Properties

Label 256.4.g.b.97.5
Level $256$
Weight $4$
Character 256.97
Analytic conductor $15.104$
Analytic rank $0$
Dimension $44$
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] = [256,4,Mod(33,256)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(256, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("256.33");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 256.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(15.1044889615\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 97.5
Character \(\chi\) \(=\) 256.97
Dual form 256.4.g.b.161.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.143768 + 0.0595506i) q^{3} +(0.767542 - 1.85301i) q^{5} +(-5.47741 - 5.47741i) q^{7} +(-19.0748 + 19.0748i) q^{9} +O(q^{10})\) \(q+(-0.143768 + 0.0595506i) q^{3} +(0.767542 - 1.85301i) q^{5} +(-5.47741 - 5.47741i) q^{7} +(-19.0748 + 19.0748i) q^{9} +(36.9342 + 15.2986i) q^{11} +(-4.49594 - 10.8542i) q^{13} +0.312111i q^{15} +53.8999i q^{17} +(31.9796 + 77.2056i) q^{19} +(1.11366 + 0.461293i) q^{21} +(50.0867 - 50.0867i) q^{23} +(85.5438 + 85.5438i) q^{25} +(3.21429 - 7.75999i) q^{27} +(-156.098 + 64.6581i) q^{29} +207.668 q^{31} -6.22100 q^{33} +(-14.3538 + 5.94555i) q^{35} +(-73.7055 + 177.941i) q^{37} +(1.29274 + 1.29274i) q^{39} +(-293.943 + 293.943i) q^{41} +(342.438 + 141.843i) q^{43} +(20.7050 + 49.9864i) q^{45} +510.799i q^{47} -282.996i q^{49} +(-3.20978 - 7.74908i) q^{51} +(590.228 + 244.481i) q^{53} +(56.6971 - 56.6971i) q^{55} +(-9.19528 - 9.19528i) q^{57} +(257.808 - 622.403i) q^{59} +(-424.302 + 175.752i) q^{61} +208.961 q^{63} -23.5637 q^{65} +(-482.813 + 199.988i) q^{67} +(-4.21817 + 10.1836i) q^{69} +(-199.873 - 199.873i) q^{71} +(-127.360 + 127.360i) q^{73} +(-17.3927 - 7.20427i) q^{75} +(-118.507 - 286.101i) q^{77} +237.438i q^{79} -727.039i q^{81} +(-9.62194 - 23.2294i) q^{83} +(99.8771 + 41.3704i) q^{85} +(18.5915 - 18.5915i) q^{87} +(329.123 + 329.123i) q^{89} +(-34.8265 + 84.0787i) q^{91} +(-29.8560 + 12.3667i) q^{93} +167.608 q^{95} +776.518 q^{97} +(-996.329 + 412.693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(255\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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
\(3\) −0.143768 + 0.0595506i −0.0276682 + 0.0114605i −0.396475 0.918046i \(-0.629767\pi\)
0.368806 + 0.929506i \(0.379767\pi\)
\(4\) 0 0
\(5\) 0.767542 1.85301i 0.0686510 0.165738i −0.885830 0.464010i \(-0.846410\pi\)
0.954481 + 0.298272i \(0.0964102\pi\)
\(6\) 0 0
\(7\) −5.47741 5.47741i −0.295752 0.295752i 0.543595 0.839348i \(-0.317063\pi\)
−0.839348 + 0.543595i \(0.817063\pi\)
\(8\) 0 0
\(9\) −19.0748 + 19.0748i −0.706473 + 0.706473i
\(10\) 0 0
\(11\) 36.9342 + 15.2986i 1.01237 + 0.419338i 0.826319 0.563202i \(-0.190431\pi\)
0.186052 + 0.982540i \(0.440431\pi\)
\(12\) 0 0
\(13\) −4.49594 10.8542i −0.0959191 0.231569i 0.868636 0.495451i \(-0.164997\pi\)
−0.964555 + 0.263882i \(0.914997\pi\)
\(14\) 0 0
\(15\) 0.312111i 0.00537245i
\(16\) 0 0
\(17\) 53.8999i 0.768980i 0.923129 + 0.384490i \(0.125623\pi\)
−0.923129 + 0.384490i \(0.874377\pi\)
\(18\) 0 0
\(19\) 31.9796 + 77.2056i 0.386138 + 0.932220i 0.990750 + 0.135700i \(0.0433282\pi\)
−0.604612 + 0.796520i \(0.706672\pi\)
\(20\) 0 0
\(21\) 1.11366 + 0.461293i 0.0115724 + 0.00479344i
\(22\) 0 0
\(23\) 50.0867 50.0867i 0.454078 0.454078i −0.442628 0.896706i \(-0.645954\pi\)
0.896706 + 0.442628i \(0.145954\pi\)
\(24\) 0 0
\(25\) 85.5438 + 85.5438i 0.684351 + 0.684351i
\(26\) 0 0
\(27\) 3.21429 7.75999i 0.0229108 0.0553115i
\(28\) 0 0
\(29\) −156.098 + 64.6581i −0.999543 + 0.414024i −0.821629 0.570022i \(-0.806935\pi\)
−0.177913 + 0.984046i \(0.556935\pi\)
\(30\) 0 0
\(31\) 207.668 1.20317 0.601584 0.798810i \(-0.294537\pi\)
0.601584 + 0.798810i \(0.294537\pi\)
\(32\) 0 0
\(33\) −6.22100 −0.0328163
\(34\) 0 0
\(35\) −14.3538 + 5.94555i −0.0693211 + 0.0287138i
\(36\) 0 0
\(37\) −73.7055 + 177.941i −0.327489 + 0.790629i 0.671288 + 0.741197i \(0.265741\pi\)
−0.998777 + 0.0494328i \(0.984259\pi\)
\(38\) 0 0
\(39\) 1.29274 + 1.29274i 0.00530781 + 0.00530781i
\(40\) 0 0
\(41\) −293.943 + 293.943i −1.11966 + 1.11966i −0.127875 + 0.991790i \(0.540815\pi\)
−0.991790 + 0.127875i \(0.959185\pi\)
\(42\) 0 0
\(43\) 342.438 + 141.843i 1.21445 + 0.503041i 0.895641 0.444778i \(-0.146717\pi\)
0.318808 + 0.947819i \(0.396717\pi\)
\(44\) 0 0
\(45\) 20.7050 + 49.9864i 0.0685894 + 0.165590i
\(46\) 0 0
\(47\) 510.799i 1.58527i 0.609697 + 0.792635i \(0.291291\pi\)
−0.609697 + 0.792635i \(0.708709\pi\)
\(48\) 0 0
\(49\) 282.996i 0.825061i
\(50\) 0 0
\(51\) −3.20978 7.74908i −0.00881291 0.0212762i
\(52\) 0 0
\(53\) 590.228 + 244.481i 1.52970 + 0.633622i 0.979506 0.201414i \(-0.0645538\pi\)
0.550194 + 0.835037i \(0.314554\pi\)
\(54\) 0 0
\(55\) 56.6971 56.6971i 0.139001 0.139001i
\(56\) 0 0
\(57\) −9.19528 9.19528i −0.0213675 0.0213675i
\(58\) 0 0
\(59\) 257.808 622.403i 0.568877 1.37339i −0.333626 0.942706i \(-0.608272\pi\)
0.902503 0.430685i \(-0.141728\pi\)
\(60\) 0 0
\(61\) −424.302 + 175.752i −0.890596 + 0.368897i −0.780597 0.625035i \(-0.785085\pi\)
−0.109999 + 0.993932i \(0.535085\pi\)
\(62\) 0 0
\(63\) 208.961 0.417882
\(64\) 0 0
\(65\) −23.5637 −0.0449648
\(66\) 0 0
\(67\) −482.813 + 199.988i −0.880373 + 0.364663i −0.776642 0.629943i \(-0.783078\pi\)
−0.103732 + 0.994605i \(0.533078\pi\)
\(68\) 0 0
