Properties

Label 600.2.d.b.349.2
Level $600$
Weight $2$
Character 600.349
Analytic conductor $4.791$
Analytic rank $0$
Dimension $2$
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] = [600,2,Mod(349,600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("600.349");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 24)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 349.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 600.349
Dual form 600.2.d.b.349.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +1.00000 q^{3} -2.00000i q^{4} +(-1.00000 + 1.00000i) q^{6} +2.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +1.00000 q^{3} -2.00000i q^{4} +(-1.00000 + 1.00000i) q^{6} +2.00000i q^{7} +(2.00000 + 2.00000i) q^{8} +1.00000 q^{9} -2.00000i q^{12} +4.00000 q^{13} +(-2.00000 - 2.00000i) q^{14} -4.00000 q^{16} +2.00000i q^{17} +(-1.00000 + 1.00000i) q^{18} -4.00000i q^{19} +2.00000i q^{21} +4.00000i q^{23} +(2.00000 + 2.00000i) q^{24} +(-4.00000 + 4.00000i) q^{26} +1.00000 q^{27} +4.00000 q^{28} +6.00000i q^{29} +2.00000 q^{31} +(4.00000 - 4.00000i) q^{32} +(-2.00000 - 2.00000i) q^{34} -2.00000i q^{36} +8.00000 q^{37} +(4.00000 + 4.00000i) q^{38} +4.00000 q^{39} +2.00000 q^{41} +(-2.00000 - 2.00000i) q^{42} +4.00000 q^{43} +(-4.00000 - 4.00000i) q^{46} +12.0000i q^{47} -4.00000 q^{48} +3.00000 q^{49} +2.00000i q^{51} -8.00000i q^{52} -6.00000 q^{53} +(-1.00000 + 1.00000i) q^{54} +(-4.00000 + 4.00000i) q^{56} -4.00000i q^{57} +(-6.00000 - 6.00000i) q^{58} -4.00000i q^{59} +(-2.00000 + 2.00000i) q^{62} +2.00000i q^{63} +8.00000i q^{64} -12.0000 q^{67} +4.00000 q^{68} +4.00000i q^{69} +12.0000 q^{71} +(2.00000 + 2.00000i) q^{72} -6.00000i q^{73} +(-8.00000 + 8.00000i) q^{74} -8.00000 q^{76} +(-4.00000 + 4.00000i) q^{78} -10.0000 q^{79} +1.00000 q^{81} +(-2.00000 + 2.00000i) q^{82} -16.0000 q^{83} +4.00000 q^{84} +(-4.00000 + 4.00000i) q^{86} +6.00000i q^{87} +10.0000 q^{89} +8.00000i q^{91} +8.00000 q^{92} +2.00000 q^{93} +(-12.0000 - 12.0000i) q^{94} +(4.00000 - 4.00000i) q^{96} +2.00000i q^{97} +(-3.00000 + 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{3} - 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 2 q^{3} - 2 q^{6} + 4 q^{8} + 2 q^{9} + 8 q^{13} - 4 q^{14} - 8 q^{16} - 2 q^{18} + 4 q^{24} - 8 q^{26} + 2 q^{27} + 8 q^{28} + 4 q^{31} + 8 q^{32} - 4 q^{34} + 16 q^{37} + 8 q^{38} + 8 q^{39} + 4 q^{41} - 4 q^{42} + 8 q^{43} - 8 q^{46} - 8 q^{48} + 6 q^{49} - 12 q^{53} - 2 q^{54} - 8 q^{56} - 12 q^{58} - 4 q^{62} - 24 q^{67} + 8 q^{68} + 24 q^{71} + 4 q^{72} - 16 q^{74} - 16 q^{76} - 8 q^{78} - 20 q^{79} + 2 q^{81} - 4 q^{82} - 32 q^{83} + 8 q^{84} - 8 q^{86} + 20 q^{89} + 16 q^{92} + 4 q^{93} - 24 q^{94} + 8 q^{96} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.00000i −0.707107 + 0.707107i
\(3\) 1.00000 0.577350
\(4\) 2.00000i 1.00000i
\(5\) 0 0
\(6\) −1.00000 + 1.00000i −0.408248 + 0.408248i
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 2.00000i 0.577350i
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −2.00000 2.00000i −0.534522 0.534522i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) −1.00000 + 1.00000i −0.235702 + 0.235702i
\(19\) 4.00000i 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) 0 0
\(21\) 2.00000i 0.436436i
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 2.00000 + 2.00000i 0.408248 + 0.408248i
\(25\) 0 0
\(26\) −4.00000 + 4.00000i −0.784465 + 0.784465i
\(27\) 1.00000 0.192450
\(28\) 4.00000 0.755929
\(29\) 6.00000i 1.11417i 0.830455 + 0.557086i \(0.188081\pi\)
−0.830455 + 0.557086i \(0.811919\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 4.00000 4.00000i 0.707107 0.707107i
\(33\) 0 0
\(34\) −2.00000 2.00000i −0.342997 0.342997i
\(35\) 0 0
\(36\) 2.00000i 0.333333i
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 4.00000 + 4.00000i 0.648886 + 0.648886i
\(39\) 4.00000 0.640513
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −2.00000 2.00000i −0.308607 0.308607i
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −4.00000 4.00000i −0.589768 0.589768i
\(47\) 12.0000i 1.75038i 0.483779 + 0.875190i \(0.339264\pi\)
−0.483779 + 0.875190i \(0.660736\pi\)
\(48\) −4.00000 −0.577350
\(49\) 3.00000 0.428571
\(50\) 0 0
\(51\) 2.00000i 0.280056i
\(52\) 8.00000i 1.10940i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −1.00000 + 1.00000i −0.136083 + 0.136083i
\(55\) 0 0
\(56\) −4.00000 + 4.00000i −0.534522 + 0.534522i
\(57\) 4.00000i 0.529813i
\(58\) −6.00000 6.00000i −0.787839 0.787839i
\(59\) 4.00000i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838471\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) −2.00000 + 2.00000i −0.254000 + 0.254000i
\(63\) 2.00000i 0.251976i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 4.00000 0.485071
\(69\) 4.00000i 0.481543i
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 2.00000 + 2.00000i 0.235702 + 0.235702i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) −8.00000 + 8.00000i −0.929981 + 0.929981i
\(75\) 0 0
\(76\) −8.00000 −0.917663
\(77\) 0 0
\(78\) −4.00000 + 4.00000i −0.452911 + 0.452911i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −2.00000 + 2.00000i −0.220863 + 0.220863i
\(83\) −16.0000 −1.75623 −0.878114 0.478451i \(-0.841198\pi\)
−0.878114 + 0.478451i \(0.841198\pi\)
\(84\) 4.00000 0.436436
\(85\) 0 0
