Properties

Label 912.2.ci.f.127.2
Level $912$
Weight $2$
Character 912.127
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 127.2
Root \(-0.489413 + 1.79677i\) of defining polynomial
Character \(\chi\) \(=\) 912.127
Dual form 912.2.ci.f.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.939693 - 0.342020i) q^{3} +(-0.0537040 - 0.304570i) q^{5} +(-4.22544 - 2.43956i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\) \(q+(-0.939693 - 0.342020i) q^{3} +(-0.0537040 - 0.304570i) q^{5} +(-4.22544 - 2.43956i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-1.67322 + 0.966032i) q^{11} +(1.49685 + 4.11257i) q^{13} +(-0.0537040 + 0.304570i) q^{15} +(-3.57294 + 2.99805i) q^{17} +(3.42972 + 2.69017i) q^{19} +(3.13624 + 3.73762i) q^{21} +(7.72421 + 1.36199i) q^{23} +(4.60858 - 1.67739i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(5.51775 - 6.57580i) q^{29} +(1.67069 - 2.89373i) q^{31} +(1.90271 - 0.335499i) q^{33} +(-0.516095 + 1.41796i) q^{35} -1.17512i q^{37} -4.37651i q^{39} +(-3.68090 + 10.1132i) q^{41} +(-2.64198 + 0.465852i) q^{43} +(0.154634 - 0.267835i) q^{45} +(-5.72472 + 6.82246i) q^{47} +(8.40289 + 14.5542i) q^{49} +(4.38286 - 1.59523i) q^{51} +(11.3935 + 2.00898i) q^{53} +(0.384083 + 0.457733i) q^{55} +(-2.30279 - 3.70097i) q^{57} +(2.80526 - 2.35389i) q^{59} +(-0.0154881 + 0.0878376i) q^{61} +(-1.66876 - 4.58487i) q^{63} +(1.17218 - 0.676759i) q^{65} +(-3.50277 - 2.93917i) q^{67} +(-6.79255 - 3.92168i) q^{69} +(2.43826 + 13.8280i) q^{71} +(-11.0620 - 4.02625i) q^{73} -4.90435 q^{75} +9.42677 q^{77} +(-4.56918 - 1.66304i) q^{79} +(0.173648 + 0.984808i) q^{81} +(9.83589 + 5.67875i) q^{83} +(1.10500 + 0.927204i) q^{85} +(-7.43404 + 4.29205i) q^{87} +(4.29457 + 11.7992i) q^{89} +(3.70800 - 21.0291i) q^{91} +(-2.55965 + 2.14780i) q^{93} +(0.635157 - 1.18906i) q^{95} +(-10.0001 - 11.9176i) q^{97} +(-1.90271 - 0.335499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\) \(1\) \(-1\)

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
\(3\) −0.939693 0.342020i −0.542532 0.197465i
\(4\) 0 0
\(5\) −0.0537040 0.304570i −0.0240172 0.136208i 0.970441 0.241336i \(-0.0775857\pi\)
−0.994459 + 0.105128i \(0.966475\pi\)
\(6\) 0 0
\(7\) −4.22544 2.43956i −1.59707 0.922067i −0.992049 0.125854i \(-0.959833\pi\)
−0.605017 0.796212i \(-0.706834\pi\)
\(8\) 0 0
\(9\) 0.766044 + 0.642788i 0.255348 + 0.214263i
\(10\) 0 0
\(11\) −1.67322 + 0.966032i −0.504494 + 0.291270i −0.730567 0.682841i \(-0.760744\pi\)
0.226074 + 0.974110i \(0.427411\pi\)
\(12\) 0 0
\(13\) 1.49685 + 4.11257i 0.415153 + 1.14062i 0.954414 + 0.298485i \(0.0964811\pi\)
−0.539262 + 0.842138i \(0.681297\pi\)
\(14\) 0 0
\(15\) −0.0537040 + 0.304570i −0.0138663 + 0.0786398i
\(16\) 0 0
\(17\) −3.57294 + 2.99805i −0.866564 + 0.727134i −0.963372 0.268169i \(-0.913581\pi\)
0.0968075 + 0.995303i \(0.469137\pi\)
\(18\) 0 0
\(19\) 3.42972 + 2.69017i 0.786832 + 0.617167i
\(20\) 0 0
\(21\) 3.13624 + 3.73762i 0.684383 + 0.815616i
\(22\) 0 0
\(23\) 7.72421 + 1.36199i 1.61061 + 0.283994i 0.905257 0.424864i \(-0.139678\pi\)
0.705352 + 0.708858i \(0.250789\pi\)
\(24\) 0 0
\(25\) 4.60858 1.67739i 0.921717 0.335477i
\(26\) 0 0
\(27\) −0.500000 0.866025i −0.0962250 0.166667i
\(28\) 0 0
\(29\) 5.51775 6.57580i 1.02462 1.22109i 0.0496481 0.998767i \(-0.484190\pi\)
0.974972 0.222328i \(-0.0713655\pi\)
\(30\) 0 0
\(31\) 1.67069 2.89373i 0.300066 0.519729i −0.676085 0.736824i \(-0.736325\pi\)
0.976151 + 0.217095i \(0.0696581\pi\)
\(32\) 0 0
\(33\) 1.90271 0.335499i 0.331220 0.0584030i
\(34\) 0 0
\(35\) −0.516095 + 1.41796i −0.0872359 + 0.239679i
\(36\) 0 0
\(37\) 1.17512i 0.193189i −0.995324 0.0965943i \(-0.969205\pi\)
0.995324 0.0965943i \(-0.0307949\pi\)
\(38\) 0 0
\(39\) 4.37651i 0.700802i
\(40\) 0 0
\(41\) −3.68090 + 10.1132i −0.574860 + 1.57942i 0.221867 + 0.975077i \(0.428785\pi\)
−0.796727 + 0.604339i \(0.793437\pi\)
\(42\) 0 0
\(43\) −2.64198 + 0.465852i −0.402898 + 0.0710418i −0.371425 0.928463i \(-0.621131\pi\)
−0.0314728 + 0.999505i \(0.510020\pi\)
\(44\) 0 0
\(45\) 0.154634 0.267835i 0.0230515 0.0399265i
\(46\) 0 0
\(47\) −5.72472 + 6.82246i −0.835036 + 0.995157i 0.164925 + 0.986306i \(0.447262\pi\)
−0.999961 + 0.00885122i \(0.997183\pi\)
\(48\) 0 0
\(49\) 8.40289 + 14.5542i 1.20041 + 2.07918i
\(50\) 0 0
\(51\) 4.38286 1.59523i 0.613722 0.223377i
\(52\) 0 0
\(53\) 11.3935 + 2.00898i 1.56501 + 0.275954i 0.887939 0.459961i \(-0.152137\pi\)
0.677074 + 0.735915i \(0.263248\pi\)
\(54\) 0 0
\(55\) 0.384083 + 0.457733i 0.0517898 + 0.0617207i
\(56\) 0 0
\(57\) −2.30279 3.70097i −0.305012 0.490205i
\(58\) 0 0
\(59\) 2.80526 2.35389i 0.365213 0.306450i −0.441651 0.897187i \(-0.645607\pi\)
0.806865 + 0.590737i \(0.201163\pi\)
\(60\) 0 0
\(61\) −0.0154881 + 0.0878376i −0.00198305 + 0.0112465i −0.985783 0.168022i \(-0.946262\pi\)
0.983800 + 0.179269i \(0.0573731\pi\)
\(62\) 0 0
\(63\) −1.66876 4.58487i −0.210244 0.577639i
\(64\) 0 0
\(65\) 1.17218 0.676759i 0.145391 0.0839417i
\(66\) 0 0
\(67\) −3.50277 2.93917i −0.427931 0.359077i 0.403239 0.915095i \(-0.367884\pi\)
−0.831171 + 0.556018i \(0.812329\pi\)
\(68\) 0 0
\(69\) −6.79255 3.92168i −0.817728 0.472115i
\(70\) 0 0
\(71\) 2.43826 + 13.8280i 0.289368 + 1.64109i 0.689252 + 0.724521i \(0.257939\pi\)
−0.399885 + 0.916566i \(0.630950\pi\)
\(72\) 0 0
\(73\) −11.0620 4.02625i −1.29471 0.471237i −0.399443 0.916758i \(-0.630796\pi\)
−0.895272 + 0.445521i \(0.853019\pi\)
\(74\) 0 0
\(75\) −4.90435 −0.566306
