Properties

Label 2646.2.f.n.883.2
Level $2646$
Weight $2$
Character 2646.883
Analytic conductor $21.128$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2646,2,Mod(883,2646)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.883");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.f (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: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 883.2
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 2646.883
Dual form 2646.2.f.n.1765.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.880438 - 1.52496i) q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.880438 - 1.52496i) q^{5} -1.00000 q^{8} -1.76088 q^{10} +(3.06238 - 5.30420i) q^{11} +(0.380438 + 0.658939i) q^{13} +(-0.500000 + 0.866025i) q^{16} +6.84213 q^{17} +1.94282 q^{19} +(-0.880438 + 1.52496i) q^{20} +(-3.06238 - 5.30420i) q^{22} +(-0.210533 - 0.364654i) q^{23} +(0.949657 - 1.64485i) q^{25} +0.760877 q^{26} +(-0.732287 + 1.26836i) q^{29} +(3.85185 + 6.67160i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.42107 - 5.92546i) q^{34} -2.88564 q^{37} +(0.971410 - 1.68253i) q^{38} +(0.880438 + 1.52496i) q^{40} +(-3.47141 - 6.01266i) q^{41} +(4.33009 - 7.49994i) q^{43} -6.12476 q^{44} -0.421067 q^{46} +(-0.830095 + 1.43777i) q^{47} +(-0.949657 - 1.64485i) q^{50} +(0.380438 - 0.658939i) q^{52} -0.225450 q^{53} -10.7850 q^{55} +(0.732287 + 1.26836i) q^{58} +(-0.993163 - 1.72021i) q^{59} +(-5.17511 + 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(0.669905 - 1.16031i) q^{65} +(-3.39248 - 5.87594i) q^{67} +(-3.42107 - 5.92546i) q^{68} -10.7850 q^{71} +0.306707 q^{73} +(-1.44282 + 2.49904i) q^{74} +(-0.971410 - 1.68253i) q^{76} +(6.72257 - 11.6438i) q^{79} +1.76088 q^{80} -6.94282 q^{82} +(-1.56238 + 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +(-4.33009 - 7.49994i) q^{86} +(-3.06238 + 5.30420i) q^{88} -2.60301 q^{89} +(-0.210533 + 0.364654i) q^{92} +(0.830095 + 1.43777i) q^{94} +(-1.71053 - 2.96273i) q^{95} +(1.81806 - 3.14897i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{4} - 5 q^{5} - 6 q^{8} - 10 q^{10} + q^{11} + 2 q^{13} - 3 q^{16} + 8 q^{17} - 6 q^{19} - 5 q^{20} - q^{22} + 7 q^{23} - 2 q^{25} + 4 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} + 18 q^{37} - 3 q^{38} + 5 q^{40} - 12 q^{41} + 18 q^{43} - 2 q^{44} + 14 q^{46} + 3 q^{47} + 2 q^{50} + 2 q^{52} + 18 q^{53} - 14 q^{55} - 5 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} - 4 q^{68} - 14 q^{71} - 50 q^{73} + 9 q^{74} + 3 q^{76} + 7 q^{79} + 10 q^{80} - 24 q^{82} + 8 q^{83} + 14 q^{85} - 18 q^{86} - q^{88} + 18 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.880438 1.52496i −0.393744 0.681985i 0.599196 0.800602i \(-0.295487\pi\)
−0.992940 + 0.118618i \(0.962154\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.76088 −0.556838
\(11\) 3.06238 5.30420i 0.923343 1.59928i 0.129138 0.991627i \(-0.458779\pi\)
0.794205 0.607650i \(-0.207888\pi\)
\(12\) 0 0
\(13\) 0.380438 + 0.658939i 0.105515 + 0.182757i 0.913948 0.405831i \(-0.133018\pi\)
−0.808434 + 0.588587i \(0.799684\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.84213 1.65946 0.829731 0.558164i \(-0.188494\pi\)
0.829731 + 0.558164i \(0.188494\pi\)
\(18\) 0 0
\(19\) 1.94282 0.445713 0.222857 0.974851i \(-0.428462\pi\)
0.222857 + 0.974851i \(0.428462\pi\)
\(20\) −0.880438 + 1.52496i −0.196872 + 0.340992i
\(21\) 0 0
\(22\) −3.06238 5.30420i −0.652902 1.13086i
\(23\) −0.210533 0.364654i −0.0438992 0.0760357i 0.843241 0.537536i \(-0.180645\pi\)
−0.887140 + 0.461500i \(0.847311\pi\)
\(24\) 0 0
\(25\) 0.949657 1.64485i 0.189931 0.328971i
\(26\) 0.760877 0.149220
\(27\) 0 0
\(28\) 0 0
\(29\) −0.732287 + 1.26836i −0.135982 + 0.235528i −0.925972 0.377592i \(-0.876752\pi\)
0.789990 + 0.613120i \(0.210086\pi\)
\(30\) 0 0
\(31\) 3.85185 + 6.67160i 0.691812 + 1.19825i 0.971243 + 0.238088i \(0.0765208\pi\)
−0.279431 + 0.960166i \(0.590146\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 3.42107 5.92546i 0.586708 1.01621i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.88564 −0.474396 −0.237198 0.971461i \(-0.576229\pi\)
−0.237198 + 0.971461i \(0.576229\pi\)
\(38\) 0.971410 1.68253i 0.157584 0.272943i
\(39\) 0 0
\(40\) 0.880438 + 1.52496i 0.139210 + 0.241118i
\(41\) −3.47141 6.01266i −0.542143 0.939020i −0.998781 0.0493667i \(-0.984280\pi\)
0.456638 0.889653i \(-0.349054\pi\)
\(42\) 0 0
\(43\) 4.33009 7.49994i 0.660333 1.14373i −0.320195 0.947352i \(-0.603748\pi\)
0.980528 0.196379i \(-0.0629183\pi\)
\(44\) −6.12476 −0.923343
\(45\) 0 0
\(46\) −0.421067 −0.0620829
\(47\) −0.830095 + 1.43777i −0.121082 + 0.209720i −0.920195 0.391461i \(-0.871970\pi\)
0.799113 + 0.601181i \(0.205303\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.949657 1.64485i −0.134302 0.232617i
\(51\) 0 0
\(52\) 0.380438 0.658939i 0.0527573 0.0913783i
\(53\) −0.225450 −0.0309680 −0.0154840 0.999880i \(-0.504929\pi\)
−0.0154840 + 0.999880i \(0.504929\pi\)
\(54\) 0 0
\(55\) −10.7850 −1.45424
\(56\) 0 0
\(57\) 0 0
\(58\) 0.732287 + 1.26836i 0.0961540 + 0.166544i
\(59\) −0.993163 1.72021i −0.129299 0.223952i 0.794106 0.607779i \(-0.207939\pi\)
−0.923405 + 0.383827i \(0.874606\pi\)
\(60\) 0 0
\(61\) −5.17511 + 8.96355i −0.662605 + 1.14766i 0.317324 + 0.948317i \(0.397216\pi\)
−0.979929 + 0.199348i \(0.936118\pi\)
\(62\) 7.70370 0.978370
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.669905 1.16031i 0.0830915 0.143919i
\(66\) 0 0
\(67\) −3.39248 5.87594i −0.414457 0.717861i 0.580914 0.813965i \(-0.302695\pi\)
−0.995371 + 0.0961042i \(0.969362\pi\)
\(68\) −3.42107 5.92546i −0.414865 0.718568i
\(69\) 0 0
\(70\) 0 0
\(71\) −10.7850 −1.27994 −0.639969 0.768401i \(-0.721053\pi\)
−0.639969 + 0.768401i \(0.721053\pi\)
\(72\) 0 0
\(73\) 0.306707 0.0358973 0.0179487 0.999839i \(-0.494286\pi\)
