Properties

Label 360.2.bs.a.113.13
Level $360$
Weight $2$
Character 360.113
Analytic conductor $2.875$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(113,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.113");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bs (of order \(12\), degree \(4\), 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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 113.13
Character \(\chi\) \(=\) 360.113
Dual form 360.2.bs.a.137.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.836139 + 1.51686i) q^{3} +(-2.22494 - 0.222822i) q^{5} +(-3.21063 - 0.860287i) q^{7} +(-1.60174 + 2.53662i) q^{9} +O(q^{10})\) \(q+(0.836139 + 1.51686i) q^{3} +(-2.22494 - 0.222822i) q^{5} +(-3.21063 - 0.860287i) q^{7} +(-1.60174 + 2.53662i) q^{9} +(-4.57804 + 2.64314i) q^{11} +(0.0106047 - 0.00284152i) q^{13} +(-1.52237 - 3.56124i) q^{15} +(1.03890 + 1.03890i) q^{17} +1.41336i q^{19} +(-1.37960 - 5.58941i) q^{21} +(2.17810 + 8.12879i) q^{23} +(4.90070 + 0.991532i) q^{25} +(-5.18698 - 0.308662i) q^{27} +(-3.79806 - 6.57844i) q^{29} +(4.47022 - 7.74265i) q^{31} +(-7.83715 - 4.73424i) q^{33} +(6.95177 + 2.62949i) q^{35} +(3.32005 - 3.32005i) q^{37} +(0.0131772 + 0.0137100i) q^{39} +(-0.0575667 - 0.0332362i) q^{41} +(-2.47585 + 9.23998i) q^{43} +(4.12900 - 5.28691i) q^{45} +(-2.64609 + 9.87536i) q^{47} +(3.50590 + 2.02413i) q^{49} +(-0.707201 + 2.44452i) q^{51} +(-3.88735 + 3.88735i) q^{53} +(10.7748 - 4.86072i) q^{55} +(-2.14387 + 1.18176i) q^{57} +(-1.02489 + 1.77516i) q^{59} +(1.37933 + 2.38907i) q^{61} +(7.32483 - 6.76619i) q^{63} +(-0.0242279 + 0.00395924i) q^{65} +(0.704972 + 2.63099i) q^{67} +(-10.5091 + 10.1007i) q^{69} -5.53347i q^{71} +(-2.33627 - 2.33627i) q^{73} +(2.59365 + 8.26275i) q^{75} +(16.9723 - 4.54771i) q^{77} +(-0.510169 + 0.294546i) q^{79} +(-3.86883 - 8.12601i) q^{81} +(-6.39688 - 1.71404i) q^{83} +(-2.07999 - 2.54297i) q^{85} +(6.80288 - 11.2616i) q^{87} +10.0611 q^{89} -0.0364923 q^{91} +(15.4823 + 0.306780i) q^{93} +(0.314927 - 3.14463i) q^{95} +(15.4120 + 4.12964i) q^{97} +(0.628236 - 15.8464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 0
\(3\) 0.836139 + 1.51686i 0.482745 + 0.875761i
\(4\) 0 0
\(5\) −2.22494 0.222822i −0.995023 0.0996492i
\(6\) 0 0
\(7\) −3.21063 0.860287i −1.21351 0.325158i −0.405369 0.914153i \(-0.632857\pi\)
−0.808137 + 0.588995i \(0.799524\pi\)
\(8\) 0 0
\(9\) −1.60174 + 2.53662i −0.533915 + 0.845538i
\(10\) 0 0
\(11\) −4.57804 + 2.64314i −1.38033 + 0.796935i −0.992199 0.124668i \(-0.960214\pi\)
−0.388134 + 0.921603i \(0.626880\pi\)
\(12\) 0 0
\(13\) 0.0106047 0.00284152i 0.00294121 0.000788095i −0.257348 0.966319i \(-0.582849\pi\)
0.260289 + 0.965531i \(0.416182\pi\)
\(14\) 0 0
\(15\) −1.52237 3.56124i −0.393073 0.919507i
\(16\) 0 0
\(17\) 1.03890 + 1.03890i 0.251969 + 0.251969i 0.821778 0.569808i \(-0.192983\pi\)
−0.569808 + 0.821778i \(0.692983\pi\)
\(18\) 0 0
\(19\) 1.41336i 0.324246i 0.986771 + 0.162123i \(0.0518342\pi\)
−0.986771 + 0.162123i \(0.948166\pi\)
\(20\) 0 0
\(21\) −1.37960 5.58941i −0.301053 1.21971i
\(22\) 0 0
\(23\) 2.17810 + 8.12879i 0.454166 + 1.69497i 0.690528 + 0.723305i \(0.257378\pi\)
−0.236363 + 0.971665i \(0.575955\pi\)
\(24\) 0 0
\(25\) 4.90070 + 0.991532i 0.980140 + 0.198306i
\(26\) 0 0
\(27\) −5.18698 0.308662i −0.998234 0.0594020i
\(28\) 0 0
\(29\) −3.79806 6.57844i −0.705283 1.22159i −0.966589 0.256330i \(-0.917487\pi\)
0.261306 0.965256i \(-0.415847\pi\)
\(30\) 0 0
\(31\) 4.47022 7.74265i 0.802875 1.39062i −0.114841 0.993384i \(-0.536636\pi\)
0.917716 0.397236i \(-0.130031\pi\)
\(32\) 0 0
\(33\) −7.83715 4.73424i −1.36427 0.824125i
\(34\) 0 0
\(35\) 6.95177 + 2.62949i 1.17506 + 0.444464i
\(36\) 0 0
\(37\) 3.32005 3.32005i 0.545813 0.545813i −0.379414 0.925227i \(-0.623874\pi\)
0.925227 + 0.379414i \(0.123874\pi\)
\(38\) 0 0
\(39\) 0.0131772 + 0.0137100i 0.00211004 + 0.00219535i
\(40\) 0 0
\(41\) −0.0575667 0.0332362i −0.00899041 0.00519062i 0.495498 0.868609i \(-0.334986\pi\)
−0.504488 + 0.863418i \(0.668319\pi\)
\(42\) 0 0
\(43\) −2.47585 + 9.23998i −0.377563 + 1.40908i 0.472001 + 0.881598i \(0.343532\pi\)
−0.849564 + 0.527486i \(0.823135\pi\)
\(44\) 0 0
\(45\) 4.12900 5.28691i 0.615514 0.788126i
\(46\) 0 0
\(47\) −2.64609 + 9.87536i −0.385972 + 1.44047i 0.450656 + 0.892698i \(0.351190\pi\)
−0.836628 + 0.547771i \(0.815477\pi\)
\(48\) 0 0
\(49\) 3.50590 + 2.02413i 0.500843 + 0.289162i
\(50\) 0 0
\(51\) −0.707201 + 2.44452i −0.0990279 + 0.342302i
\(52\) 0 0
\(53\) −3.88735 + 3.88735i −0.533969 + 0.533969i −0.921751 0.387782i \(-0.873241\pi\)
0.387782 + 0.921751i \(0.373241\pi\)
\(54\) 0 0
\(55\) 10.7748 4.86072i 1.45288 0.655420i
\(56\) 0 0
\(57\) −2.14387 + 1.18176i −0.283962 + 0.156528i
\(58\) 0 0
\(59\) −1.02489 + 1.77516i −0.133429 + 0.231106i −0.924996 0.379976i \(-0.875932\pi\)
0.791567 + 0.611082i \(0.209266\pi\)
\(60\) 0 0
\(61\) 1.37933 + 2.38907i 0.176605 + 0.305889i 0.940716 0.339197i \(-0.110155\pi\)
−0.764111 + 0.645085i \(0.776822\pi\)
\(62\) 0 0
\(63\) 7.32483 6.76619i 0.922842 0.852459i
\(64\) 0 0
\(65\) −0.0242279 + 0.00395924i −0.00300511 + 0.000491083i
\(66\) 0 0
\(67\) 0.704972 + 2.63099i 0.0861260 + 0.321427i 0.995525 0.0944981i \(-0.0301246\pi\)
−0.909399 + 0.415925i \(0.863458\pi\)
\(68\) 0 0
\(69\) −10.5091 + 10.1007i −1.26514 + 1.21598i
\(70\) 0 0
\(71\) 5.53347i 0.656703i −0.944556 0.328351i \(-0.893507\pi\)
0.944556 0.328351i \(-0.106493\pi\)
\(72\) 0 0
\(73\) −2.33627 2.33627i −0.273439 0.273439i 0.557044 0.830483i \(-0.311936\pi\)
−0.830483 + 0.557044i \(0.811936\pi\)
\(74\) 0 0
