Properties

Label 1368.2.g.b.685.11
Level $1368$
Weight $2$
Character 1368.685
Analytic conductor $10.924$
Analytic rank $0$
Dimension $16$
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] = [1368,2,Mod(685,1368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1368.685");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.g (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.9235349965\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 4 x^{12} + 4 x^{11} - 10 x^{10} + 24 x^{9} - 40 x^{8} + 48 x^{7} - 40 x^{6} + 32 x^{5} + 64 x^{4} - 128 x^{3} + 192 x^{2} - 256 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 152)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 685.11
Root \(1.14052 - 0.836196i\) of defining polynomial
Character \(\chi\) \(=\) 1368.685
Dual form 1368.2.g.b.685.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.836196 - 1.14052i) q^{2} +(-0.601554 - 1.90739i) q^{4} -0.594041i q^{5} -3.48756 q^{7} +(-2.67842 - 0.908869i) q^{8} +O(q^{10})\) \(q+(0.836196 - 1.14052i) q^{2} +(-0.601554 - 1.90739i) q^{4} -0.594041i q^{5} -3.48756 q^{7} +(-2.67842 - 0.908869i) q^{8} +(-0.677513 - 0.496734i) q^{10} +4.83520i q^{11} -0.215597i q^{13} +(-2.91629 + 3.97762i) q^{14} +(-3.27627 + 2.29479i) q^{16} -1.29720 q^{17} -1.00000i q^{19} +(-1.13307 + 0.357348i) q^{20} +(5.51462 + 4.04317i) q^{22} -4.52815 q^{23} +4.64712 q^{25} +(-0.245891 - 0.180281i) q^{26} +(2.09796 + 6.65214i) q^{28} +9.41093i q^{29} -1.22031 q^{31} +(-0.122350 + 5.65553i) q^{32} +(-1.08471 + 1.47948i) q^{34} +2.07176i q^{35} +5.62653i q^{37} +(-1.14052 - 0.836196i) q^{38} +(-0.539905 + 1.59109i) q^{40} +0.450021 q^{41} +0.794359i q^{43} +(9.22260 - 2.90863i) q^{44} +(-3.78642 + 5.16442i) q^{46} -12.1986 q^{47} +5.16310 q^{49} +(3.88590 - 5.30011i) q^{50} +(-0.411227 + 0.129693i) q^{52} -2.56409i q^{53} +2.87231 q^{55} +(9.34118 + 3.16974i) q^{56} +(10.7333 + 7.86938i) q^{58} -2.75191i q^{59} -7.76665i q^{61} +(-1.02042 + 1.39178i) q^{62} +(6.34792 + 4.86867i) q^{64} -0.128073 q^{65} +4.11631i q^{67} +(0.780337 + 2.47427i) q^{68} +(2.36287 + 1.73239i) q^{70} +7.82788 q^{71} +3.08931 q^{73} +(6.41714 + 4.70488i) q^{74} +(-1.90739 + 0.601554i) q^{76} -16.8631i q^{77} -10.0731 q^{79} +(1.36320 + 1.94624i) q^{80} +(0.376306 - 0.513256i) q^{82} +11.6296i q^{83} +0.770591i q^{85} +(0.905979 + 0.664240i) q^{86} +(4.39456 - 12.9507i) q^{88} -13.7091 q^{89} +0.751907i q^{91} +(2.72392 + 8.63694i) q^{92} +(-10.2004 + 13.9127i) q^{94} -0.594041 q^{95} +2.08846 q^{97} +(4.31736 - 5.88860i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{4} - 8 q^{7} + 12 q^{8} - 8 q^{10} - 4 q^{14} + 2 q^{16} + 8 q^{17} - 8 q^{20} + 20 q^{22} - 24 q^{25} + 10 q^{26} - 14 q^{28} + 16 q^{31} + 20 q^{32} - 2 q^{38} + 28 q^{40} - 16 q^{41} + 28 q^{44} - 48 q^{46} - 24 q^{47} + 24 q^{49} - 12 q^{50} + 8 q^{52} + 16 q^{55} + 48 q^{56} + 38 q^{58} + 16 q^{62} + 14 q^{64} - 16 q^{65} + 26 q^{68} - 32 q^{70} - 48 q^{71} + 20 q^{74} - 4 q^{76} - 48 q^{79} - 4 q^{80} - 12 q^{82} - 48 q^{86} + 40 q^{88} + 16 q^{89} - 62 q^{92} - 36 q^{94} - 16 q^{95} + 32 q^{97} + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).

\(n\) \(343\) \(685\) \(1009\) \(1217\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.836196 1.14052i 0.591280 0.806467i
\(3\) 0 0
\(4\) −0.601554 1.90739i −0.300777 0.953695i
\(5\) 0.594041i 0.265663i −0.991139 0.132832i \(-0.957593\pi\)
0.991139 0.132832i \(-0.0424069\pi\)
\(6\) 0 0
\(7\) −3.48756 −1.31818 −0.659088 0.752066i \(-0.729057\pi\)
−0.659088 + 0.752066i \(0.729057\pi\)
\(8\) −2.67842 0.908869i −0.946966 0.321334i
\(9\) 0 0
\(10\) −0.677513 0.496734i −0.214248 0.157081i
\(11\) 4.83520i 1.45787i 0.684585 + 0.728933i \(0.259984\pi\)
−0.684585 + 0.728933i \(0.740016\pi\)
\(12\) 0 0
\(13\) 0.215597i 0.0597957i −0.999553 0.0298979i \(-0.990482\pi\)
0.999553 0.0298979i \(-0.00951821\pi\)
\(14\) −2.91629 + 3.97762i −0.779410 + 1.06306i
\(15\) 0 0
\(16\) −3.27627 + 2.29479i −0.819067 + 0.573699i
\(17\) −1.29720 −0.314618 −0.157309 0.987549i \(-0.550282\pi\)
−0.157309 + 0.987549i \(0.550282\pi\)
\(18\) 0 0
\(19\) 1.00000i 0.229416i
\(20\) −1.13307 + 0.357348i −0.253362 + 0.0799053i
\(21\) 0 0
\(22\) 5.51462 + 4.04317i 1.17572 + 0.862007i
\(23\) −4.52815 −0.944184 −0.472092 0.881549i \(-0.656501\pi\)
−0.472092 + 0.881549i \(0.656501\pi\)
\(24\) 0 0
\(25\) 4.64712 0.929423
\(26\) −0.245891 0.180281i −0.0482233 0.0353560i
\(27\) 0 0
\(28\) 2.09796 + 6.65214i 0.396477 + 1.25714i
\(29\) 9.41093i 1.74757i 0.486316 + 0.873783i \(0.338340\pi\)
−0.486316 + 0.873783i \(0.661660\pi\)
\(30\) 0 0
\(31\) −1.22031 −0.219174 −0.109587 0.993977i \(-0.534953\pi\)
−0.109587 + 0.993977i \(0.534953\pi\)
\(32\) −0.122350 + 5.65553i −0.0216286 + 0.999766i
\(33\) 0 0
\(34\) −1.08471 + 1.47948i −0.186027 + 0.253729i
\(35\) 2.07176i 0.350191i
\(36\) 0 0
\(37\) 5.62653i 0.924995i 0.886621 + 0.462498i \(0.153047\pi\)
−0.886621 + 0.462498i \(0.846953\pi\)
\(38\) −1.14052 0.836196i −0.185016 0.135649i
\(39\) 0 0
\(40\) −0.539905 + 1.59109i −0.0853665 + 0.251574i
\(41\) 0.450021 0.0702815 0.0351407 0.999382i \(-0.488812\pi\)
0.0351407 + 0.999382i \(0.488812\pi\)
\(42\) 0 0
\(43\) 0.794359i 0.121139i 0.998164 + 0.0605693i \(0.0192916\pi\)
−0.998164 + 0.0605693i \(0.980708\pi\)
\(44\) 9.22260 2.90863i 1.39036 0.438493i
\(45\) 0 0
\(46\) −3.78642 + 5.16442i −0.558277 + 0.761453i
\(47\) −12.1986 −1.77935 −0.889676 0.456593i \(-0.849070\pi\)
−0.889676 + 0.456593i \(0.849070\pi\)
\(48\) 0 0
\(49\) 5.16310 0.737586
\(50\) 3.88590 5.30011i 0.549549 0.749549i
\(51\) 0 0
\(52\) −0.411227 + 0.129693i −0.0570269 + 0.0179852i
\(53\) 2.56409i 0.352205i −0.984372 0.176103i \(-0.943651\pi\)
