Properties

Label 63.2.p.a.17.1
Level $63$
Weight $2$
Character 63.17
Analytic conductor $0.503$
Analytic rank $0$
Dimension $4$
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] = [63,2,Mod(17,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.p (of order \(6\), degree \(2\), 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: \(0.503057532734\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 63.17
Dual form 63.2.p.a.26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.22474 + 2.12132i) q^{5} +(-0.500000 + 2.59808i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.22474 + 2.12132i) q^{5} +(-0.500000 + 2.59808i) q^{7} -2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +(1.22474 + 0.707107i) q^{11} -5.19615i q^{13} +(-1.22474 - 3.53553i) q^{14} +(2.00000 + 3.46410i) q^{16} +(2.44949 - 4.24264i) q^{17} +(1.50000 - 0.866025i) q^{19} -2.00000 q^{22} +(-4.89898 + 2.82843i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(3.67423 + 6.36396i) q^{26} +2.82843i q^{29} +(1.50000 + 0.866025i) q^{31} +6.92820i q^{34} +(-6.12372 + 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} +(-1.22474 + 2.12132i) q^{38} +(6.00000 - 3.46410i) q^{40} +7.34847 q^{41} -1.00000 q^{43} +(4.00000 - 6.92820i) q^{46} +(-6.12372 - 10.6066i) q^{47} +(-6.50000 - 2.59808i) q^{49} -1.41421i q^{50} +(-2.44949 - 1.41421i) q^{53} +3.46410i q^{55} +(7.34847 + 1.41421i) q^{56} +(-2.00000 - 3.46410i) q^{58} +(2.44949 - 4.24264i) q^{59} +(-3.00000 + 1.73205i) q^{61} -2.44949 q^{62} -8.00000 q^{64} +(11.0227 - 6.36396i) q^{65} +(-5.50000 + 9.52628i) q^{67} +(6.00000 - 6.92820i) q^{70} +7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} +(-1.22474 - 0.707107i) q^{74} +(-2.44949 + 2.82843i) q^{77} +(-2.50000 - 4.33013i) q^{79} +(-4.89898 + 8.48528i) q^{80} +(-9.00000 + 5.19615i) q^{82} -7.34847 q^{83} +12.0000 q^{85} +(1.22474 - 0.707107i) q^{86} +(2.00000 - 3.46410i) q^{88} +(-2.44949 - 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} +(15.0000 + 8.66025i) q^{94} +(3.67423 + 2.12132i) q^{95} -10.3923i q^{97} +(9.79796 - 1.41421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{7} - 12 q^{10} + 8 q^{16} + 6 q^{19} - 8 q^{22} - 2 q^{25} + 6 q^{31} + 2 q^{37} + 24 q^{40} - 4 q^{43} + 16 q^{46} - 26 q^{49} - 8 q^{58} - 12 q^{61} - 32 q^{64} - 22 q^{67} + 24 q^{70} + 6 q^{73} - 10 q^{79} - 36 q^{82} + 48 q^{85} + 8 q^{88} + 54 q^{91} + 60 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 0.707107i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0
\(4\) 0 0
\(5\) 1.22474 + 2.12132i 0.547723 + 0.948683i 0.998430 + 0.0560116i \(0.0178384\pi\)
−0.450708 + 0.892672i \(0.648828\pi\)
\(6\) 0 0
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) −3.00000 1.73205i −0.948683 0.547723i
\(11\) 1.22474 + 0.707107i 0.369274 + 0.213201i 0.673141 0.739514i \(-0.264945\pi\)
−0.303867 + 0.952714i \(0.598278\pi\)
\(12\) 0 0
\(13\) 5.19615i 1.44115i −0.693375 0.720577i \(-0.743877\pi\)
0.693375 0.720577i \(-0.256123\pi\)
\(14\) −1.22474 3.53553i −0.327327 0.944911i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 2.44949 4.24264i 0.594089 1.02899i −0.399586 0.916696i \(-0.630846\pi\)
0.993675 0.112296i \(-0.0358205\pi\)
\(18\) 0 0
\(19\) 1.50000 0.866025i 0.344124 0.198680i −0.317970 0.948101i \(-0.603001\pi\)
0.662094 + 0.749421i \(0.269668\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) −4.89898 + 2.82843i −1.02151 + 0.589768i −0.914540 0.404495i \(-0.867447\pi\)
−0.106967 + 0.994263i \(0.534114\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 3.67423 + 6.36396i 0.720577 + 1.24808i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.82843i 0.525226i 0.964901 + 0.262613i \(0.0845842\pi\)
−0.964901 + 0.262613i \(0.915416\pi\)
\(30\) 0 0
\(31\) 1.50000 + 0.866025i 0.269408 + 0.155543i 0.628619 0.777714i \(-0.283621\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 6.92820i 1.18818i
\(35\) −6.12372 + 2.12132i −1.03510 + 0.358569i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −1.22474 + 2.12132i −0.198680 + 0.344124i
\(39\) 0 0
\(40\) 6.00000 3.46410i 0.948683 0.547723i
\(41\) 7.34847 1.14764 0.573819 0.818982i \(-0.305461\pi\)
0.573819 + 0.818982i \(0.305461\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) −6.12372 10.6066i −0.893237 1.54713i −0.835971 0.548773i \(-0.815095\pi\)
−0.0572655 0.998359i \(-0.518238\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 1.41421i 0.200000i
\(51\) 0 0
\(52\) 0 0
\(53\) −2.44949 1.41421i −0.336463 0.194257i 0.322244 0.946657i \(-0.395563\pi\)
−0.658707 + 0.752400i \(0.728896\pi\)
\(54\) 0 0
\(55\) 3.46410i 0.467099i
\(56\) 7.34847 + 1.41421i 0.981981 + 0.188982i
\(57\) 0 0
\(58\) −2.00000 3.46410i −0.262613 0.454859i
\(59\) 2.44949 4.24264i 0.318896 0.552345i −0.661362 0.750067i \(-0.730021\pi\)
0.980258 + 0.197722i \(0.0633545\pi\)
\(60\) 0 0
\(61\) −3.00000 + 1.73205i −0.384111 + 0.221766i −0.679605 0.733578i \(-0.737849\pi\)
0.295495 + 0.955344i \(0.404516\pi\)
\(62\) −2.44949 −0.311086
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 11.0227 6.36396i 1.36720 0.789352i
\(66\) 0 0
\(67\) −5.50000 + 9.52628i −0.671932 + 1.16382i 0.305424 + 0.952217i \(0.401202\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 6.00000 6.92820i 0.717137 0.828079i
\(71\) 7.07107i 0.839181i 0.907713 + 0.419591i \(0.137826\pi\)
−0.907713 + 0.419591i \(0.862174\pi\)
\(72\) 0 0
\(73\) 1.50000 + 0.866025i 0.175562 + 0.101361i 0.585206 0.810885i \(-0.301014\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −1.22474 0.707107i −0.142374 0.0821995i
\(75\) 0 0
\(76\) 0 0
\(77\) −2.44949 + 2.82843i −0.279145 + 0.322329i
\(78\) 0 0