\(75\) 2.59365 + 8.26275i 0.299489 + 0.954100i
\(76\) 0 0
\(77\) 16.9723 4.54771i 1.93417 0.518260i
\(78\) 0 0
\(79\) −0.510169 + 0.294546i −0.0573985 + 0.0331390i −0.528425 0.848980i \(-0.677217\pi\)
0.471026 + 0.882119i \(0.343884\pi\)
\(80\) 0 0
\(81\) −3.86883 8.12601i −0.429871 0.902891i
\(82\) 0 0
\(83\) −6.39688 1.71404i −0.702149 0.188140i −0.109956 0.993936i \(-0.535071\pi\)
−0.592193 + 0.805796i \(0.701738\pi\)
\(84\) 0 0
\(85\) −2.07999 2.54297i −0.225607 0.275824i
\(86\) 0 0
\(87\) 6.80288 11.2616i 0.729345 1.20737i
\(88\) 0 0
\(89\) 10.0611 1.06647 0.533235 0.845967i \(-0.320976\pi\)
0.533235 + 0.845967i \(0.320976\pi\)
\(90\) 0 0
\(91\) −0.0364923 −0.00382543
\(92\) 0 0
\(93\) 15.4823 + 0.306780i 1.60543 + 0.0318116i
\(94\) 0 0
\(95\) 0.314927 3.14463i 0.0323109 0.322632i
\(96\) 0 0
\(97\) 15.4120 + 4.12964i 1.56485 + 0.419301i 0.934196 0.356760i \(-0.116118\pi\)
0.630658 + 0.776061i \(0.282785\pi\)
\(98\) 0 0
\(99\) 0.628236 15.8464i 0.0631401 1.59262i
\(100\) 0 0
\(101\) −10.2579 + 5.92241i −1.02070 + 0.589301i −0.914307 0.405023i \(-0.867264\pi\)
−0.106393 + 0.994324i \(0.533930\pi\)
\(102\) 0 0
\(103\) −11.7082 + 3.13719i −1.15364 + 0.309117i −0.784423 0.620227i \(-0.787041\pi\)
−0.369217 + 0.929343i \(0.620374\pi\)
\(104\) 0 0
\(105\) 1.82408 + 12.7435i 0.178012 + 1.24364i
\(106\) 0 0
\(107\) 3.81441 + 3.81441i 0.368753 + 0.368753i 0.867022 0.498269i \(-0.166031\pi\)
−0.498269 + 0.867022i \(0.666031\pi\)
\(108\) 0 0
\(109\) 1.04526i 0.100117i 0.998746 + 0.0500587i \(0.0159409\pi\)
−0.998746 + 0.0500587i \(0.984059\pi\)
\(110\) 0 0
\(111\) 7.81209 + 2.26004i 0.741490 + 0.214513i
\(112\) 0 0
\(113\) 2.13774 + 7.97816i 0.201102 + 0.750522i 0.990602 + 0.136773i \(0.0436730\pi\)
−0.789501 + 0.613750i \(0.789660\pi\)
\(114\) 0 0
\(115\) −3.03487 18.5714i −0.283003 1.73179i
\(116\) 0 0
\(117\) −0.00977816 + 0.0314514i −0.000903991 + 0.00290768i
\(118\) 0 0
\(119\) −2.44177 4.22926i −0.223836 0.387696i
\(120\) 0 0
\(121\) 8.47233 14.6745i 0.770212 1.33405i
\(122\) 0 0
\(123\) 0.00228091 0.115111i 0.000205663 0.0103792i
\(124\) 0 0
\(125\) −10.6828 3.29808i −0.955500 0.294990i
\(126\) 0 0
\(127\) −2.00572 + 2.00572i −0.177979 + 0.177979i −0.790474 0.612495i \(-0.790166\pi\)
0.612495 + 0.790474i \(0.290166\pi\)
\(128\) 0 0
\(129\) −16.0859 + 3.97039i −1.41629 + 0.349573i
\(130\) 0 0
\(131\) −1.96773 1.13607i −0.171921 0.0992587i 0.411570 0.911378i \(-0.364980\pi\)
−0.583491 + 0.812119i \(0.698314\pi\)
\(132\) 0 0
\(133\) 1.21589 4.53777i 0.105431 0.393475i
\(134\) 0 0
\(135\) 11.4719 + 1.84253i 0.987346 + 0.158580i
\(136\) 0 0
\(137\) 3.58696 13.3867i 0.306455 1.14370i −0.625231 0.780439i \(-0.714995\pi\)
0.931686 0.363265i \(-0.118338\pi\)
\(138\) 0 0
\(139\) 1.21060 + 0.698941i 0.102682 + 0.0592834i 0.550462 0.834861i \(-0.314452\pi\)
−0.447780 + 0.894144i \(0.647785\pi\)
\(140\) 0 0
\(141\) −17.1921 + 4.24341i −1.44783 + 0.357359i
\(142\) 0 0
\(143\) −0.0410382 + 0.0410382i −0.00343179 + 0.00343179i
\(144\) 0 0
\(145\) 6.98464 + 15.4829i 0.580042 + 1.28579i
\(146\) 0 0
\(147\) −0.138911 + 7.01043i −0.0114572 + 0.578210i
\(148\) 0 0
\(149\) −7.12858 + 12.3471i −0.583996 + 1.01151i 0.411003 + 0.911634i \(0.365178\pi\)
−0.995000 + 0.0998776i \(0.968155\pi\)
\(150\) 0 0
\(151\) −6.63051 11.4844i −0.539583 0.934586i −0.998926 0.0463267i \(-0.985248\pi\)
0.459343 0.888259i \(-0.348085\pi\)
\(152\) 0 0
\(153\) −4.29932 + 0.971234i −0.347580 + 0.0785196i
\(154\) 0 0
\(155\) −11.6712 + 16.2308i −0.937453 + 1.30369i
\(156\) 0 0
\(157\) 4.83404 + 18.0409i 0.385798 + 1.43982i 0.836905 + 0.547349i \(0.184363\pi\)
−0.451106 + 0.892470i \(0.648970\pi\)
\(158\) 0 0
\(159\) −9.14695 2.64621i −0.725400 0.209858i
\(160\) 0 0
\(161\) 27.9724i 2.20453i
\(162\) 0 0
\(163\) −0.256781 0.256781i −0.0201126 0.0201126i 0.696979 0.717092i \(-0.254527\pi\)
−0.717092 + 0.696979i \(0.754527\pi\)
\(164\) 0 0
\(165\) 16.3823 + 12.2797i 1.27536 + 0.955972i
\(166\) 0 0
\(167\) −3.56639 + 0.955610i −0.275975 + 0.0739473i −0.394152 0.919045i \(-0.628962\pi\)
0.118177 + 0.992993i \(0.462295\pi\)
\(168\) 0 0
\(169\) −11.2582 + 6.49994i −0.866017 + 0.499995i
\(170\) 0 0
\(171\) −3.58514 2.26383i −0.274163 0.173120i
\(172\) 0 0
\(173\) 9.99572 + 2.67834i 0.759960 + 0.203631i 0.617932 0.786232i \(-0.287971\pi\)
0.142029 + 0.989863i \(0.454638\pi\)
\(174\) 0 0
\(175\) −14.8814 7.39946i −1.12492 0.559346i
\(176\) 0 0
\(177\) −3.54962 0.0703355i −0.266806 0.00528674i
\(178\) 0 0
\(179\) 3.94287 0.294704 0.147352 0.989084i \(-0.452925\pi\)
0.147352 + 0.989084i \(0.452925\pi\)
\(180\) 0 0
\(181\) −15.9901 −1.18854 −0.594268 0.804267i \(-0.702558\pi\)
−0.594268 + 0.804267i \(0.702558\pi\)
\(182\) 0 0
\(183\) −2.47058 + 4.08984i −0.182630 + 0.302330i
\(184\) 0 0
\(185\) −8.12669 + 6.64713i −0.597486 + 0.488707i
\(186\) 0 0
\(187\) −7.50205 2.01017i −0.548605 0.146998i
\(188\) 0 0
\(189\) 16.3879 + 5.45329i 1.19205 + 0.396668i
\(190\) 0 0
\(191\) 13.6180 7.86236i 0.985364 0.568900i 0.0814788 0.996675i \(-0.474036\pi\)
0.903885 + 0.427775i \(0.140702\pi\)
\(192\) 0 0
\(193\) −18.9076 + 5.06628i −1.36100 + 0.364679i −0.864184 0.503177i \(-0.832164\pi\)
−0.496817 + 0.867856i \(0.665498\pi\)
\(194\) 0 0
\(195\) −0.0262635 0.0334400i −0.00188077 0.00239469i
\(196\) 0 0
\(197\) −5.05729 5.05729i −0.360317 0.360317i 0.503612 0.863930i \(-0.332004\pi\)
−0.863930 + 0.503612i \(0.832004\pi\)
\(198\) 0 0
\(199\) 17.3561i 1.23034i 0.788394 + 0.615171i \(0.210913\pi\)
−0.788394 + 0.615171i \(0.789087\pi\)
\(200\) 0 0
\(201\) −3.40140 + 3.26922i −0.239916 + 0.230593i