0.984372 0.176103i \(-0.0563490\pi\)
\(54\) 0 0
\(55\) 2.87231 0.387302
\(56\) 9.34118 + 3.16974i 1.24827 + 0.423574i
\(57\) 0 0
\(58\) 10.7333 + 7.86938i 1.40935 + 1.03330i
\(59\) 2.75191i 0.358268i −0.983825 0.179134i \(-0.942670\pi\)
0.983825 0.179134i \(-0.0573295\pi\)
\(60\) 0 0
\(61\) 7.76665i 0.994417i −0.867631 0.497209i \(-0.834358\pi\)
0.867631 0.497209i \(-0.165642\pi\)
\(62\) −1.02042 + 1.39178i −0.129593 + 0.176757i
\(63\) 0 0
\(64\) 6.34792 + 4.86867i 0.793489 + 0.608584i
\(65\) −0.128073 −0.0158855
\(66\) 0 0
\(67\) 4.11631i 0.502887i 0.967872 + 0.251443i \(0.0809053\pi\)
−0.967872 + 0.251443i \(0.919095\pi\)
\(68\) 0.780337 + 2.47427i 0.0946297 + 0.300049i
\(69\) 0 0
\(70\) 2.36287 + 1.73239i 0.282417 + 0.207061i
\(71\) 7.82788 0.928999 0.464499 0.885573i \(-0.346234\pi\)
0.464499 + 0.885573i \(0.346234\pi\)
\(72\) 0 0
\(73\) 3.08931 0.361577 0.180788 0.983522i \(-0.442135\pi\)
0.180788 + 0.983522i \(0.442135\pi\)
\(74\) 6.41714 + 4.70488i 0.745978 + 0.546931i
\(75\) 0 0
\(76\) −1.90739 + 0.601554i −0.218793 + 0.0690030i
\(77\) 16.8631i 1.92172i
\(78\) 0 0
\(79\) −10.0731 −1.13331 −0.566654 0.823956i \(-0.691763\pi\)
−0.566654 + 0.823956i \(0.691763\pi\)
\(80\) 1.36320 + 1.94624i 0.152411 + 0.217596i
\(81\) 0 0
\(82\) 0.376306 0.513256i 0.0415560 0.0566797i
\(83\) 11.6296i 1.27651i 0.769825 + 0.638255i \(0.220343\pi\)
−0.769825 + 0.638255i \(0.779657\pi\)
\(84\) 0 0
\(85\) 0.770591i 0.0835823i
\(86\) 0.905979 + 0.664240i 0.0976943 + 0.0716268i
\(87\) 0 0
\(88\) 4.39456 12.9507i 0.468462 1.38055i
\(89\) −13.7091 −1.45317 −0.726583 0.687079i \(-0.758893\pi\)
−0.726583 + 0.687079i \(0.758893\pi\)
\(90\) 0 0
\(91\) 0.751907i 0.0788213i
\(92\) 2.72392 + 8.63694i 0.283989 + 0.900463i
\(93\) 0 0
\(94\) −10.2004 + 13.9127i −1.05209 + 1.43499i
\(95\) −0.594041 −0.0609473
\(96\) 0 0
\(97\) 2.08846 0.212051 0.106026 0.994363i \(-0.466187\pi\)
0.106026 + 0.994363i \(0.466187\pi\)
\(98\) 4.31736 5.88860i 0.436120 0.594839i
\(99\) 0 0
\(100\) −2.79549 8.86386i −0.279549 0.886386i
\(101\) 2.77074i 0.275699i −0.990453 0.137849i \(-0.955981\pi\)
0.990453 0.137849i \(-0.0440190\pi\)
\(102\) 0 0
\(103\) −14.3363 −1.41260 −0.706301 0.707912i \(-0.749637\pi\)
−0.706301 + 0.707912i \(0.749637\pi\)
\(104\) −0.195949 + 0.577459i −0.0192144 + 0.0566245i
\(105\) 0 0
\(106\) −2.92439 2.14408i −0.284042 0.208252i
\(107\) 2.42388i 0.234325i −0.993113 0.117163i \(-0.962620\pi\)
0.993113 0.117163i \(-0.0373799\pi\)
\(108\) 0 0
\(109\) 0.00123810i 0.000118589i −1.00000 5.92945e-5i \(-0.999981\pi\)
1.00000 5.92945e-5i \(-1.88740e-5\pi\)
\(110\) 2.40181 3.27591i 0.229003 0.312346i
\(111\) 0 0
\(112\) 11.4262 8.00324i 1.07967 0.756235i
\(113\) −1.81614 −0.170848 −0.0854242 0.996345i \(-0.527225\pi\)
−0.0854242 + 0.996345i \(0.527225\pi\)
\(114\) 0 0
\(115\) 2.68990i 0.250835i
\(116\) 17.9503 5.66118i 1.66664 0.525627i
\(117\) 0 0
\(118\) −3.13859 2.30113i −0.288931 0.211836i
\(119\) 4.52407 0.414721
\(120\) 0 0
\(121\) −12.3791 −1.12538
\(122\) −8.85798 6.49444i −0.801964 0.587979i
\(123\) 0 0
\(124\) 0.734083 + 2.32761i 0.0659226 + 0.209025i
\(125\) 5.73078i 0.512577i
\(126\) 0 0
\(127\) −16.1269 −1.43103 −0.715517 0.698596i \(-0.753809\pi\)
−0.715517 + 0.698596i \(0.753809\pi\)
\(128\) 10.8609 3.16874i 0.959977 0.280079i
\(129\) 0 0
\(130\) −0.107094 + 0.146070i −0.00939279 + 0.0128111i
\(131\) 11.1477i 0.973983i 0.873407 + 0.486992i \(0.161906\pi\)
−0.873407 + 0.486992i \(0.838094\pi\)
\(132\) 0 0
\(133\) 3.48756i 0.302410i
\(134\) 4.69471 + 3.44204i 0.405562 + 0.297347i
\(135\) 0 0
\(136\) 3.47446 + 1.17899i 0.297932 + 0.101097i
\(137\) −11.1666 −0.954025 −0.477013 0.878896i \(-0.658280\pi\)
−0.477013 + 0.878896i \(0.658280\pi\)
\(138\) 0 0
\(139\) 13.0534i 1.10718i −0.832790 0.553589i \(-0.813258\pi\)
0.832790 0.553589i \(-0.186742\pi\)
\(140\) 3.95164 1.24627i 0.333975 0.105329i
\(141\) 0 0
\(142\) 6.54564 8.92783i 0.549298 0.749207i
\(143\) 1.04245 0.0871742
\(144\) 0 0
\(145\) 5.59048 0.464264
\(146\) 2.58327 3.52341i 0.213793 0.291600i
\(147\) 0 0
\(148\) 10.7320 3.38466i 0.882163 0.278217i
\(149\) 14.3811i 1.17814i −0.808080 0.589072i \(-0.799493\pi\)
0.808080 0.589072i \(-0.200507\pi\)
\(150\) 0 0
\(151\) 17.3489 1.41184 0.705918 0.708293i \(-0.250535\pi\)
0.705918 + 0.708293i \(0.250535\pi\)
\(152\) −0.908869 + 2.67842i −0.0737190 + 0.217249i
\(153\) 0 0
\(154\) −19.2326 14.1008i −1.54981 1.13628i
\(155\) 0.724915i 0.0582266i
\(156\) 0 0
\(157\) 9.63293i 0.768791i 0.923168 + 0.384396i \(0.125590\pi\)
−0.923168 + 0.384396i \(0.874410\pi\)
\(158\) −8.42306 + 11.4885i −0.670102 + 0.913976i
\(159\) 0 0
\(160\) 3.35962 + 0.0726808i 0.265601 + 0.00574592i
\(161\) 15.7922 1.24460
\(162\) 0 0
\(163\) 22.5365i 1.76520i 0.470129 + 0.882598i \(0.344207\pi\)
−0.470129 + 0.882598i \(0.655793\pi\)
\(164\) −0.270712 0.858365i −0.0211390 0.0670271i
\(165\) 0 0
\(166\) 13.2637 + 9.72458i 1.02946 + 0.754774i
\(167\) −16.5108 −1.27765 −0.638823 0.769353i \(-0.720579\pi\)
−0.638823 + 0.769353i \(0.720579\pi\)
\(168\) 0 0
\(169\) 12.9535 0.996424
\(170\) 0.878871 + 0.644365i 0.0674064 + 0.0494205i
\(171\) 0 0
\(172\) 1.51515 0.477850i 0.115529 0.0364357i
\(173\) 5.14911i 0.391479i 0.980656 + 0.195740i \(0.0627108\pi\)
−0.980656 + 0.195740i \(0.937289\pi\)
\(174\) 0 0
\(175\) −16.2071 −1.22514
\(176\) −11.0958 15.8414i −0.836376 1.19409i
\(177\) 0 0
\(178\) −11.4635 + 15.6355i −0.859227 + 1.17193i
\(179\) 9.31580i 0.696295i −0.937440 0.348148i \(-0.886811\pi\)
0.937440 0.348148i \(-0.113189\pi\)
\(180\) 0 0
\(181\) 5.15517i 0.383180i −0.981475 0.191590i \(-0.938636\pi\)
0.981475 0.191590i \(-0.0613645\pi\)