0.0179487 + 0.999839i \(0.494286\pi\)
\(74\) −1.44282 + 2.49904i −0.167724 + 0.290507i
\(75\) 0 0
\(76\) −0.971410 1.68253i −0.111428 0.193000i
\(77\) 0 0
\(78\) 0 0
\(79\) 6.72257 11.6438i 0.756348 1.31003i −0.188353 0.982101i \(-0.560315\pi\)
0.944701 0.327932i \(-0.106352\pi\)
\(80\) 1.76088 0.196872
\(81\) 0 0
\(82\) −6.94282 −0.766706
\(83\) −1.56238 + 2.70612i −0.171494 + 0.297036i −0.938942 0.344075i \(-0.888193\pi\)
0.767449 + 0.641110i \(0.221526\pi\)
\(84\) 0 0
\(85\) −6.02408 10.4340i −0.653403 1.13173i
\(86\) −4.33009 7.49994i −0.466926 0.808740i
\(87\) 0 0
\(88\) −3.06238 + 5.30420i −0.326451 + 0.565430i
\(89\) −2.60301 −0.275919 −0.137959 0.990438i \(-0.544054\pi\)
−0.137959 + 0.990438i \(0.544054\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.210533 + 0.364654i −0.0219496 + 0.0380178i
\(93\) 0 0
\(94\) 0.830095 + 1.43777i 0.0856178 + 0.148294i
\(95\) −1.71053 2.96273i −0.175497 0.303970i
\(96\) 0 0
\(97\) 1.81806 3.14897i 0.184596 0.319729i −0.758845 0.651272i \(-0.774236\pi\)
0.943440 + 0.331543i \(0.107569\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.89931 −0.189931
\(101\) 4.00520 6.93721i 0.398532 0.690278i −0.595013 0.803716i \(-0.702853\pi\)
0.993545 + 0.113438i \(0.0361863\pi\)
\(102\) 0 0
\(103\) −3.41423 5.91362i −0.336414 0.582686i 0.647341 0.762200i \(-0.275881\pi\)
−0.983755 + 0.179514i \(0.942548\pi\)
\(104\) −0.380438 0.658939i −0.0373051 0.0646142i
\(105\) 0 0
\(106\) −0.112725 + 0.195246i −0.0109488 + 0.0189639i
\(107\) 3.54583 0.342788 0.171394 0.985203i \(-0.445173\pi\)
0.171394 + 0.985203i \(0.445173\pi\)
\(108\) 0 0
\(109\) −0.703697 −0.0674019 −0.0337010 0.999432i \(-0.510729\pi\)
−0.0337010 + 0.999432i \(0.510729\pi\)
\(110\) −5.39248 + 9.34004i −0.514152 + 0.890538i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.25116 7.36323i −0.399916 0.692674i 0.593799 0.804613i \(-0.297627\pi\)
−0.993715 + 0.111939i \(0.964294\pi\)
\(114\) 0 0
\(115\) −0.370723 + 0.642111i −0.0345701 + 0.0598772i
\(116\) 1.46457 0.135982
\(117\) 0 0
\(118\) −1.98633 −0.182856
\(119\) 0 0
\(120\) 0 0
\(121\) −13.2564 22.9607i −1.20512 2.08734i
\(122\) 5.17511 + 8.96355i 0.468532 + 0.811521i
\(123\) 0 0
\(124\) 3.85185 6.67160i 0.345906 0.599127i
\(125\) −12.1488 −1.08663
\(126\) 0 0
\(127\) −18.9532 −1.68183 −0.840913 0.541170i \(-0.817982\pi\)
−0.840913 + 0.541170i \(0.817982\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −0.669905 1.16031i −0.0587546 0.101766i
\(131\) 3.64652 + 6.31595i 0.318598 + 0.551827i 0.980196 0.198031i \(-0.0634548\pi\)
−0.661598 + 0.749859i \(0.730121\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.78495 −0.586131
\(135\) 0 0
\(136\) −6.84213 −0.586708
\(137\) −4.09097 + 7.08577i −0.349515 + 0.605378i −0.986163 0.165776i \(-0.946987\pi\)
0.636648 + 0.771154i \(0.280320\pi\)
\(138\) 0 0
\(139\) 6.23229 + 10.7946i 0.528616 + 0.915589i 0.999443 + 0.0333640i \(0.0106220\pi\)
−0.470828 + 0.882225i \(0.656045\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.39248 + 9.34004i −0.452527 + 0.783799i
\(143\) 4.66019 0.389705
\(144\) 0 0
\(145\) 2.57893 0.214169
\(146\) 0.153353 0.265616i 0.0126916 0.0219825i
\(147\) 0 0
\(148\) 1.44282 + 2.49904i 0.118599 + 0.205420i
\(149\) 4.41423 + 7.64567i 0.361628 + 0.626358i 0.988229 0.152982i \(-0.0488878\pi\)
−0.626601 + 0.779340i \(0.715554\pi\)
\(150\) 0 0
\(151\) 7.49316 12.9785i 0.609785 1.05618i −0.381491 0.924373i \(-0.624589\pi\)
0.991276 0.131806i \(-0.0420775\pi\)
\(152\) −1.94282 −0.157584
\(153\) 0 0
\(154\) 0 0
\(155\) 6.78263 11.7479i 0.544794 0.943611i
\(156\) 0 0
\(157\) 9.49028 + 16.4377i 0.757407 + 1.31187i 0.944169 + 0.329462i \(0.106868\pi\)
−0.186761 + 0.982405i \(0.559799\pi\)
\(158\) −6.72257 11.6438i −0.534819 0.926334i
\(159\) 0 0
\(160\) 0.880438 1.52496i 0.0696048 0.120559i
\(161\) 0 0
\(162\) 0 0
\(163\) 15.0377 1.17785 0.588924 0.808189i \(-0.299552\pi\)
0.588924 + 0.808189i \(0.299552\pi\)
\(164\) −3.47141 + 6.01266i −0.271072 + 0.469510i
\(165\) 0 0
\(166\) 1.56238 + 2.70612i 0.121264 + 0.210036i
\(167\) 0.572097 + 0.990901i 0.0442702 + 0.0766782i 0.887311 0.461171i \(-0.152570\pi\)
−0.843041 + 0.537849i \(0.819237\pi\)
\(168\) 0 0
\(169\) 6.21053 10.7570i 0.477733 0.827458i
\(170\) −12.0482 −0.924051
\(171\) 0 0
\(172\) −8.66019 −0.660333
\(173\) −0.248838 + 0.431001i −0.0189188 + 0.0327684i −0.875330 0.483526i \(-0.839356\pi\)
0.856411 + 0.516295i \(0.172689\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.06238 + 5.30420i 0.230836 + 0.399819i
\(177\) 0 0
\(178\) −1.30150 + 2.25427i −0.0975519 + 0.168965i
\(179\) 8.82846 0.659870 0.329935 0.944004i \(-0.392973\pi\)
0.329935 + 0.944004i \(0.392973\pi\)
\(180\) 0 0
\(181\) −1.32941 −0.0988140 −0.0494070 0.998779i \(-0.515733\pi\)
−0.0494070 + 0.998779i \(0.515733\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.210533 + 0.364654i 0.0155207 + 0.0268827i
\(185\) 2.54063 + 4.40050i 0.186791 + 0.323531i
\(186\) 0 0
\(187\) 20.9532 36.2920i 1.53225 2.65394i
\(188\) 1.66019 0.121082
\(189\) 0 0
\(190\) −3.42107 −0.248190
\(191\) −8.08414 + 14.0021i −0.584947 + 1.01316i 0.409934 + 0.912115i \(0.365552\pi\)
−0.994882 + 0.101044i \(0.967782\pi\)
\(192\) 0 0
\(193\) 7.08414 + 12.2701i 0.509927 + 0.883220i 0.999934 + 0.0115011i \(0.00366101\pi\)
−0.490007 + 0.871719i \(0.663006\pi\)
\(194\) −1.81806 3.14897i −0.130529 0.226083i
\(195\) 0 0
\(196\) 0 0
\(197\) −15.8421 −1.12871 −0.564353 0.825534i \(-0.690874\pi\)
−0.564353 + 0.825534i \(0.690874\pi\)
\(198\) 0 0
\(199\) −8.94282 −0.633940 −0.316970 0.948436i \(-0.602665\pi\)
−0.316970 + 0.948436i \(0.602665\pi\)
\(200\) −0.949657 + 1.64485i −0.0671509 + 0.116309i
\(201\) 0 0
\(202\) −4.00520 6.93721i −0.281805 0.488101i
\(203\) 0 0
\(204\) 0 0
\(205\) −6.11273 + 10.5876i −0.426931 + 0.739467i
\(206\) −6.82846 −0.475761
\(207\) 0 0
