Properties

Label 1805.2.b.k.1084.5
Level $1805$
Weight $2$
Character 1805.1084
Analytic conductor $14.413$
Analytic rank $0$
Dimension $24$
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] = [1805,2,Mod(1084,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1084");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (of order \(2\), degree \(1\), 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: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1084.5
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.k.1084.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.78468i q^{2} +2.38377i q^{3} -1.18508 q^{4} +(-1.16534 + 1.90840i) q^{5} +4.25426 q^{6} -4.23911i q^{7} -1.45438i q^{8} -2.68235 q^{9} +O(q^{10})\) \(q-1.78468i q^{2} +2.38377i q^{3} -1.18508 q^{4} +(-1.16534 + 1.90840i) q^{5} +4.25426 q^{6} -4.23911i q^{7} -1.45438i q^{8} -2.68235 q^{9} +(3.40588 + 2.07976i) q^{10} -0.490889 q^{11} -2.82495i q^{12} +4.16199i q^{13} -7.56544 q^{14} +(-4.54918 - 2.77790i) q^{15} -4.96575 q^{16} +2.03619i q^{17} +4.78713i q^{18} +(1.38102 - 2.26160i) q^{20} +10.1050 q^{21} +0.876080i q^{22} +4.39525i q^{23} +3.46689 q^{24} +(-2.28396 - 4.44787i) q^{25} +7.42782 q^{26} +0.757211i q^{27} +5.02367i q^{28} +3.26270 q^{29} +(-4.95766 + 8.11882i) q^{30} +4.08833 q^{31} +5.95351i q^{32} -1.17017i q^{33} +3.63395 q^{34} +(8.08990 + 4.94000i) q^{35} +3.17879 q^{36} +2.14440i q^{37} -9.92123 q^{39} +(2.77553 + 1.69484i) q^{40} +4.36602 q^{41} -18.0343i q^{42} +10.6241i q^{43} +0.581742 q^{44} +(3.12585 - 5.11898i) q^{45} +7.84410 q^{46} -2.62142i q^{47} -11.8372i q^{48} -10.9700 q^{49} +(-7.93801 + 4.07614i) q^{50} -4.85381 q^{51} -4.93228i q^{52} +11.4341i q^{53} +1.35138 q^{54} +(0.572053 - 0.936812i) q^{55} -6.16526 q^{56} -5.82287i q^{58} +0.542306 q^{59} +(5.39112 + 3.29203i) q^{60} -13.6423 q^{61} -7.29635i q^{62} +11.3708i q^{63} +0.693606 q^{64} +(-7.94274 - 4.85014i) q^{65} -2.08837 q^{66} +7.15699i q^{67} -2.41305i q^{68} -10.4772 q^{69} +(8.81632 - 14.4379i) q^{70} +6.03858 q^{71} +3.90114i q^{72} +2.05419i q^{73} +3.82707 q^{74} +(10.6027 - 5.44444i) q^{75} +2.08093i q^{77} +17.7062i q^{78} -5.34029 q^{79} +(5.78678 - 9.47662i) q^{80} -9.85206 q^{81} -7.79193i q^{82} +8.11578i q^{83} -11.9753 q^{84} +(-3.88587 - 2.37286i) q^{85} +18.9605 q^{86} +7.77752i q^{87} +0.713937i q^{88} +4.34099 q^{89} +(-9.13574 - 5.57863i) q^{90} +17.6431 q^{91} -5.20871i q^{92} +9.74562i q^{93} -4.67839 q^{94} -14.1918 q^{96} -5.64669i q^{97} +19.5780i q^{98} +1.31674 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} + 12 q^{40} + 60 q^{41} + 30 q^{44} + 9 q^{45} + 6 q^{46} - 12 q^{49} + 18 q^{50} + 30 q^{51} + 24 q^{54} + 33 q^{55} + 18 q^{56} - 60 q^{59} - 42 q^{60} + 30 q^{61} + 18 q^{65} + 36 q^{66} - 66 q^{69} + 9 q^{70} + 96 q^{71} - 24 q^{74} + 36 q^{75} - 72 q^{79} - 42 q^{80} - 96 q^{81} + 54 q^{84} - 27 q^{85} + 108 q^{86} - 84 q^{89} - 93 q^{90} + 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.78468i 1.26196i −0.775800 0.630979i \(-0.782653\pi\)
0.775800 0.630979i \(-0.217347\pi\)
\(3\) 2.38377i 1.37627i 0.725583 + 0.688134i \(0.241570\pi\)
−0.725583 + 0.688134i \(0.758430\pi\)
\(4\) −1.18508 −0.592538
\(5\) −1.16534 + 1.90840i −0.521156 + 0.853461i
\(6\) 4.25426 1.73679
\(7\) 4.23911i 1.60223i −0.598509 0.801116i \(-0.704240\pi\)
0.598509 0.801116i \(-0.295760\pi\)
\(8\) 1.45438i 0.514199i
\(9\) −2.68235 −0.894116
\(10\) 3.40588 + 2.07976i 1.07703 + 0.657677i
\(11\) −0.490889 −0.148009 −0.0740043 0.997258i \(-0.523578\pi\)
−0.0740043 + 0.997258i \(0.523578\pi\)
\(12\) 2.82495i 0.815492i
\(13\) 4.16199i 1.15433i 0.816628 + 0.577165i \(0.195841\pi\)
−0.816628 + 0.577165i \(0.804159\pi\)
\(14\) −7.56544 −2.02195
\(15\) −4.54918 2.77790i −1.17459 0.717251i
\(16\) −4.96575 −1.24144
\(17\) 2.03619i 0.493850i 0.969035 + 0.246925i \(0.0794201\pi\)
−0.969035 + 0.246925i \(0.920580\pi\)
\(18\) 4.78713i 1.12834i
\(19\) 0 0
\(20\) 1.38102 2.26160i 0.308805 0.505709i
\(21\) 10.1050 2.20510
\(22\) 0.876080i 0.186781i
\(23\) 4.39525i 0.916472i 0.888830 + 0.458236i \(0.151519\pi\)
−0.888830 + 0.458236i \(0.848481\pi\)
\(24\) 3.46689 0.707677
\(25\) −2.28396 4.44787i −0.456793 0.889573i
\(26\) 7.42782 1.45672
\(27\) 0.757211i 0.145725i
\(28\) 5.02367i 0.949384i
\(29\) 3.26270 0.605869 0.302934 0.953011i \(-0.402034\pi\)
0.302934 + 0.953011i \(0.402034\pi\)
\(30\) −4.95766 + 8.11882i −0.905140 + 1.48229i
\(31\) 4.08833 0.734285 0.367143 0.930165i \(-0.380336\pi\)
0.367143 + 0.930165i \(0.380336\pi\)
\(32\) 5.95351i 1.05244i
\(33\) 1.17017i 0.203700i
\(34\) 3.63395 0.623218
\(35\) 8.08990 + 4.94000i 1.36744 + 0.835013i
\(36\) 3.17879 0.529798
\(37\) 2.14440i 0.352538i 0.984342 + 0.176269i \(0.0564028\pi\)
−0.984342 + 0.176269i \(0.943597\pi\)
\(38\) 0 0
\(39\) −9.92123 −1.58867
\(40\) 2.77553 + 1.69484i 0.438849 + 0.267978i
\(41\) 4.36602 0.681857 0.340929 0.940089i \(-0.389259\pi\)
0.340929 + 0.940089i \(0.389259\pi\)
\(42\) 18.0343i 2.78275i
\(43\) 10.6241i 1.62015i 0.586324 + 0.810077i \(0.300575\pi\)
−0.586324 + 0.810077i \(0.699425\pi\)
\(44\) 0.581742 0.0877008
\(45\) 3.12585 5.11898i 0.465974 0.763093i
\(46\) 7.84410 1.15655
\(47\) 2.62142i 0.382373i −0.981554 0.191187i \(-0.938766\pi\)
0.981554 0.191187i \(-0.0612336\pi\)
\(48\) 11.8372i 1.70855i
\(49\) −10.9700 −1.56715
\(50\) −7.93801 + 4.07614i −1.12260 + 0.576453i
\(51\) −4.85381 −0.679670
\(52\) 4.93228i 0.683985i
\(53\) 11.4341i 1.57059i 0.619121 + 0.785296i \(0.287489\pi\)
−0.619121 + 0.785296i \(0.712511\pi\)
\(54\) 1.35138 0.183899
\(55\) 0.572053 0.936812i 0.0771356 0.126320i
\(56\) −6.16526 −0.823867
\(57\) 0 0
\(58\) 5.82287i 0.764581i
\(59\) 0.542306 0.0706022 0.0353011 0.999377i \(-0.488761\pi\)
0.0353011 + 0.999377i \(0.488761\pi\)
\(60\) 5.39112 + 3.29203i 0.695991 + 0.424999i
