Properties

Label 1260.2.c.c.811.1
Level $1260$
Weight $2$
Character 1260.811
Analytic conductor $10.061$
Analytic rank $0$
Dimension $8$
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] = [1260,2,Mod(811,1260)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1260, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1260.811");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.0611506547\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.342102016.5
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 811.1
Root \(-0.599676 + 1.28078i\) of defining polynomial
Character \(\chi\) \(=\) 1260.811
Dual form 1260.2.c.c.811.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.28078 - 0.599676i) q^{2} +(1.28078 + 1.53610i) q^{4} -1.00000i q^{5} +(2.60399 - 0.468213i) q^{7} +(-0.719224 - 2.73546i) q^{8} +O(q^{10})\) \(q+(-1.28078 - 0.599676i) q^{2} +(1.28078 + 1.53610i) q^{4} -1.00000i q^{5} +(2.60399 - 0.468213i) q^{7} +(-0.719224 - 2.73546i) q^{8} +(-0.599676 + 1.28078i) q^{10} +2.39871i q^{11} +2.00000i q^{13} +(-3.61591 - 0.961876i) q^{14} +(-0.719224 + 3.93481i) q^{16} +7.12311i q^{17} -2.39871 q^{19} +(1.53610 - 1.28078i) q^{20} +(1.43845 - 3.07221i) q^{22} +5.73384i q^{23} -1.00000 q^{25} +(1.19935 - 2.56155i) q^{26} +(4.05436 + 3.40032i) q^{28} +2.00000 q^{29} -6.67026 q^{31} +(3.28078 - 4.60831i) q^{32} +(4.27156 - 9.12311i) q^{34} +(-0.468213 - 2.60399i) q^{35} +2.00000 q^{37} +(3.07221 + 1.43845i) q^{38} +(-2.73546 + 0.719224i) q^{40} -7.12311i q^{41} +7.60669i q^{43} +(-3.68466 + 3.07221i) q^{44} +(3.43845 - 7.34376i) q^{46} -10.0054 q^{47} +(6.56155 - 2.43845i) q^{49} +(1.28078 + 0.599676i) q^{50} +(-3.07221 + 2.56155i) q^{52} -2.00000 q^{53} +2.39871 q^{55} +(-3.15363 - 6.78636i) q^{56} +(-2.56155 - 1.19935i) q^{58} +10.9418 q^{59} +2.00000i q^{61} +(8.54312 + 4.00000i) q^{62} +(-6.96543 + 3.93481i) q^{64} +2.00000 q^{65} +14.2770i q^{67} +(-10.9418 + 9.12311i) q^{68} +(-0.961876 + 3.61591i) q^{70} +6.14441i q^{71} -9.36932i q^{73} +(-2.56155 - 1.19935i) q^{74} +(-3.07221 - 3.68466i) q^{76} +(1.12311 + 6.24621i) q^{77} +4.27156i q^{79} +(3.93481 + 0.719224i) q^{80} +(-4.27156 + 9.12311i) q^{82} +0.936426 q^{83} +7.12311 q^{85} +(4.56155 - 9.74247i) q^{86} +(6.56155 - 1.72521i) q^{88} -12.0000i q^{89} +(0.936426 + 5.20798i) q^{91} +(-8.80776 + 7.34376i) q^{92} +(12.8147 + 6.00000i) q^{94} +2.39871i q^{95} +7.12311i q^{97} +(-9.86616 - 0.811703i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 2 q^{4} - 14 q^{8} + 6 q^{14} - 14 q^{16} + 28 q^{22} - 8 q^{25} + 14 q^{28} + 16 q^{29} + 18 q^{32} + 16 q^{37} + 20 q^{44} + 44 q^{46} + 36 q^{49} + 2 q^{50} - 16 q^{53} - 2 q^{56} - 4 q^{58} + 2 q^{64} + 16 q^{65} + 4 q^{70} - 4 q^{74} - 24 q^{77} + 24 q^{85} + 20 q^{86} + 36 q^{88} + 12 q^{92} - 26 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28078 0.599676i −0.905646 0.424035i
\(3\) 0 0
\(4\) 1.28078 + 1.53610i 0.640388 + 0.768051i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 2.60399 0.468213i 0.984217 0.176968i
\(8\) −0.719224 2.73546i −0.254284 0.967130i
\(9\) 0 0
\(10\) −0.599676 + 1.28078i −0.189634 + 0.405017i
\(11\) 2.39871i 0.723237i 0.932326 + 0.361618i \(0.117776\pi\)
−0.932326 + 0.361618i \(0.882224\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) −3.61591 0.961876i −0.966392 0.257072i
\(15\) 0 0
\(16\) −0.719224 + 3.93481i −0.179806 + 0.983702i
\(17\) 7.12311i 1.72761i 0.503829 + 0.863803i \(0.331924\pi\)
−0.503829 + 0.863803i \(0.668076\pi\)
\(18\) 0 0
\(19\) −2.39871 −0.550301 −0.275150 0.961401i \(-0.588728\pi\)
−0.275150 + 0.961401i \(0.588728\pi\)
\(20\) 1.53610 1.28078i 0.343483 0.286390i
\(21\) 0 0
\(22\) 1.43845 3.07221i 0.306678 0.654996i
\(23\) 5.73384i 1.19559i 0.801650 + 0.597794i \(0.203956\pi\)
−0.801650 + 0.597794i \(0.796044\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 1.19935 2.56155i 0.235212 0.502362i
\(27\) 0 0
\(28\) 4.05436 + 3.40032i 0.766201 + 0.642601i
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) −6.67026 −1.19801 −0.599007 0.800743i \(-0.704438\pi\)
−0.599007 + 0.800743i \(0.704438\pi\)
\(32\) 3.28078 4.60831i 0.579965 0.814642i
\(33\) 0 0
\(34\) 4.27156 9.12311i 0.732566 1.56460i
\(35\) −0.468213 2.60399i −0.0791425 0.440155i
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 3.07221 + 1.43845i 0.498378 + 0.233347i
\(39\) 0 0
\(40\) −2.73546 + 0.719224i −0.432514 + 0.113719i
\(41\) 7.12311i 1.11244i −0.831034 0.556221i \(-0.812251\pi\)
0.831034 0.556221i \(-0.187749\pi\)
\(42\) 0 0
\(43\) 7.60669i 1.16001i 0.814613 + 0.580005i \(0.196949\pi\)
−0.814613 + 0.580005i \(0.803051\pi\)
\(44\) −3.68466 + 3.07221i −0.555483 + 0.463152i
\(45\) 0 0
\(46\) 3.43845 7.34376i 0.506971 1.08278i
\(47\) −10.0054 −1.45944 −0.729719 0.683748i \(-0.760349\pi\)
−0.729719 + 0.683748i \(0.760349\pi\)
\(48\) 0 0
\(49\) 6.56155 2.43845i 0.937365 0.348350i
\(50\) 1.28078 + 0.599676i 0.181129 + 0.0848071i
\(51\) 0 0
\(52\) −3.07221 + 2.56155i −0.426038 + 0.355223i
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 0 0
\(55\) 2.39871 0.323441
\(56\) −3.15363 6.78636i −0.421421 0.906865i
\(57\) 0 0
\(58\) −2.56155 1.19935i −0.336348 0.157483i
\(59\) 10.9418 1.42450 0.712252 0.701924i \(-0.247675\pi\)
0.712252 + 0.701924i \(0.247675\pi\)
\(60\) 0 0
\(61\) 2.00000i 0.256074i 0.991769 + 0.128037i \(0.0408676\pi\)
−0.991769 + 0.128037i \(0.959132\pi\)
\(62\) 8.54312 + 4.00000i 1.08498 + 0.508001i
\(63\) 0 0
\(64\) −6.96543 + 3.93481i −0.870679 + 0.491851i
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 14.2770i 1.74421i 0.489321 + 0.872104i \(0.337245\pi\)
−0.489321 + 0.872104i \(0.662755\pi\)
\(68\) −10.9418 + 9.12311i −1.32689 + 1.10634i
\(69\) 0 0
\(70\) −0.961876 + 3.61591i −0.114966 + 0.432184i
\(71\) 6.14441i 0.729207i 0.931163 + 0.364604i \(0.118796\pi\)