\(86\) −4.00000 + 4.00000i −0.431331 + 0.431331i
\(87\) 6.00000i 0.643268i
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) 8.00000i 0.838628i
\(92\) 8.00000 0.834058
\(93\) 2.00000 0.207390
\(94\) −12.0000 12.0000i −1.23771 1.23771i
\(95\) 0 0
\(96\) 4.00000 4.00000i 0.408248 0.408248i
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) −3.00000 + 3.00000i −0.303046 + 0.303046i
\(99\) 0 0
\(100\) 0 0
\(101\) 10.0000i 0.995037i −0.867453 0.497519i \(-0.834245\pi\)
0.867453 0.497519i \(-0.165755\pi\)
\(102\) −2.00000 2.00000i −0.198030 0.198030i
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 8.00000 + 8.00000i 0.784465 + 0.784465i
\(105\) 0 0
\(106\) 6.00000 6.00000i 0.582772 0.582772i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 2.00000i 0.192450i
\(109\) 4.00000i 0.383131i −0.981480 0.191565i \(-0.938644\pi\)
0.981480 0.191565i \(-0.0613564\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) 8.00000i 0.755929i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 4.00000 + 4.00000i 0.374634 + 0.374634i
\(115\) 0 0
\(116\) 12.0000 1.11417
\(117\) 4.00000 0.369800
\(118\) 4.00000 + 4.00000i 0.368230 + 0.368230i
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 0 0
\(123\) 2.00000 0.180334
\(124\) 4.00000i 0.359211i
\(125\) 0 0
\(126\) −2.00000 2.00000i −0.178174 0.178174i
\(127\) 2.00000i 0.177471i 0.996055 + 0.0887357i \(0.0282826\pi\)
−0.996055 + 0.0887357i \(0.971717\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) 4.00000 0.352180
\(130\) 0 0
\(131\) 20.0000i 1.74741i −0.486458 0.873704i \(-0.661711\pi\)
0.486458 0.873704i \(-0.338289\pi\)
\(132\) 0 0
\(133\) 8.00000 0.693688
\(134\) 12.0000 12.0000i 1.03664 1.03664i
\(135\) 0 0
\(136\) −4.00000 + 4.00000i −0.342997 + 0.342997i
\(137\) 18.0000i 1.53784i −0.639343 0.768922i \(-0.720793\pi\)
0.639343 0.768922i \(-0.279207\pi\)
\(138\) −4.00000 4.00000i −0.340503 0.340503i
\(139\) 4.00000i 0.339276i −0.985506 0.169638i \(-0.945740\pi\)
0.985506 0.169638i \(-0.0542598\pi\)
\(140\) 0 0
\(141\) 12.0000i 1.01058i
\(142\) −12.0000 + 12.0000i −1.00702 + 1.00702i
\(143\) 0 0
\(144\) −4.00000 −0.333333
\(145\) 0 0
\(146\) 6.00000 + 6.00000i 0.496564 + 0.496564i
\(147\) 3.00000 0.247436
\(148\) 16.0000i 1.31519i
\(149\) 6.00000i 0.491539i 0.969328 + 0.245770i \(0.0790407\pi\)
−0.969328 + 0.245770i \(0.920959\pi\)
\(150\) 0 0
\(151\) −18.0000 −1.46482 −0.732410 0.680864i \(-0.761604\pi\)
−0.732410 + 0.680864i \(0.761604\pi\)
\(152\) 8.00000 8.00000i 0.648886 0.648886i
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) 0 0
\(156\) 8.00000i 0.640513i
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 10.0000 10.0000i 0.795557 0.795557i
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) −8.00000 −0.630488
\(162\) −1.00000 + 1.00000i −0.0785674 + 0.0785674i
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 0 0
\(166\) 16.0000 16.0000i 1.24184 1.24184i
\(167\) 8.00000i 0.619059i −0.950890 0.309529i \(-0.899829\pi\)
0.950890 0.309529i \(-0.100171\pi\)
\(168\) −4.00000 + 4.00000i −0.308607 + 0.308607i
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 4.00000i 0.305888i
\(172\) 8.00000i 0.609994i
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −6.00000 6.00000i −0.454859 0.454859i
\(175\) 0 0
\(176\) 0 0
\(177\) 4.00000i 0.300658i
\(178\) −10.0000 + 10.0000i −0.749532 + 0.749532i
\(179\) 4.00000i 0.298974i −0.988764 0.149487i \(-0.952238\pi\)
0.988764 0.149487i \(-0.0477622\pi\)
\(180\) 0 0
\(181\) 20.0000i 1.48659i −0.668965 0.743294i \(-0.733262\pi\)
0.668965 0.743294i \(-0.266738\pi\)
\(182\) −8.00000 8.00000i −0.592999 0.592999i
\(183\) 0 0
\(184\) −8.00000 + 8.00000i −0.589768 + 0.589768i
\(185\) 0 0
\(186\) −2.00000 + 2.00000i −0.146647 + 0.146647i
\(187\) 0 0
\(188\) 24.0000 1.75038
\(189\) 2.00000i 0.145479i
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 8.00000i 0.577350i
\(193\) 6.00000i 0.431889i −0.976406 0.215945i \(-0.930717\pi\)
0.976406 0.215945i \(-0.0692831\pi\)
\(194\) −2.00000 2.00000i −0.143592 0.143592i
\(195\) 0 0
\(196\) 6.00000i 0.428571i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) −10.0000 −0.708881 −0.354441 0.935079i \(-0.615329\pi\)
−0.354441 + 0.935079i \(0.615329\pi\)
\(200\) 0 0
\(201\) −12.0000 −0.846415
\(202\) 10.0000 + 10.0000i 0.703598 + 0.703598i
\(203\) −12.0000 −0.842235
\(204\) 4.00000 0.280056
\(205\) 0 0
\(206\) 6.00000 + 6.00000i 0.418040 + 0.418040i
\(207\) 4.00000i 0.278019i
\(208\) −16.0000 −1.10940
\(209\) 0 0
\(210\) 0 0
\(211\) 20.0000i 1.37686i 0.725304 + 0.688428i \(0.241699\pi\)
−0.725304 + 0.688428i \(0.758301\pi\)
\(212\) 12.0000i 0.824163i
\(213\) 12.0000 0.822226
\(214\) 12.0000 12.0000i 0.820303 0.820303i
\(215\) 0 0
\(216\) 2.00000 + 2.00000i 0.136083 + 0.136083i
\(217\) 4.00000i 0.271538i
\(218\) 4.00000 + 4.00000i 0.270914 + 0.270914i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) 8.00000i 0.538138i
\(222\) −8.00000 + 8.00000i −0.536925 + 0.536925i
\(223\) 14.0000i 0.937509i 0.883328 + 0.468755i \(0.155297\pi\)
−0.883328 + 0.468755i \(0.844703\pi\)
\(224\) 8.00000 + 8.00000i 0.534522 + 0.534522i
\(225\) 0 0
\(226\) 6.00000 + 6.00000i 0.399114 + 0.399114i
\(227\) 8.00000 0.530979 0.265489 0.964114i \(-0.414466\pi\)
0.265489 + 0.964114i \(0.414466\pi\)
\(228\) −8.00000 −0.529813
