Properties

Label 810.2.e.h.271.1
Level $810$
Weight $2$
Character 810.271
Analytic conductor $6.468$
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] = [810,2,Mod(271,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.271");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.e (of order \(3\), degree \(2\), 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: \(6.46788256372\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 90)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.271
Dual form 810.2.e.h.541.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -1.00000 q^{10} +(-3.00000 - 5.19615i) q^{11} +(2.00000 - 3.46410i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(3.00000 - 5.19615i) q^{22} +(-0.500000 - 0.866025i) q^{25} +4.00000 q^{26} +2.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{34} +2.00000 q^{35} +8.00000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-4.00000 - 6.92820i) q^{43} +6.00000 q^{44} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +(2.00000 + 3.46410i) q^{52} -6.00000 q^{53} +6.00000 q^{55} +(1.00000 + 1.73205i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(-3.00000 + 5.19615i) q^{59} +(-1.00000 - 1.73205i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(2.00000 - 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} +(1.00000 + 1.73205i) q^{70} -12.0000 q^{71} -10.0000 q^{73} +(4.00000 + 6.92820i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(2.00000 + 3.46410i) q^{79} +1.00000 q^{80} +(-6.00000 - 10.3923i) q^{83} +(3.00000 - 5.19615i) q^{85} +(4.00000 - 6.92820i) q^{86} +(3.00000 + 5.19615i) q^{88} +12.0000 q^{89} -8.00000 q^{91} +(2.00000 - 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} - q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} - 6 q^{11} + 4 q^{13} + 2 q^{14} - q^{16} - 12 q^{17} - 8 q^{19} - q^{20} + 6 q^{22} - q^{25} + 8 q^{26} + 4 q^{28} + 6 q^{29} + 4 q^{31} + q^{32} - 6 q^{34} + 4 q^{35} + 16 q^{37} - 4 q^{38} + q^{40} - 8 q^{43} + 12 q^{44} + 3 q^{49} + q^{50} + 4 q^{52} - 12 q^{53} + 12 q^{55} + 2 q^{56} - 6 q^{58} - 6 q^{59} - 2 q^{61} + 8 q^{62} + 2 q^{64} + 4 q^{65} + 4 q^{67} + 6 q^{68} + 2 q^{70} - 24 q^{71} - 20 q^{73} + 8 q^{74} + 4 q^{76} - 12 q^{77} + 4 q^{79} + 2 q^{80} - 12 q^{83} + 6 q^{85} + 8 q^{86} + 6 q^{88} + 24 q^{89} - 16 q^{91} + 4 q^{95} - 2 q^{97} + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.00000 −0.316228
\(11\) −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i \(-0.806886\pi\)
−0.0829925 0.996550i \(-0.526448\pi\)
\(12\) 0 0
\(13\) 2.00000 3.46410i 0.554700 0.960769i −0.443227 0.896410i \(-0.646166\pi\)
0.997927 0.0643593i \(-0.0205004\pi\)
\(14\) 1.00000 1.73205i 0.267261 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 0 0
\(22\) 3.00000 5.19615i 0.639602 1.10782i
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 4.00000 0.784465
\(27\) 0 0
\(28\) 2.00000 0.377964
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −3.00000 5.19615i −0.514496 0.891133i
\(35\) 2.00000 0.338062
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) −2.00000 3.46410i −0.324443 0.561951i
\(39\) 0 0
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 0 0
\(43\) −4.00000 6.92820i −0.609994 1.05654i −0.991241 0.132068i \(-0.957838\pi\)
0.381246 0.924473i \(-0.375495\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) 0 0
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) 0 0
\(58\) −3.00000 + 5.19615i −0.393919 + 0.682288i
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 + 3.46410i 0.248069 + 0.429669i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) 0 0
\(70\) 1.00000 + 1.73205i 0.119523 + 0.207020i
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −10.0000 −1.17041 −0.585206 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 4.00000 + 6.92820i 0.464991 + 0.805387i
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) −6.00000 + 10.3923i −0.683763 + 1.18431i
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 1.00000 0.111803
\(81\) 0 0
\(82\) 0 0
\(83\) −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) 0 0
\(85\) 3.00000 5.19615i 0.325396 0.563602i
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 0 0
\(88\) 3.00000 + 5.19615i 0.319801 + 0.553912i
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.00000 3.46410i 0.205196 0.355409i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) −1.00000 + 1.73205i −0.0985329 + 0.170664i −0.911078 0.412235i \(-0.864748\pi\)
