Properties

Label 304.2.u.f.225.1
Level $304$
Weight $2$
Character 304.225
Analytic conductor $2.427$
Analytic rank $0$
Dimension $18$
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] = [304,2,Mod(17,304)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(304, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("304.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.u (of order \(9\), degree \(6\), 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: \(2.42745222145\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 21 x^{16} - 34 x^{15} + 204 x^{14} - 267 x^{13} + 1304 x^{12} - 972 x^{11} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 225.1
Root \(-0.976256 + 1.69092i\) of defining polynomial
Character \(\chi\) \(=\) 304.225
Dual form 304.2.u.f.177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.83476 + 0.667798i) q^{3} +(0.302047 - 1.71299i) q^{5} +(0.962609 + 1.66729i) q^{7} +(0.622259 - 0.522138i) q^{9} +O(q^{10})\) \(q+(-1.83476 + 0.667798i) q^{3} +(0.302047 - 1.71299i) q^{5} +(0.962609 + 1.66729i) q^{7} +(0.622259 - 0.522138i) q^{9} +(2.27748 - 3.94470i) q^{11} +(2.57934 + 0.938803i) q^{13} +(0.589750 + 3.34464i) q^{15} +(3.84088 + 3.22288i) q^{17} +(4.18751 + 1.21026i) q^{19} +(-2.87957 - 2.41625i) q^{21} +(-0.198055 - 1.12322i) q^{23} +(1.85536 + 0.675294i) q^{25} +(2.13575 - 3.69923i) q^{27} +(3.83721 - 3.21980i) q^{29} +(0.999936 + 1.73194i) q^{31} +(-1.54436 + 8.75848i) q^{33} +(3.14680 - 1.14534i) q^{35} -7.06608 q^{37} -5.35941 q^{39} +(-10.3600 + 3.77075i) q^{41} +(-1.05998 + 6.01147i) q^{43} +(-0.706466 - 1.22363i) q^{45} +(6.72021 - 5.63892i) q^{47} +(1.64677 - 2.85228i) q^{49} +(-9.19933 - 3.34828i) q^{51} +(0.00933315 + 0.0529309i) q^{53} +(-6.06934 - 5.09278i) q^{55} +(-8.49130 + 0.575879i) q^{57} +(-2.83451 - 2.37844i) q^{59} +(-2.60306 - 14.7627i) q^{61} +(1.46955 + 0.534871i) q^{63} +(2.38724 - 4.13483i) q^{65} +(-9.72449 + 8.15982i) q^{67} +(1.11347 + 1.92859i) q^{69} +(0.359347 - 2.03796i) q^{71} +(0.670002 - 0.243861i) q^{73} -3.85509 q^{75} +8.76928 q^{77} +(-10.5802 + 3.85086i) q^{79} +(-1.87142 + 10.6133i) q^{81} +(4.99262 + 8.64748i) q^{83} +(6.68089 - 5.60593i) q^{85} +(-4.89018 + 8.47005i) q^{87} +(15.2229 + 5.54068i) q^{89} +(0.917642 + 5.20421i) q^{91} +(-2.99123 - 2.50994i) q^{93} +(3.33799 - 6.80762i) q^{95} +(0.285278 + 0.239377i) q^{97} +(-0.642497 - 3.64378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 9 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 9 q^{7} - 6 q^{9} + 3 q^{11} + 3 q^{13} - 33 q^{15} + 9 q^{17} + 24 q^{19} - 15 q^{21} - 6 q^{23} + 6 q^{25} + 12 q^{27} - 3 q^{29} + 6 q^{31} - 45 q^{33} + 15 q^{35} + 48 q^{37} - 12 q^{39} - 18 q^{41} + 39 q^{43} - 42 q^{45} + 27 q^{47} - 18 q^{49} - 48 q^{51} + 39 q^{53} + 27 q^{55} - 6 q^{57} - 9 q^{59} - 24 q^{61} - 3 q^{63} + 27 q^{65} - 39 q^{67} - 3 q^{69} + 12 q^{73} - 90 q^{75} + 60 q^{77} - 63 q^{79} - 6 q^{81} + 27 q^{83} - 30 q^{85} - 18 q^{87} + 66 q^{89} - 108 q^{91} + 60 q^{93} + 75 q^{95} - 81 q^{97} - 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/304\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(191\) \(229\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.83476 + 0.667798i −1.05930 + 0.385554i −0.812165 0.583428i \(-0.801711\pi\)
−0.247135 + 0.968981i \(0.579489\pi\)
\(4\) 0 0
\(5\) 0.302047 1.71299i 0.135079 0.766073i −0.839725 0.543012i \(-0.817284\pi\)
0.974804 0.223061i \(-0.0716050\pi\)
\(6\) 0 0
\(7\) 0.962609 + 1.66729i 0.363832 + 0.630176i 0.988588 0.150644i \(-0.0481348\pi\)
−0.624756 + 0.780820i \(0.714802\pi\)
\(8\) 0 0
\(9\) 0.622259 0.522138i 0.207420 0.174046i
\(10\) 0 0
\(11\) 2.27748 3.94470i 0.686685 1.18937i −0.286220 0.958164i \(-0.592399\pi\)
0.972904 0.231209i \(-0.0742680\pi\)
\(12\) 0 0
\(13\) 2.57934 + 0.938803i 0.715381 + 0.260377i 0.673963 0.738765i \(-0.264591\pi\)
0.0414171 + 0.999142i \(0.486813\pi\)
\(14\) 0 0
\(15\) 0.589750 + 3.34464i 0.152273 + 0.863581i
\(16\) 0 0
\(17\) 3.84088 + 3.22288i 0.931550 + 0.781663i 0.976095 0.217344i \(-0.0697393\pi\)
−0.0445449 + 0.999007i \(0.514184\pi\)
\(18\) 0 0
\(19\) 4.18751 + 1.21026i 0.960682 + 0.277652i
\(20\) 0 0
\(21\) −2.87957 2.41625i −0.628374 0.527268i
\(22\) 0 0
\(23\) −0.198055 1.12322i −0.0412972 0.234208i 0.957172 0.289520i \(-0.0934958\pi\)
−0.998469 + 0.0553120i \(0.982385\pi\)
\(24\) 0 0
\(25\) 1.85536 + 0.675294i 0.371071 + 0.135059i
\(26\) 0 0
\(27\) 2.13575 3.69923i 0.411026 0.711918i
\(28\) 0 0
\(29\) 3.83721 3.21980i 0.712552 0.597902i −0.212762 0.977104i \(-0.568246\pi\)
0.925314 + 0.379202i \(0.123801\pi\)
\(30\) 0 0
\(31\) 0.999936 + 1.73194i 0.179594 + 0.311066i 0.941741 0.336338i \(-0.109188\pi\)
−0.762148 + 0.647403i \(0.775855\pi\)
\(32\) 0 0
\(33\) −1.54436 + 8.75848i −0.268838 + 1.52466i
\(34\) 0 0
\(35\) 3.14680 1.14534i 0.531907 0.193598i
\(36\) 0 0
\(37\) −7.06608 −1.16166 −0.580828 0.814026i \(-0.697271\pi\)
−0.580828 + 0.814026i \(0.697271\pi\)
\(38\) 0 0
\(39\) −5.35941 −0.858192
\(40\) 0 0
\(41\) −10.3600 + 3.77075i −1.61797 + 0.588892i −0.982993 0.183642i \(-0.941211\pi\)
−0.634974 + 0.772534i \(0.718989\pi\)
\(42\) 0 0
\(43\) −1.05998 + 6.01147i −0.161646 + 0.916741i 0.790809 + 0.612063i \(0.209660\pi\)
−0.952455 + 0.304678i \(0.901451\pi\)
\(44\) 0 0
\(45\) −0.706466 1.22363i −0.105314 0.182409i
\(46\) 0 0
\(47\) 6.72021 5.63892i 0.980243 0.822522i −0.00388290 0.999992i \(-0.501236\pi\)
0.984126 + 0.177471i \(0.0567915\pi\)
\(48\) 0 0
\(49\) 1.64677 2.85228i 0.235252 0.407469i
\(50\) 0 0
\(51\) −9.19933 3.34828i −1.28816 0.468853i
\(52\) 0 0
\(53\) 0.00933315 + 0.0529309i 0.00128201 + 0.00727062i 0.985442 0.170012i \(-0.0543805\pi\)