\(79\) −2.50000 4.33013i −0.281272 0.487177i 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) −4.89898 + 8.48528i −0.547723 + 0.948683i
\(81\) 0 0
\(82\) −9.00000 + 5.19615i −0.993884 + 0.573819i
\(83\) −7.34847 −0.806599 −0.403300 0.915068i \(-0.632137\pi\)
−0.403300 + 0.915068i \(0.632137\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) 1.22474 0.707107i 0.132068 0.0762493i
\(87\) 0 0
\(88\) 2.00000 3.46410i 0.213201 0.369274i
\(89\) −2.44949 4.24264i −0.259645 0.449719i 0.706502 0.707712i \(-0.250272\pi\)
−0.966147 + 0.257993i \(0.916939\pi\)
\(90\) 0 0
\(91\) 13.5000 + 2.59808i 1.41518 + 0.272352i
\(92\) 0 0
\(93\) 0 0
\(94\) 15.0000 + 8.66025i 1.54713 + 0.893237i
\(95\) 3.67423 + 2.12132i 0.376969 + 0.217643i
\(96\) 0 0
\(97\) 10.3923i 1.05518i −0.849500 0.527589i \(-0.823096\pi\)
0.849500 0.527589i \(-0.176904\pi\)
\(98\) 9.79796 1.41421i 0.989743 0.142857i
\(99\) 0 0
\(100\) 0 0
\(101\) −8.57321 + 14.8492i −0.853067 + 1.47755i 0.0253604 + 0.999678i \(0.491927\pi\)
−0.878427 + 0.477876i \(0.841407\pi\)
\(102\) 0 0
\(103\) −7.50000 + 4.33013i −0.738997 + 0.426660i −0.821705 0.569914i \(-0.806977\pi\)
0.0827075 + 0.996574i \(0.473643\pi\)
\(104\) −14.6969 −1.44115
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) 2.44949 1.41421i 0.236801 0.136717i −0.376905 0.926252i \(-0.623012\pi\)
0.613706 + 0.789535i \(0.289678\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) −2.44949 4.24264i −0.233550 0.404520i
\(111\) 0 0
\(112\) −10.0000 + 3.46410i −0.944911 + 0.327327i
\(113\) 1.41421i 0.133038i −0.997785 0.0665190i \(-0.978811\pi\)
0.997785 0.0665190i \(-0.0211893\pi\)
\(114\) 0 0
\(115\) −12.0000 6.92820i −1.11901 0.646058i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.92820i 0.637793i
\(119\) 9.79796 + 8.48528i 0.898177 + 0.777844i
\(120\) 0 0
\(121\) −4.50000 7.79423i −0.409091 0.708566i
\(122\) 2.44949 4.24264i 0.221766 0.384111i
\(123\) 0 0
\(124\) 0 0
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) 9.79796 5.65685i 0.866025 0.500000i
\(129\) 0 0
\(130\) −9.00000 + 15.5885i −0.789352 + 1.36720i
\(131\) 1.22474 + 2.12132i 0.107006 + 0.185341i 0.914556 0.404459i \(-0.132540\pi\)
−0.807550 + 0.589799i \(0.799207\pi\)
\(132\) 0 0
\(133\) 1.50000 + 4.33013i 0.130066 + 0.375470i
\(134\) 15.5563i 1.34386i
\(135\) 0 0
\(136\) −12.0000 6.92820i −1.02899 0.594089i
\(137\) −9.79796 5.65685i −0.837096 0.483298i 0.0191800 0.999816i \(-0.493894\pi\)
−0.856276 + 0.516518i \(0.827228\pi\)
\(138\) 0 0
\(139\) 5.19615i 0.440732i −0.975417 0.220366i \(-0.929275\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.00000 8.66025i −0.419591 0.726752i
\(143\) 3.67423 6.36396i 0.307255 0.532181i
\(144\) 0 0
\(145\) −6.00000 + 3.46410i −0.498273 + 0.287678i
\(146\) −2.44949 −0.202721
\(147\) 0 0
\(148\) 0 0
\(149\) −4.89898 + 2.82843i −0.401340 + 0.231714i −0.687062 0.726599i \(-0.741100\pi\)
0.285722 + 0.958313i \(0.407767\pi\)
\(150\) 0 0
\(151\) 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i \(-0.480389\pi\)
0.833597 0.552372i \(-0.186277\pi\)
\(152\) −2.44949 4.24264i −0.198680 0.344124i
\(153\) 0 0
\(154\) 1.00000 5.19615i 0.0805823 0.418718i
\(155\) 4.24264i 0.340777i
\(156\) 0 0
\(157\) 15.0000 + 8.66025i 1.19713 + 0.691164i 0.959914 0.280293i \(-0.0904318\pi\)
0.237216 + 0.971457i \(0.423765\pi\)
\(158\) 6.12372 + 3.53553i 0.487177 + 0.281272i
\(159\) 0 0
\(160\) 0 0
\(161\) −4.89898 14.1421i −0.386094 1.11456i
\(162\) 0 0
\(163\) 5.00000 + 8.66025i 0.391630 + 0.678323i 0.992665 0.120900i \(-0.0385779\pi\)
−0.601035 + 0.799223i \(0.705245\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 9.00000 5.19615i 0.698535 0.403300i
\(167\) 7.34847 0.568642 0.284321 0.958729i \(-0.408232\pi\)
0.284321 + 0.958729i \(0.408232\pi\)
\(168\) 0 0
\(169\) −14.0000 −1.07692
\(170\) −14.6969 + 8.48528i −1.12720 + 0.650791i
\(171\) 0 0
\(172\) 0 0
\(173\) 4.89898 + 8.48528i 0.372463 + 0.645124i 0.989944 0.141462i \(-0.0451802\pi\)
−0.617481 + 0.786586i \(0.711847\pi\)
\(174\) 0 0
\(175\) −2.00000 1.73205i −0.151186 0.130931i
\(176\) 5.65685i 0.426401i
\(177\) 0 0
\(178\) 6.00000 + 3.46410i 0.449719 + 0.259645i
\(179\) 8.57321 + 4.94975i 0.640792 + 0.369961i 0.784920 0.619598i \(-0.212704\pi\)
−0.144127 + 0.989559i \(0.546038\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i 0.815086 + 0.579340i \(0.196690\pi\)
−0.815086 + 0.579340i \(0.803310\pi\)
\(182\) −18.3712 + 6.36396i −1.36176 + 0.471728i
\(183\) 0 0
\(184\) 8.00000 + 13.8564i 0.589768 + 1.02151i
\(185\) −1.22474 + 2.12132i −0.0900450 + 0.155963i
\(186\) 0 0
\(187\) 6.00000 3.46410i 0.438763 0.253320i
\(188\) 0 0
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) −1.22474 + 0.707107i −0.0886194 + 0.0511645i −0.543655 0.839309i \(-0.682960\pi\)
0.455035 + 0.890473i \(0.349627\pi\)
\(192\) 0 0
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) 7.34847 + 12.7279i 0.527589 + 0.913812i
\(195\) 0 0
\(196\) 0 0
\(197\) 19.7990i 1.41062i 0.708899 + 0.705310i \(0.249192\pi\)
−0.708899 + 0.705310i \(0.750808\pi\)
\(198\) 0 0
\(199\) −12.0000 6.92820i −0.850657 0.491127i 0.0102152 0.999948i \(-0.496748\pi\)
−0.860873 + 0.508821i \(0.830082\pi\)
\(200\) 2.44949 + 1.41421i 0.173205 + 0.100000i
\(201\) 0 0
\(202\) 24.2487i 1.70613i
\(203\) −7.34847 1.41421i −0.515761 0.0992583i
\(204\) 0 0
\(205\) 9.00000 + 15.5885i 0.628587 + 1.08875i
\(206\) 6.12372 10.6066i 0.426660 0.738997i
\(207\) 0 0
\(208\) 18.0000 10.3923i 1.24808 0.720577i
\(209\) 2.44949 0.169435
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −2.00000 + 3.46410i −0.136717 + 0.236801i
\(215\) −1.22474 2.12132i −0.0835269 0.144673i
