Properties

Label 912.2.bo.c.481.1
Level $912$
Weight $2$
Character 912.481
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
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(289,912)]
 
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([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("912.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bo (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 481.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 912.481
Dual form 912.2.bo.c.529.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.939693 + 0.342020i) q^{3} +(-0.0812519 - 0.460802i) q^{5} +(-2.20574 + 3.82045i) q^{7} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\) \(q+(0.939693 + 0.342020i) q^{3} +(-0.0812519 - 0.460802i) q^{5} +(-2.20574 + 3.82045i) q^{7} +(0.766044 + 0.642788i) q^{9} +(-2.76604 - 4.79093i) q^{11} +(-5.62449 + 2.04715i) q^{13} +(0.0812519 - 0.460802i) q^{15} +(-3.33022 + 2.79439i) q^{17} +(-4.34002 - 0.405223i) q^{19} +(-3.37939 + 2.83564i) q^{21} +(0.549163 - 3.11446i) q^{23} +(4.49273 - 1.63522i) q^{25} +(0.500000 + 0.866025i) q^{27} +(-1.15657 - 0.970481i) q^{29} +(-1.09240 + 1.89209i) q^{31} +(-0.960637 - 5.44804i) q^{33} +(1.93969 + 0.705990i) q^{35} -2.75877 q^{37} -5.98545 q^{39} +(1.84002 + 0.669713i) q^{41} +(-0.624485 - 3.54163i) q^{43} +(0.233956 - 0.405223i) q^{45} +(7.08512 + 5.94512i) q^{47} +(-6.23055 - 10.7916i) q^{49} +(-4.08512 + 1.48686i) q^{51} +(-0.464508 + 2.63435i) q^{53} +(-1.98293 + 1.66387i) q^{55} +(-3.93969 - 1.86516i) q^{57} +(-1.01707 + 0.853427i) q^{59} +(-1.15270 + 6.53731i) q^{61} +(-4.14543 + 1.50881i) q^{63} +(1.40033 + 2.42544i) q^{65} +(1.90760 + 1.60067i) q^{67} +(1.58125 - 2.73881i) q^{69} +(1.31908 + 7.48086i) q^{71} +(-2.97431 - 1.08256i) q^{73} +4.78106 q^{75} +24.4047 q^{77} +(1.18732 + 0.432149i) q^{79} +(0.173648 + 0.984808i) q^{81} +(-8.96838 + 15.5337i) q^{83} +(1.55825 + 1.30753i) q^{85} +(-0.754900 - 1.30753i) q^{87} +(-11.7280 + 4.26865i) q^{89} +(4.58512 - 26.0035i) q^{91} +(-1.67365 + 1.40436i) q^{93} +(0.165907 + 2.03282i) q^{95} +(-6.36618 + 5.34186i) q^{97} +(0.960637 - 5.44804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{5} - 3 q^{7} - 12 q^{11} - 21 q^{13} + 3 q^{15} + 3 q^{17} - 6 q^{19} - 9 q^{21} + 15 q^{23} + 9 q^{25} + 3 q^{27} + 15 q^{29} - 3 q^{31} + 3 q^{33} + 6 q^{35} + 6 q^{37} - 9 q^{41} + 9 q^{43} + 6 q^{45} + 21 q^{47} - 3 q^{51} + 30 q^{53} + 9 q^{55} - 18 q^{57} - 27 q^{59} - 9 q^{61} - 9 q^{63} - 6 q^{65} + 15 q^{67} + 12 q^{69} - 9 q^{71} + 12 q^{73} - 6 q^{75} + 42 q^{77} - 15 q^{79} + 3 q^{83} - 36 q^{85} - 6 q^{87} - 48 q^{89} + 6 q^{91} - 9 q^{93} + 48 q^{95} + 18 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{7}{9}\right)\) \(1\) \(1\) \(1\)

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
\(5\) −0.0812519 0.460802i −0.0363370 0.206077i 0.961234 0.275734i \(-0.0889208\pi\)
−0.997571 + 0.0696565i \(0.977810\pi\)
\(6\) 0 0
\(7\) −2.20574 + 3.82045i −0.833690 + 1.44399i 0.0614021 + 0.998113i \(0.480443\pi\)
−0.895092 + 0.445881i \(0.852891\pi\)
\(8\) 0 0
\(9\) 0.766044 + 0.642788i 0.255348 + 0.214263i
\(10\) 0 0
\(11\) −2.76604 4.79093i −0.833994 1.44452i −0.894847 0.446373i \(-0.852716\pi\)
0.0608533 0.998147i \(-0.480618\pi\)
\(12\) 0 0
\(13\) −5.62449 + 2.04715i −1.55995 + 0.567776i −0.970725 0.240192i \(-0.922790\pi\)
−0.589226 + 0.807968i \(0.700567\pi\)
\(14\) 0 0
\(15\) 0.0812519 0.460802i 0.0209792 0.118979i
\(16\) 0 0
\(17\) −3.33022 + 2.79439i −0.807698 + 0.677739i −0.950057 0.312076i \(-0.898976\pi\)
0.142360 + 0.989815i \(0.454531\pi\)
\(18\) 0 0
\(19\) −4.34002 0.405223i −0.995669 0.0929645i
\(20\) 0 0
\(21\) −3.37939 + 2.83564i −0.737442 + 0.618788i
\(22\) 0 0
\(23\) 0.549163 3.11446i 0.114508 0.649409i −0.872484 0.488643i \(-0.837492\pi\)
0.986992 0.160767i \(-0.0513967\pi\)
\(24\) 0 0
\(25\) 4.49273 1.63522i 0.898545 0.327044i
\(26\) 0 0
\(27\) 0.500000 + 0.866025i 0.0962250 + 0.166667i
\(28\) 0 0
\(29\) −1.15657 0.970481i −0.214770 0.180214i 0.529055 0.848587i \(-0.322546\pi\)
−0.743826 + 0.668374i \(0.766991\pi\)
\(30\) 0 0
\(31\) −1.09240 + 1.89209i −0.196200 + 0.339829i −0.947293 0.320368i \(-0.896194\pi\)
0.751093 + 0.660196i \(0.229527\pi\)
\(32\) 0 0
\(33\) −0.960637 5.44804i −0.167225 0.948383i
\(34\) 0 0
\(35\) 1.93969 + 0.705990i 0.327868 + 0.119334i
\(36\) 0 0
\(37\) −2.75877 −0.453539 −0.226770 0.973948i \(-0.572816\pi\)
−0.226770 + 0.973948i \(0.572816\pi\)
\(38\) 0 0
\(39\) −5.98545 −0.958439
\(40\) 0 0
\(41\) 1.84002 + 0.669713i 0.287363 + 0.104592i 0.481680 0.876347i \(-0.340027\pi\)
−0.194317 + 0.980939i \(0.562249\pi\)
\(42\) 0 0
\(43\) −0.624485 3.54163i −0.0952331 0.540094i −0.994676 0.103055i \(-0.967138\pi\)
0.899443 0.437039i \(-0.143973\pi\)
\(44\) 0 0
\(45\) 0.233956 0.405223i 0.0348760 0.0604071i
\(46\) 0 0
\(47\) 7.08512 + 5.94512i 1.03347 + 0.867185i 0.991260 0.131923i \(-0.0421153\pi\)
0.0422114 + 0.999109i \(0.486560\pi\)
\(48\) 0 0
\(49\) −6.23055 10.7916i −0.890079 1.54166i
\(50\) 0 0
\(51\) −4.08512 + 1.48686i −0.572032 + 0.208202i
\(52\) 0 0
\(53\) −0.464508 + 2.63435i −0.0638050 + 0.361856i 0.936143 + 0.351621i \(0.114369\pi\)
−0.999948 + 0.0102357i \(0.996742\pi\)
\(54\) 0 0
\(55\) −1.98293 + 1.66387i −0.267378 + 0.224357i
\(56\) 0 0
\(57\) −3.93969 1.86516i −0.521825 0.247046i
\(58\) 0 0
\(59\) −1.01707 + 0.853427i −0.132412 + 0.111107i −0.706588 0.707625i \(-0.749767\pi\)
0.574177 + 0.818731i \(0.305322\pi\)
\(60\) 0 0
\(61\) −1.15270 + 6.53731i −0.147589 + 0.837016i 0.817664 + 0.575696i \(0.195269\pi\)