0.812545 + 0.582899i \(0.198082\pi\)
\(104\) −2.00000 + 3.46410i −0.196116 + 0.339683i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 3.00000 + 5.19615i 0.286039 + 0.495434i
\(111\) 0 0
\(112\) −1.00000 + 1.73205i −0.0944911 + 0.163663i
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) −6.00000 −0.552345
\(119\) 6.00000 + 10.3923i 0.550019 + 0.952661i
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 1.00000 1.73205i 0.0905357 0.156813i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −2.00000 + 3.46410i −0.175412 + 0.303822i
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 0 0
\(133\) 4.00000 + 6.92820i 0.346844 + 0.600751i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 6.00000 0.514496
\(137\) −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 0 0
\(139\) −10.0000 + 17.3205i −0.848189 + 1.46911i 0.0346338 + 0.999400i \(0.488974\pi\)
−0.882823 + 0.469706i \(0.844360\pi\)
\(140\) −1.00000 + 1.73205i −0.0845154 + 0.146385i
\(141\) 0 0
\(142\) −6.00000 10.3923i −0.503509 0.872103i
\(143\) −24.0000 −2.00698
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) −5.00000 8.66025i −0.413803 0.716728i
\(147\) 0 0
\(148\) −4.00000 + 6.92820i −0.328798 + 0.569495i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) 4.00000 0.324443
\(153\) 0 0
\(154\) −12.0000 −0.966988
\(155\) 2.00000 + 3.46410i 0.160644 + 0.278243i
\(156\) 0 0
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) −2.00000 + 3.46410i −0.159111 + 0.275589i
\(159\) 0 0
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 0 0
\(162\) 0 0
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) 12.0000 20.7846i 0.928588 1.60836i 0.142901 0.989737i \(-0.454357\pi\)
0.785687 0.618624i \(-0.212310\pi\)
\(168\) 0 0
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) 6.00000 0.460179
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) −9.00000 15.5885i −0.684257 1.18517i −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 0 0
\(175\) −1.00000 + 1.73205i −0.0755929 + 0.130931i
\(176\) −3.00000 + 5.19615i −0.226134 + 0.391675i
\(177\) 0 0
\(178\) 6.00000 + 10.3923i 0.449719 + 0.778936i
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −4.00000 6.92820i −0.296500 0.513553i
\(183\) 0 0
\(184\) 0 0
\(185\) −4.00000 + 6.92820i −0.294086 + 0.509372i
\(186\) 0 0
\(187\) 18.0000 + 31.1769i 1.31629 + 2.27988i
\(188\) 0 0
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0 0
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) 0 0
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) −3.00000 + 5.19615i −0.211079 + 0.365600i
\(203\) 6.00000 10.3923i 0.421117 0.729397i
\(204\) 0 0
\(205\) 0 0
\(206\) −2.00000 −0.139347
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) 12.0000 + 20.7846i 0.830057 + 1.43770i
\(210\) 0 0
\(211\) 2.00000 3.46410i 0.137686 0.238479i −0.788935 0.614477i \(-0.789367\pi\)
0.926620 + 0.375999i \(0.122700\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 8.00000 0.545595
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) 0 0
\(220\) −3.00000 + 5.19615i −0.202260 + 0.350325i
\(221\) −12.0000 + 20.7846i −0.807207 + 1.39812i
\(222\) 0 0
\(223\) −13.0000 22.5167i −0.870544 1.50783i −0.861435 0.507869i \(-0.830434\pi\)
−0.00910984 0.999959i \(-0.502900\pi\)
\(224\) −2.00000 −0.133631
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.00000 5.19615i −0.195283 0.338241i
\(237\) 0 0
\(238\) −6.00000 + 10.3923i −0.388922 + 0.673633i
\(239\) 6.00000 10.3923i 0.388108 0.672222i −0.604087 0.796918i \(-0.706462\pi\)
0.992195 + 0.124696i \(0.0397955\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) −25.0000 −1.60706
\(243\) 0 0
\(244\) 2.00000 0.128037
\(245\) 1.50000 + 2.59808i 0.0958315 + 0.165985i
\(246\) 0 0
\(247\) −8.00000 + 13.8564i −0.509028 + 0.881662i
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.00000 + 1.73205i 0.0627456 + 0.108679i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 0 0
\(259\) −8.00000 13.8564i −0.497096 0.860995i
\(260\) −4.00000 −0.248069
\(261\) 0 0
\(262\) 6.00000 0.370681
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) 3.00000 5.19615i 0.184289 0.319197i
\(266\) −4.00000 + 6.92820i −0.245256 + 0.424795i
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 3.00000 + 5.19615i 0.181902 + 0.315063i
\(273\) 0 0
\(274\) 3.00000 5.19615i 0.181237 0.313911i
\(275\) −3.00000 + 5.19615i −0.180907 + 0.313340i
\(276\) 0 0
\(277\) −4.00000 6.92820i −0.240337 0.416275i 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) −20.0000 −1.19952
