Properties

Label 1008.2.t.i.193.4
Level $1008$
Weight $2$
Character 1008.193
Analytic conductor $8.049$
Analytic rank $0$
Dimension $10$
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] = [1008,2,Mod(193,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.193");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.t (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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 193.4
Root \(-0.335166 + 0.580525i\) of defining polynomial
Character \(\chi\) \(=\) 1008.193
Dual form 1008.2.t.i.961.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.377302 + 1.69046i) q^{3} +1.42494 q^{5} +(-2.21529 + 1.44655i) q^{7} +(-2.71529 + 1.27563i) q^{9} +O(q^{10})\) \(q+(0.377302 + 1.69046i) q^{3} +1.42494 q^{5} +(-2.21529 + 1.44655i) q^{7} +(-2.71529 + 1.27563i) q^{9} +4.93077 q^{11} +(-1.37730 + 2.38556i) q^{13} +(0.537632 + 2.40879i) q^{15} +(0.559839 - 0.969670i) q^{17} +(2.00752 + 3.47713i) q^{19} +(-3.28116 - 3.19906i) q^{21} -5.43661 q^{23} -2.96955 q^{25} +(-3.18087 - 4.10878i) q^{27} +(3.40555 + 5.89858i) q^{29} +(1.25292 + 2.17012i) q^{31} +(1.86039 + 8.33526i) q^{33} +(-3.15664 + 2.06124i) q^{35} +(0.709787 + 1.22939i) q^{37} +(-4.55234 - 1.42819i) q^{39} +(0.124384 - 0.215440i) q^{41} +(0.498313 + 0.863104i) q^{43} +(-3.86911 + 1.81769i) q^{45} +(-4.73790 + 8.20628i) q^{47} +(2.81498 - 6.40905i) q^{49} +(1.85041 + 0.580525i) q^{51} +(-0.410229 + 0.710537i) q^{53} +7.02604 q^{55} +(-5.12050 + 4.70556i) q^{57} +(-3.29204 - 5.70197i) q^{59} +(-0.0376322 + 0.0651809i) q^{61} +(4.16988 - 6.75368i) q^{63} +(-1.96257 + 3.39927i) q^{65} +(-6.29385 - 10.9013i) q^{67} +(-2.05125 - 9.19035i) q^{69} -0.0804951 q^{71} +(5.34551 - 9.25869i) q^{73} +(-1.12042 - 5.01990i) q^{75} +(-10.9231 + 7.13261i) q^{77} +(-0.922457 + 1.59774i) q^{79} +(5.74555 - 6.92738i) q^{81} +(7.23583 + 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} +(-8.68637 + 7.98248i) q^{87} +(6.76292 + 11.7137i) q^{89} +(-0.399711 - 7.27703i) q^{91} +(-3.19576 + 2.93679i) q^{93} +(2.86059 + 4.95469i) q^{95} +(2.70160 + 4.67930i) q^{97} +(-13.3885 + 6.28982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.377302 + 1.69046i 0.217836 + 0.975985i
\(4\) 0 0
\(5\) 1.42494 0.637251 0.318626 0.947881i \(-0.396779\pi\)
0.318626 + 0.947881i \(0.396779\pi\)
\(6\) 0 0
\(7\) −2.21529 + 1.44655i −0.837299 + 0.546745i
\(8\) 0 0
\(9\) −2.71529 + 1.27563i −0.905095 + 0.425209i
\(10\) 0 0
\(11\) 4.93077 1.48668 0.743342 0.668911i \(-0.233239\pi\)
0.743342 + 0.668911i \(0.233239\pi\)
\(12\) 0 0
\(13\) −1.37730 + 2.38556i −0.381995 + 0.661635i −0.991347 0.131265i \(-0.958096\pi\)
0.609352 + 0.792900i \(0.291429\pi\)
\(14\) 0 0
\(15\) 0.537632 + 2.40879i 0.138816 + 0.621948i
\(16\) 0 0
\(17\) 0.559839 0.969670i 0.135781 0.235180i −0.790115 0.612959i \(-0.789979\pi\)
0.925896 + 0.377780i \(0.123312\pi\)
\(18\) 0 0
\(19\) 2.00752 + 3.47713i 0.460557 + 0.797709i 0.998989 0.0449606i \(-0.0143162\pi\)
−0.538431 + 0.842669i \(0.680983\pi\)
\(20\) 0 0
\(21\) −3.28116 3.19906i −0.716009 0.698092i
\(22\) 0 0
\(23\) −5.43661 −1.13361 −0.566806 0.823851i \(-0.691821\pi\)
−0.566806 + 0.823851i \(0.691821\pi\)
\(24\) 0 0
\(25\) −2.96955 −0.593911
\(26\) 0 0
\(27\) −3.18087 4.10878i −0.612160 0.790734i
\(28\) 0 0
\(29\) 3.40555 + 5.89858i 0.632394 + 1.09534i 0.987061 + 0.160346i \(0.0512611\pi\)
−0.354667 + 0.934993i \(0.615406\pi\)
\(30\) 0 0
\(31\) 1.25292 + 2.17012i 0.225031 + 0.389765i 0.956329 0.292294i \(-0.0944184\pi\)
−0.731298 + 0.682058i \(0.761085\pi\)
\(32\) 0 0
\(33\) 1.86039 + 8.33526i 0.323853 + 1.45098i
\(34\) 0 0
\(35\) −3.15664 + 2.06124i −0.533570 + 0.348414i
\(36\) 0 0
\(37\) 0.709787 + 1.22939i 0.116688 + 0.202110i 0.918453 0.395529i \(-0.129439\pi\)
−0.801765 + 0.597639i \(0.796106\pi\)
\(38\) 0 0
\(39\) −4.55234 1.42819i −0.728958 0.228694i
\(40\) 0 0
\(41\) 0.124384 0.215440i 0.0194256 0.0336460i −0.856149 0.516729i \(-0.827150\pi\)
0.875575 + 0.483083i \(0.160483\pi\)
\(42\) 0 0
\(43\) 0.498313 + 0.863104i 0.0759921 + 0.131622i 0.901517 0.432743i \(-0.142454\pi\)
−0.825525 + 0.564365i \(0.809121\pi\)
\(44\) 0 0
\(45\) −3.86911 + 1.81769i −0.576773 + 0.270965i
\(46\) 0 0
\(47\) −4.73790 + 8.20628i −0.691093 + 1.19701i 0.280387 + 0.959887i \(0.409537\pi\)
−0.971480 + 0.237122i \(0.923796\pi\)
\(48\) 0 0
\(49\) 2.81498 6.40905i 0.402140 0.915578i
\(50\) 0 0
\(51\) 1.85041 + 0.580525i 0.259110 + 0.0812898i
\(52\) 0 0
\(53\) −0.410229 + 0.710537i −0.0563493 + 0.0975998i −0.892824 0.450406i \(-0.851279\pi\)
0.836475 + 0.548005i \(0.184613\pi\)
\(54\) 0 0
\(55\) 7.02604 0.947392
\(56\) 0 0
\(57\) −5.12050 + 4.70556i −0.678226 + 0.623267i
\(58\) 0 0
\(59\) −3.29204 5.70197i −0.428586 0.742334i 0.568161 0.822917i \(-0.307655\pi\)
−0.996748 + 0.0805836i \(0.974322\pi\)
\(60\) 0 0
\(61\) −0.0376322 + 0.0651809i −0.00481831 + 0.00834556i −0.868425 0.495821i \(-0.834867\pi\)
0.863606 + 0.504167i \(0.168200\pi\)
\(62\) 0 0
\(63\) 4.16988 6.75368i 0.525355 0.850883i
\(64\) 0 0
\(65\) −1.96257 + 3.39927i −0.243427 + 0.421628i
\(66\) 0 0
\(67\) −6.29385 10.9013i −0.768916 1.33180i −0.938151 0.346226i \(-0.887463\pi\)
0.169235 0.985576i \(-0.445870\pi\)
\(68\) 0 0
\(69\) −2.05125 9.19035i −0.246941 1.10639i
\(70\) 0 0
\(71\) −0.0804951 −0.00955301 −0.00477651 0.999989i \(-0.501520\pi\)
−0.00477651 + 0.999989i \(0.501520\pi\)
\(72\) 0 0
\(73\) 5.34551 9.25869i 0.625644 1.08365i −0.362772 0.931878i \(-0.618170\pi\)
0.988416 0.151769i \(-0.0484971\pi\)
\(74\) 0 0
\(75\) −1.12042 5.01990i −0.129375 0.579648i
\(76\) 0 0
\(77\) −10.9231 + 7.13261i −1.24480 + 0.812837i
\(78\) 0 0