\(76\) 0 0
\(77\) 9.42677 1.07428
\(78\) 0 0
\(79\) −4.56918 1.66304i −0.514073 0.187107i 0.0719402 0.997409i \(-0.477081\pi\)
−0.586013 + 0.810302i \(0.699303\pi\)
\(80\) 0 0
\(81\) 0.173648 + 0.984808i 0.0192942 + 0.109423i
\(82\) 0 0
\(83\) 9.83589 + 5.67875i 1.07963 + 0.623324i 0.930796 0.365538i \(-0.119115\pi\)
0.148833 + 0.988862i \(0.452448\pi\)
\(84\) 0 0
\(85\) 1.10500 + 0.927204i 0.119854 + 0.100569i
\(86\) 0 0
\(87\) −7.43404 + 4.29205i −0.797013 + 0.460156i
\(88\) 0 0
\(89\) 4.29457 + 11.7992i 0.455224 + 1.25072i 0.929003 + 0.370073i \(0.120667\pi\)
−0.473779 + 0.880644i \(0.657110\pi\)
\(90\) 0 0
\(91\) 3.70800 21.0291i 0.388704 2.20445i
\(92\) 0 0
\(93\) −2.55965 + 2.14780i −0.265424 + 0.222717i
\(94\) 0 0
\(95\) 0.635157 1.18906i 0.0651657 0.121995i
\(96\) 0 0
\(97\) −10.0001 11.9176i −1.01535 1.21005i −0.977537 0.210764i \(-0.932405\pi\)
−0.0378147 0.999285i \(-0.512040\pi\)
\(98\) 0 0
\(99\) −1.90271 0.335499i −0.191230 0.0337190i
\(100\) 0 0
\(101\) −1.72450 + 0.627668i −0.171595 + 0.0624553i −0.426389 0.904540i \(-0.640214\pi\)
0.254794 + 0.966995i \(0.417992\pi\)
\(102\) 0 0
\(103\) 4.82401 + 8.35543i 0.475324 + 0.823285i 0.999601 0.0282629i \(-0.00899757\pi\)
−0.524277 + 0.851548i \(0.675664\pi\)
\(104\) 0 0
\(105\) 0.969941 1.15593i 0.0946565 0.112807i
\(106\) 0 0
\(107\) −5.55236 + 9.61698i −0.536767 + 0.929708i 0.462308 + 0.886719i \(0.347021\pi\)
−0.999076 + 0.0429890i \(0.986312\pi\)
\(108\) 0 0
\(109\) 10.1146 1.78347i 0.968802 0.170826i 0.333211 0.942852i \(-0.391868\pi\)
0.635590 + 0.772026i \(0.280757\pi\)
\(110\) 0 0
\(111\) −0.401915 + 1.10425i −0.0381481 + 0.104811i
\(112\) 0 0
\(113\) 5.00185i 0.470535i −0.971931 0.235267i \(-0.924403\pi\)
0.971931 0.235267i \(-0.0755966\pi\)
\(114\) 0 0
\(115\) 2.42571i 0.226199i
\(116\) 0 0
\(117\) −1.49685 + 4.11257i −0.138384 + 0.380208i
\(118\) 0 0
\(119\) 22.4111 3.95169i 2.05443 0.362251i
\(120\) 0 0
\(121\) −3.63356 + 6.29352i −0.330324 + 0.572138i
\(122\) 0 0
\(123\) 6.91783 8.24435i 0.623760 0.743368i
\(124\) 0 0
\(125\) −1.53155 2.65273i −0.136986 0.237267i
\(126\) 0 0
\(127\) −5.78923 + 2.10711i −0.513711 + 0.186976i −0.585851 0.810419i \(-0.699240\pi\)
0.0721394 + 0.997395i \(0.477017\pi\)
\(128\) 0 0
\(129\) 2.64198 + 0.465852i 0.232613 + 0.0410160i
\(130\) 0 0
\(131\) 6.89310 + 8.21488i 0.602253 + 0.717737i 0.977911 0.209021i \(-0.0670278\pi\)
−0.375658 + 0.926758i \(0.622583\pi\)
\(132\) 0 0
\(133\) −7.92925 19.7342i −0.687553 1.71117i
\(134\) 0 0
\(135\) −0.236914 + 0.198794i −0.0203903 + 0.0171095i
\(136\) 0 0
\(137\) −1.36935 + 7.76599i −0.116992 + 0.663494i 0.868753 + 0.495246i \(0.164922\pi\)
−0.985745 + 0.168248i \(0.946189\pi\)
\(138\) 0 0
\(139\) 2.10120 + 5.77301i 0.178222 + 0.489660i 0.996349 0.0853774i \(-0.0272096\pi\)
−0.818127 + 0.575038i \(0.804987\pi\)
\(140\) 0 0
\(141\) 7.71289 4.45304i 0.649543 0.375014i
\(142\) 0 0
\(143\) −6.47744 5.43522i −0.541671 0.454516i
\(144\) 0 0
\(145\) −2.29912 1.32740i −0.190931 0.110234i
\(146\) 0 0
\(147\) −2.91829 16.5505i −0.240697 1.36506i
\(148\) 0 0
\(149\) −10.3028 3.74990i −0.844036 0.307204i −0.116430 0.993199i \(-0.537145\pi\)
−0.727606 + 0.685995i \(0.759367\pi\)
\(150\) 0 0
\(151\) −1.66027 −0.135110 −0.0675552 0.997716i \(-0.521520\pi\)
−0.0675552 + 0.997716i \(0.521520\pi\)
\(152\) 0 0
\(153\) −4.66414 −0.377073
\(154\) 0 0
\(155\) −0.971067 0.353439i −0.0779980 0.0283889i
\(156\) 0 0
\(157\) 2.28210 + 12.9424i 0.182132 + 1.03292i 0.929586 + 0.368606i \(0.120165\pi\)
−0.747454 + 0.664313i \(0.768724\pi\)
\(158\) 0 0
\(159\) −10.0192 5.78462i −0.794578 0.458750i
\(160\) 0 0
\(161\) −29.3155 24.5987i −2.31039 1.93865i
\(162\) 0 0
\(163\) −7.53822 + 4.35219i −0.590439 + 0.340890i −0.765271 0.643708i \(-0.777395\pi\)
0.174832 + 0.984598i \(0.444062\pi\)
\(164\) 0 0
\(165\) −0.204366 0.561492i −0.0159099 0.0437121i
\(166\) 0 0
\(167\) −2.27477 + 12.9009i −0.176027 + 0.998300i 0.760924 + 0.648841i \(0.224746\pi\)
−0.936951 + 0.349459i \(0.886365\pi\)
\(168\) 0 0
\(169\) −4.71411 + 3.95561i −0.362624 + 0.304278i
\(170\) 0 0
\(171\) 0.898110 + 4.26537i 0.0686802 + 0.326181i
\(172\) 0 0
\(173\) −4.41217 5.25822i −0.335451 0.399775i 0.571780 0.820407i \(-0.306253\pi\)
−0.907232 + 0.420632i \(0.861808\pi\)
\(174\) 0 0
\(175\) −23.5654 4.15521i −1.78138 0.314105i
\(176\) 0 0
\(177\) −3.44116 + 1.25248i −0.258653 + 0.0941420i
\(178\) 0 0
\(179\) −0.0507409 0.0878858i −0.00379255 0.00656889i 0.864123 0.503281i \(-0.167874\pi\)
−0.867915 + 0.496712i \(0.834541\pi\)
\(180\) 0 0
\(181\) 11.7409 13.9923i 0.872695 1.04004i −0.126151 0.992011i \(-0.540262\pi\)
0.998846 0.0480268i \(-0.0152933\pi\)
\(182\) 0 0
\(183\) 0.0445963 0.0772431i 0.00329665 0.00570997i
\(184\) 0 0
\(185\) −0.357907 + 0.0631087i −0.0263138 + 0.00463984i
\(186\) 0 0
\(187\) 3.08208 8.46796i 0.225384 0.619238i
\(188\) 0 0
\(189\) 4.87912i 0.354904i
\(190\) 0 0
\(191\) 4.24962i 0.307492i 0.988110 + 0.153746i \(0.0491337\pi\)
−0.988110 + 0.153746i \(0.950866\pi\)
\(192\) 0 0
\(193\) −0.483847 + 1.32936i −0.0348281 + 0.0956894i −0.955888 0.293732i \(-0.905103\pi\)
0.921060 + 0.389421i \(0.127325\pi\)
\(194\) 0 0
\(195\) −1.33296 + 0.235036i −0.0954549 + 0.0168313i
\(196\) 0 0
\(197\) 8.55243 14.8132i 0.609335 1.05540i −0.382015 0.924156i \(-0.624770\pi\)
0.991350 0.131243i \(-0.0418970\pi\)
\(198\) 0 0
\(199\) 15.4265 18.3846i 1.09356 1.30325i 0.144027 0.989574i \(-0.453995\pi\)
0.949530 0.313677i \(-0.101561\pi\)