\(279\) 0 0
\(280\) −2.00000 −0.119523
\(281\) −6.00000 10.3923i −0.357930 0.619953i 0.629685 0.776851i \(-0.283184\pi\)
−0.987615 + 0.156898i \(0.949851\pi\)
\(282\) 0 0
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) −12.0000 20.7846i −0.709575 1.22902i
\(287\) 0 0
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) 0 0
\(292\) 5.00000 8.66025i 0.292603 0.506803i
\(293\) 9.00000 15.5885i 0.525786 0.910687i −0.473763 0.880652i \(-0.657105\pi\)
0.999549 0.0300351i \(-0.00956192\pi\)
\(294\) 0 0
\(295\) −3.00000 5.19615i −0.174667 0.302532i
\(296\) −8.00000 −0.464991
\(297\) 0 0
\(298\) −6.00000 −0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −8.00000 + 13.8564i −0.461112 + 0.798670i
\(302\) −8.00000 + 13.8564i −0.460348 + 0.797347i
\(303\) 0 0
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) −6.00000 10.3923i −0.341882 0.592157i
\(309\) 0 0
\(310\) −2.00000 + 3.46410i −0.113592 + 0.196748i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 0 0
\(313\) 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) 18.0000 31.1769i 1.00781 1.74557i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) −4.00000 −0.221880
\(326\) 10.0000 + 17.3205i 0.553849 + 0.959294i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) 12.0000 0.658586
\(333\) 0 0
\(334\) 24.0000 1.31322
\(335\) 2.00000 + 3.46410i 0.109272 + 0.189264i
\(336\) 0 0
\(337\) −7.00000 + 12.1244i −0.381314 + 0.660456i −0.991250 0.131995i \(-0.957862\pi\)
0.609936 + 0.792451i \(0.291195\pi\)
\(338\) 1.50000 2.59808i 0.0815892 0.141317i
\(339\) 0 0
\(340\) 3.00000 + 5.19615i 0.162698 + 0.281801i
\(341\) −24.0000 −1.29967
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 4.00000 + 6.92820i 0.215666 + 0.373544i
\(345\) 0 0
\(346\) 9.00000 15.5885i 0.483843 0.838041i
\(347\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) 0 0
\(349\) 11.0000 + 19.0526i 0.588817 + 1.01986i 0.994388 + 0.105797i \(0.0337393\pi\)
−0.405571 + 0.914063i \(0.632927\pi\)
\(350\) −2.00000 −0.106904
\(351\) 0 0
\(352\) −6.00000 −0.319801
\(353\) 15.0000 + 25.9808i 0.798369 + 1.38282i 0.920677 + 0.390324i \(0.127637\pi\)
−0.122308 + 0.992492i \(0.539030\pi\)
\(354\) 0 0
\(355\) 6.00000 10.3923i 0.318447 0.551566i
\(356\) −6.00000 + 10.3923i −0.317999 + 0.550791i
\(357\) 0 0
\(358\) 3.00000 + 5.19615i 0.158555 + 0.274625i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 1.00000 + 1.73205i 0.0525588 + 0.0910346i
\(363\) 0 0
\(364\) 4.00000 6.92820i 0.209657 0.363137i
\(365\) 5.00000 8.66025i 0.261712 0.453298i
\(366\) 0 0
\(367\) −13.0000 22.5167i −0.678594 1.17536i −0.975404 0.220423i \(-0.929256\pi\)
0.296810 0.954937i \(-0.404077\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −8.00000 −0.415900
\(371\) 6.00000 + 10.3923i 0.311504 + 0.539542i
\(372\) 0 0
\(373\) 14.0000 24.2487i 0.724893 1.25555i −0.234126 0.972206i \(-0.575223\pi\)
0.959018 0.283344i \(-0.0914439\pi\)
\(374\) −18.0000 + 31.1769i −0.930758 + 1.61212i
\(375\) 0 0
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 2.00000 + 3.46410i 0.102598 + 0.177705i
\(381\) 0 0
\(382\) 6.00000 10.3923i 0.306987 0.531717i
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) −6.00000 10.3923i −0.305788 0.529641i
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) 9.00000 + 15.5885i 0.456318 + 0.790366i 0.998763 0.0497253i \(-0.0158346\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.50000 + 2.59808i −0.0757614 + 0.131223i
\(393\) 0 0
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) −4.00000 −0.201262
\(396\) 0 0
\(397\) −16.0000 −0.803017 −0.401508 0.915855i \(-0.631514\pi\)
−0.401508 + 0.915855i \(0.631514\pi\)
\(398\) −8.00000 13.8564i −0.401004 0.694559i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 18.0000 31.1769i 0.898877 1.55690i 0.0699455 0.997551i \(-0.477717\pi\)
0.828932 0.559350i \(-0.188949\pi\)
\(402\) 0 0
\(403\) −8.00000 13.8564i −0.398508 0.690237i
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 12.0000 0.595550
\(407\) −24.0000 41.5692i −1.18964 2.06051i
\(408\) 0 0
\(409\) 11.0000 19.0526i 0.543915 0.942088i −0.454759 0.890614i \(-0.650275\pi\)
0.998674 0.0514740i \(-0.0163919\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −1.00000 1.73205i −0.0492665 0.0853320i
\(413\) 12.0000 0.590481
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) 0 0
\(418\) −12.0000 + 20.7846i −0.586939 + 1.01661i
