93\) −1.76895 + 0.473988i −0.183431 + 0.0491503i
\(94\) 0 0
\(95\) −3.05204 5.28630i −0.313133 0.542363i
\(96\) 0 0
\(97\) 2.47736 9.24563i 0.251538 0.938751i −0.718446 0.695582i \(-0.755146\pi\)
0.969984 0.243169i \(-0.0781869\pi\)
\(98\) 0 0
\(99\) 6.03406 + 4.53699i 0.606445 + 0.455984i
\(100\) 0 0
\(101\) −5.29946 + 9.17893i −0.527316 + 0.913338i 0.472177 + 0.881504i \(0.343468\pi\)
−0.999493 + 0.0318341i \(0.989865\pi\)
\(102\) 0 0
\(103\) 19.3794i 1.90951i −0.297391 0.954756i \(-0.596116\pi\)
0.297391 0.954756i \(-0.403884\pi\)
\(104\) 0 0
\(105\) 3.69455i 0.360551i
\(106\) 0 0
\(107\) 8.94884 + 5.16662i 0.865117 + 0.499476i 0.865723 0.500524i \(-0.166859\pi\)
−0.000605486 1.00000i \(0.500193\pi\)
\(108\) 0 0
\(109\) 8.97324 8.97324i 0.859481 0.859481i −0.131796 0.991277i \(-0.542074\pi\)
0.991277 + 0.131796i \(0.0420744\pi\)
\(110\) 0 0
\(111\) −4.33561 1.16172i −0.411518 0.110266i
\(112\) 0 0
\(113\) −6.83614 11.8405i −0.643090 1.11386i −0.984739 0.174037i \(-0.944319\pi\)
0.341649 0.939828i \(-0.389015\pi\)
\(114\) 0 0
\(115\) −1.71599 6.40415i −0.160017 0.597190i
\(116\) 0 0
\(117\) −5.09921 6.43076i −0.471423 0.594524i
\(118\) 0 0
\(119\) 2.83733 0.760260i 0.260098 0.0696930i
\(120\) 0 0
\(121\) 7.62448 7.92889i 0.693135 0.720808i
\(122\) 0 0
\(123\) −0.810978 0.217301i −0.0731235 0.0195934i
\(124\) 0 0
\(125\) −2.57924 + 2.57924i −0.230695 + 0.230695i
\(126\) 0 0
\(127\) 8.81504 15.2681i 0.782208 1.35482i −0.148445 0.988921i \(-0.547427\pi\)
0.930653 0.365903i \(-0.119240\pi\)
\(128\) 0 0
\(129\) 9.36913 0.824906
\(130\) 0 0
\(131\) 4.79234i 0.418709i −0.977840 0.209354i \(-0.932864\pi\)
0.977840 0.209354i \(-0.0671362\pi\)
\(132\) 0 0
\(133\) 1.19461 2.06912i 0.103586 0.179416i
\(134\) 0 0
\(135\) −10.5723 10.5723i −0.909923 0.909923i
\(136\) 0 0
\(137\) −1.80559 0.483806i −0.154262 0.0413343i 0.180862 0.983509i \(-0.442111\pi\)
−0.335123 + 0.942174i \(0.608778\pi\)
\(138\) 0 0
\(139\) −10.1020 + 5.83242i −0.856844 + 0.494699i −0.862954 0.505282i \(-0.831388\pi\)
0.00611025 + 0.999981i \(0.498055\pi\)
\(140\) 0 0
\(141\) −0.0593418 0.221467i −0.00499748 0.0186509i
\(142\) 0 0
\(143\) −10.1990 + 6.24336i −0.852887 + 0.522096i
\(144\) 0 0
\(145\) 6.86705 + 25.6282i 0.570278 + 2.12830i
\(146\) 0 0
\(147\) −3.90498 + 2.25454i −0.322077 + 0.185951i
\(148\) 0 0
\(149\) −12.3285 3.30342i −1.00999 0.270626i −0.284366 0.958716i \(-0.591783\pi\)
−0.725626 + 0.688089i \(0.758450\pi\)
\(150\) 0 0
\(151\) 1.00976 + 1.00976i 0.0821735 + 0.0821735i 0.746999 0.664825i \(-0.231494\pi\)
−0.664825 + 0.746999i \(0.731494\pi\)
\(152\) 0 0
\(153\) 2.56422 4.44135i 0.207305 0.359062i
\(154\) 0 0
\(155\) 7.17034i 0.575936i
\(156\) 0 0
\(157\) 16.1466 1.28864 0.644319 0.764757i \(-0.277141\pi\)
0.644319 + 0.764757i \(0.277141\pi\)
\(158\) 0 0
\(159\) 0.775186 1.34266i 0.0614763 0.106480i
\(160\) 0 0
\(161\) 1.83501 1.83501i 0.144619 0.144619i
\(162\) 0 0
\(163\) 1.89449 + 0.507626i 0.148388 + 0.0397604i 0.332248 0.943192i \(-0.392193\pi\)
−0.183861 + 0.982952i \(0.558859\pi\)
\(164\) 0 0
\(165\) −7.39998 + 5.79412i −0.576088 + 0.451072i
\(166\) 0 0
\(167\) −3.50682 + 0.939648i −0.271366 + 0.0727122i −0.391936 0.919993i \(-0.628194\pi\)
0.120570 + 0.992705i \(0.461528\pi\)
\(168\) 0 0
\(169\) 12.4435 3.76278i 0.957195 0.289445i
\(170\) 0 0
\(171\) −1.07962 4.02919i −0.0825605 0.308120i
\(172\) 0 0
\(173\) 7.82822 + 13.5589i 0.595168 + 1.03086i 0.993523 + 0.113630i \(0.0362479\pi\)
−0.398355 + 0.917231i \(0.630419\pi\)
\(174\) 0 0
\(175\) −7.67578 2.05672i −0.580234 0.155473i
\(176\) 0 0
\(177\) −1.02459 + 1.02459i −0.0770131 + 0.0770131i
\(178\) 0 0
\(179\) 11.2126 + 6.47359i 0.838068 + 0.483859i 0.856607 0.515969i \(-0.172568\pi\)
−0.0185390 + 0.999828i \(0.505901\pi\)
\(180\) 0 0
\(181\) 1.43232i 0.106463i −0.998582 0.0532317i \(-0.983048\pi\)
0.998582 0.0532317i \(-0.0169522\pi\)
\(182\) 0 0
\(183\) 2.46575i 0.182273i
\(184\) 0 0
\(185\) −8.78709 + 15.2197i −0.646040 + 1.11897i
\(186\) 0 0
\(187\) −5.97251 4.49071i −0.436753 0.328393i
\(188\) 0 0
\(189\) 1.51467 5.65282i 0.110176 0.411182i
\(190\) 0 0
\(191\) 2.76875 + 4.79561i 0.200340 + 0.346998i 0.948638 0.316364i \(-0.102462\pi\)
−0.748298 + 0.663362i \(0.769129\pi\)
\(192\) 0 0
\(193\) −14.1165 + 3.78251i −1.01613 + 0.272271i −0.728188 0.685378i \(-0.759637\pi\)
−0.287940 + 0.957648i \(0.592970\pi\)
\(194\) 0 0
\(195\) 9.37604 4.05977i 0.671432 0.290726i
\(196\) 0 0
\(197\) −0.448559 1.67404i −0.0319585 0.119271i 0.948104 0.317961i \(-0.102998\pi\)
−0.980062 + 0.198690i \(0.936331\pi\)
\(198\) 0 0
\(199\) 10.5093 6.06753i 0.744983 0.430116i −0.0788956 0.996883i \(-0.525139\pi\)