\(200\) 0 0
\(201\) 2.28627 + 3.95994i 0.161261 + 0.279312i
\(202\) 0 0
\(203\) −39.3570 + 14.3248i −2.76232 + 1.00540i
\(204\) 0 0
\(205\) 3.27786 + 0.577975i 0.228936 + 0.0403675i
\(206\) 0 0
\(207\) 5.04162 + 6.00837i 0.350417 + 0.417610i
\(208\) 0 0
\(209\) −8.33746 1.18802i −0.576714 0.0821769i
\(210\) 0 0
\(211\) 4.76878 4.00148i 0.328296 0.275473i −0.463709 0.885988i \(-0.653482\pi\)
0.792005 + 0.610514i \(0.209037\pi\)
\(212\) 0 0
\(213\) 2.43826 13.8280i 0.167067 0.947482i
\(214\) 0 0
\(215\) 0.283770 + 0.779651i 0.0193529 + 0.0531718i
\(216\) 0 0
\(217\) −14.1188 + 8.15151i −0.958449 + 0.553361i
\(218\) 0 0
\(219\) 9.01786 + 7.56688i 0.609371 + 0.511323i
\(220\) 0 0
\(221\) −17.6779 10.2063i −1.18914 0.686551i
\(222\) 0 0
\(223\) −1.85361 10.5124i −0.124127 0.703960i −0.981822 0.189801i \(-0.939216\pi\)
0.857695 0.514158i \(-0.171896\pi\)
\(224\) 0 0
\(225\) 4.60858 + 1.67739i 0.307239 + 0.111826i
\(226\) 0 0
\(227\) −6.02146 −0.399658 −0.199829 0.979831i \(-0.564039\pi\)
−0.199829 + 0.979831i \(0.564039\pi\)
\(228\) 0 0
\(229\) 1.01550 0.0671064 0.0335532 0.999437i \(-0.489318\pi\)
0.0335532 + 0.999437i \(0.489318\pi\)
\(230\) 0 0
\(231\) −8.85827 3.22414i −0.582831 0.212133i
\(232\) 0 0
\(233\) 0.117889 + 0.668580i 0.00772315 + 0.0438002i 0.988426 0.151705i \(-0.0484764\pi\)
−0.980703 + 0.195505i \(0.937365\pi\)
\(234\) 0 0
\(235\) 2.38536 + 1.37719i 0.155604 + 0.0898378i
\(236\) 0 0
\(237\) 3.72483 + 3.12550i 0.241954 + 0.203023i
\(238\) 0 0
\(239\) 20.1517 11.6346i 1.30350 0.752578i 0.322500 0.946570i \(-0.395477\pi\)
0.981003 + 0.193992i \(0.0621435\pi\)
\(240\) 0 0
\(241\) −3.09156 8.49400i −0.199145 0.547147i 0.799416 0.600778i \(-0.205143\pi\)
−0.998561 + 0.0536317i \(0.982920\pi\)
\(242\) 0 0
\(243\) 0.173648 0.984808i 0.0111395 0.0631754i
\(244\) 0 0
\(245\) 3.98152 3.34089i 0.254370 0.213442i
\(246\) 0 0
\(247\) −5.92973 + 18.1318i −0.377300 + 1.15370i
\(248\) 0 0
\(249\) −7.30047 8.70036i −0.462648 0.551363i
\(250\) 0 0
\(251\) 23.1936 + 4.08966i 1.46397 + 0.258137i 0.848152 0.529753i \(-0.177715\pi\)
0.615816 + 0.787890i \(0.288827\pi\)
\(252\) 0 0
\(253\) −14.2400 + 5.18294i −0.895261 + 0.325848i
\(254\) 0 0
\(255\) −0.721236 1.24922i −0.0451656 0.0782291i
\(256\) 0 0
\(257\) −7.52214 + 8.96454i −0.469219 + 0.559193i −0.947806 0.318847i \(-0.896704\pi\)
0.478588 + 0.878040i \(0.341149\pi\)
\(258\) 0 0
\(259\) −2.86678 + 4.96540i −0.178133 + 0.308535i
\(260\) 0 0
\(261\) 8.45368 1.49061i 0.523270 0.0922666i
\(262\) 0 0
\(263\) 2.36698 6.50322i 0.145954 0.401006i −0.845076 0.534647i \(-0.820445\pi\)
0.991030 + 0.133641i \(0.0426669\pi\)
\(264\) 0 0
\(265\) 3.57800i 0.219795i
\(266\) 0 0
\(267\) 12.5565i 0.768445i
\(268\) 0 0
\(269\) −0.0460123 + 0.126418i −0.00280542 + 0.00770783i −0.941087 0.338163i \(-0.890194\pi\)
0.938282 + 0.345871i \(0.112417\pi\)
\(270\) 0 0
\(271\) 11.0397 1.94659i 0.670611 0.118247i 0.172033 0.985091i \(-0.444967\pi\)
0.498579 + 0.866844i \(0.333855\pi\)
\(272\) 0 0
\(273\) −10.6768 + 18.4927i −0.646186 + 1.11923i
\(274\) 0 0
\(275\) −6.09075 + 7.25867i −0.367286 + 0.437714i
\(276\) 0 0
\(277\) −13.6972 23.7242i −0.822982 1.42545i −0.903452 0.428690i \(-0.858975\pi\)
0.0804693 0.996757i \(-0.474358\pi\)
\(278\) 0 0
\(279\) 3.13988 1.14282i 0.187980 0.0684190i
\(280\) 0 0
\(281\) −3.81377 0.672470i −0.227510 0.0401162i 0.0587307 0.998274i \(-0.481295\pi\)
−0.286241 + 0.958158i \(0.592406\pi\)
\(282\) 0 0
\(283\) 14.7694 + 17.6015i 0.877949 + 1.04630i 0.998563 + 0.0535994i \(0.0170694\pi\)
−0.120613 + 0.992700i \(0.538486\pi\)
\(284\) 0 0
\(285\) −1.00354 + 0.900119i −0.0594443 + 0.0533184i
\(286\) 0 0
\(287\) 40.2252 33.7529i 2.37442 1.99237i
\(288\) 0 0
\(289\) 0.825554 4.68195i 0.0485620 0.275409i
\(290\) 0 0
\(291\) 5.32092 + 14.6191i 0.311918 + 0.856987i
\(292\) 0 0
\(293\) −7.37553 + 4.25827i −0.430883 + 0.248770i −0.699723 0.714414i \(-0.746693\pi\)
0.268840 + 0.963185i \(0.413360\pi\)
\(294\) 0 0
\(295\) −0.867579 0.727985i −0.0505124 0.0423849i
\(296\) 0 0
\(297\) 1.67322 + 0.966032i 0.0970899 + 0.0560549i
\(298\) 0 0
\(299\) 5.96075 + 33.8051i 0.344719 + 1.95500i
\(300\) 0 0
\(301\) 12.3000 + 4.47684i 0.708960 + 0.258040i
\(302\) 0 0
\(303\) 1.83518 0.105428
\(304\) 0 0
\(305\) 0.0275845 0.00157948
\(306\) 0 0
\(307\) −8.73075 3.17773i −0.498290 0.181363i 0.0806347 0.996744i \(-0.474305\pi\)
−0.578925 + 0.815381i \(0.696527\pi\)
\(308\) 0 0
\(309\) −1.67536 9.50144i −0.0953080 0.540518i
\(310\) 0 0
\(311\) 11.9799 + 6.91660i 0.679318 + 0.392204i 0.799598 0.600536i \(-0.205046\pi\)
−0.120280 + 0.992740i \(0.538379\pi\)
\(312\) 0 0
\(313\) 11.5289 + 9.67394i 0.651655 + 0.546803i 0.907573 0.419895i \(-0.137933\pi\)
−0.255918 + 0.966699i \(0.582378\pi\)
\(314\) 0 0
\(315\) −1.30680 + 0.754480i −0.0736297 + 0.0425101i
\(316\) 0 0
\(317\) 6.66678 + 18.3168i 0.374443 + 1.02878i 0.973623 + 0.228161i \(0.0732712\pi\)
−0.599180 + 0.800614i \(0.704507\pi\)
\(318\) 0 0
\(319\) −2.87996 + 16.3331i −0.161247 + 0.914476i
\(320\) 0 0
\(321\) 8.50672 7.13798i 0.474799 0.398403i
\(322\) 0 0
\(323\) −20.3194 + 0.670666i −1.13060 + 0.0373168i
\(324\) 0 0
\(325\) 13.7968 + 16.4423i 0.765306 + 0.912057i
\(326\) 0 0
\(327\) −10.1146 1.78347i −0.559338 0.0986264i
\(328\) 0 0
\(329\) 40.8332 14.8621i 2.25121 0.819373i
\(330\) 0 0
\(331\) 5.61585 + 9.72694i 0.308675 + 0.534641i 0.978073 0.208263i \(-0.0667811\pi\)
−0.669398 + 0.742904i \(0.733448\pi\)