\(419\) 3.00000 5.19615i 0.146560 0.253849i −0.783394 0.621525i \(-0.786513\pi\)
0.929954 + 0.367677i \(0.119847\pi\)
\(420\) 0 0
\(421\) −7.00000 12.1244i −0.341159 0.590905i 0.643489 0.765455i \(-0.277486\pi\)
−0.984648 + 0.174550i \(0.944153\pi\)
\(422\) 4.00000 0.194717
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 0 0
\(427\) −2.00000 + 3.46410i −0.0967868 + 0.167640i
\(428\) −6.00000 + 10.3923i −0.290021 + 0.502331i
\(429\) 0 0
\(430\) 4.00000 + 6.92820i 0.192897 + 0.334108i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 38.0000 1.82616 0.913082 0.407777i \(-0.133696\pi\)
0.913082 + 0.407777i \(0.133696\pi\)
\(434\) −4.00000 6.92820i −0.192006 0.332564i
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 0 0
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) 12.0000 + 20.7846i 0.570137 + 0.987507i 0.996551 + 0.0829786i \(0.0264433\pi\)
−0.426414 + 0.904528i \(0.640223\pi\)
\(444\) 0 0
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 13.0000 22.5167i 0.615568 1.06619i
\(447\) 0 0
\(448\) −1.00000 1.73205i −0.0472456 0.0818317i
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) 0 0
\(454\) 0 0
\(455\) 4.00000 6.92820i 0.187523 0.324799i
\(456\) 0 0
\(457\) −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i \(-0.958593\pi\)
0.383437 0.923567i \(-0.374740\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) 9.00000 + 15.5885i 0.419172 + 0.726027i 0.995856 0.0909401i \(-0.0289872\pi\)
−0.576685 + 0.816967i \(0.695654\pi\)
\(462\) 0 0
\(463\) 17.0000 29.4449i 0.790057 1.36842i −0.135874 0.990726i \(-0.543384\pi\)
0.925931 0.377693i \(-0.123282\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) 3.00000 5.19615i 0.138086 0.239172i
\(473\) −24.0000 + 41.5692i −1.10352 + 1.91135i
\(474\) 0 0
\(475\) 2.00000 + 3.46410i 0.0917663 + 0.158944i
\(476\) −12.0000 −0.550019
\(477\) 0 0
\(478\) 12.0000 0.548867
\(479\) −18.0000 31.1769i −0.822441 1.42451i −0.903859 0.427830i \(-0.859278\pi\)
0.0814184 0.996680i \(-0.474055\pi\)
\(480\) 0 0
\(481\) 16.0000 27.7128i 0.729537 1.26360i
\(482\) −5.00000 + 8.66025i −0.227744 + 0.394464i
\(483\) 0 0
\(484\) −12.5000 21.6506i −0.568182 0.984120i
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 1.00000 + 1.73205i 0.0452679 + 0.0784063i
\(489\) 0 0
\(490\) −1.50000 + 2.59808i −0.0677631 + 0.117369i
\(491\) 3.00000 5.19615i 0.135388 0.234499i −0.790358 0.612646i \(-0.790105\pi\)
0.925746 + 0.378147i \(0.123439\pi\)
\(492\) 0 0
\(493\) −18.0000 31.1769i −0.810679 1.40414i
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 12.0000 + 20.7846i 0.538274 + 0.932317i
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 9.00000 + 15.5885i 0.401690 + 0.695747i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) 0 0
\(508\) −1.00000 + 1.73205i −0.0443678 + 0.0768473i
\(509\) −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) 0 0
\(511\) 10.0000 + 17.3205i 0.442374 + 0.766214i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) −1.00000 1.73205i −0.0440653 0.0763233i
\(516\) 0 0
\(517\) 0 0
\(518\) 8.00000 13.8564i 0.351500 0.608816i
\(519\) 0 0
\(520\) −2.00000 3.46410i −0.0877058 0.151911i
\(521\) 12.0000 0.525730 0.262865 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 0 0
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 3.00000 + 5.19615i 0.131056 + 0.226995i
\(525\) 0 0
\(526\) 12.0000 20.7846i 0.523225 0.906252i
\(527\) −12.0000 + 20.7846i −0.522728 + 0.905392i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 6.00000 0.260623
\(531\) 0 0
\(532\) −8.00000 −0.346844
\(533\) 0 0
\(534\) 0 0
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) 0 0
\(538\) 9.00000 + 15.5885i 0.388018 + 0.672066i
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 4.00000 + 6.92820i 0.171815 + 0.297592i
\(543\) 0 0
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) −1.00000 + 1.73205i −0.0428353 + 0.0741929i
\(546\) 0 0
\(547\) 20.0000 + 34.6410i 0.855138 + 1.48114i 0.876517 + 0.481371i \(0.159861\pi\)
−0.0213785 + 0.999771i \(0.506805\pi\)
\(548\) 6.00000 0.256307
\(549\) 0 0
\(550\) −6.00000 −0.255841
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 0 0
\(553\) 4.00000 6.92820i 0.170097 0.294617i
\(554\) 4.00000 6.92820i 0.169944 0.294351i
\(555\) 0 0
\(556\) −10.0000 17.3205i −0.424094 0.734553i
\(557\) 42.0000 1.77960 0.889799 0.456354i \(-0.150845\pi\)
0.889799 + 0.456354i \(0.150845\pi\)
\(558\) 0 0
\(559\) −32.0000 −1.35346
\(560\) −1.00000 1.73205i −0.0422577 0.0731925i
\(561\) 0 0
