Properties

Label 576.2.y.a.47.18
Level $576$
Weight $2$
Character 576.47
Analytic conductor $4.599$
Analytic rank $0$
Dimension $88$
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] = [576,2,Mod(47,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.y (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: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 47.18
Character \(\chi\) \(=\) 576.47
Dual form 576.2.y.a.527.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.49488 - 0.874828i) q^{3} +(0.473330 - 1.76649i) q^{5} +(-1.40613 + 2.43549i) q^{7} +(1.46935 - 2.61553i) q^{9} +O(q^{10})\) \(q+(1.49488 - 0.874828i) q^{3} +(0.473330 - 1.76649i) q^{5} +(-1.40613 + 2.43549i) q^{7} +(1.46935 - 2.61553i) q^{9} +(-1.55262 - 5.79446i) q^{11} +(0.296913 - 1.10810i) q^{13} +(-0.837802 - 3.05478i) q^{15} +0.699378i q^{17} +(2.01481 - 2.01481i) q^{19} +(0.0286324 + 4.87090i) q^{21} +(4.91498 - 2.83767i) q^{23} +(1.43368 + 0.827735i) q^{25} +(-0.0916271 - 5.19534i) q^{27} +(1.45175 + 5.41802i) q^{29} +(-5.15522 + 2.97637i) q^{31} +(-7.39014 - 7.30377i) q^{33} +(3.63671 + 3.63671i) q^{35} +(3.48490 - 3.48490i) q^{37} +(-0.525542 - 1.91622i) q^{39} +(-1.55998 - 2.70196i) q^{41} +(-7.09570 + 1.90129i) q^{43} +(-3.92482 - 3.83361i) q^{45} +(-2.83634 + 4.91269i) q^{47} +(-0.454420 - 0.787079i) q^{49} +(0.611835 + 1.04549i) q^{51} +(4.45605 + 4.45605i) q^{53} -10.9708 q^{55} +(1.24929 - 4.77451i) q^{57} +(13.6570 + 3.65938i) q^{59} +(-13.2354 + 3.54643i) q^{61} +(4.30400 + 7.25638i) q^{63} +(-1.81690 - 1.04899i) q^{65} +(12.8958 + 3.45542i) q^{67} +(4.86486 - 8.54175i) q^{69} -7.21910i q^{71} +3.75535i q^{73} +(2.86731 - 0.0168548i) q^{75} +(16.2956 + 4.36638i) q^{77} +(-2.96345 - 1.71095i) q^{79} +(-4.68200 - 7.68628i) q^{81} +(-1.15222 + 0.308735i) q^{83} +(1.23544 + 0.331036i) q^{85} +(6.91004 + 6.82927i) q^{87} -0.391835 q^{89} +(2.28126 + 2.28126i) q^{91} +(-5.10265 + 8.95925i) q^{93} +(-2.60547 - 4.51280i) q^{95} +(-0.875387 + 1.51622i) q^{97} +(-17.4369 - 4.45318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 0
\(3\) 1.49488 0.874828i 0.863071 0.505082i
\(4\) 0 0
\(5\) 0.473330 1.76649i 0.211679 0.789999i −0.775630 0.631188i \(-0.782568\pi\)
0.987309 0.158810i \(-0.0507658\pi\)
\(6\) 0 0
\(7\) −1.40613 + 2.43549i −0.531468 + 0.920530i 0.467857 + 0.883804i \(0.345026\pi\)
−0.999325 + 0.0367260i \(0.988307\pi\)
\(8\) 0 0
\(9\) 1.46935 2.61553i 0.489784 0.871844i
\(10\) 0 0
\(11\) −1.55262 5.79446i −0.468133 1.74710i −0.646288 0.763093i \(-0.723680\pi\)
0.178156 0.984002i \(-0.442987\pi\)
\(12\) 0 0
\(13\) 0.296913 1.10810i 0.0823489 0.307330i −0.912450 0.409188i \(-0.865812\pi\)
0.994799 + 0.101858i \(0.0324787\pi\)
\(14\) 0 0
\(15\) −0.837802 3.05478i −0.216320 0.788741i
\(16\) 0 0
\(17\) 0.699378i 0.169624i 0.996397 + 0.0848120i \(0.0270290\pi\)
−0.996397 + 0.0848120i \(0.972971\pi\)
\(18\) 0 0
\(19\) 2.01481 2.01481i 0.462228 0.462228i −0.437157 0.899385i \(-0.644015\pi\)
0.899385 + 0.437157i \(0.144015\pi\)
\(20\) 0 0
\(21\) 0.0286324 + 4.87090i 0.00624810 + 1.06292i
\(22\) 0 0
\(23\) 4.91498 2.83767i 1.02485 0.591695i 0.109341 0.994004i \(-0.465126\pi\)
0.915504 + 0.402310i \(0.131792\pi\)
\(24\) 0 0
\(25\) 1.43368 + 0.827735i 0.286736 + 0.165547i
\(26\) 0 0
\(27\) −0.0916271 5.19534i −0.0176336 0.999845i
\(28\) 0 0
\(29\) 1.45175 + 5.41802i 0.269584 + 1.00610i 0.959385 + 0.282101i \(0.0910315\pi\)
−0.689801 + 0.723999i \(0.742302\pi\)
\(30\) 0 0
\(31\) −5.15522 + 2.97637i −0.925905 + 0.534572i −0.885514 0.464612i \(-0.846194\pi\)
−0.0403909 + 0.999184i \(0.512860\pi\)
\(32\) 0 0
\(33\) −7.39014 7.30377i −1.28646 1.27142i
\(34\) 0 0
\(35\) 3.63671 + 3.63671i 0.614717 + 0.614717i
\(36\) 0 0
\(37\) 3.48490 3.48490i 0.572913 0.572913i −0.360028 0.932941i \(-0.617233\pi\)
0.932941 + 0.360028i \(0.117233\pi\)
\(38\) 0 0
\(39\) −0.525542 1.91622i −0.0841540 0.306841i
\(40\) 0 0
\(41\) −1.55998 2.70196i −0.243628 0.421975i 0.718117 0.695922i \(-0.245004\pi\)
−0.961745 + 0.273947i \(0.911671\pi\)
\(42\) 0 0
\(43\) −7.09570 + 1.90129i −1.08208 + 0.289944i −0.755450 0.655207i \(-0.772581\pi\)
−0.326635 + 0.945151i \(0.605915\pi\)
\(44\) 0 0
\(45\) −3.92482 3.83361i −0.585078 0.571480i
\(46\) 0 0
\(47\) −2.83634 + 4.91269i −0.413723 + 0.716589i −0.995293 0.0969068i \(-0.969105\pi\)
0.581570 + 0.813496i \(0.302438\pi\)
\(48\) 0 0
\(49\) −0.454420 0.787079i −0.0649172 0.112440i
\(50\) 0 0
\(51\) 0.611835 + 1.04549i 0.0856741 + 0.146398i
\(52\) 0 0
\(53\) 4.45605 + 4.45605i 0.612086 + 0.612086i 0.943489 0.331403i \(-0.107522\pi\)
−0.331403 + 0.943489i \(0.607522\pi\)
\(54\) 0 0
\(55\) −10.9708 −1.47930
\(56\) 0 0
\(57\) 1.24929 4.77451i 0.165473 0.632399i
\(58\) 0 0
\(59\) 13.6570 + 3.65938i 1.77799 + 0.476411i 0.990215 0.139552i \(-0.0445663\pi\)
0.787775 + 0.615963i \(0.211233\pi\)
\(60\) 0 0
\(61\) −13.2354 + 3.54643i −1.69463 + 0.454074i −0.971577 0.236724i \(-0.923926\pi\)
−0.723048 + 0.690797i \(0.757260\pi\)
\(62\) 0 0
\(63\) 4.30400 + 7.25638i 0.542253 + 0.914219i
\(64\) 0 0
\(65\) −1.81690 1.04899i −0.225359 0.130111i
\(66\) 0 0
\(67\) 12.8958 + 3.45542i 1.57547 + 0.422146i 0.937520 0.347930i \(-0.113115\pi\)
0.637952 + 0.770077i \(0.279782\pi\)
\(68\) 0 0
\(69\) 4.86486 8.54175i 0.585660 1.02831i
\(70\) 0 0
\(71\) 7.21910i 0.856749i −0.903601 0.428375i \(-0.859086\pi\)
0.903601 0.428375i \(-0.140914\pi\)
\(72\) 0 0
\(73\) 3.75535i 0.439531i 0.975553 + 0.219765i \(0.0705292\pi\)
−0.975553 + 0.219765i \(0.929471\pi\)
\(74\) 0 0
\(75\) 2.86731 0.0168548i 0.331088 0.00194622i
\(76\) 0 0
