Properties

Label 804.2.q.a.241.4
Level $804$
Weight $2$
Character 804.241
Analytic conductor $6.420$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [804,2,Mod(25,804)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(804, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("804.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 804.q (of order \(11\), degree \(10\), 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: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 241.4
Character \(\chi\) \(=\) 804.241
Dual form 804.2.q.a.397.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.415415 - 0.909632i) q^{3} +(0.346311 + 0.101686i) q^{5} +(-0.316787 - 0.365591i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(0.415415 - 0.909632i) q^{3} +(0.346311 + 0.101686i) q^{5} +(-0.316787 - 0.365591i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-3.26532 - 0.958785i) q^{11} +(-5.29213 - 3.40105i) q^{13} +(0.236360 - 0.272774i) q^{15} +(-0.245080 - 1.70457i) q^{17} +(-0.00809343 + 0.00934032i) q^{19} +(-0.464151 + 0.136287i) q^{21} +(2.00963 - 4.40047i) q^{23} +(-4.09668 - 2.63277i) q^{25} +(-0.959493 + 0.281733i) q^{27} +6.45535 q^{29} +(-3.57798 + 2.29943i) q^{31} +(-2.22860 + 2.57195i) q^{33} +(-0.0725312 - 0.158821i) q^{35} +6.61092 q^{37} +(-5.29213 + 3.40105i) q^{39} +(-0.766467 - 5.33089i) q^{41} +(0.267804 + 1.86262i) q^{43} +(-0.149936 - 0.328315i) q^{45} +(-1.75439 + 3.84157i) q^{47} +(0.962901 - 6.69712i) q^{49} +(-1.65234 - 0.485171i) q^{51} +(0.891886 - 6.20320i) q^{53} +(-1.03332 - 0.664076i) q^{55} +(0.00513412 + 0.0112422i) q^{57} +(-3.05821 + 1.96539i) q^{59} +(-13.0035 + 3.81817i) q^{61} +(-0.0688443 + 0.478823i) q^{63} +(-1.48689 - 1.71596i) q^{65} +(2.10117 + 7.91107i) q^{67} +(-3.16798 - 3.65604i) q^{69} +(0.831647 - 5.78423i) q^{71} +(-0.109491 + 0.0321495i) q^{73} +(-4.09668 + 2.63277i) q^{75} +(0.683887 + 1.49750i) q^{77} +(-10.4984 - 6.74689i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(15.8816 + 4.66324i) q^{83} +(0.0884571 - 0.615233i) q^{85} +(2.68165 - 5.87200i) q^{87} +(3.11906 + 6.82978i) q^{89} +(0.433084 + 3.01216i) q^{91} +(0.605286 + 4.20986i) q^{93} +(-0.00375263 + 0.00241167i) q^{95} +3.84463 q^{97} +(1.41373 + 3.09564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 6 q^{3} - 2 q^{5} - 2 q^{7} - 6 q^{9} + 7 q^{11} - 2 q^{13} + 9 q^{15} - 19 q^{17} + 2 q^{19} - 2 q^{21} + 4 q^{23} + 16 q^{25} - 6 q^{27} + 16 q^{29} - 28 q^{31} - 4 q^{33} + 28 q^{35} + 2 q^{37} - 2 q^{39} + 32 q^{41} + 19 q^{43} - 2 q^{45} + 2 q^{47} - 70 q^{49} - 19 q^{51} + 31 q^{53} - 5 q^{55} + 13 q^{57} + 59 q^{59} + 32 q^{61} + 9 q^{63} + 28 q^{65} + 7 q^{67} + 4 q^{69} + 16 q^{71} + 19 q^{73} + 16 q^{75} - 46 q^{77} + 48 q^{79} - 6 q^{81} + 60 q^{83} - 66 q^{85} + 5 q^{87} - 22 q^{89} + 24 q^{91} + 5 q^{93} + 103 q^{95} - 46 q^{97} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(1\)

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
\(3\) 0.415415 0.909632i 0.239840 0.525176i
\(4\) 0 0
\(5\) 0.346311 + 0.101686i 0.154875 + 0.0454754i 0.358251 0.933625i \(-0.383373\pi\)
−0.203376 + 0.979101i \(0.565191\pi\)
\(6\) 0 0
\(7\) −0.316787 0.365591i −0.119734 0.138181i 0.692718 0.721209i \(-0.256413\pi\)
−0.812452 + 0.583028i \(0.801868\pi\)
\(8\) 0 0
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 0 0
\(11\) −3.26532 0.958785i −0.984531 0.289085i −0.250438 0.968133i \(-0.580575\pi\)
−0.734094 + 0.679048i \(0.762393\pi\)
\(12\) 0 0
\(13\) −5.29213 3.40105i −1.46777 0.943281i −0.998174 0.0604010i \(-0.980762\pi\)
−0.469599 0.882880i \(-0.655602\pi\)
\(14\) 0 0
\(15\) 0.236360 0.272774i 0.0610279 0.0704299i
\(16\) 0 0
\(17\) −0.245080 1.70457i −0.0594407 0.413419i −0.997717 0.0675325i \(-0.978487\pi\)
0.938276 0.345886i \(-0.112422\pi\)
\(18\) 0 0
\(19\) −0.00809343 + 0.00934032i −0.00185676 + 0.00214282i −0.756677 0.653789i \(-0.773179\pi\)
0.754820 + 0.655931i \(0.227724\pi\)
\(20\) 0 0
\(21\) −0.464151 + 0.136287i −0.101286 + 0.0297403i
\(22\) 0 0
\(23\) 2.00963 4.40047i 0.419036 0.917561i −0.575944 0.817489i \(-0.695366\pi\)
0.994980 0.100072i \(-0.0319072\pi\)
\(24\) 0 0
\(25\) −4.09668 2.63277i −0.819335 0.526555i
\(26\) 0 0
\(27\) −0.959493 + 0.281733i −0.184655 + 0.0542195i
\(28\) 0 0
\(29\) 6.45535 1.19873 0.599365 0.800476i \(-0.295420\pi\)
0.599365 + 0.800476i \(0.295420\pi\)
\(30\) 0 0
\(31\) −3.57798 + 2.29943i −0.642624 + 0.412989i −0.820964 0.570980i \(-0.806564\pi\)
0.178340 + 0.983969i \(0.442927\pi\)
\(32\) 0 0
\(33\) −2.22860 + 2.57195i −0.387950 + 0.447719i
\(34\) 0 0
\(35\) −0.0725312 0.158821i −0.0122600 0.0268457i
\(36\) 0 0
\(37\) 6.61092 1.08683 0.543414 0.839465i \(-0.317131\pi\)
0.543414 + 0.839465i \(0.317131\pi\)
\(38\) 0 0
\(39\) −5.29213 + 3.40105i −0.847419 + 0.544603i
\(40\) 0 0
\(41\) −0.766467 5.33089i −0.119702 0.832546i −0.957884 0.287155i \(-0.907290\pi\)
0.838182 0.545391i \(-0.183619\pi\)
\(42\) 0 0
\(43\) 0.267804 + 1.86262i 0.0408398 + 0.284047i 0.999999 + 0.00118115i \(0.000375972\pi\)
−0.959160 + 0.282866i \(0.908715\pi\)
\(44\) 0 0
\(45\) −0.149936 0.328315i −0.0223512 0.0489423i
\(46\) 0 0
\(47\) −1.75439 + 3.84157i −0.255904 + 0.560351i −0.993360 0.115044i \(-0.963299\pi\)
0.737457 + 0.675394i \(0.236027\pi\)
\(48\) 0 0
\(49\) 0.962901 6.69712i 0.137557 0.956732i
\(50\) 0 0
\(51\) −1.65234 0.485171i −0.231374 0.0679375i
\(52\) 0 0
\(53\) 0.891886 6.20320i 0.122510 0.852075i −0.832187 0.554495i \(-0.812911\pi\)
0.954697 0.297580i \(-0.0961795\pi\)
\(54\) 0 0
\(55\) −1.03332 0.664076i −0.139333 0.0895440i
\(56\) 0 0
\(57\) 0.00513412 + 0.0112422i 0.000680031 + 0.00148906i
\(58\) 0 0
