Properties

Label 525.2.b.j.251.2
Level $525$
Weight $2$
Character 525.251
Analytic conductor $4.192$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(251,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 525.251
Dual form 525.2.b.j.251.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.73205i q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(1.73205 + 2.44949i) q^{6} +(-2.44949 + 1.00000i) q^{7} -1.73205i q^{8} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q-1.73205i q^{2} +(-1.41421 + 1.00000i) q^{3} -1.00000 q^{4} +(1.73205 + 2.44949i) q^{6} +(-2.44949 + 1.00000i) q^{7} -1.73205i q^{8} +(1.00000 - 2.82843i) q^{9} +2.82843i q^{11} +(1.41421 - 1.00000i) q^{12} +4.00000i q^{13} +(1.73205 + 4.24264i) q^{14} -5.00000 q^{16} -2.82843 q^{17} +(-4.89898 - 1.73205i) q^{18} +(2.46410 - 3.86370i) q^{21} +4.89898 q^{22} +3.46410i q^{23} +(1.73205 + 2.44949i) q^{24} +6.92820 q^{26} +(1.41421 + 5.00000i) q^{27} +(2.44949 - 1.00000i) q^{28} +5.65685i q^{29} +9.79796i q^{31} +5.19615i q^{32} +(-2.82843 - 4.00000i) q^{33} +4.89898i q^{34} +(-1.00000 + 2.82843i) q^{36} +(-4.00000 - 5.65685i) q^{39} -3.46410 q^{41} +(-6.69213 - 4.26795i) q^{42} +4.89898 q^{43} -2.82843i q^{44} +6.00000 q^{46} -2.82843 q^{47} +(7.07107 - 5.00000i) q^{48} +(5.00000 - 4.89898i) q^{49} +(4.00000 - 2.82843i) q^{51} -4.00000i q^{52} +(8.66025 - 2.44949i) q^{54} +(1.73205 + 4.24264i) q^{56} +9.79796 q^{58} -6.92820 q^{59} -9.79796i q^{61} +16.9706 q^{62} +(0.378937 + 7.92820i) q^{63} -1.00000 q^{64} +(-6.92820 + 4.89898i) q^{66} +4.89898 q^{67} +2.82843 q^{68} +(-3.46410 - 4.89898i) q^{69} +2.82843i q^{71} +(-4.89898 - 1.73205i) q^{72} -8.00000i q^{73} +(-2.82843 - 6.92820i) q^{77} +(-9.79796 + 6.92820i) q^{78} -8.00000 q^{79} +(-7.00000 - 5.65685i) q^{81} +6.00000i q^{82} +2.82843 q^{83} +(-2.46410 + 3.86370i) q^{84} -8.48528i q^{86} +(-5.65685 - 8.00000i) q^{87} +4.89898 q^{88} -10.3923 q^{89} +(-4.00000 - 9.79796i) q^{91} -3.46410i q^{92} +(-9.79796 - 13.8564i) q^{93} +4.89898i q^{94} +(-5.19615 - 7.34847i) q^{96} +8.00000i q^{97} +(-8.48528 - 8.66025i) q^{98} +(8.00000 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 8 q^{9} - 40 q^{16} - 8 q^{21} - 8 q^{36} - 32 q^{39} + 48 q^{46} + 40 q^{49} + 32 q^{51} - 8 q^{64} - 64 q^{79} - 56 q^{81} + 8 q^{84} - 32 q^{91} + 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 1.22474i −0.790569 0.612372i \(-0.790215\pi\)
0.790569 0.612372i \(-0.209785\pi\)
\(3\) −1.41421 + 1.00000i −0.816497 + 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) 1.73205 + 2.44949i 0.707107 + 1.00000i
\(7\) −2.44949 + 1.00000i −0.925820 + 0.377964i
\(8\) 1.73205i 0.612372i
\(9\) 1.00000 2.82843i 0.333333 0.942809i
\(10\) 0 0
\(11\) 2.82843i 0.852803i 0.904534 + 0.426401i \(0.140219\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 1.41421 1.00000i 0.408248 0.288675i
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 1.73205 + 4.24264i 0.462910 + 1.13389i
\(15\) 0 0
\(16\) −5.00000 −1.25000
\(17\) −2.82843 −0.685994 −0.342997 0.939336i \(-0.611442\pi\)
−0.342997 + 0.939336i \(0.611442\pi\)
\(18\) −4.89898 1.73205i −1.15470 0.408248i
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 2.46410 3.86370i 0.537711 0.843129i
\(22\) 4.89898 1.04447
\(23\) 3.46410i 0.722315i 0.932505 + 0.361158i \(0.117618\pi\)
−0.932505 + 0.361158i \(0.882382\pi\)
\(24\) 1.73205 + 2.44949i 0.353553 + 0.500000i
\(25\) 0 0
\(26\) 6.92820 1.35873
\(27\) 1.41421 + 5.00000i 0.272166 + 0.962250i
\(28\) 2.44949 1.00000i 0.462910 0.188982i
\(29\) 5.65685i 1.05045i 0.850963 + 0.525226i \(0.176019\pi\)
−0.850963 + 0.525226i \(0.823981\pi\)
\(30\) 0 0
\(31\) 9.79796i 1.75977i 0.475191 + 0.879883i \(0.342379\pi\)
−0.475191 + 0.879883i \(0.657621\pi\)
\(32\) 5.19615i 0.918559i
\(33\) −2.82843 4.00000i −0.492366 0.696311i
\(34\) 4.89898i 0.840168i
\(35\) 0 0
\(36\) −1.00000 + 2.82843i −0.166667 + 0.471405i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) −4.00000 5.65685i −0.640513 0.905822i
\(40\) 0 0
\(41\) −3.46410 −0.541002 −0.270501 0.962720i \(-0.587189\pi\)
−0.270501 + 0.962720i \(0.587189\pi\)
\(42\) −6.69213 4.26795i −1.03262 0.658559i
\(43\) 4.89898 0.747087 0.373544 0.927613i \(-0.378143\pi\)
0.373544 + 0.927613i \(0.378143\pi\)
\(44\) 2.82843i 0.426401i
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) −2.82843 −0.412568 −0.206284 0.978492i \(-0.566137\pi\)
−0.206284 + 0.978492i \(0.566137\pi\)
\(48\) 7.07107 5.00000i 1.02062 0.721688i
\(49\) 5.00000 4.89898i 0.714286 0.699854i
\(50\) 0 0
\(51\) 4.00000 2.82843i 0.560112 0.396059i
\(52\) 4.00000i 0.554700i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 8.66025 2.44949i 1.17851 0.333333i
\(55\) 0 0
\(56\) 1.73205 + 4.24264i 0.231455 + 0.566947i
\(57\) 0 0
\(58\) 9.79796 1.28654
\(59\) −6.92820 −0.901975 −0.450988 0.892530i \(-0.648928\pi\)
−0.450988 + 0.892530i \(0.648928\pi\)
\(60\) 0 0
\(61\) 9.79796i 1.25450i −0.778818 0.627250i \(-0.784180\pi\)
0.778818 0.627250i \(-0.215820\pi\)
\(62\) 16.9706 2.15526
\(63\) 0.378937 + 7.92820i 0.0477416 + 0.998860i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −6.92820 + 4.89898i −0.852803 + 0.603023i
\(67\) 4.89898 0.598506 0.299253 0.954174i \(-0.403263\pi\)
0.299253 + 0.954174i \(0.403263\pi\)
\(68\) 2.82843 0.342997
\(69\) −3.46410 4.89898i −0.417029 0.589768i
\(70\) 0 0
\(71\) 2.82843i 0.335673i 0.985815 + 0.167836i \(0.0536780\pi\)
−0.985815 + 0.167836i \(0.946322\pi\)
\(72\) −4.89898 1.73205i −0.577350 0.204124i
\(73\) 8.00000i 0.936329i −0.883641 0.468165i \(-0.844915\pi\)
0.883641 0.468165i \(-0.155085\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.82843 6.92820i −0.322329 0.789542i