\(229\) 4.00000i 0.264327i −0.991228 0.132164i \(-0.957808\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −12.0000 + 12.0000i −0.787839 + 0.787839i
\(233\) 14.0000i 0.917170i 0.888650 + 0.458585i \(0.151644\pi\)
−0.888650 + 0.458585i \(0.848356\pi\)
\(234\) −4.00000 + 4.00000i −0.261488 + 0.261488i
\(235\) 0 0
\(236\) −8.00000 −0.520756
\(237\) −10.0000 −0.649570
\(238\) 4.00000 4.00000i 0.259281 0.259281i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) −11.0000 + 11.0000i −0.707107 + 0.707107i
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) −2.00000 + 2.00000i −0.127515 + 0.127515i
\(247\) 16.0000i 1.01806i
\(248\) 4.00000 + 4.00000i 0.254000 + 0.254000i
\(249\) −16.0000 −1.01396
\(250\) 0 0
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 4.00000 0.251976
\(253\) 0 0
\(254\) −2.00000 2.00000i −0.125491 0.125491i
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 18.0000i 1.12281i −0.827541 0.561405i \(-0.810261\pi\)
0.827541 0.561405i \(-0.189739\pi\)
\(258\) −4.00000 + 4.00000i −0.249029 + 0.249029i
\(259\) 16.0000i 0.994192i
\(260\) 0 0
\(261\) 6.00000i 0.371391i
\(262\) 20.0000 + 20.0000i 1.23560 + 1.23560i
\(263\) 16.0000i 0.986602i −0.869859 0.493301i \(-0.835790\pi\)
0.869859 0.493301i \(-0.164210\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −8.00000 + 8.00000i −0.490511 + 0.490511i
\(267\) 10.0000 0.611990
\(268\) 24.0000i 1.46603i
\(269\) 6.00000i 0.365826i 0.983129 + 0.182913i \(0.0585527\pi\)
−0.983129 + 0.182913i \(0.941447\pi\)
\(270\) 0 0
\(271\) −18.0000 −1.09342 −0.546711 0.837321i \(-0.684120\pi\)
−0.546711 + 0.837321i \(0.684120\pi\)
\(272\) 8.00000i 0.485071i
\(273\) 8.00000i 0.484182i
\(274\) 18.0000 + 18.0000i 1.08742 + 1.08742i
\(275\) 0 0
\(276\) 8.00000 0.481543
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) 4.00000 + 4.00000i 0.239904 + 0.239904i
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) −12.0000 12.0000i −0.714590 0.714590i
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 24.0000i 1.42414i
\(285\) 0 0
\(286\) 0 0
\(287\) 4.00000i 0.236113i
\(288\) 4.00000 4.00000i 0.235702 0.235702i
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 2.00000i 0.117242i
\(292\) −12.0000 −0.702247
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −3.00000 + 3.00000i −0.174964 + 0.174964i
\(295\) 0 0
\(296\) 16.0000 + 16.0000i 0.929981 + 0.929981i
\(297\) 0 0
\(298\) −6.00000 6.00000i −0.347571 0.347571i
\(299\) 16.0000i 0.925304i
\(300\) 0 0
\(301\) 8.00000i 0.461112i
\(302\) 18.0000 18.0000i 1.03578 1.03578i
\(303\) 10.0000i 0.574485i
\(304\) 16.0000i 0.917663i
\(305\) 0 0
\(306\) −2.00000 2.00000i −0.114332 0.114332i
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 8.00000 + 8.00000i 0.452911 + 0.452911i
\(313\) 14.0000i 0.791327i 0.918396 + 0.395663i \(0.129485\pi\)
−0.918396 + 0.395663i \(0.870515\pi\)
\(314\) −8.00000 + 8.00000i −0.451466 + 0.451466i
\(315\) 0 0
\(316\) 20.0000i 1.12509i
\(317\) −22.0000 −1.23564 −0.617822 0.786318i \(-0.711985\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) 6.00000 6.00000i 0.336463 0.336463i
\(319\) 0 0
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) 8.00000 8.00000i 0.445823 0.445823i
\(323\) 8.00000 0.445132
\(324\) 2.00000i 0.111111i
\(325\) 0 0
\(326\) −4.00000 + 4.00000i −0.221540 + 0.221540i
\(327\) 4.00000i 0.221201i
\(328\) 4.00000 + 4.00000i 0.220863 + 0.220863i
\(329\) −24.0000 −1.32316
\(330\) 0 0
\(331\) 20.0000i 1.09930i 0.835395 + 0.549650i \(0.185239\pi\)
−0.835395 + 0.549650i \(0.814761\pi\)
\(332\) 32.0000i 1.75623i
\(333\) 8.00000 0.438397
\(334\) 8.00000 + 8.00000i 0.437741 + 0.437741i
\(335\) 0 0
\(336\) 8.00000i 0.436436i
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) −3.00000 + 3.00000i −0.163178 + 0.163178i
\(339\) 6.00000i 0.325875i
\(340\) 0 0
\(341\) 0 0
\(342\) 4.00000 + 4.00000i 0.216295 + 0.216295i
\(343\) 20.0000i 1.07990i
\(344\) 8.00000 + 8.00000i 0.431331 + 0.431331i
\(345\) 0 0
\(346\) 6.00000 6.00000i 0.322562 0.322562i
\(347\) 8.00000 0.429463 0.214731 0.976673i \(-0.431112\pi\)
0.214731 + 0.976673i \(0.431112\pi\)
\(348\) 12.0000 0.643268
\(349\) 16.0000i 0.856460i 0.903670 + 0.428230i \(0.140863\pi\)
−0.903670 + 0.428230i \(0.859137\pi\)
\(350\) 0 0
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) 6.00000i 0.319348i −0.987170 0.159674i \(-0.948956\pi\)
0.987170 0.159674i \(-0.0510443\pi\)
\(354\) 4.00000 + 4.00000i 0.212598 + 0.212598i
\(355\) 0 0
\(356\) 20.0000i 1.06000i
\(357\) −4.00000 −0.211702
\(358\) 4.00000 + 4.00000i 0.211407 + 0.211407i
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) 20.0000 + 20.0000i 1.05118 + 1.05118i
\(363\) 11.0000 0.577350
\(364\) 16.0000 0.838628
\(365\) 0 0
\(366\) 0 0
\(367\) 18.0000i 0.939592i −0.882775 0.469796i \(-0.844327\pi\)
0.882775 0.469796i \(-0.155673\pi\)
\(368\) 16.0000i 0.834058i
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) 12.0000i 0.623009i
\(372\) 4.00000i 0.207390i
\(373\) −16.0000 −0.828449 −0.414224 0.910175i \(-0.635947\pi\)
−0.414224 + 0.910175i \(0.635947\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −24.0000 + 24.0000i −1.23771 + 1.23771i
\(377\) 24.0000i 1.23606i
\(378\) −2.00000 2.00000i −0.102869 0.102869i
\(379\) 4.00000i 0.205466i −0.994709 0.102733i \(-0.967241\pi\)
0.994709 0.102733i \(-0.0327588\pi\)
\(380\) 0 0
\(381\) 2.00000i 0.102463i