\(216\) 0 0
\(217\) −3.00000 + 3.46410i −0.203653 + 0.235159i
\(218\) 1.41421i 0.0957826i
\(219\) 0 0
\(220\) 0 0
\(221\) −22.0454 12.7279i −1.48293 0.856173i
\(222\) 0 0
\(223\) 20.7846i 1.39184i 0.718119 + 0.695920i \(0.245003\pi\)
−0.718119 + 0.695920i \(0.754997\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 + 1.73205i 0.0665190 + 0.115214i
\(227\) 13.4722 23.3345i 0.894181 1.54877i 0.0593658 0.998236i \(-0.481092\pi\)
0.834815 0.550530i \(-0.185575\pi\)
\(228\) 0 0
\(229\) 19.5000 11.2583i 1.28860 0.743971i 0.310192 0.950674i \(-0.399607\pi\)
0.978404 + 0.206702i \(0.0662732\pi\)
\(230\) 19.5959 1.29212
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) −8.57321 + 4.94975i −0.561650 + 0.324269i −0.753807 0.657095i \(-0.771785\pi\)
0.192158 + 0.981364i \(0.438452\pi\)
\(234\) 0 0
\(235\) 15.0000 25.9808i 0.978492 1.69480i
\(236\) 0 0
\(237\) 0 0
\(238\) −18.0000 3.46410i −1.16677 0.224544i
\(239\) 26.8701i 1.73808i −0.494742 0.869040i \(-0.664738\pi\)
0.494742 0.869040i \(-0.335262\pi\)
\(240\) 0 0
\(241\) −12.0000 6.92820i −0.772988 0.446285i 0.0609515 0.998141i \(-0.480586\pi\)
−0.833939 + 0.551856i \(0.813920\pi\)
\(242\) 11.0227 + 6.36396i 0.708566 + 0.409091i
\(243\) 0 0
\(244\) 0 0
\(245\) −2.44949 16.9706i −0.156492 1.08421i
\(246\) 0 0
\(247\) −4.50000 7.79423i −0.286328 0.495935i
\(248\) 2.44949 4.24264i 0.155543 0.269408i
\(249\) 0 0
\(250\) −12.0000 + 6.92820i −0.758947 + 0.438178i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) −13.4722 + 7.77817i −0.845321 + 0.488046i
\(255\) 0 0
\(256\) 0 0
\(257\) 1.22474 + 2.12132i 0.0763975 + 0.132324i 0.901693 0.432377i \(-0.142325\pi\)
−0.825296 + 0.564701i \(0.808992\pi\)
\(258\) 0 0
\(259\) −2.50000 + 0.866025i −0.155342 + 0.0538122i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.00000 1.73205i −0.185341 0.107006i
\(263\) 12.2474 + 7.07107i 0.755210 + 0.436021i 0.827573 0.561358i \(-0.189721\pi\)
−0.0723633 + 0.997378i \(0.523054\pi\)
\(264\) 0 0
\(265\) 6.92820i 0.425596i
\(266\) −4.89898 4.24264i −0.300376 0.260133i
\(267\) 0 0
\(268\) 0 0
\(269\) −8.57321 + 14.8492i −0.522718 + 0.905374i 0.476932 + 0.878940i \(0.341749\pi\)
−0.999651 + 0.0264343i \(0.991585\pi\)
\(270\) 0 0
\(271\) −12.0000 + 6.92820i −0.728948 + 0.420858i −0.818037 0.575165i \(-0.804938\pi\)
0.0890891 + 0.996024i \(0.471604\pi\)
\(272\) 19.5959 1.18818
\(273\) 0 0
\(274\) 16.0000 0.966595
\(275\) −1.22474 + 0.707107i −0.0738549 + 0.0426401i
\(276\) 0 0
\(277\) −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i \(0.409482\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(278\) 3.67423 + 6.36396i 0.220366 + 0.381685i
\(279\) 0 0
\(280\) 6.00000 + 17.3205i 0.358569 + 1.03510i
\(281\) 22.6274i 1.34984i −0.737892 0.674919i \(-0.764178\pi\)
0.737892 0.674919i \(-0.235822\pi\)
\(282\) 0 0
\(283\) 1.50000 + 0.866025i 0.0891657 + 0.0514799i 0.543920 0.839137i \(-0.316940\pi\)
−0.454754 + 0.890617i \(0.650273\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 10.3923i 0.614510i
\(287\) −3.67423 + 19.0919i −0.216883 + 1.12696i
\(288\) 0 0
\(289\) −3.50000 6.06218i −0.205882 0.356599i
\(290\) 4.89898 8.48528i 0.287678 0.498273i
\(291\) 0 0
\(292\) 0 0
\(293\) −14.6969 −0.858604 −0.429302 0.903161i \(-0.641240\pi\)
−0.429302 + 0.903161i \(0.641240\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) 2.44949 1.41421i 0.142374 0.0821995i
\(297\) 0 0
\(298\) 4.00000 6.92820i 0.231714 0.401340i
\(299\) 14.6969 + 25.4558i 0.849946 + 1.47215i
\(300\) 0 0
\(301\) 0.500000 2.59808i 0.0288195 0.149751i
\(302\) 31.1127i 1.79033i
\(303\) 0 0
\(304\) 6.00000 + 3.46410i 0.344124 + 0.198680i
\(305\) −7.34847 4.24264i −0.420772 0.242933i
\(306\) 0 0
\(307\) 15.5885i 0.889680i −0.895610 0.444840i \(-0.853260\pi\)
0.895610 0.444840i \(-0.146740\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −3.00000 5.19615i −0.170389 0.295122i
\(311\) −8.57321 + 14.8492i −0.486142 + 0.842023i −0.999873 0.0159282i \(-0.994930\pi\)
0.513731 + 0.857951i \(0.328263\pi\)
\(312\) 0 0
\(313\) 10.5000 6.06218i 0.593495 0.342655i −0.172983 0.984925i \(-0.555341\pi\)
0.766478 + 0.642270i \(0.222007\pi\)
\(314\) −24.4949 −1.38233
\(315\) 0 0
\(316\) 0 0
\(317\) −12.2474 + 7.07107i −0.687885 + 0.397151i −0.802819 0.596222i \(-0.796668\pi\)
0.114934 + 0.993373i \(0.463334\pi\)
\(318\) 0 0
\(319\) −2.00000 + 3.46410i −0.111979 + 0.193952i
\(320\) −9.79796 16.9706i −0.547723 0.948683i
\(321\) 0 0
\(322\) 16.0000 + 13.8564i 0.891645 + 0.772187i
\(323\) 8.48528i 0.472134i
\(324\) 0 0
\(325\) 4.50000 + 2.59808i 0.249615 + 0.144115i
\(326\) −12.2474 7.07107i −0.678323 0.391630i
\(327\) 0 0
\(328\) 20.7846i 1.14764i
\(329\) 30.6186 10.6066i 1.68806 0.584761i
\(330\) 0 0
\(331\) 15.5000 + 26.8468i 0.851957 + 1.47563i 0.879440 + 0.476011i \(0.157918\pi\)
−0.0274825 + 0.999622i \(0.508749\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −9.00000 + 5.19615i −0.492458 + 0.284321i
\(335\) −26.9444 −1.47213
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 17.1464 9.89949i 0.932643 0.538462i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.22474 + 2.12132i 0.0663237 + 0.114876i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 2.82843i 0.152499i
\(345\) 0 0
\(346\) −12.0000 6.92820i −0.645124 0.372463i
\(347\) 26.9444 + 15.5563i 1.44645 + 0.835109i 0.998268 0.0588334i \(-0.0187381\pi\)
0.448183 + 0.893942i \(0.352071\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i −0.960539 0.278144i \(-0.910281\pi\)
0.960539 0.278144i \(-0.0897191\pi\)
\(350\) 3.67423 + 0.707107i 0.196396 + 0.0377964i
\(351\) 0 0
\(352\) 0 0