−0.931163 + 0.364604i \(0.881204\pi\)
\(72\) 0 0
\(73\) 9.36932i 1.09660i −0.836283 0.548298i \(-0.815276\pi\)
0.836283 0.548298i \(-0.184724\pi\)
\(74\) −2.56155 1.19935i −0.297774 0.139422i
\(75\) 0 0
\(76\) −3.07221 3.68466i −0.352406 0.422659i
\(77\) 1.12311 + 6.24621i 0.127990 + 0.711822i
\(78\) 0 0
\(79\) 4.27156i 0.480588i 0.970700 + 0.240294i \(0.0772438\pi\)
−0.970700 + 0.240294i \(0.922756\pi\)
\(80\) 3.93481 + 0.719224i 0.439925 + 0.0804116i
\(81\) 0 0
\(82\) −4.27156 + 9.12311i −0.471715 + 1.00748i
\(83\) 0.936426 0.102786 0.0513931 0.998679i \(-0.483634\pi\)
0.0513931 + 0.998679i \(0.483634\pi\)
\(84\) 0 0
\(85\) 7.12311 0.772609
\(86\) 4.56155 9.74247i 0.491885 1.05056i
\(87\) 0 0
\(88\) 6.56155 1.72521i 0.699464 0.183908i
\(89\) 12.0000i 1.27200i −0.771690 0.635999i \(-0.780588\pi\)
0.771690 0.635999i \(-0.219412\pi\)
\(90\) 0 0
\(91\) 0.936426 + 5.20798i 0.0981642 + 0.545945i
\(92\) −8.80776 + 7.34376i −0.918273 + 0.765640i
\(93\) 0 0
\(94\) 12.8147 + 6.00000i 1.32173 + 0.618853i
\(95\) 2.39871i 0.246102i
\(96\) 0 0
\(97\) 7.12311i 0.723242i 0.932325 + 0.361621i \(0.117777\pi\)
−0.932325 + 0.361621i \(0.882223\pi\)
\(98\) −9.86616 0.811703i −0.996633 0.0819944i
\(99\) 0 0
\(100\) −1.28078 1.53610i −0.128078 0.153610i
\(101\) 6.87689i 0.684277i 0.939650 + 0.342138i \(0.111151\pi\)
−0.939650 + 0.342138i \(0.888849\pi\)
\(102\) 0 0
\(103\) −1.46228 −0.144083 −0.0720413 0.997402i \(-0.522951\pi\)
−0.0720413 + 0.997402i \(0.522951\pi\)
\(104\) 5.47091 1.43845i 0.536467 0.141051i
\(105\) 0 0
\(106\) 2.56155 + 1.19935i 0.248800 + 0.116491i
\(107\) 9.47954i 0.916422i 0.888843 + 0.458211i \(0.151510\pi\)
−0.888843 + 0.458211i \(0.848490\pi\)
\(108\) 0 0
\(109\) 1.12311 0.107574 0.0537870 0.998552i \(-0.482871\pi\)
0.0537870 + 0.998552i \(0.482871\pi\)
\(110\) −3.07221 1.43845i −0.292923 0.137151i
\(111\) 0 0
\(112\) −0.0305236 + 10.5830i −0.00288420 + 0.999996i
\(113\) 14.4924 1.36333 0.681666 0.731663i \(-0.261256\pi\)
0.681666 + 0.731663i \(0.261256\pi\)
\(114\) 0 0
\(115\) 5.73384 0.534683
\(116\) 2.56155 + 3.07221i 0.237834 + 0.285247i
\(117\) 0 0
\(118\) −14.0140 6.56155i −1.29010 0.604040i
\(119\) 3.33513 + 18.5485i 0.305731 + 1.70034i
\(120\) 0 0
\(121\) 5.24621 0.476928
\(122\) 1.19935 2.56155i 0.108584 0.231912i
\(123\) 0 0
\(124\) −8.54312 10.2462i −0.767195 0.920137i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 13.2252i 1.17355i −0.809750 0.586776i \(-0.800397\pi\)
0.809750 0.586776i \(-0.199603\pi\)
\(128\) 11.2808 0.862603i 0.997089 0.0762440i
\(129\) 0 0
\(130\) −2.56155 1.19935i −0.224663 0.105190i
\(131\) −13.8664 −1.21151 −0.605756 0.795651i \(-0.707129\pi\)
−0.605756 + 0.795651i \(0.707129\pi\)
\(132\) 0 0
\(133\) −6.24621 + 1.12311i −0.541615 + 0.0973856i
\(134\) 8.56155 18.2856i 0.739606 1.57963i
\(135\) 0 0
\(136\) 19.4849 5.12311i 1.67082 0.439303i
\(137\) 14.0000 1.19610 0.598050 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) −1.34700 −0.114251 −0.0571255 0.998367i \(-0.518194\pi\)
−0.0571255 + 0.998367i \(0.518194\pi\)
\(140\) 3.40032 4.05436i 0.287380 0.342656i
\(141\) 0 0
\(142\) 3.68466 7.86962i 0.309210 0.660404i
\(143\) −4.79741 −0.401180
\(144\) 0 0
\(145\) 2.00000i 0.166091i
\(146\) −5.61856 + 12.0000i −0.464995 + 0.993127i
\(147\) 0 0
\(148\) 2.56155 + 3.07221i 0.210558 + 0.252534i
\(149\) 19.3693 1.58680 0.793398 0.608703i \(-0.208310\pi\)
0.793398 + 0.608703i \(0.208310\pi\)
\(150\) 0 0
\(151\) 14.6875i 1.19525i −0.801774 0.597627i \(-0.796110\pi\)
0.801774 0.597627i \(-0.203890\pi\)
\(152\) 1.72521 + 6.56155i 0.139933 + 0.532212i
\(153\) 0 0
\(154\) 2.30726 8.67350i 0.185924 0.698931i
\(155\) 6.67026i 0.535769i
\(156\) 0 0
\(157\) 16.2462i 1.29659i 0.761390 + 0.648294i \(0.224517\pi\)
−0.761390 + 0.648294i \(0.775483\pi\)
\(158\) 2.56155 5.47091i 0.203786 0.435242i
\(159\) 0 0
\(160\) −4.60831 3.28078i −0.364319 0.259368i
\(161\) 2.68466 + 14.9309i 0.211581 + 1.17672i
\(162\) 0 0
\(163\) 0.936426i 0.0733466i 0.999327 + 0.0366733i \(0.0116761\pi\)
−0.999327 + 0.0366733i \(0.988324\pi\)
\(164\) 10.9418 9.12311i 0.854413 0.712395i
\(165\) 0 0
\(166\) −1.19935 0.561553i −0.0930878 0.0435850i
\(167\) −2.28343 −0.176697 −0.0883484 0.996090i \(-0.528159\pi\)
−0.0883484 + 0.996090i \(0.528159\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −9.12311 4.27156i −0.699710 0.327614i
\(171\) 0 0
\(172\) −11.6847 + 9.74247i −0.890947 + 0.742856i
\(173\) 0.246211i 0.0187191i −0.999956 0.00935955i \(-0.997021\pi\)
0.999956 0.00935955i \(-0.00297928\pi\)
\(174\) 0 0
\(175\) −2.60399 + 0.468213i −0.196843 + 0.0353936i
\(176\) −9.43845 1.72521i −0.711450 0.130042i
\(177\) 0 0
\(178\) −7.19612 + 15.3693i −0.539372 + 1.15198i
\(179\) 0.525853i 0.0393041i −0.999807 0.0196520i \(-0.993744\pi\)
0.999807 0.0196520i \(-0.00625584\pi\)
\(180\) 0 0
\(181\) 6.87689i 0.511156i −0.966789 0.255578i \(-0.917734\pi\)
0.966789 0.255578i \(-0.0822657\pi\)
\(182\) 1.92375 7.23182i 0.142598 0.536058i
\(183\) 0 0
\(184\) 15.6847 4.12391i 1.15629 0.304019i
\(185\) 2.00000i 0.147043i
\(186\) 0 0
\(187\) −17.0862 −1.24947
\(188\) −12.8147 15.3693i −0.934606 1.12092i
\(189\) 0 0
\(190\) 1.43845 3.07221i 0.104356 0.222881i
\(191\) 1.34700i 0.0974655i −0.998812 0.0487327i \(-0.984482\pi\)
0.998812 0.0487327i \(-0.0155183\pi\)
\(192\) 0 0
\(193\) 10.4924 0.755261 0.377631 0.925956i \(-0.376739\pi\)
0.377631 + 0.925956i \(0.376739\pi\)
\(194\) 4.27156 9.12311i 0.306680 0.655001i
\(195\) 0 0
\(196\) 12.1496 + 6.95611i 0.867828 + 0.496865i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 16.0345 1.13666 0.568329 0.822802i \(-0.307590\pi\)
0.568329 + 0.822802i \(0.307590\pi\)
\(200\) 0.719224 + 2.73546i 0.0508568 + 0.193426i
\(201\) 0 0
\(202\) 4.12391 8.80776i 0.290157 0.619712i
\(203\) 5.20798 0.936426i 0.365529 0.0657242i