\(332\) 0 0
\(333\) 0.755353 0.900194i 0.0413931 0.0493304i
\(334\) 0 0
\(335\) −0.707072 + 1.22469i −0.0386315 + 0.0669117i
\(336\) 0 0
\(337\) −12.3862 + 2.18402i −0.674720 + 0.118971i −0.500502 0.865736i \(-0.666851\pi\)
−0.174219 + 0.984707i \(0.555740\pi\)
\(338\) 0 0
\(339\) −1.71073 + 4.70021i −0.0929144 + 0.255280i
\(340\) 0 0
\(341\) 6.45578i 0.349600i
\(342\) 0 0
\(343\) 47.8436i 2.58331i
\(344\) 0 0
\(345\) −0.829642 + 2.27942i −0.0446664 + 0.122720i
\(346\) 0 0
\(347\) 2.60502 0.459335i 0.139845 0.0246584i −0.103288 0.994652i \(-0.532936\pi\)
0.243132 + 0.969993i \(0.421825\pi\)
\(348\) 0 0
\(349\) 2.38187 4.12552i 0.127499 0.220834i −0.795208 0.606336i \(-0.792639\pi\)
0.922707 + 0.385502i \(0.125972\pi\)
\(350\) 0 0
\(351\) 2.81317 3.35260i 0.150156 0.178949i
\(352\) 0 0
\(353\) −0.924355 1.60103i −0.0491984 0.0852142i 0.840377 0.542002i \(-0.182333\pi\)
−0.889576 + 0.456787i \(0.849000\pi\)
\(354\) 0 0
\(355\) 4.08067 1.48524i 0.216579 0.0788285i
\(356\) 0 0
\(357\) −22.4111 3.95169i −1.18612 0.209146i
\(358\) 0 0
\(359\) −7.12135 8.48690i −0.375851 0.447921i 0.544649 0.838664i \(-0.316663\pi\)
−0.920500 + 0.390743i \(0.872218\pi\)
\(360\) 0 0
\(361\) 4.52597 + 18.4531i 0.238209 + 0.971214i
\(362\) 0 0
\(363\) 5.56694 4.67122i 0.292189 0.245175i
\(364\) 0 0
\(365\) −0.632202 + 3.58540i −0.0330910 + 0.187668i
\(366\) 0 0
\(367\) 9.71428 + 26.6898i 0.507081 + 1.39319i 0.884234 + 0.467043i \(0.154681\pi\)
−0.377153 + 0.926151i \(0.623097\pi\)
\(368\) 0 0
\(369\) −9.32037 + 5.38112i −0.485199 + 0.280130i
\(370\) 0 0
\(371\) −43.2414 36.2838i −2.24498 1.88376i
\(372\) 0 0
\(373\) −17.1406 9.89614i −0.887508 0.512403i −0.0143814 0.999897i \(-0.504578\pi\)
−0.873127 + 0.487494i \(0.837911\pi\)
\(374\) 0 0
\(375\) 0.531903 + 3.01657i 0.0274674 + 0.155775i
\(376\) 0 0
\(377\) 35.3027 + 12.8491i 1.81818 + 0.661764i
\(378\) 0 0
\(379\) −18.4749 −0.948991 −0.474496 0.880258i \(-0.657370\pi\)
−0.474496 + 0.880258i \(0.657370\pi\)
\(380\) 0 0
\(381\) 6.16077 0.315626
\(382\) 0 0
\(383\) −8.81762 3.20935i −0.450559 0.163990i 0.106766 0.994284i \(-0.465950\pi\)
−0.557326 + 0.830294i \(0.688173\pi\)
\(384\) 0 0
\(385\) −0.506255 2.87112i −0.0258011 0.146326i
\(386\) 0 0
\(387\) −2.32332 1.34137i −0.118101 0.0681856i
\(388\) 0 0
\(389\) 21.7806 + 18.2761i 1.10432 + 0.926634i 0.997708 0.0676671i \(-0.0215556\pi\)
0.106611 + 0.994301i \(0.466000\pi\)
\(390\) 0 0
\(391\) −31.6814 + 18.2913i −1.60220 + 0.925029i
\(392\) 0 0
\(393\) −3.66774 10.0770i −0.185013 0.508319i
\(394\) 0 0
\(395\) −0.261131 + 1.48095i −0.0131389 + 0.0745146i
\(396\) 0 0
\(397\) 28.2230 23.6819i 1.41647 1.18856i 0.463274 0.886215i \(-0.346675\pi\)
0.953198 0.302346i \(-0.0977698\pi\)
\(398\) 0 0
\(399\) 0.701578 + 21.2560i 0.0351228 + 1.06413i
\(400\) 0 0
\(401\) −4.62124 5.50738i −0.230774 0.275025i 0.638214 0.769859i \(-0.279673\pi\)
−0.868988 + 0.494834i \(0.835229\pi\)
\(402\) 0 0
\(403\) 14.4015 + 2.53937i 0.717388 + 0.126495i
\(404\) 0 0
\(405\) 0.290618 0.105776i 0.0144409 0.00525606i
\(406\) 0 0
\(407\) 1.13520 + 1.96623i 0.0562700 + 0.0974625i
\(408\) 0 0
\(409\) 1.20702 1.43847i 0.0596834 0.0711279i −0.735377 0.677658i \(-0.762995\pi\)
0.795060 + 0.606531i \(0.207439\pi\)
\(410\) 0 0
\(411\) 3.94290 6.82930i 0.194489 0.336864i
\(412\) 0 0
\(413\) −17.5959 + 3.10263i −0.865837 + 0.152670i
\(414\) 0 0
\(415\) 1.20135 3.30069i 0.0589722 0.162025i
\(416\) 0 0
\(417\) 6.14351i 0.300849i
\(418\) 0 0
\(419\) 39.3106i 1.92045i −0.279226 0.960225i \(-0.590078\pi\)
0.279226 0.960225i \(-0.409922\pi\)
\(420\) 0 0
\(421\) −4.70770 + 12.9343i −0.229439 + 0.630379i −0.999975 0.00701724i \(-0.997766\pi\)
0.770536 + 0.637396i \(0.219989\pi\)
\(422\) 0 0
\(423\) −8.77078 + 1.54653i −0.426450 + 0.0751946i
\(424\) 0 0
\(425\) −11.4373 + 19.8100i −0.554790 + 0.960924i
\(426\) 0 0
\(427\) 0.279729 0.333368i 0.0135370 0.0161328i
\(428\) 0 0
\(429\) 4.22785 + 7.32285i 0.204122 + 0.353550i
\(430\) 0 0
\(431\) −17.7538 + 6.46186i −0.855171 + 0.311257i −0.732147 0.681147i \(-0.761482\pi\)
−0.123024 + 0.992404i \(0.539259\pi\)
\(432\) 0 0
\(433\) −28.8391 5.08511i −1.38592 0.244375i −0.569574 0.821940i \(-0.692892\pi\)
−0.816345 + 0.577565i \(0.804003\pi\)
\(434\) 0 0
\(435\) 1.70647 + 2.03369i 0.0818189 + 0.0975080i
\(436\) 0 0
\(437\) 22.8279 + 25.4507i 1.09201 + 1.21747i
\(438\) 0 0
\(439\) −8.42847 + 7.07233i −0.402269 + 0.337544i −0.821370 0.570396i \(-0.806790\pi\)
0.419101 + 0.907940i \(0.362345\pi\)
\(440\) 0 0
\(441\) −2.91829 + 16.5505i −0.138966 + 0.788118i
\(442\) 0 0
\(443\) −1.70401 4.68173i −0.0809600 0.222436i 0.892608 0.450834i \(-0.148873\pi\)
−0.973568 + 0.228398i \(0.926651\pi\)
\(444\) 0 0
\(445\) 3.36306 1.94167i 0.159425 0.0920438i
\(446\) 0 0
\(447\) 8.39890 + 7.04751i 0.397254 + 0.333336i
\(448\) 0 0
\(449\) 24.3367 + 14.0508i 1.14852 + 0.663099i 0.948527 0.316697i \(-0.102574\pi\)
0.199995 + 0.979797i \(0.435907\pi\)
\(450\) 0 0
\(451\) −3.61072 20.4774i −0.170022 0.964245i
\(452\) 0 0
\(453\) 1.56014 + 0.567844i 0.0733017 + 0.0266797i
\(454\) 0 0
\(455\) −6.60398 −0.309599
\(456\) 0 0
\(457\) 19.8941 0.930607 0.465304 0.885151i \(-0.345945\pi\)
0.465304 + 0.885151i \(0.345945\pi\)
\(458\) 0 0
\(459\) 4.38286 + 1.59523i 0.204574 + 0.0744589i
\(460\) 0 0
\(461\) 1.56088 + 8.85219i 0.0726974 + 0.412287i 0.999339 + 0.0363424i \(0.0115707\pi\)
−0.926642 + 0.375945i \(0.877318\pi\)
\(462\) 0 0
