Properties

Label 912.2.ci.f.751.3
Level $912$
Weight $2$
Character 912.751
Analytic conductor $7.282$
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] = [912,2,Mod(79,912)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(912, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 0, 0, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("912.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.ci (of order \(18\), degree \(6\), 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: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 6 x^{17} - 3 x^{16} + 100 x^{15} - 171 x^{14} - 471 x^{13} + 1537 x^{12} + 321 x^{11} - 3936 x^{10} - 1317 x^{9} + 4941 x^{8} + 21078 x^{7} - 14829 x^{6} + \cdots + 1367631 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 751.3
Root \(-2.15607 - 0.0639189i\) of defining polynomial
Character \(\chi\) \(=\) 912.751
Dual form 912.2.ci.f.895.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.766044 - 0.642788i) q^{3} +(3.02685 + 1.10168i) q^{5} +(1.81645 + 1.04873i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\) \(q+(0.766044 - 0.642788i) q^{3} +(3.02685 + 1.10168i) q^{5} +(1.81645 + 1.04873i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-1.32141 + 0.762916i) q^{11} +(3.47269 - 4.13859i) q^{13} +(3.02685 - 1.10168i) q^{15} +(-0.0697157 - 0.395377i) q^{17} +(-1.70519 + 4.01152i) q^{19} +(2.06559 - 0.364219i) q^{21} +(-0.994583 - 2.73259i) q^{23} +(4.11792 + 3.45534i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(-0.725223 - 0.127876i) q^{29} +(-2.72904 + 4.72684i) q^{31} +(-0.521865 + 1.43381i) q^{33} +(4.34276 + 5.17550i) q^{35} +3.91535i q^{37} -5.40255i q^{39} +(3.82246 + 4.55543i) q^{41} +(2.67537 - 7.35052i) q^{43} +(1.61056 - 2.78956i) q^{45} +(-9.18147 - 1.61894i) q^{47} +(-1.30035 - 2.25226i) q^{49} +(-0.307549 - 0.258064i) q^{51} +(-0.116137 - 0.319084i) q^{53} +(-4.84021 + 0.853459i) q^{55} +(1.27230 + 4.16908i) q^{57} +(1.81685 + 10.3039i) q^{59} +(-2.45154 + 0.892288i) q^{61} +(1.34822 - 1.60674i) q^{63} +(15.0708 - 8.70110i) q^{65} +(1.74510 - 9.89698i) q^{67} +(-2.51837 - 1.45398i) q^{69} +(-1.09275 - 0.397729i) q^{71} +(4.32157 - 3.62623i) q^{73} +5.37556 q^{75} -3.20036 q^{77} +(8.16316 - 6.84971i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-11.4897 - 6.63357i) q^{83} +(0.224562 - 1.27355i) q^{85} +(-0.637750 + 0.368205i) q^{87} +(-0.157877 + 0.188151i) q^{89} +(10.6482 - 3.87563i) q^{91} +(0.947786 + 5.37516i) q^{93} +(-9.58081 + 10.2637i) q^{95} +(15.3071 - 2.69906i) q^{97} +(0.521865 + 1.43381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{13} + 12 q^{17} + 3 q^{19} + 15 q^{21} + 6 q^{23} + 24 q^{25} - 9 q^{27} + 12 q^{29} + 12 q^{31} + 6 q^{33} - 36 q^{35} + 12 q^{41} + 21 q^{43} - 6 q^{45} - 24 q^{47} - 3 q^{49} - 6 q^{51} + 6 q^{53} + 12 q^{55} + 54 q^{59} - 24 q^{61} + 12 q^{63} + 36 q^{65} - 21 q^{67} + 15 q^{73} + 18 q^{75} - 60 q^{79} + 54 q^{85} + 18 q^{87} + 36 q^{89} + 24 q^{91} + 24 q^{93} - 6 q^{95} - 6 q^{97} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\) \(1\) \(-1\)

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
\(3\) 0.766044 0.642788i 0.442276 0.371114i
\(4\) 0 0
\(5\) 3.02685 + 1.10168i 1.35365 + 0.492688i 0.914085 0.405522i \(-0.132910\pi\)
0.439565 + 0.898211i \(0.355133\pi\)
\(6\) 0 0
\(7\) 1.81645 + 1.04873i 0.686553 + 0.396381i 0.802319 0.596895i \(-0.203599\pi\)
−0.115767 + 0.993276i \(0.536932\pi\)
\(8\) 0 0
\(9\) 0.173648 0.984808i 0.0578827 0.328269i
\(10\) 0 0
\(11\) −1.32141 + 0.762916i −0.398420 + 0.230028i −0.685802 0.727788i \(-0.740548\pi\)
0.287382 + 0.957816i \(0.407215\pi\)
\(12\) 0 0
\(13\) 3.47269 4.13859i 0.963151 1.14784i −0.0258107 0.999667i \(-0.508217\pi\)
0.988962 0.148172i \(-0.0473388\pi\)
\(14\) 0 0
\(15\) 3.02685 1.10168i 0.781530 0.284454i
\(16\) 0 0
\(17\) −0.0697157 0.395377i −0.0169085 0.0958931i 0.975186 0.221389i \(-0.0710590\pi\)
−0.992094 + 0.125496i \(0.959948\pi\)
\(18\) 0 0
\(19\) −1.70519 + 4.01152i −0.391199 + 0.920306i
\(20\) 0 0
\(21\) 2.06559 0.364219i 0.450748 0.0794791i
\(22\) 0 0
\(23\) −0.994583 2.73259i −0.207385 0.569785i 0.791773 0.610815i \(-0.209158\pi\)
−0.999158 + 0.0410302i \(0.986936\pi\)
\(24\) 0 0
\(25\) 4.11792 + 3.45534i 0.823583 + 0.691068i
\(26\) 0 0
\(27\) −0.500000 0.866025i −0.0962250 0.166667i
\(28\) 0 0
\(29\) −0.725223 0.127876i −0.134671 0.0237460i 0.105907 0.994376i \(-0.466226\pi\)
−0.240577 + 0.970630i \(0.577337\pi\)
\(30\) 0 0
\(31\) −2.72904 + 4.72684i −0.490150 + 0.848965i −0.999936 0.0113364i \(-0.996391\pi\)
0.509786 + 0.860302i \(0.329725\pi\)
\(32\) 0 0
\(33\) −0.521865 + 1.43381i −0.0908451 + 0.249595i
\(34\) 0 0
\(35\) 4.34276 + 5.17550i 0.734060 + 0.874819i
\(36\) 0 0
\(37\) 3.91535i 0.643679i 0.946794 + 0.321839i \(0.104301\pi\)
−0.946794 + 0.321839i \(0.895699\pi\)
\(38\) 0 0
\(39\) 5.40255i 0.865100i
\(40\) 0 0
\(41\) 3.82246 + 4.55543i 0.596967 + 0.711438i 0.976929 0.213564i \(-0.0685073\pi\)
−0.379962 + 0.925002i \(0.624063\pi\)
\(42\) 0 0
\(43\) 2.67537 7.35052i 0.407990 1.12094i −0.550255 0.834996i \(-0.685470\pi\)
0.958245 0.285947i \(-0.0923082\pi\)
\(44\) 0 0
\(45\) 1.61056 2.78956i 0.240087 0.415844i
\(46\) 0 0
\(47\) −9.18147 1.61894i −1.33925 0.236147i −0.542299 0.840185i \(-0.682446\pi\)
−0.796955 + 0.604039i \(0.793557\pi\)
\(48\) 0 0
\(49\) −1.30035 2.25226i −0.185764 0.321752i
\(50\) 0 0
\(51\) −0.307549 0.258064i −0.0430655 0.0361362i
\(52\) 0 0
\(53\) −0.116137 0.319084i −0.0159527 0.0438296i 0.931461 0.363842i \(-0.118535\pi\)
−0.947413 + 0.320012i \(0.896313\pi\)
\(54\) 0 0