\(59\) −3.05821 + 1.96539i −0.398145 + 0.255872i −0.724358 0.689424i \(-0.757864\pi\)
0.326213 + 0.945296i \(0.394227\pi\)
\(60\) 0 0
\(61\) −13.0035 + 3.81817i −1.66493 + 0.488867i −0.972555 0.232674i \(-0.925252\pi\)
−0.692372 + 0.721541i \(0.743434\pi\)
\(62\) 0 0
\(63\) −0.0688443 + 0.478823i −0.00867357 + 0.0603260i
\(64\) 0 0
\(65\) −1.48689 1.71596i −0.184425 0.212838i
\(66\) 0 0
\(67\) 2.10117 + 7.91107i 0.256699 + 0.966491i
\(68\) 0 0
\(69\) −3.16798 3.65604i −0.381379 0.440135i
\(70\) 0 0
\(71\) 0.831647 5.78423i 0.0986983 0.686462i −0.879058 0.476716i \(-0.841827\pi\)
0.977756 0.209746i \(-0.0672638\pi\)
\(72\) 0 0
\(73\) −0.109491 + 0.0321495i −0.0128150 + 0.00376282i −0.288134 0.957590i \(-0.593035\pi\)
0.275319 + 0.961353i \(0.411217\pi\)
\(74\) 0 0
\(75\) −4.09668 + 2.63277i −0.473043 + 0.304007i
\(76\) 0 0
\(77\) 0.683887 + 1.49750i 0.0779361 + 0.170656i
\(78\) 0 0
\(79\) −10.4984 6.74689i −1.18116 0.759084i −0.205559 0.978645i \(-0.565901\pi\)
−0.975599 + 0.219560i \(0.929538\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0 0
\(83\) 15.8816 + 4.66324i 1.74323 + 0.511858i 0.989400 0.145216i \(-0.0463876\pi\)
0.753827 + 0.657073i \(0.228206\pi\)
\(84\) 0 0
\(85\) 0.0884571 0.615233i 0.00959452 0.0667314i
\(86\) 0 0
\(87\) 2.68165 5.87200i 0.287503 0.629544i
\(88\) 0 0
\(89\) 3.11906 + 6.82978i 0.330619 + 0.723955i 0.999817 0.0191293i \(-0.00608941\pi\)
−0.669198 + 0.743084i \(0.733362\pi\)
\(90\) 0 0
\(91\) 0.433084 + 3.01216i 0.0453995 + 0.315761i
\(92\) 0 0
\(93\) 0.605286 + 4.20986i 0.0627653 + 0.436542i
\(94\) 0 0
\(95\) −0.00375263 + 0.00241167i −0.000385012 + 0.000247432i
\(96\) 0 0
\(97\) 3.84463 0.390363 0.195182 0.980767i \(-0.437470\pi\)
0.195182 + 0.980767i \(0.437470\pi\)
\(98\) 0 0
\(99\) 1.41373 + 3.09564i 0.142085 + 0.311123i
\(100\) 0 0
\(101\) 10.1832 11.7521i 1.01327 1.16937i 0.0277828 0.999614i \(-0.491155\pi\)
0.985485 0.169760i \(-0.0542992\pi\)
\(102\) 0 0
\(103\) −9.92897 + 6.38096i −0.978330 + 0.628735i −0.929012 0.370048i \(-0.879341\pi\)
−0.0493178 + 0.998783i \(0.515705\pi\)
\(104\) 0 0
\(105\) −0.174599 −0.0170392
\(106\) 0 0
\(107\) 5.93932 1.74394i 0.574176 0.168593i 0.0182622 0.999833i \(-0.494187\pi\)
0.555914 + 0.831240i \(0.312368\pi\)
\(108\) 0 0
\(109\) 12.6532 + 8.13171i 1.21195 + 0.778876i 0.980985 0.194085i \(-0.0621736\pi\)
0.230970 + 0.972961i \(0.425810\pi\)
\(110\) 0 0
\(111\) 2.74627 6.01350i 0.260665 0.570776i
\(112\) 0 0
\(113\) −0.424988 + 0.124788i −0.0399796 + 0.0117391i −0.301661 0.953415i \(-0.597541\pi\)
0.261682 + 0.965154i \(0.415723\pi\)
\(114\) 0 0
\(115\) 1.14342 1.31958i 0.106625 0.123051i
\(116\) 0 0
\(117\) 0.895270 + 6.22674i 0.0827677 + 0.575662i
\(118\) 0 0
\(119\) −0.545538 + 0.629584i −0.0500094 + 0.0577139i
\(120\) 0 0
\(121\) 0.489266 + 0.314432i 0.0444788 + 0.0285848i
\(122\) 0 0
\(123\) −5.16755 1.51733i −0.465943 0.136813i
\(124\) 0 0
\(125\) −2.33281 2.69220i −0.208653 0.240798i
\(126\) 0 0
\(127\) −6.19395 7.14820i −0.549624 0.634300i 0.411171 0.911558i \(-0.365120\pi\)
−0.960796 + 0.277258i \(0.910574\pi\)
\(128\) 0 0
\(129\) 1.80555 + 0.530157i 0.158970 + 0.0466777i
\(130\) 0 0
\(131\) −7.53434 + 16.4979i −0.658279 + 1.44143i 0.225839 + 0.974165i \(0.427488\pi\)
−0.884118 + 0.467265i \(0.845240\pi\)
\(132\) 0 0
\(133\) 0.00597863 0.000518413
\(134\) 0 0
\(135\) −0.360931 −0.0310640
\(136\) 0 0
\(137\) 1.87899 4.11442i 0.160533 0.351519i −0.812224 0.583346i \(-0.801743\pi\)
0.972757 + 0.231827i \(0.0744705\pi\)
\(138\) 0 0
\(139\) 0.250731 + 0.0736213i 0.0212667 + 0.00624448i 0.292349 0.956312i \(-0.405563\pi\)
−0.271082 + 0.962556i \(0.587381\pi\)
\(140\) 0 0
\(141\) 2.76562 + 3.19169i 0.232907 + 0.268789i
\(142\) 0 0
\(143\) 14.0196 + 16.1795i 1.17238 + 1.35300i
\(144\) 0 0
\(145\) 2.23556 + 0.656420i 0.185653 + 0.0545127i
\(146\) 0 0
\(147\) −5.69191 3.65797i −0.469461 0.301704i
\(148\) 0 0
\(149\) 14.8396 17.1259i 1.21571 1.40301i 0.326695 0.945130i \(-0.394065\pi\)
0.889016 0.457876i \(-0.151390\pi\)
\(150\) 0 0
\(151\) −0.313856 2.18292i −0.0255412 0.177643i 0.973058 0.230562i \(-0.0740565\pi\)
−0.998599 + 0.0529191i \(0.983147\pi\)
\(152\) 0 0
\(153\) −1.12773 + 1.30147i −0.0911719 + 0.105218i
\(154\) 0 0
\(155\) −1.47291 + 0.432487i −0.118307 + 0.0347382i
\(156\) 0 0
\(157\) 1.26122 2.76168i 0.100656 0.220406i −0.852604 0.522558i \(-0.824978\pi\)
0.953260 + 0.302152i \(0.0977050\pi\)
\(158\) 0 0
\(159\) −5.27213 3.38819i −0.418107 0.268701i
\(160\) 0 0
\(161\) −2.24539 + 0.659307i −0.176962 + 0.0519607i
\(162\) 0 0
\(163\) 0.397413 0.0311278 0.0155639 0.999879i \(-0.495046\pi\)
0.0155639 + 0.999879i \(0.495046\pi\)
\(164\) 0 0
\(165\) −1.03332 + 0.664076i −0.0804440 + 0.0516982i
\(166\) 0 0
\(167\) 9.13533 10.5427i 0.706913 0.815821i −0.282756 0.959192i \(-0.591249\pi\)
0.989669 + 0.143371i \(0.0457942\pi\)
\(168\) 0 0
\(169\) 11.0391 + 24.1724i 0.849165 + 1.85941i
\(170\) 0 0
\(171\) 0.0123590 0.000945118
\(172\) 0 0
\(173\) 18.1921 11.6914i 1.38312 0.888879i 0.383721 0.923449i \(-0.374642\pi\)
0.999402 + 0.0345699i \(0.0110061\pi\)
\(174\) 0 0
\(175\) 0.335253 + 2.33174i 0.0253428 + 0.176263i
\(176\) 0 0
\(177\) 0.517358 + 3.59830i 0.0388870 + 0.270465i
\(178\) 0 0
\(179\) −0.0580196 0.127045i −0.00433659 0.00949581i 0.907451 0.420157i \(-0.138025\pi\)
−0.911788 + 0.410661i \(0.865298\pi\)
\(180\) 0 0
\(181\) −1.28347 + 2.81040i −0.0953993 + 0.208895i −0.951315 0.308220i \(-0.900267\pi\)
0.855916 + 0.517115i \(0.172994\pi\)
\(182\) 0 0
\(183\) −1.92872 + 13.4145i −0.142575 + 0.991630i
\(184\) 0 0
\(185\) 2.28944 + 0.672239i 0.168323 + 0.0494240i
\(186\) 0 0