−0.984160 + 0.177282i \(0.943269\pi\)
\(54\) 0 0
\(55\) −6.06934 5.09278i −0.818389 0.686710i
\(56\) 0 0
\(57\) −8.49130 + 0.575879i −1.12470 + 0.0762770i
\(58\) 0 0
\(59\) −2.83451 2.37844i −0.369022 0.309646i 0.439353 0.898315i \(-0.355208\pi\)
−0.808375 + 0.588669i \(0.799652\pi\)
\(60\) 0 0
\(61\) −2.60306 14.7627i −0.333288 1.89017i −0.443518 0.896266i \(-0.646270\pi\)
0.110229 0.993906i \(-0.464842\pi\)
\(62\) 0 0
\(63\) 1.46955 + 0.534871i 0.185145 + 0.0673874i
\(64\) 0 0
\(65\) 2.38724 4.13483i 0.296101 0.512862i
\(66\) 0 0
\(67\) −9.72449 + 8.15982i −1.18804 + 0.996880i −0.188144 + 0.982141i \(0.560247\pi\)
−0.999891 + 0.0147389i \(0.995308\pi\)
\(68\) 0 0
\(69\) 1.11347 + 1.92859i 0.134046 + 0.232174i
\(70\) 0 0
\(71\) 0.359347 2.03796i 0.0426466 0.241861i −0.956031 0.293265i \(-0.905258\pi\)
0.998678 + 0.0514034i \(0.0163694\pi\)
\(72\) 0 0
\(73\) 0.670002 0.243861i 0.0784178 0.0285418i −0.302513 0.953145i \(-0.597826\pi\)
0.380931 + 0.924603i \(0.375603\pi\)
\(74\) 0 0
\(75\) −3.85509 −0.445148
\(76\) 0 0
\(77\) 8.76928 0.999352
\(78\) 0 0
\(79\) −10.5802 + 3.85086i −1.19036 + 0.433256i −0.859850 0.510546i \(-0.829443\pi\)
−0.330511 + 0.943802i \(0.607221\pi\)
\(80\) 0 0
\(81\) −1.87142 + 10.6133i −0.207935 + 1.17926i
\(82\) 0 0
\(83\) 4.99262 + 8.64748i 0.548012 + 0.949184i 0.998411 + 0.0563567i \(0.0179484\pi\)
−0.450399 + 0.892827i \(0.648718\pi\)
\(84\) 0 0
\(85\) 6.68089 5.60593i 0.724645 0.608049i
\(86\) 0 0
\(87\) −4.89018 + 8.47005i −0.524283 + 0.908084i
\(88\) 0 0
\(89\) 15.2229 + 5.54068i 1.61362 + 0.587311i 0.982152 0.188088i \(-0.0602289\pi\)
0.631472 + 0.775399i \(0.282451\pi\)
\(90\) 0 0
\(91\) 0.917642 + 5.20421i 0.0961950 + 0.545549i
\(92\) 0 0
\(93\) −2.99123 2.50994i −0.310176 0.260269i
\(94\) 0 0
\(95\) 3.33799 6.80762i 0.342470 0.698447i
\(96\) 0 0
\(97\) 0.285278 + 0.239377i 0.0289656 + 0.0243050i 0.657156 0.753755i \(-0.271759\pi\)
−0.628190 + 0.778060i \(0.716204\pi\)
\(98\) 0 0
\(99\) −0.642497 3.64378i −0.0645734 0.366214i
\(100\) 0 0
\(101\) −17.4750 6.36040i −1.73883 0.632883i −0.739637 0.673006i \(-0.765003\pi\)
−0.999195 + 0.0401224i \(0.987225\pi\)
\(102\) 0 0
\(103\) 4.48973 7.77645i 0.442387 0.766236i −0.555479 0.831530i \(-0.687465\pi\)
0.997866 + 0.0652941i \(0.0207986\pi\)
\(104\) 0 0
\(105\) −5.00877 + 4.20286i −0.488806 + 0.410157i
\(106\) 0 0
\(107\) 3.74332 + 6.48362i 0.361881 + 0.626796i 0.988270 0.152714i \(-0.0488015\pi\)
−0.626390 + 0.779510i \(0.715468\pi\)
\(108\) 0 0
\(109\) −2.91266 + 16.5185i −0.278982 + 1.58219i 0.447039 + 0.894515i \(0.352479\pi\)
−0.726021 + 0.687672i \(0.758633\pi\)
\(110\) 0 0
\(111\) 12.9646 4.71871i 1.23054 0.447881i
\(112\) 0 0
\(113\) 10.6659 1.00336 0.501682 0.865052i \(-0.332715\pi\)
0.501682 + 0.865052i \(0.332715\pi\)
\(114\) 0 0
\(115\) −1.98389 −0.184999
\(116\) 0 0
\(117\) 2.09520 0.762592i 0.193702 0.0705016i
\(118\) 0 0
\(119\) −1.67620 + 9.50623i −0.153657 + 0.871435i
\(120\) 0 0
\(121\) −4.87379 8.44164i −0.443071 0.767422i
\(122\) 0 0
\(123\) 16.4901 13.8368i 1.48686 1.24763i
\(124\) 0 0
\(125\) 6.06572 10.5061i 0.542534 0.939697i
\(126\) 0 0
\(127\) 10.3628 + 3.77175i 0.919550 + 0.334689i 0.758059 0.652185i \(-0.226148\pi\)
0.161491 + 0.986874i \(0.448370\pi\)
\(128\) 0 0
\(129\) −2.06963 11.7375i −0.182221 1.03343i
\(130\) 0 0
\(131\) −10.7437 9.01505i −0.938683 0.787648i 0.0386728 0.999252i \(-0.487687\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(132\) 0 0
\(133\) 2.01309 + 8.14680i 0.174557 + 0.706417i
\(134\) 0 0
\(135\) −5.69166 4.77587i −0.489860 0.411041i
\(136\) 0 0
\(137\) 1.53142 + 8.68510i 0.130838 + 0.742019i 0.977668 + 0.210155i \(0.0673969\pi\)
−0.846830 + 0.531863i \(0.821492\pi\)
\(138\) 0 0
\(139\) 5.75603 + 2.09502i 0.488220 + 0.177698i 0.574388 0.818583i \(-0.305240\pi\)
−0.0861681 + 0.996281i \(0.527462\pi\)
\(140\) 0 0
\(141\) −8.56431 + 14.8338i −0.721245 + 1.24923i
\(142\) 0 0
\(143\) 9.57769 8.03663i 0.800926 0.672057i
\(144\) 0 0
\(145\) −4.35647 7.54564i −0.361786 0.626631i
\(146\) 0 0
\(147\) −1.11667 + 6.33297i −0.0921016 + 0.522334i
\(148\) 0 0
\(149\) 2.28488 0.831630i 0.187185 0.0681298i −0.246727 0.969085i \(-0.579355\pi\)
0.433912 + 0.900955i \(0.357133\pi\)
\(150\) 0 0
\(151\) −11.4850 −0.934636 −0.467318 0.884089i \(-0.654780\pi\)
−0.467318 + 0.884089i \(0.654780\pi\)
\(152\) 0 0
\(153\) 4.07281 0.329267
\(154\) 0 0
\(155\) 3.26882 1.18975i 0.262558 0.0955634i
\(156\) 0 0
\(157\) −0.462101 + 2.62071i −0.0368797 + 0.209155i −0.997679 0.0680888i \(-0.978310\pi\)
0.960800 + 0.277244i \(0.0894210\pi\)
\(158\) 0 0
\(159\) −0.0524713 0.0908830i −0.00416124 0.00720749i
\(160\) 0 0
\(161\) 1.68209 1.41144i 0.132567 0.111237i
\(162\) 0 0
\(163\) −2.05611 + 3.56129i −0.161047 + 0.278942i −0.935245 0.354002i \(-0.884820\pi\)
0.774197 + 0.632944i \(0.218154\pi\)
\(164\) 0 0
\(165\) 14.5367 + 5.29094i 1.13168 + 0.411899i
\(166\) 0 0
\(167\) −2.59827 14.7355i −0.201060 1.14027i −0.903521 0.428545i \(-0.859027\pi\)
0.702461 0.711722i \(-0.252085\pi\)
\(168\) 0 0
\(169\) −4.18693 3.51325i −0.322071 0.270250i
\(170\) 0 0
\(171\) 3.23764 1.43336i 0.247589 0.109612i
\(172\) 0 0
\(173\) −4.88231 4.09674i −0.371195 0.311470i 0.438039 0.898956i \(-0.355673\pi\)
−0.809234 + 0.587486i \(0.800118\pi\)
\(174\) 0 0
\(175\) 0.660072 + 3.74346i 0.0498968 + 0.282979i
\(176\) 0 0
\(177\) 6.78897 + 2.47098i 0.510290 + 0.185730i
\(178\) 0 0
\(179\) 1.59062 2.75504i 0.118889 0.205922i −0.800439 0.599415i \(-0.795400\pi\)
0.919328 + 0.393493i \(0.128733\pi\)
\(180\) 0 0
