Properties

Label 605.2.b.d.364.1
Level $605$
Weight $2$
Character 605.364
Analytic conductor $4.831$
Analytic rank $0$
Dimension $4$
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] = [605,2,Mod(364,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.364");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.b (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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 4x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 364.1
Root \(-1.93185i\) of defining polynomial
Character \(\chi\) \(=\) 605.364
Dual form 605.2.b.d.364.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.93185i q^{2} -0.517638i q^{3} -1.73205 q^{4} +(-1.73205 - 1.41421i) q^{5} -1.00000 q^{6} -0.896575i q^{7} -0.517638i q^{8} +2.73205 q^{9} +O(q^{10})\) \(q-1.93185i q^{2} -0.517638i q^{3} -1.73205 q^{4} +(-1.73205 - 1.41421i) q^{5} -1.00000 q^{6} -0.896575i q^{7} -0.517638i q^{8} +2.73205 q^{9} +(-2.73205 + 3.34607i) q^{10} +0.896575i q^{12} -4.24264i q^{13} -1.73205 q^{14} +(-0.732051 + 0.896575i) q^{15} -4.46410 q^{16} -1.03528i q^{17} -5.27792i q^{18} -6.19615 q^{19} +(3.00000 + 2.44949i) q^{20} -0.464102 q^{21} +6.31319i q^{23} -0.267949 q^{24} +(1.00000 + 4.89898i) q^{25} -8.19615 q^{26} -2.96713i q^{27} +1.55291i q^{28} +6.92820 q^{29} +(1.73205 + 1.41421i) q^{30} -5.26795 q^{31} +7.58871i q^{32} -2.00000 q^{34} +(-1.26795 + 1.55291i) q^{35} -4.73205 q^{36} +6.69213i q^{37} +11.9700i q^{38} -2.19615 q^{39} +(-0.732051 + 0.896575i) q^{40} -1.73205 q^{41} +0.896575i q^{42} -10.6945i q^{43} +(-4.73205 - 3.86370i) q^{45} +12.1962 q^{46} +4.10394i q^{47} +2.31079i q^{48} +6.19615 q^{49} +(9.46410 - 1.93185i) q^{50} -0.535898 q^{51} +7.34847i q^{52} -11.9700i q^{53} -5.73205 q^{54} -0.464102 q^{56} +3.20736i q^{57} -13.3843i q^{58} +4.73205 q^{59} +(1.26795 - 1.55291i) q^{60} -8.26795 q^{61} +10.1769i q^{62} -2.44949i q^{63} +5.73205 q^{64} +(-6.00000 + 7.34847i) q^{65} -14.9372i q^{67} +1.79315i q^{68} +3.26795 q^{69} +(3.00000 + 2.44949i) q^{70} +2.19615 q^{71} -1.41421i q^{72} -4.89898i q^{73} +12.9282 q^{74} +(2.53590 - 0.517638i) q^{75} +10.7321 q^{76} +4.24264i q^{78} +5.46410 q^{79} +(7.73205 + 6.31319i) q^{80} +6.66025 q^{81} +3.34607i q^{82} +9.89949i q^{83} +0.803848 q^{84} +(-1.46410 + 1.79315i) q^{85} -20.6603 q^{86} -3.58630i q^{87} +6.46410 q^{89} +(-7.46410 + 9.14162i) q^{90} -3.80385 q^{91} -10.9348i q^{92} +2.72689i q^{93} +7.92820 q^{94} +(10.7321 + 8.76268i) q^{95} +3.92820 q^{96} +0.656339i q^{97} -11.9700i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{6} + 4 q^{9} - 4 q^{10} + 4 q^{15} - 4 q^{16} - 4 q^{19} + 12 q^{20} + 12 q^{21} - 8 q^{24} + 4 q^{25} - 12 q^{26} - 28 q^{31} - 8 q^{34} - 12 q^{35} - 12 q^{36} + 12 q^{39} + 4 q^{40} - 12 q^{45} + 28 q^{46} + 4 q^{49} + 24 q^{50} - 16 q^{51} - 16 q^{54} + 12 q^{56} + 12 q^{59} + 12 q^{60} - 40 q^{61} + 16 q^{64} - 24 q^{65} + 20 q^{69} + 12 q^{70} - 12 q^{71} + 24 q^{74} + 24 q^{75} + 36 q^{76} + 8 q^{79} + 24 q^{80} - 8 q^{81} + 24 q^{84} + 8 q^{85} - 48 q^{86} + 12 q^{89} - 16 q^{90} - 36 q^{91} + 4 q^{94} + 36 q^{95} - 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.93185i 1.36603i −0.730406 0.683013i \(-0.760669\pi\)
0.730406 0.683013i \(-0.239331\pi\)
\(3\) 0.517638i 0.298858i −0.988772 0.149429i \(-0.952256\pi\)
0.988772 0.149429i \(-0.0477436\pi\)
\(4\) −1.73205 −0.866025
\(5\) −1.73205 1.41421i −0.774597 0.632456i
\(6\) −1.00000 −0.408248
\(7\) 0.896575i 0.338874i −0.985541 0.169437i \(-0.945805\pi\)
0.985541 0.169437i \(-0.0541949\pi\)
\(8\) 0.517638i 0.183013i
\(9\) 2.73205 0.910684
\(10\) −2.73205 + 3.34607i −0.863950 + 1.05812i
\(11\) 0 0
\(12\) 0.896575i 0.258819i
\(13\) 4.24264i 1.17670i −0.808608 0.588348i \(-0.799778\pi\)
0.808608 0.588348i \(-0.200222\pi\)
\(14\) −1.73205 −0.462910
\(15\) −0.732051 + 0.896575i −0.189015 + 0.231495i
\(16\) −4.46410 −1.11603
\(17\) 1.03528i 0.251091i −0.992088 0.125546i \(-0.959932\pi\)
0.992088 0.125546i \(-0.0400682\pi\)
\(18\) 5.27792i 1.24402i
\(19\) −6.19615 −1.42149 −0.710747 0.703447i \(-0.751643\pi\)
−0.710747 + 0.703447i \(0.751643\pi\)
\(20\) 3.00000 + 2.44949i 0.670820 + 0.547723i
\(21\) −0.464102 −0.101275
\(22\) 0 0
\(23\) 6.31319i 1.31639i 0.752847 + 0.658196i \(0.228680\pi\)
−0.752847 + 0.658196i \(0.771320\pi\)
\(24\) −0.267949 −0.0546949
\(25\) 1.00000 + 4.89898i 0.200000 + 0.979796i
\(26\) −8.19615 −1.60740
\(27\) 2.96713i 0.571024i
\(28\) 1.55291i 0.293473i
\(29\) 6.92820 1.28654 0.643268 0.765641i \(-0.277578\pi\)
0.643268 + 0.765641i \(0.277578\pi\)
\(30\) 1.73205 + 1.41421i 0.316228 + 0.258199i
\(31\) −5.26795 −0.946152 −0.473076 0.881022i \(-0.656856\pi\)
−0.473076 + 0.881022i \(0.656856\pi\)
\(32\) 7.58871i 1.34151i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) −1.26795 + 1.55291i −0.214323 + 0.262490i
\(36\) −4.73205 −0.788675
\(37\) 6.69213i 1.10018i 0.835106 + 0.550090i \(0.185406\pi\)
−0.835106 + 0.550090i \(0.814594\pi\)
\(38\) 11.9700i 1.94180i
\(39\) −2.19615 −0.351666
\(40\) −0.732051 + 0.896575i −0.115747 + 0.141761i
\(41\) −1.73205 −0.270501 −0.135250 0.990811i \(-0.543184\pi\)
−0.135250 + 0.990811i \(0.543184\pi\)
\(42\) 0.896575i 0.138345i
\(43\) 10.6945i 1.63090i −0.578827 0.815451i \(-0.696489\pi\)
0.578827 0.815451i \(-0.303511\pi\)
\(44\) 0 0
\(45\) −4.73205 3.86370i −0.705412 0.575967i
\(46\) 12.1962 1.79822
\(47\) 4.10394i 0.598621i 0.954156 + 0.299311i \(0.0967567\pi\)
−0.954156 + 0.299311i \(0.903243\pi\)
\(48\) 2.31079i 0.333534i
\(49\) 6.19615 0.885165
\(50\) 9.46410 1.93185i 1.33843 0.273205i
\(51\) −0.535898 −0.0750408
\(52\) 7.34847i 1.01905i
\(53\) 11.9700i 1.64421i −0.569334 0.822106i \(-0.692799\pi\)
0.569334 0.822106i \(-0.307201\pi\)
\(54\) −5.73205 −0.780033
\(55\) 0 0
\(56\) −0.464102 −0.0620182
