Properties

Label 1350.2.q.h.557.4
Level $1350$
Weight $2$
Character 1350.557
Analytic conductor $10.780$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1350,2,Mod(143,1350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1350, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1350.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1350.q (of order \(12\), 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: \(10.7798042729\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: 16.0.9349208943630483456.9
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + \cdots + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 557.4
Root \(0.500000 + 0.589118i\) of defining polynomial
Character \(\chi\) \(=\) 1350.557
Dual form 1350.2.q.h.143.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.521929 - 1.94786i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.521929 - 1.94786i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.70563 - 0.984748i) q^{11} +(-1.05248 - 3.92790i) q^{13} +(1.00829 - 1.74641i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.35877 - 2.35877i) q^{17} -3.70753i q^{19} +(1.90239 - 0.509743i) q^{22} +(-6.05338 + 1.62200i) q^{23} -4.06647i q^{26} +(1.42594 - 1.42594i) q^{28} +(3.74863 + 6.49281i) q^{29} +(3.48837 - 6.04204i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.88889 - 1.66790i) q^{34} +(-4.26692 - 4.26692i) q^{37} +(0.959578 - 3.58120i) q^{38} +(-6.13601 - 3.54263i) q^{41} +(9.09714 + 2.43757i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(7.49533 + 2.00837i) q^{47} +(2.54041 + 1.46671i) q^{49} +(1.05248 - 3.92790i) q^{52} +(7.03027 + 7.03027i) q^{53} +(1.74641 - 1.00829i) q^{56} +(1.94043 + 7.24179i) q^{58} +(-1.34967 + 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(4.93330 - 4.93330i) q^{62} +1.00000i q^{64} +(8.18285 - 2.19259i) q^{67} +(3.22213 - 0.863368i) q^{68} -5.68481i q^{71} +(-1.14928 + 1.14928i) q^{73} +(-3.01717 - 5.22589i) q^{74} +(1.85376 - 3.21081i) q^{76} +(-1.02794 - 3.83631i) q^{77} +(-10.0535 + 5.80440i) q^{79} +(-5.01003 - 5.01003i) q^{82} +(-0.440961 + 1.64569i) q^{83} +(8.15627 + 4.70902i) q^{86} +(1.90239 + 0.509743i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(-6.05338 - 1.62200i) q^{92} +(6.72013 + 3.87987i) q^{94} +(-2.60421 + 9.71905i) q^{97} +(2.07424 + 2.07424i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{7} + 8 q^{16} - 8 q^{22} - 24 q^{23} + 16 q^{28} - 8 q^{31} + 24 q^{38} - 24 q^{41} - 32 q^{46} + 48 q^{47} - 24 q^{56} - 16 q^{58} - 24 q^{61} + 16 q^{67} - 24 q^{68} - 16 q^{73} + 16 q^{76} - 72 q^{77} + 16 q^{82} + 48 q^{83} + 48 q^{86} - 8 q^{88} - 24 q^{92} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).

\(n\) \(1001\) \(1027\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.683013 + 0.183013i
\(3\) 0 0
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.521929 1.94786i 0.197270 0.736223i −0.794397 0.607399i \(-0.792213\pi\)
0.991667 0.128824i \(-0.0411204\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.70563 0.984748i 0.514268 0.296913i −0.220318 0.975428i \(-0.570710\pi\)
0.734586 + 0.678515i \(0.237376\pi\)
\(12\) 0 0
\(13\) −1.05248 3.92790i −0.291905 1.08940i −0.943644 0.330961i \(-0.892627\pi\)
0.651739 0.758443i \(-0.274040\pi\)
\(14\) 1.00829 1.74641i 0.269476 0.466747i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 2.35877 2.35877i 0.572085 0.572085i −0.360626 0.932711i \(-0.617437\pi\)
0.932711 + 0.360626i \(0.117437\pi\)
\(18\) 0 0
\(19\) 3.70753i 0.850565i −0.905061 0.425282i \(-0.860175\pi\)
0.905061 0.425282i \(-0.139825\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.90239 0.509743i 0.405590 0.108678i
\(23\) −6.05338 + 1.62200i −1.26222 + 0.338210i −0.827044 0.562137i \(-0.809979\pi\)
−0.435173 + 0.900347i \(0.643313\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 4.06647i 0.797499i
\(27\) 0 0
\(28\) 1.42594 1.42594i 0.269476 0.269476i
\(29\) 3.74863 + 6.49281i 0.696103 + 1.20569i 0.969808 + 0.243872i \(0.0784175\pi\)
−0.273705 + 0.961814i \(0.588249\pi\)
\(30\) 0 0
\(31\) 3.48837 6.04204i 0.626530 1.08518i −0.361713 0.932289i \(-0.617808\pi\)
0.988243 0.152892i \(-0.0488587\pi\)
\(32\) 0.258819 + 0.965926i 0.0457532 + 0.170753i
\(33\) 0 0
\(34\) 2.88889 1.66790i 0.495440 0.286042i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.26692 4.26692i −0.701478 0.701478i 0.263250 0.964728i \(-0.415206\pi\)
−0.964728 + 0.263250i \(0.915206\pi\)
\(38\) 0.959578 3.58120i 0.155664 0.580947i
\(39\) 0 0
\(40\) 0 0
\(41\) −6.13601 3.54263i −0.958284 0.553266i −0.0626396 0.998036i \(-0.519952\pi\)
−0.895644 + 0.444771i \(0.853285\pi\)
\(42\) 0 0
\(43\) 9.09714 + 2.43757i 1.38730 + 0.371726i 0.873767 0.486344i \(-0.161670\pi\)
0.513533 + 0.858070i \(0.328336\pi\)
\(44\) 1.96950 0.296913
\(45\) 0 0
\(46\) −6.26692 −0.924007
\(47\) 7.49533 + 2.00837i 1.09331 + 0.292951i 0.760036 0.649881i \(-0.225181\pi\)
0.333270 + 0.942831i \(0.391848\pi\)
\(48\) 0 0
\(49\) 2.54041 + 1.46671i 0.362916 + 0.209530i
\(50\) 0 0
\(51\) 0 0
\(52\) 1.05248 3.92790i 0.145953 0.544702i
\(53\) 7.03027 + 7.03027i 0.965682 + 0.965682i 0.999430 0.0337485i \(-0.0107445\pi\)
−0.0337485 + 0.999430i \(0.510745\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.74641 1.00829i 0.233373 0.134738i
\(57\) 0 0
\(58\) 1.94043 + 7.24179i 0.254791 + 0.950894i
\(59\) −1.34967 + 2.33769i −0.175712 + 0.304341i −0.940407 0.340050i \(-0.889556\pi\)
0.764696 + 0.644392i \(0.222889\pi\)
\(60\) 0 0
\(61\) −4.37353 7.57518i −0.559973 0.969902i −0.997498 0.0706960i \(-0.977478\pi\)
0.437524 0.899207i \(-0.355855\pi\)
\(62\) 4.93330 4.93330i 0.626530 0.626530i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) 8.18285 2.19259i 0.999694 0.267867i 0.278377 0.960472i \(-0.410204\pi\)
0.721317 + 0.692605i \(0.243537\pi\)
