Properties

Label 256.3.h.b.31.5
Level $256$
Weight $3$
Character 256.31
Analytic conductor $6.975$
Analytic rank $0$
Dimension $28$
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] = [256,3,Mod(31,256)]
 
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([4, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("256.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 256.h (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: \(6.97549476762\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 31.5
Character \(\chi\) \(=\) 256.31
Dual form 256.3.h.b.223.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37292 - 0.568682i) q^{3} +(-2.28872 - 0.948019i) q^{5} +(-6.37744 + 6.37744i) q^{7} +(-4.80245 + 4.80245i) q^{9} +O(q^{10})\) \(q+(1.37292 - 0.568682i) q^{3} +(-2.28872 - 0.948019i) q^{5} +(-6.37744 + 6.37744i) q^{7} +(-4.80245 + 4.80245i) q^{9} +(1.79646 + 0.744117i) q^{11} +(-16.7036 + 6.91888i) q^{13} -3.68135 q^{15} -6.19811i q^{17} +(8.50083 + 20.5228i) q^{19} +(-5.12898 + 12.3825i) q^{21} +(23.6476 + 23.6476i) q^{23} +(-13.3382 - 13.3382i) q^{25} +(-8.98045 + 21.6807i) q^{27} +(-14.5725 - 35.1811i) q^{29} -14.1609i q^{31} +2.88956 q^{33} +(20.6421 - 8.55025i) q^{35} +(30.0695 + 12.4552i) q^{37} +(-18.9981 + 18.9981i) q^{39} +(-56.9700 + 56.9700i) q^{41} +(-54.5034 - 22.5760i) q^{43} +(15.5443 - 6.43866i) q^{45} +34.8047 q^{47} -32.3435i q^{49} +(-3.52475 - 8.50951i) q^{51} +(-3.92967 + 9.48706i) q^{53} +(-3.40615 - 3.40615i) q^{55} +(23.3419 + 23.3419i) q^{57} +(-9.41777 + 22.7365i) q^{59} +(-3.00467 - 7.25391i) q^{61} -61.2547i q^{63} +44.7892 q^{65} +(55.9040 - 23.1562i) q^{67} +(45.9141 + 19.0183i) q^{69} +(6.27499 - 6.27499i) q^{71} +(66.4597 - 66.4597i) q^{73} +(-25.8974 - 10.7271i) q^{75} +(-16.2024 + 6.71124i) q^{77} -75.8508 q^{79} -26.2523i q^{81} +(1.23390 + 2.97891i) q^{83} +(-5.87593 + 14.1857i) q^{85} +(-40.0138 - 40.0138i) q^{87} +(36.7030 + 36.7030i) q^{89} +(62.4018 - 150.651i) q^{91} +(-8.05304 - 19.4417i) q^{93} -55.0300i q^{95} +90.0528 q^{97} +(-12.2010 + 5.05381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} - 8 q^{15} + 4 q^{19} + 4 q^{21} - 68 q^{23} - 4 q^{25} + 100 q^{27} + 4 q^{29} - 8 q^{33} - 92 q^{35} + 4 q^{37} + 188 q^{39} - 4 q^{41} - 92 q^{43} + 40 q^{45} - 8 q^{47} - 224 q^{51} + 164 q^{53} + 252 q^{55} - 4 q^{57} - 124 q^{59} + 68 q^{61} - 8 q^{65} + 164 q^{67} - 188 q^{69} - 260 q^{71} - 4 q^{73} + 488 q^{75} - 220 q^{77} - 520 q^{79} + 484 q^{83} - 96 q^{85} - 452 q^{87} - 4 q^{89} + 196 q^{91} - 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(3\) 1.37292 0.568682i 0.457640 0.189561i −0.141940 0.989875i \(-0.545334\pi\)
0.599580 + 0.800315i \(0.295334\pi\)
\(4\) 0 0
\(5\) −2.28872 0.948019i −0.457744 0.189604i 0.141883 0.989883i \(-0.454684\pi\)
−0.599627 + 0.800280i \(0.704684\pi\)
\(6\) 0 0
\(7\) −6.37744 + 6.37744i −0.911063 + 0.911063i −0.996356 0.0852929i \(-0.972817\pi\)
0.0852929 + 0.996356i \(0.472817\pi\)
\(8\) 0 0
\(9\) −4.80245 + 4.80245i −0.533606 + 0.533606i
\(10\) 0 0
\(11\) 1.79646 + 0.744117i 0.163314 + 0.0676470i 0.462843 0.886440i \(-0.346829\pi\)
−0.299529 + 0.954087i \(0.596829\pi\)
\(12\) 0 0
\(13\) −16.7036 + 6.91888i −1.28490 + 0.532221i −0.917460 0.397827i \(-0.869764\pi\)
−0.367436 + 0.930049i \(0.619764\pi\)
\(14\) 0 0
\(15\) −3.68135 −0.245423
\(16\) 0 0
\(17\) 6.19811i 0.364595i −0.983243 0.182297i \(-0.941647\pi\)
0.983243 0.182297i \(-0.0583533\pi\)
\(18\) 0 0
\(19\) 8.50083 + 20.5228i 0.447412 + 1.08015i 0.973288 + 0.229587i \(0.0737375\pi\)
−0.525876 + 0.850561i \(0.676262\pi\)
\(20\) 0 0
\(21\) −5.12898 + 12.3825i −0.244237 + 0.589641i
\(22\) 0 0
\(23\) 23.6476 + 23.6476i 1.02815 + 1.02815i 0.999592 + 0.0285625i \(0.00909295\pi\)
0.0285625 + 0.999592i \(0.490907\pi\)
\(24\) 0 0
\(25\) −13.3382 13.3382i −0.533527 0.533527i
\(26\) 0 0
\(27\) −8.98045 + 21.6807i −0.332609 + 0.802990i
\(28\) 0 0
\(29\) −14.5725 35.1811i −0.502500 1.21314i −0.948118 0.317919i \(-0.897016\pi\)
0.445618 0.895223i \(-0.352984\pi\)
\(30\) 0 0
\(31\) 14.1609i 0.456803i −0.973567 0.228401i \(-0.926650\pi\)
0.973567 0.228401i \(-0.0733498\pi\)
\(32\) 0 0
\(33\) 2.88956 0.0875623
\(34\) 0 0
\(35\) 20.6421 8.55025i 0.589775 0.244293i
\(36\) 0 0
\(37\) 30.0695 + 12.4552i 0.812689 + 0.336627i 0.750027 0.661408i \(-0.230041\pi\)
0.0626629 + 0.998035i \(0.480041\pi\)
\(38\) 0 0
\(39\) −18.9981 + 18.9981i −0.487131 + 0.487131i
\(40\) 0 0
\(41\) −56.9700 + 56.9700i −1.38951 + 1.38951i −0.563170 + 0.826341i \(0.690418\pi\)
−0.826341 + 0.563170i \(0.809582\pi\)
\(42\) 0 0
\(43\) −54.5034 22.5760i −1.26752 0.525024i −0.355310 0.934748i \(-0.615625\pi\)
−0.912209 + 0.409724i \(0.865625\pi\)
\(44\) 0 0
\(45\) 15.5443 6.43866i 0.345429 0.143081i
\(46\) 0 0
\(47\) 34.8047 0.740525 0.370263 0.928927i \(-0.379268\pi\)
0.370263 + 0.928927i \(0.379268\pi\)
\(48\) 0 0
\(49\) 32.3435i 0.660072i
\(50\) 0 0
\(51\) −3.52475 8.50951i −0.0691128 0.166853i
\(52\) 0 0
\(53\) −3.92967 + 9.48706i −0.0741447 + 0.179001i −0.956606 0.291383i \(-0.905885\pi\)
0.882462 + 0.470384i \(0.155885\pi\)
\(54\) 0 0
\(55\) −3.40615 3.40615i −0.0619300 0.0619300i
\(56\) 0 0
\(57\) 23.3419 + 23.3419i 0.409507 + 0.409507i
\(58\) 0 0
\(59\) −9.41777 + 22.7365i −0.159623 + 0.385365i −0.983375 0.181586i \(-0.941877\pi\)
0.823752 + 0.566951i \(0.191877\pi\)
\(60\) 0 0