\(187\) −0.834050 + 5.80095i −0.0609918 + 0.424207i
\(188\) 0 0
\(189\) 0.406954 + 0.261533i 0.0296015 + 0.0190237i
\(190\) 0 0
\(191\) 9.29299 + 20.3488i 0.672417 + 1.47239i 0.870483 + 0.492199i \(0.163807\pi\)
−0.198066 + 0.980189i \(0.563466\pi\)
\(192\) 0 0
\(193\) −3.67935 + 2.36457i −0.264845 + 0.170206i −0.666323 0.745663i \(-0.732133\pi\)
0.401478 + 0.915869i \(0.368497\pi\)
\(194\) 0 0
\(195\) −2.17856 + 0.639684i −0.156010 + 0.0458087i
\(196\) 0 0
\(197\) 1.19873 8.33732i 0.0854057 0.594010i −0.901508 0.432762i \(-0.857539\pi\)
0.986914 0.161248i \(-0.0515518\pi\)
\(198\) 0 0
\(199\) 9.53969 + 11.0094i 0.676250 + 0.780435i 0.985341 0.170598i \(-0.0545700\pi\)
−0.309090 + 0.951033i \(0.600025\pi\)
\(200\) 0 0
\(201\) 8.06902 + 1.37508i 0.569145 + 0.0969910i
\(202\) 0 0
\(203\) −2.04497 2.36002i −0.143529 0.165641i
\(204\) 0 0
\(205\) 0.276642 1.92409i 0.0193215 0.134384i
\(206\) 0 0
\(207\) −4.64167 + 1.36292i −0.322619 + 0.0947294i
\(208\) 0 0
\(209\) 0.0353830 0.0227393i 0.00244749 0.00157291i
\(210\) 0 0
\(211\) −7.16513 15.6894i −0.493268 1.08011i −0.978599 0.205775i \(-0.934028\pi\)
0.485331 0.874330i \(-0.338699\pi\)
\(212\) 0 0
\(213\) −4.91604 3.15935i −0.336842 0.216475i
\(214\) 0 0
\(215\) −0.0966590 + 0.672278i −0.00659209 + 0.0458490i
\(216\) 0 0
\(217\) 1.97411 + 0.579650i 0.134011 + 0.0393492i
\(218\) 0 0
\(219\) −0.0162401 + 0.112952i −0.00109740 + 0.00763259i
\(220\) 0 0
\(221\) −4.50033 + 9.85434i −0.302725 + 0.662874i
\(222\) 0 0
\(223\) 1.13456 + 2.48435i 0.0759760 + 0.166364i 0.943809 0.330492i \(-0.107215\pi\)
−0.867833 + 0.496857i \(0.834488\pi\)
\(224\) 0 0
\(225\) 0.693035 + 4.82016i 0.0462023 + 0.321344i
\(226\) 0 0
\(227\) 1.35758 + 9.44214i 0.0901054 + 0.626697i 0.983967 + 0.178353i \(0.0570769\pi\)
−0.893861 + 0.448344i \(0.852014\pi\)
\(228\) 0 0
\(229\) 13.2872 8.53919i 0.878046 0.564286i −0.0221583 0.999754i \(-0.507054\pi\)
0.900204 + 0.435469i \(0.143417\pi\)
\(230\) 0 0
\(231\) 1.64627 0.108317
\(232\) 0 0
\(233\) 7.80506 + 17.0907i 0.511326 + 1.11965i 0.972620 + 0.232401i \(0.0746581\pi\)
−0.461294 + 0.887247i \(0.652615\pi\)
\(234\) 0 0
\(235\) −0.998198 + 1.15198i −0.0651153 + 0.0751470i
\(236\) 0 0
\(237\) −10.4984 + 6.74689i −0.681942 + 0.438258i
\(238\) 0 0
\(239\) −26.7542 −1.73058 −0.865292 0.501268i \(-0.832867\pi\)
−0.865292 + 0.501268i \(0.832867\pi\)
\(240\) 0 0
\(241\) 10.9130 3.20436i 0.702971 0.206411i 0.0893370 0.996001i \(-0.471525\pi\)
0.613634 + 0.789591i \(0.289707\pi\)
\(242\) 0 0
\(243\) 0.841254 + 0.540641i 0.0539664 + 0.0346821i
\(244\) 0 0
\(245\) 1.01447 2.22137i 0.0648120 0.141918i
\(246\) 0 0
\(247\) 0.0745984 0.0219041i 0.00474658 0.00139372i
\(248\) 0 0
\(249\) 10.8393 12.5092i 0.686911 0.792737i
\(250\) 0 0
\(251\) 0.294427 + 2.04778i 0.0185840 + 0.129255i 0.997001 0.0773837i \(-0.0246567\pi\)
−0.978417 + 0.206639i \(0.933748\pi\)
\(252\) 0 0
\(253\) −10.7812 + 12.4421i −0.677806 + 0.782230i
\(254\) 0 0
\(255\) −0.522889 0.336040i −0.0327446 0.0210437i
\(256\) 0 0
\(257\) −5.92971 1.74112i −0.369885 0.108608i 0.0915069 0.995804i \(-0.470832\pi\)
−0.461392 + 0.887196i \(0.652650\pi\)
\(258\) 0 0
\(259\) −2.09425 2.41689i −0.130130 0.150178i
\(260\) 0 0
\(261\) −4.22736 4.87863i −0.261667 0.301980i
\(262\) 0 0
\(263\) −1.84159 0.540739i −0.113557 0.0333434i 0.224460 0.974483i \(-0.427938\pi\)
−0.338017 + 0.941140i \(0.609756\pi\)
\(264\) 0 0
\(265\) 0.939650 2.05755i 0.0577222 0.126394i
\(266\) 0 0
\(267\) 7.50829 0.459500
\(268\) 0 0
\(269\) −10.4964 −0.639976 −0.319988 0.947422i \(-0.603679\pi\)
−0.319988 + 0.947422i \(0.603679\pi\)
\(270\) 0 0
\(271\) 6.05691 13.2628i 0.367931 0.805656i −0.631608 0.775288i \(-0.717605\pi\)
0.999539 0.0303683i \(-0.00966801\pi\)
\(272\) 0 0
\(273\) 2.91987 + 0.857351i 0.176719 + 0.0518893i
\(274\) 0 0
\(275\) 10.8527 + 12.5247i 0.654442 + 0.755267i
\(276\) 0 0
\(277\) −9.20310 10.6209i −0.552961 0.638151i 0.408610 0.912709i \(-0.366014\pi\)
−0.961570 + 0.274559i \(0.911468\pi\)
\(278\) 0 0
\(279\) 4.08087 + 1.19825i 0.244315 + 0.0717374i
\(280\) 0 0
\(281\) −21.6976 13.9442i −1.29437 0.831843i −0.301785 0.953376i \(-0.597582\pi\)
−0.992587 + 0.121533i \(0.961219\pi\)
\(282\) 0 0
\(283\) −14.3017 + 16.5051i −0.850150 + 0.981125i −0.999971 0.00758776i \(-0.997585\pi\)
0.149821 + 0.988713i \(0.452130\pi\)
\(284\) 0 0
\(285\) 0.000634832 0.00441535i 3.76042e−5 0.000261543i
\(286\) 0 0
\(287\) −1.70612 + 1.96897i −0.100709 + 0.116225i
\(288\) 0 0
\(289\) 13.4659 3.95394i 0.792111 0.232585i
\(290\) 0 0
\(291\) 1.59712 3.49720i 0.0936247 0.205009i
\(292\) 0 0
\(293\) 17.5244 + 11.2622i 1.02378 + 0.657946i 0.940925 0.338615i \(-0.109959\pi\)
0.0828589 + 0.996561i \(0.473595\pi\)
\(294\) 0 0
\(295\) −1.25895 + 0.369660i −0.0732987 + 0.0215224i
\(296\) 0 0
\(297\) 3.40317 0.197472
\(298\) 0 0
\(299\) −25.6014 + 16.4530i −1.48057 + 0.951503i
\(300\) 0 0
\(301\) 0.596121 0.687960i 0.0343598 0.0396534i
\(302\) 0 0
\(303\) −6.45979 14.1450i −0.371105 0.812607i
\(304\) 0 0
\(305\) −4.89151 −0.280087
\(306\) 0 0
\(307\) 12.7081 8.16698i 0.725287 0.466114i −0.125185 0.992133i \(-0.539952\pi\)
0.850472 + 0.526020i \(0.176316\pi\)
\(308\) 0 0
\(309\) 1.67968 + 11.6825i 0.0955538 + 0.664592i
\(310\) 0 0
\(311\) −2.06658 14.3734i −0.117185 0.815039i −0.960632 0.277826i \(-0.910386\pi\)
0.843447 0.537213i \(-0.180523\pi\)
\(312\) 0 0
\(313\) 0.889116 + 1.94689i 0.0502558 + 0.110045i 0.933094 0.359632i \(-0.117098\pi\)
−0.882838 + 0.469677i \(0.844370\pi\)
\(314\) 0 0
\(315\) −0.0725312 + 0.158821i −0.00408667 + 0.00894856i
\(316\) 0 0
\(317\) 2.09440 14.5669i 0.117633 0.818157i −0.842516 0.538671i \(-0.818927\pi\)