\(202\) 0 0
\(203\) 6.53485 + 24.3884i 0.458657 + 1.71173i
\(204\) 0 0
\(205\) 0.120677 + 0.0867755i 0.00842842 + 0.00606067i
\(206\) 0 0
\(207\) −24.1084 7.49523i −1.67565 0.520954i
\(208\) 0 0
\(209\) −3.73569 6.47041i −0.258403 0.447567i
\(210\) 0 0
\(211\) −13.5587 + 23.4844i −0.933421 + 1.61673i −0.155996 + 0.987758i \(0.549859\pi\)
−0.777425 + 0.628975i \(0.783475\pi\)
\(212\) 0 0
\(213\) 8.39352 4.62675i 0.575115 0.317020i
\(214\) 0 0
\(215\) 7.56748 20.0067i 0.516098 1.36445i
\(216\) 0 0
\(217\) −21.0131 + 21.0131i −1.42646 + 1.42646i
\(218\) 0 0
\(219\) 1.59035 5.49724i 0.107466 0.371469i
\(220\) 0 0
\(221\) 0.0139692 + 0.00806513i 0.000939671 + 0.000542519i
\(222\) 0 0
\(223\) 3.20378 11.9567i 0.214541 0.800677i −0.771787 0.635881i \(-0.780637\pi\)
0.986328 0.164796i \(-0.0526965\pi\)
\(224\) 0 0
\(225\) −10.3648 + 10.8430i −0.690987 + 0.722867i
\(226\) 0 0
\(227\) 6.57784 24.5488i 0.436586 1.62936i −0.300655 0.953733i \(-0.597205\pi\)
0.737242 0.675629i \(-0.236128\pi\)
\(228\) 0 0
\(229\) 10.5518 + 6.09206i 0.697280 + 0.402575i 0.806333 0.591461i \(-0.201449\pi\)
−0.109054 + 0.994036i \(0.534782\pi\)
\(230\) 0 0
\(231\) 21.0894 + 21.9421i 1.38758 + 1.44368i
\(232\) 0 0
\(233\) 14.2997 14.2997i 0.936806 0.936806i −0.0613130 0.998119i \(-0.519529\pi\)
0.998119 + 0.0613130i \(0.0195288\pi\)
\(234\) 0 0
\(235\) 8.08785 21.3824i 0.527593 1.39484i
\(236\) 0 0
\(237\) −0.873358 0.527575i −0.0567307 0.0342697i
\(238\) 0 0
\(239\) 12.7785 22.1330i 0.826573 1.43167i −0.0741389 0.997248i \(-0.523621\pi\)
0.900711 0.434418i \(-0.143046\pi\)
\(240\) 0 0
\(241\) 13.5509 + 23.4709i 0.872892 + 1.51189i 0.858991 + 0.511990i \(0.171092\pi\)
0.0139008 + 0.999903i \(0.495575\pi\)
\(242\) 0 0
\(243\) 9.09116 12.6630i 0.583198 0.812330i
\(244\) 0 0
\(245\) −7.34939 5.28477i −0.469536 0.337631i
\(246\) 0 0
\(247\) 0.00401608 + 0.0149882i 0.000255537 + 0.000953677i
\(248\) 0 0
\(249\) −2.74872 11.1364i −0.174193 0.705738i
\(250\) 0 0
\(251\) 8.32014i 0.525163i −0.964910 0.262581i \(-0.915426\pi\)
0.964910 0.262581i \(-0.0845738\pi\)
\(252\) 0 0
\(253\) −31.4569 31.4569i −1.97768 1.97768i
\(254\) 0 0
\(255\) 2.11817 5.28133i 0.132645 0.330730i
\(256\) 0 0
\(257\) −3.27846 + 0.878461i −0.204505 + 0.0547969i −0.359617 0.933100i \(-0.617093\pi\)
0.155112 + 0.987897i \(0.450426\pi\)
\(258\) 0 0
\(259\) −13.5157 + 7.80328i −0.839823 + 0.484872i
\(260\) 0 0
\(261\) 22.7705 + 0.902747i 1.40946 + 0.0558786i
\(262\) 0 0
\(263\) −1.54654 0.414393i −0.0953636 0.0255526i 0.210822 0.977525i \(-0.432386\pi\)
−0.306185 + 0.951972i \(0.599053\pi\)
\(264\) 0 0
\(265\) 9.51531 7.78293i 0.584521 0.478102i
\(266\) 0 0
\(267\) 8.41244 + 15.2612i 0.514833 + 0.933973i
\(268\) 0 0
\(269\) 10.5660 0.644220 0.322110 0.946702i \(-0.395608\pi\)
0.322110 + 0.946702i \(0.395608\pi\)
\(270\) 0 0
\(271\) −0.0835748 −0.00507681 −0.00253840 0.999997i \(-0.500808\pi\)
−0.00253840 + 0.999997i \(0.500808\pi\)
\(272\) 0 0
\(273\) −0.0305126 0.0553538i −0.00184671 0.00335016i
\(274\) 0 0
\(275\) −25.0564 + 8.41393i −1.51096 + 0.507379i
\(276\) 0 0
\(277\) −14.1104 3.78086i −0.847810 0.227170i −0.191342 0.981523i \(-0.561284\pi\)
−0.656469 + 0.754353i \(0.727951\pi\)
\(278\) 0 0
\(279\) 12.4800 + 23.7410i 0.747156 + 1.42133i
\(280\) 0 0
\(281\) −16.4207 + 9.48051i −0.979578 + 0.565560i −0.902143 0.431437i \(-0.858007\pi\)
−0.0774356 + 0.996997i \(0.524673\pi\)
\(282\) 0 0
\(283\) 7.52400 2.01605i 0.447255 0.119842i −0.0281594 0.999603i \(-0.508965\pi\)
0.475415 + 0.879762i \(0.342298\pi\)
\(284\) 0 0
\(285\) 5.03329 2.15165i 0.298147 0.127453i
\(286\) 0 0
\(287\) 0.156233 + 0.156233i 0.00922214 + 0.00922214i
\(288\) 0 0
\(289\) 14.8414i 0.873023i
\(290\) 0 0
\(291\) 6.62250 + 26.8309i 0.388218 + 1.57285i
\(292\) 0 0
\(293\) 3.87427 + 14.4590i 0.226337 + 0.844703i 0.981864 + 0.189585i \(0.0607143\pi\)
−0.755527 + 0.655118i \(0.772619\pi\)
\(294\) 0 0
\(295\) 2.67586 3.72125i 0.155794 0.216660i
\(296\) 0 0
\(297\) 24.5620 12.2968i 1.42523 0.713533i
\(298\) 0 0
\(299\) 0.0461962 + 0.0800142i 0.00267160 + 0.00462734i
\(300\) 0 0
\(301\) 15.8981 27.5363i 0.916349 1.58716i
\(302\) 0 0
\(303\) −17.5605 10.6079i −1.00883 0.609407i
\(304\) 0 0
\(305\) −2.53658 5.62287i −0.145244 0.321965i
\(306\) 0 0
\(307\) −9.29999 + 9.29999i −0.530779 + 0.530779i −0.920804 0.390025i \(-0.872466\pi\)
0.390025 + 0.920804i \(0.372466\pi\)
\(308\) 0 0
\(309\) −14.5483 15.1365i −0.827626 0.861088i
\(310\) 0 0
\(311\) 2.84114 + 1.64033i 0.161106 + 0.0930146i 0.578385 0.815764i \(-0.303683\pi\)
−0.417279 + 0.908778i \(0.637016\pi\)
\(312\) 0 0
\(313\) −0.140261 + 0.523461i −0.00792802 + 0.0295878i −0.969777 0.243995i \(-0.921542\pi\)
0.961849 + 0.273583i \(0.0882087\pi\)
\(314\) 0 0
\(315\) −17.8050 + 13.4222i −1.00320 + 0.756256i
\(316\) 0 0
\(317\) 1.25232 4.67373i 0.0703375 0.262503i −0.921798 0.387670i \(-0.873280\pi\)
0.992136 + 0.125167i \(0.0399467\pi\)
\(318\) 0 0
\(319\) 34.7754 + 20.0776i 1.94705 + 1.12413i
\(320\) 0 0
\(321\) −2.59656 + 8.97531i −0.144926 + 0.500953i
\(322\) 0 0
\(323\) −1.46833 + 1.46833i −0.0817001 + 0.0817001i
\(324\) 0 0
\(325\) 0.0547879 0.00341054i 0.00303908 0.000189182i
\(326\) 0 0
\(327\) −1.58551 + 0.873980i −0.0876790 + 0.0483312i
\(328\) 0 0
\(329\) 16.9913 29.4298i 0.936760 1.62252i
\(330\) 0 0
\(331\) 4.54691 + 7.87548i 0.249921 + 0.432876i 0.963504 0.267695i \(-0.0862620\pi\)
−0.713583 + 0.700571i \(0.752929\pi\)
\(332\) 0 0
\(333\) 3.10382 + 13.7396i 0.170088 + 0.752924i
\(334\) 0 0
\(335\) −0.982275 6.01087i −0.0536674 0.328409i
\(336\) 0 0