\(55\) −4.84021 + 0.853459i −0.652653 + 0.115080i
\(56\) 0 0
\(57\) 1.27230 + 4.16908i 0.168520 + 0.552208i
\(58\) 0 0
\(59\) 1.81685 + 10.3039i 0.236534 + 1.34145i 0.839359 + 0.543578i \(0.182931\pi\)
−0.602825 + 0.797874i \(0.705958\pi\)
\(60\) 0 0
\(61\) −2.45154 + 0.892288i −0.313888 + 0.114246i −0.494160 0.869371i \(-0.664524\pi\)
0.180272 + 0.983617i \(0.442302\pi\)
\(62\) 0 0
\(63\) 1.34822 1.60674i 0.169859 0.202431i
\(64\) 0 0
\(65\) 15.0708 8.70110i 1.86930 1.07924i
\(66\) 0 0
\(67\) 1.74510 9.89698i 0.213198 1.20911i −0.670807 0.741632i \(-0.734052\pi\)
0.884006 0.467476i \(-0.154837\pi\)
\(68\) 0 0
\(69\) −2.51837 1.45398i −0.303176 0.175039i
\(70\) 0 0
\(71\) −1.09275 0.397729i −0.129686 0.0472017i 0.276362 0.961054i \(-0.410871\pi\)
−0.406048 + 0.913852i \(0.633093\pi\)
\(72\) 0 0
\(73\) 4.32157 3.62623i 0.505801 0.424418i −0.353848 0.935303i \(-0.615127\pi\)
0.859649 + 0.510886i \(0.170682\pi\)
\(74\) 0 0
\(75\) 5.37556 0.620716
\(76\) 0 0
\(77\) −3.20036 −0.364715
\(78\) 0 0
\(79\) 8.16316 6.84971i 0.918428 0.770652i −0.0552759 0.998471i \(-0.517604\pi\)
0.973704 + 0.227819i \(0.0731594\pi\)
\(80\) 0 0
\(81\) −0.939693 0.342020i −0.104410 0.0380022i
\(82\) 0 0
\(83\) −11.4897 6.63357i −1.26116 0.728129i −0.287858 0.957673i \(-0.592943\pi\)
−0.973298 + 0.229544i \(0.926276\pi\)
\(84\) 0 0
\(85\) 0.224562 1.27355i 0.0243572 0.138136i
\(86\) 0 0
\(87\) −0.637750 + 0.368205i −0.0683740 + 0.0394758i
\(88\) 0 0
\(89\) −0.157877 + 0.188151i −0.0167350 + 0.0199439i −0.774347 0.632761i \(-0.781921\pi\)
0.757612 + 0.652705i \(0.226366\pi\)
\(90\) 0 0
\(91\) 10.6482 3.87563i 1.11624 0.406277i
\(92\) 0 0
\(93\) 0.947786 + 5.37516i 0.0982808 + 0.557378i
\(94\) 0 0
\(95\) −9.58081 + 10.2637i −0.982970 + 1.05303i
\(96\) 0 0
\(97\) 15.3071 2.69906i 1.55421 0.274048i 0.670435 0.741969i \(-0.266108\pi\)
0.883771 + 0.467920i \(0.154997\pi\)
\(98\) 0 0
\(99\) 0.521865 + 1.43381i 0.0524494 + 0.144104i
\(100\) 0 0
\(101\) 3.78201 + 3.17348i 0.376324 + 0.315773i 0.811257 0.584689i \(-0.198784\pi\)
−0.434933 + 0.900463i \(0.643228\pi\)
\(102\) 0 0
\(103\) 5.11152 + 8.85342i 0.503654 + 0.872353i 0.999991 + 0.00422386i \(0.00134450\pi\)
−0.496338 + 0.868130i \(0.665322\pi\)
\(104\) 0 0
\(105\) 6.65349 + 1.17319i 0.649314 + 0.114492i
\(106\) 0 0
\(107\) −8.32768 + 14.4240i −0.805067 + 1.39442i 0.111178 + 0.993800i \(0.464537\pi\)
−0.916246 + 0.400617i \(0.868796\pi\)
\(108\) 0 0
\(109\) −1.95854 + 5.38104i −0.187594 + 0.515410i −0.997462 0.0712020i \(-0.977317\pi\)
0.809868 + 0.586612i \(0.199539\pi\)
\(110\) 0 0
\(111\) 2.51674 + 2.99933i 0.238878 + 0.284684i
\(112\) 0 0
\(113\) 16.6565i 1.56692i −0.621445 0.783458i \(-0.713454\pi\)
0.621445 0.783458i \(-0.286546\pi\)
\(114\) 0 0
\(115\) 9.36688i 0.873466i
\(116\) 0 0
\(117\) −3.47269 4.13859i −0.321050 0.382613i
\(118\) 0 0
\(119\) 0.288008 0.791295i 0.0264016 0.0725379i
\(120\) 0 0
\(121\) −4.33592 + 7.51003i −0.394174 + 0.682730i
\(122\) 0 0
\(123\) 5.85634 + 1.03263i 0.528049 + 0.0931092i
\(124\) 0 0
\(125\) 0.604858 + 1.04764i 0.0541001 + 0.0937041i
\(126\) 0 0
\(127\) −7.69721 6.45873i −0.683017 0.573120i 0.233869 0.972268i \(-0.424861\pi\)
−0.916886 + 0.399149i \(0.869306\pi\)
\(128\) 0 0
\(129\) −2.67537 7.35052i −0.235553 0.647177i
\(130\) 0 0
\(131\) −15.1931 + 2.67895i −1.32742 + 0.234061i −0.791999 0.610522i \(-0.790960\pi\)
−0.535425 + 0.844583i \(0.679848\pi\)
\(132\) 0 0
\(133\) −7.30439 + 5.49844i −0.633371 + 0.476775i
\(134\) 0 0
\(135\) −0.559340 3.17218i −0.0481403 0.273017i
\(136\) 0 0
\(137\) −13.7733 + 5.01306i −1.17673 + 0.428295i −0.855046 0.518552i \(-0.826471\pi\)
−0.321685 + 0.946847i \(0.604249\pi\)
\(138\) 0 0
\(139\) 9.24652 11.0196i 0.784280 0.934669i −0.214838 0.976650i \(-0.568922\pi\)
0.999118 + 0.0419811i \(0.0133669\pi\)
\(140\) 0 0
\(141\) −8.07404 + 4.66155i −0.679957 + 0.392573i
\(142\) 0 0
\(143\) −1.43145 + 8.11814i −0.119704 + 0.678873i
\(144\) 0 0
\(145\) −2.05426 1.18603i −0.170597 0.0984945i
\(146\) 0 0
\(147\) −2.44385 0.889488i −0.201565 0.0733638i
\(148\) 0 0
\(149\) −15.5901 + 13.0817i −1.27719 + 1.07169i −0.283569 + 0.958952i \(0.591518\pi\)
−0.993625 + 0.112740i \(0.964037\pi\)
\(150\) 0 0
\(151\) 5.81477 0.473199 0.236600 0.971607i \(-0.423967\pi\)
0.236600 + 0.971607i \(0.423967\pi\)
\(152\) 0 0
\(153\) −0.401477 −0.0324575
\(154\) 0 0
\(155\) −13.4679 + 11.3009i −1.08177 + 0.907711i
\(156\) 0 0
\(157\) −20.7381 7.54804i −1.65508 0.602400i −0.665501 0.746397i \(-0.731782\pi\)
−0.989578 + 0.143997i \(0.954004\pi\)
\(158\) 0 0
\(159\) −0.294070 0.169781i −0.0233212 0.0134645i
\(160\) 0 0
\(161\) 1.05914 6.00666i 0.0834716 0.473391i
\(162\) 0 0
\(163\) 12.5945 7.27141i 0.986474 0.569541i 0.0822556 0.996611i \(-0.473788\pi\)
0.904218 + 0.427070i \(0.140454\pi\)
\(164\) 0 0
\(165\) −3.15922 + 3.76501i −0.245945 + 0.293106i
\(166\) 0 0
\(167\) 19.7550 7.19023i 1.52869 0.556397i 0.565388 0.824825i \(-0.308727\pi\)
0.963300 + 0.268429i \(0.0865044\pi\)
\(168\) 0 0
\(169\) −2.81093 15.9416i −0.216226 1.22628i
\(170\) 0 0
\(171\) 3.65447 + 2.37588i 0.279465 + 0.181688i
\(172\) 0 0
\(173\) −24.5257 + 4.32455i −1.86466 + 0.328789i −0.988258 0.152795i \(-0.951173\pi\)
−0.876400 + 0.481584i \(0.840062\pi\)
\(174\) 0 0
\(175\) 3.85627 + 10.5950i 0.291507 + 0.800908i
\(176\) 0 0
\(177\) 8.01500 + 6.72538i 0.602444 + 0.505511i
\(178\) 0 0
\(179\) 12.0720 + 20.9094i 0.902307 + 1.56284i 0.824491 + 0.565874i \(0.191461\pi\)
0.0778159 + 0.996968i \(0.475205\pi\)
\(180\) 0 0
\(181\) −11.0659 1.95121i −0.822520 0.145033i −0.253478 0.967341i \(-0.581575\pi\)
−0.569042 + 0.822308i \(0.692686\pi\)