\(61\) −13.6423 −1.74671 −0.873356 0.487083i \(-0.838061\pi\)
−0.873356 + 0.487083i \(0.838061\pi\)
\(62\) 7.29635i 0.926637i
\(63\) 11.3708i 1.43258i
\(64\) 0.693606 0.0867007
\(65\) −7.94274 4.85014i −0.985176 0.601586i
\(66\) −2.08837 −0.257061
\(67\) 7.15699i 0.874365i 0.899373 + 0.437182i \(0.144024\pi\)
−0.899373 + 0.437182i \(0.855976\pi\)
\(68\) 2.41305i 0.292625i
\(69\) −10.4772 −1.26131
\(70\) 8.81632 14.4379i 1.05375 1.72566i
\(71\) 6.03858 0.716647 0.358324 0.933597i \(-0.383348\pi\)
0.358324 + 0.933597i \(0.383348\pi\)
\(72\) 3.90114i 0.459754i
\(73\) 2.05419i 0.240425i 0.992748 + 0.120212i \(0.0383576\pi\)
−0.992748 + 0.120212i \(0.961642\pi\)
\(74\) 3.82707 0.444888
\(75\) 10.6027 5.44444i 1.22429 0.628670i
\(76\) 0 0
\(77\) 2.08093i 0.237144i
\(78\) 17.7062i 2.00483i
\(79\) −5.34029 −0.600830 −0.300415 0.953809i \(-0.597125\pi\)
−0.300415 + 0.953809i \(0.597125\pi\)
\(80\) 5.78678 9.47662i 0.646982 1.05952i
\(81\) −9.85206 −1.09467
\(82\) 7.79193i 0.860475i
\(83\) 8.11578i 0.890823i 0.895326 + 0.445411i \(0.146943\pi\)
−0.895326 + 0.445411i \(0.853057\pi\)
\(84\) −11.9753 −1.30661
\(85\) −3.88587 2.37286i −0.421482 0.257373i
\(86\) 18.9605 2.04457
\(87\) 7.77752i 0.833838i
\(88\) 0.713937i 0.0761060i
\(89\) 4.34099 0.460144 0.230072 0.973174i \(-0.426104\pi\)
0.230072 + 0.973174i \(0.426104\pi\)
\(90\) −9.13574 5.57863i −0.962992 0.588039i
\(91\) 17.6431 1.84950
\(92\) 5.20871i 0.543045i
\(93\) 9.74562i 1.01057i
\(94\) −4.67839 −0.482539
\(95\) 0 0
\(96\) −14.1918 −1.44844
\(97\) 5.64669i 0.573335i −0.958030 0.286667i \(-0.907453\pi\)
0.958030 0.286667i \(-0.0925475\pi\)
\(98\) 19.5780i 1.97768i
\(99\) 1.31674 0.132337
\(100\) 2.70667 + 5.27106i 0.270667 + 0.527106i
\(101\) −3.30082 −0.328444 −0.164222 0.986423i \(-0.552511\pi\)
−0.164222 + 0.986423i \(0.552511\pi\)
\(102\) 8.66250i 0.857715i
\(103\) 3.41567i 0.336556i −0.985740 0.168278i \(-0.946179\pi\)
0.985740 0.168278i \(-0.0538206\pi\)
\(104\) 6.05310 0.593556
\(105\) −11.7758 + 19.2844i −1.14920 + 1.88197i
\(106\) 20.4062 1.98202
\(107\) 1.75252i 0.169422i 0.996406 + 0.0847110i \(0.0269967\pi\)
−0.996406 + 0.0847110i \(0.973003\pi\)
\(108\) 0.897354i 0.0863479i
\(109\) 3.51923 0.337081 0.168541 0.985695i \(-0.446095\pi\)
0.168541 + 0.985695i \(0.446095\pi\)
\(110\) −1.67191 1.02093i −0.159410 0.0973419i
\(111\) −5.11176 −0.485186
\(112\) 21.0503i 1.98907i
\(113\) 13.2583i 1.24723i 0.781731 + 0.623616i \(0.214337\pi\)
−0.781731 + 0.623616i \(0.785663\pi\)
\(114\) 0 0
\(115\) −8.38788 5.12196i −0.782174 0.477625i
\(116\) −3.86655 −0.359000
\(117\) 11.1639i 1.03210i
\(118\) 0.967842i 0.0890971i
\(119\) 8.63165 0.791262
\(120\) −4.04011 + 6.61621i −0.368810 + 0.603975i
\(121\) −10.7590 −0.978093
\(122\) 24.3470i 2.20428i
\(123\) 10.4076i 0.938419i
\(124\) −4.84498 −0.435092
\(125\) 11.1499 + 0.824566i 0.997277 + 0.0737514i
\(126\) 20.2931 1.80786
\(127\) 19.8082i 1.75769i 0.477105 + 0.878846i \(0.341686\pi\)
−0.477105 + 0.878846i \(0.658314\pi\)
\(128\) 10.6692i 0.943029i
\(129\) −25.3253 −2.22977
\(130\) −8.65594 + 14.1752i −0.759176 + 1.24325i
\(131\) −3.43004 −0.299684 −0.149842 0.988710i \(-0.547876\pi\)
−0.149842 + 0.988710i \(0.547876\pi\)
\(132\) 1.38674i 0.120700i
\(133\) 0 0
\(134\) 12.7729 1.10341
\(135\) −1.44506 0.882409i −0.124371 0.0759457i
\(136\) 2.96139 0.253937
\(137\) 0.608296i 0.0519702i −0.999662 0.0259851i \(-0.991728\pi\)
0.999662 0.0259851i \(-0.00827225\pi\)
\(138\) 18.6985i 1.59172i
\(139\) 8.45799 0.717397 0.358699 0.933453i \(-0.383221\pi\)
0.358699 + 0.933453i \(0.383221\pi\)
\(140\) −9.58716 5.85428i −0.810263 0.494777i
\(141\) 6.24885 0.526248
\(142\) 10.7769i 0.904379i
\(143\) 2.04308i 0.170851i
\(144\) 13.3199 1.10999
\(145\) −3.80216 + 6.22653i −0.315752 + 0.517085i
\(146\) 3.66607 0.303406
\(147\) 26.1500i 2.15682i
\(148\) 2.54128i 0.208892i
\(149\) 4.63735 0.379907 0.189953 0.981793i \(-0.439166\pi\)
0.189953 + 0.981793i \(0.439166\pi\)
\(150\) −9.71657 18.9224i −0.793355 1.54500i
\(151\) 14.2109 1.15646 0.578232 0.815872i \(-0.303743\pi\)
0.578232 + 0.815872i \(0.303743\pi\)
\(152\) 0 0
\(153\) 5.46178i 0.441559i
\(154\) 3.71380 0.299266
\(155\) −4.76429 + 7.80215i −0.382677 + 0.626684i
\(156\) 11.7574 0.941347
\(157\) 10.7281i 0.856194i −0.903733 0.428097i \(-0.859184\pi\)
0.903733 0.428097i \(-0.140816\pi\)
\(158\) 9.53071i 0.758222i
\(159\) −27.2562 −2.16156
\(160\) −11.3617 6.93786i −0.898218 0.548486i
\(161\) 18.6319 1.46840
\(162\) 17.5828i 1.38143i
\(163\) 16.9366i 1.32658i −0.748363 0.663289i \(-0.769160\pi\)
0.748363 0.663289i \(-0.230840\pi\)
\(164\) −5.17406 −0.404027
\(165\) 2.23314 + 1.36364i 0.173850 + 0.106159i
\(166\) 14.4841 1.12418
\(167\) 16.2567i 1.25798i −0.777412 0.628991i \(-0.783468\pi\)
0.777412 0.628991i \(-0.216532\pi\)
\(168\) 14.6965i 1.13386i
\(169\) −4.32219 −0.332476
\(170\) −4.23479 + 6.93503i −0.324794 + 0.531892i
\(171\) 0 0
\(172\) 12.5903i 0.960003i
\(173\) 8.59112i 0.653171i 0.945168 + 0.326585i \(0.105898\pi\)
−0.945168 + 0.326585i \(0.894102\pi\)
\(174\) 13.8804 1.05227
\(175\) −18.8550 + 9.68197i −1.42530 + 0.731888i
\(176\) 2.43763 0.183743
\(177\) 1.29273i 0.0971677i
\(178\) 7.74728i 0.580683i
\(179\) 23.5276 1.75853 0.879267 0.476330i \(-0.158033\pi\)
0.879267 + 0.476330i \(0.158033\pi\)
\(180\) −3.70437 + 6.06639i −0.276107 + 0.452162i
\(181\) −16.6135 −1.23487 −0.617434 0.786623i \(-0.711828\pi\)
−0.617434 + 0.786623i \(0.711828\pi\)
\(182\) 31.4873i 2.33400i
\(183\) 32.5200i 2.40394i
\(184\) 6.39234 0.471250
\(185\) −4.09237 2.49896i −0.300877 0.183727i
\(186\) 17.3928 1.27530
\(187\) 0.999546i 0.0730941i
\(188\) 3.10658i 0.226571i
\(189\) 3.20990 0.233486
\(190\) 0 0
\(191\) −12.8109 −0.926965 −0.463482 0.886106i \(-0.653400\pi\)
−0.463482 + 0.886106i \(0.653400\pi\)
\(192\) 1.65339i 0.119323i