0.960150 0.279486i \(-0.0901642\pi\)
\(318\) 0 0
\(319\) −21.0788 6.18930i −1.18019 0.346534i
\(320\) 0 0
\(321\) 0.880938 6.12706i 0.0491692 0.341979i
\(322\) 0 0
\(323\) 0.0179048 + 0.0115067i 0.000996248 + 0.000640250i
\(324\) 0 0
\(325\) 12.7260 + 27.8660i 0.705910 + 1.54573i
\(326\) 0 0
\(327\) 12.6532 8.13171i 0.699723 0.449684i
\(328\) 0 0
\(329\) 1.96021 0.575570i 0.108070 0.0317322i
\(330\) 0 0
\(331\) 0.00165880 0.0115372i 9.11758e−5 0.000634141i −0.989776 0.142632i \(-0.954443\pi\)
0.989867 + 0.141998i \(0.0453526\pi\)
\(332\) 0 0
\(333\) −4.32923 4.99620i −0.237240 0.273790i
\(334\) 0 0
\(335\) −0.0767868 + 2.95335i −0.00419531 + 0.161359i
\(336\) 0 0
\(337\) −5.80458 6.69884i −0.316196 0.364909i 0.575297 0.817945i \(-0.304887\pi\)
−0.891492 + 0.453036i \(0.850341\pi\)
\(338\) 0 0
\(339\) −0.0630355 + 0.438422i −0.00342362 + 0.0238118i
\(340\) 0 0
\(341\) 13.8879 4.07786i 0.752072 0.220828i
\(342\) 0 0
\(343\) −5.60212 + 3.60026i −0.302486 + 0.194396i
\(344\) 0 0
\(345\) −0.725337 1.58827i −0.0390508 0.0855094i
\(346\) 0 0
\(347\) 19.0107 + 12.2175i 1.02055 + 0.655868i 0.940103 0.340891i \(-0.110729\pi\)
0.0804476 + 0.996759i \(0.474365\pi\)
\(348\) 0 0
\(349\) 1.03753 7.21619i 0.0555378 0.386274i −0.943027 0.332716i \(-0.892035\pi\)
0.998565 0.0535574i \(-0.0170560\pi\)
\(350\) 0 0
\(351\) 6.03595 + 1.77231i 0.322175 + 0.0945992i
\(352\) 0 0
\(353\) −0.335004 + 2.33001i −0.0178305 + 0.124014i −0.996793 0.0800285i \(-0.974499\pi\)
0.978962 + 0.204042i \(0.0654080\pi\)
\(354\) 0 0
\(355\) 0.876185 1.91858i 0.0465030 0.101827i
\(356\) 0 0
\(357\) 0.346065 + 0.757777i 0.0183157 + 0.0401058i
\(358\) 0 0
\(359\) −4.97431 34.5971i −0.262534 1.82596i −0.513642 0.858004i \(-0.671704\pi\)
0.251108 0.967959i \(-0.419205\pi\)
\(360\) 0 0
\(361\) 2.70396 + 18.8065i 0.142314 + 0.989813i
\(362\) 0 0
\(363\) 0.489266 0.314432i 0.0256798 0.0165034i
\(364\) 0 0
\(365\) −0.0411872 −0.00215584
\(366\) 0 0
\(367\) −14.3373 31.3943i −0.748401 1.63877i −0.769219 0.638985i \(-0.779354\pi\)
0.0208184 0.999783i \(-0.493373\pi\)
\(368\) 0 0
\(369\) −3.52689 + 4.07025i −0.183603 + 0.211889i
\(370\) 0 0
\(371\) −2.55037 + 1.63903i −0.132409 + 0.0850940i
\(372\) 0 0
\(373\) −13.6966 −0.709185 −0.354593 0.935021i \(-0.615380\pi\)
−0.354593 + 0.935021i \(0.615380\pi\)
\(374\) 0 0
\(375\) −3.41800 + 1.00361i −0.176505 + 0.0518264i
\(376\) 0 0
\(377\) −34.1626 21.9550i −1.75946 1.13074i
\(378\) 0 0
\(379\) 5.52834 12.1054i 0.283972 0.621812i −0.712864 0.701303i \(-0.752602\pi\)
0.996836 + 0.0794908i \(0.0253294\pi\)
\(380\) 0 0
\(381\) −9.07529 + 2.66475i −0.464941 + 0.136519i
\(382\) 0 0
\(383\) 6.35593 7.33513i 0.324773 0.374808i −0.569759 0.821812i \(-0.692964\pi\)
0.894532 + 0.447004i \(0.147509\pi\)
\(384\) 0 0
\(385\) 0.0845623 + 0.588144i 0.00430970 + 0.0299746i
\(386\) 0 0
\(387\) 1.23230 1.42215i 0.0626413 0.0722919i
\(388\) 0 0
\(389\) −19.8390 12.7497i −1.00588 0.646438i −0.0695541 0.997578i \(-0.522158\pi\)
−0.936323 + 0.351140i \(0.885794\pi\)
\(390\) 0 0
\(391\) −7.99342 2.34708i −0.404245 0.118697i
\(392\) 0 0
\(393\) 11.8771 + 13.7070i 0.599123 + 0.691425i
\(394\) 0 0
\(395\) −2.94964 3.40406i −0.148412 0.171277i
\(396\) 0 0
\(397\) −28.7646 8.44605i −1.44365 0.423895i −0.536216 0.844081i \(-0.680147\pi\)
−0.907438 + 0.420186i \(0.861965\pi\)
\(398\) 0 0
\(399\) 0.00248361 0.00543835i 0.000124336 0.000272258i
\(400\) 0 0
\(401\) −15.3172 −0.764903 −0.382451 0.923976i \(-0.624920\pi\)
−0.382451 + 0.923976i \(0.624920\pi\)
\(402\) 0 0
\(403\) 26.7556 1.33279
\(404\) 0 0
\(405\) −0.149936 + 0.328315i −0.00745040 + 0.0163141i
\(406\) 0 0
\(407\) −21.5868 6.33845i −1.07002 0.314185i
\(408\) 0 0
\(409\) −16.0416 18.5130i −0.793204 0.915407i 0.204784 0.978807i \(-0.434351\pi\)
−0.997988 + 0.0634006i \(0.979805\pi\)
\(410\) 0 0
\(411\) −2.96205 3.41838i −0.146107 0.168616i
\(412\) 0 0
\(413\) 1.68733 + 0.495445i 0.0830282 + 0.0243793i
\(414\) 0 0
\(415\) 5.02577 + 3.22987i 0.246705 + 0.158548i
\(416\) 0 0
\(417\) 0.171126 0.197490i 0.00838007 0.00967111i
\(418\) 0 0
\(419\) 2.26899 + 15.7812i 0.110848 + 0.770961i 0.967099 + 0.254402i \(0.0818785\pi\)
−0.856251 + 0.516560i \(0.827212\pi\)
\(420\) 0 0
\(421\) 16.9469 19.5578i 0.825942 0.953188i −0.173557 0.984824i \(-0.555526\pi\)
0.999499 + 0.0316357i \(0.0100716\pi\)
\(422\) 0 0
\(423\) 4.05214 1.18982i 0.197022 0.0578509i
\(424\) 0 0
\(425\) −3.48373 + 7.62831i −0.168986 + 0.370027i
\(426\) 0 0
\(427\) 5.51522 + 3.54442i 0.266900 + 0.171526i
\(428\) 0 0
\(429\) 20.5414 6.03149i 0.991747 0.291203i
\(430\) 0 0
\(431\) −23.5278 −1.13329 −0.566647 0.823961i \(-0.691760\pi\)
−0.566647 + 0.823961i \(0.691760\pi\)
\(432\) 0 0
\(433\) 0.684418 0.439849i 0.0328911 0.0211378i −0.524092 0.851662i \(-0.675595\pi\)
0.556983 + 0.830524i \(0.311959\pi\)
\(434\) 0 0
\(435\) 1.52579 1.76085i 0.0731559 0.0844264i
\(436\) 0 0
\(437\) 0.0248370 + 0.0543854i 0.00118811 + 0.00260161i
\(438\) 0 0
\(439\) 21.7815 1.03957 0.519787 0.854296i \(-0.326011\pi\)
0.519787 + 0.854296i \(0.326011\pi\)
\(440\) 0 0
\(441\) −5.69191 + 3.65797i −0.271043 + 0.174189i
\(442\) 0 0
\(443\) −0.0403283 0.280490i −0.00191606 0.0133265i 0.988841 0.148975i \(-0.0475973\pi\)
−0.990757 + 0.135648i \(0.956688\pi\)
\(444\) 0 0
\(445\) 0.385670 + 2.68239i 0.0182825 + 0.127158i
\(446\) 0 0
\(447\) −9.41362 20.6130i −0.445249 0.974959i
\(448\) 0 0
\(449\) 7.81069 17.1030i 0.368609 0.807142i −0.630901 0.775863i \(-0.717315\pi\)
0.999511 0.0312789i \(-0.00995800\pi\)
\(450\) 0 0
\(451\) −2.60842 + 18.1420i −0.122826 + 0.854271i
\(452\) 0 0
\(453\) −2.11603 0.621322i −0.0994198 0.0291923i