0.823878 + 0.566767i \(0.191806\pi\)
\(200\) 0 0
\(201\) −1.23995 + 4.62755i −0.0874591 + 0.326402i
\(202\) 0 0
\(203\) −7.34335 + 7.34335i −0.515402 + 0.515402i
\(204\) 0 0
\(205\) −1.64363 + 2.84685i −0.114796 + 0.198833i
\(206\) 0 0
\(207\) 4.53076i 0.314910i
\(208\) 0 0
\(209\) −6.01783 + 0.852245i −0.416262 + 0.0589510i
\(210\) 0 0
\(211\) 18.1711 + 10.4911i 1.25095 + 0.722237i 0.971299 0.237864i \(-0.0764471\pi\)
0.279653 + 0.960101i \(0.409780\pi\)
\(212\) 0 0
\(213\) 5.21842 + 5.21842i 0.357560 + 0.357560i
\(214\) 0 0
\(215\) 9.49432 35.4333i 0.647507 2.41653i
\(216\) 0 0
\(217\) −2.43055 + 1.40328i −0.164997 + 0.0952609i
\(218\) 0 0
\(219\) −6.18640 + 1.65764i −0.418038 + 0.112013i
\(220\) 0 0
\(221\) 5.04720 + 6.36517i 0.339512 + 0.428167i
\(222\) 0 0
\(223\) −15.0234 + 4.02550i −1.00604 + 0.269567i −0.723973 0.689828i \(-0.757686\pi\)
−0.282065 + 0.959395i \(0.591019\pi\)
\(224\) 0 0
\(225\) −12.0151 + 6.93693i −0.801008 + 0.462462i
\(226\) 0 0
\(227\) −14.3793 3.85293i −0.954391 0.255728i −0.252166 0.967684i \(-0.581143\pi\)
−0.702224 + 0.711956i \(0.747810\pi\)
\(228\) 0 0
\(229\) 16.4206 16.4206i 1.08511 1.08511i 0.0890819 0.996024i \(-0.471607\pi\)
0.996024 0.0890819i \(-0.0283933\pi\)
\(230\) 0 0
\(231\) −3.41228 1.37445i −0.224511 0.0904322i
\(232\) 0 0
\(233\) 22.3223 1.46238 0.731192 0.682172i \(-0.238964\pi\)
0.731192 + 0.682172i \(0.238964\pi\)
\(234\) 0 0
\(235\) −0.897704 −0.0585598
\(236\) 0 0
\(237\) −6.76654 3.90666i −0.439534 0.253765i
\(238\) 0 0
\(239\) −17.2343 + 17.2343i −1.11479 + 1.11479i −0.122302 + 0.992493i \(0.539028\pi\)
−0.992493 + 0.122302i \(0.960972\pi\)
\(240\) 0 0
\(241\) 5.78938 21.6063i 0.372927 1.39178i −0.483424 0.875387i \(-0.660607\pi\)
0.856350 0.516395i \(-0.172726\pi\)
\(242\) 0 0
\(243\) −8.01343 13.8797i −0.514062 0.890381i
\(244\) 0 0
\(245\) 4.56933 + 17.0530i 0.291924 + 1.08948i
\(246\) 0 0
\(247\) 6.56373 + 0.758015i 0.417640 + 0.0482313i
\(248\) 0 0
\(249\) 0.472643 + 1.76393i 0.0299525 + 0.111784i
\(250\) 0 0
\(251\) −26.6613 + 15.3929i −1.68285 + 0.971593i −0.723094 + 0.690749i \(0.757281\pi\)
−0.959754 + 0.280843i \(0.909386\pi\)
\(252\) 0 0
\(253\) −6.55324 0.797599i −0.411998 0.0501446i
\(254\) 0 0
\(255\) 4.51453 + 4.51453i 0.282711 + 0.282711i
\(256\) 0 0
\(257\) −17.0388 9.83734i −1.06285 0.613636i −0.136630 0.990622i \(-0.543627\pi\)
−0.926219 + 0.376986i \(0.876961\pi\)
\(258\) 0 0
\(259\) −6.87876 −0.427425
\(260\) 0 0
\(261\) 18.1312i 1.12230i
\(262\) 0 0
\(263\) 22.5690 + 13.0302i 1.39166 + 0.803477i 0.993499 0.113838i \(-0.0363144\pi\)
0.398163 + 0.917315i \(0.369648\pi\)
\(264\) 0 0
\(265\) −4.29229 4.29229i −0.263674 0.263674i
\(266\) 0 0
\(267\) 6.60453 + 1.76968i 0.404191 + 0.108303i
\(268\) 0 0
\(269\) 7.68975 + 13.3190i 0.468852 + 0.812076i 0.999366 0.0356006i \(-0.0113344\pi\)
−0.530514 + 0.847676i \(0.678001\pi\)
\(270\) 0 0
\(271\) −20.5357 + 5.50253i −1.24746 + 0.334255i −0.821353 0.570420i \(-0.806781\pi\)
−0.426103 + 0.904675i \(0.640114\pi\)
\(272\) 0 0
\(273\) 3.21111 + 2.38370i 0.194345 + 0.144268i
\(274\) 0 0
\(275\) 7.91834 + 18.5997i 0.477494 + 1.12160i
\(276\) 0 0
\(277\) 14.2317 + 24.6500i 0.855100 + 1.48108i 0.876552 + 0.481307i \(0.159838\pi\)
−0.0214521 + 0.999770i \(0.506829\pi\)
\(278\) 0 0
\(279\) −1.26821 + 4.73301i −0.0759255 + 0.283358i
\(280\) 0 0
\(281\) −20.1079 20.1079i −1.19954 1.19954i −0.974305 0.225231i \(-0.927686\pi\)
−0.225231 0.974305i \(-0.572314\pi\)
\(282\) 0 0
\(283\) 6.21048 10.7569i 0.369175 0.639429i −0.620262 0.784395i \(-0.712974\pi\)
0.989437 + 0.144965i \(0.0463071\pi\)
\(284\) 0 0
\(285\) 5.19299 0.307606
\(286\) 0 0
\(287\) −1.28668 −0.0759500
\(288\) 0 0
\(289\) 5.96194 10.3264i 0.350702 0.607434i
\(290\) 0 0
\(291\) 5.75803 + 5.75803i 0.337542 + 0.337542i
\(292\) 0 0
\(293\) 8.07865 30.1499i 0.471960 1.76138i −0.160756 0.986994i \(-0.551393\pi\)
0.632716 0.774384i \(-0.281940\pi\)
\(294\) 0 0
\(295\) 2.83664 + 4.91321i 0.165156 + 0.286058i
\(296\) 0 0
\(297\) −13.6977 + 5.83145i −0.794823 + 0.338375i
\(298\) 0 0
\(299\) 6.67329 + 2.64048i 0.385926 + 0.152703i
\(300\) 0 0
\(301\) 13.8690 3.71620i 0.799398 0.214198i
\(302\) 0 0
\(303\) −4.50846 7.80888i −0.259004 0.448608i
\(304\) 0 0
\(305\) −9.32526 2.49870i −0.533963 0.143075i
\(306\) 0 0
\(307\) 2.73282 + 2.73282i 0.155970 + 0.155970i 0.780778 0.624808i \(-0.214823\pi\)
−0.624808 + 0.780778i \(0.714823\pi\)
\(308\) 0 0
\(309\) 14.2780 + 8.24342i 0.812248 + 0.468952i
\(310\) 0 0
\(311\) 27.0223i 1.53229i 0.642667 + 0.766146i \(0.277828\pi\)
−0.642667 + 0.766146i \(0.722172\pi\)
\(312\) 0 0