\(562\) 6.00000 10.3923i 0.253095 0.438373i
\(563\) 12.0000 20.7846i 0.505740 0.875967i −0.494238 0.869326i \(-0.664553\pi\)
0.999978 0.00664037i \(-0.00211371\pi\)
\(564\) 0 0
\(565\) −3.00000 5.19615i −0.126211 0.218604i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) −18.0000 31.1769i −0.754599 1.30700i −0.945573 0.325409i \(-0.894498\pi\)
0.190974 0.981595i \(-0.438835\pi\)
\(570\) 0 0
\(571\) −22.0000 + 38.1051i −0.920671 + 1.59465i −0.122292 + 0.992494i \(0.539025\pi\)
−0.798379 + 0.602155i \(0.794309\pi\)
\(572\) 12.0000 20.7846i 0.501745 0.869048i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −22.0000 −0.915872 −0.457936 0.888985i \(-0.651411\pi\)
−0.457936 + 0.888985i \(0.651411\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) 0 0
\(580\) 3.00000 5.19615i 0.124568 0.215758i
\(581\) −12.0000 + 20.7846i −0.497844 + 0.862291i
\(582\) 0 0
\(583\) 18.0000 + 31.1769i 0.745484 + 1.29122i
\(584\) 10.0000 0.413803
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) 18.0000 + 31.1769i 0.742940 + 1.28681i 0.951151 + 0.308725i \(0.0999023\pi\)
−0.208212 + 0.978084i \(0.566764\pi\)
\(588\) 0 0
\(589\) −8.00000 + 13.8564i −0.329634 + 0.570943i
\(590\) 3.00000 5.19615i 0.123508 0.213922i
\(591\) 0 0
\(592\) −4.00000 6.92820i −0.164399 0.284747i
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) 5.00000 + 8.66025i 0.203954 + 0.353259i 0.949799 0.312861i \(-0.101287\pi\)
−0.745845 + 0.666120i \(0.767954\pi\)
\(602\) −16.0000 −0.652111
\(603\) 0 0
\(604\) −16.0000 −0.651031
\(605\) −12.5000 21.6506i −0.508197 0.880223i
\(606\) 0 0
\(607\) −19.0000 + 32.9090i −0.771186 + 1.33573i 0.165727 + 0.986172i \(0.447003\pi\)
−0.936913 + 0.349562i \(0.886330\pi\)
\(608\) −2.00000 + 3.46410i −0.0811107 + 0.140488i
\(609\) 0 0
\(610\) 1.00000 + 1.73205i 0.0404888 + 0.0701287i
\(611\) 0 0
\(612\) 0 0
\(613\) 8.00000 0.323117 0.161558 0.986863i \(-0.448348\pi\)
0.161558 + 0.986863i \(0.448348\pi\)
\(614\) −8.00000 13.8564i −0.322854 0.559199i
\(615\) 0 0
\(616\) 6.00000 10.3923i 0.241747 0.418718i
\(617\) 15.0000 25.9808i 0.603877 1.04595i −0.388351 0.921512i \(-0.626955\pi\)
0.992228 0.124434i \(-0.0397116\pi\)
\(618\) 0 0
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) −4.00000 −0.160644
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) −12.0000 20.7846i −0.480770 0.832718i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −5.00000 + 8.66025i −0.199840 + 0.346133i
\(627\) 0 0
\(628\) 2.00000 + 3.46410i 0.0798087 + 0.138233i
\(629\) −48.0000 −1.91389
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −2.00000 3.46410i −0.0795557 0.137795i
\(633\) 0 0
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) −1.00000 + 1.73205i −0.0396838 + 0.0687343i
\(636\) 0 0
\(637\) −6.00000 10.3923i −0.237729 0.411758i
\(638\) 36.0000 1.42525
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) −12.0000 20.7846i −0.473972 0.820943i 0.525584 0.850741i \(-0.323847\pi\)
−0.999556 + 0.0297987i \(0.990513\pi\)
\(642\) 0 0
\(643\) 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i \(-0.808201\pi\)
0.902764 + 0.430137i \(0.141535\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 12.0000 + 20.7846i 0.472134 + 0.817760i
\(647\) −48.0000 −1.88707 −0.943537 0.331266i \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) −2.00000 3.46410i −0.0784465 0.135873i
\(651\) 0 0
\(652\) −10.0000 + 17.3205i −0.391630 + 0.678323i
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) 3.00000 + 5.19615i 0.117220 + 0.203030i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 15.0000 + 25.9808i 0.584317 + 1.01207i 0.994960 + 0.100271i \(0.0319709\pi\)
−0.410643 + 0.911796i \(0.634696\pi\)
\(660\) 0 0
\(661\) −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i \(-0.845717\pi\)
0.845922 + 0.533306i \(0.179051\pi\)
\(662\) −2.00000 + 3.46410i −0.0777322 + 0.134636i
\(663\) 0 0
\(664\) 6.00000 + 10.3923i 0.232845 + 0.403300i
\(665\) −8.00000 −0.310227
\(666\) 0 0
\(667\) 0 0
\(668\) 12.0000 + 20.7846i 0.464294 + 0.804181i
\(669\) 0 0
\(670\) −2.00000 + 3.46410i −0.0772667 + 0.133830i
\(671\) −6.00000 + 10.3923i −0.231627 + 0.401190i
\(672\) 0 0
\(673\) −7.00000 12.1244i −0.269830 0.467360i 0.698988 0.715134i \(-0.253634\pi\)
−0.968818 + 0.247774i \(0.920301\pi\)
\(674\) −14.0000 −0.539260
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 0 0
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) −3.00000 + 5.19615i −0.115045 + 0.199263i
\(681\) 0 0