\(77\) 16.2956 + 4.36638i 1.85705 + 0.497596i
\(78\) 0 0
\(79\) −2.96345 1.71095i −0.333415 0.192497i 0.323942 0.946077i \(-0.394992\pi\)
−0.657356 + 0.753580i \(0.728325\pi\)
\(80\) 0 0
\(81\) −4.68200 7.68628i −0.520223 0.854031i
\(82\) 0 0
\(83\) −1.15222 + 0.308735i −0.126472 + 0.0338881i −0.321500 0.946910i \(-0.604187\pi\)
0.195028 + 0.980798i \(0.437520\pi\)
\(84\) 0 0
\(85\) 1.23544 + 0.331036i 0.134003 + 0.0359059i
\(86\) 0 0
\(87\) 6.91004 + 6.82927i 0.740834 + 0.732175i
\(88\) 0 0
\(89\) −0.391835 −0.0415344 −0.0207672 0.999784i \(-0.506611\pi\)
−0.0207672 + 0.999784i \(0.506611\pi\)
\(90\) 0 0
\(91\) 2.28126 + 2.28126i 0.239141 + 0.239141i
\(92\) 0 0
\(93\) −5.10265 + 8.95925i −0.529120 + 0.929031i
\(94\) 0 0
\(95\) −2.60547 4.51280i −0.267315 0.463004i
\(96\) 0 0
\(97\) −0.875387 + 1.51622i −0.0888821 + 0.153948i −0.907039 0.421047i \(-0.861663\pi\)
0.818157 + 0.574995i \(0.194996\pi\)
\(98\) 0 0
\(99\) −17.4369 4.45318i −1.75248 0.447561i
\(100\) 0 0
\(101\) −0.816427 + 0.218761i −0.0812375 + 0.0217675i −0.299209 0.954188i \(-0.596723\pi\)
0.217971 + 0.975955i \(0.430056\pi\)
\(102\) 0 0
\(103\) 5.30341 + 9.18577i 0.522560 + 0.905101i 0.999655 + 0.0262492i \(0.00835635\pi\)
−0.477095 + 0.878852i \(0.658310\pi\)
\(104\) 0 0
\(105\) 8.61796 + 2.25496i 0.841026 + 0.220062i
\(106\) 0 0
\(107\) −6.39894 + 6.39894i −0.618609 + 0.618609i −0.945174 0.326566i \(-0.894109\pi\)
0.326566 + 0.945174i \(0.394109\pi\)
\(108\) 0 0
\(109\) 1.52592 + 1.52592i 0.146157 + 0.146157i 0.776399 0.630242i \(-0.217044\pi\)
−0.630242 + 0.776399i \(0.717044\pi\)
\(110\) 0 0
\(111\) 2.16083 8.25820i 0.205097 0.783834i
\(112\) 0 0
\(113\) 5.75213 3.32099i 0.541115 0.312413i −0.204416 0.978884i \(-0.565529\pi\)
0.745531 + 0.666471i \(0.232196\pi\)
\(114\) 0 0
\(115\) −2.68630 10.0254i −0.250499 0.934876i
\(116\) 0 0
\(117\) −2.46199 2.40477i −0.227611 0.222321i
\(118\) 0 0
\(119\) −1.70333 0.983418i −0.156144 0.0901498i
\(120\) 0 0
\(121\) −21.6389 + 12.4932i −1.96717 + 1.13575i
\(122\) 0 0
\(123\) −4.69574 2.67441i −0.423400 0.241143i
\(124\) 0 0
\(125\) 8.60659 8.60659i 0.769797 0.769797i
\(126\) 0 0
\(127\) 13.8224i 1.22654i 0.789874 + 0.613270i \(0.210146\pi\)
−0.789874 + 0.613270i \(0.789854\pi\)
\(128\) 0 0
\(129\) −8.94395 + 9.04972i −0.787471 + 0.796784i
\(130\) 0 0
\(131\) −2.40595 + 8.97914i −0.210209 + 0.784511i 0.777589 + 0.628773i \(0.216442\pi\)
−0.987798 + 0.155739i \(0.950224\pi\)
\(132\) 0 0
\(133\) 2.07396 + 7.74013i 0.179835 + 0.671154i
\(134\) 0 0
\(135\) −9.22090 2.29725i −0.793608 0.197716i
\(136\) 0 0
\(137\) −5.96603 + 10.3335i −0.509712 + 0.882848i 0.490224 + 0.871596i \(0.336915\pi\)
−0.999937 + 0.0112514i \(0.996419\pi\)
\(138\) 0 0
\(139\) 0.323448 1.20712i 0.0274345 0.102387i −0.950851 0.309649i \(-0.899789\pi\)
0.978286 + 0.207262i \(0.0664552\pi\)
\(140\) 0 0
\(141\) 0.0577550 + 9.82521i 0.00486385 + 0.827432i
\(142\) 0 0
\(143\) −6.88181 −0.575486
\(144\) 0 0
\(145\) 10.2580 0.851884
\(146\) 0 0
\(147\) −1.36786 0.779052i −0.112819 0.0642551i
\(148\) 0 0
\(149\) −0.930902 + 3.47417i −0.0762625 + 0.284615i −0.993517 0.113687i \(-0.963734\pi\)
0.917254 + 0.398302i \(0.130401\pi\)
\(150\) 0 0
\(151\) 5.43126 9.40721i 0.441989 0.765548i −0.555848 0.831284i \(-0.687606\pi\)
0.997837 + 0.0657361i \(0.0209395\pi\)
\(152\) 0 0
\(153\) 1.82924 + 1.02763i 0.147886 + 0.0830792i
\(154\) 0 0
\(155\) 2.81761 + 10.5155i 0.226316 + 0.844621i
\(156\) 0 0
\(157\) 2.55352 9.52986i 0.203793 0.760565i −0.786021 0.618199i \(-0.787862\pi\)
0.989814 0.142366i \(-0.0454709\pi\)
\(158\) 0 0
\(159\) 10.5596 + 2.76300i 0.837428 + 0.219120i
\(160\) 0 0
\(161\) 15.9606i 1.25787i
\(162\) 0 0
\(163\) 3.66703 3.66703i 0.287224 0.287224i −0.548758 0.835981i \(-0.684899\pi\)
0.835981 + 0.548758i \(0.184899\pi\)
\(164\) 0 0
\(165\) −16.4000 + 9.59752i −1.27674 + 0.747166i
\(166\) 0 0
\(167\) 17.4253 10.0605i 1.34841 0.778505i 0.360385 0.932803i \(-0.382645\pi\)
0.988024 + 0.154299i \(0.0493118\pi\)
\(168\) 0 0
\(169\) 10.1186 + 5.84198i 0.778355 + 0.449383i
\(170\) 0 0
\(171\) −2.30932 8.23025i −0.176598 0.629383i
\(172\) 0 0
\(173\) −2.70826 10.1074i −0.205906 0.768450i −0.989172 0.146763i \(-0.953114\pi\)
0.783266 0.621687i \(-0.213552\pi\)
\(174\) 0 0
\(175\) −4.03189 + 2.32781i −0.304782 + 0.175966i
\(176\) 0 0
\(177\) 23.6169 6.47717i 1.77516 0.486854i
\(178\) 0 0
\(179\) 12.4542 + 12.4542i 0.930872 + 0.930872i 0.997760 0.0668885i \(-0.0213072\pi\)
−0.0668885 + 0.997760i \(0.521307\pi\)
\(180\) 0 0
\(181\) −9.12083 + 9.12083i −0.677946 + 0.677946i −0.959535 0.281589i \(-0.909139\pi\)
0.281589 + 0.959535i \(0.409139\pi\)
\(182\) 0 0
\(183\) −16.6829 + 16.8802i −1.23324 + 1.24782i
\(184\) 0 0
\(185\) −4.50653 7.80554i −0.331327 0.573875i
\(186\) 0 0
\(187\) 4.05252 1.08587i 0.296349 0.0794066i
\(188\) 0 0
\(189\) 12.7821 + 7.08219i 0.929759 + 0.515153i
\(190\) 0 0
\(191\) 1.76985 3.06547i 0.128062 0.221810i −0.794864 0.606788i \(-0.792458\pi\)
0.922926 + 0.384978i \(0.125791\pi\)
\(192\) 0 0
\(193\) 7.43004 + 12.8692i 0.534826 + 0.926346i 0.999172 + 0.0406916i \(0.0129561\pi\)
−0.464346 + 0.885654i \(0.653711\pi\)
\(194\) 0 0
\(195\) −3.63374 + 0.0213600i −0.260218 + 0.00152962i
\(196\) 0 0
\(197\) −11.9105 11.9105i −0.848589 0.848589i 0.141368 0.989957i \(-0.454850\pi\)
−0.989957 + 0.141368i \(0.954850\pi\)
\(198\) 0 0
\(199\) −15.5983 −1.10574 −0.552868 0.833269i \(-0.686467\pi\)
−0.552868 + 0.833269i \(0.686467\pi\)
\(200\) 0 0
\(201\) 22.3006 6.11615i 1.57296 0.431400i
\(202\) 0 0
\(203\) −15.2369 4.08272i −1.06942 0.286551i
