Properties

Label 576.3.q.g.257.1
Level $576$
Weight $3$
Character 576.257
Analytic conductor $15.695$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,3,Mod(65,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.65");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 576.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(15.6948632272\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.1
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 576.257
Dual form 576.3.q.g.65.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.686141 + 2.92048i) q^{3} +(-6.55842 - 3.78651i) q^{5} +(4.55842 + 7.89542i) q^{7} +(-8.05842 - 4.00772i) q^{9} +O(q^{10})\) \(q+(-0.686141 + 2.92048i) q^{3} +(-6.55842 - 3.78651i) q^{5} +(4.55842 + 7.89542i) q^{7} +(-8.05842 - 4.00772i) q^{9} +(-0.383156 + 0.221215i) q^{11} +(-5.55842 + 9.62747i) q^{13} +(15.5584 - 16.5557i) q^{15} -8.01544i q^{17} -8.11684 q^{19} +(-26.1861 + 7.89542i) q^{21} +(-20.4416 - 11.8020i) q^{23} +(16.1753 + 28.0164i) q^{25} +(17.2337 - 20.7846i) q^{27} +(45.9090 - 26.5055i) q^{29} +(14.6753 - 25.4183i) q^{31} +(-0.383156 - 1.27078i) q^{33} -69.0420i q^{35} -18.4674 q^{37} +(-24.3030 - 22.8391i) q^{39} +(-38.9674 - 22.4978i) q^{41} +(-11.5000 - 19.9186i) q^{43} +(37.6753 + 56.7976i) q^{45} +(7.32473 - 4.22894i) q^{47} +(-17.0584 + 29.5461i) q^{49} +(23.4090 + 5.49972i) q^{51} -60.5841i q^{53} +3.35053 q^{55} +(5.56930 - 23.7051i) q^{57} +(65.9674 + 38.0863i) q^{59} +(2.67527 + 4.63370i) q^{61} +(-5.09105 - 81.8935i) q^{63} +(72.9090 - 42.0940i) q^{65} +(54.8505 - 95.0039i) q^{67} +(48.4932 - 51.6014i) q^{69} -16.0309i q^{71} -4.35053 q^{73} +(-92.9198 + 28.0164i) q^{75} +(-3.49317 - 2.01678i) q^{77} +(0.792110 + 1.37197i) q^{79} +(48.8763 + 64.5918i) q^{81} +(-7.32473 + 4.22894i) q^{83} +(-30.3505 + 52.5687i) q^{85} +(45.9090 + 152.263i) q^{87} +64.1236i q^{89} -101.351 q^{91} +(64.1644 + 60.2994i) q^{93} +(53.2337 + 30.7345i) q^{95} +(-57.6168 - 99.7953i) q^{97} +(3.97420 - 0.247063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{3} - 9 q^{5} + q^{7} - 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{3} - 9 q^{5} + q^{7} - 15 q^{9} - 36 q^{11} - 5 q^{13} + 45 q^{15} + 2 q^{19} - 99 q^{21} - 99 q^{23} + 13 q^{25} + 63 q^{29} + 7 q^{31} - 36 q^{33} + 64 q^{37} - 57 q^{39} - 18 q^{41} - 46 q^{43} + 99 q^{45} + 81 q^{47} - 51 q^{49} - 27 q^{51} - 90 q^{55} + 51 q^{57} + 126 q^{59} - 41 q^{61} - 141 q^{63} + 171 q^{65} + 116 q^{67} - 99 q^{69} + 86 q^{73} - 297 q^{75} + 279 q^{77} - 83 q^{79} - 63 q^{81} - 81 q^{83} - 18 q^{85} + 63 q^{87} - 302 q^{91} + 159 q^{93} + 144 q^{95} - 196 q^{97} + 171 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.686141 + 2.92048i −0.228714 + 0.973494i
\(4\) 0 0
\(5\) −6.55842 3.78651i −1.31168 0.757301i −0.329309 0.944222i \(-0.606816\pi\)
−0.982375 + 0.186921i \(0.940149\pi\)
\(6\) 0 0
\(7\) 4.55842 + 7.89542i 0.651203 + 1.12792i 0.982831 + 0.184507i \(0.0590688\pi\)
−0.331628 + 0.943410i \(0.607598\pi\)
\(8\) 0 0
\(9\) −8.05842 4.00772i −0.895380 0.445302i
\(10\) 0 0
\(11\) −0.383156 + 0.221215i −0.0348324 + 0.0201105i −0.517315 0.855795i \(-0.673068\pi\)
0.482483 + 0.875906i \(0.339735\pi\)
\(12\) 0 0
\(13\) −5.55842 + 9.62747i −0.427571 + 0.740575i −0.996657 0.0817036i \(-0.973964\pi\)
0.569086 + 0.822278i \(0.307297\pi\)
\(14\) 0 0
\(15\) 15.5584 16.5557i 1.03723 1.10371i
\(16\) 0 0
\(17\) 8.01544i 0.471497i −0.971814 0.235748i \(-0.924246\pi\)
0.971814 0.235748i \(-0.0757541\pi\)
\(18\) 0 0
\(19\) −8.11684 −0.427202 −0.213601 0.976921i \(-0.568519\pi\)
−0.213601 + 0.976921i \(0.568519\pi\)
\(20\) 0 0
\(21\) −26.1861 + 7.89542i −1.24696 + 0.375972i
\(22\) 0 0
\(23\) −20.4416 11.8020i −0.888764 0.513128i −0.0152262 0.999884i \(-0.504847\pi\)
−0.873538 + 0.486756i \(0.838180\pi\)
\(24\) 0 0
\(25\) 16.1753 + 28.0164i 0.647011 + 1.12066i
\(26\) 0 0
\(27\) 17.2337 20.7846i 0.638285 0.769800i
\(28\) 0 0
\(29\) 45.9090 26.5055i 1.58307 0.913984i 0.588659 0.808381i \(-0.299656\pi\)
0.994408 0.105603i \(-0.0336772\pi\)
\(30\) 0 0
\(31\) 14.6753 25.4183i 0.473396 0.819945i −0.526141 0.850398i \(-0.676361\pi\)
0.999536 + 0.0304523i \(0.00969476\pi\)
\(32\) 0 0
\(33\) −0.383156 1.27078i −0.0116108 0.0385086i
\(34\) 0 0
\(35\) 69.0420i 1.97263i
\(36\) 0 0
\(37\) −18.4674 −0.499118 −0.249559 0.968360i \(-0.580286\pi\)
−0.249559 + 0.968360i \(0.580286\pi\)
\(38\) 0 0
\(39\) −24.3030 22.8391i −0.623153 0.585617i
\(40\) 0 0
\(41\) −38.9674 22.4978i −0.950424 0.548727i −0.0572112 0.998362i \(-0.518221\pi\)
−0.893213 + 0.449635i \(0.851554\pi\)
\(42\) 0 0
\(43\) −11.5000 19.9186i −0.267442 0.463223i 0.700759 0.713398i \(-0.252845\pi\)
−0.968200 + 0.250176i \(0.919512\pi\)
\(44\) 0 0
\(45\) 37.6753 + 56.7976i 0.837228 + 1.26217i
\(46\) 0 0
\(47\) 7.32473 4.22894i 0.155845 0.0899774i −0.420049 0.907501i \(-0.637987\pi\)
0.575895 + 0.817524i \(0.304654\pi\)
\(48\) 0 0
\(49\) −17.0584 + 29.5461i −0.348131 + 0.602981i
\(50\) 0 0
\(51\) 23.4090 + 5.49972i 0.458999 + 0.107838i
\(52\) 0 0
\(53\) 60.5841i 1.14310i −0.820569 0.571548i \(-0.806343\pi\)
0.820569 0.571548i \(-0.193657\pi\)
\(54\) 0 0
\(55\) 3.35053 0.0609188
\(56\) 0 0
\(57\) 5.56930 23.7051i 0.0977070 0.415879i
\(58\) 0 0
\(59\) 65.9674 + 38.0863i 1.11809 + 0.645530i 0.940913 0.338649i \(-0.109970\pi\)
0.177178 + 0.984179i \(0.443303\pi\)
\(60\) 0 0
\(61\) 2.67527 + 4.63370i 0.0438568 + 0.0759622i 0.887121 0.461538i \(-0.152702\pi\)
−0.843264 + 0.537500i \(0.819369\pi\)
\(62\) 0 0
\(63\) −5.09105 81.8935i −0.0808103 1.29990i
\(64\) 0 0
\(65\) 72.9090 42.0940i 1.12168 0.647600i