\(204\) 0 0
\(205\) −7.12311 −0.497499
\(206\) 1.87285 + 0.876894i 0.130488 + 0.0610961i
\(207\) 0 0
\(208\) −7.86962 1.43845i −0.545660 0.0997384i
\(209\) 5.75379i 0.397998i
\(210\) 0 0
\(211\) 18.4332i 1.26900i 0.772924 + 0.634498i \(0.218793\pi\)
−0.772924 + 0.634498i \(0.781207\pi\)
\(212\) −2.56155 3.07221i −0.175928 0.211000i
\(213\) 0 0
\(214\) 5.68466 12.1412i 0.388595 0.829954i
\(215\) 7.60669 0.518772
\(216\) 0 0
\(217\) −17.3693 + 3.12311i −1.17911 + 0.212010i
\(218\) −1.43845 0.673500i −0.0974239 0.0456152i
\(219\) 0 0
\(220\) 3.07221 + 3.68466i 0.207128 + 0.248420i
\(221\) −14.2462 −0.958304
\(222\) 0 0
\(223\) 12.9300 0.865854 0.432927 0.901429i \(-0.357481\pi\)
0.432927 + 0.901429i \(0.357481\pi\)
\(224\) 6.38545 13.5361i 0.426646 0.904419i
\(225\) 0 0
\(226\) −18.5616 8.69076i −1.23470 0.578101i
\(227\) 14.2770 0.947595 0.473797 0.880634i \(-0.342883\pi\)
0.473797 + 0.880634i \(0.342883\pi\)
\(228\) 0 0
\(229\) 21.1231i 1.39585i −0.716169 0.697927i \(-0.754106\pi\)
0.716169 0.697927i \(-0.245894\pi\)
\(230\) −7.34376 3.43845i −0.484233 0.226724i
\(231\) 0 0
\(232\) −1.43845 5.47091i −0.0944387 0.359183i
\(233\) −24.2462 −1.58842 −0.794211 0.607642i \(-0.792116\pi\)
−0.794211 + 0.607642i \(0.792116\pi\)
\(234\) 0 0
\(235\) 10.0054i 0.652680i
\(236\) 14.0140 + 16.8078i 0.912236 + 1.09409i
\(237\) 0 0
\(238\) 6.85155 25.7565i 0.444120 1.66955i
\(239\) 12.8147i 0.828912i −0.910069 0.414456i \(-0.863972\pi\)
0.910069 0.414456i \(-0.136028\pi\)
\(240\) 0 0
\(241\) 15.6155i 1.00588i 0.864320 + 0.502942i \(0.167749\pi\)
−0.864320 + 0.502942i \(0.832251\pi\)
\(242\) −6.71922 3.14603i −0.431928 0.202234i
\(243\) 0 0
\(244\) −3.07221 + 2.56155i −0.196678 + 0.163987i
\(245\) −2.43845 6.56155i −0.155787 0.419202i
\(246\) 0 0
\(247\) 4.79741i 0.305252i
\(248\) 4.79741 + 18.2462i 0.304636 + 1.15864i
\(249\) 0 0
\(250\) 0.599676 1.28078i 0.0379269 0.0810034i
\(251\) −16.5604 −1.04528 −0.522641 0.852553i \(-0.675053\pi\)
−0.522641 + 0.852553i \(0.675053\pi\)
\(252\) 0 0
\(253\) −13.7538 −0.864693
\(254\) −7.93087 + 16.9386i −0.497627 + 1.06282i
\(255\) 0 0
\(256\) −14.9654 5.66001i −0.935340 0.353751i
\(257\) 13.3693i 0.833955i −0.908917 0.416978i \(-0.863089\pi\)
0.908917 0.416978i \(-0.136911\pi\)
\(258\) 0 0
\(259\) 5.20798 0.936426i 0.323608 0.0581867i
\(260\) 2.56155 + 3.07221i 0.158861 + 0.190530i
\(261\) 0 0
\(262\) 17.7597 + 8.31534i 1.09720 + 0.513724i
\(263\) 1.98813i 0.122593i −0.998120 0.0612967i \(-0.980476\pi\)
0.998120 0.0612967i \(-0.0195236\pi\)
\(264\) 0 0
\(265\) 2.00000i 0.122859i
\(266\) 8.67350 + 2.30726i 0.531806 + 0.141467i
\(267\) 0 0
\(268\) −21.9309 + 18.2856i −1.33964 + 1.11697i
\(269\) 16.2462i 0.990549i −0.868737 0.495274i \(-0.835067\pi\)
0.868737 0.495274i \(-0.164933\pi\)
\(270\) 0 0
\(271\) −23.7565 −1.44310 −0.721552 0.692360i \(-0.756571\pi\)
−0.721552 + 0.692360i \(0.756571\pi\)
\(272\) −28.0281 5.12311i −1.69945 0.310634i
\(273\) 0 0
\(274\) −17.9309 8.39547i −1.08324 0.507189i
\(275\) 2.39871i 0.144647i
\(276\) 0 0
\(277\) −4.24621 −0.255130 −0.127565 0.991830i \(-0.540716\pi\)
−0.127565 + 0.991830i \(0.540716\pi\)
\(278\) 1.72521 + 0.807764i 0.103471 + 0.0484465i
\(279\) 0 0
\(280\) −6.78636 + 3.15363i −0.405562 + 0.188465i
\(281\) 4.63068 0.276243 0.138122 0.990415i \(-0.455893\pi\)
0.138122 + 0.990415i \(0.455893\pi\)
\(282\) 0 0
\(283\) 24.6929 1.46784 0.733921 0.679235i \(-0.237688\pi\)
0.733921 + 0.679235i \(0.237688\pi\)
\(284\) −9.43845 + 7.86962i −0.560069 + 0.466976i
\(285\) 0 0
\(286\) 6.14441 + 2.87689i 0.363327 + 0.170114i
\(287\) −3.33513 18.5485i −0.196867 1.09488i
\(288\) 0 0
\(289\) −33.7386 −1.98463
\(290\) −1.19935 + 2.56155i −0.0704284 + 0.150420i
\(291\) 0 0
\(292\) 14.3922 12.0000i 0.842242 0.702247i
\(293\) 32.2462i 1.88384i 0.335832 + 0.941922i \(0.390983\pi\)
−0.335832 + 0.941922i \(0.609017\pi\)
\(294\) 0 0
\(295\) 10.9418i 0.637058i
\(296\) −1.43845 5.47091i −0.0836080 0.317990i
\(297\) 0 0
\(298\) −24.8078 11.6153i −1.43708 0.672858i
\(299\) −11.4677 −0.663193
\(300\) 0 0
\(301\) 3.56155 + 19.8078i 0.205284 + 1.14170i
\(302\) −8.80776 + 18.8114i −0.506830 + 1.08248i
\(303\) 0 0
\(304\) 1.72521 9.43845i 0.0989473 0.541332i
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) −31.3632 −1.78999 −0.894996 0.446074i \(-0.852822\pi\)
−0.894996 + 0.446074i \(0.852822\pi\)
\(308\) −8.15638 + 9.72521i −0.464753 + 0.554145i
\(309\) 0 0
\(310\) 4.00000 8.54312i 0.227185 0.485216i
\(311\) 9.36426 0.530999 0.265499 0.964111i \(-0.414463\pi\)
0.265499 + 0.964111i \(0.414463\pi\)
\(312\) 0 0
\(313\) 7.61553i 0.430455i −0.976564 0.215228i \(-0.930951\pi\)
0.976564 0.215228i \(-0.0690493\pi\)
\(314\) 9.74247 20.8078i 0.549799 1.17425i
\(315\) 0 0
\(316\) −6.56155 + 5.47091i −0.369116 + 0.307763i
\(317\) 4.24621 0.238491 0.119245 0.992865i \(-0.461952\pi\)
0.119245 + 0.992865i \(0.461952\pi\)
\(318\) 0 0
\(319\) 4.79741i 0.268603i
\(320\) 3.93481 + 6.96543i 0.219962 + 0.389380i
\(321\) 0 0
\(322\) 5.51524 20.7330i 0.307352 1.15541i
\(323\) 17.0862i 0.950703i
\(324\) 0 0
\(325\) 2.00000i 0.110940i
\(326\) 0.561553 1.19935i 0.0311015 0.0664260i
\(327\) 0 0
\(328\) −19.4849 + 5.12311i −1.07588 + 0.282876i
\(329\) −26.0540 + 4.68466i −1.43640 + 0.258274i
\(330\) 0 0
\(331\) 29.0798i 1.59837i −0.601086 0.799184i \(-0.705265\pi\)
0.601086 0.799184i \(-0.294735\pi\)
\(332\) 1.19935 + 1.43845i 0.0658230 + 0.0789450i
\(333\) 0 0
\(334\) 2.92456 + 1.36932i 0.160025 + 0.0749257i
\(335\) 14.2770 0.780033
\(336\) 0 0
\(337\) 4.24621 0.231306 0.115653 0.993290i \(-0.463104\pi\)
0.115653 + 0.993290i \(0.463104\pi\)
\(338\) −11.5270 5.39709i −0.626985 0.293563i
\(339\) 0 0
\(340\) 9.12311 + 10.9418i 0.494770 + 0.593404i
\(341\) 16.0000i 0.866449i
\(342\) 0 0
\(343\) 15.9445 9.42190i 0.860923 0.508735i