\(68\) 3.22213 0.863368i 0.390741 0.104699i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.68481i 0.674663i −0.941386 0.337332i \(-0.890476\pi\)
0.941386 0.337332i \(-0.109524\pi\)
\(72\) 0 0
\(73\) −1.14928 + 1.14928i −0.134513 + 0.134513i −0.771157 0.636645i \(-0.780322\pi\)
0.636645 + 0.771157i \(0.280322\pi\)
\(74\) −3.01717 5.22589i −0.350739 0.607498i
\(75\) 0 0
\(76\) 1.85376 3.21081i 0.212641 0.368305i
\(77\) −1.02794 3.83631i −0.117144 0.437188i
\(78\) 0 0
\(79\) −10.0535 + 5.80440i −1.13111 + 0.653046i −0.944214 0.329334i \(-0.893176\pi\)
−0.186895 + 0.982380i \(0.559842\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −5.01003 5.01003i −0.553266 0.553266i
\(83\) −0.440961 + 1.64569i −0.0484017 + 0.180638i −0.985895 0.167366i \(-0.946474\pi\)
0.937493 + 0.348004i \(0.113140\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.15627 + 4.70902i 0.879513 + 0.507787i
\(87\) 0 0
\(88\) 1.90239 + 0.509743i 0.202795 + 0.0543388i
\(89\) 2.04989 0.217288 0.108644 0.994081i \(-0.465349\pi\)
0.108644 + 0.994081i \(0.465349\pi\)
\(90\) 0 0
\(91\) −8.20034 −0.859629
\(92\) −6.05338 1.62200i −0.631109 0.169105i
\(93\) 0 0
\(94\) 6.72013 + 3.87987i 0.693128 + 0.400178i
\(95\) 0 0
\(96\) 0 0
\(97\) −2.60421 + 9.71905i −0.264418 + 0.986820i 0.698188 + 0.715914i \(0.253990\pi\)
−0.962606 + 0.270906i \(0.912677\pi\)
\(98\) 2.07424 + 2.07424i 0.209530 + 0.209530i
\(99\) 0 0
\(100\) 0 0
\(101\) 4.09014 2.36144i 0.406984 0.234972i −0.282509 0.959265i \(-0.591167\pi\)
0.689493 + 0.724292i \(0.257833\pi\)
\(102\) 0 0
\(103\) −1.03662 3.86872i −0.102141 0.381196i 0.895864 0.444329i \(-0.146558\pi\)
−0.998005 + 0.0631321i \(0.979891\pi\)
\(104\) 2.03323 3.52166i 0.199375 0.345327i
\(105\) 0 0
\(106\) 4.97115 + 8.61029i 0.482841 + 0.836305i
\(107\) −5.40296 + 5.40296i −0.522324 + 0.522324i −0.918273 0.395949i \(-0.870416\pi\)
0.395949 + 0.918273i \(0.370416\pi\)
\(108\) 0 0
\(109\) 4.35357i 0.416996i −0.978023 0.208498i \(-0.933142\pi\)
0.978023 0.208498i \(-0.0668575\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.94786 0.521929i 0.184056 0.0493176i
\(113\) 2.86451 0.767544i 0.269471 0.0722045i −0.121553 0.992585i \(-0.538788\pi\)
0.391024 + 0.920380i \(0.372121\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.49726i 0.696103i
\(117\) 0 0
\(118\) −1.90872 + 1.90872i −0.175712 + 0.175712i
\(119\) −3.36345 5.82566i −0.308327 0.534037i
\(120\) 0 0
\(121\) −3.56054 + 6.16704i −0.323686 + 0.560640i
\(122\) −2.26391 8.44902i −0.204965 0.764938i
\(123\) 0 0
\(124\) 6.04204 3.48837i 0.542591 0.313265i
\(125\) 0 0
\(126\) 0 0
\(127\) 3.41734 + 3.41734i 0.303240 + 0.303240i 0.842280 0.539040i \(-0.181213\pi\)
−0.539040 + 0.842280i \(0.681213\pi\)
\(128\) −0.258819 + 0.965926i −0.0228766 + 0.0853766i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.411267 + 0.237445i 0.0359326 + 0.0207457i 0.517859 0.855466i \(-0.326729\pi\)
−0.481926 + 0.876212i \(0.660063\pi\)
\(132\) 0 0
\(133\) −7.22176 1.93506i −0.626206 0.167791i
\(134\) 8.47151 0.731827
\(135\) 0 0
\(136\) 3.33580 0.286042
\(137\) 9.51618 + 2.54985i 0.813022 + 0.217849i 0.641293 0.767296i \(-0.278398\pi\)
0.171728 + 0.985144i \(0.445065\pi\)
\(138\) 0 0
\(139\) 0.608318 + 0.351212i 0.0515968 + 0.0297894i 0.525577 0.850746i \(-0.323850\pi\)
−0.473980 + 0.880536i \(0.657183\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.47134 5.49111i 0.123472 0.460803i
\(143\) −5.66314 5.66314i −0.473575 0.473575i
\(144\) 0 0
\(145\) 0 0
\(146\) −1.40757 + 0.812661i −0.116491 + 0.0672563i
\(147\) 0 0
\(148\) −1.56180 5.82872i −0.128379 0.479118i
\(149\) −4.05609 + 7.02536i −0.332288 + 0.575540i −0.982960 0.183819i \(-0.941154\pi\)
0.650672 + 0.759359i \(0.274487\pi\)
\(150\) 0 0
\(151\) 4.61739 + 7.99755i 0.375758 + 0.650832i 0.990440 0.137943i \(-0.0440491\pi\)
−0.614682 + 0.788775i \(0.710716\pi\)
\(152\) 2.62162 2.62162i 0.212641 0.212641i
\(153\) 0 0
\(154\) 3.97164i 0.320044i
\(155\) 0 0
\(156\) 0 0
\(157\) −10.4848 + 2.80938i −0.836775 + 0.224213i −0.651667 0.758505i \(-0.725930\pi\)
−0.185108 + 0.982718i \(0.559264\pi\)
\(158\) −11.2132 + 3.00458i −0.892077 + 0.239031i
\(159\) 0 0
\(160\) 0 0
\(161\) 12.6377i 0.995993i
\(162\) 0 0
\(163\) −9.68197 + 9.68197i −0.758351 + 0.758351i −0.976022 0.217671i \(-0.930154\pi\)
0.217671 + 0.976022i \(0.430154\pi\)
\(164\) −3.54263 6.13601i −0.276633 0.479142i
\(165\) 0 0
\(166\) −0.851871 + 1.47548i −0.0661180 + 0.114520i
\(167\) 1.32254 + 4.93579i 0.102341 + 0.381943i 0.998030 0.0627387i \(-0.0199835\pi\)
−0.895689 + 0.444682i \(0.853317\pi\)
\(168\) 0 0
\(169\) −3.06239 + 1.76807i −0.235568 + 0.136005i
\(170\) 0 0
\(171\) 0 0
\(172\) 6.65957 + 6.65957i 0.507787 + 0.507787i
\(173\) −1.91916 + 7.16239i −0.145911 + 0.544546i 0.853802 + 0.520597i \(0.174291\pi\)
−0.999713 + 0.0239492i \(0.992376\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.70563 + 0.984748i 0.128567 + 0.0742282i
\(177\) 0 0
\(178\) 1.98004 + 0.530550i 0.148410 + 0.0397664i
\(179\) −2.73426 −0.204369 −0.102184 0.994765i \(-0.532583\pi\)
−0.102184 + 0.994765i \(0.532583\pi\)
\(180\) 0 0
\(181\) −22.7081 −1.68788 −0.843941 0.536437i \(-0.819770\pi\)
−0.843941 + 0.536437i \(0.819770\pi\)
\(182\) −7.92092 2.12240i −0.587138 0.157323i
\(183\) 0 0
\(184\) −5.42731 3.13346i −0.400107 0.231002i
\(185\) 0 0
\(186\) 0 0
\(187\) 1.70040 6.34598i 0.124346 0.464064i
\(188\) 5.48696 + 5.48696i 0.400178 + 0.400178i
\(189\) 0 0
\(190\) 0 0
\(191\) 1.11154 0.641749i 0.0804283 0.0464353i −0.459246 0.888309i \(-0.651881\pi\)
0.539675 + 0.841874i \(0.318547\pi\)
\(192\) 0 0
\(193\) −1.41494 5.28063i −0.101850 0.380108i 0.896119 0.443814i \(-0.146375\pi\)
−0.997969 + 0.0637057i \(0.979708\pi\)
\(194\) −5.03095 + 8.71386i −0.361201 + 0.625619i
\(195\) 0 0
\(196\) 1.46671 + 2.54041i 0.104765 + 0.181458i