\(181\) −3.48401 + 2.92343i −0.258964 + 0.217297i −0.763021 0.646374i \(-0.776285\pi\)
0.504057 + 0.863671i \(0.331840\pi\)
\(182\) 0 0
\(183\) 14.6345 + 25.3477i 1.08181 + 1.87376i
\(184\) 0 0
\(185\) −2.13428 + 12.1041i −0.156916 + 0.889913i
\(186\) 0 0
\(187\) 21.4608 7.81110i 1.56937 0.571204i
\(188\) 0 0
\(189\) 8.22358 0.598178
\(190\) 0 0
\(191\) 0.968712 0.0700935 0.0350468 0.999386i \(-0.488842\pi\)
0.0350468 + 0.999386i \(0.488842\pi\)
\(192\) 0 0
\(193\) −14.2895 + 5.20094i −1.02858 + 0.374372i −0.800540 0.599280i \(-0.795454\pi\)
−0.228039 + 0.973652i \(0.573231\pi\)
\(194\) 0 0
\(195\) −1.61879 + 9.18062i −0.115924 + 0.657438i
\(196\) 0 0
\(197\) −8.22940 14.2537i −0.586320 1.01554i −0.994709 0.102729i \(-0.967243\pi\)
0.408389 0.912808i \(-0.366091\pi\)
\(198\) 0 0
\(199\) −16.8080 + 14.1036i −1.19149 + 0.999775i −0.191653 + 0.981463i \(0.561385\pi\)
−0.999832 + 0.0183119i \(0.994171\pi\)
\(200\) 0 0
\(201\) 12.3930 21.4653i 0.874135 1.51405i
\(202\) 0 0
\(203\) 9.06207 + 3.29832i 0.636033 + 0.231497i
\(204\) 0 0
\(205\) 3.33004 + 18.8856i 0.232580 + 1.31903i
\(206\) 0 0
\(207\) −0.709718 0.595524i −0.0493288 0.0413918i
\(208\) 0 0
\(209\) 14.3111 13.7622i 0.989917 0.951949i
\(210\) 0 0
\(211\) −14.0895 11.8225i −0.969962 0.813895i 0.0125831 0.999921i \(-0.495995\pi\)
−0.982545 + 0.186026i \(0.940439\pi\)
\(212\) 0 0
\(213\) 0.701629 + 3.97914i 0.0480748 + 0.272646i
\(214\) 0 0
\(215\) 9.97744 + 3.63149i 0.680456 + 0.247666i
\(216\) 0 0
\(217\) −1.92509 + 3.33436i −0.130684 + 0.226351i
\(218\) 0 0
\(219\) −1.06644 + 0.894853i −0.0720636 + 0.0604685i
\(220\) 0 0
\(221\) 6.88129 + 11.9187i 0.462886 + 0.801741i
\(222\) 0 0
\(223\) 3.38895 19.2197i 0.226941 1.28705i −0.631998 0.774970i \(-0.717765\pi\)
0.858939 0.512077i \(-0.171124\pi\)
\(224\) 0 0
\(225\) 1.50711 0.548543i 0.100474 0.0365695i
\(226\) 0 0
\(227\) −7.30867 −0.485094 −0.242547 0.970140i \(-0.577983\pi\)
−0.242547 + 0.970140i \(0.577983\pi\)
\(228\) 0 0
\(229\) 21.1319 1.39644 0.698218 0.715885i \(-0.253977\pi\)
0.698218 + 0.715885i \(0.253977\pi\)
\(230\) 0 0
\(231\) −16.0895 + 5.85611i −1.05861 + 0.385304i
\(232\) 0 0
\(233\) 0.826691 4.68840i 0.0541583 0.307147i −0.945681 0.325097i \(-0.894603\pi\)
0.999839 + 0.0179503i \(0.00571406\pi\)
\(234\) 0 0
\(235\) −7.62961 13.2149i −0.497701 0.862044i
\(236\) 0 0
\(237\) 16.8405 14.1308i 1.09391 0.917896i
\(238\) 0 0
\(239\) −10.4370 + 18.0774i −0.675114 + 1.16933i 0.301322 + 0.953522i \(0.402572\pi\)
−0.976436 + 0.215809i \(0.930761\pi\)
\(240\) 0 0
\(241\) −6.64094 2.41710i −0.427781 0.155699i 0.119152 0.992876i \(-0.461982\pi\)
−0.546933 + 0.837177i \(0.684205\pi\)
\(242\) 0 0
\(243\) −1.42875 8.10284i −0.0916543 0.519797i
\(244\) 0 0
\(245\) −4.38854 3.68242i −0.280373 0.235261i
\(246\) 0 0
\(247\) 9.66483 + 7.05292i 0.614959 + 0.448767i
\(248\) 0 0
\(249\) −14.9350 12.5320i −0.946470 0.794182i
\(250\) 0 0
\(251\) 2.11124 + 11.9734i 0.133260 + 0.755756i 0.976055 + 0.217522i \(0.0697973\pi\)
−0.842795 + 0.538234i \(0.819092\pi\)
\(252\) 0 0
\(253\) −4.88185 1.77685i −0.306919 0.111709i
\(254\) 0 0
\(255\) −8.51421 + 14.7470i −0.533180 + 0.923495i
\(256\) 0 0
\(257\) −0.252279 + 0.211687i −0.0157367 + 0.0132047i −0.650622 0.759402i \(-0.725492\pi\)
0.634885 + 0.772606i \(0.281047\pi\)
\(258\) 0 0
\(259\) −6.80187 11.7812i −0.422648 0.732047i
\(260\) 0 0
\(261\) 0.706560 4.00710i 0.0437350 0.248033i
\(262\) 0 0
\(263\) −8.33131 + 3.03235i −0.513731 + 0.186983i −0.585859 0.810413i \(-0.699243\pi\)
0.0721288 + 0.997395i \(0.477021\pi\)
\(264\) 0 0
\(265\) 0.0934893 0.00574300
\(266\) 0 0
\(267\) −31.6304 −1.93575
\(268\) 0 0
\(269\) −10.8291 + 3.94146i −0.660261 + 0.240315i −0.650349 0.759636i \(-0.725377\pi\)
−0.00991170 + 0.999951i \(0.503155\pi\)
\(270\) 0 0
\(271\) 0.516800 2.93092i 0.0313934 0.178041i −0.965079 0.261958i \(-0.915632\pi\)
0.996473 + 0.0839170i \(0.0267431\pi\)
\(272\) 0 0
\(273\) −5.15901 8.93567i −0.312238 0.540812i
\(274\) 0 0
\(275\) 6.88936 5.78086i 0.415444 0.348599i
\(276\) 0 0
\(277\) −15.8352 + 27.4274i −0.951445 + 1.64795i −0.209144 + 0.977885i \(0.567068\pi\)
−0.742301 + 0.670066i \(0.766266\pi\)
\(278\) 0 0
\(279\) 1.52653 + 0.555612i 0.0913910 + 0.0332636i
\(280\) 0 0
\(281\) −2.59294 14.7053i −0.154682 0.877245i −0.959076 0.283149i \(-0.908621\pi\)
0.804394 0.594096i \(-0.202490\pi\)
\(282\) 0 0
\(283\) 14.2583 + 11.9642i 0.847571 + 0.711196i 0.959253 0.282548i \(-0.0911796\pi\)
−0.111683 + 0.993744i \(0.535624\pi\)
\(284\) 0 0
\(285\) −1.57829 + 14.7195i −0.0934899 + 0.871906i
\(286\) 0 0
\(287\) −16.2596 13.6434i −0.959774 0.805346i
\(288\) 0 0
\(289\) 1.41338 + 8.01566i 0.0831399 + 0.471510i
\(290\) 0 0
\(291\) −0.683273 0.248691i −0.0400542 0.0145785i
\(292\) 0 0
\(293\) −5.68375 + 9.84455i −0.332048 + 0.575125i −0.982913 0.184069i \(-0.941073\pi\)
0.650865 + 0.759193i \(0.274406\pi\)
\(294\) 0 0
\(295\) −4.93040 + 4.13709i −0.287059 + 0.240871i
\(296\) 0 0
\(297\) −9.72825 16.8498i −0.564490 0.977726i
\(298\) 0 0
\(299\) 0.543636 3.08311i 0.0314393 0.178301i
\(300\) 0 0
\(301\) −11.0432 + 4.01940i −0.636520 + 0.231674i
\(302\) 0 0
\(303\) 36.3100 2.08595
\(304\) 0 0
\(305\) −26.0747 −1.49303
\(306\) 0 0
\(307\) −10.0165 + 3.64570i −0.571670 + 0.208071i −0.611649 0.791130i \(-0.709493\pi\)
0.0399784 + 0.999201i \(0.487271\pi\)
\(308\) 0 0
\(309\) −3.04449 + 17.2662i −0.173195 + 0.982238i
\(310\) 0 0
\(311\) −12.7091 22.0128i −0.720668 1.24823i −0.960733 0.277476i \(-0.910502\pi\)
0.240065 0.970757i \(-0.422831\pi\)
\(312\) 0 0
\(313\) −1.29381 + 1.08564i −0.0731305 + 0.0613638i −0.678620 0.734489i \(-0.737422\pi\)
0.605490 + 0.795853i \(0.292977\pi\)