\(208\) −0.760877 −0.0527573
\(209\) 5.94966 10.3051i 0.411546 0.712819i
\(210\) 0 0
\(211\) 11.3856 + 19.7205i 0.783820 + 1.35762i 0.929702 + 0.368314i \(0.120065\pi\)
−0.145882 + 0.989302i \(0.546602\pi\)
\(212\) 0.112725 + 0.195246i 0.00774199 + 0.0134095i
\(213\) 0 0
\(214\) 1.77292 3.07078i 0.121194 0.209914i
\(215\) −15.2495 −1.04001
\(216\) 0 0
\(217\) 0 0
\(218\) −0.351848 + 0.609419i −0.0238302 + 0.0412751i
\(219\) 0 0
\(220\) 5.39248 + 9.34004i 0.363561 + 0.629706i
\(221\) 2.60301 + 4.50855i 0.175097 + 0.303278i
\(222\) 0 0
\(223\) 6.44282 11.1593i 0.431443 0.747281i −0.565555 0.824711i \(-0.691338\pi\)
0.996998 + 0.0774293i \(0.0246712\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −8.50232 −0.565566
\(227\) −10.9984 + 19.0497i −0.729987 + 1.26437i 0.226901 + 0.973918i \(0.427141\pi\)
−0.956888 + 0.290457i \(0.906193\pi\)
\(228\) 0 0
\(229\) −1.89931 3.28971i −0.125510 0.217390i 0.796422 0.604741i \(-0.206723\pi\)
−0.921932 + 0.387351i \(0.873390\pi\)
\(230\) 0.370723 + 0.642111i 0.0244448 + 0.0423396i
\(231\) 0 0
\(232\) 0.732287 1.26836i 0.0480770 0.0832718i
\(233\) −6.67059 −0.437005 −0.218503 0.975836i \(-0.570117\pi\)
−0.218503 + 0.975836i \(0.570117\pi\)
\(234\) 0 0
\(235\) 2.92339 0.190701
\(236\) −0.993163 + 1.72021i −0.0646494 + 0.111976i
\(237\) 0 0
\(238\) 0 0
\(239\) 7.82038 + 13.5453i 0.505858 + 0.876172i 0.999977 + 0.00677786i \(0.00215748\pi\)
−0.494119 + 0.869394i \(0.664509\pi\)
\(240\) 0 0
\(241\) 10.7060 18.5434i 0.689635 1.19448i −0.282320 0.959320i \(-0.591104\pi\)
0.971956 0.235163i \(-0.0755625\pi\)
\(242\) −26.5127 −1.70430
\(243\) 0 0
\(244\) 10.3502 0.662605
\(245\) 0 0
\(246\) 0 0
\(247\) 0.739123 + 1.28020i 0.0470293 + 0.0814571i
\(248\) −3.85185 6.67160i −0.244593 0.423647i
\(249\) 0 0
\(250\) −6.07442 + 10.5212i −0.384180 + 0.665419i
\(251\) −23.6030 −1.48981 −0.744904 0.667171i \(-0.767505\pi\)
−0.744904 + 0.667171i \(0.767505\pi\)
\(252\) 0 0
\(253\) −2.57893 −0.162136
\(254\) −9.47661 + 16.4140i −0.594616 + 1.02990i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.1300 17.5456i −0.631890 1.09447i −0.987165 0.159704i \(-0.948946\pi\)
0.355275 0.934762i \(-0.384387\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.33981 −0.0830915
\(261\) 0 0
\(262\) 7.29303 0.450565
\(263\) −11.2443 + 19.4757i −0.693355 + 1.20093i 0.277377 + 0.960761i \(0.410535\pi\)
−0.970732 + 0.240165i \(0.922799\pi\)
\(264\) 0 0
\(265\) 0.198495 + 0.343803i 0.0121935 + 0.0211197i
\(266\) 0 0
\(267\) 0 0
\(268\) −3.39248 + 5.87594i −0.207228 + 0.358930i
\(269\) 25.3412 1.54508 0.772540 0.634966i \(-0.218986\pi\)
0.772540 + 0.634966i \(0.218986\pi\)
\(270\) 0 0
\(271\) −13.7576 −0.835715 −0.417858 0.908513i \(-0.637219\pi\)
−0.417858 + 0.908513i \(0.637219\pi\)
\(272\) −3.42107 + 5.92546i −0.207433 + 0.359284i
\(273\) 0 0
\(274\) 4.09097 + 7.08577i 0.247145 + 0.428067i
\(275\) −5.81642 10.0743i −0.350743 0.607505i
\(276\) 0 0
\(277\) 1.64132 2.84284i 0.0986171 0.170810i −0.812495 0.582968i \(-0.801891\pi\)
0.911112 + 0.412158i \(0.135225\pi\)
\(278\) 12.4646 0.747575
\(279\) 0 0
\(280\) 0 0
\(281\) −0.634479 + 1.09895i −0.0378498 + 0.0655578i −0.884330 0.466863i \(-0.845384\pi\)
0.846480 + 0.532421i \(0.178718\pi\)
\(282\) 0 0
\(283\) −4.09617 7.09478i −0.243492 0.421741i 0.718214 0.695822i \(-0.244960\pi\)
−0.961707 + 0.274081i \(0.911626\pi\)
\(284\) 5.39248 + 9.34004i 0.319985 + 0.554230i
\(285\) 0 0
\(286\) 2.33009 4.03584i 0.137781 0.238644i
\(287\) 0 0
\(288\) 0 0
\(289\) 29.8148 1.75381
\(290\) 1.28947 2.23342i 0.0757201 0.131151i
\(291\) 0 0
\(292\) −0.153353 0.265616i −0.00897433 0.0155440i
\(293\) 7.72545 + 13.3809i 0.451326 + 0.781719i 0.998469 0.0553202i \(-0.0176180\pi\)
−0.547143 + 0.837039i \(0.684285\pi\)
\(294\) 0 0
\(295\) −1.74884 + 3.02908i −0.101821 + 0.176360i
\(296\) 2.88564 0.167724
\(297\) 0 0
\(298\) 8.82846 0.511419
\(299\) 0.160190 0.277457i 0.00926402 0.0160458i
\(300\) 0 0
\(301\) 0 0
\(302\) −7.49316 12.9785i −0.431183 0.746831i
\(303\) 0 0
\(304\) −0.971410 + 1.68253i −0.0557142 + 0.0964998i
\(305\) 18.2255 1.04359
\(306\) 0 0
\(307\) −4.89931 −0.279619 −0.139809 0.990178i \(-0.544649\pi\)
−0.139809 + 0.990178i \(0.544649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −6.78263 11.7479i −0.385228 0.667234i
\(311\) 3.84501 + 6.65976i 0.218031 + 0.377640i 0.954206 0.299151i \(-0.0967034\pi\)
−0.736175 + 0.676791i \(0.763370\pi\)
\(312\) 0 0
\(313\) −0.861564 + 1.49227i −0.0486985 + 0.0843482i −0.889347 0.457233i \(-0.848841\pi\)
0.840649 + 0.541581i \(0.182174\pi\)
\(314\) 18.9806 1.07114
\(315\) 0 0
\(316\) −13.4451 −0.756348
\(317\) 16.6014 28.7544i 0.932426 1.61501i 0.153266 0.988185i \(-0.451021\pi\)
0.779161 0.626824i \(-0.215646\pi\)
\(318\) 0 0
\(319\) 4.48508 + 7.76839i 0.251116 + 0.434946i
\(320\) −0.880438 1.52496i −0.0492180 0.0852481i
\(321\) 0 0
\(322\) 0 0
\(323\) 13.2930 0.739644
\(324\) 0 0
\(325\) 1.44514 0.0801621
\(326\) 7.51887 13.0231i 0.416432 0.721281i
\(327\) 0 0
\(328\) 3.47141 + 6.01266i 0.191677 + 0.331994i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.44445 + 2.50187i −0.0793944 + 0.137515i −0.902989 0.429664i \(-0.858632\pi\)
0.823594 + 0.567179i \(0.191965\pi\)
\(332\) 3.12476 0.171494
\(333\) 0 0
\(334\) 1.14419 0.0626075
\(335\) −5.97373 + 10.3468i −0.326380 + 0.565307i
\(336\) 0 0
\(337\) −4.36156 7.55445i −0.237590 0.411517i 0.722433 0.691441i \(-0.243024\pi\)
−0.960022 + 0.279924i \(0.909691\pi\)
\(338\) −6.21053 10.7570i −0.337808 0.585101i
\(339\) 0 0
\(340\) −6.02408 + 10.4340i −0.326701 + 0.565863i
\(341\) 47.1833 2.55512
\(342\) 0 0
\(343\) 0 0
\(344\) −4.33009 + 7.49994i −0.233463 + 0.404370i
\(345\) 0 0
\(346\) 0.248838 + 0.431001i 0.0133776 + 0.0231707i
\(347\) 4.84733 + 8.39583i 0.260219 + 0.450712i 0.966300 0.257419i \(-0.0828720\pi\)