\(463\) −5.60293 3.23485i −0.260390 0.150336i 0.364122 0.931351i \(-0.381369\pi\)
−0.624513 + 0.781015i \(0.714702\pi\)
\(464\) 0 0
\(465\) 0.791621 + 0.664249i 0.0367105 + 0.0308038i
\(466\) 0 0
\(467\) −2.56688 + 1.48199i −0.118781 + 0.0685781i −0.558213 0.829697i \(-0.688513\pi\)
0.439432 + 0.898276i \(0.355180\pi\)
\(468\) 0 0
\(469\) 7.63046 + 20.9645i 0.352342 + 0.968051i
\(470\) 0 0
\(471\) 2.28210 12.9424i 0.105154 0.596356i
\(472\) 0 0
\(473\) 3.97058 3.33171i 0.182567 0.153192i
\(474\) 0 0
\(475\) 20.3186 + 6.64491i 0.932282 + 0.304889i
\(476\) 0 0
\(477\) 7.43656 + 8.86255i 0.340497 + 0.405788i
\(478\) 0 0
\(479\) −23.4427 4.13358i −1.07112 0.188868i −0.389837 0.920884i \(-0.627469\pi\)
−0.681288 + 0.732016i \(0.738580\pi\)
\(480\) 0 0
\(481\) 4.83277 1.75898i 0.220355 0.0802028i
\(482\) 0 0
\(483\) 19.1344 + 33.1417i 0.870643 + 1.50800i
\(484\) 0 0
\(485\) −3.09271 + 3.68574i −0.140433 + 0.167361i
\(486\) 0 0
\(487\) 1.96250 3.39914i 0.0889292 0.154030i −0.818130 0.575034i \(-0.804989\pi\)
0.907059 + 0.421004i \(0.138322\pi\)
\(488\) 0 0
\(489\) 8.57215 1.51150i 0.387646 0.0683525i
\(490\) 0 0
\(491\) 12.0457 33.0952i 0.543613 1.49356i −0.298578 0.954385i \(-0.596512\pi\)
0.842191 0.539179i \(-0.181265\pi\)
\(492\) 0 0
\(493\) 40.0374i 1.80319i
\(494\) 0 0
\(495\) 0.597528i 0.0268569i
\(496\) 0 0
\(497\) 23.4316 64.3778i 1.05105 2.88774i
\(498\) 0 0
\(499\) 42.8558 7.55664i 1.91849 0.338281i 0.919937 0.392066i \(-0.128240\pi\)
0.998553 + 0.0537847i \(0.0171285\pi\)
\(500\) 0 0
\(501\) 6.54995 11.3448i 0.292630 0.506850i
\(502\) 0 0
\(503\) −17.5162 + 20.8750i −0.781008 + 0.930769i −0.998979 0.0451861i \(-0.985612\pi\)
0.217970 + 0.975955i \(0.430056\pi\)
\(504\) 0 0
\(505\) 0.283782 + 0.491525i 0.0126281 + 0.0218726i
\(506\) 0 0
\(507\) 5.78271 2.10474i 0.256819 0.0934746i
\(508\) 0 0
\(509\) 29.8085 + 5.25604i 1.32124 + 0.232970i 0.789401 0.613877i \(-0.210391\pi\)
0.531836 + 0.846847i \(0.321502\pi\)
\(510\) 0 0
\(511\) 36.9197 + 43.9992i 1.63323 + 1.94641i
\(512\) 0 0
\(513\) 0.614895 4.31531i 0.0271483 0.190526i
\(514\) 0 0
\(515\) 2.28575 1.91797i 0.100722 0.0845159i
\(516\) 0 0
\(517\) 2.98799 16.9457i 0.131411 0.745272i
\(518\) 0 0
\(519\) 2.34767 + 6.45016i 0.103051 + 0.283131i
\(520\) 0 0
\(521\) −32.1911 + 18.5856i −1.41032 + 0.814248i −0.995418 0.0956187i \(-0.969517\pi\)
−0.414901 + 0.909867i \(0.636184\pi\)
\(522\) 0 0
\(523\) −2.31904 1.94591i −0.101405 0.0850886i 0.590676 0.806909i \(-0.298861\pi\)
−0.692080 + 0.721820i \(0.743306\pi\)
\(524\) 0 0
\(525\) 20.7230 + 11.9645i 0.904428 + 0.522172i
\(526\) 0 0
\(527\) 2.70625 + 15.3479i 0.117886 + 0.668566i
\(528\) 0 0
\(529\) 36.1955 + 13.1741i 1.57372 + 0.572786i
\(530\) 0 0
\(531\) 3.66200 0.158917
\(532\) 0 0
\(533\) −47.1010 −2.04017
\(534\) 0 0
\(535\) 3.22723 + 1.17462i 0.139525 + 0.0507831i
\(536\) 0 0
\(537\) 0.0176221 + 0.0999401i 0.000760451 + 0.00431273i
\(538\) 0 0
\(539\) −28.1197 16.2349i −1.21120 0.699288i
\(540\) 0 0
\(541\) 7.33536 + 6.15510i 0.315372 + 0.264628i 0.786708 0.617325i \(-0.211784\pi\)
−0.471336 + 0.881954i \(0.656228\pi\)
\(542\) 0 0
\(543\) −15.8185 + 9.13281i −0.678837 + 0.391926i
\(544\) 0 0
\(545\) −1.08639 2.98482i −0.0465357 0.127856i
\(546\) 0 0
\(547\) 0.835008 4.73557i 0.0357024 0.202478i −0.961739 0.273967i \(-0.911664\pi\)
0.997441 + 0.0714891i \(0.0227751\pi\)
\(548\) 0 0
\(549\) −0.0683255 + 0.0573319i −0.00291606 + 0.00244687i
\(550\) 0 0
\(551\) 36.6143 7.70946i 1.55982 0.328434i
\(552\) 0 0
\(553\) 15.2497 + 18.1739i 0.648483 + 0.772831i
\(554\) 0 0
\(555\) 0.357907 + 0.0631087i 0.0151923 + 0.00267881i
\(556\) 0 0
\(557\) −14.1305 + 5.14308i −0.598728 + 0.217919i −0.623564 0.781772i \(-0.714316\pi\)
0.0248360 + 0.999692i \(0.492094\pi\)
\(558\) 0 0
\(559\) −5.87051 10.1680i −0.248296 0.430062i
\(560\) 0 0
\(561\) −5.79242 + 6.90314i −0.244556 + 0.291451i
\(562\) 0 0
\(563\) −0.563769 + 0.976476i −0.0237600 + 0.0411536i −0.877661 0.479282i \(-0.840897\pi\)
0.853901 + 0.520436i \(0.174230\pi\)
\(564\) 0 0
\(565\) −1.52342 + 0.268620i −0.0640906 + 0.0113009i
\(566\) 0 0
\(567\) 1.66876 4.58487i 0.0700812 0.192546i
\(568\) 0 0
\(569\) 8.03677i 0.336919i 0.985709 + 0.168460i \(0.0538792\pi\)
−0.985709 + 0.168460i \(0.946121\pi\)
\(570\) 0 0
\(571\) 8.88393i 0.371781i 0.982570 + 0.185890i \(0.0595169\pi\)
−0.982570 + 0.185890i \(0.940483\pi\)
\(572\) 0 0
\(573\) 1.45346 3.99334i 0.0607190 0.166824i
\(574\) 0 0
\(575\) 37.8822 6.67966i 1.57980 0.278561i
\(576\) 0 0
\(577\) −10.0755 + 17.4513i −0.419450 + 0.726508i −0.995884 0.0906351i \(-0.971110\pi\)
0.576434 + 0.817143i \(0.304444\pi\)
\(578\) 0 0
\(579\) 0.909335 1.08370i 0.0377907 0.0450372i
\(580\) 0 0
\(581\) −27.7073 47.9905i −1.14949 1.99098i
\(582\) 0 0
\(583\) −21.0045 + 7.64501i −0.869917 + 0.316624i
\(584\) 0 0
\(585\) 1.33296 + 0.235036i 0.0551109 + 0.00971754i
\(586\) 0 0
\(587\) 14.9114 + 17.7707i 0.615458 + 0.733474i 0.980282 0.197602i \(-0.0633155\pi\)
−0.364825 + 0.931076i \(0.618871\pi\)
\(588\) 0 0
\(589\) 13.5146 5.43023i 0.556861 0.223749i
\(590\) 0 0
\(591\) −13.1031 + 10.9948i −0.538989 + 0.452265i
\(592\) 0 0
\(593\) 2.99379 16.9786i 0.122940 0.697229i −0.859570 0.511019i \(-0.829268\pi\)
0.982510 0.186211i \(-0.0596207\pi\)
\(594\) 0 0
\(595\) −2.40714 6.61355i −0.0986829 0.271129i
\(596\) 0 0
\(597\) −20.7841 + 11.9997i −0.850636 + 0.491115i
\(598\) 0 0
\(599\) −23.4281 19.6585i −0.957246 0.803225i 0.0232565 0.999730i \(-0.492597\pi\)