\(344\) 20.8078 5.47091i 1.12188 0.294972i
\(345\) 0 0
\(346\) −0.147647 + 0.315342i −0.00793756 + 0.0169529i
\(347\) 9.47954i 0.508889i 0.967087 + 0.254444i \(0.0818925\pi\)
−0.967087 + 0.254444i \(0.918107\pi\)
\(348\) 0 0
\(349\) 27.8617i 1.49140i −0.666279 0.745702i \(-0.732114\pi\)
0.666279 0.745702i \(-0.267886\pi\)
\(350\) 3.61591 + 0.961876i 0.193278 + 0.0514145i
\(351\) 0 0
\(352\) 11.0540 + 7.86962i 0.589179 + 0.419452i
\(353\) 5.36932i 0.285780i −0.989739 0.142890i \(-0.954361\pi\)
0.989739 0.142890i \(-0.0456395\pi\)
\(354\) 0 0
\(355\) 6.14441 0.326111
\(356\) 18.4332 15.3693i 0.976959 0.814572i
\(357\) 0 0
\(358\) −0.315342 + 0.673500i −0.0166663 + 0.0355956i
\(359\) 16.5604i 0.874023i −0.899456 0.437012i \(-0.856037\pi\)
0.899456 0.437012i \(-0.143963\pi\)
\(360\) 0 0
\(361\) −13.2462 −0.697169
\(362\) −4.12391 + 8.80776i −0.216748 + 0.462926i
\(363\) 0 0
\(364\) −6.80065 + 8.10871i −0.356451 + 0.425012i
\(365\) −9.36932 −0.490412
\(366\) 0 0
\(367\) 7.08084 0.369617 0.184808 0.982775i \(-0.440834\pi\)
0.184808 + 0.982775i \(0.440834\pi\)
\(368\) −22.5616 4.12391i −1.17610 0.214974i
\(369\) 0 0
\(370\) −1.19935 + 2.56155i −0.0623514 + 0.133169i
\(371\) −5.20798 + 0.936426i −0.270385 + 0.0486168i
\(372\) 0 0
\(373\) 22.4924 1.16461 0.582307 0.812969i \(-0.302150\pi\)
0.582307 + 0.812969i \(0.302150\pi\)
\(374\) 21.8836 + 10.2462i 1.13158 + 0.529819i
\(375\) 0 0
\(376\) 7.19612 + 27.3693i 0.371111 + 1.41146i
\(377\) 4.00000i 0.206010i
\(378\) 0 0
\(379\) 22.4095i 1.15110i −0.817767 0.575549i \(-0.804788\pi\)
0.817767 0.575549i \(-0.195212\pi\)
\(380\) −3.68466 + 3.07221i −0.189019 + 0.157601i
\(381\) 0 0
\(382\) −0.807764 + 1.72521i −0.0413288 + 0.0882692i
\(383\) −17.4968 −0.894045 −0.447023 0.894523i \(-0.647516\pi\)
−0.447023 + 0.894523i \(0.647516\pi\)
\(384\) 0 0
\(385\) 6.24621 1.12311i 0.318336 0.0572388i
\(386\) −13.4384 6.29206i −0.683999 0.320257i
\(387\) 0 0
\(388\) −10.9418 + 9.12311i −0.555487 + 0.463156i
\(389\) −1.12311 −0.0569437 −0.0284719 0.999595i \(-0.509064\pi\)
−0.0284719 + 0.999595i \(0.509064\pi\)
\(390\) 0 0
\(391\) −40.8427 −2.06551
\(392\) −11.3895 16.1950i −0.575256 0.817973i
\(393\) 0 0
\(394\) 23.0540 + 10.7942i 1.16144 + 0.543803i
\(395\) 4.27156 0.214925
\(396\) 0 0
\(397\) 14.0000i 0.702640i −0.936255 0.351320i \(-0.885733\pi\)
0.936255 0.351320i \(-0.114267\pi\)
\(398\) −20.5366 9.61553i −1.02941 0.481983i
\(399\) 0 0
\(400\) 0.719224 3.93481i 0.0359612 0.196740i
\(401\) −6.00000 −0.299626 −0.149813 0.988714i \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) 0 0
\(403\) 13.3405i 0.664539i
\(404\) −10.5636 + 8.80776i −0.525560 + 0.438203i
\(405\) 0 0
\(406\) −7.23182 1.92375i −0.358909 0.0954742i
\(407\) 4.79741i 0.237799i
\(408\) 0 0
\(409\) 8.87689i 0.438934i −0.975620 0.219467i \(-0.929568\pi\)
0.975620 0.219467i \(-0.0704319\pi\)
\(410\) 9.12311 + 4.27156i 0.450558 + 0.210957i
\(411\) 0 0
\(412\) −1.87285 2.24621i −0.0922688 0.110663i
\(413\) 28.4924 5.12311i 1.40202 0.252092i
\(414\) 0 0
\(415\) 0.936426i 0.0459674i
\(416\) 9.21662 + 6.56155i 0.451882 + 0.321707i
\(417\) 0 0
\(418\) −3.45041 + 7.36932i −0.168765 + 0.360445i
\(419\) 11.9935 0.585922 0.292961 0.956124i \(-0.405359\pi\)
0.292961 + 0.956124i \(0.405359\pi\)
\(420\) 0 0
\(421\) −17.6155 −0.858528 −0.429264 0.903179i \(-0.641227\pi\)
−0.429264 + 0.903179i \(0.641227\pi\)
\(422\) 11.0540 23.6089i 0.538099 1.14926i
\(423\) 0 0
\(424\) 1.43845 + 5.47091i 0.0698572 + 0.265691i
\(425\) 7.12311i 0.345521i
\(426\) 0 0
\(427\) 0.936426 + 5.20798i 0.0453168 + 0.252032i
\(428\) −14.5616 + 12.1412i −0.703859 + 0.586866i
\(429\) 0 0
\(430\) −9.74247 4.56155i −0.469824 0.219978i
\(431\) 36.5712i 1.76157i −0.473515 0.880786i \(-0.657015\pi\)
0.473515 0.880786i \(-0.342985\pi\)
\(432\) 0 0
\(433\) 11.6155i 0.558207i −0.960261 0.279103i \(-0.909963\pi\)
0.960261 0.279103i \(-0.0900372\pi\)
\(434\) 24.1191 + 6.41597i 1.15775 + 0.307976i
\(435\) 0 0
\(436\) 1.43845 + 1.72521i 0.0688891 + 0.0826224i
\(437\) 13.7538i 0.657933i
\(438\) 0 0
\(439\) 18.1379 0.865677 0.432838 0.901472i \(-0.357512\pi\)
0.432838 + 0.901472i \(0.357512\pi\)
\(440\) −1.72521 6.56155i −0.0822460 0.312810i
\(441\) 0 0
\(442\) 18.2462 + 8.54312i 0.867884 + 0.406355i
\(443\) 30.3115i 1.44014i 0.693900 + 0.720071i \(0.255891\pi\)
−0.693900 + 0.720071i \(0.744109\pi\)
\(444\) 0 0
\(445\) −12.0000 −0.568855
\(446\) −16.5604 7.75379i −0.784157 0.367153i
\(447\) 0 0
\(448\) −16.2956 + 13.5075i −0.769895 + 0.638170i
\(449\) −25.6155 −1.20887 −0.604436 0.796654i \(-0.706601\pi\)
−0.604436 + 0.796654i \(0.706601\pi\)
\(450\) 0 0
\(451\) 17.0862 0.804559
\(452\) 18.5616 + 22.2619i 0.873062 + 1.04711i
\(453\) 0 0
\(454\) −18.2856 8.56155i −0.858185 0.401814i
\(455\) 5.20798 0.936426i 0.244154 0.0439003i
\(456\) 0 0
\(457\) 6.00000 0.280668 0.140334 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) −12.6670 + 27.0540i −0.591891 + 1.26415i
\(459\) 0 0
\(460\) 7.34376 + 8.80776i 0.342405 + 0.410664i
\(461\) 37.6155i 1.75193i 0.482375 + 0.875965i \(0.339774\pi\)
−0.482375 + 0.875965i \(0.660226\pi\)
\(462\) 0 0
\(463\) 21.9989i 1.02238i 0.859469 + 0.511188i \(0.170795\pi\)
−0.859469 + 0.511188i \(0.829205\pi\)
\(464\) −1.43845 + 7.86962i −0.0667782 + 0.365338i
\(465\) 0 0
\(466\) 31.0540 + 14.5399i 1.43855 + 0.673547i
\(467\) −1.98813 −0.0919998 −0.0459999 0.998941i \(-0.514647\pi\)
−0.0459999 + 0.998941i \(0.514647\pi\)
\(468\) 0 0
\(469\) 6.68466 + 37.1771i 0.308669 + 1.71668i
\(470\) 6.00000 12.8147i 0.276759 0.591097i
\(471\) 0 0
\(472\) −7.86962 29.9309i −0.362228 1.37768i
\(473\) −18.2462 −0.838962
\(474\) 0 0
\(475\) 2.39871 0.110060
\(476\) −24.2209 + 28.8796i −1.11016 + 1.32369i
\(477\) 0 0
\(478\) −7.68466 + 16.4127i −0.351488 + 0.750701i