\(79\) −0.922457 + 1.59774i −0.103785 + 0.179760i −0.913241 0.407420i \(-0.866429\pi\)
0.809456 + 0.587180i \(0.199762\pi\)
\(80\) 0 0
\(81\) 5.74555 6.92738i 0.638395 0.769709i
\(82\) 0 0
\(83\) 7.23583 + 12.5328i 0.794236 + 1.37566i 0.923323 + 0.384023i \(0.125462\pi\)
−0.129088 + 0.991633i \(0.541205\pi\)
\(84\) 0 0
\(85\) 0.797736 1.38172i 0.0865266 0.149868i
\(86\) 0 0
\(87\) −8.68637 + 7.98248i −0.931277 + 0.855811i
\(88\) 0 0
\(89\) 6.76292 + 11.7137i 0.716868 + 1.24165i 0.962235 + 0.272222i \(0.0877584\pi\)
−0.245366 + 0.969430i \(0.578908\pi\)
\(90\) 0 0
\(91\) −0.399711 7.27703i −0.0419011 0.762840i
\(92\) 0 0
\(93\) −3.19576 + 2.93679i −0.331385 + 0.304531i
\(94\) 0 0
\(95\) 2.86059 + 4.95469i 0.293491 + 0.508341i
\(96\) 0 0
\(97\) 2.70160 + 4.67930i 0.274306 + 0.475111i 0.969960 0.243266i \(-0.0782187\pi\)
−0.695654 + 0.718377i \(0.744885\pi\)
\(98\) 0 0
\(99\) −13.3885 + 6.28982i −1.34559 + 0.632151i
\(100\) 0 0
\(101\) −5.13540 −0.510991 −0.255496 0.966810i \(-0.582239\pi\)
−0.255496 + 0.966810i \(0.582239\pi\)
\(102\) 0 0
\(103\) 14.2112 1.40027 0.700137 0.714009i \(-0.253122\pi\)
0.700137 + 0.714009i \(0.253122\pi\)
\(104\) 0 0
\(105\) −4.67545 4.55846i −0.456277 0.444860i
\(106\) 0 0
\(107\) −3.83015 6.63401i −0.370274 0.641334i 0.619333 0.785128i \(-0.287403\pi\)
−0.989608 + 0.143794i \(0.954070\pi\)
\(108\) 0 0
\(109\) −0.849394 + 1.47119i −0.0813572 + 0.140915i −0.903833 0.427885i \(-0.859259\pi\)
0.822476 + 0.568800i \(0.192592\pi\)
\(110\) 0 0
\(111\) −1.81042 + 1.66371i −0.171838 + 0.157913i
\(112\) 0 0
\(113\) −0.300351 + 0.520224i −0.0282547 + 0.0489385i −0.879807 0.475331i \(-0.842328\pi\)
0.851552 + 0.524270i \(0.175662\pi\)
\(114\) 0 0
\(115\) −7.74683 −0.722395
\(116\) 0 0
\(117\) 0.696689 8.23439i 0.0644090 0.761270i
\(118\) 0 0
\(119\) 0.162473 + 2.95793i 0.0148939 + 0.271153i
\(120\) 0 0
\(121\) 13.3125 1.21023
\(122\) 0 0
\(123\) 0.411122 + 0.128980i 0.0370696 + 0.0116298i
\(124\) 0 0
\(125\) −11.3561 −1.01572
\(126\) 0 0
\(127\) −7.25977 −0.644200 −0.322100 0.946706i \(-0.604389\pi\)
−0.322100 + 0.946706i \(0.604389\pi\)
\(128\) 0 0
\(129\) −1.27103 + 1.16803i −0.111908 + 0.102839i
\(130\) 0 0
\(131\) 20.4530 1.78698 0.893492 0.449079i \(-0.148248\pi\)
0.893492 + 0.449079i \(0.148248\pi\)
\(132\) 0 0
\(133\) −9.47708 4.79886i −0.821767 0.416114i
\(134\) 0 0
\(135\) −4.53255 5.85475i −0.390100 0.503896i
\(136\) 0 0
\(137\) 12.2116 1.04331 0.521655 0.853157i \(-0.325315\pi\)
0.521655 + 0.853157i \(0.325315\pi\)
\(138\) 0 0
\(139\) 1.24092 2.14933i 0.105253 0.182304i −0.808588 0.588375i \(-0.799768\pi\)
0.913842 + 0.406071i \(0.133101\pi\)
\(140\) 0 0
\(141\) −15.6600 4.91296i −1.31881 0.413746i
\(142\) 0 0
\(143\) −6.79117 + 11.7626i −0.567906 + 0.983642i
\(144\) 0 0
\(145\) 4.85269 + 8.40511i 0.402994 + 0.698006i
\(146\) 0 0
\(147\) 11.8963 + 2.34046i 0.981191 + 0.193038i
\(148\) 0 0
\(149\) −8.55593 −0.700929 −0.350465 0.936576i \(-0.613976\pi\)
−0.350465 + 0.936576i \(0.613976\pi\)
\(150\) 0 0
\(151\) 17.6592 1.43709 0.718544 0.695482i \(-0.244809\pi\)
0.718544 + 0.695482i \(0.244809\pi\)
\(152\) 0 0
\(153\) −0.283187 + 3.34708i −0.0228943 + 0.270595i
\(154\) 0 0
\(155\) 1.78533 + 3.09228i 0.143401 + 0.248378i
\(156\) 0 0
\(157\) −3.16074 5.47457i −0.252255 0.436918i 0.711891 0.702289i \(-0.247839\pi\)
−0.964146 + 0.265371i \(0.914505\pi\)
\(158\) 0 0
\(159\) −1.35591 0.425387i −0.107531 0.0337354i
\(160\) 0 0
\(161\) 12.0436 7.86433i 0.949172 0.619796i
\(162\) 0 0
\(163\) 4.01134 + 6.94784i 0.314192 + 0.544197i 0.979265 0.202581i \(-0.0649331\pi\)
−0.665073 + 0.746778i \(0.731600\pi\)
\(164\) 0 0
\(165\) 2.65094 + 11.8772i 0.206376 + 0.924640i
\(166\) 0 0
\(167\) −1.06038 + 1.83663i −0.0820545 + 0.142123i −0.904132 0.427253i \(-0.859482\pi\)
0.822078 + 0.569375i \(0.192815\pi\)
\(168\) 0 0
\(169\) 2.70608 + 4.68706i 0.208160 + 0.360543i
\(170\) 0 0
\(171\) −9.88652 6.88056i −0.756041 0.526169i
\(172\) 0 0
\(173\) 9.14404 15.8379i 0.695208 1.20414i −0.274902 0.961472i \(-0.588646\pi\)
0.970110 0.242664i \(-0.0780212\pi\)
\(174\) 0 0
\(175\) 6.57841 4.29561i 0.497281 0.324718i
\(176\) 0 0
\(177\) 8.39684 7.71641i 0.631145 0.580001i
\(178\) 0 0
\(179\) −3.81276 + 6.60389i −0.284979 + 0.493598i −0.972604 0.232468i \(-0.925320\pi\)
0.687625 + 0.726066i \(0.258653\pi\)
\(180\) 0 0
\(181\) 15.5305 1.15438 0.577188 0.816611i \(-0.304150\pi\)
0.577188 + 0.816611i \(0.304150\pi\)
\(182\) 0 0
\(183\) −0.124384 0.0390227i −0.00919475 0.00288464i
\(184\) 0 0
\(185\) 1.01140 + 1.75180i 0.0743597 + 0.128795i
\(186\) 0 0
\(187\) 2.76044 4.78122i 0.201863 0.349638i
\(188\) 0 0
\(189\) 12.9901 + 4.50082i 0.944891 + 0.327386i
\(190\) 0 0
\(191\) 7.41624 12.8453i 0.536620 0.929454i −0.462463 0.886639i \(-0.653034\pi\)
0.999083 0.0428150i \(-0.0136326\pi\)
\(192\) 0 0
\(193\) −8.28387 14.3481i −0.596286 1.03280i −0.993364 0.115013i \(-0.963309\pi\)
0.397078 0.917785i \(-0.370024\pi\)
\(194\) 0 0
\(195\) −6.48680 2.03509i −0.464529 0.145736i
\(196\) 0 0
\(197\) −4.03740 −0.287653 −0.143826 0.989603i \(-0.545941\pi\)
−0.143826 + 0.989603i \(0.545941\pi\)
\(198\) 0 0
\(199\) 12.6407 21.8943i 0.896076 1.55205i 0.0636081 0.997975i \(-0.479739\pi\)
0.832468 0.554074i \(-0.186927\pi\)
\(200\) 0 0
\(201\) 16.0534 14.7525i 1.13232 1.04056i
\(202\) 0 0
\(203\) −16.0769 8.14075i −1.12837 0.571368i
\(204\) 0 0
\(205\) 0.177240 0.306988i 0.0123790 0.0214410i
\(206\) 0 0
\(207\) 14.7619 6.93508i 1.02603 0.482022i
\(208\) 0 0
\(209\) 9.89864 + 17.1449i 0.684703 + 1.18594i
\(210\) 0 0
\(211\) 3.76246 6.51678i 0.259019 0.448634i −0.706961 0.707253i \(-0.749934\pi\)
0.965979 + 0.258619i \(0.0832675\pi\)