\(313\) −9.41276 −0.532041 −0.266020 0.963967i \(-0.585709\pi\)
−0.266020 + 0.963967i \(0.585709\pi\)
\(314\) 0 0
\(315\) −8.56080 4.94258i −0.482346 0.278483i
\(316\) 0 0
\(317\) 19.6344 + 19.6344i 1.10278 + 1.10278i 0.994074 + 0.108704i \(0.0346700\pi\)
0.108704 + 0.994074i \(0.465330\pi\)
\(318\) 0 0
\(319\) 26.2248 + 3.19184i 1.46831 + 0.178709i
\(320\) 0 0
\(321\) −7.61313 + 4.39544i −0.424924 + 0.245330i
\(322\) 0 0
\(323\) 1.06861 + 3.98810i 0.0594589 + 0.221904i
\(324\) 0 0
\(325\) −3.21502 21.7396i −0.178337 1.20590i
\(326\) 0 0
\(327\) 2.79420 + 10.4281i 0.154520 + 0.576675i
\(328\) 0 0
\(329\) −0.175686 0.304298i −0.00968591 0.0167765i
\(330\) 0 0
\(331\) −5.27309 + 19.6794i −0.289835 + 1.08168i 0.655398 + 0.755284i \(0.272501\pi\)
−0.945233 + 0.326396i \(0.894166\pi\)
\(332\) 0 0
\(333\) −8.49207 + 8.49207i −0.465362 + 0.465362i
\(334\) 0 0
\(335\) 16.2445 + 9.37876i 0.887531 + 0.512417i
\(336\) 0 0
\(337\) 13.3095 0.725017 0.362508 0.931981i \(-0.381920\pi\)
0.362508 + 0.931981i \(0.381920\pi\)
\(338\) 0 0
\(339\) 11.6315 0.631739
\(340\) 0 0
\(341\) 6.62251 + 2.66752i 0.358629 + 0.144454i
\(342\) 0 0
\(343\) −11.3396 + 11.3396i −0.612280 + 0.612280i
\(344\) 0 0
\(345\) 5.44826 + 1.45986i 0.293324 + 0.0785961i
\(346\) 0 0
\(347\) −10.0919 + 5.82657i −0.541763 + 0.312787i −0.745793 0.666178i \(-0.767929\pi\)
0.204030 + 0.978965i \(0.434596\pi\)
\(348\) 0 0
\(349\) −10.6872 + 2.86364i −0.572075 + 0.153287i −0.533248 0.845959i \(-0.679029\pi\)
−0.0388271 + 0.999246i \(0.512362\pi\)
\(350\) 0 0
\(351\) 16.0101 2.36770i 0.854558 0.126378i
\(352\) 0 0
\(353\) −27.1593 + 7.27732i −1.44554 + 0.387333i −0.894472 0.447124i \(-0.852448\pi\)
−0.551073 + 0.834457i \(0.685781\pi\)
\(354\) 0 0
\(355\) 25.0238 14.4475i 1.32813 0.766794i
\(356\) 0 0
\(357\) −0.646783 + 2.41383i −0.0342314 + 0.127753i
\(358\) 0 0
\(359\) −18.0346 18.0346i −0.951831 0.951831i 0.0470606 0.998892i \(-0.485015\pi\)
−0.998892 + 0.0470606i \(0.985015\pi\)
\(360\) 0 0
\(361\) −13.5462 7.82088i −0.712956 0.411625i
\(362\) 0 0
\(363\) 2.59848 + 8.99014i 0.136385 + 0.471860i
\(364\) 0 0
\(365\) 25.0763i 1.31255i
\(366\) 0 0
\(367\) −11.5716 + 20.0426i −0.604033 + 1.04622i 0.388170 + 0.921588i \(0.373107\pi\)
−0.992203 + 0.124628i \(0.960226\pi\)
\(368\) 0 0
\(369\) −1.58845 + 1.58845i −0.0826912 + 0.0826912i
\(370\) 0 0
\(371\) 0.614944 2.29500i 0.0319263 0.119151i
\(372\) 0 0
\(373\) 10.2469 5.91605i 0.530564 0.306321i −0.210682 0.977555i \(-0.567568\pi\)
0.741246 + 0.671233i \(0.234235\pi\)
\(374\) 0 0
\(375\) −0.803156 2.99742i −0.0414748 0.154786i
\(376\) 0 0
\(377\) −26.7052 10.5667i −1.37539 0.544212i
\(378\) 0 0
\(379\) −0.613944 + 0.164506i −0.0315362 + 0.00845010i −0.274553 0.961572i \(-0.588530\pi\)
0.243016 + 0.970022i \(0.421863\pi\)
\(380\) 0 0
\(381\) 7.49930 + 12.9892i 0.384201 + 0.665455i
\(382\) 0 0
\(383\) 2.82017 10.5250i 0.144104 0.537803i −0.855690 0.517489i \(-0.826867\pi\)
0.999794 0.0203137i \(-0.00646651\pi\)
\(384\) 0 0
\(385\) −8.65593 + 11.5121i −0.441147 + 0.586713i
\(386\) 0 0
\(387\) 12.5340 21.7096i 0.637141 1.10356i
\(388\) 0 0
\(389\) 8.15316i 0.413381i −0.978406 0.206691i \(-0.933731\pi\)
0.978406 0.206691i \(-0.0662694\pi\)
\(390\) 0 0
\(391\) 4.48455i 0.226793i
\(392\) 0 0
\(393\) 3.53081 + 2.03852i 0.178106 + 0.102830i
\(394\) 0 0
\(395\) −21.6316 + 21.6316i −1.08841 + 1.08841i
\(396\) 0 0
\(397\) 9.78973 + 2.62315i 0.491333 + 0.131652i 0.495975 0.868337i \(-0.334811\pi\)
−0.00464195 + 0.999989i \(0.501478\pi\)
\(398\) 0 0
\(399\) 1.01630 + 1.76029i 0.0508787 + 0.0881245i
\(400\) 0 0
\(401\) −5.86068 21.8724i −0.292669 1.09225i −0.943051 0.332647i \(-0.892058\pi\)
0.650383 0.759607i \(-0.274609\pi\)
\(402\) 0 0
\(403\) −6.23208 4.62626i −0.310442 0.230451i
\(404\) 0 0
\(405\) −9.68448 + 2.59495i −0.481226 + 0.128944i
\(406\) 0 0
\(407\) 10.7879 + 13.7778i 0.534735 + 0.682939i
\(408\) 0 0
\(409\) 10.2938 + 2.75821i 0.508995 + 0.136385i 0.504171 0.863604i \(-0.331798\pi\)
0.00482332 + 0.999988i \(0.498465\pi\)
\(410\) 0 0
\(411\) 1.12449 1.12449i 0.0554671 0.0554671i
\(412\) 0 0
\(413\) −1.11030 + 1.92309i −0.0546342 + 0.0946292i
\(414\) 0 0
\(415\) 7.14999 0.350979
\(416\) 0 0
\(417\) 9.92373i 0.485967i
\(418\) 0 0
\(419\) 6.62367 11.4725i 0.323587 0.560470i −0.657638 0.753334i \(-0.728444\pi\)
0.981225 + 0.192864i \(0.0617777\pi\)
\(420\) 0 0
\(421\) −12.2658 12.2658i −0.597798 0.597798i 0.341928 0.939726i \(-0.388920\pi\)
−0.939726 + 0.341928i \(0.888920\pi\)
\(422\) 0 0
\(423\) −0.592557 0.158775i −0.0288111 0.00771992i
\(424\) 0 0
\(425\) 11.8926 6.86618i 0.576874 0.333058i
\(426\) 0 0