\(353\) −8.57321 + 14.8492i −0.456306 + 0.790345i −0.998762 0.0497387i \(-0.984161\pi\)
0.542456 + 0.840084i \(0.317494\pi\)
\(354\) 0 0
\(355\) −15.0000 + 8.66025i −0.796117 + 0.459639i
\(356\) 0 0
\(357\) 0 0
\(358\) −14.0000 −0.739923
\(359\) 24.4949 14.1421i 1.29279 0.746393i 0.313643 0.949541i \(-0.398450\pi\)
0.979148 + 0.203148i \(0.0651171\pi\)
\(360\) 0 0
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) −11.0227 19.0919i −0.579340 1.00345i
\(363\) 0 0
\(364\) 0 0
\(365\) 4.24264i 0.222070i
\(366\) 0 0
\(367\) 1.50000 + 0.866025i 0.0782994 + 0.0452062i 0.538639 0.842537i \(-0.318939\pi\)
−0.460339 + 0.887743i \(0.652272\pi\)
\(368\) −19.5959 11.3137i −1.02151 0.589768i
\(369\) 0 0
\(370\) 3.46410i 0.180090i
\(371\) 4.89898 5.65685i 0.254342 0.293689i
\(372\) 0 0
\(373\) −14.5000 25.1147i −0.750782 1.30039i −0.947444 0.319921i \(-0.896344\pi\)
0.196663 0.980471i \(-0.436990\pi\)
\(374\) −4.89898 + 8.48528i −0.253320 + 0.438763i
\(375\) 0 0
\(376\) −30.0000 + 17.3205i −1.54713 + 0.893237i
\(377\) 14.6969 0.756931
\(378\) 0 0
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.00000 1.73205i 0.0511645 0.0886194i
\(383\) −9.79796 16.9706i −0.500652 0.867155i −1.00000 0.000753393i \(-0.999760\pi\)
0.499347 0.866402i \(-0.333573\pi\)
\(384\) 0 0
\(385\) −9.00000 1.73205i −0.458682 0.0882735i
\(386\) 15.5563i 0.791797i
\(387\) 0 0
\(388\) 0 0
\(389\) 23.2702 + 13.4350i 1.17984 + 0.681183i 0.955978 0.293437i \(-0.0947991\pi\)
0.223865 + 0.974620i \(0.428132\pi\)
\(390\) 0 0
\(391\) 27.7128i 1.40150i
\(392\) −7.34847 + 18.3848i −0.371154 + 0.928571i
\(393\) 0 0
\(394\) −14.0000 24.2487i −0.705310 1.22163i
\(395\) 6.12372 10.6066i 0.308118 0.533676i
\(396\) 0 0
\(397\) 1.50000 0.866025i 0.0752828 0.0434646i −0.461886 0.886939i \(-0.652827\pi\)
0.537169 + 0.843475i \(0.319494\pi\)
\(398\) 19.5959 0.982255
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 17.1464 9.89949i 0.856252 0.494357i −0.00650355 0.999979i \(-0.502070\pi\)
0.862755 + 0.505622i \(0.168737\pi\)
\(402\) 0 0
\(403\) 4.50000 7.79423i 0.224161 0.388258i
\(404\) 0 0
\(405\) 0 0
\(406\) 10.0000 3.46410i 0.496292 0.171920i
\(407\) 1.41421i 0.0701000i
\(408\) 0 0
\(409\) 28.5000 + 16.4545i 1.40923 + 0.813622i 0.995314 0.0966915i \(-0.0308260\pi\)
0.413920 + 0.910313i \(0.364159\pi\)
\(410\) −22.0454 12.7279i −1.08875 0.628587i
\(411\) 0 0
\(412\) 0 0
\(413\) 9.79796 + 8.48528i 0.482126 + 0.417533i
\(414\) 0 0
\(415\) −9.00000 15.5885i −0.441793 0.765207i
\(416\) 0 0
\(417\) 0 0
\(418\) −3.00000 + 1.73205i −0.146735 + 0.0847174i
\(419\) −36.7423 −1.79498 −0.897491 0.441034i \(-0.854612\pi\)
−0.897491 + 0.441034i \(0.854612\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) 26.9444 15.5563i 1.31163 0.757271i
\(423\) 0 0
\(424\) −4.00000 + 6.92820i −0.194257 + 0.336463i
\(425\) 2.44949 + 4.24264i 0.118818 + 0.205798i
\(426\) 0 0
\(427\) −3.00000 8.66025i −0.145180 0.419099i
\(428\) 0 0
\(429\) 0 0
\(430\) 3.00000 + 1.73205i 0.144673 + 0.0835269i
\(431\) −13.4722 7.77817i −0.648933 0.374661i 0.139114 0.990276i \(-0.455574\pi\)
−0.788047 + 0.615615i \(0.788908\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i 0.927200 + 0.374567i \(0.122209\pi\)
−0.927200 + 0.374567i \(0.877791\pi\)
\(434\) 1.22474 6.36396i 0.0587896 0.305480i
\(435\) 0 0
\(436\) 0 0
\(437\) −4.89898 + 8.48528i −0.234350 + 0.405906i
\(438\) 0 0
\(439\) 24.0000 13.8564i 1.14546 0.661330i 0.197681 0.980266i \(-0.436659\pi\)
0.947776 + 0.318936i \(0.103326\pi\)
\(440\) 9.79796 0.467099
\(441\) 0 0
\(442\) 36.0000 1.71235
\(443\) −34.2929 + 19.7990i −1.62930 + 0.940678i −0.645002 + 0.764181i \(0.723143\pi\)
−0.984301 + 0.176497i \(0.943523\pi\)
\(444\) 0 0
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) −14.6969 25.4558i −0.695920 1.20537i
\(447\) 0 0
\(448\) 4.00000 20.7846i 0.188982 0.981981i
\(449\) 7.07107i 0.333704i 0.985982 + 0.166852i \(0.0533603\pi\)
−0.985982 + 0.166852i \(0.946640\pi\)
\(450\) 0 0
\(451\) 9.00000 + 5.19615i 0.423793 + 0.244677i
\(452\) 0 0
\(453\) 0 0
\(454\) 38.1051i 1.78836i
\(455\) 11.0227 + 31.8198i 0.516752 + 1.49174i
\(456\) 0 0
\(457\) −2.50000 4.33013i −0.116945 0.202555i 0.801611 0.597847i \(-0.203977\pi\)
−0.918556 + 0.395292i \(0.870643\pi\)
\(458\) −15.9217 + 27.5772i −0.743971 + 1.28860i
\(459\) 0 0
\(460\) 0 0
\(461\) 14.6969 0.684505 0.342252 0.939608i \(-0.388810\pi\)
0.342252 + 0.939608i \(0.388810\pi\)
\(462\) 0 0
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) −9.79796 + 5.65685i −0.454859 + 0.262613i
\(465\) 0 0
\(466\) 7.00000 12.1244i 0.324269 0.561650i
\(467\) −13.4722 23.3345i −0.623419 1.07979i −0.988844 0.148952i \(-0.952410\pi\)
0.365426 0.930841i \(-0.380923\pi\)
\(468\) 0 0
\(469\) −22.0000 19.0526i −1.01587 0.879765i
\(470\) 42.4264i 1.95698i
\(471\) 0 0
\(472\) −12.0000 6.92820i −0.552345 0.318896i
\(473\) −1.22474 0.707107i −0.0563138 0.0325128i
\(474\) 0 0
\(475\) 1.73205i 0.0794719i
\(476\) 0 0
\(477\) 0 0
\(478\) 19.0000 + 32.9090i 0.869040 + 1.50522i
\(479\) 2.44949 4.24264i 0.111920 0.193851i −0.804624 0.593784i \(-0.797633\pi\)
0.916544 + 0.399933i \(0.130967\pi\)
\(480\) 0 0
\(481\) 4.50000 2.59808i 0.205182 0.118462i
\(482\) 19.5959 0.892570
\(483\) 0 0
\(484\) 0 0
\(485\) 22.0454 12.7279i 1.00103 0.577945i
\(486\) 0 0
\(487\) −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i \(-0.959191\pi\)
0.606621 + 0.794991i \(0.292524\pi\)
\(488\) 4.89898 + 8.48528i 0.221766 + 0.384111i
\(489\) 0 0
\(490\) 15.0000 + 19.0526i 0.677631 + 0.860707i
\(491\) 11.3137i 0.510581i 0.966864 + 0.255290i \(0.0821710\pi\)
−0.966864 + 0.255290i \(0.917829\pi\)
\(492\) 0 0
\(493\) 12.0000 + 6.92820i 0.540453 + 0.312031i
