Properties

Label 360.2.m.c.179.11
Level $360$
Weight $2$
Character 360.179
Analytic conductor $2.875$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(179,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.179");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.m (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 17x^{12} - 104x^{10} + 713x^{8} + 238x^{6} + 1004x^{4} - 152x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 179.11
Root \(-0.645096 + 0.854135i\) of defining polynomial
Character \(\chi\) \(=\) 360.179
Dual form 360.2.m.c.179.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.927153 + 1.06789i) q^{2} +(-0.280776 + 1.98019i) q^{4} +(-2.18650 + 0.468213i) q^{5} -3.02045 q^{7} +(-2.37495 + 1.53610i) q^{8} +O(q^{10})\) \(q+(0.927153 + 1.06789i) q^{2} +(-0.280776 + 1.98019i) q^{4} +(-2.18650 + 0.468213i) q^{5} -3.02045 q^{7} +(-2.37495 + 1.53610i) q^{8} +(-2.52722 - 1.90083i) q^{10} +3.62258i q^{11} +1.69614 q^{13} +(-2.80042 - 3.22550i) q^{14} +(-3.84233 - 1.11198i) q^{16} -6.60421 q^{17} +5.12311 q^{19} +(-0.313235 - 4.46115i) q^{20} +(-3.86852 + 3.35869i) q^{22} +6.67026i q^{23} +(4.56155 - 2.04750i) q^{25} +(1.57258 + 1.81129i) q^{26} +(0.848071 - 5.98107i) q^{28} +6.82867 q^{29} -1.73642i q^{31} +(-2.37495 - 5.13416i) q^{32} +(-6.12311 - 7.05256i) q^{34} +(6.60421 - 1.41421i) q^{35} +0.371834 q^{37} +(4.74990 + 5.47091i) q^{38} +(4.47360 - 4.47067i) q^{40} +5.83095i q^{41} +5.24477i q^{43} +(-7.17341 - 1.01714i) q^{44} +(-7.12311 + 6.18435i) q^{46} +0.525853i q^{47} +2.12311 q^{49} +(6.41575 + 2.97289i) q^{50} +(-0.476236 + 3.35869i) q^{52} -10.0054i q^{53} +(-1.69614 - 7.92077i) q^{55} +(7.17341 - 4.63972i) q^{56} +(6.33122 + 7.29226i) q^{58} +4.86270i q^{59} +(1.85431 - 1.60993i) q^{62} +(3.28078 - 7.29634i) q^{64} +(-3.70861 + 0.794156i) q^{65} +13.4347i q^{67} +(1.85431 - 13.0776i) q^{68} +(7.63333 + 5.74137i) q^{70} -2.45567 q^{71} -14.5845i q^{73} +(0.344747 + 0.397078i) q^{74} +(-1.43845 + 10.1447i) q^{76} -10.9418i q^{77} +14.1051i q^{79} +(8.92189 + 0.632320i) q^{80} +(-6.22681 + 5.40618i) q^{82} +5.79119 q^{83} +(14.4401 - 3.09218i) q^{85} +(-5.60083 + 4.86270i) q^{86} +(-5.56466 - 8.60345i) q^{88} -10.2477i q^{89} -5.12311 q^{91} +(-13.2084 - 1.87285i) q^{92} +(-0.561553 + 0.487546i) q^{94} +(-11.2017 + 2.39871i) q^{95} +9.33976i q^{97} +(1.96844 + 2.26724i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{4} - 8 q^{10} - 12 q^{16} + 16 q^{19} + 40 q^{25} - 32 q^{34} - 28 q^{40} - 48 q^{46} - 32 q^{49} + 36 q^{64} + 32 q^{70} - 56 q^{76} - 16 q^{91} + 24 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.927153 + 1.06789i 0.655596 + 0.755112i
\(3\) 0 0
\(4\) −0.280776 + 1.98019i −0.140388 + 0.990097i
\(5\) −2.18650 + 0.468213i −0.977832 + 0.209391i
\(6\) 0 0
\(7\) −3.02045 −1.14162 −0.570811 0.821081i \(-0.693371\pi\)
−0.570811 + 0.821081i \(0.693371\pi\)
\(8\) −2.37495 + 1.53610i −0.839672 + 0.543094i
\(9\) 0 0
\(10\) −2.52722 1.90083i −0.799176 0.601097i
\(11\) 3.62258i 1.09225i 0.837704 + 0.546125i \(0.183898\pi\)
−0.837704 + 0.546125i \(0.816102\pi\)
\(12\) 0 0
\(13\) 1.69614 0.470425 0.235212 0.971944i \(-0.424421\pi\)
0.235212 + 0.971944i \(0.424421\pi\)
\(14\) −2.80042 3.22550i −0.748443 0.862052i
\(15\) 0 0
\(16\) −3.84233 1.11198i −0.960582 0.277996i
\(17\) −6.60421 −1.60176 −0.800878 0.598828i \(-0.795633\pi\)
−0.800878 + 0.598828i \(0.795633\pi\)
\(18\) 0 0
\(19\) 5.12311 1.17532 0.587661 0.809108i \(-0.300049\pi\)
0.587661 + 0.809108i \(0.300049\pi\)