\(182\) 0 0
\(183\) −1.30444 + 2.25935i −0.0964268 + 0.167016i
\(184\) 0 0
\(185\) −4.31348 + 11.8512i −0.317133 + 0.871316i
\(186\) 0 0
\(187\) 0.393763 + 0.469268i 0.0287948 + 0.0343163i
\(188\) 0 0
\(189\) 2.09745i 0.152567i
\(190\) 0 0
\(191\) 0.336347i 0.0243372i −0.999926 0.0121686i \(-0.996127\pi\)
0.999926 0.0121686i \(-0.00387349\pi\)
\(192\) 0 0
\(193\) 0.535482 + 0.638163i 0.0385449 + 0.0459360i 0.784972 0.619531i \(-0.212677\pi\)
−0.746428 + 0.665467i \(0.768233\pi\)
\(194\) 0 0
\(195\) 5.95190 16.3527i 0.426225 1.17104i
\(196\) 0 0
\(197\) −5.01903 + 8.69322i −0.357591 + 0.619366i −0.987558 0.157256i \(-0.949735\pi\)
0.629967 + 0.776622i \(0.283069\pi\)
\(198\) 0 0
\(199\) −4.64607 0.819227i −0.329351 0.0580735i 0.00652776 0.999979i \(-0.497922\pi\)
−0.335879 + 0.941905i \(0.609033\pi\)
\(200\) 0 0
\(201\) −5.02483 8.70325i −0.354424 0.613880i
\(202\) 0 0
\(203\) −1.18322 0.992841i −0.0830459 0.0696838i
\(204\) 0 0
\(205\) 6.55137 + 17.9998i 0.457568 + 1.25716i
\(206\) 0 0
\(207\) −2.86379 + 0.504963i −0.199047 + 0.0350973i
\(208\) 0 0
\(209\) −0.807194 6.60178i −0.0558348 0.456655i
\(210\) 0 0
\(211\) 2.37181 + 13.4512i 0.163282 + 0.926020i 0.950818 + 0.309751i \(0.100246\pi\)
−0.787536 + 0.616269i \(0.788643\pi\)
\(212\) 0 0
\(213\) −1.09275 + 0.397729i −0.0748740 + 0.0272519i
\(214\) 0 0
\(215\) 16.1959 19.3015i 1.10455 1.31635i
\(216\) 0 0
\(217\) −9.91432 + 5.72404i −0.673028 + 0.388573i
\(218\) 0 0
\(219\) 0.979620 5.55570i 0.0661966 0.375419i
\(220\) 0 0
\(221\) −1.87841 1.08450i −0.126355 0.0729513i
\(222\) 0 0
\(223\) −14.4781 5.26960i −0.969526 0.352878i −0.191766 0.981441i \(-0.561422\pi\)
−0.777759 + 0.628562i \(0.783644\pi\)
\(224\) 0 0
\(225\) 4.11792 3.45534i 0.274528 0.230356i
\(226\) 0 0
\(227\) −11.5959 −0.769648 −0.384824 0.922990i \(-0.625738\pi\)
−0.384824 + 0.922990i \(0.625738\pi\)
\(228\) 0 0
\(229\) −21.6883 −1.43320 −0.716600 0.697484i \(-0.754303\pi\)
−0.716600 + 0.697484i \(0.754303\pi\)
\(230\) 0 0
\(231\) −2.45162 + 2.05715i −0.161305 + 0.135351i
\(232\) 0 0
\(233\) 17.5176 + 6.37589i 1.14762 + 0.417698i 0.844658 0.535306i \(-0.179804\pi\)
0.302958 + 0.953004i \(0.402026\pi\)
\(234\) 0 0
\(235\) −26.0074 15.0154i −1.69654 0.979495i
\(236\) 0 0
\(237\) 1.85044 10.4944i 0.120199 0.681682i
\(238\) 0 0
\(239\) −0.148903 + 0.0859691i −0.00963173 + 0.00556088i −0.504808 0.863232i \(-0.668437\pi\)
0.495176 + 0.868792i \(0.335103\pi\)
\(240\) 0 0
\(241\) 8.11891 9.67573i 0.522985 0.623269i −0.438299 0.898829i \(-0.644419\pi\)
0.961284 + 0.275560i \(0.0888634\pi\)
\(242\) 0 0
\(243\) −0.939693 + 0.342020i −0.0602813 + 0.0219406i
\(244\) 0 0
\(245\) −1.45467 8.24985i −0.0929355 0.527063i
\(246\) 0 0
\(247\) 10.6804 + 20.9879i 0.679580 + 1.33543i
\(248\) 0 0
\(249\) −13.0656 + 2.30381i −0.827998 + 0.145998i
\(250\) 0 0
\(251\) 1.00146 + 2.75149i 0.0632117 + 0.173673i 0.967278 0.253720i \(-0.0816543\pi\)
−0.904066 + 0.427393i \(0.859432\pi\)
\(252\) 0 0
\(253\) 3.39899 + 2.85209i 0.213693 + 0.179309i
\(254\) 0 0
\(255\) −0.646601 1.11995i −0.0404917 0.0701337i
\(256\) 0 0
\(257\) 13.2464 + 2.33571i 0.826290 + 0.145697i 0.570774 0.821107i \(-0.306643\pi\)
0.255517 + 0.966805i \(0.417754\pi\)
\(258\) 0 0
\(259\) −4.10613 + 7.11202i −0.255142 + 0.441920i
\(260\) 0 0
\(261\) −0.251867 + 0.692000i −0.0155902 + 0.0428337i
\(262\) 0 0
\(263\) −19.8129 23.6121i −1.22172 1.45599i −0.849292 0.527924i \(-0.822971\pi\)
−0.372426 0.928062i \(-0.621474\pi\)
\(264\) 0 0
\(265\) 1.09377i 0.0671896i
\(266\) 0 0
\(267\) 0.245613i 0.0150313i
\(268\) 0 0
\(269\) −11.5225 13.7320i −0.702539 0.837253i 0.290272 0.956944i \(-0.406254\pi\)
−0.992811 + 0.119691i \(0.961810\pi\)
\(270\) 0 0
\(271\) 4.98801 13.7044i 0.303000 0.832486i −0.690975 0.722879i \(-0.742819\pi\)
0.993975 0.109607i \(-0.0349593\pi\)
\(272\) 0 0
\(273\) 5.66579 9.81344i 0.342909 0.593937i
\(274\) 0 0
\(275\) −8.07759 1.42430i −0.487097 0.0858883i
\(276\) 0 0
\(277\) −10.0315 17.3750i −0.602732 1.04396i −0.992406 0.123009i \(-0.960746\pi\)
0.389674 0.920953i \(-0.372588\pi\)
\(278\) 0 0
\(279\) 4.18113 + 3.50839i 0.250318 + 0.210042i
\(280\) 0 0
\(281\) 1.48132 + 4.06990i 0.0883682 + 0.242790i 0.976003 0.217759i \(-0.0698748\pi\)
−0.887634 + 0.460549i \(0.847653\pi\)
\(282\) 0 0
\(283\) 4.82206 0.850259i 0.286642 0.0505426i −0.0284787 0.999594i \(-0.509066\pi\)
0.315120 + 0.949052i \(0.397955\pi\)
\(284\) 0 0
\(285\) −0.741943 + 14.0209i −0.0439489 + 0.830525i
\(286\) 0 0
\(287\) 2.16590 + 12.2834i 0.127849 + 0.725066i
\(288\) 0 0
\(289\) 15.8233 5.75921i 0.930783 0.338777i
\(290\) 0 0
\(291\) 9.99103 11.9068i 0.585685 0.697992i
\(292\) 0 0
\(293\) 5.64527 3.25930i 0.329800 0.190410i −0.325952 0.945386i \(-0.605685\pi\)
0.655752 + 0.754976i \(0.272352\pi\)
\(294\) 0 0
\(295\) −5.85229 + 33.1900i −0.340733 + 1.93239i
\(296\) 0 0
\(297\) 1.32141 + 0.762916i 0.0766759 + 0.0442689i
\(298\) 0 0
\(299\) −14.7630 5.37328i −0.853764 0.310745i
\(300\) 0 0
\(301\) 12.5684 10.5461i 0.724428 0.607867i
\(302\) 0 0
\(303\) 4.93706 0.283627
\(304\) 0 0
\(305\) −8.40348 −0.481182
\(306\) 0 0
\(307\) −17.8847 + 15.0071i −1.02074 + 0.856499i −0.989720 0.143020i \(-0.954319\pi\)
−0.0310157 + 0.999519i \(0.509874\pi\)
\(308\) 0 0
\(309\) 9.60652 + 3.49649i 0.546496 + 0.198908i
\(310\) 0 0
\(311\) 10.0195 + 5.78478i 0.568155 + 0.328025i 0.756412 0.654095i \(-0.226950\pi\)
−0.188257 + 0.982120i \(0.560284\pi\)
\(312\) 0 0
\(313\) −5.04399 + 28.6059i −0.285103 + 1.61690i 0.419815 + 0.907610i \(0.362095\pi\)
−0.704918 + 0.709289i \(0.749016\pi\)
\(314\) 0 0