\(66\) 0 0
\(67\) 54.8505 95.0039i 0.818665 1.41797i −0.0880017 0.996120i \(-0.528048\pi\)
0.906666 0.421848i \(-0.138619\pi\)
\(68\) 0 0
\(69\) 48.4932 51.6014i 0.702800 0.747847i
\(70\) 0 0
\(71\) 16.0309i 0.225787i −0.993607 0.112894i \(-0.963988\pi\)
0.993607 0.112894i \(-0.0360119\pi\)
\(72\) 0 0
\(73\) −4.35053 −0.0595963 −0.0297982 0.999556i \(-0.509486\pi\)
−0.0297982 + 0.999556i \(0.509486\pi\)
\(74\) 0 0
\(75\) −92.9198 + 28.0164i −1.23893 + 0.373552i
\(76\) 0 0
\(77\) −3.49317 2.01678i −0.0453659 0.0261920i
\(78\) 0 0
\(79\) 0.792110 + 1.37197i 0.0100267 + 0.0173668i 0.870995 0.491291i \(-0.163475\pi\)
−0.860969 + 0.508658i \(0.830142\pi\)
\(80\) 0 0
\(81\) 48.8763 + 64.5918i 0.603411 + 0.797430i
\(82\) 0 0
\(83\) −7.32473 + 4.22894i −0.0882498 + 0.0509511i −0.543475 0.839425i \(-0.682892\pi\)
0.455226 + 0.890376i \(0.349559\pi\)
\(84\) 0 0
\(85\) −30.3505 + 52.5687i −0.357065 + 0.618455i
\(86\) 0 0
\(87\) 45.9090 + 152.263i 0.527689 + 1.75015i
\(88\) 0 0
\(89\) 64.1236i 0.720489i 0.932858 + 0.360245i \(0.117307\pi\)
−0.932858 + 0.360245i \(0.882693\pi\)
\(90\) 0 0
\(91\) −101.351 −1.11374
\(92\) 0 0
\(93\) 64.1644 + 60.2994i 0.689940 + 0.648380i
\(94\) 0 0
\(95\) 53.2337 + 30.7345i 0.560355 + 0.323521i
\(96\) 0 0
\(97\) −57.6168 99.7953i −0.593988 1.02882i −0.993689 0.112172i \(-0.964219\pi\)
0.399701 0.916646i \(-0.369114\pi\)
\(98\) 0 0
\(99\) 3.97420 0.247063i 0.0401435 0.00249558i
\(100\) 0 0
\(101\) −114.558 + 66.1403i −1.13424 + 0.654855i −0.944998 0.327075i \(-0.893937\pi\)
−0.189244 + 0.981930i \(0.560604\pi\)
\(102\) 0 0
\(103\) 62.6753 108.557i 0.608498 1.05395i −0.382990 0.923752i \(-0.625106\pi\)
0.991488 0.130197i \(-0.0415609\pi\)
\(104\) 0 0
\(105\) 201.636 + 47.3725i 1.92034 + 0.451167i
\(106\) 0 0
\(107\) 36.5378i 0.341475i 0.985317 + 0.170737i \(0.0546149\pi\)
−0.985317 + 0.170737i \(0.945385\pi\)
\(108\) 0 0
\(109\) −134.701 −1.23579 −0.617895 0.786261i \(-0.712014\pi\)
−0.617895 + 0.786261i \(0.712014\pi\)
\(110\) 0 0
\(111\) 12.6712 53.9336i 0.114155 0.485889i
\(112\) 0 0
\(113\) −164.727 95.1051i −1.45776 0.841638i −0.458859 0.888509i \(-0.651742\pi\)
−0.998901 + 0.0468711i \(0.985075\pi\)
\(114\) 0 0
\(115\) 89.3763 + 154.804i 0.777185 + 1.34612i
\(116\) 0 0
\(117\) 83.3763 55.3056i 0.712618 0.472697i
\(118\) 0 0
\(119\) 63.2853 36.5378i 0.531809 0.307040i
\(120\) 0 0
\(121\) −60.4021 + 104.620i −0.499191 + 0.864624i
\(122\) 0 0
\(123\) 92.4416 98.3668i 0.751558 0.799730i
\(124\) 0 0
\(125\) 55.6657i 0.445325i
\(126\) 0 0
\(127\) −184.103 −1.44963 −0.724816 0.688943i \(-0.758075\pi\)
−0.724816 + 0.688943i \(0.758075\pi\)
\(128\) 0 0
\(129\) 66.0625 19.9186i 0.512112 0.154408i
\(130\) 0 0
\(131\) −109.194 63.0433i −0.833544 0.481247i 0.0215207 0.999768i \(-0.493149\pi\)
−0.855064 + 0.518522i \(0.826483\pi\)
\(132\) 0 0
\(133\) −37.0000 64.0859i −0.278195 0.481849i
\(134\) 0 0
\(135\) −191.727 + 71.0588i −1.42020 + 0.526361i
\(136\) 0 0
\(137\) 107.617 62.1326i 0.785524 0.453523i −0.0528602 0.998602i \(-0.516834\pi\)
0.838385 + 0.545079i \(0.183500\pi\)
\(138\) 0 0
\(139\) −13.3832 + 23.1803i −0.0962817 + 0.166765i −0.910143 0.414295i \(-0.864028\pi\)
0.813861 + 0.581059i \(0.197362\pi\)
\(140\) 0 0
\(141\) 7.32473 + 24.2934i 0.0519485 + 0.172294i
\(142\) 0 0
\(143\) 4.91843i 0.0343946i
\(144\) 0 0
\(145\) −401.454 −2.76865
\(146\) 0 0
\(147\) −74.5842 70.0916i −0.507376 0.476813i
\(148\) 0 0
\(149\) −69.8437 40.3243i −0.468750 0.270633i 0.246966 0.969024i \(-0.420566\pi\)
−0.715716 + 0.698391i \(0.753900\pi\)
\(150\) 0 0
\(151\) 49.9742 + 86.5579i 0.330955 + 0.573231i 0.982699 0.185208i \(-0.0592958\pi\)
−0.651744 + 0.758439i \(0.725963\pi\)
\(152\) 0 0
\(153\) −32.1237 + 64.5918i −0.209959 + 0.422169i
\(154\) 0 0
\(155\) −192.493 + 111.136i −1.24189 + 0.717006i
\(156\) 0 0
\(157\) −34.7269 + 60.1487i −0.221190 + 0.383113i −0.955170 0.296059i \(-0.904327\pi\)
0.733979 + 0.679172i \(0.237661\pi\)
\(158\) 0 0
\(159\) 176.935 + 41.5692i 1.11280 + 0.261442i
\(160\) 0 0
\(161\) 215.193i 1.33660i
\(162\) 0 0
\(163\) 162.467 0.996732 0.498366 0.866967i \(-0.333934\pi\)
0.498366 + 0.866967i \(0.333934\pi\)
\(164\) 0 0
\(165\) −2.29894 + 9.78517i −0.0139329 + 0.0593040i
\(166\) 0 0
\(167\) −83.7269 48.3397i −0.501358 0.289459i 0.227916 0.973681i \(-0.426809\pi\)
−0.729274 + 0.684221i \(0.760142\pi\)
\(168\) 0 0
\(169\) 22.7079 + 39.3312i 0.134366 + 0.232729i
\(170\) 0 0
\(171\) 65.4090 + 32.5301i 0.382509 + 0.190234i
\(172\) 0 0
\(173\) 24.2731 14.0141i 0.140307 0.0810064i −0.428203 0.903682i \(-0.640853\pi\)
0.568510 + 0.822676i \(0.307520\pi\)
\(174\) 0 0
\(175\) −147.467 + 255.421i −0.842671 + 1.45955i
\(176\) 0 0
\(177\) −156.493 + 166.524i −0.884142 + 0.940813i
\(178\) 0 0
\(179\) 35.6012i 0.198889i −0.995043 0.0994447i \(-0.968293\pi\)
0.995043 0.0994447i \(-0.0317067\pi\)
\(180\) 0 0
\(181\) 19.6358 0.108485 0.0542426 0.998528i \(-0.482726\pi\)
0.0542426 + 0.998528i \(0.482726\pi\)
\(182\) 0 0
\(183\) −15.3682 + 4.63370i −0.0839794 + 0.0253207i
\(184\) 0 0
\(185\) 121.117 + 69.9268i 0.654686 + 0.377983i
\(186\) 0 0
\(187\) 1.77314 + 3.07117i 0.00948202 + 0.0164233i
\(188\) 0 0
\(189\) 242.662 + 41.3222i 1.28392 + 0.218636i
\(190\) 0 0
\(191\) −188.662 + 108.924i −0.987757 + 0.570282i −0.904603 0.426255i \(-0.859833\pi\)
−0.0831540 + 0.996537i \(0.526499\pi\)
\(192\) 0 0
\(193\) 24.5000 42.4352i 0.126943 0.219872i −0.795548 0.605891i \(-0.792817\pi\)
0.922491 + 0.386019i \(0.126150\pi\)
\(194\) 0 0
\(195\) 72.9090 + 241.812i 0.373892 + 1.24006i
\(196\) 0 0
\(197\) 359.965i 1.82723i −0.406575 0.913617i \(-0.633277\pi\)