\(78\) −9.79796 + 6.92820i −1.10940 + 0.784465i
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) −7.00000 5.65685i −0.777778 0.628539i
\(82\) 6.00000i 0.662589i
\(83\) 2.82843 0.310460 0.155230 0.987878i \(-0.450388\pi\)
0.155230 + 0.987878i \(0.450388\pi\)
\(84\) −2.46410 + 3.86370i −0.268856 + 0.421565i
\(85\) 0 0
\(86\) 8.48528i 0.914991i
\(87\) −5.65685 8.00000i −0.606478 0.857690i
\(88\) 4.89898 0.522233
\(89\) −10.3923 −1.10158 −0.550791 0.834643i \(-0.685674\pi\)
−0.550791 + 0.834643i \(0.685674\pi\)
\(90\) 0 0
\(91\) −4.00000 9.79796i −0.419314 1.02711i
\(92\) 3.46410i 0.361158i
\(93\) −9.79796 13.8564i −1.01600 1.43684i
\(94\) 4.89898i 0.505291i
\(95\) 0 0
\(96\) −5.19615 7.34847i −0.530330 0.750000i
\(97\) 8.00000i 0.812277i 0.913812 + 0.406138i \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) −8.48528 8.66025i −0.857143 0.874818i
\(99\) 8.00000 + 2.82843i 0.804030 + 0.284268i
\(100\) 0 0
\(101\) −17.3205 −1.72345 −0.861727 0.507371i \(-0.830617\pi\)
−0.861727 + 0.507371i \(0.830617\pi\)
\(102\) −4.89898 6.92820i −0.485071 0.685994i
\(103\) 10.0000i 0.985329i 0.870219 + 0.492665i \(0.163977\pi\)
−0.870219 + 0.492665i \(0.836023\pi\)
\(104\) 6.92820 0.679366
\(105\) 0 0
\(106\) 0 0
\(107\) 10.3923i 1.00466i 0.864675 + 0.502331i \(0.167524\pi\)
−0.864675 + 0.502331i \(0.832476\pi\)
\(108\) −1.41421 5.00000i −0.136083 0.481125i
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 12.2474 5.00000i 1.15728 0.472456i
\(113\) 6.92820i 0.651751i −0.945413 0.325875i \(-0.894341\pi\)
0.945413 0.325875i \(-0.105659\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.65685i 0.525226i
\(117\) 11.3137 + 4.00000i 1.04595 + 0.369800i
\(118\) 12.0000i 1.10469i
\(119\) 6.92820 2.82843i 0.635107 0.259281i
\(120\) 0 0
\(121\) 3.00000 0.272727
\(122\) −16.9706 −1.53644
\(123\) 4.89898 3.46410i 0.441726 0.312348i
\(124\) 9.79796i 0.879883i
\(125\) 0 0
\(126\) 13.7321 0.656339i 1.22335 0.0584713i
\(127\) −14.6969 −1.30414 −0.652071 0.758158i \(-0.726100\pi\)
−0.652071 + 0.758158i \(0.726100\pi\)
\(128\) 12.1244i 1.07165i
\(129\) −6.92820 + 4.89898i −0.609994 + 0.431331i
\(130\) 0 0
\(131\) 6.92820 0.605320 0.302660 0.953099i \(-0.402125\pi\)
0.302660 + 0.953099i \(0.402125\pi\)
\(132\) 2.82843 + 4.00000i 0.246183 + 0.348155i
\(133\) 0 0
\(134\) 8.48528i 0.733017i
\(135\) 0 0
\(136\) 4.89898i 0.420084i
\(137\) 6.92820i 0.591916i −0.955201 0.295958i \(-0.904361\pi\)
0.955201 0.295958i \(-0.0956389\pi\)
\(138\) −8.48528 + 6.00000i −0.722315 + 0.510754i
\(139\) 9.79796i 0.831052i −0.909581 0.415526i \(-0.863598\pi\)
0.909581 0.415526i \(-0.136402\pi\)
\(140\) 0 0
\(141\) 4.00000 2.82843i 0.336861 0.238197i
\(142\) 4.89898 0.411113
\(143\) −11.3137 −0.946100
\(144\) −5.00000 + 14.1421i −0.416667 + 1.17851i
\(145\) 0 0
\(146\) −13.8564 −1.14676
\(147\) −2.17209 + 11.9282i −0.179151 + 0.983822i
\(148\) 0 0
\(149\) 11.3137i 0.926855i −0.886135 0.463428i \(-0.846619\pi\)
0.886135 0.463428i \(-0.153381\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) −2.82843 + 8.00000i −0.228665 + 0.646762i
\(154\) −12.0000 + 4.89898i −0.966988 + 0.394771i
\(155\) 0 0
\(156\) 4.00000 + 5.65685i 0.320256 + 0.452911i
\(157\) 4.00000i 0.319235i −0.987179 0.159617i \(-0.948974\pi\)
0.987179 0.159617i \(-0.0510260\pi\)
\(158\) 13.8564i 1.10236i
\(159\) 0 0
\(160\) 0 0
\(161\) −3.46410 8.48528i −0.273009 0.668734i
\(162\) −9.79796 + 12.1244i −0.769800 + 0.952579i
\(163\) −14.6969 −1.15115 −0.575577 0.817748i \(-0.695222\pi\)
−0.575577 + 0.817748i \(0.695222\pi\)
\(164\) 3.46410 0.270501
\(165\) 0 0
\(166\) 4.89898i 0.380235i
\(167\) 14.1421 1.09435 0.547176 0.837018i \(-0.315703\pi\)
0.547176 + 0.837018i \(0.315703\pi\)
\(168\) −6.69213 4.26795i −0.516309 0.329279i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) −4.89898 −0.373544
\(173\) 19.7990 1.50529 0.752645 0.658427i \(-0.228778\pi\)
0.752645 + 0.658427i \(0.228778\pi\)
\(174\) −13.8564 + 9.79796i −1.05045 + 0.742781i
\(175\) 0 0
\(176\) 14.1421i 1.06600i
\(177\) 9.79796 6.92820i 0.736460 0.520756i
\(178\) 18.0000i 1.34916i
\(179\) 2.82843i 0.211407i −0.994398 0.105703i \(-0.966291\pi\)
0.994398 0.105703i \(-0.0337094\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −16.9706 + 6.92820i −1.25794 + 0.513553i
\(183\) 9.79796 + 13.8564i 0.724286 + 1.02430i
\(184\) 6.00000 0.442326
\(185\) 0 0
\(186\) −24.0000 + 16.9706i −1.75977 + 1.24434i
\(187\) 8.00000i 0.585018i
\(188\) 2.82843 0.206284
\(189\) −8.46410 10.8332i −0.615673 0.788002i
\(190\) 0 0
\(191\) 19.7990i 1.43260i 0.697790 + 0.716302i \(0.254167\pi\)
−0.697790 + 0.716302i \(0.745833\pi\)
\(192\) 1.41421 1.00000i 0.102062 0.0721688i
\(193\) 9.79796 0.705273 0.352636 0.935760i \(-0.385285\pi\)
0.352636 + 0.935760i \(0.385285\pi\)
\(194\) 13.8564 0.994832
\(195\) 0 0
\(196\) −5.00000 + 4.89898i −0.357143 + 0.349927i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 4.89898 13.8564i 0.348155 0.984732i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 0 0
\(201\) −6.92820 + 4.89898i −0.488678 + 0.345547i
\(202\) 30.0000i 2.11079i
\(203\) −5.65685 13.8564i −0.397033 0.972529i
\(204\) −4.00000 + 2.82843i −0.280056 + 0.198030i
\(205\) 0 0
\(206\) 17.3205 1.20678
\(207\) 9.79796 + 3.46410i 0.681005 + 0.240772i
\(208\) 20.0000i 1.38675i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −2.82843 4.00000i −0.193801 0.274075i
\(214\) 18.0000 1.23045
\(215\) 0 0
\(216\) 8.66025 2.44949i 0.589256 0.166667i
\(217\) −9.79796 24.0000i −0.665129 1.62923i
\(218\) 17.3205i 1.17309i
\(219\) 8.00000 + 11.3137i 0.540590 + 0.764510i
\(220\) 0 0