\(182\) 0.857562 + 0.628741i 0.0635667 + 0.0466054i
\(183\) 0 0
\(184\) 12.1283 + 4.11549i 0.894110 + 0.303398i
\(185\) 3.34239 0.245737
\(186\) 0 0
\(187\) 6.27223i 0.458671i
\(188\) 7.33813 + 23.2675i 0.535188 + 1.69696i
\(189\) 0 0
\(190\) −0.496734 + 0.677513i −0.0360369 + 0.0491520i
\(191\) 14.8805 1.07672 0.538359 0.842715i \(-0.319044\pi\)
0.538359 + 0.842715i \(0.319044\pi\)
\(192\) 0 0
\(193\) −21.2754 −1.53144 −0.765719 0.643175i \(-0.777617\pi\)
−0.765719 + 0.643175i \(0.777617\pi\)
\(194\) 1.74636 2.38193i 0.125382 0.171012i
\(195\) 0 0
\(196\) −3.10588 9.84805i −0.221849 0.703432i
\(197\) 3.69169i 0.263022i 0.991315 + 0.131511i \(0.0419829\pi\)
−0.991315 + 0.131511i \(0.958017\pi\)
\(198\) 0 0
\(199\) 11.6857 0.828377 0.414188 0.910191i \(-0.364065\pi\)
0.414188 + 0.910191i \(0.364065\pi\)
\(200\) −12.4469 4.22362i −0.880132 0.298655i
\(201\) 0 0
\(202\) −3.16007 2.31688i −0.222342 0.163015i
\(203\) 32.8212i 2.30360i
\(204\) 0 0
\(205\) 0.267331i 0.0186712i
\(206\) −11.9880 + 16.3508i −0.835243 + 1.13922i
\(207\) 0 0
\(208\) 0.494750 + 0.706352i 0.0343047 + 0.0489767i
\(209\) 4.83520 0.334458
\(210\) 0 0
\(211\) 7.61611i 0.524315i 0.965025 + 0.262157i \(0.0844340\pi\)
−0.965025 + 0.262157i \(0.915566\pi\)
\(212\) −4.89072 + 1.54244i −0.335896 + 0.105935i
\(213\) 0 0
\(214\) −2.76447 2.02684i −0.188976 0.138552i
\(215\) 0.471882 0.0321821
\(216\) 0 0
\(217\) 4.25591 0.288910
\(218\) −0.00141208 0.00103530i −9.56380e−5 7.01192e-5i
\(219\) 0 0
\(220\) −1.72785 5.47860i −0.116491 0.369367i
\(221\) 0.279672i 0.0188128i
\(222\) 0 0
\(223\) −1.95477 −0.130901 −0.0654505 0.997856i \(-0.520848\pi\)
−0.0654505 + 0.997856i \(0.520848\pi\)
\(224\) 0.426703 19.7240i 0.0285103 1.31787i
\(225\) 0 0
\(226\) −1.51865 + 2.07134i −0.101019 + 0.137784i
\(227\) 13.3709i 0.887461i −0.896160 0.443730i \(-0.853655\pi\)
0.896160 0.443730i \(-0.146345\pi\)
\(228\) 0 0
\(229\) 11.5800i 0.765225i −0.923909 0.382613i \(-0.875024\pi\)
0.923909 0.382613i \(-0.124976\pi\)
\(230\) 3.06788 + 2.24929i 0.202290 + 0.148314i
\(231\) 0 0
\(232\) 8.55330 25.2065i 0.561552 1.65489i
\(233\) −1.58872 −0.104080 −0.0520401 0.998645i \(-0.516572\pi\)
−0.0520401 + 0.998645i \(0.516572\pi\)
\(234\) 0 0
\(235\) 7.24648i 0.472708i
\(236\) −5.24896 + 1.65542i −0.341678 + 0.107759i
\(237\) 0 0
\(238\) 3.78301 5.15978i 0.245216 0.334459i
\(239\) −23.8219 −1.54091 −0.770455 0.637494i \(-0.779971\pi\)
−0.770455 + 0.637494i \(0.779971\pi\)
\(240\) 0 0
\(241\) 22.8554 1.47225 0.736123 0.676848i \(-0.236654\pi\)
0.736123 + 0.676848i \(0.236654\pi\)
\(242\) −10.3514 + 14.1186i −0.665412 + 0.907578i
\(243\) 0 0
\(244\) −14.8140 + 4.67206i −0.948370 + 0.299098i
\(245\) 3.06710i 0.195950i
\(246\) 0 0
\(247\) −0.215597 −0.0137181
\(248\) 3.26851 + 1.10910i 0.207551 + 0.0704281i
\(249\) 0 0
\(250\) −6.53605 4.79205i −0.413376 0.303076i
\(251\) 2.63524i 0.166335i −0.996536 0.0831676i \(-0.973496\pi\)
0.996536 0.0831676i \(-0.0265037\pi\)
\(252\) 0 0
\(253\) 21.8945i 1.37649i
\(254\) −13.4853 + 18.3930i −0.846141 + 1.15408i
\(255\) 0 0
\(256\) 5.46784 15.0367i 0.341740 0.939795i
\(257\) −20.0579 −1.25118 −0.625588 0.780153i \(-0.715141\pi\)
−0.625588 + 0.780153i \(0.715141\pi\)
\(258\) 0 0
\(259\) 19.6229i 1.21931i
\(260\) 0.0770429 + 0.244285i 0.00477800 + 0.0151499i
\(261\) 0 0
\(262\) 12.7142 + 9.32170i 0.785485 + 0.575896i
\(263\) −4.03667 −0.248912 −0.124456 0.992225i \(-0.539718\pi\)
−0.124456 + 0.992225i \(0.539718\pi\)
\(264\) 0 0
\(265\) −1.52318 −0.0935679
\(266\) 3.97762 + 2.91629i 0.243884 + 0.178809i
\(267\) 0 0
\(268\) 7.85140 2.47618i 0.479601 0.151257i
\(269\) 14.3095i 0.872467i 0.899834 + 0.436233i \(0.143688\pi\)
−0.899834 + 0.436233i \(0.856312\pi\)
\(270\) 0 0
\(271\) 9.85034 0.598366 0.299183 0.954196i \(-0.403286\pi\)
0.299183 + 0.954196i \(0.403286\pi\)
\(272\) 4.24998 2.97681i 0.257693 0.180496i
\(273\) 0 0
\(274\) −9.33745 + 12.7357i −0.564096 + 0.769390i
\(275\) 22.4697i 1.35498i
\(276\) 0 0
\(277\) 16.9641i 1.01928i −0.860389 0.509638i \(-0.829779\pi\)
0.860389 0.509638i \(-0.170221\pi\)
\(278\) −14.8877 10.9152i −0.892902 0.654652i
\(279\) 0 0
\(280\) 1.88295 5.54904i 0.112528 0.331619i
\(281\) 10.2078 0.608944 0.304472 0.952521i \(-0.401520\pi\)
0.304472 + 0.952521i \(0.401520\pi\)
\(282\) 0 0
\(283\) 18.7709i 1.11581i −0.829903 0.557907i \(-0.811604\pi\)
0.829903 0.557907i \(-0.188396\pi\)
\(284\) −4.70889 14.9308i −0.279421 0.885981i
\(285\) 0 0
\(286\) 0.871694 1.18893i 0.0515443 0.0703031i
\(287\) −1.56948 −0.0926433
\(288\) 0 0
\(289\) −15.3173 −0.901016
\(290\) 4.67473 6.37603i 0.274510 0.374413i
\(291\) 0 0
\(292\) −1.85839 5.89253i −0.108754 0.344834i
\(293\) 19.8271i 1.15831i −0.815217 0.579155i \(-0.803382\pi\)
0.815217 0.579155i \(-0.196618\pi\)
\(294\) 0 0
\(295\) −1.63475 −0.0951786
\(296\) 5.11377 15.0702i 0.297232 0.875939i
\(297\) 0 0
\(298\) −16.4019 12.0254i −0.950134 0.696613i
\(299\) 0.976253i 0.0564582i
\(300\) 0 0
\(301\) 2.77038i 0.159682i
\(302\) 14.5071 19.7867i 0.834790 1.13860i
\(303\) 0 0
\(304\) 2.29479 + 3.27627i 0.131615 + 0.187907i
\(305\) −4.61371 −0.264180
\(306\) 0 0
\(307\) 18.3935i 1.04977i 0.851173 + 0.524886i \(0.175892\pi\)
−0.851173 + 0.524886i \(0.824108\pi\)
\(308\) −32.1644 + 10.1440i −1.83274 + 0.578010i
\(309\) 0 0
\(310\) 0.826777 + 0.606171i 0.0469578 + 0.0344282i
\(311\) −19.1747 −1.08730 −0.543648 0.839313i \(-0.682957\pi\)
−0.543648 + 0.839313i \(0.682957\pi\)
\(312\) 0 0
\(313\) 14.2274 0.804183 0.402091 0.915600i \(-0.368283\pi\)
0.402091 + 0.915600i \(0.368283\pi\)
\(314\) 10.9865 + 8.05501i 0.620004 + 0.454571i
\(315\) 0 0
\(316\) 6.05949 + 19.2133i 0.340873 + 1.08083i