0.406575 0.913617i \(-0.366723\pi\)
\(198\) 0 0
\(199\) 61.0652 0.306861 0.153430 0.988159i \(-0.450968\pi\)
0.153430 + 0.988159i \(0.450968\pi\)
\(200\) 0 0
\(201\) 239.822 + 225.376i 1.19314 + 1.12127i
\(202\) 0 0
\(203\) 418.545 + 241.647i 2.06180 + 1.19038i
\(204\) 0 0
\(205\) 170.376 + 295.100i 0.831104 + 1.43951i
\(206\) 0 0
\(207\) 117.428 + 177.029i 0.567285 + 0.855214i
\(208\) 0 0
\(209\) 3.11002 1.79557i 0.0148805 0.00859124i
\(210\) 0 0
\(211\) −193.493 + 335.140i −0.917029 + 1.58834i −0.113126 + 0.993581i \(0.536087\pi\)
−0.803903 + 0.594761i \(0.797247\pi\)
\(212\) 0 0
\(213\) 46.8179 + 10.9994i 0.219802 + 0.0516406i
\(214\) 0 0
\(215\) 174.179i 0.810136i
\(216\) 0 0
\(217\) 267.584 1.23311
\(218\) 0 0
\(219\) 2.98508 12.7056i 0.0136305 0.0580167i
\(220\) 0 0
\(221\) 77.1684 + 44.5532i 0.349178 + 0.201598i
\(222\) 0 0
\(223\) 51.3763 + 88.9864i 0.230387 + 0.399042i 0.957922 0.287028i \(-0.0926674\pi\)
−0.727535 + 0.686071i \(0.759334\pi\)
\(224\) 0 0
\(225\) −18.0652 290.594i −0.0802900 1.29153i
\(226\) 0 0
\(227\) −293.552 + 169.482i −1.29318 + 0.746617i −0.979216 0.202818i \(-0.934990\pi\)
−0.313962 + 0.949435i \(0.601657\pi\)
\(228\) 0 0
\(229\) −148.376 + 256.995i −0.647932 + 1.12225i 0.335685 + 0.941974i \(0.391032\pi\)
−0.983616 + 0.180276i \(0.942301\pi\)
\(230\) 0 0
\(231\) 8.28679 8.81795i 0.0358736 0.0381729i
\(232\) 0 0
\(233\) 346.537i 1.48728i −0.668578 0.743642i \(-0.733097\pi\)
0.668578 0.743642i \(-0.266903\pi\)
\(234\) 0 0
\(235\) −64.0516 −0.272560
\(236\) 0 0
\(237\) −4.55033 + 1.37197i −0.0191997 + 0.00578892i
\(238\) 0 0
\(239\) 140.026 + 80.8439i 0.585882 + 0.338259i 0.763468 0.645846i \(-0.223495\pi\)
−0.177586 + 0.984105i \(0.556829\pi\)
\(240\) 0 0
\(241\) 162.370 + 281.232i 0.673732 + 1.16694i 0.976838 + 0.213982i \(0.0686433\pi\)
−0.303105 + 0.952957i \(0.598023\pi\)
\(242\) 0 0
\(243\) −222.175 + 98.4233i −0.914302 + 0.405034i
\(244\) 0 0
\(245\) 223.753 129.184i 0.913276 0.527280i
\(246\) 0 0
\(247\) 45.1168 78.1447i 0.182659 0.316375i
\(248\) 0 0
\(249\) −7.32473 24.2934i −0.0294166 0.0975638i
\(250\) 0 0
\(251\) 384.012i 1.52993i −0.644074 0.764963i \(-0.722757\pi\)
0.644074 0.764963i \(-0.277243\pi\)
\(252\) 0 0
\(253\) 10.4431 0.0412770
\(254\) 0 0
\(255\) −132.701 124.708i −0.520396 0.489050i
\(256\) 0 0
\(257\) −11.2011 6.46694i −0.0435839 0.0251632i 0.478050 0.878333i \(-0.341344\pi\)
−0.521634 + 0.853170i \(0.674677\pi\)
\(258\) 0 0
\(259\) −84.1821 145.808i −0.325027 0.562964i
\(260\) 0 0
\(261\) −476.181 + 29.6026i −1.82445 + 0.113420i
\(262\) 0 0
\(263\) 42.8437 24.7358i 0.162904 0.0940526i −0.416332 0.909213i \(-0.636684\pi\)
0.579236 + 0.815160i \(0.303351\pi\)
\(264\) 0 0
\(265\) −229.402 + 397.336i −0.865668 + 1.49938i
\(266\) 0 0
\(267\) −187.272 43.9978i −0.701392 0.164786i
\(268\) 0 0
\(269\) 21.4434i 0.0797154i −0.999205 0.0398577i \(-0.987310\pi\)
0.999205 0.0398577i \(-0.0126905\pi\)
\(270\) 0 0
\(271\) 326.907 1.20630 0.603150 0.797628i \(-0.293912\pi\)
0.603150 + 0.797628i \(0.293912\pi\)
\(272\) 0 0
\(273\) 69.5407 295.992i 0.254728 1.08422i
\(274\) 0 0
\(275\) −12.3953 7.15643i −0.0450738 0.0260234i
\(276\) 0 0
\(277\) −238.727 413.487i −0.861830 1.49273i −0.870161 0.492768i \(-0.835985\pi\)
0.00833105 0.999965i \(-0.497348\pi\)
\(278\) 0 0
\(279\) −220.129 + 146.017i −0.788993 + 0.523359i
\(280\) 0 0
\(281\) −103.064 + 59.5039i −0.366775 + 0.211758i −0.672049 0.740507i \(-0.734585\pi\)
0.305274 + 0.952265i \(0.401252\pi\)
\(282\) 0 0
\(283\) 195.675 338.920i 0.691432 1.19760i −0.279937 0.960018i \(-0.590313\pi\)
0.971369 0.237577i \(-0.0763532\pi\)
\(284\) 0 0
\(285\) −126.285 + 134.380i −0.443106 + 0.471508i
\(286\) 0 0
\(287\) 410.218i 1.42933i
\(288\) 0 0
\(289\) 224.753 0.777691
\(290\) 0 0
\(291\) 330.984 99.7953i 1.13740 0.342939i
\(292\) 0 0
\(293\) −62.0910 35.8483i −0.211915 0.122349i 0.390286 0.920694i \(-0.372376\pi\)
−0.602201 + 0.798345i \(0.705709\pi\)
\(294\) 0 0
\(295\) −288.428 499.572i −0.977722 1.69346i
\(296\) 0 0
\(297\) −2.00532 + 11.7761i −0.00675192 + 0.0396502i
\(298\) 0 0
\(299\) 227.246 131.200i 0.760020 0.438797i
\(300\) 0 0
\(301\) 104.844 181.595i 0.348318 0.603304i
\(302\) 0 0
\(303\) −114.558 379.947i −0.378081 1.25395i
\(304\) 0 0
\(305\) 40.5196i 0.132851i
\(306\) 0 0
\(307\) −172.351 −0.561402 −0.280701 0.959795i \(-0.590567\pi\)
−0.280701 + 0.959795i \(0.590567\pi\)
\(308\) 0 0
\(309\) 274.034 + 257.527i 0.886841 + 0.833421i
\(310\) 0 0
\(311\) 524.246 + 302.673i 1.68568 + 0.973227i 0.957763 + 0.287559i \(0.0928438\pi\)
0.727915 + 0.685667i \(0.240489\pi\)
\(312\) 0 0
\(313\) −163.734 283.595i −0.523111 0.906055i −0.999638 0.0268949i \(-0.991438\pi\)
0.476527 0.879160i \(-0.341895\pi\)
\(314\) 0 0
\(315\) −276.701 + 556.369i −0.878416 + 1.76625i
\(316\) 0 0
\(317\) 59.7921 34.5210i 0.188619 0.108899i −0.402717 0.915325i \(-0.631934\pi\)
0.591336 + 0.806425i \(0.298601\pi\)
\(318\) 0 0
\(319\) −11.7269 + 20.3115i −0.0367613 + 0.0636725i
\(320\) 0 0
\(321\) −106.708 25.0701i −0.332423 0.0780999i
\(322\) 0 0
\(323\) 65.0601i 0.201424i
\(324\) 0 0
\(325\) −359.636 −1.10657
\(326\) 0 0
\(327\) 92.4239 393.392i 0.282642 1.20303i
\(328\) 0 0
\(329\) 66.7785 + 38.5546i 0.202974 + 0.117187i
\(330\) 0 0
\(331\) −254.895 441.492i −0.770076 1.33381i −0.937521 0.347930i \(-0.886885\pi\)
0.167444 0.985882i \(-0.446449\pi\)
\(332\) 0 0
\(333\) 148.818 + 74.0121i 0.446901 + 0.222259i
\(334\) 0 0
\(335\) −719.466 + 415.384i −2.14766 + 1.23995i
\(336\) 0 0
\(337\) 168.720 292.232i 0.500653 0.867156i −0.499347 0.866402i \(-0.666427\pi\)
