Properties

Label 1323.2.h.g.802.4
Level $1323$
Weight $2$
Character 1323.802
Analytic conductor $10.564$
Analytic rank $0$
Dimension $12$
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] = [1323,2,Mod(226,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), 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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{5} \)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 802.4
Root \(-1.29589 + 0.748185i\) of defining polynomial
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.g.226.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.239123 q^{2} -1.94282 q^{4} +(1.29589 - 2.24456i) q^{5} +0.942820 q^{8} +O(q^{10})\) \(q-0.239123 q^{2} -1.94282 q^{4} +(1.29589 - 2.24456i) q^{5} +0.942820 q^{8} +(-0.309879 + 0.536725i) q^{10} +(2.09097 + 3.62167i) q^{11} +(1.84155 + 3.18966i) q^{13} +3.66019 q^{16} +(-0.855536 + 1.48183i) q^{17} +(-3.57780 - 6.19694i) q^{19} +(-2.51769 + 4.36077i) q^{20} +(-0.500000 - 0.866025i) q^{22} +(-2.56238 + 4.43818i) q^{23} +(-0.858685 - 1.48729i) q^{25} +(-0.440358 - 0.762722i) q^{26} +(-1.06238 + 1.84010i) q^{29} +6.53585 q^{31} -2.76088 q^{32} +(0.204579 - 0.354341i) q^{34} +(-0.830095 - 1.43777i) q^{37} +(0.855536 + 1.48183i) q^{38} +(1.22180 - 2.11621i) q^{40} +(5.10948 + 8.84988i) q^{41} +(0.830095 - 1.43777i) q^{43} +(-4.06238 - 7.03625i) q^{44} +(0.612725 - 1.06127i) q^{46} +9.33824 q^{47} +(0.205332 + 0.355645i) q^{50} +(-3.57780 - 6.19694i) q^{52} +(5.32326 - 9.22015i) q^{53} +10.8387 q^{55} +(0.254040 - 0.440011i) q^{58} +6.06429 q^{59} +7.98597 q^{61} -1.56287 q^{62} -6.66019 q^{64} +9.54583 q^{65} +8.26320 q^{67} +(1.66215 - 2.87893i) q^{68} -6.23912 q^{71} +(3.57780 - 6.19694i) q^{73} +(0.198495 + 0.343803i) q^{74} +(6.95103 + 12.0395i) q^{76} -9.82846 q^{79} +(4.74322 - 8.21550i) q^{80} +(-1.22180 - 2.11621i) q^{82} +(-3.44733 + 5.97094i) q^{83} +(2.21737 + 3.84060i) q^{85} +(-0.198495 + 0.343803i) q^{86} +(1.97141 + 3.41458i) q^{88} +(2.51769 + 4.36077i) q^{89} +(4.97825 - 8.62258i) q^{92} -2.23299 q^{94} -18.5458 q^{95} +(1.53167 - 2.65294i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{2} + 12 q^{4} - 24 q^{8} + 8 q^{11} + 12 q^{16} - 6 q^{22} + 4 q^{23} - 12 q^{25} + 22 q^{29} - 32 q^{32} + 6 q^{37} - 6 q^{43} - 14 q^{44} - 12 q^{46} + 56 q^{50} + 28 q^{53} - 18 q^{58} - 48 q^{64} + 12 q^{65} - 76 q^{71} + 36 q^{74} - 12 q^{79} + 30 q^{85} - 36 q^{86} + 6 q^{88} + 62 q^{92} - 120 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.239123 −0.169086 −0.0845428 0.996420i \(-0.526943\pi\)
−0.0845428 + 0.996420i \(0.526943\pi\)
\(3\) 0 0
\(4\) −1.94282 −0.971410
\(5\) 1.29589 2.24456i 0.579542 1.00380i −0.415990 0.909369i \(-0.636565\pi\)
0.995532 0.0944264i \(-0.0301017\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.942820 0.333337
\(9\) 0 0
\(10\) −0.309879 + 0.536725i −0.0979922 + 0.169727i
\(11\) 2.09097 + 3.62167i 0.630452 + 1.09197i 0.987459 + 0.157873i \(0.0504636\pi\)
−0.357008 + 0.934101i \(0.616203\pi\)
\(12\) 0 0
\(13\) 1.84155 + 3.18966i 0.510755 + 0.884653i 0.999922 + 0.0124633i \(0.00396730\pi\)
−0.489168 + 0.872190i \(0.662699\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.66019 0.915047
\(17\) −0.855536 + 1.48183i −0.207498 + 0.359397i −0.950926 0.309419i \(-0.899865\pi\)
0.743428 + 0.668816i \(0.233199\pi\)
\(18\) 0 0
\(19\) −3.57780 6.19694i −0.820805 1.42168i −0.905084 0.425233i \(-0.860192\pi\)
0.0842790 0.996442i \(-0.473141\pi\)
\(20\) −2.51769 + 4.36077i −0.562973 + 0.975097i
\(21\) 0 0
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) −2.56238 + 4.43818i −0.534294 + 0.925424i 0.464904 + 0.885361i \(0.346089\pi\)
−0.999197 + 0.0400622i \(0.987244\pi\)
\(24\) 0 0
\(25\) −0.858685 1.48729i −0.171737 0.297457i
\(26\) −0.440358 0.762722i −0.0863613 0.149582i
\(27\) 0 0
\(28\) 0 0
\(29\) −1.06238 + 1.84010i −0.197279 + 0.341698i −0.947645 0.319325i \(-0.896544\pi\)
0.750366 + 0.661023i \(0.229877\pi\)
\(30\) 0 0
\(31\) 6.53585 1.17387 0.586937 0.809633i \(-0.300334\pi\)
0.586937 + 0.809633i \(0.300334\pi\)
\(32\) −2.76088 −0.488059
\(33\) 0 0
\(34\) 0.204579 0.354341i 0.0350850 0.0607689i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.830095 1.43777i −0.136467 0.236367i 0.789690 0.613506i \(-0.210241\pi\)
−0.926157 + 0.377139i \(0.876908\pi\)
\(38\) 0.855536 + 1.48183i 0.138786 + 0.240385i
\(39\) 0 0
\(40\) 1.22180 2.11621i 0.193183 0.334602i
\(41\) 5.10948 + 8.84988i 0.797967 + 1.38212i 0.920938 + 0.389708i \(0.127424\pi\)
−0.122972 + 0.992410i \(0.539242\pi\)
\(42\) 0 0
\(43\) 0.830095 1.43777i 0.126588 0.219257i −0.795764 0.605606i \(-0.792931\pi\)
0.922353 + 0.386349i \(0.126264\pi\)
\(44\) −4.06238 7.03625i −0.612427 1.06075i
\(45\) 0 0
\(46\) 0.612725 1.06127i 0.0903414 0.156476i
\(47\) 9.33824 1.36212 0.681061 0.732226i \(-0.261519\pi\)
0.681061 + 0.732226i \(0.261519\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.205332 + 0.355645i 0.0290383 + 0.0502958i
\(51\) 0 0
\(52\) −3.57780 6.19694i −0.496152 0.859361i
\(53\) 5.32326 9.22015i 0.731206 1.26649i −0.225162 0.974321i \(-0.572291\pi\)
0.956368 0.292164i \(-0.0943754\pi\)
\(54\) 0 0
\(55\) 10.8387 1.46149
\(56\) 0 0
\(57\) 0 0
\(58\) 0.254040 0.440011i 0.0333571 0.0577762i
\(59\) 6.06429 0.789504 0.394752 0.918788i \(-0.370831\pi\)
0.394752 + 0.918788i \(0.370831\pi\)
\(60\) 0 0
\(61\) 7.98597 1.02250 0.511249 0.859433i \(-0.329183\pi\)
0.511249 + 0.859433i \(0.329183\pi\)
\(62\) −1.56287 −0.198485
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) 9.54583 1.18401
\(66\) 0 0
\(67\) 8.26320 1.00951 0.504755 0.863262i \(-0.331583\pi\)
0.504755 + 0.863262i \(0.331583\pi\)
\(68\) 1.66215 2.87893i 0.201566 0.349122i
\(69\) 0 0
\(70\) 0 0