\(427\) −0.978021 3.65002i −0.0473298 0.176637i
\(428\) 0 0
\(429\) −0.261511 10.1700i −0.0126259 0.491012i
\(430\) 0 0
\(431\) −0.933615 3.48430i −0.0449707 0.167833i 0.939788 0.341757i \(-0.111022\pi\)
−0.984759 + 0.173924i \(0.944355\pi\)
\(432\) 0 0
\(433\) −21.3849 + 12.3466i −1.02769 + 0.593338i −0.916322 0.400441i \(-0.868857\pi\)
−0.111369 + 0.993779i \(0.535523\pi\)
\(434\) 0 0
\(435\) −21.8029 5.84207i −1.04537 0.280106i
\(436\) 0 0
\(437\) 2.57925 + 2.57925i 0.123382 + 0.123382i
\(438\) 0 0
\(439\) 18.3260 31.7415i 0.874650 1.51494i 0.0175150 0.999847i \(-0.494425\pi\)
0.857135 0.515092i \(-0.172242\pi\)
\(440\) 0 0
\(441\) 12.0645i 0.574501i
\(442\) 0 0
\(443\) −14.7224 −0.699482 −0.349741 0.936846i \(-0.613730\pi\)
−0.349741 + 0.936846i \(0.613730\pi\)
\(444\) 0 0
\(445\) 13.3856 23.1845i 0.634537 1.09905i
\(446\) 0 0
\(447\) 7.67801 7.67801i 0.363157 0.363157i
\(448\) 0 0
\(449\) −29.7484 7.97105i −1.40391 0.376177i −0.524164 0.851617i \(-0.675622\pi\)
−0.879748 + 0.475440i \(0.842289\pi\)
\(450\) 0 0
\(451\) 2.01788 + 2.57714i 0.0950181 + 0.121353i
\(452\) 0 0
\(453\) −1.17348 + 0.314433i −0.0551349 + 0.0147733i
\(454\) 0 0
\(455\) 12.2690 9.72859i 0.575179 0.456083i
\(456\) 0 0
\(457\) −1.61053 6.01059i −0.0753376 0.281164i 0.917972 0.396645i \(-0.129826\pi\)
−0.993310 + 0.115481i \(0.963159\pi\)
\(458\) 0 0
\(459\) 5.05659 + 8.75826i 0.236021 + 0.408801i
\(460\) 0 0
\(461\) −25.5259 6.83963i −1.18886 0.318553i −0.390423 0.920635i \(-0.627671\pi\)
−0.798434 + 0.602082i \(0.794338\pi\)
\(462\) 0 0
\(463\) −2.72391 + 2.72391i −0.126591 + 0.126591i −0.767564 0.640973i \(-0.778531\pi\)
0.640973 + 0.767564i \(0.278531\pi\)
\(464\) 0 0
\(465\) −5.28283 3.05005i −0.244986 0.141442i
\(466\) 0 0
\(467\) 14.5570i 0.673615i −0.941573 0.336808i \(-0.890653\pi\)
0.941573 0.336808i \(-0.109347\pi\)
\(468\) 0 0
\(469\) 7.34193i 0.339019i
\(470\) 0 0
\(471\) −6.86827 + 11.8962i −0.316473 + 0.548148i
\(472\) 0 0
\(473\) −29.1940 21.9509i −1.34234 1.00930i
\(474\) 0 0
\(475\) 2.89089 10.7889i 0.132643 0.495030i
\(476\) 0 0
\(477\) −2.07409 3.59243i −0.0949661 0.164486i
\(478\) 0 0
\(479\) 32.4291 8.68935i 1.48172 0.397026i 0.574790 0.818301i \(-0.305084\pi\)
0.906933 + 0.421275i \(0.138417\pi\)
\(480\) 0 0
\(481\) −7.55875 17.4569i −0.344650 0.795967i
\(482\) 0 0
\(483\) 0.571407 + 2.13252i 0.0259999 + 0.0970330i
\(484\) 0 0
\(485\) 27.6114 15.9414i 1.25377 0.723864i
\(486\) 0 0
\(487\) 4.95078 18.4765i 0.224341 0.837252i −0.758326 0.651875i \(-0.773983\pi\)
0.982667 0.185377i \(-0.0593507\pi\)
\(488\) 0 0
\(489\) −1.17986 + 1.17986i −0.0533550 + 0.0533550i
\(490\) 0 0
\(491\) 6.13533 10.6267i 0.276884 0.479577i −0.693725 0.720240i \(-0.744032\pi\)
0.970609 + 0.240663i \(0.0773650\pi\)
\(492\) 0 0
\(493\) 17.9463i 0.808261i
\(494\) 0 0
\(495\) 3.52608 + 24.8982i 0.158486 + 1.11909i
\(496\) 0 0
\(497\) 9.79464 + 5.65494i 0.439349 + 0.253659i
\(498\) 0 0
\(499\) 26.6447 + 26.6447i 1.19278 + 1.19278i 0.976283 + 0.216498i \(0.0694634\pi\)
0.216498 + 0.976283i \(0.430537\pi\)
\(500\) 0 0
\(501\) 0.799396 2.98339i 0.0357144 0.133288i
\(502\) 0 0
\(503\) −33.6811 + 19.4458i −1.50177 + 0.867044i −0.501767 + 0.865003i \(0.667317\pi\)
−0.999998 + 0.00204172i \(0.999350\pi\)
\(504\) 0 0
\(505\) −34.1012 + 9.13740i −1.51749 + 0.406609i
\(506\) 0 0
\(507\) −2.52083 + 10.7685i −0.111954 + 0.478246i
\(508\) 0 0
\(509\) 28.4307 7.61798i 1.26017 0.337661i 0.433911 0.900956i \(-0.357133\pi\)
0.826256 + 0.563295i \(0.190466\pi\)
\(510\) 0 0
\(511\) −8.50019 + 4.90759i −0.376026 + 0.217099i
\(512\) 0 0
\(513\) 7.94549 + 2.12899i 0.350802 + 0.0939972i
\(514\) 0 0
\(515\) 45.6448 45.6448i 2.01135 2.01135i
\(516\) 0 0
\(517\) −0.333965 + 0.829117i −0.0146878 + 0.0364645i
\(518\) 0 0
\(519\) −13.3195 −0.584663
\(520\) 0 0
\(521\) −32.5137 −1.42445 −0.712226 0.701950i \(-0.752313\pi\)
−0.712226 + 0.701950i \(0.752313\pi\)
\(522\) 0 0
\(523\) −2.72175 1.57140i −0.119014 0.0687127i 0.439311 0.898335i \(-0.355223\pi\)
−0.558325 + 0.829622i \(0.688556\pi\)
\(524\) 0 0
\(525\) 4.78036 4.78036i 0.208632 0.208632i
\(526\) 0 0
\(527\) 1.25527 4.68473i 0.0546804 0.204070i
\(528\) 0 0
\(529\) −9.51904 16.4875i −0.413871 0.716846i
\(530\) 0 0
\(531\) 1.00342 + 3.74483i 0.0435449 + 0.162512i
\(532\) 0 0
\(533\) −1.41387 3.26533i −0.0612415 0.141437i
\(534\) 0 0
\(535\) 8.90835 + 33.2464i 0.385142 + 1.43737i
\(536\) 0 0
\(537\) −9.53899 + 5.50734i −0.411638 + 0.237659i
\(538\) 0 0
\(539\) 17.4500 + 2.12385i 0.751624 + 0.0914806i
\(540\) 0 0
\(541\) 15.3196 + 15.3196i 0.658641 + 0.658641i 0.955058 0.296417i \(-0.0957920\pi\)
−0.296417 + 0.955058i \(0.595792\pi\)