\(57\) 3.20736i 0.424826i
\(58\) 13.3843i 1.75744i
\(59\) 4.73205 0.616061 0.308030 0.951377i \(-0.400330\pi\)
0.308030 + 0.951377i \(0.400330\pi\)
\(60\) 1.26795 1.55291i 0.163692 0.200480i
\(61\) −8.26795 −1.05860 −0.529301 0.848434i \(-0.677546\pi\)
−0.529301 + 0.848434i \(0.677546\pi\)
\(62\) 10.1769i 1.29247i
\(63\) 2.44949i 0.308607i
\(64\) 5.73205 0.716506
\(65\) −6.00000 + 7.34847i −0.744208 + 0.911465i
\(66\) 0 0
\(67\) 14.9372i 1.82487i −0.409226 0.912433i \(-0.634201\pi\)
0.409226 0.912433i \(-0.365799\pi\)
\(68\) 1.79315i 0.217451i
\(69\) 3.26795 0.393415
\(70\) 3.00000 + 2.44949i 0.358569 + 0.292770i
\(71\) 2.19615 0.260635 0.130318 0.991472i \(-0.458400\pi\)
0.130318 + 0.991472i \(0.458400\pi\)
\(72\) 1.41421i 0.166667i
\(73\) 4.89898i 0.573382i −0.958023 0.286691i \(-0.907445\pi\)
0.958023 0.286691i \(-0.0925553\pi\)
\(74\) 12.9282 1.50287
\(75\) 2.53590 0.517638i 0.292820 0.0597717i
\(76\) 10.7321 1.23105
\(77\) 0 0
\(78\) 4.24264i 0.480384i
\(79\) 5.46410 0.614759 0.307380 0.951587i \(-0.400548\pi\)
0.307380 + 0.951587i \(0.400548\pi\)
\(80\) 7.73205 + 6.31319i 0.864470 + 0.705836i
\(81\) 6.66025 0.740028
\(82\) 3.34607i 0.369511i
\(83\) 9.89949i 1.08661i 0.839535 + 0.543305i \(0.182827\pi\)
−0.839535 + 0.543305i \(0.817173\pi\)
\(84\) 0.803848 0.0877070
\(85\) −1.46410 + 1.79315i −0.158804 + 0.194495i
\(86\) −20.6603 −2.22785
\(87\) 3.58630i 0.384492i
\(88\) 0 0
\(89\) 6.46410 0.685193 0.342597 0.939483i \(-0.388694\pi\)
0.342597 + 0.939483i \(0.388694\pi\)
\(90\) −7.46410 + 9.14162i −0.786785 + 0.963611i
\(91\) −3.80385 −0.398752
\(92\) 10.9348i 1.14003i
\(93\) 2.72689i 0.282765i
\(94\) 7.92820 0.817732
\(95\) 10.7321 + 8.76268i 1.10109 + 0.899032i
\(96\) 3.92820 0.400921
\(97\) 0.656339i 0.0666411i 0.999445 + 0.0333206i \(0.0106082\pi\)
−0.999445 + 0.0333206i \(0.989392\pi\)
\(98\) 11.9700i 1.20916i
\(99\) 0 0
\(100\) −1.73205 8.48528i −0.173205 0.848528i
\(101\) −1.39230 −0.138540 −0.0692698 0.997598i \(-0.522067\pi\)
−0.0692698 + 0.997598i \(0.522067\pi\)
\(102\) 1.03528i 0.102508i
\(103\) 4.24264i 0.418040i −0.977911 0.209020i \(-0.932973\pi\)
0.977911 0.209020i \(-0.0670273\pi\)
\(104\) −2.19615 −0.215350
\(105\) 0.803848 + 0.656339i 0.0784475 + 0.0640521i
\(106\) −23.1244 −2.24604
\(107\) 4.38134i 0.423560i −0.977317 0.211780i \(-0.932074\pi\)
0.977317 0.211780i \(-0.0679261\pi\)
\(108\) 5.13922i 0.494521i
\(109\) 1.19615 0.114571 0.0572853 0.998358i \(-0.481756\pi\)
0.0572853 + 0.998358i \(0.481756\pi\)
\(110\) 0 0
\(111\) 3.46410 0.328798
\(112\) 4.00240i 0.378192i
\(113\) 2.82843i 0.266076i −0.991111 0.133038i \(-0.957527\pi\)
0.991111 0.133038i \(-0.0424732\pi\)
\(114\) 6.19615 0.580323
\(115\) 8.92820 10.9348i 0.832559 1.01967i
\(116\) −12.0000 −1.11417
\(117\) 11.5911i 1.07160i
\(118\) 9.14162i 0.841554i
\(119\) −0.928203 −0.0850883
\(120\) 0.464102 + 0.378937i 0.0423665 + 0.0345921i
\(121\) 0 0
\(122\) 15.9725i 1.44608i
\(123\) 0.896575i 0.0808415i
\(124\) 9.12436 0.819391
\(125\) 5.19615 9.89949i 0.464758 0.885438i
\(126\) −4.73205 −0.421565
\(127\) 3.34607i 0.296915i −0.988919 0.148458i \(-0.952569\pi\)
0.988919 0.148458i \(-0.0474309\pi\)
\(128\) 4.10394i 0.362740i
\(129\) −5.53590 −0.487409
\(130\) 14.1962 + 11.5911i 1.24508 + 1.01661i
\(131\) 21.1244 1.84564 0.922822 0.385227i \(-0.125877\pi\)
0.922822 + 0.385227i \(0.125877\pi\)
\(132\) 0 0
\(133\) 5.55532i 0.481707i
\(134\) −28.8564 −2.49281
\(135\) −4.19615 + 5.13922i −0.361147 + 0.442313i
\(136\) −0.535898 −0.0459529
\(137\) 13.7632i 1.17587i −0.808908 0.587935i \(-0.799941\pi\)
0.808908 0.587935i \(-0.200059\pi\)
\(138\) 6.31319i 0.537415i
\(139\) −16.5885 −1.40701 −0.703507 0.710688i \(-0.748384\pi\)
−0.703507 + 0.710688i \(0.748384\pi\)
\(140\) 2.19615 2.68973i 0.185609 0.227323i
\(141\) 2.12436 0.178903
\(142\) 4.24264i 0.356034i
\(143\) 0 0
\(144\) −12.1962 −1.01635
\(145\) −12.0000 9.79796i −0.996546 0.813676i
\(146\) −9.46410 −0.783255
\(147\) 3.20736i 0.264539i
\(148\) 11.5911i 0.952783i
\(149\) 13.7321 1.12497 0.562487 0.826806i \(-0.309845\pi\)
0.562487 + 0.826806i \(0.309845\pi\)
\(150\) −1.00000 4.89898i −0.0816497 0.400000i
\(151\) −6.19615 −0.504236 −0.252118 0.967697i \(-0.581127\pi\)
−0.252118 + 0.967697i \(0.581127\pi\)
\(152\) 3.20736i 0.260152i
\(153\) 2.82843i 0.228665i
\(154\) 0 0
\(155\) 9.12436 + 7.45001i 0.732886 + 0.598399i
\(156\) 3.80385 0.304552
\(157\) 12.0716i 0.963417i −0.876331 0.481709i \(-0.840016\pi\)
0.876331 0.481709i \(-0.159984\pi\)
\(158\) 10.5558i 0.839777i
\(159\) −6.19615 −0.491387
\(160\) 10.7321 13.1440i 0.848443 1.03913i
\(161\) 5.66025 0.446091
\(162\) 12.8666i 1.01090i
\(163\) 7.58871i 0.594393i 0.954816 + 0.297197i \(0.0960517\pi\)
−0.954816 + 0.297197i \(0.903948\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) 19.1244 1.48434
\(167\) 1.93185i 0.149491i −0.997203 0.0747456i \(-0.976186\pi\)
0.997203 0.0747456i \(-0.0238145\pi\)
\(168\) 0.240237i 0.0185347i
\(169\) −5.00000 −0.384615
\(170\) 3.46410 + 2.82843i 0.265684 + 0.216930i
\(171\) −16.9282 −1.29453
\(172\) 18.5235i 1.41240i
\(173\) 7.62587i 0.579784i 0.957059 + 0.289892i \(0.0936194\pi\)
−0.957059 + 0.289892i \(0.906381\pi\)
\(174\) −6.92820 −0.525226
\(175\) 4.39230 0.896575i 0.332027 0.0677747i
\(176\) 0 0
\(177\) 2.44949i 0.184115i
\(178\) 12.4877i 0.935992i
\(179\) 8.53590 0.638003 0.319002 0.947754i \(-0.396652\pi\)
0.319002 + 0.947754i \(0.396652\pi\)
\(180\) 8.19615 + 6.69213i 0.610905 + 0.498802i
\(181\) 3.39230 0.252148 0.126074 0.992021i \(-0.459762\pi\)
0.126074 + 0.992021i \(0.459762\pi\)
\(182\) 7.34847i 0.544705i
\(183\) 4.27981i 0.316372i
\(184\) 3.26795 0.240916
\(185\) 9.46410 11.5911i 0.695815 0.852195i
\(186\) 5.26795 0.386265
\(187\) 0 0
\(188\) 7.10823i 0.518421i