\(71\) −6.23912 −0.740448 −0.370224 0.928943i \(-0.620719\pi\)
−0.370224 + 0.928943i \(0.620719\pi\)
\(72\) 0 0
\(73\) 3.57780 6.19694i 0.418750 0.725297i −0.577064 0.816699i \(-0.695802\pi\)
0.995814 + 0.0914022i \(0.0291349\pi\)
\(74\) 0.198495 + 0.343803i 0.0230746 + 0.0399663i
\(75\) 0 0
\(76\) 6.95103 + 12.0395i 0.797338 + 1.38103i
\(77\) 0 0
\(78\) 0 0
\(79\) −9.82846 −1.10579 −0.552894 0.833252i \(-0.686477\pi\)
−0.552894 + 0.833252i \(0.686477\pi\)
\(80\) 4.74322 8.21550i 0.530308 0.918521i
\(81\) 0 0
\(82\) −1.22180 2.11621i −0.134925 0.233696i
\(83\) −3.44733 + 5.97094i −0.378393 + 0.655396i −0.990829 0.135124i \(-0.956857\pi\)
0.612436 + 0.790521i \(0.290190\pi\)
\(84\) 0 0
\(85\) 2.21737 + 3.84060i 0.240508 + 0.416571i
\(86\) −0.198495 + 0.343803i −0.0214043 + 0.0370733i
\(87\) 0 0
\(88\) 1.97141 + 3.41458i 0.210153 + 0.363996i
\(89\) 2.51769 + 4.36077i 0.266875 + 0.462240i 0.968053 0.250745i \(-0.0806757\pi\)
−0.701178 + 0.712986i \(0.747342\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.97825 8.62258i 0.519018 0.898966i
\(93\) 0 0
\(94\) −2.23299 −0.230315
\(95\) −18.5458 −1.90276
\(96\) 0 0
\(97\) 1.53167 2.65294i 0.155518 0.269365i −0.777730 0.628599i \(-0.783629\pi\)
0.933247 + 0.359234i \(0.116962\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.66827 + 2.88953i 0.166827 + 0.288953i
\(101\) 5.54984 + 9.61260i 0.552229 + 0.956489i 0.998113 + 0.0613986i \(0.0195561\pi\)
−0.445884 + 0.895091i \(0.647111\pi\)
\(102\) 0 0
\(103\) 3.99298 6.91605i 0.393440 0.681459i −0.599460 0.800404i \(-0.704618\pi\)
0.992901 + 0.118946i \(0.0379515\pi\)
\(104\) 1.73625 + 3.00728i 0.170254 + 0.294888i
\(105\) 0 0
\(106\) −1.27292 + 2.20475i −0.123636 + 0.214145i
\(107\) 1.97825 + 3.42642i 0.191244 + 0.331245i 0.945663 0.325149i \(-0.105414\pi\)
−0.754419 + 0.656394i \(0.772081\pi\)
\(108\) 0 0
\(109\) −3.63160 + 6.29012i −0.347844 + 0.602484i −0.985866 0.167534i \(-0.946420\pi\)
0.638022 + 0.770018i \(0.279753\pi\)
\(110\) −2.59179 −0.247117
\(111\) 0 0
\(112\) 0 0
\(113\) 3.46457 + 6.00082i 0.325920 + 0.564509i 0.981698 0.190444i \(-0.0609928\pi\)
−0.655778 + 0.754953i \(0.727659\pi\)
\(114\) 0 0
\(115\) 6.64115 + 11.5028i 0.619291 + 1.07264i
\(116\) 2.06402 3.57498i 0.191639 0.331929i
\(117\) 0 0
\(118\) −1.45011 −0.133494
\(119\) 0 0
\(120\) 0 0
\(121\) −3.24433 + 5.61934i −0.294939 + 0.510849i
\(122\) −1.90963 −0.172890
\(123\) 0 0
\(124\) −12.6980 −1.14031
\(125\) 8.50788 0.760968
\(126\) 0 0
\(127\) 9.11109 0.808479 0.404239 0.914653i \(-0.367536\pi\)
0.404239 + 0.914653i \(0.367536\pi\)
\(128\) 7.11436 0.628827
\(129\) 0 0
\(130\) −2.28263 −0.200200
\(131\) 2.15143 3.72639i 0.187971 0.325576i −0.756602 0.653875i \(-0.773142\pi\)
0.944574 + 0.328299i \(0.106475\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.97592 −0.170694
\(135\) 0 0
\(136\) −0.806617 + 1.39710i −0.0691668 + 0.119800i
\(137\) 10.2947 + 17.8309i 0.879533 + 1.52340i 0.851854 + 0.523779i \(0.175478\pi\)
0.0276785 + 0.999617i \(0.491189\pi\)
\(138\) 0 0
\(139\) −7.88067 13.6497i −0.668429 1.15775i −0.978343 0.206989i \(-0.933634\pi\)
0.309914 0.950765i \(-0.399700\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.49192 0.125199
\(143\) −7.70127 + 13.3390i −0.644012 + 1.11546i
\(144\) 0 0
\(145\) 2.75347 + 4.76915i 0.228663 + 0.396056i
\(146\) −0.855536 + 1.48183i −0.0708047 + 0.122637i
\(147\) 0 0
\(148\) 1.61273 + 2.79332i 0.132565 + 0.229610i
\(149\) 3.03379 5.25468i 0.248538 0.430480i −0.714582 0.699551i \(-0.753383\pi\)
0.963120 + 0.269071i \(0.0867166\pi\)
\(150\) 0 0
\(151\) −2.24433 3.88728i −0.182641 0.316343i 0.760138 0.649761i \(-0.225131\pi\)
−0.942779 + 0.333418i \(0.891798\pi\)
\(152\) −3.37323 5.84260i −0.273605 0.473897i
\(153\) 0 0
\(154\) 0 0
\(155\) 8.46978 14.6701i 0.680309 1.17833i
\(156\) 0 0
\(157\) −1.02891 −0.0821163 −0.0410582 0.999157i \(-0.513073\pi\)
−0.0410582 + 0.999157i \(0.513073\pi\)
\(158\) 2.35021 0.186973
\(159\) 0 0
\(160\) −3.57780 + 6.19694i −0.282850 + 0.489911i
\(161\) 0 0
\(162\) 0 0
\(163\) −3.41423 5.91362i −0.267423 0.463190i 0.700772 0.713385i \(-0.252839\pi\)
−0.968196 + 0.250194i \(0.919505\pi\)
\(164\) −9.92680 17.1937i −0.775153 1.34260i
\(165\) 0 0
\(166\) 0.824336 1.42779i 0.0639809 0.110818i
\(167\) −8.99716 15.5835i −0.696221 1.20589i −0.969767 0.244032i \(-0.921530\pi\)
0.273546 0.961859i \(-0.411803\pi\)
\(168\) 0 0
\(169\) −0.282630 + 0.489530i −0.0217408 + 0.0376561i
\(170\) −0.530225 0.918376i −0.0406664 0.0704362i
\(171\) 0 0
\(172\) −1.61273 + 2.79332i −0.122969 + 0.212989i
\(173\) −0.830357 −0.0631309 −0.0315654 0.999502i \(-0.510049\pi\)
−0.0315654 + 0.999502i \(0.510049\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 7.65335 + 13.2560i 0.576893 + 0.999208i
\(177\) 0 0
\(178\) −0.602038 1.04276i −0.0451247 0.0781582i
\(179\) 3.78947 6.56355i 0.283238 0.490583i −0.688942 0.724816i \(-0.741925\pi\)
0.972180 + 0.234233i \(0.0752580\pi\)
\(180\) 0 0
\(181\) −0.409157 −0.0304124 −0.0152062 0.999884i \(-0.504840\pi\)
−0.0152062 + 0.999884i \(0.504840\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.41586 + 4.18440i −0.178100 + 0.308478i
\(185\) −4.30286 −0.316353
\(186\) 0 0
\(187\) −7.15561 −0.523270
\(188\) −18.1425 −1.32318
\(189\) 0 0
\(190\) 4.43474 0.321730
\(191\) −16.0241 −1.15946 −0.579731 0.814808i \(-0.696842\pi\)
−0.579731 + 0.814808i \(0.696842\pi\)
\(192\) 0 0
\(193\) −12.3743 −0.890721 −0.445360 0.895351i \(-0.646924\pi\)
−0.445360 + 0.895351i \(0.646924\pi\)
\(194\) −0.366259 + 0.634379i −0.0262959 + 0.0455458i
\(195\) 0 0
\(196\) 0 0
\(197\) −23.1021 −1.64595 −0.822977 0.568075i \(-0.807688\pi\)
−0.822977 + 0.568075i \(0.807688\pi\)
\(198\) 0 0
\(199\) −3.37323 + 5.84260i −0.239122 + 0.414171i −0.960463 0.278409i \(-0.910193\pi\)