\(69\) −4.21817 + 10.1836i −0.00735953 + 0.0177675i
\(70\) 0 0
\(71\) −199.873 199.873i −0.334092 0.334092i 0.520046 0.854138i \(-0.325915\pi\)
−0.854138 + 0.520046i \(0.825915\pi\)
\(72\) 0 0
\(73\) −127.360 + 127.360i −0.204197 + 0.204197i −0.801796 0.597598i \(-0.796122\pi\)
0.597598 + 0.801796i \(0.296122\pi\)
\(74\) 0 0
\(75\) −17.3927 7.20427i −0.0267777 0.0110917i
\(76\) 0 0
\(77\) −118.507 286.101i −0.175391 0.423431i
\(78\) 0 0
\(79\) 237.438i 0.338150i 0.985603 + 0.169075i \(0.0540780\pi\)
−0.985603 + 0.169075i \(0.945922\pi\)
\(80\) 0 0
\(81\) 727.039i 0.997310i
\(82\) 0 0
\(83\) −9.62194 23.2294i −0.0127246 0.0307200i 0.917390 0.397991i \(-0.130292\pi\)
−0.930114 + 0.367271i \(0.880292\pi\)
\(84\) 0 0
\(85\) 99.8771 + 41.3704i 0.127449 + 0.0527912i
\(86\) 0 0
\(87\) 18.5915 18.5915i 0.0229106 0.0229106i
\(88\) 0 0
\(89\) 329.123 + 329.123i 0.391989 + 0.391989i 0.875396 0.483407i \(-0.160601\pi\)
−0.483407 + 0.875396i \(0.660601\pi\)
\(90\) 0 0
\(91\) −34.8265 + 84.0787i −0.0401188 + 0.0968554i
\(92\) 0 0
\(93\) −29.8560 + 12.3667i −0.0332894 + 0.0137889i
\(94\) 0 0
\(95\) 167.608 0.181013
\(96\) 0 0
\(97\) 776.518 0.812819 0.406410 0.913691i \(-0.366781\pi\)
0.406410 + 0.913691i \(0.366781\pi\)
\(98\) 0 0
\(99\) −996.329 + 412.693i −1.01146 + 0.418962i
\(100\) 0 0
\(101\) 370.061 893.405i 0.364578 0.880170i −0.630040 0.776563i \(-0.716962\pi\)
0.994618 0.103607i \(-0.0330384\pi\)
\(102\) 0 0
\(103\) −1445.50 1445.50i −1.38281 1.38281i −0.839595 0.543212i \(-0.817208\pi\)
−0.543212 0.839595i \(-0.682792\pi\)
\(104\) 0 0
\(105\) 1.70956 1.70956i 0.00158891 0.00158891i
\(106\) 0 0
\(107\) 8.88527 + 3.68040i 0.00802777 + 0.00332521i 0.386694 0.922208i \(-0.373617\pi\)
−0.378666 + 0.925533i \(0.623617\pi\)
\(108\) 0 0
\(109\) −648.092 1564.63i −0.569505 1.37491i −0.901973 0.431791i \(-0.857882\pi\)
0.332469 0.943114i \(-0.392118\pi\)
\(110\) 0 0
\(111\) 29.9714i 0.0256285i
\(112\) 0 0
\(113\) 729.808i 0.607562i −0.952742 0.303781i \(-0.901751\pi\)
0.952742 0.303781i \(-0.0982492\pi\)
\(114\) 0 0
\(115\) −54.3675 131.255i −0.0440852 0.106431i
\(116\) 0 0
\(117\) 292.799 + 121.281i 0.231362 + 0.0958331i
\(118\) 0 0
\(119\) 295.232 295.232i 0.227427 0.227427i
\(120\) 0 0
\(121\) 188.928 + 188.928i 0.141944 + 0.141944i
\(122\) 0 0
\(123\) 24.7551 59.7642i 0.0181471 0.0438110i
\(124\) 0 0
\(125\) 455.798 188.798i 0.326143 0.135093i
\(126\) 0 0
\(127\) −1559.09 −1.08934 −0.544671 0.838650i \(-0.683346\pi\)
−0.544671 + 0.838650i \(0.683346\pi\)
\(128\) 0 0
\(129\) −57.6784 −0.0393667
\(130\) 0 0
\(131\) −508.328 + 210.556i −0.339029 + 0.140431i −0.545701 0.837980i \(-0.683737\pi\)
0.206672 + 0.978410i \(0.433737\pi\)
\(132\) 0 0
\(133\) 247.721 598.052i 0.161505 0.389907i
\(134\) 0 0
\(135\) −11.9122 11.9122i −0.00759438 0.00759438i
\(136\) 0 0
\(137\) −118.150 + 118.150i −0.0736806 + 0.0736806i −0.742987 0.669306i \(-0.766591\pi\)
0.669306 + 0.742987i \(0.266591\pi\)
\(138\) 0 0
\(139\) −1.49385 0.618775i −0.000911562 0.000377581i 0.382228 0.924068i \(-0.375157\pi\)
−0.383139 + 0.923691i \(0.625157\pi\)
\(140\) 0 0
\(141\) −30.4184 73.4365i −0.0181680 0.0438615i
\(142\) 0 0
\(143\) 469.671i 0.274657i
\(144\) 0 0
\(145\) 338.880i 0.194086i
\(146\) 0 0
\(147\) 16.8526 + 40.6858i 0.00945563 + 0.0228279i
\(148\) 0 0
\(149\) 527.451 + 218.478i 0.290003 + 0.120123i 0.522942 0.852368i \(-0.324834\pi\)
−0.232939 + 0.972491i \(0.574834\pi\)
\(150\) 0 0
\(151\) −893.493 + 893.493i −0.481533 + 0.481533i −0.905621 0.424088i \(-0.860595\pi\)
0.424088 + 0.905621i \(0.360595\pi\)
\(152\) 0 0
\(153\) −1028.13 1028.13i −0.543263 0.543263i
\(154\) 0 0
\(155\) 159.394 384.810i 0.0825987 0.199411i
\(156\) 0 0
\(157\) 277.684 115.020i 0.141157 0.0584690i −0.310987 0.950414i \(-0.600659\pi\)
0.452143 + 0.891945i \(0.350659\pi\)
\(158\) 0 0
\(159\) −99.4149 −0.0495856
\(160\) 0 0
\(161\) −548.690 −0.268589
\(162\) 0 0
\(163\) 2082.24 862.493i 1.00058 0.414452i 0.178567 0.983928i \(-0.442854\pi\)
0.822008 + 0.569476i \(0.192854\pi\)
\(164\) 0 0
\(165\) −4.77488 + 11.5276i −0.00225287 + 0.00543891i
\(166\) 0 0
\(167\) 1423.70 + 1423.70i 0.659697 + 0.659697i 0.955308 0.295611i \(-0.0955234\pi\)
−0.295611 + 0.955308i \(0.595523\pi\)
\(168\) 0 0
\(169\) 1455.91 1455.91i 0.662683 0.662683i
\(170\) 0 0
\(171\) −2082.68 862.675i −0.931384 0.385792i
\(172\) 0 0
\(173\) 1398.51 + 3376.31i 0.614606 + 1.48379i 0.857889 + 0.513835i \(0.171776\pi\)
−0.243283 + 0.969955i \(0.578224\pi\)
\(174\) 0 0
\(175\) 937.117i 0.404796i
\(176\) 0 0
\(177\) 104.834i 0.0445188i
\(178\) 0 0
\(179\) −664.405 1604.01i −0.277430 0.669775i 0.722333 0.691545i \(-0.243070\pi\)
−0.999763 + 0.0217704i \(0.993070\pi\)
\(180\) 0 0
\(181\) −2978.79 1233.86i −1.22327 0.506695i −0.324822 0.945775i \(-0.605304\pi\)
−0.898448 + 0.439080i \(0.855304\pi\)
\(182\) 0 0
\(183\) 50.5350 50.5350i 0.0204134 0.0204134i
\(184\) 0 0
\(185\) 273.154 + 273.154i 0.108555 + 0.108555i
\(186\) 0 0
\(187\) −824.596 + 1990.75i −0.322462 + 0.778493i
\(188\) 0 0
\(189\) −60.1106 + 24.8986i −0.0231344 + 0.00958259i
\(190\) 0 0
\(191\) 3559.03 1.34829 0.674143 0.738601i \(-0.264513\pi\)
0.674143 + 0.738601i \(0.264513\pi\)
\(192\) 0 0
\(193\) 150.055 0.0559648 0.0279824 0.999608i \(-0.491092\pi\)
0.0279824 + 0.999608i \(0.491092\pi\)
\(194\) 0 0
\(195\) 3.38770 1.40323i 0.00124409 0.000515320i
\(196\) 0 0