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 4.00000i 0.182384i
\(482\) 9.36426 20.0000i 0.426531 0.910975i
\(483\) 0 0
\(484\) 6.71922 + 8.05872i 0.305419 + 0.366305i
\(485\) 7.12311 0.323444
\(486\) 0 0
\(487\) 19.0744i 0.864342i −0.901792 0.432171i \(-0.857748\pi\)
0.901792 0.432171i \(-0.142252\pi\)
\(488\) 5.47091 1.43845i 0.247657 0.0651154i
\(489\) 0 0
\(490\) −0.811703 + 9.86616i −0.0366690 + 0.445708i
\(491\) 13.6358i 0.615376i 0.951487 + 0.307688i \(0.0995553\pi\)
−0.951487 + 0.307688i \(0.900445\pi\)
\(492\) 0 0
\(493\) 14.2462i 0.641617i
\(494\) −2.87689 + 6.14441i −0.129438 + 0.276450i
\(495\) 0 0
\(496\) 4.79741 26.2462i 0.215410 1.17849i
\(497\) 2.87689 + 16.0000i 0.129046 + 0.717698i
\(498\) 0 0
\(499\) 27.2069i 1.21795i 0.793190 + 0.608974i \(0.208419\pi\)
−0.793190 + 0.608974i \(0.791581\pi\)
\(500\) −1.53610 + 1.28078i −0.0686966 + 0.0572781i
\(501\) 0 0
\(502\) 21.2101 + 9.93087i 0.946655 + 0.443236i
\(503\) 21.4731 0.957437 0.478718 0.877968i \(-0.341101\pi\)
0.478718 + 0.877968i \(0.341101\pi\)
\(504\) 0 0
\(505\) 6.87689 0.306018
\(506\) 17.6155 + 8.24782i 0.783106 + 0.366660i
\(507\) 0 0
\(508\) 20.3153 16.9386i 0.901348 0.751528i
\(509\) 17.6155i 0.780795i −0.920646 0.390397i \(-0.872338\pi\)
0.920646 0.390397i \(-0.127662\pi\)
\(510\) 0 0
\(511\) −4.38684 24.3976i −0.194062 1.07929i
\(512\) 15.7732 + 16.2236i 0.697083 + 0.716990i
\(513\) 0 0
\(514\) −8.01726 + 17.1231i −0.353626 + 0.755268i
\(515\) 1.46228i 0.0644357i
\(516\) 0 0
\(517\) 24.0000i 1.05552i
\(518\) −7.23182 1.92375i −0.317748 0.0845248i
\(519\) 0 0
\(520\) −1.43845 5.47091i −0.0630801 0.239915i
\(521\) 26.2462i 1.14987i 0.818200 + 0.574934i \(0.194972\pi\)
−0.818200 + 0.574934i \(0.805028\pi\)
\(522\) 0 0
\(523\) 17.2015 0.752170 0.376085 0.926585i \(-0.377270\pi\)
0.376085 + 0.926585i \(0.377270\pi\)
\(524\) −17.7597 21.3002i −0.775838 0.930503i
\(525\) 0 0
\(526\) −1.19224 + 2.54635i −0.0519840 + 0.111026i
\(527\) 47.5130i 2.06970i
\(528\) 0 0
\(529\) −9.87689 −0.429430
\(530\) 1.19935 2.56155i 0.0520966 0.111267i
\(531\) 0 0
\(532\) −9.72521 8.15638i −0.421641 0.353624i
\(533\) 14.2462 0.617072
\(534\) 0 0
\(535\) 9.47954 0.409836
\(536\) 39.0540 10.2683i 1.68687 0.443524i
\(537\) 0 0
\(538\) −9.74247 + 20.8078i −0.420028 + 0.897086i
\(539\) 5.84912 + 15.7392i 0.251939 + 0.677937i
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 30.4268 + 14.2462i 1.30694 + 0.611927i
\(543\) 0 0
\(544\) 32.8255 + 23.3693i 1.40738 + 1.00195i
\(545\) 1.12311i 0.0481086i
\(546\) 0 0
\(547\) 1.75757i 0.0751484i 0.999294 + 0.0375742i \(0.0119631\pi\)
−0.999294 + 0.0375742i \(0.988037\pi\)
\(548\) 17.9309 + 21.5054i 0.765969 + 0.918667i
\(549\) 0 0
\(550\) −1.43845 + 3.07221i −0.0613356 + 0.130999i
\(551\) −4.79741 −0.204377
\(552\) 0 0
\(553\) 2.00000 + 11.1231i 0.0850487 + 0.473003i
\(554\) 5.43845 + 2.54635i 0.231057 + 0.108184i
\(555\) 0 0
\(556\) −1.72521 2.06913i −0.0731650 0.0877507i
\(557\) −6.49242 −0.275093 −0.137546 0.990495i \(-0.543922\pi\)
−0.137546 + 0.990495i \(0.543922\pi\)
\(558\) 0 0
\(559\) −15.2134 −0.643457
\(560\) 10.5830 + 0.0305236i 0.447212 + 0.00128986i
\(561\) 0 0
\(562\) −5.93087 2.77691i −0.250179 0.117137i
\(563\) 26.7963 1.12933 0.564665 0.825320i \(-0.309005\pi\)
0.564665 + 0.825320i \(0.309005\pi\)
\(564\) 0 0
\(565\) 14.4924i 0.609701i
\(566\) −31.6261 14.8078i −1.32934 0.622417i
\(567\) 0 0
\(568\) 16.8078 4.41921i 0.705238 0.185426i
\(569\) 37.1231 1.55628 0.778141 0.628090i \(-0.216163\pi\)
0.778141 + 0.628090i \(0.216163\pi\)
\(570\) 0 0
\(571\) 28.0281i 1.17294i 0.809972 + 0.586469i \(0.199482\pi\)
−0.809972 + 0.586469i \(0.800518\pi\)
\(572\) −6.14441 7.36932i −0.256911 0.308127i
\(573\) 0 0
\(574\) −6.85155 + 25.7565i −0.285978 + 1.07506i
\(575\) 5.73384i 0.239118i
\(576\) 0 0
\(577\) 4.38447i 0.182528i 0.995827 + 0.0912640i \(0.0290907\pi\)
−0.995827 + 0.0912640i \(0.970909\pi\)
\(578\) 43.2116 + 20.2323i 1.79737 + 0.841551i
\(579\) 0 0
\(580\) 3.07221 2.56155i 0.127566 0.106363i
\(581\) 2.43845 0.438447i 0.101164 0.0181899i
\(582\) 0 0
\(583\) 4.79741i 0.198688i
\(584\) −25.6294 + 6.73863i −1.06055 + 0.278847i
\(585\) 0 0
\(586\) 19.3373 41.3002i 0.798816 1.70609i
\(587\) 8.65840 0.357370 0.178685 0.983906i \(-0.442816\pi\)
0.178685 + 0.983906i \(0.442816\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) −6.56155 + 14.0140i −0.270135 + 0.576948i
\(591\) 0 0
\(592\) −1.43845 + 7.86962i −0.0591198 + 0.323439i
\(593\) 13.3693i 0.549012i −0.961585 0.274506i \(-0.911486\pi\)
0.961585 0.274506i \(-0.0885143\pi\)
\(594\) 0 0
\(595\) 18.5485 3.33513i 0.760415 0.136727i
\(596\) 24.8078 + 29.7533i 1.01617 + 1.21874i
\(597\) 0 0
\(598\) 14.6875 + 6.87689i 0.600618 + 0.281217i
\(599\) 10.1207i 0.413520i −0.978392 0.206760i \(-0.933708\pi\)
0.978392 0.206760i \(-0.0662919\pi\)
\(600\) 0 0
\(601\) 8.87689i 0.362096i 0.983474 + 0.181048i \(0.0579489\pi\)
−0.983474 + 0.181048i \(0.942051\pi\)
\(602\) 7.31670 27.5051i 0.298206 1.12102i
\(603\) 0 0
\(604\) 22.5616 18.8114i 0.918017 0.765427i
\(605\) 5.24621i 0.213289i
\(606\) 0 0
\(607\) 7.90198 0.320732 0.160366 0.987058i \(-0.448733\pi\)
0.160366 + 0.987058i \(0.448733\pi\)
\(608\) −7.86962 + 11.0540i −0.319155 + 0.448298i
\(609\) 0 0
\(610\) −2.56155 1.19935i −0.103714 0.0485604i
\(611\) 20.0108i 0.809550i
\(612\) 0 0
\(613\) 11.7538 0.474731 0.237366 0.971420i \(-0.423716\pi\)
0.237366 + 0.971420i \(0.423716\pi\)
\(614\) 40.1692 + 18.8078i 1.62110 + 0.759020i
\(615\) 0 0
\(616\) 16.2785 7.56463i 0.655878 0.304788i
\(617\) 26.0000 1.04672 0.523360 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 0 0
\(619\) −48.8600 −1.96385 −0.981925 0.189273i \(-0.939387\pi\)
−0.981925 + 0.189273i \(0.939387\pi\)
\(620\) −10.2462 + 8.54312i −0.411498 + 0.343100i
\(621\) 0 0