\(542\) 0 0
\(543\) 1.05528 + 0.609265i 0.0452863 + 0.0261460i
\(544\) 0 0
\(545\) 42.2697 1.81064
\(546\) 0 0
\(547\) 24.8203i 1.06124i 0.847610 + 0.530620i \(0.178041\pi\)
−0.847610 + 0.530620i \(0.821959\pi\)
\(548\) 0 0
\(549\) −5.71349 3.29868i −0.243846 0.140784i
\(550\) 0 0
\(551\) −10.3217 10.3217i −0.439718 0.439718i
\(552\) 0 0
\(553\) −11.5660 3.09910i −0.491836 0.131787i
\(554\) 0 0
\(555\) −7.47552 12.9480i −0.317318 0.549611i
\(556\) 0 0
\(557\) 10.0888 2.70328i 0.427475 0.114542i −0.0386655 0.999252i \(-0.512311\pi\)
0.466141 + 0.884711i \(0.345644\pi\)
\(558\) 0 0
\(559\) 24.6710 + 31.1133i 1.04347 + 1.31595i
\(560\) 0 0
\(561\) 5.84911 2.49011i 0.246950 0.105132i
\(562\) 0 0
\(563\) −12.5165 21.6792i −0.527507 0.913669i −0.999486 0.0320595i \(-0.989793\pi\)
0.471979 0.881610i \(-0.343540\pi\)
\(564\) 0 0
\(565\) 11.7870 43.9896i 0.495882 1.85066i
\(566\) 0 0
\(567\) −2.77493 2.77493i −0.116536 0.116536i
\(568\) 0 0
\(569\) −13.0072 + 22.5291i −0.545290 + 0.944471i 0.453298 + 0.891359i \(0.350247\pi\)
−0.998589 + 0.0531117i \(0.983086\pi\)
\(570\) 0 0
\(571\) −10.7284 −0.448969 −0.224485 0.974478i \(-0.572070\pi\)
−0.224485 + 0.974478i \(0.572070\pi\)
\(572\) 0 0
\(573\) −4.71096 −0.196803
\(574\) 0 0
\(575\) 6.06598 10.5066i 0.252969 0.438155i
\(576\) 0 0
\(577\) −11.7775 11.7775i −0.490303 0.490303i 0.418099 0.908402i \(-0.362697\pi\)
−0.908402 + 0.418099i \(0.862697\pi\)
\(578\) 0 0
\(579\) 3.21793 12.0095i 0.133732 0.499096i
\(580\) 0 0
\(581\) 1.39930 + 2.42366i 0.0580527 + 0.100550i
\(582\) 0 0
\(583\) −5.56117 + 2.36753i −0.230320 + 0.0980529i
\(584\) 0 0
\(585\) 3.13621 27.1568i 0.129666 1.12279i
\(586\) 0 0
\(587\) 10.6926 2.86507i 0.441330 0.118254i −0.0313096 0.999510i \(-0.509968\pi\)
0.472640 + 0.881256i \(0.343301\pi\)
\(588\) 0 0
\(589\) −1.97243 3.41634i −0.0812724 0.140768i
\(590\) 0 0
\(591\) 1.42417 + 0.381606i 0.0585827 + 0.0156972i
\(592\) 0 0
\(593\) −25.2426 25.2426i −1.03659 1.03659i −0.999305 0.0372841i \(-0.988129\pi\)
−0.0372841 0.999305i \(-0.511871\pi\)
\(594\) 0 0
\(595\) 8.47348 + 4.89217i 0.347379 + 0.200559i
\(596\) 0 0
\(597\) 10.3238i 0.422524i
\(598\) 0 0
\(599\) 12.6365 0.516313 0.258157 0.966103i \(-0.416885\pi\)
0.258157 + 0.966103i \(0.416885\pi\)
\(600\) 0 0
\(601\) 25.2519 + 14.5792i 1.03005 + 0.594698i 0.916998 0.398892i \(-0.130605\pi\)
0.113049 + 0.993589i \(0.463938\pi\)
\(602\) 0 0
\(603\) 9.06388 + 9.06388i 0.369110 + 0.369110i
\(604\) 0 0
\(605\) 36.6332 0.716979i 1.48935 0.0291493i
\(606\) 0 0
\(607\) −11.8673 + 6.85161i −0.481680 + 0.278098i −0.721116 0.692814i \(-0.756371\pi\)
0.239436 + 0.970912i \(0.423037\pi\)
\(608\) 0 0
\(609\) −2.28666 8.53393i −0.0926602 0.345812i
\(610\) 0 0
\(611\) 0.579194 0.780236i 0.0234317 0.0315650i
\(612\) 0 0
\(613\) −6.75784 25.2206i −0.272946 1.01865i −0.957205 0.289411i \(-0.906541\pi\)
0.684259 0.729239i \(-0.260126\pi\)
\(614\) 0 0
\(615\) −1.39830 2.42193i −0.0563849 0.0976615i
\(616\) 0 0
\(617\) 1.62323 6.05799i 0.0653489 0.243885i −0.925523 0.378691i \(-0.876374\pi\)
0.990872 + 0.134806i \(0.0430410\pi\)
\(618\) 0 0
\(619\) −25.7346 + 25.7346i −1.03436 + 1.03436i −0.0349708 + 0.999388i \(0.511134\pi\)
−0.999388 + 0.0349708i \(0.988866\pi\)
\(620\) 0 0
\(621\) 7.73757 + 4.46729i 0.310498 + 0.179266i
\(622\) 0 0
\(623\) 10.4786 0.419815
\(624\) 0 0
\(625\) 18.3255 0.733019
\(626\) 0 0
\(627\) 1.93190 4.79623i 0.0771527 0.191543i
\(628\) 0 0
\(629\) 8.40545 8.40545i 0.335147 0.335147i
\(630\) 0 0
\(631\) −35.4237 9.49175i −1.41019 0.377860i −0.528200 0.849120i \(-0.677133\pi\)
−0.881994 + 0.471260i \(0.843799\pi\)
\(632\) 0 0
\(633\) −15.4589 + 8.92520i −0.614436 + 0.354745i
\(634\) 0 0
\(635\) 56.7235 15.1990i 2.25100 0.603154i
\(636\) 0 0
\(637\) −17.7696 7.03107i −0.704059 0.278581i
\(638\) 0 0
\(639\) 19.0730 5.11061i 0.754518 0.202172i
\(640\) 0 0
\(641\) 27.6323 15.9535i 1.09141 0.630125i 0.157458 0.987526i \(-0.449670\pi\)
0.933951 + 0.357401i \(0.116337\pi\)
\(642\) 0 0
\(643\) −4.48792 + 16.7492i −0.176986 + 0.660523i 0.819218 + 0.573482i \(0.194408\pi\)
−0.996205 + 0.0870407i \(0.972259\pi\)
\(644\) 0 0
\(645\) 22.0673 + 22.0673i 0.868899 + 0.868899i
\(646\) 0 0
\(647\) −23.3562 13.4847i −0.918226 0.530138i −0.0351571 0.999382i \(-0.511193\pi\)
−0.883069 + 0.469244i \(0.844526\pi\)
\(648\) 0 0
\(649\) 5.59311 0.792096i 0.219549 0.0310925i
\(650\) 0 0
\(651\) 2.38765i 0.0935795i
\(652\) 0 0
\(653\) −11.9838 + 20.7566i −0.468963 + 0.812268i −0.999371 0.0354749i \(-0.988706\pi\)
0.530407 + 0.847743i \(0.322039\pi\)
\(654\) 0 0
\(655\) 11.2875 11.2875i 0.441039 0.441039i