\(197\) −12.0386 + 12.0386i −0.857716 + 0.857716i −0.991069 0.133353i \(-0.957426\pi\)
0.133353 + 0.991069i \(0.457426\pi\)
\(198\) 0 0
\(199\) 4.43831i 0.314623i −0.987549 0.157312i \(-0.949717\pi\)
0.987549 0.157312i \(-0.0502827\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 4.56196 1.22237i 0.320978 0.0860058i
\(203\) 14.6036 3.91303i 1.02497 0.274641i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.00520i 0.279055i
\(207\) 0 0
\(208\) 2.87542 2.87542i 0.199375 0.199375i
\(209\) −3.65098 6.32368i −0.252543 0.437418i
\(210\) 0 0
\(211\) 12.0425 20.8582i 0.829038 1.43594i −0.0697556 0.997564i \(-0.522222\pi\)
0.898794 0.438372i \(-0.144445\pi\)
\(212\) 2.57326 + 9.60353i 0.176732 + 0.659573i
\(213\) 0 0
\(214\) −6.61725 + 3.82047i −0.452346 + 0.261162i
\(215\) 0 0
\(216\) 0 0
\(217\) −9.94838 9.94838i −0.675340 0.675340i
\(218\) 1.12679 4.20523i 0.0763156 0.284814i
\(219\) 0 0
\(220\) 0 0
\(221\) −11.7476 6.78245i −0.790226 0.456237i
\(222\) 0 0
\(223\) 16.2073 + 4.34272i 1.08532 + 0.290810i 0.756773 0.653678i \(-0.226775\pi\)
0.328546 + 0.944488i \(0.393441\pi\)
\(224\) 2.01658 0.134738
\(225\) 0 0
\(226\) 2.96556 0.197266
\(227\) 7.18543 + 1.92533i 0.476914 + 0.127789i 0.489265 0.872135i \(-0.337265\pi\)
−0.0123515 + 0.999924i \(0.503932\pi\)
\(228\) 0 0
\(229\) −7.74183 4.46975i −0.511595 0.295369i 0.221894 0.975071i \(-0.428776\pi\)
−0.733489 + 0.679701i \(0.762109\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.94043 + 7.24179i −0.127396 + 0.475447i
\(233\) −15.0591 15.0591i −0.986558 0.986558i 0.0133533 0.999911i \(-0.495749\pi\)
−0.999911 + 0.0133533i \(0.995749\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2.33769 + 1.34967i −0.152171 + 0.0878558i
\(237\) 0 0
\(238\) −1.74105 6.49768i −0.112855 0.421182i
\(239\) −5.42731 + 9.40038i −0.351064 + 0.608060i −0.986436 0.164146i \(-0.947513\pi\)
0.635372 + 0.772206i \(0.280847\pi\)
\(240\) 0 0
\(241\) 11.6659 + 20.2059i 0.751467 + 1.30158i 0.947112 + 0.320904i \(0.103987\pi\)
−0.195645 + 0.980675i \(0.562680\pi\)
\(242\) −5.03537 + 5.03537i −0.323686 + 0.323686i
\(243\) 0 0
\(244\) 8.74707i 0.559973i
\(245\) 0 0
\(246\) 0 0
\(247\) −14.5628 + 3.90209i −0.926609 + 0.248284i
\(248\) 6.73901 1.80571i 0.427928 0.114663i
\(249\) 0 0
\(250\) 0 0
\(251\) 13.3860i 0.844914i 0.906383 + 0.422457i \(0.138832\pi\)
−0.906383 + 0.422457i \(0.861168\pi\)
\(252\) 0 0
\(253\) −8.72759 + 8.72759i −0.548699 + 0.548699i
\(254\) 2.41643 + 4.18538i 0.151620 + 0.262614i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.95494 7.29595i −0.121946 0.455109i 0.877766 0.479089i \(-0.159033\pi\)
−0.999712 + 0.0239802i \(0.992366\pi\)
\(258\) 0 0
\(259\) −10.5384 + 6.08436i −0.654825 + 0.378063i
\(260\) 0 0
\(261\) 0 0
\(262\) 0.335798 + 0.335798i 0.0207457 + 0.0207457i
\(263\) 2.88569 10.7695i 0.177939 0.664078i −0.818093 0.575086i \(-0.804969\pi\)
0.996032 0.0889923i \(-0.0283647\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −6.47485 3.73826i −0.396998 0.229207i
\(267\) 0 0
\(268\) 8.18285 + 2.19259i 0.499847 + 0.133934i
\(269\) −13.4707 −0.821326 −0.410663 0.911787i \(-0.634703\pi\)
−0.410663 + 0.911787i \(0.634703\pi\)
\(270\) 0 0
\(271\) 20.4402 1.24165 0.620827 0.783947i \(-0.286797\pi\)
0.620827 + 0.783947i \(0.286797\pi\)
\(272\) 3.22213 + 0.863368i 0.195371 + 0.0523494i
\(273\) 0 0
\(274\) 8.53197 + 4.92594i 0.515435 + 0.297587i
\(275\) 0 0
\(276\) 0 0
\(277\) −6.27326 + 23.4121i −0.376924 + 1.40670i 0.473590 + 0.880745i \(0.342958\pi\)
−0.850514 + 0.525953i \(0.823709\pi\)
\(278\) 0.496689 + 0.496689i 0.0297894 + 0.0297894i
\(279\) 0 0
\(280\) 0 0
\(281\) −19.5424 + 11.2828i −1.16580 + 0.673076i −0.952687 0.303952i \(-0.901694\pi\)
−0.213114 + 0.977027i \(0.568360\pi\)
\(282\) 0 0
\(283\) −0.549660 2.05136i −0.0326739 0.121941i 0.947663 0.319273i \(-0.103439\pi\)
−0.980337 + 0.197333i \(0.936772\pi\)
\(284\) 2.84241 4.92319i 0.168666 0.292138i
\(285\) 0 0
\(286\) −4.00444 6.93590i −0.236788 0.410128i
\(287\) −10.1031 + 10.1031i −0.596368 + 0.596368i
\(288\) 0 0
\(289\) 5.87245i 0.345438i
\(290\) 0 0
\(291\) 0 0
\(292\) −1.56994 + 0.420664i −0.0918738 + 0.0246175i
\(293\) −3.53204 + 0.946406i −0.206344 + 0.0552896i −0.360510 0.932755i \(-0.617397\pi\)
0.154167 + 0.988045i \(0.450731\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 6.03434i 0.350739i
\(297\) 0 0
\(298\) −5.73618 + 5.73618i −0.332288 + 0.332288i
\(299\) 12.7421 + 22.0700i 0.736895 + 1.27634i
\(300\) 0 0
\(301\) 9.49611 16.4477i 0.547347 0.948032i
\(302\) 2.39014 + 8.92011i 0.137537 + 0.513295i
\(303\) 0 0
\(304\) 3.21081 1.85376i 0.184153 0.106321i
\(305\) 0 0
\(306\) 0 0
\(307\) 10.5436 + 10.5436i 0.601754 + 0.601754i 0.940778 0.339024i \(-0.110097\pi\)
−0.339024 + 0.940778i \(0.610097\pi\)
\(308\) 1.02794 3.83631i 0.0585721 0.218594i
\(309\) 0 0
\(310\) 0 0
\(311\) 9.08436 + 5.24485i 0.515127 + 0.297408i 0.734938 0.678134i \(-0.237211\pi\)
−0.219812 + 0.975542i \(0.570544\pi\)
\(312\) 0 0
\(313\) −17.0518 4.56901i −0.963824 0.258256i −0.257606 0.966250i \(-0.582934\pi\)
−0.706218 + 0.707994i \(0.749600\pi\)
\(314\) −10.8546 −0.612562
\(315\) 0 0
\(316\) −11.6088 −0.653046
\(317\) −22.3972 6.00131i −1.25795 0.337067i −0.432549 0.901611i \(-0.642386\pi\)
−0.825403 + 0.564543i \(0.809052\pi\)
\(318\) 0 0
\(319\) 12.7876 + 7.38291i 0.715966 + 0.413363i
\(320\) 0 0
\(321\) 0 0
\(322\) −3.27089 + 12.2071i −0.182279 + 0.680276i
\(323\) −8.74518 8.74518i −0.486595 0.486595i
\(324\) 0 0
\(325\) 0 0
\(326\) −11.8579 + 6.84619i −0.656751 + 0.379175i
\(327\) 0 0
\(328\) −1.83380 6.84383i −0.101255 0.377887i
\(329\) 7.82405 13.5517i 0.431354 0.747127i
\(330\) 0 0
\(331\) 12.9130 + 22.3659i 0.709761 + 1.22934i 0.964946 + 0.262450i \(0.0845303\pi\)
−0.255185 + 0.966892i \(0.582136\pi\)
\(332\) −1.20473 + 1.20473i −0.0661180 + 0.0661180i
\(333\) 0 0
\(334\) 5.10991i 0.279602i