\(682\) −12.0000 20.7846i −0.459504 0.795884i
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 0 0
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) −12.0000 + 20.7846i −0.457164 + 0.791831i
\(690\) 0 0
\(691\) −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i \(-0.851021\pi\)
0.0555386 0.998457i \(-0.482312\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 0 0
\(695\) −10.0000 17.3205i −0.379322 0.657004i
\(696\) 0 0
\(697\) 0 0
\(698\) −11.0000 + 19.0526i −0.416356 + 0.721150i
\(699\) 0 0
\(700\) −1.00000 1.73205i −0.0377964 0.0654654i
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) 0 0
\(703\) −32.0000 −1.20690
\(704\) −3.00000 5.19615i −0.113067 0.195837i
\(705\) 0 0
\(706\) −15.0000 + 25.9808i −0.564532 + 0.977799i
\(707\) 6.00000 10.3923i 0.225653 0.390843i
\(708\) 0 0
\(709\) 17.0000 + 29.4449i 0.638448 + 1.10583i 0.985773 + 0.168080i \(0.0537568\pi\)
−0.347325 + 0.937745i \(0.612910\pi\)
\(710\) 12.0000 0.450352
\(711\) 0 0
\(712\) −12.0000 −0.449719
\(713\) 0 0
\(714\) 0 0
\(715\) 12.0000 20.7846i 0.448775 0.777300i
\(716\) −3.00000 + 5.19615i −0.112115 + 0.194189i
\(717\) 0 0
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) −1.50000 2.59808i −0.0558242 0.0966904i
\(723\) 0 0
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 0 0
\(727\) 5.00000 + 8.66025i 0.185440 + 0.321191i 0.943725 0.330732i \(-0.107296\pi\)
−0.758285 + 0.651923i \(0.773962\pi\)
\(728\) 8.00000 0.296500
\(729\) 0 0
\(730\) 10.0000 0.370117
\(731\) 24.0000 + 41.5692i 0.887672 + 1.53749i
\(732\) 0 0
\(733\) −16.0000 + 27.7128i −0.590973 + 1.02360i 0.403128 + 0.915144i \(0.367923\pi\)
−0.994102 + 0.108453i \(0.965410\pi\)
\(734\) 13.0000 22.5167i 0.479839 0.831105i
\(735\) 0 0
\(736\) 0 0
\(737\) −24.0000 −0.884051
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −4.00000 6.92820i −0.147043 0.254686i
\(741\) 0 0
\(742\) −6.00000 + 10.3923i −0.220267 + 0.381514i
\(743\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 0 0
\(745\) −3.00000 5.19615i −0.109911 0.190372i
\(746\) 28.0000 1.02515
\(747\) 0 0
\(748\) −36.0000 −1.31629
\(749\) −12.0000 20.7846i −0.438470 0.759453i
\(750\) 0 0
\(751\) −10.0000 + 17.3205i −0.364905 + 0.632034i −0.988761 0.149505i \(-0.952232\pi\)
0.623856 + 0.781540i \(0.285565\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 12.0000 + 20.7846i 0.437014 + 0.756931i
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −40.0000 −1.45382 −0.726912 0.686730i \(-0.759045\pi\)
−0.726912 + 0.686730i \(0.759045\pi\)
\(758\) 10.0000 + 17.3205i 0.363216 + 0.629109i
\(759\) 0 0
\(760\) −2.00000 + 3.46410i −0.0725476 + 0.125656i
\(761\) −18.0000 + 31.1769i −0.652499 + 1.13016i 0.330015 + 0.943976i \(0.392946\pi\)
−0.982514 + 0.186187i \(0.940387\pi\)
\(762\) 0 0
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 0 0
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 0 0
\(769\) −7.00000 + 12.1244i −0.252426 + 0.437215i −0.964193 0.265200i \(-0.914562\pi\)
0.711767 + 0.702416i \(0.247895\pi\)
\(770\) 6.00000 10.3923i 0.216225 0.374513i
\(771\) 0 0
\(772\) 5.00000 + 8.66025i 0.179954 + 0.311689i
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 1.00000 + 1.73205i 0.0358979 + 0.0621770i
\(777\) 0 0
\(778\) −9.00000 + 15.5885i −0.322666 + 0.558873i
\(779\) 0 0
\(780\) 0 0
\(781\) 36.0000 + 62.3538i 1.28818 + 2.23120i
\(782\) 0 0
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) 2.00000 + 3.46410i 0.0713831 + 0.123639i
\(786\) 0 0
\(787\) 14.0000 24.2487i 0.499046 0.864373i −0.500953 0.865474i \(-0.667017\pi\)
0.999999 + 0.00110111i \(0.000350496\pi\)
\(788\) 9.00000 15.5885i 0.320612 0.555316i
\(789\) 0 0
\(790\) −2.00000 3.46410i −0.0711568 0.123247i
\(791\) 12.0000 0.426671
\(792\) 0 0
\(793\) −8.00000 −0.284088
\(794\) −8.00000 13.8564i −0.283909 0.491745i
\(795\) 0 0
\(796\) 8.00000 13.8564i 0.283552 0.491127i
\(797\) −9.00000 + 15.5885i −0.318796 + 0.552171i −0.980237 0.197826i \(-0.936612\pi\)
0.661441 + 0.749997i \(0.269945\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) 36.0000 1.27120
\(803\) 30.0000 + 51.9615i 1.05868 + 1.83368i
\(804\) 0 0
\(805\) 0 0
\(806\) 8.00000 13.8564i 0.281788 0.488071i
\(807\) 0 0
\(808\) −3.00000 5.19615i −0.105540 0.182800i
\(809\) −24.0000 −0.843795 −0.421898 0.906644i \(-0.638636\pi\)
−0.421898 + 0.906644i \(0.638636\pi\)
\(810\) 0 0
\(811\) −52.0000 −1.82597 −0.912983 0.407997i \(-0.866228\pi\)
−0.912983 + 0.407997i \(0.866228\pi\)
\(812\) 6.00000 + 10.3923i 0.210559 + 0.364698i