−0.965252 + 0.261320i \(0.915842\pi\)
\(62\) 0 0
\(63\) −4.14543 + 1.50881i −0.522275 + 0.190093i
\(64\) 0 0
\(65\) 1.40033 + 2.42544i 0.173690 + 0.300839i
\(66\) 0 0
\(67\) 1.90760 + 1.60067i 0.233051 + 0.195553i 0.751833 0.659354i \(-0.229170\pi\)
−0.518782 + 0.854907i \(0.673614\pi\)
\(68\) 0 0
\(69\) 1.58125 2.73881i 0.190360 0.329714i
\(70\) 0 0
\(71\) 1.31908 + 7.48086i 0.156546 + 0.887815i 0.957359 + 0.288901i \(0.0932898\pi\)
−0.800813 + 0.598914i \(0.795599\pi\)
\(72\) 0 0
\(73\) −2.97431 1.08256i −0.348116 0.126704i 0.162043 0.986784i \(-0.448192\pi\)
−0.510160 + 0.860080i \(0.670414\pi\)
\(74\) 0 0
\(75\) 4.78106 0.552069
\(76\) 0 0
\(77\) 24.4047 2.78117
\(78\) 0 0
\(79\) 1.18732 + 0.432149i 0.133584 + 0.0486205i 0.407947 0.913006i \(-0.366245\pi\)
−0.274363 + 0.961626i \(0.588467\pi\)
\(80\) 0 0
\(81\) 0.173648 + 0.984808i 0.0192942 + 0.109423i
\(82\) 0 0
\(83\) −8.96838 + 15.5337i −0.984407 + 1.70504i −0.339867 + 0.940474i \(0.610382\pi\)
−0.644541 + 0.764570i \(0.722951\pi\)
\(84\) 0 0
\(85\) 1.55825 + 1.30753i 0.169016 + 0.141821i
\(86\) 0 0
\(87\) −0.754900 1.30753i −0.0809338 0.140181i
\(88\) 0 0
\(89\) −11.7280 + 4.26865i −1.24317 + 0.452476i −0.878088 0.478500i \(-0.841181\pi\)
−0.365081 + 0.930976i \(0.618959\pi\)
\(90\) 0 0
\(91\) 4.58512 26.0035i 0.480651 2.72591i
\(92\) 0 0
\(93\) −1.67365 + 1.40436i −0.173549 + 0.145625i
\(94\) 0 0
\(95\) 0.165907 + 2.03282i 0.0170217 + 0.208563i
\(96\) 0 0
\(97\) −6.36618 + 5.34186i −0.646388 + 0.542384i −0.905972 0.423337i \(-0.860859\pi\)
0.259585 + 0.965720i \(0.416414\pi\)
\(98\) 0 0
\(99\) 0.960637 5.44804i 0.0965477 0.547549i
\(100\) 0 0
\(101\) −1.16637 + 0.424525i −0.116059 + 0.0422419i −0.399397 0.916778i \(-0.630780\pi\)
0.283338 + 0.959020i \(0.408558\pi\)
\(102\) 0 0
\(103\) 1.69207 + 2.93075i 0.166724 + 0.288775i 0.937266 0.348614i \(-0.113348\pi\)
−0.770542 + 0.637389i \(0.780014\pi\)
\(104\) 0 0
\(105\) 1.58125 + 1.32683i 0.154314 + 0.129485i
\(106\) 0 0
\(107\) 7.90807 13.6972i 0.764502 1.32416i −0.176007 0.984389i \(-0.556318\pi\)
0.940509 0.339768i \(-0.110348\pi\)
\(108\) 0 0
\(109\) −1.00980 5.72686i −0.0967213 0.548534i −0.994206 0.107489i \(-0.965719\pi\)
0.897485 0.441045i \(-0.145392\pi\)
\(110\) 0 0
\(111\) −2.59240 0.943555i −0.246059 0.0895583i
\(112\) 0 0
\(113\) 12.1361 1.14167 0.570834 0.821066i \(-0.306620\pi\)
0.570834 + 0.821066i \(0.306620\pi\)
\(114\) 0 0
\(115\) −1.47977 −0.137989
\(116\) 0 0
\(117\) −5.62449 2.04715i −0.519984 0.189259i
\(118\) 0 0
\(119\) −3.33022 18.8866i −0.305281 1.73133i
\(120\) 0 0
\(121\) −9.80200 + 16.9776i −0.891091 + 1.54342i
\(122\) 0 0
\(123\) 1.50000 + 1.25865i 0.135250 + 0.113489i
\(124\) 0 0
\(125\) −2.28833 3.96351i −0.204675 0.354507i
\(126\) 0 0
\(127\) 0.426022 0.155059i 0.0378033 0.0137593i −0.323049 0.946382i \(-0.604708\pi\)
0.360853 + 0.932623i \(0.382486\pi\)
\(128\) 0 0
\(129\) 0.624485 3.54163i 0.0549829 0.311823i
\(130\) 0 0
\(131\) 8.27972 6.94751i 0.723402 0.607006i −0.204922 0.978778i \(-0.565694\pi\)
0.928324 + 0.371772i \(0.121250\pi\)
\(132\) 0 0
\(133\) 11.1211 15.6870i 0.964320 1.36024i
\(134\) 0 0
\(135\) 0.358441 0.300767i 0.0308497 0.0258859i
\(136\) 0 0
\(137\) 1.90508 10.8042i 0.162762 0.923068i −0.788580 0.614932i \(-0.789184\pi\)
0.951342 0.308136i \(-0.0997053\pi\)
\(138\) 0 0
\(139\) −12.6493 + 4.60397i −1.07290 + 0.390504i −0.817260 0.576269i \(-0.804508\pi\)
−0.255639 + 0.966772i \(0.582286\pi\)
\(140\) 0 0
\(141\) 4.62449 + 8.00984i 0.389452 + 0.674550i
\(142\) 0 0
\(143\) 25.3653 + 21.2840i 2.12115 + 1.77986i
\(144\) 0 0
\(145\) −0.353226 + 0.611806i −0.0293338 + 0.0508077i
\(146\) 0 0
\(147\) −2.16385 12.2718i −0.178471 1.01216i
\(148\) 0 0
\(149\) −7.69594 2.80109i −0.630476 0.229474i 0.00696263 0.999976i \(-0.497784\pi\)
−0.637438 + 0.770501i \(0.720006\pi\)
\(150\) 0 0
\(151\) −21.1411 −1.72044 −0.860221 0.509921i \(-0.829675\pi\)
−0.860221 + 0.509921i \(0.829675\pi\)
\(152\) 0 0
\(153\) −4.34730 −0.351458
\(154\) 0 0
\(155\) 0.960637 + 0.349643i 0.0771602 + 0.0280840i
\(156\) 0 0
\(157\) 3.41013 + 19.3398i 0.272158 + 1.54348i 0.747847 + 0.663871i \(0.231088\pi\)
−0.475689 + 0.879614i \(0.657801\pi\)
\(158\) 0 0
\(159\) −1.33750 + 2.31661i −0.106070 + 0.183719i
\(160\) 0 0
\(161\) 10.6873 + 8.96773i 0.842279 + 0.706756i
\(162\) 0 0
\(163\) 2.27584 + 3.94188i 0.178258 + 0.308752i 0.941284 0.337616i \(-0.109621\pi\)
−0.763026 + 0.646368i \(0.776287\pi\)
\(164\) 0 0
\(165\) −2.43242 + 0.885328i −0.189364 + 0.0689227i
\(166\) 0 0
\(167\) −3.32383 + 18.8504i −0.257205 + 1.45868i 0.533142 + 0.846026i \(0.321011\pi\)
−0.790348 + 0.612658i \(0.790100\pi\)
\(168\) 0 0
\(169\) 17.4855 14.6720i 1.34503 1.12862i
\(170\) 0 0
\(171\) −3.06418 3.10013i −0.234324 0.237073i
\(172\) 0 0
\(173\) 4.25284 3.56856i 0.323337 0.271312i −0.466641 0.884447i \(-0.654536\pi\)
0.789979 + 0.613134i \(0.210092\pi\)
\(174\) 0 0
\(175\) −3.66250 + 20.7711i −0.276859 + 1.57015i
\(176\) 0 0
\(177\) −1.24763 + 0.454099i −0.0937773 + 0.0341322i
\(178\) 0 0
\(179\) −4.17499 7.23130i −0.312054 0.540493i 0.666753 0.745279i \(-0.267684\pi\)
−0.978807 + 0.204786i \(0.934350\pi\)
\(180\) 0 0
\(181\) −9.64337 8.09175i −0.716786 0.601455i 0.209708 0.977764i \(-0.432749\pi\)
−0.926494 + 0.376309i \(0.877193\pi\)
\(182\) 0 0
\(183\) −3.31908 + 5.74881i −0.245353 + 0.424964i
\(184\) 0 0
\(185\) 0.224155 + 1.27125i 0.0164802 + 0.0934640i
\(186\) 0 0
\(187\) 22.5993 + 8.22546i 1.65262 + 0.601505i
\(188\) 0 0
\(189\) −4.41147 −0.320888
\(190\) 0 0
\(191\) 6.71688 0.486016 0.243008 0.970024i \(-0.421866\pi\)