\(335\) 0 0
\(336\) 0 0
\(337\) 30.9889 8.30344i 1.68807 0.452317i 0.718180 0.695858i \(-0.244976\pi\)
0.969891 + 0.243541i \(0.0783089\pi\)
\(338\) −3.41565 + 0.915220i −0.185787 + 0.0497814i
\(339\) 0 0
\(340\) 0 0
\(341\) 13.7407i 0.744099i
\(342\) 0 0
\(343\) 14.1644 14.1644i 0.764806 0.764806i
\(344\) 4.70902 + 8.15627i 0.253894 + 0.439757i
\(345\) 0 0
\(346\) −3.70753 + 6.42162i −0.199318 + 0.345229i
\(347\) −3.83170 14.3001i −0.205696 0.767670i −0.989236 0.146328i \(-0.953255\pi\)
0.783540 0.621342i \(-0.213412\pi\)
\(348\) 0 0
\(349\) 13.3741 7.72151i 0.715897 0.413323i −0.0973439 0.995251i \(-0.531035\pi\)
0.813241 + 0.581928i \(0.197701\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.39264 + 1.39264i 0.0742282 + 0.0742282i
\(353\) −5.39774 + 20.1446i −0.287293 + 1.07219i 0.659855 + 0.751393i \(0.270618\pi\)
−0.947148 + 0.320798i \(0.896049\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.77526 + 1.02494i 0.0940883 + 0.0543219i
\(357\) 0 0
\(358\) −2.64110 0.707680i −0.139586 0.0374020i
\(359\) 3.39466 0.179163 0.0895815 0.995979i \(-0.471447\pi\)
0.0895815 + 0.995979i \(0.471447\pi\)
\(360\) 0 0
\(361\) 5.25425 0.276540
\(362\) −21.9344 5.87729i −1.15284 0.308904i
\(363\) 0 0
\(364\) −7.10170 4.10017i −0.372230 0.214907i
\(365\) 0 0
\(366\) 0 0
\(367\) −5.68801 + 21.2279i −0.296912 + 1.10809i 0.642776 + 0.766054i \(0.277783\pi\)
−0.939687 + 0.342035i \(0.888884\pi\)
\(368\) −4.43138 4.43138i −0.231002 0.231002i
\(369\) 0 0
\(370\) 0 0
\(371\) 17.3633 10.0247i 0.901458 0.520457i
\(372\) 0 0
\(373\) 0.381044 + 1.42207i 0.0197297 + 0.0736322i 0.975089 0.221815i \(-0.0711981\pi\)
−0.955359 + 0.295447i \(0.904531\pi\)
\(374\) 3.28492 5.68965i 0.169859 0.294205i
\(375\) 0 0
\(376\) 3.87987 + 6.72013i 0.200089 + 0.346564i
\(377\) 21.5578 21.5578i 1.11028 1.11028i
\(378\) 0 0
\(379\) 30.1323i 1.54779i 0.633314 + 0.773895i \(0.281694\pi\)
−0.633314 + 0.773895i \(0.718306\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.23976 0.332194i 0.0634318 0.0169965i
\(383\) −16.5638 + 4.43826i −0.846372 + 0.226785i −0.655843 0.754897i \(-0.727687\pi\)
−0.190528 + 0.981682i \(0.561020\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 5.46691i 0.278258i
\(387\) 0 0
\(388\) −7.11484 + 7.11484i −0.361201 + 0.361201i
\(389\) −15.1070 26.1660i −0.765953 1.32667i −0.939741 0.341886i \(-0.888934\pi\)
0.173789 0.984783i \(-0.444399\pi\)
\(390\) 0 0
\(391\) −10.4526 + 18.1044i −0.528610 + 0.915580i
\(392\) 0.759224 + 2.83346i 0.0383466 + 0.143112i
\(393\) 0 0
\(394\) −14.7442 + 8.51258i −0.742803 + 0.428858i
\(395\) 0 0
\(396\) 0 0
\(397\) 2.16969 + 2.16969i 0.108893 + 0.108893i 0.759454 0.650561i \(-0.225466\pi\)
−0.650561 + 0.759454i \(0.725466\pi\)
\(398\) 1.14872 4.28708i 0.0575801 0.214892i
\(399\) 0 0
\(400\) 0 0
\(401\) 12.3209 + 7.11346i 0.615275 + 0.355229i 0.775027 0.631928i \(-0.217736\pi\)
−0.159752 + 0.987157i \(0.551069\pi\)
\(402\) 0 0
\(403\) −27.4040 7.34287i −1.36509 0.365774i
\(404\) 4.72288 0.234972
\(405\) 0 0
\(406\) 15.1188 0.750333
\(407\) −11.4796 3.07596i −0.569025 0.152470i
\(408\) 0 0
\(409\) −10.2963 5.94456i −0.509118 0.293939i 0.223353 0.974738i \(-0.428300\pi\)
−0.732471 + 0.680798i \(0.761633\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 1.03662 3.86872i 0.0510706 0.190598i
\(413\) 3.84907 + 3.84907i 0.189401 + 0.189401i
\(414\) 0 0
\(415\) 0 0
\(416\) 3.52166 2.03323i 0.172664 0.0996874i
\(417\) 0 0
\(418\) −1.88989 7.05315i −0.0924373 0.344981i
\(419\) 19.6354 34.0095i 0.959251 1.66147i 0.234926 0.972013i \(-0.424515\pi\)
0.724325 0.689458i \(-0.242151\pi\)
\(420\) 0 0
\(421\) −12.2493 21.2163i −0.596992 1.03402i −0.993262 0.115887i \(-0.963029\pi\)
0.396270 0.918134i \(-0.370304\pi\)
\(422\) 17.0306 17.0306i 0.829038 0.829038i
\(423\) 0 0
\(424\) 9.94230i 0.482841i
\(425\) 0 0
\(426\) 0 0
\(427\) −17.0381 + 4.56534i −0.824531 + 0.220932i
\(428\) −7.38058 + 1.97762i −0.356754 + 0.0955920i
\(429\) 0 0
\(430\) 0 0
\(431\) 6.10703i 0.294165i 0.989124 + 0.147083i \(0.0469883\pi\)
−0.989124 + 0.147083i \(0.953012\pi\)
\(432\) 0 0
\(433\) −10.2605 + 10.2605i −0.493088 + 0.493088i −0.909278 0.416190i \(-0.863365\pi\)
0.416190 + 0.909278i \(0.363365\pi\)
\(434\) −7.03457 12.1842i −0.337670 0.584862i
\(435\) 0 0
\(436\) 2.17679 3.77030i 0.104249 0.180565i
\(437\) 6.01360 + 22.4431i 0.287670 + 1.07360i
\(438\) 0 0
\(439\) 1.96604 1.13510i 0.0938342 0.0541752i −0.452349 0.891841i \(-0.649414\pi\)
0.546183 + 0.837666i \(0.316080\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −9.59184 9.59184i −0.456237 0.456237i
\(443\) 7.20031 26.8719i 0.342097 1.27672i −0.553870 0.832603i \(-0.686850\pi\)
0.895967 0.444120i \(-0.146484\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 14.5310 + 8.38950i 0.688065 + 0.397254i
\(447\) 0 0
\(448\) 1.94786 + 0.521929i 0.0920279 + 0.0246588i
\(449\) −11.7712 −0.555516 −0.277758 0.960651i \(-0.589591\pi\)
−0.277758 + 0.960651i \(0.589591\pi\)
\(450\) 0 0
\(451\) −13.9544 −0.657086
\(452\) 2.86451 + 0.767544i 0.134735 + 0.0361022i
\(453\) 0 0
\(454\) 6.44228 + 3.71945i 0.302351 + 0.174562i
\(455\) 0 0
\(456\) 0 0
\(457\) 10.0741 37.5970i 0.471246 1.75871i −0.164058 0.986451i \(-0.552458\pi\)
0.635303 0.772263i \(-0.280875\pi\)
\(458\) −6.32118 6.32118i −0.295369 0.295369i
\(459\) 0 0
\(460\) 0 0
\(461\) 2.62200 1.51381i 0.122119 0.0705053i −0.437696 0.899123i \(-0.644205\pi\)
0.559815 + 0.828618i \(0.310872\pi\)
\(462\) 0 0
\(463\) −1.76940 6.60350i −0.0822311 0.306891i 0.912544 0.408978i \(-0.134115\pi\)
−0.994775 + 0.102087i \(0.967448\pi\)
\(464\) −3.74863 + 6.49281i −0.174026 + 0.301421i
\(465\) 0 0
\(466\) −10.6484 18.4436i −0.493279 0.854384i
\(467\) −8.05359 + 8.05359i −0.372676 + 0.372676i −0.868451 0.495775i \(-0.834884\pi\)
0.495775 + 0.868451i \(0.334884\pi\)
\(468\) 0 0