1.00000 0.000754096i \(-0.000240036\pi\)
\(338\) 0 0
\(339\) 390.778 415.826i 1.15274 1.22663i
\(340\) 0 0
\(341\) 12.9856i 0.0380808i
\(342\) 0 0
\(343\) 135.687 0.395590
\(344\) 0 0
\(345\) −513.428 + 154.804i −1.48820 + 0.448708i
\(346\) 0 0
\(347\) 186.407 + 107.622i 0.537197 + 0.310151i 0.743942 0.668244i \(-0.232954\pi\)
−0.206745 + 0.978395i \(0.566287\pi\)
\(348\) 0 0
\(349\) 181.012 + 313.522i 0.518659 + 0.898345i 0.999765 + 0.0216818i \(0.00690207\pi\)
−0.481105 + 0.876663i \(0.659765\pi\)
\(350\) 0 0
\(351\) 104.311 + 281.446i 0.297183 + 0.801842i
\(352\) 0 0
\(353\) −506.486 + 292.420i −1.43481 + 0.828385i −0.997482 0.0709189i \(-0.977407\pi\)
−0.437323 + 0.899304i \(0.644074\pi\)
\(354\) 0 0
\(355\) −60.7011 + 105.137i −0.170989 + 0.296161i
\(356\) 0 0
\(357\) 63.2853 + 209.894i 0.177270 + 0.587937i
\(358\) 0 0
\(359\) 393.693i 1.09664i −0.836269 0.548319i \(-0.815268\pi\)
0.836269 0.548319i \(-0.184732\pi\)
\(360\) 0 0
\(361\) −295.117 −0.817498
\(362\) 0 0
\(363\) −264.095 248.187i −0.727535 0.683711i
\(364\) 0 0
\(365\) 28.5326 + 16.4733i 0.0781716 + 0.0451324i
\(366\) 0 0
\(367\) 190.428 + 329.831i 0.518877 + 0.898722i 0.999759 + 0.0219364i \(0.00698314\pi\)
−0.480882 + 0.876785i \(0.659684\pi\)
\(368\) 0 0
\(369\) 223.851 + 337.467i 0.606641 + 0.914546i
\(370\) 0 0
\(371\) 478.337 276.168i 1.28932 0.744388i
\(372\) 0 0
\(373\) 66.4416 115.080i 0.178128 0.308526i −0.763112 0.646267i \(-0.776329\pi\)
0.941239 + 0.337741i \(0.109663\pi\)
\(374\) 0 0
\(375\) 162.571 + 38.1945i 0.433522 + 0.101852i
\(376\) 0 0
\(377\) 589.316i 1.56317i
\(378\) 0 0
\(379\) 507.622 1.33937 0.669686 0.742644i \(-0.266429\pi\)
0.669686 + 0.742644i \(0.266429\pi\)
\(380\) 0 0
\(381\) 126.321 537.670i 0.331550 1.41121i
\(382\) 0 0
\(383\) −287.466 165.968i −0.750564 0.433338i 0.0753339 0.997158i \(-0.475998\pi\)
−0.825898 + 0.563820i \(0.809331\pi\)
\(384\) 0 0
\(385\) 15.2731 + 26.4539i 0.0396705 + 0.0687113i
\(386\) 0 0
\(387\) 12.8437 + 206.601i 0.0331879 + 0.533853i
\(388\) 0 0
\(389\) −296.662 + 171.278i −0.762626 + 0.440302i −0.830238 0.557409i \(-0.811795\pi\)
0.0676116 + 0.997712i \(0.478462\pi\)
\(390\) 0 0
\(391\) −94.5979 + 163.848i −0.241938 + 0.419049i
\(392\) 0 0
\(393\) 259.039 275.643i 0.659133 0.701382i
\(394\) 0 0
\(395\) 11.9973i 0.0303730i
\(396\) 0 0
\(397\) 24.8043 0.0624792 0.0312396 0.999512i \(-0.490055\pi\)
0.0312396 + 0.999512i \(0.490055\pi\)
\(398\) 0 0
\(399\) 212.549 64.0859i 0.532704 0.160616i
\(400\) 0 0
\(401\) 52.0842 + 30.0708i 0.129886 + 0.0749896i 0.563535 0.826092i \(-0.309441\pi\)
−0.433649 + 0.901082i \(0.642774\pi\)
\(402\) 0 0
\(403\) 163.143 + 282.571i 0.404820 + 0.701170i
\(404\) 0 0
\(405\) −75.9742 608.691i −0.187591 1.50294i
\(406\) 0 0
\(407\) 7.07589 4.08526i 0.0173855 0.0100375i
\(408\) 0 0
\(409\) 240.720 416.939i 0.588558 1.01941i −0.405864 0.913933i \(-0.633029\pi\)
0.994422 0.105478i \(-0.0336373\pi\)
\(410\) 0 0
\(411\) 107.617 + 356.925i 0.261841 + 0.868430i
\(412\) 0 0
\(413\) 694.453i 1.68149i
\(414\) 0 0
\(415\) 64.0516 0.154341
\(416\) 0 0
\(417\) −58.5149 54.9902i −0.140324 0.131871i
\(418\) 0 0
\(419\) −479.531 276.857i −1.14447 0.660758i −0.196933 0.980417i \(-0.563098\pi\)
−0.947533 + 0.319659i \(0.896432\pi\)
\(420\) 0 0
\(421\) −190.947 330.730i −0.453556 0.785581i 0.545048 0.838405i \(-0.316511\pi\)
−0.998604 + 0.0528233i \(0.983178\pi\)
\(422\) 0 0
\(423\) −75.9742 + 4.72306i −0.179608 + 0.0111656i
\(424\) 0 0
\(425\) 224.564 129.652i 0.528385 0.305063i
\(426\) 0 0
\(427\) −24.3900 + 42.2447i −0.0571194 + 0.0989337i
\(428\) 0 0
\(429\) 14.3642 + 3.37474i 0.0334829 + 0.00786652i
\(430\) 0 0
\(431\) 821.321i 1.90562i −0.303570 0.952809i \(-0.598179\pi\)
0.303570 0.952809i \(-0.401821\pi\)
\(432\) 0 0
\(433\) −199.155 −0.459942 −0.229971 0.973198i \(-0.573863\pi\)
−0.229971 + 0.973198i \(0.573863\pi\)
\(434\) 0 0
\(435\) 275.454 1172.44i 0.633227 2.69526i
\(436\) 0 0
\(437\) 165.921 + 95.7946i 0.379682 + 0.219210i
\(438\) 0 0
\(439\) −240.830 417.130i −0.548588 0.950182i −0.998372 0.0570445i \(-0.981832\pi\)
0.449784 0.893137i \(-0.351501\pi\)
\(440\) 0 0
\(441\) 255.876 169.729i 0.580218 0.384873i
\(442\) 0 0
\(443\) −467.902 + 270.143i −1.05621 + 0.609805i −0.924382 0.381468i \(-0.875419\pi\)
−0.131830 + 0.991272i \(0.542085\pi\)
\(444\) 0 0
\(445\) 242.804 420.549i 0.545628 0.945055i
\(446\) 0 0
\(447\) 165.689 176.309i 0.370669 0.394428i
\(448\) 0 0
\(449\) 300.318i 0.668859i 0.942421 + 0.334429i \(0.108544\pi\)
−0.942421 + 0.334429i \(0.891456\pi\)
\(450\) 0 0
\(451\) 19.9074 0.0441407
\(452\) 0 0
\(453\) −287.080 + 86.5579i −0.633731 + 0.191077i
\(454\) 0 0
\(455\) 664.700 + 383.764i 1.46088 + 0.843438i
\(456\) 0 0
\(457\) −77.8505 134.841i −0.170351 0.295057i 0.768191 0.640220i \(-0.221157\pi\)
−0.938543 + 0.345163i \(0.887824\pi\)
\(458\) 0 0
\(459\) −166.598 138.136i −0.362958 0.300949i
\(460\) 0 0
\(461\) −261.143 + 150.771i −0.566470 + 0.327052i −0.755738 0.654874i \(-0.772722\pi\)
0.189268 + 0.981925i \(0.439388\pi\)
\(462\) 0 0
\(463\) 119.390 206.790i 0.257862 0.446630i −0.707807 0.706406i \(-0.750315\pi\)
0.965669 + 0.259776i \(0.0836488\pi\)
\(464\) 0 0
\(465\) −192.493 638.428i −0.413964 1.37296i
\(466\) 0 0
\(467\) 423.152i 0.906107i −0.891483 0.453054i \(-0.850335\pi\)
0.891483 0.453054i \(-0.149665\pi\)
\(468\) 0 0
\(469\) 1000.13 2.13247
\(470\) 0 0
\(471\) −151.836 142.690i −0.322369 0.302950i
\(472\) 0 0
\(473\) 8.81259 + 5.08795i 0.0186313 + 0.0107568i
\(474\) 0 0
\(475\) −131.292 227.405i −0.276404 0.478747i
\(476\) 0 0