\(494\) 11.0227 + 6.36396i 0.495935 + 0.286328i
\(495\) 0 0
\(496\) 6.92820i 0.311086i
\(497\) −18.3712 3.53553i −0.824060 0.158590i
\(498\) 0 0
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −22.0454 −0.982956 −0.491478 0.870890i \(-0.663543\pi\)
−0.491478 + 0.870890i \(0.663543\pi\)
\(504\) 0 0
\(505\) −42.0000 −1.86898
\(506\) 9.79796 5.65685i 0.435572 0.251478i
\(507\) 0 0
\(508\) 0 0
\(509\) 1.22474 + 2.12132i 0.0542859 + 0.0940259i 0.891891 0.452250i \(-0.149378\pi\)
−0.837605 + 0.546276i \(0.816045\pi\)
\(510\) 0 0
\(511\) −3.00000 + 3.46410i −0.132712 + 0.153243i
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) −3.00000 1.73205i −0.132324 0.0763975i
\(515\) −18.3712 10.6066i −0.809531 0.467383i
\(516\) 0 0
\(517\) 17.3205i 0.761755i
\(518\) 2.44949 2.82843i 0.107624 0.124274i
\(519\) 0 0
\(520\) −18.0000 31.1769i −0.789352 1.36720i
\(521\) 2.44949 4.24264i 0.107314 0.185873i −0.807367 0.590049i \(-0.799108\pi\)
0.914681 + 0.404176i \(0.132442\pi\)
\(522\) 0 0
\(523\) 1.50000 0.866025i 0.0655904 0.0378686i −0.466846 0.884339i \(-0.654610\pi\)
0.532437 + 0.846470i \(0.321276\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −20.0000 −0.872041
\(527\) 7.34847 4.24264i 0.320104 0.184812i
\(528\) 0 0
\(529\) 4.50000 7.79423i 0.195652 0.338880i
\(530\) 4.89898 + 8.48528i 0.212798 + 0.368577i
\(531\) 0 0
\(532\) 0 0
\(533\) 38.1838i 1.65392i
\(534\) 0 0
\(535\) 6.00000 + 3.46410i 0.259403 + 0.149766i
\(536\) 26.9444 + 15.5563i 1.16382 + 0.671932i
\(537\) 0 0
\(538\) 24.2487i 1.04544i
\(539\) −6.12372 7.77817i −0.263767 0.335030i
\(540\) 0 0
\(541\) −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i \(-0.285749\pi\)
−0.988847 + 0.148933i \(0.952416\pi\)
\(542\) 9.79796 16.9706i 0.420858 0.728948i
\(543\) 0 0
\(544\) 0 0
\(545\) 2.44949 0.104925
\(546\) 0 0
\(547\) −10.0000 −0.427569 −0.213785 0.976881i \(-0.568579\pi\)
−0.213785 + 0.976881i \(0.568579\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.00000 1.73205i 0.0426401 0.0738549i
\(551\) 2.44949 + 4.24264i 0.104352 + 0.180743i
\(552\) 0 0
\(553\) 12.5000 4.33013i 0.531554 0.184136i
\(554\) 32.5269i 1.38194i
\(555\) 0 0
\(556\) 0 0
\(557\) −13.4722 7.77817i −0.570835 0.329572i 0.186648 0.982427i \(-0.440238\pi\)
−0.757483 + 0.652855i \(0.773571\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) −19.5959 16.9706i −0.828079 0.717137i
\(561\) 0 0
\(562\) 16.0000 + 27.7128i 0.674919 + 1.16899i
\(563\) 13.4722 23.3345i 0.567785 0.983433i −0.428999 0.903305i \(-0.641134\pi\)
0.996785 0.0801281i \(-0.0255329\pi\)
\(564\) 0 0
\(565\) 3.00000 1.73205i 0.126211 0.0728679i
\(566\) −2.44949 −0.102960
\(567\) 0 0
\(568\) 20.0000 0.839181
\(569\) −1.22474 + 0.707107i −0.0513440 + 0.0296435i −0.525452 0.850823i \(-0.676104\pi\)
0.474108 + 0.880467i \(0.342771\pi\)
\(570\) 0 0
\(571\) −5.50000 + 9.52628i −0.230168 + 0.398662i −0.957857 0.287244i \(-0.907261\pi\)
0.727690 + 0.685907i \(0.240594\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −9.00000 25.9808i −0.375653 1.08442i
\(575\) 5.65685i 0.235907i
\(576\) 0 0
\(577\) 1.50000 + 0.866025i 0.0624458 + 0.0360531i 0.530898 0.847436i \(-0.321855\pi\)
−0.468452 + 0.883489i \(0.655188\pi\)
\(578\) 8.57321 + 4.94975i 0.356599 + 0.205882i
\(579\) 0 0
\(580\) 0 0
\(581\) 3.67423 19.0919i 0.152433 0.792065i
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 2.44949 4.24264i 0.101361 0.175562i
\(585\) 0 0
\(586\) 18.0000 10.3923i 0.743573 0.429302i
\(587\) 14.6969 0.606608 0.303304 0.952894i \(-0.401910\pi\)
0.303304 + 0.952894i \(0.401910\pi\)
\(588\) 0 0
\(589\) 3.00000 0.123613
\(590\) −14.6969 + 8.48528i −0.605063 + 0.349334i
\(591\) 0 0
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) 8.57321 + 14.8492i 0.352060 + 0.609785i 0.986610 0.163096i \(-0.0521481\pi\)
−0.634550 + 0.772881i \(0.718815\pi\)
\(594\) 0 0
\(595\) −6.00000 + 31.1769i −0.245976 + 1.27813i
\(596\) 0 0
\(597\) 0 0
\(598\) −36.0000 20.7846i −1.47215 0.849946i
\(599\) 4.89898 + 2.82843i 0.200167 + 0.115566i 0.596733 0.802440i \(-0.296465\pi\)
−0.396566 + 0.918006i \(0.629798\pi\)
\(600\) 0 0
\(601\) 25.9808i 1.05978i −0.848067 0.529889i \(-0.822234\pi\)
0.848067 0.529889i \(-0.177766\pi\)
\(602\) 1.22474 + 3.53553i 0.0499169 + 0.144098i
\(603\) 0 0
\(604\) 0 0
\(605\) 11.0227 19.0919i 0.448137 0.776195i
\(606\) 0 0
\(607\) −34.5000 + 19.9186i −1.40031 + 0.808470i −0.994424 0.105453i \(-0.966371\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 12.0000 0.485866
\(611\) −55.1135 + 31.8198i −2.22965 + 1.28729i
\(612\) 0 0
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) 11.0227 + 19.0919i 0.444840 + 0.770486i
\(615\) 0 0
\(616\) 8.00000 + 6.92820i 0.322329 + 0.279145i
\(617\) 24.0416i 0.967880i 0.875101 + 0.483940i \(0.160795\pi\)
−0.875101 + 0.483940i \(0.839205\pi\)
\(618\) 0 0
\(619\) −25.5000 14.7224i −1.02493 0.591744i −0.109403 0.993997i \(-0.534894\pi\)
−0.915529 + 0.402253i \(0.868227\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.2487i 0.972285i
\(623\) 12.2474 4.24264i 0.490684 0.169978i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −8.57321 + 14.8492i −0.342655 + 0.593495i
\(627\) 0 0
\(628\) 0 0
\(629\) 4.89898 0.195335
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) −12.2474 + 7.07107i −0.487177 + 0.281272i
\(633\) 0 0
\(634\) 10.0000 17.3205i 0.397151 0.687885i
\(635\) 13.4722 + 23.3345i 0.534628 + 0.926002i
\(636\) 0 0
\(637\) −13.5000 + 33.7750i −0.534889 + 1.33821i
\(638\) 5.65685i 0.223957i
\(639\) 0 0
\(640\) 24.0000 + 13.8564i 0.948683 + 0.547723i
\(641\) 12.2474 + 7.07107i 0.483745 + 0.279290i 0.721976 0.691918i \(-0.243234\pi\)