0.721341 + 0.692580i \(0.243526\pi\)
\(200\) −0.809585 1.40224i −0.0572463 0.0991536i
\(201\) 0 0
\(202\) −1.32710 2.29860i −0.0933741 0.161729i
\(203\) 0 0
\(204\) 0 0
\(205\) 26.4854 1.84982
\(206\) −0.954815 + 1.65379i −0.0665251 + 0.115225i
\(207\) 0 0
\(208\) 6.74043 + 11.6748i 0.467365 + 0.809500i
\(209\) 14.9622 25.9153i 1.03496 1.79260i
\(210\) 0 0
\(211\) −8.44282 14.6234i −0.581228 1.00672i −0.995334 0.0964875i \(-0.969239\pi\)
0.414106 0.910228i \(-0.364094\pi\)
\(212\) −10.3421 + 17.9131i −0.710301 + 1.23028i
\(213\) 0 0
\(214\) −0.473045 0.819338i −0.0323367 0.0560088i
\(215\) −2.15143 3.72639i −0.146726 0.254138i
\(216\) 0 0
\(217\) 0 0
\(218\) 0.868400 1.50411i 0.0588155 0.101871i
\(219\) 0 0
\(220\) −21.0577 −1.41971
\(221\) −6.30206 −0.423922
\(222\) 0 0
\(223\) −2.25071 + 3.89834i −0.150719 + 0.261052i −0.931492 0.363762i \(-0.881492\pi\)
0.780773 + 0.624815i \(0.214825\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.828460 1.43494i −0.0551084 0.0954505i
\(227\) 3.03215 + 5.25183i 0.201251 + 0.348576i 0.948932 0.315482i \(-0.102166\pi\)
−0.747681 + 0.664058i \(0.768833\pi\)
\(228\) 0 0
\(229\) −5.52466 + 9.56899i −0.365080 + 0.632336i −0.988789 0.149320i \(-0.952292\pi\)
0.623709 + 0.781656i \(0.285625\pi\)
\(230\) −1.58805 2.75059i −0.104713 0.181369i
\(231\) 0 0
\(232\) −1.00163 + 1.73488i −0.0657605 + 0.113901i
\(233\) −4.06922 7.04809i −0.266583 0.461736i 0.701394 0.712774i \(-0.252561\pi\)
−0.967977 + 0.251038i \(0.919228\pi\)
\(234\) 0 0
\(235\) 12.1014 20.9602i 0.789407 1.36729i
\(236\) −11.7818 −0.766932
\(237\) 0 0
\(238\) 0 0
\(239\) 10.5813 + 18.3273i 0.684445 + 1.18549i 0.973611 + 0.228214i \(0.0732886\pi\)
−0.289166 + 0.957279i \(0.593378\pi\)
\(240\) 0 0
\(241\) 6.84573 + 11.8572i 0.440972 + 0.763786i 0.997762 0.0668671i \(-0.0213004\pi\)
−0.556790 + 0.830654i \(0.687967\pi\)
\(242\) 0.775794 1.34371i 0.0498699 0.0863772i
\(243\) 0 0
\(244\) −15.5153 −0.993265
\(245\) 0 0
\(246\) 0 0
\(247\) 13.1774 22.8240i 0.838460 1.45225i
\(248\) 6.16213 0.391296
\(249\) 0 0
\(250\) −2.03443 −0.128669
\(251\) 15.2040 0.959667 0.479833 0.877360i \(-0.340697\pi\)
0.479833 + 0.877360i \(0.340697\pi\)
\(252\) 0 0
\(253\) −21.4315 −1.34738
\(254\) −2.17867 −0.136702
\(255\) 0 0
\(256\) 11.6192 0.726198
\(257\) −12.8107 + 22.1889i −0.799112 + 1.38410i 0.121082 + 0.992642i \(0.461363\pi\)
−0.920195 + 0.391461i \(0.871970\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −18.5458 −1.15016
\(261\) 0 0
\(262\) −0.514457 + 0.891066i −0.0317833 + 0.0550502i
\(263\) 3.55034 + 6.14938i 0.218924 + 0.379187i 0.954479 0.298278i \(-0.0964121\pi\)
−0.735556 + 0.677464i \(0.763079\pi\)
\(264\) 0 0
\(265\) −13.7968 23.8967i −0.847528 1.46796i
\(266\) 0 0
\(267\) 0 0
\(268\) −16.0539 −0.980649
\(269\) 8.21572 14.2301i 0.500922 0.867622i −0.499078 0.866557i \(-0.666328\pi\)
0.999999 0.00106448i \(-0.000338834\pi\)
\(270\) 0 0
\(271\) 6.34899 + 10.9968i 0.385674 + 0.668007i 0.991862 0.127314i \(-0.0406357\pi\)
−0.606189 + 0.795321i \(0.707302\pi\)
\(272\) −3.13143 + 5.42379i −0.189871 + 0.328865i
\(273\) 0 0
\(274\) −2.46169 4.26378i −0.148716 0.257584i
\(275\) 3.59097 6.21975i 0.216544 0.375065i
\(276\) 0 0
\(277\) 0.414230 + 0.717468i 0.0248887 + 0.0431084i 0.878201 0.478291i \(-0.158744\pi\)
−0.853313 + 0.521399i \(0.825410\pi\)
\(278\) 1.88445 + 3.26396i 0.113022 + 0.195760i
\(279\) 0 0
\(280\) 0 0
\(281\) 2.60985 4.52039i 0.155690 0.269664i −0.777620 0.628735i \(-0.783573\pi\)
0.933310 + 0.359071i \(0.116906\pi\)
\(282\) 0 0
\(283\) 7.35417 0.437160 0.218580 0.975819i \(-0.429858\pi\)
0.218580 + 0.975819i \(0.429858\pi\)
\(284\) 12.1215 0.719278
\(285\) 0 0
\(286\) 1.84155 3.18966i 0.108893 0.188609i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.03611 + 12.1869i 0.413889 + 0.716877i
\(290\) −0.658419 1.14041i −0.0386637 0.0669674i
\(291\) 0 0
\(292\) −6.95103 + 12.0395i −0.406778 + 0.704561i
\(293\) −3.91286 6.77728i −0.228592 0.395933i 0.728799 0.684728i \(-0.240079\pi\)
−0.957391 + 0.288795i \(0.906745\pi\)
\(294\) 0 0
\(295\) 7.85868 13.6116i 0.457550 0.792500i
\(296\) −0.782630 1.35556i −0.0454895 0.0787900i
\(297\) 0 0
\(298\) −0.725450 + 1.25652i −0.0420242 + 0.0727881i
\(299\) −18.8750 −1.09157
\(300\) 0 0
\(301\) 0 0
\(302\) 0.536670 + 0.929540i 0.0308819 + 0.0534890i
\(303\) 0 0
\(304\) −13.0954 22.6820i −0.751075 1.30090i
\(305\) 10.3490 17.9249i 0.592580 1.02638i
\(306\) 0 0
\(307\) −22.6709 −1.29390 −0.646948 0.762534i \(-0.723955\pi\)
−0.646948 + 0.762534i \(0.723955\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.02532 + 3.50796i −0.115030 + 0.199239i
\(311\) −32.3176 −1.83256 −0.916281 0.400536i \(-0.868824\pi\)
−0.916281 + 0.400536i \(0.868824\pi\)
\(312\) 0 0
\(313\) 24.3196 1.37462 0.687312 0.726362i \(-0.258791\pi\)
0.687312 + 0.726362i \(0.258791\pi\)
\(314\) 0.246037 0.0138847
\(315\) 0 0
\(316\) 19.0949 1.07417
\(317\) −5.13844 −0.288603 −0.144302 0.989534i \(-0.546094\pi\)
−0.144302 + 0.989534i \(0.546094\pi\)
\(318\) 0 0
\(319\) −8.88564 −0.497500
\(320\) −8.63090 + 14.9492i −0.482482 + 0.835684i
\(321\) 0 0
\(322\) 0 0
\(323\) 12.2438 0.681262
\(324\) 0 0
\(325\) 3.16263 5.47783i 0.175431 0.303855i
\(326\) 0.816422 + 1.41408i 0.0452174 + 0.0783189i
\(327\) 0 0
\(328\) 4.81732 + 8.34384i 0.265992 + 0.460712i
\(329\) 0 0
\(330\) 0 0
\(331\) −11.6979 −0.642977 −0.321488 0.946913i \(-0.604183\pi\)
−0.321488 + 0.946913i \(0.604183\pi\)
\(332\) 6.69753 11.6005i 0.367575 0.636658i
\(333\) 0 0
\(334\) 2.15143 + 3.72639i 0.117721 + 0.203899i
\(335\) 10.7082 18.5472i 0.585053 1.01334i
\(336\) 0 0
\(337\) 16.8473 + 29.1804i 0.917733 + 1.58956i 0.802850 + 0.596181i \(0.203316\pi\)