\(477\) −242.804 + 488.212i −0.509024 + 1.02351i
\(478\) 0 0
\(479\) 379.284 218.980i 0.791824 0.457160i −0.0487802 0.998810i \(-0.515533\pi\)
0.840604 + 0.541650i \(0.182200\pi\)
\(480\) 0 0
\(481\) 102.649 177.794i 0.213408 0.369634i
\(482\) 0 0
\(483\) 628.467 + 147.653i 1.30117 + 0.305699i
\(484\) 0 0
\(485\) 872.666i 1.79931i
\(486\) 0 0
\(487\) −401.945 −0.825350 −0.412675 0.910878i \(-0.635405\pi\)
−0.412675 + 0.910878i \(0.635405\pi\)
\(488\) 0 0
\(489\) −111.475 + 474.483i −0.227966 + 0.970313i
\(490\) 0 0
\(491\) −241.084 139.190i −0.491007 0.283483i 0.233985 0.972240i \(-0.424823\pi\)
−0.724992 + 0.688757i \(0.758157\pi\)
\(492\) 0 0
\(493\) −212.454 367.981i −0.430941 0.746411i
\(494\) 0 0
\(495\) −27.0000 13.4280i −0.0545455 0.0271273i
\(496\) 0 0
\(497\) 126.571 73.0756i 0.254669 0.147033i
\(498\) 0 0
\(499\) −272.655 + 472.252i −0.546402 + 0.946397i 0.452115 + 0.891960i \(0.350670\pi\)
−0.998517 + 0.0544369i \(0.982664\pi\)
\(500\) 0 0
\(501\) 198.624 211.355i 0.396454 0.421866i
\(502\) 0 0
\(503\) 306.460i 0.609264i 0.952470 + 0.304632i \(0.0985335\pi\)
−0.952470 + 0.304632i \(0.901466\pi\)
\(504\) 0 0
\(505\) 1001.76 1.98369
\(506\) 0 0
\(507\) −130.447 + 39.3312i −0.257292 + 0.0775764i
\(508\) 0 0
\(509\) −480.208 277.248i −0.943434 0.544692i −0.0523989 0.998626i \(-0.516687\pi\)
−0.891035 + 0.453934i \(0.850020\pi\)
\(510\) 0 0
\(511\) −19.8316 34.3493i −0.0388093 0.0672197i
\(512\) 0 0
\(513\) −139.883 + 168.705i −0.272677 + 0.328860i
\(514\) 0 0
\(515\) −822.102 + 474.641i −1.59631 + 0.921632i
\(516\) 0 0
\(517\) −1.87101 + 3.24069i −0.00361898 + 0.00626825i
\(518\) 0 0
\(519\) 24.2731 + 80.5049i 0.0467691 + 0.155115i
\(520\) 0 0
\(521\) 154.167i 0.295905i 0.988994 + 0.147953i \(0.0472683\pi\)
−0.988994 + 0.147953i \(0.952732\pi\)
\(522\) 0 0
\(523\) 480.598 0.918925 0.459463 0.888197i \(-0.348042\pi\)
0.459463 + 0.888197i \(0.348042\pi\)
\(524\) 0 0
\(525\) −644.769 605.930i −1.22813 1.15415i
\(526\) 0 0
\(527\) −203.739 117.629i −0.386602 0.223204i
\(528\) 0 0
\(529\) 14.0721 + 24.3735i 0.0266013 + 0.0460748i
\(530\) 0 0
\(531\) −378.954 571.294i −0.713660 1.07588i
\(532\) 0 0
\(533\) 433.194 250.105i 0.812747 0.469240i
\(534\) 0 0
\(535\) 138.351 239.630i 0.258599 0.447907i
\(536\) 0 0
\(537\) 103.973 + 24.4274i 0.193618 + 0.0454887i
\(538\) 0 0
\(539\) 15.0943i 0.0280043i
\(540\) 0 0
\(541\) 300.543 0.555533 0.277766 0.960649i \(-0.410406\pi\)
0.277766 + 0.960649i \(0.410406\pi\)
\(542\) 0 0
\(543\) −13.4729 + 57.3460i −0.0248120 + 0.105610i
\(544\) 0 0
\(545\) 883.426 + 510.046i 1.62097 + 0.935865i
\(546\) 0 0
\(547\) 50.6032 + 87.6473i 0.0925104 + 0.160233i 0.908567 0.417739i \(-0.137178\pi\)
−0.816056 + 0.577972i \(0.803844\pi\)
\(548\) 0 0
\(549\) −2.98785 48.0620i −0.00544236 0.0875446i
\(550\) 0 0
\(551\) −372.636 + 215.141i −0.676290 + 0.390456i
\(552\) 0 0
\(553\) −7.22154 + 12.5081i −0.0130588 + 0.0226186i
\(554\) 0 0
\(555\) −287.323 + 305.740i −0.517700 + 0.550883i
\(556\) 0 0
\(557\) 433.041i 0.777452i 0.921353 + 0.388726i \(0.127085\pi\)
−0.921353 + 0.388726i \(0.872915\pi\)
\(558\) 0 0
\(559\) 255.687 0.457401
\(560\) 0 0
\(561\) −10.1859 + 3.07117i −0.0181567 + 0.00547445i
\(562\) 0 0
\(563\) 902.201 + 520.886i 1.60249 + 0.925197i 0.990988 + 0.133954i \(0.0427673\pi\)
0.611501 + 0.791244i \(0.290566\pi\)
\(564\) 0 0
\(565\) 720.232 + 1247.48i 1.27475 + 2.20793i
\(566\) 0 0
\(567\) −287.181 + 680.336i −0.506491 + 1.19989i
\(568\) 0 0
\(569\) 257.445 148.636i 0.452452 0.261223i −0.256413 0.966567i \(-0.582541\pi\)
0.708865 + 0.705344i \(0.249207\pi\)
\(570\) 0 0
\(571\) 339.524 588.073i 0.594613 1.02990i −0.398988 0.916956i \(-0.630638\pi\)
0.993601 0.112945i \(-0.0360282\pi\)
\(572\) 0 0
\(573\) −188.662 625.720i −0.329252 1.09201i
\(574\) 0 0
\(575\) 763.599i 1.32800i
\(576\) 0 0
\(577\) −148.351 −0.257107 −0.128553 0.991703i \(-0.541033\pi\)
−0.128553 + 0.991703i \(0.541033\pi\)
\(578\) 0 0
\(579\) 107.121 + 100.668i 0.185010 + 0.173866i
\(580\) 0 0
\(581\) −66.7785 38.5546i −0.114937 0.0663590i
\(582\) 0 0
\(583\) 13.4021 + 23.2132i 0.0229882 + 0.0398168i
\(584\) 0 0
\(585\) −756.232 + 47.0124i −1.29270 + 0.0803631i
\(586\) 0 0
\(587\) 456.497 263.559i 0.777678 0.448993i −0.0579287 0.998321i \(-0.518450\pi\)
0.835607 + 0.549328i \(0.185116\pi\)
\(588\) 0 0
\(589\) −119.117 + 206.316i −0.202236 + 0.350283i
\(590\) 0 0
\(591\) 1051.27 + 246.987i 1.77880 + 0.417913i
\(592\) 0 0
\(593\) 473.848i 0.799069i −0.916718 0.399534i \(-0.869172\pi\)
0.916718 0.399534i \(-0.130828\pi\)
\(594\) 0 0
\(595\) −553.402 −0.930088
\(596\) 0 0
\(597\) −41.8993 + 178.340i −0.0701832 + 0.298727i
\(598\) 0 0
\(599\) 601.414 + 347.227i 1.00403 + 0.579677i 0.909438 0.415839i \(-0.136512\pi\)
0.0945922 + 0.995516i \(0.469845\pi\)
\(600\) 0 0
\(601\) −93.3559 161.697i −0.155334 0.269047i 0.777846 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(602\) 0 0
\(603\) −822.758 + 545.756i −1.36444 + 0.905068i
\(604\) 0 0
\(605\) 792.285 457.426i 1.30956 0.756076i
\(606\) 0 0
\(607\) −411.194 + 712.209i −0.677420 + 1.17333i 0.298335 + 0.954461i \(0.403569\pi\)
−0.975755 + 0.218865i \(0.929764\pi\)
\(608\) 0 0
\(609\) −992.906 + 1056.55i −1.63039 + 1.73489i
\(610\) 0 0
\(611\) 94.0249i 0.153887i
\(612\) 0 0
\(613\) 482.206 0.786634 0.393317 0.919403i \(-0.371328\pi\)
0.393317 + 0.919403i \(0.371328\pi\)
\(614\) 0 0
\(615\) −978.737 + 295.100i −1.59144 + 0.479838i
\(616\) 0 0
\(617\) −595.916 344.052i −0.965828 0.557621i −0.0678661 0.997694i \(-0.521619\pi\)
−0.897962 + 0.440073i \(0.854952\pi\)
\(618\) 0 0