\(469\) 17.0835i 0.788841i
\(470\) 0 0
\(471\) 0 0
\(472\) −2.60736 + 0.698639i −0.120013 + 0.0321575i
\(473\) 17.9168 4.80079i 0.823814 0.220740i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.72689i 0.308327i
\(477\) 0 0
\(478\) −7.67538 + 7.67538i −0.351064 + 0.351064i
\(479\) 16.5711 + 28.7020i 0.757154 + 1.31143i 0.944296 + 0.329097i \(0.106744\pi\)
−0.187142 + 0.982333i \(0.559922\pi\)
\(480\) 0 0
\(481\) −12.2692 + 21.2509i −0.559428 + 0.968958i
\(482\) 6.03872 + 22.5368i 0.275056 + 1.02652i
\(483\) 0 0
\(484\) −6.16704 + 3.56054i −0.280320 + 0.161843i
\(485\) 0 0
\(486\) 0 0
\(487\) 14.8248 + 14.8248i 0.671777 + 0.671777i 0.958126 0.286349i \(-0.0924415\pi\)
−0.286349 + 0.958126i \(0.592442\pi\)
\(488\) 2.26391 8.44902i 0.102482 0.382469i
\(489\) 0 0
\(490\) 0 0
\(491\) −16.1505 9.32449i −0.728861 0.420808i 0.0891441 0.996019i \(-0.471587\pi\)
−0.818005 + 0.575210i \(0.804920\pi\)
\(492\) 0 0
\(493\) 24.1572 + 6.47289i 1.08798 + 0.291524i
\(494\) −15.0765 −0.678325
\(495\) 0 0
\(496\) 6.97674 0.313265
\(497\) −11.0732 2.96707i −0.496703 0.133091i
\(498\) 0 0
\(499\) 19.6189 + 11.3270i 0.878263 + 0.507065i 0.870085 0.492901i \(-0.164064\pi\)
0.00817742 + 0.999967i \(0.497397\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −3.46454 + 12.9298i −0.154630 + 0.577087i
\(503\) 9.64801 + 9.64801i 0.430183 + 0.430183i 0.888691 0.458507i \(-0.151616\pi\)
−0.458507 + 0.888691i \(0.651616\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −10.6891 + 6.17134i −0.475187 + 0.274349i
\(507\) 0 0
\(508\) 1.25084 + 4.66818i 0.0554968 + 0.207117i
\(509\) 13.5882 23.5355i 0.602286 1.04319i −0.390188 0.920735i \(-0.627590\pi\)
0.992474 0.122455i \(-0.0390768\pi\)
\(510\) 0 0
\(511\) 1.63879 + 2.83847i 0.0724959 + 0.125567i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 7.55332i 0.333163i
\(515\) 0 0
\(516\) 0 0
\(517\) 14.7620 3.95547i 0.649233 0.173961i
\(518\) −11.7541 + 3.14949i −0.516444 + 0.138381i
\(519\) 0 0
\(520\) 0 0
\(521\) 18.3542i 0.804114i 0.915615 + 0.402057i \(0.131705\pi\)
−0.915615 + 0.402057i \(0.868295\pi\)
\(522\) 0 0
\(523\) 25.8576 25.8576i 1.13067 1.13067i 0.140607 0.990066i \(-0.455095\pi\)
0.990066 0.140607i \(-0.0449053\pi\)
\(524\) 0.237445 + 0.411267i 0.0103728 + 0.0179663i
\(525\) 0 0
\(526\) 5.57472 9.65570i 0.243069 0.421009i
\(527\) −6.02350 22.4800i −0.262388 0.979244i
\(528\) 0 0
\(529\) 14.0940 8.13716i 0.612781 0.353789i
\(530\) 0 0
\(531\) 0 0
\(532\) −5.28669 5.28669i −0.229207 0.229207i
\(533\) −7.45708 + 27.8302i −0.323002 + 1.20546i
\(534\) 0 0
\(535\) 0 0
\(536\) 7.33654 + 4.23576i 0.316890 + 0.182957i
\(537\) 0 0
\(538\) −13.0117 3.48649i −0.560976 0.150313i
\(539\) 5.77735 0.248848
\(540\) 0 0
\(541\) −4.54804 −0.195536 −0.0977678 0.995209i \(-0.531170\pi\)
−0.0977678 + 0.995209i \(0.531170\pi\)
\(542\) 19.7437 + 5.29032i 0.848066 + 0.227239i
\(543\) 0 0
\(544\) 2.88889 + 1.66790i 0.123860 + 0.0715106i
\(545\) 0 0
\(546\) 0 0
\(547\) 5.79252 21.6180i 0.247670 0.924319i −0.724352 0.689430i \(-0.757861\pi\)
0.972022 0.234888i \(-0.0754724\pi\)
\(548\) 6.96632 + 6.96632i 0.297587 + 0.297587i
\(549\) 0 0
\(550\) 0 0
\(551\) 24.0723 13.8981i 1.02551 0.592080i
\(552\) 0 0
\(553\) 6.05896 + 22.6124i 0.257653 + 0.961575i
\(554\) −12.1190 + 20.9907i −0.514887 + 0.891811i
\(555\) 0 0
\(556\) 0.351212 + 0.608318i 0.0148947 + 0.0257984i
\(557\) −20.5740 + 20.5740i −0.871749 + 0.871749i −0.992663 0.120914i \(-0.961417\pi\)
0.120914 + 0.992663i \(0.461417\pi\)
\(558\) 0 0
\(559\) 38.2982i 1.61984i
\(560\) 0 0
\(561\) 0 0
\(562\) −21.7967 + 5.84041i −0.919438 + 0.246363i
\(563\) 34.2529 9.17805i 1.44359 0.386809i 0.549800 0.835296i \(-0.314704\pi\)
0.893789 + 0.448487i \(0.148037\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2.12372i 0.0892668i
\(567\) 0 0
\(568\) 4.01977 4.01977i 0.168666 0.168666i
\(569\) 12.0592 + 20.8872i 0.505549 + 0.875637i 0.999979 + 0.00641982i \(0.00204351\pi\)
−0.494430 + 0.869217i \(0.664623\pi\)
\(570\) 0 0
\(571\) 2.24726 3.89236i 0.0940448 0.162890i −0.815165 0.579229i \(-0.803354\pi\)
0.909210 + 0.416339i \(0.136687\pi\)
\(572\) −2.07285 7.73599i −0.0866703 0.323458i
\(573\) 0 0
\(574\) −12.3737 + 7.14398i −0.516470 + 0.298184i
\(575\) 0 0
\(576\) 0 0
\(577\) −0.186522 0.186522i −0.00776502 0.00776502i 0.703214 0.710979i \(-0.251748\pi\)
−0.710979 + 0.703214i \(0.751748\pi\)
\(578\) −1.51990 + 5.67235i −0.0632196 + 0.235939i
\(579\) 0 0
\(580\) 0 0
\(581\) 2.97543 + 1.71786i 0.123441 + 0.0712689i
\(582\) 0 0
\(583\) 18.9141 + 5.06802i 0.783342 + 0.209896i
\(584\) −1.62532 −0.0672563
\(585\) 0 0
\(586\) −3.65663 −0.151054
\(587\) 43.6620 + 11.6992i 1.80212 + 0.482878i 0.994307 0.106555i \(-0.0339820\pi\)
0.807818 + 0.589433i \(0.200649\pi\)
\(588\) 0 0
\(589\) −22.4010 12.9332i −0.923017 0.532904i
\(590\) 0 0
\(591\) 0 0
\(592\) 1.56180 5.82872i 0.0641897 0.239559i
\(593\) 3.60323 + 3.60323i 0.147967 + 0.147967i 0.777209 0.629242i \(-0.216635\pi\)
−0.629242 + 0.777209i \(0.716635\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −7.02536 + 4.05609i −0.287770 + 0.166144i
\(597\) 0 0
\(598\) 6.59580 + 24.6159i 0.269722 + 1.00662i
\(599\) −23.4581 + 40.6307i −0.958473 + 1.66012i −0.232260 + 0.972654i \(0.574612\pi\)
−0.726213 + 0.687470i \(0.758721\pi\)
\(600\) 0 0
\(601\) −20.5688 35.6263i −0.839020 1.45323i −0.890715 0.454563i \(-0.849795\pi\)
0.0516943 0.998663i \(-0.483538\pi\)
\(602\) 13.4295 13.4295i 0.547347 0.547347i
\(603\) 0 0
\(604\) 9.23478i 0.375758i
\(605\) 0 0
\(606\) 0 0
\(607\) 15.9755 4.28061i 0.648424 0.173745i 0.0804079 0.996762i \(-0.474378\pi\)
0.568016 + 0.823017i \(0.307711\pi\)
\(608\) 3.58120 0.959578i 0.145237 0.0389160i
\(609\) 0 0
\(610\) 0 0
\(611\) 31.5547i 1.27657i
\(612\) 0 0
\(613\) 21.1512 21.1512i 0.854290 0.854290i −0.136368 0.990658i \(-0.543543\pi\)