\(622\) −11.9935 5.61553i −0.480897 0.225162i
\(623\) −5.61856 31.2479i −0.225103 1.25192i
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −4.56685 + 9.75379i −0.182528 + 0.389840i
\(627\) 0 0
\(628\) −24.9559 + 20.8078i −0.995847 + 0.830320i
\(629\) 14.2462i 0.568034i
\(630\) 0 0
\(631\) 7.19612i 0.286473i 0.989688 + 0.143236i \(0.0457509\pi\)
−0.989688 + 0.143236i \(0.954249\pi\)
\(632\) 11.6847 3.07221i 0.464791 0.122206i
\(633\) 0 0
\(634\) −5.43845 2.54635i −0.215988 0.101129i
\(635\) −13.2252 −0.524828
\(636\) 0 0
\(637\) 4.87689 + 13.1231i 0.193230 + 0.519956i
\(638\) 2.87689 6.14441i 0.113897 0.243260i
\(639\) 0 0
\(640\) −0.862603 11.2808i −0.0340974 0.445912i
\(641\) −1.12311 −0.0443600 −0.0221800 0.999754i \(-0.507061\pi\)
−0.0221800 + 0.999754i \(0.507061\pi\)
\(642\) 0 0
\(643\) 4.91269 0.193738 0.0968688 0.995297i \(-0.469117\pi\)
0.0968688 + 0.995297i \(0.469117\pi\)
\(644\) −19.4969 + 23.2470i −0.768286 + 0.916061i
\(645\) 0 0
\(646\) −10.2462 + 21.8836i −0.403132 + 0.861000i
\(647\) −37.7382 −1.48364 −0.741820 0.670599i \(-0.766037\pi\)
−0.741820 + 0.670599i \(0.766037\pi\)
\(648\) 0 0
\(649\) 26.2462i 1.03025i
\(650\) −1.19935 + 2.56155i −0.0470425 + 0.100472i
\(651\) 0 0
\(652\) −1.43845 + 1.19935i −0.0563339 + 0.0469703i
\(653\) −42.9848 −1.68213 −0.841063 0.540936i \(-0.818070\pi\)
−0.841063 + 0.540936i \(0.818070\pi\)
\(654\) 0 0
\(655\) 13.8664i 0.541804i
\(656\) 28.0281 + 5.12311i 1.09431 + 0.200024i
\(657\) 0 0
\(658\) 36.1786 + 9.62395i 1.41039 + 0.375181i
\(659\) 4.27156i 0.166396i −0.996533 0.0831981i \(-0.973487\pi\)
0.996533 0.0831981i \(-0.0265134\pi\)
\(660\) 0 0
\(661\) 4.24621i 0.165158i 0.996585 + 0.0825792i \(0.0263158\pi\)
−0.996585 + 0.0825792i \(0.973684\pi\)
\(662\) −17.4384 + 37.2447i −0.677764 + 1.44756i
\(663\) 0 0
\(664\) −0.673500 2.56155i −0.0261369 0.0994075i
\(665\) 1.12311 + 6.24621i 0.0435522 + 0.242218i
\(666\) 0 0
\(667\) 11.4677i 0.444030i
\(668\) −2.92456 3.50758i −0.113155 0.135712i
\(669\) 0 0
\(670\) −18.2856 8.56155i −0.706434 0.330762i
\(671\) −4.79741 −0.185202
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −5.43845 2.54635i −0.209481 0.0980818i
\(675\) 0 0
\(676\) 11.5270 + 13.8249i 0.443346 + 0.531728i
\(677\) 16.7386i 0.643318i −0.946856 0.321659i \(-0.895760\pi\)
0.946856 0.321659i \(-0.104240\pi\)
\(678\) 0 0
\(679\) 3.33513 + 18.5485i 0.127991 + 0.711827i
\(680\) −5.12311 19.4849i −0.196462 0.747213i
\(681\) 0 0
\(682\) −9.59482 + 20.4924i −0.367405 + 0.784695i
\(683\) 7.60669i 0.291062i −0.989354 0.145531i \(-0.953511\pi\)
0.989354 0.145531i \(-0.0464890\pi\)
\(684\) 0 0
\(685\) 14.0000i 0.534913i
\(686\) −26.0715 + 2.50580i −0.995413 + 0.0956718i
\(687\) 0 0
\(688\) −29.9309 5.47091i −1.14110 0.208577i
\(689\) 4.00000i 0.152388i
\(690\) 0 0
\(691\) −22.4095 −0.852497 −0.426249 0.904606i \(-0.640165\pi\)
−0.426249 + 0.904606i \(0.640165\pi\)
\(692\) 0.378206 0.315342i 0.0143772 0.0119875i
\(693\) 0 0
\(694\) 5.68466 12.1412i 0.215787 0.460873i
\(695\) 1.34700i 0.0510946i
\(696\) 0 0
\(697\) 50.7386 1.92186
\(698\) −16.7080 + 35.6847i −0.632408 + 1.35068i
\(699\) 0 0
\(700\) −4.05436 3.40032i −0.153240 0.128520i
\(701\) −2.87689 −0.108659 −0.0543294 0.998523i \(-0.517302\pi\)
−0.0543294 + 0.998523i \(0.517302\pi\)
\(702\) 0 0
\(703\) −4.79741 −0.180938
\(704\) −9.43845 16.7080i −0.355725 0.629707i
\(705\) 0 0
\(706\) −3.21985 + 6.87689i −0.121181 + 0.258815i
\(707\) 3.21985 + 17.9074i 0.121095 + 0.673476i
\(708\) 0 0
\(709\) −4.73863 −0.177963 −0.0889816 0.996033i \(-0.528361\pi\)
−0.0889816 + 0.996033i \(0.528361\pi\)
\(710\) −7.86962 3.68466i −0.295341 0.138283i
\(711\) 0 0
\(712\) −32.8255 + 8.63068i −1.23019 + 0.323449i
\(713\) 38.2462i 1.43233i
\(714\) 0 0
\(715\) 4.79741i 0.179413i
\(716\) 0.807764 0.673500i 0.0301876 0.0251699i
\(717\) 0 0
\(718\) −9.93087 + 21.2101i −0.370617 + 0.791556i
\(719\) 37.9182 1.41411 0.707055 0.707159i \(-0.250023\pi\)
0.707055 + 0.707159i \(0.250023\pi\)
\(720\) 0 0
\(721\) −3.80776 + 0.684658i −0.141809 + 0.0254980i
\(722\) 16.9654 + 7.94344i 0.631388 + 0.295624i
\(723\) 0 0
\(724\) 10.5636 8.80776i 0.392594 0.327338i
\(725\) −2.00000 −0.0742781
\(726\) 0 0
\(727\) 22.2942 0.826847 0.413423 0.910539i \(-0.364333\pi\)
0.413423 + 0.910539i \(0.364333\pi\)
\(728\) 13.5727 6.30726i 0.503038 0.233763i
\(729\) 0 0
\(730\) 12.0000 + 5.61856i 0.444140 + 0.207952i
\(731\) −54.1833 −2.00404
\(732\) 0 0
\(733\) 48.7386i 1.80020i −0.435681 0.900101i \(-0.643492\pi\)
0.435681 0.900101i \(-0.356508\pi\)
\(734\) −9.06897 4.24621i −0.334742 0.156731i
\(735\) 0 0
\(736\) 26.4233 + 18.8114i 0.973975 + 0.693399i
\(737\) −34.2462 −1.26148
\(738\) 0 0
\(739\) 15.5087i 0.570496i 0.958454 + 0.285248i \(0.0920759\pi\)
−0.958454 + 0.285248i \(0.907924\pi\)
\(740\) 3.07221 2.56155i 0.112937 0.0941646i
\(741\) 0 0
\(742\) 7.23182 + 1.92375i 0.265488 + 0.0706232i
\(743\) 15.0981i 0.553896i −0.960885 0.276948i \(-0.910677\pi\)
0.960885 0.276948i \(-0.0893229\pi\)
\(744\) 0 0
\(745\) 19.3693i 0.709637i
\(746\) −28.8078 13.4882i −1.05473 0.493837i
\(747\) 0 0
\(748\) −21.8836 26.2462i −0.800145 0.959657i
\(749\) 4.43845 + 24.6847i 0.162177 + 0.901958i
\(750\) 0 0
\(751\) 5.09271i 0.185835i −0.995674 0.0929177i \(-0.970381\pi\)
0.995674 0.0929177i \(-0.0296194\pi\)
\(752\) 7.19612 39.3693i 0.262415 1.43565i
\(753\) 0 0
\(754\) 2.39871 5.12311i 0.0873557 0.186573i
\(755\) −14.6875 −0.534534
\(756\) 0 0
\(757\) −12.2462 −0.445096 −0.222548 0.974922i \(-0.571437\pi\)
−0.222548 + 0.974922i \(0.571437\pi\)
\(758\) −13.4384 + 28.7016i −0.488106 + 1.04249i
\(759\) 0 0
\(760\) 6.56155 1.72521i 0.238013 0.0625798i
\(761\) 35.2311i 1.27712i −0.769570 0.638562i \(-0.779529\pi\)
0.769570 0.638562i \(-0.220471\pi\)
\(762\) 0 0
\(763\) 2.92456 0.525853i 0.105876 0.0190372i