\(337\) −4.26314 15.9103i −0.232228 0.866687i −0.979379 0.202033i \(-0.935245\pi\)
0.747151 0.664655i \(-0.231421\pi\)
\(338\) 0 0
\(339\) −10.3143 + 9.91351i −0.560197 + 0.538428i
\(340\) 0 0
\(341\) 47.2616i 2.55936i
\(342\) 0 0
\(343\) 6.93760 + 6.93760i 0.374595 + 0.374595i
\(344\) 0 0
\(345\) 25.6327 20.1317i 1.38002 1.08386i
\(346\) 0 0
\(347\) 9.87351 2.64560i 0.530038 0.142023i 0.0161322 0.999870i \(-0.494865\pi\)
0.513906 + 0.857847i \(0.328198\pi\)
\(348\) 0 0
\(349\) 26.7834 15.4634i 1.43368 0.827736i 0.436282 0.899810i \(-0.356295\pi\)
0.997399 + 0.0720741i \(0.0229618\pi\)
\(350\) 0 0
\(351\) −0.0558833 + 0.0114656i −0.00298283 + 0.000611990i
\(352\) 0 0
\(353\) 18.1173 + 4.85451i 0.964285 + 0.258379i 0.706413 0.707800i \(-0.250312\pi\)
0.257872 + 0.966179i \(0.416979\pi\)
\(354\) 0 0
\(355\) −1.23298 + 12.3116i −0.0654399 + 0.653434i
\(356\) 0 0
\(357\) 4.37356 7.24008i 0.231473 0.383185i
\(358\) 0 0
\(359\) −28.2779 −1.49245 −0.746226 0.665693i \(-0.768136\pi\)
−0.746226 + 0.665693i \(0.768136\pi\)
\(360\) 0 0
\(361\) 17.0024 0.894864
\(362\) 0 0
\(363\) 29.3432 + 0.581435i 1.54012 + 0.0305174i
\(364\) 0 0
\(365\) 4.67748 + 5.71862i 0.244830 + 0.299326i
\(366\) 0 0
\(367\) 15.8161 + 4.23791i 0.825593 + 0.221217i 0.646790 0.762668i \(-0.276111\pi\)
0.178803 + 0.983885i \(0.442778\pi\)
\(368\) 0 0
\(369\) 0.176514 0.0927888i 0.00918898 0.00483039i
\(370\) 0 0
\(371\) 15.8251 9.13663i 0.821599 0.474350i
\(372\) 0 0
\(373\) −16.2614 + 4.35722i −0.841982 + 0.225608i −0.653934 0.756551i \(-0.726883\pi\)
−0.188048 + 0.982160i \(0.560216\pi\)
\(374\) 0 0
\(375\) −3.92958 18.9620i −0.202923 0.979195i
\(376\) 0 0
\(377\) −0.0589701 0.0589701i −0.00303711 0.00303711i
\(378\) 0 0
\(379\) 27.2839i 1.40148i −0.713417 0.700740i \(-0.752853\pi\)
0.713417 0.700740i \(-0.247147\pi\)
\(380\) 0 0
\(381\) −4.71947 1.36534i −0.241786 0.0699486i
\(382\) 0 0
\(383\) 2.73374 + 10.2025i 0.139688 + 0.521321i 0.999935 + 0.0114437i \(0.00364271\pi\)
−0.860247 + 0.509878i \(0.829691\pi\)
\(384\) 0 0
\(385\) −38.7756 + 6.33657i −1.97619 + 0.322941i
\(386\) 0 0
\(387\) −19.4726 21.0803i −0.989848 1.07157i
\(388\) 0 0
\(389\) 2.16870 + 3.75630i 0.109957 + 0.190452i 0.915753 0.401742i \(-0.131595\pi\)
−0.805795 + 0.592194i \(0.798262\pi\)
\(390\) 0 0
\(391\) −6.18215 + 10.7078i −0.312645 + 0.541516i
\(392\) 0 0
\(393\) 0.0779655 3.93468i 0.00393284 0.198478i
\(394\) 0 0
\(395\) 1.20073 0.541670i 0.0604151 0.0272544i
\(396\) 0 0
\(397\) −7.18346 + 7.18346i −0.360527 + 0.360527i −0.864007 0.503480i \(-0.832053\pi\)
0.503480 + 0.864007i \(0.332053\pi\)
\(398\) 0 0
\(399\) 7.89983 1.94987i 0.395486 0.0976154i
\(400\) 0 0
\(401\) 0.145839 + 0.0842005i 0.00728288 + 0.00420477i 0.503637 0.863915i \(-0.331995\pi\)
−0.496354 + 0.868120i \(0.665328\pi\)
\(402\) 0 0
\(403\) 0.0254044 0.0948106i 0.00126548 0.00472285i
\(404\) 0 0
\(405\) 6.79726 + 18.9419i 0.337759 + 0.941233i
\(406\) 0 0
\(407\) −6.42400 + 23.9747i −0.318426 + 1.18838i
\(408\) 0 0
\(409\) 3.84998 + 2.22278i 0.190369 + 0.109910i 0.592155 0.805824i \(-0.298277\pi\)
−0.401786 + 0.915733i \(0.631611\pi\)
\(410\) 0 0
\(411\) 23.3050 5.75223i 1.14955 0.283736i
\(412\) 0 0
\(413\) 4.81769 4.81769i 0.237063 0.237063i
\(414\) 0 0
\(415\) 13.8507 + 5.23900i 0.679906 + 0.257172i
\(416\) 0 0
\(417\) −0.0479666 + 2.42073i −0.00234893 + 0.118544i
\(418\) 0 0
\(419\) 13.7355 23.7906i 0.671024 1.16225i −0.306590 0.951842i \(-0.599188\pi\)
0.977614 0.210406i \(-0.0674785\pi\)
\(420\) 0 0
\(421\) −4.83154 8.36847i −0.235475 0.407854i 0.723936 0.689867i \(-0.242331\pi\)
−0.959411 + 0.282013i \(0.908998\pi\)
\(422\) 0 0
\(423\) −20.8116 22.5299i −1.01190 1.09544i
\(424\) 0 0
\(425\) 4.06122 + 6.12142i 0.196998 + 0.296932i
\(426\) 0 0
\(427\) −2.37324 8.85704i −0.114849 0.428622i
\(428\) 0 0
\(429\) −0.0965630 0.0279357i −0.00466211 0.00134875i
\(430\) 0 0
\(431\) 7.32261i 0.352718i 0.984326 + 0.176359i \(0.0564319\pi\)
−0.984326 + 0.176359i \(0.943568\pi\)
\(432\) 0 0
\(433\) 18.5489 + 18.5489i 0.891403 + 0.891403i 0.994655 0.103252i \(-0.0329248\pi\)
−0.103252 + 0.994655i \(0.532925\pi\)
\(434\) 0 0
\(435\) −17.6453 + 23.5406i −0.846029 + 1.12869i
\(436\) 0 0
\(437\) −11.4889 + 3.07844i −0.549588 + 0.147262i
\(438\) 0 0
\(439\) 0.757943 0.437599i 0.0361747 0.0208854i −0.481804 0.876279i \(-0.660018\pi\)
0.517978 + 0.855394i \(0.326685\pi\)
\(440\) 0 0
\(441\) −10.7500 + 5.65098i −0.511905 + 0.269094i
\(442\) 0 0
\(443\) −3.69784 0.990833i −0.175690 0.0470759i 0.169902 0.985461i \(-0.445655\pi\)
−0.345591 + 0.938385i \(0.612322\pi\)
\(444\) 0 0
\(445\) −22.3852 2.24183i −1.06116 0.106273i
\(446\) 0 0
\(447\) −24.6893 0.489217i −1.16776 0.0231392i
\(448\) 0 0
\(449\) 19.1148 0.902084 0.451042 0.892503i \(-0.351052\pi\)
0.451042 + 0.892503i \(0.351052\pi\)
\(450\) 0 0
\(451\) 0.351391 0.0165463
\(452\) 0 0
\(453\) 11.8762 19.6601i 0.557992 0.923712i
\(454\) 0 0
\(455\) 0.0811931 + 0.00813130i 0.00380639 + 0.000381201i
\(456\) 0 0
\(457\) 30.3972 + 8.14491i 1.42192 + 0.381003i 0.886165 0.463370i \(-0.153360\pi\)
0.535756 + 0.844373i \(0.320027\pi\)
\(458\) 0 0
\(459\) −5.06806 5.70940i −0.236557 0.266492i
\(460\) 0 0
\(461\) −12.1639 + 7.02285i −0.566531 + 0.327087i −0.755763 0.654846i \(-0.772734\pi\)
0.189232 + 0.981932i \(0.439400\pi\)
\(462\) 0 0
\(463\) −28.6925 + 7.68813i −1.33345 + 0.357298i −0.854002 0.520270i \(-0.825831\pi\)
−0.479452 + 0.877568i \(0.659165\pi\)
\(464\) 0 0
\(465\) −34.3787 4.13236i −1.59427 0.191634i
\(466\) 0 0
\(467\) 2.29536 + 2.29536i 0.106216 + 0.106216i 0.758218 0.652001i \(-0.226070\pi\)