−0.706081 + 0.708131i \(0.749539\pi\)
\(348\) 0 0
\(349\) −14.1992 + 24.5937i −0.760065 + 1.31647i 0.182752 + 0.983159i \(0.441500\pi\)
−0.942817 + 0.333312i \(0.891834\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.12476 0.326451
\(353\) 2.19686 3.80507i 0.116927 0.202524i −0.801621 0.597832i \(-0.796029\pi\)
0.918548 + 0.395308i \(0.129362\pi\)
\(354\) 0 0
\(355\) 9.49549 + 16.4467i 0.503968 + 0.872898i
\(356\) 1.30150 + 2.25427i 0.0689796 + 0.119476i
\(357\) 0 0
\(358\) 4.41423 7.64567i 0.233299 0.404086i
\(359\) 32.1592 1.69730 0.848650 0.528955i \(-0.177416\pi\)
0.848650 + 0.528955i \(0.177416\pi\)
\(360\) 0 0
\(361\) −15.2255 −0.801339
\(362\) −0.664703 + 1.15130i −0.0349360 + 0.0605110i
\(363\) 0 0
\(364\) 0 0
\(365\) −0.270036 0.467717i −0.0141343 0.0244814i
\(366\) 0 0
\(367\) 17.3015 29.9671i 0.903131 1.56427i 0.0797249 0.996817i \(-0.474596\pi\)
0.823406 0.567452i \(-0.192071\pi\)
\(368\) 0.421067 0.0219496
\(369\) 0 0
\(370\) 5.08126 0.264162
\(371\) 0 0
\(372\) 0 0
\(373\) −5.48796 9.50543i −0.284156 0.492172i 0.688248 0.725475i \(-0.258380\pi\)
−0.972404 + 0.233303i \(0.925047\pi\)
\(374\) −20.9532 36.2920i −1.08347 1.87662i
\(375\) 0 0
\(376\) 0.830095 1.43777i 0.0428089 0.0741472i
\(377\) −1.11436 −0.0573925
\(378\) 0 0
\(379\) 33.9877 1.74583 0.872916 0.487871i \(-0.162226\pi\)
0.872916 + 0.487871i \(0.162226\pi\)
\(380\) −1.71053 + 2.96273i −0.0877485 + 0.151985i
\(381\) 0 0
\(382\) 8.08414 + 14.0021i 0.413620 + 0.716411i
\(383\) 10.5120 + 18.2074i 0.537140 + 0.930354i 0.999056 + 0.0434304i \(0.0138287\pi\)
−0.461916 + 0.886923i \(0.652838\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.1683 0.721146
\(387\) 0 0
\(388\) −3.63611 −0.184596
\(389\) 6.86909 11.8976i 0.348277 0.603233i −0.637667 0.770312i \(-0.720100\pi\)
0.985943 + 0.167080i \(0.0534337\pi\)
\(390\) 0 0
\(391\) −1.44050 2.49501i −0.0728491 0.126178i
\(392\) 0 0
\(393\) 0 0
\(394\) −7.92107 + 13.7197i −0.399058 + 0.691188i
\(395\) −23.6752 −1.19123
\(396\) 0 0
\(397\) −7.15787 −0.359243 −0.179622 0.983736i \(-0.557487\pi\)
−0.179622 + 0.983736i \(0.557487\pi\)
\(398\) −4.47141 + 7.74471i −0.224132 + 0.388207i
\(399\) 0 0
\(400\) 0.949657 + 1.64485i 0.0474828 + 0.0822427i
\(401\) −4.63968 8.03616i −0.231695 0.401307i 0.726612 0.687048i \(-0.241094\pi\)
−0.958307 + 0.285741i \(0.907760\pi\)
\(402\) 0 0
\(403\) −2.93078 + 5.07626i −0.145993 + 0.252867i
\(404\) −8.01040 −0.398532
\(405\) 0 0
\(406\) 0 0
\(407\) −8.83693 + 15.3060i −0.438030 + 0.758691i
\(408\) 0 0
\(409\) 7.58414 + 13.1361i 0.375011 + 0.649539i 0.990329 0.138741i \(-0.0443055\pi\)
−0.615317 + 0.788279i \(0.710972\pi\)
\(410\) 6.11273 + 10.5876i 0.301886 + 0.522882i
\(411\) 0 0
\(412\) −3.41423 + 5.91362i −0.168207 + 0.291343i
\(413\) 0 0
\(414\) 0 0
\(415\) 5.50232 0.270098
\(416\) −0.380438 + 0.658939i −0.0186525 + 0.0323071i
\(417\) 0 0
\(418\) −5.94966 10.3051i −0.291007 0.504039i
\(419\) −4.16827 7.21966i −0.203633 0.352703i 0.746063 0.665875i \(-0.231942\pi\)
−0.949696 + 0.313172i \(0.898608\pi\)
\(420\) 0 0
\(421\) −3.50232 + 6.06620i −0.170693 + 0.295649i −0.938662 0.344838i \(-0.887934\pi\)
0.767969 + 0.640486i \(0.221267\pi\)
\(422\) 22.7713 1.10849
\(423\) 0 0
\(424\) 0.225450 0.0109488
\(425\) 6.49768 11.2543i 0.315184 0.545914i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.77292 3.07078i −0.0856971 0.148432i
\(429\) 0 0
\(430\) −7.62476 + 13.2065i −0.367699 + 0.636873i
\(431\) −3.45090 −0.166224 −0.0831120 0.996540i \(-0.526486\pi\)
−0.0831120 + 0.996540i \(0.526486\pi\)
\(432\) 0 0
\(433\) −28.2599 −1.35809 −0.679043 0.734099i \(-0.737605\pi\)
−0.679043 + 0.734099i \(0.737605\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.351848 + 0.609419i 0.0168505 + 0.0291859i
\(437\) −0.409028 0.708458i −0.0195665 0.0338901i
\(438\) 0 0
\(439\) −14.4480 + 25.0247i −0.689566 + 1.19436i 0.282412 + 0.959293i \(0.408866\pi\)
−0.971978 + 0.235071i \(0.924468\pi\)
\(440\) 10.7850 0.514152
\(441\) 0 0
\(442\) 5.20602 0.247625
\(443\) −6.88044 + 11.9173i −0.326899 + 0.566207i −0.981895 0.189426i \(-0.939337\pi\)
0.654995 + 0.755633i \(0.272671\pi\)
\(444\) 0 0
\(445\) 2.29179 + 3.96950i 0.108641 + 0.188172i
\(446\) −6.44282 11.1593i −0.305076 0.528408i
\(447\) 0 0
\(448\) 0 0
\(449\) 20.2003 0.953309 0.476655 0.879091i \(-0.341849\pi\)
0.476655 + 0.879091i \(0.341849\pi\)
\(450\) 0 0
\(451\) −42.5231 −2.00234
\(452\) −4.25116 + 7.36323i −0.199958 + 0.346337i
\(453\) 0 0
\(454\) 10.9984 + 19.0497i 0.516179 + 0.894048i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0149 + 17.3463i −0.468478 + 0.811428i −0.999351 0.0360237i \(-0.988531\pi\)
0.530873 + 0.847451i \(0.321864\pi\)
\(458\) −3.79863 −0.177498
\(459\) 0 0
\(460\) 0.741446 0.0345701
\(461\) 5.97661 10.3518i 0.278359 0.482131i −0.692618 0.721304i \(-0.743543\pi\)
0.970977 + 0.239173i \(0.0768763\pi\)
\(462\) 0 0
\(463\) 6.64527 + 11.5100i 0.308832 + 0.534913i 0.978107 0.208102i \(-0.0667286\pi\)
−0.669275 + 0.743015i \(0.733395\pi\)
\(464\) −0.732287 1.26836i −0.0339956 0.0588820i
\(465\) 0 0
\(466\) −3.33530 + 5.77690i −0.154505 + 0.267610i
\(467\) 11.2301 0.519667 0.259833 0.965653i \(-0.416332\pi\)
0.259833 + 0.965653i \(0.416332\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.46169 2.53173i 0.0674230 0.116780i
\(471\) 0 0
\(472\) 0.993163 + 1.72021i 0.0457141 + 0.0791791i
\(473\) −26.5208 45.9354i −1.21943 2.11211i
\(474\) 0 0
\(475\) 1.84501 3.19565i 0.0846550 0.146627i
\(476\) 0 0
\(477\) 0 0
\(478\) 15.6408 0.715392
\(479\) 16.3135 28.2559i 0.745385 1.29104i −0.204630 0.978839i \(-0.565599\pi\)
0.950015 0.312205i \(-0.101068\pi\)
\(480\) 0 0
\(481\) −1.09781 1.90146i −0.0500557 0.0866991i
\(482\) −10.7060 18.5434i −0.487646 0.844627i
\(483\) 0 0
\(484\) −13.2564 + 22.9607i −0.602562 + 1.04367i
\(485\) −6.40275 −0.290734