0.114883 + 0.993379i \(0.463351\pi\)
\(338\) 0.0675835 0.117058i 0.00367606 0.00636711i
\(339\) 0 0
\(340\) −4.30795 7.46159i −0.233631 0.404661i
\(341\) 13.6663 + 23.6707i 0.740071 + 1.28184i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.782630 1.35556i 0.0421966 0.0730866i
\(345\) 0 0
\(346\) 0.198558 0.0106745
\(347\) −27.3114 −1.46615 −0.733075 0.680148i \(-0.761916\pi\)
−0.733075 + 0.680148i \(0.761916\pi\)
\(348\) 0 0
\(349\) 11.4585 19.8467i 0.613358 1.06237i −0.377312 0.926086i \(-0.623152\pi\)
0.990670 0.136281i \(-0.0435150\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5.77292 9.99898i −0.307697 0.532948i
\(353\) −5.13466 8.89349i −0.273290 0.473353i 0.696412 0.717642i \(-0.254779\pi\)
−0.969702 + 0.244289i \(0.921445\pi\)
\(354\) 0 0
\(355\) −8.08525 + 14.0041i −0.429120 + 0.743258i
\(356\) −4.89142 8.47218i −0.259245 0.449025i
\(357\) 0 0
\(358\) −0.906150 + 1.56950i −0.0478915 + 0.0829505i
\(359\) 5.05034 + 8.74745i 0.266547 + 0.461673i 0.967968 0.251075i \(-0.0807839\pi\)
−0.701421 + 0.712747i \(0.747451\pi\)
\(360\) 0 0
\(361\) −16.1014 + 27.8884i −0.847441 + 1.46781i
\(362\) 0.0978390 0.00514231
\(363\) 0 0
\(364\) 0 0
\(365\) −9.27292 16.0612i −0.485367 0.840680i
\(366\) 0 0
\(367\) −3.88768 6.73367i −0.202935 0.351494i 0.746538 0.665343i \(-0.231715\pi\)
−0.949473 + 0.313849i \(0.898381\pi\)
\(368\) −9.37880 + 16.2446i −0.488904 + 0.846806i
\(369\) 0 0
\(370\) 1.02891 0.0534907
\(371\) 0 0
\(372\) 0 0
\(373\) −12.0555 + 20.8808i −0.624212 + 1.08117i 0.364480 + 0.931211i \(0.381247\pi\)
−0.988693 + 0.149957i \(0.952087\pi\)
\(374\) 1.71107 0.0884775
\(375\) 0 0
\(376\) 8.80428 0.454046
\(377\) −7.82573 −0.403045
\(378\) 0 0
\(379\) −13.3581 −0.686161 −0.343081 0.939306i \(-0.611470\pi\)
−0.343081 + 0.939306i \(0.611470\pi\)
\(380\) 36.0312 1.84836
\(381\) 0 0
\(382\) 3.83173 0.196048
\(383\) 4.62020 8.00242i 0.236081 0.408905i −0.723505 0.690319i \(-0.757470\pi\)
0.959586 + 0.281414i \(0.0908035\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.95898 0.150608
\(387\) 0 0
\(388\) −2.97577 + 5.15418i −0.151072 + 0.261664i
\(389\) 5.22421 + 9.04859i 0.264878 + 0.458782i 0.967532 0.252750i \(-0.0813351\pi\)
−0.702654 + 0.711532i \(0.748002\pi\)
\(390\) 0 0
\(391\) −4.38442 7.59404i −0.221730 0.384047i
\(392\) 0 0
\(393\) 0 0
\(394\) 5.52424 0.278307
\(395\) −12.7366 + 22.0605i −0.640850 + 1.10999i
\(396\) 0 0
\(397\) −0.204579 0.354341i −0.0102675 0.0177838i 0.860846 0.508866i \(-0.169935\pi\)
−0.871114 + 0.491082i \(0.836602\pi\)
\(398\) 0.806617 1.39710i 0.0404321 0.0700304i
\(399\) 0 0
\(400\) −3.14295 5.44375i −0.157147 0.272187i
\(401\) 7.62640 13.2093i 0.380844 0.659641i −0.610339 0.792140i \(-0.708967\pi\)
0.991183 + 0.132499i \(0.0423001\pi\)
\(402\) 0 0
\(403\) 12.0361 + 20.8472i 0.599562 + 1.03847i
\(404\) −10.7823 18.6756i −0.536441 0.929143i
\(405\) 0 0
\(406\) 0 0
\(407\) 3.47141 6.01266i 0.172071 0.298036i
\(408\) 0 0
\(409\) 6.12670 0.302946 0.151473 0.988461i \(-0.451598\pi\)
0.151473 + 0.988461i \(0.451598\pi\)
\(410\) −6.33327 −0.312778
\(411\) 0 0
\(412\) −7.75765 + 13.4366i −0.382192 + 0.661976i
\(413\) 0 0
\(414\) 0 0
\(415\) 8.93474 + 15.4754i 0.438589 + 0.759659i
\(416\) −5.08430 8.80626i −0.249278 0.431763i
\(417\) 0 0
\(418\) −3.57780 + 6.19694i −0.174996 + 0.303102i
\(419\) −0.781437 1.35349i −0.0381757 0.0661223i 0.846306 0.532697i \(-0.178821\pi\)
−0.884482 + 0.466574i \(0.845488\pi\)
\(420\) 0 0
\(421\) −11.6316 + 20.1465i −0.566889 + 0.981881i 0.429982 + 0.902838i \(0.358520\pi\)
−0.996871 + 0.0790438i \(0.974813\pi\)
\(422\) 2.01887 + 3.49679i 0.0982773 + 0.170221i
\(423\) 0 0
\(424\) 5.01887 8.69295i 0.243738 0.422167i
\(425\) 2.93854 0.142540
\(426\) 0 0
\(427\) 0 0
\(428\) −3.84338 6.65692i −0.185777 0.321775i
\(429\) 0 0
\(430\) 0.514457 + 0.891066i 0.0248093 + 0.0429710i
\(431\) 0.502879 0.871011i 0.0242228 0.0419551i −0.853660 0.520831i \(-0.825622\pi\)
0.877883 + 0.478876i \(0.158956\pi\)
\(432\) 0 0
\(433\) −13.1071 −0.629889 −0.314945 0.949110i \(-0.601986\pi\)
−0.314945 + 0.949110i \(0.601986\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.05555 12.2206i 0.337899 0.585259i
\(437\) 36.6708 1.75420
\(438\) 0 0
\(439\) −18.6141 −0.888402 −0.444201 0.895927i \(-0.646512\pi\)
−0.444201 + 0.895927i \(0.646512\pi\)
\(440\) 10.2190 0.487170
\(441\) 0 0
\(442\) 1.50697 0.0716792
\(443\) 1.11901 0.0531656 0.0265828 0.999647i \(-0.491537\pi\)
0.0265828 + 0.999647i \(0.491537\pi\)
\(444\) 0 0
\(445\) 13.0506 0.618660
\(446\) 0.538197 0.932185i 0.0254844 0.0441402i
\(447\) 0 0
\(448\) 0 0
\(449\) 39.4419 1.86138 0.930689 0.365813i \(-0.119209\pi\)
0.930689 + 0.365813i \(0.119209\pi\)
\(450\) 0 0
\(451\) −21.3676 + 37.0097i −1.00616 + 1.74272i
\(452\) −6.73104 11.6585i −0.316602 0.548370i
\(453\) 0 0
\(454\) −0.725057 1.25584i −0.0340286 0.0589393i
\(455\) 0 0
\(456\) 0 0
\(457\) −34.2405 −1.60170 −0.800852 0.598863i \(-0.795619\pi\)
−0.800852 + 0.598863i \(0.795619\pi\)
\(458\) 1.32107 2.28817i 0.0617297 0.106919i
\(459\) 0 0
\(460\) −12.9026 22.3479i −0.601585 1.04198i
\(461\) −10.1938 + 17.6561i −0.474772 + 0.822328i −0.999583 0.0288903i \(-0.990803\pi\)
0.524811 + 0.851219i \(0.324136\pi\)
\(462\) 0 0
\(463\) −3.40451 5.89679i −0.158221 0.274047i 0.776006 0.630725i \(-0.217243\pi\)
−0.934227 + 0.356678i \(0.883909\pi\)
\(464\) −3.88852 + 6.73511i −0.180520 + 0.312670i
\(465\) 0 0
\(466\) 0.973045 + 1.68536i 0.0450754 + 0.0780729i
\(467\) −12.3956 21.4698i −0.573598 0.993502i −0.996192 0.0871825i \(-0.972214\pi\)
0.422594 0.906319i \(-0.361120\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.89372 + 5.01207i −0.133477 + 0.231190i
\(471\) 0 0
\(472\) 5.71754 0.263171
\(473\) 6.94282 0.319231
\(474\) 0 0