\(61\) −3.00467 7.25391i −0.0492568 0.118916i 0.897336 0.441348i \(-0.145500\pi\)
−0.946593 + 0.322432i \(0.895500\pi\)
\(62\) 0 0
\(63\) 61.2547i 0.972297i
\(64\) 0 0
\(65\) 44.7892 0.689065
\(66\) 0 0
\(67\) 55.9040 23.1562i 0.834388 0.345615i 0.0757497 0.997127i \(-0.475865\pi\)
0.758638 + 0.651512i \(0.225865\pi\)
\(68\) 0 0
\(69\) 45.9141 + 19.0183i 0.665422 + 0.275627i
\(70\) 0 0
\(71\) 6.27499 6.27499i 0.0883801 0.0883801i −0.661535 0.749915i \(-0.730095\pi\)
0.749915 + 0.661535i \(0.230095\pi\)
\(72\) 0 0
\(73\) 66.4597 66.4597i 0.910406 0.910406i −0.0858977 0.996304i \(-0.527376\pi\)
0.996304 + 0.0858977i \(0.0273758\pi\)
\(74\) 0 0
\(75\) −25.8974 10.7271i −0.345299 0.143027i
\(76\) 0 0
\(77\) −16.2024 + 6.71124i −0.210420 + 0.0871589i
\(78\) 0 0
\(79\) −75.8508 −0.960136 −0.480068 0.877231i \(-0.659388\pi\)
−0.480068 + 0.877231i \(0.659388\pi\)
\(80\) 0 0
\(81\) 26.2523i 0.324103i
\(82\) 0 0
\(83\) 1.23390 + 2.97891i 0.0148663 + 0.0358905i 0.931138 0.364666i \(-0.118817\pi\)
−0.916272 + 0.400556i \(0.868817\pi\)
\(84\) 0 0
\(85\) −5.87593 + 14.1857i −0.0691286 + 0.166891i
\(86\) 0 0
\(87\) −40.0138 40.0138i −0.459928 0.459928i
\(88\) 0 0
\(89\) 36.7030 + 36.7030i 0.412393 + 0.412393i 0.882572 0.470178i \(-0.155810\pi\)
−0.470178 + 0.882572i \(0.655810\pi\)
\(90\) 0 0
\(91\) 62.4018 150.651i 0.685734 1.65551i
\(92\) 0 0
\(93\) −8.05304 19.4417i −0.0865918 0.209051i
\(94\) 0 0
\(95\) 55.0300i 0.579263i
\(96\) 0 0
\(97\) 90.0528 0.928379 0.464189 0.885736i \(-0.346346\pi\)
0.464189 + 0.885736i \(0.346346\pi\)
\(98\) 0 0
\(99\) −12.2010 + 5.05381i −0.123242 + 0.0510486i
\(100\) 0 0
\(101\) 20.0870 + 8.32031i 0.198881 + 0.0823793i 0.479901 0.877323i \(-0.340673\pi\)
−0.281020 + 0.959702i \(0.590673\pi\)
\(102\) 0 0
\(103\) 4.88882 4.88882i 0.0474642 0.0474642i −0.682976 0.730441i \(-0.739315\pi\)
0.730441 + 0.682976i \(0.239315\pi\)
\(104\) 0 0
\(105\) 23.4776 23.4776i 0.223596 0.223596i
\(106\) 0 0
\(107\) 51.9710 + 21.5271i 0.485710 + 0.201188i 0.612080 0.790795i \(-0.290333\pi\)
−0.126371 + 0.991983i \(0.540333\pi\)
\(108\) 0 0
\(109\) 49.8054 20.6301i 0.456931 0.189267i −0.142333 0.989819i \(-0.545460\pi\)
0.599263 + 0.800552i \(0.295460\pi\)
\(110\) 0 0
\(111\) 48.3661 0.435730
\(112\) 0 0
\(113\) 62.0870i 0.549442i 0.961524 + 0.274721i \(0.0885855\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(114\) 0 0
\(115\) −31.7043 76.5410i −0.275690 0.665574i
\(116\) 0 0
\(117\) 46.9909 113.446i 0.401632 0.969624i
\(118\) 0 0
\(119\) 39.5281 + 39.5281i 0.332169 + 0.332169i
\(120\) 0 0
\(121\) −82.8864 82.8864i −0.685011 0.685011i
\(122\) 0 0
\(123\) −45.8174 + 110.613i −0.372499 + 0.899292i
\(124\) 0 0
\(125\) 41.5830 + 100.390i 0.332664 + 0.803122i
\(126\) 0 0
\(127\) 177.045i 1.39406i 0.717043 + 0.697029i \(0.245495\pi\)
−0.717043 + 0.697029i \(0.754505\pi\)
\(128\) 0 0
\(129\) −87.6673 −0.679592
\(130\) 0 0
\(131\) −88.7654 + 36.7678i −0.677598 + 0.280670i −0.694823 0.719181i \(-0.744517\pi\)
0.0172241 + 0.999852i \(0.494517\pi\)
\(132\) 0 0
\(133\) −185.097 76.6695i −1.39170 0.576462i
\(134\) 0 0
\(135\) 41.1075 41.1075i 0.304500 0.304500i
\(136\) 0 0
\(137\) −58.5583 + 58.5583i −0.427433 + 0.427433i −0.887753 0.460320i \(-0.847735\pi\)
0.460320 + 0.887753i \(0.347735\pi\)
\(138\) 0 0
\(139\) 166.832 + 69.1039i 1.20023 + 0.497151i 0.891072 0.453861i \(-0.149954\pi\)
0.309155 + 0.951012i \(0.399954\pi\)
\(140\) 0 0
\(141\) 47.7840 19.7928i 0.338894 0.140374i
\(142\) 0 0
\(143\) −35.1558 −0.245845
\(144\) 0 0
\(145\) 94.3348i 0.650585i
\(146\) 0 0
\(147\) −18.3932 44.4050i −0.125124 0.302075i
\(148\) 0 0
\(149\) −18.0040 + 43.4655i −0.120832 + 0.291715i −0.972709 0.232027i \(-0.925464\pi\)
0.851877 + 0.523742i \(0.175464\pi\)
\(150\) 0 0
\(151\) −68.3596 68.3596i −0.452713 0.452713i 0.443541 0.896254i \(-0.353722\pi\)
−0.896254 + 0.443541i \(0.853722\pi\)
\(152\) 0 0
\(153\) 29.7661 + 29.7661i 0.194550 + 0.194550i
\(154\) 0 0
\(155\) −13.4248 + 32.4103i −0.0866115 + 0.209099i
\(156\) 0 0
\(157\) 74.5650 + 180.016i 0.474936 + 1.14660i 0.961956 + 0.273206i \(0.0880840\pi\)
−0.487020 + 0.873391i \(0.661916\pi\)
\(158\) 0 0
\(159\) 15.2597i 0.0959730i
\(160\) 0 0
\(161\) −301.622 −1.87343
\(162\) 0 0
\(163\) −267.123 + 110.646i −1.63879 + 0.678811i −0.996175 0.0873756i \(-0.972152\pi\)
−0.642619 + 0.766186i \(0.722152\pi\)
\(164\) 0 0
\(165\) −6.61339 2.73936i −0.0400812 0.0166022i
\(166\) 0 0
\(167\) 99.3059 99.3059i 0.594646 0.594646i −0.344237 0.938883i \(-0.611862\pi\)
0.938883 + 0.344237i \(0.111862\pi\)
\(168\) 0 0
\(169\) 111.640 111.640i 0.660592 0.660592i
\(170\) 0 0
\(171\) −139.385 57.7350i −0.815115 0.337632i
\(172\) 0 0
\(173\) −187.259 + 77.5652i −1.08242 + 0.448354i −0.851358 0.524585i \(-0.824220\pi\)
−0.231063 + 0.972939i \(0.574220\pi\)
\(174\) 0 0
\(175\) 170.127 0.972153
\(176\) 0 0
\(177\) 36.5711i 0.206617i
\(178\) 0 0
\(179\) 101.230 + 244.390i 0.565528 + 1.36531i 0.905290 + 0.424795i \(0.139654\pi\)
−0.339761 + 0.940512i \(0.610346\pi\)
\(180\) 0 0
\(181\) −6.07796 + 14.6735i −0.0335799 + 0.0810690i −0.939780 0.341780i \(-0.888970\pi\)
0.906200 + 0.422849i \(0.138970\pi\)
\(182\) 0 0
\(183\) −8.25033 8.25033i −0.0450838 0.0450838i
\(184\) 0 0
\(185\) −57.0130 57.0130i −0.308178 0.308178i
\(186\) 0 0
\(187\) 4.61212 11.1346i 0.0246637 0.0595435i
\(188\) 0 0
\(189\) −80.9953 195.540i −0.428546 1.03460i
\(190\) 0 0