\(486\) 0 0
\(487\) −3.69794 −0.167570 −0.0837848 0.996484i \(-0.526701\pi\)
−0.0837848 + 0.996484i \(0.526701\pi\)
\(488\) 5.17511 8.96355i 0.234266 0.405761i
\(489\) 0 0
\(490\) 0 0
\(491\) 18.7804 + 32.5287i 0.847549 + 1.46800i 0.883389 + 0.468641i \(0.155256\pi\)
−0.0358393 + 0.999358i \(0.511410\pi\)
\(492\) 0 0
\(493\) −5.01040 + 8.67827i −0.225657 + 0.390850i
\(494\) 1.47825 0.0665095
\(495\) 0 0
\(496\) −7.70370 −0.345906
\(497\) 0 0
\(498\) 0 0
\(499\) 15.8977 + 27.5356i 0.711678 + 1.23266i 0.964227 + 0.265078i \(0.0853977\pi\)
−0.252549 + 0.967584i \(0.581269\pi\)
\(500\) 6.07442 + 10.5212i 0.271656 + 0.470523i
\(501\) 0 0
\(502\) −11.8015 + 20.4408i −0.526727 + 0.912318i
\(503\) 30.8252 1.37443 0.687214 0.726455i \(-0.258834\pi\)
0.687214 + 0.726455i \(0.258834\pi\)
\(504\) 0 0
\(505\) −14.1053 −0.627679
\(506\) −1.28947 + 2.23342i −0.0573238 + 0.0992877i
\(507\) 0 0
\(508\) 9.47661 + 16.4140i 0.420457 + 0.728252i
\(509\) −4.00808 6.94220i −0.177655 0.307708i 0.763422 0.645900i \(-0.223518\pi\)
−0.941077 + 0.338193i \(0.890184\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −20.2599 −0.893627
\(515\) −6.01204 + 10.4132i −0.264922 + 0.458858i
\(516\) 0 0
\(517\) 5.08414 + 8.80598i 0.223600 + 0.387287i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.669905 + 1.16031i −0.0293773 + 0.0508829i
\(521\) −29.7292 −1.30246 −0.651229 0.758881i \(-0.725746\pi\)
−0.651229 + 0.758881i \(0.725746\pi\)
\(522\) 0 0
\(523\) 26.9396 1.17798 0.588992 0.808139i \(-0.299525\pi\)
0.588992 + 0.808139i \(0.299525\pi\)
\(524\) 3.64652 6.31595i 0.159299 0.275914i
\(525\) 0 0
\(526\) 11.2443 + 19.4757i 0.490276 + 0.849183i
\(527\) 26.3549 + 45.6480i 1.14804 + 1.98846i
\(528\) 0 0
\(529\) 11.4114 19.7650i 0.496146 0.859350i
\(530\) 0.396990 0.0172441
\(531\) 0 0
\(532\) 0 0
\(533\) 2.64132 4.57489i 0.114408 0.198161i
\(534\) 0 0
\(535\) −3.12188 5.40726i −0.134971 0.233776i
\(536\) 3.39248 + 5.87594i 0.146533 + 0.253802i
\(537\) 0 0
\(538\) 12.6706 21.9461i 0.546268 0.946164i
\(539\) 0 0
\(540\) 0 0
\(541\) −14.3114 −0.615293 −0.307647 0.951501i \(-0.599541\pi\)
−0.307647 + 0.951501i \(0.599541\pi\)
\(542\) −6.87880 + 11.9144i −0.295470 + 0.511769i
\(543\) 0 0
\(544\) 3.42107 + 5.92546i 0.146677 + 0.254052i
\(545\) 0.619562 + 1.07311i 0.0265391 + 0.0459671i
\(546\) 0 0
\(547\) 1.02463 1.77471i 0.0438101 0.0758813i −0.843289 0.537461i \(-0.819384\pi\)
0.887099 + 0.461579i \(0.152717\pi\)
\(548\) 8.18194 0.349515
\(549\) 0 0
\(550\) −11.6328 −0.496026
\(551\) −1.42270 + 2.46419i −0.0606091 + 0.104978i
\(552\) 0 0
\(553\) 0 0
\(554\) −1.64132 2.84284i −0.0697328 0.120781i
\(555\) 0 0
\(556\) 6.23229 10.7946i 0.264308 0.457795i
\(557\) 17.6868 0.749412 0.374706 0.927144i \(-0.377744\pi\)
0.374706 + 0.927144i \(0.377744\pi\)
\(558\) 0 0
\(559\) 6.58934 0.278699
\(560\) 0 0
\(561\) 0 0
\(562\) 0.634479 + 1.09895i 0.0267639 + 0.0463564i
\(563\) −0.468531 0.811520i −0.0197462 0.0342015i 0.855983 0.517003i \(-0.172952\pi\)
−0.875730 + 0.482802i \(0.839619\pi\)
\(564\) 0 0
\(565\) −7.48577 + 12.9657i −0.314929 + 0.545473i
\(566\) −8.19235 −0.344350
\(567\) 0 0
\(568\) 10.7850 0.452527
\(569\) 11.7632 20.3745i 0.493139 0.854142i −0.506830 0.862046i \(-0.669183\pi\)
0.999969 + 0.00790437i \(0.00251607\pi\)
\(570\) 0 0
\(571\) 0.242002 + 0.419160i 0.0101275 + 0.0175413i 0.871045 0.491204i \(-0.163443\pi\)
−0.860917 + 0.508745i \(0.830110\pi\)
\(572\) −2.33009 4.03584i −0.0974262 0.168747i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.799737 −0.0333514
\(576\) 0 0
\(577\) −4.46130 −0.185727 −0.0928633 0.995679i \(-0.529602\pi\)
−0.0928633 + 0.995679i \(0.529602\pi\)
\(578\) 14.9074 25.8204i 0.620066 1.07399i
\(579\) 0 0
\(580\) −1.28947 2.23342i −0.0535422 0.0927378i
\(581\) 0 0
\(582\) 0 0
\(583\) −0.690415 + 1.19583i −0.0285941 + 0.0495264i
\(584\) −0.306707 −0.0126916
\(585\) 0 0
\(586\) 15.4509 0.638271
\(587\) 8.31518 14.4023i 0.343204 0.594447i −0.641822 0.766854i \(-0.721821\pi\)
0.985026 + 0.172407i \(0.0551544\pi\)
\(588\) 0 0
\(589\) 7.48345 + 12.9617i 0.308350 + 0.534078i
\(590\) 1.74884 + 3.02908i 0.0719985 + 0.124705i
\(591\) 0 0
\(592\) 1.44282 2.49904i 0.0592995 0.102710i
\(593\) −41.5264 −1.70528 −0.852642 0.522495i \(-0.825001\pi\)
−0.852642 + 0.522495i \(0.825001\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.41423 7.64567i 0.180814 0.313179i
\(597\) 0 0
\(598\) −0.160190 0.277457i −0.00655065 0.0113461i
\(599\) 7.53831 + 13.0567i 0.308007 + 0.533483i 0.977926 0.208950i \(-0.0670047\pi\)
−0.669919 + 0.742434i \(0.733671\pi\)
\(600\) 0 0
\(601\) 8.05555 13.9526i 0.328593 0.569139i −0.653640 0.756805i \(-0.726759\pi\)
0.982233 + 0.187666i \(0.0600924\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −14.9863 −0.609785
\(605\) −23.3428 + 40.4310i −0.949021 + 1.64375i
\(606\) 0 0
\(607\) 9.78659 + 16.9509i 0.397225 + 0.688014i 0.993382 0.114853i \(-0.0366398\pi\)
−0.596157 + 0.802868i \(0.703306\pi\)
\(608\) 0.971410 + 1.68253i 0.0393959 + 0.0682357i
\(609\) 0 0
\(610\) 9.11273 15.7837i 0.368963 0.639063i
\(611\) −1.26320 −0.0511036
\(612\) 0 0
\(613\) 5.55159 0.224226 0.112113 0.993695i \(-0.464238\pi\)
0.112113 + 0.993695i \(0.464238\pi\)
\(614\) −2.44966 + 4.24293i −0.0988601 + 0.171231i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.634479 1.09895i −0.0255431 0.0442420i 0.852971 0.521958i \(-0.174798\pi\)
−0.878514 + 0.477716i \(0.841465\pi\)
\(618\) 0 0
\(619\) 2.25116 3.89913i 0.0904818 0.156719i −0.817232 0.576309i \(-0.804493\pi\)
0.907714 + 0.419589i \(0.137826\pi\)
\(620\) −13.5653 −0.544794
\(621\) 0 0
\(622\) 7.69002 0.308342
\(623\) 0 0
\(624\) 0 0
\(625\) 5.94802 + 10.3023i 0.237921 + 0.412091i
\(626\) 0.861564 + 1.49227i 0.0344350 + 0.0596432i
\(627\) 0 0
\(628\) 9.49028 16.4377i 0.378704 0.655934i
\(629\) −19.7439 −0.787242