\(197\) −1519.90 + 3669.37i −0.549689 + 1.32707i 0.368022 + 0.929817i \(0.380035\pi\)
−0.917711 + 0.397249i \(0.869965\pi\)
\(198\) 0 0
\(199\) 3083.86 + 3083.86i 1.09854 + 1.09854i 0.994582 + 0.103955i \(0.0331499\pi\)
0.103955 + 0.994582i \(0.466850\pi\)
\(200\) 0 0
\(201\) 57.5037 57.5037i 0.0201791 0.0201791i
\(202\) 0 0
\(203\) 1209.17 + 500.856i 0.418066 + 0.173168i
\(204\) 0 0
\(205\) 319.066 + 770.294i 0.108705 + 0.262437i
\(206\) 0 0
\(207\) 1910.78i 0.641587i
\(208\) 0 0
\(209\) 3340.77i 1.10567i
\(210\) 0 0
\(211\) 868.746 + 2097.34i 0.283445 + 0.684297i 0.999911 0.0133249i \(-0.00424156\pi\)
−0.716466 + 0.697622i \(0.754242\pi\)
\(212\) 0 0
\(213\) 40.6379 + 16.8328i 0.0130726 + 0.00541485i
\(214\) 0 0
\(215\) 525.671 525.671i 0.166746 0.166746i
\(216\) 0 0
\(217\) −1137.48 1137.48i −0.355840 0.355840i
\(218\) 0 0
\(219\) 10.7260 25.8947i 0.00330956 0.00798998i
\(220\) 0 0
\(221\) 585.038 242.331i 0.178072 0.0737599i
\(222\) 0 0
\(223\) −3747.63 −1.12538 −0.562690 0.826668i \(-0.690234\pi\)
−0.562690 + 0.826668i \(0.690234\pi\)
\(224\) 0 0
\(225\) −3263.46 −0.966950
\(226\) 0 0
\(227\) 5533.41 2292.01i 1.61791 0.670159i 0.624107 0.781339i \(-0.285463\pi\)
0.993800 + 0.111180i \(0.0354629\pi\)
\(228\) 0 0
\(229\) −719.189 + 1736.28i −0.207534 + 0.501032i −0.993034 0.117830i \(-0.962406\pi\)
0.785500 + 0.618862i \(0.212406\pi\)
\(230\) 0 0
\(231\) 34.0750 + 34.0750i 0.00970549 + 0.00970549i
\(232\) 0 0
\(233\) −575.901 + 575.901i −0.161925 + 0.161925i −0.783419 0.621494i \(-0.786526\pi\)
0.621494 + 0.783419i \(0.286526\pi\)
\(234\) 0 0
\(235\) 946.515 + 392.059i 0.262740 + 0.108830i
\(236\) 0 0
\(237\) −14.1396 34.1360i −0.00387538 0.00935599i
\(238\) 0 0
\(239\) 3712.45i 1.00476i −0.864646 0.502381i \(-0.832457\pi\)
0.864646 0.502381i \(-0.167543\pi\)
\(240\) 0 0
\(241\) 6285.59i 1.68004i 0.542553 + 0.840021i \(0.317458\pi\)
−0.542553 + 0.840021i \(0.682542\pi\)
\(242\) 0 0
\(243\) 130.082 + 314.045i 0.0343405 + 0.0829052i
\(244\) 0 0
\(245\) −524.394 217.211i −0.136744 0.0566413i
\(246\) 0 0
\(247\) 694.223 694.223i 0.178835 0.178835i
\(248\) 0 0
\(249\) 2.76665 + 2.76665i 0.000704135 + 0.000704135i
\(250\) 0 0
\(251\) −639.477 + 1543.83i −0.160810 + 0.388231i −0.983662 0.180026i \(-0.942382\pi\)
0.822852 + 0.568256i \(0.192382\pi\)
\(252\) 0 0
\(253\) 2616.17 1083.65i 0.650108 0.269283i
\(254\) 0 0
\(255\) −16.8228 −0.00413130
\(256\) 0 0
\(257\) 42.7546 0.0103773 0.00518864 0.999987i \(-0.498348\pi\)
0.00518864 + 0.999987i \(0.498348\pi\)
\(258\) 0 0
\(259\) 1378.37 570.939i 0.330686 0.136975i
\(260\) 0 0
\(261\) 1744.20 4210.88i 0.413653 0.998646i
\(262\) 0 0
\(263\) 2360.67 + 2360.67i 0.553479 + 0.553479i 0.927443 0.373964i \(-0.122002\pi\)
−0.373964 + 0.927443i \(0.622002\pi\)
\(264\) 0 0
\(265\) 906.050 906.050i 0.210031 0.210031i
\(266\) 0 0
\(267\) −66.9169 27.7179i −0.0153380 0.00635321i
\(268\) 0 0
\(269\) 1665.10 + 4019.90i 0.377408 + 0.911143i 0.992450 + 0.122649i \(0.0391389\pi\)
−0.615042 + 0.788494i \(0.710861\pi\)
\(270\) 0 0
\(271\) 4547.41i 1.01932i −0.860376 0.509660i \(-0.829771\pi\)
0.860376 0.509660i \(-0.170229\pi\)
\(272\) 0 0
\(273\) 14.1618i 0.00313959i
\(274\) 0 0
\(275\) 1850.79 + 4468.20i 0.405843 + 0.979791i
\(276\) 0 0
\(277\) −6747.39 2794.86i −1.46358 0.606234i −0.498194 0.867065i \(-0.666003\pi\)
−0.965384 + 0.260831i \(0.916003\pi\)
\(278\) 0 0
\(279\) −3961.21 + 3961.21i −0.850005 + 0.850005i
\(280\) 0 0
\(281\) 3178.42 + 3178.42i 0.674764 + 0.674764i 0.958811 0.284046i \(-0.0916770\pi\)
−0.284046 + 0.958811i \(0.591677\pi\)
\(282\) 0 0
\(283\) −1868.13 + 4510.06i −0.392399 + 0.947334i 0.597018 + 0.802228i \(0.296352\pi\)
−0.989416 + 0.145106i \(0.953648\pi\)
\(284\) 0 0
\(285\) −24.0967 + 9.98118i −0.00500830 + 0.00207451i
\(286\) 0 0
\(287\) 3220.10 0.662287
\(288\) 0 0
\(289\) 2007.80 0.408670
\(290\) 0 0
\(291\) −111.638 + 46.2421i −0.0224892 + 0.00931533i
\(292\) 0 0
\(293\) −509.398 + 1229.79i −0.101568 + 0.245206i −0.966492 0.256696i \(-0.917366\pi\)
0.864925 + 0.501902i \(0.167366\pi\)
\(294\) 0 0
\(295\) −955.441 955.441i −0.188569 0.188569i
\(296\) 0 0
\(297\) 237.435 237.435i 0.0463884 0.0463884i
\(298\) 0 0
\(299\) −768.835 318.462i −0.148705 0.0615957i
\(300\) 0 0
\(301\) −1098.74 2652.60i −0.210401 0.507952i
\(302\) 0 0
\(303\) 150.480i 0.0285309i
\(304\) 0 0
\(305\) 921.133i 0.172931i
\(306\) 0 0
\(307\) −2519.05 6081.52i −0.468305 1.13059i −0.964903 0.262607i \(-0.915418\pi\)
0.496598 0.867981i \(-0.334582\pi\)
\(308\) 0 0
\(309\) 293.897 + 121.736i 0.0541074 + 0.0224120i
\(310\) 0 0
\(311\) 5470.06 5470.06i 0.997358 0.997358i −0.00263825 0.999997i \(-0.500840\pi\)
0.999997 + 0.00263825i \(0.000839783\pi\)
\(312\) 0 0
\(313\) −4168.95 4168.95i −0.752853 0.752853i 0.222158 0.975011i \(-0.428690\pi\)
−0.975011 + 0.222158i \(0.928690\pi\)
\(314\) 0 0
\(315\) 160.386 387.206i 0.0286880 0.0692590i
\(316\) 0 0
\(317\) −3013.16 + 1248.09i −0.533868 + 0.221135i −0.633296 0.773909i \(-0.718299\pi\)
0.0994284 + 0.995045i \(0.468299\pi\)
\(318\) 0 0
\(319\) −6754.55 −1.18552
\(320\) 0 0
\(321\) −1.49659 −0.000260222
\(322\) 0 0
\(323\) −4161.38 + 1723.70i −0.716858 + 0.296932i
\(324\) 0 0
\(325\) 543.906 1313.11i 0.0928322 0.224117i
\(326\) 0 0
\(327\) 186.350 + 186.350i 0.0315143 + 0.0315143i
\(328\) 0 0
\(329\) 2797.85 2797.85i 0.468847 0.468847i