\(382\) 8.00000 8.00000i 0.409316 0.409316i
\(383\) 24.0000i 1.22634i 0.789950 + 0.613171i \(0.210106\pi\)
−0.789950 + 0.613171i \(0.789894\pi\)
\(384\) −8.00000 8.00000i −0.408248 0.408248i
\(385\) 0 0
\(386\) 6.00000 + 6.00000i 0.305392 + 0.305392i
\(387\) 4.00000 0.203331
\(388\) 4.00000 0.203069
\(389\) 34.0000i 1.72387i −0.507020 0.861934i \(-0.669253\pi\)
0.507020 0.861934i \(-0.330747\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) 6.00000 + 6.00000i 0.303046 + 0.303046i
\(393\) 20.0000i 1.00887i
\(394\) 2.00000 2.00000i 0.100759 0.100759i
\(395\) 0 0
\(396\) 0 0
\(397\) −32.0000 −1.60603 −0.803017 0.595956i \(-0.796773\pi\)
−0.803017 + 0.595956i \(0.796773\pi\)
\(398\) 10.0000 10.0000i 0.501255 0.501255i
\(399\) 8.00000 0.400501
\(400\) 0 0
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 12.0000 12.0000i 0.598506 0.598506i
\(403\) 8.00000 0.398508
\(404\) −20.0000 −0.995037
\(405\) 0 0
\(406\) 12.0000 12.0000i 0.595550 0.595550i
\(407\) 0 0
\(408\) −4.00000 + 4.00000i −0.198030 + 0.198030i
\(409\) −10.0000 −0.494468 −0.247234 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) 0 0
\(411\) 18.0000i 0.887875i
\(412\) −12.0000 −0.591198
\(413\) 8.00000 0.393654
\(414\) −4.00000 4.00000i −0.196589 0.196589i
\(415\) 0 0
\(416\) 16.0000 16.0000i 0.784465 0.784465i
\(417\) 4.00000i 0.195881i
\(418\) 0 0
\(419\) 24.0000i 1.17248i −0.810139 0.586238i \(-0.800608\pi\)
0.810139 0.586238i \(-0.199392\pi\)
\(420\) 0 0
\(421\) 20.0000i 0.974740i −0.873195 0.487370i \(-0.837956\pi\)
0.873195 0.487370i \(-0.162044\pi\)
\(422\) −20.0000 20.0000i −0.973585 0.973585i
\(423\) 12.0000i 0.583460i
\(424\) −12.0000 12.0000i −0.582772 0.582772i
\(425\) 0 0
\(426\) −12.0000 + 12.0000i −0.581402 + 0.581402i
\(427\) 0 0
\(428\) 24.0000i 1.16008i
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) −4.00000 −0.192450
\(433\) 14.0000i 0.672797i 0.941720 + 0.336399i \(0.109209\pi\)
−0.941720 + 0.336399i \(0.890791\pi\)
\(434\) −4.00000 4.00000i −0.192006 0.192006i
\(435\) 0 0
\(436\) −8.00000 −0.383131
\(437\) 16.0000 0.765384
\(438\) 6.00000 + 6.00000i 0.286691 + 0.286691i
\(439\) 30.0000 1.43182 0.715911 0.698192i \(-0.246012\pi\)
0.715911 + 0.698192i \(0.246012\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) −8.00000 8.00000i −0.380521 0.380521i
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 16.0000i 0.759326i
\(445\) 0 0
\(446\) −14.0000 14.0000i −0.662919 0.662919i
\(447\) 6.00000i 0.283790i
\(448\) −16.0000 −0.755929
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −12.0000 −0.564433
\(453\) −18.0000 −0.845714
\(454\) −8.00000 + 8.00000i −0.375459 + 0.375459i
\(455\) 0 0
\(456\) 8.00000 8.00000i 0.374634 0.374634i
\(457\) 22.0000i 1.02912i 0.857455 + 0.514558i \(0.172044\pi\)
−0.857455 + 0.514558i \(0.827956\pi\)
\(458\) 4.00000 + 4.00000i 0.186908 + 0.186908i
\(459\) 2.00000i 0.0933520i
\(460\) 0 0
\(461\) 30.0000i 1.39724i 0.715493 + 0.698620i \(0.246202\pi\)
−0.715493 + 0.698620i \(0.753798\pi\)
\(462\) 0 0
\(463\) 26.0000i 1.20832i −0.796862 0.604161i \(-0.793508\pi\)
0.796862 0.604161i \(-0.206492\pi\)
\(464\) 24.0000i 1.11417i
\(465\) 0 0
\(466\) −14.0000 14.0000i −0.648537 0.648537i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 8.00000i 0.369800i
\(469\) 24.0000i 1.10822i
\(470\) 0 0
\(471\) 8.00000 0.368621
\(472\) 8.00000 8.00000i 0.368230 0.368230i
\(473\) 0 0
\(474\) 10.0000 10.0000i 0.459315 0.459315i
\(475\) 0 0
\(476\) 8.00000i 0.366679i
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −20.0000 −0.913823 −0.456912 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) 0 0
\(481\) 32.0000 1.45907
\(482\) −2.00000 + 2.00000i −0.0910975 + 0.0910975i
\(483\) −8.00000 −0.364013
\(484\) 22.0000i 1.00000i
\(485\) 0 0
\(486\) −1.00000 + 1.00000i −0.0453609 + 0.0453609i
\(487\) 38.0000i 1.72194i −0.508652 0.860972i \(-0.669856\pi\)
0.508652 0.860972i \(-0.330144\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 20.0000i 0.902587i −0.892375 0.451294i \(-0.850963\pi\)
0.892375 0.451294i \(-0.149037\pi\)
\(492\) 4.00000i 0.180334i
\(493\) −12.0000 −0.540453
\(494\) 16.0000 + 16.0000i 0.719874 + 0.719874i
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 24.0000i 1.07655i
\(498\) 16.0000 16.0000i 0.716977 0.716977i
\(499\) 36.0000i 1.61158i 0.592200 + 0.805791i \(0.298259\pi\)
−0.592200 + 0.805791i \(0.701741\pi\)
\(500\) 0 0
\(501\) 8.00000i 0.357414i
\(502\) 0 0
\(503\) 36.0000i 1.60516i −0.596544 0.802580i \(-0.703460\pi\)
0.596544 0.802580i \(-0.296540\pi\)
\(504\) −4.00000 + 4.00000i −0.178174 + 0.178174i
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) 4.00000 0.177471
\(509\) 6.00000i 0.265945i 0.991120 + 0.132973i \(0.0424523\pi\)
−0.991120 + 0.132973i \(0.957548\pi\)
\(510\) 0 0
\(511\) 12.0000 0.530849
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 4.00000i 0.176604i
\(514\) 18.0000 + 18.0000i 0.793946 + 0.793946i
\(515\) 0 0
\(516\) 8.00000i 0.352180i
\(517\) 0 0
\(518\) −16.0000 16.0000i −0.703000 0.703000i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) −6.00000 6.00000i −0.262613 0.262613i
\(523\) −36.0000 −1.57417 −0.787085 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) −40.0000 −1.74741
\(525\) 0 0
\(526\) 16.0000 + 16.0000i 0.697633 + 0.697633i
\(527\) 4.00000i 0.174243i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 0 0