\(204\) 0 0
\(205\) −5.51137 + 1.47677i −0.384931 + 0.103142i
\(206\) 0 0
\(207\) −0.200159 17.0248i −0.0139120 1.18331i
\(208\) 0 0
\(209\) −14.8029 8.54648i −1.02394 0.591172i
\(210\) 0 0
\(211\) −15.6018 4.18049i −1.07407 0.287797i −0.321907 0.946771i \(-0.604324\pi\)
−0.752165 + 0.658975i \(0.770990\pi\)
\(212\) 0 0
\(213\) −6.31547 10.7917i −0.432729 0.739436i
\(214\) 0 0
\(215\) 13.4344i 0.916220i
\(216\) 0 0
\(217\) 16.7407i 1.13643i
\(218\) 0 0
\(219\) 3.28529 + 5.61381i 0.221999 + 0.379346i
\(220\) 0 0
\(221\) 0.774977 + 0.207655i 0.0521306 + 0.0139684i
\(222\) 0 0
\(223\) 13.9254 + 8.03982i 0.932512 + 0.538386i 0.887605 0.460605i \(-0.152368\pi\)
0.0449068 + 0.998991i \(0.485701\pi\)
\(224\) 0 0
\(225\) 4.27155 2.53360i 0.284770 0.168907i
\(226\) 0 0
\(227\) −10.6697 + 2.85895i −0.708176 + 0.189755i −0.594890 0.803807i \(-0.702804\pi\)
−0.113286 + 0.993562i \(0.536138\pi\)
\(228\) 0 0
\(229\) −0.390566 0.104652i −0.0258093 0.00691559i 0.245891 0.969297i \(-0.420919\pi\)
−0.271701 + 0.962382i \(0.587586\pi\)
\(230\) 0 0
\(231\) 28.1798 7.72858i 1.85409 0.508503i
\(232\) 0 0
\(233\) −11.6252 −0.761590 −0.380795 0.924659i \(-0.624350\pi\)
−0.380795 + 0.924659i \(0.624350\pi\)
\(234\) 0 0
\(235\) 7.33569 + 7.33569i 0.478528 + 0.478528i
\(236\) 0 0
\(237\) −5.92680 + 0.0348392i −0.384987 + 0.00226305i
\(238\) 0 0
\(239\) −1.55685 2.69654i −0.100704 0.174425i 0.811271 0.584671i \(-0.198776\pi\)
−0.911975 + 0.410246i \(0.865443\pi\)
\(240\) 0 0
\(241\) −7.16669 + 12.4131i −0.461647 + 0.799596i −0.999043 0.0437337i \(-0.986075\pi\)
0.537396 + 0.843330i \(0.319408\pi\)
\(242\) 0 0
\(243\) −13.7232 7.39414i −0.880345 0.474334i
\(244\) 0 0
\(245\) −1.60546 + 0.430181i −0.102569 + 0.0274833i
\(246\) 0 0
\(247\) −1.63437 2.83082i −0.103993 0.180121i
\(248\) 0 0
\(249\) −1.45234 + 1.46951i −0.0920382 + 0.0931266i
\(250\) 0 0
\(251\) 3.06176 3.06176i 0.193257 0.193257i −0.603845 0.797102i \(-0.706365\pi\)
0.797102 + 0.603845i \(0.206365\pi\)
\(252\) 0 0
\(253\) −24.0739 24.0739i −1.51351 1.51351i
\(254\) 0 0
\(255\) 2.13645 0.585940i 0.133789 0.0366930i
\(256\) 0 0
\(257\) 2.78074 1.60546i 0.173458 0.100146i −0.410757 0.911745i \(-0.634736\pi\)
0.584215 + 0.811599i \(0.301402\pi\)
\(258\) 0 0
\(259\) 3.58722 + 13.3877i 0.222899 + 0.831870i
\(260\) 0 0
\(261\) 16.3041 + 4.16388i 1.00920 + 0.257737i
\(262\) 0 0
\(263\) −2.63762 1.52283i −0.162643 0.0939018i 0.416469 0.909150i \(-0.363267\pi\)
−0.579112 + 0.815248i \(0.696601\pi\)
\(264\) 0 0
\(265\) 9.98076 5.76240i 0.613113 0.353981i
\(266\) 0 0
\(267\) −0.585748 + 0.342788i −0.0358472 + 0.0209783i
\(268\) 0 0
\(269\) 1.99648 1.99648i 0.121727 0.121727i −0.643619 0.765346i \(-0.722568\pi\)
0.765346 + 0.643619i \(0.222568\pi\)
\(270\) 0 0
\(271\) 13.9357i 0.846534i −0.906005 0.423267i \(-0.860883\pi\)
0.906005 0.423267i \(-0.139117\pi\)
\(272\) 0 0
\(273\) 5.40593 + 1.41451i 0.327182 + 0.0856099i
\(274\) 0 0
\(275\) 2.57032 9.59256i 0.154996 0.578453i
\(276\) 0 0
\(277\) −8.09885 30.2253i −0.486613 1.81606i −0.572686 0.819774i \(-0.694099\pi\)
0.0860738 0.996289i \(-0.472568\pi\)
\(278\) 0 0
\(279\) 0.209943 + 17.8570i 0.0125689 + 1.06907i
\(280\) 0 0
\(281\) 11.3745 19.7012i 0.678544 1.17527i −0.296875 0.954916i \(-0.595944\pi\)
0.975419 0.220357i \(-0.0707222\pi\)
\(282\) 0 0
\(283\) −0.633463 + 2.36412i −0.0376555 + 0.140532i −0.982194 0.187867i \(-0.939843\pi\)
0.944539 + 0.328399i \(0.106509\pi\)
\(284\) 0 0
\(285\) −7.84279 4.46678i −0.464567 0.264589i
\(286\) 0 0
\(287\) 8.77415 0.517921
\(288\) 0 0
\(289\) 16.5109 0.971228
\(290\) 0 0
\(291\) 0.0178251 + 3.03238i 0.00104492 + 0.177761i
\(292\) 0 0
\(293\) 2.01774 7.53030i 0.117877 0.439925i −0.881609 0.471981i \(-0.843539\pi\)
0.999486 + 0.0320565i \(0.0102057\pi\)
\(294\) 0 0
\(295\) 12.9285 22.3929i 0.752728 1.30376i
\(296\) 0 0
\(297\) −29.9620 + 8.59733i −1.73857 + 0.498868i
\(298\) 0 0
\(299\) −1.68508 6.28881i −0.0974508 0.363691i
\(300\) 0 0
\(301\) 5.34693 19.9550i 0.308192 1.15019i
\(302\) 0 0
\(303\) −1.02908 + 1.04125i −0.0591194 + 0.0598185i
\(304\) 0 0
\(305\) 25.0589i 1.43487i
\(306\) 0 0
\(307\) 24.0831 24.0831i 1.37450 1.37450i 0.520843 0.853652i \(-0.325618\pi\)
0.853652 0.520843i \(-0.174382\pi\)
\(308\) 0 0
\(309\) 15.9639 + 9.09209i 0.908157 + 0.517231i
\(310\) 0 0
\(311\) −9.09165 + 5.24907i −0.515540 + 0.297647i −0.735108 0.677950i \(-0.762869\pi\)
0.219568 + 0.975597i \(0.429535\pi\)
\(312\) 0 0
\(313\) 19.1380 + 11.0493i 1.08174 + 0.624544i 0.931366 0.364085i \(-0.118618\pi\)
0.150376 + 0.988629i \(0.451952\pi\)
\(314\) 0 0
\(315\) 14.8555 4.16832i 0.837015 0.234858i
\(316\) 0 0
\(317\) −5.71597 21.3323i −0.321041 1.19814i −0.918232 0.396042i \(-0.870383\pi\)
0.597192 0.802099i \(-0.296283\pi\)
\(318\) 0 0
\(319\) 29.1405 16.8243i 1.63155 0.941978i
\(320\) 0 0
\(321\) −3.96770 + 15.1636i −0.221455 + 0.846352i
\(322\) 0 0
\(323\) 1.40911 + 1.40911i 0.0784050 + 0.0784050i
\(324\) 0 0
\(325\) 1.34289 1.34289i 0.0744900 0.0744900i
\(326\) 0 0
\(327\) 3.61599 + 0.946157i 0.199965 + 0.0523226i
\(328\) 0 0
\(329\) −7.97655 13.8158i −0.439761 0.761689i
\(330\) 0 0
\(331\) −3.16734 + 0.848686i −0.174093 + 0.0466480i −0.344812 0.938672i \(-0.612057\pi\)
0.170720 + 0.985320i \(0.445391\pi\)
\(332\) 0 0
\(333\) −3.99431 14.2354i −0.218887 0.780095i
\(334\) 0 0
\(335\) 12.2079 21.1447i 0.666990 1.15526i
\(336\) 0 0
\(337\) −11.5710 20.0416i −0.630315 1.09174i −0.987487 0.157699i \(-0.949593\pi\)
0.357172 0.934038i \(-0.383741\pi\)
\(338\) 0 0
\(339\) 5.69347 9.99662i 0.309227 0.542942i