0.243008 + 0.970024i \(0.421866\pi\)
\(192\) 0 0
\(193\) 11.7763 + 4.28623i 0.847677 + 0.308529i 0.729093 0.684415i \(-0.239942\pi\)
0.118584 + 0.992944i \(0.462164\pi\)
\(194\) 0 0
\(195\) 0.486329 + 2.75811i 0.0348268 + 0.197512i
\(196\) 0 0
\(197\) 2.03596 3.52638i 0.145056 0.251245i −0.784338 0.620334i \(-0.786997\pi\)
0.929394 + 0.369089i \(0.120330\pi\)
\(198\) 0 0
\(199\) 5.48158 + 4.59959i 0.388579 + 0.326057i 0.816059 0.577968i \(-0.196154\pi\)
−0.427480 + 0.904025i \(0.640599\pi\)
\(200\) 0 0
\(201\) 1.24510 + 2.15658i 0.0878226 + 0.152113i
\(202\) 0 0
\(203\) 6.25877 2.27801i 0.439280 0.159885i
\(204\) 0 0
\(205\) 0.159100 0.902302i 0.0111120 0.0630195i
\(206\) 0 0
\(207\) 2.42262 2.03282i 0.168384 0.141291i
\(208\) 0 0
\(209\) 10.0633 + 21.9136i 0.696093 + 1.51580i
\(210\) 0 0
\(211\) 2.03209 1.70513i 0.139895 0.117386i −0.570155 0.821537i \(-0.693117\pi\)
0.710050 + 0.704151i \(0.248672\pi\)
\(212\) 0 0
\(213\) −1.31908 + 7.48086i −0.0903817 + 0.512580i
\(214\) 0 0
\(215\) −1.58125 + 0.575529i −0.107840 + 0.0392507i
\(216\) 0 0
\(217\) −4.81908 8.34689i −0.327140 0.566624i
\(218\) 0 0
\(219\) −2.42468 2.03455i −0.163845 0.137482i
\(220\) 0 0
\(221\) 13.0103 22.5344i 0.875165 1.51583i
\(222\) 0 0
\(223\) −2.42246 13.7384i −0.162220 0.919993i −0.951885 0.306456i \(-0.900857\pi\)
0.789665 0.613538i \(-0.210254\pi\)
\(224\) 0 0
\(225\) 4.49273 + 1.63522i 0.299515 + 0.109015i
\(226\) 0 0
\(227\) 23.6117 1.56717 0.783583 0.621287i \(-0.213390\pi\)
0.783583 + 0.621287i \(0.213390\pi\)
\(228\) 0 0
\(229\) 8.61081 0.569019 0.284509 0.958673i \(-0.408169\pi\)
0.284509 + 0.958673i \(0.408169\pi\)
\(230\) 0 0
\(231\) 22.9329 + 8.34689i 1.50887 + 0.549185i
\(232\) 0 0
\(233\) −2.68139 15.2069i −0.175664 0.996238i −0.937375 0.348322i \(-0.886752\pi\)
0.761711 0.647916i \(-0.224359\pi\)
\(234\) 0 0
\(235\) 2.16385 3.74789i 0.141154 0.244486i
\(236\) 0 0
\(237\) 0.967911 + 0.812174i 0.0628726 + 0.0527564i
\(238\) 0 0
\(239\) 3.87939 + 6.71929i 0.250937 + 0.434635i 0.963784 0.266684i \(-0.0859281\pi\)
−0.712847 + 0.701319i \(0.752595\pi\)
\(240\) 0 0
\(241\) 12.4846 4.54401i 0.804202 0.292706i 0.0929755 0.995668i \(-0.470362\pi\)
0.711227 + 0.702963i \(0.248140\pi\)
\(242\) 0 0
\(243\) −0.173648 + 0.984808i −0.0111395 + 0.0631754i
\(244\) 0 0
\(245\) −4.46657 + 3.74789i −0.285358 + 0.239444i
\(246\) 0 0
\(247\) 25.2399 6.60549i 1.60598 0.420297i
\(248\) 0 0
\(249\) −13.7404 + 11.5295i −0.870759 + 0.730654i
\(250\) 0 0
\(251\) 3.06506 17.3828i 0.193465 1.09719i −0.721124 0.692806i \(-0.756374\pi\)
0.914588 0.404386i \(-0.132515\pi\)
\(252\) 0 0
\(253\) −16.4402 + 5.98373i −1.03358 + 0.376194i
\(254\) 0 0
\(255\) 1.01707 + 1.76162i 0.0636917 + 0.110317i
\(256\) 0 0
\(257\) 6.05303 + 5.07910i 0.377578 + 0.316825i 0.811751 0.584004i \(-0.198515\pi\)
−0.434173 + 0.900830i \(0.642959\pi\)
\(258\) 0 0
\(259\) 6.08512 10.5397i 0.378111 0.654908i
\(260\) 0 0
\(261\) −0.262174 1.48686i −0.0162282 0.0920345i
\(262\) 0 0
\(263\) −23.8405 8.67723i −1.47007 0.535061i −0.521949 0.852977i \(-0.674795\pi\)
−0.948119 + 0.317916i \(0.897017\pi\)
\(264\) 0 0
\(265\) 1.25166 0.0768888
\(266\) 0 0
\(267\) −12.4807 −0.763807
\(268\) 0 0
\(269\) −18.9538 6.89863i −1.15564 0.420617i −0.308099 0.951354i \(-0.599693\pi\)
−0.847536 + 0.530737i \(0.821915\pi\)
\(270\) 0 0
\(271\) −3.56165 20.1991i −0.216355 1.22701i −0.878540 0.477669i \(-0.841482\pi\)
0.662185 0.749341i \(-0.269629\pi\)
\(272\) 0 0
\(273\) 13.2023 22.8671i 0.799042 1.38398i
\(274\) 0 0
\(275\) −20.2613 17.0012i −1.22180 1.02521i
\(276\) 0 0
\(277\) −4.56758 7.91128i −0.274439 0.475343i 0.695554 0.718474i \(-0.255159\pi\)
−0.969994 + 0.243131i \(0.921826\pi\)
\(278\) 0 0
\(279\) −2.05303 + 0.747243i −0.122912 + 0.0447363i
\(280\) 0 0
\(281\) −0.595800 + 3.37895i −0.0355424 + 0.201571i −0.997408 0.0719508i \(-0.977078\pi\)
0.961866 + 0.273522i \(0.0881886\pi\)
\(282\) 0 0
\(283\) −8.61200 + 7.22632i −0.511930 + 0.429560i −0.861808 0.507235i \(-0.830668\pi\)
0.349878 + 0.936795i \(0.386223\pi\)
\(284\) 0 0
\(285\) −0.539363 + 1.96697i −0.0319491 + 0.116513i
\(286\) 0 0
\(287\) −6.61721 + 5.55250i −0.390602 + 0.327754i
\(288\) 0 0
\(289\) 0.329755 1.87014i 0.0193974 0.110008i
\(290\) 0 0
\(291\) −7.80928 + 2.84234i −0.457788 + 0.166621i
\(292\) 0 0
\(293\) 7.26604 + 12.5852i 0.424487 + 0.735233i 0.996372 0.0851007i \(-0.0271212\pi\)
−0.571886 + 0.820333i \(0.693788\pi\)
\(294\) 0 0
\(295\) 0.475900 + 0.399328i 0.0277080 + 0.0232498i
\(296\) 0 0
\(297\) 2.76604 4.79093i 0.160502 0.277998i
\(298\) 0 0
\(299\) 3.28699 + 18.6414i 0.190091 + 1.07806i
\(300\) 0 0
\(301\) 14.9081 + 5.42609i 0.859287 + 0.312755i
\(302\) 0 0
\(303\) −1.24123 −0.0713068
\(304\) 0 0
\(305\) 3.10607 0.177853
\(306\) 0 0
\(307\) −24.1532 8.79104i −1.37849 0.501731i −0.456773 0.889583i \(-0.650995\pi\)
−0.921721 + 0.387853i \(0.873217\pi\)
\(308\) 0 0
\(309\) 0.587649 + 3.33272i 0.0334302 + 0.189592i
\(310\) 0 0
\(311\) 2.91875 5.05542i 0.165507 0.286667i −0.771328 0.636438i \(-0.780407\pi\)
0.936835 + 0.349771i \(0.113741\pi\)
\(312\) 0 0
\(313\) −12.6480 10.6129i −0.714905 0.599876i 0.211066 0.977472i \(-0.432307\pi\)
−0.925971 + 0.377596i \(0.876751\pi\)
\(314\) 0 0
\(315\) 1.03209 + 1.78763i 0.0581516 + 0.100722i
\(316\) 0 0
\(317\) 25.3243 9.21729i 1.42235 0.517695i 0.487624 0.873054i \(-0.337864\pi\)
0.934730 + 0.355359i \(0.115641\pi\)
\(318\) 0 0
\(319\) −1.45037 + 8.22546i −0.0812051 + 0.460537i
\(320\) 0 0
\(321\) 12.1159 10.1664i 0.676242 0.567434i
\(322\) 0 0
\(323\) 15.5856 10.7782i 0.867205 0.599716i
\(324\) 0 0