0.990658 + 0.136368i \(0.0435429\pi\)
\(614\) 7.45544 + 12.9132i 0.300877 + 0.521134i
\(615\) 0 0
\(616\) 1.98582 3.43954i 0.0800110 0.138583i
\(617\) −2.72427 10.1671i −0.109675 0.409312i 0.889159 0.457599i \(-0.151290\pi\)
−0.998834 + 0.0482869i \(0.984624\pi\)
\(618\) 0 0
\(619\) −2.77044 + 1.59951i −0.111353 + 0.0642898i −0.554642 0.832089i \(-0.687145\pi\)
0.443289 + 0.896379i \(0.353812\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 7.41734 + 7.41734i 0.297408 + 0.297408i
\(623\) 1.06990 3.99290i 0.0428644 0.159972i
\(624\) 0 0
\(625\) 0 0
\(626\) −15.2882 8.82666i −0.611040 0.352784i
\(627\) 0 0
\(628\) −10.4848 2.80938i −0.418388 0.112107i
\(629\) −20.1293 −0.802609
\(630\) 0 0
\(631\) 21.2335 0.845291 0.422645 0.906295i \(-0.361102\pi\)
0.422645 + 0.906295i \(0.361102\pi\)
\(632\) −11.2132 3.00458i −0.446039 0.119516i
\(633\) 0 0
\(634\) −20.0808 11.5936i −0.797510 0.460442i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.08736 11.5222i 0.122326 0.456525i
\(638\) 10.4410 + 10.4410i 0.413363 + 0.413363i
\(639\) 0 0
\(640\) 0 0
\(641\) −42.6583 + 24.6288i −1.68490 + 0.972778i −0.726582 + 0.687080i \(0.758892\pi\)
−0.958320 + 0.285698i \(0.907775\pi\)
\(642\) 0 0
\(643\) 5.25595 + 19.6155i 0.207274 + 0.773559i 0.988744 + 0.149616i \(0.0478036\pi\)
−0.781470 + 0.623943i \(0.785530\pi\)
\(644\) −6.31887 + 10.9446i −0.248998 + 0.431278i
\(645\) 0 0
\(646\) −6.18378 10.7106i −0.243298 0.421404i
\(647\) 29.0632 29.0632i 1.14259 1.14259i 0.154619 0.987974i \(-0.450585\pi\)
0.987974 0.154619i \(-0.0494151\pi\)
\(648\) 0 0
\(649\) 5.31632i 0.208684i
\(650\) 0 0
\(651\) 0 0
\(652\) −13.2258 + 3.54385i −0.517963 + 0.138788i
\(653\) 2.75027 0.736931i 0.107626 0.0288384i −0.204604 0.978845i \(-0.565591\pi\)
0.312230 + 0.950006i \(0.398924\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 7.08526i 0.276633i
\(657\) 0 0
\(658\) 11.0649 11.0649i 0.431354 0.431354i
\(659\) −18.8486 32.6467i −0.734236 1.27173i −0.955058 0.296420i \(-0.904207\pi\)
0.220822 0.975314i \(-0.429126\pi\)
\(660\) 0 0
\(661\) 3.68907 6.38966i 0.143488 0.248529i −0.785320 0.619091i \(-0.787501\pi\)
0.928808 + 0.370561i \(0.120835\pi\)
\(662\) 6.68424 + 24.9459i 0.259791 + 0.969551i
\(663\) 0 0
\(664\) −1.47548 + 0.851871i −0.0572598 + 0.0330590i
\(665\) 0 0
\(666\) 0 0
\(667\) −33.2232 33.2232i −1.28641 1.28641i
\(668\) −1.32254 + 4.93579i −0.0511707 + 0.190971i
\(669\) 0 0
\(670\) 0 0
\(671\) −14.9193 8.61365i −0.575953 0.332526i
\(672\) 0 0
\(673\) 6.88414 + 1.84460i 0.265364 + 0.0711041i 0.389048 0.921218i \(-0.372804\pi\)
−0.123684 + 0.992322i \(0.539471\pi\)
\(674\) 32.0820 1.23575
\(675\) 0 0
\(676\) −3.53614 −0.136005
\(677\) 8.09727 + 2.16966i 0.311203 + 0.0833867i 0.411040 0.911617i \(-0.365166\pi\)
−0.0998372 + 0.995004i \(0.531832\pi\)
\(678\) 0 0
\(679\) 17.5722 + 10.1453i 0.674358 + 0.389341i
\(680\) 0 0
\(681\) 0 0
\(682\) 3.55635 13.2725i 0.136180 0.508229i
\(683\) 15.8873 + 15.8873i 0.607911 + 0.607911i 0.942400 0.334488i \(-0.108564\pi\)
−0.334488 + 0.942400i \(0.608564\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 17.3478 10.0158i 0.662342 0.382403i
\(687\) 0 0
\(688\) 2.43757 + 9.09714i 0.0929315 + 0.346825i
\(689\) 20.2150 35.0134i 0.770131 1.33391i
\(690\) 0 0
\(691\) 9.16297 + 15.8707i 0.348576 + 0.603751i 0.985997 0.166765i \(-0.0533321\pi\)
−0.637421 + 0.770516i \(0.719999\pi\)
\(692\) −5.24323 + 5.24323i −0.199318 + 0.199318i
\(693\) 0 0
\(694\) 14.8046i 0.561973i
\(695\) 0 0
\(696\) 0 0
\(697\) −22.8296 + 6.11718i −0.864734 + 0.231705i
\(698\) 14.9168 3.99695i 0.564610 0.151287i
\(699\) 0 0
\(700\) 0 0
\(701\) 21.1738i 0.799724i 0.916575 + 0.399862i \(0.130942\pi\)
−0.916575 + 0.399862i \(0.869058\pi\)
\(702\) 0 0
\(703\) −15.8197 + 15.8197i −0.596652 + 0.596652i
\(704\) 0.984748 + 1.70563i 0.0371141 + 0.0642835i
\(705\) 0 0
\(706\) −10.4276 + 18.0612i −0.392449 + 0.679742i
\(707\) −2.46501 9.19953i −0.0927062 0.345984i
\(708\) 0 0
\(709\) 20.4846 11.8268i 0.769316 0.444165i −0.0633143 0.997994i \(-0.520167\pi\)
0.832631 + 0.553829i \(0.186834\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.44949 + 1.44949i 0.0543219 + 0.0543219i
\(713\) −11.3163 + 42.2329i −0.423798 + 1.58163i
\(714\) 0 0
\(715\) 0 0
\(716\) −2.36794 1.36713i −0.0884942 0.0510921i
\(717\) 0 0
\(718\) 3.27899 + 0.878601i 0.122371 + 0.0327891i
\(719\) 21.3695 0.796947 0.398473 0.917180i \(-0.369540\pi\)
0.398473 + 0.917180i \(0.369540\pi\)
\(720\) 0 0
\(721\) −8.07679 −0.300795
\(722\) 5.07522 + 1.35990i 0.188880 + 0.0506102i
\(723\) 0 0
\(724\) −19.6658 11.3541i −0.730874 0.421970i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.796213 2.97151i 0.0295299 0.110207i −0.949588 0.313501i \(-0.898498\pi\)
0.979118 + 0.203294i \(0.0651647\pi\)
\(728\) −5.79852 5.79852i −0.214907 0.214907i
\(729\) 0 0
\(730\) 0 0
\(731\) 27.2077 15.7084i 1.00631 0.580994i
\(732\) 0 0
\(733\) 6.30661 + 23.5366i 0.232940 + 0.869343i 0.979067 + 0.203540i \(0.0652446\pi\)
−0.746127 + 0.665804i \(0.768089\pi\)
\(734\) −10.9884 + 19.0324i −0.405589 + 0.702500i
\(735\) 0 0
\(736\) −3.13346 5.42731i −0.115501 0.200053i
\(737\) 11.7978 11.7978i 0.434578 0.434578i
\(738\) 0 0
\(739\) 5.68805i 0.209238i 0.994512 + 0.104619i \(0.0333624\pi\)
−0.994512 + 0.104619i \(0.966638\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 19.3663 5.18917i 0.710958 0.190500i
\(743\) −15.1100 + 4.04871i −0.554332 + 0.148533i −0.525101 0.851040i \(-0.675973\pi\)
−0.0292311 + 0.999573i \(0.509306\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.47224i 0.0539025i
\(747\) 0 0
\(748\) 4.64558 4.64558i 0.169859 0.169859i
\(749\) 7.70428 + 13.3442i 0.281508 + 0.487586i
\(750\) 0 0
\(751\) −21.6240 + 37.4538i −0.789070 + 1.36671i 0.137467 + 0.990506i \(0.456104\pi\)
−0.926537 + 0.376203i \(0.877229\pi\)