\(340\) 0 0
\(341\) 25.2506 + 25.2506i 1.36739 + 1.36739i
\(342\) 0 0
\(343\) −17.1300 −0.924931
\(344\) 0 0
\(345\) −12.7862 12.6368i −0.688388 0.680342i
\(346\) 0 0
\(347\) −7.59002 2.03374i −0.407454 0.109177i 0.0492700 0.998785i \(-0.484311\pi\)
−0.456724 + 0.889609i \(0.650977\pi\)
\(348\) 0 0
\(349\) 20.9793 5.62138i 1.12299 0.300905i 0.350900 0.936413i \(-0.385876\pi\)
0.772095 + 0.635508i \(0.219209\pi\)
\(350\) 0 0
\(351\) −5.78414 1.44103i −0.308735 0.0769168i
\(352\) 0 0
\(353\) −0.108858 0.0628489i −0.00579390 0.00334511i 0.497100 0.867693i \(-0.334398\pi\)
−0.502894 + 0.864348i \(0.667731\pi\)
\(354\) 0 0
\(355\) −12.7525 3.41701i −0.676831 0.181356i
\(356\) 0 0
\(357\) −3.40660 + 0.0200249i −0.180297 + 0.00105983i
\(358\) 0 0
\(359\) 4.07414i 0.215025i 0.994204 + 0.107512i \(0.0342886\pi\)
−0.994204 + 0.107512i \(0.965711\pi\)
\(360\) 0 0
\(361\) 10.8811i 0.572691i
\(362\) 0 0
\(363\) −21.4182 + 37.6062i −1.12416 + 1.97381i
\(364\) 0 0
\(365\) 6.63379 + 1.77752i 0.347229 + 0.0930396i
\(366\) 0 0
\(367\) −4.96310 2.86545i −0.259072 0.149575i 0.364839 0.931071i \(-0.381124\pi\)
−0.623911 + 0.781495i \(0.714457\pi\)
\(368\) 0 0
\(369\) −9.35922 + 0.110035i −0.487222 + 0.00572822i
\(370\) 0 0
\(371\) −17.1185 + 4.58689i −0.888748 + 0.238139i
\(372\) 0 0
\(373\) 19.7409 + 5.28955i 1.02214 + 0.273882i 0.730695 0.682704i \(-0.239196\pi\)
0.291448 + 0.956587i \(0.405863\pi\)
\(374\) 0 0
\(375\) 5.33657 20.3951i 0.275579 1.05320i
\(376\) 0 0
\(377\) 6.43473 0.331405
\(378\) 0 0
\(379\) 2.85273 + 2.85273i 0.146535 + 0.146535i 0.776568 0.630033i \(-0.216959\pi\)
−0.630033 + 0.776568i \(0.716959\pi\)
\(380\) 0 0
\(381\) 12.0922 + 20.6629i 0.619503 + 1.05859i
\(382\) 0 0
\(383\) −7.78731 13.4880i −0.397913 0.689206i 0.595555 0.803314i \(-0.296932\pi\)
−0.993468 + 0.114109i \(0.963599\pi\)
\(384\) 0 0
\(385\) 15.4263 26.7192i 0.786200 1.36174i
\(386\) 0 0
\(387\) −5.45322 + 21.3527i −0.277203 + 1.08542i
\(388\) 0 0
\(389\) −26.9587 + 7.22357i −1.36686 + 0.366250i −0.866332 0.499469i \(-0.833529\pi\)
−0.500531 + 0.865719i \(0.666862\pi\)
\(390\) 0 0
\(391\) 1.98460 + 3.43743i 0.100366 + 0.173838i
\(392\) 0 0
\(393\) 4.25858 + 15.5276i 0.214817 + 0.783262i
\(394\) 0 0
\(395\) −4.42507 + 4.42507i −0.222649 + 0.222649i
\(396\) 0 0
\(397\) 27.4204 + 27.4204i 1.37619 + 1.37619i 0.850961 + 0.525230i \(0.176021\pi\)
0.525230 + 0.850961i \(0.323979\pi\)
\(398\) 0 0
\(399\) 9.87161 + 9.75623i 0.494199 + 0.488423i
\(400\) 0 0
\(401\) −14.6316 + 8.44757i −0.730669 + 0.421852i −0.818667 0.574269i \(-0.805286\pi\)
0.0879981 + 0.996121i \(0.471953\pi\)
\(402\) 0 0
\(403\) 1.76745 + 6.59620i 0.0880428 + 0.328580i
\(404\) 0 0
\(405\) −15.7939 + 4.63257i −0.784803 + 0.230194i
\(406\) 0 0
\(407\) −25.6038 14.7824i −1.26913 0.732735i
\(408\) 0 0
\(409\) −14.9737 + 8.64508i −0.740402 + 0.427471i −0.822216 0.569176i \(-0.807262\pi\)
0.0818133 + 0.996648i \(0.473929\pi\)
\(410\) 0 0
\(411\) 0.121483 + 20.6666i 0.00599233 + 1.01941i
\(412\) 0 0
\(413\) −28.1160 + 28.1160i −1.38350 + 1.38350i
\(414\) 0 0
\(415\) 2.18151i 0.107086i
\(416\) 0 0
\(417\) −0.572508 2.08747i −0.0280359 0.102224i
\(418\) 0 0
\(419\) −0.788205 + 2.94162i −0.0385063 + 0.143708i −0.982503 0.186248i \(-0.940367\pi\)
0.943996 + 0.329956i \(0.107034\pi\)
\(420\) 0 0
\(421\) −2.38357 8.89561i −0.116168 0.433546i 0.883203 0.468990i \(-0.155382\pi\)
−0.999372 + 0.0354445i \(0.988715\pi\)
\(422\) 0 0
\(423\) 8.68170 + 14.6370i 0.422119 + 0.711676i
\(424\) 0 0
\(425\) −0.578900 + 1.00268i −0.0280808 + 0.0486373i
\(426\) 0 0
\(427\) 9.97350 37.2216i 0.482651 1.80128i
\(428\) 0 0
\(429\) −10.2875 + 6.02040i −0.496685 + 0.290667i
\(430\) 0 0
\(431\) −7.28002 −0.350666 −0.175333 0.984509i \(-0.556100\pi\)
−0.175333 + 0.984509i \(0.556100\pi\)
\(432\) 0 0
\(433\) −19.9763 −0.960002 −0.480001 0.877268i \(-0.659364\pi\)
−0.480001 + 0.877268i \(0.659364\pi\)
\(434\) 0 0
\(435\) 15.3346 8.97401i 0.735236 0.430271i
\(436\) 0 0
\(437\) 4.18539 15.6201i 0.200214 0.747210i
\(438\) 0 0
\(439\) −15.3133 + 26.5235i −0.730866 + 1.26590i 0.225647 + 0.974209i \(0.427550\pi\)
−0.956513 + 0.291688i \(0.905783\pi\)
\(440\) 0 0
\(441\) −2.72633 + 0.0320532i −0.129825 + 0.00152634i
\(442\) 0 0
\(443\) −7.70884 28.7698i −0.366258 1.36689i −0.865708 0.500550i \(-0.833131\pi\)
0.499450 0.866343i \(-0.333536\pi\)
\(444\) 0 0
\(445\) −0.185467 + 0.692173i −0.00879199 + 0.0328121i
\(446\) 0 0
\(447\) 1.64771 + 6.00786i 0.0779342 + 0.284162i
\(448\) 0 0
\(449\) 26.8028i 1.26490i −0.774599 0.632452i \(-0.782048\pi\)
0.774599 0.632452i \(-0.217952\pi\)
\(450\) 0 0
\(451\) −13.2344 + 13.2344i −0.623181 + 0.623181i
\(452\) 0 0
\(453\) −0.110594 18.8141i −0.00519616 0.883964i
\(454\) 0 0
\(455\) 5.10961 2.95004i 0.239542 0.138300i
\(456\) 0 0
\(457\) −3.25342 1.87837i −0.152189 0.0878662i 0.421972 0.906609i \(-0.361338\pi\)
−0.574161 + 0.818743i \(0.694671\pi\)
\(458\) 0 0
\(459\) 3.63351 0.0640819i 0.169598 0.00299109i
\(460\) 0 0
\(461\) 1.05208 + 3.92641i 0.0490002 + 0.182871i 0.986088 0.166221i \(-0.0531566\pi\)
−0.937088 + 0.349092i \(0.886490\pi\)
\(462\) 0 0
\(463\) −20.2888 + 11.7137i −0.942899 + 0.544383i −0.890868 0.454263i \(-0.849903\pi\)
−0.0520310 + 0.998645i \(0.516569\pi\)
\(464\) 0 0
\(465\) 13.4112 + 13.2545i 0.621930 + 0.614661i
\(466\) 0 0
\(467\) −13.2570 13.2570i −0.613463 0.613463i 0.330384 0.943847i \(-0.392822\pi\)
−0.943847 + 0.330384i \(0.892822\pi\)
\(468\) 0 0
\(469\) −26.5489 + 26.5489i −1.22591 + 1.22591i
\(470\) 0 0