\(330\) 0 0
\(331\) −5175.95 2143.95i −0.859504 0.356018i −0.0909902 0.995852i \(-0.529003\pi\)
−0.768513 + 0.639834i \(0.779003\pi\)
\(332\) 0 0
\(333\) −1988.26 4800.09i −0.327196 0.789920i
\(334\) 0 0
\(335\) 1048.16i 0.170946i
\(336\) 0 0
\(337\) 6275.84i 1.01444i −0.861816 0.507220i \(-0.830673\pi\)
0.861816 0.507220i \(-0.169327\pi\)
\(338\) 0 0
\(339\) 43.4605 + 104.923i 0.00696298 + 0.0168101i
\(340\) 0 0
\(341\) 7670.04 + 3177.03i 1.21805 + 0.504534i
\(342\) 0 0
\(343\) −3428.84 + 3428.84i −0.539766 + 0.539766i
\(344\) 0 0
\(345\) 15.6326 + 15.6326i 0.00243951 + 0.00243951i
\(346\) 0 0
\(347\) 2873.53 6937.32i 0.444551 1.07324i −0.529782 0.848134i \(-0.677726\pi\)
0.974334 0.225108i \(-0.0722736\pi\)
\(348\) 0 0
\(349\) 4992.75 2068.06i 0.765775 0.317194i 0.0346154 0.999401i \(-0.488979\pi\)
0.731160 + 0.682206i \(0.238979\pi\)
\(350\) 0 0
\(351\) −98.6794 −0.0150060
\(352\) 0 0
\(353\) 1773.18 0.267356 0.133678 0.991025i \(-0.457321\pi\)
0.133678 + 0.991025i \(0.457321\pi\)
\(354\) 0 0
\(355\) −523.777 + 216.956i −0.0783076 + 0.0324361i
\(356\) 0 0
\(357\) −24.8636 + 60.0261i −0.00368606 + 0.00889894i
\(358\) 0 0
\(359\) −7338.52 7338.52i −1.07886 1.07886i −0.996612 0.0822522i \(-0.973789\pi\)
−0.0822522 0.996612i \(-0.526211\pi\)
\(360\) 0 0
\(361\) −87.9631 + 87.9631i −0.0128245 + 0.0128245i
\(362\) 0 0
\(363\) −38.4125 15.9110i −0.00555409 0.00230058i
\(364\) 0 0
\(365\) 138.246 + 333.754i 0.0198249 + 0.0478617i
\(366\) 0 0
\(367\) 8883.05i 1.26346i 0.775187 + 0.631732i \(0.217656\pi\)
−0.775187 + 0.631732i \(0.782344\pi\)
\(368\) 0 0
\(369\) 11213.8i 1.58203i
\(370\) 0 0
\(371\) −1893.80 4572.04i −0.265017 0.639808i
\(372\) 0 0
\(373\) 3736.23 + 1547.60i 0.518645 + 0.214830i 0.626622 0.779323i \(-0.284437\pi\)
−0.107976 + 0.994153i \(0.534437\pi\)
\(374\) 0 0
\(375\) −54.2861 + 54.2861i −0.00747553 + 0.00747553i
\(376\) 0 0
\(377\) 1403.62 + 1403.62i 0.191751 + 0.191751i
\(378\) 0 0
\(379\) 619.566 1495.76i 0.0839708 0.202724i −0.876317 0.481735i \(-0.840007\pi\)
0.960288 + 0.279012i \(0.0900068\pi\)
\(380\) 0 0
\(381\) 224.147 92.8445i 0.0301401 0.0124844i
\(382\) 0 0
\(383\) 2505.69 0.334294 0.167147 0.985932i \(-0.446545\pi\)
0.167147 + 0.985932i \(0.446545\pi\)
\(384\) 0 0
\(385\) −621.106 −0.0822195
\(386\) 0 0
\(387\) −9237.54 + 3826.31i −1.21336 + 0.502590i
\(388\) 0 0
\(389\) 1376.18 3322.40i 0.179371 0.433039i −0.808464 0.588545i \(-0.799701\pi\)
0.987835 + 0.155506i \(0.0497009\pi\)
\(390\) 0 0
\(391\) 2699.67 + 2699.67i 0.349177 + 0.349177i
\(392\) 0 0
\(393\) 60.5425 60.5425i 0.00777091 0.00777091i
\(394\) 0 0
\(395\) 439.975 + 182.244i 0.0560444 + 0.0232143i
\(396\) 0 0
\(397\) −134.074 323.683i −0.0169495 0.0409198i 0.915178 0.403049i \(-0.132050\pi\)
−0.932128 + 0.362130i \(0.882050\pi\)
\(398\) 0 0
\(399\) 100.733i 0.0126389i
\(400\) 0 0
\(401\) 1126.07i 0.140233i −0.997539 0.0701166i \(-0.977663\pi\)
0.997539 0.0701166i \(-0.0223371\pi\)
\(402\) 0 0
\(403\) −933.661 2254.06i −0.115407 0.278617i
\(404\) 0 0
\(405\) −1347.21 558.033i −0.165292 0.0684663i
\(406\) 0 0
\(407\) −5444.51 + 5444.51i −0.663082 + 0.663082i
\(408\) 0 0
\(409\) −5373.28 5373.28i −0.649612 0.649612i 0.303287 0.952899i \(-0.401916\pi\)
−0.952899 + 0.303287i \(0.901916\pi\)
\(410\) 0 0
\(411\) 9.95029 24.0221i 0.00119419 0.00288303i
\(412\) 0 0
\(413\) −4821.28 + 1997.04i −0.574430 + 0.237937i
\(414\) 0 0
\(415\) −50.4296 −0.00596504
\(416\) 0 0
\(417\) 0.251617 2.95485e−5
\(418\) 0 0
\(419\) 6114.35 2532.65i 0.712901 0.295293i 0.00339649 0.999994i \(-0.498919\pi\)
0.709504 + 0.704701i \(0.248919\pi\)
\(420\) 0 0
\(421\) 1033.34 2494.70i 0.119624 0.288799i −0.852713 0.522380i \(-0.825044\pi\)
0.972337 + 0.233581i \(0.0750444\pi\)
\(422\) 0 0
\(423\) −9743.36 9743.36i −1.11995 1.11995i
\(424\) 0 0
\(425\) −4610.81 + 4610.81i −0.526252 + 0.526252i
\(426\) 0 0
\(427\) 3286.74 + 1361.41i 0.372498 + 0.154294i
\(428\) 0 0
\(429\) 27.9692 + 67.5237i 0.00314771 + 0.00759924i
\(430\) 0 0
\(431\) 1487.87i 0.166283i 0.996538 + 0.0831417i \(0.0264954\pi\)
−0.996538 + 0.0831417i \(0.973505\pi\)
\(432\) 0 0
\(433\) 3672.70i 0.407618i −0.979011 0.203809i \(-0.934668\pi\)
0.979011 0.203809i \(-0.0653321\pi\)
\(434\) 0 0
\(435\) −20.1805 48.7200i −0.00222432 0.00536999i
\(436\) 0 0
\(437\) 5468.72 + 2265.22i 0.598637 + 0.247964i
\(438\) 0 0
\(439\) 7362.81 7362.81i 0.800473 0.800473i −0.182696 0.983169i \(-0.558482\pi\)
0.983169 + 0.182696i \(0.0584825\pi\)
\(440\) 0 0
\(441\) 5398.08 + 5398.08i 0.582883 + 0.582883i
\(442\) 0 0
\(443\) 4893.54 11814.0i 0.524828 1.26705i −0.410044 0.912066i \(-0.634487\pi\)
0.934873 0.354983i \(-0.115513\pi\)
\(444\) 0 0
\(445\) 862.485 357.253i 0.0918780 0.0380571i
\(446\) 0 0
\(447\) −88.8411 −0.00940054
\(448\) 0 0
\(449\) 4998.86 0.525414 0.262707 0.964876i \(-0.415385\pi\)
0.262707 + 0.964876i \(0.415385\pi\)
\(450\) 0 0
\(451\) −15353.5 + 6359.63i −1.60303 + 0.663999i
\(452\) 0 0
\(453\) 75.2476 181.664i 0.00780450 0.0188417i
\(454\) 0 0
\(455\) 129.068 + 129.068i 0.0132984 + 0.0132984i
\(456\) 0 0
\(457\) −4394.36 + 4394.36i −0.449801 + 0.449801i −0.895288 0.445487i \(-0.853031\pi\)
0.445487 + 0.895288i \(0.353031\pi\)
\(458\) 0 0
\(459\) 418.263 + 173.250i 0.0425334 + 0.0176179i
\(460\) 0 0
\(461\) −3050.81 7365.31i −0.308222 0.744115i −0.999763 0.0217769i \(-0.993068\pi\)