\(221\) 11.3137i 0.761042i
\(222\) 0 0
\(223\) 26.0000i 1.74109i −0.492090 0.870544i \(-0.663767\pi\)
0.492090 0.870544i \(-0.336233\pi\)
\(224\) −5.19615 12.7279i −0.347183 0.850420i
\(225\) 0 0
\(226\) −12.0000 −0.798228
\(227\) −2.82843 −0.187729 −0.0938647 0.995585i \(-0.529922\pi\)
−0.0938647 + 0.995585i \(0.529922\pi\)
\(228\) 0 0
\(229\) 19.5959i 1.29493i 0.762093 + 0.647467i \(0.224172\pi\)
−0.762093 + 0.647467i \(0.775828\pi\)
\(230\) 0 0
\(231\) 10.9282 + 6.96953i 0.719023 + 0.458562i
\(232\) 9.79796 0.643268
\(233\) 20.7846i 1.36165i 0.732448 + 0.680823i \(0.238378\pi\)
−0.732448 + 0.680823i \(0.761622\pi\)
\(234\) 6.92820 19.5959i 0.452911 1.28103i
\(235\) 0 0
\(236\) 6.92820 0.450988
\(237\) 11.3137 8.00000i 0.734904 0.519656i
\(238\) −4.89898 12.0000i −0.317554 0.777844i
\(239\) 2.82843i 0.182956i −0.995807 0.0914779i \(-0.970841\pi\)
0.995807 0.0914779i \(-0.0291591\pi\)
\(240\) 0 0
\(241\) 9.79796i 0.631142i −0.948902 0.315571i \(-0.897804\pi\)
0.948902 0.315571i \(-0.102196\pi\)
\(242\) 5.19615i 0.334021i
\(243\) 15.5563 + 1.00000i 0.997940 + 0.0641500i
\(244\) 9.79796i 0.627250i
\(245\) 0 0
\(246\) −6.00000 8.48528i −0.382546 0.541002i
\(247\) 0 0
\(248\) 16.9706 1.07763
\(249\) −4.00000 + 2.82843i −0.253490 + 0.179244i
\(250\) 0 0
\(251\) 20.7846 1.31191 0.655956 0.754799i \(-0.272265\pi\)
0.655956 + 0.754799i \(0.272265\pi\)
\(252\) −0.378937 7.92820i −0.0238708 0.499430i
\(253\) −9.79796 −0.615992
\(254\) 25.4558i 1.59724i
\(255\) 0 0
\(256\) 19.0000 1.18750
\(257\) 14.1421 0.882162 0.441081 0.897467i \(-0.354595\pi\)
0.441081 + 0.897467i \(0.354595\pi\)
\(258\) 8.48528 + 12.0000i 0.528271 + 0.747087i
\(259\) 0 0
\(260\) 0 0
\(261\) 16.0000 + 5.65685i 0.990375 + 0.350150i
\(262\) 12.0000i 0.741362i
\(263\) 3.46410i 0.213606i −0.994280 0.106803i \(-0.965939\pi\)
0.994280 0.106803i \(-0.0340614\pi\)
\(264\) −6.92820 + 4.89898i −0.426401 + 0.301511i
\(265\) 0 0
\(266\) 0 0
\(267\) 14.6969 10.3923i 0.899438 0.635999i
\(268\) −4.89898 −0.299253
\(269\) 10.3923 0.633630 0.316815 0.948487i \(-0.397387\pi\)
0.316815 + 0.948487i \(0.397387\pi\)
\(270\) 0 0
\(271\) 29.3939i 1.78555i 0.450502 + 0.892775i \(0.351245\pi\)
−0.450502 + 0.892775i \(0.648755\pi\)
\(272\) 14.1421 0.857493
\(273\) 15.4548 + 9.85641i 0.935368 + 0.596537i
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 3.46410 + 4.89898i 0.208514 + 0.294884i
\(277\) −19.5959 −1.17740 −0.588702 0.808350i \(-0.700361\pi\)
−0.588702 + 0.808350i \(0.700361\pi\)
\(278\) −16.9706 −1.01783
\(279\) 27.7128 + 9.79796i 1.65912 + 0.586588i
\(280\) 0 0
\(281\) 28.2843i 1.68730i 0.536895 + 0.843649i \(0.319597\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −4.89898 6.92820i −0.291730 0.412568i
\(283\) 14.0000i 0.832214i −0.909316 0.416107i \(-0.863394\pi\)
0.909316 0.416107i \(-0.136606\pi\)
\(284\) 2.82843i 0.167836i
\(285\) 0 0
\(286\) 19.5959i 1.15873i
\(287\) 8.48528 3.46410i 0.500870 0.204479i
\(288\) 14.6969 + 5.19615i 0.866025 + 0.306186i
\(289\) −9.00000 −0.529412
\(290\) 0 0
\(291\) −8.00000 11.3137i −0.468968 0.663221i
\(292\) 8.00000i 0.468165i
\(293\) 2.82843 0.165238 0.0826192 0.996581i \(-0.473671\pi\)
0.0826192 + 0.996581i \(0.473671\pi\)
\(294\) 20.6603 + 3.76217i 1.20493 + 0.219414i
\(295\) 0 0
\(296\) 0 0
\(297\) −14.1421 + 4.00000i −0.820610 + 0.232104i
\(298\) −19.5959 −1.13516
\(299\) −13.8564 −0.801337
\(300\) 0 0
\(301\) −12.0000 + 4.89898i −0.691669 + 0.282372i
\(302\) 13.8564i 0.797347i
\(303\) 24.4949 17.3205i 1.40720 0.995037i
\(304\) 0 0
\(305\) 0 0
\(306\) 13.8564 + 4.89898i 0.792118 + 0.280056i
\(307\) 10.0000i 0.570730i −0.958419 0.285365i \(-0.907885\pi\)
0.958419 0.285365i \(-0.0921148\pi\)
\(308\) 2.82843 + 6.92820i 0.161165 + 0.394771i
\(309\) −10.0000 14.1421i −0.568880 0.804518i
\(310\) 0 0
\(311\) 27.7128 1.57145 0.785725 0.618576i \(-0.212290\pi\)
0.785725 + 0.618576i \(0.212290\pi\)
\(312\) −9.79796 + 6.92820i −0.554700 + 0.392232i
\(313\) 16.0000i 0.904373i 0.891923 + 0.452187i \(0.149356\pi\)
−0.891923 + 0.452187i \(0.850644\pi\)
\(314\) −6.92820 −0.390981
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) 13.8564i 0.778253i 0.921184 + 0.389127i \(0.127223\pi\)
−0.921184 + 0.389127i \(0.872777\pi\)
\(318\) 0 0
\(319\) −16.0000 −0.895828
\(320\) 0 0
\(321\) −10.3923 14.6969i −0.580042 0.820303i
\(322\) −14.6969 + 6.00000i −0.819028 + 0.334367i
\(323\) 0 0
\(324\) 7.00000 + 5.65685i 0.388889 + 0.314270i
\(325\) 0 0
\(326\) 25.4558i 1.40987i
\(327\) −14.1421 + 10.0000i −0.782062 + 0.553001i
\(328\) 6.00000i 0.331295i
\(329\) 6.92820 2.82843i 0.381964 0.155936i
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) −2.82843 −0.155230
\(333\) 0 0
\(334\) 24.4949i 1.34030i
\(335\) 0 0
\(336\) −12.3205 + 19.3185i −0.672139 + 1.05391i
\(337\) 19.5959 1.06746 0.533729 0.845656i \(-0.320790\pi\)
0.533729 + 0.845656i \(0.320790\pi\)
\(338\) 5.19615i 0.282633i
\(339\) 6.92820 + 9.79796i 0.376288 + 0.532152i
\(340\) 0 0
\(341\) −27.7128 −1.50073
\(342\) 0 0
\(343\) −7.34847 + 17.0000i −0.396780 + 0.917914i
\(344\) 8.48528i 0.457496i
\(345\) 0 0
\(346\) 34.2929i 1.84360i
\(347\) 17.3205i 0.929814i 0.885360 + 0.464907i \(0.153912\pi\)
−0.885360 + 0.464907i \(0.846088\pi\)
\(348\) 5.65685 + 8.00000i 0.303239 + 0.428845i
\(349\) 19.5959i 1.04895i −0.851427 0.524473i \(-0.824262\pi\)
0.851427 0.524473i \(-0.175738\pi\)
\(350\) 0 0
\(351\) −20.0000 + 5.65685i −1.06752 + 0.301941i
\(352\) −14.6969 −0.783349
\(353\) −31.1127 −1.65596 −0.827981 0.560756i \(-0.810510\pi\)
−0.827981 + 0.560756i \(0.810510\pi\)
\(354\) −12.0000 16.9706i −0.637793 0.901975i
\(355\) 0 0
\(356\) 10.3923 0.550791