\(314\) 0 0
\(315\) 1.36010 2.35576i 0.0766330 0.132732i
\(316\) 0 0
\(317\) −18.4942 6.73135i −1.03874 0.378070i −0.234337 0.972155i \(-0.575292\pi\)
−0.804402 + 0.594085i \(0.797514\pi\)
\(318\) 0 0
\(319\) −3.96201 22.4697i −0.221830 1.25806i
\(320\) 0 0
\(321\) −11.1979 9.39611i −0.625003 0.524440i
\(322\) 0 0
\(323\) 12.1832 + 18.1443i 0.677892 + 1.00958i
\(324\) 0 0
\(325\) 4.15163 + 3.48363i 0.230291 + 0.193237i
\(326\) 0 0
\(327\) −5.68700 32.2526i −0.314492 1.78357i
\(328\) 0 0
\(329\) 15.8706 + 5.77644i 0.874977 + 0.318466i
\(330\) 0 0
\(331\) 4.50354 7.80036i 0.247537 0.428747i −0.715305 0.698813i \(-0.753712\pi\)
0.962842 + 0.270066i \(0.0870455\pi\)
\(332\) 0 0
\(333\) −4.39693 + 3.68946i −0.240950 + 0.202181i
\(334\) 0 0
\(335\) 11.0404 + 19.1226i 0.603204 + 1.04478i
\(336\) 0 0
\(337\) −1.90637 + 10.8115i −0.103846 + 0.588942i 0.887828 + 0.460174i \(0.152213\pi\)
−0.991675 + 0.128767i \(0.958898\pi\)
\(338\) 0 0
\(339\) −19.5694 + 7.12267i −1.06286 + 0.386850i
\(340\) 0 0
\(341\) 9.10931 0.493297
\(342\) 0 0
\(343\) 19.8173 1.07003
\(344\) 0 0
\(345\) 3.63997 1.32484i 0.195969 0.0713270i
\(346\) 0 0
\(347\) −0.486415 + 2.75859i −0.0261121 + 0.148089i −0.995076 0.0991121i \(-0.968400\pi\)
0.968964 + 0.247201i \(0.0795109\pi\)
\(348\) 0 0
\(349\) −16.8890 29.2526i −0.904048 1.56586i −0.822190 0.569213i \(-0.807248\pi\)
−0.0818576 0.996644i \(-0.526085\pi\)
\(350\) 0 0
\(351\) 8.98169 7.53653i 0.479407 0.402270i
\(352\) 0 0
\(353\) −1.25317 + 2.17056i −0.0666996 + 0.115527i −0.897447 0.441123i \(-0.854580\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(354\) 0 0
\(355\) −3.38246 1.23112i −0.179523 0.0653409i
\(356\) 0 0
\(357\) −3.27281 18.5610i −0.173215 0.982354i
\(358\) 0 0
\(359\) −16.3680 13.7343i −0.863868 0.724871i 0.0989298 0.995094i \(-0.468458\pi\)
−0.962798 + 0.270223i \(0.912903\pi\)
\(360\) 0 0
\(361\) 16.0705 + 10.1360i 0.845818 + 0.533471i
\(362\) 0 0
\(363\) 14.5795 + 12.2337i 0.765228 + 0.642102i
\(364\) 0 0
\(365\) −0.215360 1.22137i −0.0112724 0.0639292i
\(366\) 0 0
\(367\) 3.36473 + 1.22466i 0.175638 + 0.0639268i 0.428342 0.903617i \(-0.359098\pi\)
−0.252705 + 0.967543i \(0.581320\pi\)
\(368\) 0 0
\(369\) −4.47779 + 7.75575i −0.233104 + 0.403748i
\(370\) 0 0
\(371\) −0.0792670 + 0.0665129i −0.00411534 + 0.00345318i
\(372\) 0 0
\(373\) 17.7609 + 30.7627i 0.919622 + 1.59283i 0.799989 + 0.600014i \(0.204838\pi\)
0.119633 + 0.992818i \(0.461828\pi\)
\(374\) 0 0
\(375\) −4.11317 + 23.3269i −0.212403 + 1.20460i
\(376\) 0 0
\(377\) 12.9202 4.70258i 0.665426 0.242195i
\(378\) 0 0
\(379\) 7.31674 0.375836 0.187918 0.982185i \(-0.439826\pi\)
0.187918 + 0.982185i \(0.439826\pi\)
\(380\) 0 0
\(381\) −21.5320 −1.10312
\(382\) 0 0
\(383\) 6.92985 2.52226i 0.354099 0.128881i −0.158845 0.987304i \(-0.550777\pi\)
0.512944 + 0.858422i \(0.328555\pi\)
\(384\) 0 0
\(385\) 2.64873 15.0217i 0.134992 0.765576i
\(386\) 0 0
\(387\) 2.47923 + 4.29415i 0.126026 + 0.218284i
\(388\) 0 0
\(389\) 6.00096 5.03540i 0.304261 0.255305i −0.477854 0.878439i \(-0.658585\pi\)
0.782115 + 0.623134i \(0.214141\pi\)
\(390\) 0 0
\(391\) 2.85931 4.95247i 0.144602 0.250457i
\(392\) 0 0
\(393\) 25.7324 + 9.36582i 1.29803 + 0.472443i
\(394\) 0 0
\(395\) 3.40080 + 19.2869i 0.171113 + 0.970428i
\(396\) 0 0
\(397\) 15.3729 + 12.8994i 0.771546 + 0.647404i 0.941104 0.338116i \(-0.109790\pi\)
−0.169558 + 0.985520i \(0.554234\pi\)
\(398\) 0 0
\(399\) −9.13396 13.6031i −0.457270 0.681006i
\(400\) 0 0
\(401\) 4.85171 + 4.07107i 0.242283 + 0.203300i 0.755841 0.654755i \(-0.227228\pi\)
−0.513558 + 0.858055i \(0.671673\pi\)
\(402\) 0 0
\(403\) 0.953225 + 5.40601i 0.0474835 + 0.269292i
\(404\) 0 0
\(405\) 17.6153 + 6.41145i 0.875312 + 0.318587i
\(406\) 0 0
\(407\) −16.0928 + 27.8736i −0.797691 + 1.38164i
\(408\) 0 0
\(409\) 14.9939 12.5813i 0.741398 0.622107i −0.191814 0.981431i \(-0.561437\pi\)
0.933213 + 0.359324i \(0.116993\pi\)
\(410\) 0 0
\(411\) −8.60968 14.9124i −0.424684 0.735575i
\(412\) 0 0
\(413\) 1.23701 7.01545i 0.0608695 0.345208i
\(414\) 0 0
\(415\) 16.3211 5.94038i 0.801169 0.291602i
\(416\) 0 0
\(417\) −11.9600 −0.585683
\(418\) 0 0
\(419\) 9.06493 0.442851 0.221426 0.975177i \(-0.428929\pi\)
0.221426 + 0.975177i \(0.428929\pi\)
\(420\) 0 0
\(421\) 23.5586 8.57464i 1.14818 0.417902i 0.303317 0.952890i \(-0.401906\pi\)
0.844860 + 0.534987i \(0.179684\pi\)
\(422\) 0 0
\(423\) 1.23742 7.01775i 0.0601653 0.341215i
\(424\) 0 0
\(425\) 4.94980 + 8.57331i 0.240101 + 0.415867i
\(426\) 0 0
\(427\) 22.1080 18.5508i 1.06988 0.897735i
\(428\) 0 0
\(429\) −12.2059 + 21.1413i −0.589307 + 1.02071i
\(430\) 0 0
\(431\) 6.18508 + 2.25119i 0.297925 + 0.108436i 0.486658 0.873593i \(-0.338216\pi\)
−0.188733 + 0.982028i \(0.560438\pi\)
\(432\) 0 0
\(433\) −3.41428 19.3634i −0.164080 0.930544i −0.950008 0.312226i \(-0.898925\pi\)
0.785928 0.618318i \(-0.212186\pi\)
\(434\) 0 0
\(435\) 13.0321 + 10.9352i 0.624839 + 0.524302i
\(436\) 0 0
\(437\) 0.530035 4.94321i 0.0253550 0.236466i
\(438\) 0 0
\(439\) 12.9204 + 10.8415i 0.616657 + 0.517437i 0.896751 0.442536i \(-0.145921\pi\)
−0.280094 + 0.959973i \(0.590366\pi\)
\(440\) 0 0
\(441\) −0.464568 2.63470i −0.0221223 0.125462i
\(442\) 0 0
\(443\) −35.5201 12.9283i −1.68761 0.614240i −0.693290 0.720659i \(-0.743839\pi\)
−0.994321 + 0.106419i \(0.966062\pi\)
\(444\) 0 0
\(445\) 14.0892 24.4032i 0.667891 1.15682i
\(446\) 0 0
\(447\) −3.63686 + 3.05168i −0.172017 + 0.144340i
\(448\) 0 0
\(449\) 7.02262 + 12.1635i 0.331418 + 0.574033i 0.982790 0.184726i \(-0.0591397\pi\)
−0.651372 + 0.758758i \(0.725806\pi\)
\(450\) 0 0