\(656\) 0 0
\(657\) −4.43519 + 16.5524i −0.173033 + 0.645769i
\(658\) 0 0
\(659\) −24.5922 + 14.1983i −0.957976 + 0.553088i −0.895549 0.444962i \(-0.853217\pi\)
−0.0624263 + 0.998050i \(0.519884\pi\)
\(660\) 0 0
\(661\) −6.87192 25.6464i −0.267287 0.997528i −0.960836 0.277118i \(-0.910621\pi\)
0.693549 0.720409i \(-0.256046\pi\)
\(662\) 0 0
\(663\) −6.83654 + 1.01104i −0.265509 + 0.0392655i
\(664\) 0 0
\(665\) 7.68714 2.05976i 0.298094 0.0798742i
\(666\) 0 0
\(667\) −7.92741 13.7307i −0.306951 0.531654i
\(668\) 0 0
\(669\) 3.42465 12.7810i 0.132405 0.494141i
\(670\) 0 0
\(671\) −5.77698 + 7.68321i −0.223018 + 0.296607i
\(672\) 0 0
\(673\) −10.2110 + 17.6859i −0.393604 + 0.681742i −0.992922 0.118769i \(-0.962105\pi\)
0.599318 + 0.800511i \(0.295439\pi\)
\(674\) 0 0
\(675\) 27.3590i 1.05305i
\(676\) 0 0
\(677\) 6.22223i 0.239140i 0.992826 + 0.119570i \(0.0381516\pi\)
−0.992826 + 0.119570i \(0.961848\pi\)
\(678\) 0 0
\(679\) 10.8074 + 6.23968i 0.414752 + 0.239457i
\(680\) 0 0
\(681\) 8.95523 8.95523i 0.343165 0.343165i
\(682\) 0 0
\(683\) −31.5467 8.45291i −1.20710 0.323442i −0.401477 0.915869i \(-0.631503\pi\)
−0.805624 + 0.592427i \(0.798170\pi\)
\(684\) 0 0
\(685\) −3.11322 5.39225i −0.118950 0.206027i
\(686\) 0 0
\(687\) 5.11326 + 19.0829i 0.195083 + 0.728060i
\(688\) 0 0
\(689\) 6.50000 0.961268i 0.247630 0.0366214i
\(690\) 0 0
\(691\) −38.2930 + 10.2606i −1.45673 + 0.390331i −0.898360 0.439259i \(-0.855241\pi\)
−0.558374 + 0.829590i \(0.688574\pi\)
\(692\) 0 0
\(693\) −7.74975 + 6.06798i −0.294389 + 0.230504i
\(694\) 0 0
\(695\) −37.5308 10.0563i −1.42362 0.381459i
\(696\) 0 0
\(697\) 1.57224 1.57224i 0.0595530 0.0595530i
\(698\) 0 0
\(699\) −9.49524 + 16.4462i −0.359143 + 0.622054i
\(700\) 0 0
\(701\) 2.28042 0.0861301 0.0430651 0.999072i \(-0.486288\pi\)
0.0430651 + 0.999072i \(0.486288\pi\)
\(702\) 0 0
\(703\) 9.66865i 0.364660i
\(704\) 0 0
\(705\) 0.381856 0.661394i 0.0143815 0.0249095i
\(706\) 0 0
\(707\) −9.77117 9.77117i −0.367483 0.367483i
\(708\) 0 0
\(709\) 23.9911 + 6.42839i 0.901004 + 0.241423i 0.679448 0.733724i \(-0.262220\pi\)
0.221557 + 0.975147i \(0.428886\pi\)
\(710\) 0 0
\(711\) −18.1046 + 10.4527i −0.678975 + 0.392006i
\(712\) 0 0
\(713\) −1.10898 4.13877i −0.0415316 0.154998i
\(714\) 0 0
\(715\) −38.7271 9.31688i −1.44831 0.348432i
\(716\) 0 0
\(717\) −5.36663 20.0285i −0.200420 0.747979i
\(718\) 0 0
\(719\) 12.6090 7.27981i 0.470236 0.271491i −0.246102 0.969244i \(-0.579150\pi\)
0.716339 + 0.697753i \(0.245817\pi\)
\(720\) 0 0
\(721\) 24.4053 + 6.53939i 0.908902 + 0.243540i
\(722\) 0 0
\(723\) 13.4560 + 13.4560i 0.500436 + 0.500436i
\(724\) 0 0
\(725\) −24.2749 + 42.0454i −0.901548 + 1.56153i
\(726\) 0 0
\(727\) 49.0752i 1.82010i 0.414498 + 0.910050i \(0.363957\pi\)
−0.414498 + 0.910050i \(0.636043\pi\)
\(728\) 0 0
\(729\) 4.60465 0.170543
\(730\) 0 0
\(731\) −12.4062 + 21.4882i −0.458860 + 0.794769i
\(732\) 0 0
\(733\) −14.5746 + 14.5746i −0.538327 + 0.538327i −0.923037 0.384711i \(-0.874301\pi\)
0.384711 + 0.923037i \(0.374301\pi\)
\(734\) 0 0
\(735\) −14.5076 3.88731i −0.535123 0.143386i
\(736\) 0 0
\(737\) 14.7055 11.5143i 0.541684 0.424133i
\(738\) 0 0
\(739\) 9.83259 2.63463i 0.361698 0.0969166i −0.0733933 0.997303i \(-0.523383\pi\)
0.435091 + 0.900386i \(0.356716\pi\)
\(740\) 0 0
\(741\) −3.35049 + 4.51347i −0.123083 + 0.165806i
\(742\) 0 0
\(743\) −3.92786 14.6590i −0.144099 0.537785i −0.999794 0.0203043i \(-0.993537\pi\)
0.855695 0.517481i \(-0.173130\pi\)
\(744\) 0 0
\(745\) −21.2570 36.8182i −0.778797 1.34892i
\(746\) 0 0
\(747\) 4.71958 + 1.26461i 0.172680 + 0.0462695i
\(748\) 0 0
\(749\) −9.52623 + 9.52623i −0.348081 + 0.348081i
\(750\) 0 0
\(751\) 9.02621 + 5.21129i 0.329371 + 0.190163i 0.655562 0.755141i \(-0.272432\pi\)
−0.326191 + 0.945304i \(0.605765\pi\)
\(752\) 0 0
\(753\) 26.1907i 0.954443i
\(754\) 0 0
\(755\) 4.75664i 0.173112i
\(756\) 0 0
\(757\) −14.7634 + 25.5710i −0.536585 + 0.929392i 0.462500 + 0.886619i \(0.346953\pi\)
−0.999085 + 0.0427728i \(0.986381\pi\)
\(758\) 0 0
\(759\) 3.37519 4.48890i 0.122512 0.162937i
\(760\) 0 0
\(761\) −7.06369 + 26.3620i −0.256059 + 0.955623i 0.711440 + 0.702747i \(0.248043\pi\)
−0.967499 + 0.252877i \(0.918623\pi\)
\(762\) 0 0
\(763\) 8.27246 + 14.3283i 0.299483 + 0.518720i
\(764\) 0 0
\(765\) 16.5004 4.42126i 0.596572 0.159851i
\(766\) 0 0
\(767\) −6.10048 0.704517i −0.220276 0.0254386i
\(768\) 0 0
\(769\) −0.529669 1.97675i −0.0191003 0.0712834i 0.955718 0.294285i \(-0.0950813\pi\)
−0.974818 + 0.223001i \(0.928415\pi\)
\(770\) 0 0
\(771\) 14.4956 8.36901i 0.522045 0.301403i
\(772\) 0 0