\(212\) 0 0
\(213\) −0.0303710 0.136073i −0.00208099 0.00932360i
\(214\) 0 0
\(215\) 0.710065 + 1.22987i 0.0484261 + 0.0838764i
\(216\) 0 0
\(217\) −5.91476 2.99502i −0.401520 0.203315i
\(218\) 0 0
\(219\) 17.6683 + 5.54302i 1.19391 + 0.374563i
\(220\) 0 0
\(221\) 1.54214 + 2.67106i 0.103735 + 0.179675i
\(222\) 0 0
\(223\) −6.49230 11.2450i −0.434757 0.753020i 0.562519 0.826784i \(-0.309832\pi\)
−0.997276 + 0.0737638i \(0.976499\pi\)
\(224\) 0 0
\(225\) 8.06319 3.78804i 0.537546 0.252536i
\(226\) 0 0
\(227\) 28.9665 1.92257 0.961286 0.275551i \(-0.0888603\pi\)
0.961286 + 0.275551i \(0.0888603\pi\)
\(228\) 0 0
\(229\) 15.4358 1.02003 0.510013 0.860167i \(-0.329640\pi\)
0.510013 + 0.860167i \(0.329640\pi\)
\(230\) 0 0
\(231\) −16.1787 15.7738i −1.06448 1.03784i
\(232\) 0 0
\(233\) −2.47324 4.28378i −0.162027 0.280640i 0.773568 0.633713i \(-0.218470\pi\)
−0.935596 + 0.353073i \(0.885137\pi\)
\(234\) 0 0
\(235\) −6.75121 + 11.6934i −0.440400 + 0.762795i
\(236\) 0 0
\(237\) −3.04896 0.956542i −0.198051 0.0621341i
\(238\) 0 0
\(239\) −6.51732 + 11.2883i −0.421571 + 0.730182i −0.996093 0.0883069i \(-0.971854\pi\)
0.574523 + 0.818489i \(0.305188\pi\)
\(240\) 0 0
\(241\) 14.5825 0.939339 0.469670 0.882842i \(-0.344373\pi\)
0.469670 + 0.882842i \(0.344373\pi\)
\(242\) 0 0
\(243\) 13.8782 + 7.09889i 0.890290 + 0.455394i
\(244\) 0 0
\(245\) 4.01117 9.13249i 0.256265 0.583453i
\(246\) 0 0
\(247\) −11.0599 −0.703722
\(248\) 0 0
\(249\) −18.4561 + 16.9605i −1.16961 + 1.07483i
\(250\) 0 0
\(251\) 14.0715 0.888187 0.444094 0.895980i \(-0.353526\pi\)
0.444094 + 0.895980i \(0.353526\pi\)
\(252\) 0 0
\(253\) −26.8067 −1.68532
\(254\) 0 0
\(255\) 2.63672 + 0.827212i 0.165118 + 0.0518020i
\(256\) 0 0
\(257\) −8.36215 −0.521617 −0.260808 0.965391i \(-0.583989\pi\)
−0.260808 + 0.965391i \(0.583989\pi\)
\(258\) 0 0
\(259\) −3.35075 1.69670i −0.208206 0.105428i
\(260\) 0 0
\(261\) −16.7714 11.6721i −1.03812 0.722487i
\(262\) 0 0
\(263\) −3.27066 −0.201678 −0.100839 0.994903i \(-0.532153\pi\)
−0.100839 + 0.994903i \(0.532153\pi\)
\(264\) 0 0
\(265\) −0.584551 + 1.01247i −0.0359087 + 0.0621956i
\(266\) 0 0
\(267\) −17.2499 + 15.8520i −1.05568 + 0.970129i
\(268\) 0 0
\(269\) −7.69349 + 13.3255i −0.469081 + 0.812471i −0.999375 0.0353420i \(-0.988748\pi\)
0.530295 + 0.847813i \(0.322081\pi\)
\(270\) 0 0
\(271\) −4.06308 7.03747i −0.246815 0.427496i 0.715825 0.698279i \(-0.246051\pi\)
−0.962640 + 0.270783i \(0.912717\pi\)
\(272\) 0 0
\(273\) 12.1507 3.42133i 0.735393 0.207069i
\(274\) 0 0
\(275\) −14.6422 −0.882958
\(276\) 0 0
\(277\) 12.8457 0.771826 0.385913 0.922535i \(-0.373887\pi\)
0.385913 + 0.922535i \(0.373887\pi\)
\(278\) 0 0
\(279\) −6.17029 4.29423i −0.369406 0.257089i
\(280\) 0 0
\(281\) −0.724081 1.25415i −0.0431951 0.0748161i 0.843620 0.536941i \(-0.180420\pi\)
−0.886815 + 0.462125i \(0.847087\pi\)
\(282\) 0 0
\(283\) −8.71926 15.1022i −0.518306 0.897732i −0.999774 0.0212686i \(-0.993229\pi\)
0.481468 0.876464i \(-0.340104\pi\)
\(284\) 0 0
\(285\) −7.29639 + 6.70513i −0.432201 + 0.397178i
\(286\) 0 0
\(287\) 0.0360979 + 0.657189i 0.00213079 + 0.0387926i
\(288\) 0 0
\(289\) 7.87316 + 13.6367i 0.463127 + 0.802160i
\(290\) 0 0
\(291\) −6.89084 + 6.33244i −0.403948 + 0.371214i
\(292\) 0 0
\(293\) −0.900048 + 1.55893i −0.0525814 + 0.0910736i −0.891118 0.453772i \(-0.850078\pi\)
0.838537 + 0.544845i \(0.183412\pi\)
\(294\) 0 0
\(295\) −4.69094 8.12495i −0.273117 0.473053i
\(296\) 0 0
\(297\) −15.6842 20.2594i −0.910088 1.17557i
\(298\) 0 0
\(299\) 7.48786 12.9693i 0.433034 0.750037i
\(300\) 0 0
\(301\) −2.35243 1.19119i −0.135592 0.0686589i
\(302\) 0 0
\(303\) −1.93760 8.68117i −0.111312 0.498720i
\(304\) 0 0
\(305\) −0.0536236 + 0.0928787i −0.00307048 + 0.00531822i
\(306\) 0 0
\(307\) −1.06478 −0.0607699 −0.0303850 0.999538i \(-0.509673\pi\)
−0.0303850 + 0.999538i \(0.509673\pi\)
\(308\) 0 0
\(309\) 5.36193 + 24.0234i 0.305029 + 1.36665i
\(310\) 0 0
\(311\) −8.46463 14.6612i −0.479985 0.831359i 0.519751 0.854318i \(-0.326025\pi\)
−0.999736 + 0.0229591i \(0.992691\pi\)
\(312\) 0 0
\(313\) 4.13928 7.16944i 0.233966 0.405241i −0.725006 0.688743i \(-0.758163\pi\)
0.958972 + 0.283502i \(0.0914963\pi\)
\(314\) 0 0
\(315\) 5.94181 9.62356i 0.334783 0.542226i
\(316\) 0 0
\(317\) −3.27371 + 5.67023i −0.183870 + 0.318472i −0.943195 0.332239i \(-0.892196\pi\)
0.759325 + 0.650711i \(0.225529\pi\)
\(318\) 0 0
\(319\) 16.7920 + 29.0846i 0.940171 + 1.62842i
\(320\) 0 0
\(321\) 9.76938 8.97773i 0.545274 0.501088i
\(322\) 0 0
\(323\) 4.49556 0.250140
\(324\) 0 0
\(325\) 4.08997 7.08404i 0.226871 0.392952i
\(326\) 0 0
\(327\) −2.80747 0.880779i −0.155253 0.0487072i
\(328\) 0 0
\(329\) −1.37500 25.0329i −0.0758062 1.38011i
\(330\) 0 0
\(331\) −13.3629 + 23.1453i −0.734493 + 1.27218i 0.220453 + 0.975398i \(0.429246\pi\)
−0.954946 + 0.296781i \(0.904087\pi\)
\(332\) 0 0
\(333\) −3.49551 2.43271i −0.191553 0.133312i
\(334\) 0 0
\(335\) −8.96834 15.5336i −0.489993 0.848692i
\(336\) 0 0
\(337\) −4.76164 + 8.24740i −0.259383 + 0.449264i −0.966077 0.258255i \(-0.916853\pi\)
0.706694 + 0.707520i \(0.250186\pi\)
\(338\) 0 0
\(339\) −0.992739 0.311449i −0.0539182 0.0169156i
\(340\) 0 0
\(341\) 6.17786 + 10.7004i 0.334550 + 0.579457i
\(342\) 0 0
\(343\) 3.03502 + 18.2699i 0.163876 + 0.986481i
\(344\) 0 0
\(345\) −2.92290 13.0957i −0.157363 0.705048i
\(346\) 0 0
\(347\) −9.35156 16.1974i −0.502018 0.869521i −0.999997 0.00233189i \(-0.999258\pi\)
0.497979 0.867189i \(-0.334076\pi\)
\(348\) 0 0
\(349\) −15.0542 26.0747i −0.805834 1.39574i −0.915727 0.401801i \(-0.868384\pi\)
0.109893 0.993943i \(-0.464949\pi\)