\(325\) −21.9217 + 18.3945i −1.21600 + 1.02034i
\(326\) 0 0
\(327\) 1.00980 5.72686i 0.0558421 0.316696i
\(328\) 0 0
\(329\) −38.3410 + 13.9550i −2.11381 + 0.769362i
\(330\) 0 0
\(331\) 14.2442 + 24.6717i 0.782933 + 1.35608i 0.930226 + 0.366987i \(0.119611\pi\)
−0.147293 + 0.989093i \(0.547056\pi\)
\(332\) 0 0
\(333\) −2.11334 1.77330i −0.115810 0.0971764i
\(334\) 0 0
\(335\) 0.582596 1.00909i 0.0318306 0.0551323i
\(336\) 0 0
\(337\) 2.89780 + 16.4343i 0.157853 + 0.895231i 0.956131 + 0.292941i \(0.0946339\pi\)
−0.798277 + 0.602290i \(0.794255\pi\)
\(338\) 0 0
\(339\) 11.4042 + 4.15079i 0.619391 + 0.225440i
\(340\) 0 0
\(341\) 12.0865 0.654519
\(342\) 0 0
\(343\) 24.0915 1.30082
\(344\) 0 0
\(345\) −1.39053 0.506111i −0.0748636 0.0272481i
\(346\) 0 0
\(347\) 3.25237 + 18.4451i 0.174597 + 0.990186i 0.938608 + 0.344984i \(0.112116\pi\)
−0.764012 + 0.645202i \(0.776773\pi\)
\(348\) 0 0
\(349\) 0.820422 1.42101i 0.0439162 0.0760651i −0.843232 0.537550i \(-0.819350\pi\)
0.887148 + 0.461485i \(0.152683\pi\)
\(350\) 0 0
\(351\) −4.58512 3.84737i −0.244736 0.205358i
\(352\) 0 0
\(353\) 5.95336 + 10.3115i 0.316866 + 0.548827i 0.979832 0.199822i \(-0.0640363\pi\)
−0.662967 + 0.748649i \(0.730703\pi\)
\(354\) 0 0
\(355\) 3.34002 1.21567i 0.177270 0.0645210i
\(356\) 0 0
\(357\) 3.33022 18.8866i 0.176254 0.999586i
\(358\) 0 0
\(359\) −1.75877 + 1.47578i −0.0928244 + 0.0778889i −0.688019 0.725693i \(-0.741519\pi\)
0.595195 + 0.803582i \(0.297075\pi\)
\(360\) 0 0
\(361\) 18.6716 + 3.51735i 0.982715 + 0.185124i
\(362\) 0 0
\(363\) −15.0175 + 12.6012i −0.788216 + 0.661392i
\(364\) 0 0
\(365\) −0.257178 + 1.45853i −0.0134613 + 0.0763429i
\(366\) 0 0
\(367\) −20.1989 + 7.35181i −1.05438 + 0.383761i −0.810312 0.585998i \(-0.800703\pi\)
−0.244063 + 0.969759i \(0.578480\pi\)
\(368\) 0 0
\(369\) 0.979055 + 1.69577i 0.0509676 + 0.0882785i
\(370\) 0 0
\(371\) −9.03983 7.58532i −0.469325 0.393810i
\(372\) 0 0
\(373\) −13.9907 + 24.2325i −0.724409 + 1.25471i 0.234807 + 0.972042i \(0.424554\pi\)
−0.959217 + 0.282672i \(0.908779\pi\)
\(374\) 0 0
\(375\) −0.794730 4.50714i −0.0410397 0.232748i
\(376\) 0 0
\(377\) 8.49185 + 3.09078i 0.437352 + 0.159183i
\(378\) 0 0
\(379\) −8.88981 −0.456639 −0.228320 0.973586i \(-0.573323\pi\)
−0.228320 + 0.973586i \(0.573323\pi\)
\(380\) 0 0
\(381\) 0.453363 0.0232265
\(382\) 0 0
\(383\) −23.5069 8.55580i −1.20114 0.437181i −0.337521 0.941318i \(-0.609588\pi\)
−0.863624 + 0.504137i \(0.831811\pi\)
\(384\) 0 0
\(385\) −1.98293 11.2457i −0.101059 0.573136i
\(386\) 0 0
\(387\) 1.79813 3.11446i 0.0914043 0.158317i
\(388\) 0 0
\(389\) −17.8739 14.9980i −0.906244 0.760429i 0.0651569 0.997875i \(-0.479245\pi\)
−0.971401 + 0.237446i \(0.923690\pi\)
\(390\) 0 0
\(391\) 6.87417 + 11.9064i 0.347642 + 0.602133i
\(392\) 0 0
\(393\) 10.1566 3.69669i 0.512331 0.186473i
\(394\) 0 0
\(395\) 0.102663 0.582232i 0.00516555 0.0292953i
\(396\) 0 0
\(397\) 2.90239 2.43539i 0.145667 0.122229i −0.567042 0.823689i \(-0.691912\pi\)
0.712709 + 0.701460i \(0.247468\pi\)
\(398\) 0 0
\(399\) 15.8157 10.9373i 0.791774 0.547552i
\(400\) 0 0
\(401\) −16.7456 + 14.0512i −0.836234 + 0.701683i −0.956713 0.291032i \(-0.906001\pi\)
0.120479 + 0.992716i \(0.461557\pi\)
\(402\) 0 0
\(403\) 2.27079 12.8783i 0.113116 0.641514i
\(404\) 0 0
\(405\) 0.439693 0.160035i 0.0218485 0.00795220i
\(406\) 0 0
\(407\) 7.63088 + 13.2171i 0.378249 + 0.655146i
\(408\) 0 0
\(409\) −6.06418 5.08845i −0.299854 0.251608i 0.480429 0.877033i \(-0.340481\pi\)
−0.780284 + 0.625426i \(0.784925\pi\)
\(410\) 0 0
\(411\) 5.48545 9.50108i 0.270577 0.468654i
\(412\) 0 0
\(413\) −1.01707 5.76811i −0.0500469 0.283830i
\(414\) 0 0
\(415\) 7.88666 + 2.87051i 0.387141 + 0.140908i
\(416\) 0 0
\(417\) −13.4611 −0.659193
\(418\) 0 0
\(419\) −6.22937 −0.304325 −0.152162 0.988356i \(-0.548624\pi\)
−0.152162 + 0.988356i \(0.548624\pi\)
\(420\) 0 0
\(421\) 3.35591 + 1.22145i 0.163557 + 0.0595300i 0.422501 0.906362i \(-0.361152\pi\)
−0.258944 + 0.965892i \(0.583374\pi\)
\(422\) 0 0
\(423\) 1.60607 + 9.10846i 0.0780896 + 0.442868i
\(424\) 0 0
\(425\) −10.3923 + 18.0001i −0.504103 + 0.873131i
\(426\) 0 0
\(427\) −22.4329 18.8234i −1.08560 0.910929i
\(428\) 0 0
\(429\) 16.5560 + 28.6759i 0.799332 + 1.38448i
\(430\) 0 0
\(431\) −24.2520 + 8.82699i −1.16818 + 0.425181i −0.852011 0.523523i \(-0.824617\pi\)
−0.316164 + 0.948704i \(0.602395\pi\)
\(432\) 0 0
\(433\) 4.53209 25.7028i 0.217798 1.23520i −0.658186 0.752856i \(-0.728676\pi\)
0.875984 0.482340i \(-0.160213\pi\)
\(434\) 0 0
\(435\) −0.541174 + 0.454099i −0.0259473 + 0.0217724i
\(436\) 0 0
\(437\) −3.64543 + 13.2943i −0.174385 + 0.635952i
\(438\) 0 0
\(439\) −17.3366 + 14.5472i −0.827432 + 0.694298i −0.954700 0.297571i \(-0.903824\pi\)
0.127268 + 0.991868i \(0.459379\pi\)
\(440\) 0 0
\(441\) 2.16385 12.2718i 0.103040 0.584371i
\(442\) 0 0
\(443\) 13.5432 4.92933i 0.643458 0.234200i 0.000379869 1.00000i \(-0.499879\pi\)
0.643079 + 0.765800i \(0.277657\pi\)
\(444\) 0 0
\(445\) 2.91993 + 5.05747i 0.138418 + 0.239747i
\(446\) 0 0
\(447\) −6.27379 5.26433i −0.296740 0.248994i
\(448\) 0 0
\(449\) −18.1361 + 31.4126i −0.855895 + 1.48245i 0.0199166 + 0.999802i \(0.493660\pi\)
−0.875812 + 0.482653i \(0.839673\pi\)
\(450\) 0 0
\(451\) −1.88103 10.6679i −0.0885744 0.502331i
\(452\) 0 0
\(453\) −19.8662 7.23070i −0.933395 0.339728i
\(454\) 0 0
\(455\) −12.3550 −0.579213
\(456\) 0 0
\(457\) −40.4543 −1.89237 −0.946186 0.323623i \(-0.895099\pi\)
−0.946186 + 0.323623i \(0.895099\pi\)
\(458\) 0 0
\(459\) −4.08512 1.48686i −0.190677 0.0694008i
\(460\) 0 0