\(471\) −4.51977 16.4799i −0.208260 0.759354i
\(472\) 0 0
\(473\) 22.0339 + 38.1638i 1.01312 + 1.75477i
\(474\) 0 0
\(475\) 4.55631 1.22086i 0.209058 0.0560169i
\(476\) 0 0
\(477\) 18.2025 5.10743i 0.833434 0.233853i
\(478\) 0 0
\(479\) −17.6429 + 30.5584i −0.806124 + 1.39625i 0.109405 + 0.993997i \(0.465105\pi\)
−0.915529 + 0.402251i \(0.868228\pi\)
\(480\) 0 0
\(481\) −2.82689 4.89631i −0.128895 0.223252i
\(482\) 0 0
\(483\) 13.9627 + 23.8592i 0.635326 + 1.08563i
\(484\) 0 0
\(485\) 2.26403 + 2.26403i 0.102804 + 0.102804i
\(486\) 0 0
\(487\) 12.1433 0.550266 0.275133 0.961406i \(-0.411278\pi\)
0.275133 + 0.961406i \(0.411278\pi\)
\(488\) 0 0
\(489\) 2.27376 8.68979i 0.102823 0.392966i
\(490\) 0 0
\(491\) 0.746514 + 0.200028i 0.0336897 + 0.00902713i 0.275625 0.961265i \(-0.411115\pi\)
−0.241935 + 0.970293i \(0.577782\pi\)
\(492\) 0 0
\(493\) −3.78924 + 1.01532i −0.170659 + 0.0457279i
\(494\) 0 0
\(495\) −16.1199 + 28.6944i −0.724537 + 1.28972i
\(496\) 0 0
\(497\) 17.5821 + 10.1510i 0.788664 + 0.455335i
\(498\) 0 0
\(499\) −0.785369 0.210439i −0.0351579 0.00942054i 0.241197 0.970476i \(-0.422460\pi\)
−0.276355 + 0.961056i \(0.589127\pi\)
\(500\) 0 0
\(501\) 17.2476 30.2834i 0.770565 1.35296i
\(502\) 0 0
\(503\) 5.40486i 0.240991i 0.992714 + 0.120495i \(0.0384483\pi\)
−0.992714 + 0.120495i \(0.961552\pi\)
\(504\) 0 0
\(505\) 1.54576i 0.0687852i
\(506\) 0 0
\(507\) 20.2369 0.118957i 0.898751 0.00528308i
\(508\) 0 0
\(509\) −27.7030 7.42301i −1.22792 0.329019i −0.414148 0.910210i \(-0.635920\pi\)
−0.813768 + 0.581191i \(0.802587\pi\)
\(510\) 0 0
\(511\) −9.14614 5.28052i −0.404601 0.233597i
\(512\) 0 0
\(513\) −10.6522 10.2830i −0.470307 0.454005i
\(514\) 0 0
\(515\) 18.7368 5.02052i 0.825644 0.221231i
\(516\) 0 0
\(517\) 32.8701 + 8.80753i 1.44563 + 0.387355i
\(518\) 0 0
\(519\) −12.8908 12.7401i −0.565841 0.559228i
\(520\) 0 0
\(521\) −12.8208 −0.561689 −0.280845 0.959753i \(-0.590615\pi\)
−0.280845 + 0.959753i \(0.590615\pi\)
\(522\) 0 0
\(523\) 2.08204 + 2.08204i 0.0910411 + 0.0910411i 0.751161 0.660120i \(-0.229494\pi\)
−0.660120 + 0.751161i \(0.729494\pi\)
\(524\) 0 0
\(525\) −3.99077 + 7.00701i −0.174171 + 0.305811i
\(526\) 0 0
\(527\) −2.08161 3.60545i −0.0906762 0.157056i
\(528\) 0 0
\(529\) 4.60471 7.97560i 0.200205 0.346765i
\(530\) 0 0
\(531\) 29.6382 30.3434i 1.28619 1.31679i
\(532\) 0 0
\(533\) −3.45721 + 0.926356i −0.149748 + 0.0401249i
\(534\) 0 0
\(535\) 8.27485 + 14.3325i 0.357753 + 0.619647i
\(536\) 0 0
\(537\) 29.5129 + 7.72231i 1.27358 + 0.333242i
\(538\) 0 0
\(539\) −3.85515 + 3.85515i −0.166053 + 0.166053i
\(540\) 0 0
\(541\) 22.7002 + 22.7002i 0.975956 + 0.975956i 0.999718 0.0237613i \(-0.00756417\pi\)
−0.0237613 + 0.999718i \(0.507564\pi\)
\(542\) 0 0
\(543\) −5.65542 + 21.6137i −0.242697 + 0.927534i
\(544\) 0 0
\(545\) 3.41779 1.97326i 0.146402 0.0845253i
\(546\) 0 0
\(547\) 5.33444 + 19.9084i 0.228084 + 0.851222i 0.981145 + 0.193271i \(0.0619098\pi\)
−0.753061 + 0.657951i \(0.771424\pi\)
\(548\) 0 0
\(549\) −10.1718 + 39.8287i −0.434120 + 1.69985i
\(550\) 0 0
\(551\) 13.8413 + 7.99125i 0.589657 + 0.340439i
\(552\) 0 0
\(553\) 8.33402 4.81165i 0.354399 0.204612i
\(554\) 0 0
\(555\) −13.5652 7.72594i −0.575813 0.327948i
\(556\) 0 0
\(557\) −10.7551 + 10.7551i −0.455708 + 0.455708i −0.897244 0.441535i \(-0.854434\pi\)
0.441535 + 0.897244i \(0.354434\pi\)
\(558\) 0 0
\(559\) 8.42723i 0.356434i
\(560\) 0 0
\(561\) 5.10809 5.16850i 0.215664 0.218214i
\(562\) 0 0
\(563\) 5.56420 20.7659i 0.234503 0.875177i −0.743869 0.668325i \(-0.767012\pi\)
0.978372 0.206852i \(-0.0663218\pi\)
\(564\) 0 0
\(565\) −3.14385 11.7330i −0.132263 0.493611i
\(566\) 0 0
\(567\) 25.3034 0.595062i 1.06264 0.0249902i
\(568\) 0 0
\(569\) 1.88272 3.26097i 0.0789277 0.136707i −0.823860 0.566794i \(-0.808184\pi\)
0.902788 + 0.430087i \(0.141517\pi\)
\(570\) 0 0
\(571\) 4.37466 16.3264i 0.183074 0.683241i −0.811961 0.583712i \(-0.801600\pi\)
0.995035 0.0995287i \(-0.0317335\pi\)
\(572\) 0 0
\(573\) −0.0360386 6.13083i −0.00150553 0.256119i
\(574\) 0 0
\(575\) 9.39535 0.391813
\(576\) 0 0
\(577\) −9.76787 −0.406642 −0.203321 0.979112i \(-0.565173\pi\)
−0.203321 + 0.979112i \(0.565173\pi\)
\(578\) 0 0
\(579\) 22.3654 + 12.7380i 0.929473 + 0.529371i
\(580\) 0 0
\(581\) 0.868246 3.24034i 0.0360209 0.134432i
\(582\) 0 0
\(583\) 18.9019 32.7390i 0.782835 1.35591i
\(584\) 0 0
\(585\) −5.41333 + 3.21083i −0.223814 + 0.132751i
\(586\) 0 0
\(587\) 5.94132 + 22.1733i 0.245224 + 0.915190i 0.973271 + 0.229662i \(0.0737620\pi\)
−0.728046 + 0.685528i \(0.759571\pi\)
\(588\) 0 0
\(589\) −4.38996 + 16.3836i −0.180885 + 0.675073i
\(590\) 0 0
\(591\) −28.2245 7.38518i −1.16100 0.303786i
\(592\) 0 0
\(593\) 1.37926i 0.0566394i −0.999599 0.0283197i \(-0.990984\pi\)
0.999599 0.0283197i \(-0.00901564\pi\)
\(594\) 0 0
\(595\) −2.54344 + 2.54344i −0.104271 + 0.104271i
\(596\) 0 0
\(597\) −23.3177 + 13.6459i −0.954330 + 0.558488i
\(598\) 0 0
\(599\) −26.6820 + 15.4049i −1.09020 + 0.629425i −0.933629 0.358242i \(-0.883376\pi\)
−0.156568 + 0.987667i \(0.550043\pi\)
\(600\) 0 0
\(601\) 2.43951 + 1.40845i 0.0995098 + 0.0574520i 0.548929 0.835869i \(-0.315036\pi\)
−0.449419 + 0.893321i \(0.648369\pi\)
\(602\) 0 0
\(603\) 27.9862 28.6521i 1.13969 1.16680i
\(604\) 0 0
\(605\) 11.8268 + 44.1382i 0.480828 + 1.79447i
\(606\) 0 0
\(607\) −26.2297 + 15.1437i −1.06463 + 0.614666i −0.926710 0.375777i \(-0.877376\pi\)
−0.137922 + 0.990443i \(0.544042\pi\)
\(608\) 0 0
\(609\) −26.3491 + 7.22648i −1.06772 + 0.292832i
\(610\) 0 0
\(611\) 4.60158 + 4.60158i 0.186160 + 0.186160i