−0.980503 + 0.196504i \(0.937041\pi\)
\(600\) 0 0
\(601\) 26.6795 + 15.4034i 1.08828 + 0.628318i 0.933118 0.359571i \(-0.117077\pi\)
0.155161 + 0.987889i \(0.450410\pi\)
\(602\) 0 0
\(603\) −0.794013 4.50307i −0.0323347 0.183379i
\(604\) 0 0
\(605\) 2.11196 + 0.768689i 0.0858632 + 0.0312517i
\(606\) 0 0
\(607\) −26.8497 −1.08979 −0.544897 0.838503i \(-0.683431\pi\)
−0.544897 + 0.838503i \(0.683431\pi\)
\(608\) 0 0
\(609\) 41.8828 1.69718
\(610\) 0 0
\(611\) −36.6269 13.3311i −1.48177 0.539319i
\(612\) 0 0
\(613\) −4.87921 27.6714i −0.197069 1.11764i −0.909441 0.415833i \(-0.863490\pi\)
0.712372 0.701802i \(-0.247621\pi\)
\(614\) 0 0
\(615\) −2.88250 1.66421i −0.116234 0.0671075i
\(616\) 0 0
\(617\) −4.01928 3.37258i −0.161810 0.135775i 0.558287 0.829648i \(-0.311459\pi\)
−0.720098 + 0.693873i \(0.755903\pi\)
\(618\) 0 0
\(619\) −24.7817 + 14.3077i −0.996062 + 0.575077i −0.907081 0.420956i \(-0.861695\pi\)
−0.0889816 + 0.996033i \(0.528361\pi\)
\(620\) 0 0
\(621\) −2.68259 7.37035i −0.107649 0.295762i
\(622\) 0 0
\(623\) 10.6385 60.3338i 0.426222 2.41722i
\(624\) 0 0
\(625\) 18.0591 15.1534i 0.722363 0.606134i
\(626\) 0 0
\(627\) 7.42832 + 3.96795i 0.296659 + 0.158465i
\(628\) 0 0
\(629\) 3.52307 + 4.19863i 0.140474 + 0.167410i
\(630\) 0 0
\(631\) −2.25046 0.396817i −0.0895893 0.0157970i 0.128674 0.991687i \(-0.458928\pi\)
−0.218263 + 0.975890i \(0.570039\pi\)
\(632\) 0 0
\(633\) −5.84977 + 2.12914i −0.232508 + 0.0846258i
\(634\) 0 0
\(635\) 0.952668 + 1.65007i 0.0378055 + 0.0654810i
\(636\) 0 0
\(637\) −47.2775 + 56.3431i −1.87320 + 2.23239i
\(638\) 0 0
\(639\) −7.02068 + 12.1602i −0.277734 + 0.481049i
\(640\) 0 0
\(641\) −19.3186 + 3.40639i −0.763039 + 0.134544i −0.541607 0.840632i \(-0.682184\pi\)
−0.221432 + 0.975176i \(0.571073\pi\)
\(642\) 0 0
\(643\) −12.4853 + 34.3032i −0.492374 + 1.35279i 0.406128 + 0.913816i \(0.366879\pi\)
−0.898502 + 0.438970i \(0.855344\pi\)
\(644\) 0 0
\(645\) 0.829687i 0.0326689i
\(646\) 0 0
\(647\) 33.1703i 1.30406i −0.758193 0.652030i \(-0.773918\pi\)
0.758193 0.652030i \(-0.226082\pi\)
\(648\) 0 0
\(649\) −2.41987 + 6.64853i −0.0949882 + 0.260978i
\(650\) 0 0
\(651\) 16.0554 2.83099i 0.629259 0.110955i
\(652\) 0 0
\(653\) −11.3118 + 19.5927i −0.442666 + 0.766720i −0.997886 0.0649835i \(-0.979301\pi\)
0.555220 + 0.831703i \(0.312634\pi\)
\(654\) 0 0
\(655\) 2.13182 2.54061i 0.0832972 0.0992697i
\(656\) 0 0
\(657\) −5.88599 10.1948i −0.229634 0.397738i
\(658\) 0 0
\(659\) −39.1922 + 14.2648i −1.52671 + 0.555678i −0.962814 0.270166i \(-0.912922\pi\)
−0.563899 + 0.825844i \(0.690699\pi\)
\(660\) 0 0
\(661\) −23.4769 4.13960i −0.913144 0.161012i −0.302713 0.953082i \(-0.597892\pi\)
−0.610431 + 0.792070i \(0.709004\pi\)
\(662\) 0 0
\(663\) 13.1210 + 15.6370i 0.509577 + 0.607290i
\(664\) 0 0
\(665\) −5.58461 + 3.47482i −0.216562 + 0.134748i
\(666\) 0 0
\(667\) 51.5764 43.2777i 1.99705 1.67572i
\(668\) 0 0
\(669\) −1.85361 + 10.5124i −0.0716648 + 0.406431i
\(670\) 0 0
\(671\) −0.0589389 0.161933i −0.00227531 0.00625137i
\(672\) 0 0
\(673\) 31.3177 18.0813i 1.20721 0.696982i 0.245059 0.969508i \(-0.421193\pi\)
0.962148 + 0.272527i \(0.0878593\pi\)
\(674\) 0 0
\(675\) −3.75695 3.15246i −0.144605 0.121338i
\(676\) 0 0
\(677\) −13.1741 7.60605i −0.506320 0.292324i 0.225000 0.974359i \(-0.427762\pi\)
−0.731320 + 0.682035i \(0.761095\pi\)
\(678\) 0 0
\(679\) 13.1809 + 74.7528i 0.505838 + 2.86875i
\(680\) 0 0
\(681\) 5.65832 + 2.05946i 0.216827 + 0.0789186i
\(682\) 0 0
\(683\) −0.959626 −0.0367191 −0.0183595 0.999831i \(-0.505844\pi\)
−0.0183595 + 0.999831i \(0.505844\pi\)
\(684\) 0 0
\(685\) 2.43883 0.0931830
\(686\) 0 0
\(687\) −0.954261 0.347323i −0.0364073 0.0132512i
\(688\) 0 0
\(689\) 8.79230 + 49.8636i 0.334960 + 1.89965i
\(690\) 0 0
\(691\) 0.625152 + 0.360932i 0.0237819 + 0.0137305i 0.511844 0.859079i \(-0.328963\pi\)
−0.488062 + 0.872809i \(0.662296\pi\)
\(692\) 0 0
\(693\) 7.22132 + 6.05941i 0.274315 + 0.230178i
\(694\) 0 0
\(695\) 1.64545 0.949998i 0.0624153 0.0360355i
\(696\) 0 0
\(697\) −17.1682 47.1693i −0.650293 1.78667i
\(698\) 0 0
\(699\) 0.117889 0.668580i 0.00445896 0.0252880i
\(700\) 0 0
\(701\) 6.66025 5.58862i 0.251554 0.211079i −0.508287 0.861188i \(-0.669721\pi\)
0.759841 + 0.650109i \(0.225277\pi\)
\(702\) 0 0
\(703\) 3.16127 4.03033i 0.119230 0.152007i
\(704\) 0 0
\(705\) −1.77048 2.10997i −0.0666801 0.0794662i
\(706\) 0 0
\(707\) 8.81802 + 1.55485i 0.331636 + 0.0584763i
\(708\) 0 0
\(709\) −21.7859 + 7.92940i −0.818185 + 0.297795i −0.717001 0.697073i \(-0.754486\pi\)
−0.101185 + 0.994868i \(0.532263\pi\)
\(710\) 0 0
\(711\) −2.43121 4.21098i −0.0911774 0.157924i
\(712\) 0 0
\(713\) 16.8460 20.0763i 0.630888 0.751863i
\(714\) 0 0
\(715\) −1.30754 + 2.26473i −0.0488993 + 0.0846961i
\(716\) 0 0
\(717\) −22.9156 + 4.04064i −0.855800 + 0.150901i
\(718\) 0 0
\(719\) −0.209863 + 0.576593i −0.00782656 + 0.0215033i −0.943544 0.331246i \(-0.892531\pi\)
0.935718 + 0.352749i \(0.114753\pi\)
\(720\) 0 0
\(721\) 47.0738i 1.75312i
\(722\) 0 0
\(723\) 9.03912i 0.336169i
\(724\) 0 0
\(725\) 14.3988 39.5605i 0.534760 1.46924i
\(726\) 0 0
\(727\) 11.7510 2.07202i 0.435821 0.0768470i 0.0485666 0.998820i \(-0.484535\pi\)
0.387254 + 0.921973i \(0.373424\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) 8.04298 9.58525i 0.297480 0.354523i
\(732\) 0 0
\(733\) −7.25030 12.5579i −0.267796 0.463836i 0.700496 0.713656i \(-0.252962\pi\)
−0.968292 + 0.249820i \(0.919629\pi\)
\(734\) 0 0