\(813\) 0 0
\(814\) 24.0000 41.5692i 0.841200 1.45700i
\(815\) −10.0000 + 17.3205i −0.350285 + 0.606711i
\(816\) 0 0
\(817\) 16.0000 + 27.7128i 0.559769 + 0.969549i
\(818\) 22.0000 0.769212
\(819\) 0 0
\(820\) 0 0
\(821\) 15.0000 + 25.9808i 0.523504 + 0.906735i 0.999626 + 0.0273557i \(0.00870868\pi\)
−0.476122 + 0.879379i \(0.657958\pi\)
\(822\) 0 0
\(823\) −7.00000 + 12.1244i −0.244005 + 0.422628i −0.961851 0.273573i \(-0.911795\pi\)
0.717847 + 0.696201i \(0.245128\pi\)
\(824\) 1.00000 1.73205i 0.0348367 0.0603388i
\(825\) 0 0
\(826\) 6.00000 + 10.3923i 0.208767 + 0.361595i
\(827\) 24.0000 0.834562 0.417281 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 0 0
\(829\) 26.0000 0.903017 0.451509 0.892267i \(-0.350886\pi\)
0.451509 + 0.892267i \(0.350886\pi\)
\(830\) 6.00000 + 10.3923i 0.208263 + 0.360722i
\(831\) 0 0
\(832\) 2.00000 3.46410i 0.0693375 0.120096i
\(833\) −9.00000 + 15.5885i −0.311832 + 0.540108i
\(834\) 0 0
\(835\) 12.0000 + 20.7846i 0.415277 + 0.719281i
\(836\) −24.0000 −0.830057
\(837\) 0 0
\(838\) 6.00000 0.207267
\(839\) −24.0000 41.5692i −0.828572 1.43513i −0.899158 0.437623i \(-0.855820\pi\)
0.0705865 0.997506i \(-0.477513\pi\)
\(840\) 0 0
\(841\) −3.50000 + 6.06218i −0.120690 + 0.209041i
\(842\) 7.00000 12.1244i 0.241236 0.417833i
\(843\) 0 0
\(844\) 2.00000 + 3.46410i 0.0688428 + 0.119239i
\(845\) 3.00000 0.103203
\(846\) 0 0
\(847\) 50.0000 1.71802
\(848\) 3.00000 + 5.19615i 0.103020 + 0.178437i
\(849\) 0 0
\(850\) −3.00000 + 5.19615i −0.102899 + 0.178227i
\(851\) 0 0
\(852\) 0 0
\(853\) −4.00000 6.92820i −0.136957 0.237217i 0.789386 0.613897i \(-0.210399\pi\)
−0.926343 + 0.376680i \(0.877066\pi\)
\(854\) −4.00000 −0.136877
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −21.0000 36.3731i −0.717346 1.24248i −0.962048 0.272882i \(-0.912023\pi\)
0.244701 0.969599i \(-0.421310\pi\)
\(858\) 0 0
\(859\) −10.0000 + 17.3205i −0.341196 + 0.590968i −0.984655 0.174512i \(-0.944165\pi\)
0.643459 + 0.765480i \(0.277499\pi\)
\(860\) −4.00000 + 6.92820i −0.136399 + 0.236250i
\(861\) 0 0
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 18.0000 0.612018
\(866\) 19.0000 + 32.9090i 0.645646 + 1.11829i
\(867\) 0 0
\(868\) 4.00000 6.92820i 0.135769 0.235159i
\(869\) 12.0000 20.7846i 0.407072 0.705070i
\(870\) 0 0
\(871\) −8.00000 13.8564i −0.271070 0.469506i
\(872\) −2.00000 −0.0677285
\(873\) 0 0
\(874\) 0 0
\(875\) −1.00000 1.73205i −0.0338062 0.0585540i
\(876\) 0 0
\(877\) 14.0000 24.2487i 0.472746 0.818821i −0.526767 0.850010i \(-0.676596\pi\)
0.999514 + 0.0311889i \(0.00992933\pi\)
\(878\) 4.00000 6.92820i 0.134993 0.233816i
\(879\) 0 0
\(880\) −3.00000 5.19615i −0.101130 0.175162i
\(881\) −36.0000 −1.21287 −0.606435 0.795133i \(-0.707401\pi\)
−0.606435 + 0.795133i \(0.707401\pi\)
\(882\) 0 0
\(883\) −4.00000 −0.134611 −0.0673054 0.997732i \(-0.521440\pi\)
−0.0673054 + 0.997732i \(0.521440\pi\)
\(884\) −12.0000 20.7846i −0.403604 0.699062i
\(885\) 0 0
\(886\) −12.0000 + 20.7846i −0.403148 + 0.698273i
\(887\) −24.0000 + 41.5692i −0.805841 + 1.39576i 0.109881 + 0.993945i \(0.464953\pi\)
−0.915722 + 0.401813i \(0.868380\pi\)
\(888\) 0 0
\(889\) −2.00000 3.46410i −0.0670778 0.116182i
\(890\) −12.0000 −0.402241
\(891\) 0 0
\(892\) 26.0000 0.870544
\(893\) 0 0
\(894\) 0 0
\(895\) −3.00000 + 5.19615i −0.100279 + 0.173688i
\(896\) 1.00000 1.73205i 0.0334077 0.0578638i
\(897\) 0 0
\(898\) −6.00000 10.3923i −0.200223 0.346796i
\(899\) 24.0000 0.800445
\(900\) 0 0
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) 0 0
\(904\) 3.00000 5.19615i 0.0997785 0.172821i
\(905\) −1.00000 + 1.73205i −0.0332411 + 0.0575753i
\(906\) 0 0
\(907\) 20.0000 + 34.6410i 0.664089 + 1.15024i 0.979531 + 0.201291i \(0.0645138\pi\)
−0.315442 + 0.948945i \(0.602153\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 8.00000 0.265197
\(911\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(912\) 0 0
\(913\) −36.0000 + 62.3538i −1.19143 + 2.06361i
\(914\) 13.0000 22.5167i 0.430002 0.744785i
\(915\) 0 0
\(916\) −7.00000 12.1244i −0.231287 0.400600i
\(917\) −12.0000 −0.396275
\(918\) 0 0
\(919\) −52.0000 −1.71532 −0.857661 0.514216i \(-0.828083\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −9.00000 + 15.5885i −0.296399 + 0.513378i
\(923\) −24.0000 + 41.5692i −0.789970 + 1.36827i
\(924\) 0 0
\(925\) −4.00000 6.92820i −0.131519 0.227798i
\(926\) 34.0000 1.11731
\(927\) 0 0
\(928\) 6.00000 0.196960
\(929\) −18.0000 31.1769i −0.590561 1.02288i −0.994157 0.107944i \(-0.965573\pi\)