\(315\) 5.85098 3.37807i 0.329665 0.190332i
\(316\) 0 0
\(317\) −0.836331 + 0.996701i −0.0469730 + 0.0559803i −0.789019 0.614368i \(-0.789411\pi\)
0.742046 + 0.670349i \(0.233855\pi\)
\(318\) 0 0
\(319\) 1.05587 0.384307i 0.0591176 0.0215171i
\(320\) 0 0
\(321\) 2.89217 + 16.4023i 0.161425 + 0.915489i
\(322\) 0 0
\(323\) 1.70494 + 0.394529i 0.0948656 + 0.0219522i
\(324\) 0 0
\(325\) 28.6005 5.04304i 1.58647 0.279737i
\(326\) 0 0
\(327\) 1.95854 + 5.38104i 0.108307 + 0.297572i
\(328\) 0 0
\(329\) −14.9798 12.5696i −0.825865 0.692983i
\(330\) 0 0
\(331\) 2.43410 + 4.21599i 0.133790 + 0.231732i 0.925135 0.379639i \(-0.123952\pi\)
−0.791344 + 0.611371i \(0.790618\pi\)
\(332\) 0 0
\(333\) 3.85586 + 0.679893i 0.211300 + 0.0372579i
\(334\) 0 0
\(335\) 16.1855 28.0342i 0.884310 1.53167i
\(336\) 0 0
\(337\) −2.15510 + 5.92109i −0.117396 + 0.322542i −0.984448 0.175675i \(-0.943789\pi\)
0.867053 + 0.498217i \(0.166012\pi\)
\(338\) 0 0
\(339\) −10.7066 12.7597i −0.581504 0.693009i
\(340\) 0 0
\(341\) 8.32811i 0.450993i
\(342\) 0 0
\(343\) 20.1370i 1.08730i
\(344\) 0 0
\(345\) −6.02091 7.17545i −0.324155 0.386313i
\(346\) 0 0
\(347\) −1.14064 + 3.13389i −0.0612329 + 0.168236i −0.966537 0.256529i \(-0.917421\pi\)
0.905304 + 0.424765i \(0.139643\pi\)
\(348\) 0 0
\(349\) −12.4520 + 21.5674i −0.666539 + 1.15448i 0.312327 + 0.949975i \(0.398891\pi\)
−0.978866 + 0.204504i \(0.934442\pi\)
\(350\) 0 0
\(351\) −5.32047 0.938142i −0.283986 0.0500743i
\(352\) 0 0
\(353\) 14.5254 + 25.1587i 0.773109 + 1.33906i 0.935851 + 0.352396i \(0.114633\pi\)
−0.162742 + 0.986669i \(0.552034\pi\)
\(354\) 0 0
\(355\) −2.86942 2.40773i −0.152293 0.127789i
\(356\) 0 0
\(357\) −0.288008 0.791295i −0.0152430 0.0418798i
\(358\) 0 0
\(359\) −12.5139 + 2.20653i −0.660456 + 0.116456i −0.493822 0.869563i \(-0.664401\pi\)
−0.166633 + 0.986019i \(0.553290\pi\)
\(360\) 0 0
\(361\) −13.1846 13.6809i −0.693927 0.720045i
\(362\) 0 0
\(363\) 1.50585 + 8.54009i 0.0790366 + 0.448239i
\(364\) 0 0
\(365\) 17.0757 6.21505i 0.893784 0.325311i
\(366\) 0 0
\(367\) −0.130303 + 0.155289i −0.00680174 + 0.00810600i −0.769435 0.638726i \(-0.779462\pi\)
0.762633 + 0.646832i \(0.223906\pi\)
\(368\) 0 0
\(369\) 5.14998 2.97334i 0.268097 0.154786i
\(370\) 0 0
\(371\) 0.123675 0.701396i 0.00642089 0.0364147i
\(372\) 0 0
\(373\) 29.8215 + 17.2174i 1.54410 + 0.891485i 0.998574 + 0.0533902i \(0.0170027\pi\)
0.545524 + 0.838095i \(0.316331\pi\)
\(374\) 0 0
\(375\) 1.13676 + 0.413747i 0.0587021 + 0.0213658i
\(376\) 0 0
\(377\) −3.04770 + 2.55733i −0.156965 + 0.131709i
\(378\) 0 0
\(379\) 18.0115 0.925190 0.462595 0.886570i \(-0.346918\pi\)
0.462595 + 0.886570i \(0.346918\pi\)
\(380\) 0 0
\(381\) −10.0480 −0.514775
\(382\) 0 0
\(383\) 7.54762 6.33320i 0.385665 0.323612i −0.429256 0.903183i \(-0.641224\pi\)
0.814922 + 0.579571i \(0.196780\pi\)
\(384\) 0 0
\(385\) −9.68702 3.52579i −0.493697 0.179691i
\(386\) 0 0
\(387\) −6.77428 3.91113i −0.344356 0.198814i
\(388\) 0 0
\(389\) 4.56302 25.8782i 0.231354 1.31208i −0.618802 0.785547i \(-0.712382\pi\)
0.850157 0.526530i \(-0.176507\pi\)
\(390\) 0 0
\(391\) −1.01107 + 0.583740i −0.0511319 + 0.0295210i
\(392\) 0 0
\(393\) −9.91656 + 11.8181i −0.500225 + 0.596144i
\(394\) 0 0
\(395\) 32.2549 11.7398i 1.62292 0.590695i
\(396\) 0 0
\(397\) −1.55629 8.82617i −0.0781081 0.442973i −0.998632 0.0522869i \(-0.983349\pi\)
0.920524 0.390686i \(-0.127762\pi\)
\(398\) 0 0
\(399\) −2.06116 + 8.90722i −0.103187 + 0.445919i
\(400\) 0 0
\(401\) 14.2316 2.50941i 0.710692 0.125314i 0.193396 0.981121i \(-0.438050\pi\)
0.517296 + 0.855807i \(0.326939\pi\)
\(402\) 0 0
\(403\) 10.0853 + 27.7092i 0.502386 + 1.38029i
\(404\) 0 0
\(405\) −2.46751 2.07049i −0.122612 0.102883i
\(406\) 0 0
\(407\) −2.98708 5.17377i −0.148064 0.256454i
\(408\) 0 0
\(409\) −17.0972 3.01469i −0.845401 0.149067i −0.265862 0.964011i \(-0.585656\pi\)
−0.579539 + 0.814944i \(0.696768\pi\)
\(410\) 0 0
\(411\) −7.32861 + 12.6935i −0.361494 + 0.626125i
\(412\) 0 0
\(413\) −7.50574 + 20.6219i −0.369333 + 1.01474i
\(414\) 0 0
\(415\) −27.4695 32.7369i −1.34842 1.60699i
\(416\) 0 0
\(417\) 14.3850i 0.704438i
\(418\) 0 0
\(419\) 8.21138i 0.401152i 0.979678 + 0.200576i \(0.0642814\pi\)
−0.979678 + 0.200576i \(0.935719\pi\)
\(420\) 0 0
\(421\) 3.67005 + 4.37379i 0.178867 + 0.213166i 0.848027 0.529953i \(-0.177790\pi\)
−0.669160 + 0.743118i \(0.733346\pi\)
\(422\) 0 0
\(423\) −3.18869 + 8.76085i −0.155039 + 0.425967i
\(424\) 0 0
\(425\) 1.07908 1.86902i 0.0523431 0.0906609i
\(426\) 0 0
\(427\) −5.38886 0.950202i −0.260785 0.0459835i
\(428\) 0 0
\(429\) 4.12169 + 7.13897i 0.198997 + 0.344673i
\(430\) 0 0
\(431\) 13.8723 + 11.6402i 0.668205 + 0.560690i 0.912533 0.409002i \(-0.134123\pi\)
−0.244329 + 0.969692i \(0.578568\pi\)
\(432\) 0 0
\(433\) −3.75295 10.3112i −0.180355 0.495522i 0.816264 0.577679i \(-0.196041\pi\)
−0.996619 + 0.0821567i \(0.973819\pi\)
\(434\) 0 0
\(435\) −2.33602 + 0.411904i −0.112004 + 0.0197493i
\(436\) 0 0
\(437\) 12.6578 + 0.669814i 0.605505 + 0.0320415i
\(438\) 0 0
\(439\) 1.64492 + 9.32880i 0.0785077 + 0.445239i 0.998570 + 0.0534665i \(0.0170270\pi\)
−0.920062 + 0.391773i \(0.871862\pi\)
\(440\) 0 0
\(441\) −2.44385 + 0.889488i −0.116374 + 0.0423566i
\(442\) 0 0
\(443\) 9.19553 10.9588i 0.436893 0.520668i −0.502005 0.864865i \(-0.667404\pi\)
0.938898 + 0.344196i \(0.111849\pi\)
\(444\) 0 0
\(445\) −0.685154 + 0.395574i −0.0324794 + 0.0187520i
\(446\) 0 0
\(447\) −3.53399 + 20.0423i −0.167152 + 0.947967i
\(448\) 0 0
\(449\) −24.3612 14.0650i −1.14968 0.663767i −0.200869 0.979618i \(-0.564377\pi\)