−0.652001 + 0.758218i \(0.726070\pi\)
\(468\) 0 0
\(469\) 9.05362i 0.418058i
\(470\) 0 0
\(471\) −23.3236 + 22.4173i −1.07470 + 1.03293i
\(472\) 0 0
\(473\) −13.0880 48.8450i −0.601786 2.24590i
\(474\) 0 0
\(475\) −1.40139 + 6.92644i −0.0643001 + 0.317807i
\(476\) 0 0
\(477\) −3.63418 16.0873i −0.166398 0.736585i
\(478\) 0 0
\(479\) 1.90847 + 3.30557i 0.0872003 + 0.151035i 0.906327 0.422578i \(-0.138875\pi\)
−0.819126 + 0.573613i \(0.805541\pi\)
\(480\) 0 0
\(481\) 0.0257741 0.0446421i 0.00117520 0.00203550i
\(482\) 0 0
\(483\) 42.4302 23.3888i 1.93064 1.06423i
\(484\) 0 0
\(485\) −33.3706 12.6223i −1.51528 0.573151i
\(486\) 0 0
\(487\) 0.907013 0.907013i 0.0411007 0.0411007i −0.686258 0.727358i \(-0.740748\pi\)
0.727358 + 0.686258i \(0.240748\pi\)
\(488\) 0 0
\(489\) 0.174797 0.604206i 0.00790459 0.0273231i
\(490\) 0 0
\(491\) −26.7642 15.4523i −1.20785 0.697354i −0.245563 0.969381i \(-0.578973\pi\)
−0.962290 + 0.272026i \(0.912306\pi\)
\(492\) 0 0
\(493\) 2.88852 10.7801i 0.130092 0.485512i
\(494\) 0 0
\(495\) −4.92871 + 35.1172i −0.221529 + 1.57840i
\(496\) 0 0
\(497\) −4.76038 + 17.7660i −0.213532 + 0.796912i
\(498\) 0 0
\(499\) 34.6894 + 20.0280i 1.55291 + 0.896574i 0.997903 + 0.0647306i \(0.0206188\pi\)
0.555010 + 0.831844i \(0.312715\pi\)
\(500\) 0 0
\(501\) −4.43152 4.61069i −0.197986 0.205991i
\(502\) 0 0
\(503\) −13.8659 + 13.8659i −0.618248 + 0.618248i −0.945082 0.326834i \(-0.894018\pi\)
0.326834 + 0.945082i \(0.394018\pi\)
\(504\) 0 0
\(505\) 24.1429 10.8913i 1.07434 0.484656i
\(506\) 0 0
\(507\) −19.2730 11.6423i −0.855942 0.517054i
\(508\) 0 0
\(509\) −15.0026 + 25.9852i −0.664978 + 1.15178i 0.314313 + 0.949319i \(0.398226\pi\)
−0.979291 + 0.202457i \(0.935108\pi\)
\(510\) 0 0
\(511\) 5.49104 + 9.51076i 0.242909 + 0.420731i
\(512\) 0 0
\(513\) 0.436249 7.33105i 0.0192609 0.323674i
\(514\) 0 0
\(515\) 26.7490 4.37122i 1.17870 0.192619i
\(516\) 0 0
\(517\) −13.9880 52.2038i −0.615190 2.29592i
\(518\) 0 0
\(519\) 4.29513 + 17.4016i 0.188535 + 0.763845i
\(520\) 0 0
\(521\) 21.0626i 0.922769i 0.887200 + 0.461384i \(0.152647\pi\)
−0.887200 + 0.461384i \(0.847353\pi\)
\(522\) 0 0
\(523\) 20.7483 + 20.7483i 0.907258 + 0.907258i 0.996050 0.0887920i \(-0.0283006\pi\)
−0.0887920 + 0.996050i \(0.528301\pi\)
\(524\) 0 0
\(525\) −1.21892 28.7599i −0.0531981 1.25519i
\(526\) 0 0
\(527\) 12.6879 3.39971i 0.552693 0.148094i
\(528\) 0 0
\(529\) −41.4145 + 23.9107i −1.80063 + 1.03960i
\(530\) 0 0
\(531\) −2.86129 5.44310i −0.124169 0.236210i
\(532\) 0 0
\(533\) −0.000704918 0 0.000188882i −3.05334e−5 0 8.18140e-6i
\(534\) 0 0
\(535\) −7.63689 9.33676i −0.330172 0.403664i
\(536\) 0 0
\(537\) 3.29678 + 5.98078i 0.142267 + 0.258090i
\(538\) 0 0
\(539\) −21.4002 −0.921774
\(540\) 0 0
\(541\) 11.6900 0.502590 0.251295 0.967911i \(-0.419144\pi\)
0.251295 + 0.967911i \(0.419144\pi\)
\(542\) 0 0
\(543\) −13.3700 24.2548i −0.573760 1.04087i
\(544\) 0 0
\(545\) 0.232907 2.32563i 0.00997663 0.0996192i
\(546\) 0 0
\(547\) 10.4949 + 2.81211i 0.448731 + 0.120237i 0.476105 0.879388i \(-0.342048\pi\)
−0.0273747 + 0.999625i \(0.508715\pi\)
\(548\) 0 0
\(549\) −8.26948 0.327847i −0.352933 0.0139922i
\(550\) 0 0
\(551\) 9.29768 5.36802i 0.396095 0.228685i
\(552\) 0 0
\(553\) 1.89136 0.506789i 0.0804288 0.0215508i
\(554\) 0 0
\(555\) −16.8778 6.76915i −0.716424 0.287334i
\(556\) 0 0
\(557\) 20.1366 + 20.1366i 0.853213 + 0.853213i 0.990528 0.137314i \(-0.0438470\pi\)
−0.137314 + 0.990528i \(0.543847\pi\)
\(558\) 0 0
\(559\) 0.105022i 0.00444197i
\(560\) 0 0
\(561\) −3.22361 13.0604i −0.136101 0.551409i
\(562\) 0 0
\(563\) −0.103875 0.387669i −0.00437783 0.0163383i 0.963702 0.266979i \(-0.0860254\pi\)
−0.968080 + 0.250641i \(0.919359\pi\)
\(564\) 0 0
\(565\) −2.97863 18.2273i −0.125312 0.766826i
\(566\) 0 0
\(567\) 5.43071 + 29.4180i 0.228068 + 1.23544i
\(568\) 0 0
\(569\) 17.1817 + 29.7596i 0.720295 + 1.24759i 0.960882 + 0.276959i \(0.0893267\pi\)
−0.240587 + 0.970628i \(0.577340\pi\)
\(570\) 0 0
\(571\) 18.3967 31.8640i 0.769878 1.33347i −0.167751 0.985829i \(-0.553650\pi\)
0.937629 0.347638i \(-0.113016\pi\)
\(572\) 0 0
\(573\) 23.3127 + 14.0826i 0.973900 + 0.588310i
\(574\) 0 0
\(575\) 2.61427 + 41.9964i 0.109023 + 1.75137i
\(576\) 0 0
\(577\) −27.4388 + 27.4388i −1.14229 + 1.14229i −0.154262 + 0.988030i \(0.549300\pi\)
−0.988030 + 0.154262i \(0.950700\pi\)
\(578\) 0 0
\(579\) −23.4942 24.4441i −0.976387 1.01586i
\(580\) 0 0
\(581\) 19.0635 + 11.0063i 0.790886 + 0.456619i
\(582\) 0 0
\(583\) 7.52168 28.0713i 0.311516 1.16259i
\(584\) 0 0
\(585\) 0.0287639 0.0677986i 0.00118924 0.00280313i
\(586\) 0 0
\(587\) 1.19051 4.44305i 0.0491377 0.183384i −0.936995 0.349342i \(-0.886405\pi\)
0.986133 + 0.165958i \(0.0530717\pi\)
\(588\) 0 0
\(589\) 10.9431 + 6.31801i 0.450903 + 0.260329i
\(590\) 0 0
\(591\) 3.44262 11.8998i 0.141610 0.489493i
\(592\) 0 0
\(593\) −29.2955 + 29.2955i −1.20302 + 1.20302i −0.229782 + 0.973242i \(0.573801\pi\)
−0.973242 + 0.229782i \(0.926199\pi\)
\(594\) 0 0
\(595\) 4.49040 + 9.95393i 0.184089 + 0.408071i
\(596\) 0 0
\(597\) −26.3268 + 14.5121i −1.07749 + 0.593941i
\(598\) 0 0
\(599\) −13.0523 + 22.6072i −0.533301 + 0.923704i 0.465943 + 0.884815i \(0.345715\pi\)
−0.999244 + 0.0388889i \(0.987618\pi\)
\(600\) 0 0
\(601\) 10.2193 + 17.7004i 0.416855 + 0.722014i 0.995621 0.0934795i \(-0.0297990\pi\)
−0.578766 + 0.815494i \(0.696466\pi\)
\(602\) 0 0
\(603\) −7.80299 2.42593i −0.317762 0.0987915i
\(604\) 0 0
\(605\) −22.1202 + 30.7620i −0.899315 + 1.25065i
\(606\) 0 0
\(607\) 3.47319 + 12.9621i 0.140973 + 0.526117i 0.999902 + 0.0140223i \(0.00446357\pi\)