\(191\) 370.577i 1.94019i 0.242716 + 0.970097i \(0.421962\pi\)
−0.242716 + 0.970097i \(0.578038\pi\)
\(192\) 0 0
\(193\) −132.679 −0.687456 −0.343728 0.939069i \(-0.611690\pi\)
−0.343728 + 0.939069i \(0.611690\pi\)
\(194\) 0 0
\(195\) 61.4920 25.4708i 0.315344 0.130620i
\(196\) 0 0
\(197\) −116.390 48.2104i −0.590814 0.244723i 0.0671870 0.997740i \(-0.478598\pi\)
−0.658001 + 0.753017i \(0.728598\pi\)
\(198\) 0 0
\(199\) −89.9950 + 89.9950i −0.452236 + 0.452236i −0.896096 0.443860i \(-0.853609\pi\)
0.443860 + 0.896096i \(0.353609\pi\)
\(200\) 0 0
\(201\) 63.5832 63.5832i 0.316334 0.316334i
\(202\) 0 0
\(203\) 317.301 + 131.430i 1.56306 + 0.647440i
\(204\) 0 0
\(205\) 184.397 76.3797i 0.899498 0.372584i
\(206\) 0 0
\(207\) −227.132 −1.09726
\(208\) 0 0
\(209\) 43.1940i 0.206670i
\(210\) 0 0
\(211\) −20.9287 50.5264i −0.0991883 0.239462i 0.866494 0.499187i \(-0.166368\pi\)
−0.965683 + 0.259725i \(0.916368\pi\)
\(212\) 0 0
\(213\) 5.04658 12.1835i 0.0236929 0.0571996i
\(214\) 0 0
\(215\) 103.340 + 103.340i 0.480653 + 0.480653i
\(216\) 0 0
\(217\) 90.3102 + 90.3102i 0.416176 + 0.416176i
\(218\) 0 0
\(219\) 53.4494 129.038i 0.244061 0.589215i
\(220\) 0 0
\(221\) 42.8840 + 103.531i 0.194045 + 0.468466i
\(222\) 0 0
\(223\) 52.7540i 0.236565i −0.992980 0.118283i \(-0.962261\pi\)
0.992980 0.118283i \(-0.0377388\pi\)
\(224\) 0 0
\(225\) 128.112 0.569386
\(226\) 0 0
\(227\) 327.101 135.490i 1.44097 0.596871i 0.480939 0.876754i \(-0.340296\pi\)
0.960034 + 0.279883i \(0.0902957\pi\)
\(228\) 0 0
\(229\) −245.430 101.660i −1.07175 0.443932i −0.224139 0.974557i \(-0.571957\pi\)
−0.847606 + 0.530625i \(0.821957\pi\)
\(230\) 0 0
\(231\) −18.4280 + 18.4280i −0.0797748 + 0.0797748i
\(232\) 0 0
\(233\) −31.8772 + 31.8772i −0.136812 + 0.136812i −0.772196 0.635384i \(-0.780842\pi\)
0.635384 + 0.772196i \(0.280842\pi\)
\(234\) 0 0
\(235\) −79.6582 32.9955i −0.338971 0.140406i
\(236\) 0 0
\(237\) −104.137 + 43.1350i −0.439397 + 0.182004i
\(238\) 0 0
\(239\) 90.0511 0.376783 0.188391 0.982094i \(-0.439673\pi\)
0.188391 + 0.982094i \(0.439673\pi\)
\(240\) 0 0
\(241\) 20.9972i 0.0871252i −0.999051 0.0435626i \(-0.986129\pi\)
0.999051 0.0435626i \(-0.0138708\pi\)
\(242\) 0 0
\(243\) −95.7533 231.169i −0.394046 0.951312i
\(244\) 0 0
\(245\) −30.6623 + 74.0253i −0.125152 + 0.302144i
\(246\) 0 0
\(247\) −283.990 283.990i −1.14976 1.14976i
\(248\) 0 0
\(249\) 3.38810 + 3.38810i 0.0136068 + 0.0136068i
\(250\) 0 0
\(251\) −105.207 + 253.991i −0.419150 + 1.01192i 0.563444 + 0.826154i \(0.309476\pi\)
−0.982594 + 0.185764i \(0.940524\pi\)
\(252\) 0 0
\(253\) 24.8853 + 60.0783i 0.0983607 + 0.237464i
\(254\) 0 0
\(255\) 22.8174i 0.0894801i
\(256\) 0 0
\(257\) 236.584 0.920561 0.460281 0.887773i \(-0.347749\pi\)
0.460281 + 0.887773i \(0.347749\pi\)
\(258\) 0 0
\(259\) −271.199 + 112.334i −1.04710 + 0.433723i
\(260\) 0 0
\(261\) 238.939 + 98.9720i 0.915477 + 0.379203i
\(262\) 0 0
\(263\) 32.0070 32.0070i 0.121700 0.121700i −0.643634 0.765334i \(-0.722574\pi\)
0.765334 + 0.643634i \(0.222574\pi\)
\(264\) 0 0
\(265\) 17.9878 17.9878i 0.0678786 0.0678786i
\(266\) 0 0
\(267\) 71.2626 + 29.5179i 0.266901 + 0.110554i
\(268\) 0 0
\(269\) −115.344 + 47.7769i −0.428787 + 0.177609i −0.586630 0.809855i \(-0.699546\pi\)
0.157844 + 0.987464i \(0.449546\pi\)
\(270\) 0 0
\(271\) −55.4325 −0.204548 −0.102274 0.994756i \(-0.532612\pi\)
−0.102274 + 0.994756i \(0.532612\pi\)
\(272\) 0 0
\(273\) 242.319i 0.887615i
\(274\) 0 0
\(275\) −14.0363 33.8866i −0.0510410 0.123224i
\(276\) 0 0
\(277\) 35.7881 86.4001i 0.129199 0.311914i −0.846022 0.533148i \(-0.821009\pi\)
0.975221 + 0.221235i \(0.0710087\pi\)
\(278\) 0 0
\(279\) 68.0069 + 68.0069i 0.243752 + 0.243752i
\(280\) 0 0
\(281\) 13.8509 + 13.8509i 0.0492914 + 0.0492914i 0.731323 0.682031i \(-0.238903\pi\)
−0.682031 + 0.731323i \(0.738903\pi\)
\(282\) 0 0
\(283\) 135.615 327.403i 0.479205 1.15690i −0.480778 0.876843i \(-0.659646\pi\)
0.959982 0.280060i \(-0.0903544\pi\)
\(284\) 0 0
\(285\) −31.2945 75.5517i −0.109805 0.265094i
\(286\) 0 0
\(287\) 726.645i 2.53186i
\(288\) 0 0
\(289\) 250.583 0.867071
\(290\) 0 0
\(291\) 123.635 51.2114i 0.424863 0.175984i
\(292\) 0 0
\(293\) 412.791 + 170.984i 1.40884 + 0.583562i 0.952031 0.306002i \(-0.0989914\pi\)
0.456811 + 0.889564i \(0.348991\pi\)
\(294\) 0 0
\(295\) 43.1093 43.1093i 0.146133 0.146133i
\(296\) 0 0
\(297\) −32.2660 + 32.2660i −0.108640 + 0.108640i
\(298\) 0 0
\(299\) −558.615 231.386i −1.86828 0.773866i
\(300\) 0 0
\(301\) 491.569 203.615i 1.63312 0.676461i
\(302\) 0 0
\(303\) 32.3094 0.106632
\(304\) 0 0
\(305\) 19.4507i 0.0637726i
\(306\) 0 0
\(307\) 42.3557 + 102.256i 0.137967 + 0.333081i 0.977728 0.209874i \(-0.0673054\pi\)
−0.839762 + 0.542955i \(0.817305\pi\)
\(308\) 0 0
\(309\) 3.93177 9.49213i 0.0127242 0.0307189i
\(310\) 0 0
\(311\) 337.326 + 337.326i 1.08465 + 1.08465i 0.996069 + 0.0885790i \(0.0282326\pi\)
0.0885790 + 0.996069i \(0.471767\pi\)
\(312\) 0 0
\(313\) −70.0735 70.0735i −0.223877 0.223877i 0.586252 0.810129i \(-0.300603\pi\)
−0.810129 + 0.586252i \(0.800603\pi\)
\(314\) 0 0
\(315\) −58.0707 + 140.195i −0.184351 + 0.445063i
\(316\) 0 0
\(317\) −32.8632 79.3388i −0.103669 0.250280i 0.863530 0.504297i \(-0.168248\pi\)
−0.967200 + 0.254017i \(0.918248\pi\)
\(318\) 0 0
\(319\) 74.0450i 0.232116i
\(320\) 0 0
\(321\) 83.5940 0.260417
\(322\) 0 0
\(323\) 127.203 52.6891i 0.393816 0.163124i