\(475\) −6.14441 + 10.6424i −0.281925 + 0.488309i
\(476\) 0 0
\(477\) 0 0
\(478\) −2.53022 4.38248i −0.115730 0.200450i
\(479\) 5.54984 + 9.61260i 0.253579 + 0.439211i 0.964508 0.264052i \(-0.0850590\pi\)
−0.710930 + 0.703263i \(0.751726\pi\)
\(480\) 0 0
\(481\) 3.05733 5.29545i 0.139402 0.241452i
\(482\) −1.63697 2.83532i −0.0745621 0.129145i
\(483\) 0 0
\(484\) 6.30314 10.9174i 0.286506 0.496244i
\(485\) −3.96978 6.87585i −0.180258 0.312216i
\(486\) 0 0
\(487\) 5.01887 8.69295i 0.227427 0.393915i −0.729618 0.683855i \(-0.760302\pi\)
0.957045 + 0.289940i \(0.0936354\pi\)
\(488\) 7.52933 0.340837
\(489\) 0 0
\(490\) 0 0
\(491\) −6.19398 10.7283i −0.279530 0.484161i 0.691738 0.722149i \(-0.256845\pi\)
−0.971268 + 0.237988i \(0.923512\pi\)
\(492\) 0 0
\(493\) −1.81781 3.14854i −0.0818702 0.141803i
\(494\) −3.15103 + 5.45774i −0.141772 + 0.245556i
\(495\) 0 0
\(496\) 23.9225 1.07415
\(497\) 0 0
\(498\) 0 0
\(499\) −5.11109 + 8.85267i −0.228804 + 0.396300i −0.957454 0.288586i \(-0.906815\pi\)
0.728650 + 0.684886i \(0.240148\pi\)
\(500\) −16.5293 −0.739212
\(501\) 0 0
\(502\) −3.63562 −0.162266
\(503\) −8.45753 −0.377102 −0.188551 0.982063i \(-0.560379\pi\)
−0.188551 + 0.982063i \(0.560379\pi\)
\(504\) 0 0
\(505\) 28.7680 1.28016
\(506\) 5.12476 0.227824
\(507\) 0 0
\(508\) −17.7012 −0.785364
\(509\) 5.28286 9.15018i 0.234159 0.405574i −0.724869 0.688886i \(-0.758100\pi\)
0.959028 + 0.283312i \(0.0914332\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −17.0071 −0.751616
\(513\) 0 0
\(514\) 3.06335 5.30587i 0.135118 0.234032i
\(515\) −10.3490 17.9249i −0.456030 0.789867i
\(516\) 0 0
\(517\) 19.5260 + 33.8200i 0.858752 + 1.48740i
\(518\) 0 0
\(519\) 0 0
\(520\) 9.00000 0.394676
\(521\) −9.87788 + 17.1090i −0.432758 + 0.749558i −0.997110 0.0759760i \(-0.975793\pi\)
0.564352 + 0.825534i \(0.309126\pi\)
\(522\) 0 0
\(523\) −16.2641 28.1702i −0.711179 1.23180i −0.964415 0.264394i \(-0.914828\pi\)
0.253236 0.967405i \(-0.418505\pi\)
\(524\) −4.17984 + 7.23970i −0.182597 + 0.316268i
\(525\) 0 0
\(526\) −0.848970 1.47046i −0.0370168 0.0641150i
\(527\) −5.59166 + 9.68504i −0.243577 + 0.421887i
\(528\) 0 0
\(529\) −1.63160 2.82601i −0.0709391 0.122870i
\(530\) 3.29913 + 5.71426i 0.143305 + 0.248211i
\(531\) 0 0
\(532\) 0 0
\(533\) −18.8187 + 32.5950i −0.815130 + 1.41185i
\(534\) 0 0
\(535\) 10.2544 0.443336
\(536\) 7.79071 0.336507
\(537\) 0 0
\(538\) −1.96457 + 3.40274i −0.0846987 + 0.146702i
\(539\) 0 0
\(540\) 0 0
\(541\) −7.61109 13.1828i −0.327226 0.566773i 0.654734 0.755859i \(-0.272781\pi\)
−0.981960 + 0.189087i \(0.939447\pi\)
\(542\) −1.51819 2.62959i −0.0652119 0.112950i
\(543\) 0 0
\(544\) 2.36203 4.09116i 0.101271 0.175407i
\(545\) 9.41234 + 16.3027i 0.403180 + 0.698329i
\(546\) 0 0
\(547\) −11.6871 + 20.2427i −0.499706 + 0.865517i −1.00000 0.000339172i \(-0.999892\pi\)
0.500294 + 0.865856i \(0.333225\pi\)
\(548\) −20.0007 34.6422i −0.854387 1.47984i
\(549\) 0 0
\(550\) −0.858685 + 1.48729i −0.0366144 + 0.0634181i
\(551\) 15.2040 0.647711
\(552\) 0 0
\(553\) 0 0
\(554\) −0.0990521 0.171563i −0.00420832 0.00728902i
\(555\) 0 0
\(556\) 15.3107 + 26.5189i 0.649319 + 1.12465i
\(557\) 13.8337 23.9606i 0.586151 1.01524i −0.408580 0.912723i \(-0.633976\pi\)
0.994731 0.102521i \(-0.0326908\pi\)
\(558\) 0 0
\(559\) 6.11465 0.258622
\(560\) 0 0
\(561\) 0 0
\(562\) −0.624075 + 1.08093i −0.0263250 + 0.0455963i
\(563\) −8.55824 −0.360687 −0.180343 0.983604i \(-0.557721\pi\)
−0.180343 + 0.983604i \(0.557721\pi\)
\(564\) 0 0
\(565\) 17.9589 0.755536
\(566\) −1.75855 −0.0739175
\(567\) 0 0
\(568\) −5.88237 −0.246819
\(569\) −13.7278 −0.575498 −0.287749 0.957706i \(-0.592907\pi\)
−0.287749 + 0.957706i \(0.592907\pi\)
\(570\) 0 0
\(571\) 10.7174 0.448508 0.224254 0.974531i \(-0.428005\pi\)
0.224254 + 0.974531i \(0.428005\pi\)
\(572\) 14.9622 25.9153i 0.625600 1.08357i
\(573\) 0 0
\(574\) 0 0
\(575\) 8.80111 0.367032
\(576\) 0 0
\(577\) 22.8177 39.5214i 0.949912 1.64530i 0.204307 0.978907i \(-0.434506\pi\)
0.745605 0.666389i \(-0.232161\pi\)
\(578\) −1.68250 2.91417i −0.0699827 0.121214i
\(579\) 0 0
\(580\) −5.34950 9.26560i −0.222126 0.384733i
\(581\) 0 0
\(582\) 0 0
\(583\) 44.5231 1.84396
\(584\) 3.37323 5.84260i 0.139585 0.241768i
\(585\) 0 0
\(586\) 0.935657 + 1.62060i 0.0386516 + 0.0669466i
\(587\) −5.10948 + 8.84988i −0.210891 + 0.365274i −0.951994 0.306118i \(-0.900970\pi\)
0.741103 + 0.671392i \(0.234303\pi\)
\(588\) 0 0
\(589\) −23.3840 40.5023i −0.963521 1.66887i
\(590\) −1.87919 + 3.25486i −0.0773652 + 0.134000i
\(591\) 0 0
\(592\) −3.03831 5.26250i −0.124874 0.216287i
\(593\) 5.69804 + 9.86929i 0.233990 + 0.405283i 0.958979 0.283478i \(-0.0914883\pi\)
−0.724988 + 0.688761i \(0.758155\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −5.89411 + 10.2089i −0.241432 + 0.418173i
\(597\) 0 0
\(598\) 4.51346 0.184569
\(599\) 34.5746 1.41268 0.706339 0.707874i \(-0.250345\pi\)
0.706339 + 0.707874i \(0.250345\pi\)
\(600\) 0 0
\(601\) 19.4207 33.6376i 0.792187 1.37211i −0.132423 0.991193i \(-0.542276\pi\)
0.924610 0.380915i \(-0.124391\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.36032 + 7.55230i 0.177419 + 0.307299i
\(605\) 8.40861 + 14.5641i 0.341858 + 0.592116i
\(606\) 0 0
\(607\) 20.6662 35.7950i 0.838817 1.45287i −0.0520683 0.998644i \(-0.516581\pi\)
0.890885 0.454229i \(-0.150085\pi\)
\(608\) 9.87788 + 17.1090i 0.400601 + 0.693861i
\(609\) 0 0
\(610\) −2.47468 + 4.28627i −0.100197 + 0.173546i
\(611\) 17.1969 + 29.7858i 0.695710 + 1.20501i
\(612\) 0 0
\(613\) 14.3285 24.8176i 0.578721 1.00237i −0.416905 0.908950i \(-0.636885\pi\)
0.995626 0.0934244i \(-0.0297813\pi\)
\(614\) 5.42114 0.218779
\(615\) 0 0
\(616\) 0 0
\(617\) −16.8518 29.1883i −0.678430 1.17508i −0.975454 0.220205i \(-0.929327\pi\)