\(735\) −4.88406 + 1.77765i −0.180151 + 0.0655697i
\(736\) 0 0
\(737\) 8.70023 + 1.53408i 0.320477 + 0.0565087i
\(738\) 0 0
\(739\) 13.4373 + 16.0140i 0.494300 + 0.589084i 0.954306 0.298832i \(-0.0965970\pi\)
−0.460005 + 0.887916i \(0.652153\pi\)
\(740\) 0 0
\(741\) 11.7736 15.0102i 0.432512 0.551414i
\(742\) 0 0
\(743\) 21.1026 17.7072i 0.774179 0.649613i −0.167597 0.985856i \(-0.553601\pi\)
0.941775 + 0.336242i \(0.109156\pi\)
\(744\) 0 0
\(745\) −0.588810 + 3.33931i −0.0215723 + 0.122343i
\(746\) 0 0
\(747\) 3.88450 + 10.6726i 0.142126 + 0.390489i
\(748\) 0 0
\(749\) 46.9224 27.0906i 1.71451 0.989870i
\(750\) 0 0
\(751\) 8.44207 + 7.08374i 0.308055 + 0.258489i 0.783688 0.621155i \(-0.213336\pi\)
−0.475632 + 0.879644i \(0.657781\pi\)
\(752\) 0 0
\(753\) −20.3961 11.7757i −0.743276 0.429130i
\(754\) 0 0
\(755\) 0.0891629 + 0.505668i 0.00324497 + 0.0184031i
\(756\) 0 0
\(757\) 4.41383 + 1.60650i 0.160423 + 0.0583893i 0.420983 0.907068i \(-0.361685\pi\)
−0.260560 + 0.965458i \(0.583907\pi\)
\(758\) 0 0
\(759\) 15.1539 0.550051
\(760\) 0 0
\(761\) −17.2111 −0.623903 −0.311951 0.950098i \(-0.600983\pi\)
−0.311951 + 0.950098i \(0.600983\pi\)
\(762\) 0 0
\(763\) −47.0895 17.1392i −1.70475 0.620479i
\(764\) 0 0
\(765\) 0.250483 + 1.42056i 0.00905622 + 0.0513604i
\(766\) 0 0
\(767\) 13.8796 + 8.01339i 0.501163 + 0.289347i
\(768\) 0 0
\(769\) −33.4711 28.0856i −1.20700 1.01279i −0.999402 0.0345770i \(-0.988992\pi\)
−0.207596 0.978215i \(-0.566564\pi\)
\(770\) 0 0
\(771\) 10.1346 5.85119i 0.364987 0.210725i
\(772\) 0 0
\(773\) 3.71914 + 10.2183i 0.133768 + 0.367525i 0.988434 0.151654i \(-0.0484599\pi\)
−0.854665 + 0.519179i \(0.826238\pi\)
\(774\) 0 0
\(775\) 2.84563 16.1384i 0.102218 0.579708i
\(776\) 0 0
\(777\) 4.39215 3.68546i 0.157568 0.132215i
\(778\) 0 0
\(779\) −39.8307 + 24.7832i −1.42708 + 0.887950i
\(780\) 0 0
\(781\) −17.4381 20.7819i −0.623983 0.743634i
\(782\) 0 0
\(783\) −8.45368 1.49061i −0.302110 0.0532701i
\(784\) 0 0
\(785\) 3.81933 1.39012i 0.136318 0.0496156i
\(786\) 0 0
\(787\) 16.3719 + 28.3569i 0.583594 + 1.01082i 0.995049 + 0.0993850i \(0.0316875\pi\)
−0.411455 + 0.911430i \(0.634979\pi\)
\(788\) 0 0
\(789\) −4.44846 + 5.30147i −0.158369 + 0.188737i
\(790\) 0 0
\(791\) −12.2023 + 21.1350i −0.433864 + 0.751475i
\(792\) 0 0
\(793\) −0.384422 + 0.0677840i −0.0136512 + 0.00240708i
\(794\) 0 0
\(795\) −1.22375 + 3.36222i −0.0434019 + 0.119246i
\(796\) 0 0
\(797\) 29.9518i 1.06095i 0.847701 + 0.530474i \(0.177986\pi\)
−0.847701 + 0.530474i \(0.822014\pi\)
\(798\) 0 0
\(799\) 41.5392i 1.46955i
\(800\) 0 0
\(801\) −4.29457 + 11.7992i −0.151741 + 0.416906i
\(802\) 0 0
\(803\) 22.3987 3.94949i 0.790433 0.139375i
\(804\) 0 0
\(805\) −5.91766 + 10.2497i −0.208570 + 0.361254i
\(806\) 0 0
\(807\) 0.0864749 0.103057i 0.00304406 0.00362777i
\(808\) 0 0
\(809\) 6.12900 + 10.6157i 0.215484 + 0.373230i 0.953422 0.301639i \(-0.0975337\pi\)
−0.737938 + 0.674868i \(0.764200\pi\)
\(810\) 0 0
\(811\) 17.4324 6.34486i 0.612133 0.222798i −0.0173033 0.999850i \(-0.505508\pi\)
0.629436 + 0.777052i \(0.283286\pi\)
\(812\) 0 0
\(813\) −11.0397 1.94659i −0.387178 0.0682699i
\(814\) 0 0
\(815\) 1.73038 + 2.06219i 0.0606127 + 0.0722353i
\(816\) 0 0
\(817\) −10.3145 5.50963i −0.360858 0.192758i
\(818\) 0 0
\(819\) 16.3577 13.7258i 0.571585 0.479617i
\(820\) 0 0
\(821\) −5.28063 + 29.9479i −0.184295 + 1.04519i 0.742562 + 0.669777i \(0.233610\pi\)
−0.926857 + 0.375413i \(0.877501\pi\)
\(822\) 0 0
\(823\) −1.26735 3.48202i −0.0441770 0.121375i 0.915642 0.401994i \(-0.131683\pi\)
−0.959819 + 0.280618i \(0.909460\pi\)
\(824\) 0 0
\(825\) 8.20605 4.73776i 0.285698 0.164948i
\(826\) 0 0
\(827\) 10.7645 + 9.03246i 0.374317 + 0.314089i 0.810467 0.585785i \(-0.199214\pi\)
−0.436149 + 0.899874i \(0.643658\pi\)
\(828\) 0 0
\(829\) 12.3753 + 7.14490i 0.429813 + 0.248153i 0.699267 0.714861i \(-0.253510\pi\)
−0.269454 + 0.963013i \(0.586843\pi\)
\(830\) 0 0
\(831\) 4.75697 + 26.9781i 0.165018 + 0.935861i
\(832\) 0 0
\(833\) −73.6573 26.8091i −2.55208 0.928879i
\(834\) 0 0
\(835\) 4.05139 0.140204
\(836\) 0 0
\(837\) −3.34139 −0.115495
\(838\) 0 0
\(839\) −32.4254 11.8019i −1.11945 0.407447i −0.284999 0.958528i \(-0.591993\pi\)
−0.834452 + 0.551081i \(0.814215\pi\)
\(840\) 0 0
\(841\) −7.75975 44.0077i −0.267578 1.51751i
\(842\) 0 0
\(843\) 3.35377 + 1.93630i 0.115510 + 0.0666897i
\(844\) 0 0
\(845\) 1.45793 + 1.22335i 0.0501543 + 0.0420844i
\(846\) 0 0
\(847\) 30.7068 17.7286i 1.05510 0.609161i
\(848\) 0 0
\(849\) −7.85863 21.5914i −0.269707 0.741015i
\(850\) 0 0
\(851\) 1.60050 9.07687i 0.0548644 0.311151i
\(852\) 0 0
\(853\) −20.3538 + 17.0789i −0.696902 + 0.584770i −0.920890 0.389821i \(-0.872537\pi\)
0.223988 + 0.974592i \(0.428092\pi\)
\(854\) 0 0
\(855\) 1.25087 0.502605i 0.0427790 0.0171887i
\(856\) 0 0
\(857\) 11.2820 + 13.4453i 0.385384 + 0.459283i 0.923506 0.383584i \(-0.125310\pi\)
−0.538122 + 0.842867i \(0.680866\pi\)
\(858\) 0 0
\(859\) −8.34593 1.47161i −0.284759 0.0502107i 0.0294441 0.999566i \(-0.490626\pi\)
−0.314203 + 0.949356i \(0.601737\pi\)
\(860\) 0 0
\(861\) −49.3435 + 17.9596i −1.68162 + 0.612060i
\(862\) 0 0
\(863\) −3.29230 5.70244i −0.112071 0.194113i 0.804534 0.593907i \(-0.202415\pi\)
−0.916605 + 0.399793i \(0.869082\pi\)
\(864\) 0 0
\(865\) −1.36455 + 1.62620i −0.0463960 + 0.0552926i
\(866\) 0 0
\(867\) −2.37709 + 4.11723i −0.0807301 + 0.139829i
\(868\) 0 0
\(869\) 9.25178 1.63134i 0.313845 0.0553394i