−0.238231 + 0.971209i \(0.576567\pi\)
\(642\) 0 0
\(643\) 25.9808i 1.02458i 0.858812 + 0.512291i \(0.171203\pi\)
−0.858812 + 0.512291i \(0.828797\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) −8.57321 + 14.8492i −0.337048 + 0.583784i −0.983876 0.178852i \(-0.942762\pi\)
0.646828 + 0.762636i \(0.276095\pi\)
\(648\) 0 0
\(649\) 6.00000 3.46410i 0.235521 0.135978i
\(650\) −7.34847 −0.288231
\(651\) 0 0
\(652\) 0 0
\(653\) 6.12372 3.53553i 0.239640 0.138356i −0.375371 0.926875i \(-0.622485\pi\)
0.615011 + 0.788518i \(0.289151\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) 14.6969 + 25.4558i 0.573819 + 0.993884i
\(657\) 0 0
\(658\) −30.0000 + 34.6410i −1.16952 + 1.35045i
\(659\) 22.6274i 0.881439i −0.897645 0.440720i \(-0.854723\pi\)
0.897645 0.440720i \(-0.145277\pi\)
\(660\) 0 0
\(661\) −25.5000 14.7224i −0.991835 0.572636i −0.0860127 0.996294i \(-0.527413\pi\)
−0.905822 + 0.423658i \(0.860746\pi\)
\(662\) −37.9671 21.9203i −1.47563 0.851957i
\(663\) 0 0
\(664\) 20.7846i 0.806599i
\(665\) −7.34847 + 8.48528i −0.284961 + 0.329045i
\(666\) 0 0
\(667\) −8.00000 13.8564i −0.309761 0.536522i
\(668\) 0 0
\(669\) 0 0
\(670\) 33.0000 19.0526i 1.27490 0.736065i
\(671\) −4.89898 −0.189123
\(672\) 0 0
\(673\) 35.0000 1.34915 0.674575 0.738206i \(-0.264327\pi\)
0.674575 + 0.738206i \(0.264327\pi\)
\(674\) −28.1691 + 16.2635i −1.08503 + 0.626445i
\(675\) 0 0
\(676\) 0 0
\(677\) 4.89898 + 8.48528i 0.188283 + 0.326116i 0.944678 0.327999i \(-0.106374\pi\)
−0.756395 + 0.654115i \(0.773041\pi\)
\(678\) 0 0
\(679\) 27.0000 + 5.19615i 1.03616 + 0.199410i
\(680\) 33.9411i 1.30158i
\(681\) 0 0
\(682\) −3.00000 1.73205i −0.114876 0.0663237i
\(683\) 41.6413 + 24.0416i 1.59336 + 0.919927i 0.992725 + 0.120405i \(0.0384193\pi\)
0.600636 + 0.799522i \(0.294914\pi\)
\(684\) 0 0
\(685\) 27.7128i 1.05885i
\(686\) −1.22474 + 26.1630i −0.0467610 + 0.998906i
\(687\) 0 0
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −7.34847 + 12.7279i −0.279954 + 0.484895i
\(690\) 0 0
\(691\) 37.5000 21.6506i 1.42657 0.823629i 0.429719 0.902963i \(-0.358613\pi\)
0.996848 + 0.0793336i \(0.0252792\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −44.0000 −1.67022
\(695\) 11.0227 6.36396i 0.418115 0.241399i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 7.34847 + 12.7279i 0.278144 + 0.481759i
\(699\) 0 0
\(700\) 0 0
\(701\) 5.65685i 0.213656i −0.994277 0.106828i \(-0.965931\pi\)
0.994277 0.106828i \(-0.0340695\pi\)
\(702\) 0 0
\(703\) 1.50000 + 0.866025i 0.0565736 + 0.0326628i
\(704\) −9.79796 5.65685i −0.369274 0.213201i
\(705\) 0 0
\(706\) 24.2487i 0.912612i
\(707\) −34.2929 29.6985i −1.28972 1.11693i
\(708\) 0 0
\(709\) 20.0000 + 34.6410i 0.751116 + 1.30097i 0.947282 + 0.320400i \(0.103817\pi\)
−0.196167 + 0.980571i \(0.562849\pi\)
\(710\) 12.2474 21.2132i 0.459639 0.796117i
\(711\) 0 0
\(712\) −12.0000 + 6.92820i −0.449719 + 0.259645i
\(713\) −9.79796 −0.366936
\(714\) 0 0
\(715\) 18.0000 0.673162
\(716\) 0 0
\(717\) 0 0
\(718\) −20.0000 + 34.6410i −0.746393 + 1.29279i
\(719\) −13.4722 23.3345i −0.502428 0.870231i −0.999996 0.00280593i \(-0.999107\pi\)
0.497568 0.867425i \(-0.334226\pi\)
\(720\) 0 0
\(721\) −7.50000 21.6506i −0.279315 0.806312i
\(722\) 22.6274i 0.842105i
\(723\) 0 0
\(724\) 0 0
\(725\) −2.44949 1.41421i −0.0909718 0.0525226i
\(726\) 0 0
\(727\) 25.9808i 0.963573i −0.876289 0.481787i \(-0.839988\pi\)
0.876289 0.481787i \(-0.160012\pi\)
\(728\) 7.34847 38.1838i 0.272352 1.41518i
\(729\) 0 0
\(730\) −3.00000 5.19615i −0.111035 0.192318i
\(731\) −2.44949 + 4.24264i −0.0905977 + 0.156920i
\(732\) 0 0
\(733\) −34.5000 + 19.9186i −1.27429 + 0.735710i −0.975792 0.218702i \(-0.929818\pi\)
−0.298495 + 0.954411i \(0.596485\pi\)
\(734\) −2.44949 −0.0904123
\(735\) 0 0
\(736\) 0 0
\(737\) −13.4722 + 7.77817i −0.496255 + 0.286513i
\(738\) 0 0
\(739\) 0.500000 0.866025i 0.0183928 0.0318573i −0.856683 0.515844i \(-0.827478\pi\)
0.875075 + 0.483987i \(0.160812\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −2.00000 + 10.3923i −0.0734223 + 0.381514i
\(743\) 24.0416i 0.882002i 0.897507 + 0.441001i \(0.145376\pi\)
−0.897507 + 0.441001i \(0.854624\pi\)
\(744\) 0 0
\(745\) −12.0000 6.92820i −0.439646 0.253830i
\(746\) 35.5176 + 20.5061i 1.30039 + 0.750782i
\(747\) 0 0
\(748\) 0 0
\(749\) 2.44949 + 7.07107i 0.0895024 + 0.258371i
\(750\) 0 0
\(751\) −14.5000 25.1147i −0.529113 0.916450i −0.999424 0.0339490i \(-0.989192\pi\)
0.470311 0.882501i \(-0.344142\pi\)
\(752\) 24.4949 42.4264i 0.893237 1.54713i
\(753\) 0 0
\(754\) −18.0000 + 10.3923i −0.655521 + 0.378465i
\(755\) 53.8888 1.96121
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 8.57321 4.94975i 0.311393 0.179783i
\(759\) 0 0
\(760\) 6.00000 10.3923i 0.217643 0.376969i
\(761\) 12.2474 + 21.2132i 0.443970 + 0.768978i 0.997980 0.0635319i \(-0.0202365\pi\)
−0.554010 + 0.832510i \(0.686903\pi\)
\(762\) 0 0
\(763\) 2.00000 + 1.73205i 0.0724049 + 0.0627044i
\(764\) 0 0
\(765\) 0 0
\(766\) 24.0000 + 13.8564i 0.867155 + 0.500652i
\(767\) −22.0454 12.7279i −0.796014 0.459579i
\(768\) 0 0
\(769\) 25.9808i 0.936890i 0.883493 + 0.468445i \(0.155186\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 12.2474 4.24264i 0.441367 0.152894i
\(771\) 0 0
\(772\) 0 0
\(773\) 13.4722 23.3345i 0.484561 0.839284i −0.515282 0.857021i \(-0.672313\pi\)
0.999843 + 0.0177365i \(0.00564599\pi\)
\(774\) 0 0
\(775\) −1.50000 + 0.866025i −0.0538816 + 0.0311086i
\(776\) −29.3939 −1.05518
\(777\) 0 0
\(778\) −38.0000 −1.36237
\(779\) 11.0227 6.36396i 0.394929 0.228013i
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) −19.5959 33.9411i −0.700749 1.21373i