\(531\) 4.00000i 0.173585i
\(532\) 16.0000i 0.693688i
\(533\) 8.00000 0.346518
\(534\) −10.0000 + 10.0000i −0.432742 + 0.432742i
\(535\) 0 0
\(536\) −24.0000 24.0000i −1.03664 1.03664i
\(537\) 4.00000i 0.172613i
\(538\) −6.00000 6.00000i −0.258678 0.258678i
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000i 0.859867i 0.902861 + 0.429934i \(0.141463\pi\)
−0.902861 + 0.429934i \(0.858537\pi\)
\(542\) 18.0000 18.0000i 0.773166 0.773166i
\(543\) 20.0000i 0.858282i
\(544\) 8.00000 + 8.00000i 0.342997 + 0.342997i
\(545\) 0 0
\(546\) −8.00000 8.00000i −0.342368 0.342368i
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −36.0000 −1.53784
\(549\) 0 0
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) −8.00000 + 8.00000i −0.340503 + 0.340503i
\(553\) 20.0000i 0.850487i
\(554\) −28.0000 + 28.0000i −1.18961 + 1.18961i
\(555\) 0 0
\(556\) −8.00000 −0.339276
\(557\) −42.0000 −1.77960 −0.889799 0.456354i \(-0.849155\pi\)
−0.889799 + 0.456354i \(0.849155\pi\)
\(558\) −2.00000 + 2.00000i −0.0846668 + 0.0846668i
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 18.0000 18.0000i 0.759284 0.759284i
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 24.0000 1.01058
\(565\) 0 0
\(566\) −4.00000 + 4.00000i −0.168133 + 0.168133i
\(567\) 2.00000i 0.0839921i
\(568\) 24.0000 + 24.0000i 1.00702 + 1.00702i
\(569\) 30.0000 1.25767 0.628833 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 0 0
\(571\) 20.0000i 0.836974i −0.908223 0.418487i \(-0.862561\pi\)
0.908223 0.418487i \(-0.137439\pi\)
\(572\) 0 0
\(573\) −8.00000 −0.334205
\(574\) −4.00000 4.00000i −0.166957 0.166957i
\(575\) 0 0
\(576\) 8.00000i 0.333333i
\(577\) 42.0000i 1.74848i 0.485491 + 0.874241i \(0.338641\pi\)
−0.485491 + 0.874241i \(0.661359\pi\)
\(578\) −13.0000 + 13.0000i −0.540729 + 0.540729i
\(579\) 6.00000i 0.249351i
\(580\) 0 0
\(581\) 32.0000i 1.32758i
\(582\) −2.00000 2.00000i −0.0829027 0.0829027i
\(583\) 0 0
\(584\) 12.0000 12.0000i 0.496564 0.496564i
\(585\) 0 0
\(586\) 6.00000 6.00000i 0.247858 0.247858i
\(587\) 28.0000 1.15568 0.577842 0.816149i \(-0.303895\pi\)
0.577842 + 0.816149i \(0.303895\pi\)
\(588\) 6.00000i 0.247436i
\(589\) 8.00000i 0.329634i
\(590\) 0 0
\(591\) −2.00000 −0.0822690
\(592\) −32.0000 −1.31519
\(593\) 6.00000i 0.246390i −0.992382 0.123195i \(-0.960686\pi\)
0.992382 0.123195i \(-0.0393141\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) −10.0000 −0.409273
\(598\) −16.0000 16.0000i −0.654289 0.654289i
\(599\) 20.0000 0.817178 0.408589 0.912719i \(-0.366021\pi\)
0.408589 + 0.912719i \(0.366021\pi\)
\(600\) 0 0
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −8.00000 8.00000i −0.326056 0.326056i
\(603\) −12.0000 −0.488678
\(604\) 36.0000i 1.46482i
\(605\) 0 0
\(606\) 10.0000 + 10.0000i 0.406222 + 0.406222i
\(607\) 2.00000i 0.0811775i 0.999176 + 0.0405887i \(0.0129233\pi\)
−0.999176 + 0.0405887i \(0.987077\pi\)
\(608\) −16.0000 16.0000i −0.648886 0.648886i
\(609\) −12.0000 −0.486265
\(610\) 0 0
\(611\) 48.0000i 1.94187i
\(612\) 4.00000 0.161690
\(613\) −16.0000 −0.646234 −0.323117 0.946359i \(-0.604731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(614\) 12.0000 12.0000i 0.484281 0.484281i
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000i 0.0805170i 0.999189 + 0.0402585i \(0.0128181\pi\)
−0.999189 + 0.0402585i \(0.987182\pi\)
\(618\) 6.00000 + 6.00000i 0.241355 + 0.241355i
\(619\) 36.0000i 1.44696i 0.690344 + 0.723481i \(0.257459\pi\)
−0.690344 + 0.723481i \(0.742541\pi\)
\(620\) 0 0
\(621\) 4.00000i 0.160514i
\(622\) 8.00000 8.00000i 0.320771 0.320771i
\(623\) 20.0000i 0.801283i
\(624\) −16.0000 −0.640513
\(625\) 0 0
\(626\) −14.0000 14.0000i −0.559553 0.559553i
\(627\) 0 0
\(628\) 16.0000i 0.638470i
\(629\) 16.0000i 0.637962i
\(630\) 0 0
\(631\) 22.0000 0.875806 0.437903 0.899022i \(-0.355721\pi\)
0.437903 + 0.899022i \(0.355721\pi\)
\(632\) −20.0000 20.0000i −0.795557 0.795557i
\(633\) 20.0000i 0.794929i
\(634\) 22.0000 22.0000i 0.873732 0.873732i
\(635\) 0 0
\(636\) 12.0000i 0.475831i
\(637\) 12.0000 0.475457
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) 22.0000 0.868948 0.434474 0.900684i \(-0.356934\pi\)
0.434474 + 0.900684i \(0.356934\pi\)
\(642\) 12.0000 12.0000i 0.473602 0.473602i
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 16.0000i 0.630488i
\(645\) 0 0
\(646\) −8.00000 + 8.00000i −0.314756 + 0.314756i
\(647\) 12.0000i 0.471769i 0.971781 + 0.235884i \(0.0757987\pi\)
−0.971781 + 0.235884i \(0.924201\pi\)
\(648\) 2.00000 + 2.00000i 0.0785674 + 0.0785674i
\(649\) 0 0
\(650\) 0 0
\(651\) 4.00000i 0.156772i
\(652\) 8.00000i 0.313304i
\(653\) −6.00000 −0.234798 −0.117399 0.993085i \(-0.537456\pi\)
−0.117399 + 0.993085i \(0.537456\pi\)
\(654\) 4.00000 + 4.00000i 0.156412 + 0.156412i
\(655\) 0 0
\(656\) −8.00000 −0.312348
\(657\) 6.00000i 0.234082i
\(658\) 24.0000 24.0000i 0.935617 0.935617i
\(659\) 36.0000i 1.40236i 0.712984 + 0.701180i \(0.247343\pi\)
−0.712984 + 0.701180i \(0.752657\pi\)
\(660\) 0 0
\(661\) 40.0000i 1.55582i −0.628376 0.777910i \(-0.716280\pi\)
0.628376 0.777910i \(-0.283720\pi\)
\(662\) −20.0000 20.0000i −0.777322 0.777322i
\(663\) 8.00000i 0.310694i
\(664\) −32.0000 32.0000i −1.24184 1.24184i
\(665\) 0 0
\(666\) −8.00000 + 8.00000i −0.309994 + 0.309994i
\(667\) −24.0000 −0.929284
\(668\) −16.0000 −0.619059
\(669\) 14.0000i 0.541271i