\(189\) −2.66025 −0.193505
\(190\) 16.9282 20.7327i 1.22810 1.50411i
\(191\) −10.7321 −0.776544 −0.388272 0.921545i \(-0.626928\pi\)
−0.388272 + 0.921545i \(0.626928\pi\)
\(192\) 2.96713i 0.214134i
\(193\) 10.2784i 0.739858i −0.929060 0.369929i \(-0.879382\pi\)
0.929060 0.369929i \(-0.120618\pi\)
\(194\) 1.26795 0.0910334
\(195\) 3.80385 + 3.10583i 0.272399 + 0.222413i
\(196\) −10.7321 −0.766575
\(197\) 2.55103i 0.181753i 0.995862 + 0.0908765i \(0.0289669\pi\)
−0.995862 + 0.0908765i \(0.971033\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 2.53590 0.517638i 0.179315 0.0366025i
\(201\) −7.73205 −0.545377
\(202\) 2.68973i 0.189248i
\(203\) 6.21166i 0.435973i
\(204\) 0.928203 0.0649872
\(205\) 3.00000 + 2.44949i 0.209529 + 0.171080i
\(206\) −8.19615 −0.571053
\(207\) 17.2480i 1.19882i
\(208\) 18.9396i 1.31322i
\(209\) 0 0
\(210\) 1.26795 1.55291i 0.0874968 0.107161i
\(211\) 11.1244 0.765832 0.382916 0.923783i \(-0.374920\pi\)
0.382916 + 0.923783i \(0.374920\pi\)
\(212\) 20.7327i 1.42393i
\(213\) 1.13681i 0.0778931i
\(214\) −8.46410 −0.578594
\(215\) −15.1244 + 18.5235i −1.03147 + 1.26329i
\(216\) −1.53590 −0.104505
\(217\) 4.72311i 0.320626i
\(218\) 2.31079i 0.156506i
\(219\) −2.53590 −0.171360
\(220\) 0 0
\(221\) −4.39230 −0.295458
\(222\) 6.69213i 0.449146i
\(223\) 5.79555i 0.388099i 0.980992 + 0.194050i \(0.0621623\pi\)
−0.980992 + 0.194050i \(0.937838\pi\)
\(224\) 6.80385 0.454601
\(225\) 2.73205 + 13.3843i 0.182137 + 0.892284i
\(226\) −5.46410 −0.363467
\(227\) 21.5278i 1.42885i −0.699713 0.714424i \(-0.746689\pi\)
0.699713 0.714424i \(-0.253311\pi\)
\(228\) 5.55532i 0.367910i
\(229\) 17.9282 1.18473 0.592365 0.805670i \(-0.298195\pi\)
0.592365 + 0.805670i \(0.298195\pi\)
\(230\) −21.1244 17.2480i −1.39290 1.13730i
\(231\) 0 0
\(232\) 3.58630i 0.235452i
\(233\) 13.0053i 0.852007i 0.904721 + 0.426004i \(0.140079\pi\)
−0.904721 + 0.426004i \(0.859921\pi\)
\(234\) −22.3923 −1.46383
\(235\) 5.80385 7.10823i 0.378601 0.463690i
\(236\) −8.19615 −0.533524
\(237\) 2.82843i 0.183726i
\(238\) 1.79315i 0.116233i
\(239\) 11.6603 0.754239 0.377120 0.926165i \(-0.376915\pi\)
0.377120 + 0.926165i \(0.376915\pi\)
\(240\) 3.26795 4.00240i 0.210945 0.258354i
\(241\) −10.1244 −0.652167 −0.326084 0.945341i \(-0.605729\pi\)
−0.326084 + 0.945341i \(0.605729\pi\)
\(242\) 0 0
\(243\) 12.3490i 0.792188i
\(244\) 14.3205 0.916777
\(245\) −10.7321 8.76268i −0.685646 0.559827i
\(246\) 1.73205 0.110432
\(247\) 26.2880i 1.67267i
\(248\) 2.72689i 0.173158i
\(249\) 5.12436 0.324743
\(250\) −19.1244 10.0382i −1.20953 0.634871i
\(251\) −14.1962 −0.896053 −0.448027 0.894020i \(-0.647873\pi\)
−0.448027 + 0.894020i \(0.647873\pi\)
\(252\) 4.24264i 0.267261i
\(253\) 0 0
\(254\) −6.46410 −0.405594
\(255\) 0.928203 + 0.757875i 0.0581263 + 0.0474600i
\(256\) 19.3923 1.21202
\(257\) 5.00052i 0.311924i 0.987763 + 0.155962i \(0.0498477\pi\)
−0.987763 + 0.155962i \(0.950152\pi\)
\(258\) 10.6945i 0.665813i
\(259\) 6.00000 0.372822
\(260\) 10.3923 12.7279i 0.644503 0.789352i
\(261\) 18.9282 1.17163
\(262\) 40.8091i 2.52120i
\(263\) 21.4906i 1.32517i 0.748988 + 0.662584i \(0.230540\pi\)
−0.748988 + 0.662584i \(0.769460\pi\)
\(264\) 0 0
\(265\) −16.9282 + 20.7327i −1.03989 + 1.27360i
\(266\) 10.7321 0.658024
\(267\) 3.34607i 0.204776i
\(268\) 25.8719i 1.58038i
\(269\) 19.7321 1.20308 0.601542 0.798841i \(-0.294553\pi\)
0.601542 + 0.798841i \(0.294553\pi\)
\(270\) 9.92820 + 8.10634i 0.604211 + 0.493336i
\(271\) 4.53590 0.275536 0.137768 0.990465i \(-0.456007\pi\)
0.137768 + 0.990465i \(0.456007\pi\)
\(272\) 4.62158i 0.280224i
\(273\) 1.96902i 0.119170i
\(274\) −26.5885 −1.60627
\(275\) 0 0
\(276\) −5.66025 −0.340707
\(277\) 22.7017i 1.36402i 0.731345 + 0.682008i \(0.238893\pi\)
−0.731345 + 0.682008i \(0.761107\pi\)
\(278\) 32.0464i 1.92202i
\(279\) −14.3923 −0.861645
\(280\) 0.803848 + 0.656339i 0.0480391 + 0.0392237i
\(281\) 17.3205 1.03325 0.516627 0.856210i \(-0.327187\pi\)
0.516627 + 0.856210i \(0.327187\pi\)
\(282\) 4.10394i 0.244386i
\(283\) 30.1146i 1.79013i 0.445939 + 0.895063i \(0.352870\pi\)
−0.445939 + 0.895063i \(0.647130\pi\)
\(284\) −3.80385 −0.225717
\(285\) 4.53590 5.55532i 0.268683 0.329069i
\(286\) 0 0
\(287\) 1.55291i 0.0916656i
\(288\) 20.7327i 1.22169i
\(289\) 15.9282 0.936953
\(290\) −18.9282 + 23.1822i −1.11150 + 1.36131i
\(291\) 0.339746 0.0199163
\(292\) 8.48528i 0.496564i
\(293\) 9.41902i 0.550265i 0.961406 + 0.275133i \(0.0887217\pi\)
−0.961406 + 0.275133i \(0.911278\pi\)
\(294\) −6.19615 −0.361367
\(295\) −8.19615 6.69213i −0.477198 0.389631i
\(296\) 3.46410 0.201347
\(297\) 0 0
\(298\) 26.5283i 1.53674i
\(299\) 26.7846 1.54899
\(300\) −4.39230 + 0.896575i −0.253590 + 0.0517638i
\(301\) −9.58846 −0.552669
\(302\) 11.9700i 0.688799i
\(303\) 0.720710i 0.0414037i
\(304\) 27.6603 1.58642
\(305\) 14.3205 + 11.6926i 0.819990 + 0.669519i
\(306\) −5.46410 −0.312362
\(307\) 17.6269i 1.00602i −0.864280 0.503010i \(-0.832226\pi\)
0.864280 0.503010i \(-0.167774\pi\)
\(308\) 0 0
\(309\) −2.19615 −0.124935
\(310\) 14.3923 17.6269i 0.817428 1.00114i
\(311\) −28.0526 −1.59071 −0.795357 0.606141i \(-0.792717\pi\)
−0.795357 + 0.606141i \(0.792717\pi\)
\(312\) 1.13681i 0.0643593i
\(313\) 17.1464i 0.969173i −0.874743 0.484587i \(-0.838970\pi\)
0.874743 0.484587i \(-0.161030\pi\)
\(314\) −23.3205 −1.31605
\(315\) −3.46410 + 4.24264i −0.195180 + 0.239046i
\(316\) −9.46410 −0.532397
\(317\) 6.96953i 0.391448i 0.980659 + 0.195724i \(0.0627057\pi\)
−0.980659 + 0.195724i \(0.937294\pi\)
\(318\) 11.9700i 0.671247i
\(319\) 0 0
\(320\) −9.92820 8.10634i −0.555003 0.453158i
\(321\) −2.26795 −0.126585
\(322\) 10.9348i 0.609371i
\(323\) 6.41473i 0.356925i
\(324\) −11.5359 −0.640883
\(325\) 20.7846 4.24264i 1.15292 0.235339i
\(326\) 14.6603 0.811956
\(327\) 0.619174i 0.0342404i