\(357\) −6.96953 + 10.9282i −0.368867 + 0.578382i
\(358\) −4.89898 −0.258919
\(359\) 31.1127i 1.64207i 0.570881 + 0.821033i \(0.306602\pi\)
−0.570881 + 0.821033i \(0.693398\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) −4.24264 + 3.00000i −0.222681 + 0.157459i
\(364\) 4.00000 + 9.79796i 0.209657 + 0.513553i
\(365\) 0 0
\(366\) 24.0000 16.9706i 1.25450 0.887066i
\(367\) 10.0000i 0.521996i −0.965339 0.260998i \(-0.915948\pi\)
0.965339 0.260998i \(-0.0840516\pi\)
\(368\) 17.3205i 0.902894i
\(369\) −3.46410 + 9.79796i −0.180334 + 0.510061i
\(370\) 0 0
\(371\) 0 0
\(372\) 9.79796 + 13.8564i 0.508001 + 0.718421i
\(373\) 9.79796 0.507319 0.253660 0.967294i \(-0.418366\pi\)
0.253660 + 0.967294i \(0.418366\pi\)
\(374\) −13.8564 −0.716498
\(375\) 0 0
\(376\) 4.89898i 0.252646i
\(377\) −22.6274 −1.16537
\(378\) −18.7637 + 14.6603i −0.965101 + 0.754042i
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 0 0
\(381\) 20.7846 14.6969i 1.06483 0.752947i
\(382\) 34.2929 1.75458
\(383\) −14.1421 −0.722629 −0.361315 0.932444i \(-0.617672\pi\)
−0.361315 + 0.932444i \(0.617672\pi\)
\(384\) −12.1244 17.1464i −0.618718 0.875000i
\(385\) 0 0
\(386\) 16.9706i 0.863779i
\(387\) 4.89898 13.8564i 0.249029 0.704361i
\(388\) 8.00000i 0.406138i
\(389\) 22.6274i 1.14726i 0.819116 + 0.573628i \(0.194464\pi\)
−0.819116 + 0.573628i \(0.805536\pi\)
\(390\) 0 0
\(391\) 9.79796i 0.495504i
\(392\) −8.48528 8.66025i −0.428571 0.437409i
\(393\) −9.79796 + 6.92820i −0.494242 + 0.349482i
\(394\) 0 0
\(395\) 0 0
\(396\) −8.00000 2.82843i −0.402015 0.142134i
\(397\) 20.0000i 1.00377i 0.864934 + 0.501886i \(0.167360\pi\)
−0.864934 + 0.501886i \(0.832640\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 22.6274i 1.12996i −0.825105 0.564980i \(-0.808884\pi\)
0.825105 0.564980i \(-0.191116\pi\)
\(402\) 8.48528 + 12.0000i 0.423207 + 0.598506i
\(403\) −39.1918 −1.95228
\(404\) 17.3205 0.861727
\(405\) 0 0
\(406\) −24.0000 + 9.79796i −1.19110 + 0.486265i
\(407\) 0 0
\(408\) −4.89898 6.92820i −0.242536 0.342997i
\(409\) 9.79796i 0.484478i −0.970217 0.242239i \(-0.922118\pi\)
0.970217 0.242239i \(-0.0778818\pi\)
\(410\) 0 0
\(411\) 6.92820 + 9.79796i 0.341743 + 0.483298i
\(412\) 10.0000i 0.492665i
\(413\) 16.9706 6.92820i 0.835067 0.340915i
\(414\) 6.00000 16.9706i 0.294884 0.834058i
\(415\) 0 0
\(416\) −20.7846 −1.01905
\(417\) 9.79796 + 13.8564i 0.479808 + 0.678551i
\(418\) 0 0
\(419\) −6.92820 −0.338465 −0.169232 0.985576i \(-0.554129\pi\)
−0.169232 + 0.985576i \(0.554129\pi\)
\(420\) 0 0
\(421\) 26.0000 1.26716 0.633581 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) 6.92820i 0.337260i
\(423\) −2.82843 + 8.00000i −0.137523 + 0.388973i
\(424\) 0 0
\(425\) 0 0
\(426\) −6.92820 + 4.89898i −0.335673 + 0.237356i
\(427\) 9.79796 + 24.0000i 0.474156 + 1.16144i
\(428\) 10.3923i 0.502331i
\(429\) 16.0000 11.3137i 0.772487 0.546231i
\(430\) 0 0
\(431\) 2.82843i 0.136241i 0.997677 + 0.0681203i \(0.0217002\pi\)
−0.997677 + 0.0681203i \(0.978300\pi\)
\(432\) −7.07107 25.0000i −0.340207 1.20281i
\(433\) 16.0000i 0.768911i 0.923144 + 0.384455i \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) −41.5692 + 16.9706i −1.99539 + 0.814613i
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) 0 0
\(438\) 19.5959 13.8564i 0.936329 0.662085i
\(439\) 39.1918i 1.87052i 0.353956 + 0.935262i \(0.384836\pi\)
−0.353956 + 0.935262i \(0.615164\pi\)
\(440\) 0 0
\(441\) −8.85641 19.0411i −0.421734 0.906720i
\(442\) −19.5959 −0.932083
\(443\) 17.3205i 0.822922i 0.911427 + 0.411461i \(0.134981\pi\)
−0.911427 + 0.411461i \(0.865019\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −45.0333 −2.13239
\(447\) 11.3137 + 16.0000i 0.535120 + 0.756774i
\(448\) 2.44949 1.00000i 0.115728 0.0472456i
\(449\) 5.65685i 0.266963i 0.991051 + 0.133482i \(0.0426157\pi\)
−0.991051 + 0.133482i \(0.957384\pi\)
\(450\) 0 0
\(451\) 9.79796i 0.461368i
\(452\) 6.92820i 0.325875i
\(453\) −11.3137 + 8.00000i −0.531564 + 0.375873i
\(454\) 4.89898i 0.229920i
\(455\) 0 0
\(456\) 0 0
\(457\) −19.5959 −0.916658 −0.458329 0.888783i \(-0.651552\pi\)
−0.458329 + 0.888783i \(0.651552\pi\)
\(458\) 33.9411 1.58596
\(459\) −4.00000 14.1421i −0.186704 0.660098i
\(460\) 0 0
\(461\) 3.46410 0.161339 0.0806696 0.996741i \(-0.474294\pi\)
0.0806696 + 0.996741i \(0.474294\pi\)
\(462\) 12.0716 18.9282i 0.561621 0.880620i
\(463\) −4.89898 −0.227675 −0.113837 0.993499i \(-0.536314\pi\)
−0.113837 + 0.993499i \(0.536314\pi\)
\(464\) 28.2843i 1.31306i
\(465\) 0 0
\(466\) 36.0000 1.66767
\(467\) −2.82843 −0.130884 −0.0654420 0.997856i \(-0.520846\pi\)
−0.0654420 + 0.997856i \(0.520846\pi\)
\(468\) −11.3137 4.00000i −0.522976 0.184900i
\(469\) −12.0000 + 4.89898i −0.554109 + 0.226214i
\(470\) 0 0
\(471\) 4.00000 + 5.65685i 0.184310 + 0.260654i
\(472\) 12.0000i 0.552345i
\(473\) 13.8564i 0.637118i
\(474\) −13.8564 19.5959i −0.636446 0.900070i
\(475\) 0 0
\(476\) −6.92820 + 2.82843i −0.317554 + 0.129641i
\(477\) 0 0
\(478\) −4.89898 −0.224074
\(479\) 27.7128 1.26623 0.633115 0.774057i \(-0.281776\pi\)
0.633115 + 0.774057i \(0.281776\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −16.9706 −0.772988
\(483\) 13.3843 + 8.53590i 0.609005 + 0.388397i
\(484\) −3.00000 −0.136364
\(485\) 0 0
\(486\) 1.73205 26.9444i 0.0785674 1.22222i
\(487\) −14.6969 −0.665982 −0.332991 0.942930i \(-0.608058\pi\)
−0.332991 + 0.942930i \(0.608058\pi\)
\(488\) −16.9706 −0.768221
\(489\) 20.7846 14.6969i 0.939913 0.664619i
\(490\) 0 0
\(491\) 14.1421i 0.638226i −0.947717 0.319113i \(-0.896615\pi\)
0.947717 0.319113i \(-0.103385\pi\)
\(492\) −4.89898 + 3.46410i −0.220863 + 0.156174i
\(493\) 16.0000i 0.720604i