\(783\) 0 0
\(784\) −4.00000 27.7128i −0.142857 0.989743i
\(785\) 42.4264i 1.51426i
\(786\) 0 0
\(787\) −39.0000 22.5167i −1.39020 0.802632i −0.396863 0.917878i \(-0.629901\pi\)
−0.993337 + 0.115246i \(0.963234\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 17.3205i 0.616236i
\(791\) 3.67423 + 0.707107i 0.130641 + 0.0251418i
\(792\) 0 0
\(793\) 9.00000 + 15.5885i 0.319599 + 0.553562i
\(794\) −1.22474 + 2.12132i −0.0434646 + 0.0752828i
\(795\) 0 0
\(796\) 0 0
\(797\) 29.3939 1.04118 0.520592 0.853805i \(-0.325711\pi\)
0.520592 + 0.853805i \(0.325711\pi\)
\(798\) 0 0
\(799\) −60.0000 −2.12265
\(800\) 0 0
\(801\) 0 0
\(802\) −14.0000 + 24.2487i −0.494357 + 0.856252i
\(803\) 1.22474 + 2.12132i 0.0432203 + 0.0748598i
\(804\) 0 0
\(805\) 24.0000 27.7128i 0.845889 0.976748i
\(806\) 12.7279i 0.448322i
\(807\) 0 0
\(808\) 42.0000 + 24.2487i 1.47755 + 0.853067i
\(809\) −35.5176 20.5061i −1.24873 0.720956i −0.277876 0.960617i \(-0.589630\pi\)
−0.970857 + 0.239661i \(0.922964\pi\)
\(810\) 0 0
\(811\) 31.1769i 1.09477i −0.836881 0.547385i \(-0.815623\pi\)
0.836881 0.547385i \(-0.184377\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −1.00000 1.73205i −0.0350500 0.0607083i
\(815\) −12.2474 + 21.2132i −0.429009 + 0.743066i
\(816\) 0 0
\(817\) −1.50000 + 0.866025i −0.0524784 + 0.0302984i
\(818\) −46.5403 −1.62724
\(819\) 0 0
\(820\) 0 0
\(821\) 20.8207 12.0208i 0.726646 0.419529i −0.0905478 0.995892i \(-0.528862\pi\)
0.817194 + 0.576363i \(0.195528\pi\)
\(822\) 0 0
\(823\) 17.0000 29.4449i 0.592583 1.02638i −0.401300 0.915947i \(-0.631442\pi\)
0.993883 0.110437i \(-0.0352250\pi\)
\(824\) 12.2474 + 21.2132i 0.426660 + 0.738997i
\(825\) 0 0
\(826\) −18.0000 3.46410i −0.626300 0.120532i
\(827\) 7.07107i 0.245885i 0.992414 + 0.122943i \(0.0392331\pi\)
−0.992414 + 0.122943i \(0.960767\pi\)
\(828\) 0 0
\(829\) 1.50000 + 0.866025i 0.0520972 + 0.0300783i 0.525822 0.850594i \(-0.323758\pi\)
−0.473725 + 0.880673i \(0.657091\pi\)
\(830\) 22.0454 + 12.7279i 0.765207 + 0.441793i
\(831\) 0 0
\(832\) 41.5692i 1.44115i
\(833\) −26.9444 + 21.2132i −0.933568 + 0.734994i
\(834\) 0 0
\(835\) 9.00000 + 15.5885i 0.311458 + 0.539461i
\(836\) 0 0
\(837\) 0 0
\(838\) 45.0000 25.9808i 1.55450 0.897491i
\(839\) 14.6969 0.507395 0.253697 0.967284i \(-0.418353\pi\)
0.253697 + 0.967284i \(0.418353\pi\)
\(840\) 0 0
\(841\) 21.0000 0.724138
\(842\) 1.22474 0.707107i 0.0422075 0.0243685i
\(843\) 0 0
\(844\) 0 0
\(845\) −17.1464 29.6985i −0.589855 1.02166i
\(846\) 0 0
\(847\) 22.5000 7.79423i 0.773109 0.267813i
\(848\) 11.3137i 0.388514i
\(849\) 0 0
\(850\) −6.00000 3.46410i −0.205798 0.118818i
\(851\) −4.89898 2.82843i −0.167935 0.0969572i
\(852\) 0 0
\(853\) 36.3731i 1.24539i 0.782465 + 0.622695i \(0.213962\pi\)
−0.782465 + 0.622695i \(0.786038\pi\)
\(854\) 9.79796 + 8.48528i 0.335279 + 0.290360i
\(855\) 0 0
\(856\) −4.00000 6.92820i −0.136717 0.236801i
\(857\) −19.5959 + 33.9411i −0.669384 + 1.15941i 0.308693 + 0.951162i \(0.400108\pi\)
−0.978077 + 0.208245i \(0.933225\pi\)
\(858\) 0 0
\(859\) 33.0000 19.0526i 1.12595 0.650065i 0.183033 0.983107i \(-0.441408\pi\)
0.942912 + 0.333042i \(0.108075\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 22.0000 0.749323
\(863\) 35.5176 20.5061i 1.20903 0.698036i 0.246485 0.969147i \(-0.420724\pi\)
0.962548 + 0.271111i \(0.0873910\pi\)
\(864\) 0 0
\(865\) −12.0000 + 20.7846i −0.408012 + 0.706698i
\(866\) −11.0227 19.0919i −0.374567 0.648769i
\(867\) 0 0
\(868\) 0 0
\(869\) 7.07107i 0.239870i
\(870\) 0 0
\(871\) 49.5000 + 28.5788i 1.67724 + 0.968357i
\(872\) −2.44949 1.41421i −0.0829502 0.0478913i
\(873\) 0 0
\(874\) 13.8564i 0.468700i
\(875\) −4.89898 + 25.4558i −0.165616 + 0.860565i
\(876\) 0 0
\(877\) −10.0000 17.3205i −0.337676 0.584872i 0.646319 0.763067i \(-0.276307\pi\)
−0.983995 + 0.178195i \(0.942974\pi\)
\(878\) −19.5959 + 33.9411i −0.661330 + 1.14546i
\(879\) 0 0
\(880\) −12.0000 + 6.92820i −0.404520 + 0.233550i
\(881\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(882\) 0 0
\(883\) 11.0000 0.370179 0.185090 0.982722i \(-0.440742\pi\)
0.185090 + 0.982722i \(0.440742\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 28.0000 48.4974i 0.940678 1.62930i
\(887\) −20.8207 36.0624i −0.699089 1.21086i −0.968783 0.247912i \(-0.920256\pi\)
0.269693 0.962946i \(-0.413078\pi\)
\(888\) 0 0
\(889\) −5.50000 + 28.5788i −0.184464 + 0.958503i
\(890\) 16.9706i 0.568855i
\(891\) 0 0
\(892\) 0 0
\(893\) −18.3712 10.6066i −0.614768 0.354936i
\(894\) 0 0
\(895\) 24.2487i 0.810545i
\(896\) 9.79796 + 28.2843i 0.327327 + 0.944911i
\(897\) 0 0
\(898\) −5.00000 8.66025i −0.166852 0.288996i
\(899\) −2.44949 + 4.24264i −0.0816951 + 0.141500i
\(900\) 0 0
\(901\) −12.0000 + 6.92820i −0.399778 + 0.230812i
\(902\) −14.6969 −0.489355
\(903\) 0 0
\(904\) −4.00000 −0.133038
\(905\) −33.0681 + 19.0919i −1.09922 + 0.634636i
\(906\) 0 0
\(907\) −2.50000 + 4.33013i −0.0830111 + 0.143780i −0.904542 0.426385i \(-0.859787\pi\)
0.821531 + 0.570164i \(0.193120\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) −36.0000 31.1769i −1.19339 1.03350i
\(911\) 53.7401i 1.78049i 0.455483 + 0.890245i \(0.349467\pi\)
−0.455483 + 0.890245i \(0.650533\pi\)
\(912\) 0 0
\(913\) −9.00000 5.19615i −0.297857 0.171968i
\(914\) 6.12372 + 3.53553i 0.202555 + 0.116945i
\(915\) 0 0
\(916\) 0 0
\(917\) −6.12372 + 2.12132i −0.202223 + 0.0700522i
\(918\) 0 0
\(919\) −8.50000 14.7224i −0.280389 0.485648i 0.691091 0.722767i \(-0.257130\pi\)
−0.971481 + 0.237119i \(0.923797\pi\)
\(920\) −19.5959 + 33.9411i −0.646058 + 1.11901i
\(921\) 0 0
\(922\) −18.0000 + 10.3923i −0.592798 + 0.342252i