\(461\) −6.81996 38.6779i −0.317637 1.80141i −0.557037 0.830488i \(-0.688062\pi\)
0.239400 0.970921i \(-0.423049\pi\)
\(462\) 0 0
\(463\) 10.4167 18.0422i 0.484105 0.838494i −0.515729 0.856752i \(-0.672479\pi\)
0.999833 + 0.0182582i \(0.00581209\pi\)
\(464\) 0 0
\(465\) 0.783119 + 0.657115i 0.0363163 + 0.0304730i
\(466\) 0 0
\(467\) −5.96198 10.3265i −0.275888 0.477851i 0.694471 0.719521i \(-0.255638\pi\)
−0.970359 + 0.241669i \(0.922305\pi\)
\(468\) 0 0
\(469\) −10.3229 + 3.75725i −0.476669 + 0.173493i
\(470\) 0 0
\(471\) −3.41013 + 19.3398i −0.157130 + 0.891131i
\(472\) 0 0
\(473\) −15.2404 + 12.7882i −0.700752 + 0.588001i
\(474\) 0 0
\(475\) −20.1612 + 5.27633i −0.925057 + 0.242095i
\(476\) 0 0
\(477\) −2.04916 + 1.71945i −0.0938247 + 0.0787283i
\(478\) 0 0
\(479\) 1.28564 7.29125i 0.0587426 0.333146i −0.941247 0.337719i \(-0.890345\pi\)
0.999990 + 0.00457323i \(0.00145571\pi\)
\(480\) 0 0
\(481\) 15.5167 5.64760i 0.707499 0.257509i
\(482\) 0 0
\(483\) 6.97565 + 12.0822i 0.317403 + 0.549758i
\(484\) 0 0
\(485\) 2.97881 + 2.49952i 0.135261 + 0.113497i
\(486\) 0 0
\(487\) −11.2934 + 19.5607i −0.511752 + 0.886381i 0.488155 + 0.872757i \(0.337670\pi\)
−0.999907 + 0.0136238i \(0.995663\pi\)
\(488\) 0 0
\(489\) 0.790393 + 4.48254i 0.0357428 + 0.202707i
\(490\) 0 0
\(491\) 15.0680 + 5.48432i 0.680011 + 0.247504i 0.658852 0.752272i \(-0.271042\pi\)
0.0211590 + 0.999776i \(0.493264\pi\)
\(492\) 0 0
\(493\) 6.56355 0.295607
\(494\) 0 0
\(495\) −2.58853 −0.116346
\(496\) 0 0
\(497\) −31.4898 11.4613i −1.41251 0.514112i
\(498\) 0 0
\(499\) 6.09879 + 34.5880i 0.273019 + 1.54837i 0.745183 + 0.666860i \(0.232362\pi\)
−0.472164 + 0.881511i \(0.656527\pi\)
\(500\) 0 0
\(501\) −9.57057 + 16.5767i −0.427582 + 0.740593i
\(502\) 0 0
\(503\) −30.7395 25.7935i −1.37061 1.15007i −0.972545 0.232715i \(-0.925239\pi\)
−0.398061 0.917359i \(-0.630317\pi\)
\(504\) 0 0
\(505\) 0.290393 + 0.502975i 0.0129223 + 0.0223821i
\(506\) 0 0
\(507\) 21.4491 7.80683i 0.952587 0.346713i
\(508\) 0 0
\(509\) 0.745100 4.22567i 0.0330260 0.187300i −0.963832 0.266511i \(-0.914129\pi\)
0.996858 + 0.0792114i \(0.0252402\pi\)
\(510\) 0 0
\(511\) 10.6964 8.97535i 0.473181 0.397046i
\(512\) 0 0
\(513\) −1.81908 3.96118i −0.0803142 0.174890i
\(514\) 0 0
\(515\) 1.21301 1.01784i 0.0534517 0.0448513i
\(516\) 0 0
\(517\) 8.88490 50.3888i 0.390758 2.21610i
\(518\) 0 0
\(519\) 5.21688 1.89879i 0.228996 0.0833476i
\(520\) 0 0
\(521\) −4.38532 7.59559i −0.192124 0.332769i 0.753830 0.657070i \(-0.228204\pi\)
−0.945954 + 0.324301i \(0.894871\pi\)
\(522\) 0 0
\(523\) −22.9800 19.2825i −1.00484 0.843165i −0.0171965 0.999852i \(-0.505474\pi\)
−0.987648 + 0.156687i \(0.949919\pi\)
\(524\) 0 0
\(525\) −10.5458 + 18.2658i −0.460255 + 0.797184i
\(526\) 0 0
\(527\) −1.64930 9.35365i −0.0718446 0.407451i
\(528\) 0 0
\(529\) 12.2147 + 4.44577i 0.531072 + 0.193294i
\(530\) 0 0
\(531\) −1.32770 −0.0576171
\(532\) 0 0
\(533\) −11.7202 −0.507657
\(534\) 0 0
\(535\) −6.95424 2.53114i −0.300658 0.109431i
\(536\) 0 0
\(537\) −1.44996 8.22313i −0.0625704 0.354854i
\(538\) 0 0
\(539\) −34.4680 + 59.7003i −1.48464 + 2.57147i
\(540\) 0 0
\(541\) 3.83544 + 3.21831i 0.164898 + 0.138366i 0.721503 0.692411i \(-0.243452\pi\)
−0.556605 + 0.830778i \(0.687896\pi\)
\(542\) 0 0
\(543\) −6.29426 10.9020i −0.270113 0.467849i
\(544\) 0 0
\(545\) −2.55690 + 0.930637i −0.109526 + 0.0398641i
\(546\) 0 0
\(547\) −2.35803 + 13.3731i −0.100822 + 0.571790i 0.891985 + 0.452065i \(0.149313\pi\)
−0.992807 + 0.119725i \(0.961799\pi\)
\(548\) 0 0
\(549\) −5.08512 + 4.26692i −0.217028 + 0.182108i
\(550\) 0 0
\(551\) 4.62630 + 4.68058i 0.197087 + 0.199399i
\(552\) 0 0
\(553\) −4.26991 + 3.58288i −0.181575 + 0.152360i
\(554\) 0 0
\(555\) −0.224155 + 1.27125i −0.00951487 + 0.0539615i
\(556\) 0 0
\(557\) 22.2961 8.11511i 0.944715 0.343848i 0.176689 0.984267i \(-0.443461\pi\)
0.768026 + 0.640419i \(0.221239\pi\)
\(558\) 0 0
\(559\) 10.7626 + 18.6414i 0.455211 + 0.788449i
\(560\) 0 0
\(561\) 18.4231 + 15.4588i 0.777823 + 0.652671i
\(562\) 0 0
\(563\) −7.37211 + 12.7689i −0.310697 + 0.538144i −0.978514 0.206183i \(-0.933896\pi\)
0.667816 + 0.744326i \(0.267229\pi\)
\(564\) 0 0
\(565\) −0.986081 5.59234i −0.0414847 0.235272i
\(566\) 0 0
\(567\) −4.14543 1.50881i −0.174092 0.0633642i
\(568\) 0 0
\(569\) 23.9668 1.00474 0.502370 0.864653i \(-0.332462\pi\)
0.502370 + 0.864653i \(0.332462\pi\)
\(570\) 0 0
\(571\) 41.0847 1.71934 0.859671 0.510848i \(-0.170669\pi\)
0.859671 + 0.510848i \(0.170669\pi\)
\(572\) 0 0
\(573\) 6.31180 + 2.29731i 0.263679 + 0.0959714i
\(574\) 0 0
\(575\) −2.62558 14.8904i −0.109494 0.620973i
\(576\) 0 0
\(577\) 3.72756 6.45632i 0.155180 0.268780i −0.777944 0.628333i \(-0.783737\pi\)
0.933125 + 0.359553i \(0.117071\pi\)
\(578\) 0 0
\(579\) 9.60014 + 8.05547i 0.398968 + 0.334774i
\(580\) 0 0
\(581\) −39.5638 68.5265i −1.64138 2.84296i
\(582\) 0 0
\(583\) 13.9058 5.06132i 0.575921 0.209618i
\(584\) 0 0
\(585\) −0.486329 + 2.75811i −0.0201072 + 0.114034i
\(586\) 0 0
\(587\) −4.53462 + 3.80499i −0.187164 + 0.157049i −0.731555 0.681782i \(-0.761205\pi\)
0.544391 + 0.838831i \(0.316761\pi\)
\(588\) 0 0
\(589\) 5.50774 7.76903i 0.226943 0.320117i
\(590\) 0 0
\(591\) 3.11927 2.61738i 0.128310 0.107665i
\(592\) 0 0
\(593\) −0.870767 + 4.93837i −0.0357581 + 0.202794i −0.997453 0.0713281i \(-0.977276\pi\)
0.961695 + 0.274122i \(0.0883874\pi\)
\(594\) 0 0
\(595\) −8.43242 + 3.06915i −0.345695 + 0.125823i
\(596\) 0 0
\(597\) 3.57785 + 6.19702i 0.146432 + 0.253627i
\(598\) 0 0
\(599\) −3.68164 3.08926i −0.150428 0.126224i 0.564468 0.825455i \(-0.309081\pi\)