\(328\) 0.896575i 0.0495051i
\(329\) 3.67949 0.202857
\(330\) 0 0
\(331\) −7.80385 −0.428938 −0.214469 0.976731i \(-0.568802\pi\)
−0.214469 + 0.976731i \(0.568802\pi\)
\(332\) 17.1464i 0.941033i
\(333\) 18.2832i 1.00192i
\(334\) −3.73205 −0.204209
\(335\) −21.1244 + 25.8719i −1.15415 + 1.41354i
\(336\) 2.07180 0.113026
\(337\) 7.82894i 0.426470i −0.977001 0.213235i \(-0.931600\pi\)
0.977001 0.213235i \(-0.0683999\pi\)
\(338\) 9.65926i 0.525394i
\(339\) −1.46410 −0.0795191
\(340\) 2.53590 3.10583i 0.137528 0.168437i
\(341\) 0 0
\(342\) 32.7028i 1.76836i
\(343\) 11.8313i 0.638833i
\(344\) −5.53590 −0.298476
\(345\) −5.66025 4.62158i −0.304738 0.248817i
\(346\) 14.7321 0.792000
\(347\) 2.96713i 0.159284i 0.996824 + 0.0796419i \(0.0253777\pi\)
−0.996824 + 0.0796419i \(0.974622\pi\)
\(348\) 6.21166i 0.332980i
\(349\) −27.3205 −1.46243 −0.731217 0.682145i \(-0.761047\pi\)
−0.731217 + 0.682145i \(0.761047\pi\)
\(350\) −1.73205 8.48528i −0.0925820 0.453557i
\(351\) −12.5885 −0.671922
\(352\) 0 0
\(353\) 1.69161i 0.0900356i −0.998986 0.0450178i \(-0.985666\pi\)
0.998986 0.0450178i \(-0.0143345\pi\)
\(354\) −4.73205 −0.251506
\(355\) −3.80385 3.10583i −0.201887 0.164840i
\(356\) −11.1962 −0.593395
\(357\) 0.480473i 0.0254293i
\(358\) 16.4901i 0.871528i
\(359\) −18.3397 −0.967935 −0.483967 0.875086i \(-0.660805\pi\)
−0.483967 + 0.875086i \(0.660805\pi\)
\(360\) −2.00000 + 2.44949i −0.105409 + 0.129099i
\(361\) 19.3923 1.02065
\(362\) 6.55343i 0.344441i
\(363\) 0 0
\(364\) 6.58846 0.345329
\(365\) −6.92820 + 8.48528i −0.362639 + 0.444140i
\(366\) 8.26795 0.432173
\(367\) 29.6341i 1.54689i 0.633865 + 0.773444i \(0.281468\pi\)
−0.633865 + 0.773444i \(0.718532\pi\)
\(368\) 28.1827i 1.46913i
\(369\) −4.73205 −0.246341
\(370\) −22.3923 18.2832i −1.16412 0.950500i
\(371\) −10.7321 −0.557180
\(372\) 4.72311i 0.244882i
\(373\) 34.1170i 1.76651i 0.468892 + 0.883255i \(0.344653\pi\)
−0.468892 + 0.883255i \(0.655347\pi\)
\(374\) 0 0
\(375\) −5.12436 2.68973i −0.264621 0.138897i
\(376\) 2.12436 0.109555
\(377\) 29.3939i 1.51386i
\(378\) 5.13922i 0.264333i
\(379\) 5.46410 0.280672 0.140336 0.990104i \(-0.455182\pi\)
0.140336 + 0.990104i \(0.455182\pi\)
\(380\) −18.5885 15.1774i −0.953568 0.778585i
\(381\) −1.73205 −0.0887357
\(382\) 20.7327i 1.06078i
\(383\) 23.7642i 1.21430i 0.794589 + 0.607148i \(0.207686\pi\)
−0.794589 + 0.607148i \(0.792314\pi\)
\(384\) 2.12436 0.108408
\(385\) 0 0
\(386\) −19.8564 −1.01066
\(387\) 29.2180i 1.48523i
\(388\) 1.13681i 0.0577129i
\(389\) 18.1244 0.918941 0.459471 0.888193i \(-0.348039\pi\)
0.459471 + 0.888193i \(0.348039\pi\)
\(390\) 6.00000 7.34847i 0.303822 0.372104i
\(391\) 6.53590 0.330535
\(392\) 3.20736i 0.161996i
\(393\) 10.9348i 0.551586i
\(394\) 4.92820 0.248279
\(395\) −9.46410 7.72741i −0.476191 0.388808i
\(396\) 0 0
\(397\) 16.0096i 0.803500i −0.915749 0.401750i \(-0.868402\pi\)
0.915749 0.401750i \(-0.131598\pi\)
\(398\) 3.86370i 0.193670i
\(399\) 2.87564 0.143962
\(400\) −4.46410 21.8695i −0.223205 1.09348i
\(401\) −32.3205 −1.61401 −0.807005 0.590545i \(-0.798913\pi\)
−0.807005 + 0.590545i \(0.798913\pi\)
\(402\) 14.9372i 0.744999i
\(403\) 22.3500i 1.11333i
\(404\) 2.41154 0.119979
\(405\) −11.5359 9.41902i −0.573223 0.468035i
\(406\) −12.0000 −0.595550
\(407\) 0 0
\(408\) 0.277401i 0.0137334i
\(409\) 1.87564 0.0927446 0.0463723 0.998924i \(-0.485234\pi\)
0.0463723 + 0.998924i \(0.485234\pi\)
\(410\) 4.73205 5.79555i 0.233699 0.286222i
\(411\) −7.12436 −0.351419
\(412\) 7.34847i 0.362033i
\(413\) 4.24264i 0.208767i
\(414\) 33.3205 1.63761
\(415\) 14.0000 17.1464i 0.687233 0.841685i
\(416\) 32.1962 1.57855
\(417\) 8.58682i 0.420498i
\(418\) 0 0
\(419\) 29.6603 1.44900 0.724499 0.689276i \(-0.242071\pi\)
0.724499 + 0.689276i \(0.242071\pi\)
\(420\) −1.39230 1.13681i −0.0679375 0.0554708i
\(421\) 21.0526 1.02604 0.513019 0.858377i \(-0.328527\pi\)
0.513019 + 0.858377i \(0.328527\pi\)
\(422\) 21.4906i 1.04615i
\(423\) 11.2122i 0.545154i
\(424\) −6.19615 −0.300912
\(425\) 5.07180 1.03528i 0.246018 0.0502183i
\(426\) −2.19615 −0.106404
\(427\) 7.41284i 0.358732i
\(428\) 7.58871i 0.366814i
\(429\) 0 0
\(430\) 35.7846 + 29.2180i 1.72569 + 1.40902i
\(431\) −18.9282 −0.911739 −0.455870 0.890047i \(-0.650672\pi\)
−0.455870 + 0.890047i \(0.650672\pi\)
\(432\) 13.2456i 0.637277i
\(433\) 20.2523i 0.973261i −0.873608 0.486631i \(-0.838226\pi\)
0.873608 0.486631i \(-0.161774\pi\)
\(434\) 9.12436 0.437983
\(435\) −5.07180 + 6.21166i −0.243174 + 0.297826i
\(436\) −2.07180 −0.0992211
\(437\) 39.1175i 1.87124i
\(438\) 4.89898i 0.234082i
\(439\) 20.2487 0.966418 0.483209 0.875505i \(-0.339471\pi\)
0.483209 + 0.875505i \(0.339471\pi\)
\(440\) 0 0
\(441\) 16.9282 0.806105
\(442\) 8.48528i 0.403604i
\(443\) 9.17878i 0.436097i 0.975938 + 0.218049i \(0.0699691\pi\)
−0.975938 + 0.218049i \(0.930031\pi\)
\(444\) −6.00000 −0.284747
\(445\) −11.1962 9.14162i −0.530749 0.433354i
\(446\) 11.1962 0.530153
\(447\) 7.10823i 0.336208i
\(448\) 5.13922i 0.242805i
\(449\) 10.5167 0.496312 0.248156 0.968720i \(-0.420175\pi\)
0.248156 + 0.968720i \(0.420175\pi\)
\(450\) 25.8564 5.27792i 1.21888 0.248803i
\(451\) 0 0
\(452\) 4.89898i 0.230429i
\(453\) 3.20736i 0.150695i
\(454\) −41.5885 −1.95184
\(455\) 6.58846 + 5.37945i 0.308872 + 0.252193i
\(456\) 1.66025 0.0777485
\(457\) 21.2132i 0.992312i −0.868233 0.496156i \(-0.834744\pi\)
0.868233 0.496156i \(-0.165256\pi\)
\(458\) 34.6346i 1.61837i
\(459\) −3.07180 −0.143379
\(460\) −15.4641 + 18.9396i −0.721017 + 0.883062i
\(461\) −33.0000 −1.53696 −0.768482 0.639872i \(-0.778987\pi\)
−0.768482 + 0.639872i \(0.778987\pi\)
\(462\) 0 0
\(463\) 17.8671i 0.830356i 0.909740 + 0.415178i \(0.136281\pi\)
−0.909740 + 0.415178i \(0.863719\pi\)
\(464\) −30.9282 −1.43581