\(317\) 0.777938i 0.0436934i 0.999761 + 0.0218467i \(0.00695457\pi\)
−0.999761 + 0.0218467i \(0.993045\pi\)
\(318\) 0 0
\(319\) −45.5037 −2.54772
\(320\) 2.89219 3.77092i 0.161678 0.210801i
\(321\) 0 0
\(322\) 13.2054 18.0113i 0.735906 1.00373i
\(323\) 1.29720i 0.0721782i
\(324\) 0 0
\(325\) 1.00190i 0.0555755i
\(326\) 25.7033 + 18.8449i 1.42357 + 1.04372i
\(327\) 0 0
\(328\) −1.20535 0.409010i −0.0665542 0.0225838i
\(329\) 42.5435 2.34550
\(330\) 0 0
\(331\) 16.3988i 0.901359i 0.892686 + 0.450680i \(0.148818\pi\)
−0.892686 + 0.450680i \(0.851182\pi\)
\(332\) 22.1821 6.99580i 1.21740 0.383945i
\(333\) 0 0
\(334\) −13.8063 + 18.8309i −0.755446 + 1.03038i
\(335\) 2.44525 0.133599
\(336\) 0 0
\(337\) 24.6109 1.34064 0.670320 0.742072i \(-0.266157\pi\)
0.670320 + 0.742072i \(0.266157\pi\)
\(338\) 10.8317 14.7737i 0.589165 0.803583i
\(339\) 0 0
\(340\) 1.46982 0.463552i 0.0797120 0.0251396i
\(341\) 5.90045i 0.319527i
\(342\) 0 0
\(343\) 6.40629 0.345907
\(344\) 0.721968 2.12763i 0.0389259 0.114714i
\(345\) 0 0
\(346\) 5.87264 + 4.30566i 0.315715 + 0.231474i
\(347\) 13.4635i 0.722760i 0.932419 + 0.361380i \(0.117694\pi\)
−0.932419 + 0.361380i \(0.882306\pi\)
\(348\) 0 0
\(349\) 2.83422i 0.151712i 0.997119 + 0.0758560i \(0.0241689\pi\)
−0.997119 + 0.0758560i \(0.975831\pi\)
\(350\) −13.5523 + 18.4845i −0.724402 + 0.988037i
\(351\) 0 0
\(352\) −27.3456 0.591585i −1.45753 0.0315316i
\(353\) 5.02227 0.267308 0.133654 0.991028i \(-0.457329\pi\)
0.133654 + 0.991028i \(0.457329\pi\)
\(354\) 0 0
\(355\) 4.65008i 0.246801i
\(356\) 8.24678 + 26.1487i 0.437079 + 1.38588i
\(357\) 0 0
\(358\) −10.6248 7.78983i −0.561539 0.411705i
\(359\) −23.6898 −1.25030 −0.625149 0.780505i \(-0.714962\pi\)
−0.625149 + 0.780505i \(0.714962\pi\)
\(360\) 0 0
\(361\) −1.00000 −0.0526316
\(362\) −5.87955 4.31073i −0.309022 0.226567i
\(363\) 0 0
\(364\) 1.43418 0.452312i 0.0751714 0.0237076i
\(365\) 1.83518i 0.0960577i
\(366\) 0 0
\(367\) −16.9338 −0.883938 −0.441969 0.897030i \(-0.645720\pi\)
−0.441969 + 0.897030i \(0.645720\pi\)
\(368\) 14.8354 10.3912i 0.773349 0.541677i
\(369\) 0 0
\(370\) 2.79489 3.81205i 0.145299 0.198179i
\(371\) 8.94244i 0.464268i
\(372\) 0 0
\(373\) 12.8599i 0.665860i −0.942952 0.332930i \(-0.891963\pi\)
0.942952 0.332930i \(-0.108037\pi\)
\(374\) −7.15357 5.24481i −0.369903 0.271203i
\(375\) 0 0
\(376\) 32.6731 + 11.0869i 1.68499 + 0.571765i
\(377\) 2.02896 0.104497
\(378\) 0 0
\(379\) 20.7810i 1.06745i 0.845659 + 0.533723i \(0.179207\pi\)
−0.845659 + 0.533723i \(0.820793\pi\)
\(380\) 0.357348 + 1.13307i 0.0183315 + 0.0581251i
\(381\) 0 0
\(382\) 12.4430 16.9715i 0.636642 0.868338i
\(383\) 15.6170 0.797993 0.398996 0.916953i \(-0.369359\pi\)
0.398996 + 0.916953i \(0.369359\pi\)
\(384\) 0 0
\(385\) −10.0173 −0.510531
\(386\) −17.7904 + 24.2650i −0.905508 + 1.23505i
\(387\) 0 0
\(388\) −1.25632 3.98351i −0.0637801 0.202232i
\(389\) 10.1133i 0.512764i 0.966576 + 0.256382i \(0.0825304\pi\)
−0.966576 + 0.256382i \(0.917470\pi\)
\(390\) 0 0
\(391\) 5.87392 0.297057
\(392\) −13.8290 4.69258i −0.698469 0.237011i
\(393\) 0 0
\(394\) 4.21043 + 3.08698i 0.212119 + 0.155520i
\(395\) 5.98381i 0.301078i
\(396\) 0 0
\(397\) 4.60677i 0.231207i −0.993295 0.115604i \(-0.963120\pi\)
0.993295 0.115604i \(-0.0368802\pi\)
\(398\) 9.77153 13.3277i 0.489802 0.668058i
\(399\) 0 0
\(400\) −15.2252 + 10.6642i −0.761259 + 0.533209i
\(401\) 4.00112 0.199806 0.0999032 0.994997i \(-0.468147\pi\)
0.0999032 + 0.994997i \(0.468147\pi\)
\(402\) 0 0
\(403\) 0.263095i 0.0131057i
\(404\) −5.28488 + 1.66675i −0.262933 + 0.0829239i
\(405\) 0 0
\(406\) −37.4331 27.4450i −1.85778 1.36207i
\(407\) −27.2054 −1.34852
\(408\) 0 0
\(409\) −14.5111 −0.717529 −0.358765 0.933428i \(-0.616802\pi\)
−0.358765 + 0.933428i \(0.616802\pi\)
\(410\) −0.304895 0.223541i −0.0150577 0.0110399i
\(411\) 0 0
\(412\) 8.62408 + 27.3450i 0.424878 + 1.34719i
\(413\) 9.59745i 0.472260i
\(414\) 0 0
\(415\) 6.90843 0.339122
\(416\) 1.21931 + 0.0263782i 0.0597817 + 0.00129330i
\(417\) 0 0
\(418\) 4.04317 5.51462i 0.197758 0.269729i
\(419\) 5.02078i 0.245281i −0.992451 0.122641i \(-0.960864\pi\)
0.992451 0.122641i \(-0.0391362\pi\)
\(420\) 0 0
\(421\) 4.10152i 0.199896i −0.994993 0.0999479i \(-0.968132\pi\)
0.994993 0.0999479i \(-0.0318676\pi\)
\(422\) 8.68630 + 6.36856i 0.422842 + 0.310017i
\(423\) 0 0
\(424\) −2.33042 + 6.86773i −0.113175 + 0.333526i
\(425\) −6.02825 −0.292413
\(426\) 0 0
\(427\) 27.0867i 1.31082i
\(428\) −4.62328 + 1.45809i −0.223475 + 0.0704797i
\(429\) 0 0
\(430\) 0.394585 0.538189i 0.0190286 0.0259538i
\(431\) 16.2920 0.784760 0.392380 0.919803i \(-0.371652\pi\)
0.392380 + 0.919803i \(0.371652\pi\)
\(432\) 0 0
\(433\) 7.44858 0.357956 0.178978 0.983853i \(-0.442721\pi\)
0.178978 + 0.983853i \(0.442721\pi\)
\(434\) 3.55878 4.85394i 0.170827 0.232997i
\(435\) 0 0
\(436\) −0.00236155 0.000744786i −0.000113098 3.56688e-5i
\(437\) 4.52815i 0.216611i
\(438\) 0 0
\(439\) 15.8898 0.758379 0.379189 0.925319i \(-0.376203\pi\)
0.379189 + 0.925319i \(0.376203\pi\)
\(440\) −7.69325 2.61055i −0.366761 0.124453i
\(441\) 0 0
\(442\) 0.318971 + 0.233861i 0.0151719 + 0.0111236i
\(443\) 15.1742i 0.720949i 0.932769 + 0.360474i \(0.117385\pi\)
−0.932769 + 0.360474i \(0.882615\pi\)
\(444\) 0 0
\(445\) 8.14379i 0.386053i
\(446\) −1.63457 + 2.22945i −0.0773991 + 0.105567i
\(447\) 0 0
\(448\) −22.1388 16.9798i −1.04596 0.802220i
\(449\) 24.3909 1.15108 0.575538 0.817775i \(-0.304793\pi\)
0.575538 + 0.817775i \(0.304793\pi\)
\(450\) 0 0
\(451\) 2.17594i 0.102461i
\(452\) 1.09251 + 3.46409i 0.0513872 + 0.162937i
\(453\) 0 0
\(454\) −15.2498 11.1807i −0.715708 0.524738i
\(455\) 0.446664 0.0209399
\(456\) 0 0