\(619\) 380.253 + 658.617i 0.614302 + 1.06400i 0.990507 + 0.137465i \(0.0438955\pi\)
−0.376205 + 0.926536i \(0.622771\pi\)
\(620\) 0 0
\(621\) −597.583 + 221.479i −0.962291 + 0.356649i
\(622\) 0 0
\(623\) −506.282 + 292.302i −0.812652 + 0.469185i
\(624\) 0 0
\(625\) 193.603 335.331i 0.309765 0.536529i
\(626\) 0 0
\(627\) 3.11002 + 10.3148i 0.00496016 + 0.0164510i
\(628\) 0 0
\(629\) 148.024i 0.235333i
\(630\) 0 0
\(631\) −1008.08 −1.59758 −0.798792 0.601607i \(-0.794527\pi\)
−0.798792 + 0.601607i \(0.794527\pi\)
\(632\) 0 0
\(633\) −846.007 795.046i −1.33650 1.25600i
\(634\) 0 0
\(635\) 1207.43 + 697.108i 1.90146 + 1.09781i
\(636\) 0 0
\(637\) −189.636 328.459i −0.297701 0.515634i
\(638\) 0 0
\(639\) −64.2473 + 129.184i −0.100544 + 0.202165i
\(640\) 0 0
\(641\) −488.095 + 281.802i −0.761458 + 0.439628i −0.829819 0.558032i \(-0.811556\pi\)
0.0683607 + 0.997661i \(0.478223\pi\)
\(642\) 0 0
\(643\) 288.500 499.697i 0.448678 0.777133i −0.549622 0.835413i \(-0.685228\pi\)
0.998300 + 0.0582801i \(0.0185617\pi\)
\(644\) 0 0
\(645\) −508.687 119.512i −0.788663 0.185289i
\(646\) 0 0
\(647\) 1024.52i 1.58349i 0.610853 + 0.791744i \(0.290827\pi\)
−0.610853 + 0.791744i \(0.709173\pi\)
\(648\) 0 0
\(649\) −33.7011 −0.0519277
\(650\) 0 0
\(651\) −183.600 + 781.475i −0.282028 + 1.20042i
\(652\) 0 0
\(653\) −345.885 199.697i −0.529686 0.305814i 0.211203 0.977442i \(-0.432262\pi\)
−0.740888 + 0.671628i \(0.765595\pi\)
\(654\) 0 0
\(655\) 477.428 + 826.929i 0.728898 + 1.26249i
\(656\) 0 0
\(657\) 35.0584 + 17.4357i 0.0533614 + 0.0265384i
\(658\) 0 0
\(659\) −646.308 + 373.146i −0.980741 + 0.566231i −0.902494 0.430703i \(-0.858266\pi\)
−0.0782470 + 0.996934i \(0.524932\pi\)
\(660\) 0 0
\(661\) 475.624 823.804i 0.719552 1.24630i −0.241626 0.970369i \(-0.577681\pi\)
0.961178 0.275931i \(-0.0889860\pi\)
\(662\) 0 0
\(663\) −183.065 + 194.799i −0.276117 + 0.293815i
\(664\) 0 0
\(665\) 560.403i 0.842711i
\(666\) 0 0
\(667\) −1251.27 −1.87596
\(668\) 0 0
\(669\) −295.135 + 88.9864i −0.441158 + 0.133014i
\(670\) 0 0
\(671\) −2.05009 1.18362i −0.00305527 0.00176396i
\(672\) 0 0
\(673\) 172.115 + 298.113i 0.255743 + 0.442961i 0.965097 0.261892i \(-0.0843464\pi\)
−0.709354 + 0.704853i \(0.751013\pi\)
\(674\) 0 0
\(675\) 861.069 + 146.629i 1.27566 + 0.217228i
\(676\) 0 0
\(677\) −853.610 + 492.832i −1.26087 + 0.727965i −0.973243 0.229778i \(-0.926200\pi\)
−0.287628 + 0.957742i \(0.592867\pi\)
\(678\) 0 0
\(679\) 525.284 909.818i 0.773614 1.33994i
\(680\) 0 0
\(681\) −293.552 973.600i −0.431060 1.42966i
\(682\) 0 0
\(683\) 166.658i 0.244009i 0.992530 + 0.122004i \(0.0389322\pi\)
−0.992530 + 0.122004i \(0.961068\pi\)
\(684\) 0 0
\(685\) −941.062 −1.37381
\(686\) 0 0
\(687\) −648.743 609.665i −0.944313 0.887431i
\(688\) 0 0
\(689\) 583.272 + 336.752i 0.846548 + 0.488755i
\(690\) 0 0
\(691\) 449.077 + 777.825i 0.649895 + 1.12565i 0.983148 + 0.182813i \(0.0585204\pi\)
−0.333253 + 0.942838i \(0.608146\pi\)
\(692\) 0 0
\(693\) 20.0668 + 30.2518i 0.0289564 + 0.0436534i
\(694\) 0 0
\(695\) 175.545 101.351i 0.252582 0.145829i
\(696\) 0 0
\(697\) −180.330 + 312.341i −0.258723 + 0.448122i
\(698\) 0 0
\(699\) 1012.06 + 237.773i 1.44786 + 0.340162i
\(700\) 0 0
\(701\) 730.549i 1.04215i −0.853510 0.521076i \(-0.825531\pi\)
0.853510 0.521076i \(-0.174469\pi\)
\(702\) 0 0
\(703\) 149.897 0.213224
\(704\) 0 0
\(705\) 43.9484 187.061i 0.0623382 0.265335i
\(706\) 0 0
\(707\) −1044.41 602.991i −1.47724 0.852887i
\(708\) 0 0
\(709\) −114.961 199.118i −0.162145 0.280843i 0.773493 0.633805i \(-0.218508\pi\)
−0.935638 + 0.352962i \(0.885174\pi\)
\(710\) 0 0
\(711\) −0.884663 14.2305i −0.00124425 0.0200148i
\(712\) 0 0
\(713\) −599.971 + 346.394i −0.841474 + 0.485825i
\(714\) 0 0
\(715\) −18.6237 + 32.2571i −0.0260471 + 0.0451149i
\(716\) 0 0
\(717\) −332.181 + 353.472i −0.463292 + 0.492988i
\(718\) 0 0
\(719\) 907.095i 1.26161i 0.775943 + 0.630803i \(0.217275\pi\)
−0.775943 + 0.630803i \(0.782725\pi\)
\(720\) 0 0
\(721\) 1142.80 1.58502
\(722\) 0 0
\(723\) −932.742 + 281.232i −1.29010 + 0.388980i
\(724\) 0 0
\(725\) 1485.18 + 857.469i 2.04852 + 1.18272i
\(726\) 0 0
\(727\) 107.871 + 186.838i 0.148378 + 0.256999i 0.930628 0.365966i \(-0.119261\pi\)
−0.782250 + 0.622965i \(0.785928\pi\)
\(728\) 0 0
\(729\) −135.000 716.391i −0.185185 0.982704i
\(730\) 0 0
\(731\) −159.656 + 92.1776i −0.218408 + 0.126098i
\(732\) 0 0
\(733\) 314.634 544.963i 0.429242 0.743469i −0.567564 0.823329i \(-0.692114\pi\)
0.996806 + 0.0798604i \(0.0254475\pi\)
\(734\) 0 0
\(735\) 223.753 + 742.104i 0.304425 + 1.00966i
\(736\) 0 0
\(737\) 48.5351i 0.0658549i
\(738\) 0 0
\(739\) 547.649 0.741068 0.370534 0.928819i \(-0.379175\pi\)
0.370534 + 0.928819i \(0.379175\pi\)
\(740\) 0 0
\(741\) 197.264 + 185.381i 0.266213 + 0.250177i
\(742\) 0 0
\(743\) 462.583 + 267.072i 0.622588 + 0.359451i 0.777876 0.628418i \(-0.216297\pi\)
−0.155288 + 0.987869i \(0.549631\pi\)
\(744\) 0 0
\(745\) 305.376 + 528.927i 0.409901 + 0.709970i
\(746\) 0 0
\(747\) 75.9742 4.72306i 0.101706 0.00632271i
\(748\) 0 0
\(749\) −288.481 + 166.555i −0.385155 + 0.222369i
\(750\) 0 0
\(751\) −225.545 + 390.655i −0.300326 + 0.520180i −0.976210 0.216828i \(-0.930429\pi\)
0.675884 + 0.737008i \(0.263762\pi\)
\(752\) 0 0
\(753\) 1121.50 + 263.486i 1.48937 + 0.349915i
\(754\) 0 0
\(755\) 756.911i 1.00253i
\(756\) 0 0
\(757\) 352.391 0.465511 0.232755 0.972535i \(-0.425226\pi\)
0.232755 + 0.972535i \(0.425226\pi\)
\(758\) 0 0
\(759\) −7.16543 + 30.4988i −0.00944061 + 0.0401829i
\(760\) 0 0
\(761\) −929.923 536.891i −1.22197 0.705507i −0.256636 0.966508i \(-0.582614\pi\)