\(350\) 0 0
\(351\) 14.1827 1.92913i 0.757019 0.102970i
\(352\) 0 0
\(353\) 6.25933 0.333150 0.166575 0.986029i \(-0.446729\pi\)
0.166575 + 0.986029i \(0.446729\pi\)
\(354\) 0 0
\(355\) −0.114700 −0.00608767
\(356\) 0 0
\(357\) −4.93895 + 1.39069i −0.261397 + 0.0736030i
\(358\) 0 0
\(359\) 5.09755 + 8.82921i 0.269038 + 0.465988i 0.968614 0.248571i \(-0.0799608\pi\)
−0.699575 + 0.714559i \(0.746628\pi\)
\(360\) 0 0
\(361\) 1.43970 2.49364i 0.0757739 0.131244i
\(362\) 0 0
\(363\) 5.02285 + 22.5042i 0.263631 + 1.18117i
\(364\) 0 0
\(365\) 7.61701 13.1931i 0.398693 0.690556i
\(366\) 0 0
\(367\) 28.6557 1.49581 0.747906 0.663804i \(-0.231059\pi\)
0.747906 + 0.663804i \(0.231059\pi\)
\(368\) 0 0
\(369\) −0.0629181 + 0.743649i −0.00327538 + 0.0387128i
\(370\) 0 0
\(371\) −0.119054 2.16746i −0.00618097 0.112529i
\(372\) 0 0
\(373\) −16.0734 −0.832249 −0.416124 0.909308i \(-0.636612\pi\)
−0.416124 + 0.909308i \(0.636612\pi\)
\(374\) 0 0
\(375\) −4.28469 19.1970i −0.221260 0.991330i
\(376\) 0 0
\(377\) −18.7619 −0.966286
\(378\) 0 0
\(379\) 1.01893 0.0523388 0.0261694 0.999658i \(-0.491669\pi\)
0.0261694 + 0.999658i \(0.491669\pi\)
\(380\) 0 0
\(381\) −2.73913 12.2723i −0.140330 0.628730i
\(382\) 0 0
\(383\) 11.5865 0.592044 0.296022 0.955181i \(-0.404340\pi\)
0.296022 + 0.955181i \(0.404340\pi\)
\(384\) 0 0
\(385\) −15.5647 + 10.1635i −0.793250 + 0.517981i
\(386\) 0 0
\(387\) −2.45406 1.70791i −0.124747 0.0868181i
\(388\) 0 0
\(389\) 17.8135 0.903181 0.451590 0.892225i \(-0.350857\pi\)
0.451590 + 0.892225i \(0.350857\pi\)
\(390\) 0 0
\(391\) −3.04363 + 5.27172i −0.153923 + 0.266602i
\(392\) 0 0
\(393\) 7.71695 + 34.5749i 0.389269 + 1.74407i
\(394\) 0 0
\(395\) −1.31444 + 2.27668i −0.0661369 + 0.114552i
\(396\) 0 0
\(397\) −6.54229 11.3316i −0.328348 0.568715i 0.653836 0.756636i \(-0.273159\pi\)
−0.982184 + 0.187921i \(0.939825\pi\)
\(398\) 0 0
\(399\) 4.53653 17.8312i 0.227111 0.892677i
\(400\) 0 0
\(401\) 14.1033 0.704285 0.352143 0.935946i \(-0.385453\pi\)
0.352143 + 0.935946i \(0.385453\pi\)
\(402\) 0 0
\(403\) −6.90259 −0.343842
\(404\) 0 0
\(405\) 8.18706 9.87108i 0.406818 0.490498i
\(406\) 0 0
\(407\) 3.49980 + 6.06183i 0.173479 + 0.300474i
\(408\) 0 0
\(409\) 1.32300 + 2.29150i 0.0654179 + 0.113307i 0.896879 0.442275i \(-0.145829\pi\)
−0.831461 + 0.555583i \(0.812495\pi\)
\(410\) 0 0
\(411\) 4.60747 + 20.6432i 0.227270 + 1.01825i
\(412\) 0 0
\(413\) 15.5410 + 7.86940i 0.764722 + 0.387228i
\(414\) 0 0
\(415\) 10.3106 + 17.8585i 0.506128 + 0.876639i
\(416\) 0 0
\(417\) 4.10155 + 1.28677i 0.200854 + 0.0630133i
\(418\) 0 0
\(419\) −16.7567 + 29.0235i −0.818619 + 1.41789i 0.0880816 + 0.996113i \(0.471926\pi\)
−0.906700 + 0.421776i \(0.861407\pi\)
\(420\) 0 0
\(421\) −2.41950 4.19071i −0.117919 0.204242i 0.801024 0.598633i \(-0.204289\pi\)
−0.918943 + 0.394390i \(0.870956\pi\)
\(422\) 0 0
\(423\) 2.39660 28.3262i 0.116527 1.37727i
\(424\) 0 0
\(425\) −1.66247 + 2.87949i −0.0806418 + 0.139676i
\(426\) 0 0
\(427\) −0.0109214 0.198831i −0.000528522 0.00962212i
\(428\) 0 0
\(429\) −22.4466 7.04210i −1.08373 0.339996i
\(430\) 0 0
\(431\) −17.6643 + 30.5954i −0.850858 + 1.47373i 0.0295774 + 0.999562i \(0.490584\pi\)
−0.880435 + 0.474166i \(0.842749\pi\)
\(432\) 0 0
\(433\) 5.47404 0.263066 0.131533 0.991312i \(-0.458010\pi\)
0.131533 + 0.991312i \(0.458010\pi\)
\(434\) 0 0
\(435\) −12.3775 + 11.3745i −0.593458 + 0.545367i
\(436\) 0 0
\(437\) −10.9141 18.9038i −0.522093 0.904292i
\(438\) 0 0
\(439\) 3.19906 5.54093i 0.152683 0.264454i −0.779530 0.626365i \(-0.784542\pi\)
0.932213 + 0.361911i \(0.117875\pi\)
\(440\) 0 0
\(441\) 0.532064 + 20.9933i 0.0253364 + 0.999679i
\(442\) 0 0
\(443\) −3.19341 + 5.53115i −0.151723 + 0.262793i −0.931861 0.362815i \(-0.881816\pi\)
0.780138 + 0.625608i \(0.215149\pi\)
\(444\) 0 0
\(445\) 9.63674 + 16.6913i 0.456825 + 0.791245i
\(446\) 0 0
\(447\) −3.22817 14.4634i −0.152687 0.684097i
\(448\) 0 0
\(449\) −11.7460 −0.554327 −0.277163 0.960823i \(-0.589394\pi\)
−0.277163 + 0.960823i \(0.589394\pi\)
\(450\) 0 0
\(451\) 0.613311 1.06229i 0.0288797 0.0500210i
\(452\) 0 0
\(453\) 6.66287 + 29.8522i 0.313049 + 1.40258i
\(454\) 0 0
\(455\) −0.569564 10.3693i −0.0267016 0.486121i
\(456\) 0 0
\(457\) −5.26120 + 9.11266i −0.246108 + 0.426272i −0.962443 0.271485i \(-0.912485\pi\)
0.716334 + 0.697757i \(0.245819\pi\)
\(458\) 0 0
\(459\) −5.76494 + 0.784145i −0.269084 + 0.0366007i
\(460\) 0 0
\(461\) −3.54278 6.13627i −0.165004 0.285794i 0.771653 0.636044i \(-0.219430\pi\)
−0.936657 + 0.350249i \(0.886097\pi\)
\(462\) 0 0
\(463\) −16.3760 + 28.3641i −0.761059 + 1.31819i 0.181246 + 0.983438i \(0.441987\pi\)
−0.942305 + 0.334755i \(0.891346\pi\)
\(464\) 0 0
\(465\) −4.55376 + 4.18475i −0.211176 + 0.194063i
\(466\) 0 0
\(467\) −1.96216 3.39856i −0.0907978 0.157266i 0.817049 0.576568i \(-0.195608\pi\)
−0.907847 + 0.419301i \(0.862275\pi\)
\(468\) 0 0
\(469\) 29.7119 + 15.0450i 1.37197 + 0.694716i
\(470\) 0 0
\(471\) 8.06196 7.40867i 0.371476 0.341373i
\(472\) 0 0
\(473\) 2.45707 + 4.25577i 0.112976 + 0.195681i
\(474\) 0 0
\(475\) −5.96145 10.3255i −0.273530 0.473768i
\(476\) 0 0
\(477\) 0.207509 2.45261i 0.00950117 0.112297i
\(478\) 0 0
\(479\) −16.0865 −0.735010 −0.367505 0.930022i \(-0.619788\pi\)
−0.367505 + 0.930022i \(0.619788\pi\)
\(480\) 0 0
\(481\) −3.91036 −0.178297
\(482\) 0 0
\(483\) 17.8384 + 17.3920i 0.811675 + 0.791365i
\(484\) 0 0
\(485\) 3.84961 + 6.66771i 0.174802 + 0.302765i
\(486\) 0 0
\(487\) 1.75172 3.03407i 0.0793781 0.137487i −0.823604 0.567166i \(-0.808040\pi\)
0.902982 + 0.429679i \(0.141373\pi\)
\(488\) 0 0
\(489\) −10.2315 + 9.40242i −0.462686 + 0.425192i