\(454\) 0 0
\(455\) −0.156314 + 1.08718i −0.00732809 + 0.0509680i
\(456\) 0 0
\(457\) 15.7983 + 10.1529i 0.739011 + 0.474934i 0.855203 0.518293i \(-0.173432\pi\)
−0.116192 + 0.993227i \(0.537069\pi\)
\(458\) 0 0
\(459\) 0.715385 + 1.56648i 0.0333913 + 0.0731168i
\(460\) 0 0
\(461\) −8.41443 + 5.40762i −0.391899 + 0.251858i −0.721720 0.692185i \(-0.756648\pi\)
0.329821 + 0.944044i \(0.393012\pi\)
\(462\) 0 0
\(463\) −2.55241 + 0.749456i −0.118621 + 0.0348302i −0.340504 0.940243i \(-0.610598\pi\)
0.221883 + 0.975073i \(0.428780\pi\)
\(464\) 0 0
\(465\) −0.218467 + 1.51947i −0.0101312 + 0.0704638i
\(466\) 0 0
\(467\) 17.2311 + 19.8857i 0.797360 + 0.920202i 0.998233 0.0594150i \(-0.0189235\pi\)
−0.200874 + 0.979617i \(0.564378\pi\)
\(468\) 0 0
\(469\) 2.22660 3.27429i 0.102815 0.151193i
\(470\) 0 0
\(471\) −1.98818 2.29449i −0.0916107 0.105724i
\(472\) 0 0
\(473\) 0.911384 6.33882i 0.0419055 0.291459i
\(474\) 0 0
\(475\) 0.0577471 0.0169561i 0.00264962 0.000777999i
\(476\) 0 0
\(477\) −5.27213 + 3.38819i −0.241394 + 0.155135i
\(478\) 0 0
\(479\) −9.09262 19.9101i −0.415453 0.909714i −0.995467 0.0951079i \(-0.969680\pi\)
0.580014 0.814606i \(-0.303047\pi\)
\(480\) 0 0
\(481\) −34.9859 22.4840i −1.59522 1.02518i
\(482\) 0 0
\(483\) −0.333044 + 2.31637i −0.0151540 + 0.105398i
\(484\) 0 0
\(485\) 1.33144 + 0.390946i 0.0604575 + 0.0177519i
\(486\) 0 0
\(487\) 3.82785 26.6233i 0.173456 1.20642i −0.698056 0.716043i \(-0.745952\pi\)
0.871513 0.490373i \(-0.163139\pi\)
\(488\) 0 0
\(489\) 0.165091 0.361499i 0.00746568 0.0163476i
\(490\) 0 0
\(491\) −7.57606 16.5893i −0.341903 0.748663i 0.658088 0.752941i \(-0.271365\pi\)
−0.999991 + 0.00427818i \(0.998638\pi\)
\(492\) 0 0
\(493\) −1.58208 11.0036i −0.0712533 0.495577i
\(494\) 0 0
\(495\) 0.174807 + 1.21581i 0.00785699 + 0.0546466i
\(496\) 0 0
\(497\) −2.37812 + 1.52832i −0.106673 + 0.0685547i
\(498\) 0 0
\(499\) −7.15432 −0.320271 −0.160136 0.987095i \(-0.551193\pi\)
−0.160136 + 0.987095i \(0.551193\pi\)
\(500\) 0 0
\(501\) −5.79505 12.6894i −0.258904 0.566920i
\(502\) 0 0
\(503\) −17.2759 + 19.9375i −0.770295 + 0.888967i −0.996369 0.0851426i \(-0.972865\pi\)
0.226074 + 0.974110i \(0.427411\pi\)
\(504\) 0 0
\(505\) 4.72159 3.03438i 0.210108 0.135028i
\(506\) 0 0
\(507\) 26.5738 1.18018
\(508\) 0 0
\(509\) −23.2723 + 6.83336i −1.03153 + 0.302883i −0.753331 0.657642i \(-0.771554\pi\)
−0.278194 + 0.960525i \(0.589736\pi\)
\(510\) 0 0
\(511\) 0.0464389 + 0.0298445i 0.00205434 + 0.00132024i
\(512\) 0 0
\(513\) 0.00513412 0.0112422i 0.000226677 0.000496353i
\(514\) 0 0
\(515\) −4.08737 + 1.20016i −0.180111 + 0.0528854i
\(516\) 0 0
\(517\) 9.41188 10.8619i 0.413934 0.477705i
\(518\) 0 0
\(519\) −3.07756 21.4049i −0.135090 0.939572i
\(520\) 0 0
\(521\) −15.2091 + 17.5522i −0.666321 + 0.768975i −0.983796 0.179291i \(-0.942620\pi\)
0.317475 + 0.948267i \(0.397165\pi\)
\(522\) 0 0
\(523\) 22.7730 + 14.6353i 0.995796 + 0.639959i 0.933679 0.358110i \(-0.116579\pi\)
0.0621164 + 0.998069i \(0.480215\pi\)
\(524\) 0 0
\(525\) 2.26029 + 0.663681i 0.0986472 + 0.0289654i
\(526\) 0 0
\(527\) 4.79642 + 5.53537i 0.208936 + 0.241124i
\(528\) 0 0
\(529\) −0.263707 0.304334i −0.0114655 0.0132319i
\(530\) 0 0
\(531\) 3.48805 + 1.02418i 0.151368 + 0.0444458i
\(532\) 0 0
\(533\) −14.0744 + 30.8186i −0.609629 + 1.33490i
\(534\) 0 0
\(535\) 2.23419 0.0965924
\(536\) 0 0
\(537\) −0.139667 −0.00602706
\(538\) 0 0
\(539\) −9.56528 + 20.9450i −0.412006 + 0.902167i
\(540\) 0 0
\(541\) 2.02083 + 0.593371i 0.0868825 + 0.0255110i 0.324885 0.945754i \(-0.394674\pi\)
−0.238002 + 0.971265i \(0.576493\pi\)
\(542\) 0 0
\(543\) 2.02326 + 2.33496i 0.0868263 + 0.100203i
\(544\) 0 0
\(545\) 3.55506 + 4.10275i 0.152282 + 0.175743i
\(546\) 0 0
\(547\) 9.77059 + 2.86890i 0.417760 + 0.122665i 0.483856 0.875148i \(-0.339236\pi\)
−0.0660954 + 0.997813i \(0.521054\pi\)
\(548\) 0 0
\(549\) 11.4011 + 7.32701i 0.486585 + 0.312709i
\(550\) 0 0
\(551\) −0.0522460 + 0.0602951i −0.00222575 + 0.00256866i
\(552\) 0 0
\(553\) 0.859138 + 5.97544i 0.0365343 + 0.254101i
\(554\) 0 0
\(555\) 1.56256 1.80329i 0.0663268 0.0765452i
\(556\) 0 0
\(557\) −28.1413 + 8.26303i −1.19238 + 0.350116i −0.816937 0.576728i \(-0.804329\pi\)
−0.375448 + 0.926843i \(0.622511\pi\)
\(558\) 0 0
\(559\) 4.91760 10.7680i 0.207992 0.455440i
\(560\) 0 0
\(561\) 4.93025 + 3.16848i 0.208155 + 0.133773i
\(562\) 0 0
\(563\) −17.3773 + 5.10245i −0.732367 + 0.215042i −0.626592 0.779348i \(-0.715551\pi\)
−0.105776 + 0.994390i \(0.533733\pi\)
\(564\) 0 0
\(565\) −0.159867 −0.00672567
\(566\) 0 0
\(567\) 0.406954 0.261533i 0.0170904 0.0109834i
\(568\) 0 0
\(569\) 3.08010 3.55462i 0.129124 0.149017i −0.687506 0.726179i \(-0.741294\pi\)
0.816630 + 0.577162i \(0.195840\pi\)
\(570\) 0 0
\(571\) −7.52286 16.4728i −0.314822 0.689364i 0.684387 0.729119i \(-0.260070\pi\)
−0.999209 + 0.0397544i \(0.987342\pi\)
\(572\) 0 0
\(573\) 22.3704 0.934536
\(574\) 0 0
\(575\) −19.8182 + 12.7364i −0.826477 + 0.531144i
\(576\) 0 0
\(577\) 6.32996 + 44.0259i 0.263520 + 1.83282i 0.505843 + 0.862625i \(0.331181\pi\)
−0.242324 + 0.970195i \(0.577910\pi\)
\(578\) 0 0
\(579\) 0.622435 + 4.32913i 0.0258675 + 0.179912i
\(580\) 0 0
\(581\) −3.32622 7.28341i −0.137995 0.302167i
\(582\) 0 0
\(583\) −8.85983 + 19.4003i −0.366937 + 0.803479i
\(584\) 0 0
\(585\) −0.323131 + 2.24743i −0.0133598 + 0.0929196i
\(586\) 0 0
\(587\) 25.6027 + 7.51762i 1.05673 + 0.310285i 0.763535 0.645766i \(-0.223462\pi\)
0.293199 + 0.956051i \(0.405280\pi\)
\(588\) 0 0
\(589\) 0.00748074 0.0520297i 0.000308239 0.00214385i
\(590\) 0 0
\(591\) −7.08593 4.55385i −0.291476 0.187320i