−0.965339 + 0.261001i \(0.915947\pi\)
\(762\) 0 0
\(763\) −614.024 1063.52i −0.804750 1.39387i
\(764\) 0 0
\(765\) 455.258 301.984i 0.595108 0.394750i
\(766\) 0 0
\(767\) −733.349 + 423.399i −0.956126 + 0.552020i
\(768\) 0 0
\(769\) −177.988 + 308.284i −0.231454 + 0.400889i −0.958236 0.285978i \(-0.907681\pi\)
0.726782 + 0.686868i \(0.241015\pi\)
\(770\) 0 0
\(771\) 26.5721 28.2753i 0.0344644 0.0366735i
\(772\) 0 0
\(773\) 370.790i 0.479677i −0.970813 0.239838i \(-0.922906\pi\)
0.970813 0.239838i \(-0.0770945\pi\)
\(774\) 0 0
\(775\) 949.505 1.22517
\(776\) 0 0
\(777\) 483.589 145.808i 0.622380 0.187655i
\(778\) 0 0
\(779\) 316.292 + 182.611i 0.406023 + 0.234418i
\(780\) 0 0
\(781\) 3.54628 + 6.14233i 0.00454069 + 0.00786470i
\(782\) 0 0
\(783\) 240.273 1410.99i 0.306862 1.80203i
\(784\) 0 0
\(785\) 455.507 262.987i 0.580263 0.335015i
\(786\) 0 0
\(787\) −576.531 + 998.581i −0.732568 + 1.26885i 0.223214 + 0.974769i \(0.428345\pi\)
−0.955782 + 0.294076i \(0.904988\pi\)
\(788\) 0 0
\(789\) 42.8437 + 142.096i 0.0543013 + 0.180097i
\(790\) 0 0
\(791\) 1734.12i 2.19231i
\(792\) 0 0
\(793\) −59.4810 −0.0750076
\(794\) 0 0
\(795\) −1003.01 942.593i −1.26165 1.18565i
\(796\) 0 0
\(797\) 761.882 + 439.873i 0.955937 + 0.551910i 0.894920 0.446226i \(-0.147232\pi\)
0.0610167 + 0.998137i \(0.480566\pi\)
\(798\) 0 0
\(799\) −33.8968 58.7110i −0.0424240 0.0734806i
\(800\) 0 0
\(801\) 256.989 516.735i 0.320836 0.645112i
\(802\) 0 0
\(803\) 1.66693 0.962404i 0.00207588 0.00119851i
\(804\) 0 0
\(805\) −814.830 + 1411.33i −1.01221 + 1.75320i
\(806\) 0 0
\(807\) 62.6252 + 14.7132i 0.0776025 + 0.0182320i
\(808\) 0 0
\(809\) 884.508i 1.09334i 0.837350 + 0.546668i \(0.184104\pi\)
−0.837350 + 0.546668i \(0.815896\pi\)
\(810\) 0 0
\(811\) −961.464 −1.18553 −0.592765 0.805376i \(-0.701964\pi\)
−0.592765 + 0.805376i \(0.701964\pi\)
\(812\) 0 0
\(813\) −224.304 + 954.727i −0.275897 + 1.17433i
\(814\) 0 0
\(815\) −1065.53 615.184i −1.30740 0.754827i
\(816\) 0 0
\(817\) 93.3437 + 161.676i 0.114252 + 0.197890i
\(818\) 0 0
\(819\) 816.725 + 406.185i 0.997223 + 0.495952i
\(820\) 0 0
\(821\) −778.064 + 449.215i −0.947702 + 0.547156i −0.892366 0.451312i \(-0.850956\pi\)
−0.0553360 + 0.998468i \(0.517623\pi\)
\(822\) 0 0
\(823\) 108.091 187.219i 0.131338 0.227484i −0.792855 0.609411i \(-0.791406\pi\)
0.924193 + 0.381927i \(0.124739\pi\)
\(824\) 0 0
\(825\) 29.4051 31.2899i 0.0356426 0.0379272i
\(826\) 0 0
\(827\) 113.883i 0.137706i 0.997627 + 0.0688528i \(0.0219339\pi\)
−0.997627 + 0.0688528i \(0.978066\pi\)
\(828\) 0 0
\(829\) −101.326 −0.122227 −0.0611135 0.998131i \(-0.519465\pi\)
−0.0611135 + 0.998131i \(0.519465\pi\)
\(830\) 0 0
\(831\) 1371.38 413.487i 1.65028 0.497578i
\(832\) 0 0
\(833\) 236.825 + 136.731i 0.284303 + 0.164143i
\(834\) 0 0
\(835\) 366.077 + 634.065i 0.438416 + 0.759359i
\(836\) 0 0
\(837\) −275.401 743.071i −0.329033 0.887779i
\(838\) 0 0
\(839\) −60.4689 + 34.9117i −0.0720726 + 0.0416111i −0.535603 0.844470i \(-0.679916\pi\)
0.463531 + 0.886081i \(0.346582\pi\)
\(840\) 0 0
\(841\) 984.588 1705.36i 1.17073 2.02777i
\(842\) 0 0
\(843\) −103.064 341.824i −0.122258 0.405485i
\(844\) 0 0
\(845\) 343.934i 0.407023i
\(846\) 0 0
\(847\) −1101.35 −1.30030
\(848\) 0 0
\(849\) 855.547 + 804.012i 1.00771 + 0.947011i
\(850\) 0 0
\(851\) 377.502 + 217.951i 0.443598 + 0.256112i
\(852\) 0 0
\(853\) −573.325 993.028i −0.672127 1.16416i −0.977300 0.211862i \(-0.932047\pi\)
0.305172 0.952297i \(-0.401286\pi\)
\(854\) 0 0
\(855\) −305.804 461.017i −0.357666 0.539201i
\(856\) 0 0
\(857\) 217.871 125.788i 0.254225 0.146777i −0.367472 0.930035i \(-0.619777\pi\)
0.621697 + 0.783258i \(0.286443\pi\)
\(858\) 0 0
\(859\) 244.266 423.082i 0.284361 0.492528i −0.688093 0.725623i \(-0.741552\pi\)
0.972454 + 0.233095i \(0.0748852\pi\)
\(860\) 0 0
\(861\) 1198.03 + 281.467i 1.39145 + 0.326908i
\(862\) 0 0
\(863\) 596.889i 0.691644i 0.938300 + 0.345822i \(0.112400\pi\)
−0.938300 + 0.345822i \(0.887600\pi\)
\(864\) 0 0
\(865\) −212.258 −0.245385
\(866\) 0 0
\(867\) −154.212 + 656.386i −0.177868 + 0.757077i
\(868\) 0 0
\(869\) −0.607003 0.350454i −0.000698508 0.000403284i
\(870\) 0 0
\(871\) 609.765 + 1056.14i 0.700074 + 1.21256i
\(872\) 0 0
\(873\) 64.3490 + 1035.10i 0.0737102 + 1.18569i
\(874\) 0 0
\(875\) 439.504 253.748i 0.502290 0.289997i
\(876\) 0 0
\(877\) 358.208 620.434i 0.408447 0.707451i −0.586269 0.810116i \(-0.699404\pi\)
0.994716 + 0.102666i \(0.0327372\pi\)
\(878\) 0 0
\(879\) 147.297 156.739i 0.167574 0.178315i
\(880\) 0 0
\(881\) 1200.86i 1.36306i 0.731790 + 0.681531i \(0.238685\pi\)
−0.731790 + 0.681531i \(0.761315\pi\)
\(882\) 0 0
\(883\) 22.8938 0.0259273 0.0129636 0.999916i \(-0.495873\pi\)
0.0129636 + 0.999916i \(0.495873\pi\)
\(884\) 0 0
\(885\) 1656.89 499.572i 1.87219 0.564488i
\(886\) 0 0
\(887\) −521.857 301.294i −0.588340 0.339678i 0.176101 0.984372i \(-0.443651\pi\)
−0.764441 + 0.644694i \(0.776985\pi\)
\(888\) 0 0
\(889\) −839.220 1453.57i −0.944005 1.63506i
\(890\) 0 0
\(891\) −33.0160 13.9366i −0.0370549 0.0156415i
\(892\) 0 0
\(893\) −59.4537 + 34.3256i −0.0665775 + 0.0384385i
\(894\) 0 0
\(895\) −134.804 + 233.488i −0.150619 + 0.260880i
\(896\) 0 0
\(897\) 227.246 + 753.689i 0.253340 + 0.840233i
\(898\) 0 0
\(899\) 1555.90i 1.73071i
\(900\) 0 0
\(901\) −485.609 −0.538966
\(902\) 0 0
\(903\) 458.406 + 430.794i 0.507648 + 0.477069i
\(904\) 0 0
\(905\) −128.780 74.3511i −0.142298 0.0821560i
\(906\) 0 0
\(907\) −211.473 366.281i −0.233156 0.403838i 0.725579 0.688139i \(-0.241572\pi\)
−0.958735 + 0.284300i \(0.908239\pi\)
\(908\) 0 0