\(773\) −13.1969 + 49.2516i −0.474660 + 1.77146i 0.148024 + 0.988984i \(0.452709\pi\)
−0.622685 + 0.782473i \(0.713958\pi\)
\(774\) 0 0
\(775\) −9.27766 + 9.27766i −0.333263 + 0.333263i
\(776\) 0 0
\(777\) 2.92601 5.06801i 0.104970 0.181814i
\(778\) 0 0
\(779\) 1.80853i 0.0647972i
\(780\) 0 0
\(781\) −4.03428 28.4867i −0.144358 1.01933i
\(782\) 0 0
\(783\) −30.9643 17.8772i −1.10657 0.638880i
\(784\) 0 0
\(785\) 38.0304 + 38.0304i 1.35736 + 1.35736i
\(786\) 0 0
\(787\) −8.34148 + 31.1308i −0.297342 + 1.10969i 0.641998 + 0.766706i \(0.278106\pi\)
−0.939340 + 0.342988i \(0.888561\pi\)
\(788\) 0 0
\(789\) −19.2003 + 11.0853i −0.683549 + 0.394647i
\(790\) 0 0
\(791\) 17.2181 4.61357i 0.612205 0.164040i
\(792\) 0 0
\(793\) 8.18834 6.49287i 0.290776 0.230569i
\(794\) 0 0
\(795\) 4.98821 1.33659i 0.176914 0.0474039i
\(796\) 0 0
\(797\) −38.4816 + 22.2174i −1.36309 + 0.786979i −0.990034 0.140831i \(-0.955023\pi\)
−0.373054 + 0.927810i \(0.621689\pi\)
\(798\) 0 0
\(799\) 0.586514 + 0.157156i 0.0207494 + 0.00555977i
\(800\) 0 0
\(801\) 12.9362 12.9362i 0.457077 0.457077i
\(802\) 0 0
\(803\) 23.1604 + 9.32890i 0.817312 + 0.329210i
\(804\) 0 0
\(805\) 8.64406 0.304663
\(806\) 0 0
\(807\) −13.0839 −0.460576
\(808\) 0 0
\(809\) 33.0435 + 19.0777i 1.16175 + 0.670735i 0.951722 0.306960i \(-0.0993119\pi\)
0.210026 + 0.977696i \(0.432645\pi\)
\(810\) 0 0
\(811\) 28.0114 28.0114i 0.983612 0.983612i −0.0162560 0.999868i \(-0.505175\pi\)
0.999868 + 0.0162560i \(0.00517467\pi\)
\(812\) 0 0
\(813\) 4.68122 17.4706i 0.164178 0.612719i
\(814\) 0 0
\(815\) 3.26650 + 5.65775i 0.114421 + 0.198182i
\(816\) 0 0
\(817\) 5.22342 + 19.4941i 0.182744 + 0.682011i
\(818\) 0 0
\(819\) 9.81920 4.25166i 0.343111 0.148565i
\(820\) 0 0
\(821\) −9.93329 37.0716i −0.346674 1.29381i −0.890644 0.454701i \(-0.849746\pi\)
0.543970 0.839105i \(-0.316921\pi\)
\(822\) 0 0
\(823\) −29.3415 + 16.9403i −1.02278 + 0.590502i −0.914908 0.403662i \(-0.867737\pi\)
−0.107872 + 0.994165i \(0.534404\pi\)
\(824\) 0 0
\(825\) −17.0718 2.07782i −0.594363 0.0723403i
\(826\) 0 0
\(827\) −18.7312 18.7312i −0.651348 0.651348i 0.301970 0.953318i \(-0.402356\pi\)
−0.953318 + 0.301970i \(0.902356\pi\)
\(828\) 0 0
\(829\) 7.29942 + 4.21432i 0.253519 + 0.146369i 0.621375 0.783514i \(-0.286574\pi\)
−0.367855 + 0.929883i \(0.619908\pi\)
\(830\) 0 0
\(831\) −24.2149 −0.840007
\(832\) 0 0
\(833\) 11.9415i 0.413747i
\(834\) 0 0
\(835\) −10.4728 6.04650i −0.362428 0.209248i
\(836\) 0 0
\(837\) −6.83252 6.83252i −0.236167 0.236167i
\(838\) 0 0
\(839\) 40.4936 + 10.8502i 1.39800 + 0.374592i 0.877625 0.479348i \(-0.159127\pi\)
0.520371 + 0.853940i \(0.325794\pi\)
\(840\) 0 0
\(841\) 17.2240 + 29.8328i 0.593931 + 1.02872i
\(842\) 0 0
\(843\) 23.3680 6.26144i 0.804837 0.215656i
\(844\) 0 0
\(845\) 38.1711 + 20.4460i 1.31312 + 0.703362i
\(846\) 0 0
\(847\) 7.41238 + 12.2774i 0.254692 + 0.421855i
\(848\) 0 0
\(849\) 5.28350 + 9.15129i 0.181329 + 0.314071i
\(850\) 0 0
\(851\) 2.71806 10.1439i 0.0931738 0.347729i
\(852\) 0 0
\(853\) 39.8564 + 39.8564i 1.36466 + 1.36466i 0.867877 + 0.496778i \(0.165484\pi\)
0.496778 + 0.867877i \(0.334516\pi\)
\(854\) 0 0
\(855\) 6.94719 12.0329i 0.237589 0.411516i
\(856\) 0 0
\(857\) −1.14977 −0.0392753 −0.0196376 0.999807i \(-0.506251\pi\)
−0.0196376 + 0.999807i \(0.506251\pi\)
\(858\) 0 0
\(859\) 21.7178 0.741003 0.370502 0.928832i \(-0.379186\pi\)
0.370502 + 0.928832i \(0.379186\pi\)
\(860\) 0 0
\(861\) 0.547313 0.947973i 0.0186524 0.0323068i
\(862\) 0 0
\(863\) −5.73837 5.73837i −0.195336 0.195336i 0.602661 0.797997i \(-0.294107\pi\)
−0.797997 + 0.602661i \(0.794107\pi\)
\(864\) 0 0
\(865\) −13.4975 + 50.3734i −0.458930 + 1.71275i
\(866\) 0 0
\(867\) 5.07206 + 8.78506i 0.172256 + 0.298356i
\(868\) 0 0
\(869\) 11.9315 + 28.0263i 0.404748 + 0.950728i
\(870\) 0 0
\(871\) −18.6324 + 8.06772i −0.631334 + 0.273364i
\(872\) 0 0
\(873\) 21.0453 5.63907i 0.712275 0.190854i
\(874\) 0 0
\(875\) −2.37781 4.11849i −0.0803847 0.139230i
\(876\) 0 0
\(877\) −22.1321 5.93027i −0.747347 0.200251i −0.135006 0.990845i \(-0.543105\pi\)
−0.612341 + 0.790594i \(0.709772\pi\)
\(878\) 0 0
\(879\) 18.7769 + 18.7769i 0.633330 + 0.633330i
\(880\) 0 0
\(881\) −3.31381 1.91323i −0.111645 0.0644583i 0.443138 0.896454i \(-0.353865\pi\)
−0.554783 + 0.831995i \(0.687199\pi\)
\(882\) 0 0
\(883\) 40.7711i 1.37206i 0.727575 + 0.686028i \(0.240647\pi\)
−0.727575 + 0.686028i \(0.759353\pi\)
\(884\) 0 0
\(885\) −4.82649 −0.162241
\(886\) 0 0
\(887\) 4.23262 + 2.44371i 0.142118 + 0.0820516i 0.569373 0.822079i \(-0.307186\pi\)
−0.427255 + 0.904131i \(0.640519\pi\)
\(888\) 0 0
\(889\) 16.2532 + 16.2532i 0.545115 + 0.545115i