\(193\) 9.63983i 0.693890i 0.937885 + 0.346945i \(0.112781\pi\)
−0.937885 + 0.346945i \(0.887219\pi\)
\(194\) −10.0775 −0.723525
\(195\) 11.5616 18.9336i 0.827944 1.35587i
\(196\) 13.0003 0.928596
\(197\) 3.10241i 0.221038i −0.993874 0.110519i \(-0.964749\pi\)
0.993874 0.110519i \(-0.0352513\pi\)
\(198\) 2.34995i 0.167004i
\(199\) −0.524290 −0.0371659 −0.0185830 0.999827i \(-0.505915\pi\)
−0.0185830 + 0.999827i \(0.505915\pi\)
\(200\) −6.46887 + 3.32174i −0.457418 + 0.234883i
\(201\) −17.0606 −1.20336
\(202\) 5.89091i 0.414483i
\(203\) 13.8309i 0.970742i
\(204\) 5.75214 0.402731
\(205\) −5.08789 + 8.33209i −0.355354 + 0.581939i
\(206\) −6.09586 −0.424719
\(207\) 11.7896i 0.819432i
\(208\) 20.6674i 1.43303i
\(209\) 0 0
\(210\) 34.4165 + 21.0160i 2.37497 + 1.45025i
\(211\) −19.0637 −1.31240 −0.656201 0.754586i \(-0.727838\pi\)
−0.656201 + 0.754586i \(0.727838\pi\)
\(212\) 13.5503i 0.930636i
\(213\) 14.3946i 0.986299i
\(214\) 3.12768 0.213804
\(215\) −20.2749 12.3806i −1.38274 0.844353i
\(216\) 1.10127 0.0749319
\(217\) 17.3309i 1.17650i
\(218\) 6.28069i 0.425382i
\(219\) −4.89671 −0.330889
\(220\) −0.677927 + 1.11019i −0.0457058 + 0.0748493i
\(221\) −8.47463 −0.570065
\(222\) 9.12284i 0.612285i
\(223\) 3.16283i 0.211799i −0.994377 0.105899i \(-0.966228\pi\)
0.994377 0.105899i \(-0.0337721\pi\)
\(224\) 25.2376 1.68626
\(225\) 6.12638 + 11.9307i 0.408426 + 0.795381i
\(226\) 23.6617 1.57395
\(227\) 9.04654i 0.600440i 0.953870 + 0.300220i \(0.0970600\pi\)
−0.953870 + 0.300220i \(0.902940\pi\)
\(228\) 0 0
\(229\) 17.8920 1.18234 0.591168 0.806549i \(-0.298667\pi\)
0.591168 + 0.806549i \(0.298667\pi\)
\(230\) −9.14105 + 14.9697i −0.602743 + 0.987071i
\(231\) −4.96046 −0.326374
\(232\) 4.74519i 0.311537i
\(233\) 6.44330i 0.422114i 0.977474 + 0.211057i \(0.0676906\pi\)
−0.977474 + 0.211057i \(0.932309\pi\)
\(234\) −19.9240 −1.30247
\(235\) 5.00271 + 3.05485i 0.326341 + 0.199276i
\(236\) −0.642674 −0.0418345
\(237\) 12.7300i 0.826903i
\(238\) 15.4047i 0.998539i
\(239\) 13.4742 0.871571 0.435785 0.900051i \(-0.356471\pi\)
0.435785 + 0.900051i \(0.356471\pi\)
\(240\) 22.5901 + 13.7943i 1.45818 + 0.890421i
\(241\) −17.6351 −1.13598 −0.567990 0.823036i \(-0.692279\pi\)
−0.567990 + 0.823036i \(0.692279\pi\)
\(242\) 19.2014i 1.23431i
\(243\) 21.2134i 1.36084i
\(244\) 16.1671 1.03499
\(245\) 12.7838 20.9352i 0.816729 1.33750i
\(246\) 18.5742 1.18424
\(247\) 0 0
\(248\) 5.94596i 0.377569i
\(249\) −19.3461 −1.22601
\(250\) 1.47158 19.8990i 0.0930712 1.25852i
\(251\) 17.7326 1.11927 0.559636 0.828738i \(-0.310941\pi\)
0.559636 + 0.828738i \(0.310941\pi\)
\(252\) 13.4752i 0.848859i
\(253\) 2.15758i 0.135646i
\(254\) 35.3513 2.21813
\(255\) 5.65635 9.26301i 0.354214 0.580072i
\(256\) 20.4282 1.27676
\(257\) 27.7475i 1.73084i −0.501046 0.865421i \(-0.667051\pi\)
0.501046 0.865421i \(-0.332949\pi\)
\(258\) 45.1975i 2.81387i
\(259\) 9.09035 0.564847
\(260\) 9.41276 + 5.74779i 0.583754 + 0.356463i
\(261\) −8.75170 −0.541716
\(262\) 6.12152i 0.378189i
\(263\) 5.56032i 0.342864i −0.985196 0.171432i \(-0.945161\pi\)
0.985196 0.171432i \(-0.0548393\pi\)
\(264\) −1.70186 −0.104742
\(265\) −21.8208 13.3246i −1.34044 0.818523i
\(266\) 0 0
\(267\) 10.3479i 0.633282i
\(268\) 8.48158i 0.518095i
\(269\) 4.62765 0.282153 0.141076 0.989999i \(-0.454944\pi\)
0.141076 + 0.989999i \(0.454944\pi\)
\(270\) −1.57482 + 2.57897i −0.0958403 + 0.156951i
\(271\) −7.60838 −0.462176 −0.231088 0.972933i \(-0.574229\pi\)
−0.231088 + 0.972933i \(0.574229\pi\)
\(272\) 10.1112i 0.613083i
\(273\) 42.0571i 2.54541i
\(274\) −1.08561 −0.0655843
\(275\) 1.12117 + 2.18341i 0.0676093 + 0.131665i
\(276\) 12.4163 0.747376
\(277\) 7.53544i 0.452761i 0.974039 + 0.226380i \(0.0726892\pi\)
−0.974039 + 0.226380i \(0.927311\pi\)
\(278\) 15.0948i 0.905325i
\(279\) −10.9663 −0.656536
\(280\) 7.18462 11.7658i 0.429363 0.703139i
\(281\) −18.2549 −1.08900 −0.544499 0.838762i \(-0.683280\pi\)
−0.544499 + 0.838762i \(0.683280\pi\)
\(282\) 11.1522i 0.664103i
\(283\) 30.9333i 1.83880i 0.393328 + 0.919398i \(0.371324\pi\)
−0.393328 + 0.919398i \(0.628676\pi\)
\(284\) −7.15618 −0.424641
\(285\) 0 0
\(286\) −3.64624 −0.215607
\(287\) 18.5080i 1.09249i
\(288\) 15.9694i 0.941004i
\(289\) 12.8539 0.756112
\(290\) 11.1124 + 6.78563i 0.652540 + 0.398466i
\(291\) 13.4604 0.789063
\(292\) 2.43437i 0.142461i
\(293\) 21.8992i 1.27937i −0.768639 0.639683i \(-0.779066\pi\)
0.768639 0.639683i \(-0.220934\pi\)
\(294\) −46.6694 −2.72181
\(295\) −0.631971 + 1.03494i −0.0367948 + 0.0602563i
\(296\) 3.11877 0.181275
\(297\) 0.371707i 0.0215686i
\(298\) 8.27618i 0.479426i
\(299\) −18.2930 −1.05791
\(300\) −12.5650 + 6.45208i −0.725440 + 0.372511i
\(301\) 45.0365 2.59586
\(302\) 25.3618i 1.45941i
\(303\) 7.86840i 0.452028i
\(304\) 0 0
\(305\) 15.8979 26.0349i 0.910309 1.49075i
\(306\) −9.74752 −0.557229
\(307\) 5.45543i 0.311358i −0.987808 0.155679i \(-0.950243\pi\)
0.987808 0.155679i \(-0.0497565\pi\)
\(308\) 2.46607i 0.140517i
\(309\) 8.14215 0.463191
\(310\) 13.9243 + 8.50273i 0.790849 + 0.482922i
\(311\) 6.69721 0.379764 0.189882 0.981807i \(-0.439189\pi\)
0.189882 + 0.981807i \(0.439189\pi\)
\(312\) 14.4292i 0.816892i
\(313\) 4.58279i 0.259035i −0.991577 0.129517i \(-0.958657\pi\)
0.991577 0.129517i \(-0.0413428\pi\)
\(314\) −19.1462 −1.08048
\(315\) −21.6999 13.2508i −1.22265 0.746598i
\(316\) 6.32866 0.356015
\(317\) 27.6794i 1.55463i −0.629113 0.777314i \(-0.716582\pi\)
0.629113 0.777314i \(-0.283418\pi\)
\(318\) 48.6435i 2.72779i
\(319\) −1.60163 −0.0896738
\(320\) −0.808286 + 1.32368i −0.0451846 + 0.0739957i
\(321\) −4.17759 −0.233170
\(322\) 33.2520i 1.85306i
\(323\) 0 0
\(324\) 11.6754 0.648636
\(325\) 18.5120 9.50584i 1.02686 0.527289i
\(326\) −30.2264 −1.67409
\(327\) 8.38903i 0.463914i
\(328\) 6.34983i 0.350611i