\(465\) 3.85641 4.72311i 0.178837 0.219029i
\(466\) 25.1244 1.16386
\(467\) 17.7656i 0.822094i −0.911614 0.411047i \(-0.865163\pi\)
0.911614 0.411047i \(-0.134837\pi\)
\(468\) 20.0764i 0.928032i
\(469\) −13.3923 −0.618399
\(470\) −13.7321 11.2122i −0.633412 0.517179i
\(471\) −6.24871 −0.287925
\(472\) 2.44949i 0.112747i
\(473\) 0 0
\(474\) −5.46410 −0.250974
\(475\) −6.19615 30.3548i −0.284299 1.39277i
\(476\) 1.60770 0.0736886
\(477\) 32.7028i 1.49736i
\(478\) 22.5259i 1.03031i
\(479\) −9.46410 −0.432426 −0.216213 0.976346i \(-0.569371\pi\)
−0.216213 + 0.976346i \(0.569371\pi\)
\(480\) −6.80385 5.55532i −0.310552 0.253564i
\(481\) 28.3923 1.29458
\(482\) 19.5588i 0.890877i
\(483\) 2.92996i 0.133318i
\(484\) 0 0
\(485\) 0.928203 1.13681i 0.0421475 0.0516200i
\(486\) −23.8564 −1.08215
\(487\) 12.7279i 0.576757i 0.957516 + 0.288379i \(0.0931162\pi\)
−0.957516 + 0.288379i \(0.906884\pi\)
\(488\) 4.27981i 0.193738i
\(489\) 3.92820 0.177639
\(490\) −16.9282 + 20.7327i −0.764738 + 0.936609i
\(491\) −15.7128 −0.709109 −0.354555 0.935035i \(-0.615368\pi\)
−0.354555 + 0.935035i \(0.615368\pi\)
\(492\) 1.55291i 0.0700108i
\(493\) 7.17260i 0.323038i
\(494\) 50.7846 2.28491
\(495\) 0 0
\(496\) 23.5167 1.05593
\(497\) 1.96902i 0.0883225i
\(498\) 9.89949i 0.443607i
\(499\) −38.3923 −1.71868 −0.859338 0.511408i \(-0.829124\pi\)
−0.859338 + 0.511408i \(0.829124\pi\)
\(500\) −9.00000 + 17.1464i −0.402492 + 0.766812i
\(501\) −1.00000 −0.0446767
\(502\) 27.4249i 1.22403i
\(503\) 34.2557i 1.52739i −0.645580 0.763693i \(-0.723384\pi\)
0.645580 0.763693i \(-0.276616\pi\)
\(504\) −1.26795 −0.0564789
\(505\) 2.41154 + 1.96902i 0.107312 + 0.0876201i
\(506\) 0 0
\(507\) 2.58819i 0.114946i
\(508\) 5.79555i 0.257136i
\(509\) 21.9282 0.971951 0.485975 0.873973i \(-0.338465\pi\)
0.485975 + 0.873973i \(0.338465\pi\)
\(510\) 1.46410 1.79315i 0.0648315 0.0794021i
\(511\) −4.39230 −0.194304
\(512\) 29.2552i 1.29291i
\(513\) 18.3848i 0.811708i
\(514\) 9.66025 0.426096
\(515\) −6.00000 + 7.34847i −0.264392 + 0.323812i
\(516\) 9.58846 0.422108
\(517\) 0 0
\(518\) 11.5911i 0.509284i
\(519\) 3.94744 0.173273
\(520\) 3.80385 + 3.10583i 0.166810 + 0.136200i
\(521\) 39.2487 1.71952 0.859759 0.510701i \(-0.170614\pi\)
0.859759 + 0.510701i \(0.170614\pi\)
\(522\) 36.5665i 1.60047i
\(523\) 8.66115i 0.378726i 0.981907 + 0.189363i \(0.0606422\pi\)
−0.981907 + 0.189363i \(0.939358\pi\)
\(524\) −36.5885 −1.59837
\(525\) −0.464102 2.27362i −0.0202551 0.0992291i
\(526\) 41.5167 1.81021
\(527\) 5.45378i 0.237570i
\(528\) 0 0
\(529\) −16.8564 −0.732887
\(530\) 40.0526 + 32.7028i 1.73977 + 1.42052i
\(531\) 12.9282 0.561036
\(532\) 9.62209i 0.417171i
\(533\) 7.34847i 0.318298i
\(534\) −6.46410 −0.279729
\(535\) −6.19615 + 7.58871i −0.267883 + 0.328088i
\(536\) −7.73205 −0.333974
\(537\) 4.41851i 0.190673i
\(538\) 38.1194i 1.64344i
\(539\) 0 0
\(540\) 7.26795 8.90138i 0.312763 0.383055i
\(541\) −23.3923 −1.00571 −0.502857 0.864370i \(-0.667718\pi\)
−0.502857 + 0.864370i \(0.667718\pi\)
\(542\) 8.76268i 0.376389i
\(543\) 1.75599i 0.0753566i
\(544\) 7.85641 0.336841
\(545\) −2.07180 1.69161i −0.0887460 0.0724608i
\(546\) 3.80385 0.162790
\(547\) 20.2523i 0.865924i 0.901412 + 0.432962i \(0.142532\pi\)
−0.901412 + 0.432962i \(0.857468\pi\)
\(548\) 23.8386i 1.01833i
\(549\) −22.5885 −0.964052
\(550\) 0 0
\(551\) −42.9282 −1.82880
\(552\) 1.69161i 0.0719999i
\(553\) 4.89898i 0.208326i
\(554\) 43.8564 1.86328
\(555\) −6.00000 4.89898i −0.254686 0.207950i
\(556\) 28.7321 1.21851
\(557\) 6.48906i 0.274950i 0.990505 + 0.137475i \(0.0438987\pi\)
−0.990505 + 0.137475i \(0.956101\pi\)
\(558\) 27.8038i 1.17703i
\(559\) −45.3731 −1.91908
\(560\) 5.66025 6.93237i 0.239189 0.292946i
\(561\) 0 0
\(562\) 33.4607i 1.41145i
\(563\) 6.07296i 0.255945i 0.991778 + 0.127972i \(0.0408469\pi\)
−0.991778 + 0.127972i \(0.959153\pi\)
\(564\) −3.67949 −0.154935
\(565\) −4.00000 + 4.89898i −0.168281 + 0.206102i
\(566\) 58.1769 2.44536
\(567\) 5.97142i 0.250776i
\(568\) 1.13681i 0.0476996i
\(569\) −5.87564 −0.246320 −0.123160 0.992387i \(-0.539303\pi\)
−0.123160 + 0.992387i \(0.539303\pi\)
\(570\) −10.7321 8.76268i −0.449516 0.367028i
\(571\) 35.7128 1.49453 0.747267 0.664524i \(-0.231365\pi\)
0.747267 + 0.664524i \(0.231365\pi\)
\(572\) 0 0
\(573\) 5.55532i 0.232077i
\(574\) 3.00000 0.125218
\(575\) −30.9282 + 6.31319i −1.28980 + 0.263278i
\(576\) 15.6603 0.652511
\(577\) 20.7327i 0.863115i 0.902085 + 0.431557i \(0.142036\pi\)
−0.902085 + 0.431557i \(0.857964\pi\)
\(578\) 30.7709i 1.27990i
\(579\) −5.32051 −0.221113
\(580\) 20.7846 + 16.9706i 0.863034 + 0.704664i
\(581\) 8.87564 0.368224
\(582\) 0.656339i 0.0272061i
\(583\) 0 0
\(584\) −2.53590 −0.104936
\(585\) −16.3923 + 20.0764i −0.677738 + 0.830057i
\(586\) 18.1962 0.751676
\(587\) 35.9473i 1.48370i 0.670564 + 0.741852i \(0.266052\pi\)
−0.670564 + 0.741852i \(0.733948\pi\)
\(588\) 5.55532i 0.229097i
\(589\) 32.6410 1.34495
\(590\) −12.9282 + 15.8338i −0.532246 + 0.651865i
\(591\) 1.32051 0.0543184
\(592\) 29.8744i 1.22783i
\(593\) 30.2533i 1.24235i −0.783670 0.621177i \(-0.786655\pi\)
0.783670 0.621177i \(-0.213345\pi\)
\(594\) 0 0
\(595\) 1.60770 + 1.31268i 0.0659091 + 0.0538145i
\(596\) −23.7846 −0.974256
\(597\) 1.03528i 0.0423710i
\(598\) 51.7439i 2.11597i
\(599\) −20.4449 −0.835354 −0.417677 0.908595i \(-0.637156\pi\)
−0.417677 + 0.908595i \(0.637156\pi\)
\(600\) −0.267949 1.31268i −0.0109390 0.0535898i
\(601\) 20.0000 0.815817 0.407909 0.913023i \(-0.366258\pi\)
0.407909 + 0.913023i \(0.366258\pi\)
\(602\) 18.5235i 0.754961i
\(603\) 40.8091i 1.66188i
\(604\) 10.7321 0.436681
\(605\) 0 0
\(606\) 1.39230 0.0565585
\(607\) 31.4916i 1.27821i 0.769121 + 0.639103i \(0.220694\pi\)
−0.769121 + 0.639103i \(0.779306\pi\)
\(608\) 47.0208i 1.90694i