0.691540 0.722338i \(-0.256932\pi\)
\(462\) 0 0
\(463\) 616.179i 0.0618493i 0.999522 + 0.0309247i \(0.00984520\pi\)
−0.999522 + 0.0309247i \(0.990155\pi\)
\(464\) 0 0
\(465\) 64.8153i 0.00646396i
\(466\) 0 0
\(467\) 7113.42 + 17173.3i 0.704860 + 1.70168i 0.712461 + 0.701712i \(0.247580\pi\)
−0.00760112 + 0.999971i \(0.502420\pi\)
\(468\) 0 0
\(469\) 3739.98 + 1549.15i 0.368222 + 0.152523i
\(470\) 0 0
\(471\) −33.0725 + 33.0725i −0.00323546 + 0.00323546i
\(472\) 0 0
\(473\) 10477.7 + 10477.7i 1.01853 + 1.01853i
\(474\) 0 0
\(475\) −3868.80 + 9340.12i −0.373711 + 0.902219i
\(476\) 0 0
\(477\) −15921.9 + 6595.06i −1.52833 + 0.633054i
\(478\) 0 0
\(479\) 10609.5 1.01203 0.506014 0.862525i \(-0.331118\pi\)
0.506014 + 0.862525i \(0.331118\pi\)
\(480\) 0 0
\(481\) 2262.77 0.214498
\(482\) 0 0
\(483\) 78.8841 32.6749i 0.00743137 0.00307817i
\(484\) 0 0
\(485\) 596.010 1438.89i 0.0558008 0.134715i
\(486\) 0 0
\(487\) 2513.20 + 2513.20i 0.233848 + 0.233848i 0.814297 0.580449i \(-0.197123\pi\)
−0.580449 + 0.814297i \(0.697123\pi\)
\(488\) 0 0
\(489\) −247.998 + 247.998i −0.0229342 + 0.0229342i
\(490\) 0 0
\(491\) 14882.3 + 6164.44i 1.36788 + 0.566593i 0.941212 0.337817i \(-0.109688\pi\)
0.426665 + 0.904410i \(0.359688\pi\)
\(492\) 0 0
\(493\) −3485.07 8413.69i −0.318376 0.768628i
\(494\) 0 0
\(495\) 2162.97i 0.196400i
\(496\) 0 0
\(497\) 2189.57i 0.197617i
\(498\) 0 0
\(499\) −4424.27 10681.1i −0.396909 0.958222i −0.988395 0.151907i \(-0.951459\pi\)
0.591486 0.806315i \(-0.298541\pi\)
\(500\) 0 0
\(501\) −289.465 119.900i −0.0258131 0.0106921i
\(502\) 0 0
\(503\) 9855.92 9855.92i 0.873666 0.873666i −0.119204 0.992870i \(-0.538034\pi\)
0.992870 + 0.119204i \(0.0380342\pi\)
\(504\) 0 0
\(505\) −1371.45 1371.45i −0.120849 0.120849i
\(506\) 0 0
\(507\) −122.613 + 296.014i −0.0107405 + 0.0259299i
\(508\) 0 0
\(509\) −6891.66 + 2854.62i −0.600132 + 0.248583i −0.662003 0.749501i \(-0.730293\pi\)
0.0618706 + 0.998084i \(0.480293\pi\)
\(510\) 0 0
\(511\) 1395.21 0.120784
\(512\) 0 0
\(513\) 701.906 0.0604092
\(514\) 0 0
\(515\) −3788.00 + 1569.04i −0.324115 + 0.134253i
\(516\) 0 0
\(517\) −7814.53 + 18865.9i −0.664763 + 1.60488i
\(518\) 0 0
\(519\) −402.122 402.122i −0.0340100 0.0340100i
\(520\) 0 0
\(521\) −14514.6 + 14514.6i −1.22053 + 1.22053i −0.253088 + 0.967443i \(0.581446\pi\)
−0.967443 + 0.253088i \(0.918554\pi\)
\(522\) 0 0
\(523\) 5451.43 + 2258.06i 0.455783 + 0.188791i 0.598750 0.800936i \(-0.295664\pi\)
−0.142967 + 0.989727i \(0.545664\pi\)
\(524\) 0 0
\(525\) 55.8059 + 134.727i 0.00463918 + 0.0112000i
\(526\) 0 0
\(527\) 11193.3i 0.925212i
\(528\) 0 0
\(529\) 7149.65i 0.587626i
\(530\) 0 0
\(531\) 6954.57 + 16789.8i 0.568367 + 1.37216i
\(532\) 0 0
\(533\) 4512.06 + 1868.96i 0.366677 + 0.151883i
\(534\) 0 0
\(535\) 13.6396 13.6396i 0.00110223 0.00110223i
\(536\) 0 0
\(537\) 191.040 + 191.040i 0.0153519 + 0.0153519i
\(538\) 0 0
\(539\) 4329.46 10452.2i 0.345979 0.835268i
\(540\) 0 0
\(541\) 10798.7 4472.96i 0.858172 0.355466i 0.0901796 0.995926i \(-0.471256\pi\)
0.767992 + 0.640459i \(0.221256\pi\)
\(542\) 0 0
\(543\) 501.732 0.0396526
\(544\) 0 0
\(545\) −3396.72 −0.266971
\(546\) 0 0
\(547\) 19366.3 8021.78i 1.51379 0.627032i 0.537453 0.843294i \(-0.319386\pi\)
0.976335 + 0.216262i \(0.0693865\pi\)
\(548\) 0 0
\(549\) 4741.04 11445.9i 0.368566 0.889797i
\(550\) 0 0
\(551\) −9983.93 9983.93i −0.771923 0.771923i
\(552\) 0 0
\(553\) 1300.54 1300.54i 0.100009 0.100009i
\(554\) 0 0
\(555\) −55.5373 23.0043i −0.00424761 0.00175942i
\(556\) 0 0
\(557\) 4652.66 + 11232.5i 0.353931 + 0.854466i 0.996127 + 0.0879250i \(0.0280236\pi\)
−0.642196 + 0.766541i \(0.721976\pi\)
\(558\) 0 0
\(559\) 4354.59i 0.329480i
\(560\) 0 0
\(561\) 335.311i 0.0252350i
\(562\) 0 0
\(563\) −3815.91 9212.42i −0.285651 0.689622i 0.714297 0.699843i \(-0.246747\pi\)
−0.999948 + 0.0102205i \(0.996747\pi\)
\(564\) 0 0
\(565\) −1352.34 560.158i −0.100696 0.0417098i
\(566\) 0 0
\(567\) −3982.29 + 3982.29i −0.294957 + 0.294957i
\(568\) 0 0
\(569\) 7598.85 + 7598.85i 0.559860 + 0.559860i 0.929268 0.369407i \(-0.120439\pi\)
−0.369407 + 0.929268i \(0.620439\pi\)
\(570\) 0 0
\(571\) −5406.36 + 13052.1i −0.396233 + 0.956591i 0.592318 + 0.805704i \(0.298213\pi\)
−0.988551 + 0.150887i \(0.951787\pi\)
\(572\) 0 0
\(573\) −511.675 + 211.943i −0.0373046 + 0.0154521i
\(574\) 0 0
\(575\) 8569.21 0.621497
\(576\) 0 0
\(577\) −13340.9 −0.962548 −0.481274 0.876570i \(-0.659826\pi\)
−0.481274 + 0.876570i \(0.659826\pi\)
\(578\) 0 0
\(579\) −21.5731 + 8.93589i −0.00154844 + 0.000641386i
\(580\) 0 0
\(581\) −74.5337 + 179.940i −0.00532217 + 0.0128489i
\(582\) 0 0
\(583\) 18059.4 + 18059.4i 1.28292 + 1.28292i
\(584\) 0 0
\(585\) 449.471 449.471i 0.0317664 0.0317664i
\(586\) 0 0
\(587\) 8254.52 + 3419.14i 0.580410 + 0.240414i 0.653519 0.756910i \(-0.273292\pi\)
−0.0731089 + 0.997324i \(0.523292\pi\)
\(588\) 0 0
\(589\) 6641.13 + 16033.1i 0.464589 + 1.12162i
\(590\) 0 0
\(591\) 618.050i 0.0430172i
\(592\) 0 0
\(593\) 3054.91i 0.211552i −0.994390 0.105776i \(-0.966267\pi\)
0.994390 0.105776i \(-0.0337326\pi\)
\(594\) 0 0
\(595\) −320.465 773.670i −0.0220803 0.0533065i
\(596\) 0 0
\(597\) −627.006 259.714i −0.0429843 0.0178047i
\(598\) 0 0
\(599\) −17187.4 + 17187.4i −1.17239 + 1.17239i −0.190748 + 0.981639i \(0.561091\pi\)
−0.981639 + 0.190748i \(0.938909\pi\)
\(600\) 0 0