\(670\) 0 0
\(671\) 0 0
\(672\) 8.00000 + 8.00000i 0.308607 + 0.308607i
\(673\) 14.0000i 0.539660i 0.962908 + 0.269830i \(0.0869676\pi\)
−0.962908 + 0.269830i \(0.913032\pi\)
\(674\) −2.00000 2.00000i −0.0770371 0.0770371i
\(675\) 0 0
\(676\) 6.00000i 0.230769i
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 6.00000 + 6.00000i 0.230429 + 0.230429i
\(679\) −4.00000 −0.153506
\(680\) 0 0
\(681\) 8.00000 0.306561
\(682\) 0 0
\(683\) −16.0000 −0.612223 −0.306111 0.951996i \(-0.599028\pi\)
−0.306111 + 0.951996i \(0.599028\pi\)
\(684\) −8.00000 −0.305888
\(685\) 0 0
\(686\) −20.0000 20.0000i −0.763604 0.763604i
\(687\) 4.00000i 0.152610i
\(688\) −16.0000 −0.609994
\(689\) −24.0000 −0.914327
\(690\) 0 0
\(691\) 20.0000i 0.760836i −0.924815 0.380418i \(-0.875780\pi\)
0.924815 0.380418i \(-0.124220\pi\)
\(692\) 12.0000i 0.456172i
\(693\) 0 0
\(694\) −8.00000 + 8.00000i −0.303676 + 0.303676i
\(695\) 0 0
\(696\) −12.0000 + 12.0000i −0.454859 + 0.454859i
\(697\) 4.00000i 0.151511i
\(698\) −16.0000 16.0000i −0.605609 0.605609i
\(699\) 14.0000i 0.529529i
\(700\) 0 0
\(701\) 50.0000i 1.88847i 0.329267 + 0.944237i \(0.393198\pi\)
−0.329267 + 0.944237i \(0.606802\pi\)
\(702\) −4.00000 + 4.00000i −0.150970 + 0.150970i
\(703\) 32.0000i 1.20690i
\(704\) 0 0
\(705\) 0 0
\(706\) 6.00000 + 6.00000i 0.225813 + 0.225813i
\(707\) 20.0000 0.752177
\(708\) −8.00000 −0.300658
\(709\) 4.00000i 0.150223i −0.997175 0.0751116i \(-0.976069\pi\)
0.997175 0.0751116i \(-0.0239313\pi\)
\(710\) 0 0
\(711\) −10.0000 −0.375029
\(712\) 20.0000 + 20.0000i 0.749532 + 0.749532i
\(713\) 8.00000i 0.299602i
\(714\) 4.00000 4.00000i 0.149696 0.149696i
\(715\) 0 0
\(716\) −8.00000 −0.298974
\(717\) 0 0
\(718\) −20.0000 + 20.0000i −0.746393 + 0.746393i
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) −3.00000 + 3.00000i −0.111648 + 0.111648i
\(723\) 2.00000 0.0743808
\(724\) −40.0000 −1.48659
\(725\) 0 0
\(726\) −11.0000 + 11.0000i −0.408248 + 0.408248i
\(727\) 42.0000i 1.55769i 0.627214 + 0.778847i \(0.284195\pi\)
−0.627214 + 0.778847i \(0.715805\pi\)
\(728\) −16.0000 + 16.0000i −0.592999 + 0.592999i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 8.00000i 0.295891i
\(732\) 0 0
\(733\) 4.00000 0.147743 0.0738717 0.997268i \(-0.476464\pi\)
0.0738717 + 0.997268i \(0.476464\pi\)
\(734\) 18.0000 + 18.0000i 0.664392 + 0.664392i
\(735\) 0 0
\(736\) 16.0000 + 16.0000i 0.589768 + 0.589768i
\(737\) 0 0
\(738\) −2.00000 + 2.00000i −0.0736210 + 0.0736210i
\(739\) 44.0000i 1.61857i −0.587419 0.809283i \(-0.699856\pi\)
0.587419 0.809283i \(-0.300144\pi\)
\(740\) 0 0
\(741\) 16.0000i 0.587775i
\(742\) 12.0000 + 12.0000i 0.440534 + 0.440534i
\(743\) 16.0000i 0.586983i −0.955962 0.293492i \(-0.905183\pi\)
0.955962 0.293492i \(-0.0948173\pi\)
\(744\) 4.00000 + 4.00000i 0.146647 + 0.146647i
\(745\) 0 0
\(746\) 16.0000 16.0000i 0.585802 0.585802i
\(747\) −16.0000 −0.585409
\(748\) 0 0
\(749\) 24.0000i 0.876941i
\(750\) 0 0
\(751\) 2.00000 0.0729810 0.0364905 0.999334i \(-0.488382\pi\)
0.0364905 + 0.999334i \(0.488382\pi\)
\(752\) 48.0000i 1.75038i
\(753\) 0 0
\(754\) −24.0000 24.0000i −0.874028 0.874028i
\(755\) 0 0
\(756\) 4.00000 0.145479
\(757\) −12.0000 −0.436147 −0.218074 0.975932i \(-0.569977\pi\)
−0.218074 + 0.975932i \(0.569977\pi\)
\(758\) 4.00000 + 4.00000i 0.145287 + 0.145287i
\(759\) 0 0
\(760\) 0 0
\(761\) −38.0000 −1.37750 −0.688749 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) −2.00000 2.00000i −0.0724524 0.0724524i
\(763\) 8.00000 0.289619
\(764\) 16.0000i 0.578860i
\(765\) 0 0
\(766\) −24.0000 24.0000i −0.867155 0.867155i
\(767\) 16.0000i 0.577727i
\(768\) 16.0000 0.577350
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 18.0000i 0.648254i
\(772\) −12.0000 −0.431889
\(773\) 34.0000 1.22290 0.611448 0.791285i \(-0.290588\pi\)
0.611448 + 0.791285i \(0.290588\pi\)
\(774\) −4.00000 + 4.00000i −0.143777 + 0.143777i
\(775\) 0 0
\(776\) −4.00000 + 4.00000i −0.143592 + 0.143592i
\(777\) 16.0000i 0.573997i
\(778\) 34.0000 + 34.0000i 1.21896 + 1.21896i
\(779\) 8.00000i 0.286630i
\(780\) 0 0
\(781\) 0 0
\(782\) 8.00000 8.00000i 0.286079 0.286079i
\(783\) 6.00000i 0.214423i
\(784\) −12.0000 −0.428571
\(785\) 0 0
\(786\) 20.0000 + 20.0000i 0.713376 + 0.713376i
\(787\) −12.0000 −0.427754 −0.213877 0.976861i \(-0.568609\pi\)
−0.213877 + 0.976861i \(0.568609\pi\)
\(788\) 4.00000i 0.142494i
\(789\) 16.0000i 0.569615i
\(790\) 0 0
\(791\) 12.0000 0.426671
\(792\) 0 0
\(793\) 0 0
\(794\) 32.0000 32.0000i 1.13564 1.13564i
\(795\) 0 0
\(796\) 20.0000i 0.708881i
\(797\) −2.00000 −0.0708436 −0.0354218 0.999372i \(-0.511277\pi\)
−0.0354218 + 0.999372i \(0.511277\pi\)
\(798\) −8.00000 + 8.00000i −0.283197 + 0.283197i
\(799\) −24.0000 −0.849059
\(800\) 0 0
\(801\) 10.0000 0.353333
\(802\) 18.0000 18.0000i 0.635602 0.635602i
\(803\) 0 0
\(804\) 24.0000i 0.846415i
\(805\) 0 0
\(806\) −8.00000 + 8.00000i −0.281788 + 0.281788i
\(807\) 6.00000i 0.211210i
\(808\) 20.0000 20.0000i 0.703598 0.703598i
\(809\) 30.0000 1.05474 0.527372 0.849635i \(-0.323177\pi\)
0.527372 + 0.849635i \(0.323177\pi\)
\(810\) 0 0
\(811\) 20.0000i 0.702295i 0.936320 + 0.351147i \(0.114208\pi\)
−0.936320 + 0.351147i \(0.885792\pi\)
\(812\) 24.0000i 0.842235i
\(813\) −18.0000 −0.631288
\(814\) 0 0
\(815\) 0 0
\(816\) 8.00000i 0.280056i
\(817\) 16.0000i 0.559769i