0.297024 0.954870i \(-0.404006\pi\)
\(618\) 0 0
\(619\) −0.719036 1.24541i −0.0289005 0.0500571i 0.851213 0.524820i \(-0.175867\pi\)
−0.880114 + 0.474763i \(0.842534\pi\)
\(620\) −16.4552 + 28.5013i −0.660859 + 1.14464i
\(621\) 0 0
\(622\) 7.72789 0.309860
\(623\) 0 0
\(624\) 0 0
\(625\) 15.3187 26.5328i 0.612750 1.06131i
\(626\) −5.81538 −0.232429
\(627\) 0 0
\(628\) 1.99900 0.0797686
\(629\) 2.84071 0.113266
\(630\) 0 0
\(631\) −30.7680 −1.22486 −0.612428 0.790527i \(-0.709807\pi\)
−0.612428 + 0.790527i \(0.709807\pi\)
\(632\) −9.26647 −0.368600
\(633\) 0 0
\(634\) 1.22872 0.0487987
\(635\) 11.8070 20.4503i 0.468547 0.811547i
\(636\) 0 0
\(637\) 0 0
\(638\) 2.12476 0.0841202
\(639\) 0 0
\(640\) 9.21946 15.9686i 0.364431 0.631213i
\(641\) 4.61956 + 8.00132i 0.182462 + 0.316033i 0.942718 0.333590i \(-0.108260\pi\)
−0.760257 + 0.649623i \(0.774927\pi\)
\(642\) 0 0
\(643\) 12.7795 + 22.1348i 0.503976 + 0.872912i 0.999989 + 0.00459728i \(0.00146337\pi\)
−0.496013 + 0.868315i \(0.665203\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.92777 −0.115192
\(647\) 14.1556 24.5181i 0.556512 0.963908i −0.441272 0.897374i \(-0.645472\pi\)
0.997784 0.0665343i \(-0.0211942\pi\)
\(648\) 0 0
\(649\) 12.6803 + 21.9629i 0.497744 + 0.862118i
\(650\) −0.756258 + 1.30988i −0.0296629 + 0.0513776i
\(651\) 0 0
\(652\) 6.63323 + 11.4891i 0.259778 + 0.449948i
\(653\) −4.17511 + 7.23150i −0.163385 + 0.282990i −0.936080 0.351786i \(-0.885574\pi\)
0.772696 + 0.634776i \(0.218908\pi\)
\(654\) 0 0
\(655\) −5.57605 9.65801i −0.217874 0.377370i
\(656\) 18.7017 + 32.3922i 0.730177 + 1.26470i
\(657\) 0 0
\(658\) 0 0
\(659\) −16.7862 + 29.0745i −0.653897 + 1.13258i 0.328272 + 0.944583i \(0.393534\pi\)
−0.982169 + 0.188000i \(0.939799\pi\)
\(660\) 0 0
\(661\) −16.9534 −0.659410 −0.329705 0.944084i \(-0.606949\pi\)
−0.329705 + 0.944084i \(0.606949\pi\)
\(662\) 2.79725 0.108718
\(663\) 0 0
\(664\) −3.25021 + 5.62952i −0.126133 + 0.218468i
\(665\) 0 0
\(666\) 0 0
\(667\) −5.44445 9.43007i −0.210810 0.365134i
\(668\) 17.4799 + 30.2760i 0.676316 + 1.17141i
\(669\) 0 0
\(670\) −2.56059 + 4.43507i −0.0989242 + 0.171342i
\(671\) 16.6984 + 28.9225i 0.644636 + 1.11654i
\(672\) 0 0
\(673\) 22.2157 38.4788i 0.856354 1.48325i −0.0190299 0.999819i \(-0.506058\pi\)
0.875384 0.483429i \(-0.160609\pi\)
\(674\) −4.02859 6.97772i −0.155175 0.268772i
\(675\) 0 0
\(676\) 0.549100 0.951068i 0.0211192 0.0365796i
\(677\) 14.3736 0.552423 0.276212 0.961097i \(-0.410921\pi\)
0.276212 + 0.961097i \(0.410921\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2.09058 + 3.62099i 0.0801701 + 0.138859i
\(681\) 0 0
\(682\) −3.26793 5.66021i −0.125135 0.216741i
\(683\) −16.1546 + 27.9806i −0.618138 + 1.07065i 0.371687 + 0.928358i \(0.378780\pi\)
−0.989825 + 0.142289i \(0.954554\pi\)
\(684\) 0 0
\(685\) 53.3632 2.03890
\(686\) 0 0
\(687\) 0 0
\(688\) 3.03831 5.26250i 0.115834 0.200631i
\(689\) 39.2122 1.49387
\(690\) 0 0
\(691\) −28.9962 −1.10307 −0.551533 0.834153i \(-0.685957\pi\)
−0.551533 + 0.834153i \(0.685957\pi\)
\(692\) 1.61323 0.0613259
\(693\) 0 0
\(694\) 6.53078 0.247905
\(695\) −40.8500 −1.54953
\(696\) 0 0
\(697\) −17.4854 −0.662306
\(698\) −2.73999 + 4.74580i −0.103710 + 0.179631i
\(699\) 0 0
\(700\) 0 0
\(701\) 26.3912 0.996783 0.498392 0.866952i \(-0.333924\pi\)
0.498392 + 0.866952i \(0.333924\pi\)
\(702\) 0 0
\(703\) −5.93984 + 10.2881i −0.224025 + 0.388023i
\(704\) −13.9263 24.1210i −0.524866 0.909095i
\(705\) 0 0
\(706\) 1.22782 + 2.12664i 0.0462095 + 0.0800372i
\(707\) 0 0
\(708\) 0 0
\(709\) −7.88564 −0.296151 −0.148076 0.988976i \(-0.547308\pi\)
−0.148076 + 0.988976i \(0.547308\pi\)
\(710\) 1.93337 3.34870i 0.0725581 0.125674i
\(711\) 0 0
\(712\) 2.37373 + 4.11142i 0.0889592 + 0.154082i
\(713\) −16.7473 + 29.0073i −0.627193 + 1.08633i
\(714\) 0 0
\(715\) 19.9601 + 34.5718i 0.746464 + 1.29291i
\(716\) −7.36225 + 12.7518i −0.275140 + 0.476557i
\(717\) 0 0
\(718\) −1.20765 2.09172i −0.0450693 0.0780623i
\(719\) −16.5754 28.7095i −0.618159 1.07068i −0.989822 0.142314i \(-0.954546\pi\)
0.371663 0.928368i \(-0.378788\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.85021 6.66877i 0.143290 0.248186i
\(723\) 0 0
\(724\) 0.794919 0.0295429
\(725\) 3.64900 0.135521
\(726\) 0 0
\(727\) −16.5502 + 28.6658i −0.613814 + 1.06316i 0.376777 + 0.926304i \(0.377032\pi\)
−0.990591 + 0.136853i \(0.956301\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.21737 + 3.84060i 0.0820685 + 0.142147i
\(731\) 1.42035 + 2.46012i 0.0525337 + 0.0909910i
\(732\) 0 0
\(733\) 22.2795 38.5892i 0.822911 1.42532i −0.0805946 0.996747i \(-0.525682\pi\)
0.903505 0.428577i \(-0.140985\pi\)
\(734\) 0.929636 + 1.61018i 0.0343135 + 0.0594327i
\(735\) 0 0
\(736\) 7.07442 12.2533i 0.260767 0.451661i
\(737\) 17.2781 + 29.9266i 0.636448 + 1.10236i
\(738\) 0 0
\(739\) −19.9045 + 34.4756i −0.732199 + 1.26821i 0.223742 + 0.974648i \(0.428173\pi\)
−0.955941 + 0.293558i \(0.905161\pi\)
\(740\) 8.35969 0.307308
\(741\) 0 0
\(742\) 0 0
\(743\) 5.37072 + 9.30237i 0.197033 + 0.341271i 0.947565 0.319563i \(-0.103536\pi\)
−0.750532 + 0.660834i \(0.770203\pi\)
\(744\) 0 0
\(745\) −7.86295 13.6190i −0.288076 0.498962i
\(746\) 2.88276 4.99309i 0.105545 0.182810i
\(747\) 0 0
\(748\) 13.9021 0.508310
\(749\) 0 0
\(750\) 0 0
\(751\) −9.85705 + 17.0729i −0.359689 + 0.622999i −0.987909 0.155036i \(-0.950450\pi\)
0.628220 + 0.778036i \(0.283784\pi\)
\(752\) 34.1797 1.24641
\(753\) 0 0
\(754\) 1.87131 0.0681492
\(755\) −11.6336 −0.423391
\(756\) 0 0
\(757\) 35.3549 1.28499 0.642497 0.766288i \(-0.277898\pi\)
0.642497 + 0.766288i \(0.277898\pi\)
\(758\) 3.19424 0.116020
\(759\) 0 0
\(760\) −17.4854 −0.634261