\(592\) 0 0
\(593\) 2.02496 + 4.43403i 0.0831549 + 0.182084i 0.946642 0.322287i \(-0.104452\pi\)
−0.863487 + 0.504371i \(0.831724\pi\)
\(594\) 0 0
\(595\) −0.252946 + 0.162558i −0.0103698 + 0.00666424i
\(596\) 0 0
\(597\) 13.9774 4.10414i 0.572058 0.167971i
\(598\) 0 0
\(599\) −3.62118 + 25.1858i −0.147957 + 1.02907i 0.771600 + 0.636108i \(0.219457\pi\)
−0.919557 + 0.392957i \(0.871452\pi\)
\(600\) 0 0
\(601\) −21.9986 25.3878i −0.897343 1.03559i −0.999168 0.0407869i \(-0.987014\pi\)
0.101825 0.994802i \(-0.467532\pi\)
\(602\) 0 0
\(603\) 4.60281 6.76861i 0.187441 0.275639i
\(604\) 0 0
\(605\) 0.137465 + 0.158643i 0.00558875 + 0.00644976i
\(606\) 0 0
\(607\) 3.78775 26.3444i 0.153740 1.06929i −0.756138 0.654412i \(-0.772916\pi\)
0.909879 0.414875i \(-0.136175\pi\)
\(608\) 0 0
\(609\) −2.99626 + 0.879782i −0.121415 + 0.0356506i
\(610\) 0 0
\(611\) 22.3498 14.3634i 0.904177 0.581079i
\(612\) 0 0
\(613\) 8.96390 + 19.6282i 0.362049 + 0.792776i 0.999747 + 0.0224896i \(0.00715928\pi\)
−0.637699 + 0.770286i \(0.720113\pi\)
\(614\) 0 0
\(615\) −1.63529 1.05094i −0.0659413 0.0423779i
\(616\) 0 0
\(617\) 6.15146 42.7844i 0.247649 1.72243i −0.364081 0.931367i \(-0.618617\pi\)
0.611730 0.791067i \(-0.290474\pi\)
\(618\) 0 0
\(619\) 27.1633 + 7.97586i 1.09178 + 0.320577i 0.777583 0.628780i \(-0.216445\pi\)
0.314201 + 0.949357i \(0.398263\pi\)
\(620\) 0 0
\(621\) −0.688467 + 4.78839i −0.0276272 + 0.192152i
\(622\) 0 0
\(623\) 1.50883 3.30388i 0.0604501 0.132367i
\(624\) 0 0
\(625\) 9.58067 + 20.9787i 0.383227 + 0.839150i
\(626\) 0 0
\(627\) −0.00598574 0.0416318i −0.000239048 0.00166261i
\(628\) 0 0
\(629\) −1.62020 11.2688i −0.0646018 0.449315i
\(630\) 0 0
\(631\) 35.5930 22.8742i 1.41693 0.910608i 0.416936 0.908936i \(-0.363104\pi\)
0.999999 0.00167236i \(-0.000532329\pi\)
\(632\) 0 0
\(633\) −17.2481 −0.685551
\(634\) 0 0
\(635\) −1.41816 3.10534i −0.0562780 0.123232i
\(636\) 0 0
\(637\) −27.8730 + 32.1672i −1.10437 + 1.27451i
\(638\) 0 0
\(639\) −4.91604 + 3.15935i −0.194476 + 0.124982i
\(640\) 0 0
\(641\) −39.8487 −1.57393 −0.786965 0.616998i \(-0.788349\pi\)
−0.786965 + 0.616998i \(0.788349\pi\)
\(642\) 0 0
\(643\) 2.96632 0.870989i 0.116980 0.0343485i −0.222719 0.974883i \(-0.571493\pi\)
0.339699 + 0.940534i \(0.389675\pi\)
\(644\) 0 0
\(645\) 0.571372 + 0.367198i 0.0224978 + 0.0144584i
\(646\) 0 0
\(647\) 1.01944 2.23227i 0.0400785 0.0877597i −0.888534 0.458811i \(-0.848275\pi\)
0.928612 + 0.371052i \(0.121003\pi\)
\(648\) 0 0
\(649\) 11.8704 3.48547i 0.465955 0.136817i
\(650\) 0 0
\(651\) 1.34734 1.55491i 0.0528065 0.0609419i
\(652\) 0 0
\(653\) 2.89304 + 20.1215i 0.113213 + 0.787417i 0.964759 + 0.263136i \(0.0847568\pi\)
−0.851545 + 0.524281i \(0.824334\pi\)
\(654\) 0 0
\(655\) −4.28684 + 4.94727i −0.167501 + 0.193306i
\(656\) 0 0
\(657\) 0.0959984 + 0.0616945i 0.00374526 + 0.00240693i
\(658\) 0 0
\(659\) 13.9359 + 4.09195i 0.542865 + 0.159400i 0.541657 0.840600i \(-0.317797\pi\)
0.00120823 + 0.999999i \(0.499615\pi\)
\(660\) 0 0
\(661\) 19.3716 + 22.3561i 0.753469 + 0.869550i 0.994900 0.100868i \(-0.0321621\pi\)
−0.241431 + 0.970418i \(0.577617\pi\)
\(662\) 0 0
\(663\) 7.09432 + 8.18728i 0.275520 + 0.317968i
\(664\) 0 0
\(665\) 0.00207047 0.000607944i 8.02893e−5 2.35751e-5i
\(666\) 0 0
\(667\) 12.9728 28.4066i 0.502310 1.09991i
\(668\) 0 0
\(669\) 2.73116 0.105593
\(670\) 0 0
\(671\) 46.1214 1.78050
\(672\) 0 0
\(673\) −6.93892 + 15.1941i −0.267476 + 0.585690i −0.994942 0.100453i \(-0.967971\pi\)
0.727466 + 0.686144i \(0.240698\pi\)
\(674\) 0 0
\(675\) 4.67247 + 1.37196i 0.179843 + 0.0528068i
\(676\) 0 0
\(677\) 16.0968 + 18.5767i 0.618651 + 0.713962i 0.975450 0.220220i \(-0.0706774\pi\)
−0.356799 + 0.934181i \(0.616132\pi\)
\(678\) 0 0
\(679\) −1.21793 1.40556i −0.0467398 0.0539406i
\(680\) 0 0
\(681\) 9.15283 + 2.68751i 0.350737 + 0.102986i
\(682\) 0 0
\(683\) 43.1265 + 27.7157i 1.65019 + 1.06051i 0.930548 + 0.366170i \(0.119331\pi\)
0.719643 + 0.694344i \(0.244305\pi\)
\(684\) 0 0
\(685\) 1.06910 1.23380i 0.0408480 0.0471412i
\(686\) 0 0
\(687\) −2.24780 15.6338i −0.0857590 0.596467i
\(688\) 0 0
\(689\) −25.8174 + 29.7948i −0.983563 + 1.13509i
\(690\) 0 0
\(691\) −32.9442 + 9.67329i −1.25326 + 0.367989i −0.839981 0.542616i \(-0.817434\pi\)
−0.413276 + 0.910606i \(0.635616\pi\)
\(692\) 0 0
\(693\) 0.683887 1.49750i 0.0259787 0.0568854i
\(694\) 0 0
\(695\) 0.0793447 + 0.0509918i 0.00300972 + 0.00193423i
\(696\) 0 0
\(697\) −8.89903 + 2.61299i −0.337075 + 0.0989741i
\(698\) 0 0
\(699\) 18.7886 0.710649
\(700\) 0 0
\(701\) 25.3423 16.2865i 0.957164 0.615132i 0.0339523 0.999423i \(-0.489191\pi\)
0.923212 + 0.384291i \(0.125554\pi\)
\(702\) 0 0
\(703\) −0.0535050 + 0.0617481i −0.00201798 + 0.00232887i
\(704\) 0 0
\(705\) 0.633213 + 1.38654i 0.0238482 + 0.0522203i
\(706\) 0 0
\(707\) −7.52236 −0.282907
\(708\) 0 0
\(709\) −30.4312 + 19.5570i −1.14287 + 0.734477i −0.968207 0.250151i \(-0.919520\pi\)
−0.174662 + 0.984628i \(0.555883\pi\)
\(710\) 0 0
\(711\) 1.77601 + 12.3524i 0.0666055 + 0.463251i
\(712\) 0 0
\(713\) 2.92815 + 20.3658i 0.109660 + 0.762704i
\(714\) 0 0
\(715\) 3.20992 + 7.02876i 0.120044 + 0.262861i
\(716\) 0 0
\(717\) −11.1141 + 24.3365i −0.415063 + 0.908861i
\(718\) 0 0
\(719\) 2.10243 14.6227i 0.0784074 0.545336i −0.912321 0.409476i \(-0.865711\pi\)
0.990728 0.135859i \(-0.0433795\pi\)
\(720\) 0 0
\(721\) 5.47819 + 1.60854i 0.204018 + 0.0599052i
\(722\) 0 0
\(723\) 1.61866 11.2580i 0.0601984 0.418689i
\(724\) 0 0
\(725\) −26.4455 16.9955i −0.982161 0.631197i
\(726\) 0 0
\(727\) −6.54582 14.3333i −0.242771 0.531594i 0.748547 0.663082i \(-0.230752\pi\)