\(630\) 0 0
\(631\) −1.69905 −0.0676381 −0.0338191 0.999428i \(-0.510767\pi\)
−0.0338191 + 0.999428i \(0.510767\pi\)
\(632\) −6.72257 + 11.6438i −0.267410 + 0.463167i
\(633\) 0 0
\(634\) −16.6014 28.7544i −0.659325 1.14198i
\(635\) 16.6871 + 28.9030i 0.662209 + 1.14698i
\(636\) 0 0
\(637\) 0 0
\(638\) 8.97017 0.355132
\(639\) 0 0
\(640\) −1.76088 −0.0696048
\(641\) −0.474289 + 0.821492i −0.0187333 + 0.0324470i −0.875240 0.483689i \(-0.839297\pi\)
0.856507 + 0.516136i \(0.172630\pi\)
\(642\) 0 0
\(643\) 9.84897 + 17.0589i 0.388405 + 0.672738i 0.992235 0.124375i \(-0.0396927\pi\)
−0.603830 + 0.797113i \(0.706359\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.64652 11.5121i 0.261504 0.452938i
\(647\) −23.4542 −0.922079 −0.461039 0.887380i \(-0.652523\pi\)
−0.461039 + 0.887380i \(0.652523\pi\)
\(648\) 0 0
\(649\) −12.1658 −0.477549
\(650\) 0.722572 1.25153i 0.0283416 0.0490891i
\(651\) 0 0
\(652\) −7.51887 13.0231i −0.294462 0.510023i
\(653\) 11.3954 + 19.7373i 0.445935 + 0.772382i 0.998117 0.0613420i \(-0.0195380\pi\)
−0.552182 + 0.833724i \(0.686205\pi\)
\(654\) 0 0
\(655\) 6.42107 11.1216i 0.250892 0.434557i
\(656\) 6.94282 0.271072
\(657\) 0 0
\(658\) 0 0
\(659\) 13.2398 22.9320i 0.515750 0.893305i −0.484083 0.875022i \(-0.660847\pi\)
0.999833 0.0182828i \(-0.00581993\pi\)
\(660\) 0 0
\(661\) −13.3691 23.1559i −0.519997 0.900662i −0.999730 0.0232469i \(-0.992600\pi\)
0.479732 0.877415i \(-0.340734\pi\)
\(662\) 1.44445 + 2.50187i 0.0561403 + 0.0972379i
\(663\) 0 0
\(664\) 1.56238 2.70612i 0.0606322 0.105018i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.616683 0.0238781
\(668\) 0.572097 0.990901i 0.0221351 0.0383391i
\(669\) 0 0
\(670\) 5.97373 + 10.3468i 0.230785 + 0.399732i
\(671\) 31.6963 + 54.8996i 1.22362 + 2.11938i
\(672\) 0 0
\(673\) −10.3856 + 17.9885i −0.400337 + 0.693404i −0.993766 0.111482i \(-0.964440\pi\)
0.593429 + 0.804886i \(0.297774\pi\)
\(674\) −8.72313 −0.336002
\(675\) 0 0
\(676\) −12.4211 −0.477733
\(677\) 10.3490 17.9249i 0.397743 0.688911i −0.595704 0.803204i \(-0.703127\pi\)
0.993447 + 0.114293i \(0.0364602\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6.02408 + 10.4340i 0.231013 + 0.400126i
\(681\) 0 0
\(682\) 23.5917 40.8620i 0.903371 1.56469i
\(683\) 28.5836 1.09372 0.546860 0.837224i \(-0.315823\pi\)
0.546860 + 0.837224i \(0.315823\pi\)
\(684\) 0 0
\(685\) 14.4074 0.550478
\(686\) 0 0
\(687\) 0 0
\(688\) 4.33009 + 7.49994i 0.165083 + 0.285933i
\(689\) −0.0857699 0.148558i −0.00326757 0.00565960i
\(690\) 0 0
\(691\) −3.34897 + 5.80059i −0.127401 + 0.220665i −0.922669 0.385593i \(-0.873997\pi\)
0.795268 + 0.606258i \(0.207330\pi\)
\(692\) 0.497677 0.0189188
\(693\) 0 0
\(694\) 9.69467 0.368005
\(695\) 10.9743 19.0080i 0.416278 0.721016i
\(696\) 0 0
\(697\) −23.7518 41.1394i −0.899665 1.55827i
\(698\) 14.1992 + 24.5937i 0.537447 + 0.930886i
\(699\) 0 0
\(700\) 0 0
\(701\) 25.1442 0.949683 0.474842 0.880071i \(-0.342505\pi\)
0.474842 + 0.880071i \(0.342505\pi\)
\(702\) 0 0
\(703\) −5.60628 −0.211445
\(704\) 3.06238 5.30420i 0.115418 0.199910i
\(705\) 0 0
\(706\) −2.19686 3.80507i −0.0826799 0.143206i
\(707\) 0 0
\(708\) 0 0
\(709\) −4.43310 + 7.67836i −0.166489 + 0.288367i −0.937183 0.348838i \(-0.886576\pi\)
0.770694 + 0.637205i \(0.219910\pi\)
\(710\) 18.9910 0.712719
\(711\) 0 0
\(712\) 2.60301 0.0975519
\(713\) 1.62188 2.80919i 0.0607401 0.105205i
\(714\) 0 0
\(715\) −4.10301 7.10662i −0.153444 0.265773i
\(716\) −4.41423 7.64567i −0.164968 0.285732i
\(717\) 0 0
\(718\) 16.0796 27.8507i 0.600086 1.03938i
\(719\) −23.6030 −0.880244 −0.440122 0.897938i \(-0.645065\pi\)
−0.440122 + 0.897938i \(0.645065\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −7.61273 + 13.1856i −0.283316 + 0.490718i
\(723\) 0 0
\(724\) 0.664703 + 1.15130i 0.0247035 + 0.0427877i
\(725\) 1.39084 + 2.40901i 0.0516546 + 0.0894683i
\(726\) 0 0
\(727\) −3.25692 + 5.64115i −0.120792 + 0.209219i −0.920080 0.391730i \(-0.871877\pi\)
0.799288 + 0.600948i \(0.205210\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −0.540073 −0.0199890
\(731\) 29.6271 51.3156i 1.09580 1.89798i
\(732\) 0 0
\(733\) −11.5991 20.0901i −0.428421 0.742047i 0.568312 0.822813i \(-0.307597\pi\)
−0.996733 + 0.0807664i \(0.974263\pi\)
\(734\) −17.3015 29.9671i −0.638610 1.10611i
\(735\) 0 0
\(736\) 0.210533 0.364654i 0.00776036 0.0134413i
\(737\) −41.5562 −1.53074
\(738\) 0 0
\(739\) 15.1568 0.557550 0.278775 0.960356i \(-0.410072\pi\)
0.278775 + 0.960356i \(0.410072\pi\)
\(740\) 2.54063 4.40050i 0.0933954 0.161765i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.21737 + 9.03675i 0.191407 + 0.331526i 0.945717 0.324992i \(-0.105362\pi\)
−0.754310 + 0.656518i \(0.772028\pi\)
\(744\) 0 0
\(745\) 7.77292 13.4631i 0.284778 0.493249i
\(746\) −10.9759 −0.401857
\(747\) 0 0
\(748\) −41.9064 −1.53225
\(749\) 0 0
\(750\) 0 0
\(751\) −20.1059 34.8244i −0.733674 1.27076i −0.955303 0.295630i \(-0.904470\pi\)
0.221628 0.975131i \(-0.428863\pi\)
\(752\) −0.830095 1.43777i −0.0302704 0.0524300i
\(753\) 0 0
\(754\) −0.557180 + 0.965064i −0.0202913 + 0.0351456i
\(755\) −26.3891 −0.960397
\(756\) 0 0
\(757\) −21.5206 −0.782181 −0.391091 0.920352i \(-0.627902\pi\)
−0.391091 + 0.920352i \(0.627902\pi\)
\(758\) 16.9939 29.4342i 0.617244 1.06910i
\(759\) 0 0
\(760\) 1.71053 + 2.96273i 0.0620476 + 0.107470i
\(761\) 11.8313 + 20.4925i 0.428886 + 0.742852i 0.996774 0.0802535i \(-0.0255730\pi\)
−0.567889 + 0.823105i \(0.692240\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 16.1683 0.584947
\(765\) 0 0
\(766\) 21.0241 0.759631
\(767\) 0.755675 1.30887i 0.0272858 0.0472605i
\(768\) 0 0
\(769\) 5.62764 + 9.74736i 0.202938 + 0.351499i 0.949474 0.313846i \(-0.101618\pi\)
−0.746536 + 0.665345i \(0.768284\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 7.08414 12.2701i 0.254964 0.441610i