\(494\) 0 0
\(495\) 0 0
\(496\) 48.9898i 2.19971i
\(497\) −2.82843 6.92820i −0.126872 0.310772i
\(498\) 4.89898 + 6.92820i 0.219529 + 0.310460i
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) −20.0000 + 14.1421i −0.893534 + 0.631824i
\(502\) 36.0000i 1.60676i
\(503\) 19.7990 0.882793 0.441397 0.897312i \(-0.354483\pi\)
0.441397 + 0.897312i \(0.354483\pi\)
\(504\) 13.7321 0.656339i 0.611674 0.0292357i
\(505\) 0 0
\(506\) 16.9706i 0.754434i
\(507\) 4.24264 3.00000i 0.188422 0.133235i
\(508\) 14.6969 0.652071
\(509\) 3.46410 0.153544 0.0767718 0.997049i \(-0.475539\pi\)
0.0767718 + 0.997049i \(0.475539\pi\)
\(510\) 0 0
\(511\) 8.00000 + 19.5959i 0.353899 + 0.866872i
\(512\) 8.66025i 0.382733i
\(513\) 0 0
\(514\) 24.4949i 1.08042i
\(515\) 0 0
\(516\) 6.92820 4.89898i 0.304997 0.215666i
\(517\) 8.00000i 0.351840i
\(518\) 0 0
\(519\) −28.0000 + 19.7990i −1.22906 + 0.869079i
\(520\) 0 0
\(521\) −10.3923 −0.455295 −0.227648 0.973744i \(-0.573103\pi\)
−0.227648 + 0.973744i \(0.573103\pi\)
\(522\) 9.79796 27.7128i 0.428845 1.21296i
\(523\) 26.0000i 1.13690i −0.822718 0.568450i \(-0.807543\pi\)
0.822718 0.568450i \(-0.192457\pi\)
\(524\) −6.92820 −0.302660
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) 27.7128i 1.20719i
\(528\) 14.1421 + 20.0000i 0.615457 + 0.870388i
\(529\) 11.0000 0.478261
\(530\) 0 0
\(531\) −6.92820 + 19.5959i −0.300658 + 0.850390i
\(532\) 0 0
\(533\) 13.8564i 0.600188i
\(534\) −18.0000 25.4558i −0.778936 1.10158i
\(535\) 0 0
\(536\) 8.48528i 0.366508i
\(537\) 2.82843 + 4.00000i 0.122056 + 0.172613i
\(538\) 18.0000i 0.776035i
\(539\) 13.8564 + 14.1421i 0.596838 + 0.609145i
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 50.9117 2.18684
\(543\) 0 0
\(544\) 14.6969i 0.630126i
\(545\) 0 0
\(546\) 17.0718 26.7685i 0.730605 1.14559i
\(547\) −34.2929 −1.46626 −0.733128 0.680090i \(-0.761941\pi\)
−0.733128 + 0.680090i \(0.761941\pi\)
\(548\) 6.92820i 0.295958i
\(549\) −27.7128 9.79796i −1.18275 0.418167i
\(550\) 0 0
\(551\) 0 0
\(552\) −8.48528 + 6.00000i −0.361158 + 0.255377i
\(553\) 19.5959 8.00000i 0.833303 0.340195i
\(554\) 33.9411i 1.44202i
\(555\) 0 0
\(556\) 9.79796i 0.415526i
\(557\) 41.5692i 1.76134i −0.473726 0.880672i \(-0.657091\pi\)
0.473726 0.880672i \(-0.342909\pi\)
\(558\) 16.9706 48.0000i 0.718421 2.03200i
\(559\) 19.5959i 0.828819i
\(560\) 0 0
\(561\) 8.00000 + 11.3137i 0.337760 + 0.477665i
\(562\) 48.9898 2.06651
\(563\) −14.1421 −0.596020 −0.298010 0.954563i \(-0.596323\pi\)
−0.298010 + 0.954563i \(0.596323\pi\)
\(564\) −4.00000 + 2.82843i −0.168430 + 0.119098i
\(565\) 0 0
\(566\) −24.2487 −1.01925
\(567\) 22.8033 + 6.85641i 0.957648 + 0.287942i
\(568\) 4.89898 0.205557
\(569\) 28.2843i 1.18574i −0.805299 0.592869i \(-0.797995\pi\)
0.805299 0.592869i \(-0.202005\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 11.3137 0.473050
\(573\) −19.7990 28.0000i −0.827115 1.16972i
\(574\) −6.00000 14.6969i −0.250435 0.613438i
\(575\) 0 0
\(576\) −1.00000 + 2.82843i −0.0416667 + 0.117851i
\(577\) 8.00000i 0.333044i 0.986038 + 0.166522i \(0.0532537\pi\)
−0.986038 + 0.166522i \(0.946746\pi\)
\(578\) 15.5885i 0.648394i
\(579\) −13.8564 + 9.79796i −0.575853 + 0.407189i
\(580\) 0 0
\(581\) −6.92820 + 2.82843i −0.287430 + 0.117343i
\(582\) −19.5959 + 13.8564i −0.812277 + 0.574367i
\(583\) 0 0
\(584\) −13.8564 −0.573382
\(585\) 0 0
\(586\) 4.89898i 0.202375i
\(587\) −19.7990 −0.817192 −0.408596 0.912715i \(-0.633981\pi\)
−0.408596 + 0.912715i \(0.633981\pi\)
\(588\) 2.17209 11.9282i 0.0895754 0.491911i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 19.7990 0.813047 0.406524 0.913640i \(-0.366741\pi\)
0.406524 + 0.913640i \(0.366741\pi\)
\(594\) 6.92820 + 24.4949i 0.284268 + 1.00504i
\(595\) 0 0
\(596\) 11.3137i 0.463428i
\(597\) 0 0
\(598\) 24.0000i 0.981433i
\(599\) 36.7696i 1.50236i −0.660096 0.751182i \(-0.729484\pi\)
0.660096 0.751182i \(-0.270516\pi\)
\(600\) 0 0
\(601\) 9.79796i 0.399667i −0.979830 0.199834i \(-0.935960\pi\)
0.979830 0.199834i \(-0.0640401\pi\)
\(602\) 8.48528 + 20.7846i 0.345834 + 0.847117i
\(603\) 4.89898 13.8564i 0.199502 0.564276i
\(604\) −8.00000 −0.325515
\(605\) 0 0
\(606\) −30.0000 42.4264i −1.21867 1.72345i
\(607\) 10.0000i 0.405887i −0.979190 0.202944i \(-0.934949\pi\)
0.979190 0.202944i \(-0.0650509\pi\)
\(608\) 0 0
\(609\) 21.8564 + 13.9391i 0.885666 + 0.564839i
\(610\) 0 0
\(611\) 11.3137i 0.457704i
\(612\) 2.82843 8.00000i 0.114332 0.323381i
\(613\) 29.3939 1.18721 0.593604 0.804757i \(-0.297705\pi\)
0.593604 + 0.804757i \(0.297705\pi\)
\(614\) −17.3205 −0.698999
\(615\) 0 0
\(616\) −12.0000 + 4.89898i −0.483494 + 0.197386i
\(617\) 48.4974i 1.95243i 0.216799 + 0.976216i \(0.430439\pi\)
−0.216799 + 0.976216i \(0.569561\pi\)
\(618\) −24.4949 + 17.3205i −0.985329 + 0.696733i
\(619\) 9.79796i 0.393813i 0.980422 + 0.196907i \(0.0630896\pi\)
−0.980422 + 0.196907i \(0.936910\pi\)
\(620\) 0 0
\(621\) −17.3205 + 4.89898i −0.695048 + 0.196589i
\(622\) 48.0000i 1.92462i
\(623\) 25.4558 10.3923i 1.01987 0.416359i
\(624\) 20.0000 + 28.2843i 0.800641 + 1.13228i
\(625\) 0 0
\(626\) 27.7128 1.10763
\(627\) 0 0
\(628\) 4.00000i 0.159617i
\(629\) 0 0
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 13.8564i 0.551178i
\(633\) 5.65685 4.00000i 0.224840 0.158986i
\(634\) 24.0000 0.953162
\(635\) 0 0
\(636\) 0 0
\(637\) 19.5959 + 20.0000i 0.776419 + 0.792429i
\(638\) 27.7128i 1.09716i
\(639\) 8.00000 + 2.82843i 0.316475 + 0.111891i
\(640\) 0 0
\(641\) 5.65685i 0.223432i −0.993740 0.111716i \(-0.964365\pi\)
0.993740 0.111716i \(-0.0356347\pi\)
\(642\) −25.4558 + 18.0000i −1.00466 + 0.710403i