−0.948809 + 0.315851i \(0.897710\pi\)
\(450\) 0 0
\(451\) −8.52643 3.10337i −0.401494 0.146132i
\(452\) 0 0
\(453\) 4.45437 3.73766i 0.209285 0.175611i
\(454\) 0 0
\(455\) 36.5003 1.71116
\(456\) 0 0
\(457\) 31.3287 1.46549 0.732747 0.680501i \(-0.238238\pi\)
0.732747 + 0.680501i \(0.238238\pi\)
\(458\) 0 0
\(459\) −0.307549 + 0.258064i −0.0143552 + 0.0120454i
\(460\) 0 0
\(461\) 22.9582 + 8.35612i 1.06927 + 0.389183i 0.815904 0.578187i \(-0.196240\pi\)
0.253368 + 0.967370i \(0.418462\pi\)
\(462\) 0 0
\(463\) 28.1155 + 16.2325i 1.30664 + 0.754388i 0.981534 0.191290i \(-0.0612670\pi\)
0.325105 + 0.945678i \(0.394600\pi\)
\(464\) 0 0
\(465\) −3.05292 + 17.3140i −0.141576 + 0.802917i
\(466\) 0 0
\(467\) 30.6095 17.6724i 1.41644 0.817782i 0.420455 0.907313i \(-0.361870\pi\)
0.995984 + 0.0895318i \(0.0285371\pi\)
\(468\) 0 0
\(469\) 13.5491 16.1472i 0.625640 0.745609i
\(470\) 0 0
\(471\) −20.7381 + 7.54804i −0.955560 + 0.347796i
\(472\) 0 0
\(473\) 2.07257 + 11.7541i 0.0952968 + 0.540455i
\(474\) 0 0
\(475\) −20.8830 + 10.6271i −0.958179 + 0.487604i
\(476\) 0 0
\(477\) −0.334404 + 0.0589644i −0.0153113 + 0.00269979i
\(478\) 0 0
\(479\) 6.88844 + 18.9258i 0.314741 + 0.864743i 0.991683 + 0.128707i \(0.0410825\pi\)
−0.676942 + 0.736036i \(0.736695\pi\)
\(480\) 0 0
\(481\) 16.2040 + 13.5968i 0.738840 + 0.619960i
\(482\) 0 0
\(483\) −3.04966 5.28217i −0.138764 0.240347i
\(484\) 0 0
\(485\) 49.3060 + 8.69398i 2.23887 + 0.394773i
\(486\) 0 0
\(487\) 11.5623 20.0265i 0.523938 0.907488i −0.475673 0.879622i \(-0.657796\pi\)
0.999612 0.0278660i \(-0.00887117\pi\)
\(488\) 0 0
\(489\) 4.97394 13.6658i 0.224929 0.617988i
\(490\) 0 0
\(491\) −10.8736 12.9587i −0.490719 0.584816i 0.462681 0.886525i \(-0.346887\pi\)
−0.953400 + 0.301709i \(0.902443\pi\)
\(492\) 0 0
\(493\) 0.295652i 0.0133155i
\(494\) 0 0
\(495\) 4.91487i 0.220907i
\(496\) 0 0
\(497\) −1.56782 1.86845i −0.0703261 0.0838114i
\(498\) 0 0
\(499\) 4.04525 11.1142i 0.181090 0.497541i −0.815620 0.578588i \(-0.803604\pi\)
0.996710 + 0.0810466i \(0.0258263\pi\)
\(500\) 0 0
\(501\) 10.5114 18.2063i 0.469615 0.813397i
\(502\) 0 0
\(503\) −40.7110 7.17845i −1.81521 0.320071i −0.840210 0.542261i \(-0.817568\pi\)
−0.975003 + 0.222190i \(0.928679\pi\)
\(504\) 0 0
\(505\) 7.95141 + 13.7723i 0.353833 + 0.612857i
\(506\) 0 0
\(507\) −12.4004 10.4051i −0.550719 0.462108i
\(508\) 0 0
\(509\) −7.07846 19.4479i −0.313747 0.862013i −0.991892 0.127085i \(-0.959438\pi\)
0.678145 0.734928i \(-0.262784\pi\)
\(510\) 0 0
\(511\) 11.6528 2.05471i 0.515490 0.0908949i
\(512\) 0 0
\(513\) 4.32668 0.529019i 0.191027 0.0233568i
\(514\) 0 0
\(515\) 5.71816 + 32.4293i 0.251972 + 1.42901i
\(516\) 0 0
\(517\) 13.3676 4.86540i 0.587906 0.213980i
\(518\) 0 0
\(519\) −16.0080 + 19.0776i −0.702675 + 0.837416i
\(520\) 0 0
\(521\) 10.7254 6.19234i 0.469890 0.271291i −0.246304 0.969193i \(-0.579216\pi\)
0.716194 + 0.697902i \(0.245883\pi\)
\(522\) 0 0
\(523\) 5.64093 31.9913i 0.246661 1.39888i −0.569943 0.821684i \(-0.693035\pi\)
0.816604 0.577199i \(-0.195854\pi\)
\(524\) 0 0
\(525\) 9.76442 + 5.63749i 0.426154 + 0.246040i
\(526\) 0 0
\(527\) 2.05914 + 0.749466i 0.0896976 + 0.0326473i
\(528\) 0 0
\(529\) 11.1411 9.34853i 0.484398 0.406458i
\(530\) 0 0
\(531\) 10.4628 0.454049
\(532\) 0 0
\(533\) 32.1273 1.39159
\(534\) 0 0
\(535\) −41.0973 + 34.4848i −1.77679 + 1.49091i
\(536\) 0 0
\(537\) 22.6880 + 8.25777i 0.979061 + 0.356349i
\(538\) 0 0
\(539\) 3.43657 + 1.98411i 0.148024 + 0.0854616i
\(540\) 0 0
\(541\) −6.72312 + 38.1287i −0.289049 + 1.63928i 0.401402 + 0.915902i \(0.368523\pi\)
−0.690452 + 0.723378i \(0.742588\pi\)
\(542\) 0 0
\(543\) −9.73117 + 5.61830i −0.417605 + 0.241104i
\(544\) 0 0
\(545\) −11.8564 + 14.1299i −0.507873 + 0.605260i
\(546\) 0 0
\(547\) 13.9476 5.07652i 0.596358 0.217056i −0.0261658 0.999658i \(-0.508330\pi\)
0.622523 + 0.782601i \(0.286108\pi\)
\(548\) 0 0
\(549\) 0.453026 + 2.56924i 0.0193347 + 0.109652i
\(550\) 0 0
\(551\) 1.74963 2.69119i 0.0745365 0.114649i
\(552\) 0 0
\(553\) 22.0114 3.88121i 0.936021 0.165046i
\(554\) 0 0
\(555\) 4.31348 + 11.8512i 0.183097 + 0.503055i
\(556\) 0 0
\(557\) 1.53033 + 1.28410i 0.0648423 + 0.0544092i 0.674633 0.738153i \(-0.264302\pi\)
−0.609790 + 0.792563i \(0.708746\pi\)
\(558\) 0 0
\(559\) −21.1301 36.5983i −0.893706 1.54794i
\(560\) 0 0
\(561\) 0.603279 + 0.106374i 0.0254705 + 0.00449113i
\(562\) 0 0
\(563\) −2.52511 + 4.37363i −0.106421 + 0.184326i −0.914318 0.404997i \(-0.867272\pi\)
0.807897 + 0.589324i \(0.200606\pi\)
\(564\) 0 0
\(565\) 18.3503 50.4170i 0.772002 2.12106i
\(566\) 0 0
\(567\) −1.34822 1.60674i −0.0566198 0.0674768i
\(568\) 0 0
\(569\) 30.0760i 1.26085i 0.776250 + 0.630425i \(0.217119\pi\)
−0.776250 + 0.630425i \(0.782881\pi\)
\(570\) 0 0
\(571\) 30.2742i 1.26694i 0.773769 + 0.633468i \(0.218369\pi\)
−0.773769 + 0.633468i \(0.781631\pi\)
\(572\) 0 0
\(573\) −0.216200 0.257657i −0.00903188 0.0107638i
\(574\) 0 0
\(575\) 5.34644 14.6892i 0.222962 0.612583i
\(576\) 0 0
\(577\) −8.10084 + 14.0311i −0.337242 + 0.584121i −0.983913 0.178648i \(-0.942828\pi\)
0.646671 + 0.762769i \(0.276161\pi\)
\(578\) 0 0
\(579\) 0.820406 + 0.144660i 0.0340949 + 0.00601186i
\(580\) 0 0
\(581\) −13.9136 24.0991i −0.577233 0.999798i
\(582\) 0 0
\(583\) 0.396899 + 0.333038i 0.0164379 + 0.0137930i
\(584\) 0 0
\(585\) −5.95190 16.3527i −0.246081 0.676102i
\(586\) 0 0
\(587\) 44.5886 7.86217i 1.84037 0.324507i 0.858317 0.513120i \(-0.171510\pi\)
0.982051 + 0.188613i \(0.0603992\pi\)
\(588\) 0 0
\(589\) −14.3083 19.0078i −0.589562 0.783202i
\(590\) 0 0
\(591\) 1.74309 + 9.88556i 0.0717012 + 0.406638i