\(890\) 0 0
\(891\) −1.20615 + 9.90993i −0.0404074 + 0.331995i
\(892\) 0 0
\(893\) 0.427715 0.246941i 0.0143129 0.00826358i
\(894\) 0 0
\(895\) 11.1619 + 41.6566i 0.373100 + 1.39243i
\(896\) 0 0
\(897\) −4.78402 + 3.79345i −0.159734 + 0.126659i
\(898\) 0 0
\(899\) 4.43793 + 16.5626i 0.148013 + 0.552392i
\(900\) 0 0
\(901\) 2.05294 + 3.55579i 0.0683932 + 0.118461i
\(902\) 0 0
\(903\) −3.16152 + 11.7989i −0.105209 + 0.392644i
\(904\) 0 0
\(905\) 3.37357 3.37357i 0.112141 0.112141i
\(906\) 0 0
\(907\) −12.7500 7.36123i −0.423357 0.244426i 0.273155 0.961970i \(-0.411933\pi\)
−0.696513 + 0.717544i \(0.745266\pi\)
\(908\) 0 0
\(909\) −24.1257 −0.800199
\(910\) 0 0
\(911\) 27.7740 0.920193 0.460096 0.887869i \(-0.347815\pi\)
0.460096 + 0.887869i \(0.347815\pi\)
\(912\) 0 0
\(913\) 2.65995 6.60371i 0.0880315 0.218551i
\(914\) 0 0
\(915\) 5.80763 5.80763i 0.191994 0.191994i
\(916\) 0 0
\(917\) 6.03520 + 1.61713i 0.199300 + 0.0534022i
\(918\) 0 0
\(919\) −4.79012 + 2.76558i −0.158011 + 0.0912279i −0.576921 0.816800i \(-0.695746\pi\)
0.418909 + 0.908028i \(0.362413\pi\)
\(920\) 0 0
\(921\) −3.17590 + 0.850979i −0.104649 + 0.0280407i
\(922\) 0 0
\(923\) −3.58822 + 31.0708i −0.118108 + 1.02271i
\(924\) 0 0
\(925\) −31.0622 + 8.32310i −1.02132 + 0.273662i
\(926\) 0 0
\(927\) 38.2024 22.0561i 1.25473 0.724419i
\(928\) 0 0
\(929\) −5.87990 + 21.9441i −0.192913 + 0.719963i 0.799884 + 0.600155i \(0.204894\pi\)
−0.992797 + 0.119808i \(0.961772\pi\)
\(930\) 0 0
\(931\) −6.86803 6.86803i −0.225091 0.225091i
\(932\) 0 0
\(933\) −19.9090 11.4944i −0.651790 0.376311i
\(934\) 0 0
\(935\) −3.49012 24.6442i −0.114139 0.805953i
\(936\) 0 0
\(937\) 41.6793i 1.36160i −0.732468 0.680801i \(-0.761632\pi\)
0.732468 0.680801i \(-0.238368\pi\)
\(938\) 0 0
\(939\) 4.00390 6.93496i 0.130662 0.226314i
\(940\) 0 0
\(941\) −24.4550 + 24.4550i −0.797211 + 0.797211i −0.982655 0.185444i \(-0.940628\pi\)
0.185444 + 0.982655i \(0.440628\pi\)
\(942\) 0 0
\(943\) 0.508414 1.89743i 0.0165562 0.0617887i
\(944\) 0 0
\(945\) 16.8817 9.74667i 0.549163 0.317059i
\(946\) 0 0
\(947\) 4.26863 + 15.9307i 0.138712 + 0.517679i 0.999955 + 0.00948635i \(0.00301964\pi\)
−0.861243 + 0.508193i \(0.830314\pi\)
\(948\) 0 0
\(949\) −21.7950 16.1791i −0.707494 0.525195i
\(950\) 0 0
\(951\) −22.8178 + 6.11400i −0.739917 + 0.198260i
\(952\) 0 0
\(953\) −0.733554 1.27055i −0.0237621 0.0411572i 0.853900 0.520437i \(-0.174231\pi\)
−0.877662 + 0.479280i \(0.840898\pi\)
\(954\) 0 0
\(955\) −4.77391 + 17.8165i −0.154480 + 0.576528i
\(956\) 0 0
\(957\) −13.5069 + 17.9637i −0.436615 + 0.580685i
\(958\) 0 0
\(959\) 1.21855 2.11060i 0.0393492 0.0681547i
\(960\) 0 0
\(961\) 26.3661i 0.850518i
\(962\) 0 0
\(963\) 23.5209i 0.757952i
\(964\) 0 0
\(965\) −42.1579 24.3399i −1.35711 0.783528i
\(966\) 0 0
\(967\) 33.6688 33.6688i 1.08272 1.08272i 0.0864611 0.996255i \(-0.472444\pi\)
0.996255 0.0864611i \(-0.0275558\pi\)
\(968\) 0 0
\(969\) −3.39283 0.909107i −0.108993 0.0292047i
\(970\) 0 0
\(971\) −27.0273 46.8126i −0.867346 1.50229i −0.864699 0.502291i \(-0.832491\pi\)
−0.00264743 0.999996i \(-0.500843\pi\)
\(972\) 0 0
\(973\) −3.93618 14.6900i −0.126188 0.470940i
\(974\) 0 0
\(975\) 17.3845 + 6.87868i 0.556750 + 0.220294i
\(976\) 0 0
\(977\) −2.17510 + 0.582816i −0.0695875 + 0.0186459i −0.293445 0.955976i \(-0.594802\pi\)
0.223857 + 0.974622i \(0.428135\pi\)
\(978\) 0 0
\(979\) −16.4334 20.9880i −0.525214 0.670779i
\(980\) 0 0
\(981\) 27.9014 + 7.47617i 0.890825 + 0.238696i
\(982\) 0 0
\(983\) −14.7853 + 14.7853i −0.471578 + 0.471578i −0.902425 0.430847i \(-0.858215\pi\)
0.430847 + 0.902425i \(0.358215\pi\)
\(984\) 0 0
\(985\) 2.88641 4.99941i 0.0919687 0.159294i
\(986\) 0 0
\(987\) 0.298927 0.00951494
\(988\) 0 0
\(989\) 21.9207i 0.697039i
\(990\) 0 0
\(991\) 17.6694 30.6043i 0.561286 0.972177i −0.436098 0.899899i \(-0.643640\pi\)
0.997385 0.0722775i \(-0.0230267\pi\)
\(992\) 0 0
\(993\) −12.2560 12.2560i −0.388934 0.388934i
\(994\) 0 0
\(995\) 39.0437 + 10.4617i 1.23777 + 0.331659i
\(996\) 0 0
\(997\) −0.117556 + 0.0678713i −0.00372305 + 0.00214950i −0.501860 0.864949i \(-0.667351\pi\)
0.498137 + 0.867098i \(0.334018\pi\)
\(998\) 0 0
\(999\) −6.12953 22.8757i −0.193930 0.723756i
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.bc.a.241.5 yes 56
11.10 odd 2 inner 572.2.bc.a.241.6 yes 56
13.2 odd 12 inner 572.2.bc.a.197.6 yes 56
143.54 even 12 inner 572.2.bc.a.197.5 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.bc.a.197.5 56 143.54 even 12 inner
572.2.bc.a.197.6 yes 56 13.2 odd 12 inner
572.2.bc.a.241.5 yes 56 1.1 even 1 trivial
572.2.bc.a.241.6 yes 56 11.10 odd 2 inner