\(818\) 10.0000 10.0000i 0.349642 0.349642i
\(819\) 8.00000i 0.279543i
\(820\) 0 0
\(821\) 10.0000i 0.349002i −0.984657 0.174501i \(-0.944169\pi\)
0.984657 0.174501i \(-0.0558313\pi\)
\(822\) 18.0000 + 18.0000i 0.627822 + 0.627822i
\(823\) 14.0000i 0.488009i 0.969774 + 0.244005i \(0.0784612\pi\)
−0.969774 + 0.244005i \(0.921539\pi\)
\(824\) 12.0000 12.0000i 0.418040 0.418040i
\(825\) 0 0
\(826\) −8.00000 + 8.00000i −0.278356 + 0.278356i
\(827\) −12.0000 −0.417281 −0.208640 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 8.00000 0.278019
\(829\) 4.00000i 0.138926i −0.997585 0.0694629i \(-0.977871\pi\)
0.997585 0.0694629i \(-0.0221285\pi\)
\(830\) 0 0
\(831\) 28.0000 0.971309
\(832\) 32.0000i 1.10940i
\(833\) 6.00000i 0.207888i
\(834\) 4.00000 + 4.00000i 0.138509 + 0.138509i
\(835\) 0 0
\(836\) 0 0
\(837\) 2.00000 0.0691301
\(838\) 24.0000 + 24.0000i 0.829066 + 0.829066i
\(839\) −20.0000 −0.690477 −0.345238 0.938515i \(-0.612202\pi\)
−0.345238 + 0.938515i \(0.612202\pi\)
\(840\) 0 0
\(841\) −7.00000 −0.241379
\(842\) 20.0000 + 20.0000i 0.689246 + 0.689246i
\(843\) −18.0000 −0.619953
\(844\) 40.0000 1.37686
\(845\) 0 0
\(846\) −12.0000 12.0000i −0.412568 0.412568i
\(847\) 22.0000i 0.755929i
\(848\) 24.0000 0.824163
\(849\) 4.00000 0.137280
\(850\) 0 0
\(851\) 32.0000i 1.09695i
\(852\) 24.0000i 0.822226i
\(853\) 24.0000 0.821744 0.410872 0.911693i \(-0.365224\pi\)
0.410872 + 0.911693i \(0.365224\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −24.0000 24.0000i −0.820303 0.820303i
\(857\) 18.0000i 0.614868i −0.951569 0.307434i \(-0.900530\pi\)
0.951569 0.307434i \(-0.0994704\pi\)
\(858\) 0 0
\(859\) 44.0000i 1.50126i −0.660722 0.750630i \(-0.729750\pi\)
0.660722 0.750630i \(-0.270250\pi\)
\(860\) 0 0
\(861\) 4.00000i 0.136320i
\(862\) −12.0000 + 12.0000i −0.408722 + 0.408722i
\(863\) 24.0000i 0.816970i 0.912765 + 0.408485i \(0.133943\pi\)
−0.912765 + 0.408485i \(0.866057\pi\)
\(864\) 4.00000 4.00000i 0.136083 0.136083i
\(865\) 0 0
\(866\) −14.0000 14.0000i −0.475739 0.475739i
\(867\) 13.0000 0.441503
\(868\) 8.00000 0.271538
\(869\) 0 0
\(870\) 0 0
\(871\) −48.0000 −1.62642
\(872\) 8.00000 8.00000i 0.270914 0.270914i
\(873\) 2.00000i 0.0676897i
\(874\) −16.0000 + 16.0000i −0.541208 + 0.541208i
\(875\) 0 0
\(876\) −12.0000 −0.405442
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) −30.0000 + 30.0000i −1.01245 + 1.01245i
\(879\) −6.00000 −0.202375
\(880\) 0 0
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) −3.00000 + 3.00000i −0.101015 + 0.101015i
\(883\) 4.00000 0.134611 0.0673054 0.997732i \(-0.478560\pi\)
0.0673054 + 0.997732i \(0.478560\pi\)
\(884\) 16.0000 0.538138
\(885\) 0 0
\(886\) −24.0000 + 24.0000i −0.806296 + 0.806296i
\(887\) 48.0000i 1.61168i −0.592132 0.805841i \(-0.701714\pi\)
0.592132 0.805841i \(-0.298286\pi\)
\(888\) 16.0000 + 16.0000i 0.536925 + 0.536925i
\(889\) −4.00000 −0.134156
\(890\) 0 0
\(891\) 0 0
\(892\) 28.0000 0.937509
\(893\) 48.0000 1.60626
\(894\) −6.00000 6.00000i −0.200670 0.200670i
\(895\) 0 0
\(896\) 16.0000 16.0000i 0.534522 0.534522i
\(897\) 16.0000i 0.534224i
\(898\) 30.0000 30.0000i 1.00111 1.00111i
\(899\) 12.0000i 0.400222i
\(900\) 0 0
\(901\) 12.0000i 0.399778i
\(902\) 0 0
\(903\) 8.00000i 0.266223i
\(904\) 12.0000 12.0000i 0.399114 0.399114i
\(905\) 0 0
\(906\) 18.0000 18.0000i 0.598010 0.598010i
\(907\) 28.0000 0.929725 0.464862 0.885383i \(-0.346104\pi\)
0.464862 + 0.885383i \(0.346104\pi\)
\(908\) 16.0000i 0.530979i
\(909\) 10.0000i 0.331679i
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 16.0000i 0.529813i
\(913\) 0 0
\(914\) −22.0000 22.0000i −0.727695 0.727695i
\(915\) 0 0
\(916\) −8.00000 −0.264327
\(917\) 40.0000 1.32092
\(918\) −2.00000 2.00000i −0.0660098 0.0660098i
\(919\) −30.0000 −0.989609 −0.494804 0.869004i \(-0.664760\pi\)
−0.494804 + 0.869004i \(0.664760\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) −30.0000 30.0000i −0.987997 0.987997i
\(923\) 48.0000 1.57994
\(924\) 0 0
\(925\) 0 0
\(926\) 26.0000 + 26.0000i 0.854413 + 0.854413i
\(927\) 6.00000i 0.197066i
\(928\) 24.0000 + 24.0000i 0.787839 + 0.787839i
\(929\) 50.0000 1.64045 0.820223 0.572043i \(-0.193849\pi\)
0.820223 + 0.572043i \(0.193849\pi\)
\(930\) 0 0
\(931\) 12.0000i 0.393284i
\(932\) 28.0000 0.917170
\(933\) −8.00000 −0.261908
\(934\) −8.00000 + 8.00000i −0.261768 + 0.261768i
\(935\) 0 0
\(936\) 8.00000 + 8.00000i 0.261488 + 0.261488i
\(937\) 38.0000i 1.24141i −0.784046 0.620703i \(-0.786847\pi\)
0.784046 0.620703i \(-0.213153\pi\)
\(938\) 24.0000 + 24.0000i 0.783628 + 0.783628i
\(939\) 14.0000i 0.456873i
\(940\) 0 0
\(941\) 30.0000i 0.977972i 0.872292 + 0.488986i \(0.162633\pi\)
−0.872292 + 0.488986i \(0.837367\pi\)
\(942\) −8.00000 + 8.00000i −0.260654 + 0.260654i
\(943\) 8.00000i 0.260516i
\(944\) 16.0000i 0.520756i
\(945\) 0 0
\(946\) 0 0
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 20.0000i 0.649570i
\(949\) 24.0000i 0.779073i
\(950\) 0 0
\(951\) −22.0000 −0.713399
\(952\) −8.00000 8.00000i −0.259281 0.259281i
\(953\) 6.00000i 0.194359i −0.995267 0.0971795i \(-0.969018\pi\)
0.995267 0.0971795i \(-0.0309821\pi\)
\(954\) 6.00000 6.00000i 0.194257 0.194257i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 20.0000 20.0000i 0.646171 0.646171i
\(959\) 36.0000 1.16250
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) −32.0000 + 32.0000i −1.03172 + 1.03172i