−0.714896 + 0.699231i \(0.753526\pi\)
\(600\) 0 0
\(601\) −4.42468 + 7.66377i −0.180486 + 0.312612i −0.942046 0.335483i \(-0.891101\pi\)
0.761560 + 0.648095i \(0.224434\pi\)
\(602\) 0 0
\(603\) 0.432419 + 2.45237i 0.0176094 + 0.0998681i
\(604\) 0 0
\(605\) 8.61974 + 3.13733i 0.350442 + 0.127551i
\(606\) 0 0
\(607\) −0.715948 −0.0290594 −0.0145297 0.999894i \(-0.504625\pi\)
−0.0145297 + 0.999894i \(0.504625\pi\)
\(608\) 0 0
\(609\) 6.66044 0.269895
\(610\) 0 0
\(611\) −52.0207 18.9340i −2.10453 0.765987i
\(612\) 0 0
\(613\) 4.23870 + 24.0389i 0.171200 + 0.970921i 0.942440 + 0.334377i \(0.108526\pi\)
−0.771240 + 0.636545i \(0.780363\pi\)
\(614\) 0 0
\(615\) 0.458111 0.793471i 0.0184728 0.0319959i
\(616\) 0 0
\(617\) −33.2918 27.9351i −1.34028 1.12463i −0.981555 0.191182i \(-0.938768\pi\)
−0.358722 0.933444i \(-0.616788\pi\)
\(618\) 0 0
\(619\) 11.8648 + 20.5505i 0.476888 + 0.825994i 0.999649 0.0264848i \(-0.00843137\pi\)
−0.522761 + 0.852479i \(0.675098\pi\)
\(620\) 0 0
\(621\) 2.97178 1.08164i 0.119253 0.0434047i
\(622\) 0 0
\(623\) 9.56077 54.2218i 0.383044 2.17235i
\(624\) 0 0
\(625\) 16.6721 13.9895i 0.666882 0.559581i
\(626\) 0 0
\(627\) 1.96151 + 24.0339i 0.0783353 + 0.959822i
\(628\) 0 0
\(629\) 9.18732 7.70908i 0.366322 0.307381i
\(630\) 0 0
\(631\) 4.48293 25.4239i 0.178462 1.01211i −0.755609 0.655023i \(-0.772659\pi\)
0.934071 0.357087i \(-0.116230\pi\)
\(632\) 0 0
\(633\) 2.49273 0.907278i 0.0990770 0.0360611i
\(634\) 0 0
\(635\) −0.106067 0.183713i −0.00420913 0.00729043i
\(636\) 0 0
\(637\) 57.1357 + 47.9425i 2.26380 + 1.89955i
\(638\) 0 0
\(639\) −3.79813 + 6.57856i −0.150252 + 0.260244i
\(640\) 0 0
\(641\) −1.87645 10.6419i −0.0741153 0.420329i −0.999179 0.0405163i \(-0.987100\pi\)
0.925064 0.379812i \(-0.124011\pi\)
\(642\) 0 0
\(643\) 13.5360 + 4.92669i 0.533806 + 0.194290i 0.594837 0.803846i \(-0.297217\pi\)
−0.0610309 + 0.998136i \(0.519439\pi\)
\(644\) 0 0
\(645\) −1.68273 −0.0662576
\(646\) 0 0
\(647\) 24.9463 0.980738 0.490369 0.871515i \(-0.336862\pi\)
0.490369 + 0.871515i \(0.336862\pi\)
\(648\) 0 0
\(649\) 6.90198 + 2.51211i 0.270926 + 0.0986091i
\(650\) 0 0
\(651\) −1.67365 9.49173i −0.0655954 0.372010i
\(652\) 0 0
\(653\) −17.8071 + 30.8427i −0.696844 + 1.20697i 0.272711 + 0.962096i \(0.412080\pi\)
−0.969555 + 0.244873i \(0.921254\pi\)
\(654\) 0 0
\(655\) −3.87417 3.25082i −0.151376 0.127020i
\(656\) 0 0
\(657\) −1.58260 2.74114i −0.0617430 0.106942i
\(658\) 0 0
\(659\) −46.0163 + 16.7485i −1.79254 + 0.652431i −0.793501 + 0.608569i \(0.791744\pi\)
−0.999038 + 0.0438619i \(0.986034\pi\)
\(660\) 0 0
\(661\) −5.90966 + 33.5154i −0.229859 + 1.30360i 0.623315 + 0.781971i \(0.285785\pi\)
−0.853174 + 0.521626i \(0.825326\pi\)
\(662\) 0 0
\(663\) 19.9329 16.7257i 0.774129 0.649571i
\(664\) 0 0
\(665\) −8.13223 3.85002i −0.315354 0.149297i
\(666\) 0 0
\(667\) −3.65767 + 3.06915i −0.141626 + 0.118838i
\(668\) 0 0
\(669\) 2.42246 13.7384i 0.0936576 0.531158i
\(670\) 0 0
\(671\) 34.5082 12.5600i 1.33217 0.484872i
\(672\) 0 0
\(673\) 14.1493 + 24.5073i 0.545415 + 0.944687i 0.998581 + 0.0532607i \(0.0169614\pi\)
−0.453165 + 0.891427i \(0.649705\pi\)
\(674\) 0 0
\(675\) 3.66250 + 3.07321i 0.140970 + 0.118288i
\(676\) 0 0
\(677\) −12.5025 + 21.6550i −0.480511 + 0.832270i −0.999750 0.0223595i \(-0.992882\pi\)
0.519239 + 0.854629i \(0.326215\pi\)
\(678\) 0 0
\(679\) −6.36618 36.1044i −0.244312 1.38556i
\(680\) 0 0
\(681\) 22.1878 + 8.07569i 0.850238 + 0.309461i
\(682\) 0 0
\(683\) 40.1284 1.53547 0.767734 0.640768i \(-0.221384\pi\)
0.767734 + 0.640768i \(0.221384\pi\)
\(684\) 0 0
\(685\) −5.13341 −0.196137
\(686\) 0 0
\(687\) 8.09152 + 2.94507i 0.308711 + 0.112362i
\(688\) 0 0
\(689\) −2.78029 15.7678i −0.105921 0.600705i
\(690\) 0 0
\(691\) 1.44087 2.49567i 0.0548135 0.0949397i −0.837317 0.546718i \(-0.815877\pi\)
0.892130 + 0.451778i \(0.149210\pi\)
\(692\) 0 0
\(693\) 18.6951 + 15.6870i 0.710167 + 0.595901i
\(694\) 0 0
\(695\) 3.14930 + 5.45475i 0.119460 + 0.206910i
\(696\) 0 0
\(697\) −7.99912 + 2.91144i −0.302988 + 0.110279i
\(698\) 0 0
\(699\) 2.68139 15.2069i 0.101419 0.575178i
\(700\) 0 0
\(701\) 11.8491 9.94258i 0.447535 0.375526i −0.390985 0.920397i \(-0.627866\pi\)
0.838520 + 0.544871i \(0.183421\pi\)
\(702\) 0 0
\(703\) 11.9731 + 1.11792i 0.451575 + 0.0421630i
\(704\) 0 0
\(705\) 3.31521 2.78179i 0.124858 0.104768i
\(706\) 0 0
\(707\) 0.950837 5.39246i 0.0357599 0.202804i
\(708\) 0 0
\(709\) −43.8353 + 15.9548i −1.64627 + 0.599193i −0.988119 0.153692i \(-0.950884\pi\)
−0.658152 + 0.752885i \(0.728661\pi\)
\(710\) 0 0
\(711\) 0.631759 + 1.09424i 0.0236928 + 0.0410372i
\(712\) 0 0
\(713\) 5.29292 + 4.44129i 0.198221 + 0.166327i
\(714\) 0 0
\(715\) 7.74675 13.4178i 0.289712 0.501796i
\(716\) 0 0
\(717\) 1.34730 + 7.64090i 0.0503157 + 0.285355i
\(718\) 0 0
\(719\) −10.8020 3.93161i −0.402847 0.146624i 0.132647 0.991163i \(-0.457652\pi\)
−0.535494 + 0.844539i \(0.679875\pi\)
\(720\) 0 0
\(721\) −14.9290 −0.555986
\(722\) 0 0
\(723\) 13.2858 0.494104
\(724\) 0 0
\(725\) −6.78312 2.46885i −0.251919 0.0916909i
\(726\) 0 0
\(727\) −3.02687 17.1663i −0.112261 0.636661i −0.988070 0.154004i \(-0.950783\pi\)
0.875810 0.482657i \(-0.160328\pi\)
\(728\) 0 0
\(729\) −0.500000 + 0.866025i −0.0185185 + 0.0320750i
\(730\) 0 0
\(731\) 11.9764 + 10.0494i 0.442962 + 0.371689i
\(732\) 0 0
\(733\) 21.9393 + 38.0000i 0.810346 + 1.40356i 0.912622 + 0.408804i \(0.134054\pi\)
−0.102276 + 0.994756i \(0.532613\pi\)
\(734\) 0 0
\(735\) −5.47906 + 1.99421i −0.202098 + 0.0735577i
\(736\) 0 0