\(609\) −3.21539 −0.130294
\(610\) 22.5885 27.6651i 0.914580 1.12013i
\(611\) 17.4115 0.704396
\(612\) 4.89898i 0.198030i
\(613\) 6.69213i 0.270293i −0.990826 0.135146i \(-0.956850\pi\)
0.990826 0.135146i \(-0.0431504\pi\)
\(614\) −34.0526 −1.37425
\(615\) 1.26795 1.55291i 0.0511286 0.0626195i
\(616\) 0 0
\(617\) 1.69161i 0.0681019i −0.999420 0.0340509i \(-0.989159\pi\)
0.999420 0.0340509i \(-0.0108408\pi\)
\(618\) 4.24264i 0.170664i
\(619\) 28.7846 1.15695 0.578476 0.815700i \(-0.303648\pi\)
0.578476 + 0.815700i \(0.303648\pi\)
\(620\) −15.8038 12.9038i −0.634698 0.518229i
\(621\) 18.7321 0.751691
\(622\) 54.1934i 2.17296i
\(623\) 5.79555i 0.232194i
\(624\) 9.80385 0.392468
\(625\) −23.0000 + 9.79796i −0.920000 + 0.391918i
\(626\) −33.1244 −1.32392
\(627\) 0 0
\(628\) 20.9086i 0.834344i
\(629\) 6.92820 0.276246
\(630\) 8.19615 + 6.69213i 0.326543 + 0.266621i
\(631\) 19.3205 0.769137 0.384569 0.923096i \(-0.374350\pi\)
0.384569 + 0.923096i \(0.374350\pi\)
\(632\) 2.82843i 0.112509i
\(633\) 5.75839i 0.228875i
\(634\) 13.4641 0.534728
\(635\) −4.73205 + 5.79555i −0.187786 + 0.229990i
\(636\) 10.7321 0.425553
\(637\) 26.2880i 1.04157i
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 5.80385 7.10823i 0.229417 0.280978i
\(641\) 19.8564 0.784281 0.392140 0.919905i \(-0.371735\pi\)
0.392140 + 0.919905i \(0.371735\pi\)
\(642\) 4.38134i 0.172918i
\(643\) 27.6651i 1.09100i 0.838109 + 0.545502i \(0.183661\pi\)
−0.838109 + 0.545502i \(0.816339\pi\)
\(644\) −9.80385 −0.386326
\(645\) 9.58846 + 7.82894i 0.377545 + 0.308264i
\(646\) 12.3923 0.487569
\(647\) 18.9767i 0.746053i 0.927821 + 0.373026i \(0.121680\pi\)
−0.927821 + 0.373026i \(0.878320\pi\)
\(648\) 3.44760i 0.135435i
\(649\) 0 0
\(650\) −8.19615 40.1528i −0.321480 1.57492i
\(651\) 2.44486 0.0958218
\(652\) 13.1440i 0.514760i
\(653\) 31.9449i 1.25010i 0.780584 + 0.625050i \(0.214922\pi\)
−0.780584 + 0.625050i \(0.785078\pi\)
\(654\) −1.19615 −0.0467733
\(655\) −36.5885 29.8744i −1.42963 1.16729i
\(656\) 7.73205 0.301886
\(657\) 13.3843i 0.522170i
\(658\) 7.10823i 0.277108i
\(659\) −11.3205 −0.440984 −0.220492 0.975389i \(-0.570766\pi\)
−0.220492 + 0.975389i \(0.570766\pi\)
\(660\) 0 0
\(661\) −1.58846 −0.0617838 −0.0308919 0.999523i \(-0.509835\pi\)
−0.0308919 + 0.999523i \(0.509835\pi\)
\(662\) 15.0759i 0.585941i
\(663\) 2.27362i 0.0883003i
\(664\) 5.12436 0.198864
\(665\) 7.85641 9.62209i 0.304658 0.373129i
\(666\) 35.3205 1.36864
\(667\) 43.7391i 1.69358i
\(668\) 3.34607i 0.129463i
\(669\) 3.00000 0.115987
\(670\) 49.9808 + 40.8091i 1.93093 + 1.57659i
\(671\) 0 0
\(672\) 3.52193i 0.135861i
\(673\) 1.61729i 0.0623418i 0.999514 + 0.0311709i \(0.00992361\pi\)
−0.999514 + 0.0311709i \(0.990076\pi\)
\(674\) −15.1244 −0.582568
\(675\) 14.5359 2.96713i 0.559487 0.114205i
\(676\) 8.66025 0.333087
\(677\) 9.04008i 0.347439i −0.984795 0.173719i \(-0.944421\pi\)
0.984795 0.173719i \(-0.0555786\pi\)
\(678\) 2.82843i 0.108625i
\(679\) 0.588457 0.0225829
\(680\) 0.928203 + 0.757875i 0.0355950 + 0.0290632i
\(681\) −11.1436 −0.427023
\(682\) 0 0
\(683\) 22.4887i 0.860507i −0.902708 0.430253i \(-0.858424\pi\)
0.902708 0.430253i \(-0.141576\pi\)
\(684\) 29.3205 1.12110
\(685\) −19.4641 + 23.8386i −0.743685 + 0.910825i
\(686\) −22.8564 −0.872662
\(687\) 9.28032i 0.354066i
\(688\) 47.7415i 1.82013i
\(689\) −50.7846 −1.93474
\(690\) −8.92820 + 10.9348i −0.339891 + 0.416280i
\(691\) −27.9090 −1.06171 −0.530854 0.847464i \(-0.678129\pi\)
−0.530854 + 0.847464i \(0.678129\pi\)
\(692\) 13.2084i 0.502108i
\(693\) 0 0
\(694\) 5.73205 0.217586
\(695\) 28.7321 + 23.4596i 1.08987 + 0.889874i
\(696\) −1.85641 −0.0703669
\(697\) 1.79315i 0.0679204i
\(698\) 52.7792i 1.99772i
\(699\) 6.73205 0.254630
\(700\) −7.60770 + 1.55291i −0.287544 + 0.0586946i
\(701\) 10.1436 0.383118 0.191559 0.981481i \(-0.438646\pi\)
0.191559 + 0.981481i \(0.438646\pi\)
\(702\) 24.3190i 0.917863i
\(703\) 41.4655i 1.56390i
\(704\) 0 0
\(705\) −3.67949 3.00429i −0.138578 0.113148i
\(706\) −3.26795 −0.122991
\(707\) 1.24831i 0.0469474i
\(708\) 4.24264i 0.159448i
\(709\) −23.3923 −0.878516 −0.439258 0.898361i \(-0.644759\pi\)
−0.439258 + 0.898361i \(0.644759\pi\)
\(710\) −6.00000 + 7.34847i −0.225176 + 0.275783i
\(711\) 14.9282 0.559851
\(712\) 3.34607i 0.125399i
\(713\) 33.2576i 1.24551i
\(714\) 0.928203 0.0347371
\(715\) 0 0
\(716\) −14.7846 −0.552527
\(717\) 6.03579i 0.225411i
\(718\) 35.4297i 1.32222i
\(719\) 39.8038 1.48443 0.742217 0.670160i \(-0.233775\pi\)
0.742217 + 0.670160i \(0.233775\pi\)
\(720\) 21.1244 + 17.2480i 0.787258 + 0.642794i
\(721\) −3.80385 −0.141663
\(722\) 37.4631i 1.39423i
\(723\) 5.24075i 0.194906i
\(724\) −5.87564 −0.218367
\(725\) 6.92820 + 33.9411i 0.257307 + 1.26054i
\(726\) 0 0
\(727\) 4.00240i 0.148441i 0.997242 + 0.0742205i \(0.0236469\pi\)
−0.997242 + 0.0742205i \(0.976353\pi\)
\(728\) 1.96902i 0.0729766i
\(729\) 13.5885 0.503276
\(730\) 16.3923 + 13.3843i 0.606706 + 0.495374i
\(731\) −11.0718 −0.409505
\(732\) 7.41284i 0.273986i
\(733\) 34.7733i 1.28438i −0.766545 0.642191i \(-0.778026\pi\)
0.766545 0.642191i \(-0.221974\pi\)
\(734\) 57.2487 2.11309
\(735\) −4.53590 + 5.55532i −0.167309 + 0.204911i
\(736\) −47.9090 −1.76595
\(737\) 0 0
\(738\) 9.14162i 0.336508i
\(739\) 25.0718 0.922281 0.461140 0.887327i \(-0.347440\pi\)
0.461140 + 0.887327i \(0.347440\pi\)
\(740\) −16.3923 + 20.0764i −0.602593 + 0.738023i
\(741\) 13.6077 0.499891
\(742\) 20.7327i 0.761122i
\(743\) 8.04197i 0.295031i 0.989060 + 0.147516i \(0.0471277\pi\)
−0.989060 + 0.147516i \(0.952872\pi\)
\(744\) 1.41154 0.0517497
\(745\) −23.7846 19.4201i −0.871401 0.711496i
\(746\) 65.9090 2.41310
\(747\) 27.0459i 0.989559i
\(748\) 0 0
\(749\) −3.92820 −0.143533
\(750\) −5.19615 + 9.89949i −0.189737 + 0.361478i