\(329\) −11.1125 −0.612651
\(330\) 2.43366 3.98544i 0.133969 0.219391i
\(331\) −14.1302 −0.776665 −0.388332 0.921519i \(-0.626949\pi\)
−0.388332 + 0.921519i \(0.626949\pi\)
\(332\) 9.61782i 0.527847i
\(333\) 5.75203i 0.315209i
\(334\) −29.0130 −1.58752
\(335\) −13.6584 8.34032i −0.746237 0.455681i
\(336\) −50.1791 −2.73749
\(337\) 14.9974i 0.816962i 0.912767 + 0.408481i \(0.133941\pi\)
−0.912767 + 0.408481i \(0.866059\pi\)
\(338\) 7.71372i 0.419571i
\(339\) −31.6046 −1.71653
\(340\) 4.60505 + 2.81202i 0.249744 + 0.152503i
\(341\) −2.00692 −0.108681
\(342\) 0 0
\(343\) 16.8294i 0.908703i
\(344\) 15.4514 0.833082
\(345\) 12.2096 19.9948i 0.657341 1.07648i
\(346\) 15.3324 0.824274
\(347\) 20.9133i 1.12268i −0.827584 0.561342i \(-0.810285\pi\)
0.827584 0.561342i \(-0.189715\pi\)
\(348\) 9.21696i 0.494081i
\(349\) 3.13055 0.167574 0.0837872 0.996484i \(-0.473298\pi\)
0.0837872 + 0.996484i \(0.473298\pi\)
\(350\) 17.2792 + 33.6501i 0.923612 + 1.79867i
\(351\) −3.15151 −0.168215
\(352\) 2.92251i 0.155771i
\(353\) 8.04538i 0.428212i −0.976810 0.214106i \(-0.931316\pi\)
0.976810 0.214106i \(-0.0686838\pi\)
\(354\) 2.30711 0.122622
\(355\) −7.03700 + 11.5240i −0.373485 + 0.611631i
\(356\) −5.14441 −0.272653
\(357\) 20.5758i 1.08899i
\(358\) 41.9891i 2.21920i
\(359\) −30.5842 −1.61417 −0.807087 0.590432i \(-0.798957\pi\)
−0.807087 + 0.590432i \(0.798957\pi\)
\(360\) −7.44493 4.54616i −0.392382 0.239603i
\(361\) 0 0
\(362\) 29.6497i 1.55835i
\(363\) 25.6470i 1.34612i
\(364\) −20.9085 −1.09590
\(365\) −3.92021 2.39383i −0.205193 0.125299i
\(366\) −58.0377 −3.03368
\(367\) 9.95175i 0.519477i −0.965679 0.259739i \(-0.916364\pi\)
0.965679 0.259739i \(-0.0836364\pi\)
\(368\) 21.8257i 1.13774i
\(369\) −11.7112 −0.609659
\(370\) −4.45984 + 7.30357i −0.231856 + 0.379694i
\(371\) 48.4703 2.51645
\(372\) 11.5493i 0.598804i
\(373\) 9.27611i 0.480299i 0.970736 + 0.240149i \(0.0771964\pi\)
−0.970736 + 0.240149i \(0.922804\pi\)
\(374\) −1.78387 −0.0922416
\(375\) −1.96557 + 26.5787i −0.101502 + 1.37252i
\(376\) −3.81253 −0.196616
\(377\) 13.5793i 0.699372i
\(378\) 5.72864i 0.294649i
\(379\) 21.1472 1.08626 0.543129 0.839649i \(-0.317239\pi\)
0.543129 + 0.839649i \(0.317239\pi\)
\(380\) 0 0
\(381\) −47.2181 −2.41906
\(382\) 22.8634i 1.16979i
\(383\) 15.1501i 0.774136i 0.922051 + 0.387068i \(0.126512\pi\)
−0.922051 + 0.387068i \(0.873488\pi\)
\(384\) −25.4328 −1.29786
\(385\) −3.97125 2.42499i −0.202394 0.123589i
\(386\) 17.2040 0.875660
\(387\) 28.4974i 1.44860i
\(388\) 6.69177i 0.339723i
\(389\) 31.4483 1.59449 0.797247 0.603653i \(-0.206289\pi\)
0.797247 + 0.603653i \(0.206289\pi\)
\(390\) −33.7905 20.6337i −1.71105 1.04483i
\(391\) −8.94958 −0.452600
\(392\) 15.9546i 0.805827i
\(393\) 8.17642i 0.412446i
\(394\) −5.53681 −0.278940
\(395\) 6.22326 10.1914i 0.313126 0.512785i
\(396\) −1.56043 −0.0784147
\(397\) 9.38559i 0.471049i −0.971868 0.235525i \(-0.924319\pi\)
0.971868 0.235525i \(-0.0756808\pi\)
\(398\) 0.935689i 0.0469019i
\(399\) 0 0
\(400\) 11.3416 + 22.0870i 0.567079 + 1.10435i
\(401\) 6.16049 0.307640 0.153820 0.988099i \(-0.450842\pi\)
0.153820 + 0.988099i \(0.450842\pi\)
\(402\) 30.4477i 1.51859i
\(403\) 17.0156i 0.847607i
\(404\) 3.91173 0.194616
\(405\) 11.4810 18.8016i 0.570495 0.934261i
\(406\) −24.6838 −1.22504
\(407\) 1.05266i 0.0521786i
\(408\) 7.05927i 0.349486i
\(409\) −2.28482 −0.112977 −0.0564885 0.998403i \(-0.517990\pi\)
−0.0564885 + 0.998403i \(0.517990\pi\)
\(410\) 14.8701 + 9.08025i 0.734382 + 0.448442i
\(411\) 1.45004 0.0715250
\(412\) 4.04783i 0.199422i
\(413\) 2.29889i 0.113121i
\(414\) −21.0406 −1.03409
\(415\) −15.4881 9.45765i −0.760283 0.464258i
\(416\) −24.7785 −1.21486
\(417\) 20.1619i 0.987332i
\(418\) 0 0
\(419\) 22.6494 1.10649 0.553247 0.833017i \(-0.313389\pi\)
0.553247 + 0.833017i \(0.313389\pi\)
\(420\) 13.9553 22.8536i 0.680947 1.11514i
\(421\) −22.9969 −1.12080 −0.560400 0.828222i \(-0.689353\pi\)
−0.560400 + 0.828222i \(0.689353\pi\)
\(422\) 34.0226i 1.65620i
\(423\) 7.03155i 0.341886i
\(424\) 16.6294 0.807597
\(425\) 9.05672 4.65059i 0.439315 0.225587i
\(426\) 25.6897 1.24467
\(427\) 57.8310i 2.79864i
\(428\) 2.07687i 0.100389i
\(429\) 4.87022 0.235137
\(430\) −22.0955 + 36.1842i −1.06554 + 1.74496i
\(431\) 25.6319 1.23465 0.617323 0.786710i \(-0.288217\pi\)
0.617323 + 0.786710i \(0.288217\pi\)
\(432\) 3.76012i 0.180909i
\(433\) 2.36330i 0.113573i 0.998386 + 0.0567864i \(0.0180854\pi\)
−0.998386 + 0.0567864i \(0.981915\pi\)
\(434\) −30.9300 −1.48469
\(435\) −14.8426 9.06346i −0.711648 0.434560i
\(436\) −4.17056 −0.199734
\(437\) 0 0
\(438\) 8.73906i 0.417568i
\(439\) 6.31659 0.301474 0.150737 0.988574i \(-0.451835\pi\)
0.150737 + 0.988574i \(0.451835\pi\)
\(440\) −1.36248 0.831980i −0.0649535 0.0396631i
\(441\) 29.4254 1.40121
\(442\) 15.1245i 0.719399i
\(443\) 31.5246i 1.49778i 0.662694 + 0.748890i \(0.269413\pi\)
−0.662694 + 0.748890i \(0.730587\pi\)
\(444\) 6.05782 0.287492
\(445\) −5.05874 + 8.28434i −0.239807 + 0.392716i
\(446\) −5.64463 −0.267281
\(447\) 11.0544i 0.522854i
\(448\) 2.94027i 0.138915i
\(449\) 15.0828 0.711803 0.355902 0.934523i \(-0.384174\pi\)
0.355902 + 0.934523i \(0.384174\pi\)
\(450\) 21.2925 10.9336i 1.00374 0.515416i
\(451\) −2.14323 −0.100921
\(452\) 15.7121i 0.739033i
\(453\) 33.8754i 1.59161i
\(454\) 16.1452 0.757730
\(455\) −20.5603 + 33.6701i −0.963880 + 1.57848i
\(456\) 0 0
\(457\) 20.1347i 0.941861i −0.882170 0.470930i \(-0.843918\pi\)
0.882170 0.470930i \(-0.156082\pi\)
\(458\) 31.9314i 1.49206i
\(459\) −1.54183 −0.0719664
\(460\) 9.94028 + 6.06992i 0.463468 + 0.283011i
\(461\) −7.48489 −0.348606 −0.174303 0.984692i \(-0.555767\pi\)
−0.174303 + 0.984692i \(0.555767\pi\)
\(462\) 8.85283i 0.411871i
\(463\) 21.5973i 1.00371i −0.864952 0.501855i \(-0.832651\pi\)
0.864952 0.501855i \(-0.167349\pi\)