\(752\) 2.00837 + 7.49533i 0.0732376 + 0.273327i
\(753\) 0 0
\(754\) 26.4028 15.2437i 0.961533 0.555141i
\(755\) 0 0
\(756\) 0 0
\(757\) −22.7266 22.7266i −0.826013 0.826013i 0.160950 0.986963i \(-0.448544\pi\)
−0.986963 + 0.160950i \(0.948544\pi\)
\(758\) −7.79880 + 29.1055i −0.283265 + 1.05716i
\(759\) 0 0
\(760\) 0 0
\(761\) 24.8744 + 14.3612i 0.901696 + 0.520595i 0.877750 0.479119i \(-0.159044\pi\)
0.0239461 + 0.999713i \(0.492377\pi\)
\(762\) 0 0
\(763\) −8.48016 2.27225i −0.307002 0.0822611i
\(764\) 1.28350 0.0464353
\(765\) 0 0
\(766\) −17.1481 −0.619587
\(767\) 10.6027 + 2.84099i 0.382842 + 0.102582i
\(768\) 0 0
\(769\) 29.3558 + 16.9486i 1.05860 + 0.611180i 0.925043 0.379861i \(-0.124028\pi\)
0.133552 + 0.991042i \(0.457362\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.41494 5.28063i 0.0509248 0.190054i
\(773\) −30.1093 30.1093i −1.08296 1.08296i −0.996232 0.0867231i \(-0.972360\pi\)
−0.0867231 0.996232i \(-0.527640\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −8.71386 + 5.03095i −0.312809 + 0.180601i
\(777\) 0 0
\(778\) −7.81993 29.1844i −0.280358 1.04631i
\(779\) −13.1344 + 22.7494i −0.470588 + 0.815083i
\(780\) 0 0
\(781\) −5.59811 9.69621i −0.200316 0.346958i
\(782\) −14.7822 + 14.7822i −0.528610 + 0.528610i
\(783\) 0 0
\(784\) 2.93342i 0.104765i
\(785\) 0 0
\(786\) 0 0
\(787\) 10.2212 2.73876i 0.364346 0.0976263i −0.0720011 0.997405i \(-0.522939\pi\)
0.436347 + 0.899778i \(0.356272\pi\)
\(788\) −16.4450 + 4.40644i −0.585831 + 0.156973i
\(789\) 0 0
\(790\) 0 0
\(791\) 5.98028i 0.212634i
\(792\) 0 0
\(793\) −25.1515 + 25.1515i −0.893157 + 0.893157i
\(794\) 1.53420 + 2.65731i 0.0544467 + 0.0943045i
\(795\) 0 0
\(796\) 2.21916 3.84369i 0.0786559 0.136236i
\(797\) −3.52110 13.1409i −0.124724 0.465476i 0.875106 0.483932i \(-0.160792\pi\)
−0.999830 + 0.0184558i \(0.994125\pi\)
\(798\) 0 0
\(799\) 22.4170 12.9425i 0.793056 0.457871i
\(800\) 0 0
\(801\) 0 0
\(802\) 10.0599 + 10.0599i 0.355229 + 0.355229i
\(803\) −0.828496 + 3.09199i −0.0292370 + 0.109114i
\(804\) 0 0
\(805\) 0 0
\(806\) −24.5697 14.1853i −0.865432 0.499657i
\(807\) 0 0
\(808\) 4.56196 + 1.22237i 0.160489 + 0.0430029i
\(809\) 33.4429 1.17579 0.587895 0.808937i \(-0.299957\pi\)
0.587895 + 0.808937i \(0.299957\pi\)
\(810\) 0 0
\(811\) 21.1960 0.744294 0.372147 0.928174i \(-0.378622\pi\)
0.372147 + 0.928174i \(0.378622\pi\)
\(812\) 14.6036 + 3.91303i 0.512487 + 0.137320i
\(813\) 0 0
\(814\) −10.2924 5.94230i −0.360747 0.208278i
\(815\) 0 0
\(816\) 0 0
\(817\) 9.03736 33.7279i 0.316177 1.17999i
\(818\) −8.40687 8.40687i −0.293939 0.293939i
\(819\) 0 0
\(820\) 0 0
\(821\) 38.4941 22.2246i 1.34345 0.775643i 0.356141 0.934432i \(-0.384092\pi\)
0.987313 + 0.158789i \(0.0507589\pi\)
\(822\) 0 0
\(823\) −6.59989 24.6311i −0.230058 0.858588i −0.980315 0.197441i \(-0.936737\pi\)
0.750257 0.661146i \(-0.229930\pi\)
\(824\) 2.00260 3.46860i 0.0697638 0.120834i
\(825\) 0 0
\(826\) 2.72171 + 4.71413i 0.0947003 + 0.164026i
\(827\) −10.7808 + 10.7808i −0.374885 + 0.374885i −0.869253 0.494368i \(-0.835400\pi\)
0.494368 + 0.869253i \(0.335400\pi\)
\(828\) 0 0
\(829\) 4.02079i 0.139648i −0.997559 0.0698239i \(-0.977756\pi\)
0.997559 0.0698239i \(-0.0222437\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 3.92790 1.05248i 0.136176 0.0364881i
\(833\) 9.45186 2.53262i 0.327488 0.0877500i
\(834\) 0 0
\(835\) 0 0
\(836\) 7.30196i 0.252543i
\(837\) 0 0
\(838\) 27.7686 27.7686i 0.959251 0.959251i
\(839\) −16.7880 29.0777i −0.579588 1.00388i −0.995527 0.0944825i \(-0.969880\pi\)
0.415939 0.909393i \(-0.363453\pi\)
\(840\) 0 0
\(841\) −13.6044 + 23.5635i −0.469118 + 0.812536i
\(842\) −6.34068 23.6637i −0.218514 0.815506i
\(843\) 0 0
\(844\) 20.8582 12.0425i 0.717968 0.414519i
\(845\) 0 0
\(846\) 0 0
\(847\) 10.1542 + 10.1542i 0.348903 + 0.348903i
\(848\) −2.57326 + 9.60353i −0.0883660 + 0.329786i
\(849\) 0 0
\(850\) 0 0
\(851\) 32.7503 + 18.9084i 1.12266 + 0.648171i
\(852\) 0 0
\(853\) −22.9734 6.15572i −0.786596 0.210768i −0.156905 0.987614i \(-0.550152\pi\)
−0.629691 + 0.776846i \(0.716818\pi\)
\(854\) −17.6391 −0.603599
\(855\) 0 0
\(856\) −7.64094 −0.261162
\(857\) 11.4475 + 3.06736i 0.391040 + 0.104779i 0.448981 0.893541i \(-0.351787\pi\)
−0.0579412 + 0.998320i \(0.518454\pi\)
\(858\) 0 0
\(859\) −34.6670 20.0150i −1.18282 0.682904i −0.226158 0.974091i \(-0.572617\pi\)
−0.956666 + 0.291187i \(0.905950\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −1.58062 + 5.89894i −0.0538360 + 0.200919i
\(863\) 1.78680 + 1.78680i 0.0608233 + 0.0608233i 0.736864 0.676041i \(-0.236306\pi\)
−0.676041 + 0.736864i \(0.736306\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −12.5665 + 7.25527i −0.427027 + 0.246544i
\(867\) 0 0
\(868\) −3.64136 13.5897i −0.123596 0.461266i
\(869\) −11.4317 + 19.8004i −0.387795 + 0.671681i
\(870\) 0 0
\(871\) −17.2246 29.8338i −0.583632 1.01088i
\(872\) 3.07844 3.07844i 0.104249 0.104249i
\(873\) 0 0
\(874\) 23.2348i 0.785928i
\(875\) 0 0
\(876\) 0 0
\(877\) −6.66309 + 1.78537i −0.224996 + 0.0602876i −0.369556 0.929208i \(-0.620490\pi\)
0.144559 + 0.989496i \(0.453824\pi\)
\(878\) 2.19284 0.587569i 0.0740047 0.0198295i
\(879\) 0 0
\(880\) 0 0
\(881\) 3.01999i 0.101746i 0.998705 + 0.0508731i \(0.0162004\pi\)
−0.998705 + 0.0508731i \(0.983800\pi\)
\(882\) 0 0
\(883\) 8.50404 8.50404i 0.286184 0.286184i −0.549385 0.835569i \(-0.685138\pi\)
0.835569 + 0.549385i \(0.185138\pi\)
\(884\) −6.78245 11.7476i −0.228119 0.395113i
\(885\) 0 0
\(886\) 13.9099 24.0927i 0.467313 0.809410i
\(887\) −4.61020 17.2055i −0.154796 0.577705i −0.999123 0.0418769i \(-0.986666\pi\)
0.844327 0.535828i \(-0.180000\pi\)
\(888\) 0 0
\(889\) 8.44013 4.87291i 0.283073 0.163432i
\(890\) 0 0
\(891\) 0 0
\(892\) 11.8645 + 11.8645i 0.397254 + 0.397254i
\(893\) 7.44607 27.7891i 0.249173 0.929928i
\(894\) 0 0
\(895\) 0 0