\(592\) 0 0
\(593\) 11.8547 4.31475i 0.486814 0.177186i −0.0869401 0.996214i \(-0.527709\pi\)
0.573754 + 0.819028i \(0.305487\pi\)
\(594\) 0 0
\(595\) 1.74352 2.07784i 0.0714772 0.0851832i
\(596\) 0 0
\(597\) −4.08568 + 2.35887i −0.167216 + 0.0965421i
\(598\) 0 0
\(599\) 7.32116 41.5203i 0.299134 1.69647i −0.350772 0.936461i \(-0.614081\pi\)
0.649907 0.760014i \(-0.274808\pi\)
\(600\) 0 0
\(601\) −5.65341 3.26400i −0.230607 0.133141i 0.380245 0.924886i \(-0.375840\pi\)
−0.610852 + 0.791745i \(0.709173\pi\)
\(602\) 0 0
\(603\) −9.44358 3.43718i −0.384572 0.139973i
\(604\) 0 0
\(605\) −21.3979 + 17.9550i −0.869948 + 0.729973i
\(606\) 0 0
\(607\) 20.5432 0.833823 0.416911 0.908947i \(-0.363113\pi\)
0.416911 + 0.908947i \(0.363113\pi\)
\(608\) 0 0
\(609\) −1.54459 −0.0625898
\(610\) 0 0
\(611\) −38.5845 + 32.3763i −1.56096 + 1.30980i
\(612\) 0 0
\(613\) 14.5887 + 5.30984i 0.589230 + 0.214462i 0.619391 0.785083i \(-0.287380\pi\)
−0.0301606 + 0.999545i \(0.509602\pi\)
\(614\) 0 0
\(615\) 16.5887 + 9.57747i 0.668919 + 0.386201i
\(616\) 0 0
\(617\) 2.31200 13.1120i 0.0930777 0.527870i −0.902242 0.431231i \(-0.858080\pi\)
0.995319 0.0966394i \(-0.0308094\pi\)
\(618\) 0 0
\(619\) 14.8667 8.58327i 0.597542 0.344991i −0.170532 0.985352i \(-0.554549\pi\)
0.768074 + 0.640361i \(0.221215\pi\)
\(620\) 0 0
\(621\) −1.86920 + 2.22763i −0.0750086 + 0.0893917i
\(622\) 0 0
\(623\) −0.484094 + 0.176196i −0.0193948 + 0.00705914i
\(624\) 0 0
\(625\) −3.99064 22.6320i −0.159625 0.905281i
\(626\) 0 0
\(627\) −4.86189 4.53840i −0.194165 0.181246i
\(628\) 0 0
\(629\) 1.54804 0.272961i 0.0617244 0.0108837i
\(630\) 0 0
\(631\) 4.13920 + 11.3724i 0.164779 + 0.452726i 0.994410 0.105585i \(-0.0336716\pi\)
−0.829631 + 0.558312i \(0.811449\pi\)
\(632\) 0 0
\(633\) 10.4632 + 8.77966i 0.415874 + 0.348960i
\(634\) 0 0
\(635\) −16.1829 28.0295i −0.642197 1.11232i
\(636\) 0 0
\(637\) −13.8369 2.43982i −0.548238 0.0966691i
\(638\) 0 0
\(639\) −0.581440 + 1.00708i −0.0230014 + 0.0398396i
\(640\) 0 0
\(641\) 5.12178 14.0720i 0.202298 0.555809i −0.796510 0.604626i \(-0.793323\pi\)
0.998808 + 0.0488164i \(0.0155449\pi\)
\(642\) 0 0
\(643\) −6.47730 7.71935i −0.255440 0.304421i 0.623050 0.782182i \(-0.285893\pi\)
−0.878490 + 0.477760i \(0.841449\pi\)
\(644\) 0 0
\(645\) 25.1964i 0.992106i
\(646\) 0 0
\(647\) 34.3782i 1.35155i −0.737110 0.675773i \(-0.763810\pi\)
0.737110 0.675773i \(-0.236190\pi\)
\(648\) 0 0
\(649\) −10.2618 12.2295i −0.402811 0.480051i
\(650\) 0 0
\(651\) −3.91547 + 10.7577i −0.153459 + 0.421626i
\(652\) 0 0
\(653\) −8.12795 + 14.0780i −0.318071 + 0.550916i −0.980086 0.198576i \(-0.936368\pi\)
0.662014 + 0.749491i \(0.269702\pi\)
\(654\) 0 0
\(655\) −48.9385 8.62918i −1.91219 0.337170i
\(656\) 0 0
\(657\) −2.82070 4.88560i −0.110046 0.190605i
\(658\) 0 0
\(659\) −24.1316 20.2488i −0.940034 0.788783i 0.0375568 0.999294i \(-0.488042\pi\)
−0.977591 + 0.210512i \(0.932487\pi\)
\(660\) 0 0
\(661\) 14.6013 + 40.1168i 0.567925 + 1.56036i 0.807737 + 0.589542i \(0.200692\pi\)
−0.239812 + 0.970819i \(0.577086\pi\)
\(662\) 0 0
\(663\) −2.13604 + 0.376642i −0.0829571 + 0.0146276i
\(664\) 0 0
\(665\) −28.1669 + 8.59584i −1.09226 + 0.333332i
\(666\) 0 0
\(667\) 0.371860 + 2.10892i 0.0143985 + 0.0816578i
\(668\) 0 0
\(669\) −14.4781 + 5.26960i −0.559756 + 0.203734i
\(670\) 0 0
\(671\) 2.55875 3.04940i 0.0987793 0.117721i
\(672\) 0 0
\(673\) −6.57314 + 3.79500i −0.253376 + 0.146287i −0.621309 0.783566i \(-0.713399\pi\)
0.367933 + 0.929852i \(0.380066\pi\)
\(674\) 0 0
\(675\) 0.933456 5.29389i 0.0359287 0.203762i
\(676\) 0 0
\(677\) −19.8392 11.4542i −0.762482 0.440219i 0.0677044 0.997705i \(-0.478433\pi\)
−0.830186 + 0.557486i \(0.811766\pi\)
\(678\) 0 0
\(679\) 30.6352 + 11.1503i 1.17567 + 0.427909i
\(680\) 0 0
\(681\) −8.88299 + 7.45371i −0.340397 + 0.285627i
\(682\) 0 0
\(683\) 36.2226 1.38602 0.693010 0.720928i \(-0.256284\pi\)
0.693010 + 0.720928i \(0.256284\pi\)
\(684\) 0 0
\(685\) −47.2125 −1.80390
\(686\) 0 0
\(687\) −16.6142 + 13.9409i −0.633870 + 0.531880i
\(688\) 0 0
\(689\) −1.72387 0.627436i −0.0656741 0.0239034i
\(690\) 0 0
\(691\) 23.9484 + 13.8266i 0.911042 + 0.525990i 0.880766 0.473551i \(-0.157028\pi\)
0.0302754 + 0.999542i \(0.490362\pi\)
\(692\) 0 0
\(693\) −0.555737 + 3.15174i −0.0211107 + 0.119725i
\(694\) 0 0
\(695\) 40.1280 23.1679i 1.52214 0.878809i
\(696\) 0 0
\(697\) 1.53463 1.82890i 0.0581281 0.0692744i
\(698\) 0 0
\(699\) 17.5176 6.37589i 0.662577 0.241158i
\(700\) 0 0
\(701\) 5.63438 + 31.9542i 0.212808 + 1.20689i 0.884671 + 0.466217i \(0.154383\pi\)
−0.671863 + 0.740675i \(0.734506\pi\)
\(702\) 0 0
\(703\) −15.7065 6.67643i −0.592382 0.251806i
\(704\) 0 0
\(705\) −29.5745 + 5.21479i −1.11384 + 0.196400i
\(706\) 0 0
\(707\) 3.54171 + 9.73076i 0.133200 + 0.365963i
\(708\) 0 0
\(709\) −19.9454 16.7362i −0.749064 0.628539i 0.186191 0.982514i \(-0.440386\pi\)
−0.935255 + 0.353974i \(0.884830\pi\)
\(710\) 0 0
\(711\) −5.32813 9.22859i −0.199820 0.346099i
\(712\) 0 0
\(713\) 15.6308 + 2.75613i 0.585377 + 0.103218i
\(714\) 0 0
\(715\) −13.2764 + 22.9954i −0.496510 + 0.859980i
\(716\) 0 0
\(717\) −0.0588064 + 0.161569i −0.00219616 + 0.00603391i
\(718\) 0 0
\(719\) −31.5963 37.6550i −1.17834 1.40429i −0.895462 0.445138i \(-0.853155\pi\)
−0.282880 0.959155i \(-0.591290\pi\)
\(720\) 0 0
\(721\) 21.4424i 0.798556i
\(722\) 0 0
\(723\) 12.6308i 0.469744i
\(724\) 0 0
\(725\) −2.54455 3.03248i −0.0945023 0.112623i
\(726\) 0 0
\(727\) −11.4331 + 31.4123i −0.424031 + 1.16502i 0.525349 + 0.850887i \(0.323935\pi\)