\(601\) −16155.9 16155.9i −1.09653 1.09653i −0.994814 0.101716i \(-0.967567\pi\)
−0.101716 0.994814i \(-0.532433\pi\)
\(602\) 0 0
\(603\) 5394.83 13024.3i 0.364336 0.879584i
\(604\) 0 0
\(605\) 495.095 205.075i 0.0332702 0.0137810i
\(606\) 0 0
\(607\) −5713.13 −0.382025 −0.191012 0.981588i \(-0.561177\pi\)
−0.191012 + 0.981588i \(0.561177\pi\)
\(608\) 0 0
\(609\) −203.667 −0.0135517
\(610\) 0 0
\(611\) 5544.29 2296.52i 0.367100 0.152058i
\(612\) 0 0
\(613\) −6320.21 + 15258.3i −0.416429 + 1.00535i 0.566945 + 0.823755i \(0.308125\pi\)
−0.983374 + 0.181592i \(0.941875\pi\)
\(614\) 0 0
\(615\) −91.7430 91.7430i −0.00601534 0.00601534i
\(616\) 0 0
\(617\) 4724.98 4724.98i 0.308299 0.308299i −0.535951 0.844249i \(-0.680047\pi\)
0.844249 + 0.535951i \(0.180047\pi\)
\(618\) 0 0
\(619\) −24539.1 10164.4i −1.59339 0.660006i −0.602933 0.797792i \(-0.706001\pi\)
−0.990462 + 0.137786i \(0.956001\pi\)
\(620\) 0 0
\(621\) −227.679 549.665i −0.0147125 0.0355190i
\(622\) 0 0
\(623\) 3605.49i 0.231863i
\(624\) 0 0
\(625\) 14132.6i 0.904489i
\(626\) 0 0
\(627\) −198.945 480.296i −0.0126716 0.0305920i
\(628\) 0 0
\(629\) −9591.00 3972.72i −0.607978 0.251833i
\(630\) 0 0
\(631\) 15837.8 15837.8i 0.999194 0.999194i −0.000805461 1.00000i \(-0.500256\pi\)
1.00000 0.000805461i \(0.000256386\pi\)
\(632\) 0 0
\(633\) −249.796 249.796i −0.0156848 0.0156848i
\(634\) 0 0
\(635\) −1196.66 + 2889.00i −0.0747844 + 0.180546i
\(636\) 0 0
\(637\) −3071.68 + 1272.33i −0.191059 + 0.0791391i
\(638\) 0 0
\(639\) 7625.06 0.472054
\(640\) 0 0
\(641\) 4.03221 0.000248460 0.000124230 1.00000i \(-0.499960\pi\)
0.000124230 1.00000i \(0.499960\pi\)
\(642\) 0 0
\(643\) −6758.04 + 2799.27i −0.414481 + 0.171683i −0.580172 0.814494i \(-0.697015\pi\)
0.165691 + 0.986178i \(0.447015\pi\)
\(644\) 0 0
\(645\) −44.2706 + 106.879i −0.00270256 + 0.00652456i
\(646\) 0 0
\(647\) 17744.9 + 17744.9i 1.07824 + 1.07824i 0.996667 + 0.0815765i \(0.0259955\pi\)
0.0815765 + 0.996667i \(0.474005\pi\)
\(648\) 0 0
\(649\) 19043.9 19043.9i 1.15183 1.15183i
\(650\) 0 0
\(651\) 231.271 + 95.7956i 0.0139235 + 0.00576732i
\(652\) 0 0
\(653\) −1174.68 2835.93i −0.0703963 0.169952i 0.884765 0.466037i \(-0.154319\pi\)
−0.955161 + 0.296085i \(0.904319\pi\)
\(654\) 0 0
\(655\) 1103.55i 0.0658308i
\(656\) 0 0
\(657\) 4858.74i 0.288520i
\(658\) 0 0
\(659\) 1291.33 + 3117.55i 0.0763325 + 0.184283i 0.957440 0.288634i \(-0.0932011\pi\)
−0.881107 + 0.472917i \(0.843201\pi\)
\(660\) 0 0
\(661\) −5796.90 2401.15i −0.341109 0.141292i 0.205551 0.978646i \(-0.434101\pi\)
−0.546661 + 0.837354i \(0.684101\pi\)
\(662\) 0 0
\(663\) −69.6788 + 69.6788i −0.00408160 + 0.00408160i
\(664\) 0 0
\(665\) −918.059 918.059i −0.0535351 0.0535351i
\(666\) 0 0
\(667\) −4579.94 + 11057.0i −0.265871 + 0.641870i
\(668\) 0 0
\(669\) 538.789 223.174i 0.0311372 0.0128974i
\(670\) 0 0
\(671\) −18360.0 −1.05631
\(672\) 0 0
\(673\) 19927.1 1.14135 0.570677 0.821174i \(-0.306681\pi\)
0.570677 + 0.821174i \(0.306681\pi\)
\(674\) 0 0
\(675\) 938.782 388.856i 0.0535315 0.0221735i
\(676\) 0 0
\(677\) 1135.03 2740.21i 0.0644356 0.155561i −0.888382 0.459105i \(-0.848170\pi\)
0.952817 + 0.303544i \(0.0981700\pi\)
\(678\) 0 0
\(679\) −4253.31 4253.31i −0.240393 0.240393i
\(680\) 0 0
\(681\) −659.036 + 659.036i −0.0370841 + 0.0370841i
\(682\) 0 0
\(683\) −14514.9 6012.25i −0.813171 0.336826i −0.0629526 0.998017i \(-0.520052\pi\)
−0.750218 + 0.661190i \(0.770052\pi\)
\(684\) 0 0
\(685\) 128.248 + 309.618i 0.00715344 + 0.0172699i
\(686\) 0 0
\(687\) 292.449i 0.0162411i
\(688\) 0 0
\(689\) 7505.60i 0.415008i
\(690\) 0 0
\(691\) −10219.6 24672.3i −0.562621 1.35829i −0.907663 0.419701i \(-0.862135\pi\)
0.345041 0.938588i \(-0.387865\pi\)
\(692\) 0 0
\(693\) 7717.79 + 3196.81i 0.423051 + 0.175234i
\(694\) 0 0
\(695\) −2.29319 + 2.29319i −0.000125159 + 0.000125159i
\(696\) 0 0
\(697\) −15843.5 15843.5i −0.860999 0.860999i
\(698\) 0 0
\(699\) 48.5008 117.091i 0.00262442 0.00633591i
\(700\) 0 0
\(701\) 18637.8 7720.05i 1.00420 0.415952i 0.180862 0.983508i \(-0.442111\pi\)
0.823334 + 0.567557i \(0.192111\pi\)
\(702\) 0 0
\(703\) −16095.1 −0.863497
\(704\) 0 0
\(705\) −159.426 −0.00851677
\(706\) 0 0
\(707\) −6920.52 + 2866.57i −0.368137 + 0.152487i
\(708\) 0 0
\(709\) 7105.65 17154.6i 0.376387 0.908678i −0.616250 0.787550i \(-0.711349\pi\)
0.992637 0.121128i \(-0.0386510\pi\)
\(710\) 0 0
\(711\) −4529.07 4529.07i −0.238894 0.238894i
\(712\) 0 0
\(713\) 10401.4 10401.4i 0.546332 0.546332i
\(714\) 0 0
\(715\) −870.305 360.492i −0.0455211 0.0188554i
\(716\) 0 0
\(717\) 221.079 + 533.731i 0.0115151 + 0.0277999i
\(718\) 0 0
\(719\) 26810.6i 1.39064i −0.718702 0.695318i \(-0.755264\pi\)
0.718702 0.695318i \(-0.244736\pi\)
\(720\) 0 0
\(721\) 15835.2i 0.817937i
\(722\) 0 0
\(723\) −374.311 903.666i −0.0192542 0.0464837i
\(724\) 0 0
\(725\) −18884.4 7822.16i −0.967376 0.400700i
\(726\) 0 0
\(727\) −17418.8 + 17418.8i −0.888623 + 0.888623i −0.994391 0.105768i \(-0.966270\pi\)
0.105768 + 0.994391i \(0.466270\pi\)
\(728\) 0 0
\(729\) 13843.1 + 13843.1i 0.703305 + 0.703305i
\(730\) 0 0
\(731\) −7645.30 + 18457.4i −0.386829 + 0.933887i
\(732\) 0 0
\(733\) 34809.3 14418.5i 1.75404 0.726547i 0.756690 0.653774i \(-0.226815\pi\)
0.997349 0.0727727i \(-0.0231848\pi\)
\(734\) 0 0
\(735\) 88.3261 0.00443260
\(736\) 0 0
\(737\) −20891.9 −1.04418
\(738\) 0 0