\(457\) −10.6860 −0.499869 −0.249934 0.968263i \(-0.580409\pi\)
−0.249934 + 0.968263i \(0.580409\pi\)
\(458\) −13.2071 9.68311i −0.617129 0.452462i
\(459\) 0 0
\(460\) 5.13069 1.61812i 0.239220 0.0754453i
\(461\) 21.8232i 1.01641i 0.861236 + 0.508205i \(0.169691\pi\)
−0.861236 + 0.508205i \(0.830309\pi\)
\(462\) 0 0
\(463\) 0.0258442 0.00120108 0.000600541 1.00000i \(-0.499809\pi\)
0.000600541 1.00000i \(0.499809\pi\)
\(464\) −21.5961 30.8327i −1.00258 1.43137i
\(465\) 0 0
\(466\) −1.32848 + 1.81196i −0.0615405 + 0.0839372i
\(467\) 4.66985i 0.216095i 0.994146 + 0.108047i \(0.0344598\pi\)
−0.994146 + 0.108047i \(0.965540\pi\)
\(468\) 0 0
\(469\) 14.3559i 0.662893i
\(470\) 8.26473 + 6.05947i 0.381223 + 0.279503i
\(471\) 0 0
\(472\) −2.50112 + 7.37078i −0.115123 + 0.339267i
\(473\) −3.84088 −0.176604
\(474\) 0 0
\(475\) 4.64712i 0.213224i
\(476\) −2.72147 8.62917i −0.124739 0.395517i
\(477\) 0 0
\(478\) −19.9198 + 27.1692i −0.911109 + 1.24269i
\(479\) 30.5428 1.39554 0.697768 0.716324i \(-0.254177\pi\)
0.697768 + 0.716324i \(0.254177\pi\)
\(480\) 0 0
\(481\) 1.21306 0.0553108
\(482\) 19.1116 26.0670i 0.870509 1.18732i
\(483\) 0 0
\(484\) 7.44671 + 23.6118i 0.338487 + 1.07326i
\(485\) 1.24063i 0.0563342i
\(486\) 0 0
\(487\) −2.37133 −0.107455 −0.0537277 0.998556i \(-0.517110\pi\)
−0.0537277 + 0.998556i \(0.517110\pi\)
\(488\) −7.05886 + 20.8024i −0.319540 + 0.941679i
\(489\) 0 0
\(490\) −3.49807 2.56469i −0.158027 0.115861i
\(491\) 41.3206i 1.86477i −0.361466 0.932385i \(-0.617724\pi\)
0.361466 0.932385i \(-0.382276\pi\)
\(492\) 0 0
\(493\) 12.2079i 0.549815i
\(494\) −0.180281 + 0.245891i −0.00811122 + 0.0110632i
\(495\) 0 0
\(496\) 3.99807 2.80036i 0.179518 0.125740i
\(497\) −27.3002 −1.22458
\(498\) 0 0
\(499\) 15.8610i 0.710035i −0.934860 0.355018i \(-0.884475\pi\)
0.934860 0.355018i \(-0.115525\pi\)
\(500\) −10.9308 + 3.44737i −0.488842 + 0.154171i
\(501\) 0 0
\(502\) −3.00554 2.20358i −0.134144 0.0983506i
\(503\) 18.6879 0.833254 0.416627 0.909078i \(-0.363212\pi\)
0.416627 + 0.909078i \(0.363212\pi\)
\(504\) 0 0
\(505\) −1.64593 −0.0732431
\(506\) −24.9710 18.3081i −1.11010 0.813893i
\(507\) 0 0
\(508\) 9.70121 + 30.7603i 0.430422 + 1.36477i
\(509\) 33.2172i 1.47233i 0.676804 + 0.736163i \(0.263364\pi\)
−0.676804 + 0.736163i \(0.736636\pi\)
\(510\) 0 0
\(511\) −10.7742 −0.476622
\(512\) −12.5774 18.8098i −0.555849 0.831283i
\(513\) 0 0
\(514\) −16.7723 + 22.8763i −0.739795 + 1.00903i
\(515\) 8.51637i 0.375276i
\(516\) 0 0
\(517\) 58.9827i 2.59406i
\(518\) −22.3802 16.4086i −0.983330 0.720951i
\(519\) 0 0
\(520\) 0.343034 + 0.116402i 0.0150431 + 0.00510455i
\(521\) 10.9831 0.481178 0.240589 0.970627i \(-0.422659\pi\)
0.240589 + 0.970627i \(0.422659\pi\)
\(522\) 0 0
\(523\) 8.00433i 0.350005i 0.984568 + 0.175002i \(0.0559933\pi\)
−0.984568 + 0.175002i \(0.944007\pi\)
\(524\) 21.2631 6.70597i 0.928882 0.292952i
\(525\) 0 0
\(526\) −3.37544 + 4.60388i −0.147176 + 0.200739i
\(527\) 1.58299 0.0689561
\(528\) 0 0
\(529\) −2.49589 −0.108517
\(530\) −1.27367 + 1.73721i −0.0553248 + 0.0754594i
\(531\) 0 0
\(532\) 6.65214 2.09796i 0.288407 0.0909580i
\(533\) 0.0970230i 0.00420253i
\(534\) 0 0
\(535\) −1.43988 −0.0622516
\(536\) 3.74118 11.0252i 0.161594 0.476217i
\(537\) 0 0
\(538\) 16.3202 + 11.9656i 0.703615 + 0.515872i
\(539\) 24.9646i 1.07530i
\(540\) 0 0
\(541\) 24.4359i 1.05058i 0.850923 + 0.525291i \(0.176044\pi\)
−0.850923 + 0.525291i \(0.823956\pi\)
\(542\) 8.23681 11.2345i 0.353801 0.482562i
\(543\) 0 0
\(544\) 0.158712 7.33636i 0.00680473 0.314544i
\(545\) −0.000735485 0 −3.15047e−5 0
\(546\) 0 0
\(547\) 5.25284i 0.224595i −0.993675 0.112298i \(-0.964179\pi\)
0.993675 0.112298i \(-0.0358210\pi\)
\(548\) 6.71730 + 21.2990i 0.286949 + 0.909849i
\(549\) 0 0
\(550\) 25.6271 + 18.7891i 1.09274 + 0.801169i
\(551\) 9.41093 0.400919
\(552\) 0 0
\(553\) 35.1305 1.49390
\(554\) −19.3479 14.1853i −0.822012 0.602677i
\(555\) 0 0
\(556\) −24.8980 + 7.85234i −1.05591 + 0.333014i
\(557\) 3.56791i 0.151177i −0.997139 0.0755886i \(-0.975916\pi\)
0.997139 0.0755886i \(-0.0240836\pi\)
\(558\) 0 0
\(559\) 0.171261 0.00724357
\(560\) −4.75425 6.78762i −0.200904 0.286829i
\(561\) 0 0
\(562\) 8.53568 11.6421i 0.360056 0.491093i
\(563\) 17.0555i 0.718805i 0.933183 + 0.359403i \(0.117020\pi\)
−0.933183 + 0.359403i \(0.882980\pi\)
\(564\) 0 0
\(565\) 1.07886i 0.0453881i
\(566\) −21.4085 15.6961i −0.899867 0.659758i
\(567\) 0 0
\(568\) −20.9664 7.11452i −0.879731 0.298519i
\(569\) 0.858816 0.0360034 0.0180017 0.999838i \(-0.494270\pi\)
0.0180017 + 0.999838i \(0.494270\pi\)
\(570\) 0 0
\(571\) 40.5440i 1.69671i 0.529426 + 0.848356i \(0.322407\pi\)
−0.529426 + 0.848356i \(0.677593\pi\)
\(572\) −0.627091 1.98836i −0.0262200 0.0831376i
\(573\) 0 0
\(574\) −1.31239 + 1.79001i −0.0547781 + 0.0747138i
\(575\) −21.0428 −0.877546
\(576\) 0 0
\(577\) 36.5405 1.52120 0.760600 0.649220i \(-0.224905\pi\)
0.760600 + 0.649220i \(0.224905\pi\)
\(578\) −12.8082 + 17.4696i −0.532752 + 0.726639i
\(579\) 0 0
\(580\) −3.36297 10.6632i −0.139640 0.442766i
\(581\) 40.5588i 1.68266i
\(582\) 0 0
\(583\) 12.3979 0.513468
\(584\) −8.27450 2.80778i −0.342401 0.116187i
\(585\) 0 0
\(586\) −22.6131 16.5793i −0.934139 0.684885i
\(587\) 30.4022i 1.25483i −0.778684 0.627416i \(-0.784113\pi\)
0.778684 0.627416i \(-0.215887\pi\)
\(588\) 0 0
\(589\) 1.22031i 0.0502821i
\(590\) −1.36697 + 1.86445i −0.0562771 + 0.0767583i
\(591\) 0 0
\(592\) −12.9117 18.4340i −0.530668 0.757633i
\(593\) 16.3814 0.672703 0.336351 0.941737i \(-0.390807\pi\)
0.336351 + 0.941737i \(0.390807\pi\)
\(594\) 0 0
\(595\) 2.68749i 0.110176i
\(596\) −27.4303 + 8.65100i −1.12359 + 0.354359i
\(597\) 0 0