\(764\) 2.06913 1.72521i 0.0748585 0.0624158i
\(765\) 0 0
\(766\) 22.4095 + 10.4924i 0.809688 + 0.379107i
\(767\) 21.8836i 0.790173i
\(768\) 0 0
\(769\) 55.2311i 1.99168i 0.0911037 + 0.995841i \(0.470961\pi\)
−0.0911037 + 0.995841i \(0.529039\pi\)
\(770\) −8.67350 2.30726i −0.312571 0.0831478i
\(771\) 0 0
\(772\) 13.4384 + 16.1174i 0.483660 + 0.580079i
\(773\) 16.7386i 0.602047i −0.953617 0.301023i \(-0.902672\pi\)
0.953617 0.301023i \(-0.0973282\pi\)
\(774\) 0 0
\(775\) 6.67026 0.239603
\(776\) 19.4849 5.12311i 0.699469 0.183909i
\(777\) 0 0
\(778\) 1.43845 + 0.673500i 0.0515708 + 0.0241461i
\(779\) 17.0862i 0.612178i
\(780\) 0 0
\(781\) −14.7386 −0.527390
\(782\) 52.3104 + 24.4924i 1.87062 + 0.875847i
\(783\) 0 0
\(784\) 4.87560 + 27.5722i 0.174129 + 0.984723i
\(785\) 16.2462 0.579852
\(786\) 0 0
\(787\) −0.936426 −0.0333800 −0.0166900 0.999861i \(-0.505313\pi\)
−0.0166900 + 0.999861i \(0.505313\pi\)
\(788\) −23.0540 27.6499i −0.821264 0.984985i
\(789\) 0 0
\(790\) −5.47091 2.56155i −0.194646 0.0911360i
\(791\) 37.7382 6.78554i 1.34181 0.241266i
\(792\) 0 0
\(793\) −4.00000 −0.142044
\(794\) −8.39547 + 17.9309i −0.297944 + 0.636343i
\(795\) 0 0
\(796\) 20.5366 + 24.6307i 0.727902 + 0.873011i
\(797\) 20.2462i 0.717158i 0.933499 + 0.358579i \(0.116739\pi\)
−0.933499 + 0.358579i \(0.883261\pi\)
\(798\) 0 0
\(799\) 71.2695i 2.52133i
\(800\) −3.28078 + 4.60831i −0.115993 + 0.162928i
\(801\) 0 0
\(802\) 7.68466 + 3.59806i 0.271355 + 0.127052i
\(803\) 22.4742 0.793098
\(804\) 0 0
\(805\) 14.9309 2.68466i 0.526244 0.0946218i
\(806\) −8.00000 + 17.0862i −0.281788 + 0.601837i
\(807\) 0 0
\(808\) 18.8114 4.94602i 0.661784 0.174001i
\(809\) 18.9848 0.667472 0.333736 0.942667i \(-0.391691\pi\)
0.333736 + 0.942667i \(0.391691\pi\)
\(810\) 0 0
\(811\) 9.06897 0.318455 0.159227 0.987242i \(-0.449100\pi\)
0.159227 + 0.987242i \(0.449100\pi\)
\(812\) 8.10871 + 6.80065i 0.284560 + 0.238656i
\(813\) 0 0
\(814\) 2.87689 6.14441i 0.100835 0.215362i
\(815\) 0.936426 0.0328016
\(816\) 0 0
\(817\) 18.2462i 0.638354i
\(818\) −5.32326 + 11.3693i −0.186124 + 0.397519i
\(819\) 0 0
\(820\) −9.12311 10.9418i −0.318593 0.382105i
\(821\) 25.6155 0.893988 0.446994 0.894537i \(-0.352495\pi\)
0.446994 + 0.894537i \(0.352495\pi\)
\(822\) 0 0
\(823\) 32.1843i 1.12188i −0.827858 0.560938i \(-0.810441\pi\)
0.827858 0.560938i \(-0.189559\pi\)
\(824\) 1.05171 + 4.00000i 0.0366379 + 0.139347i
\(825\) 0 0
\(826\) −39.5646 10.5247i −1.37663 0.366200i
\(827\) 0.115279i 0.00400866i −0.999998 0.00200433i \(-0.999362\pi\)
0.999998 0.00200433i \(-0.000637998\pi\)
\(828\) 0 0
\(829\) 32.2462i 1.11996i 0.828507 + 0.559979i \(0.189191\pi\)
−0.828507 + 0.559979i \(0.810809\pi\)
\(830\) −0.561553 + 1.19935i −0.0194918 + 0.0416301i
\(831\) 0 0
\(832\) −7.86962 13.9309i −0.272830 0.482966i
\(833\) 17.3693 + 46.7386i 0.601811 + 1.61940i
\(834\) 0 0
\(835\) 2.28343i 0.0790212i
\(836\) 8.83841 7.36932i 0.305683 0.254873i
\(837\) 0 0
\(838\) −15.3610 7.19224i −0.530638 0.248452i
\(839\) −35.2242 −1.21607 −0.608037 0.793909i \(-0.708043\pi\)
−0.608037 + 0.793909i \(0.708043\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 22.5616 + 10.5636i 0.777522 + 0.364046i
\(843\) 0 0
\(844\) −28.3153 + 23.6089i −0.974654 + 0.812650i
\(845\) 9.00000i 0.309609i
\(846\) 0 0
\(847\) 13.6611 2.45635i 0.469401 0.0844010i
\(848\) 1.43845 7.86962i 0.0493965 0.270244i
\(849\) 0 0
\(850\) −4.27156 + 9.12311i −0.146513 + 0.312920i
\(851\) 11.4677i 0.393107i
\(852\) 0 0
\(853\) 7.75379i 0.265485i 0.991151 + 0.132742i \(0.0423783\pi\)
−0.991151 + 0.132742i \(0.957622\pi\)
\(854\) 1.92375 7.23182i 0.0658295 0.247468i
\(855\) 0 0
\(856\) 25.9309 6.81791i 0.886299 0.233031i
\(857\) 15.6155i 0.533416i 0.963777 + 0.266708i \(0.0859360\pi\)
−0.963777 + 0.266708i \(0.914064\pi\)
\(858\) 0 0
\(859\) −41.3686 −1.41148 −0.705739 0.708472i \(-0.749385\pi\)
−0.705739 + 0.708472i \(0.749385\pi\)
\(860\) 9.74247 + 11.6847i 0.332215 + 0.398444i
\(861\) 0 0
\(862\) −21.9309 + 46.8395i −0.746968 + 1.59536i
\(863\) 41.7792i 1.42218i 0.703101 + 0.711090i \(0.251798\pi\)
−0.703101 + 0.711090i \(0.748202\pi\)
\(864\) 0 0
\(865\) −0.246211 −0.00837143
\(866\) −6.96556 + 14.8769i −0.236699 + 0.505537i
\(867\) 0 0
\(868\) −27.0436 22.6811i −0.917920 0.769845i
\(869\) −10.2462 −0.347579
\(870\) 0 0
\(871\) −28.5539 −0.967512
\(872\) −0.807764 3.07221i −0.0273543 0.104038i
\(873\) 0 0
\(874\) −8.24782 + 17.6155i −0.278987 + 0.595854i
\(875\) 0.468213 + 2.60399i 0.0158285 + 0.0880310i
\(876\) 0 0
\(877\) −48.7386 −1.64579 −0.822893 0.568196i \(-0.807642\pi\)
−0.822893 + 0.568196i \(0.807642\pi\)
\(878\) −23.2306 10.8769i −0.783996 0.367077i
\(879\) 0 0
\(880\) −1.72521 + 9.43845i −0.0581567 + 0.318170i
\(881\) 6.63068i 0.223393i −0.993742 0.111697i \(-0.964371\pi\)
0.993742 0.111697i \(-0.0356285\pi\)
\(882\) 0 0
\(883\) 13.4558i 0.452824i 0.974032 + 0.226412i \(0.0726996\pi\)
−0.974032 + 0.226412i \(0.927300\pi\)
\(884\) −18.2462 21.8836i −0.613686 0.736027i
\(885\) 0 0
\(886\) 18.1771 38.8222i 0.610671 1.30426i
\(887\) −17.7274 −0.595227 −0.297613 0.954686i \(-0.596191\pi\)
−0.297613 + 0.954686i \(0.596191\pi\)
\(888\) 0 0
\(889\) −6.19224 34.4384i −0.207681 1.15503i
\(890\) 15.3693 + 7.19612i 0.515181 + 0.241214i
\(891\) 0 0
\(892\) 16.5604 + 19.8617i 0.554483 + 0.665020i
\(893\) 24.0000 0.803129
\(894\) 0 0
\(895\) −0.525853 −0.0175773
\(896\) 28.9712 7.52802i 0.967859 0.251493i
\(897\) 0 0
\(898\) 32.8078 + 15.3610i 1.09481 + 0.512604i
\(899\) −13.3405 −0.444932
\(900\) 0 0
\(901\) 14.2462i 0.474610i
\(902\) −21.8836 10.2462i −0.728646 0.341162i
\(903\) 0 0
\(904\) −10.4233 39.6434i −0.346674 1.31852i
\(905\) −6.87689 −0.228596
\(906\) 0 0
\(907\) 14.5075i 0.481714i −0.970561 0.240857i \(-0.922572\pi\)
0.970561 0.240857i \(-0.0774285\pi\)