\(464\) −16.2017 −0.752147
\(465\) −18.5985 11.3570i −0.862486 0.526666i
\(466\) 11.4992 0.532691
\(467\) 27.0503i 1.25174i 0.779927 + 0.625870i \(0.215256\pi\)
−0.779927 + 0.625870i \(0.784744\pi\)
\(468\) 13.2301i 0.611561i
\(469\) 30.3392 1.40094
\(470\) 5.45192 8.92823i 0.251478 0.411828i
\(471\) 25.5732 1.17835
\(472\) 0.788717i 0.0363036i
\(473\) 5.21524i 0.239797i
\(474\) −22.7190 −1.04352
\(475\) 0 0
\(476\) −10.2292 −0.468853
\(477\) 30.6702i 1.40429i
\(478\) 24.0470i 1.09989i
\(479\) 38.0534 1.73870 0.869352 0.494193i \(-0.164536\pi\)
0.869352 + 0.494193i \(0.164536\pi\)
\(480\) 16.5383 27.0836i 0.754865 1.23619i
\(481\) −8.92499 −0.406944
\(482\) 31.4731i 1.43356i
\(483\) 44.4142i 2.02092i
\(484\) 12.7503 0.579558
\(485\) 10.7761 + 6.58032i 0.489319 + 0.298797i
\(486\) −37.8591 −1.71732
\(487\) 18.3353i 0.830851i 0.909627 + 0.415426i \(0.136367\pi\)
−0.909627 + 0.415426i \(0.863633\pi\)
\(488\) 19.8410i 0.898158i
\(489\) 40.3730 1.82573
\(490\) −37.3626 22.8150i −1.68787 1.03068i
\(491\) −15.0675 −0.679986 −0.339993 0.940428i \(-0.610425\pi\)
−0.339993 + 0.940428i \(0.610425\pi\)
\(492\) 12.3338i 0.556049i
\(493\) 6.64350i 0.299208i
\(494\) 0 0
\(495\) −1.53444 + 2.51285i −0.0689682 + 0.112944i
\(496\) −20.3016 −0.911568
\(497\) 25.5982i 1.14824i
\(498\) 34.5266i 1.54717i
\(499\) −34.5299 −1.54577 −0.772886 0.634545i \(-0.781188\pi\)
−0.772886 + 0.634545i \(0.781188\pi\)
\(500\) −13.2135 0.977174i −0.590925 0.0437005i
\(501\) 38.7522 1.73132
\(502\) 31.6470i 1.41247i
\(503\) 30.8704i 1.37644i −0.725501 0.688221i \(-0.758392\pi\)
0.725501 0.688221i \(-0.241608\pi\)
\(504\) 16.5374 0.736632
\(505\) 3.84658 6.29929i 0.171171 0.280315i
\(506\) −3.85059 −0.171179
\(507\) 10.3031i 0.457577i
\(508\) 23.4742i 1.04150i
\(509\) −10.1777 −0.451118 −0.225559 0.974230i \(-0.572421\pi\)
−0.225559 + 0.974230i \(0.572421\pi\)
\(510\) −16.5315 10.0948i −0.732027 0.447003i
\(511\) 8.70794 0.385217
\(512\) 15.1195i 0.668194i
\(513\) 0 0
\(514\) −49.5204 −2.18425
\(515\) 6.51845 + 3.98041i 0.287237 + 0.175398i
\(516\) 30.0124 1.32122
\(517\) 1.28683i 0.0565946i
\(518\) 16.2234i 0.712813i
\(519\) −20.4792 −0.898938
\(520\) −7.05392 + 11.5517i −0.309335 + 0.506577i
\(521\) 16.5423 0.724732 0.362366 0.932036i \(-0.381969\pi\)
0.362366 + 0.932036i \(0.381969\pi\)
\(522\) 15.6190i 0.683624i
\(523\) 7.99801i 0.349729i −0.984593 0.174864i \(-0.944051\pi\)
0.984593 0.174864i \(-0.0559487\pi\)
\(524\) 4.06486 0.177574
\(525\) −23.0796 44.9459i −1.00727 1.96160i
\(526\) −9.92338 −0.432680
\(527\) 8.32463i 0.362626i
\(528\) 5.81075i 0.252880i
\(529\) 3.68180 0.160078
\(530\) −23.7801 + 38.9431i −1.03294 + 1.69158i
\(531\) −1.45465 −0.0631266
\(532\) 0 0
\(533\) 18.1713i 0.787088i
\(534\) 18.4677 0.799176
\(535\) −3.34450 2.04228i −0.144595 0.0882953i
\(536\) 10.4089 0.449598
\(537\) 56.0843i 2.42021i
\(538\) 8.25886i 0.356065i
\(539\) 5.38507 0.231952
\(540\) 1.71251 + 1.04572i 0.0736946 + 0.0450007i
\(541\) 5.20048 0.223586 0.111793 0.993732i \(-0.464341\pi\)
0.111793 + 0.993732i \(0.464341\pi\)
\(542\) 13.5785i 0.583247i
\(543\) 39.6026i 1.69951i
\(544\) −12.1225 −0.519748
\(545\) −4.10110 + 6.71609i −0.175672 + 0.287686i
\(546\) 75.0585 3.21221
\(547\) 11.0339i 0.471777i −0.971780 0.235889i \(-0.924200\pi\)
0.971780 0.235889i \(-0.0758001\pi\)
\(548\) 0.720878i 0.0307944i
\(549\) 36.5933 1.56176
\(550\) 3.89668 2.00093i 0.166155 0.0853201i
\(551\) 0 0
\(552\) 15.2379i 0.648566i
\(553\) 22.6381i 0.962669i
\(554\) 13.4483 0.571365
\(555\) 5.95694 9.75526i 0.252858 0.414088i
\(556\) −10.0234 −0.425086
\(557\) 21.2817i 0.901735i 0.892591 + 0.450867i \(0.148885\pi\)
−0.892591 + 0.450867i \(0.851115\pi\)
\(558\) 19.5713i 0.828521i
\(559\) −44.2173 −1.87019
\(560\) −40.1724 24.5308i −1.69759 1.03662i
\(561\) 2.38269 0.100597
\(562\) 32.5792i 1.37427i
\(563\) 14.7072i 0.619833i 0.950764 + 0.309917i \(0.100301\pi\)
−0.950764 + 0.309917i \(0.899699\pi\)
\(564\) −7.40537 −0.311822
\(565\) −25.3020 15.4504i −1.06446 0.650003i
\(566\) 55.2061 2.32048
\(567\) 41.7639i 1.75392i
\(568\) 8.78236i 0.368500i
\(569\) −40.6551 −1.70435 −0.852174 0.523258i \(-0.824716\pi\)
−0.852174 + 0.523258i \(0.824716\pi\)
\(570\) 0 0
\(571\) −24.3240 −1.01793 −0.508964 0.860788i \(-0.669972\pi\)
−0.508964 + 0.860788i \(0.669972\pi\)
\(572\) 2.42120i 0.101236i
\(573\) 30.5382i 1.27575i
\(574\) −33.0308 −1.37868
\(575\) 19.5495 10.0386i 0.815269 0.418638i
\(576\) −1.86049 −0.0775204
\(577\) 33.6876i 1.40243i −0.712949 0.701216i \(-0.752641\pi\)
0.712949 0.701216i \(-0.247359\pi\)
\(578\) 22.9401i 0.954182i
\(579\) −22.9791 −0.954979
\(580\) 4.50585 7.37892i 0.187095 0.306393i
\(581\) 34.4037 1.42730
\(582\) 24.0225i 0.995764i
\(583\) 5.61287i 0.232461i
\(584\) 2.98757 0.123626
\(585\) 21.3052 + 13.0098i 0.880861 + 0.537887i
\(586\) −39.0830 −1.61451
\(587\) 2.24977i 0.0928580i 0.998922 + 0.0464290i \(0.0147841\pi\)
−0.998922 + 0.0464290i \(0.985216\pi\)
\(588\) 30.9898i 1.27800i
\(589\) 0 0
\(590\) 1.84703 + 1.12787i 0.0760409 + 0.0464335i
\(591\) 7.39543 0.304207
\(592\) 10.6486i 0.437653i
\(593\) 31.3871i 1.28891i −0.764640 0.644457i \(-0.777083\pi\)
0.764640 0.644457i \(-0.222917\pi\)
\(594\) −0.663377 −0.0272187
\(595\) −10.0588 + 16.4726i −0.412371 + 0.675312i
\(596\) −5.49562 −0.225109
\(597\) 1.24979i 0.0511503i
\(598\) 32.6471i 1.33504i
\(599\) −10.4068 −0.425212 −0.212606 0.977138i \(-0.568195\pi\)
−0.212606 + 0.977138i \(0.568195\pi\)
\(600\) −7.91826 15.4203i −0.323262 0.629530i
\(601\) −1.29592 −0.0528616 −0.0264308 0.999651i \(-0.508414\pi\)
−0.0264308 + 0.999651i \(0.508414\pi\)
\(602\) 80.3757i 3.27587i
\(603\) 19.1975i 0.781783i
\(604\) −16.8410 −0.685249
\(605\) 12.5379 20.5325i 0.509739 0.834765i
\(606\) −14.0426 −0.570440
\(607\) 5.50902i 0.223604i −0.993730 0.111802i \(-0.964338\pi\)