\(751\) −20.6410 −0.753201 −0.376601 0.926376i \(-0.622907\pi\)
−0.376601 + 0.926376i \(0.622907\pi\)
\(752\) 18.3204i 0.668076i
\(753\) 7.34847i 0.267793i
\(754\) −56.7846 −2.06797
\(755\) 10.7321 + 8.76268i 0.390579 + 0.318907i
\(756\) 4.60770 0.167580
\(757\) 35.0779i 1.27493i −0.770480 0.637465i \(-0.779983\pi\)
0.770480 0.637465i \(-0.220017\pi\)
\(758\) 10.5558i 0.383405i
\(759\) 0 0
\(760\) 4.53590 5.55532i 0.164534 0.201513i
\(761\) 7.85641 0.284795 0.142397 0.989810i \(-0.454519\pi\)
0.142397 + 0.989810i \(0.454519\pi\)
\(762\) 3.34607i 0.121215i
\(763\) 1.07244i 0.0388250i
\(764\) 18.5885 0.672507
\(765\) −4.00000 + 4.89898i −0.144620 + 0.177123i
\(766\) 45.9090 1.65876
\(767\) 20.0764i 0.724916i
\(768\) 10.0382i 0.362222i
\(769\) −17.8564 −0.643918 −0.321959 0.946754i \(-0.604341\pi\)
−0.321959 + 0.946754i \(0.604341\pi\)
\(770\) 0 0
\(771\) 2.58846 0.0932210
\(772\) 17.8028i 0.640736i
\(773\) 51.6424i 1.85745i −0.370774 0.928723i \(-0.620907\pi\)
0.370774 0.928723i \(-0.379093\pi\)
\(774\) −56.4449 −2.02887
\(775\) −5.26795 25.8076i −0.189230 0.927035i
\(776\) 0.339746 0.0121962
\(777\) 3.10583i 0.111421i
\(778\) 35.0136i 1.25530i
\(779\) 10.7321 0.384516
\(780\) −6.58846 5.37945i −0.235905 0.192615i
\(781\) 0 0
\(782\) 12.6264i 0.451519i
\(783\) 20.5569i 0.734642i
\(784\) −27.6603 −0.987866
\(785\) −17.0718 + 20.9086i −0.609319 + 0.746260i
\(786\) −21.1244 −0.753481
\(787\) 4.65874i 0.166066i 0.996547 + 0.0830331i \(0.0264607\pi\)
−0.996547 + 0.0830331i \(0.973539\pi\)
\(788\) 4.41851i 0.157403i
\(789\) 11.1244 0.396038
\(790\) −14.9282 + 18.2832i −0.531122 + 0.650488i
\(791\) −2.53590 −0.0901662
\(792\) 0 0
\(793\) 35.0779i 1.24565i
\(794\) −30.9282 −1.09760
\(795\) 10.7321 + 8.76268i 0.380627 + 0.310780i
\(796\) −3.46410 −0.122782
\(797\) 7.90327i 0.279948i −0.990155 0.139974i \(-0.955298\pi\)
0.990155 0.139974i \(-0.0447019\pi\)
\(798\) 5.55532i 0.196656i
\(799\) 4.24871 0.150309
\(800\) −37.1769 + 7.58871i −1.31440 + 0.268301i
\(801\) 17.6603 0.623994
\(802\) 62.4384i 2.20478i
\(803\) 0 0
\(804\) 13.3923 0.472310
\(805\) −9.80385 8.00481i −0.345540 0.282132i
\(806\) 43.1769 1.52084
\(807\) 10.2141i 0.359552i
\(808\) 0.720710i 0.0253545i
\(809\) 21.4641 0.754638 0.377319 0.926083i \(-0.376846\pi\)
0.377319 + 0.926083i \(0.376846\pi\)
\(810\) −18.1962 + 22.2856i −0.639348 + 0.783038i
\(811\) −32.9808 −1.15811 −0.579056 0.815288i \(-0.696579\pi\)
−0.579056 + 0.815288i \(0.696579\pi\)
\(812\) 10.7589i 0.377564i
\(813\) 2.34795i 0.0823463i
\(814\) 0 0
\(815\) 10.7321 13.1440i 0.375927 0.460415i
\(816\) 2.39230 0.0837474
\(817\) 66.2650i 2.31832i
\(818\) 3.62347i 0.126692i
\(819\) −10.3923 −0.363137
\(820\) −5.19615 4.24264i −0.181458 0.148159i
\(821\) 18.8038 0.656259 0.328129 0.944633i \(-0.393582\pi\)
0.328129 + 0.944633i \(0.393582\pi\)
\(822\) 13.7632i 0.480047i
\(823\) 48.3978i 1.68704i 0.537096 + 0.843521i \(0.319521\pi\)
−0.537096 + 0.843521i \(0.680479\pi\)
\(824\) −2.19615 −0.0765066
\(825\) 0 0
\(826\) −8.19615 −0.285181
\(827\) 26.7314i 0.929540i −0.885431 0.464770i \(-0.846137\pi\)
0.885431 0.464770i \(-0.153863\pi\)
\(828\) 29.8744i 1.03821i
\(829\) −41.9808 −1.45805 −0.729026 0.684486i \(-0.760027\pi\)
−0.729026 + 0.684486i \(0.760027\pi\)
\(830\) −33.1244 27.0459i −1.14976 0.938778i
\(831\) 11.7513 0.407648
\(832\) 24.3190i 0.843111i
\(833\) 6.41473i 0.222257i
\(834\) 16.5885 0.574411
\(835\) −2.73205 + 3.34607i −0.0945465 + 0.115795i
\(836\) 0 0
\(837\) 15.6307i 0.540275i
\(838\) 57.2992i 1.97937i
\(839\) −2.78461 −0.0961354 −0.0480677 0.998844i \(-0.515306\pi\)
−0.0480677 + 0.998844i \(0.515306\pi\)
\(840\) 0.339746 0.416102i 0.0117223 0.0143569i
\(841\) 19.0000 0.655172
\(842\) 40.6704i 1.40160i
\(843\) 8.96575i 0.308797i
\(844\) −19.2679 −0.663230
\(845\) 8.66025 + 7.07107i 0.297922 + 0.243252i
\(846\) 21.6603 0.744695
\(847\) 0 0
\(848\) 53.4355i 1.83498i
\(849\) 15.5885 0.534994
\(850\) −2.00000 9.79796i −0.0685994 0.336067i
\(851\) −42.2487 −1.44827
\(852\) 1.96902i 0.0674574i
\(853\) 12.4233i 0.425366i −0.977121 0.212683i \(-0.931780\pi\)
0.977121 0.212683i \(-0.0682202\pi\)
\(854\) 14.3205 0.490038
\(855\) 29.3205 + 23.9401i 1.00274 + 0.818734i
\(856\) −2.26795 −0.0775169
\(857\) 24.4206i 0.834191i 0.908863 + 0.417095i \(0.136952\pi\)
−0.908863 + 0.417095i \(0.863048\pi\)
\(858\) 0 0
\(859\) 11.8038 0.402742 0.201371 0.979515i \(-0.435460\pi\)
0.201371 + 0.979515i \(0.435460\pi\)
\(860\) 26.1962 32.0836i 0.893281 1.09404i
\(861\) 0.803848 0.0273951
\(862\) 36.5665i 1.24546i
\(863\) 9.76079i 0.332261i −0.986104 0.166131i \(-0.946873\pi\)
0.986104 0.166131i \(-0.0531273\pi\)
\(864\) 22.5167 0.766032
\(865\) 10.7846 13.2084i 0.366688 0.449099i
\(866\) −39.1244 −1.32950
\(867\) 8.24504i 0.280016i
\(868\) 8.18067i 0.277670i
\(869\) 0 0
\(870\) 12.0000 + 9.79796i 0.406838 + 0.332182i
\(871\) −63.3731 −2.14731
\(872\) 0.619174i 0.0209679i
\(873\) 1.79315i 0.0606890i
\(874\) −75.5692 −2.55617
\(875\) −8.87564 4.65874i −0.300052 0.157494i
\(876\) 4.39230 0.148402
\(877\) 55.9865i 1.89053i 0.326302 + 0.945265i \(0.394197\pi\)
−0.326302 + 0.945265i \(0.605803\pi\)
\(878\) 39.1175i 1.32015i
\(879\) 4.87564 0.164451
\(880\) 0 0
\(881\) 38.9090 1.31088 0.655438 0.755249i \(-0.272484\pi\)
0.655438 + 0.755249i \(0.272484\pi\)
\(882\) 32.7028i 1.10116i
\(883\) 47.0208i 1.58238i −0.611574 0.791188i \(-0.709463\pi\)
0.611574 0.791188i \(-0.290537\pi\)
\(884\) 7.60770 0.255874
\(885\) −3.46410 + 4.24264i −0.116445 + 0.142615i
\(886\) 17.7321 0.595720
\(887\) 8.34658i 0.280251i 0.990134 + 0.140125i \(0.0447506\pi\)
−0.990134 + 0.140125i \(0.955249\pi\)
\(888\) 1.79315i 0.0601742i
\(889\) −3.00000 −0.100617
\(890\) −17.6603 + 21.6293i −0.591973 + 0.725016i
\(891\) 0 0
\(892\) 10.0382i 0.336104i
\(893\) 25.4286i 0.850937i