\(643\) 22.0000i 0.867595i 0.901010 + 0.433798i \(0.142827\pi\)
−0.901010 + 0.433798i \(0.857173\pi\)
\(644\) 3.46410 + 8.48528i 0.136505 + 0.334367i
\(645\) 0 0
\(646\) 0 0
\(647\) −19.7990 −0.778379 −0.389189 0.921158i \(-0.627245\pi\)
−0.389189 + 0.921158i \(0.627245\pi\)
\(648\) −9.79796 + 12.1244i −0.384900 + 0.476290i
\(649\) 19.5959i 0.769207i
\(650\) 0 0
\(651\) 37.8564 + 24.1432i 1.48371 + 0.946245i
\(652\) 14.6969 0.575577
\(653\) 27.7128i 1.08449i −0.840222 0.542243i \(-0.817575\pi\)
0.840222 0.542243i \(-0.182425\pi\)
\(654\) 17.3205 + 24.4949i 0.677285 + 0.957826i
\(655\) 0 0
\(656\) 17.3205 0.676252
\(657\) −22.6274 8.00000i −0.882780 0.312110i
\(658\) −4.89898 12.0000i −0.190982 0.467809i
\(659\) 2.82843i 0.110180i −0.998481 0.0550899i \(-0.982455\pi\)
0.998481 0.0550899i \(-0.0175446\pi\)
\(660\) 0 0
\(661\) 9.79796i 0.381096i 0.981678 + 0.190548i \(0.0610266\pi\)
−0.981678 + 0.190548i \(0.938973\pi\)
\(662\) 48.4974i 1.88491i
\(663\) 11.3137 + 16.0000i 0.439388 + 0.621389i
\(664\) 4.89898i 0.190117i
\(665\) 0 0
\(666\) 0 0
\(667\) −19.5959 −0.758757
\(668\) −14.1421 −0.547176
\(669\) 26.0000 + 36.7696i 1.00522 + 1.42159i
\(670\) 0 0
\(671\) 27.7128 1.06984
\(672\) 20.0764 + 12.8038i 0.774464 + 0.493919i
\(673\) −9.79796 −0.377684 −0.188842 0.982008i \(-0.560473\pi\)
−0.188842 + 0.982008i \(0.560473\pi\)
\(674\) 33.9411i 1.30736i
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −2.82843 −0.108705 −0.0543526 0.998522i \(-0.517310\pi\)
−0.0543526 + 0.998522i \(0.517310\pi\)
\(678\) 16.9706 12.0000i 0.651751 0.460857i
\(679\) −8.00000 19.5959i −0.307012 0.752022i
\(680\) 0 0
\(681\) 4.00000 2.82843i 0.153280 0.108386i
\(682\) 48.0000i 1.83801i
\(683\) 10.3923i 0.397650i −0.980035 0.198825i \(-0.936287\pi\)
0.980035 0.198825i \(-0.0637126\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 29.4449 + 12.7279i 1.12421 + 0.485954i
\(687\) −19.5959 27.7128i −0.747631 1.05731i
\(688\) −24.4949 −0.933859
\(689\) 0 0
\(690\) 0 0
\(691\) 9.79796i 0.372732i −0.982480 0.186366i \(-0.940329\pi\)
0.982480 0.186366i \(-0.0596710\pi\)
\(692\) −19.7990 −0.752645
\(693\) −22.4243 + 1.07180i −0.851830 + 0.0407142i
\(694\) 30.0000 1.13878
\(695\) 0 0
\(696\) −13.8564 + 9.79796i −0.525226 + 0.371391i
\(697\) 9.79796 0.371124
\(698\) −33.9411 −1.28469
\(699\) −20.7846 29.3939i −0.786146 1.11178i
\(700\) 0 0
\(701\) 22.6274i 0.854626i −0.904104 0.427313i \(-0.859460\pi\)
0.904104 0.427313i \(-0.140540\pi\)
\(702\) 9.79796 + 34.6410i 0.369800 + 1.30744i
\(703\) 0 0
\(704\) 2.82843i 0.106600i
\(705\) 0 0
\(706\) 53.8888i 2.02813i
\(707\) 42.4264 17.3205i 1.59561 0.651405i
\(708\) −9.79796 + 6.92820i −0.368230 + 0.260378i
\(709\) −38.0000 −1.42712 −0.713560 0.700594i \(-0.752918\pi\)
−0.713560 + 0.700594i \(0.752918\pi\)
\(710\) 0 0
\(711\) −8.00000 + 22.6274i −0.300023 + 0.848594i
\(712\) 18.0000i 0.674579i
\(713\) −33.9411 −1.27111
\(714\) 18.9282 + 12.0716i 0.708370 + 0.451768i
\(715\) 0 0
\(716\) 2.82843i 0.105703i
\(717\) 2.82843 + 4.00000i 0.105630 + 0.149383i
\(718\) 53.8888 2.01111
\(719\) 41.5692 1.55027 0.775135 0.631795i \(-0.217682\pi\)
0.775135 + 0.631795i \(0.217682\pi\)
\(720\) 0 0
\(721\) −10.0000 24.4949i −0.372419 0.912238i
\(722\) 32.9090i 1.22474i
\(723\) 9.79796 + 13.8564i 0.364390 + 0.515325i
\(724\) 0 0
\(725\) 0 0
\(726\) 5.19615 + 7.34847i 0.192847 + 0.272727i
\(727\) 10.0000i 0.370879i −0.982656 0.185440i \(-0.940629\pi\)
0.982656 0.185440i \(-0.0593710\pi\)
\(728\) −16.9706 + 6.92820i −0.628971 + 0.256776i
\(729\) −23.0000 + 14.1421i −0.851852 + 0.523783i
\(730\) 0 0
\(731\) −13.8564 −0.512498
\(732\) −9.79796 13.8564i −0.362143 0.512148i
\(733\) 28.0000i 1.03420i 0.855924 + 0.517102i \(0.172989\pi\)
−0.855924 + 0.517102i \(0.827011\pi\)
\(734\) −17.3205 −0.639312
\(735\) 0 0
\(736\) −18.0000 −0.663489
\(737\) 13.8564i 0.510407i
\(738\) 16.9706 + 6.00000i 0.624695 + 0.220863i
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.2487i 0.889599i 0.895630 + 0.444799i \(0.146725\pi\)
−0.895630 + 0.444799i \(0.853275\pi\)
\(744\) −24.0000 + 16.9706i −0.879883 + 0.622171i
\(745\) 0 0
\(746\) 16.9706i 0.621336i
\(747\) 2.82843 8.00000i 0.103487 0.292705i
\(748\) 8.00000i 0.292509i
\(749\) −10.3923 25.4558i −0.379727 0.930136i
\(750\) 0 0
\(751\) 8.00000 0.291924 0.145962 0.989290i \(-0.453372\pi\)
0.145962 + 0.989290i \(0.453372\pi\)
\(752\) 14.1421 0.515711
\(753\) −29.3939 + 20.7846i −1.07117 + 0.757433i
\(754\) 39.1918i 1.42728i
\(755\) 0 0
\(756\) 8.46410 + 10.8332i 0.307836 + 0.394001i
\(757\) 29.3939 1.06834 0.534169 0.845378i \(-0.320624\pi\)
0.534169 + 0.845378i \(0.320624\pi\)
\(758\) 48.4974i 1.76151i
\(759\) 13.8564 9.79796i 0.502956 0.355643i
\(760\) 0 0
\(761\) 38.1051 1.38131 0.690655 0.723185i \(-0.257322\pi\)
0.690655 + 0.723185i \(0.257322\pi\)
\(762\) −25.4558 36.0000i −0.922168 1.30414i
\(763\) −24.4949 + 10.0000i −0.886775 + 0.362024i
\(764\) 19.7990i 0.716302i
\(765\) 0 0
\(766\) 24.4949i 0.885037i
\(767\) 27.7128i 1.00065i
\(768\) −26.8701 + 19.0000i −0.969590 + 0.685603i
\(769\) 19.5959i 0.706647i 0.935501 + 0.353323i \(0.114948\pi\)
−0.935501 + 0.353323i \(0.885052\pi\)
\(770\) 0 0
\(771\) −20.0000 + 14.1421i −0.720282 + 0.509317i
\(772\) −9.79796 −0.352636
\(773\) 2.82843 0.101731 0.0508657 0.998706i \(-0.483802\pi\)
0.0508657 + 0.998706i \(0.483802\pi\)
\(774\) −24.0000 8.48528i −0.862662 0.304997i
\(775\) 0 0
\(776\) 13.8564 0.497416
\(777\) 0 0
\(778\) 39.1918 1.40510
\(779\) 0 0
\(780\) 0 0
\(781\) −8.00000 −0.286263
\(782\) −16.9706 −0.606866
\(783\) −28.2843 + 8.00000i −1.01080 + 0.285897i
\(784\) −25.0000 + 24.4949i −0.892857 + 0.874818i
\(785\) 0 0