\(451\) −8.72026 + 49.4551i −0.410621 + 2.32875i
\(452\) 0 0
\(453\) 21.0722 7.66966i 0.990059 0.360352i
\(454\) 0 0
\(455\) 9.19193 0.430924
\(456\) 0 0
\(457\) −10.9491 −0.512177 −0.256089 0.966653i \(-0.582434\pi\)
−0.256089 + 0.966653i \(0.582434\pi\)
\(458\) 0 0
\(459\) 20.1254 7.32503i 0.939371 0.341903i
\(460\) 0 0
\(461\) 1.36371 7.73396i 0.0635141 0.360206i −0.936442 0.350823i \(-0.885902\pi\)
0.999956 0.00938355i \(-0.00298692\pi\)
\(462\) 0 0
\(463\) −9.88710 17.1250i −0.459492 0.795864i 0.539442 0.842023i \(-0.318635\pi\)
−0.998934 + 0.0461588i \(0.985302\pi\)
\(464\) 0 0
\(465\) −5.20300 + 4.36583i −0.241283 + 0.202461i
\(466\) 0 0
\(467\) 4.56124 7.90030i 0.211069 0.365582i −0.740980 0.671527i \(-0.765639\pi\)
0.952049 + 0.305944i \(0.0989722\pi\)
\(468\) 0 0
\(469\) −22.9657 8.35881i −1.06046 0.385974i
\(470\) 0 0
\(471\) −0.902258 5.11696i −0.0415739 0.235777i
\(472\) 0 0
\(473\) 21.2994 + 17.8723i 0.979347 + 0.821769i
\(474\) 0 0
\(475\) 6.95205 + 5.07326i 0.318982 + 0.232777i
\(476\) 0 0
\(477\) 0.0334449 + 0.0280636i 0.00153134 + 0.00128494i
\(478\) 0 0
\(479\) 6.06849 + 34.4161i 0.277276 + 1.57251i 0.731637 + 0.681694i \(0.238757\pi\)
−0.454361 + 0.890818i \(0.650132\pi\)
\(480\) 0 0
\(481\) −18.2258 6.63366i −0.831026 0.302469i
\(482\) 0 0
\(483\) −2.14367 + 3.71295i −0.0975405 + 0.168945i
\(484\) 0 0
\(485\) 0.496218 0.416376i 0.0225321 0.0189067i
\(486\) 0 0
\(487\) −14.9182 25.8391i −0.676009 1.17088i −0.976173 0.216994i \(-0.930375\pi\)
0.300164 0.953888i \(-0.402959\pi\)
\(488\) 0 0
\(489\) 1.39425 7.90719i 0.0630502 0.357575i
\(490\) 0 0
\(491\) −6.74192 + 2.45386i −0.304259 + 0.110741i −0.489638 0.871926i \(-0.662871\pi\)
0.185379 + 0.982667i \(0.440649\pi\)
\(492\) 0 0
\(493\) 25.1153 1.13114
\(494\) 0 0
\(495\) −6.43583 −0.289269
\(496\) 0 0
\(497\) 3.74377 1.36262i 0.167931 0.0611220i
\(498\) 0 0
\(499\) 2.81846 15.9843i 0.126172 0.715556i −0.854433 0.519561i \(-0.826095\pi\)
0.980605 0.195994i \(-0.0627935\pi\)
\(500\) 0 0
\(501\) 14.6075 + 25.3010i 0.652617 + 1.13037i
\(502\) 0 0
\(503\) −14.2611 + 11.9665i −0.635869 + 0.533558i −0.902747 0.430173i \(-0.858453\pi\)
0.266877 + 0.963731i \(0.414008\pi\)
\(504\) 0 0
\(505\) −16.1736 + 28.0135i −0.719715 + 1.24658i
\(506\) 0 0
\(507\) 10.0282 + 3.64995i 0.445366 + 0.162100i
\(508\) 0 0
\(509\) −0.734939 4.16805i −0.0325756 0.184745i 0.964178 0.265255i \(-0.0854562\pi\)
−0.996754 + 0.0805099i \(0.974345\pi\)
\(510\) 0 0
\(511\) 1.05154 + 0.882344i 0.0465172 + 0.0390326i
\(512\) 0 0
\(513\) 13.4205 12.9058i 0.592531 0.569804i
\(514\) 0 0
\(515\) −11.9649 10.0397i −0.527236 0.442403i
\(516\) 0 0
\(517\) −6.93877 39.3517i −0.305167 1.73069i
\(518\) 0 0
\(519\) 11.6937 + 4.25615i 0.513295 + 0.186824i
\(520\) 0 0
\(521\) −6.40530 + 11.0943i −0.280621 + 0.486050i −0.971538 0.236884i \(-0.923874\pi\)
0.690917 + 0.722934i \(0.257207\pi\)
\(522\) 0 0
\(523\) −24.7911 + 20.8022i −1.08404 + 0.909618i −0.996250 0.0865209i \(-0.972425\pi\)
−0.0877905 + 0.996139i \(0.527981\pi\)
\(524\) 0 0
\(525\) −3.71095 6.42755i −0.161959 0.280521i
\(526\) 0 0
\(527\) −1.74120 + 9.87485i −0.0758479 + 0.430155i
\(528\) 0 0
\(529\) 20.3905 7.42154i 0.886545 0.322676i
\(530\) 0 0
\(531\) −3.00567 −0.130435
\(532\) 0 0
\(533\) −30.2621 −1.31080
\(534\) 0 0
\(535\) 12.2370 4.45392i 0.529054 0.192560i
\(536\) 0 0
\(537\) −1.07860 + 6.11706i −0.0465451 + 0.263971i
\(538\) 0 0
\(539\) −7.50094 12.9920i −0.323088 0.559605i
\(540\) 0 0
\(541\) 14.1268 11.8538i 0.607359 0.509634i −0.286443 0.958097i \(-0.592473\pi\)
0.893801 + 0.448463i \(0.148028\pi\)
\(542\) 0 0
\(543\) 4.44006 7.69040i 0.190541 0.330027i
\(544\) 0 0
\(545\) 27.4163 + 9.97872i 1.17439 + 0.427442i
\(546\) 0 0
\(547\) −5.66428 32.1238i −0.242187 1.37351i −0.826935 0.562297i \(-0.809918\pi\)
0.584748 0.811215i \(-0.301193\pi\)
\(548\) 0 0
\(549\) −9.32795 7.82708i −0.398107 0.334052i
\(550\) 0 0
\(551\) 19.9652 8.83894i 0.850544 0.376552i
\(552\) 0 0
\(553\) −16.6051 13.9333i −0.706119 0.592504i
\(554\) 0 0
\(555\) −4.16722 23.6335i −0.176888 1.00318i
\(556\) 0 0
\(557\) −12.2636 4.46359i −0.519625 0.189128i 0.0688747 0.997625i \(-0.478059\pi\)
−0.588500 + 0.808497i \(0.700281\pi\)
\(558\) 0 0
\(559\) −8.37765 + 14.5105i −0.354337 + 0.613730i
\(560\) 0 0
\(561\) −34.1592 + 28.6630i −1.44220 + 1.21015i
\(562\) 0 0
\(563\) −9.12500 15.8050i −0.384573 0.666100i 0.607137 0.794597i \(-0.292318\pi\)
−0.991710 + 0.128498i \(0.958985\pi\)
\(564\) 0 0
\(565\) 3.22160 18.2706i 0.135534 0.768649i
\(566\) 0 0
\(567\) −19.4969 + 7.09631i −0.818795 + 0.298017i
\(568\) 0 0
\(569\) −34.4274 −1.44327 −0.721636 0.692273i \(-0.756610\pi\)
−0.721636 + 0.692273i \(0.756610\pi\)
\(570\) 0 0
\(571\) −16.6525 −0.696884 −0.348442 0.937330i \(-0.613289\pi\)
−0.348442 + 0.937330i \(0.613289\pi\)
\(572\) 0 0
\(573\) −1.77735 + 0.646904i −0.0742500 + 0.0270248i
\(574\) 0 0
\(575\) 0.391044 2.21772i 0.0163077 0.0924855i
\(576\) 0 0
\(577\) 18.7394 + 32.4576i 0.780130 + 1.35123i 0.931865 + 0.362804i \(0.118181\pi\)
−0.151735 + 0.988421i \(0.548486\pi\)
\(578\) 0 0
\(579\) 22.7446 19.0850i 0.945233 0.793144i
\(580\) 0 0
\(581\) −9.61189 + 16.6483i −0.398769 + 0.690687i
\(582\) 0 0
\(583\) 0.230053 + 0.0837324i 0.00952781 + 0.00346784i
\(584\) 0 0
\(585\) −0.673464 3.81940i −0.0278443 0.157913i
\(586\) 0 0
\(587\) 26.0297 + 21.8415i 1.07436 + 0.901494i 0.995440 0.0953871i \(-0.0304089\pi\)
0.0789185 + 0.996881i \(0.474853\pi\)
\(588\) 0 0
\(589\) 2.09115 + 8.46270i 0.0861643 + 0.348700i
\(590\) 0 0
\(591\) 24.6176 + 20.6566i 1.01263 + 0.849700i
\(592\) 0 0
\(593\) 3.29313 + 18.6762i 0.135232 + 0.766941i 0.974698 + 0.223528i \(0.0717574\pi\)