\(612\) 0 0
\(613\) 3.66344 3.66344i 0.147965 0.147965i −0.629243 0.777208i \(-0.716635\pi\)
0.777208 + 0.629243i \(0.216635\pi\)
\(614\) 0 0
\(615\) −6.94694 + 7.02910i −0.280128 + 0.283441i
\(616\) 0 0
\(617\) −13.2053 22.8722i −0.531624 0.920799i −0.999319 0.0369091i \(-0.988249\pi\)
0.467695 0.883890i \(-0.345085\pi\)
\(618\) 0 0
\(619\) −47.2262 + 12.6542i −1.89818 + 0.508617i −0.900981 + 0.433858i \(0.857152\pi\)
−0.997202 + 0.0747583i \(0.976181\pi\)
\(620\) 0 0
\(621\) −15.1930 25.2750i −0.609674 1.01425i
\(622\) 0 0
\(623\) 0.550972 0.954312i 0.0220742 0.0382337i
\(624\) 0 0
\(625\) −6.99103 12.1088i −0.279641 0.484353i
\(626\) 0 0
\(627\) −29.6054 + 0.174028i −1.18232 + 0.00695000i
\(628\) 0 0
\(629\) 2.43726 + 2.43726i 0.0971799 + 0.0971799i
\(630\) 0 0
\(631\) 36.5500 1.45503 0.727516 0.686090i \(-0.240675\pi\)
0.727516 + 0.686090i \(0.240675\pi\)
\(632\) 0 0
\(633\) −26.9801 + 7.39954i −1.07236 + 0.294105i
\(634\) 0 0
\(635\) 24.4171 + 6.54255i 0.968964 + 0.259633i
\(636\) 0 0
\(637\) −1.00708 + 0.269847i −0.0399020 + 0.0106917i
\(638\) 0 0
\(639\) −18.8818 10.6074i −0.746952 0.419623i
\(640\) 0 0
\(641\) −5.95425 3.43769i −0.235179 0.135780i 0.377780 0.925895i \(-0.376688\pi\)
−0.612959 + 0.790115i \(0.710021\pi\)
\(642\) 0 0
\(643\) −28.3564 7.59808i −1.11827 0.299639i −0.348086 0.937463i \(-0.613168\pi\)
−0.770183 + 0.637823i \(0.779835\pi\)
\(644\) 0 0
\(645\) 11.7528 + 20.0829i 0.462766 + 0.790764i
\(646\) 0 0
\(647\) 1.90726i 0.0749821i −0.999297 0.0374911i \(-0.988063\pi\)
0.999297 0.0374911i \(-0.0119366\pi\)
\(648\) 0 0
\(649\) 84.8166i 3.32934i
\(650\) 0 0
\(651\) −14.6452 25.0254i −0.573991 0.980821i
\(652\) 0 0
\(653\) −22.1710 5.94070i −0.867618 0.232478i −0.202560 0.979270i \(-0.564926\pi\)
−0.665057 + 0.746792i \(0.731593\pi\)
\(654\) 0 0
\(655\) 14.7228 + 8.50019i 0.575266 + 0.332130i
\(656\) 0 0
\(657\) 9.82224 + 5.51794i 0.383202 + 0.215275i
\(658\) 0 0
\(659\) 14.4059 3.86006i 0.561175 0.150366i 0.0329291 0.999458i \(-0.489516\pi\)
0.528246 + 0.849091i \(0.322850\pi\)
\(660\) 0 0
\(661\) −36.4336 9.76236i −1.41710 0.379712i −0.532648 0.846337i \(-0.678803\pi\)
−0.884455 + 0.466625i \(0.845470\pi\)
\(662\) 0 0
\(663\) 1.34016 0.367552i 0.0520476 0.0142745i
\(664\) 0 0
\(665\) 14.6545 0.568278
\(666\) 0 0
\(667\) 22.5099 + 22.5099i 0.871586 + 0.871586i
\(668\) 0 0
\(669\) 27.8503 0.163711i 1.07675 0.00632943i
\(670\) 0 0
\(671\) 41.0993 + 71.1860i 1.58662 + 2.74811i
\(672\) 0 0
\(673\) −11.2966 + 19.5664i −0.435454 + 0.754228i −0.997333 0.0729916i \(-0.976745\pi\)
0.561879 + 0.827220i \(0.310079\pi\)
\(674\) 0 0
\(675\) 4.16901 7.52430i 0.160465 0.289611i
\(676\) 0 0
\(677\) 30.3860 8.14191i 1.16783 0.312919i 0.377741 0.925911i \(-0.376701\pi\)
0.790089 + 0.612992i \(0.210034\pi\)
\(678\) 0 0
\(679\) −2.46182 4.26400i −0.0944760 0.163637i
\(680\) 0 0
\(681\) −13.4489 + 13.6080i −0.515365 + 0.521459i
\(682\) 0 0
\(683\) 24.1502 24.1502i 0.924081 0.924081i −0.0732336 0.997315i \(-0.523332\pi\)
0.997315 + 0.0732336i \(0.0233319\pi\)
\(684\) 0 0
\(685\) 15.4301 + 15.4301i 0.589553 + 0.589553i
\(686\) 0 0
\(687\) −0.675403 + 0.185236i −0.0257682 + 0.00706718i
\(688\) 0 0
\(689\) 6.26079 3.61467i 0.238517 0.137708i
\(690\) 0 0
\(691\) 10.7138 + 39.9843i 0.407571 + 1.52108i 0.799264 + 0.600980i \(0.205223\pi\)
−0.391693 + 0.920096i \(0.628111\pi\)
\(692\) 0 0
\(693\) 35.3643 36.2058i 1.34338 1.37534i
\(694\) 0 0
\(695\) −1.97928 1.14273i −0.0750782 0.0433464i
\(696\) 0 0
\(697\) 1.88969 1.09101i 0.0715772 0.0413251i
\(698\) 0 0
\(699\) −17.3783 + 10.1700i −0.657307 + 0.384666i
\(700\) 0 0
\(701\) 21.1814 21.1814i 0.800009 0.800009i −0.183088 0.983097i \(-0.558609\pi\)
0.983097 + 0.183088i \(0.0586092\pi\)
\(702\) 0 0
\(703\) 14.0428i 0.529633i
\(704\) 0 0
\(705\) 17.3835 + 4.54854i 0.654699 + 0.171308i
\(706\) 0 0
\(707\) 0.615214 2.29601i 0.0231375 0.0863503i
\(708\) 0 0
\(709\) 4.24787 + 15.8532i 0.159532 + 0.595381i 0.998675 + 0.0514698i \(0.0163906\pi\)
−0.839143 + 0.543911i \(0.816943\pi\)
\(710\) 0 0
\(711\) −8.82940 + 5.23701i −0.331128 + 0.196403i
\(712\) 0 0
\(713\) −16.8919 + 29.2576i −0.632606 + 1.09571i
\(714\) 0 0
\(715\) −3.25736 + 12.1566i −0.121819 + 0.454633i
\(716\) 0 0
\(717\) −4.68631 2.66904i −0.175014 0.0996771i
\(718\) 0 0
\(719\) −23.3461 −0.870664 −0.435332 0.900270i \(-0.643369\pi\)
−0.435332 + 0.900270i \(0.643369\pi\)
\(720\) 0 0
\(721\) −29.8292 −1.11090
\(722\) 0 0
\(723\) 0.145932 + 24.8257i 0.00542726 + 0.923278i
\(724\) 0 0
\(725\) −2.40334 + 8.96937i −0.0892576 + 0.333114i
\(726\) 0 0
\(727\) 2.90255 5.02736i 0.107650 0.186454i −0.807168 0.590322i \(-0.799001\pi\)
0.914818 + 0.403867i \(0.132334\pi\)
\(728\) 0 0
\(729\) −26.9832 + 0.952068i −0.999378 + 0.0352618i
\(730\) 0 0
\(731\) −1.32972 4.96258i −0.0491814 0.183548i
\(732\) 0 0
\(733\) −0.240792 + 0.898647i −0.00889384 + 0.0331923i −0.970230 0.242185i \(-0.922136\pi\)
0.961336 + 0.275377i \(0.0888027\pi\)
\(734\) 0 0
\(735\) −2.02364 + 2.04757i −0.0746430 + 0.0755257i
\(736\) 0 0
\(737\) 80.0891i 2.95012i
\(738\) 0 0
\(739\) −5.91328 + 5.91328i −0.217523 + 0.217523i −0.807454 0.589931i \(-0.799155\pi\)
0.589931 + 0.807454i \(0.299155\pi\)
\(740\) 0 0
\(741\) −4.91968 2.80195i −0.180729 0.102932i
\(742\) 0 0
\(743\) −20.3899 + 11.7721i −0.748032 + 0.431876i −0.824982 0.565158i \(-0.808815\pi\)
0.0769504 + 0.997035i \(0.475482\pi\)
\(744\) 0 0
\(745\) 5.69647 + 3.28886i 0.208703 + 0.120494i
\(746\) 0 0
\(747\) −0.885505 + 3.46730i −0.0323989 + 0.126862i
\(748\) 0 0