\(324\) 0 0
\(325\) 315.081 + 130.511i 0.969480 + 0.401572i
\(326\) 0 0
\(327\) 56.6469 56.6469i 0.173232 0.173232i
\(328\) 0 0
\(329\) −221.965 + 221.965i −0.674665 + 0.674665i
\(330\) 0 0
\(331\) −124.865 51.7206i −0.377234 0.156256i 0.186006 0.982549i \(-0.440446\pi\)
−0.563240 + 0.826293i \(0.690446\pi\)
\(332\) 0 0
\(333\) −204.223 + 84.5919i −0.613282 + 0.254030i
\(334\) 0 0
\(335\) −149.901 −0.447466
\(336\) 0 0
\(337\) 323.529i 0.960027i 0.877261 + 0.480014i \(0.159368\pi\)
−0.877261 + 0.480014i \(0.840632\pi\)
\(338\) 0 0
\(339\) 35.3077 + 85.2404i 0.104153 + 0.251447i
\(340\) 0 0
\(341\) 10.5373 25.4394i 0.0309013 0.0746024i
\(342\) 0 0
\(343\) −106.226 106.226i −0.309696 0.309696i
\(344\) 0 0
\(345\) −87.0550 87.0550i −0.252333 0.252333i
\(346\) 0 0
\(347\) 135.065 326.076i 0.389236 0.939700i −0.600866 0.799350i \(-0.705177\pi\)
0.990102 0.140350i \(-0.0448226\pi\)
\(348\) 0 0
\(349\) −187.869 453.555i −0.538305 1.29958i −0.925905 0.377756i \(-0.876696\pi\)
0.387600 0.921828i \(-0.373304\pi\)
\(350\) 0 0
\(351\) 424.282i 1.20878i
\(352\) 0 0
\(353\) −70.5556 −0.199874 −0.0999372 0.994994i \(-0.531864\pi\)
−0.0999372 + 0.994994i \(0.531864\pi\)
\(354\) 0 0
\(355\) −20.3105 + 8.41289i −0.0572127 + 0.0236983i
\(356\) 0 0
\(357\) 76.7478 + 31.7900i 0.214980 + 0.0890475i
\(358\) 0 0
\(359\) −409.567 + 409.567i −1.14086 + 1.14086i −0.152561 + 0.988294i \(0.548752\pi\)
−0.988294 + 0.152561i \(0.951248\pi\)
\(360\) 0 0
\(361\) −93.6563 + 93.6563i −0.259436 + 0.259436i
\(362\) 0 0
\(363\) −160.932 66.6604i −0.443340 0.183637i
\(364\) 0 0
\(365\) −215.113 + 89.1026i −0.589350 + 0.244117i
\(366\) 0 0
\(367\) 513.680 1.39967 0.699837 0.714303i \(-0.253256\pi\)
0.699837 + 0.714303i \(0.253256\pi\)
\(368\) 0 0
\(369\) 547.191i 1.48290i
\(370\) 0 0
\(371\) −35.4419 85.5644i −0.0955308 0.230632i
\(372\) 0 0
\(373\) 46.5164 112.301i 0.124709 0.301074i −0.849178 0.528106i \(-0.822902\pi\)
0.973887 + 0.227032i \(0.0729023\pi\)
\(374\) 0 0
\(375\) 114.180 + 114.180i 0.304481 + 0.304481i
\(376\) 0 0
\(377\) 486.828 + 486.828i 1.29132 + 1.29132i
\(378\) 0 0
\(379\) −172.090 + 415.462i −0.454064 + 1.09621i 0.516699 + 0.856167i \(0.327160\pi\)
−0.970763 + 0.240040i \(0.922840\pi\)
\(380\) 0 0
\(381\) 100.683 + 243.069i 0.264259 + 0.637977i
\(382\) 0 0
\(383\) 430.627i 1.12435i 0.827017 + 0.562177i \(0.190036\pi\)
−0.827017 + 0.562177i \(0.809964\pi\)
\(384\) 0 0
\(385\) 43.4451 0.112844
\(386\) 0 0
\(387\) 370.170 153.329i 0.956512 0.396200i
\(388\) 0 0
\(389\) −55.8615 23.1386i −0.143603 0.0594823i 0.309725 0.950826i \(-0.399763\pi\)
−0.453327 + 0.891344i \(0.649763\pi\)
\(390\) 0 0
\(391\) 146.570 146.570i 0.374860 0.374860i
\(392\) 0 0
\(393\) −100.959 + 100.959i −0.256892 + 0.256892i
\(394\) 0 0
\(395\) 173.601 + 71.9080i 0.439497 + 0.182046i
\(396\) 0 0
\(397\) 67.6641 28.0274i 0.170439 0.0705979i −0.295833 0.955240i \(-0.595597\pi\)
0.466271 + 0.884642i \(0.345597\pi\)
\(398\) 0 0
\(399\) −297.723 −0.746174
\(400\) 0 0
\(401\) 536.024i 1.33672i −0.743839 0.668359i \(-0.766997\pi\)
0.743839 0.668359i \(-0.233003\pi\)
\(402\) 0 0
\(403\) 97.9774 + 236.538i 0.243120 + 0.586944i
\(404\) 0 0
\(405\) −24.8877 + 60.0842i −0.0614511 + 0.148356i
\(406\) 0 0
\(407\) 44.7505 + 44.7505i 0.109952 + 0.109952i
\(408\) 0 0
\(409\) −540.379 540.379i −1.32122 1.32122i −0.912790 0.408430i \(-0.866077\pi\)
−0.408430 0.912790i \(-0.633923\pi\)
\(410\) 0 0
\(411\) −47.0948 + 113.697i −0.114586 + 0.276635i
\(412\) 0 0
\(413\) −84.9395 205.062i −0.205665 0.496518i
\(414\) 0 0
\(415\) 7.98765i 0.0192474i
\(416\) 0 0
\(417\) 268.345 0.643512
\(418\) 0 0
\(419\) 341.184 141.323i 0.814281 0.337286i 0.0636205 0.997974i \(-0.479735\pi\)
0.750661 + 0.660688i \(0.229735\pi\)
\(420\) 0 0
\(421\) −339.196 140.500i −0.805692 0.333728i −0.0584581 0.998290i \(-0.518618\pi\)
−0.747234 + 0.664561i \(0.768618\pi\)
\(422\) 0 0
\(423\) −167.148 + 167.148i −0.395149 + 0.395149i
\(424\) 0 0
\(425\) −82.6714 + 82.6714i −0.194521 + 0.194521i
\(426\) 0 0
\(427\) 65.4234 + 27.0993i 0.153216 + 0.0634643i
\(428\) 0 0
\(429\) −48.2661 + 19.9925i −0.112508 + 0.0466025i
\(430\) 0 0
\(431\) 154.504 0.358478 0.179239 0.983806i \(-0.442637\pi\)
0.179239 + 0.983806i \(0.442637\pi\)
\(432\) 0 0
\(433\) 506.808i 1.17046i 0.810868 + 0.585228i \(0.198995\pi\)
−0.810868 + 0.585228i \(0.801005\pi\)
\(434\) 0 0
\(435\) 53.6465 + 129.514i 0.123325 + 0.297734i
\(436\) 0 0
\(437\) −284.291 + 686.338i −0.650550 + 1.57057i
\(438\) 0 0
\(439\) −144.746 144.746i −0.329718 0.329718i 0.522761 0.852479i \(-0.324902\pi\)
−0.852479 + 0.522761i \(0.824902\pi\)
\(440\) 0 0
\(441\) 155.328 + 155.328i 0.352218 + 0.352218i
\(442\) 0 0
\(443\) −230.959 + 557.584i −0.521351 + 1.25865i 0.415713 + 0.909496i \(0.363532\pi\)
−0.937064 + 0.349158i \(0.886468\pi\)
\(444\) 0 0
\(445\) −49.2078 118.798i −0.110579 0.266962i
\(446\) 0 0
\(447\) 69.9132i 0.156405i
\(448\) 0 0
\(449\) −0.201052 −0.000447778 −0.000223889 1.00000i \(-0.500071\pi\)
−0.000223889 1.00000i \(0.500071\pi\)
\(450\) 0 0
\(451\) −144.736 + 59.9518i −0.320923 + 0.132931i
\(452\) 0 0
\(453\) −132.727 54.9774i −0.292996 0.121363i
\(454\) 0 0
\(455\) −285.641 + 285.641i −0.627782 + 0.627782i
\(456\) 0 0
\(457\) 226.835 226.835i 0.496358 0.496358i −0.413944 0.910302i \(-0.635849\pi\)
0.910302 + 0.413944i \(0.135849\pi\)
\(458\) 0 0
\(459\) 134.379 + 55.6618i 0.292766 + 0.121268i