\(739\) 35885.8 14864.4i 1.78630 0.739911i 0.795278 0.606245i \(-0.207325\pi\)
0.991026 0.133666i \(-0.0426749\pi\)
\(740\) 0 0
\(741\) −58.4656 + 141.148i −0.00289850 + 0.00699759i
\(742\) 0 0
\(743\) −19477.4 19477.4i −0.961718 0.961718i 0.0375762 0.999294i \(-0.488036\pi\)
−0.999294 + 0.0375762i \(0.988036\pi\)
\(744\) 0 0
\(745\) 809.682 809.682i 0.0398180 0.0398180i
\(746\) 0 0
\(747\) 626.632 + 259.559i 0.0306925 + 0.0127132i
\(748\) 0 0
\(749\) −28.5092 68.8273i −0.00139079 0.00335767i
\(750\) 0 0
\(751\) 26371.3i 1.28136i −0.767807 0.640681i \(-0.778652\pi\)
0.767807 0.640681i \(-0.221348\pi\)
\(752\) 0 0
\(753\) 260.035i 0.0125846i
\(754\) 0 0
\(755\) 969.857 + 2341.44i 0.0467506 + 0.112866i
\(756\) 0 0
\(757\) −26271.7 10882.1i −1.26137 0.522478i −0.351043 0.936359i \(-0.614173\pi\)
−0.910331 + 0.413881i \(0.864173\pi\)
\(758\) 0 0
\(759\) −311.589 + 311.589i −0.0149012 + 0.0149012i
\(760\) 0 0
\(761\) −7394.46 7394.46i −0.352233 0.352233i 0.508707 0.860940i \(-0.330124\pi\)
−0.860940 + 0.508707i \(0.830124\pi\)
\(762\) 0 0
\(763\) −5020.27 + 12120.0i −0.238199 + 0.575064i
\(764\) 0 0
\(765\) −2694.26 + 1116.00i −0.127335 + 0.0527439i
\(766\) 0 0
\(767\) −7914.75 −0.372601
\(768\) 0 0
\(769\) 4771.82 0.223766 0.111883 0.993721i \(-0.464312\pi\)
0.111883 + 0.993721i \(0.464312\pi\)
\(770\) 0 0
\(771\) −6.14675 + 2.54607i −0.000287120 + 0.000118929i
\(772\) 0 0
\(773\) 8895.17 21474.8i 0.413890 0.999219i −0.570193 0.821511i \(-0.693132\pi\)
0.984083 0.177709i \(-0.0568684\pi\)
\(774\) 0 0
\(775\) 17764.7 + 17764.7i 0.823389 + 0.823389i
\(776\) 0 0
\(777\) −164.166 + 164.166i −0.00757967 + 0.00757967i
\(778\) 0 0
\(779\) −32094.3 13293.9i −1.47612 0.611429i
\(780\) 0 0
\(781\) −4324.36 10439.9i −0.198128 0.478323i
\(782\) 0 0
\(783\) 1419.15i 0.0647718i
\(784\) 0 0
\(785\) 602.834i 0.0274090i
\(786\) 0 0
\(787\) 7111.73 + 17169.2i 0.322117 + 0.777659i 0.999131 + 0.0416884i \(0.0132737\pi\)
−0.677014 + 0.735970i \(0.736726\pi\)
\(788\) 0 0
\(789\) −479.968 198.809i −0.0216569 0.00897059i
\(790\) 0 0
\(791\) −3997.46 + 3997.46i −0.179688 + 0.179688i
\(792\) 0 0
\(793\) 3815.27 + 3815.27i 0.170850 + 0.170850i
\(794\) 0 0
\(795\) −76.3051 + 184.217i −0.00340410 + 0.00821823i
\(796\) 0 0
\(797\) −24661.7 + 10215.2i −1.09606 + 0.454004i −0.856117 0.516782i \(-0.827130\pi\)
−0.239946 + 0.970786i \(0.577130\pi\)
\(798\) 0 0
\(799\) −27532.0 −1.21904
\(800\) 0 0
\(801\) −12555.9 −0.553859
\(802\) 0 0
\(803\) −6652.40 + 2755.51i −0.292351 + 0.121096i
\(804\) 0 0
\(805\) −421.143 + 1016.73i −0.0184389 + 0.0445155i
\(806\) 0 0
\(807\) −478.775 478.775i −0.0208844 0.0208844i
\(808\) 0 0
\(809\) 22540.9 22540.9i 0.979600 0.979600i −0.0201963 0.999796i \(-0.506429\pi\)
0.999796 + 0.0201963i \(0.00642911\pi\)
\(810\) 0 0
\(811\) 12287.9 + 5089.83i 0.532044 + 0.220380i 0.632498 0.774562i \(-0.282030\pi\)
−0.100454 + 0.994942i \(0.532030\pi\)
\(812\) 0 0
\(813\) 270.801 + 653.772i 0.0116819 + 0.0282027i
\(814\) 0 0
\(815\) 4520.41i 0.194286i
\(816\) 0 0
\(817\) 30974.2i 1.32638i
\(818\) 0 0
\(819\) −939.473 2268.09i −0.0400829 0.0967686i
\(820\) 0 0
\(821\) 15862.2 + 6570.34i 0.674293 + 0.279301i 0.693439 0.720515i \(-0.256095\pi\)
−0.0191460 + 0.999817i \(0.506095\pi\)
\(822\) 0 0
\(823\) 11289.1 11289.1i 0.478146 0.478146i −0.426392 0.904538i \(-0.640216\pi\)
0.904538 + 0.426392i \(0.140216\pi\)
\(824\) 0 0
\(825\) −532.168 532.168i −0.0224578 0.0224578i
\(826\) 0 0
\(827\) −2548.49 + 6152.59i −0.107158 + 0.258702i −0.968359 0.249563i \(-0.919713\pi\)
0.861201 + 0.508265i \(0.169713\pi\)
\(828\) 0 0
\(829\) 40448.6 16754.4i 1.69462 0.701934i 0.694768 0.719234i \(-0.255507\pi\)
0.999850 + 0.0173006i \(0.00550723\pi\)
\(830\) 0 0
\(831\) 1136.49 0.0474423
\(832\) 0 0
\(833\) 15253.5 0.634455
\(834\) 0 0
\(835\) 3730.88 1545.38i 0.154626 0.0640481i
\(836\) 0 0
\(837\) 667.504 1611.50i 0.0275655 0.0665490i
\(838\) 0 0
\(839\) 2282.23 + 2282.23i 0.0939108 + 0.0939108i 0.752501 0.658591i \(-0.228847\pi\)
−0.658591 + 0.752501i \(0.728847\pi\)
\(840\) 0 0
\(841\) 2940.42 2940.42i 0.120563 0.120563i
\(842\) 0 0
\(843\) −646.232 267.678i −0.0264026 0.0109363i
\(844\) 0 0
\(845\) −1580.35 3815.30i −0.0643380 0.155326i
\(846\) 0 0
\(847\) 2069.67i 0.0839607i
\(848\) 0 0
\(849\) 759.651i 0.0307081i
\(850\) 0 0
\(851\) 5220.80 + 12604.1i 0.210302 + 0.507713i
\(852\) 0 0
\(853\) −8660.34 3587.23i −0.347625 0.143991i 0.202037 0.979378i \(-0.435244\pi\)
−0.549663 + 0.835387i \(0.685244\pi\)
\(854\) 0 0
\(855\) −3197.09 + 3197.09i −0.127881 + 0.127881i
\(856\) 0 0
\(857\) −10879.0 10879.0i −0.433630 0.433630i 0.456231 0.889861i \(-0.349199\pi\)
−0.889861 + 0.456231i \(0.849199\pi\)
\(858\) 0 0
\(859\) 816.021 1970.05i 0.0324124 0.0782506i −0.906844 0.421465i \(-0.861516\pi\)
0.939257 + 0.343215i \(0.111516\pi\)
\(860\) 0 0
\(861\) −462.947 + 191.759i −0.0183243 + 0.00759016i
\(862\) 0 0
\(863\) 17532.1 0.691541 0.345771 0.938319i \(-0.387617\pi\)
0.345771 + 0.938319i \(0.387617\pi\)
\(864\) 0 0
\(865\) 7329.74 0.288114
\(866\) 0 0
\(867\) −288.657 + 119.566i −0.0113072 + 0.00468358i
\(868\) 0 0
\(869\) −3632.48 + 8769.58i −0.141799 + 0.342333i
\(870\) 0 0
\(871\) 4341.40 + 4341.40i 0.168889 + 0.168889i
\(872\) 0 0
\(873\) −14811.9 + 14811.9i −0.574234 + 0.574234i
\(874\) 0 0
\(875\) −3530.71 1462.47i −0.136411 0.0565034i
\(876\) 0 0