\(749\) −6.58682 24.5823i −0.240677 0.898219i
\(750\) 0 0
\(751\) 13.0649 7.54301i 0.476744 0.275248i −0.242315 0.970198i \(-0.577907\pi\)
0.719059 + 0.694949i \(0.244573\pi\)
\(752\) 0 0
\(753\) 1.89846 7.25549i 0.0691838 0.264405i
\(754\) 0 0
\(755\) −14.0470 14.0470i −0.511222 0.511222i
\(756\) 0 0
\(757\) 4.48920 4.48920i 0.163163 0.163163i −0.620803 0.783966i \(-0.713193\pi\)
0.783966 + 0.620803i \(0.213193\pi\)
\(758\) 0 0
\(759\) −57.0481 14.9271i −2.07071 0.541821i
\(760\) 0 0
\(761\) 19.0628 + 33.0177i 0.691025 + 1.19689i 0.971502 + 0.237030i \(0.0761739\pi\)
−0.280477 + 0.959861i \(0.590493\pi\)
\(762\) 0 0
\(763\) −5.86202 + 1.57072i −0.212219 + 0.0568640i
\(764\) 0 0
\(765\) 2.68114 2.74493i 0.0969368 0.0992433i
\(766\) 0 0
\(767\) 8.10989 14.0467i 0.292831 0.507198i
\(768\) 0 0
\(769\) 17.5683 + 30.4291i 0.633528 + 1.09730i 0.986825 + 0.161791i \(0.0517271\pi\)
−0.353297 + 0.935511i \(0.614940\pi\)
\(770\) 0 0
\(771\) 2.75238 4.83265i 0.0991247 0.174044i
\(772\) 0 0
\(773\) −23.4773 23.4773i −0.844420 0.844420i 0.145010 0.989430i \(-0.453678\pi\)
−0.989430 + 0.145010i \(0.953678\pi\)
\(774\) 0 0
\(775\) −9.85458 −0.353987
\(776\) 0 0
\(777\) 17.0744 + 16.8748i 0.612540 + 0.605381i
\(778\) 0 0
\(779\) −8.58698 2.30087i −0.307660 0.0824374i
\(780\) 0 0
\(781\) −41.8308 + 11.2085i −1.49682 + 0.401073i
\(782\) 0 0
\(783\) 28.0155 8.03880i 1.00119 0.287283i
\(784\) 0 0
\(785\) −15.6257 9.02153i −0.557707 0.321992i
\(786\) 0 0
\(787\) 0.208763 + 0.0559379i 0.00744160 + 0.00199397i 0.262538 0.964922i \(-0.415441\pi\)
−0.255096 + 0.966916i \(0.582107\pi\)
\(788\) 0 0
\(789\) −5.27515 + 0.0310087i −0.187800 + 0.00110394i
\(790\) 0 0
\(791\) 18.6790i 0.664150i
\(792\) 0 0
\(793\) 15.7191i 0.558202i
\(794\) 0 0
\(795\) 9.87897 17.3456i 0.350371 0.615183i
\(796\) 0 0
\(797\) −2.95273 0.791183i −0.104591 0.0280251i 0.206144 0.978522i \(-0.433909\pi\)
−0.310735 + 0.950497i \(0.600575\pi\)
\(798\) 0 0
\(799\) −3.43583 1.98367i −0.121551 0.0701774i
\(800\) 0 0
\(801\) −0.575744 + 1.02486i −0.0203429 + 0.0362115i
\(802\) 0 0
\(803\) 21.7602 5.83064i 0.767902 0.205759i
\(804\) 0 0
\(805\) 28.1942 + 7.55460i 0.993714 + 0.266265i
\(806\) 0 0
\(807\) 1.23793 4.73107i 0.0435771 0.166542i
\(808\) 0 0
\(809\) 42.5506 1.49600 0.748000 0.663699i \(-0.231014\pi\)
0.748000 + 0.663699i \(0.231014\pi\)
\(810\) 0 0
\(811\) −15.1448 15.1448i −0.531806 0.531806i 0.389304 0.921109i \(-0.372716\pi\)
−0.921109 + 0.389304i \(0.872716\pi\)
\(812\) 0 0
\(813\) −12.1913 20.8323i −0.427569 0.730619i
\(814\) 0 0
\(815\) −4.74206 8.21348i −0.166107 0.287706i
\(816\) 0 0
\(817\) −10.4657 + 18.1272i −0.366150 + 0.634190i
\(818\) 0 0
\(819\) 9.31868 2.61473i 0.325621 0.0913660i
\(820\) 0 0
\(821\) 26.6973 7.15352i 0.931742 0.249660i 0.239145 0.970984i \(-0.423133\pi\)
0.692598 + 0.721324i \(0.256466\pi\)
\(822\) 0 0
\(823\) 10.1921 + 17.6532i 0.355273 + 0.615350i 0.987165 0.159706i \(-0.0510547\pi\)
−0.631892 + 0.775057i \(0.717721\pi\)
\(824\) 0 0
\(825\) −4.54951 16.5883i −0.158394 0.577532i
\(826\) 0 0
\(827\) −8.34698 + 8.34698i −0.290253 + 0.290253i −0.837180 0.546927i \(-0.815797\pi\)
0.546927 + 0.837180i \(0.315797\pi\)
\(828\) 0 0
\(829\) −2.48126 2.48126i −0.0861778 0.0861778i 0.662704 0.748882i \(-0.269409\pi\)
−0.748882 + 0.662704i \(0.769409\pi\)
\(830\) 0 0
\(831\) −38.5488 38.0982i −1.33724 1.32161i
\(832\) 0 0
\(833\) 0.550465 0.317811i 0.0190725 0.0110115i
\(834\) 0 0
\(835\) −9.52386 35.5435i −0.329587 1.23004i
\(836\) 0 0
\(837\) 15.9356 + 26.5104i 0.550815 + 0.916335i
\(838\) 0 0
\(839\) 17.7430 + 10.2439i 0.612558 + 0.353660i 0.773966 0.633227i \(-0.218270\pi\)
−0.161408 + 0.986888i \(0.551604\pi\)
\(840\) 0 0
\(841\) −2.13260 + 1.23126i −0.0735380 + 0.0424572i
\(842\) 0 0
\(843\) −0.231613 39.4017i −0.00797717 1.35707i
\(844\) 0 0
\(845\) 15.1092 15.1092i 0.519774 0.519774i
\(846\) 0 0
\(847\) 70.2684i 2.41445i
\(848\) 0 0
\(849\) 1.12124 + 4.08825i 0.0384809 + 0.140308i
\(850\) 0 0
\(851\) 7.23923 27.0172i 0.248158 0.926137i
\(852\) 0 0
\(853\) 4.06296 + 15.1632i 0.139113 + 0.519177i 0.999947 + 0.0102909i \(0.00327574\pi\)
−0.860834 + 0.508886i \(0.830058\pi\)
\(854\) 0 0
\(855\) −15.6317 + 0.183781i −0.534594 + 0.00628517i
\(856\) 0 0
\(857\) 0.102894 0.178217i 0.00351478 0.00608778i −0.864263 0.503041i \(-0.832215\pi\)
0.867777 + 0.496953i \(0.165548\pi\)
\(858\) 0 0
\(859\) 0.733242 2.73650i 0.0250179 0.0933681i −0.952288 0.305201i \(-0.901276\pi\)
0.977306 + 0.211833i \(0.0679431\pi\)
\(860\) 0 0
\(861\) 13.1163 7.67587i 0.447003 0.261593i
\(862\) 0 0
\(863\) 26.9928 0.918846 0.459423 0.888218i \(-0.348056\pi\)
0.459423 + 0.888218i \(0.348056\pi\)
\(864\) 0 0
\(865\) −19.1365 −0.650660
\(866\) 0 0
\(867\) 24.6818 14.4442i 0.838239 0.490550i
\(868\) 0 0
\(869\) −5.31292 + 19.8281i −0.180228 + 0.672621i
\(870\) 0 0
\(871\) 7.65786 13.2638i 0.259477 0.449427i
\(872\) 0 0
\(873\) 2.67945 + 4.51746i 0.0906858 + 0.152893i
\(874\) 0 0
\(875\) 8.85929 + 33.0633i 0.299499 + 1.11774i
\(876\) 0 0
\(877\) −13.9344 + 52.0038i −0.470531 + 1.75604i 0.167338 + 0.985900i \(0.446483\pi\)
−0.637869 + 0.770145i \(0.720184\pi\)
\(878\) 0 0
\(879\) −3.57143 13.0221i −0.120461 0.439224i
\(880\) 0 0
\(881\) 27.9049i 0.940139i 0.882629 + 0.470069i \(0.155771\pi\)
−0.882629 + 0.470069i \(0.844229\pi\)
\(882\) 0 0
\(883\) −3.83601 + 3.83601i −0.129092 + 0.129092i −0.768701 0.639609i \(-0.779096\pi\)
0.639609 + 0.768701i \(0.279096\pi\)
\(884\) 0 0
\(885\) −0.263257 44.7850i −0.00884929 1.50543i
\(886\) 0 0