\(909\) 1188.23 73.8684i 1.30719 0.0812634i
\(910\) 0 0
\(911\) −125.376 + 72.3861i −0.137625 + 0.0794578i −0.567232 0.823558i \(-0.691986\pi\)
0.429607 + 0.903016i \(0.358652\pi\)
\(912\) 0 0
\(913\) 1.87101 3.24069i 0.00204930 0.00354949i
\(914\) 0 0
\(915\) 118.337 + 27.8022i 0.129330 + 0.0303849i
\(916\) 0 0
\(917\) 1149.51i 1.25356i
\(918\) 0 0
\(919\) 869.093 0.945694 0.472847 0.881145i \(-0.343226\pi\)
0.472847 + 0.881145i \(0.343226\pi\)
\(920\) 0 0
\(921\) 118.257 503.347i 0.128400 0.546522i
\(922\) 0 0
\(923\) 154.337 + 89.1064i 0.167212 + 0.0965400i
\(924\) 0 0
\(925\) −298.715 517.389i −0.322935 0.559340i
\(926\) 0 0
\(927\) −940.129 + 623.611i −1.01416 + 0.672720i
\(928\) 0 0
\(929\) 82.2838 47.5066i 0.0885724 0.0511373i −0.455060 0.890461i \(-0.650382\pi\)
0.543632 + 0.839324i \(0.317049\pi\)
\(930\) 0 0
\(931\) 138.461 239.821i 0.148722 0.257595i
\(932\) 0 0
\(933\) −1243.66 + 1323.37i −1.33297 + 1.41841i
\(934\) 0 0
\(935\) 26.8560i 0.0287230i
\(936\) 0 0
\(937\) −1555.55 −1.66014 −0.830071 0.557657i \(-0.811700\pi\)
−0.830071 + 0.557657i \(0.811700\pi\)
\(938\) 0 0
\(939\) 940.578 283.595i 1.00168 0.302018i
\(940\) 0 0
\(941\) −335.246 193.554i −0.356265 0.205690i 0.311176 0.950352i \(-0.399277\pi\)
−0.667441 + 0.744662i \(0.732611\pi\)
\(942\) 0 0
\(943\) 531.036 + 919.782i 0.563135 + 0.975379i
\(944\) 0 0
\(945\) −1435.01 1189.85i −1.51853 1.25910i
\(946\) 0 0
\(947\) −839.861 + 484.894i −0.886865 + 0.512032i −0.872916 0.487871i \(-0.837774\pi\)
−0.0139492 + 0.999903i \(0.504440\pi\)
\(948\) 0 0
\(949\) 24.1821 41.8846i 0.0254817 0.0441355i
\(950\) 0 0
\(951\) 59.7921 + 198.308i 0.0628729 + 0.208526i
\(952\) 0 0
\(953\) 1294.65i 1.35850i −0.733909 0.679248i \(-0.762306\pi\)
0.733909 0.679248i \(-0.237694\pi\)
\(954\) 0 0
\(955\) 1649.76 1.72750
\(956\) 0 0
\(957\) −51.2731 48.1846i −0.0535769 0.0503497i
\(958\) 0 0
\(959\) 981.126 + 566.453i 1.02307 + 0.590671i
\(960\) 0 0
\(961\) 49.7731 + 86.2096i 0.0517931 + 0.0897082i
\(962\) 0 0
\(963\) 146.433 294.437i 0.152059 0.305750i
\(964\) 0 0
\(965\) −321.363 + 185.539i −0.333018 + 0.192268i
\(966\) 0 0
\(967\) 412.036 713.668i 0.426098 0.738023i −0.570425 0.821350i \(-0.693221\pi\)
0.996522 + 0.0833272i \(0.0265547\pi\)
\(968\) 0 0
\(969\) −190.007 44.6404i −0.196085 0.0460685i
\(970\) 0 0
\(971\) 1518.35i 1.56370i 0.623469 + 0.781848i \(0.285723\pi\)
−0.623469 + 0.781848i \(0.714277\pi\)
\(972\) 0 0
\(973\) −244.024 −0.250796
\(974\) 0 0
\(975\) 246.761 1050.31i 0.253088 1.07724i
\(976\) 0 0
\(977\) −321.497 185.616i −0.329065 0.189986i 0.326361 0.945245i \(-0.394178\pi\)
−0.655426 + 0.755259i \(0.727511\pi\)
\(978\) 0 0
\(979\) −14.1851 24.5693i −0.0144894 0.0250963i
\(980\) 0 0
\(981\) 1085.48 + 539.844i 1.10650 + 0.550300i
\(982\) 0 0
\(983\) 808.039 466.522i 0.822014 0.474590i −0.0290967 0.999577i \(-0.509263\pi\)
0.851110 + 0.524987i \(0.175930\pi\)
\(984\) 0 0
\(985\) −1363.01 + 2360.80i −1.38377 + 2.39676i
\(986\) 0 0
\(987\) −158.417 + 168.571i −0.160504 + 0.170792i
\(988\) 0 0
\(989\) 542.890i 0.548928i
\(990\) 0 0
\(991\) −1615.53 −1.63020 −0.815099 0.579321i \(-0.803318\pi\)
−0.815099 + 0.579321i \(0.803318\pi\)
\(992\) 0 0
\(993\) 1464.26 441.492i 1.47458 0.444604i
\(994\) 0 0
\(995\) −400.492 231.224i −0.402504 0.232386i
\(996\) 0 0
\(997\) 519.376 + 899.586i 0.520939 + 0.902293i 0.999704 + 0.0243496i \(0.00775149\pi\)
−0.478764 + 0.877943i \(0.658915\pi\)
\(998\) 0 0
\(999\) −318.261 + 383.837i −0.318580 + 0.384221i
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 576.3.q.g.257.1 4
3.2 odd 2 1728.3.q.h.449.2 4
4.3 odd 2 576.3.q.d.257.2 4
8.3 odd 2 36.3.g.a.5.1 4
8.5 even 2 144.3.q.b.113.2 4
9.2 odd 6 inner 576.3.q.g.65.1 4
9.7 even 3 1728.3.q.h.1601.2 4
12.11 even 2 1728.3.q.g.449.2 4
24.5 odd 2 432.3.q.b.17.1 4
24.11 even 2 108.3.g.a.17.1 4
36.7 odd 6 1728.3.q.g.1601.2 4
36.11 even 6 576.3.q.d.65.2 4
40.3 even 4 900.3.u.a.149.1 8
40.19 odd 2 900.3.p.a.401.2 4
40.27 even 4 900.3.u.a.149.4 8
72.5 odd 6 1296.3.e.e.161.4 4
72.11 even 6 36.3.g.a.29.1 yes 4
72.13 even 6 1296.3.e.e.161.1 4
72.29 odd 6 144.3.q.b.65.2 4
72.43 odd 6 108.3.g.a.89.1 4
72.59 even 6 324.3.c.b.161.4 4
72.61 even 6 432.3.q.b.305.1 4
72.67 odd 6 324.3.c.b.161.1 4
120.59 even 2 2700.3.p.b.2501.2 4
120.83 odd 4 2700.3.u.b.449.1 8
120.107 odd 4 2700.3.u.b.449.4 8
360.43 even 12 2700.3.u.b.2249.4 8
360.83 odd 12 900.3.u.a.749.4 8
360.187 even 12 2700.3.u.b.2249.1 8
360.227 odd 12 900.3.u.a.749.1 8
360.259 odd 6 2700.3.p.b.1601.2 4
360.299 even 6 900.3.p.a.101.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.3.g.a.5.1 4 8.3 odd 2
36.3.g.a.29.1 yes 4 72.11 even 6
108.3.g.a.17.1 4 24.11 even 2
108.3.g.a.89.1 4 72.43 odd 6
144.3.q.b.65.2 4 72.29 odd 6
144.3.q.b.113.2 4 8.5 even 2
324.3.c.b.161.1 4 72.67 odd 6
324.3.c.b.161.4 4 72.59 even 6
432.3.q.b.17.1 4 24.5 odd 2
432.3.q.b.305.1 4 72.61 even 6
576.3.q.d.65.2 4 36.11 even 6
576.3.q.d.257.2 4 4.3 odd 2
576.3.q.g.65.1 4 9.2 odd 6 inner
576.3.q.g.257.1 4 1.1 even 1 trivial
900.3.p.a.101.2 4 360.299 even 6
900.3.p.a.401.2 4 40.19 odd 2
900.3.u.a.149.1 8 40.3 even 4
900.3.u.a.149.4 8 40.27 even 4
900.3.u.a.749.1 8 360.227 odd 12
900.3.u.a.749.4 8 360.83 odd 12
1296.3.e.e.161.1 4 72.13 even 6
1296.3.e.e.161.4 4 72.5 odd 6
1728.3.q.g.449.2 4 12.11 even 2
1728.3.q.g.1601.2 4 36.7 odd 6
1728.3.q.h.449.2 4 3.2 odd 2
1728.3.q.h.1601.2 4 9.7 even 3
2700.3.p.b.1601.2 4 360.259 odd 6
2700.3.p.b.2501.2 4 120.59 even 2
2700.3.u.b.449.1 8 120.83 odd 4
2700.3.u.b.449.4 8 120.107 odd 4
2700.3.u.b.2249.1 8 360.187 even 12
2700.3.u.b.2249.4 8 360.43 even 12