0.403596 0.914937i \(-0.367760\pi\)
\(930\) 0 0
\(931\) −6.00000 + 10.3923i −0.196642 + 0.340594i
\(932\) 3.00000 5.19615i 0.0982683 0.170206i
\(933\) 0 0
\(934\) −6.00000 10.3923i −0.196326 0.340047i
\(935\) −36.0000 −1.17733
\(936\) 0 0
\(937\) −22.0000 −0.718709 −0.359354 0.933201i \(-0.617003\pi\)
−0.359354 + 0.933201i \(0.617003\pi\)
\(938\) −4.00000 6.92820i −0.130605 0.226214i
\(939\) 0 0
\(940\) 0 0
\(941\) 21.0000 36.3731i 0.684580 1.18573i −0.288988 0.957333i \(-0.593319\pi\)
0.973568 0.228395i \(-0.0733479\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) −48.0000 −1.56061
\(947\) −12.0000 20.7846i −0.389948 0.675409i 0.602494 0.798123i \(-0.294174\pi\)
−0.992442 + 0.122714i \(0.960840\pi\)
\(948\) 0 0
\(949\) −20.0000 + 34.6410i −0.649227 + 1.12449i
\(950\) −2.00000 + 3.46410i −0.0648886 + 0.112390i
\(951\) 0 0
\(952\) −6.00000 10.3923i −0.194461 0.336817i
\(953\) 30.0000 0.971795 0.485898 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) 0 0
\(955\) 12.0000 0.388311
\(956\) 6.00000 + 10.3923i 0.194054 + 0.336111i
\(957\) 0 0
\(958\) 18.0000 31.1769i 0.581554 1.00728i
\(959\) −6.00000 + 10.3923i −0.193750 + 0.335585i
\(960\) 0 0
\(961\) 7.50000 + 12.9904i 0.241935 + 0.419045i
\(962\) 32.0000 1.03172
\(963\) 0 0
\(964\) −10.0000 −0.322078
\(965\) 5.00000 + 8.66025i 0.160956 + 0.278783i
\(966\) 0 0
\(967\) −1.00000 + 1.73205i −0.0321578 + 0.0556990i −0.881656 0.471892i \(-0.843571\pi\)
0.849499 + 0.527591i \(0.176905\pi\)
\(968\) 12.5000 21.6506i 0.401765 0.695878i
\(969\) 0 0
\(970\) 1.00000 + 1.73205i 0.0321081 + 0.0556128i
\(971\) −6.00000 −0.192549 −0.0962746 0.995355i \(-0.530693\pi\)
−0.0962746 + 0.995355i \(0.530693\pi\)
\(972\) 0 0
\(973\) 40.0000 1.28234
\(974\) 19.0000 + 32.9090i 0.608799 + 1.05447i
\(975\) 0 0
\(976\) −1.00000 + 1.73205i −0.0320092 + 0.0554416i
\(977\) 3.00000 5.19615i 0.0959785 0.166240i −0.814038 0.580812i \(-0.802735\pi\)
0.910017 + 0.414572i \(0.136069\pi\)
\(978\) 0 0
\(979\) −36.0000 62.3538i −1.15056 1.99284i
\(980\) −3.00000 −0.0958315
\(981\) 0 0
\(982\) 6.00000 0.191468
\(983\) 24.0000 + 41.5692i 0.765481 + 1.32585i 0.939992 + 0.341197i \(0.110832\pi\)
−0.174511 + 0.984655i \(0.555834\pi\)
\(984\) 0 0
\(985\) 9.00000 15.5885i 0.286764 0.496690i
\(986\) 18.0000 31.1769i 0.573237 0.992875i
\(987\) 0 0
\(988\) −8.00000 13.8564i −0.254514 0.440831i
\(989\) 0 0
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) −2.00000 3.46410i −0.0635001 0.109985i
\(993\) 0 0
\(994\) −12.0000 + 20.7846i −0.380617 + 0.659248i
\(995\) 8.00000 13.8564i 0.253617 0.439278i
\(996\) 0 0
\(997\) −22.0000 38.1051i −0.696747 1.20680i −0.969588 0.244742i \(-0.921297\pi\)
0.272841 0.962059i \(-0.412037\pi\)
\(998\) 4.00000 0.126618
\(999\) 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 810.2.e.h.271.1 2
3.2 odd 2 810.2.e.e.271.1 2
9.2 odd 6 810.2.e.e.541.1 2
9.4 even 3 90.2.a.a.1.1 1
9.5 odd 6 90.2.a.b.1.1 yes 1
9.7 even 3 inner 810.2.e.h.541.1 2
36.23 even 6 720.2.a.b.1.1 1
36.31 odd 6 720.2.a.g.1.1 1
45.4 even 6 450.2.a.e.1.1 1
45.13 odd 12 450.2.c.d.199.2 2
45.14 odd 6 450.2.a.a.1.1 1
45.22 odd 12 450.2.c.d.199.1 2
45.23 even 12 450.2.c.a.199.1 2
45.32 even 12 450.2.c.a.199.2 2
63.13 odd 6 4410.2.a.k.1.1 1
63.41 even 6 4410.2.a.bf.1.1 1
72.5 odd 6 2880.2.a.bf.1.1 1
72.13 even 6 2880.2.a.k.1.1 1
72.59 even 6 2880.2.a.u.1.1 1
72.67 odd 6 2880.2.a.h.1.1 1
180.23 odd 12 3600.2.f.u.2449.2 2
180.59 even 6 3600.2.a.bj.1.1 1
180.67 even 12 3600.2.f.a.2449.1 2
180.103 even 12 3600.2.f.a.2449.2 2
180.139 odd 6 3600.2.a.ba.1.1 1
180.167 odd 12 3600.2.f.u.2449.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
90.2.a.a.1.1 1 9.4 even 3
90.2.a.b.1.1 yes 1 9.5 odd 6
450.2.a.a.1.1 1 45.14 odd 6
450.2.a.e.1.1 1 45.4 even 6
450.2.c.a.199.1 2 45.23 even 12
450.2.c.a.199.2 2 45.32 even 12
450.2.c.d.199.1 2 45.22 odd 12
450.2.c.d.199.2 2 45.13 odd 12
720.2.a.b.1.1 1 36.23 even 6
720.2.a.g.1.1 1 36.31 odd 6
810.2.e.e.271.1 2 3.2 odd 2
810.2.e.e.541.1 2 9.2 odd 6
810.2.e.h.271.1 2 1.1 even 1 trivial
810.2.e.h.541.1 2 9.7 even 3 inner
2880.2.a.h.1.1 1 72.67 odd 6
2880.2.a.k.1.1 1 72.13 even 6
2880.2.a.u.1.1 1 72.59 even 6
2880.2.a.bf.1.1 1 72.5 odd 6
3600.2.a.ba.1.1 1 180.139 odd 6
3600.2.a.bj.1.1 1 180.59 even 6
3600.2.f.a.2449.1 2 180.67 even 12
3600.2.f.a.2449.2 2 180.103 even 12
3600.2.f.u.2449.1 2 180.167 odd 12
3600.2.f.u.2449.2 2 180.23 odd 12
4410.2.a.k.1.1 1 63.13 odd 6
4410.2.a.bf.1.1 1 63.41 even 6