\(490\) 0 0
\(491\) 20.5546 35.6017i 0.927618 1.60668i 0.140321 0.990106i \(-0.455186\pi\)
0.787296 0.616575i \(-0.211480\pi\)
\(492\) 0 0
\(493\) 7.62624 0.343468
\(494\) 0 0
\(495\) −19.0777 + 8.96261i −0.857480 + 0.402839i
\(496\) 0 0
\(497\) 0.178320 0.116440i 0.00799873 0.00522306i
\(498\) 0 0
\(499\) −11.8297 −0.529571 −0.264785 0.964307i \(-0.585301\pi\)
−0.264785 + 0.964307i \(0.585301\pi\)
\(500\) 0 0
\(501\) −3.50482 1.09956i −0.156584 0.0491247i
\(502\) 0 0
\(503\) −21.8595 −0.974665 −0.487332 0.873217i \(-0.662030\pi\)
−0.487332 + 0.873217i \(0.662030\pi\)
\(504\) 0 0
\(505\) −7.31762 −0.325630
\(506\) 0 0
\(507\) −6.90226 + 6.34294i −0.306540 + 0.281700i
\(508\) 0 0
\(509\) 16.8966 0.748930 0.374465 0.927241i \(-0.377826\pi\)
0.374465 + 0.927241i \(0.377826\pi\)
\(510\) 0 0
\(511\) 1.55134 + 28.2432i 0.0686271 + 1.24941i
\(512\) 0 0
\(513\) 7.90108 19.3088i 0.348841 0.852503i
\(514\) 0 0
\(515\) 20.2501 0.892326
\(516\) 0 0
\(517\) −23.3615 + 40.4633i −1.02744 + 1.77957i
\(518\) 0 0
\(519\) 30.2234 + 9.48190i 1.32666 + 0.416209i
\(520\) 0 0
\(521\) −17.2466 + 29.8720i −0.755587 + 1.30872i 0.189495 + 0.981882i \(0.439315\pi\)
−0.945082 + 0.326834i \(0.894018\pi\)
\(522\) 0 0
\(523\) −0.995615 1.72445i −0.0435352 0.0754051i 0.843437 0.537229i \(-0.180529\pi\)
−0.886972 + 0.461823i \(0.847195\pi\)
\(524\) 0 0
\(525\) 9.74359 + 9.49977i 0.425245 + 0.414604i
\(526\) 0 0
\(527\) 2.80573 0.122220
\(528\) 0 0
\(529\) 6.55673 0.285075
\(530\) 0 0
\(531\) 16.2124 + 11.2831i 0.703558 + 0.489644i
\(532\) 0 0
\(533\) 0.342629 + 0.593452i 0.0148409 + 0.0257052i
\(534\) 0 0
\(535\) −5.45772 9.45305i −0.235958 0.408691i
\(536\) 0 0
\(537\) −12.6021 3.95364i −0.543823 0.170612i
\(538\) 0 0
\(539\) 13.8800 31.6016i 0.597856 1.36118i
\(540\) 0 0
\(541\) −15.0681 26.0988i −0.647830 1.12207i −0.983640 0.180145i \(-0.942343\pi\)
0.335810 0.941930i \(-0.390990\pi\)
\(542\) 0 0
\(543\) 5.85971 + 26.2537i 0.251464 + 1.12665i
\(544\) 0 0
\(545\) −1.21033 + 2.09636i −0.0518450 + 0.0897982i
\(546\) 0 0
\(547\) −7.68070 13.3034i −0.328403 0.568810i 0.653792 0.756674i \(-0.273177\pi\)
−0.982195 + 0.187864i \(0.939844\pi\)
\(548\) 0 0
\(549\) 0.0190357 0.224990i 0.000812426 0.00960232i
\(550\) 0 0
\(551\) −13.6734 + 23.6831i −0.582508 + 1.00893i
\(552\) 0 0
\(553\) −0.267709 4.87384i −0.0113842 0.207257i
\(554\) 0 0
\(555\) −2.57974 + 2.37069i −0.109504 + 0.100630i
\(556\) 0 0
\(557\) −11.6412 + 20.1631i −0.493252 + 0.854338i −0.999970 0.00777438i \(-0.997525\pi\)
0.506718 + 0.862112i \(0.330859\pi\)
\(558\) 0 0
\(559\) −2.74531 −0.116114
\(560\) 0 0
\(561\) 9.12397 + 2.86244i 0.385214 + 0.120852i
\(562\) 0 0
\(563\) 2.27942 + 3.94808i 0.0960663 + 0.166392i 0.910053 0.414492i \(-0.136041\pi\)
−0.813987 + 0.580883i \(0.802707\pi\)
\(564\) 0 0
\(565\) −0.427982 + 0.741286i −0.0180053 + 0.0311861i
\(566\) 0 0
\(567\) −2.70724 + 23.6574i −0.113693 + 0.993516i
\(568\) 0 0
\(569\) −9.09976 + 15.7612i −0.381482 + 0.660746i −0.991274 0.131815i \(-0.957919\pi\)
0.609793 + 0.792561i \(0.291253\pi\)
\(570\) 0 0
\(571\) −8.52275 14.7618i −0.356666 0.617763i 0.630736 0.775998i \(-0.282753\pi\)
−0.987402 + 0.158234i \(0.949420\pi\)
\(572\) 0 0
\(573\) 24.5126 + 7.69027i 1.02403 + 0.321266i
\(574\) 0 0
\(575\) 16.1443 0.673264
\(576\) 0 0
\(577\) −5.70473 + 9.88088i −0.237491 + 0.411346i −0.959994 0.280022i \(-0.909658\pi\)
0.722503 + 0.691368i \(0.242992\pi\)
\(578\) 0 0
\(579\) 21.1293 19.4171i 0.878103 0.806947i
\(580\) 0 0
\(581\) −34.1588 17.2968i −1.41715 0.717592i
\(582\) 0 0
\(583\) −2.02275 + 3.50350i −0.0837736 + 0.145100i
\(584\) 0 0
\(585\) 0.992739 11.7335i 0.0410447 0.485120i
\(586\) 0 0
\(587\) −2.52544 4.37420i −0.104236 0.180543i 0.809190 0.587548i \(-0.199906\pi\)
−0.913426 + 0.407005i \(0.866573\pi\)
\(588\) 0 0
\(589\) −5.03052 + 8.71312i −0.207279 + 0.359018i
\(590\) 0 0
\(591\) −1.52332 6.82504i −0.0626610 0.280745i
\(592\) 0 0
\(593\) −9.98892 17.3013i −0.410196 0.710480i 0.584715 0.811239i \(-0.301206\pi\)
−0.994911 + 0.100759i \(0.967873\pi\)
\(594\) 0 0
\(595\) 0.231513 + 4.21487i 0.00949113 + 0.172793i
\(596\) 0 0
\(597\) 41.7808 + 13.1078i 1.70997 + 0.536465i
\(598\) 0 0
\(599\) 2.19660 + 3.80463i 0.0897508 + 0.155453i 0.907406 0.420256i \(-0.138060\pi\)
−0.817655 + 0.575709i \(0.804726\pi\)
\(600\) 0 0
\(601\) 12.1778 + 21.0926i 0.496743 + 0.860385i 0.999993 0.00375637i \(-0.00119569\pi\)
−0.503250 + 0.864141i \(0.667862\pi\)
\(602\) 0 0
\(603\) 30.9955 + 21.5715i 1.26224 + 0.878457i
\(604\) 0 0
\(605\) 18.9695 0.771221
\(606\) 0 0
\(607\) −13.1256 −0.532752 −0.266376 0.963869i \(-0.585826\pi\)
−0.266376 + 0.963869i \(0.585826\pi\)
\(608\) 0 0
\(609\) 7.69574 30.2487i 0.311847 1.22574i
\(610\) 0 0
\(611\) −13.0510 22.6051i −0.527988 0.914502i
\(612\) 0 0
\(613\) −23.2403 + 40.2534i −0.938667 + 1.62582i −0.170707 + 0.985322i \(0.554605\pi\)
−0.767960 + 0.640497i \(0.778728\pi\)
\(614\) 0 0
\(615\) 0.585823 + 0.183789i 0.0236227 + 0.00741108i
\(616\) 0 0
\(617\) 14.1948 24.5862i 0.571463 0.989803i −0.424953 0.905215i \(-0.639709\pi\)
0.996416 0.0845873i \(-0.0269572\pi\)
\(618\) 0 0
\(619\) −31.9212 −1.28302 −0.641511 0.767114i \(-0.721692\pi\)
−0.641511 + 0.767114i \(0.721692\pi\)
\(620\) 0 0
\(621\) 17.2932 + 22.3378i 0.693951 + 0.896385i
\(622\) 0 0
\(623\) −31.9263 16.1663i −1.27910 0.647691i
\(624\) 0 0
\(625\) −1.33399 −0.0533594
\(626\) 0 0
\(627\) −25.2480 + 23.2020i −1.00831 + 0.926601i
\(628\) 0 0
\(629\) 1.58947 0.0633762
\(630\) 0 0
\(631\) −38.7184 −1.54135 −0.770677 0.637226i \(-0.780082\pi\)
−0.770677 + 0.637226i \(0.780082\pi\)
\(632\) 0 0