\(786\) 12.0000 + 16.9706i 0.428026 + 0.605320i
\(787\) 14.0000i 0.499046i 0.968369 + 0.249523i \(0.0802738\pi\)
−0.968369 + 0.249523i \(0.919726\pi\)
\(788\) 0 0
\(789\) 3.46410 + 4.89898i 0.123325 + 0.174408i
\(790\) 0 0
\(791\) 6.92820 + 16.9706i 0.246339 + 0.603404i
\(792\) 4.89898 13.8564i 0.174078 0.492366i
\(793\) 39.1918 1.39174
\(794\) 34.6410 1.22936
\(795\) 0 0
\(796\) 0 0
\(797\) −36.7696 −1.30244 −0.651222 0.758887i \(-0.725743\pi\)
−0.651222 + 0.758887i \(0.725743\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) −10.3923 + 29.3939i −0.367194 + 1.03858i
\(802\) −39.1918 −1.38391
\(803\) 22.6274 0.798504
\(804\) 6.92820 4.89898i 0.244339 0.172774i
\(805\) 0 0
\(806\) 67.8823i 2.39105i
\(807\) −14.6969 + 10.3923i −0.517357 + 0.365826i
\(808\) 30.0000i 1.05540i
\(809\) 22.6274i 0.795538i 0.917486 + 0.397769i \(0.130215\pi\)
−0.917486 + 0.397769i \(0.869785\pi\)
\(810\) 0 0
\(811\) 29.3939i 1.03216i 0.856541 + 0.516079i \(0.172609\pi\)
−0.856541 + 0.516079i \(0.827391\pi\)
\(812\) 5.65685 + 13.8564i 0.198517 + 0.486265i
\(813\) −29.3939 41.5692i −1.03089 1.45790i
\(814\) 0 0
\(815\) 0 0
\(816\) −20.0000 + 14.1421i −0.700140 + 0.495074i
\(817\) 0 0
\(818\) −16.9706 −0.593362
\(819\) −31.7128 + 1.51575i −1.10814 + 0.0529646i
\(820\) 0 0
\(821\) 22.6274i 0.789702i −0.918745 0.394851i \(-0.870796\pi\)
0.918745 0.394851i \(-0.129204\pi\)
\(822\) 16.9706 12.0000i 0.591916 0.418548i
\(823\) −4.89898 −0.170768 −0.0853838 0.996348i \(-0.527212\pi\)
−0.0853838 + 0.996348i \(0.527212\pi\)
\(824\) 17.3205 0.603388
\(825\) 0 0
\(826\) −12.0000 29.3939i −0.417533 1.02274i
\(827\) 10.3923i 0.361376i 0.983540 + 0.180688i \(0.0578324\pi\)
−0.983540 + 0.180688i \(0.942168\pi\)
\(828\) −9.79796 3.46410i −0.340503 0.120386i
\(829\) 29.3939i 1.02089i 0.859910 + 0.510446i \(0.170520\pi\)
−0.859910 + 0.510446i \(0.829480\pi\)
\(830\) 0 0
\(831\) 27.7128 19.5959i 0.961347 0.679775i
\(832\) 4.00000i 0.138675i
\(833\) −14.1421 + 13.8564i −0.489996 + 0.480096i
\(834\) 24.0000 16.9706i 0.831052 0.587643i
\(835\) 0 0
\(836\) 0 0
\(837\) −48.9898 + 13.8564i −1.69334 + 0.478947i
\(838\) 12.0000i 0.414533i
\(839\) 27.7128 0.956753 0.478376 0.878155i \(-0.341226\pi\)
0.478376 + 0.878155i \(0.341226\pi\)
\(840\) 0 0
\(841\) −3.00000 −0.103448
\(842\) 45.0333i 1.55195i
\(843\) −28.2843 40.0000i −0.974162 1.37767i
\(844\) 4.00000 0.137686
\(845\) 0 0
\(846\) 13.8564 + 4.89898i 0.476393 + 0.168430i
\(847\) −7.34847 + 3.00000i −0.252496 + 0.103081i
\(848\) 0 0
\(849\) 14.0000 + 19.7990i 0.480479 + 0.679500i
\(850\) 0 0
\(851\) 0 0
\(852\) 2.82843 + 4.00000i 0.0969003 + 0.137038i
\(853\) 20.0000i 0.684787i −0.939557 0.342393i \(-0.888762\pi\)
0.939557 0.342393i \(-0.111238\pi\)
\(854\) 41.5692 16.9706i 1.42247 0.580721i
\(855\) 0 0
\(856\) 18.0000 0.615227
\(857\) 48.0833 1.64249 0.821246 0.570574i \(-0.193279\pi\)
0.821246 + 0.570574i \(0.193279\pi\)
\(858\) −19.5959 27.7128i −0.668994 0.946100i
\(859\) 39.1918i 1.33721i −0.743619 0.668604i \(-0.766892\pi\)
0.743619 0.668604i \(-0.233108\pi\)
\(860\) 0 0
\(861\) −8.53590 + 13.3843i −0.290903 + 0.456134i
\(862\) 4.89898 0.166860
\(863\) 10.3923i 0.353758i −0.984233 0.176879i \(-0.943400\pi\)
0.984233 0.176879i \(-0.0566002\pi\)
\(864\) −25.9808 + 7.34847i −0.883883 + 0.250000i
\(865\) 0 0
\(866\) 27.7128 0.941720
\(867\) 12.7279 9.00000i 0.432263 0.305656i
\(868\) 9.79796 + 24.0000i 0.332564 + 0.814613i
\(869\) 22.6274i 0.767583i
\(870\) 0 0
\(871\) 19.5959i 0.663982i
\(872\) 17.3205i 0.586546i
\(873\) 22.6274 + 8.00000i 0.765822 + 0.270759i
\(874\) 0 0
\(875\) 0 0
\(876\) −8.00000 11.3137i −0.270295 0.382255i
\(877\) 48.9898 1.65427 0.827134 0.562005i \(-0.189970\pi\)
0.827134 + 0.562005i \(0.189970\pi\)
\(878\) 67.8823 2.29092
\(879\) −4.00000 + 2.82843i −0.134917 + 0.0954005i
\(880\) 0 0
\(881\) −10.3923 −0.350126 −0.175063 0.984557i \(-0.556013\pi\)
−0.175063 + 0.984557i \(0.556013\pi\)
\(882\) −32.9802 + 15.3397i −1.11050 + 0.516516i
\(883\) 14.6969 0.494591 0.247296 0.968940i \(-0.420458\pi\)
0.247296 + 0.968940i \(0.420458\pi\)
\(884\) 11.3137i 0.380521i
\(885\) 0 0
\(886\) 30.0000 1.00787
\(887\) −2.82843 −0.0949693 −0.0474846 0.998872i \(-0.515121\pi\)
−0.0474846 + 0.998872i \(0.515121\pi\)
\(888\) 0 0
\(889\) 36.0000 14.6969i 1.20740 0.492919i
\(890\) 0 0
\(891\) 16.0000 19.7990i 0.536020 0.663291i
\(892\) 26.0000i 0.870544i
\(893\) 0 0
\(894\) 27.7128 19.5959i 0.926855 0.655386i
\(895\) 0 0
\(896\) −12.1244 29.6985i −0.405046 0.992157i
\(897\) 19.5959 13.8564i 0.654289 0.462652i
\(898\) 9.79796 0.326962
\(899\) −55.4256 −1.84855
\(900\) 0 0
\(901\) 0 0
\(902\) −16.9706 −0.565058
\(903\) 12.0716 18.9282i 0.401717 0.629891i
\(904\) −12.0000 −0.399114
\(905\) 0 0
\(906\) 13.8564 + 19.5959i 0.460348 + 0.651031i
\(907\) 24.4949 0.813340 0.406670 0.913575i \(-0.366690\pi\)
0.406670 + 0.913575i \(0.366690\pi\)
\(908\) 2.82843 0.0938647
\(909\) −17.3205 + 48.9898i −0.574485 + 1.62489i
\(910\) 0 0
\(911\) 48.0833i 1.59307i −0.604593 0.796535i \(-0.706664\pi\)
0.604593 0.796535i \(-0.293336\pi\)
\(912\) 0 0
\(913\) 8.00000i 0.264761i
\(914\) 33.9411i 1.12267i
\(915\) 0 0
\(916\) 19.5959i 0.647467i
\(917\) −16.9706 + 6.92820i −0.560417 + 0.228789i
\(918\) −24.4949 + 6.92820i −0.808452 + 0.228665i
\(919\) 16.0000 0.527791 0.263896 0.964551i \(-0.414993\pi\)
0.263896 + 0.964551i \(0.414993\pi\)
\(920\) 0 0
\(921\) 10.0000 + 14.1421i 0.329511 + 0.465999i
\(922\) 6.00000i 0.197599i
\(923\) −11.3137 −0.372395
\(924\) −10.9282 6.96953i −0.359511 0.229281i
\(925\) 0 0
\(926\) 8.48528i 0.278844i
\(927\) 28.2843 + 10.0000i 0.928977 + 0.328443i
\(928\) −29.3939 −0.964901