\(896\) 1.74641 + 1.00829i 0.0583434 + 0.0336846i
\(897\) 0 0
\(898\) −11.3701 3.04660i −0.379424 0.101666i
\(899\) 52.3064 1.74452
\(900\) 0 0
\(901\) 33.1655 1.10490
\(902\) −13.4789 3.61166i −0.448798 0.120255i
\(903\) 0 0
\(904\) 2.56825 + 1.48278i 0.0854188 + 0.0493166i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.324723 + 1.21188i −0.0107822 + 0.0402399i −0.971107 0.238643i \(-0.923297\pi\)
0.960325 + 0.278883i \(0.0899641\pi\)
\(908\) 5.26010 + 5.26010i 0.174562 + 0.174562i
\(909\) 0 0
\(910\) 0 0
\(911\) 23.3987 13.5092i 0.775232 0.447581i −0.0595057 0.998228i \(-0.518952\pi\)
0.834738 + 0.550647i \(0.185619\pi\)
\(912\) 0 0
\(913\) 0.868470 + 3.24117i 0.0287422 + 0.107267i
\(914\) 19.4616 33.7085i 0.643734 1.11498i
\(915\) 0 0
\(916\) −4.46975 7.74183i −0.147685 0.255797i
\(917\) 0.677163 0.677163i 0.0223619 0.0223619i
\(918\) 0 0
\(919\) 54.3202i 1.79186i 0.444196 + 0.895930i \(0.353489\pi\)
−0.444196 + 0.895930i \(0.646511\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 2.92446 0.783607i 0.0963121 0.0258067i
\(923\) −22.3294 + 5.98314i −0.734981 + 0.196938i
\(924\) 0 0
\(925\) 0 0
\(926\) 6.83645i 0.224660i
\(927\) 0 0
\(928\) −5.30136 + 5.30136i −0.174026 + 0.174026i
\(929\) −13.9274 24.1230i −0.456944 0.791450i 0.541854 0.840473i \(-0.317723\pi\)
−0.998798 + 0.0490228i \(0.984389\pi\)
\(930\) 0 0
\(931\) 5.43786 9.41865i 0.178219 0.308684i
\(932\) −5.51203 20.5712i −0.180553 0.673831i
\(933\) 0 0
\(934\) −9.86360 + 5.69475i −0.322747 + 0.186338i
\(935\) 0 0
\(936\) 0 0
\(937\) 16.8770 + 16.8770i 0.551349 + 0.551349i 0.926830 0.375481i \(-0.122523\pi\)
−0.375481 + 0.926830i \(0.622523\pi\)
\(938\) 4.42152 16.5014i 0.144368 0.538788i
\(939\) 0 0
\(940\) 0 0
\(941\) −28.5039 16.4567i −0.929201 0.536474i −0.0426420 0.999090i \(-0.513577\pi\)
−0.886559 + 0.462616i \(0.846911\pi\)
\(942\) 0 0
\(943\) 42.8898 + 11.4923i 1.39668 + 0.374240i
\(944\) −2.69933 −0.0878558
\(945\) 0 0
\(946\) 18.5488 0.603074
\(947\) 11.5072 + 3.08335i 0.373934 + 0.100195i 0.440891 0.897560i \(-0.354662\pi\)
−0.0669572 + 0.997756i \(0.521329\pi\)
\(948\) 0 0
\(949\) 5.72383 + 3.30466i 0.185804 + 0.107274i
\(950\) 0 0
\(951\) 0 0
\(952\) 1.74105 6.49768i 0.0564277 0.210591i
\(953\) 13.4723 + 13.4723i 0.436411 + 0.436411i 0.890802 0.454391i \(-0.150143\pi\)
−0.454391 + 0.890802i \(0.650143\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −9.40038 + 5.42731i −0.304030 + 0.175532i
\(957\) 0 0
\(958\) 8.57785 + 32.0130i 0.277138 + 1.03429i
\(959\) 9.93353 17.2054i 0.320770 0.555591i
\(960\) 0 0
\(961\) −8.83746 15.3069i −0.285079 0.493772i
\(962\) −17.3513 + 17.3513i −0.559428 + 0.559428i
\(963\) 0 0
\(964\) 23.3318i 0.751467i
\(965\) 0 0
\(966\) 0 0
\(967\) −8.95826 + 2.40036i −0.288078 + 0.0771904i −0.399964 0.916531i \(-0.630978\pi\)
0.111886 + 0.993721i \(0.464311\pi\)
\(968\) −6.87844 + 1.84307i −0.221081 + 0.0592386i
\(969\) 0 0
\(970\) 0 0
\(971\) 24.7290i 0.793590i 0.917907 + 0.396795i \(0.129878\pi\)
−0.917907 + 0.396795i \(0.870122\pi\)
\(972\) 0 0
\(973\) 1.00161 1.00161i 0.0321102 0.0321102i
\(974\) 10.4827 + 18.1566i 0.335889 + 0.581776i
\(975\) 0 0
\(976\) 4.37353 7.57518i 0.139993 0.242476i
\(977\) 6.35548 + 23.7190i 0.203330 + 0.758837i 0.989952 + 0.141403i \(0.0451612\pi\)
−0.786622 + 0.617434i \(0.788172\pi\)
\(978\) 0 0
\(979\) 3.49636 2.01862i 0.111744 0.0645155i
\(980\) 0 0
\(981\) 0 0
\(982\) −13.1868 13.1868i −0.420808 0.420808i
\(983\) 10.7435 40.0954i 0.342666 1.27885i −0.552650 0.833414i \(-0.686383\pi\)
0.895316 0.445433i \(-0.146950\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 21.6587 + 12.5047i 0.689754 + 0.398230i
\(987\) 0 0
\(988\) −14.5628 3.90209i −0.463305 0.124142i
\(989\) −59.0222 −1.87680
\(990\) 0 0
\(991\) 36.6089 1.16292 0.581460 0.813575i \(-0.302481\pi\)
0.581460 + 0.813575i \(0.302481\pi\)
\(992\) 6.73901 + 1.80571i 0.213964 + 0.0573315i
\(993\) 0 0
\(994\) −9.92800 5.73193i −0.314897 0.181806i
\(995\) 0 0
\(996\) 0 0
\(997\) −3.09617 + 11.5550i −0.0980565 + 0.365952i −0.997465 0.0711569i \(-0.977331\pi\)
0.899409 + 0.437109i \(0.143998\pi\)
\(998\) 16.0188 + 16.0188i 0.507065 + 0.507065i
\(999\) 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 1350.2.q.h.557.4 16
3.2 odd 2 450.2.p.h.257.1 16
5.2 odd 4 270.2.m.b.233.2 16
5.3 odd 4 inner 1350.2.q.h.1043.3 16
5.4 even 2 270.2.m.b.17.2 16
9.2 odd 6 inner 1350.2.q.h.1007.3 16
9.7 even 3 450.2.p.h.407.1 16
15.2 even 4 90.2.l.b.23.4 16
15.8 even 4 450.2.p.h.293.1 16
15.14 odd 2 90.2.l.b.77.4 yes 16
45.2 even 12 270.2.m.b.143.2 16
45.4 even 6 810.2.f.c.647.7 16
45.7 odd 12 90.2.l.b.83.4 yes 16
45.14 odd 6 810.2.f.c.647.2 16
45.22 odd 12 810.2.f.c.323.2 16
45.29 odd 6 270.2.m.b.197.2 16
45.32 even 12 810.2.f.c.323.7 16
45.34 even 6 90.2.l.b.47.4 yes 16
45.38 even 12 inner 1350.2.q.h.143.4 16
45.43 odd 12 450.2.p.h.443.1 16
60.47 odd 4 720.2.cu.b.113.1 16
60.59 even 2 720.2.cu.b.257.2 16
180.7 even 12 720.2.cu.b.353.2 16
180.79 odd 6 720.2.cu.b.497.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.l.b.23.4 16 15.2 even 4
90.2.l.b.47.4 yes 16 45.34 even 6
90.2.l.b.77.4 yes 16 15.14 odd 2
90.2.l.b.83.4 yes 16 45.7 odd 12
270.2.m.b.17.2 16 5.4 even 2
270.2.m.b.143.2 16 45.2 even 12
270.2.m.b.197.2 16 45.29 odd 6
270.2.m.b.233.2 16 5.2 odd 4
450.2.p.h.257.1 16 3.2 odd 2
450.2.p.h.293.1 16 15.8 even 4
450.2.p.h.407.1 16 9.7 even 3
450.2.p.h.443.1 16 45.43 odd 12
720.2.cu.b.113.1 16 60.47 odd 4
720.2.cu.b.257.2 16 60.59 even 2
720.2.cu.b.353.2 16 180.7 even 12
720.2.cu.b.497.1 16 180.79 odd 6
810.2.f.c.323.2 16 45.22 odd 12
810.2.f.c.323.7 16 45.32 even 12
810.2.f.c.647.2 16 45.14 odd 6
810.2.f.c.647.7 16 45.4 even 6
1350.2.q.h.143.4 16 45.38 even 12 inner
1350.2.q.h.557.4 16 1.1 even 1 trivial
1350.2.q.h.1007.3 16 9.2 odd 6 inner
1350.2.q.h.1043.3 16 5.3 odd 4 inner