\(633\) 12.4359 + 3.90149i 0.494283 + 0.155070i
\(634\) 0 0
\(635\) −10.3447 −0.410517
\(636\) 0 0
\(637\) 11.4121 + 15.5425i 0.452163 + 0.615816i
\(638\) 0 0
\(639\) 0.218567 0.102682i 0.00864639 0.00406202i
\(640\) 0 0
\(641\) −40.4001 −1.59571 −0.797854 0.602851i \(-0.794032\pi\)
−0.797854 + 0.602851i \(0.794032\pi\)
\(642\) 0 0
\(643\) −6.27355 + 10.8661i −0.247405 + 0.428517i −0.962805 0.270198i \(-0.912911\pi\)
0.715400 + 0.698715i \(0.246244\pi\)
\(644\) 0 0
\(645\) −1.81113 + 1.66437i −0.0713132 + 0.0655344i
\(646\) 0 0
\(647\) −17.2774 + 29.9253i −0.679245 + 1.17649i 0.295964 + 0.955199i \(0.404359\pi\)
−0.975209 + 0.221287i \(0.928974\pi\)
\(648\) 0 0
\(649\) −16.2323 28.1151i −0.637173 1.10362i
\(650\) 0 0
\(651\) 2.83130 11.1287i 0.110967 0.436167i
\(652\) 0 0
\(653\) −22.2944 −0.872446 −0.436223 0.899839i \(-0.643684\pi\)
−0.436223 + 0.899839i \(0.643684\pi\)
\(654\) 0 0
\(655\) 29.1442 1.13876
\(656\) 0 0
\(657\) −2.70395 + 31.9589i −0.105491 + 1.24683i
\(658\) 0 0
\(659\) −3.57493 6.19196i −0.139259 0.241204i 0.787957 0.615730i \(-0.211139\pi\)
−0.927217 + 0.374526i \(0.877806\pi\)
\(660\) 0 0
\(661\) −21.4530 37.1577i −0.834425 1.44527i −0.894498 0.447072i \(-0.852467\pi\)
0.0600736 0.998194i \(-0.480866\pi\)
\(662\) 0 0
\(663\) −3.93346 + 3.61471i −0.152763 + 0.140384i
\(664\) 0 0
\(665\) −13.5043 6.83807i −0.523672 0.265169i
\(666\) 0 0
\(667\) −18.5146 32.0683i −0.716889 1.24169i
\(668\) 0 0
\(669\) 16.5596 15.2177i 0.640232 0.588351i
\(670\) 0 0
\(671\) −0.185556 + 0.321392i −0.00716331 + 0.0124072i
\(672\) 0 0
\(673\) −18.8270 32.6094i −0.725729 1.25700i −0.958673 0.284510i \(-0.908169\pi\)
0.232944 0.972490i \(-0.425164\pi\)
\(674\) 0 0
\(675\) 9.44578 + 12.2012i 0.363568 + 0.469626i
\(676\) 0 0
\(677\) 13.1808 22.8298i 0.506580 0.877422i −0.493391 0.869808i \(-0.664243\pi\)
0.999971 0.00761453i \(-0.00242380\pi\)
\(678\) 0 0
\(679\) −12.7537 6.45800i −0.489440 0.247835i
\(680\) 0 0
\(681\) 10.9291 + 48.9666i 0.418805 + 1.87640i
\(682\) 0 0
\(683\) −1.96588 + 3.40500i −0.0752222 + 0.130289i −0.901183 0.433439i \(-0.857300\pi\)
0.825961 + 0.563728i \(0.190633\pi\)
\(684\) 0 0
\(685\) 17.4008 0.664850
\(686\) 0 0
\(687\) 5.82396 + 26.0936i 0.222198 + 0.995531i
\(688\) 0 0
\(689\) −1.13002 1.95725i −0.0430503 0.0745653i
\(690\) 0 0
\(691\) 9.95052 17.2348i 0.378536 0.655643i −0.612314 0.790615i \(-0.709761\pi\)
0.990849 + 0.134972i \(0.0430944\pi\)
\(692\) 0 0
\(693\) 20.5607 33.3008i 0.781037 1.26499i
\(694\) 0 0
\(695\) 1.76823 3.06266i 0.0670727 0.116173i
\(696\) 0 0
\(697\) −0.139270 0.241223i −0.00527524 0.00913699i
\(698\) 0 0
\(699\) 6.30838 5.79718i 0.238605 0.219270i
\(700\) 0 0
\(701\) 43.7908 1.65396 0.826979 0.562234i \(-0.190058\pi\)
0.826979 + 0.562234i \(0.190058\pi\)
\(702\) 0 0
\(703\) −2.84983 + 4.93604i −0.107483 + 0.186166i
\(704\) 0 0
\(705\) −22.3145 7.00066i −0.840412 0.263660i
\(706\) 0 0
\(707\) 11.3764 7.42861i 0.427853 0.279382i
\(708\) 0 0
\(709\) −22.3172 + 38.6545i −0.838139 + 1.45170i 0.0533097 + 0.998578i \(0.483023\pi\)
−0.891449 + 0.453121i \(0.850310\pi\)
\(710\) 0 0
\(711\) 0.466612 5.51504i 0.0174993 0.206830i
\(712\) 0 0
\(713\) −6.81163 11.7981i −0.255097 0.441842i
\(714\) 0 0
\(715\) −9.67699 + 16.7610i −0.361899 + 0.626827i
\(716\) 0 0
\(717\) −21.5414 6.75814i −0.804480 0.252387i
\(718\) 0 0
\(719\) 19.5096 + 33.7917i 0.727586 + 1.26022i 0.957901 + 0.287100i \(0.0926912\pi\)
−0.230315 + 0.973116i \(0.573976\pi\)
\(720\) 0 0
\(721\) −31.4819 + 20.5572i −1.17245 + 0.765592i
\(722\) 0 0
\(723\) 5.50200 + 24.6510i 0.204622 + 0.916781i
\(724\) 0 0
\(725\) −10.1130 17.5162i −0.375586 0.650534i
\(726\) 0 0
\(727\) 11.2554 + 19.4949i 0.417439 + 0.723025i 0.995681 0.0928402i \(-0.0295946\pi\)
−0.578242 + 0.815865i \(0.696261\pi\)
\(728\) 0 0
\(729\) −6.76407 + 26.1390i −0.250521 + 0.968111i
\(730\) 0 0
\(731\) 1.11590 0.0412731
\(732\) 0 0
\(733\) −0.897039 −0.0331329 −0.0165664 0.999863i \(-0.505274\pi\)
−0.0165664 + 0.999863i \(0.505274\pi\)
\(734\) 0 0
\(735\) 16.9515 + 3.33501i 0.625266 + 0.123014i
\(736\) 0 0
\(737\) −31.0335 53.7517i −1.14314 1.97997i
\(738\) 0 0
\(739\) −1.79032 + 3.10092i −0.0658578 + 0.114069i −0.897074 0.441880i \(-0.854312\pi\)
0.831216 + 0.555949i \(0.187645\pi\)
\(740\) 0 0
\(741\) −4.17291 18.6962i −0.153296 0.686823i
\(742\) 0 0
\(743\) 24.7964 42.9486i 0.909691 1.57563i 0.0951977 0.995458i \(-0.469652\pi\)
0.814493 0.580173i \(-0.197015\pi\)
\(744\) 0 0
\(745\) −12.1917 −0.446668
\(746\) 0 0
\(747\) −35.6346 24.8000i −1.30380 0.907384i
\(748\) 0 0
\(749\) 18.0813 + 9.15573i 0.660676 + 0.334543i
\(750\) 0 0
\(751\) 42.9030 1.56555 0.782776 0.622304i \(-0.213803\pi\)
0.782776 + 0.622304i \(0.213803\pi\)
\(752\) 0 0
\(753\) 5.30922 + 23.7873i 0.193479 + 0.866858i
\(754\) 0 0
\(755\) 25.1633 0.915786
\(756\) 0 0
\(757\) 13.8029 0.501677 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(758\) 0 0
\(759\) −10.1142 45.3155i −0.367123 1.64485i
\(760\) 0 0
\(761\) 40.7197 1.47609 0.738044 0.674752i \(-0.235749\pi\)
0.738044 + 0.674752i \(0.235749\pi\)
\(762\) 0 0
\(763\) −0.246505 4.48781i −0.00892410 0.162470i
\(764\) 0 0
\(765\) −0.403524 + 4.76938i −0.0145894 + 0.172437i
\(766\) 0 0
\(767\) 18.1365 0.654871
\(768\) 0 0
\(769\) 5.57381 9.65413i 0.200997 0.348137i −0.747853 0.663864i \(-0.768915\pi\)
0.948850 + 0.315728i \(0.102249\pi\)
\(770\) 0 0
\(771\) −3.15506 14.1359i −0.113627 0.509090i
\(772\) 0 0
\(773\) −0.462831 + 0.801647i −0.0166469 + 0.0288332i −0.874229 0.485514i \(-0.838632\pi\)
0.857582 + 0.514347i \(0.171966\pi\)
\(774\) 0 0
\(775\) −3.72061 6.44428i −0.133648 0.231485i
\(776\) 0 0