\(773\) −0.277984 −0.00999839 −0.00499919 0.999988i \(-0.501591\pi\)
−0.00499919 + 0.999988i \(0.501591\pi\)
\(774\) 0 0
\(775\) 14.6317 0.525587
\(776\) −1.81806 + 3.14897i −0.0652644 + 0.113041i
\(777\) 0 0
\(778\) −6.86909 11.8976i −0.246269 0.426550i
\(779\) −6.74433 11.6815i −0.241641 0.418534i
\(780\) 0 0
\(781\) −33.0276 + 57.2056i −1.18182 + 2.04698i
\(782\) −2.88099 −0.103024
\(783\) 0 0
\(784\) 0 0
\(785\) 16.7112 28.9447i 0.596449 1.03308i
\(786\) 0 0
\(787\) −14.6940 25.4507i −0.523784 0.907220i −0.999617 0.0276845i \(-0.991187\pi\)
0.475833 0.879536i \(-0.342147\pi\)
\(788\) 7.92107 + 13.7197i 0.282176 + 0.488744i
\(789\) 0 0
\(790\) −11.8376 + 20.5034i −0.421164 + 0.729477i
\(791\) 0 0
\(792\) 0 0
\(793\) −7.87524 −0.279658
\(794\) −3.57893 + 6.19889i −0.127012 + 0.219991i
\(795\) 0 0
\(796\) 4.47141 + 7.74471i 0.158485 + 0.274504i
\(797\) 0.433105 + 0.750160i 0.0153414 + 0.0265720i 0.873594 0.486655i \(-0.161783\pi\)
−0.858253 + 0.513227i \(0.828450\pi\)
\(798\) 0 0
\(799\) −5.67962 + 9.83739i −0.200931 + 0.348022i
\(800\) 1.89931 0.0671509
\(801\) 0 0
\(802\) −9.27936 −0.327666
\(803\) 0.939253 1.62683i 0.0331455 0.0574097i
\(804\) 0 0
\(805\) 0 0
\(806\) 2.93078 + 5.07626i 0.103232 + 0.178804i
\(807\) 0 0
\(808\) −4.00520 + 6.93721i −0.140903 + 0.244050i
\(809\) 19.3341 0.679749 0.339875 0.940471i \(-0.389615\pi\)
0.339875 + 0.940471i \(0.389615\pi\)
\(810\) 0 0
\(811\) 47.0391 1.65177 0.825884 0.563841i \(-0.190677\pi\)
0.825884 + 0.563841i \(0.190677\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 8.83693 + 15.3060i 0.309734 + 0.536476i
\(815\) −13.2398 22.9320i −0.463770 0.803274i
\(816\) 0 0
\(817\) 8.41260 14.5710i 0.294319 0.509776i
\(818\) 15.1683 0.530346
\(819\) 0 0
\(820\) 12.2255 0.426931
\(821\) 0.705332 1.22167i 0.0246162 0.0426366i −0.853455 0.521167i \(-0.825497\pi\)
0.878071 + 0.478530i \(0.158830\pi\)
\(822\) 0 0
\(823\) 17.5196 + 30.3448i 0.610694 + 1.05775i 0.991124 + 0.132943i \(0.0424426\pi\)
−0.380430 + 0.924810i \(0.624224\pi\)
\(824\) 3.41423 + 5.91362i 0.118940 + 0.206011i
\(825\) 0 0
\(826\) 0 0
\(827\) 18.5997 0.646776 0.323388 0.946266i \(-0.395178\pi\)
0.323388 + 0.946266i \(0.395178\pi\)
\(828\) 0 0
\(829\) 38.1696 1.32569 0.662843 0.748758i \(-0.269350\pi\)
0.662843 + 0.748758i \(0.269350\pi\)
\(830\) 2.75116 4.76515i 0.0954942 0.165401i
\(831\) 0 0
\(832\) 0.380438 + 0.658939i 0.0131893 + 0.0228446i
\(833\) 0 0
\(834\) 0 0
\(835\) 1.00739 1.74485i 0.0348622 0.0603832i
\(836\) −11.8993 −0.411546
\(837\) 0 0
\(838\) −8.33654 −0.287981
\(839\) 17.3691 30.0841i 0.599648 1.03862i −0.393225 0.919442i \(-0.628641\pi\)
0.992873 0.119178i \(-0.0380259\pi\)
\(840\) 0 0
\(841\) 13.4275 + 23.2571i 0.463018 + 0.801970i
\(842\) 3.50232 + 6.06620i 0.120698 + 0.209055i
\(843\) 0 0
\(844\) 11.3856 19.7205i 0.391910 0.678808i
\(845\) −21.8720 −0.752419
\(846\) 0 0
\(847\) 0 0
\(848\) 0.112725 0.195246i 0.00387100 0.00670476i
\(849\) 0 0
\(850\) −6.49768 11.2543i −0.222868 0.386020i
\(851\) 0.607523 + 1.05226i 0.0208256 + 0.0360711i
\(852\) 0 0
\(853\) 21.1586 36.6477i 0.724455 1.25479i −0.234743 0.972058i \(-0.575425\pi\)
0.959198 0.282736i \(-0.0912419\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −3.54583 −0.121194
\(857\) −7.46169 + 12.9240i −0.254887 + 0.441477i −0.964865 0.262747i \(-0.915371\pi\)
0.709978 + 0.704224i \(0.248705\pi\)
\(858\) 0 0
\(859\) 9.70658 + 16.8123i 0.331184 + 0.573628i 0.982744 0.184969i \(-0.0592186\pi\)
−0.651560 + 0.758597i \(0.725885\pi\)
\(860\) 7.62476 + 13.2065i 0.260002 + 0.450337i
\(861\) 0 0
\(862\) −1.72545 + 2.98857i −0.0587691 + 0.101791i
\(863\) −1.08453 −0.0369177 −0.0184588 0.999830i \(-0.505876\pi\)
−0.0184588 + 0.999830i \(0.505876\pi\)
\(864\) 0 0
\(865\) 0.876348 0.0297967
\(866\) −14.1300 + 24.4738i −0.480156 + 0.831654i
\(867\) 0 0
\(868\) 0 0
\(869\) −41.1742 71.3157i −1.39674 2.41922i
\(870\) 0 0
\(871\) 2.58126 4.47087i 0.0874625 0.151490i
\(872\) 0.703697 0.0238302
\(873\) 0 0
\(874\) −0.818057 −0.0276712
\(875\) 0 0
\(876\) 0 0
\(877\) 14.2850 + 24.7423i 0.482369 + 0.835487i 0.999795 0.0202407i \(-0.00644326\pi\)
−0.517427 + 0.855728i \(0.673110\pi\)
\(878\) 14.4480 + 25.0247i 0.487597 + 0.844543i
\(879\) 0 0
\(880\) 5.39248 9.34004i 0.181780 0.314853i
\(881\) 45.9967 1.54967 0.774835 0.632164i \(-0.217833\pi\)
0.774835 + 0.632164i \(0.217833\pi\)
\(882\) 0 0
\(883\) 32.9384 1.10847 0.554233 0.832361i \(-0.313012\pi\)
0.554233 + 0.832361i \(0.313012\pi\)
\(884\) 2.60301 4.50855i 0.0875487 0.151639i
\(885\) 0 0
\(886\) 6.88044 + 11.9173i 0.231153 + 0.400368i
\(887\) 14.1699 + 24.5430i 0.475779 + 0.824073i 0.999615 0.0277459i \(-0.00883293\pi\)
−0.523836 + 0.851819i \(0.675500\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 4.58358 0.153642
\(891\) 0 0
\(892\) −12.8856 −0.431443
\(893\) −1.61273 + 2.79332i −0.0539678 + 0.0934750i
\(894\) 0 0
\(895\) −7.77292 13.4631i −0.259820 0.450021i
\(896\) 0 0
\(897\) 0 0
\(898\) 10.1001 17.4939i 0.337046 0.583780i
\(899\) −11.2826 −0.376297
\(900\) 0 0
\(901\) −1.54256 −0.0513901
\(902\) −21.2616 + 36.8261i −0.707933 + 1.22618i
\(903\) 0 0
\(904\) 4.25116 + 7.36323i 0.141392 + 0.244897i
\(905\) 1.17046 + 2.02730i 0.0389074 + 0.0673896i
\(906\) 0 0
\(907\) −3.97373 + 6.88271i −0.131946 + 0.228537i −0.924427 0.381360i \(-0.875456\pi\)
0.792481 + 0.609897i \(0.208789\pi\)
\(908\) 21.9967 0.729987
\(909\) 0 0
\(910\) 0 0
\(911\) 4.00808 6.94220i 0.132794 0.230005i −0.791959 0.610575i \(-0.790939\pi\)
0.924752 + 0.380569i \(0.124272\pi\)
\(912\) 0 0
\(913\) 9.56922 + 16.5744i 0.316695 + 0.548532i
\(914\) 10.0149 + 17.3463i 0.331264 + 0.573766i
\(915\) 0 0
\(916\) −1.89931 + 3.28971i −0.0627551 + 0.108695i
\(917\) 0 0
\(918\) 0 0
\(919\) 24.0449 0.793168 0.396584 0.917999i \(-0.370196\pi\)