\(908\) 18.2856 + 21.9309i 0.606829 + 0.727801i
\(909\) 0 0
\(910\) −7.23182 1.92375i −0.239732 0.0637718i
\(911\) 10.9418i 0.362519i 0.983435 + 0.181259i \(0.0580174\pi\)
−0.983435 + 0.181259i \(0.941983\pi\)
\(912\) 0 0
\(913\) 2.24621i 0.0743387i
\(914\) −7.68466 3.59806i −0.254186 0.119013i
\(915\) 0 0
\(916\) 32.4473 27.0540i 1.07209 0.893889i
\(917\) −36.1080 + 6.49242i −1.19239 + 0.214399i
\(918\) 0 0
\(919\) 29.9009i 0.986340i −0.869933 0.493170i \(-0.835838\pi\)
0.869933 0.493170i \(-0.164162\pi\)
\(920\) −4.12391 15.6847i −0.135961 0.517108i
\(921\) 0 0
\(922\) 22.5571 48.1771i 0.742880 1.58663i
\(923\) −12.2888 −0.404492
\(924\) 0 0
\(925\) −2.00000 −0.0657596
\(926\) 13.1922 28.1757i 0.433524 0.925911i
\(927\) 0 0
\(928\) 6.56155 9.21662i 0.215394 0.302550i
\(929\) 12.8769i 0.422477i 0.977435 + 0.211239i \(0.0677497\pi\)
−0.977435 + 0.211239i \(0.932250\pi\)
\(930\) 0 0
\(931\) −15.7392 + 5.84912i −0.515833 + 0.191697i
\(932\) −31.0540 37.2447i −1.01721 1.21999i
\(933\) 0 0
\(934\) 2.54635 + 1.19224i 0.0833192 + 0.0390112i
\(935\) 17.0862i 0.558780i
\(936\) 0 0
\(937\) 36.1080i 1.17960i 0.807551 + 0.589798i \(0.200793\pi\)
−0.807551 + 0.589798i \(0.799207\pi\)
\(938\) 13.7327 51.6242i 0.448387 1.68559i
\(939\) 0 0
\(940\) −15.3693 + 12.8147i −0.501292 + 0.417969i
\(941\) 51.3693i 1.67459i −0.546750 0.837296i \(-0.684135\pi\)
0.546750 0.837296i \(-0.315865\pi\)
\(942\) 0 0
\(943\) 40.8427 1.33002
\(944\) −7.86962 + 43.0540i −0.256134 + 1.40129i
\(945\) 0 0
\(946\) 23.3693 + 10.9418i 0.759802 + 0.355749i
\(947\) 18.8438i 0.612341i −0.951977 0.306171i \(-0.900952\pi\)
0.951977 0.306171i \(-0.0990478\pi\)
\(948\) 0 0
\(949\) 18.7386 0.608282
\(950\) −3.07221 1.43845i −0.0996755 0.0466694i
\(951\) 0 0
\(952\) 48.3399 22.4636i 1.56671 0.728051i
\(953\) −11.7538 −0.380743 −0.190371 0.981712i \(-0.560969\pi\)
−0.190371 + 0.981712i \(0.560969\pi\)
\(954\) 0 0
\(955\) −1.34700 −0.0435879
\(956\) 19.6847 16.4127i 0.636647 0.530826i
\(957\) 0 0
\(958\) 0 0
\(959\) 36.4559 6.55498i 1.17722 0.211671i
\(960\) 0 0
\(961\) 13.4924 0.435239
\(962\) 2.39871 5.12311i 0.0773374 0.165176i
\(963\) 0 0
\(964\) −23.9871 + 20.0000i −0.772571 + 0.644157i
\(965\) 10.4924i 0.337763i
\(966\) 0 0
\(967\) 55.1197i 1.77253i 0.463179 + 0.886265i \(0.346709\pi\)
−0.463179 + 0.886265i \(0.653291\pi\)
\(968\) −3.77320 14.3508i −0.121275 0.461251i
\(969\) 0 0
\(970\) −9.12311 4.27156i −0.292925 0.137151i
\(971\) 0.525853 0.0168754 0.00843771 0.999964i \(-0.497314\pi\)
0.00843771 + 0.999964i \(0.497314\pi\)
\(972\) 0 0
\(973\) −3.50758 + 0.630683i −0.112448 + 0.0202188i
\(974\) −11.4384 + 24.4300i −0.366511 + 0.782788i
\(975\) 0 0
\(976\) −7.86962 1.43845i −0.251900 0.0460436i
\(977\) 10.4924 0.335682 0.167841 0.985814i \(-0.446320\pi\)
0.167841 + 0.985814i \(0.446320\pi\)
\(978\) 0 0
\(979\) 28.7845 0.919956
\(980\) 6.95611 12.1496i 0.222205 0.388104i
\(981\) 0 0
\(982\) 8.17708 17.4644i 0.260941 0.557313i
\(983\) 12.6994 0.405048 0.202524 0.979277i \(-0.435086\pi\)
0.202524 + 0.979277i \(0.435086\pi\)
\(984\) 0 0
\(985\) 18.0000i 0.573528i
\(986\) 8.54312 18.2462i 0.272068 0.581078i
\(987\) 0 0
\(988\) 7.36932 6.14441i 0.234449 0.195480i
\(989\) −43.6155 −1.38689
\(990\) 0 0
\(991\) 34.4678i 1.09490i −0.836837 0.547452i \(-0.815598\pi\)
0.836837 0.547452i \(-0.184402\pi\)
\(992\) −21.8836 + 30.7386i −0.694806 + 0.975953i
\(993\) 0 0
\(994\) 5.91016 22.2176i 0.187459 0.704700i
\(995\) 16.0345i 0.508329i
\(996\) 0 0
\(997\) 38.4924i 1.21907i −0.792760 0.609534i \(-0.791357\pi\)
0.792760 0.609534i \(-0.208643\pi\)
\(998\) 16.3153 34.8460i 0.516453 1.10303i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1260.2.c.c.811.1 8
3.2 odd 2 140.2.g.c.111.7 yes 8
4.3 odd 2 inner 1260.2.c.c.811.3 8
7.6 odd 2 inner 1260.2.c.c.811.2 8
12.11 even 2 140.2.g.c.111.6 yes 8
15.2 even 4 700.2.c.j.699.4 8
15.8 even 4 700.2.c.i.699.5 8
15.14 odd 2 700.2.g.j.251.2 8
21.2 odd 6 980.2.o.e.31.6 16
21.5 even 6 980.2.o.e.31.5 16
21.11 odd 6 980.2.o.e.411.2 16
21.17 even 6 980.2.o.e.411.1 16
21.20 even 2 140.2.g.c.111.8 yes 8
24.5 odd 2 2240.2.k.e.1791.5 8
24.11 even 2 2240.2.k.e.1791.3 8
28.27 even 2 inner 1260.2.c.c.811.4 8
60.23 odd 4 700.2.c.i.699.3 8
60.47 odd 4 700.2.c.j.699.6 8
60.59 even 2 700.2.g.j.251.3 8
84.11 even 6 980.2.o.e.411.5 16
84.23 even 6 980.2.o.e.31.1 16
84.47 odd 6 980.2.o.e.31.2 16
84.59 odd 6 980.2.o.e.411.6 16
84.83 odd 2 140.2.g.c.111.5 8
105.62 odd 4 700.2.c.i.699.4 8
105.83 odd 4 700.2.c.j.699.5 8
105.104 even 2 700.2.g.j.251.1 8
168.83 odd 2 2240.2.k.e.1791.6 8
168.125 even 2 2240.2.k.e.1791.4 8
420.83 even 4 700.2.c.j.699.3 8
420.167 even 4 700.2.c.i.699.6 8
420.419 odd 2 700.2.g.j.251.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.g.c.111.5 8 84.83 odd 2
140.2.g.c.111.6 yes 8 12.11 even 2
140.2.g.c.111.7 yes 8 3.2 odd 2
140.2.g.c.111.8 yes 8 21.20 even 2
700.2.c.i.699.3 8 60.23 odd 4
700.2.c.i.699.4 8 105.62 odd 4
700.2.c.i.699.5 8 15.8 even 4
700.2.c.i.699.6 8 420.167 even 4
700.2.c.j.699.3 8 420.83 even 4
700.2.c.j.699.4 8 15.2 even 4
700.2.c.j.699.5 8 105.83 odd 4
700.2.c.j.699.6 8 60.47 odd 4
700.2.g.j.251.1 8 105.104 even 2
700.2.g.j.251.2 8 15.14 odd 2
700.2.g.j.251.3 8 60.59 even 2
700.2.g.j.251.4 8 420.419 odd 2
980.2.o.e.31.1 16 84.23 even 6
980.2.o.e.31.2 16 84.47 odd 6
980.2.o.e.31.5 16 21.5 even 6
980.2.o.e.31.6 16 21.2 odd 6
980.2.o.e.411.1 16 21.17 even 6
980.2.o.e.411.2 16 21.11 odd 6
980.2.o.e.411.5 16 84.11 even 6
980.2.o.e.411.6 16 84.59 odd 6
1260.2.c.c.811.1 8 1.1 even 1 trivial
1260.2.c.c.811.2 8 7.6 odd 2 inner
1260.2.c.c.811.3 8 4.3 odd 2 inner
1260.2.c.c.811.4 8 28.27 even 2 inner
2240.2.k.e.1791.3 8 24.11 even 2
2240.2.k.e.1791.4 8 168.125 even 2
2240.2.k.e.1791.5 8 24.5 odd 2
2240.2.k.e.1791.6 8 168.83 odd 2