\(598\) 1.11343 + 0.816338i 0.0455316 + 0.0333826i
\(599\) 2.24749 0.0918298 0.0459149 0.998945i \(-0.485380\pi\)
0.0459149 + 0.998945i \(0.485380\pi\)
\(600\) 0 0
\(601\) −33.1805 −1.35346 −0.676730 0.736231i \(-0.736604\pi\)
−0.676730 + 0.736231i \(0.736604\pi\)
\(602\) −3.15966 2.31658i −0.128778 0.0944167i
\(603\) 0 0
\(604\) −10.4363 33.0912i −0.424648 1.34646i
\(605\) 7.35371i 0.298971i
\(606\) 0 0
\(607\) 35.7847 1.45246 0.726228 0.687454i \(-0.241272\pi\)
0.726228 + 0.687454i \(0.241272\pi\)
\(608\) 5.65553 + 0.122350i 0.229362 + 0.00496194i
\(609\) 0 0
\(610\) −3.85796 + 5.26201i −0.156204 + 0.213052i
\(611\) 2.62998i 0.106398i
\(612\) 0 0
\(613\) 42.2856i 1.70790i 0.520355 + 0.853950i \(0.325800\pi\)
−0.520355 + 0.853950i \(0.674200\pi\)
\(614\) 20.9781 + 15.3806i 0.846606 + 0.620709i
\(615\) 0 0
\(616\) −15.3263 + 45.1664i −0.617515 + 1.81981i
\(617\) 26.2079 1.05509 0.527545 0.849527i \(-0.323113\pi\)
0.527545 + 0.849527i \(0.323113\pi\)
\(618\) 0 0
\(619\) 40.7494i 1.63786i −0.573896 0.818929i \(-0.694568\pi\)
0.573896 0.818929i \(-0.305432\pi\)
\(620\) 1.38269 0.436075i 0.0555304 0.0175132i
\(621\) 0 0
\(622\) −16.0338 + 21.8690i −0.642896 + 0.876868i
\(623\) 47.8115 1.91553
\(624\) 0 0
\(625\) 19.8313 0.793250
\(626\) 11.8969 16.2266i 0.475497 0.648546i
\(627\) 0 0
\(628\) 18.3737 5.79472i 0.733192 0.231235i
\(629\) 7.29874i 0.291020i
\(630\) 0 0
\(631\) 42.3804 1.68714 0.843569 0.537021i \(-0.180450\pi\)
0.843569 + 0.537021i \(0.180450\pi\)
\(632\) 26.9800 + 9.15510i 1.07320 + 0.364170i
\(633\) 0 0
\(634\) 0.887251 + 0.650509i 0.0352372 + 0.0258350i
\(635\) 9.58005i 0.380173i
\(636\) 0 0
\(637\) 1.11315i 0.0441045i
\(638\) −38.0500 + 51.8977i −1.50641 + 2.05465i
\(639\) 0 0
\(640\) −1.88236 6.45182i −0.0744068 0.255030i
\(641\) 40.0356 1.58131 0.790656 0.612261i \(-0.209740\pi\)
0.790656 + 0.612261i \(0.209740\pi\)
\(642\) 0 0
\(643\) 2.25369i 0.0888767i −0.999012 0.0444384i \(-0.985850\pi\)
0.999012 0.0444384i \(-0.0141498\pi\)
\(644\) −9.49986 30.1219i −0.374347 1.18697i
\(645\) 0 0
\(646\) 1.47948 + 1.08471i 0.0582093 + 0.0426775i
\(647\) 6.89272 0.270981 0.135490 0.990779i \(-0.456739\pi\)
0.135490 + 0.990779i \(0.456739\pi\)
\(648\) 0 0
\(649\) 13.3060 0.522307
\(650\) −1.14269 0.837786i −0.0448198 0.0328607i
\(651\) 0 0
\(652\) 42.9859 13.5569i 1.68346 0.530930i
\(653\) 5.75398i 0.225170i −0.993642 0.112585i \(-0.964087\pi\)
0.993642 0.112585i \(-0.0359131\pi\)
\(654\) 0 0
\(655\) 6.62222 0.258751
\(656\) −1.47439 + 1.03271i −0.0575652 + 0.0403204i
\(657\) 0 0
\(658\) 35.5747 48.5215i 1.38684 1.89157i
\(659\) 34.1024i 1.32844i −0.747537 0.664220i \(-0.768764\pi\)
0.747537 0.664220i \(-0.231236\pi\)
\(660\) 0 0
\(661\) 46.3767i 1.80384i 0.431900 + 0.901922i \(0.357843\pi\)
−0.431900 + 0.901922i \(0.642157\pi\)
\(662\) 18.7031 + 13.7126i 0.726916 + 0.532955i
\(663\) 0 0
\(664\) 10.5697 31.1489i 0.410185 1.20881i
\(665\) 2.07176 0.0803392
\(666\) 0 0
\(667\) 42.6141i 1.65002i
\(668\) 9.93215 + 31.4926i 0.384287 + 1.21848i
\(669\) 0 0
\(670\) 2.04471 2.78885i 0.0789941 0.107743i
\(671\) 37.5533 1.44973
\(672\) 0 0
\(673\) −29.1579 −1.12395 −0.561977 0.827153i \(-0.689959\pi\)
−0.561977 + 0.827153i \(0.689959\pi\)
\(674\) 20.5795 28.0691i 0.792693 1.08118i
\(675\) 0 0
\(676\) −7.79224 24.7074i −0.299701 0.950285i
\(677\) 10.0436i 0.386006i 0.981198 + 0.193003i \(0.0618228\pi\)
−0.981198 + 0.193003i \(0.938177\pi\)
\(678\) 0 0
\(679\) −7.28365 −0.279521
\(680\) 0.700366 2.06397i 0.0268578 0.0791496i
\(681\) 0 0
\(682\) −6.72955 4.93393i −0.257688 0.188930i
\(683\) 25.5866i 0.979042i 0.871991 + 0.489521i \(0.162828\pi\)
−0.871991 + 0.489521i \(0.837172\pi\)
\(684\) 0 0
\(685\) 6.63341i 0.253449i
\(686\) 5.35691 7.30648i 0.204528 0.278963i
\(687\) 0 0
\(688\) −1.82289 2.60253i −0.0694970 0.0992206i
\(689\) −0.552809 −0.0210604
\(690\) 0 0
\(691\) 42.2386i 1.60683i 0.595417 + 0.803417i \(0.296987\pi\)
−0.595417 + 0.803417i \(0.703013\pi\)
\(692\) 9.82135 3.09746i 0.373352 0.117748i
\(693\) 0 0
\(694\) 15.3554 + 11.2581i 0.582882 + 0.427353i
\(695\) −7.75428 −0.294136
\(696\) 0 0
\(697\) −0.583768 −0.0221118
\(698\) 3.23247 + 2.36996i 0.122351 + 0.0897043i
\(699\) 0 0
\(700\) 9.74945 + 30.9133i 0.368495 + 1.16841i
\(701\) 43.9811i 1.66114i 0.556911 + 0.830572i \(0.311986\pi\)
−0.556911 + 0.830572i \(0.688014\pi\)
\(702\) 0 0
\(703\) 5.62653 0.212208
\(704\) −23.5410 + 30.6934i −0.887234 + 1.15680i
\(705\) 0 0
\(706\) 4.19960 5.72798i 0.158054 0.215575i
\(707\) 9.66314i 0.363420i
\(708\) 0 0
\(709\) 11.1307i 0.418023i −0.977913 0.209012i \(-0.932975\pi\)
0.977913 0.209012i \(-0.0670246\pi\)
\(710\) −5.30350 3.88838i −0.199037 0.145928i
\(711\) 0 0
\(712\) 36.7189 + 12.4598i 1.37610 + 0.466951i
\(713\) 5.52575 0.206941
\(714\) 0 0
\(715\) 0.619259i 0.0231590i
\(716\) −17.7688 + 5.60395i −0.664053 + 0.209430i
\(717\) 0 0
\(718\) −19.8093 + 27.0186i −0.739276 + 1.00832i
\(719\) −17.8961 −0.667413 −0.333706 0.942677i \(-0.608299\pi\)
−0.333706 + 0.942677i \(0.608299\pi\)
\(720\) 0 0
\(721\) 49.9989 1.86206
\(722\) −0.836196 + 1.14052i −0.0311200 + 0.0424456i
\(723\) 0 0
\(724\) −9.83291 + 3.10111i −0.365437 + 0.115252i
\(725\) 43.7337i 1.62423i
\(726\) 0 0
\(727\) −35.8772 −1.33061 −0.665306 0.746571i \(-0.731699\pi\)
−0.665306 + 0.746571i \(0.731699\pi\)
\(728\) 0.683385 2.01393i 0.0253279 0.0746411i
\(729\) 0 0
\(730\) −2.09305 1.53457i −0.0774673 0.0567970i
\(731\) 1.03044i 0.0381123i
\(732\) 0 0
\(733\) 24.4618i 0.903516i 0.892141 + 0.451758i \(0.149203\pi\)
−0.892141 + 0.451758i \(0.850797\pi\)
\(734\) −14.1600 + 19.3133i −0.522655 + 0.712867i
\(735\) 0 0
\(736\) 0.554018 25.6091i 0.0204214 0.943963i