−0.839465 + 0.543414i \(0.817132\pi\)
\(594\) 0 0
\(595\) 15.7778 + 5.74265i 0.646827 + 0.235426i
\(596\) 0 0
\(597\) 21.4203 37.1010i 0.876673 1.51844i
\(598\) 0 0
\(599\) 25.6598 21.5311i 1.04843 0.879738i 0.0555029 0.998459i \(-0.482324\pi\)
0.992928 + 0.118721i \(0.0378794\pi\)
\(600\) 0 0
\(601\) 7.50056 + 12.9914i 0.305954 + 0.529928i 0.977473 0.211059i \(-0.0676912\pi\)
−0.671519 + 0.740987i \(0.734358\pi\)
\(602\) 0 0
\(603\) −1.79061 + 10.1550i −0.0729192 + 0.413545i
\(604\) 0 0
\(605\) −15.9326 + 5.79898i −0.647751 + 0.235762i
\(606\) 0 0
\(607\) 7.06547 0.286779 0.143389 0.989666i \(-0.454200\pi\)
0.143389 + 0.989666i \(0.454200\pi\)
\(608\) 0 0
\(609\) −18.8293 −0.763003
\(610\) 0 0
\(611\) 22.6276 8.23576i 0.915413 0.333183i
\(612\) 0 0
\(613\) −4.54668 + 25.7855i −0.183639 + 1.04147i 0.744053 + 0.668120i \(0.232901\pi\)
−0.927692 + 0.373346i \(0.878210\pi\)
\(614\) 0 0
\(615\) −18.7216 32.4268i −0.754928 1.30757i
\(616\) 0 0
\(617\) −33.3641 + 27.9958i −1.34319 + 1.12707i −0.362395 + 0.932025i \(0.618041\pi\)
−0.980794 + 0.195045i \(0.937515\pi\)
\(618\) 0 0
\(619\) 12.4919 21.6365i 0.502090 0.869646i −0.497907 0.867231i \(-0.665898\pi\)
0.999997 0.00241526i \(-0.000768802\pi\)
\(620\) 0 0
\(621\) −4.57806 1.66628i −0.183711 0.0668654i
\(622\) 0 0
\(623\) 5.41579 + 30.7145i 0.216979 + 1.23055i
\(624\) 0 0
\(625\) −8.60229 7.21818i −0.344092 0.288727i
\(626\) 0 0
\(627\) −17.0670 + 34.8072i −0.681592 + 1.39007i
\(628\) 0 0
\(629\) −27.1399 22.7731i −1.08214 0.908024i
\(630\) 0 0
\(631\) 8.07717 + 45.8079i 0.321547 + 1.82358i 0.532905 + 0.846175i \(0.321100\pi\)
−0.211358 + 0.977409i \(0.567789\pi\)
\(632\) 0 0
\(633\) 33.7459 + 12.2825i 1.34128 + 0.488186i
\(634\) 0 0
\(635\) 9.59103 16.6121i 0.380608 0.659233i
\(636\) 0 0
\(637\) 6.92531 5.81102i 0.274391 0.230241i
\(638\) 0 0
\(639\) −0.840488 1.45577i −0.0332492 0.0575893i
\(640\) 0 0
\(641\) 1.23030 6.97736i 0.0485938 0.275589i −0.950823 0.309734i \(-0.899760\pi\)
0.999417 + 0.0341454i \(0.0108709\pi\)
\(642\) 0 0
\(643\) 0.150167 0.0546563i 0.00592200 0.00215543i −0.339057 0.940766i \(-0.610108\pi\)
0.344979 + 0.938610i \(0.387886\pi\)
\(644\) 0 0
\(645\) −20.7313 −0.816295
\(646\) 0 0
\(647\) 18.8979 0.742955 0.371478 0.928442i \(-0.378851\pi\)
0.371478 + 0.928442i \(0.378851\pi\)
\(648\) 0 0
\(649\) −15.8378 + 5.76447i −0.621686 + 0.226275i
\(650\) 0 0
\(651\) 1.30541 7.40333i 0.0511629 0.290159i
\(652\) 0 0
\(653\) 5.62463 + 9.74215i 0.220109 + 0.381240i 0.954841 0.297118i \(-0.0960254\pi\)
−0.734732 + 0.678358i \(0.762692\pi\)
\(654\) 0 0
\(655\) −18.6878 + 15.6809i −0.730193 + 0.612705i
\(656\) 0 0
\(657\) 0.289586 0.501578i 0.0112978 0.0195684i
\(658\) 0 0
\(659\) −11.8940 4.32904i −0.463323 0.168636i 0.0998025 0.995007i \(-0.468179\pi\)
−0.563125 + 0.826372i \(0.690401\pi\)
\(660\) 0 0
\(661\) −0.642263 3.64245i −0.0249811 0.141675i 0.969766 0.244036i \(-0.0784715\pi\)
−0.994747 + 0.102361i \(0.967360\pi\)
\(662\) 0 0
\(663\) −20.5848 17.2727i −0.799449 0.670817i
\(664\) 0 0
\(665\) 14.5634 0.987692i 0.564746 0.0383010i
\(666\) 0 0
\(667\) −4.37653 3.67235i −0.169460 0.142194i
\(668\) 0 0
\(669\) 6.61697 + 37.5267i 0.255827 + 1.45087i
\(670\) 0 0
\(671\) −64.1629 23.3534i −2.47698 0.901548i
\(672\) 0 0
\(673\) 11.1273 19.2730i 0.428926 0.742921i −0.567852 0.823130i \(-0.692226\pi\)
0.996778 + 0.0802094i \(0.0255589\pi\)
\(674\) 0 0
\(675\) 6.46065 5.42113i 0.248671 0.208659i
\(676\) 0 0
\(677\) −11.9484 20.6952i −0.459213 0.795380i 0.539707 0.841853i \(-0.318535\pi\)
−0.998920 + 0.0464733i \(0.985202\pi\)
\(678\) 0 0
\(679\) −0.124499 + 0.706068i −0.00477783 + 0.0270964i
\(680\) 0 0
\(681\) 13.4097 4.88072i 0.513860 0.187030i
\(682\) 0 0
\(683\) −26.9375 −1.03073 −0.515367 0.856970i \(-0.672344\pi\)
−0.515367 + 0.856970i \(0.672344\pi\)
\(684\) 0 0
\(685\) 15.3401 0.586114
\(686\) 0 0
\(687\) −38.7720 + 14.1119i −1.47924 + 0.538401i
\(688\) 0 0
\(689\) −0.0256184 + 0.145289i −0.000975982 + 0.00553507i
\(690\) 0 0
\(691\) 13.6869 + 23.7063i 0.520673 + 0.901831i 0.999711 + 0.0240374i \(0.00765207\pi\)
−0.479039 + 0.877794i \(0.659015\pi\)
\(692\) 0 0
\(693\) 5.45676 4.57877i 0.207285 0.173933i
\(694\) 0 0
\(695\) 5.32735 9.22724i 0.202078 0.350009i
\(696\) 0 0
\(697\) −51.9444 18.9062i −1.96753 0.716123i
\(698\) 0 0
\(699\) 1.61412 + 9.15415i 0.0610517 + 0.346242i
\(700\) 0 0
\(701\) −17.7609 14.9032i −0.670821 0.562886i 0.242487 0.970155i \(-0.422037\pi\)
−0.913308 + 0.407269i \(0.866481\pi\)
\(702\) 0 0
\(703\) −29.5893 8.55178i −1.11598 0.322537i
\(704\) 0 0
\(705\) 22.8234 + 19.1511i 0.859579 + 0.721272i
\(706\) 0 0
\(707\) −6.21703 35.2585i −0.233815 1.32603i
\(708\) 0 0
\(709\) 0.177739 + 0.0646919i 0.00667515 + 0.00242955i 0.345356 0.938472i \(-0.387758\pi\)
−0.338680 + 0.940901i \(0.609981\pi\)
\(710\) 0 0
\(711\) −4.57292 + 7.92054i −0.171498 + 0.297043i
\(712\) 0 0
\(713\) 1.74731 1.46617i 0.0654374 0.0549085i
\(714\) 0 0
\(715\) −10.8738 18.8339i −0.406656 0.704349i
\(716\) 0 0
\(717\) 7.07734 40.1376i 0.264308 1.49896i
\(718\) 0 0
\(719\) −10.7370 + 3.90793i −0.400421 + 0.145741i −0.534377 0.845246i \(-0.679454\pi\)
0.133957 + 0.990987i \(0.457232\pi\)
\(720\) 0 0
\(721\) 17.2874 0.643818
\(722\) 0 0
\(723\) 13.7987 0.513178
\(724\) 0 0
\(725\) 9.29370 3.38263i 0.345159 0.125628i
\(726\) 0 0
\(727\) −5.22332 + 29.6229i −0.193722 + 1.09865i 0.720504 + 0.693451i \(0.243910\pi\)
−0.914226 + 0.405204i \(0.867201\pi\)
\(728\) 0 0
\(729\) −8.13313 14.0870i −0.301227 0.521741i
\(730\) 0 0
\(731\) −23.4455 + 19.6731i −0.867164 + 0.727637i
\(732\) 0 0