\(887\) 44.3036 25.5787i 1.48757 0.858849i 0.487671 0.873028i \(-0.337847\pi\)
0.999899 + 0.0141788i \(0.00451340\pi\)
\(888\) 0 0
\(889\) −33.6644 19.4361i −1.12907 0.651867i
\(890\) 0 0
\(891\) −37.2685 + 39.0636i −1.24854 + 1.30868i
\(892\) 0 0
\(893\) 4.18343 + 15.6128i 0.139993 + 0.522462i
\(894\) 0 0
\(895\) 27.8952 16.1053i 0.932434 0.538341i
\(896\) 0 0
\(897\) −8.02063 7.92688i −0.267801 0.264671i
\(898\) 0 0
\(899\) −23.6101 23.6101i −0.787442 0.787442i
\(900\) 0 0
\(901\) −3.11647 + 3.11647i −0.103825 + 0.103825i
\(902\) 0 0
\(903\) −9.46416 34.5081i −0.314947 1.14836i
\(904\) 0 0
\(905\) 11.7947 + 20.4290i 0.392069 + 0.679084i
\(906\) 0 0
\(907\) 9.99802 2.67896i 0.331979 0.0889535i −0.0889794 0.996033i \(-0.528361\pi\)
0.420958 + 0.907080i \(0.361694\pi\)
\(908\) 0 0
\(909\) −0.627443 + 2.45683i −0.0208110 + 0.0814878i
\(910\) 0 0
\(911\) 5.69107 9.85722i 0.188553 0.326584i −0.756215 0.654324i \(-0.772953\pi\)
0.944768 + 0.327739i \(0.106287\pi\)
\(912\) 0 0
\(913\) 3.57791 + 6.19712i 0.118411 + 0.205095i
\(914\) 0 0
\(915\) 21.9222 + 37.4602i 0.724727 + 1.23839i
\(916\) 0 0
\(917\) −18.4856 18.4856i −0.610447 0.610447i
\(918\) 0 0
\(919\) −11.8316 −0.390288 −0.195144 0.980775i \(-0.562517\pi\)
−0.195144 + 0.980775i \(0.562517\pi\)
\(920\) 0 0
\(921\) 14.9329 57.0700i 0.492055 1.88052i
\(922\) 0 0
\(923\) −7.99945 2.14345i −0.263305 0.0705524i
\(924\) 0 0
\(925\) 7.88080 2.11165i 0.259119 0.0694307i
\(926\) 0 0
\(927\) 31.8182 0.374084i 1.04505 0.0122865i
\(928\) 0 0
\(929\) 35.7139 + 20.6194i 1.17174 + 0.676502i 0.954088 0.299525i \(-0.0968284\pi\)
0.217647 + 0.976027i \(0.430162\pi\)
\(930\) 0 0
\(931\) −2.50138 0.670242i −0.0819794 0.0219663i
\(932\) 0 0
\(933\) −8.99893 + 15.8004i −0.294612 + 0.517281i
\(934\) 0 0
\(935\) 7.67271i 0.250924i
\(936\) 0 0
\(937\) 15.6750i 0.512081i −0.966666 0.256041i \(-0.917582\pi\)
0.966666 0.256041i \(-0.0824181\pi\)
\(938\) 0 0
\(939\) 38.2753 0.224992i 1.24907 0.00734233i
\(940\) 0 0
\(941\) 9.63753 + 2.58237i 0.314174 + 0.0841828i 0.412461 0.910975i \(-0.364669\pi\)
−0.0982863 + 0.995158i \(0.531336\pi\)
\(942\) 0 0
\(943\) −15.3345 8.85340i −0.499361 0.288306i
\(944\) 0 0
\(945\) 18.5608 19.2272i 0.603781 0.625461i
\(946\) 0 0
\(947\) 2.28712 0.612832i 0.0743214 0.0199144i −0.221467 0.975168i \(-0.571084\pi\)
0.295788 + 0.955254i \(0.404418\pi\)
\(948\) 0 0
\(949\) 4.16129 + 1.11501i 0.135081 + 0.0361949i
\(950\) 0 0
\(951\) −27.2068 26.8888i −0.882240 0.871929i
\(952\) 0 0
\(953\) 43.1152 1.39664 0.698320 0.715786i \(-0.253931\pi\)
0.698320 + 0.715786i \(0.253931\pi\)
\(954\) 0 0
\(955\) −4.57740 4.57740i −0.148121 0.148121i
\(956\) 0 0
\(957\) 28.8433 50.6432i 0.932371 1.63706i
\(958\) 0 0
\(959\) −16.7781 29.0605i −0.541792 0.938411i
\(960\) 0 0
\(961\) 2.21754 3.84089i 0.0715334 0.123900i
\(962\) 0 0
\(963\) 7.33432 + 26.1389i 0.236345 + 0.842315i
\(964\) 0 0
\(965\) 26.2502 7.03372i 0.845023 0.226423i
\(966\) 0 0
\(967\) 21.1271 + 36.5932i 0.679401 + 1.17676i 0.975162 + 0.221495i \(0.0710936\pi\)
−0.295761 + 0.955262i \(0.595573\pi\)
\(968\) 0 0
\(969\) 3.33918 + 0.873727i 0.107270 + 0.0280682i
\(970\) 0 0
\(971\) −11.0093 + 11.0093i −0.353305 + 0.353305i −0.861338 0.508033i \(-0.830373\pi\)
0.508033 + 0.861338i \(0.330373\pi\)
\(972\) 0 0
\(973\) 2.48513 + 2.48513i 0.0796697 + 0.0796697i
\(974\) 0 0
\(975\) 0.832665 3.18226i 0.0266666 0.101914i
\(976\) 0 0
\(977\) 30.5197 17.6206i 0.976413 0.563732i 0.0752275 0.997166i \(-0.476032\pi\)
0.901185 + 0.433434i \(0.142698\pi\)
\(978\) 0 0
\(979\) 0.608371 + 2.27047i 0.0194436 + 0.0725646i
\(980\) 0 0
\(981\) 6.23321 1.74898i 0.199011 0.0558406i
\(982\) 0 0
\(983\) 33.9109 + 19.5785i 1.08159 + 0.624456i 0.931325 0.364190i \(-0.118654\pi\)
0.150264 + 0.988646i \(0.451987\pi\)
\(984\) 0 0
\(985\) −26.6774 + 15.4022i −0.850013 + 0.490755i
\(986\) 0 0
\(987\) −24.0104 13.6749i −0.764261 0.435276i
\(988\) 0 0
\(989\) −29.4801 + 29.4801i −0.937411 + 0.937411i
\(990\) 0 0
\(991\) 15.1164i 0.480188i 0.970750 + 0.240094i \(0.0771783\pi\)
−0.970750 + 0.240094i \(0.922822\pi\)
\(992\) 0 0
\(993\) −3.99235 + 4.03956i −0.126693 + 0.128192i
\(994\) 0 0
\(995\) −7.38315 + 27.5543i −0.234062 + 0.873530i
\(996\) 0 0
\(997\) −10.3875 38.7668i −0.328976 1.22776i −0.910254 0.414051i \(-0.864113\pi\)
0.581277 0.813706i \(-0.302553\pi\)
\(998\) 0 0
\(999\) −18.4245 17.7859i −0.582927 0.562722i
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 576.2.y.a.47.18 88
3.2 odd 2 1728.2.z.a.1007.6 88
4.3 odd 2 144.2.u.a.83.17 yes 88
9.4 even 3 1728.2.z.a.1583.6 88
9.5 odd 6 inner 576.2.y.a.239.16 88
12.11 even 2 432.2.v.a.35.6 88
16.5 even 4 144.2.u.a.11.10 88
16.11 odd 4 inner 576.2.y.a.335.16 88
36.23 even 6 144.2.u.a.131.10 yes 88
36.31 odd 6 432.2.v.a.179.13 88
48.5 odd 4 432.2.v.a.251.13 88
48.11 even 4 1728.2.z.a.143.6 88
144.5 odd 12 144.2.u.a.59.17 yes 88
144.59 even 12 inner 576.2.y.a.527.18 88
144.85 even 12 432.2.v.a.395.6 88
144.139 odd 12 1728.2.z.a.719.6 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.10 88 16.5 even 4
144.2.u.a.59.17 yes 88 144.5 odd 12
144.2.u.a.83.17 yes 88 4.3 odd 2
144.2.u.a.131.10 yes 88 36.23 even 6
432.2.v.a.35.6 88 12.11 even 2
432.2.v.a.179.13 88 36.31 odd 6
432.2.v.a.251.13 88 48.5 odd 4
432.2.v.a.395.6 88 144.85 even 12
576.2.y.a.47.18 88 1.1 even 1 trivial
576.2.y.a.239.16 88 9.5 odd 6 inner
576.2.y.a.335.16 88 16.11 odd 4 inner
576.2.y.a.527.18 88 144.59 even 12 inner
1728.2.z.a.143.6 88 48.11 even 4
1728.2.z.a.719.6 88 144.139 odd 12
1728.2.z.a.1007.6 88 3.2 odd 2
1728.2.z.a.1583.6 88 9.4 even 3