\(737\) −19.9032 −0.733142
\(738\) 0 0
\(739\) 26.7820i 0.985193i 0.870258 + 0.492596i \(0.163952\pi\)
−0.870258 + 0.492596i \(0.836048\pi\)
\(740\) −2.01063 6.37523i −0.0739121 0.234358i
\(741\) 0 0
\(742\) 10.1990 + 7.47763i 0.374417 + 0.274512i
\(743\) −23.7835 −0.872534 −0.436267 0.899817i \(-0.643700\pi\)
−0.436267 + 0.899817i \(0.643700\pi\)
\(744\) 0 0
\(745\) −8.54295 −0.312990
\(746\) −14.6669 10.7534i −0.536994 0.393710i
\(747\) 0 0
\(748\) −11.9636 + 3.77308i −0.437432 + 0.137958i
\(749\) 8.45344i 0.308882i
\(750\) 0 0
\(751\) 22.4303 0.818494 0.409247 0.912424i \(-0.365791\pi\)
0.409247 + 0.912424i \(0.365791\pi\)
\(752\) 39.9659 27.9933i 1.45741 1.02081i
\(753\) 0 0
\(754\) 1.69661 2.31407i 0.0617869 0.0842733i
\(755\) 10.3060i 0.375073i
\(756\) 0 0
\(757\) 32.2421i 1.17186i 0.810362 + 0.585930i \(0.199271\pi\)
−0.810362 + 0.585930i \(0.800729\pi\)
\(758\) 23.7010 + 17.3769i 0.860859 + 0.631159i
\(759\) 0 0
\(760\) 1.59109 + 0.539905i 0.0577150 + 0.0195844i
\(761\) −16.3559 −0.592902 −0.296451 0.955048i \(-0.595803\pi\)
−0.296451 + 0.955048i \(0.595803\pi\)
\(762\) 0 0
\(763\) 0.00431797i 0.000156321i
\(764\) −8.95145 28.3830i −0.323852 1.02686i
\(765\) 0 0
\(766\) 13.0589 17.8115i 0.471837 0.643554i
\(767\) −0.593302 −0.0214229
\(768\) 0 0
\(769\) −19.6832 −0.709794 −0.354897 0.934905i \(-0.615484\pi\)
−0.354897 + 0.934905i \(0.615484\pi\)
\(770\) −8.37646 + 11.4249i −0.301867 + 0.411727i
\(771\) 0 0
\(772\) 12.7983 + 40.5805i 0.460621 + 1.46052i
\(773\) 33.0819i 1.18987i −0.803773 0.594936i \(-0.797177\pi\)
0.803773 0.594936i \(-0.202823\pi\)
\(774\) 0 0
\(775\) −5.67093 −0.203706
\(776\) −5.59379 1.89814i −0.200805 0.0681392i
\(777\) 0 0
\(778\) 11.5344 + 8.45668i 0.413527 + 0.303187i
\(779\) 0.450021i 0.0161237i
\(780\) 0 0
\(781\) 37.8494i 1.35436i
\(782\) 4.91175 6.69930i 0.175644 0.239566i
\(783\) 0 0
\(784\) −16.9157 + 11.8483i −0.604132 + 0.423152i
\(785\) 5.72235 0.204240
\(786\) 0 0
\(787\) 35.1617i 1.25338i −0.779269 0.626690i \(-0.784409\pi\)
0.779269 0.626690i \(-0.215591\pi\)
\(788\) 7.04149 2.22075i 0.250843 0.0791110i
\(789\) 0 0
\(790\) 6.82464 + 5.00364i 0.242810 + 0.178022i
\(791\) 6.33392 0.225208
\(792\) 0 0
\(793\) −1.67446 −0.0594619
\(794\) −5.25410 3.85216i −0.186461 0.136708i
\(795\) 0 0
\(796\) −7.02957 22.2892i −0.249157 0.790019i
\(797\) 3.75101i 0.132868i 0.997791 + 0.0664338i \(0.0211621\pi\)
−0.997791 + 0.0664338i \(0.978838\pi\)
\(798\) 0 0
\(799\) 15.8241 0.559815
\(800\) −0.568573 + 26.2819i −0.0201021 + 0.929206i
\(801\) 0 0
\(802\) 3.34572 4.56334i 0.118141 0.161137i
\(803\) 14.9374i 0.527131i
\(804\) 0 0
\(805\) 9.38121i 0.330644i
\(806\) 0.300064 + 0.219999i 0.0105693 + 0.00774913i
\(807\) 0 0
\(808\) −2.51824 + 7.42122i −0.0885913 + 0.261078i
\(809\) −23.9158 −0.840836 −0.420418 0.907331i \(-0.638117\pi\)
−0.420418 + 0.907331i \(0.638117\pi\)
\(810\) 0 0
\(811\) 52.0538i 1.82785i −0.405878 0.913927i \(-0.633034\pi\)
0.405878 0.913927i \(-0.366966\pi\)
\(812\) −62.6028 + 19.7437i −2.19693 + 0.692869i
\(813\) 0 0
\(814\) −22.7490 + 31.0282i −0.797352 + 1.08754i
\(815\) 13.3876 0.468947
\(816\) 0 0
\(817\) 0.794359 0.0277911
\(818\) −12.1341 + 16.5502i −0.424260 + 0.578663i
\(819\) 0 0
\(820\) −0.509904 + 0.160814i −0.0178066 + 0.00561587i
\(821\) 0.703590i 0.0245555i 0.999925 + 0.0122777i \(0.00390822\pi\)
−0.999925 + 0.0122777i \(0.996092\pi\)
\(822\) 0 0
\(823\) 23.4559 0.817622 0.408811 0.912619i \(-0.365943\pi\)
0.408811 + 0.912619i \(0.365943\pi\)
\(824\) 38.3988 + 13.0299i 1.33769 + 0.453916i
\(825\) 0 0
\(826\) 10.9460 + 8.02535i 0.380862 + 0.279238i
\(827\) 29.5282i 1.02680i −0.858150 0.513399i \(-0.828386\pi\)
0.858150 0.513399i \(-0.171614\pi\)
\(828\) 0 0
\(829\) 4.42946i 0.153841i 0.997037 + 0.0769207i \(0.0245088\pi\)
−0.997037 + 0.0769207i \(0.975491\pi\)
\(830\) 5.77680 7.87918i 0.200516 0.273490i
\(831\) 0 0
\(832\) 1.04967 1.36859i 0.0363907 0.0474473i
\(833\) −6.69759 −0.232058
\(834\) 0 0
\(835\) 9.80811i 0.339424i
\(836\) −2.90863 9.22260i −0.100597 0.318970i
\(837\) 0 0
\(838\) −5.72628 4.19835i −0.197811 0.145030i
\(839\) 36.4506 1.25841 0.629207 0.777237i \(-0.283380\pi\)
0.629207 + 0.777237i \(0.283380\pi\)
\(840\) 0 0
\(841\) −59.5656 −2.05399
\(842\) −4.67785 3.42967i −0.161209 0.118194i
\(843\) 0 0
\(844\) 14.5269 4.58150i 0.500036 0.157702i
\(845\) 7.69492i 0.264713i
\(846\) 0 0
\(847\) 43.1730 1.48344
\(848\) 5.88406 + 8.40065i 0.202060 + 0.288479i
\(849\) 0 0
\(850\) −5.04079 + 6.87531i −0.172898 + 0.235821i
\(851\) 25.4777i 0.873366i
\(852\) 0 0
\(853\) 52.7043i 1.80456i 0.431149 + 0.902281i \(0.358108\pi\)
−0.431149 + 0.902281i \(0.641892\pi\)
\(854\) 30.8928 + 22.6498i 1.05713 + 0.775059i
\(855\) 0 0
\(856\) −2.20299 + 6.49218i −0.0752966 + 0.221898i
\(857\) −13.7199 −0.468662 −0.234331 0.972157i \(-0.575290\pi\)
−0.234331 + 0.972157i \(0.575290\pi\)
\(858\) 0 0
\(859\) 55.0757i 1.87916i 0.342330 + 0.939580i \(0.388784\pi\)
−0.342330 + 0.939580i \(0.611216\pi\)
\(860\) −0.283862 0.900062i −0.00967962 0.0306919i
\(861\) 0 0
\(862\) 13.6233 18.5813i 0.464013 0.632883i
\(863\) −38.3384 −1.30505 −0.652527 0.757766i \(-0.726291\pi\)
−0.652527 + 0.757766i \(0.726291\pi\)
\(864\) 0 0
\(865\) 3.05878 0.104002
\(866\) 6.22847 8.49523i 0.211652 0.288680i
\(867\) 0 0
\(868\) −2.56016 8.11768i −0.0868975 0.275532i
\(869\) 48.7053i 1.65221i
\(870\) 0 0
\(871\) 0.887462 0.0300705
\(872\) −0.00112527 + 0.00331617i −3.81066e−5 + 0.000112300i
\(873\) 0 0
\(874\) 5.16442 + 3.78642i 0.174689 + 0.128077i
\(875\) 19.9865i 0.675666i
\(876\) 0 0
\(877\) 21.4788i 0.725288i −0.931928 0.362644i \(-0.881874\pi\)
0.931928 0.362644i \(-0.118126\pi\)