\(733\) 16.3368 28.2962i 0.603414 1.04514i −0.388885 0.921286i \(-0.627140\pi\)
0.992300 0.123858i \(-0.0395269\pi\)
\(734\) 0 0
\(735\) 10.5110 + 3.82570i 0.387705 + 0.141113i
\(736\) 0 0
\(737\) 10.0408 + 56.9440i 0.369856 + 2.09756i
\(738\) 0 0
\(739\) 19.5685 + 16.4199i 0.719838 + 0.604016i 0.927341 0.374218i \(-0.122089\pi\)
−0.207502 + 0.978235i \(0.566533\pi\)
\(740\) 0 0
\(741\) −22.4426 6.48627i −0.824449 0.238279i
\(742\) 0 0
\(743\) −17.6914 14.8449i −0.649035 0.544605i 0.257743 0.966214i \(-0.417021\pi\)
−0.906778 + 0.421608i \(0.861466\pi\)
\(744\) 0 0
\(745\) −0.734433 4.16518i −0.0269076 0.152600i
\(746\) 0 0
\(747\) 7.62188 + 2.77414i 0.278870 + 0.101500i
\(748\) 0 0
\(749\) −7.20671 + 12.4824i −0.263328 + 0.456097i
\(750\) 0 0
\(751\) 9.91762 8.32187i 0.361899 0.303670i −0.443648 0.896201i \(-0.646316\pi\)
0.805547 + 0.592532i \(0.201871\pi\)
\(752\) 0 0
\(753\) −11.8694 20.5585i −0.432547 0.749193i
\(754\) 0 0
\(755\) −3.46900 + 19.6737i −0.126250 + 0.715999i
\(756\) 0 0
\(757\) −16.4280 + 5.97928i −0.597084 + 0.217321i −0.622842 0.782347i \(-0.714022\pi\)
0.0257583 + 0.999668i \(0.491800\pi\)
\(758\) 0 0
\(759\) 10.1436 0.368189
\(760\) 0 0
\(761\) −4.43066 −0.160611 −0.0803057 0.996770i \(-0.525590\pi\)
−0.0803057 + 0.996770i \(0.525590\pi\)
\(762\) 0 0
\(763\) −30.3449 + 11.0446i −1.09856 + 0.399843i
\(764\) 0 0
\(765\) 1.23018 6.97669i 0.0444772 0.252243i
\(766\) 0 0
\(767\) −5.07829 8.79585i −0.183366 0.317600i
\(768\) 0 0
\(769\) 31.3561 26.3109i 1.13073 0.948794i 0.131633 0.991299i \(-0.457978\pi\)
0.999096 + 0.0425043i \(0.0135336\pi\)
\(770\) 0 0
\(771\) 0.321507 0.556867i 0.0115788 0.0200551i
\(772\) 0 0
\(773\) −7.12589 2.59361i −0.256300 0.0932857i 0.210675 0.977556i \(-0.432434\pi\)
−0.466975 + 0.884271i \(0.654656\pi\)
\(774\) 0 0
\(775\) 0.685668 + 3.88861i 0.0246299 + 0.139683i
\(776\) 0 0
\(777\) 20.3473 + 17.0734i 0.729954 + 0.612504i
\(778\) 0 0
\(779\) −47.9464 + 3.25172i −1.71786 + 0.116505i
\(780\) 0 0
\(781\) −7.22073 6.05892i −0.258378 0.216805i
\(782\) 0 0
\(783\) −3.71546 21.0714i −0.132780 0.753031i
\(784\) 0 0
\(785\) 4.34967 + 1.58315i 0.155246 + 0.0565051i
\(786\) 0 0
\(787\) 15.4525 26.7645i 0.550821 0.954050i −0.447394 0.894337i \(-0.647648\pi\)
0.998216 0.0597134i \(-0.0190187\pi\)
\(788\) 0 0
\(789\) 13.2610 11.1273i 0.472103 0.396141i
\(790\) 0 0
\(791\) 10.2671 + 17.7831i 0.365056 + 0.632295i
\(792\) 0 0
\(793\) 7.14509 40.5218i 0.253730 1.43897i
\(794\) 0 0
\(795\) −0.171530 + 0.0624320i −0.00608356 + 0.00221423i
\(796\) 0 0
\(797\) −17.9708 −0.636559 −0.318279 0.947997i \(-0.603105\pi\)
−0.318279 + 0.947997i \(0.603105\pi\)
\(798\) 0 0
\(799\) 43.9851 1.55608
\(800\) 0 0
\(801\) 12.3656 4.50071i 0.436917 0.159025i
\(802\) 0 0
\(803\) 0.563955 3.19835i 0.0199015 0.112867i
\(804\) 0 0
\(805\) −1.90971 3.30772i −0.0673086 0.116582i
\(806\) 0 0
\(807\) 17.2367 14.4633i 0.606759 0.509132i
\(808\) 0 0
\(809\) −2.52462 + 4.37277i −0.0887608 + 0.153738i −0.906988 0.421157i \(-0.861624\pi\)
0.818227 + 0.574896i \(0.194957\pi\)
\(810\) 0 0
\(811\) 18.5490 + 6.75127i 0.651342 + 0.237069i 0.646494 0.762919i \(-0.276235\pi\)
0.00484814 + 0.999988i \(0.498457\pi\)
\(812\) 0 0
\(813\) 1.00906 + 5.72265i 0.0353892 + 0.200702i
\(814\) 0 0
\(815\) 5.47942 + 4.59778i 0.191936 + 0.161053i
\(816\) 0 0
\(817\) −11.7141 + 23.8903i −0.409826 + 0.835815i
\(818\) 0 0
\(819\) 3.28832 + 2.75923i 0.114903 + 0.0964153i
\(820\) 0 0
\(821\) 0.349550 + 1.98240i 0.0121994 + 0.0691862i 0.990300 0.138948i \(-0.0443721\pi\)
−0.978100 + 0.208134i \(0.933261\pi\)
\(822\) 0 0
\(823\) 40.4124 + 14.7089i 1.40869 + 0.512721i 0.930745 0.365670i \(-0.119160\pi\)
0.477944 + 0.878390i \(0.341382\pi\)
\(824\) 0 0
\(825\) −8.77988 + 15.2072i −0.305676 + 0.529447i
\(826\) 0 0
\(827\) −25.7538 + 21.6100i −0.895547 + 0.751453i −0.969315 0.245823i \(-0.920942\pi\)
0.0737683 + 0.997275i \(0.476497\pi\)
\(828\) 0 0
\(829\) 17.3799 + 30.1028i 0.603627 + 1.04551i 0.992267 + 0.124123i \(0.0396118\pi\)
−0.388639 + 0.921390i \(0.627055\pi\)
\(830\) 0 0
\(831\) 10.7379 60.8974i 0.372492 2.11251i
\(832\) 0 0
\(833\) 15.5176 5.64794i 0.537653 0.195690i
\(834\) 0 0
\(835\) −26.0266 −0.900687
\(836\) 0 0
\(837\) 8.54246 0.295271
\(838\) 0 0
\(839\) 17.4556 6.35333i 0.602636 0.219341i −0.0226423 0.999744i \(-0.507208\pi\)
0.625278 + 0.780402i \(0.284986\pi\)
\(840\) 0 0
\(841\) −0.678741 + 3.84933i −0.0234049 + 0.132736i
\(842\) 0 0
\(843\) 14.5776 + 25.2492i 0.502080 + 0.869628i
\(844\) 0 0
\(845\) −7.28281 + 6.11101i −0.250536 + 0.210225i
\(846\) 0 0
\(847\) 9.38310 16.2520i 0.322407 0.558426i
\(848\) 0 0
\(849\) −34.1503 12.4297i −1.17204 0.426586i
\(850\) 0 0
\(851\) 1.39947 + 7.93678i 0.0479732 + 0.272069i
\(852\) 0 0
\(853\) −1.57133 1.31850i −0.0538012 0.0451446i 0.615491 0.788144i \(-0.288958\pi\)
−0.669292 + 0.743000i \(0.733402\pi\)
\(854\) 0 0
\(855\) −1.47742 5.97900i −0.0505267 0.204477i
\(856\) 0 0
\(857\) 15.4175 + 12.9368i 0.526651 + 0.441913i 0.866943 0.498407i \(-0.166081\pi\)
−0.340292 + 0.940320i \(0.610526\pi\)
\(858\) 0 0
\(859\) 1.65890 + 9.40808i 0.0566009 + 0.320999i 0.999941 0.0108268i \(-0.00344635\pi\)
−0.943341 + 0.331826i \(0.892335\pi\)
\(860\) 0 0
\(861\) 38.9435 + 14.1743i 1.32719 + 0.483058i
\(862\) 0 0
\(863\) −17.3643 + 30.0759i −0.591089 + 1.02380i 0.402997 + 0.915201i \(0.367969\pi\)
−0.994086 + 0.108595i \(0.965365\pi\)
\(864\) 0 0
\(865\) −8.49237 + 7.12594i −0.288749 + 0.242289i
\(866\) 0 0
\(867\) −7.94606 13.7630i −0.269862 0.467415i
\(868\) 0 0
\(869\) −8.90554 + 50.5058i −0.302100 + 1.71329i
\(870\) 0 0