\(894\) −13.7321 −0.459268
\(895\) −14.7846 12.0716i −0.494195 0.403509i
\(896\) 3.67949 0.122923
\(897\) 13.8647i 0.462930i
\(898\) 20.3166i 0.677975i
\(899\) −36.4974 −1.21726
\(900\) −4.73205 23.1822i −0.157735 0.772741i
\(901\) −12.3923 −0.412848
\(902\) 0 0
\(903\) 4.96335i 0.165170i
\(904\) −1.46410 −0.0486953
\(905\) −5.87564 4.79744i −0.195313 0.159472i
\(906\) 6.19615 0.205853
\(907\) 8.06918i 0.267933i −0.990986 0.133966i \(-0.957229\pi\)
0.990986 0.133966i \(-0.0427714\pi\)
\(908\) 37.2872i 1.23742i
\(909\) −3.80385 −0.126166
\(910\) 10.3923 12.7279i 0.344502 0.421927i
\(911\) 18.2487 0.604607 0.302303 0.953212i \(-0.402244\pi\)
0.302303 + 0.953212i \(0.402244\pi\)
\(912\) 14.3180i 0.474116i
\(913\) 0 0
\(914\) −40.9808 −1.35552
\(915\) 6.05256 7.41284i 0.200091 0.245061i
\(916\) −31.0526 −1.02601
\(917\) 18.9396i 0.625440i
\(918\) 5.93426i 0.195860i
\(919\) −32.9808 −1.08793 −0.543967 0.839106i \(-0.683079\pi\)
−0.543967 + 0.839106i \(0.683079\pi\)
\(920\) −5.66025 4.62158i −0.186613 0.152369i
\(921\) −9.12436 −0.300658
\(922\) 63.7511i 2.09953i
\(923\) 9.31749i 0.306689i
\(924\) 0 0
\(925\) −32.7846 + 6.69213i −1.07795 + 0.220036i
\(926\) 34.5167 1.13429
\(927\) 11.5911i 0.380702i
\(928\) 52.5761i 1.72589i
\(929\) 16.1436 0.529654 0.264827 0.964296i \(-0.414685\pi\)
0.264827 + 0.964296i \(0.414685\pi\)
\(930\) −9.12436 7.45001i −0.299199 0.244295i
\(931\) −38.3923 −1.25826
\(932\) 22.5259i 0.737860i
\(933\) 14.5211i 0.475399i
\(934\) −34.3205 −1.12300
\(935\) 0 0
\(936\) −6.00000 −0.196116
\(937\) 22.7017i 0.741634i 0.928706 + 0.370817i \(0.120922\pi\)
−0.928706 + 0.370817i \(0.879078\pi\)
\(938\) 25.8719i 0.844749i
\(939\) −8.87564 −0.289646
\(940\) −10.0526 + 12.3118i −0.327878 + 0.401567i
\(941\) −27.0000 −0.880175 −0.440087 0.897955i \(-0.645053\pi\)
−0.440087 + 0.897955i \(0.645053\pi\)
\(942\) 12.0716i 0.393313i
\(943\) 10.9348i 0.356085i
\(944\) −21.1244 −0.687539
\(945\) 4.60770 + 3.76217i 0.149888 + 0.122383i
\(946\) 0 0
\(947\) 14.3180i 0.465273i 0.972564 + 0.232636i \(0.0747352\pi\)
−0.972564 + 0.232636i \(0.925265\pi\)
\(948\) 4.89898i 0.159111i
\(949\) −20.7846 −0.674697
\(950\) −58.6410 + 11.9700i −1.90257 + 0.388360i
\(951\) 3.60770 0.116988
\(952\) 0.480473i 0.0155722i
\(953\) 31.3901i 1.01683i −0.861114 0.508413i \(-0.830233\pi\)
0.861114 0.508413i \(-0.169767\pi\)
\(954\) −63.1769 −2.04543
\(955\) 18.5885 + 15.1774i 0.601508 + 0.491130i
\(956\) −20.1962 −0.653190
\(957\) 0 0
\(958\) 18.2832i 0.590705i
\(959\) −12.3397 −0.398471
\(960\) −4.19615 + 5.13922i −0.135430 + 0.165867i
\(961\) −3.24871 −0.104797
\(962\) 54.8497i 1.76843i
\(963\) 11.9700i 0.385729i
\(964\) 17.5359 0.564793
\(965\) −14.5359 + 17.8028i −0.467927 + 0.573091i
\(966\) −5.66025 −0.182116
\(967\) 4.24264i 0.136434i 0.997671 + 0.0682171i \(0.0217310\pi\)
−0.997671 + 0.0682171i \(0.978269\pi\)
\(968\) 0 0
\(969\) 3.32051 0.106670
\(970\) −2.19615 1.79315i −0.0705142 0.0575746i
\(971\) −11.0718 −0.355311 −0.177655 0.984093i \(-0.556851\pi\)
−0.177655 + 0.984093i \(0.556851\pi\)
\(972\) 21.3891i 0.686055i
\(973\) 14.8728i 0.476800i
\(974\) 24.5885 0.787865
\(975\) −2.19615 10.7589i −0.0703332 0.344561i
\(976\) 36.9090 1.18143
\(977\) 14.9743i 0.479072i 0.970888 + 0.239536i \(0.0769952\pi\)
−0.970888 + 0.239536i \(0.923005\pi\)
\(978\) 7.58871i 0.242660i
\(979\) 0 0
\(980\) 18.5885 + 15.1774i 0.593786 + 0.484825i
\(981\) 3.26795 0.104338
\(982\) 30.3548i 0.968661i
\(983\) 15.0115i 0.478793i −0.970922 0.239396i \(-0.923050\pi\)
0.970922 0.239396i \(-0.0769495\pi\)
\(984\) 0.464102 0.0147950
\(985\) 3.60770 4.41851i 0.114951 0.140785i
\(986\) −13.8564 −0.441278
\(987\) 1.90465i 0.0606255i
\(988\) 45.5322i 1.44857i
\(989\) 67.5167 2.14690
\(990\) 0 0
\(991\) −45.9090 −1.45835 −0.729173 0.684329i \(-0.760095\pi\)
−0.729173 + 0.684329i \(0.760095\pi\)
\(992\) 39.9769i 1.26927i
\(993\) 4.03957i 0.128192i
\(994\) −3.80385 −0.120651
\(995\) −3.46410 2.82843i −0.109819 0.0896672i
\(996\) −8.87564 −0.281236
\(997\) 0.175865i 0.00556971i 0.999996 + 0.00278486i \(0.000886449\pi\)
−0.999996 + 0.00278486i \(0.999114\pi\)
\(998\) 74.1682i 2.34775i
\(999\) 19.8564 0.628229
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 605.2.b.d.364.1 4
5.2 odd 4 3025.2.a.y.1.4 4
5.3 odd 4 3025.2.a.y.1.1 4
5.4 even 2 inner 605.2.b.d.364.4 yes 4
11.2 odd 10 605.2.j.e.444.4 16
11.3 even 5 605.2.j.f.9.1 16
11.4 even 5 605.2.j.f.269.4 16
11.5 even 5 605.2.j.f.124.4 16
11.6 odd 10 605.2.j.e.124.1 16
11.7 odd 10 605.2.j.e.269.1 16
11.8 odd 10 605.2.j.e.9.4 16
11.9 even 5 605.2.j.f.444.1 16
11.10 odd 2 605.2.b.e.364.4 yes 4
55.4 even 10 605.2.j.f.269.1 16
55.9 even 10 605.2.j.f.444.4 16
55.14 even 10 605.2.j.f.9.4 16
55.19 odd 10 605.2.j.e.9.1 16
55.24 odd 10 605.2.j.e.444.1 16
55.29 odd 10 605.2.j.e.269.4 16
55.32 even 4 3025.2.a.z.1.1 4
55.39 odd 10 605.2.j.e.124.4 16
55.43 even 4 3025.2.a.z.1.4 4
55.49 even 10 605.2.j.f.124.1 16
55.54 odd 2 605.2.b.e.364.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.b.d.364.1 4 1.1 even 1 trivial
605.2.b.d.364.4 yes 4 5.4 even 2 inner
605.2.b.e.364.1 yes 4 55.54 odd 2
605.2.b.e.364.4 yes 4 11.10 odd 2
605.2.j.e.9.1 16 55.19 odd 10
605.2.j.e.9.4 16 11.8 odd 10
605.2.j.e.124.1 16 11.6 odd 10
605.2.j.e.124.4 16 55.39 odd 10
605.2.j.e.269.1 16 11.7 odd 10
605.2.j.e.269.4 16 55.29 odd 10
605.2.j.e.444.1 16 55.24 odd 10
605.2.j.e.444.4 16 11.2 odd 10
605.2.j.f.9.1 16 11.3 even 5
605.2.j.f.9.4 16 55.14 even 10
605.2.j.f.124.1 16 55.49 even 10
605.2.j.f.124.4 16 11.5 even 5
605.2.j.f.269.1 16 55.4 even 10
605.2.j.f.269.4 16 11.4 even 5
605.2.j.f.444.1 16 11.9 even 5
605.2.j.f.444.4 16 55.9 even 10
3025.2.a.y.1.1 4 5.3 odd 4
3025.2.a.y.1.4 4 5.2 odd 4
3025.2.a.z.1.1 4 55.32 even 4
3025.2.a.z.1.4 4 55.43 even 4