\(460\) 0 0
\(461\) −496.600 + 205.699i −1.07722 + 0.446201i −0.849535 0.527533i \(-0.823117\pi\)
−0.227690 + 0.973734i \(0.573117\pi\)
\(462\) 0 0
\(463\) −520.019 −1.12315 −0.561576 0.827425i \(-0.689805\pi\)
−0.561576 + 0.827425i \(0.689805\pi\)
\(464\) 0 0
\(465\) 52.1312i 0.112110i
\(466\) 0 0
\(467\) −35.4966 85.6964i −0.0760099 0.183504i 0.881307 0.472544i \(-0.156664\pi\)
−0.957317 + 0.289040i \(0.906664\pi\)
\(468\) 0 0
\(469\) −208.847 + 504.202i −0.445303 + 1.07506i
\(470\) 0 0
\(471\) 204.743 + 204.743i 0.434699 + 0.434699i
\(472\) 0 0
\(473\) −81.1137 81.1137i −0.171488 0.171488i
\(474\) 0 0
\(475\) 160.351 387.122i 0.337582 0.814994i
\(476\) 0 0
\(477\) −26.6891 64.4332i −0.0559520 0.135080i
\(478\) 0 0
\(479\) 163.116i 0.340535i 0.985398 + 0.170268i \(0.0544632\pi\)
−0.985398 + 0.170268i \(0.945537\pi\)
\(480\) 0 0
\(481\) −588.447 −1.22338
\(482\) 0 0
\(483\) −414.102 + 171.527i −0.857355 + 0.355128i
\(484\) 0 0
\(485\) −206.106 85.3718i −0.424960 0.176024i
\(486\) 0 0
\(487\) 371.724 371.724i 0.763294 0.763294i −0.213622 0.976916i \(-0.568526\pi\)
0.976916 + 0.213622i \(0.0685262\pi\)
\(488\) 0 0
\(489\) −303.817 + 303.817i −0.621302 + 0.621302i
\(490\) 0 0
\(491\) −281.201 116.477i −0.572710 0.237224i 0.0774824 0.996994i \(-0.475312\pi\)
−0.650193 + 0.759769i \(0.725312\pi\)
\(492\) 0 0
\(493\) −218.056 + 90.3220i −0.442305 + 0.183209i
\(494\) 0 0
\(495\) 32.7158 0.0660924
\(496\) 0 0
\(497\) 80.0367i 0.161040i
\(498\) 0 0
\(499\) 236.126 + 570.059i 0.473199 + 1.14240i 0.962741 + 0.270424i \(0.0871639\pi\)
−0.489542 + 0.871980i \(0.662836\pi\)
\(500\) 0 0
\(501\) 79.8656 192.813i 0.159412 0.384855i
\(502\) 0 0
\(503\) 12.8902 + 12.8902i 0.0256266 + 0.0256266i 0.719804 0.694177i \(-0.244232\pi\)
−0.694177 + 0.719804i \(0.744232\pi\)
\(504\) 0 0
\(505\) −38.0857 38.0857i −0.0754173 0.0754173i
\(506\) 0 0
\(507\) 89.7851 216.760i 0.177091 0.427535i
\(508\) 0 0
\(509\) −59.1272 142.746i −0.116163 0.280443i 0.855095 0.518472i \(-0.173499\pi\)
−0.971258 + 0.238028i \(0.923499\pi\)
\(510\) 0 0
\(511\) 847.685i 1.65888i
\(512\) 0 0
\(513\) −521.291 −1.01616
\(514\) 0 0
\(515\) −15.8238 + 6.55444i −0.0307259 + 0.0127271i
\(516\) 0 0
\(517\) 62.5251 + 25.8988i 0.120938 + 0.0500943i
\(518\) 0 0
\(519\) −212.982 + 212.982i −0.410369 + 0.410369i
\(520\) 0 0
\(521\) 119.838 119.838i 0.230015 0.230015i −0.582684 0.812699i \(-0.697997\pi\)
0.812699 + 0.582684i \(0.197997\pi\)
\(522\) 0 0
\(523\) 689.004 + 285.395i 1.31741 + 0.545688i 0.927037 0.374970i \(-0.122347\pi\)
0.390370 + 0.920658i \(0.372347\pi\)
\(524\) 0 0
\(525\) 233.570 96.7480i 0.444896 0.184282i
\(526\) 0 0
\(527\) −87.7707 −0.166548
\(528\) 0 0
\(529\) 589.413i 1.11420i
\(530\) 0 0
\(531\) −63.9626 154.419i −0.120457 0.290809i
\(532\) 0 0
\(533\) 557.438 1345.77i 1.04585 2.52490i
\(534\) 0 0
\(535\) −98.5390 98.5390i −0.184185 0.184185i
\(536\) 0 0
\(537\) 277.960 + 277.960i 0.517617 + 0.517617i
\(538\) 0 0
\(539\) 24.0673 58.1037i 0.0446519 0.107799i
\(540\) 0 0
\(541\) 294.810 + 711.735i 0.544936 + 1.31559i 0.921204 + 0.389081i \(0.127207\pi\)
−0.376267 + 0.926511i \(0.622793\pi\)
\(542\) 0 0
\(543\) 23.6020i 0.0434658i
\(544\) 0 0
\(545\) −133.549 −0.245043
\(546\) 0 0
\(547\) −518.930 + 214.948i −0.948683 + 0.392957i −0.802736 0.596335i \(-0.796623\pi\)
−0.145948 + 0.989292i \(0.546623\pi\)
\(548\) 0 0
\(549\) 49.2663 + 20.4068i 0.0897382 + 0.0371708i
\(550\) 0 0
\(551\) 598.138 598.138i 1.08555 1.08555i
\(552\) 0 0
\(553\) 483.734 483.734i 0.874745 0.874745i
\(554\) 0 0
\(555\) −110.696 45.8520i −0.199453 0.0826162i
\(556\) 0 0
\(557\) 883.511 365.962i 1.58620 0.657024i 0.596816 0.802378i \(-0.296432\pi\)
0.989380 + 0.145355i \(0.0464323\pi\)
\(558\) 0 0
\(559\) 1066.61 1.90806
\(560\) 0 0
\(561\) 17.9098i 0.0319248i
\(562\) 0 0
\(563\) −385.055 929.606i −0.683935 1.65117i −0.756656 0.653813i \(-0.773168\pi\)
0.0727214 0.997352i \(-0.476832\pi\)
\(564\) 0 0
\(565\) 58.8596 142.100i 0.104176 0.251504i
\(566\) 0 0
\(567\) 167.423 + 167.423i 0.295278 + 0.295278i
\(568\) 0 0
\(569\) −503.029 503.029i −0.884058 0.884058i 0.109886 0.993944i \(-0.464951\pi\)
−0.993944 + 0.109886i \(0.964951\pi\)
\(570\) 0 0
\(571\) 48.1525 116.250i 0.0843301 0.203591i −0.876089 0.482149i \(-0.839856\pi\)
0.960419 + 0.278558i \(0.0898564\pi\)
\(572\) 0 0
\(573\) 210.741 + 508.773i 0.367785 + 0.887910i
\(574\) 0 0
\(575\) 630.830i 1.09710i
\(576\) 0 0
\(577\) −11.8629 −0.0205595 −0.0102798 0.999947i \(-0.503272\pi\)
−0.0102798 + 0.999947i \(0.503272\pi\)
\(578\) 0 0
\(579\) −182.158 + 75.4522i −0.314607 + 0.130315i
\(580\) 0 0
\(581\) −26.8670 11.1287i −0.0462426 0.0191543i
\(582\) 0 0
\(583\) −14.1190 + 14.1190i −0.0242178 + 0.0242178i
\(584\) 0 0
\(585\) −215.098 + 215.098i −0.367689 + 0.367689i
\(586\) 0 0
\(587\) 496.631 + 205.711i 0.846049 + 0.350445i 0.763236 0.646120i \(-0.223610\pi\)
0.0828132 + 0.996565i \(0.473610\pi\)
\(588\) 0 0
\(589\) 290.621 120.379i 0.493414 0.204379i
\(590\) 0 0
\(591\) −187.211 −0.316770
\(592\) 0 0
\(593\) 410.471i 0.692193i −0.938199 0.346097i \(-0.887507\pi\)
0.938199 0.346097i \(-0.112493\pi\)
\(594\) 0 0
\(595\) −52.9954 127.942i −0.0890678 0.215029i
\(596\) 0 0
\(597\) −72.3774 + 174.735i −0.121235 + 0.292688i
\(598\) 0 0
\(599\) −565.778 565.778i −0.944537 0.944537i 0.0540033 0.998541i \(-0.482802\pi\)