\(761\) −19.5572 + 33.8741i −0.708948 + 1.22793i 0.256300 + 0.966597i \(0.417497\pi\)
−0.965248 + 0.261336i \(0.915837\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 31.1319 1.12631
\(765\) 0 0
\(766\) −1.10480 + 1.91357i −0.0399180 + 0.0691399i
\(767\) 11.1677 + 19.3430i 0.403243 + 0.698437i
\(768\) 0 0
\(769\) 18.9240 + 32.7773i 0.682415 + 1.18198i 0.974242 + 0.225507i \(0.0724038\pi\)
−0.291826 + 0.956471i \(0.594263\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 24.0410 0.865255
\(773\) 14.9133 25.8305i 0.536393 0.929059i −0.462702 0.886514i \(-0.653120\pi\)
0.999095 0.0425453i \(-0.0135467\pi\)
\(774\) 0 0
\(775\) −5.61224 9.72068i −0.201598 0.349177i
\(776\) 1.44409 2.50124i 0.0518399 0.0897894i
\(777\) 0 0
\(778\) −1.24923 2.16373i −0.0447870 0.0775734i
\(779\) 36.5614 63.3263i 1.30995 2.26890i
\(780\) 0 0
\(781\) −13.0458 22.5960i −0.466817 0.808550i
\(782\) 1.04842 + 1.81591i 0.0374913 + 0.0649369i
\(783\) 0 0
\(784\) 0 0
\(785\) −1.33336 + 2.30946i −0.0475898 + 0.0824280i
\(786\) 0 0
\(787\) 17.6206 0.628107 0.314053 0.949405i \(-0.398313\pi\)
0.314053 + 0.949405i \(0.398313\pi\)
\(788\) 44.8832 1.59890
\(789\) 0 0
\(790\) 3.04563 5.27518i 0.108359 0.187683i
\(791\) 0 0
\(792\) 0 0
\(793\) 14.7066 + 25.4725i 0.522246 + 0.904556i
\(794\) 0.0489195 + 0.0847311i 0.00173609 + 0.00300699i
\(795\) 0 0
\(796\) 6.55357 11.3511i 0.232285 0.402330i
\(797\) 5.06056 + 8.76515i 0.179254 + 0.310477i 0.941625 0.336663i \(-0.109298\pi\)
−0.762371 + 0.647140i \(0.775965\pi\)
\(798\) 0 0
\(799\) −7.98921 + 13.8377i −0.282638 + 0.489543i
\(800\) 2.37072 + 4.10621i 0.0838177 + 0.145177i
\(801\) 0 0
\(802\) −1.82365 + 3.15865i −0.0643953 + 0.111536i
\(803\) 29.9244 1.05601
\(804\) 0 0
\(805\) 0 0
\(806\) −2.87812 4.98504i −0.101377 0.175591i
\(807\) 0 0
\(808\) 5.23250 + 9.06295i 0.184079 + 0.318834i
\(809\) −23.5735 + 40.8305i −0.828799 + 1.43552i 0.0701816 + 0.997534i \(0.477642\pi\)
−0.898981 + 0.437988i \(0.855691\pi\)
\(810\) 0 0
\(811\) 21.0577 0.739435 0.369717 0.929144i \(-0.379454\pi\)
0.369717 + 0.929144i \(0.379454\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −0.830095 + 1.43777i −0.0290948 + 0.0503937i
\(815\) −17.6979 −0.619931
\(816\) 0 0
\(817\) −11.8797 −0.415617
\(818\) −1.46504 −0.0512238
\(819\) 0 0
\(820\) −51.4563 −1.79693
\(821\) −11.1604 −0.389499 −0.194750 0.980853i \(-0.562389\pi\)
−0.194750 + 0.980853i \(0.562389\pi\)
\(822\) 0 0
\(823\) 9.43474 0.328874 0.164437 0.986388i \(-0.447419\pi\)
0.164437 + 0.986388i \(0.447419\pi\)
\(824\) 3.76466 6.52059i 0.131148 0.227156i
\(825\) 0 0
\(826\) 0 0
\(827\) −17.2646 −0.600348 −0.300174 0.953884i \(-0.597045\pi\)
−0.300174 + 0.953884i \(0.597045\pi\)
\(828\) 0 0
\(829\) 24.2263 41.9612i 0.841415 1.45737i −0.0472838 0.998881i \(-0.515057\pi\)
0.888699 0.458492i \(-0.151610\pi\)
\(830\) −2.13650 3.70053i −0.0741591 0.128447i
\(831\) 0 0
\(832\) −12.2651 21.2438i −0.425215 0.736495i
\(833\) 0 0
\(834\) 0 0
\(835\) −46.6375 −1.61396
\(836\) −29.0688 + 50.3487i −1.00537 + 1.74135i
\(837\) 0 0
\(838\) 0.186860 + 0.323651i 0.00645497 + 0.0111803i
\(839\) −7.43429 + 12.8766i −0.256660 + 0.444548i −0.965345 0.260977i \(-0.915955\pi\)
0.708685 + 0.705525i \(0.249289\pi\)
\(840\) 0 0
\(841\) 12.2427 + 21.2050i 0.422162 + 0.731206i
\(842\) 2.78139 4.81750i 0.0958529 0.166022i
\(843\) 0 0
\(844\) 16.4029 + 28.4106i 0.564610 + 0.977934i
\(845\) 0.732518 + 1.26876i 0.0251994 + 0.0436466i
\(846\) 0 0
\(847\) 0 0
\(848\) 19.4841 33.7475i 0.669088 1.15889i
\(849\) 0 0
\(850\) −0.702674 −0.0241015
\(851\) 8.50808 0.291653
\(852\) 0 0
\(853\) −3.99900 + 6.92648i −0.136923 + 0.237158i −0.926331 0.376712i \(-0.877055\pi\)
0.789407 + 0.613870i \(0.210388\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.86513 + 3.23050i 0.0637488 + 0.110416i
\(857\) −21.5661 37.3536i −0.736684 1.27597i −0.953980 0.299869i \(-0.903057\pi\)
0.217296 0.976106i \(-0.430276\pi\)
\(858\) 0 0
\(859\) 1.22180 2.11621i 0.0416871 0.0722042i −0.844429 0.535667i \(-0.820060\pi\)
0.886116 + 0.463463i \(0.153393\pi\)
\(860\) 4.17984 + 7.23970i 0.142531 + 0.246872i
\(861\) 0 0
\(862\) −0.120250 + 0.208279i −0.00409573 + 0.00709401i
\(863\) 12.8594 + 22.2731i 0.437738 + 0.758185i 0.997515 0.0704589i \(-0.0224464\pi\)
−0.559777 + 0.828644i \(0.689113\pi\)
\(864\) 0 0
\(865\) −1.07605 + 1.86378i −0.0365870 + 0.0633705i
\(866\) 3.13422 0.106505
\(867\) 0 0
\(868\) 0 0
\(869\) −20.5510 35.5954i −0.697146 1.20749i
\(870\) 0 0
\(871\) 15.2171 + 26.3568i 0.515612 + 0.893067i
\(872\) −3.42395 + 5.93045i −0.115949 + 0.200830i
\(873\) 0 0
\(874\) −8.76884 −0.296611
\(875\) 0 0
\(876\) 0 0
\(877\) 10.9795 19.0170i 0.370751 0.642160i −0.618930 0.785446i \(-0.712434\pi\)
0.989681 + 0.143286i \(0.0457670\pi\)
\(878\) 4.45106 0.150216
\(879\) 0 0
\(880\) 39.6718 1.33733
\(881\) 35.0576 1.18112 0.590560 0.806994i \(-0.298907\pi\)
0.590560 + 0.806994i \(0.298907\pi\)
\(882\) 0 0
\(883\) 26.3009 0.885097 0.442549 0.896744i \(-0.354074\pi\)
0.442549 + 0.896744i \(0.354074\pi\)
\(884\) 12.2438 0.411803
\(885\) 0 0
\(886\) −0.267580 −0.00898954
\(887\) 23.9090 41.4116i 0.802785 1.39046i −0.114991 0.993366i \(-0.536684\pi\)
0.917776 0.397098i \(-0.129983\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −3.12071 −0.104607
\(891\) 0 0
\(892\) 4.37272 7.57378i 0.146410 0.253589i
\(893\) −33.4104 57.8685i −1.11804 1.93650i
\(894\) 0 0
\(895\) −9.82150 17.0113i −0.328296 0.568626i
\(896\) 0 0
\(897\) 0 0
\(898\) −9.43147 −0.314732
\(899\) −6.94357 + 12.0266i −0.231581 + 0.401110i
\(900\) 0 0
\(901\) 9.10848 + 15.7764i 0.303448 + 0.525587i
\(902\) 5.10948 8.84988i 0.170127 0.294669i
\(903\) 0 0
\(904\) 3.26647 + 5.65769i 0.108641 + 0.188172i
\(905\) −0.530225 + 0.918376i −0.0176253 + 0.0305279i