0.993730 0.111802i \(-0.0356623\pi\)
\(608\) 0 0
\(609\) 32.9698 1.33600
\(610\) −46.4638 28.3726i −1.88127 1.14877i
\(611\) 10.9103 0.441385
\(612\) 6.47263i 0.261641i
\(613\) 40.6727i 1.64275i −0.570386 0.821376i \(-0.693207\pi\)
0.570386 0.821376i \(-0.306793\pi\)
\(614\) −9.73619 −0.392921
\(615\) −19.8618 12.1284i −0.800904 0.489062i
\(616\) 3.02646 0.121939
\(617\) 30.5053i 1.22810i −0.789268 0.614049i \(-0.789540\pi\)
0.789268 0.614049i \(-0.210460\pi\)
\(618\) 14.5311i 0.584527i
\(619\) −5.80411 −0.233287 −0.116643 0.993174i \(-0.537213\pi\)
−0.116643 + 0.993174i \(0.537213\pi\)
\(620\) 5.64605 9.24615i 0.226751 0.371334i
\(621\) −3.32813 −0.133553
\(622\) 11.9524i 0.479246i
\(623\) 18.4019i 0.737258i
\(624\) 49.2663 1.97223
\(625\) −14.5670 + 20.3175i −0.582681 + 0.812701i
\(626\) −8.17881 −0.326891
\(627\) 0 0
\(628\) 12.7136i 0.507328i
\(629\) −4.36642 −0.174101
\(630\) −23.6484 + 38.7274i −0.942176 + 1.54294i
\(631\) −23.3642 −0.930116 −0.465058 0.885280i \(-0.653967\pi\)
−0.465058 + 0.885280i \(0.653967\pi\)
\(632\) 7.76679i 0.308946i
\(633\) 45.4435i 1.80622i
\(634\) −49.3987 −1.96187
\(635\) −37.8019 23.0833i −1.50012 0.916032i
\(636\) 32.3007 1.28080
\(637\) 45.6572i 1.80901i
\(638\) 2.85839i 0.113165i
\(639\) −16.1976 −0.640766
\(640\) −20.3610 12.4332i −0.804839 0.491465i
\(641\) 18.3459 0.724621 0.362311 0.932057i \(-0.381988\pi\)
0.362311 + 0.932057i \(0.381988\pi\)
\(642\) 7.45565i 0.294251i
\(643\) 15.7630i 0.621633i 0.950470 + 0.310817i \(0.100603\pi\)
−0.950470 + 0.310817i \(0.899397\pi\)
\(644\) −22.0803 −0.870084
\(645\) 29.5126 48.3307i 1.16206 1.90302i
\(646\) 0 0
\(647\) 25.0443i 0.984592i 0.870428 + 0.492296i \(0.163842\pi\)
−0.870428 + 0.492296i \(0.836158\pi\)
\(648\) 14.3286i 0.562880i
\(649\) −0.266212 −0.0104497
\(650\) −16.9649 33.0379i −0.665417 1.29585i
\(651\) 41.3127 1.61917
\(652\) 20.0712i 0.786049i
\(653\) 2.98852i 0.116950i 0.998289 + 0.0584749i \(0.0186238\pi\)
−0.998289 + 0.0584749i \(0.981376\pi\)
\(654\) 14.9717 0.585440
\(655\) 3.99716 6.54588i 0.156182 0.255769i
\(656\) −21.6805 −0.846482
\(657\) 5.51005i 0.214968i
\(658\) 19.8322i 0.773140i
\(659\) 35.7695 1.39338 0.696691 0.717372i \(-0.254655\pi\)
0.696691 + 0.717372i \(0.254655\pi\)
\(660\) −2.64644 1.61602i −0.103013 0.0629035i
\(661\) 3.22147 0.125301 0.0626503 0.998036i \(-0.480045\pi\)
0.0626503 + 0.998036i \(0.480045\pi\)
\(662\) 25.2178i 0.980118i
\(663\) 20.2015i 0.784563i
\(664\) 11.8034 0.458061
\(665\) 0 0
\(666\) −10.2655 −0.397781
\(667\) 14.3404i 0.555262i
\(668\) 19.2655i 0.745403i
\(669\) 7.53945 0.291492
\(670\) −14.8848 + 24.3758i −0.575050 + 0.941720i
\(671\) 6.69684 0.258529
\(672\) 60.1605i 2.32074i
\(673\) 0.639706i 0.0246588i −0.999924 0.0123294i \(-0.996075\pi\)
0.999924 0.0123294i \(-0.00392468\pi\)
\(674\) 26.7656 1.03097
\(675\) 3.36797 1.72944i 0.129633 0.0665663i
\(676\) 5.12213 0.197005
\(677\) 25.8005i 0.991592i −0.868439 0.495796i \(-0.834876\pi\)
0.868439 0.495796i \(-0.165124\pi\)
\(678\) 56.4041i 2.16618i
\(679\) −23.9369 −0.918616
\(680\) −3.45103 + 5.65151i −0.132341 + 0.216726i
\(681\) −21.5648 −0.826366
\(682\) 3.58170i 0.137150i
\(683\) 5.33696i 0.204213i 0.994773 + 0.102107i \(0.0325583\pi\)
−0.994773 + 0.102107i \(0.967442\pi\)
\(684\) 0 0
\(685\) 1.16087 + 0.708872i 0.0443546 + 0.0270846i
\(686\) 30.0351 1.14675
\(687\) 42.6503i 1.62721i
\(688\) 52.7564i 2.01132i
\(689\) −47.5886 −1.81298
\(690\) −35.6842 21.7901i −1.35847 0.829536i
\(691\) 13.2507 0.504079 0.252040 0.967717i \(-0.418899\pi\)
0.252040 + 0.967717i \(0.418899\pi\)
\(692\) 10.1811i 0.387029i
\(693\) 5.58178i 0.212034i
\(694\) −37.3235 −1.41678
\(695\) −9.85644 + 16.1412i −0.373876 + 0.612271i
\(696\) 11.3114 0.428759
\(697\) 8.89006i 0.336735i
\(698\) 5.58702i 0.211472i
\(699\) −15.3593 −0.580943
\(700\) 22.3446 11.4739i 0.844547 0.433672i
\(701\) 40.8699 1.54363 0.771817 0.635845i \(-0.219348\pi\)
0.771817 + 0.635845i \(0.219348\pi\)
\(702\) 5.62443i 0.212280i
\(703\) 0 0
\(704\) −0.340484 −0.0128325
\(705\) −7.28204 + 11.9253i −0.274257 + 0.449133i
\(706\) −14.3584 −0.540386
\(707\) 13.9925i 0.526244i
\(708\) 1.53199i 0.0575756i
\(709\) −7.35745 −0.276315 −0.138157 0.990410i \(-0.544118\pi\)
−0.138157 + 0.990410i \(0.544118\pi\)
\(710\) 20.5666 + 12.5588i 0.771853 + 0.471323i
\(711\) 14.3245 0.537211
\(712\) 6.31344i 0.236606i
\(713\) 17.9692i 0.672952i
\(714\) 36.7213 1.37426
\(715\) 3.89901 + 2.38088i 0.145815 + 0.0890399i
\(716\) −27.8820 −1.04200
\(717\) 32.1193i 1.19952i
\(718\) 54.5830i 2.03702i
\(719\) 31.9597 1.19190 0.595948 0.803023i \(-0.296776\pi\)
0.595948 + 0.803023i \(0.296776\pi\)
\(720\) −15.5222 + 25.4196i −0.578477 + 0.947332i
\(721\) −14.4794 −0.539240
\(722\) 0 0
\(723\) 42.0381i 1.56341i
\(724\) 19.6882 0.731707
\(725\) −7.45189 14.5121i −0.276756 0.538964i
\(726\) −45.7717 −1.69875
\(727\) 29.3883i 1.08995i 0.838452 + 0.544976i \(0.183461\pi\)
−0.838452 + 0.544976i \(0.816539\pi\)
\(728\) 25.6598i 0.951014i
\(729\) 21.0116 0.778207
\(730\) −4.27222 + 6.99632i −0.158122 + 0.258945i
\(731\) −21.6326 −0.800112
\(732\) 38.5387i 1.42443i
\(733\) 50.8285i 1.87739i −0.344745 0.938696i \(-0.612035\pi\)
0.344745 0.938696i \(-0.387965\pi\)
\(734\) −17.7607 −0.655559
\(735\) 49.9046 + 30.4737i 1.84076 + 1.12404i
\(736\) −26.1671 −0.964534
\(737\) 3.51329i 0.129414i
\(738\) 20.9007i 0.769364i
\(739\) −14.7245 −0.541650 −0.270825 0.962629i \(-0.587296\pi\)
−0.270825 + 0.962629i \(0.587296\pi\)
\(740\) 4.84978 + 2.96146i 0.178281 + 0.108865i
\(741\) 0 0
\(742\) 86.5039i 3.17566i
\(743\) 34.6568i 1.27144i 0.771922 + 0.635718i \(0.219296\pi\)
−0.771922 + 0.635718i \(0.780704\pi\)
\(744\) 14.1738 0.519636
\(745\) −5.40409 + 8.84991i −0.197991 + 0.324236i
\(746\) 16.5549 0.606117
\(747\) 21.7693i 0.796498i