−0.998541 + 0.0540033i \(0.982802\pi\)
\(600\) 0 0
\(601\) 224.391 + 224.391i 0.373362 + 0.373362i 0.868700 0.495338i \(-0.164956\pi\)
−0.495338 + 0.868700i \(0.664956\pi\)
\(602\) 0 0
\(603\) −157.270 + 379.683i −0.260812 + 0.629656i
\(604\) 0 0
\(605\) 111.126 + 268.282i 0.183679 + 0.443441i
\(606\) 0 0
\(607\) 19.8654i 0.0327271i 0.999866 + 0.0163636i \(0.00520892\pi\)
−0.999866 + 0.0163636i \(0.994791\pi\)
\(608\) 0 0
\(609\) 510.371 0.838047
\(610\) 0 0
\(611\) −581.365 + 240.809i −0.951498 + 0.394123i
\(612\) 0 0
\(613\) −905.460 375.054i −1.47710 0.611833i −0.508631 0.860985i \(-0.669848\pi\)
−0.968464 + 0.249152i \(0.919848\pi\)
\(614\) 0 0
\(615\) 209.726 209.726i 0.341019 0.341019i
\(616\) 0 0
\(617\) 673.907 673.907i 1.09223 1.09223i 0.0969409 0.995290i \(-0.469094\pi\)
0.995290 0.0969409i \(-0.0309058\pi\)
\(618\) 0 0
\(619\) −354.963 147.030i −0.573446 0.237529i 0.0770649 0.997026i \(-0.475445\pi\)
−0.650511 + 0.759497i \(0.725445\pi\)
\(620\) 0 0
\(621\) −725.062 + 300.330i −1.16757 + 0.483624i
\(622\) 0 0
\(623\) −468.143 −0.751433
\(624\) 0 0
\(625\) 202.389i 0.323822i
\(626\) 0 0
\(627\) 24.5636 + 59.3018i 0.0391764 + 0.0945803i
\(628\) 0 0
\(629\) 77.1987 186.374i 0.122732 0.296302i
\(630\) 0 0
\(631\) −494.698 494.698i −0.783991 0.783991i 0.196511 0.980502i \(-0.437039\pi\)
−0.980502 + 0.196511i \(0.937039\pi\)
\(632\) 0 0
\(633\) −57.4669 57.4669i −0.0907850 0.0907850i
\(634\) 0 0
\(635\) 167.843 405.208i 0.264319 0.638122i
\(636\) 0 0
\(637\) 223.781 + 540.255i 0.351304 + 0.848124i
\(638\) 0 0
\(639\) 60.2706i 0.0943202i
\(640\) 0 0
\(641\) 440.457 0.687141 0.343571 0.939127i \(-0.388364\pi\)
0.343571 + 0.939127i \(0.388364\pi\)
\(642\) 0 0
\(643\) 211.055 87.4220i 0.328235 0.135960i −0.212479 0.977166i \(-0.568154\pi\)
0.540715 + 0.841206i \(0.318154\pi\)
\(644\) 0 0
\(645\) 200.646 + 83.1103i 0.311079 + 0.128853i
\(646\) 0 0
\(647\) 515.935 515.935i 0.797426 0.797426i −0.185263 0.982689i \(-0.559314\pi\)
0.982689 + 0.185263i \(0.0593136\pi\)
\(648\) 0 0
\(649\) −33.8372 + 33.8372i −0.0521375 + 0.0521375i
\(650\) 0 0
\(651\) 175.346 + 72.6309i 0.269349 + 0.111568i
\(652\) 0 0
\(653\) 613.161 253.980i 0.938991 0.388943i 0.139909 0.990164i \(-0.455319\pi\)
0.799082 + 0.601222i \(0.205319\pi\)
\(654\) 0 0
\(655\) 238.016 0.363383
\(656\) 0 0
\(657\) 638.339i 0.971596i
\(658\) 0 0
\(659\) 19.4679 + 46.9996i 0.0295416 + 0.0713196i 0.937962 0.346738i \(-0.112711\pi\)
−0.908420 + 0.418058i \(0.862711\pi\)
\(660\) 0 0
\(661\) −46.1458 + 111.406i −0.0698122 + 0.168541i −0.954934 0.296817i \(-0.904075\pi\)
0.885122 + 0.465359i \(0.154075\pi\)
\(662\) 0 0
\(663\) 117.752 + 117.752i 0.177606 + 0.177606i
\(664\) 0 0
\(665\) 350.950 + 350.950i 0.527745 + 0.527745i
\(666\) 0 0
\(667\) 487.344 1176.55i 0.730650 1.76395i
\(668\) 0 0
\(669\) −30.0002 72.4270i −0.0448434 0.108262i
\(670\) 0 0
\(671\) 15.2672i 0.0227528i
\(672\) 0 0
\(673\) −352.344 −0.523542 −0.261771 0.965130i \(-0.584306\pi\)
−0.261771 + 0.965130i \(0.584306\pi\)
\(674\) 0 0
\(675\) 408.964 169.398i 0.605872 0.250961i
\(676\) 0 0
\(677\) 1178.26 + 488.051i 1.74041 + 0.720902i 0.998742 + 0.0501357i \(0.0159654\pi\)
0.741669 + 0.670766i \(0.234035\pi\)
\(678\) 0 0
\(679\) −574.306 + 574.306i −0.845812 + 0.845812i
\(680\) 0 0
\(681\) 372.033 372.033i 0.546304 0.546304i
\(682\) 0 0
\(683\) 414.446 + 171.669i 0.606802 + 0.251346i 0.664861 0.746967i \(-0.268491\pi\)
−0.0580582 + 0.998313i \(0.518491\pi\)
\(684\) 0 0
\(685\) 189.538 78.5093i 0.276698 0.114612i
\(686\) 0 0
\(687\) −394.768 −0.574626
\(688\) 0 0
\(689\) 185.657i 0.269459i
\(690\) 0 0
\(691\) −268.707 648.715i −0.388866 0.938806i −0.990181 0.139794i \(-0.955356\pi\)
0.601314 0.799012i \(-0.294644\pi\)
\(692\) 0 0
\(693\) 45.5807 110.041i 0.0657729 0.158790i
\(694\) 0 0
\(695\) −316.319 316.319i −0.455136 0.455136i
\(696\) 0 0
\(697\) 353.106 + 353.106i 0.506608 + 0.506608i
\(698\) 0 0
\(699\) −25.6368 + 61.8927i −0.0366764 + 0.0885447i
\(700\) 0 0
\(701\) −464.382 1121.12i −0.662457 1.59931i −0.793941 0.607995i \(-0.791974\pi\)
0.131484 0.991318i \(-0.458026\pi\)
\(702\) 0 0
\(703\) 722.990i 1.02844i
\(704\) 0 0
\(705\) −128.128 −0.181742
\(706\) 0 0
\(707\) −181.166 + 75.0414i −0.256246 + 0.106141i
\(708\) 0 0
\(709\) −591.984 245.208i −0.834957 0.345850i −0.0760937 0.997101i \(-0.524245\pi\)
−0.758863 + 0.651250i \(0.774245\pi\)
\(710\) 0 0
\(711\) 364.270 364.270i 0.512334 0.512334i
\(712\) 0 0
\(713\) 334.870 334.870i 0.469664 0.469664i
\(714\) 0 0
\(715\) 80.4619 + 33.3284i 0.112534 + 0.0466132i
\(716\) 0 0
\(717\) 123.633 51.2104i 0.172431 0.0714232i
\(718\) 0 0
\(719\) −906.230 −1.26040 −0.630202 0.776432i \(-0.717028\pi\)
−0.630202 + 0.776432i \(0.717028\pi\)
\(720\) 0 0
\(721\) 62.3563i 0.0864858i
\(722\) 0 0
\(723\) −11.9407 28.8274i −0.0165155 0.0398720i
\(724\) 0 0
\(725\) −274.881 + 663.622i −0.379147 + 0.915341i
\(726\) 0 0
\(727\) 317.957 + 317.957i 0.437355 + 0.437355i 0.891121 0.453766i \(-0.149920\pi\)
−0.453766 + 0.891121i \(0.649920\pi\)
\(728\) 0 0
\(729\) −95.8544 95.8544i −0.131488 0.131488i
\(730\) 0 0
\(731\) −139.929 + 337.818i −0.191421 + 0.462131i
\(732\) 0 0
\(733\) 159.623 + 385.363i 0.217766 + 0.525734i 0.994577 0.103999i \(-0.0331640\pi\)
−0.776811 + 0.629734i \(0.783164\pi\)
\(734\) 0 0
\(735\) 119.068i 0.161997i
\(736\) 0 0
\(737\) 117.660 0.159647
\(738\) 0 0