\(737\) 2.39218 13.5667i 0.0881170 0.499736i
\(738\) 0 0
\(739\) 13.6040 11.4151i 0.500432 0.419912i −0.357316 0.933984i \(-0.616308\pi\)
0.857747 + 0.514072i \(0.171864\pi\)
\(740\) 0 0
\(741\) 25.9770 + 2.42544i 0.954289 + 0.0891008i
\(742\) 0 0
\(743\) −7.98751 + 6.70232i −0.293033 + 0.245884i −0.777438 0.628960i \(-0.783481\pi\)
0.484404 + 0.874844i \(0.339036\pi\)
\(744\) 0 0
\(745\) −0.665441 + 3.77390i −0.0243799 + 0.138265i
\(746\) 0 0
\(747\) −16.8550 + 6.13473i −0.616694 + 0.224458i
\(748\) 0 0
\(749\) 34.8862 + 60.4248i 1.27472 + 2.20787i
\(750\) 0 0
\(751\) 26.0915 + 21.8934i 0.952093 + 0.798901i 0.979649 0.200719i \(-0.0643279\pi\)
−0.0275557 + 0.999620i \(0.508772\pi\)
\(752\) 0 0
\(753\) 8.82547 15.2862i 0.321618 0.557059i
\(754\) 0 0
\(755\) 1.71776 + 9.74189i 0.0625156 + 0.354544i
\(756\) 0 0
\(757\) −40.6664 14.8014i −1.47805 0.537965i −0.527774 0.849385i \(-0.676973\pi\)
−0.950272 + 0.311420i \(0.899195\pi\)
\(758\) 0 0
\(759\) −17.4953 −0.635037
\(760\) 0 0
\(761\) 14.1679 0.513585 0.256793 0.966467i \(-0.417334\pi\)
0.256793 + 0.966467i \(0.417334\pi\)
\(762\) 0 0
\(763\) 24.1065 + 8.77406i 0.872715 + 0.317642i
\(764\) 0 0
\(765\) 0.353226 + 2.00324i 0.0127709 + 0.0724275i
\(766\) 0 0
\(767\) 3.97343 6.88218i 0.143472 0.248501i
\(768\) 0 0
\(769\) −13.9722 11.7241i −0.503852 0.422782i 0.355107 0.934825i \(-0.384444\pi\)
−0.858960 + 0.512043i \(0.828889\pi\)
\(770\) 0 0
\(771\) 3.95084 + 6.84305i 0.142286 + 0.246446i
\(772\) 0 0
\(773\) 26.5437 9.66112i 0.954711 0.347486i 0.182752 0.983159i \(-0.441499\pi\)
0.771959 + 0.635673i \(0.219277\pi\)
\(774\) 0 0
\(775\) −1.81386 + 10.2869i −0.0651559 + 0.369517i
\(776\) 0 0
\(777\) 9.32295 7.82288i 0.334459 0.280644i
\(778\) 0 0
\(779\) −7.71436 3.65219i −0.276395 0.130853i
\(780\) 0 0
\(781\) 32.1917 27.0120i 1.15191 0.966566i
\(782\) 0 0
\(783\) 0.262174 1.48686i 0.00936934 0.0531361i
\(784\) 0 0
\(785\) 8.63475 3.14279i 0.308188 0.112171i
\(786\) 0 0
\(787\) 9.07057 + 15.7107i 0.323331 + 0.560026i 0.981173 0.193130i \(-0.0618639\pi\)
−0.657842 + 0.753156i \(0.728531\pi\)
\(788\) 0 0
\(789\) −19.4349 16.3079i −0.691902 0.580575i
\(790\) 0 0
\(791\) −26.7690 + 46.3653i −0.951797 + 1.64856i
\(792\) 0 0
\(793\) −6.89945 39.1287i −0.245007 1.38950i
\(794\) 0 0
\(795\) 1.17617 + 0.428092i 0.0417146 + 0.0151829i
\(796\) 0 0
\(797\) −32.8111 −1.16223 −0.581114 0.813822i \(-0.697383\pi\)
−0.581114 + 0.813822i \(0.697383\pi\)
\(798\) 0 0
\(799\) −40.2080 −1.42246
\(800\) 0 0
\(801\) −11.7280 4.26865i −0.414389 0.150825i
\(802\) 0 0
\(803\) 3.04060 + 17.2441i 0.107300 + 0.608531i
\(804\) 0 0
\(805\) 3.26399 5.65339i 0.115040 0.199256i
\(806\) 0 0
\(807\) −15.4513 12.9652i −0.543912 0.456396i
\(808\) 0 0
\(809\) 4.67112 + 8.09062i 0.164228 + 0.284451i 0.936381 0.350986i \(-0.114153\pi\)
−0.772153 + 0.635437i \(0.780820\pi\)
\(810\) 0 0
\(811\) −14.1027 + 5.13295i −0.495211 + 0.180242i −0.577539 0.816363i \(-0.695987\pi\)
0.0823275 + 0.996605i \(0.473765\pi\)
\(812\) 0 0
\(813\) 3.56165 20.1991i 0.124913 0.708414i
\(814\) 0 0
\(815\) 1.63151 1.36900i 0.0571493 0.0479540i
\(816\) 0 0
\(817\) 1.27513 + 15.6238i 0.0446111 + 0.546608i
\(818\) 0 0
\(819\) 20.2271 16.9726i 0.706794 0.593070i
\(820\) 0 0
\(821\) 6.34760 35.9990i 0.221533 1.25637i −0.647671 0.761920i \(-0.724257\pi\)
0.869203 0.494455i \(-0.164632\pi\)
\(822\) 0 0
\(823\) 21.4595 7.81060i 0.748030 0.272261i 0.0602532 0.998183i \(-0.480809\pi\)
0.687776 + 0.725923i \(0.258587\pi\)
\(824\) 0 0
\(825\) −13.2246 22.9057i −0.460422 0.797475i
\(826\) 0 0
\(827\) −1.86303 1.56326i −0.0647838 0.0543600i 0.609821 0.792539i \(-0.291241\pi\)
−0.674605 + 0.738179i \(0.735686\pi\)
\(828\) 0 0
\(829\) 11.6702 20.2135i 0.405324 0.702042i −0.589035 0.808108i \(-0.700492\pi\)
0.994359 + 0.106065i \(0.0338253\pi\)
\(830\) 0 0
\(831\) −1.58630 8.99638i −0.0550283 0.312081i
\(832\) 0 0
\(833\) 50.9051 + 18.5280i 1.76376 + 0.641956i
\(834\) 0 0
\(835\) 8.95636 0.309947
\(836\) 0 0
\(837\) −2.18479 −0.0755175
\(838\) 0 0
\(839\) −1.37851 0.501736i −0.0475914 0.0173218i 0.318115 0.948052i \(-0.396950\pi\)
−0.365706 + 0.930730i \(0.619172\pi\)
\(840\) 0 0
\(841\) −4.63997 26.3146i −0.159999 0.907399i
\(842\) 0 0
\(843\) −1.71554 + 2.97140i −0.0590862 + 0.102340i
\(844\) 0 0
\(845\) −8.18164 6.86521i −0.281457 0.236170i
\(846\) 0 0
\(847\) −43.2413 74.8961i −1.48579 2.57346i
\(848\) 0 0
\(849\) −10.5642 + 3.84505i −0.362562 + 0.131962i
\(850\) 0 0
\(851\) −1.51501 + 8.59208i −0.0519340 + 0.294533i
\(852\) 0 0
\(853\) −7.15207 + 6.00130i −0.244882 + 0.205481i −0.756965 0.653456i \(-0.773319\pi\)
0.512083 + 0.858936i \(0.328874\pi\)
\(854\) 0 0
\(855\) −1.17958 + 1.66387i −0.0403407 + 0.0569032i
\(856\) 0 0
\(857\) 26.6930 22.3981i 0.911816 0.765104i −0.0606480 0.998159i \(-0.519317\pi\)
0.972464 + 0.233055i \(0.0748723\pi\)
\(858\) 0 0
\(859\) 4.00758 22.7281i 0.136737 0.775473i −0.836898 0.547359i \(-0.815633\pi\)
0.973635 0.228114i \(-0.0732558\pi\)
\(860\) 0 0
\(861\) −8.11721 + 2.95442i −0.276634 + 0.100686i
\(862\) 0 0
\(863\) 21.5788 + 37.3755i 0.734550 + 1.27228i 0.954920 + 0.296862i \(0.0959402\pi\)
−0.220370 + 0.975416i \(0.570727\pi\)
\(864\) 0 0
\(865\) −1.98995 1.66977i −0.0676604 0.0567738i
\(866\) 0 0
\(867\) 0.949493 1.64457i 0.0322465 0.0558525i
\(868\) 0 0
\(869\) −1.21378 6.88370i −0.0411748 0.233514i
\(870\) 0 0
\(871\) −14.0061 5.09780i −0.474578 0.172732i
\(872\) 0 0
\(873\) −8.31046 −0.281266
\(874\) 0 0
\(875\) 20.1898 0.682541
\(876\) 0 0
\(877\) −42.1374 15.3368i −1.42288 0.517886i −0.487998 0.872845i \(-0.662273\pi\)