−0.949380 + 0.314130i \(0.898287\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) −3.09274 0.545334i −0.114389 0.0201699i
\(732\) 0 0
\(733\) 12.0527 + 20.8759i 0.445177 + 0.771069i 0.998065 0.0621867i \(-0.0198074\pi\)
−0.552888 + 0.833256i \(0.686474\pi\)
\(734\) 0 0
\(735\) −6.41724 5.38470i −0.236703 0.198618i
\(736\) 0 0
\(737\) 5.24456 + 14.4093i 0.193186 + 0.530774i
\(738\) 0 0
\(739\) −46.7284 + 8.23949i −1.71893 + 0.303094i −0.944244 0.329247i \(-0.893205\pi\)
−0.774690 + 0.632341i \(0.782094\pi\)
\(740\) 0 0
\(741\) 21.6724 + 9.21239i 0.796157 + 0.338426i
\(742\) 0 0
\(743\) 3.99639 + 22.6646i 0.146613 + 0.831485i 0.966058 + 0.258326i \(0.0831710\pi\)
−0.819445 + 0.573158i \(0.805718\pi\)
\(744\) 0 0
\(745\) −61.6009 + 22.4209i −2.25688 + 0.821438i
\(746\) 0 0
\(747\) −8.52795 + 10.1632i −0.312021 + 0.371853i
\(748\) 0 0
\(749\) −30.2536 + 17.4669i −1.10544 + 0.638227i
\(750\) 0 0
\(751\) −1.09632 + 6.21756i −0.0400054 + 0.226882i −0.998255 0.0590513i \(-0.981192\pi\)
0.958250 + 0.285933i \(0.0923035\pi\)
\(752\) 0 0
\(753\) 2.53579 + 1.46404i 0.0924093 + 0.0533525i
\(754\) 0 0
\(755\) 17.6005 + 6.40604i 0.640546 + 0.233140i
\(756\) 0 0
\(757\) 18.1562 15.2348i 0.659897 0.553719i −0.250159 0.968205i \(-0.580483\pi\)
0.910056 + 0.414485i \(0.136038\pi\)
\(758\) 0 0
\(759\) 4.43706 0.161055
\(760\) 0 0
\(761\) −4.15456 −0.150603 −0.0753013 0.997161i \(-0.523992\pi\)
−0.0753013 + 0.997161i \(0.523992\pi\)
\(762\) 0 0
\(763\) −9.20082 + 7.72041i −0.333092 + 0.279498i
\(764\) 0 0
\(765\) −1.21521 0.442301i −0.0439361 0.0159914i
\(766\) 0 0
\(767\) 48.9529 + 28.2630i 1.76759 + 1.02052i
\(768\) 0 0
\(769\) 0.811565 4.60261i 0.0292658 0.165974i −0.966672 0.256018i \(-0.917589\pi\)
0.995938 + 0.0900433i \(0.0287005\pi\)
\(770\) 0 0
\(771\) 11.6487 6.72540i 0.419519 0.242209i
\(772\) 0 0
\(773\) 0.966318 1.15161i 0.0347561 0.0414207i −0.748386 0.663263i \(-0.769171\pi\)
0.783142 + 0.621842i \(0.213616\pi\)
\(774\) 0 0
\(775\) −27.5708 + 10.0350i −0.990373 + 0.360466i
\(776\) 0 0
\(777\) 1.42604 + 8.08749i 0.0511590 + 0.290137i
\(778\) 0 0
\(779\) −24.7922 + 7.56598i −0.888274 + 0.271079i
\(780\) 0 0
\(781\) 1.74740 0.308114i 0.0625270 0.0110252i
\(782\) 0 0
\(783\) 0.251867 + 0.692000i 0.00900100 + 0.0247301i
\(784\) 0 0
\(785\) −54.4556 45.6937i −1.94360 1.63088i
\(786\) 0 0
\(787\) −3.80025 6.58223i −0.135464 0.234631i 0.790310 0.612707i \(-0.209919\pi\)
−0.925775 + 0.378075i \(0.876586\pi\)
\(788\) 0 0
\(789\) −30.3552 5.35243i −1.08067 0.190552i
\(790\) 0 0
\(791\) 17.4682 30.2558i 0.621096 1.07577i
\(792\) 0 0
\(793\) −4.82063 + 13.2446i −0.171185 + 0.470328i
\(794\) 0 0
\(795\) −0.703060 0.837875i −0.0249350 0.0297164i
\(796\) 0 0
\(797\) 35.7008i 1.26459i 0.774728 + 0.632294i \(0.217887\pi\)
−0.774728 + 0.632294i \(0.782113\pi\)
\(798\) 0 0
\(799\) 3.74301i 0.132418i
\(800\) 0 0
\(801\) 0.157877 + 0.188151i 0.00557832 + 0.00664798i
\(802\) 0 0
\(803\) −2.94405 + 8.08872i −0.103893 + 0.285445i
\(804\) 0 0
\(805\) 9.82330 17.0144i 0.346226 0.599680i
\(806\) 0 0
\(807\) −17.6535 3.11279i −0.621432 0.109575i
\(808\) 0 0
\(809\) −24.6049 42.6170i −0.865063 1.49833i −0.866985 0.498334i \(-0.833945\pi\)
0.00192213 0.999998i \(-0.499388\pi\)
\(810\) 0 0
\(811\) −21.7575 18.2567i −0.764010 0.641080i 0.175158 0.984540i \(-0.443957\pi\)
−0.939167 + 0.343460i \(0.888401\pi\)
\(812\) 0 0
\(813\) −4.98801 13.7044i −0.174937 0.480636i
\(814\) 0 0
\(815\) 46.1324 8.13439i 1.61595 0.284935i
\(816\) 0 0
\(817\) 24.9247 + 23.2664i 0.872006 + 0.813987i
\(818\) 0 0
\(819\) −1.96771 11.1594i −0.0687573 0.389942i
\(820\) 0 0
\(821\) 20.6181 7.50437i 0.719576 0.261904i 0.0438304 0.999039i \(-0.486044\pi\)
0.675746 + 0.737135i \(0.263822\pi\)
\(822\) 0 0
\(823\) −6.31110 + 7.52128i −0.219991 + 0.262175i −0.864741 0.502219i \(-0.832517\pi\)
0.644750 + 0.764394i \(0.276962\pi\)
\(824\) 0 0
\(825\) −7.10331 + 4.10110i −0.247306 + 0.142782i
\(826\) 0 0
\(827\) −1.74234 + 9.88131i −0.0605871 + 0.343607i 0.939413 + 0.342789i \(0.111371\pi\)
−1.00000 0.000817979i \(0.999740\pi\)
\(828\) 0 0
\(829\) 13.5109 + 7.80055i 0.469254 + 0.270924i 0.715928 0.698175i \(-0.246004\pi\)
−0.246673 + 0.969099i \(0.579337\pi\)
\(830\) 0 0
\(831\) −18.8530 6.86192i −0.654002 0.238037i
\(832\) 0 0
\(833\) −0.799840 + 0.671145i −0.0277128 + 0.0232538i
\(834\) 0 0
\(835\) 67.7169 2.34344
\(836\) 0 0
\(837\) 5.45808 0.188659
\(838\) 0 0
\(839\) −11.7747 + 9.88011i −0.406506 + 0.341099i −0.823002 0.568038i \(-0.807703\pi\)
0.416496 + 0.909138i \(0.363258\pi\)
\(840\) 0 0
\(841\) −26.7415 9.73311i −0.922120 0.335624i
\(842\) 0 0
\(843\) 3.75084 + 2.16555i 0.129186 + 0.0745854i
\(844\) 0 0
\(845\) 9.05432 51.3496i 0.311478 1.76648i
\(846\) 0 0
\(847\) −15.7519 + 9.09439i −0.541243 + 0.312487i
\(848\) 0 0
\(849\) 3.14737 3.75089i 0.108018 0.128730i
\(850\) 0 0
\(851\) 10.6990 3.89414i 0.366759 0.133489i
\(852\) 0 0
\(853\) −4.62836 26.2487i −0.158472 0.898740i −0.955543 0.294853i \(-0.904729\pi\)
0.797070 0.603886i \(-0.206382\pi\)
\(854\) 0 0
\(855\) 8.44409 + 11.2175i 0.288782 + 0.383631i
\(856\) 0 0
\(857\) −10.7571 + 1.89677i −0.367456 + 0.0647925i −0.354328 0.935121i \(-0.615290\pi\)
−0.0131287 + 0.999914i \(0.504179\pi\)
\(858\) 0 0
\(859\) 16.6810 + 45.8306i 0.569147 + 1.56372i 0.805839 + 0.592134i \(0.201714\pi\)
−0.236692 + 0.971585i \(0.576063\pi\)
\(860\) 0 0
\(861\) 9.55479 + 8.01742i 0.325626 + 0.273233i
\(862\) 0 0
\(863\) −15.3261 26.5455i −0.521706 0.903621i −0.999681 0.0252475i \(-0.991963\pi\)
0.477976 0.878373i \(-0.341371\pi\)
\(864\) 0 0
\(865\) −79.0002 13.9299i −2.68609 0.473629i