\(739\) 380.514 157.614i 0.514904 0.213280i −0.110073 0.993924i \(-0.535108\pi\)
0.624977 + 0.780643i \(0.285108\pi\)
\(740\) 0 0
\(741\) −551.395 228.395i −0.744123 0.308226i
\(742\) 0 0
\(743\) 5.76228 5.76228i 0.00775542 0.00775542i −0.703218 0.710974i \(-0.748254\pi\)
0.710974 + 0.703218i \(0.248254\pi\)
\(744\) 0 0
\(745\) 82.4123 82.4123i 0.110620 0.110620i
\(746\) 0 0
\(747\) −20.2318 8.38030i −0.0270841 0.0112186i
\(748\) 0 0
\(749\) −468.729 + 194.154i −0.625807 + 0.259218i
\(750\) 0 0
\(751\) −302.377 −0.402632 −0.201316 0.979526i \(-0.564522\pi\)
−0.201316 + 0.979526i \(0.564522\pi\)
\(752\) 0 0
\(753\) 408.539i 0.542548i
\(754\) 0 0
\(755\) 91.6499 + 221.262i 0.121391 + 0.293063i
\(756\) 0 0
\(757\) 9.31627 22.4915i 0.0123068 0.0297113i −0.917607 0.397490i \(-0.869881\pi\)
0.929914 + 0.367778i \(0.119881\pi\)
\(758\) 0 0
\(759\) 68.3309 + 68.3309i 0.0900276 + 0.0900276i
\(760\) 0 0
\(761\) −163.034 163.034i −0.214236 0.214236i 0.591828 0.806064i \(-0.298406\pi\)
−0.806064 + 0.591828i \(0.798406\pi\)
\(762\) 0 0
\(763\) −186.064 + 449.198i −0.243859 + 0.588727i
\(764\) 0 0
\(765\) −39.9075 96.3452i −0.0521667 0.125941i
\(766\) 0 0
\(767\) 444.943i 0.580109i
\(768\) 0 0
\(769\) 180.205 0.234337 0.117168 0.993112i \(-0.462618\pi\)
0.117168 + 0.993112i \(0.462618\pi\)
\(770\) 0 0
\(771\) 324.811 134.541i 0.421286 0.174502i
\(772\) 0 0
\(773\) −196.725 81.4860i −0.254495 0.105415i 0.251789 0.967782i \(-0.418981\pi\)
−0.506284 + 0.862367i \(0.668981\pi\)
\(774\) 0 0
\(775\) −188.880 + 188.880i −0.243716 + 0.243716i
\(776\) 0 0
\(777\) −308.452 + 308.452i −0.396978 + 0.396978i
\(778\) 0 0
\(779\) −1653.48 684.892i −2.12256 0.879194i
\(780\) 0 0
\(781\) 15.9421 6.60342i 0.0204124 0.00845508i
\(782\) 0 0
\(783\) 893.620 1.14128
\(784\) 0 0
\(785\) 482.695i 0.614898i
\(786\) 0 0
\(787\) −80.6847 194.790i −0.102522 0.247510i 0.864293 0.502990i \(-0.167767\pi\)
−0.966814 + 0.255480i \(0.917767\pi\)
\(788\) 0 0
\(789\) 25.7412 62.1448i 0.0326251 0.0787640i
\(790\) 0 0
\(791\) −395.956 395.956i −0.500576 0.500576i
\(792\) 0 0
\(793\) 100.378 + 100.378i 0.126580 + 0.126580i
\(794\) 0 0
\(795\) 14.4665 34.9252i 0.0181969 0.0439311i
\(796\) 0 0
\(797\) 256.509 + 619.268i 0.321843 + 0.776999i 0.999147 + 0.0412950i \(0.0131483\pi\)
−0.677304 + 0.735704i \(0.736852\pi\)
\(798\) 0 0
\(799\) 215.723i 0.269992i
\(800\) 0 0
\(801\) −352.529 −0.440111
\(802\) 0 0
\(803\) 168.846 69.9382i 0.210269 0.0870961i
\(804\) 0 0
\(805\) 690.328 + 285.943i 0.857551 + 0.355209i
\(806\) 0 0
\(807\) −131.188 + 131.188i −0.162562 + 0.162562i
\(808\) 0 0
\(809\) −1008.10 + 1008.10i −1.24611 + 1.24611i −0.288683 + 0.957425i \(0.593217\pi\)
−0.957425 + 0.288683i \(0.906783\pi\)
\(810\) 0 0
\(811\) 1271.85 + 526.816i 1.56825 + 0.649588i 0.986497 0.163780i \(-0.0523688\pi\)
0.581748 + 0.813369i \(0.302369\pi\)
\(812\) 0 0
\(813\) −76.1044 + 31.5235i −0.0936094 + 0.0387743i
\(814\) 0 0
\(815\) 716.266 0.878854
\(816\) 0 0
\(817\) 1310.48i 1.60401i
\(818\) 0 0
\(819\) 423.814 + 1023.18i 0.517477 + 1.24930i
\(820\) 0 0
\(821\) 119.922 289.516i 0.146068 0.352639i −0.833865 0.551969i \(-0.813877\pi\)
0.979932 + 0.199330i \(0.0638767\pi\)
\(822\) 0 0
\(823\) 607.735 + 607.735i 0.738439 + 0.738439i 0.972276 0.233837i \(-0.0751282\pi\)
−0.233837 + 0.972276i \(0.575128\pi\)
\(824\) 0 0
\(825\) −38.5414 38.5414i −0.0467168 0.0467168i
\(826\) 0 0
\(827\) −246.520 + 595.152i −0.298090 + 0.719652i 0.701883 + 0.712292i \(0.252343\pi\)
−0.999973 + 0.00736012i \(0.997657\pi\)
\(828\) 0 0
\(829\) −393.211 949.295i −0.474319 1.14511i −0.962236 0.272218i \(-0.912243\pi\)
0.487916 0.872890i \(-0.337757\pi\)
\(830\) 0 0
\(831\) 138.972i 0.167235i
\(832\) 0 0
\(833\) −200.469 −0.240659
\(834\) 0 0
\(835\) −321.428 + 133.140i −0.384943 + 0.159449i
\(836\) 0 0
\(837\) 307.018 + 127.171i 0.366808 + 0.151937i
\(838\) 0 0
\(839\) −575.067 + 575.067i −0.685420 + 0.685420i −0.961216 0.275796i \(-0.911059\pi\)
0.275796 + 0.961216i \(0.411059\pi\)
\(840\) 0 0
\(841\) −430.678 + 430.678i −0.512102 + 0.512102i
\(842\) 0 0
\(843\) 26.8929 + 11.1394i 0.0319015 + 0.0132140i
\(844\) 0 0
\(845\) −361.350 + 149.676i −0.427633 + 0.177131i
\(846\) 0 0
\(847\) 1057.21 1.24818
\(848\) 0 0
\(849\) 526.620i 0.620283i
\(850\) 0 0
\(851\) 416.535 + 1005.61i 0.489466 + 1.18167i
\(852\) 0 0
\(853\) −304.017 + 733.961i −0.356409 + 0.860447i 0.639390 + 0.768882i \(0.279187\pi\)
−0.995799 + 0.0915645i \(0.970813\pi\)
\(854\) 0 0
\(855\) 264.279 + 264.279i 0.309098 + 0.309098i
\(856\) 0 0
\(857\) −241.394 241.394i −0.281673 0.281673i 0.552103 0.833776i \(-0.313826\pi\)
−0.833776 + 0.552103i \(0.813826\pi\)
\(858\) 0 0
\(859\) −443.212 + 1070.01i −0.515963 + 1.24564i 0.424401 + 0.905474i \(0.360485\pi\)
−0.940364 + 0.340170i \(0.889515\pi\)
\(860\) 0 0
\(861\) −413.230 997.625i −0.479942 1.15868i
\(862\) 0 0
\(863\) 167.859i 0.194507i 0.995260 + 0.0972533i \(0.0310057\pi\)
−0.995260 + 0.0972533i \(0.968994\pi\)
\(864\) 0 0
\(865\) 502.117 0.580482
\(866\) 0 0
\(867\) 344.031 142.502i 0.396806 0.164363i
\(868\) 0 0
\(869\) −136.263 56.4418i −0.156804 0.0649503i
\(870\) 0 0
\(871\) −773.586 + 773.586i −0.888158 + 0.888158i
\(872\) 0 0
\(873\) −432.474 + 432.474i −0.495388 + 0.495388i
\(874\) 0 0
\(875\) −905.426 375.040i −1.03477 0.428617i
\(876\) 0 0
\(877\) −659.079 + 272.999i −0.751515 + 0.311288i −0.725360 0.688370i \(-0.758326\pi\)