\(777\) 1.60395 6.30447i 0.0575415 0.226172i
\(778\) 0 0
\(779\) 0.998817 0.0357863
\(780\) 0 0
\(781\) −0.396903 −0.0142023
\(782\) 0 0
\(783\) 13.4033 32.7553i 0.478996 1.17058i
\(784\) 0 0
\(785\) −4.50386 7.80092i −0.160750 0.278427i
\(786\) 0 0
\(787\) 11.5120 + 19.9393i 0.410358 + 0.710761i 0.994929 0.100582i \(-0.0320704\pi\)
−0.584571 + 0.811343i \(0.698737\pi\)
\(788\) 0 0
\(789\) −1.23403 5.52891i −0.0439325 0.196834i
\(790\) 0 0
\(791\) −0.0871659 1.58692i −0.00309926 0.0564243i
\(792\) 0 0
\(793\) −0.103662 0.179548i −0.00368114 0.00637593i
\(794\) 0 0
\(795\) −1.93209 0.606149i −0.0685242 0.0214979i
\(796\) 0 0
\(797\) 11.3925 19.7325i 0.403544 0.698960i −0.590606 0.806960i \(-0.701111\pi\)
0.994151 + 0.108000i \(0.0344447\pi\)
\(798\) 0 0
\(799\) 5.30492 + 9.18839i 0.187675 + 0.325062i
\(800\) 0 0
\(801\) −33.3056 23.1791i −1.17680 0.818995i
\(802\) 0 0
\(803\) 26.3575 45.6525i 0.930135 1.61104i
\(804\) 0 0
\(805\) 17.1614 11.2062i 0.604861 0.394966i
\(806\) 0 0
\(807\) −25.4290 7.97776i −0.895143 0.280831i
\(808\) 0 0
\(809\) 6.73753 11.6697i 0.236879 0.410286i −0.722938 0.690913i \(-0.757209\pi\)
0.959817 + 0.280627i \(0.0905422\pi\)
\(810\) 0 0
\(811\) 30.7348 1.07924 0.539622 0.841907i \(-0.318567\pi\)
0.539622 + 0.841907i \(0.318567\pi\)
\(812\) 0 0
\(813\) 10.3635 9.52372i 0.363465 0.334011i
\(814\) 0 0
\(815\) 5.71590 + 9.90023i 0.200219 + 0.346790i
\(816\) 0 0
\(817\) −2.00075 + 3.46540i −0.0699974 + 0.121239i
\(818\) 0 0
\(819\) 10.3681 + 19.2493i 0.362291 + 0.672626i
\(820\) 0 0
\(821\) 8.49319 14.7106i 0.296414 0.513405i −0.678899 0.734232i \(-0.737542\pi\)
0.975313 + 0.220827i \(0.0708757\pi\)
\(822\) 0 0
\(823\) −9.29157 16.0935i −0.323884 0.560983i 0.657402 0.753540i \(-0.271655\pi\)
−0.981286 + 0.192557i \(0.938322\pi\)
\(824\) 0 0
\(825\) −5.52453 24.7520i −0.192340 0.861754i
\(826\) 0 0
\(827\) −14.5419 −0.505670 −0.252835 0.967509i \(-0.581363\pi\)
−0.252835 + 0.967509i \(0.581363\pi\)
\(828\) 0 0
\(829\) 4.78717 8.29161i 0.166265 0.287980i −0.770839 0.637030i \(-0.780163\pi\)
0.937104 + 0.349051i \(0.113496\pi\)
\(830\) 0 0
\(831\) 4.84673 + 21.7152i 0.168131 + 0.753291i
\(832\) 0 0
\(833\) −4.63872 6.31764i −0.160722 0.218893i
\(834\) 0 0
\(835\) −1.51097 + 2.61708i −0.0522894 + 0.0905678i
\(836\) 0 0
\(837\) 4.93115 12.0508i 0.170446 0.416538i
\(838\) 0 0
\(839\) −21.2303 36.7720i −0.732952 1.26951i −0.955616 0.294615i \(-0.904809\pi\)
0.222664 0.974895i \(-0.428525\pi\)
\(840\) 0 0
\(841\) −8.69551 + 15.0611i −0.299845 + 0.519347i
\(842\) 0 0
\(843\) 1.84688 1.69722i 0.0636100 0.0584554i
\(844\) 0 0
\(845\) 3.85599 + 6.67877i 0.132650 + 0.229757i
\(846\) 0 0
\(847\) −29.4911 + 19.2572i −1.01332 + 0.661687i
\(848\) 0 0
\(849\) 22.2398 20.4376i 0.763268 0.701417i
\(850\) 0 0
\(851\) −3.85883 6.68370i −0.132279 0.229114i
\(852\) 0 0
\(853\) 7.14039 + 12.3675i 0.244482 + 0.423456i 0.961986 0.273099i \(-0.0880486\pi\)
−0.717504 + 0.696555i \(0.754715\pi\)
\(854\) 0 0
\(855\) −14.0877 9.80436i −0.481788 0.335302i
\(856\) 0 0
\(857\) 34.7790 1.18803 0.594013 0.804455i \(-0.297543\pi\)
0.594013 + 0.804455i \(0.297543\pi\)
\(858\) 0 0
\(859\) 12.6486 0.431564 0.215782 0.976442i \(-0.430770\pi\)
0.215782 + 0.976442i \(0.430770\pi\)
\(860\) 0 0
\(861\) −1.09733 + 0.308981i −0.0373969 + 0.0105300i
\(862\) 0 0
\(863\) −13.2398 22.9321i −0.450690 0.780617i 0.547739 0.836649i \(-0.315489\pi\)
−0.998429 + 0.0560318i \(0.982155\pi\)
\(864\) 0 0
\(865\) 13.0297 22.5681i 0.443022 0.767337i
\(866\) 0 0
\(867\) −20.0817 + 18.4544i −0.682011 + 0.626744i
\(868\) 0 0
\(869\) −4.54843 + 7.87811i −0.154295 + 0.267247i
\(870\) 0 0
\(871\) 34.6741 1.17489
\(872\) 0 0
\(873\) −13.3047 9.25942i −0.450294 0.313384i
\(874\) 0 0
\(875\) 25.1570 16.4272i 0.850463 0.555341i
\(876\) 0 0
\(877\) 28.4534 0.960805 0.480402 0.877048i \(-0.340491\pi\)
0.480402 + 0.877048i \(0.340491\pi\)
\(878\) 0 0
\(879\) −2.97489 0.933305i −0.100341 0.0314796i
\(880\) 0 0
\(881\) −20.3637 −0.686071 −0.343036 0.939322i \(-0.611455\pi\)
−0.343036 + 0.939322i \(0.611455\pi\)
\(882\) 0 0
\(883\) −49.1950 −1.65554 −0.827772 0.561065i \(-0.810392\pi\)
−0.827772 + 0.561065i \(0.810392\pi\)
\(884\) 0 0
\(885\) 11.9650 10.9954i 0.402198 0.369606i
\(886\) 0 0
\(887\) 4.21692 0.141590 0.0707952 0.997491i \(-0.477446\pi\)
0.0707952 + 0.997491i \(0.477446\pi\)
\(888\) 0 0
\(889\) 16.0825 10.5016i 0.539388 0.352213i
\(890\) 0 0
\(891\) 28.3300 34.1573i 0.949092 1.14431i
\(892\) 0 0
\(893\) −38.0457 −1.27315
\(894\) 0 0
\(895\) −5.43294 + 9.41013i −0.181603 + 0.314546i
\(896\) 0 0
\(897\) 24.7493 + 7.76453i 0.826355 + 0.259250i
\(898\) 0 0
\(899\) −8.53374 + 14.7809i −0.284616 + 0.492970i
\(900\) 0 0
\(901\) 0.459325 + 0.795574i 0.0153023 + 0.0265044i
\(902\) 0 0
\(903\) 1.12607 4.42612i 0.0374733 0.147292i
\(904\) 0 0
\(905\) 22.1301 0.735628
\(906\) 0 0
\(907\) −47.9851 −1.59332 −0.796659 0.604429i \(-0.793401\pi\)
−0.796659 + 0.604429i \(0.793401\pi\)
\(908\) 0 0
\(909\) 13.9441 6.55085i 0.462496 0.217278i
\(910\) 0 0
\(911\) 12.8667 + 22.2858i 0.426294 + 0.738362i 0.996540 0.0831113i \(-0.0264857\pi\)
−0.570247 + 0.821474i \(0.693152\pi\)
\(912\) 0 0
\(913\) 35.6782 + 61.7965i 1.18078 + 2.04517i
\(914\) 0 0
\(915\) −0.177240 0.0556049i −0.00585937 0.00183824i
\(916\) 0 0
\(917\) −45.3092 + 29.5863i −1.49624 + 0.977024i
\(918\) 0 0
\(919\) −1.13478 1.96550i −0.0374330 0.0648359i 0.846702 0.532068i \(-0.178585\pi\)
−0.884135 + 0.467232i \(0.845251\pi\)
\(920\) 0 0
\(921\) −0.401742 1.79996i −0.0132379 0.0593106i
\(922\) 0 0
\(923\) 0.110866 0.192026i 0.00364920 0.00632060i
\(924\) 0 0