\(866\) 0 0
\(867\) 8.41941 14.5828i 0.285938 0.495259i
\(868\) 0 0
\(869\) −5.56113 + 15.2791i −0.188648 + 0.518307i
\(870\) 0 0
\(871\) −34.8993 41.5914i −1.18252 1.40927i
\(872\) 0 0
\(873\) 15.5433i 0.526061i
\(874\) 0 0
\(875\) 2.53732i 0.0857771i
\(876\) 0 0
\(877\) 15.7467 + 18.7662i 0.531727 + 0.633688i 0.963312 0.268385i \(-0.0864898\pi\)
−0.431585 + 0.902072i \(0.642045\pi\)
\(878\) 0 0
\(879\) 2.22949 6.12548i 0.0751989 0.206607i
\(880\) 0 0
\(881\) −4.09864 + 7.09906i −0.138087 + 0.239173i −0.926772 0.375623i \(-0.877429\pi\)
0.788686 + 0.614797i \(0.210762\pi\)
\(882\) 0 0
\(883\) −13.6696 2.41031i −0.460018 0.0811136i −0.0611633 0.998128i \(-0.519481\pi\)
−0.398855 + 0.917014i \(0.630592\pi\)
\(884\) 0 0
\(885\) 16.8510 + 29.1868i 0.566440 + 0.981102i
\(886\) 0 0
\(887\) 7.29985 + 6.12530i 0.245105 + 0.205668i 0.757061 0.653344i \(-0.226634\pi\)
−0.511956 + 0.859012i \(0.671079\pi\)
\(888\) 0 0
\(889\) −7.20815 19.8042i −0.241753 0.664212i
\(890\) 0 0
\(891\) 1.50265 0.264958i 0.0503407 0.00887642i
\(892\) 0 0
\(893\) 22.1506 34.0710i 0.741242 1.14014i
\(894\) 0 0
\(895\) 13.5048 + 76.5893i 0.451414 + 2.56010i
\(896\) 0 0
\(897\) −14.7630 + 5.37328i −0.492921 + 0.179409i
\(898\) 0 0
\(899\) 2.58361 3.07903i 0.0861684 0.102691i
\(900\) 0 0
\(901\) −0.118062 + 0.0681632i −0.00393322 + 0.00227084i
\(902\) 0 0
\(903\) 2.84901 16.1576i 0.0948093 0.537690i
\(904\) 0 0
\(905\) −31.3452 18.0972i −1.04195 0.601570i
\(906\) 0 0
\(907\) −35.9397 13.0810i −1.19336 0.434347i −0.332457 0.943118i \(-0.607878\pi\)
−0.860902 + 0.508771i \(0.830100\pi\)
\(908\) 0 0
\(909\) 3.78201 3.17348i 0.125441 0.105258i
\(910\) 0 0
\(911\) 30.9861 1.02662 0.513308 0.858204i \(-0.328420\pi\)
0.513308 + 0.858204i \(0.328420\pi\)
\(912\) 0 0
\(913\) 20.2434 0.669959
\(914\) 0 0
\(915\) −6.43744 + 5.40165i −0.212815 + 0.178573i
\(916\) 0 0
\(917\) −30.4069 11.0672i −1.00412 0.365471i
\(918\) 0 0
\(919\) 22.6165 + 13.0576i 0.746048 + 0.430731i 0.824264 0.566205i \(-0.191589\pi\)
−0.0782160 + 0.996936i \(0.524922\pi\)
\(920\) 0 0
\(921\) −4.05414 + 22.9922i −0.133588 + 0.757618i
\(922\) 0 0
\(923\) −5.44082 + 3.14126i −0.179087 + 0.103396i
\(924\) 0 0
\(925\) −13.5289 + 16.1231i −0.444826 + 0.530123i
\(926\) 0 0
\(927\) 9.60652 3.49649i 0.315520 0.114840i
\(928\) 0 0
\(929\) 5.88318 + 33.3652i 0.193021 + 1.09468i 0.915209 + 0.402979i \(0.132025\pi\)
−0.722188 + 0.691696i \(0.756864\pi\)
\(930\) 0 0
\(931\) 11.2523 1.37581i 0.368781 0.0450905i
\(932\) 0 0
\(933\) 11.3938 2.00903i 0.373016 0.0657728i
\(934\) 0 0
\(935\) 0.674877 + 1.85421i 0.0220708 + 0.0606391i
\(936\) 0 0
\(937\) 7.57998 + 6.36036i 0.247627 + 0.207784i 0.758150 0.652081i \(-0.226104\pi\)
−0.510523 + 0.859864i \(0.670548\pi\)
\(938\) 0 0
\(939\) 14.5236 + 25.1556i 0.473959 + 0.820921i
\(940\) 0 0
\(941\) 46.2398 + 8.15333i 1.50738 + 0.265791i 0.865458 0.500982i \(-0.167028\pi\)
0.641918 + 0.766773i \(0.278139\pi\)
\(942\) 0 0
\(943\) 8.64638 14.9760i 0.281565 0.487685i
\(944\) 0 0
\(945\) 2.31073 6.34869i 0.0751681 0.206523i
\(946\) 0 0
\(947\) −0.876606 1.04470i −0.0284859 0.0339481i 0.751613 0.659604i \(-0.229276\pi\)
−0.780099 + 0.625656i \(0.784831\pi\)
\(948\) 0 0
\(949\) 30.4780i 0.989356i
\(950\) 0 0
\(951\) 1.30110i 0.0421911i
\(952\) 0 0
\(953\) 15.4953 + 18.4666i 0.501943 + 0.598192i 0.956213 0.292672i \(-0.0945443\pi\)
−0.454270 + 0.890864i \(0.650100\pi\)
\(954\) 0 0
\(955\) 0.370549 1.01807i 0.0119907 0.0329441i
\(956\) 0 0
\(957\) 0.561819 0.973100i 0.0181610 0.0314558i
\(958\) 0 0
\(959\) −30.2758 5.33844i −0.977656 0.172387i
\(960\) 0 0
\(961\) 0.604671 + 1.04732i 0.0195055 + 0.0337845i
\(962\) 0 0
\(963\) 12.7587 + 10.7059i 0.411145 + 0.344991i
\(964\) 0 0
\(965\) 0.917772 + 2.52156i 0.0295441 + 0.0811719i
\(966\) 0 0
\(967\) 39.7633 7.01134i 1.27870 0.225470i 0.507273 0.861785i \(-0.330654\pi\)
0.771429 + 0.636316i \(0.219542\pi\)
\(968\) 0 0
\(969\) 1.55966 0.793690i 0.0501035 0.0254970i
\(970\) 0 0
\(971\) −1.00455 5.69711i −0.0322377 0.182829i 0.964437 0.264313i \(-0.0851452\pi\)
−0.996675 + 0.0814840i \(0.974034\pi\)
\(972\) 0 0
\(973\) 28.3524 10.3194i 0.908935 0.330825i
\(974\) 0 0
\(975\) 18.6676 22.2472i 0.597843 0.712482i
\(976\) 0 0
\(977\) 30.7077 17.7291i 0.982426 0.567204i 0.0794240 0.996841i \(-0.474692\pi\)
0.903002 + 0.429637i \(0.141359\pi\)
\(978\) 0 0
\(979\) 0.0650772 0.369071i 0.00207988 0.0117956i
\(980\) 0 0
\(981\) 4.95919 + 2.86319i 0.158335 + 0.0914147i
\(982\) 0 0
\(983\) 6.74093 + 2.45350i 0.215002 + 0.0782544i 0.447276 0.894396i \(-0.352394\pi\)
−0.232274 + 0.972650i \(0.574616\pi\)
\(984\) 0 0
\(985\) −24.7691 + 20.7837i −0.789208 + 0.662224i
\(986\) 0 0
\(987\) −19.5548 −0.622435
\(988\) 0 0
\(989\) −22.7469 −0.723308
\(990\) 0 0
\(991\) −6.95401 + 5.83510i −0.220901 + 0.185358i −0.746522 0.665361i \(-0.768278\pi\)
0.525621 + 0.850719i \(0.323833\pi\)
\(992\) 0 0
\(993\) 4.57462 + 1.66502i 0.145171 + 0.0528380i
\(994\) 0 0
\(995\) −13.1604 7.59818i −0.417214 0.240879i
\(996\) 0 0
\(997\) −3.88088 + 22.0096i −0.122909 + 0.697050i 0.859619 + 0.510935i \(0.170701\pi\)
−0.982528 + 0.186115i \(0.940410\pi\)
\(998\) 0 0
\(999\) 3.39079 1.95767i 0.107280 0.0619380i
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 912.2.ci.f.751.3 yes 18
4.3 odd 2 912.2.ci.e.751.3 18
19.2 odd 18 912.2.ci.e.895.3 yes 18
76.59 even 18 inner 912.2.ci.f.895.3 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
912.2.ci.e.751.3 18 4.3 odd 2
912.2.ci.e.895.3 yes 18 19.2 odd 18
912.2.ci.f.751.3 yes 18 1.1 even 1 trivial
912.2.ci.f.895.3 yes 18 76.59 even 18 inner