−0.991318 + 0.131488i \(0.958025\pi\)
\(728\) 0 0
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) 0 0
\(731\) 3.10933 0.912982i 0.115003 0.0337679i
\(732\) 0 0
\(733\) 1.17949 8.20351i 0.0435653 0.303004i −0.956376 0.292140i \(-0.905633\pi\)
0.999941 0.0108638i \(-0.00345813\pi\)
\(734\) 0 0
\(735\) −1.59921 1.84558i −0.0589877 0.0680754i
\(736\) 0 0
\(737\) 0.724012 27.8468i 0.0266693 1.02575i
\(738\) 0 0
\(739\) 27.2921 + 31.4968i 1.00396 + 1.15863i 0.987316 + 0.158766i \(0.0507516\pi\)
0.0166404 + 0.999862i \(0.494703\pi\)
\(740\) 0 0
\(741\) 0.0110647 0.0769564i 0.000406470 0.00282706i
\(742\) 0 0
\(743\) 3.99813 1.17396i 0.146677 0.0430683i −0.207570 0.978220i \(-0.566555\pi\)
0.354247 + 0.935152i \(0.384737\pi\)
\(744\) 0 0
\(745\) 6.88060 4.42189i 0.252086 0.162006i
\(746\) 0 0
\(747\) −6.87596 15.0563i −0.251578 0.550879i
\(748\) 0 0
\(749\) −2.51907 1.61891i −0.0920448 0.0591536i
\(750\) 0 0
\(751\) 4.56899 31.7780i 0.166725 1.15960i −0.718872 0.695142i \(-0.755341\pi\)
0.885597 0.464454i \(-0.153749\pi\)
\(752\) 0 0
\(753\) 1.98504 + 0.582860i 0.0723388 + 0.0212406i
\(754\) 0 0
\(755\) 0.113280 0.787883i 0.00412270 0.0286740i
\(756\) 0 0
\(757\) −5.68403 + 12.4463i −0.206590 + 0.452368i −0.984357 0.176184i \(-0.943625\pi\)
0.777768 + 0.628552i \(0.216352\pi\)
\(758\) 0 0
\(759\) 6.83910 + 14.9755i 0.248244 + 0.543578i
\(760\) 0 0
\(761\) −5.04294 35.0745i −0.182807 1.27145i −0.850087 0.526642i \(-0.823451\pi\)
0.667281 0.744806i \(-0.267458\pi\)
\(762\) 0 0
\(763\) −1.03548 7.20191i −0.0374868 0.260727i
\(764\) 0 0
\(765\) −0.522889 + 0.336040i −0.0189051 + 0.0121496i
\(766\) 0 0
\(767\) 22.8689 0.825747
\(768\) 0 0
\(769\) −6.99199 15.3103i −0.252138 0.552105i 0.740664 0.671876i \(-0.234511\pi\)
−0.992802 + 0.119771i \(0.961784\pi\)
\(770\) 0 0
\(771\) −4.04707 + 4.67057i −0.145752 + 0.168206i
\(772\) 0 0
\(773\) −28.0384 + 18.0192i −1.00847 + 0.648106i −0.936997 0.349337i \(-0.886407\pi\)
−0.0714748 + 0.997442i \(0.522771\pi\)
\(774\) 0 0
\(775\) 20.7117 0.743986
\(776\) 0 0
\(777\) −3.06847 + 0.900983i −0.110081 + 0.0323226i
\(778\) 0 0
\(779\) 0.0559956 + 0.0359862i 0.00200625 + 0.00128934i
\(780\) 0 0
\(781\) −8.26143 + 18.0900i −0.295617 + 0.647311i
\(782\) 0 0
\(783\) −6.19387 + 1.81868i −0.221351 + 0.0649944i
\(784\) 0 0
\(785\) 0.717598 0.828153i 0.0256122 0.0295580i
\(786\) 0 0
\(787\) 4.81059 + 33.4584i 0.171479 + 1.19266i 0.875762 + 0.482744i \(0.160360\pi\)
−0.704283 + 0.709920i \(0.748731\pi\)
\(788\) 0 0
\(789\) −1.25690 + 1.45054i −0.0447467 + 0.0516404i
\(790\) 0 0
\(791\) 0.180252 + 0.115841i 0.00640902 + 0.00411883i
\(792\) 0 0
\(793\) 81.8020 + 24.0192i 2.90487 + 0.852948i
\(794\) 0 0
\(795\) −1.48126 1.70947i −0.0525350 0.0606287i
\(796\) 0 0
\(797\) 4.35293 + 5.02355i 0.154189 + 0.177943i 0.827589 0.561335i \(-0.189712\pi\)
−0.673400 + 0.739279i \(0.735167\pi\)
\(798\) 0 0
\(799\) 6.97819 + 2.04898i 0.246871 + 0.0724878i
\(800\) 0 0
\(801\) 3.11906 6.82978i 0.110206 0.241318i
\(802\) 0 0
\(803\) 0.388348 0.0137045
\(804\) 0 0
\(805\) −0.844648 −0.0297699
\(806\) 0 0
\(807\) −4.36036 + 9.54785i −0.153492 + 0.336100i
\(808\) 0 0
\(809\) 14.7625 + 4.33467i 0.519023 + 0.152399i 0.530744 0.847532i \(-0.321913\pi\)
−0.0117206 + 0.999931i \(0.503731\pi\)
\(810\) 0 0
\(811\) −20.3472 23.4819i −0.714487 0.824562i 0.276145 0.961116i \(-0.410943\pi\)
−0.990633 + 0.136553i \(0.956397\pi\)
\(812\) 0 0
\(813\) −9.54812 11.0191i −0.334867 0.386457i
\(814\) 0 0
\(815\) 0.137628 + 0.0404113i 0.00482091 + 0.00141555i
\(816\) 0 0
\(817\) −0.0195649 0.0125736i −0.000684490 0.000439895i
\(818\) 0 0
\(819\) 1.99283 2.29985i 0.0696352 0.0803633i
\(820\) 0 0
\(821\) −2.89908 20.1636i −0.101179 0.703713i −0.975761 0.218837i \(-0.929774\pi\)
0.874583 0.484876i \(-0.161135\pi\)
\(822\) 0 0
\(823\) −11.5715 + 13.3542i −0.403358 + 0.465500i −0.920696 0.390281i \(-0.872378\pi\)
0.517338 + 0.855781i \(0.326923\pi\)
\(824\) 0 0
\(825\) 15.9012 4.66902i 0.553610 0.162554i
\(826\) 0 0
\(827\) −9.62837 + 21.0832i −0.334811 + 0.733135i −0.999907 0.0136234i \(-0.995663\pi\)
0.665096 + 0.746758i \(0.268391\pi\)
\(828\) 0 0
\(829\) 27.4619 + 17.6487i 0.953790 + 0.612964i 0.922273 0.386539i \(-0.126330\pi\)
0.0315175 + 0.999503i \(0.489966\pi\)
\(830\) 0 0
\(831\) −13.4843 + 3.95934i −0.467764 + 0.137348i
\(832\) 0 0
\(833\) −11.6517 −0.403707
\(834\) 0 0
\(835\) 4.23572 2.72213i 0.146583 0.0942032i
\(836\) 0 0
\(837\) 2.78522 3.21432i 0.0962713 0.111103i
\(838\) 0 0
\(839\) 13.2510 + 29.0156i 0.457475 + 1.00173i 0.988056 + 0.154096i \(0.0492465\pi\)
−0.530581 + 0.847634i \(0.678026\pi\)
\(840\) 0 0
\(841\) 12.6716 0.436952
\(842\) 0 0
\(843\) −21.6976 + 13.9442i −0.747306 + 0.480265i
\(844\) 0 0
\(845\) 1.36499 + 9.49369i 0.0469570 + 0.326593i
\(846\) 0 0
\(847\) −0.0400393 0.278479i −0.00137577 0.00956867i
\(848\) 0 0
\(849\) 9.07240 + 19.8658i 0.311364 + 0.681792i
\(850\) 0 0
\(851\) 13.2855 29.0911i 0.455420 0.997231i
\(852\) 0 0
\(853\) 2.06241 14.3444i 0.0706157 0.491143i −0.923567 0.383437i \(-0.874740\pi\)
0.994183 0.107706i \(-0.0343505\pi\)
\(854\) 0 0
\(855\) 0.00428007 + 0.00125674i 0.000146375 + 4.29796e-5i
\(856\) 0 0
\(857\) 4.65378 32.3678i 0.158970 1.10566i −0.741566 0.670880i \(-0.765916\pi\)
0.900536 0.434782i \(-0.143174\pi\)
\(858\) 0 0
\(859\) −35.1427 22.5848i −1.19905 0.770585i −0.220261 0.975441i \(-0.570691\pi\)
−0.978792 + 0.204856i \(0.934327\pi\)
\(860\) 0 0
\(861\) 1.08229 + 2.36988i 0.0368843 + 0.0807654i
\(862\) 0 0
\(863\) −2.04483 + 1.31413i −0.0696069 + 0.0447336i −0.574981 0.818166i \(-0.694991\pi\)
0.505375 + 0.862900i \(0.331354\pi\)
\(864\) 0 0