\(748\) 1.18454i 0.0433110i
\(749\) 7.42910 0.271453
\(750\) 47.4345 + 3.50792i 1.73206 + 0.128091i
\(751\) −8.35539 −0.304893 −0.152446 0.988312i \(-0.548715\pi\)
−0.152446 + 0.988312i \(0.548715\pi\)
\(752\) 13.0173i 0.474692i
\(753\) 42.2704i 1.54042i
\(754\) 24.2348 0.882578
\(755\) −16.5605 + 27.1200i −0.602698 + 0.986998i
\(756\) −3.80398 −0.138349
\(757\) 13.8709i 0.504146i −0.967708 0.252073i \(-0.918888\pi\)
0.967708 0.252073i \(-0.0811123\pi\)
\(758\) 37.7410i 1.37081i
\(759\) 5.14317 0.186685
\(760\) 0 0
\(761\) 44.3970 1.60939 0.804696 0.593687i \(-0.202328\pi\)
0.804696 + 0.593687i \(0.202328\pi\)
\(762\) 84.2692i 3.05275i
\(763\) 14.9184i 0.540082i
\(764\) 15.1819 0.549262
\(765\) 10.4232 + 6.36483i 0.376853 + 0.230121i
\(766\) 27.0381 0.976927
\(767\) 2.25707i 0.0814983i
\(768\) 48.6961i 1.75717i
\(769\) −19.0001 −0.685160 −0.342580 0.939489i \(-0.611301\pi\)
−0.342580 + 0.939489i \(0.611301\pi\)
\(770\) −4.32784 + 7.08740i −0.155964 + 0.255412i
\(771\) 66.1436 2.38210
\(772\) 11.4239i 0.411157i
\(773\) 1.86738i 0.0671650i −0.999436 0.0335825i \(-0.989308\pi\)
0.999436 0.0335825i \(-0.0106917\pi\)
\(774\) −50.8587 −1.82808
\(775\) −9.33759 18.1843i −0.335416 0.653200i
\(776\) −8.21241 −0.294808
\(777\) 21.6693i 0.777381i
\(778\) 56.1252i 2.01218i
\(779\) 0 0
\(780\) −13.7014 + 22.4378i −0.490588 + 0.803403i
\(781\) −2.96427 −0.106070
\(782\) 15.9721i 0.571162i
\(783\) 2.47055i 0.0882904i
\(784\) 54.4744 1.94552
\(785\) 20.4734 + 12.5019i 0.730728 + 0.446211i
\(786\) −14.5923 −0.520489
\(787\) 12.9689i 0.462291i −0.972919 0.231146i \(-0.925753\pi\)
0.972919 0.231146i \(-0.0742474\pi\)
\(788\) 3.67660i 0.130973i
\(789\) 13.2545 0.471873
\(790\) −18.1884 11.1065i −0.647113 0.395152i
\(791\) 56.2032 1.99836
\(792\) 1.91503i 0.0680476i
\(793\) 56.7790i 2.01628i
\(794\) −16.7503 −0.594444
\(795\) 31.7627 52.0156i 1.12651 1.84480i
\(796\) 0.621324 0.0220222
\(797\) 29.9226i 1.05991i 0.848025 + 0.529956i \(0.177791\pi\)
−0.848025 + 0.529956i \(0.822209\pi\)
\(798\) 0 0
\(799\) 5.33772 0.188835
\(800\) 26.4804 13.5976i 0.936224 0.480748i
\(801\) −11.6441 −0.411422
\(802\) 10.9945i 0.388229i
\(803\) 1.00838i 0.0355850i
\(804\) 20.2181 0.713038
\(805\) −21.7125 + 35.5571i −0.765266 + 1.25322i
\(806\) 30.3674 1.06964
\(807\) 11.0312i 0.388318i
\(808\) 4.80064i 0.168886i
\(809\) −42.4578 −1.49274 −0.746369 0.665532i \(-0.768205\pi\)
−0.746369 + 0.665532i \(0.768205\pi\)
\(810\) −33.5549 20.4899i −1.17900 0.719941i
\(811\) −31.1514 −1.09387 −0.546936 0.837174i \(-0.684206\pi\)
−0.546936 + 0.837174i \(0.684206\pi\)
\(812\) 16.3907i 0.575202i
\(813\) 18.1366i 0.636079i
\(814\) −1.87867 −0.0658472
\(815\) 32.3218 + 19.7369i 1.13218 + 0.691354i
\(816\) 24.1028 0.843767
\(817\) 0 0
\(818\) 4.07767i 0.142572i
\(819\) −47.3250 −1.65367
\(820\) 6.02955 9.87417i 0.210561 0.344821i
\(821\) −6.20740 −0.216640 −0.108320 0.994116i \(-0.534547\pi\)
−0.108320 + 0.994116i \(0.534547\pi\)
\(822\) 2.58785i 0.0902616i
\(823\) 35.9702i 1.25384i 0.779083 + 0.626921i \(0.215685\pi\)
−0.779083 + 0.626921i \(0.784315\pi\)
\(824\) −4.96766 −0.173057
\(825\) −5.20474 + 2.67262i −0.181206 + 0.0930486i
\(826\) −4.10279 −0.142754
\(827\) 15.3837i 0.534945i 0.963565 + 0.267473i \(0.0861885\pi\)
−0.963565 + 0.267473i \(0.913811\pi\)
\(828\) 13.9716i 0.485545i
\(829\) 24.1941 0.840295 0.420148 0.907456i \(-0.361978\pi\)
0.420148 + 0.907456i \(0.361978\pi\)
\(830\) −16.8789 + 27.6413i −0.585874 + 0.959445i
\(831\) −17.9627 −0.623120
\(832\) 2.88678i 0.100081i
\(833\) 22.3371i 0.773936i
\(834\) 35.9825 1.24597
\(835\) 31.0243 + 18.9446i 1.07364 + 0.655605i
\(836\) 0 0
\(837\) 3.09573i 0.107004i
\(838\) 40.4218i 1.39635i
\(839\) −12.4265 −0.429012 −0.214506 0.976723i \(-0.568814\pi\)
−0.214506 + 0.976723i \(0.568814\pi\)
\(840\) 28.0468 + 17.1265i 0.967708 + 0.590919i
\(841\) −18.3548 −0.632923
\(842\) 41.0420i 1.41440i
\(843\) 43.5155i 1.49875i
\(844\) 22.5920 0.777649
\(845\) 5.03683 8.24846i 0.173272 0.283756i
\(846\) 12.5491 0.431446
\(847\) 45.6087i 1.56713i
\(848\) 56.7787i 1.94979i
\(849\) −73.7379 −2.53068
\(850\) −8.29982 16.1633i −0.284681 0.554398i
\(851\) −9.42518 −0.323091
\(852\) 17.0587i 0.584420i
\(853\) 23.1527i 0.792734i −0.918092 0.396367i \(-0.870271\pi\)
0.918092 0.396367i \(-0.129729\pi\)
\(854\) 103.210 3.53176
\(855\) 0 0
\(856\) 2.54882 0.0871167
\(857\) 2.84272i 0.0971054i −0.998821 0.0485527i \(-0.984539\pi\)
0.998821 0.0485527i \(-0.0154609\pi\)
\(858\) 8.69178i 0.296733i
\(859\) 25.8715 0.882725 0.441363 0.897329i \(-0.354495\pi\)
0.441363 + 0.897329i \(0.354495\pi\)
\(860\) 24.0273 + 14.6720i 0.819326 + 0.500311i
\(861\) 44.1188 1.50356
\(862\) 45.7447i 1.55807i
\(863\) 38.0032i 1.29365i 0.762641 + 0.646823i \(0.223903\pi\)
−0.762641 + 0.646823i \(0.776097\pi\)
\(864\) −4.50806 −0.153367
\(865\) −16.3953 10.0116i −0.557456 0.340404i
\(866\) 4.21773 0.143324
\(867\) 30.6407i 1.04061i
\(868\) 20.5384i 0.697119i
\(869\) 2.62149 0.0889281
\(870\) −16.1754 + 26.4893i −0.548396 + 0.898071i
\(871\) −29.7873 −1.00931
\(872\) 5.11828i 0.173327i
\(873\) 15.1464i 0.512628i
\(874\) 0 0
\(875\) 3.49542 47.2656i 0.118167 1.59787i
\(876\) 5.80298 0.196065
\(877\) 49.0943i 1.65780i 0.559400 + 0.828898i \(0.311032\pi\)
−0.559400 + 0.828898i \(0.688968\pi\)
\(878\) 11.2731i 0.380448i
\(879\) 52.2026 1.76075
\(880\) −2.84067 + 4.65197i −0.0957590 + 0.156818i
\(881\) −55.7494 −1.87825 −0.939123 0.343581i \(-0.888360\pi\)
−0.939123 + 0.343581i \(0.888360\pi\)
\(882\) 52.5150i 1.76827i
\(883\) 16.6355i 0.559828i 0.960025 + 0.279914i \(0.0903060\pi\)
−0.960025 + 0.279914i \(0.909694\pi\)
\(884\) 10.0431 0.337786
\(885\) −2.46705 1.50647i −0.0829289 0.0506395i
\(886\) 56.2613 1.89014
\(887\) 43.3883i 1.45684i 0.685133 + 0.728418i \(0.259744\pi\)
−0.685133 + 0.728418i \(0.740256\pi\)