\(925\) −2.10775 3.65073i −0.0693024 0.120035i
\(926\) 0 0
\(927\) −38.5875 + 18.1282i −1.26738 + 0.595408i
\(928\) 0 0
\(929\) −22.9248 + 39.7069i −0.752138 + 1.30274i 0.194647 + 0.980873i \(0.437644\pi\)
−0.946785 + 0.321868i \(0.895689\pi\)
\(930\) 0 0
\(931\) 27.9362 3.07824i 0.915573 0.100885i
\(932\) 0 0
\(933\) 21.5903 19.8408i 0.706836 0.649558i
\(934\) 0 0
\(935\) 3.93346 6.81294i 0.128638 0.222807i
\(936\) 0 0
\(937\) −56.2075 −1.83622 −0.918110 0.396325i \(-0.870285\pi\)
−0.918110 + 0.396325i \(0.870285\pi\)
\(938\) 0 0
\(939\) 13.6814 + 4.29222i 0.446475 + 0.140071i
\(940\) 0 0
\(941\) 17.6402 + 30.5536i 0.575053 + 0.996020i 0.996036 + 0.0889519i \(0.0283517\pi\)
−0.420983 + 0.907068i \(0.638315\pi\)
\(942\) 0 0
\(943\) −0.676229 + 1.17126i −0.0220210 + 0.0381415i
\(944\) 0 0
\(945\) 18.5101 + 6.41338i 0.602133 + 0.208627i
\(946\) 0 0
\(947\) −25.3565 + 43.9188i −0.823976 + 1.42717i 0.0787236 + 0.996896i \(0.474916\pi\)
−0.902699 + 0.430272i \(0.858418\pi\)
\(948\) 0 0
\(949\) 14.7248 + 25.5040i 0.477986 + 0.827896i
\(950\) 0 0
\(951\) −10.8204 3.39467i −0.350877 0.110080i
\(952\) 0 0
\(953\) 25.9988 0.842184 0.421092 0.907018i \(-0.361647\pi\)
0.421092 + 0.907018i \(0.361647\pi\)
\(954\) 0 0
\(955\) 10.5677 18.3038i 0.341962 0.592296i
\(956\) 0 0
\(957\) −42.8305 + 39.3598i −1.38451 + 1.27232i
\(958\) 0 0
\(959\) −27.0522 + 17.6647i −0.873562 + 0.570424i
\(960\) 0 0
\(961\) 12.3604 21.4088i 0.398722 0.690607i
\(962\) 0 0
\(963\) 18.8625 + 13.1274i 0.607834 + 0.423024i
\(964\) 0 0
\(965\) −11.8040 20.4451i −0.379984 0.658152i
\(966\) 0 0
\(967\) 12.9810 22.4838i 0.417442 0.723031i −0.578239 0.815867i \(-0.696260\pi\)
0.995681 + 0.0928360i \(0.0295932\pi\)
\(968\) 0 0
\(969\) 1.69619 + 7.59955i 0.0544893 + 0.244133i
\(970\) 0 0
\(971\) 3.97206 + 6.87981i 0.127469 + 0.220783i 0.922696 0.385530i \(-0.125981\pi\)
−0.795226 + 0.606313i \(0.792648\pi\)
\(972\) 0 0
\(973\) 0.360130 + 6.55643i 0.0115452 + 0.210189i
\(974\) 0 0
\(975\) 13.5184 + 4.24110i 0.432936 + 0.135824i
\(976\) 0 0
\(977\) 26.1274 + 45.2540i 0.835889 + 1.44780i 0.893304 + 0.449452i \(0.148381\pi\)
−0.0574149 + 0.998350i \(0.518286\pi\)
\(978\) 0 0
\(979\) 33.3464 + 57.7577i 1.06576 + 1.84594i
\(980\) 0 0
\(981\) 0.429654 5.07822i 0.0137178 0.162135i
\(982\) 0 0
\(983\) 38.8379 1.23874 0.619369 0.785100i \(-0.287389\pi\)
0.619369 + 0.785100i \(0.287389\pi\)
\(984\) 0 0
\(985\) −5.75304 −0.183307
\(986\) 0 0
\(987\) 41.7982 11.7693i 1.33045 0.374622i
\(988\) 0 0
\(989\) −2.70914 4.69236i −0.0861455 0.149208i
\(990\) 0 0
\(991\) 15.4689 26.7929i 0.491385 0.851104i −0.508565 0.861023i \(-0.669824\pi\)
0.999951 + 0.00991892i \(0.00315734\pi\)
\(992\) 0 0
\(993\) −44.1679 13.8567i −1.40163 0.439728i
\(994\) 0 0
\(995\) 18.0122 31.1981i 0.571025 0.989045i
\(996\) 0 0
\(997\) 47.0670 1.49063 0.745313 0.666714i \(-0.232300\pi\)
0.745313 + 0.666714i \(0.232300\pi\)
\(998\) 0 0
\(999\) 2.79353 6.82688i 0.0883834 0.215993i
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 1008.2.t.i.193.4 10
3.2 odd 2 3024.2.t.i.1873.1 10
4.3 odd 2 63.2.g.b.4.2 10
7.2 even 3 1008.2.q.i.625.1 10
9.2 odd 6 3024.2.q.i.2881.5 10
9.7 even 3 1008.2.q.i.529.1 10
12.11 even 2 189.2.g.b.172.4 10
21.2 odd 6 3024.2.q.i.2305.5 10
28.3 even 6 441.2.f.f.148.2 10
28.11 odd 6 441.2.f.e.148.2 10
28.19 even 6 441.2.h.f.373.4 10
28.23 odd 6 63.2.h.b.58.4 yes 10
28.27 even 2 441.2.g.f.67.2 10
36.7 odd 6 63.2.h.b.25.4 yes 10
36.11 even 6 189.2.h.b.46.2 10
36.23 even 6 567.2.e.e.487.4 10
36.31 odd 6 567.2.e.f.487.2 10
63.2 odd 6 3024.2.t.i.289.1 10
63.16 even 3 inner 1008.2.t.i.961.4 10
84.11 even 6 1323.2.f.e.442.4 10
84.23 even 6 189.2.h.b.37.2 10
84.47 odd 6 1323.2.h.f.226.2 10
84.59 odd 6 1323.2.f.f.442.4 10
84.83 odd 2 1323.2.g.f.361.4 10
252.11 even 6 1323.2.f.e.883.4 10
252.23 even 6 567.2.e.e.163.4 10
252.31 even 6 3969.2.a.ba.1.4 5
252.47 odd 6 1323.2.g.f.667.4 10
252.59 odd 6 3969.2.a.bb.1.2 5
252.67 odd 6 3969.2.a.z.1.4 5
252.79 odd 6 63.2.g.b.16.2 yes 10
252.83 odd 6 1323.2.h.f.802.2 10
252.95 even 6 3969.2.a.bc.1.2 5
252.115 even 6 441.2.f.f.295.2 10
252.151 odd 6 441.2.f.e.295.2 10
252.187 even 6 441.2.g.f.79.2 10
252.191 even 6 189.2.g.b.100.4 10
252.223 even 6 441.2.h.f.214.4 10
252.227 odd 6 1323.2.f.f.883.4 10
252.247 odd 6 567.2.e.f.163.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.2 10 4.3 odd 2
63.2.g.b.16.2 yes 10 252.79 odd 6
63.2.h.b.25.4 yes 10 36.7 odd 6
63.2.h.b.58.4 yes 10 28.23 odd 6
189.2.g.b.100.4 10 252.191 even 6
189.2.g.b.172.4 10 12.11 even 2
189.2.h.b.37.2 10 84.23 even 6
189.2.h.b.46.2 10 36.11 even 6
441.2.f.e.148.2 10 28.11 odd 6
441.2.f.e.295.2 10 252.151 odd 6
441.2.f.f.148.2 10 28.3 even 6
441.2.f.f.295.2 10 252.115 even 6
441.2.g.f.67.2 10 28.27 even 2
441.2.g.f.79.2 10 252.187 even 6
441.2.h.f.214.4 10 252.223 even 6
441.2.h.f.373.4 10 28.19 even 6
567.2.e.e.163.4 10 252.23 even 6
567.2.e.e.487.4 10 36.23 even 6
567.2.e.f.163.2 10 252.247 odd 6
567.2.e.f.487.2 10 36.31 odd 6
1008.2.q.i.529.1 10 9.7 even 3
1008.2.q.i.625.1 10 7.2 even 3
1008.2.t.i.193.4 10 1.1 even 1 trivial
1008.2.t.i.961.4 10 63.16 even 3 inner
1323.2.f.e.442.4 10 84.11 even 6
1323.2.f.e.883.4 10 252.11 even 6
1323.2.f.f.442.4 10 84.59 odd 6
1323.2.f.f.883.4 10 252.227 odd 6
1323.2.g.f.361.4 10 84.83 odd 2
1323.2.g.f.667.4 10 252.47 odd 6
1323.2.h.f.226.2 10 84.47 odd 6
1323.2.h.f.802.2 10 252.83 odd 6
3024.2.q.i.2305.5 10 21.2 odd 6
3024.2.q.i.2881.5 10 9.2 odd 6
3024.2.t.i.289.1 10 63.2 odd 6
3024.2.t.i.1873.1 10 3.2 odd 2
3969.2.a.z.1.4 5 252.67 odd 6
3969.2.a.ba.1.4 5 252.31 even 6
3969.2.a.bb.1.2 5 252.59 odd 6
3969.2.a.bc.1.2 5 252.95 even 6