\(929\) −45.0333 −1.47750 −0.738748 0.673982i \(-0.764582\pi\)
−0.738748 + 0.673982i \(0.764582\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 20.7846i 0.680823i
\(933\) −39.1918 + 27.7128i −1.28308 + 0.907277i
\(934\) 4.89898i 0.160300i
\(935\) 0 0
\(936\) 6.92820 19.5959i 0.226455 0.640513i
\(937\) 8.00000i 0.261349i 0.991425 + 0.130674i \(0.0417142\pi\)
−0.991425 + 0.130674i \(0.958286\pi\)
\(938\) 8.48528 + 20.7846i 0.277054 + 0.678642i
\(939\) −16.0000 22.6274i −0.522140 0.738418i
\(940\) 0 0
\(941\) −24.2487 −0.790485 −0.395243 0.918577i \(-0.629340\pi\)
−0.395243 + 0.918577i \(0.629340\pi\)
\(942\) 9.79796 6.92820i 0.319235 0.225733i
\(943\) 12.0000i 0.390774i
\(944\) 34.6410 1.12747
\(945\) 0 0
\(946\) 24.0000 0.780307
\(947\) 3.46410i 0.112568i 0.998415 + 0.0562841i \(0.0179253\pi\)
−0.998415 + 0.0562841i \(0.982075\pi\)
\(948\) −11.3137 + 8.00000i −0.367452 + 0.259828i
\(949\) 32.0000 1.03876
\(950\) 0 0
\(951\) −13.8564 19.5959i −0.449325 0.635441i
\(952\) −4.89898 12.0000i −0.158777 0.388922i
\(953\) 20.7846i 0.673280i 0.941634 + 0.336640i \(0.109290\pi\)
−0.941634 + 0.336640i \(0.890710\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 2.82843i 0.0914779i
\(957\) 22.6274 16.0000i 0.731441 0.517207i
\(958\) 48.0000i 1.55081i
\(959\) 6.92820 + 16.9706i 0.223723 + 0.548008i
\(960\) 0 0
\(961\) −65.0000 −2.09677
\(962\) 0 0
\(963\) 29.3939 + 10.3923i 0.947204 + 0.334887i
\(964\) 9.79796i 0.315571i
\(965\) 0 0
\(966\) 14.7846 23.1822i 0.475687 0.745876i
\(967\) 34.2929 1.10278 0.551392 0.834246i \(-0.314097\pi\)
0.551392 + 0.834246i \(0.314097\pi\)
\(968\) 5.19615i 0.167011i
\(969\) 0 0
\(970\) 0 0
\(971\) −20.7846 −0.667010 −0.333505 0.942748i \(-0.608231\pi\)
−0.333505 + 0.942748i \(0.608231\pi\)
\(972\) −15.5563 1.00000i −0.498970 0.0320750i
\(973\) 9.79796 + 24.0000i 0.314108 + 0.769405i
\(974\) 25.4558i 0.815658i
\(975\) 0 0
\(976\) 48.9898i 1.56813i
\(977\) 48.4974i 1.55157i 0.630997 + 0.775785i \(0.282646\pi\)
−0.630997 + 0.775785i \(0.717354\pi\)
\(978\) −25.4558 36.0000i −0.813988 1.15115i
\(979\) 29.3939i 0.939432i
\(980\) 0 0
\(981\) 10.0000 28.2843i 0.319275 0.903047i
\(982\) −24.4949 −0.781664
\(983\) 2.82843 0.0902128 0.0451064 0.998982i \(-0.485637\pi\)
0.0451064 + 0.998982i \(0.485637\pi\)
\(984\) −6.00000 8.48528i −0.191273 0.270501i
\(985\) 0 0
\(986\) −27.7128 −0.882556
\(987\) −6.96953 + 10.9282i −0.221843 + 0.347849i
\(988\) 0 0
\(989\) 16.9706i 0.539633i
\(990\) 0 0
\(991\) 8.00000 0.254128 0.127064 0.991894i \(-0.459445\pi\)
0.127064 + 0.991894i \(0.459445\pi\)
\(992\) −50.9117 −1.61645
\(993\) 39.5980 28.0000i 1.25660 0.888553i
\(994\) −12.0000 + 4.89898i −0.380617 + 0.155386i
\(995\) 0 0
\(996\) 4.00000 2.82843i 0.126745 0.0896221i
\(997\) 52.0000i 1.64686i −0.567420 0.823428i \(-0.692059\pi\)
0.567420 0.823428i \(-0.307941\pi\)
\(998\) 6.92820i 0.219308i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 525.2.b.j.251.2 8
3.2 odd 2 inner 525.2.b.j.251.8 8
5.2 odd 4 105.2.g.c.104.4 yes 4
5.3 odd 4 105.2.g.a.104.1 4
5.4 even 2 inner 525.2.b.j.251.7 8
7.6 odd 2 inner 525.2.b.j.251.3 8
15.2 even 4 105.2.g.c.104.1 yes 4
15.8 even 4 105.2.g.a.104.4 yes 4
15.14 odd 2 inner 525.2.b.j.251.1 8
20.3 even 4 1680.2.k.c.209.3 4
20.7 even 4 1680.2.k.a.209.1 4
21.20 even 2 inner 525.2.b.j.251.5 8
35.2 odd 12 735.2.p.a.374.1 8
35.3 even 12 735.2.p.a.509.4 8
35.12 even 12 735.2.p.c.374.2 8
35.13 even 4 105.2.g.c.104.2 yes 4
35.17 even 12 735.2.p.c.509.1 8
35.18 odd 12 735.2.p.c.509.3 8
35.23 odd 12 735.2.p.c.374.4 8
35.27 even 4 105.2.g.a.104.3 yes 4
35.32 odd 12 735.2.p.a.509.2 8
35.33 even 12 735.2.p.a.374.3 8
35.34 odd 2 inner 525.2.b.j.251.6 8
60.23 odd 4 1680.2.k.c.209.2 4
60.47 odd 4 1680.2.k.a.209.4 4
105.2 even 12 735.2.p.a.374.4 8
105.17 odd 12 735.2.p.c.509.4 8
105.23 even 12 735.2.p.c.374.1 8
105.32 even 12 735.2.p.a.509.3 8
105.38 odd 12 735.2.p.a.509.1 8
105.47 odd 12 735.2.p.c.374.3 8
105.53 even 12 735.2.p.c.509.2 8
105.62 odd 4 105.2.g.a.104.2 yes 4
105.68 odd 12 735.2.p.a.374.2 8
105.83 odd 4 105.2.g.c.104.3 yes 4
105.104 even 2 inner 525.2.b.j.251.4 8
140.27 odd 4 1680.2.k.c.209.4 4
140.83 odd 4 1680.2.k.a.209.2 4
420.83 even 4 1680.2.k.a.209.3 4
420.167 even 4 1680.2.k.c.209.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.g.a.104.1 4 5.3 odd 4
105.2.g.a.104.2 yes 4 105.62 odd 4
105.2.g.a.104.3 yes 4 35.27 even 4
105.2.g.a.104.4 yes 4 15.8 even 4
105.2.g.c.104.1 yes 4 15.2 even 4
105.2.g.c.104.2 yes 4 35.13 even 4
105.2.g.c.104.3 yes 4 105.83 odd 4
105.2.g.c.104.4 yes 4 5.2 odd 4
525.2.b.j.251.1 8 15.14 odd 2 inner
525.2.b.j.251.2 8 1.1 even 1 trivial
525.2.b.j.251.3 8 7.6 odd 2 inner
525.2.b.j.251.4 8 105.104 even 2 inner
525.2.b.j.251.5 8 21.20 even 2 inner
525.2.b.j.251.6 8 35.34 odd 2 inner
525.2.b.j.251.7 8 5.4 even 2 inner
525.2.b.j.251.8 8 3.2 odd 2 inner
735.2.p.a.374.1 8 35.2 odd 12
735.2.p.a.374.2 8 105.68 odd 12
735.2.p.a.374.3 8 35.33 even 12
735.2.p.a.374.4 8 105.2 even 12
735.2.p.a.509.1 8 105.38 odd 12
735.2.p.a.509.2 8 35.32 odd 12
735.2.p.a.509.3 8 105.32 even 12
735.2.p.a.509.4 8 35.3 even 12
735.2.p.c.374.1 8 105.23 even 12
735.2.p.c.374.2 8 35.12 even 12
735.2.p.c.374.3 8 105.47 odd 12
735.2.p.c.374.4 8 35.23 odd 12
735.2.p.c.509.1 8 35.17 even 12
735.2.p.c.509.2 8 105.53 even 12
735.2.p.c.509.3 8 35.18 odd 12
735.2.p.c.509.4 8 105.17 odd 12
1680.2.k.a.209.1 4 20.7 even 4
1680.2.k.a.209.2 4 140.83 odd 4
1680.2.k.a.209.3 4 420.83 even 4
1680.2.k.a.209.4 4 60.47 odd 4
1680.2.k.c.209.1 4 420.167 even 4
1680.2.k.c.209.2 4 60.23 odd 4
1680.2.k.c.209.3 4 20.3 even 4
1680.2.k.c.209.4 4 140.27 odd 4