\(865\) 7.48900 2.19897i 0.254633 0.0747671i
\(866\) 0 0
\(867\) 1.99730 13.8915i 0.0678319 0.471781i
\(868\) 0 0
\(869\) 27.8117 + 32.0964i 0.943448 + 1.08880i
\(870\) 0 0
\(871\) 15.7862 49.0126i 0.534897 1.66073i
\(872\) 0 0
\(873\) −2.51770 2.90558i −0.0852112 0.0983389i
\(874\) 0 0
\(875\) −0.245244 + 1.70571i −0.00829075 + 0.0576635i
\(876\) 0 0
\(877\) 51.5334 15.1316i 1.74016 0.510957i 0.751319 0.659939i \(-0.229418\pi\)
0.988840 + 0.148983i \(0.0475999\pi\)
\(878\) 0 0
\(879\) 17.5244 11.2622i 0.591082 0.379865i
\(880\) 0 0
\(881\) 17.4388 + 38.1856i 0.587527 + 1.28650i 0.936925 + 0.349530i \(0.113659\pi\)
−0.349398 + 0.936974i \(0.613614\pi\)
\(882\) 0 0
\(883\) 20.7318 + 13.3235i 0.697679 + 0.448371i 0.840808 0.541333i \(-0.182080\pi\)
−0.143129 + 0.989704i \(0.545716\pi\)
\(884\) 0 0
\(885\) −0.186731 + 1.29874i −0.00627688 + 0.0436567i
\(886\) 0 0
\(887\) 17.0476 + 5.00564i 0.572404 + 0.168073i 0.555109 0.831777i \(-0.312676\pi\)
0.0172947 + 0.999850i \(0.494495\pi\)
\(888\) 0 0
\(889\) −0.651159 + 4.52891i −0.0218392 + 0.151895i
\(890\) 0 0
\(891\) 1.41373 3.09564i 0.0473617 0.103708i
\(892\) 0 0
\(893\) −0.0216825 0.0474780i −0.000725577 0.00158879i
\(894\) 0 0
\(895\) −0.00717410 0.0498970i −0.000239804 0.00166787i
\(896\) 0 0
\(897\) 4.33099 + 30.1227i 0.144607 + 1.00577i
\(898\) 0 0
\(899\) −23.0971 + 14.8436i −0.770332 + 0.495062i
\(900\) 0 0
\(901\) −10.7924 −0.359546
\(902\) 0 0
\(903\) −0.378153 0.828039i −0.0125841 0.0275554i
\(904\) 0 0
\(905\) −0.730258 + 0.842762i −0.0242746 + 0.0280144i
\(906\) 0 0
\(907\) −33.4344 + 21.4870i −1.11017 + 0.713464i −0.961331 0.275397i \(-0.911191\pi\)
−0.148842 + 0.988861i \(0.547554\pi\)
\(908\) 0 0
\(909\) −15.5502 −0.515768
\(910\) 0 0
\(911\) 2.69374 0.790953i 0.0892475 0.0262054i −0.236804 0.971557i \(-0.576100\pi\)
0.326051 + 0.945352i \(0.394282\pi\)
\(912\) 0 0
\(913\) −47.3873 30.4540i −1.56829 1.00788i
\(914\) 0 0
\(915\) −2.03201 + 4.44947i −0.0671761 + 0.147095i
\(916\) 0 0
\(917\) 8.41827 2.47183i 0.277996 0.0816269i
\(918\) 0 0
\(919\) 2.72445 3.14418i 0.0898713 0.103717i −0.709033 0.705176i \(-0.750868\pi\)
0.798904 + 0.601459i \(0.205414\pi\)
\(920\) 0 0
\(921\) −2.14982 14.9523i −0.0708391 0.492696i
\(922\) 0 0
\(923\) −24.0736 + 27.7824i −0.792393 + 0.914470i
\(924\) 0 0
\(925\) −27.0828 17.4051i −0.890477 0.572275i
\(926\) 0 0
\(927\) 11.3245 + 3.32517i 0.371945 + 0.109213i
\(928\) 0 0
\(929\) −11.5607 13.3418i −0.379295 0.437730i 0.533716 0.845664i \(-0.320795\pi\)
−0.913012 + 0.407933i \(0.866250\pi\)
\(930\) 0 0
\(931\) 0.0547601 + 0.0631965i 0.00179469 + 0.00207118i
\(932\) 0 0
\(933\) −13.9330 4.09109i −0.456145 0.133936i
\(934\) 0 0
\(935\) −0.878717 + 1.92412i −0.0287371 + 0.0629255i
\(936\) 0 0
\(937\) 30.3590 0.991784 0.495892 0.868384i \(-0.334841\pi\)
0.495892 + 0.868384i \(0.334841\pi\)
\(938\) 0 0
\(939\) 2.14031 0.0698463
\(940\) 0 0
\(941\) 3.55087 7.77531i 0.115755 0.253468i −0.842883 0.538097i \(-0.819143\pi\)
0.958638 + 0.284629i \(0.0918706\pi\)
\(942\) 0 0
\(943\) −24.9987 7.34029i −0.814070 0.239033i
\(944\) 0 0
\(945\) 0.114338 + 0.131953i 0.00371942 + 0.00429244i
\(946\) 0 0
\(947\) 9.99231 + 11.5317i 0.324706 + 0.374731i 0.894509 0.447051i \(-0.147526\pi\)
−0.569802 + 0.821782i \(0.692980\pi\)
\(948\) 0 0
\(949\) 0.688784 + 0.202245i 0.0223589 + 0.00656516i
\(950\) 0 0
\(951\) −12.3804 7.95643i −0.401463 0.258005i
\(952\) 0 0
\(953\) 26.7761 30.9013i 0.867364 1.00099i −0.132588 0.991171i \(-0.542329\pi\)
0.999952 0.00982003i \(-0.00312586\pi\)
\(954\) 0 0
\(955\) 1.14907 + 7.99199i 0.0371832 + 0.258615i
\(956\) 0 0
\(957\) −14.3864 + 16.6028i −0.465047 + 0.536693i
\(958\) 0 0
\(959\) −2.09944 + 0.616450i −0.0677943 + 0.0199062i
\(960\) 0 0
\(961\) −5.36330 + 11.7440i −0.173010 + 0.378839i
\(962\) 0 0
\(963\) −5.20741 3.34660i −0.167807 0.107843i
\(964\) 0 0
\(965\) −1.51464 + 0.444739i −0.0487581 + 0.0143167i
\(966\) 0 0
\(967\) −15.1692 −0.487809 −0.243905 0.969799i \(-0.578428\pi\)
−0.243905 + 0.969799i \(0.578428\pi\)
\(968\) 0 0
\(969\) 0.0179048 0.0115067i 0.000575184 0.000369648i
\(970\) 0 0
\(971\) 16.9893 19.6067i 0.545212 0.629208i −0.414549 0.910027i \(-0.636061\pi\)
0.959761 + 0.280819i \(0.0906060\pi\)
\(972\) 0 0
\(973\) −0.0525130 0.114987i −0.00168349 0.00368633i
\(974\) 0 0
\(975\) 30.6343 0.981084
\(976\) 0 0
\(977\) −41.4778 + 26.6561i −1.32699 + 0.852806i −0.995871 0.0907827i \(-0.971063\pi\)
−0.331121 + 0.943588i \(0.607427\pi\)
\(978\) 0 0
\(979\) −3.63643 25.2919i −0.116221 0.808333i
\(980\) 0 0
\(981\) −2.14054 14.8878i −0.0683421 0.475330i
\(982\) 0 0
\(983\) 7.63241 + 16.7126i 0.243436 + 0.533051i 0.991428 0.130658i \(-0.0417089\pi\)
−0.747991 + 0.663708i \(0.768982\pi\)
\(984\) 0 0
\(985\) 1.26292 2.76541i 0.0402401 0.0881134i
\(986\) 0 0
\(987\) 0.290744 2.02217i 0.00925449 0.0643664i
\(988\) 0 0
\(989\) 8.73458 + 2.56470i 0.277743 + 0.0815528i
\(990\) 0 0
\(991\) −3.66522 + 25.4922i −0.116430 + 0.809785i 0.845006 + 0.534756i \(0.179597\pi\)
−0.961436 + 0.275029i \(0.911313\pi\)
\(992\) 0 0
\(993\) −0.00980551 0.00630162i −0.000311168 0.000199976i
\(994\) 0 0
\(995\) 2.18420 + 4.78273i 0.0692437 + 0.151623i
\(996\) 0 0
\(997\) −38.4572 + 24.7149i −1.21795 + 0.782730i −0.981972 0.189028i \(-0.939466\pi\)
−0.235980 + 0.971758i \(0.575830\pi\)
\(998\) 0 0
\(999\) −6.34313 + 1.86251i −0.200688 + 0.0589272i
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 804.2.q.a.241.4 60
67.62 even 11 inner 804.2.q.a.397.4 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
804.2.q.a.241.4 60 1.1 even 1 trivial
804.2.q.a.397.4 yes 60 67.62 even 11 inner