−0.934882 + 0.354959i \(0.884495\pi\)
\(878\) 0 0
\(879\) 2.52347 + 14.3113i 0.0851146 + 0.482709i
\(880\) 0 0
\(881\) 2.29932 3.98253i 0.0774659 0.134175i −0.824690 0.565585i \(-0.808650\pi\)
0.902156 + 0.431410i \(0.141984\pi\)
\(882\) 0 0
\(883\) 5.53524 + 4.64462i 0.186276 + 0.156304i 0.731157 0.682209i \(-0.238981\pi\)
−0.544881 + 0.838513i \(0.683425\pi\)
\(884\) 0 0
\(885\) 0.310622 + 0.538013i 0.0104414 + 0.0180851i
\(886\) 0 0
\(887\) 43.5676 15.8573i 1.46286 0.532437i 0.516707 0.856162i \(-0.327158\pi\)
0.946151 + 0.323725i \(0.104935\pi\)
\(888\) 0 0
\(889\) −0.347296 + 1.96962i −0.0116479 + 0.0660588i
\(890\) 0 0
\(891\) 4.23783 3.55596i 0.141973 0.119129i
\(892\) 0 0
\(893\) −28.3405 28.6730i −0.948378 0.959506i
\(894\) 0 0
\(895\) −2.99297 + 2.51140i −0.100044 + 0.0839470i
\(896\) 0 0
\(897\) −3.28699 + 18.6414i −0.109749 + 0.622420i
\(898\) 0 0
\(899\) 3.09967 1.12819i 0.103380 0.0376272i
\(900\) 0 0
\(901\) −5.81449 10.0710i −0.193709 0.335514i
\(902\) 0 0
\(903\) 12.1532 + 10.1977i 0.404432 + 0.339359i
\(904\) 0 0
\(905\) −2.94516 + 5.10116i −0.0979003 + 0.169568i
\(906\) 0 0
\(907\) 9.44222 + 53.5495i 0.313524 + 1.77808i 0.580381 + 0.814345i \(0.302904\pi\)
−0.266857 + 0.963736i \(0.585985\pi\)
\(908\) 0 0
\(909\) −1.16637 0.424525i −0.0386862 0.0140806i
\(910\) 0 0
\(911\) 16.8993 0.559899 0.279950 0.960015i \(-0.409682\pi\)
0.279950 + 0.960015i \(0.409682\pi\)
\(912\) 0 0
\(913\) 99.2277 3.28396
\(914\) 0 0
\(915\) 2.91875 + 1.06234i 0.0964908 + 0.0351198i
\(916\) 0 0
\(917\) 8.27972 + 46.9566i 0.273420 + 1.55064i
\(918\) 0 0
\(919\) −3.85100 + 6.67014i −0.127033 + 0.220027i −0.922526 0.385936i \(-0.873879\pi\)
0.795493 + 0.605963i \(0.207212\pi\)
\(920\) 0 0
\(921\) −19.6898 16.5217i −0.648802 0.544410i
\(922\) 0 0
\(923\) −22.7335 39.3757i −0.748284 1.29607i
\(924\) 0 0
\(925\) −12.3944 + 4.51119i −0.407525 + 0.148327i
\(926\) 0 0
\(927\) −0.587649 + 3.33272i −0.0193009 + 0.109461i
\(928\) 0 0
\(929\) −13.9010 + 11.6644i −0.456078 + 0.382695i −0.841686 0.539968i \(-0.818436\pi\)
0.385607 + 0.922663i \(0.373992\pi\)
\(930\) 0 0
\(931\) 22.6677 + 49.3607i 0.742904 + 1.61773i
\(932\) 0 0
\(933\) 4.47178 3.75227i 0.146400 0.122844i
\(934\) 0 0
\(935\) 1.95408 11.0821i 0.0639052 0.362424i
\(936\) 0 0
\(937\) 9.71436 3.53574i 0.317354 0.115507i −0.178432 0.983952i \(-0.557102\pi\)
0.495786 + 0.868445i \(0.334880\pi\)
\(938\) 0 0
\(939\) −8.25537 14.2987i −0.269404 0.466621i
\(940\) 0 0
\(941\) 34.5808 + 29.0168i 1.12730 + 0.945920i 0.998950 0.0458088i \(-0.0145865\pi\)
0.128353 + 0.991729i \(0.459031\pi\)
\(942\) 0 0
\(943\) 3.09627 5.36289i 0.100828 0.174640i
\(944\) 0 0
\(945\) 0.358441 + 2.03282i 0.0116601 + 0.0661276i
\(946\) 0 0
\(947\) −18.9561 6.89944i −0.615989 0.224202i 0.0151327 0.999885i \(-0.495183\pi\)
−0.631122 + 0.775684i \(0.717405\pi\)
\(948\) 0 0
\(949\) 18.9451 0.614984
\(950\) 0 0
\(951\) 26.9495 0.873899
\(952\) 0 0
\(953\) 42.0232 + 15.2952i 1.36127 + 0.495460i 0.916445 0.400160i \(-0.131045\pi\)
0.444820 + 0.895620i \(0.353268\pi\)
\(954\) 0 0
\(955\) −0.545759 3.09516i −0.0176604 0.100157i
\(956\) 0 0
\(957\) −4.17617 + 7.23335i −0.134997 + 0.233821i
\(958\) 0 0
\(959\) 37.0749 + 31.1095i 1.19721 + 1.00458i
\(960\) 0 0
\(961\) 13.1133 + 22.7130i 0.423011 + 0.732677i
\(962\) 0 0
\(963\) 14.8623 5.40944i 0.478931 0.174317i
\(964\) 0 0
\(965\) 1.01826 5.77482i 0.0327788 0.185898i
\(966\) 0 0
\(967\) 8.96270 7.52060i 0.288221 0.241846i −0.487201 0.873290i \(-0.661982\pi\)
0.775421 + 0.631444i \(0.217537\pi\)
\(968\) 0 0
\(969\) 18.3320 4.79763i 0.588910 0.154122i
\(970\) 0 0
\(971\) −27.9786 + 23.4769i −0.897877 + 0.753409i −0.969774 0.244003i \(-0.921539\pi\)
0.0718969 + 0.997412i \(0.477095\pi\)
\(972\) 0 0
\(973\) 10.3118 58.4811i 0.330581 1.87482i
\(974\) 0 0
\(975\) −26.8910 + 9.78752i −0.861201 + 0.313452i
\(976\) 0 0
\(977\) 25.0219 + 43.3392i 0.800521 + 1.38654i 0.919274 + 0.393619i \(0.128777\pi\)
−0.118753 + 0.992924i \(0.537890\pi\)
\(978\) 0 0
\(979\) 52.8911 + 44.3809i 1.69041 + 1.41842i
\(980\) 0 0
\(981\) 2.90760 5.03612i 0.0928326 0.160791i
\(982\) 0 0
\(983\) −1.71317 9.71589i −0.0546417 0.309889i 0.945221 0.326430i \(-0.105846\pi\)
−0.999863 + 0.0165411i \(0.994735\pi\)
\(984\) 0 0
\(985\) −1.79039 0.651650i −0.0570466 0.0207633i
\(986\) 0 0
\(987\) −40.8016 −1.29873
\(988\) 0 0
\(989\) −11.3732 −0.361647
\(990\) 0 0
\(991\) 32.1596 + 11.7051i 1.02158 + 0.371826i 0.797870 0.602830i \(-0.205960\pi\)
0.223712 + 0.974655i \(0.428182\pi\)
\(992\) 0 0
\(993\) 4.94697 + 28.0556i 0.156987 + 0.890319i
\(994\) 0 0
\(995\) 1.67412 2.89965i 0.0530730 0.0919252i
\(996\) 0 0
\(997\) 30.4818 + 25.5773i 0.965368 + 0.810040i 0.981818 0.189825i \(-0.0607919\pi\)
−0.0164497 + 0.999865i \(0.505236\pi\)
\(998\) 0 0
\(999\) −1.37939 2.38917i −0.0436418 0.0755898i
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.bo.c.481.1 6
4.3 odd 2 114.2.i.b.25.1 6
12.11 even 2 342.2.u.d.253.1 6
19.16 even 9 inner 912.2.bo.c.529.1 6
76.15 even 18 2166.2.a.n.1.3 3
76.23 odd 18 2166.2.a.t.1.3 3
76.35 odd 18 114.2.i.b.73.1 yes 6
228.23 even 18 6498.2.a.bo.1.1 3
228.35 even 18 342.2.u.d.73.1 6
228.167 odd 18 6498.2.a.bt.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
114.2.i.b.25.1 6 4.3 odd 2
114.2.i.b.73.1 yes 6 76.35 odd 18
342.2.u.d.73.1 6 228.35 even 18
342.2.u.d.253.1 6 12.11 even 2
912.2.bo.c.481.1 6 1.1 even 1 trivial
912.2.bo.c.529.1 6 19.16 even 9 inner
2166.2.a.n.1.3 3 76.15 even 18
2166.2.a.t.1.3 3 76.23 odd 18
6498.2.a.bo.1.1 3 228.23 even 18
6498.2.a.bt.1.1 3 228.167 odd 18