\(906\) 0 0
\(907\) 9.55718 + 16.5535i 0.317341 + 0.549651i 0.979932 0.199330i \(-0.0638767\pi\)
−0.662591 + 0.748981i \(0.730543\pi\)
\(908\) −5.89092 10.2034i −0.195497 0.338611i
\(909\) 0 0
\(910\) 0 0
\(911\) −9.02928 + 15.6392i −0.299153 + 0.518149i −0.975942 0.218028i \(-0.930038\pi\)
0.676789 + 0.736177i \(0.263371\pi\)
\(912\) 0 0
\(913\) −28.8330 −0.954234
\(914\) 8.18770 0.270825
\(915\) 0 0
\(916\) 10.7334 18.5908i 0.354642 0.614258i
\(917\) 0 0
\(918\) 0 0
\(919\) −8.10464 14.0377i −0.267348 0.463060i 0.700828 0.713330i \(-0.252814\pi\)
−0.968176 + 0.250270i \(0.919481\pi\)
\(920\) 6.26141 + 10.8451i 0.206433 + 0.357552i
\(921\) 0 0
\(922\) 2.43757 4.22199i 0.0802771 0.139044i
\(923\) −11.4897 19.9007i −0.378187 0.655039i
\(924\) 0 0
\(925\) −1.42558 + 2.46918i −0.0468728 + 0.0811860i
\(926\) 0.814099 + 1.41006i 0.0267529 + 0.0463375i
\(927\) 0 0
\(928\) 2.93310 5.08029i 0.0962839 0.166769i
\(929\) −22.6829 −0.744203 −0.372102 0.928192i \(-0.621363\pi\)
−0.372102 + 0.928192i \(0.621363\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 7.90576 + 13.6932i 0.258962 + 0.448535i
\(933\) 0 0
\(934\) 2.96407 + 5.13392i 0.0969873 + 0.167987i
\(935\) −9.27292 + 16.0612i −0.303257 + 0.525256i
\(936\) 0 0
\(937\) −51.2933 −1.67568 −0.837840 0.545915i \(-0.816182\pi\)
−0.837840 + 0.545915i \(0.816182\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −23.5108 + 40.7219i −0.766838 + 1.32820i
\(941\) −31.9318 −1.04095 −0.520474 0.853878i \(-0.674245\pi\)
−0.520474 + 0.853878i \(0.674245\pi\)
\(942\) 0 0
\(943\) −52.3697 −1.70539
\(944\) 22.1965 0.722433
\(945\) 0 0
\(946\) −1.66019 −0.0539774
\(947\) 4.49330 0.146013 0.0730063 0.997331i \(-0.476741\pi\)
0.0730063 + 0.997331i \(0.476741\pi\)
\(948\) 0 0
\(949\) 26.3549 0.855515
\(950\) 1.46927 2.54485i 0.0476695 0.0825660i
\(951\) 0 0
\(952\) 0 0
\(953\) −1.14635 −0.0371340 −0.0185670 0.999828i \(-0.505910\pi\)
−0.0185670 + 0.999828i \(0.505910\pi\)
\(954\) 0 0
\(955\) −20.7655 + 35.9669i −0.671956 + 1.16386i
\(956\) −20.5575 35.6066i −0.664876 1.15160i
\(957\) 0 0
\(958\) −1.32710 2.29860i −0.0428765 0.0742643i
\(959\) 0 0
\(960\) 0 0
\(961\) 11.7174 0.377980
\(962\) −0.731078 + 1.26626i −0.0235709 + 0.0408260i
\(963\) 0 0
\(964\) −13.3000 23.0363i −0.428365 0.741950i
\(965\) −16.0358 + 27.7748i −0.516210 + 0.894102i
\(966\) 0 0
\(967\) −24.8080 42.9686i −0.797770 1.38178i −0.921065 0.389408i \(-0.872680\pi\)
0.123295 0.992370i \(-0.460654\pi\)
\(968\) −3.05881 + 5.29802i −0.0983140 + 0.170285i
\(969\) 0 0
\(970\) 0.949266 + 1.64418i 0.0304791 + 0.0527913i
\(971\) 2.56661 + 4.44550i 0.0823664 + 0.142663i 0.904266 0.426970i \(-0.140419\pi\)
−0.821900 + 0.569632i \(0.807086\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −1.20013 + 2.07869i −0.0384546 + 0.0666054i
\(975\) 0 0
\(976\) 29.2302 0.935634
\(977\) −31.1948 −0.998011 −0.499006 0.866599i \(-0.666301\pi\)
−0.499006 + 0.866599i \(0.666301\pi\)
\(978\) 0 0
\(979\) −10.5288 + 18.2365i −0.336503 + 0.582840i
\(980\) 0 0
\(981\) 0 0
\(982\) 1.48113 + 2.56538i 0.0472646 + 0.0818647i
\(983\) −10.1700 17.6150i −0.324374 0.561832i 0.657012 0.753880i \(-0.271820\pi\)
−0.981385 + 0.192049i \(0.938487\pi\)
\(984\) 0 0
\(985\) −29.9378 + 51.8539i −0.953899 + 1.65220i
\(986\) 0.434681 + 0.752890i 0.0138431 + 0.0239769i
\(987\) 0 0
\(988\) −25.6014 + 44.3429i −0.814488 + 1.41074i
\(989\) 4.25404 + 7.36821i 0.135271 + 0.234296i
\(990\) 0 0
\(991\) 6.48276 11.2285i 0.205932 0.356684i −0.744498 0.667625i \(-0.767311\pi\)
0.950429 + 0.310941i \(0.100644\pi\)
\(992\) −18.0447 −0.572919
\(993\) 0 0
\(994\) 0 0
\(995\) 8.74269 + 15.1428i 0.277162 + 0.480059i
\(996\) 0 0
\(997\) −24.7408 42.8523i −0.783548 1.35715i −0.929863 0.367907i \(-0.880074\pi\)
0.146314 0.989238i \(-0.453259\pi\)
\(998\) 1.22218 2.11688i 0.0386875 0.0670086i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1323.2.h.g.802.4 12
3.2 odd 2 441.2.h.g.214.3 12
7.2 even 3 1323.2.g.g.667.3 12
7.3 odd 6 1323.2.f.g.883.3 12
7.4 even 3 1323.2.f.g.883.4 12
7.5 odd 6 1323.2.g.g.667.4 12
7.6 odd 2 inner 1323.2.h.g.802.3 12
9.4 even 3 1323.2.g.g.361.3 12
9.5 odd 6 441.2.g.g.67.4 12
21.2 odd 6 441.2.g.g.79.4 12
21.5 even 6 441.2.g.g.79.3 12
21.11 odd 6 441.2.f.g.295.4 yes 12
21.17 even 6 441.2.f.g.295.3 yes 12
21.20 even 2 441.2.h.g.214.4 12
63.4 even 3 1323.2.f.g.442.4 12
63.5 even 6 441.2.h.g.373.4 12
63.11 odd 6 3969.2.a.be.1.4 6
63.13 odd 6 1323.2.g.g.361.4 12
63.23 odd 6 441.2.h.g.373.3 12
63.25 even 3 3969.2.a.bd.1.3 6
63.31 odd 6 1323.2.f.g.442.3 12
63.32 odd 6 441.2.f.g.148.4 yes 12
63.38 even 6 3969.2.a.be.1.3 6
63.40 odd 6 inner 1323.2.h.g.226.3 12
63.41 even 6 441.2.g.g.67.3 12
63.52 odd 6 3969.2.a.bd.1.4 6
63.58 even 3 inner 1323.2.h.g.226.4 12
63.59 even 6 441.2.f.g.148.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.f.g.148.3 12 63.59 even 6
441.2.f.g.148.4 yes 12 63.32 odd 6
441.2.f.g.295.3 yes 12 21.17 even 6
441.2.f.g.295.4 yes 12 21.11 odd 6
441.2.g.g.67.3 12 63.41 even 6
441.2.g.g.67.4 12 9.5 odd 6
441.2.g.g.79.3 12 21.5 even 6
441.2.g.g.79.4 12 21.2 odd 6
441.2.h.g.214.3 12 3.2 odd 2
441.2.h.g.214.4 12 21.20 even 2
441.2.h.g.373.3 12 63.23 odd 6
441.2.h.g.373.4 12 63.5 even 6
1323.2.f.g.442.3 12 63.31 odd 6
1323.2.f.g.442.4 12 63.4 even 3
1323.2.f.g.883.3 12 7.3 odd 6
1323.2.f.g.883.4 12 7.4 even 3
1323.2.g.g.361.3 12 9.4 even 3
1323.2.g.g.361.4 12 63.13 odd 6
1323.2.g.g.667.3 12 7.2 even 3
1323.2.g.g.667.4 12 7.5 odd 6
1323.2.h.g.226.3 12 63.40 odd 6 inner
1323.2.h.g.226.4 12 63.58 even 3 inner
1323.2.h.g.802.3 12 7.6 odd 2 inner
1323.2.h.g.802.4 12 1.1 even 1 trivial
3969.2.a.bd.1.3 6 63.25 even 3
3969.2.a.bd.1.4 6 63.52 odd 6
3969.2.a.be.1.3 6 63.38 even 6
3969.2.a.be.1.4 6 63.11 odd 6