\(963\) −12.0000 −0.386695
\(964\) 4.00000i 0.128831i
\(965\) 0 0
\(966\) 8.00000 8.00000i 0.257396 0.257396i
\(967\) 22.0000i 0.707472i 0.935345 + 0.353736i \(0.115089\pi\)
−0.935345 + 0.353736i \(0.884911\pi\)
\(968\) 22.0000 + 22.0000i 0.707107 + 0.707107i
\(969\) 8.00000 0.256997
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 2.00000i 0.0641500i
\(973\) 8.00000 0.256468
\(974\) 38.0000 + 38.0000i 1.21760 + 1.21760i
\(975\) 0 0
\(976\) 0 0
\(977\) 2.00000i 0.0639857i 0.999488 + 0.0319928i \(0.0101854\pi\)
−0.999488 + 0.0319928i \(0.989815\pi\)
\(978\) −4.00000 + 4.00000i −0.127906 + 0.127906i
\(979\) 0 0
\(980\) 0 0
\(981\) 4.00000i 0.127710i
\(982\) 20.0000 + 20.0000i 0.638226 + 0.638226i
\(983\) 16.0000i 0.510321i −0.966899 0.255160i \(-0.917872\pi\)
0.966899 0.255160i \(-0.0821283\pi\)
\(984\) 4.00000 + 4.00000i 0.127515 + 0.127515i
\(985\) 0 0
\(986\) 12.0000 12.0000i 0.382158 0.382158i
\(987\) −24.0000 −0.763928
\(988\) −32.0000 −1.01806
\(989\) 16.0000i 0.508770i
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) 8.00000 8.00000i 0.254000 0.254000i
\(993\) 20.0000i 0.634681i
\(994\) −24.0000 24.0000i −0.761234 0.761234i
\(995\) 0 0
\(996\) 32.0000i 1.01396i
\(997\) 48.0000 1.52018 0.760088 0.649821i \(-0.225156\pi\)
0.760088 + 0.649821i \(0.225156\pi\)
\(998\) −36.0000 36.0000i −1.13956 1.13956i
\(999\) 8.00000 0.253109
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 600.2.d.b.349.2 2
3.2 odd 2 1800.2.d.i.1549.1 2
4.3 odd 2 2400.2.d.b.49.1 2
5.2 odd 4 24.2.d.a.13.1 2
5.3 odd 4 600.2.k.b.301.2 2
5.4 even 2 600.2.d.c.349.1 2
8.3 odd 2 2400.2.d.c.49.1 2
8.5 even 2 600.2.d.c.349.2 2
12.11 even 2 7200.2.d.g.2449.1 2
15.2 even 4 72.2.d.b.37.2 2
15.8 even 4 1800.2.k.a.901.1 2
15.14 odd 2 1800.2.d.b.1549.2 2
20.3 even 4 2400.2.k.a.1201.1 2
20.7 even 4 96.2.d.a.49.2 2
20.19 odd 2 2400.2.d.c.49.2 2
24.5 odd 2 1800.2.d.b.1549.1 2
24.11 even 2 7200.2.d.d.2449.1 2
35.27 even 4 1176.2.c.a.589.1 2
40.3 even 4 2400.2.k.a.1201.2 2
40.13 odd 4 600.2.k.b.301.1 2
40.19 odd 2 2400.2.d.b.49.2 2
40.27 even 4 96.2.d.a.49.1 2
40.29 even 2 inner 600.2.d.b.349.1 2
40.37 odd 4 24.2.d.a.13.2 yes 2
45.2 even 12 648.2.n.c.109.2 4
45.7 odd 12 648.2.n.k.109.1 4
45.22 odd 12 648.2.n.k.541.2 4
45.32 even 12 648.2.n.c.541.1 4
60.23 odd 4 7200.2.k.d.3601.2 2
60.47 odd 4 288.2.d.b.145.1 2
60.59 even 2 7200.2.d.d.2449.2 2
80.27 even 4 768.2.a.e.1.1 1
80.37 odd 4 768.2.a.a.1.1 1
80.67 even 4 768.2.a.d.1.1 1
80.77 odd 4 768.2.a.h.1.1 1
120.29 odd 2 1800.2.d.i.1549.2 2
120.53 even 4 1800.2.k.a.901.2 2
120.59 even 2 7200.2.d.g.2449.2 2
120.77 even 4 72.2.d.b.37.1 2
120.83 odd 4 7200.2.k.d.3601.1 2
120.107 odd 4 288.2.d.b.145.2 2
140.27 odd 4 4704.2.c.a.2353.1 2
180.7 even 12 2592.2.r.f.433.1 4
180.47 odd 12 2592.2.r.g.433.2 4
180.67 even 12 2592.2.r.f.2161.2 4
180.167 odd 12 2592.2.r.g.2161.1 4
240.77 even 4 2304.2.a.e.1.1 1
240.107 odd 4 2304.2.a.l.1.1 1
240.197 even 4 2304.2.a.o.1.1 1
240.227 odd 4 2304.2.a.b.1.1 1
280.27 odd 4 4704.2.c.a.2353.2 2
280.237 even 4 1176.2.c.a.589.2 2
360.67 even 12 2592.2.r.f.2161.1 4
360.77 even 12 648.2.n.c.541.2 4
360.157 odd 12 648.2.n.k.541.1 4
360.187 even 12 2592.2.r.f.433.2 4
360.227 odd 12 2592.2.r.g.433.1 4
360.277 odd 12 648.2.n.k.109.2 4
360.317 even 12 648.2.n.c.109.1 4
360.347 odd 12 2592.2.r.g.2161.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
24.2.d.a.13.1 2 5.2 odd 4
24.2.d.a.13.2 yes 2 40.37 odd 4
72.2.d.b.37.1 2 120.77 even 4
72.2.d.b.37.2 2 15.2 even 4
96.2.d.a.49.1 2 40.27 even 4
96.2.d.a.49.2 2 20.7 even 4
288.2.d.b.145.1 2 60.47 odd 4
288.2.d.b.145.2 2 120.107 odd 4
600.2.d.b.349.1 2 40.29 even 2 inner
600.2.d.b.349.2 2 1.1 even 1 trivial
600.2.d.c.349.1 2 5.4 even 2
600.2.d.c.349.2 2 8.5 even 2
600.2.k.b.301.1 2 40.13 odd 4
600.2.k.b.301.2 2 5.3 odd 4
648.2.n.c.109.1 4 360.317 even 12
648.2.n.c.109.2 4 45.2 even 12
648.2.n.c.541.1 4 45.32 even 12
648.2.n.c.541.2 4 360.77 even 12
648.2.n.k.109.1 4 45.7 odd 12
648.2.n.k.109.2 4 360.277 odd 12
648.2.n.k.541.1 4 360.157 odd 12
648.2.n.k.541.2 4 45.22 odd 12
768.2.a.a.1.1 1 80.37 odd 4
768.2.a.d.1.1 1 80.67 even 4
768.2.a.e.1.1 1 80.27 even 4
768.2.a.h.1.1 1 80.77 odd 4
1176.2.c.a.589.1 2 35.27 even 4
1176.2.c.a.589.2 2 280.237 even 4
1800.2.d.b.1549.1 2 24.5 odd 2
1800.2.d.b.1549.2 2 15.14 odd 2
1800.2.d.i.1549.1 2 3.2 odd 2
1800.2.d.i.1549.2 2 120.29 odd 2
1800.2.k.a.901.1 2 15.8 even 4
1800.2.k.a.901.2 2 120.53 even 4
2304.2.a.b.1.1 1 240.227 odd 4
2304.2.a.e.1.1 1 240.77 even 4
2304.2.a.l.1.1 1 240.107 odd 4
2304.2.a.o.1.1 1 240.197 even 4
2400.2.d.b.49.1 2 4.3 odd 2
2400.2.d.b.49.2 2 40.19 odd 2
2400.2.d.c.49.1 2 8.3 odd 2
2400.2.d.c.49.2 2 20.19 odd 2
2400.2.k.a.1201.1 2 20.3 even 4
2400.2.k.a.1201.2 2 40.3 even 4
2592.2.r.f.433.1 4 180.7 even 12
2592.2.r.f.433.2 4 360.187 even 12
2592.2.r.f.2161.1 4 360.67 even 12
2592.2.r.f.2161.2 4 180.67 even 12
2592.2.r.g.433.1 4 360.227 odd 12
2592.2.r.g.433.2 4 180.47 odd 12
2592.2.r.g.2161.1 4 180.167 odd 12
2592.2.r.g.2161.2 4 360.347 odd 12
4704.2.c.a.2353.1 2 140.27 odd 4
4704.2.c.a.2353.2 2 280.27 odd 4
7200.2.d.d.2449.1 2 24.11 even 2
7200.2.d.d.2449.2 2 60.59 even 2
7200.2.d.g.2449.1 2 12.11 even 2
7200.2.d.g.2449.2 2 120.59 even 2
7200.2.k.d.3601.1 2 120.83 odd 4
7200.2.k.d.3601.2 2 60.23 odd 4