−0.858929 + 0.512094i \(0.828870\pi\)
\(608\) 0 0
\(609\) −31.5298 + 30.3046i −1.27765 + 1.22800i
\(610\) 0 0
\(611\) 0.112244i 0.00454091i
\(612\) 0 0
\(613\) 1.02234 + 1.02234i 0.0412919 + 0.0412919i 0.727451 0.686159i \(-0.240705\pi\)
−0.686159 + 0.727451i \(0.740705\pi\)
\(614\) 0 0
\(615\) −0.0307242 + 0.255606i −0.00123892 + 0.0103070i
\(616\) 0 0
\(617\) −27.3812 + 7.33677i −1.10233 + 0.295367i −0.763712 0.645558i \(-0.776625\pi\)
−0.338615 + 0.940925i \(0.609958\pi\)
\(618\) 0 0
\(619\) −11.8445 + 6.83845i −0.476073 + 0.274861i −0.718778 0.695239i \(-0.755298\pi\)
0.242706 + 0.970100i \(0.421965\pi\)
\(620\) 0 0
\(621\) −8.78872 42.8361i −0.352679 1.71896i
\(622\) 0 0
\(623\) −32.3024 8.65540i −1.29417 0.346771i
\(624\) 0 0
\(625\) 23.0337 + 9.71841i 0.921349 + 0.388736i
\(626\) 0 0
\(627\) 6.69116 11.0767i 0.267219 0.442360i
\(628\) 0 0
\(629\) 6.89838 0.275056
\(630\) 0 0
\(631\) −20.5918 −0.819746 −0.409873 0.912143i \(-0.634427\pi\)
−0.409873 + 0.912143i \(0.634427\pi\)
\(632\) 0 0
\(633\) −46.9596 0.930501i −1.86648 0.0369841i
\(634\) 0 0
\(635\) 4.90953 4.01569i 0.194829 0.159358i
\(636\) 0 0
\(637\) 0.0429306 + 0.0115032i 0.00170097 + 0.000455774i
\(638\) 0 0
\(639\) 14.0363 + 8.86321i 0.555267 + 0.350623i
\(640\) 0 0
\(641\) −9.83627 + 5.67897i −0.388509 + 0.224306i −0.681514 0.731805i \(-0.738678\pi\)
0.293005 + 0.956111i \(0.405345\pi\)
\(642\) 0 0
\(643\) 21.3604 5.72351i 0.842373 0.225713i 0.188269 0.982118i \(-0.439712\pi\)
0.654104 + 0.756404i \(0.273046\pi\)
\(644\) 0 0
\(645\) 36.6749 5.24957i 1.44407 0.206701i
\(646\) 0 0
\(647\) 0.0725336 + 0.0725336i 0.00285159 + 0.00285159i 0.708531 0.705680i \(-0.249358\pi\)
−0.705680 + 0.708531i \(0.749358\pi\)
\(648\) 0 0
\(649\) 10.8357i 0.425337i
\(650\) 0 0
\(651\) −49.4439 14.3041i −1.93786 0.560623i
\(652\) 0 0
\(653\) −0.275111 1.02673i −0.0107659 0.0401790i 0.960334 0.278853i \(-0.0899541\pi\)
−0.971100 + 0.238674i \(0.923287\pi\)
\(654\) 0 0
\(655\) 4.12493 + 2.96614i 0.161174 + 0.115896i
\(656\) 0 0
\(657\) 9.66831 2.18411i 0.377197 0.0852102i
\(658\) 0 0
\(659\) −19.1407 33.1526i −0.745615 1.29144i −0.949907 0.312533i \(-0.898823\pi\)
0.204292 0.978910i \(-0.434511\pi\)
\(660\) 0 0
\(661\) 2.12766 3.68521i 0.0827562 0.143338i −0.821677 0.569954i \(-0.806961\pi\)
0.904433 + 0.426616i \(0.140294\pi\)
\(662\) 0 0
\(663\) −0.000553489 0.0279329i −2.14957e−5 0.00108483i
\(664\) 0 0
\(665\) −3.71640 + 9.82533i −0.144116 + 0.381010i
\(666\) 0 0
\(667\) 45.2022 45.2022i 1.75024 1.75024i
\(668\) 0 0
\(669\) 20.8154 5.13774i 0.804770 0.198636i
\(670\) 0 0
\(671\) −12.6293 7.29150i −0.487547 0.281485i
\(672\) 0 0
\(673\) 3.02542 11.2910i 0.116621 0.435237i −0.882782 0.469783i \(-0.844332\pi\)
0.999403 + 0.0345464i \(0.0109986\pi\)
\(674\) 0 0
\(675\) −25.1138 6.65572i −0.966629 0.256179i
\(676\) 0 0
\(677\) 3.06941 11.4552i 0.117967 0.440258i −0.881525 0.472138i \(-0.843483\pi\)
0.999492 + 0.0318792i \(0.0101492\pi\)
\(678\) 0 0
\(679\) −45.9297 26.5175i −1.76262 1.01765i
\(680\) 0 0
\(681\) 42.7372 10.5485i 1.63769 0.404221i
\(682\) 0 0
\(683\) 13.0019 13.0019i 0.497505 0.497505i −0.413156 0.910660i \(-0.635573\pi\)
0.910660 + 0.413156i \(0.135573\pi\)
\(684\) 0 0
\(685\) −10.9636 + 28.9854i −0.418898 + 1.10747i
\(686\) 0 0
\(687\) −0.418083 + 21.0994i −0.0159509 + 0.804991i
\(688\) 0 0
\(689\) −0.0301782 + 0.0522702i −0.00114970 + 0.00199133i
\(690\) 0 0
\(691\) −8.55175 14.8121i −0.325324 0.563478i 0.656254 0.754540i \(-0.272140\pi\)
−0.981578 + 0.191062i \(0.938807\pi\)
\(692\) 0 0
\(693\) −15.6495 + 50.3364i −0.594474 + 1.91212i
\(694\) 0 0
\(695\) −2.53778 1.82485i −0.0962633 0.0692205i
\(696\) 0 0
\(697\) −0.0252769 0.0943347i −0.000957431 0.00357318i
\(698\) 0 0
\(699\) 33.6473 + 9.73415i 1.27266 + 0.368180i
\(700\) 0 0
\(701\) 15.2554i 0.576189i 0.957602 + 0.288094i \(0.0930217\pi\)
−0.957602 + 0.288094i \(0.906978\pi\)
\(702\) 0 0
\(703\) 4.69242 + 4.69242i 0.176978 + 0.176978i
\(704\) 0 0
\(705\) 39.1968 5.61055i 1.47624 0.211305i
\(706\) 0 0
\(707\) 38.0294 10.1899i 1.43024 0.383232i
\(708\) 0 0
\(709\) −10.6295 + 6.13692i −0.399198 + 0.230477i −0.686138 0.727472i \(-0.740695\pi\)
0.286940 + 0.957949i \(0.407362\pi\)
\(710\) 0 0
\(711\) 0.0700095 1.76589i 0.00262556 0.0662261i
\(712\) 0 0
\(713\) 72.6749 + 19.4732i 2.72170 + 0.729277i
\(714\) 0 0
\(715\) 0.100452 0.0821633i 0.00375668 0.00307273i
\(716\) 0 0
\(717\) 44.2573 + 0.876956i 1.65282 + 0.0327505i
\(718\) 0 0
\(719\) 34.5290 1.28771 0.643857 0.765146i \(-0.277333\pi\)
0.643857 + 0.765146i \(0.277333\pi\)
\(720\) 0 0
\(721\) 40.2895 1.50046
\(722\) 0 0
\(723\) −24.2717 + 40.1798i −0.902673 + 1.49430i
\(724\) 0 0
\(725\) −12.0904 36.0049i −0.449028 1.33719i
\(726\) 0 0
\(727\) 50.0060 + 13.3991i 1.85462 + 0.496944i 0.999760 0.0219129i \(-0.00697566\pi\)
0.854861 + 0.518857i \(0.173642\pi\)
\(728\) 0 0
\(729\) 26.8095 + 3.20205i 0.992943 + 0.118594i
\(730\) 0 0
\(731\) −12.1715 + 7.02723i −0.450180 + 0.259912i
\(732\) 0 0
\(733\) 16.1801 4.33544i 0.597625 0.160133i 0.0526892 0.998611i \(-0.483221\pi\)
0.544936 + 0.838478i \(0.316554\pi\)
\(734\) 0 0
\(735\) 1.87115 15.5668i 0.0690184 0.574191i
\(736\) 0 0
\(737\) −10.1815 10.1815i −0.375039 0.375039i
\(738\) 0 0
\(739\) 20.6951i 0.761283i −0.924723 0.380642i \(-0.875703\pi\)
0.924723 0.380642i \(-0.124297\pi\)
\(740\) 0 0
\(741\) −0.0193770 + 0.0186241i −0.000711834 + 0.000684172i
\(742\) 0 0
\(743\) −12.9451 48.3118i −0.474910 1.77239i −0.621738 0.783225i \(-0.713573\pi\)
0.146828 0.989162i \(-0.453094\pi\)