−0.0261554 + 0.999658i \(0.508326\pi\)
\(878\) 0 0
\(879\) 663.964 0.755363
\(880\) 0 0
\(881\) 806.984i 0.915987i 0.888956 + 0.457993i \(0.151432\pi\)
−0.888956 + 0.457993i \(0.848568\pi\)
\(882\) 0 0
\(883\) 118.704 + 286.577i 0.134433 + 0.324549i 0.976733 0.214459i \(-0.0687989\pi\)
−0.842300 + 0.539009i \(0.818799\pi\)
\(884\) 0 0
\(885\) 34.6701 83.7011i 0.0391753 0.0945776i
\(886\) 0 0
\(887\) 727.865 + 727.865i 0.820592 + 0.820592i 0.986193 0.165601i \(-0.0529563\pi\)
−0.165601 + 0.986193i \(0.552956\pi\)
\(888\) 0 0
\(889\) −1129.10 1129.10i −1.27008 1.27008i
\(890\) 0 0
\(891\) 19.5348 47.1611i 0.0219246 0.0529306i
\(892\) 0 0
\(893\) 295.869 + 714.290i 0.331320 + 0.799877i
\(894\) 0 0
\(895\) 655.308i 0.732188i
\(896\) 0 0
\(897\) −898.518 −1.00169
\(898\) 0 0
\(899\) −498.196 + 206.359i −0.554167 + 0.229543i
\(900\) 0 0
\(901\) 58.8018 + 24.3565i 0.0652628 + 0.0270328i
\(902\) 0 0
\(903\) 559.093 559.093i 0.619151 0.619151i
\(904\) 0 0
\(905\) 27.8215 27.8215i 0.0307420 0.0307420i
\(906\) 0 0
\(907\) −711.116 294.554i −0.784031 0.324756i −0.0454897 0.998965i \(-0.514485\pi\)
−0.738541 + 0.674209i \(0.764485\pi\)
\(908\) 0 0
\(909\) −136.425 + 56.5090i −0.150082 + 0.0621661i
\(910\) 0 0
\(911\) −758.696 −0.832817 −0.416409 0.909178i \(-0.636711\pi\)
−0.416409 + 0.909178i \(0.636711\pi\)
\(912\) 0 0
\(913\) 6.26965i 0.00686708i
\(914\) 0 0
\(915\) 11.0612 + 26.7042i 0.0120888 + 0.0291849i
\(916\) 0 0
\(917\) 331.611 800.581i 0.361626 0.873043i
\(918\) 0 0
\(919\) 949.647 + 949.647i 1.03335 + 1.03335i 0.999424 + 0.0339243i \(0.0108005\pi\)
0.0339243 + 0.999424i \(0.489199\pi\)
\(920\) 0 0
\(921\) 116.302 + 116.302i 0.126278 + 0.126278i
\(922\) 0 0
\(923\) −61.3993 + 148.231i −0.0665215 + 0.160597i
\(924\) 0 0
\(925\) −234.943 567.202i −0.253992 0.613191i
\(926\) 0 0
\(927\) 46.9566i 0.0506544i
\(928\) 0 0
\(929\) 222.645 0.239661 0.119830 0.992794i \(-0.461765\pi\)
0.119830 + 0.992794i \(0.461765\pi\)
\(930\) 0 0
\(931\) 663.780 274.947i 0.712975 0.295324i
\(932\) 0 0
\(933\) 654.952 + 271.290i 0.701985 + 0.290772i
\(934\) 0 0
\(935\) −21.1117 + 21.1117i −0.0225794 + 0.0225794i
\(936\) 0 0
\(937\) −1027.40 + 1027.40i −1.09648 + 1.09648i −0.101659 + 0.994819i \(0.532415\pi\)
−0.994819 + 0.101659i \(0.967585\pi\)
\(938\) 0 0
\(939\) −136.055 56.3558i −0.144893 0.0600168i
\(940\) 0 0
\(941\) 892.441 369.661i 0.948397 0.392839i 0.145769 0.989319i \(-0.453434\pi\)
0.802628 + 0.596480i \(0.203434\pi\)
\(942\) 0 0
\(943\) −2694.40 −2.85726
\(944\) 0 0
\(945\) 524.321i 0.554837i
\(946\) 0 0
\(947\) −385.441 930.536i −0.407012 0.982615i −0.985919 0.167221i \(-0.946521\pi\)
0.578907 0.815394i \(-0.303479\pi\)
\(948\) 0 0
\(949\) −650.293 + 1569.95i −0.685240 + 1.65432i
\(950\) 0 0
\(951\) −90.2371 90.2371i −0.0948865 0.0948865i
\(952\) 0 0
\(953\) 648.910 + 648.910i 0.680913 + 0.680913i 0.960206 0.279293i \(-0.0901001\pi\)
−0.279293 + 0.960206i \(0.590100\pi\)
\(954\) 0 0
\(955\) 351.314 848.148i 0.367868 0.888113i
\(956\) 0 0
\(957\) −42.1081 101.658i −0.0440001 0.106226i
\(958\) 0 0
\(959\) 746.905i 0.778837i
\(960\) 0 0
\(961\) 760.470 0.791331
\(962\) 0 0
\(963\) −352.971 + 146.205i −0.366532 + 0.151823i
\(964\) 0 0
\(965\) 303.665 + 125.782i 0.314679 + 0.130344i
\(966\) 0 0
\(967\) −41.2757 + 41.2757i −0.0426842 + 0.0426842i −0.728127 0.685443i \(-0.759609\pi\)
0.685443 + 0.728127i \(0.259609\pi\)
\(968\) 0 0
\(969\) 144.676 144.676i 0.149304 0.149304i
\(970\) 0 0
\(971\) 213.816 + 88.5653i 0.220201 + 0.0912104i 0.490057 0.871690i \(-0.336976\pi\)
−0.269856 + 0.962901i \(0.586976\pi\)
\(972\) 0 0
\(973\) −1504.67 + 623.253i −1.54642 + 0.640547i
\(974\) 0 0
\(975\) 506.800 0.519795
\(976\) 0 0
\(977\) 314.091i 0.321485i 0.986996 + 0.160742i \(0.0513888\pi\)
−0.986996 + 0.160742i \(0.948611\pi\)
\(978\) 0 0
\(979\) 38.6240 + 93.2467i 0.0394526 + 0.0952469i
\(980\) 0 0
\(981\) −140.113 + 338.263i −0.142827 + 0.344815i
\(982\) 0 0
\(983\) −8.50847 8.50847i −0.00865562 0.00865562i 0.702766 0.711421i \(-0.251948\pi\)
−0.711421 + 0.702766i \(0.751948\pi\)
\(984\) 0 0
\(985\) 220.680 + 220.680i 0.224041 + 0.224041i
\(986\) 0 0
\(987\) −178.513 + 430.967i −0.180864 + 0.436644i
\(988\) 0 0
\(989\) −755.003 1822.74i −0.763400 1.84301i
\(990\) 0 0
\(991\) 93.7233i 0.0945745i −0.998881 0.0472872i \(-0.984942\pi\)
0.998881 0.0472872i \(-0.0150576\pi\)
\(992\) 0 0
\(993\) −200.842 −0.202257
\(994\) 0 0
\(995\) 291.291 120.657i 0.292754 0.121263i
\(996\) 0 0
\(997\) 287.749 + 119.189i 0.288614 + 0.119548i 0.522294 0.852766i \(-0.325077\pi\)
−0.233679 + 0.972314i \(0.575077\pi\)
\(998\) 0 0
\(999\) −540.075 + 540.075i −0.540616 + 0.540616i
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 256.3.h.b.31.5 28
4.3 odd 2 256.3.h.a.31.3 28
8.3 odd 2 128.3.h.a.15.5 28
8.5 even 2 32.3.h.a.27.6 yes 28
24.5 odd 2 288.3.u.a.91.2 28
32.3 odd 8 32.3.h.a.19.6 28
32.13 even 8 256.3.h.a.223.3 28
32.19 odd 8 inner 256.3.h.b.223.5 28
32.29 even 8 128.3.h.a.111.5 28
96.35 even 8 288.3.u.a.19.2 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
32.3.h.a.19.6 28 32.3 odd 8
32.3.h.a.27.6 yes 28 8.5 even 2
128.3.h.a.15.5 28 8.3 odd 2
128.3.h.a.111.5 28 32.29 even 8
256.3.h.a.31.3 28 4.3 odd 2
256.3.h.a.223.3 28 32.13 even 8
256.3.h.b.31.5 28 1.1 even 1 trivial
256.3.h.b.223.5 28 32.19 odd 8 inner
288.3.u.a.19.2 28 96.35 even 8
288.3.u.a.91.2 28 24.5 odd 2