\(871\) −32.7432 + 11.9176i −1.10946 + 0.403811i
\(872\) 0 0
\(873\) 0.302505 0.0102382
\(874\) 0 0
\(875\) 23.3557 0.789566
\(876\) 0 0
\(877\) 25.1774 9.16382i 0.850180 0.309440i 0.120066 0.992766i \(-0.461689\pi\)
0.730114 + 0.683326i \(0.239467\pi\)
\(878\) 0 0
\(879\) 3.85415 21.8580i 0.129997 0.737252i
\(880\) 0 0
\(881\) 7.87940 + 13.6475i 0.265464 + 0.459797i 0.967685 0.252162i \(-0.0811416\pi\)
−0.702221 + 0.711959i \(0.747808\pi\)
\(882\) 0 0
\(883\) −31.7063 + 26.6047i −1.06700 + 0.895320i −0.994777 0.102069i \(-0.967454\pi\)
−0.0722232 + 0.997388i \(0.523009\pi\)
\(884\) 0 0
\(885\) 6.28336 10.8831i 0.211213 0.365831i
\(886\) 0 0
\(887\) 43.7848 + 15.9363i 1.47015 + 0.535090i 0.948141 0.317851i \(-0.102961\pi\)
0.522007 + 0.852941i \(0.325183\pi\)
\(888\) 0 0
\(889\) 3.68673 + 20.9085i 0.123649 + 0.701249i
\(890\) 0 0
\(891\) 37.6044 + 31.5538i 1.25979 + 1.05709i
\(892\) 0 0
\(893\) 34.9655 15.4799i 1.17008 0.518015i
\(894\) 0 0
\(895\) −4.23892 3.55688i −0.141692 0.118893i
\(896\) 0 0
\(897\) 1.06145 + 6.01981i 0.0354409 + 0.200996i
\(898\) 0 0
\(899\) 9.41346 + 3.42622i 0.313957 + 0.114271i
\(900\) 0 0
\(901\) −0.134743 + 0.233381i −0.00448893 + 0.00777505i
\(902\) 0 0
\(903\) 17.5775 14.7493i 0.584943 0.490825i
\(904\) 0 0
\(905\) 3.95548 + 6.85108i 0.131484 + 0.227738i
\(906\) 0 0
\(907\) −0.423530 + 2.40196i −0.0140631 + 0.0797557i −0.991032 0.133628i \(-0.957337\pi\)
0.976968 + 0.213384i \(0.0684484\pi\)
\(908\) 0 0
\(909\) −14.1950 + 5.16656i −0.470819 + 0.171364i
\(910\) 0 0
\(911\) 29.8844 0.990115 0.495057 0.868860i \(-0.335147\pi\)
0.495057 + 0.868860i \(0.335147\pi\)
\(912\) 0 0
\(913\) 45.4823 1.50524
\(914\) 0 0
\(915\) 47.8407 17.4126i 1.58157 0.575643i
\(916\) 0 0
\(917\) 4.68868 26.5908i 0.154834 0.878107i
\(918\) 0 0
\(919\) 20.1737 + 34.9419i 0.665469 + 1.15263i 0.979158 + 0.203100i \(0.0651016\pi\)
−0.313689 + 0.949526i \(0.601565\pi\)
\(920\) 0 0
\(921\) 15.9432 13.3780i 0.525348 0.440819i
\(922\) 0 0
\(923\) 2.84012 4.91923i 0.0934837 0.161919i
\(924\) 0 0
\(925\) −13.1101 4.77168i −0.431057 0.156892i
\(926\) 0 0
\(927\) −1.26660 7.18323i −0.0416005 0.235928i
\(928\) 0 0
\(929\) −40.3558 33.8625i −1.32403 1.11099i −0.985433 0.170062i \(-0.945603\pi\)
−0.338597 0.940932i \(-0.609952\pi\)
\(930\) 0 0
\(931\) 10.3479 9.95096i 0.339137 0.326130i
\(932\) 0 0
\(933\) 38.0183 + 31.9012i 1.24466 + 1.04440i
\(934\) 0 0
\(935\) −6.89818 39.1215i −0.225595 1.27941i
\(936\) 0 0
\(937\) −30.0102 10.9228i −0.980391 0.356833i −0.198399 0.980121i \(-0.563574\pi\)
−0.781992 + 0.623288i \(0.785796\pi\)
\(938\) 0 0
\(939\) 1.64885 2.85589i 0.0538081 0.0931984i
\(940\) 0 0
\(941\) −1.29042 + 1.08279i −0.0420666 + 0.0352981i −0.663579 0.748107i \(-0.730963\pi\)
0.621512 + 0.783405i \(0.286519\pi\)
\(942\) 0 0
\(943\) 6.28725 + 10.8898i 0.204741 + 0.354622i
\(944\) 0 0
\(945\) 2.48391 14.0869i 0.0808015 0.458248i
\(946\) 0 0
\(947\) 29.2449 10.6443i 0.950332 0.345892i 0.180094 0.983649i \(-0.442360\pi\)
0.770238 + 0.637757i \(0.220138\pi\)
\(948\) 0 0
\(949\) 1.95710 0.0635302
\(950\) 0 0
\(951\) 38.4277 1.24610
\(952\) 0 0
\(953\) −21.9284 + 7.98128i −0.710330 + 0.258539i −0.671815 0.740719i \(-0.734485\pi\)
−0.0385151 + 0.999258i \(0.512263\pi\)
\(954\) 0 0
\(955\) 0.292596 1.65940i 0.00946819 0.0536968i
\(956\) 0 0
\(957\) 22.2745 + 38.5806i 0.720034 + 1.24713i
\(958\) 0 0
\(959\) −13.0064 + 10.9137i −0.419999 + 0.352421i
\(960\) 0 0
\(961\) 13.5003 23.3831i 0.435492 0.754295i
\(962\) 0 0
\(963\) 5.71466 + 2.07997i 0.184152 + 0.0670260i
\(964\) 0 0
\(965\) 4.59308 + 26.0487i 0.147857 + 0.838536i
\(966\) 0 0
\(967\) −41.7482 35.0309i −1.34253 1.12652i −0.980968 0.194171i \(-0.937798\pi\)
−0.361565 0.932347i \(-0.617757\pi\)
\(968\) 0 0
\(969\) −34.4700 25.1546i −1.10734 0.808081i
\(970\) 0 0
\(971\) −22.3904 18.7878i −0.718543 0.602929i 0.208439 0.978035i \(-0.433162\pi\)
−0.926982 + 0.375107i \(0.877606\pi\)
\(972\) 0 0
\(973\) 2.04780 + 11.6137i 0.0656495 + 0.372317i
\(974\) 0 0
\(975\) −9.94360 3.61918i −0.318450 0.115906i
\(976\) 0 0
\(977\) 17.0031 29.4502i 0.543977 0.942196i −0.454693 0.890648i \(-0.650251\pi\)
0.998671 0.0515482i \(-0.0164156\pi\)
\(978\) 0 0
\(979\) 56.5261 47.4310i 1.80658 1.51590i
\(980\) 0 0
\(981\) 6.81251 + 11.7996i 0.217507 + 0.376733i
\(982\) 0 0
\(983\) 5.94855 33.7359i 0.189729 1.07601i −0.729998 0.683450i \(-0.760479\pi\)
0.919727 0.392559i \(-0.128410\pi\)
\(984\) 0 0
\(985\) −26.9022 + 9.79159i −0.857175 + 0.311986i
\(986\) 0 0
\(987\) −32.9763 −1.04965
\(988\) 0 0
\(989\) 6.96216 0.221384
\(990\) 0 0
\(991\) −41.2569 + 15.0163i −1.31057 + 0.477008i −0.900424 0.435013i \(-0.856744\pi\)
−0.410144 + 0.912021i \(0.634522\pi\)
\(992\) 0 0
\(993\) −3.05385 + 17.3193i −0.0969111 + 0.549610i
\(994\) 0 0
\(995\) 19.0825 + 33.0518i 0.604955 + 1.04781i
\(996\) 0 0
\(997\) −44.1321 + 37.0312i −1.39768 + 1.17279i −0.435559 + 0.900160i \(0.643449\pi\)
−0.962119 + 0.272631i \(0.912106\pi\)
\(998\) 0 0
\(999\) −15.0914 + 26.1391i −0.477471 + 0.827003i
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 304.2.u.f.225.1 18
4.3 odd 2 152.2.q.c.73.3 yes 18
19.5 even 9 5776.2.a.cd.1.8 9
19.6 even 9 inner 304.2.u.f.177.1 18
19.14 odd 18 5776.2.a.ce.1.2 9
76.43 odd 18 2888.2.a.y.1.2 9
76.63 odd 18 152.2.q.c.25.3 18
76.71 even 18 2888.2.a.x.1.8 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.2.q.c.25.3 18 76.63 odd 18
152.2.q.c.73.3 yes 18 4.3 odd 2
304.2.u.f.177.1 18 19.6 even 9 inner
304.2.u.f.225.1 18 1.1 even 1 trivial
2888.2.a.x.1.8 9 76.71 even 18
2888.2.a.y.1.2 9 76.43 odd 18
5776.2.a.cd.1.8 9 19.5 even 9
5776.2.a.ce.1.2 9 19.14 odd 18