\(744\) 0 0
\(745\) 18.6119 25.8831i 0.681886 0.948282i
\(746\) 0 0
\(747\) 14.5940 13.4810i 0.533967 0.493243i
\(748\) 0 0
\(749\) −8.96519 15.5282i −0.327581 0.567387i
\(750\) 0 0
\(751\) −10.0420 + 17.3933i −0.366438 + 0.634690i −0.989006 0.147876i \(-0.952756\pi\)
0.622568 + 0.782566i \(0.286090\pi\)
\(752\) 0 0
\(753\) 12.6205 6.95679i 0.459917 0.253520i
\(754\) 0 0
\(755\) 12.1935 + 27.0295i 0.443767 + 0.983703i
\(756\) 0 0
\(757\) −8.40854 + 8.40854i −0.305614 + 0.305614i −0.843205 0.537592i \(-0.819334\pi\)
0.537592 + 0.843205i \(0.319334\pi\)
\(758\) 0 0
\(759\) 21.4135 74.0182i 0.777260 2.68669i
\(760\) 0 0
\(761\) −9.59644 5.54051i −0.347871 0.200843i 0.315876 0.948800i \(-0.397702\pi\)
−0.663747 + 0.747957i \(0.731035\pi\)
\(762\) 0 0
\(763\) 0.899221 3.35594i 0.0325540 0.121493i
\(764\) 0 0
\(765\) 9.78214 1.20295i 0.353674 0.0434928i
\(766\) 0 0
\(767\) −0.00582448 + 0.0217372i −0.000210310 + 0.000784886i
\(768\) 0 0
\(769\) −30.4335 17.5708i −1.09746 0.633618i −0.161907 0.986806i \(-0.551764\pi\)
−0.935553 + 0.353188i \(0.885098\pi\)
\(770\) 0 0
\(771\) −4.07375 4.23846i −0.146713 0.152644i
\(772\) 0 0
\(773\) −26.2350 + 26.2350i −0.943606 + 0.943606i −0.998493 0.0548870i \(-0.982520\pi\)
0.0548870 + 0.998493i \(0.482520\pi\)
\(774\) 0 0
\(775\) 29.5843 33.5120i 1.06270 1.20379i
\(776\) 0 0
\(777\) −23.1375 13.9768i −0.830052 0.501415i
\(778\) 0 0
\(779\) 0.0469745 0.0813623i 0.00168304 0.00291511i
\(780\) 0 0
\(781\) 14.6257 + 25.3325i 0.523350 + 0.906468i
\(782\) 0 0
\(783\) 17.6700 + 35.2945i 0.631473 + 1.26132i
\(784\) 0 0
\(785\) −6.73553 41.2170i −0.240401 1.47110i
\(786\) 0 0
\(787\) −3.04748 11.3733i −0.108631 0.405416i 0.890101 0.455764i \(-0.150634\pi\)
−0.998732 + 0.0503475i \(0.983967\pi\)
\(788\) 0 0
\(789\) −0.664542 2.69237i −0.0236583 0.0958511i
\(790\) 0 0
\(791\) 27.4540i 0.976153i
\(792\) 0 0
\(793\) 0.0214159 + 0.0214159i 0.000760502 + 0.000760502i
\(794\) 0 0
\(795\) 19.7618 + 7.92581i 0.700877 + 0.281099i
\(796\) 0 0
\(797\) −1.29699 + 0.347528i −0.0459419 + 0.0123101i −0.281717 0.959498i \(-0.590904\pi\)
0.235775 + 0.971808i \(0.424237\pi\)
\(798\) 0 0
\(799\) −13.0085 + 7.51045i −0.460207 + 0.265701i
\(800\) 0 0
\(801\) −16.1152 + 25.5210i −0.569404 + 0.901742i
\(802\) 0 0
\(803\) 16.8706 + 4.52046i 0.595351 + 0.159524i
\(804\) 0 0
\(805\) −6.23287 + 62.2368i −0.219680 + 2.19356i
\(806\) 0 0
\(807\) 8.83463 + 16.0272i 0.310994 + 0.564182i
\(808\) 0 0
\(809\) 27.2154 0.956842 0.478421 0.878131i \(-0.341209\pi\)
0.478421 + 0.878131i \(0.341209\pi\)
\(810\) 0 0
\(811\) −55.3129 −1.94230 −0.971150 0.238471i \(-0.923354\pi\)
−0.971150 + 0.238471i \(0.923354\pi\)
\(812\) 0 0
\(813\) −0.0698802 0.126772i −0.00245080 0.00444607i
\(814\) 0 0
\(815\) 0.514105 + 0.628539i 0.0180083 + 0.0220167i
\(816\) 0 0
\(817\) −13.0594 3.49925i −0.456890 0.122423i
\(818\) 0 0
\(819\) 0.0584513 0.0925669i 0.00204245 0.00323455i
\(820\) 0 0
\(821\) 35.8123 20.6762i 1.24986 0.721605i 0.278776 0.960356i \(-0.410071\pi\)
0.971081 + 0.238751i \(0.0767378\pi\)
\(822\) 0 0
\(823\) −20.4930 + 5.49108i −0.714341 + 0.191407i −0.597645 0.801761i \(-0.703897\pi\)
−0.116696 + 0.993168i \(0.537230\pi\)
\(824\) 0 0
\(825\) −33.7134 30.9719i −1.17375 1.07830i
\(826\) 0 0
\(827\) −18.1508 18.1508i −0.631166 0.631166i 0.317195 0.948360i \(-0.397259\pi\)
−0.948360 + 0.317195i \(0.897259\pi\)
\(828\) 0 0
\(829\) 26.0466i 0.904637i −0.891856 0.452319i \(-0.850597\pi\)
0.891856 0.452319i \(-0.149403\pi\)
\(830\) 0 0
\(831\) −6.06318 24.5648i −0.210330 0.852145i
\(832\) 0 0
\(833\) 1.53940 + 5.74513i 0.0533372 + 0.199057i
\(834\) 0 0
\(835\) 8.14792 1.33150i 0.281970 0.0460786i
\(836\) 0 0
\(837\) −25.5768 + 38.7811i −0.884063 + 1.34047i
\(838\) 0 0
\(839\) 23.2213 + 40.2205i 0.801690 + 1.38857i 0.918503 + 0.395413i \(0.129399\pi\)
−0.116814 + 0.993154i \(0.537268\pi\)
\(840\) 0 0
\(841\) −14.3506 + 24.8560i −0.494848 + 0.857102i
\(842\) 0 0
\(843\) −28.1106 16.9810i −0.968182 0.584855i
\(844\) 0 0
\(845\) 26.4972 11.9534i 0.911531 0.411209i
\(846\) 0 0
\(847\) −39.8258 + 39.8258i −1.36843 + 1.36843i
\(848\) 0 0
\(849\) 9.34918 + 9.72718i 0.320863 + 0.333836i
\(850\) 0 0
\(851\) 34.2194 + 19.7566i 1.17303 + 0.677247i
\(852\) 0 0
\(853\) −10.3189 + 38.5107i −0.353313 + 1.31858i 0.529281 + 0.848446i \(0.322462\pi\)
−0.882594 + 0.470136i \(0.844205\pi\)
\(854\) 0 0
\(855\) 7.47228 + 5.83574i 0.255547 + 0.199578i
\(856\) 0 0
\(857\) 9.45183 35.2747i 0.322868 1.20496i −0.593569 0.804783i \(-0.702282\pi\)
0.916438 0.400178i \(-0.131052\pi\)
\(858\) 0 0
\(859\) 33.5506 + 19.3705i 1.14473 + 0.660912i 0.947598 0.319465i \(-0.103503\pi\)
0.197135 + 0.980376i \(0.436836\pi\)
\(860\) 0 0
\(861\) −0.106352 + 0.367617i −0.00362445 + 0.0125283i
\(862\) 0 0
\(863\) −13.5234 + 13.5234i −0.460341 + 0.460341i −0.898767 0.438426i \(-0.855536\pi\)
0.438426 + 0.898767i \(0.355536\pi\)
\(864\) 0 0
\(865\) −21.6431 8.18642i −0.735886 0.278347i
\(866\) 0 0
\(867\) 22.5123 12.4095i 0.764559 0.421447i
\(868\) 0 0
\(869\) 1.55705 2.69689i 0.0528193 0.0914858i
\(870\) 0 0
\(871\) 0.0149520 + 0.0258976i 0.000506630 + 0.000877508i
\(872\) 0 0
\(873\) −35.1614 + 32.4798i −1.19003 + 1.09927i
\(874\) 0 0
\(875\) 31.4613 + 19.7792i 1.06359 + 0.668660i
\(876\) 0 0
\(877\) 0.135609 + 0.506099i 0.00457918 + 0.0170898i 0.968178 0.250264i \(-0.0805174\pi\)
−0.963598 + 0.267354i \(0.913851\pi\)
\(878\) 0 0
\(879\) −18.6929 + 17.9665i −0.630494 + 0.605993i
\(880\) 0 0
\(881\) 39.0309i 1.31499i −0.753461 0.657493i \(-0.771617\pi\)
0.753461 0.657493i \(-0.228383\pi\)
\(882\) 0 0