0.396584 + 0.917999i \(0.370196\pi\)
\(920\) 0.370723 0.642111i 0.0122224 0.0211698i
\(921\) 0 0
\(922\) −5.97661 10.3518i −0.196829 0.340918i
\(923\) −4.10301 7.10662i −0.135052 0.233917i
\(924\) 0 0
\(925\) −2.74037 + 4.74646i −0.0901027 + 0.156062i
\(926\) 13.2905 0.436754
\(927\) 0 0
\(928\) −1.46457 −0.0480770
\(929\) −13.9331 + 24.1328i −0.457130 + 0.791773i −0.998808 0.0488134i \(-0.984456\pi\)
0.541678 + 0.840586i \(0.317789\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 3.33530 + 5.77690i 0.109251 + 0.189229i
\(933\) 0 0
\(934\) 5.61505 9.72555i 0.183730 0.318230i
\(935\) −73.7921 −2.41326
\(936\) 0 0
\(937\) −53.2211 −1.73866 −0.869328 0.494235i \(-0.835448\pi\)
−0.869328 + 0.494235i \(0.835448\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −1.46169 2.53173i −0.0476752 0.0825759i
\(941\) 15.0241 + 26.0225i 0.489771 + 0.848308i 0.999931 0.0117715i \(-0.00374709\pi\)
−0.510160 + 0.860080i \(0.670414\pi\)
\(942\) 0 0
\(943\) −1.46169 + 2.53173i −0.0475993 + 0.0824445i
\(944\) 1.98633 0.0646494
\(945\) 0 0
\(946\) −53.0416 −1.72453
\(947\) −19.8445 + 34.3716i −0.644858 + 1.11693i 0.339476 + 0.940615i \(0.389750\pi\)
−0.984334 + 0.176312i \(0.943583\pi\)
\(948\) 0 0
\(949\) 0.116683 + 0.202101i 0.00378769 + 0.00656047i
\(950\) −1.84501 3.19565i −0.0598601 0.103681i
\(951\) 0 0
\(952\) 0 0
\(953\) −23.0643 −0.747126 −0.373563 0.927605i \(-0.621864\pi\)
−0.373563 + 0.927605i \(0.621864\pi\)
\(954\) 0 0
\(955\) 28.4703 0.921278
\(956\) 7.82038 13.5453i 0.252929 0.438086i
\(957\) 0 0
\(958\) −16.3135 28.2559i −0.527067 0.912906i
\(959\) 0 0
\(960\) 0 0
\(961\) −14.1735 + 24.5492i −0.457209 + 0.791909i
\(962\) −2.19562 −0.0707895
\(963\) 0 0
\(964\) −21.4120 −0.689635
\(965\) 12.4743 21.6061i 0.401562 0.695525i
\(966\) 0 0
\(967\) 15.2902 + 26.4833i 0.491698 + 0.851646i 0.999954 0.00955967i \(-0.00304298\pi\)
−0.508256 + 0.861206i \(0.669710\pi\)
\(968\) 13.2564 + 22.9607i 0.426076 + 0.737985i
\(969\) 0 0
\(970\) −3.20137 + 5.54494i −0.102790 + 0.178037i
\(971\) −26.2060 −0.840991 −0.420496 0.907295i \(-0.638144\pi\)
−0.420496 + 0.907295i \(0.638144\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −1.84897 + 3.20251i −0.0592448 + 0.102615i
\(975\) 0 0
\(976\) −5.17511 8.96355i −0.165651 0.286916i
\(977\) 10.5270 + 18.2332i 0.336787 + 0.583332i 0.983826 0.179124i \(-0.0573264\pi\)
−0.647039 + 0.762457i \(0.723993\pi\)
\(978\) 0 0
\(979\) −7.97141 + 13.8069i −0.254767 + 0.441270i
\(980\) 0 0
\(981\) 0 0
\(982\) 37.5609 1.19862
\(983\) 9.76483 16.9132i 0.311450 0.539447i −0.667227 0.744855i \(-0.732519\pi\)
0.978676 + 0.205408i \(0.0658521\pi\)
\(984\) 0 0
\(985\) 13.9480 + 24.1587i 0.444421 + 0.769760i
\(986\) 5.01040 + 8.67827i 0.159564 + 0.276373i
\(987\) 0 0
\(988\) 0.739123 1.28020i 0.0235146 0.0407286i
\(989\) −3.64652 −0.115952
\(990\) 0 0
\(991\) 14.9967 0.476387 0.238193 0.971218i \(-0.423445\pi\)
0.238193 + 0.971218i \(0.423445\pi\)
\(992\) −3.85185 + 6.67160i −0.122296 + 0.211823i
\(993\) 0 0
\(994\) 0 0
\(995\) 7.87360 + 13.6375i 0.249610 + 0.432337i
\(996\) 0 0
\(997\) −29.2821 + 50.7180i −0.927373 + 1.60626i −0.139672 + 0.990198i \(0.544605\pi\)
−0.787700 + 0.616059i \(0.788728\pi\)
\(998\) 31.7954 1.00646
\(999\) 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 2646.2.f.n.883.2 6
3.2 odd 2 882.2.f.m.295.3 6
7.2 even 3 2646.2.e.o.2125.2 6
7.3 odd 6 378.2.h.d.289.2 6
7.4 even 3 2646.2.h.p.667.2 6
7.5 odd 6 378.2.e.c.235.2 6
7.6 odd 2 2646.2.f.o.883.2 6
9.2 odd 6 7938.2.a.by.1.2 3
9.4 even 3 inner 2646.2.f.n.1765.2 6
9.5 odd 6 882.2.f.m.589.3 6
9.7 even 3 7938.2.a.bx.1.2 3
21.2 odd 6 882.2.e.p.655.1 6
21.5 even 6 126.2.e.d.25.3 6
21.11 odd 6 882.2.h.o.79.2 6
21.17 even 6 126.2.h.c.79.2 yes 6
21.20 even 2 882.2.f.l.295.1 6
28.3 even 6 3024.2.t.g.289.2 6
28.19 even 6 3024.2.q.h.2881.2 6
63.4 even 3 2646.2.e.o.1549.2 6
63.5 even 6 126.2.h.c.67.2 yes 6
63.13 odd 6 2646.2.f.o.1765.2 6
63.20 even 6 7938.2.a.cb.1.2 3
63.23 odd 6 882.2.h.o.67.2 6
63.31 odd 6 378.2.e.c.37.2 6
63.32 odd 6 882.2.e.p.373.1 6
63.34 odd 6 7938.2.a.bu.1.2 3
63.38 even 6 1134.2.g.k.163.2 6
63.40 odd 6 378.2.h.d.361.2 6
63.41 even 6 882.2.f.l.589.1 6
63.47 even 6 1134.2.g.k.487.2 6
63.52 odd 6 1134.2.g.n.163.2 6
63.58 even 3 2646.2.h.p.361.2 6
63.59 even 6 126.2.e.d.121.3 yes 6
63.61 odd 6 1134.2.g.n.487.2 6
84.47 odd 6 1008.2.q.h.529.1 6
84.59 odd 6 1008.2.t.g.961.2 6
252.31 even 6 3024.2.q.h.2305.2 6
252.59 odd 6 1008.2.q.h.625.1 6
252.103 even 6 3024.2.t.g.1873.2 6
252.131 odd 6 1008.2.t.g.193.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.e.d.25.3 6 21.5 even 6
126.2.e.d.121.3 yes 6 63.59 even 6
126.2.h.c.67.2 yes 6 63.5 even 6
126.2.h.c.79.2 yes 6 21.17 even 6
378.2.e.c.37.2 6 63.31 odd 6
378.2.e.c.235.2 6 7.5 odd 6
378.2.h.d.289.2 6 7.3 odd 6
378.2.h.d.361.2 6 63.40 odd 6
882.2.e.p.373.1 6 63.32 odd 6
882.2.e.p.655.1 6 21.2 odd 6
882.2.f.l.295.1 6 21.20 even 2
882.2.f.l.589.1 6 63.41 even 6
882.2.f.m.295.3 6 3.2 odd 2
882.2.f.m.589.3 6 9.5 odd 6
882.2.h.o.67.2 6 63.23 odd 6
882.2.h.o.79.2 6 21.11 odd 6
1008.2.q.h.529.1 6 84.47 odd 6
1008.2.q.h.625.1 6 252.59 odd 6
1008.2.t.g.193.2 6 252.131 odd 6
1008.2.t.g.961.2 6 84.59 odd 6
1134.2.g.k.163.2 6 63.38 even 6
1134.2.g.k.487.2 6 63.47 even 6
1134.2.g.n.163.2 6 63.52 odd 6
1134.2.g.n.487.2 6 63.61 odd 6
2646.2.e.o.1549.2 6 63.4 even 3
2646.2.e.o.2125.2 6 7.2 even 3
2646.2.f.n.883.2 6 1.1 even 1 trivial
2646.2.f.n.1765.2 6 9.4 even 3 inner
2646.2.f.o.883.2 6 7.6 odd 2
2646.2.f.o.1765.2 6 63.13 odd 6
2646.2.h.p.361.2 6 63.58 even 3
2646.2.h.p.667.2 6 7.4 even 3
3024.2.q.h.2305.2 6 252.31 even 6
3024.2.q.h.2881.2 6 28.19 even 6
3024.2.t.g.289.2 6 28.3 even 6
3024.2.t.g.1873.2 6 252.103 even 6
7938.2.a.bu.1.2 3 63.34 odd 6
7938.2.a.bx.1.2 3 9.7 even 3
7938.2.a.by.1.2 3 9.2 odd 6
7938.2.a.cb.1.2 3 63.20 even 6