\(888\) 7.43441i 0.249483i
\(889\) 83.9691 2.81623
\(890\) 14.7849 + 9.02822i 0.495591 + 0.302626i
\(891\) 4.83627 0.162021
\(892\) 3.74820i 0.125499i
\(893\) 0 0
\(894\) 19.7285 0.659819
\(895\) −27.4176 + 44.9000i −0.916470 + 1.50084i
\(896\) 45.2277 1.51095
\(897\) 43.6062i 1.45597i
\(898\) 26.9180i 0.898266i
\(899\) 13.3390 0.444880
\(900\) −7.26023 14.1388i −0.242008 0.471294i
\(901\) −23.2820 −0.775636
\(902\) 3.82498i 0.127358i
\(903\) 107.357i 3.57260i
\(904\) 19.2825 0.641326
\(905\) 19.3603 31.7051i 0.643559 1.05391i
\(906\) 60.4567 2.00854
\(907\) 19.8364i 0.658656i 0.944216 + 0.329328i \(0.106822\pi\)
−0.944216 + 0.329328i \(0.893178\pi\)
\(908\) 10.7208i 0.355784i
\(909\) 8.85395 0.293667
\(910\) 60.0904 + 36.6935i 1.99198 + 1.21638i
\(911\) 15.4076 0.510478 0.255239 0.966878i \(-0.417846\pi\)
0.255239 + 0.966878i \(0.417846\pi\)
\(912\) 0 0
\(913\) 3.98395i 0.131849i
\(914\) −35.9339 −1.18859
\(915\) 62.0610 + 37.8968i 2.05167 + 1.25283i
\(916\) −21.2034 −0.700579
\(917\) 14.5403i 0.480163i
\(918\) 2.75167i 0.0908186i
\(919\) 13.2561 0.437278 0.218639 0.975806i \(-0.429838\pi\)
0.218639 + 0.975806i \(0.429838\pi\)
\(920\) −7.44925 + 12.1991i −0.245595 + 0.402193i
\(921\) 13.0045 0.428512
\(922\) 13.3581i 0.439926i
\(923\) 25.1325i 0.827247i
\(924\) 5.87853 0.193389
\(925\) 9.53801 4.89774i 0.313608 0.161037i
\(926\) −38.5442 −1.26664
\(927\) 9.16200i 0.300920i
\(928\) 19.4245i 0.637641i
\(929\) −31.2016 −1.02369 −0.511846 0.859077i \(-0.671038\pi\)
−0.511846 + 0.859077i \(0.671038\pi\)
\(930\) −20.2685 + 33.1924i −0.664631 + 1.08842i
\(931\) 0 0
\(932\) 7.63580i 0.250119i
\(933\) 15.9646i 0.522658i
\(934\) 48.2762 1.57964
\(935\) 1.90753 + 1.16481i 0.0623830 + 0.0380934i
\(936\) −16.2365 −0.530707
\(937\) 16.2187i 0.529840i −0.964270 0.264920i \(-0.914654\pi\)
0.964270 0.264920i \(-0.0853456\pi\)
\(938\) 54.1458i 1.76792i
\(939\) 10.9243 0.356502
\(940\) −5.92860 3.62023i −0.193369 0.118079i
\(941\) 35.1748 1.14666 0.573332 0.819323i \(-0.305650\pi\)
0.573332 + 0.819323i \(0.305650\pi\)
\(942\) 45.6400i 1.48703i
\(943\) 19.1897i 0.624903i
\(944\) −2.69295 −0.0876482
\(945\) −3.74063 + 6.12577i −0.121683 + 0.199271i
\(946\) −9.30752 −0.302614
\(947\) 22.2784i 0.723950i −0.932188 0.361975i \(-0.882103\pi\)
0.932188 0.361975i \(-0.117897\pi\)
\(948\) 15.0860i 0.489972i
\(949\) −8.54953 −0.277530
\(950\) 0 0
\(951\) 65.9811 2.13958
\(952\) 12.5537i 0.406866i
\(953\) 4.25996i 0.137994i 0.997617 + 0.0689968i \(0.0219798\pi\)
−0.997617 + 0.0689968i \(0.978020\pi\)
\(954\) −54.7364 −1.77216
\(955\) 14.9291 24.4483i 0.483093 0.791129i
\(956\) −15.9679 −0.516439
\(957\) 3.81790i 0.123415i
\(958\) 67.9131i 2.19417i
\(959\) −2.57863 −0.0832684
\(960\) −3.15533 1.92677i −0.101838 0.0621861i
\(961\) −14.2856 −0.460825
\(962\) 15.9282i 0.513547i
\(963\) 4.70085i 0.151483i
\(964\) 20.8990 0.673111
\(965\) −18.3966 11.2337i −0.592208 0.361625i
\(966\) 79.2650 2.55031
\(967\) 1.21906i 0.0392023i −0.999808 0.0196012i \(-0.993760\pi\)
0.999808 0.0196012i \(-0.00623964\pi\)
\(968\) 15.6477i 0.502935i
\(969\) 0 0
\(970\) 11.7438 19.2319i 0.377069 0.617500i
\(971\) −4.34003 −0.139278 −0.0696391 0.997572i \(-0.522185\pi\)
−0.0696391 + 0.997572i \(0.522185\pi\)
\(972\) 25.1395i 0.806349i
\(973\) 35.8543i 1.14944i
\(974\) 32.7226 1.04850
\(975\) 22.6597 + 44.1283i 0.725692 + 1.41324i
\(976\) 67.7440 2.16843
\(977\) 21.5270i 0.688710i 0.938840 + 0.344355i \(0.111902\pi\)
−0.938840 + 0.344355i \(0.888098\pi\)
\(978\) 72.0527i 2.30399i
\(979\) −2.13095 −0.0681054
\(980\) −15.1498 + 24.8098i −0.483943 + 0.792520i
\(981\) −9.43980 −0.301389
\(982\) 26.8906i 0.858114i
\(983\) 14.5998i 0.465661i −0.972517 0.232830i \(-0.925201\pi\)
0.972517 0.232830i \(-0.0747987\pi\)
\(984\) 15.1365 0.482534
\(985\) 5.92064 + 3.61537i 0.188647 + 0.115195i
\(986\) 11.8565 0.377588
\(987\) 26.4896i 0.843172i
\(988\) 0 0
\(989\) −46.6954 −1.48483
\(990\) 4.48464 + 2.73849i 0.142531 + 0.0870349i
\(991\) 31.9286 1.01425 0.507123 0.861874i \(-0.330709\pi\)
0.507123 + 0.861874i \(0.330709\pi\)
\(992\) 24.3399i 0.772792i
\(993\) 33.6831i 1.06890i
\(994\) −45.6845 −1.44903
\(995\) 0.610976 1.00055i 0.0193692 0.0317197i
\(996\) 22.9267 0.726459
\(997\) 55.1812i 1.74761i 0.486280 + 0.873803i \(0.338353\pi\)
−0.486280 + 0.873803i \(0.661647\pi\)
\(998\) 61.6248i 1.95070i
\(999\) −1.62377 −0.0513737
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 1805.2.b.k.1084.5 24
5.2 odd 4 9025.2.a.cu.1.20 24
5.3 odd 4 9025.2.a.cu.1.5 24
5.4 even 2 inner 1805.2.b.k.1084.20 24
19.4 even 9 95.2.p.a.54.7 yes 48
19.5 even 9 95.2.p.a.44.2 48
19.18 odd 2 1805.2.b.l.1084.20 24
57.5 odd 18 855.2.da.b.424.7 48
57.23 odd 18 855.2.da.b.244.2 48
95.4 even 18 95.2.p.a.54.2 yes 48
95.18 even 4 9025.2.a.ct.1.20 24
95.23 odd 36 475.2.l.f.301.2 48
95.24 even 18 95.2.p.a.44.7 yes 48
95.37 even 4 9025.2.a.ct.1.5 24
95.42 odd 36 475.2.l.f.301.7 48
95.43 odd 36 475.2.l.f.101.2 48
95.62 odd 36 475.2.l.f.101.7 48
95.94 odd 2 1805.2.b.l.1084.5 24
285.119 odd 18 855.2.da.b.424.2 48
285.194 odd 18 855.2.da.b.244.7 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.44.2 48 19.5 even 9
95.2.p.a.44.7 yes 48 95.24 even 18
95.2.p.a.54.2 yes 48 95.4 even 18
95.2.p.a.54.7 yes 48 19.4 even 9
475.2.l.f.101.2 48 95.43 odd 36
475.2.l.f.101.7 48 95.62 odd 36
475.2.l.f.301.2 48 95.23 odd 36
475.2.l.f.301.7 48 95.42 odd 36
855.2.da.b.244.2 48 57.23 odd 18
855.2.da.b.244.7 48 285.194 odd 18
855.2.da.b.424.2 48 285.119 odd 18
855.2.da.b.424.7 48 57.5 odd 18
1805.2.b.k.1084.5 24 1.1 even 1 trivial
1805.2.b.k.1084.20 24 5.4 even 2 inner
1805.2.b.l.1084.5 24 95.94 odd 2
1805.2.b.l.1084.20 24 19.18 odd 2
9025.2.a.ct.1.5 24 95.37 even 4
9025.2.a.ct.1.20 24 95.18 even 4
9025.2.a.cu.1.5 24 5.3 odd 4
9025.2.a.cu.1.20 24 5.2 odd 4