\(923\) 36.7423 1.20939
\(924\) 0 0
\(925\) −1.00000 −0.0328798
\(926\) 15.9217 9.19239i 0.523219 0.302081i
\(927\) 0 0
\(928\) 0 0
\(929\) −28.1691 48.7904i −0.924199 1.60076i −0.792844 0.609425i \(-0.791400\pi\)
−0.131355 0.991335i \(-0.541933\pi\)
\(930\) 0 0
\(931\) −12.0000 + 1.73205i −0.393284 + 0.0567657i
\(932\) 0 0
\(933\) 0 0
\(934\) 33.0000 + 19.0526i 1.07979 + 0.623419i
\(935\) 14.6969 + 8.48528i 0.480641 + 0.277498i
\(936\) 0 0
\(937\) 46.7654i 1.52776i 0.645359 + 0.763879i \(0.276708\pi\)
−0.645359 + 0.763879i \(0.723292\pi\)
\(938\) 40.4166 + 7.77817i 1.31965 + 0.253966i
\(939\) 0 0
\(940\) 0 0
\(941\) 24.4949 42.4264i 0.798511 1.38306i −0.122075 0.992521i \(-0.538955\pi\)
0.920586 0.390540i \(-0.127712\pi\)
\(942\) 0 0
\(943\) −36.0000 + 20.7846i −1.17232 + 0.676840i
\(944\) 19.5959 0.637793
\(945\) 0 0
\(946\) 2.00000 0.0650256
\(947\) 42.8661 24.7487i 1.39296 0.804226i 0.399318 0.916812i \(-0.369247\pi\)
0.993642 + 0.112586i \(0.0359135\pi\)
\(948\) 0 0
\(949\) 4.50000 7.79423i 0.146076 0.253011i
\(950\) −1.22474 2.12132i −0.0397360 0.0688247i
\(951\) 0 0
\(952\) 24.0000 27.7128i 0.777844 0.898177i
\(953\) 5.65685i 0.183243i −0.995794 0.0916217i \(-0.970795\pi\)
0.995794 0.0916217i \(-0.0292051\pi\)
\(954\) 0 0
\(955\) −3.00000 1.73205i −0.0970777 0.0560478i
\(956\) 0 0
\(957\) 0 0
\(958\) 6.92820i 0.223840i
\(959\) 19.5959 22.6274i 0.632785 0.730677i
\(960\) 0 0
\(961\) −14.0000 24.2487i −0.451613 0.782216i
\(962\) −3.67423 + 6.36396i −0.118462 + 0.205182i
\(963\) 0 0
\(964\) 0 0
\(965\) −26.9444 −0.867371
\(966\) 0 0
\(967\) −13.0000 −0.418052 −0.209026 0.977910i \(-0.567029\pi\)
−0.209026 + 0.977910i \(0.567029\pi\)
\(968\) −22.0454 + 12.7279i −0.708566 + 0.409091i
\(969\) 0 0
\(970\) −18.0000 + 31.1769i −0.577945 + 1.00103i
\(971\) 19.5959 + 33.9411i 0.628863 + 1.08922i 0.987780 + 0.155853i \(0.0498127\pi\)
−0.358917 + 0.933369i \(0.616854\pi\)
\(972\) 0 0
\(973\) 13.5000 + 2.59808i 0.432790 + 0.0832905i
\(974\) 24.0416i 0.770344i
\(975\) 0 0
\(976\) −12.0000 6.92820i −0.384111 0.221766i
\(977\) −6.12372 3.53553i −0.195915 0.113112i 0.398833 0.917023i \(-0.369415\pi\)
−0.594749 + 0.803912i \(0.702748\pi\)
\(978\) 0 0
\(979\) 6.92820i 0.221426i
\(980\) 0 0
\(981\) 0 0
\(982\) −8.00000 13.8564i −0.255290 0.442176i
\(983\) 2.44949 4.24264i 0.0781266 0.135319i −0.824315 0.566131i \(-0.808439\pi\)
0.902442 + 0.430812i \(0.141773\pi\)
\(984\) 0 0
\(985\) −42.0000 + 24.2487i −1.33823 + 0.772628i
\(986\) −19.5959 −0.624061
\(987\) 0 0
\(988\) 0 0
\(989\) 4.89898 2.82843i 0.155778 0.0899388i
\(990\) 0 0
\(991\) −17.5000 + 30.3109i −0.555906 + 0.962857i 0.441927 + 0.897051i \(0.354295\pi\)
−0.997832 + 0.0658059i \(0.979038\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 25.0000 8.66025i 0.792952 0.274687i
\(995\) 33.9411i 1.07601i
\(996\) 0 0
\(997\) −25.5000 14.7224i −0.807593 0.466264i 0.0385262 0.999258i \(-0.487734\pi\)
−0.846119 + 0.532993i \(0.821067\pi\)
\(998\) −30.6186 17.6777i −0.969216 0.559577i
\(999\) 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 63.2.p.a.17.1 4
3.2 odd 2 inner 63.2.p.a.17.2 yes 4
4.3 odd 2 1008.2.bt.b.17.2 4
5.2 odd 4 1575.2.bc.a.899.1 8
5.3 odd 4 1575.2.bc.a.899.4 8
5.4 even 2 1575.2.bk.c.1151.2 4
7.2 even 3 441.2.p.a.215.2 4
7.3 odd 6 441.2.c.a.440.2 4
7.4 even 3 441.2.c.a.440.1 4
7.5 odd 6 inner 63.2.p.a.26.2 yes 4
7.6 odd 2 441.2.p.a.80.1 4
9.2 odd 6 567.2.s.d.458.1 4
9.4 even 3 567.2.i.d.269.1 4
9.5 odd 6 567.2.i.d.269.2 4
9.7 even 3 567.2.s.d.458.2 4
12.11 even 2 1008.2.bt.b.17.1 4
15.2 even 4 1575.2.bc.a.899.3 8
15.8 even 4 1575.2.bc.a.899.2 8
15.14 odd 2 1575.2.bk.c.1151.1 4
21.2 odd 6 441.2.p.a.215.1 4
21.5 even 6 inner 63.2.p.a.26.1 yes 4
21.11 odd 6 441.2.c.a.440.4 4
21.17 even 6 441.2.c.a.440.3 4
21.20 even 2 441.2.p.a.80.2 4
28.3 even 6 7056.2.k.b.881.4 4
28.11 odd 6 7056.2.k.b.881.2 4
28.19 even 6 1008.2.bt.b.593.1 4
35.12 even 12 1575.2.bc.a.1349.2 8
35.19 odd 6 1575.2.bk.c.26.1 4
35.33 even 12 1575.2.bc.a.1349.3 8
63.5 even 6 567.2.s.d.26.2 4
63.40 odd 6 567.2.s.d.26.1 4
63.47 even 6 567.2.i.d.215.2 4
63.61 odd 6 567.2.i.d.215.1 4
84.11 even 6 7056.2.k.b.881.3 4
84.47 odd 6 1008.2.bt.b.593.2 4
84.59 odd 6 7056.2.k.b.881.1 4
105.47 odd 12 1575.2.bc.a.1349.4 8
105.68 odd 12 1575.2.bc.a.1349.1 8
105.89 even 6 1575.2.bk.c.26.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.p.a.17.1 4 1.1 even 1 trivial
63.2.p.a.17.2 yes 4 3.2 odd 2 inner
63.2.p.a.26.1 yes 4 21.5 even 6 inner
63.2.p.a.26.2 yes 4 7.5 odd 6 inner
441.2.c.a.440.1 4 7.4 even 3
441.2.c.a.440.2 4 7.3 odd 6
441.2.c.a.440.3 4 21.17 even 6
441.2.c.a.440.4 4 21.11 odd 6
441.2.p.a.80.1 4 7.6 odd 2
441.2.p.a.80.2 4 21.20 even 2
441.2.p.a.215.1 4 21.2 odd 6
441.2.p.a.215.2 4 7.2 even 3
567.2.i.d.215.1 4 63.61 odd 6
567.2.i.d.215.2 4 63.47 even 6
567.2.i.d.269.1 4 9.4 even 3
567.2.i.d.269.2 4 9.5 odd 6
567.2.s.d.26.1 4 63.40 odd 6
567.2.s.d.26.2 4 63.5 even 6
567.2.s.d.458.1 4 9.2 odd 6
567.2.s.d.458.2 4 9.7 even 3
1008.2.bt.b.17.1 4 12.11 even 2
1008.2.bt.b.17.2 4 4.3 odd 2
1008.2.bt.b.593.1 4 28.19 even 6
1008.2.bt.b.593.2 4 84.47 odd 6
1575.2.bc.a.899.1 8 5.2 odd 4
1575.2.bc.a.899.2 8 15.8 even 4
1575.2.bc.a.899.3 8 15.2 even 4
1575.2.bc.a.899.4 8 5.3 odd 4
1575.2.bc.a.1349.1 8 105.68 odd 12
1575.2.bc.a.1349.2 8 35.12 even 12
1575.2.bc.a.1349.3 8 35.33 even 12
1575.2.bc.a.1349.4 8 105.47 odd 12
1575.2.bk.c.26.1 4 35.19 odd 6
1575.2.bk.c.26.2 4 105.89 even 6
1575.2.bk.c.1151.1 4 15.14 odd 2
1575.2.bk.c.1151.2 4 5.4 even 2
7056.2.k.b.881.1 4 84.59 odd 6
7056.2.k.b.881.2 4 28.11 odd 6
7056.2.k.b.881.3 4 84.11 even 6
7056.2.k.b.881.4 4 28.3 even 6