\(883\) 19.5869 + 19.5869i 0.659151 + 0.659151i 0.955179 0.296028i \(-0.0956621\pi\)
−0.296028 + 0.955179i \(0.595662\pi\)
\(884\) 0 0
\(885\) 7.88201 + 0.947427i 0.264951 + 0.0318474i
\(886\) 0 0
\(887\) −5.58895 + 1.49755i −0.187658 + 0.0502829i −0.351424 0.936216i \(-0.614303\pi\)
0.163766 + 0.986499i \(0.447636\pi\)
\(888\) 0 0
\(889\) 8.16514 4.71414i 0.273850 0.158107i
\(890\) 0 0
\(891\) 39.1899 + 26.9754i 1.31291 + 0.903710i
\(892\) 0 0
\(893\) −13.9574 3.73987i −0.467066 0.125150i
\(894\) 0 0
\(895\) −8.77263 0.878559i −0.293237 0.0293670i
\(896\) 0 0
\(897\) −0.0827441 + 0.136976i −0.00276274 + 0.00457350i
\(898\) 0 0
\(899\) −67.9127 −2.26502
\(900\) 0 0
\(901\) −8.07711 −0.269088
\(902\) 0 0
\(903\) 55.0617 + 1.09104i 1.83234 + 0.0363077i
\(904\) 0 0
\(905\) 35.5770 + 3.56296i 1.18262 + 0.118437i
\(906\) 0 0
\(907\) −28.1814 7.55119i −0.935749 0.250733i −0.241444 0.970415i \(-0.577621\pi\)
−0.694304 + 0.719682i \(0.744288\pi\)
\(908\) 0 0
\(909\) 1.40767 35.5065i 0.0466896 1.17768i
\(910\) 0 0
\(911\) 34.5362 19.9395i 1.14424 0.660625i 0.196759 0.980452i \(-0.436958\pi\)
0.947476 + 0.319827i \(0.103625\pi\)
\(912\) 0 0
\(913\) 33.8156 9.06087i 1.11913 0.299871i
\(914\) 0 0
\(915\) 6.40819 8.54915i 0.211848 0.282626i
\(916\) 0 0
\(917\) 5.34031 + 5.34031i 0.176353 + 0.176353i
\(918\) 0 0
\(919\) 44.3053i 1.46150i 0.682647 + 0.730748i \(0.260829\pi\)
−0.682647 + 0.730748i \(0.739171\pi\)
\(920\) 0 0
\(921\) −21.8829 6.33073i −0.721066 0.208605i
\(922\) 0 0
\(923\) −0.0157235 0.0586808i −0.000517544 0.00193150i
\(924\) 0 0
\(925\) 19.5625 12.9786i 0.643212 0.426735i
\(926\) 0 0
\(927\) 10.7956 34.7241i 0.354575 1.14049i
\(928\) 0 0
\(929\) 1.80245 + 3.12193i 0.0591363 + 0.102427i 0.894078 0.447911i \(-0.147832\pi\)
−0.834942 + 0.550339i \(0.814499\pi\)
\(930\) 0 0
\(931\) −2.86082 + 4.95509i −0.0937597 + 0.162396i
\(932\) 0 0
\(933\) −0.112572 + 5.68116i −0.00368544 + 0.185993i
\(934\) 0 0
\(935\) 16.2437 + 6.14413i 0.531226 + 0.200934i
\(936\) 0 0
\(937\) 24.9740 24.9740i 0.815864 0.815864i −0.169642 0.985506i \(-0.554261\pi\)
0.985506 + 0.169642i \(0.0542612\pi\)
\(938\) 0 0
\(939\) −0.911296 + 0.224930i −0.0297390 + 0.00734030i
\(940\) 0 0
\(941\) −12.4239 7.17294i −0.405008 0.233831i 0.283635 0.958932i \(-0.408460\pi\)
−0.688642 + 0.725101i \(0.741793\pi\)
\(942\) 0 0
\(943\) 0.144784 0.540340i 0.00471480 0.0175959i
\(944\) 0 0
\(945\) −35.2471 15.7848i −1.14659 0.513481i
\(946\) 0 0
\(947\) −13.0396 + 48.6646i −0.423731 + 1.58139i 0.342947 + 0.939355i \(0.388575\pi\)
−0.766678 + 0.642031i \(0.778092\pi\)
\(948\) 0 0
\(949\) −0.0314139 0.0181368i −0.00101974 0.000588747i
\(950\) 0 0
\(951\) 8.13653 2.00829i 0.263845 0.0651232i
\(952\) 0 0
\(953\) −5.98422 + 5.98422i −0.193848 + 0.193848i −0.797356 0.603509i \(-0.793769\pi\)
0.603509 + 0.797356i \(0.293769\pi\)
\(954\) 0 0
\(955\) −32.0511 + 14.4589i −1.03715 + 0.467878i
\(956\) 0 0
\(957\) −1.37788 + 69.5372i −0.0445404 + 2.24782i
\(958\) 0 0
\(959\) −23.0328 + 39.8940i −0.743769 + 1.28825i
\(960\) 0 0
\(961\) −24.4657 42.3758i −0.789216 1.36696i
\(962\) 0 0
\(963\) −15.7854 + 3.56598i −0.508677 + 0.114912i
\(964\) 0 0
\(965\) 43.1972 7.05912i 1.39057 0.227241i
\(966\) 0 0
\(967\) −7.16303 26.7328i −0.230347 0.859669i −0.980191 0.198054i \(-0.936538\pi\)
0.749844 0.661615i \(-0.230129\pi\)
\(968\) 0 0
\(969\) −3.45498 0.999527i −0.110990 0.0321094i
\(970\) 0 0
\(971\) 19.9390i 0.639874i −0.947439 0.319937i \(-0.896338\pi\)
0.947439 0.319937i \(-0.103662\pi\)
\(972\) 0 0
\(973\) −3.28551 3.28551i −0.105329 0.105329i
\(974\) 0 0
\(975\) 0.0509836 + 0.0802540i 0.00163278 + 0.00257018i
\(976\) 0 0
\(977\) −15.6454 + 4.19216i −0.500540 + 0.134119i −0.500250 0.865881i \(-0.666759\pi\)
−0.000289240 1.00000i \(0.500092\pi\)
\(978\) 0 0
\(979\) −46.0600 + 26.5927i −1.47208 + 0.849908i
\(980\) 0 0
\(981\) −2.65142 1.67423i −0.0846532 0.0534542i
\(982\) 0 0
\(983\) −38.0008 10.1823i −1.21204 0.324764i −0.404476 0.914549i \(-0.632546\pi\)
−0.807561 + 0.589784i \(0.799213\pi\)
\(984\) 0 0
\(985\) 10.1253 + 12.3790i 0.322618 + 0.394429i
\(986\) 0 0
\(987\) 58.8480 + 1.16607i 1.87315 + 0.0371164i
\(988\) 0 0
\(989\) −80.5025 −2.55983
\(990\) 0 0
\(991\) −34.0496 −1.08162 −0.540810 0.841145i \(-0.681882\pi\)
−0.540810 + 0.841145i \(0.681882\pi\)
\(992\) 0 0
\(993\) −8.14417 + 13.4820i −0.258448 + 0.427840i
\(994\) 0 0
\(995\) 3.86733 38.6163i 0.122603 1.22422i
\(996\) 0 0
\(997\) 6.80419 + 1.82318i 0.215491 + 0.0577406i 0.364949 0.931027i \(-0.381086\pi\)
−0.149458 + 0.988768i \(0.547753\pi\)
\(998\) 0 0
\(999\) −18.2458 + 16.1963i −0.577272 + 0.512427i
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 360.2.bs.a.113.13 72
3.2 odd 2 1080.2.bt.a.233.18 72
4.3 odd 2 720.2.cu.e.113.6 72
5.2 odd 4 inner 360.2.bs.a.257.15 yes 72
9.2 odd 6 inner 360.2.bs.a.353.15 yes 72
9.7 even 3 1080.2.bt.a.953.12 72
15.2 even 4 1080.2.bt.a.17.12 72
20.7 even 4 720.2.cu.e.257.4 72
36.11 even 6 720.2.cu.e.353.4 72
45.2 even 12 inner 360.2.bs.a.137.13 yes 72
45.7 odd 12 1080.2.bt.a.737.18 72
180.47 odd 12 720.2.cu.e.497.6 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bs.a.113.13 72 1.1 even 1 trivial
360.2.bs.a.137.13 yes 72 45.2 even 12 inner
360.2.bs.a.257.15 yes 72 5.2 odd 4 inner
360.2.bs.a.353.15 yes 72 9.2 odd 6 inner
720.2.cu.e.113.6 72 4.3 odd 2
720.2.cu.e.257.4 72 20.7 even 4
720.2.cu.e.353.4 72 36.11 even 6
720.2.cu.e.497.6 72 180.47 odd 12
1080.2.bt.a.17.12 72 15.2 even 4
1080.2.bt.a.233.18 72 3.2 odd 2
1080.2.bt.a.737.18 72 45.7 odd 12
1080.2.bt.a.953.12 72 9.7 even 3