\(877\) 1857.78 + 4485.09i 0.0715313 + 0.172692i 0.955601 0.294663i \(-0.0952072\pi\)
−0.884070 + 0.467354i \(0.845207\pi\)
\(878\) 0 0
\(879\) 207.140i 0.00794842i
\(880\) 0 0
\(881\) 24865.4i 0.950894i −0.879744 0.475447i \(-0.842286\pi\)
0.879744 0.475447i \(-0.157714\pi\)
\(882\) 0 0
\(883\) −14018.3 33843.3i −0.534264 1.28983i −0.928676 0.370893i \(-0.879052\pi\)
0.394412 0.918934i \(-0.370948\pi\)
\(884\) 0 0
\(885\) 194.259 + 80.4647i 0.00737847 + 0.00305626i
\(886\) 0 0
\(887\) 4048.92 4048.92i 0.153269 0.153269i −0.626307 0.779576i \(-0.715435\pi\)
0.779576 + 0.626307i \(0.215435\pi\)
\(888\) 0 0
\(889\) 8539.75 + 8539.75i 0.322175 + 0.322175i
\(890\) 0 0
\(891\) 11122.7 26852.6i 0.418210 1.00965i
\(892\) 0 0
\(893\) −39436.5 + 16335.1i −1.47782 + 0.612133i
\(894\) 0 0
\(895\) −3482.21 −0.130053
\(896\) 0 0
\(897\) 129.498 0.00482032
\(898\) 0 0
\(899\) −32416.6 + 13427.4i −1.20262 + 0.498141i
\(900\) 0 0
\(901\) −13177.5 + 31813.3i −0.487243 + 1.17631i
\(902\) 0 0
\(903\) 315.928 + 315.928i 0.0116428 + 0.0116428i
\(904\) 0 0
\(905\) −4572.69 + 4572.69i −0.167957 + 0.167957i
\(906\) 0 0
\(907\) 30120.4 + 12476.3i 1.10268 + 0.456745i 0.858411 0.512963i \(-0.171452\pi\)
0.244268 + 0.969708i \(0.421452\pi\)
\(908\) 0 0
\(909\) 9982.67 + 24100.3i 0.364251 + 0.879380i
\(910\) 0 0
\(911\) 26490.1i 0.963400i 0.876336 + 0.481700i \(0.159980\pi\)
−0.876336 + 0.481700i \(0.840020\pi\)
\(912\) 0 0
\(913\) 1005.16i 0.0364360i
\(914\) 0 0
\(915\) −54.8541 132.429i −0.00198188 0.00478468i
\(916\) 0 0
\(917\) 3937.62 + 1631.02i 0.141801 + 0.0587360i
\(918\) 0 0
\(919\) 2467.15 2467.15i 0.0885570 0.0885570i −0.661441 0.749998i \(-0.730055\pi\)
0.749998 + 0.661441i \(0.230055\pi\)
\(920\) 0 0
\(921\) 724.316 + 724.316i 0.0259143 + 0.0259143i
\(922\) 0 0
\(923\) −1270.84 + 3068.07i −0.0453197 + 0.109411i
\(924\) 0 0
\(925\) −21526.8 + 8916.69i −0.765185 + 0.316950i
\(926\) 0 0
\(927\) 55145.1 1.95383
\(928\) 0 0
\(929\) −13097.0 −0.462537 −0.231269 0.972890i \(-0.574288\pi\)
−0.231269 + 0.972890i \(0.574288\pi\)
\(930\) 0 0
\(931\) 21848.9 9050.10i 0.769138 0.318588i
\(932\) 0 0
\(933\) −460.673 + 1112.16i −0.0161648 + 0.0390253i
\(934\) 0 0
\(935\) 3055.97 + 3055.97i 0.106889 + 0.106889i
\(936\) 0 0
\(937\) −24748.7 + 24748.7i −0.862864 + 0.862864i −0.991670 0.128806i \(-0.958886\pi\)
0.128806 + 0.991670i \(0.458886\pi\)
\(938\) 0 0
\(939\) 847.625 + 351.098i 0.0294581 + 0.0122020i
\(940\) 0 0
\(941\) 3168.01 + 7648.26i 0.109749 + 0.264959i 0.969207 0.246249i \(-0.0791982\pi\)
−0.859457 + 0.511208i \(0.829198\pi\)
\(942\) 0 0
\(943\) 29445.3i 1.01683i
\(944\) 0 0
\(945\) 130.496i 0.00449211i
\(946\) 0 0
\(947\) 4403.80 + 10631.7i 0.151113 + 0.364820i 0.981250 0.192741i \(-0.0617376\pi\)
−0.830137 + 0.557560i \(0.811738\pi\)
\(948\) 0 0
\(949\) 1954.99 + 809.785i 0.0668723 + 0.0276994i
\(950\) 0 0
\(951\) 358.872 358.872i 0.0122368 0.0122368i
\(952\) 0 0
\(953\) −4833.37 4833.37i −0.164290 0.164290i 0.620174 0.784464i \(-0.287062\pi\)
−0.784464 + 0.620174i \(0.787062\pi\)
\(954\) 0 0
\(955\) 2731.71 6594.92i 0.0925612 0.223462i
\(956\) 0 0
\(957\) 971.088 402.238i 0.0328013 0.0135867i
\(958\) 0 0
\(959\) 1294.31 0.0435824
\(960\) 0 0
\(961\) 13334.8 0.447613
\(962\) 0 0
\(963\) −239.687 + 99.2817i −0.00802057 + 0.00332223i
\(964\) 0 0
\(965\) 115.174 278.054i 0.00384204 0.00927551i
\(966\) 0 0
\(967\) 11429.8 + 11429.8i 0.380101 + 0.380101i 0.871138 0.491037i \(-0.163382\pi\)
−0.491037 + 0.871138i \(0.663382\pi\)
\(968\) 0 0
\(969\) 495.625 495.625i 0.0164311 0.0164311i
\(970\) 0 0
\(971\) −6489.63 2688.09i −0.214482 0.0888414i 0.272856 0.962055i \(-0.412032\pi\)
−0.487338 + 0.873214i \(0.662032\pi\)
\(972\) 0 0
\(973\) 4.79317 + 11.5717i 0.000157926 + 0.000381267i
\(974\) 0 0
\(975\) 221.172i 0.00726481i
\(976\) 0 0
\(977\) 19891.1i 0.651354i −0.945481 0.325677i \(-0.894408\pi\)
0.945481 0.325677i \(-0.105592\pi\)
\(978\) 0 0
\(979\) 7120.77 + 17191.1i 0.232462 + 0.561214i
\(980\) 0 0
\(981\) 42207.2 + 17482.8i 1.37367 + 0.568994i
\(982\) 0 0
\(983\) 606.701 606.701i 0.0196854 0.0196854i −0.697196 0.716881i \(-0.745569\pi\)
0.716881 + 0.697196i \(0.245569\pi\)
\(984\) 0 0
\(985\) 5632.79 + 5632.79i 0.182209 + 0.182209i
\(986\) 0 0
\(987\) −235.628 + 568.856i −0.00759890 + 0.0183454i
\(988\) 0 0
\(989\) 24256.0 10047.2i 0.779875 0.323035i
\(990\) 0 0
\(991\) 2306.07 0.0739201 0.0369600 0.999317i \(-0.488233\pi\)
0.0369600 + 0.999317i \(0.488233\pi\)
\(992\) 0 0
\(993\) 871.808 0.0278610
\(994\) 0 0
\(995\) 8081.41 3347.43i 0.257485 0.106654i
\(996\) 0 0
\(997\) −11827.8 + 28554.9i −0.375718 + 0.907064i 0.617040 + 0.786932i \(0.288332\pi\)
−0.992758 + 0.120132i \(0.961668\pi\)
\(998\) 0 0
\(999\) 1143.91 + 1143.91i 0.0362279 + 0.0362279i
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 256.4.g.b.97.5 44
4.3 odd 2 256.4.g.a.97.7 44
8.3 odd 2 128.4.g.a.49.5 44
8.5 even 2 32.4.g.a.21.11 44
32.3 odd 8 256.4.g.a.161.7 44
32.13 even 8 32.4.g.a.29.11 yes 44
32.19 odd 8 128.4.g.a.81.5 44
32.29 even 8 inner 256.4.g.b.161.5 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.4.g.a.21.11 44 8.5 even 2
32.4.g.a.29.11 yes 44 32.13 even 8
128.4.g.a.49.5 44 8.3 odd 2
128.4.g.a.81.5 44 32.19 odd 8
256.4.g.a.97.7 44 4.3 odd 2
256.4.g.a.161.7 44 32.3 odd 8
256.4.g.b.97.5 44 1.1 even 1 trivial
256.4.g.b.161.5 44 32.29 even 8 inner