\(878\) 13.2870 18.1226i 0.448414 0.611607i
\(879\) 0 0
\(880\) −9.41044 + 6.59135i −0.317226 + 0.222194i
\(881\) 11.2383 0.378629 0.189314 0.981917i \(-0.439373\pi\)
0.189314 + 0.981917i \(0.439373\pi\)
\(882\) 0 0
\(883\) 15.7137i 0.528809i −0.964412 0.264405i \(-0.914825\pi\)
0.964412 0.264405i \(-0.0851755\pi\)
\(884\) 0.533444 0.168238i 0.0179417 0.00565845i
\(885\) 0 0
\(886\) 17.3064 + 12.6886i 0.581421 + 0.426282i
\(887\) −4.48008 −0.150426 −0.0752131 0.997167i \(-0.523964\pi\)
−0.0752131 + 0.997167i \(0.523964\pi\)
\(888\) 0 0
\(889\) 56.2437 1.88635
\(890\) 9.28812 + 6.80980i 0.311338 + 0.228265i
\(891\) 0 0
\(892\) 1.17590 + 3.72851i 0.0393720 + 0.124840i
\(893\) 12.1986i 0.408211i
\(894\) 0 0
\(895\) −5.53396 −0.184980
\(896\) −37.8781 + 11.0512i −1.26542 + 0.369194i
\(897\) 0 0
\(898\) 20.3955 27.8182i 0.680608 0.928305i
\(899\) 11.4843i 0.383022i
\(900\) 0 0
\(901\) 3.32614i 0.110810i
\(902\) 2.48170 + 1.81951i 0.0826314 + 0.0605831i
\(903\) 0 0
\(904\) 4.86440 + 1.65064i 0.161788 + 0.0548993i
\(905\) −3.06238 −0.101797
\(906\) 0 0
\(907\) 6.37021i 0.211519i 0.994392 + 0.105760i \(0.0337274\pi\)
−0.994392 + 0.105760i \(0.966273\pi\)
\(908\) −25.5036 + 8.04334i −0.846367 + 0.266928i
\(909\) 0 0
\(910\) 0.373498 0.509427i 0.0123813 0.0168873i
\(911\) 30.5275 1.01142 0.505711 0.862703i \(-0.331230\pi\)
0.505711 + 0.862703i \(0.331230\pi\)
\(912\) 0 0
\(913\) −56.2312 −1.86098
\(914\) −8.93556 + 12.1875i −0.295562 + 0.403127i
\(915\) 0 0
\(916\) −22.0875 + 6.96597i −0.729791 + 0.230162i
\(917\) 38.8785i 1.28388i
\(918\) 0 0
\(919\) −48.0650 −1.58552 −0.792758 0.609536i \(-0.791356\pi\)
−0.792758 + 0.609536i \(0.791356\pi\)
\(920\) 2.44477 7.20471i 0.0806017 0.237532i
\(921\) 0 0
\(922\) 24.8898 + 18.2485i 0.819700 + 0.600982i
\(923\) 1.68767i 0.0555502i
\(924\) 0 0
\(925\) 26.1471i 0.859712i
\(926\) 0.0216108 0.0294757i 0.000710175 0.000968632i
\(927\) 0 0
\(928\) −53.2238 1.15142i −1.74716 0.0377974i
\(929\) −47.2953 −1.55171 −0.775854 0.630912i \(-0.782681\pi\)
−0.775854 + 0.630912i \(0.782681\pi\)
\(930\) 0 0
\(931\) 5.16310i 0.169214i
\(932\) 0.955698 + 3.03030i 0.0313049 + 0.0992607i
\(933\) 0 0
\(934\) 5.32604 + 3.90491i 0.174273 + 0.127773i
\(935\) −3.72596 −0.121852
\(936\) 0 0
\(937\) −8.30237 −0.271227 −0.135613 0.990762i \(-0.543301\pi\)
−0.135613 + 0.990762i \(0.543301\pi\)
\(938\) −16.3731 12.0043i −0.534601 0.391955i
\(939\) 0 0
\(940\) 13.8219 4.35915i 0.450819 0.142180i
\(941\) 31.3955i 1.02347i −0.859145 0.511733i \(-0.829004\pi\)
0.859145 0.511733i \(-0.170996\pi\)
\(942\) 0 0
\(943\) −2.03776 −0.0663586
\(944\) 6.31506 + 9.01598i 0.205538 + 0.293445i
\(945\) 0 0
\(946\) −3.21173 + 4.38059i −0.104422 + 0.142425i
\(947\) 2.14805i 0.0698024i 0.999391 + 0.0349012i \(0.0111117\pi\)
−0.999391 + 0.0349012i \(0.988888\pi\)
\(948\) 0 0
\(949\) 0.666046i 0.0216208i
\(950\) −5.30011 3.88590i −0.171958 0.126075i
\(951\) 0 0
\(952\) −12.1174 4.11179i −0.392727 0.133264i
\(953\) −25.3661 −0.821689 −0.410844 0.911705i \(-0.634766\pi\)
−0.410844 + 0.911705i \(0.634766\pi\)
\(954\) 0 0
\(955\) 8.83965i 0.286044i
\(956\) 14.3301 + 45.4376i 0.463470 + 1.46956i
\(957\) 0 0
\(958\) 25.5398 34.8346i 0.825152 1.12545i
\(959\) 38.9442 1.25757
\(960\) 0 0
\(961\) −29.5108 −0.951963
\(962\) 1.01436 1.38351i 0.0327041 0.0446063i
\(963\) 0 0
\(964\) −13.7488 43.5942i −0.442818 1.40407i
\(965\) 12.6385i 0.406847i
\(966\) 0 0
\(967\) −12.8395 −0.412892 −0.206446 0.978458i \(-0.566190\pi\)
−0.206446 + 0.978458i \(0.566190\pi\)
\(968\) 33.1566 + 11.2510i 1.06569 + 0.361621i
\(969\) 0 0
\(970\) −1.41496 1.03741i −0.0454317 0.0333093i
\(971\) 8.77909i 0.281734i 0.990028 + 0.140867i \(0.0449891\pi\)
−0.990028 + 0.140867i \(0.955011\pi\)
\(972\) 0 0
\(973\) 45.5247i 1.45945i
\(974\) −1.98290 + 2.70454i −0.0635362 + 0.0866592i
\(975\) 0 0
\(976\) 17.8229 + 25.4456i 0.570496 + 0.814494i
\(977\) 45.9701 1.47071 0.735357 0.677680i \(-0.237014\pi\)
0.735357 + 0.677680i \(0.237014\pi\)
\(978\) 0 0
\(979\) 66.2864i 2.11852i
\(980\) −5.85014 + 1.84502i −0.186876 + 0.0589371i
\(981\) 0 0
\(982\) −47.1268 34.5521i −1.50388 1.10260i
\(983\) 51.4992 1.64257 0.821284 0.570519i \(-0.193258\pi\)
0.821284 + 0.570519i \(0.193258\pi\)
\(984\) 0 0
\(985\) 2.19302 0.0698753
\(986\) −13.9233 10.2082i −0.443407 0.325094i
\(987\) 0 0
\(988\) 0.129693 + 0.411227i 0.00412608 + 0.0130829i
\(989\) 3.59697i 0.114377i
\(990\) 0 0
\(991\) −29.4762 −0.936343 −0.468171 0.883638i \(-0.655087\pi\)
−0.468171 + 0.883638i \(0.655087\pi\)
\(992\) 0.149305 6.90151i 0.00474043 0.219123i
\(993\) 0 0
\(994\) −22.8283 + 31.1364i −0.724071 + 0.987586i
\(995\) 6.94178i 0.220069i
\(996\) 0 0
\(997\) 54.3591i 1.72157i −0.508968 0.860786i \(-0.669973\pi\)
0.508968 0.860786i \(-0.330027\pi\)
\(998\) −18.0897 13.2629i −0.572620 0.419829i
\(999\) 0 0
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 1368.2.g.b.685.11 16
3.2 odd 2 152.2.c.b.77.6 yes 16
4.3 odd 2 5472.2.g.b.2737.8 16
8.3 odd 2 5472.2.g.b.2737.9 16
8.5 even 2 inner 1368.2.g.b.685.12 16
12.11 even 2 608.2.c.b.305.16 16
24.5 odd 2 152.2.c.b.77.5 16
24.11 even 2 608.2.c.b.305.1 16
48.5 odd 4 4864.2.a.bo.1.1 8
48.11 even 4 4864.2.a.bn.1.8 8
48.29 odd 4 4864.2.a.bq.1.8 8
48.35 even 4 4864.2.a.bp.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.2.c.b.77.5 16 24.5 odd 2
152.2.c.b.77.6 yes 16 3.2 odd 2
608.2.c.b.305.1 16 24.11 even 2
608.2.c.b.305.16 16 12.11 even 2
1368.2.g.b.685.11 16 1.1 even 1 trivial
1368.2.g.b.685.12 16 8.5 even 2 inner
4864.2.a.bn.1.8 8 48.11 even 4
4864.2.a.bo.1.1 8 48.5 odd 4
4864.2.a.bp.1.1 8 48.35 even 4
4864.2.a.bq.1.8 8 48.29 odd 4
5472.2.g.b.2737.8 16 4.3 odd 2
5472.2.g.b.2737.9 16 8.3 odd 2