\(870\) 0 0
\(871\) 6.84443 18.8049i 0.231915 0.637180i
\(872\) 0 0
\(873\) 15.5573i 0.526536i
\(874\) 0 0
\(875\) 14.9453i 0.505242i
\(876\) 0 0
\(877\) −14.1004 + 38.7406i −0.476138 + 1.30818i 0.436609 + 0.899651i \(0.356179\pi\)
−0.912747 + 0.408526i \(0.866043\pi\)
\(878\) 0 0
\(879\) 8.38714 1.47888i 0.282891 0.0498814i
\(880\) 0 0
\(881\) 19.8429 34.3689i 0.668525 1.15792i −0.309792 0.950804i \(-0.600259\pi\)
0.978317 0.207114i \(-0.0664072\pi\)
\(882\) 0 0
\(883\) 1.92126 2.28967i 0.0646557 0.0770536i −0.732747 0.680501i \(-0.761762\pi\)
0.797403 + 0.603447i \(0.206207\pi\)
\(884\) 0 0
\(885\) 0.566272 + 0.980811i 0.0190350 + 0.0329696i
\(886\) 0 0
\(887\) 15.6929 5.71174i 0.526915 0.191781i −0.0648453 0.997895i \(-0.520655\pi\)
0.591760 + 0.806114i \(0.298433\pi\)
\(888\) 0 0
\(889\) 29.6025 + 5.21971i 0.992835 + 0.175064i
\(890\) 0 0
\(891\) −1.24191 1.48005i −0.0416055 0.0495834i
\(892\) 0 0
\(893\) −37.9878 + 7.99865i −1.27121 + 0.267664i
\(894\) 0 0
\(895\) −0.0240424 + 0.0201740i −0.000803650 + 0.000674342i
\(896\) 0 0
\(897\) 5.96075 33.8051i 0.199024 1.12872i
\(898\) 0 0
\(899\) −9.81009 26.9530i −0.327185 0.898933i
\(900\) 0 0
\(901\) −46.7311 + 26.9802i −1.55684 + 0.898842i
\(902\) 0 0
\(903\) −10.0271 8.41370i −0.333679 0.279990i
\(904\) 0 0
\(905\) −4.89217 2.82450i −0.162621 0.0938894i
\(906\) 0 0
\(907\) −6.35444 36.0378i −0.210996 1.19662i −0.887722 0.460380i \(-0.847713\pi\)
0.676726 0.736235i \(-0.263398\pi\)
\(908\) 0 0
\(909\) −1.72450 0.627668i −0.0571982 0.0208184i
\(910\) 0 0
\(911\) −39.5093 −1.30900 −0.654500 0.756062i \(-0.727121\pi\)
−0.654500 + 0.756062i \(0.727121\pi\)
\(912\) 0 0
\(913\) −21.9434 −0.726222
\(914\) 0 0
\(915\) −0.0259210 0.00943446i −0.000856921 0.000311894i
\(916\) 0 0
\(917\) −9.08570 51.5276i −0.300036 1.70159i
\(918\) 0 0
\(919\) −10.6452 6.14598i −0.351151 0.202737i 0.314041 0.949409i \(-0.398317\pi\)
−0.665192 + 0.746672i \(0.731650\pi\)
\(920\) 0 0
\(921\) 7.11737 + 5.97218i 0.234525 + 0.196790i
\(922\) 0 0
\(923\) −53.2191 + 30.7261i −1.75173 + 1.01136i
\(924\) 0 0
\(925\) −1.97113 5.41564i −0.0648104 0.178065i
\(926\) 0 0
\(927\) −1.67536 + 9.50144i −0.0550261 + 0.312068i
\(928\) 0 0
\(929\) −14.0512 + 11.7903i −0.461003 + 0.386828i −0.843500 0.537129i \(-0.819509\pi\)
0.382497 + 0.923957i \(0.375064\pi\)
\(930\) 0 0
\(931\) −10.3338 + 72.5222i −0.338677 + 2.37682i
\(932\) 0 0
\(933\) −8.89181 10.5968i −0.291105 0.346925i
\(934\) 0 0
\(935\) −2.74461 0.483949i −0.0897584 0.0158268i
\(936\) 0 0
\(937\) 22.4279 8.16308i 0.732686 0.266676i 0.0513849 0.998679i \(-0.483636\pi\)
0.681302 + 0.732003i \(0.261414\pi\)
\(938\) 0 0
\(939\) −7.52499 13.0337i −0.245569 0.425337i
\(940\) 0 0
\(941\) −8.40953 + 10.0221i −0.274143 + 0.326711i −0.885496 0.464647i \(-0.846181\pi\)
0.611353 + 0.791358i \(0.290626\pi\)
\(942\) 0 0
\(943\) −42.2061 + 73.1031i −1.37442 + 2.38056i
\(944\) 0 0
\(945\) 1.48604 0.262028i 0.0483407 0.00852377i
\(946\) 0 0
\(947\) 1.00032 2.74836i 0.0325061 0.0893098i −0.922378 0.386289i \(-0.873757\pi\)
0.954884 + 0.296979i \(0.0959791\pi\)
\(948\) 0 0
\(949\) 51.5202i 1.67242i
\(950\) 0 0
\(951\) 19.4924i 0.632083i
\(952\) 0 0
\(953\) 12.8554 35.3200i 0.416429 1.14413i −0.537282 0.843403i \(-0.680549\pi\)
0.953711 0.300726i \(-0.0972289\pi\)
\(954\) 0 0
\(955\) 1.29431 0.228222i 0.0418829 0.00738508i
\(956\) 0 0
\(957\) 8.29251 14.3630i 0.268059 0.464291i
\(958\) 0 0
\(959\) 24.7317 29.4741i 0.798629 0.951769i
\(960\) 0 0
\(961\) 9.91756 + 17.1777i 0.319921 + 0.554120i
\(962\) 0 0
\(963\) −10.4350 + 3.79804i −0.336264 + 0.122390i
\(964\) 0 0
\(965\) 0.430868 + 0.0759737i 0.0138701 + 0.00244568i
\(966\) 0 0
\(967\) −28.7153 34.2216i −0.923423 1.10049i −0.994678 0.103035i \(-0.967145\pi\)
0.0712544 0.997458i \(-0.477300\pi\)
\(968\) 0 0
\(969\) 19.3234 + 6.31944i 0.620757 + 0.203010i
\(970\) 0 0
\(971\) 3.13072 2.62699i 0.100470 0.0843040i −0.591169 0.806548i \(-0.701333\pi\)
0.691639 + 0.722244i \(0.256889\pi\)
\(972\) 0 0
\(973\) 5.20509 29.5195i 0.166867 0.946352i
\(974\) 0 0
\(975\) −7.34110 20.1695i −0.235103 0.645941i
\(976\) 0 0
\(977\) 39.2562 22.6646i 1.25592 0.725104i 0.283639 0.958931i \(-0.408458\pi\)
0.972278 + 0.233827i \(0.0751251\pi\)
\(978\) 0 0
\(979\) −18.5842 15.5940i −0.593953 0.498386i
\(980\) 0 0
\(981\) 8.89462 + 5.13531i 0.283983 + 0.163958i
\(982\) 0 0
\(983\) −7.11745 40.3651i −0.227011 1.28745i −0.858802 0.512307i \(-0.828791\pi\)
0.631791 0.775139i \(-0.282320\pi\)
\(984\) 0 0
\(985\) −4.97097 1.80929i −0.158388 0.0576487i
\(986\) 0 0
\(987\) −43.4538 −1.38315
\(988\) 0 0
\(989\) −21.0417 −0.669087
\(990\) 0 0
\(991\) −43.1089 15.6904i −1.36940 0.498421i −0.450452 0.892801i \(-0.648737\pi\)
−0.918948 + 0.394380i \(0.870959\pi\)
\(992\) 0 0
\(993\) −1.95036 11.0611i −0.0618929 0.351012i
\(994\) 0 0
\(995\) −6.42788 3.71114i −0.203777 0.117651i
\(996\) 0 0
\(997\) −7.05855 5.92283i −0.223547 0.187578i 0.524135 0.851635i \(-0.324389\pi\)
−0.747682 + 0.664057i \(0.768833\pi\)
\(998\) 0 0
\(999\) −1.01768 + 0.587560i −0.0321981 + 0.0185896i
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.127.2 yes 18
4.3 odd 2 912.2.ci.e.127.2 yes 18
19.3 odd 18 912.2.ci.e.79.2 18
76.3 even 18 inner 912.2.ci.f.79.2 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
912.2.ci.e.79.2 18 19.3 odd 18
912.2.ci.e.127.2 yes 18 4.3 odd 2
912.2.ci.f.79.2 yes 18 76.3 even 18 inner
912.2.ci.f.127.2 yes 18 1.1 even 1 trivial