\(20\) −0.313235 4.46115i −0.0700415 0.997544i
\(21\) 0 0
\(22\) −3.86852 + 3.35869i −0.824771 + 0.716074i
\(23\) 6.67026i 1.39085i 0.718601 + 0.695423i \(0.244783\pi\)
−0.718601 + 0.695423i \(0.755217\pi\)
\(24\) 0 0
\(25\) 4.56155 2.04750i 0.912311 0.409499i
\(26\) 1.57258 + 1.81129i 0.308409 + 0.355223i
\(27\) 0 0
\(28\) 0.848071 5.98107i 0.160270 1.13032i
\(29\) 6.82867 1.26805 0.634026 0.773312i \(-0.281401\pi\)
0.634026 + 0.773312i \(0.281401\pi\)
\(30\) 0 0
\(31\) 1.73642i 0.311870i −0.987767 0.155935i \(-0.950161\pi\)
0.987767 0.155935i \(-0.0498391\pi\)
\(32\) −2.37495 5.13416i −0.419836 0.907600i
\(33\) 0 0
\(34\) −6.12311 7.05256i −1.05010 1.20950i
\(35\) 6.60421 1.41421i 1.11631 0.239046i
\(36\) 0 0
\(37\) 0.371834 0.0611292 0.0305646 0.999533i \(-0.490269\pi\)
0.0305646 + 0.999533i \(0.490269\pi\)
\(38\) 4.74990 + 5.47091i 0.770536 + 0.887499i
\(39\) 0 0
\(40\) 4.47360 4.47067i 0.707339 0.706875i
\(41\) 5.83095i 0.910642i 0.890327 + 0.455321i \(0.150475\pi\)
−0.890327 + 0.455321i \(0.849525\pi\)
\(42\) 0 0
\(43\) 5.24477i 0.799819i 0.916555 + 0.399910i \(0.130959\pi\)
−0.916555 + 0.399910i \(0.869041\pi\)
\(44\) −7.17341 1.01714i −1.08143 0.153339i
\(45\) 0 0
\(46\) −7.12311 + 6.18435i −1.05024 + 0.911833i
\(47\) 0.525853i 0.0767035i 0.999264 + 0.0383518i \(0.0122107\pi\)
−0.999264 + 0.0383518i \(0.987789\pi\)
\(48\) 0 0
\(49\) 2.12311 0.303301
\(50\) 6.41575 + 2.97289i 0.907325 + 0.420431i
\(51\) 0 0
\(52\) −0.476236 + 3.35869i −0.0660421 + 0.465766i
\(53\) 10.0054i 1.37435i −0.726493 0.687173i \(-0.758851\pi\)
0.726493 0.687173i \(-0.241149\pi\)
\(54\) 0 0
\(55\) −1.69614 7.92077i −0.228708 1.06804i
\(56\) 7.17341 4.63972i 0.958588 0.620008i
\(57\) 0 0
\(58\) 6.33122 + 7.29226i 0.831329 + 0.957521i
\(59\) 4.86270i 0.633069i 0.948581 + 0.316535i \(0.102519\pi\)
−0.948581 + 0.316535i \(0.897481\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 1.85431 1.60993i 0.235497 0.204461i
\(63\) 0 0
\(64\) 3.28078 7.29634i 0.410097 0.912042i
\(65\) −3.70861 + 0.794156i −0.459996 + 0.0985029i
\(66\) 0 0
\(67\) 13.4347i 1.64132i 0.571420 + 0.820658i \(0.306393\pi\)
−0.571420 + 0.820658i \(0.693607\pi\)
\(68\) 1.85431 13.0776i 0.224868 1.58589i
\(69\) 0 0
\(70\) 7.63333 + 5.74137i 0.912357 + 0.686225i
\(71\) −2.45567 −0.291434 −0.145717 0.989326i \(-0.546549\pi\)
−0.145717 + 0.989326i \(0.546549\pi\)
\(72\) 0 0
\(73\) 14.5845i 1.70699i −0.521102 0.853495i \(-0.674479\pi\)
0.521102 0.853495i \(-0.325521\pi\)
\(74\) 0.344747 + 0.397078i 0.0400760 + 0.0461594i
\(75\) 0 0
\(76\) −1.43845 + 10.1447i −0.165001 + 1.16368i
\(77\) 10.9418i 1.24694i
\(78\) 0 0
\(79\) 14.1051i 1.58695i 0.608603 + 0.793475i \(0.291730\pi\)
−0.608603 + 0.793475i \(0.708270\pi\)
\(80\) 8.92189 + 0.632320i 0.997498 + 0.0706955i
\(81\) 0 0
\(82\) −6.22681 + 5.40618i −0.687636 + 0.597013i
\(83\) 5.79119 0.635666 0.317833 0.948147i \(-0.397045\pi\)
0.317833 + 0.948147i \(0.397045\pi\)
\(84\) 0 0
\(85\) 14.4401 3.09218i 1.56625 0.335394i
\(86\) −5.60083 + 4.86270i −0.603953 + 0.524358i
\(87\) 0 0
\(88\) −5.56466 8.60345i −0.593195 0.917131i
\(89\) 10.2477i 1.08625i −0.839651 0.543126i \(-0.817240\pi\)
0.839651 0.543126i \(-0.182760\pi\)
\(90\) 0 0
\(91\) −5.12311 −0.537047
\(92\) −13.2084 1.87285i −1.37707 0.195258i
\(93\) 0 0
\(94\) −0.561553 + 0.487546i −0.0579198 + 0.0502865i
\(95\) −11.2017 + 2.39871i −1.14927 + 0.246102i
\(96\) 0 0
\(97\) 9.33976i 0.948309i 0.880442 + 0.474154i \(0.157246\pi\)
−0.880442 + 0.474154i \(0.842754\pi\)
\(98\) 1.96844 + 2.26724i 0.198843 + 0.229026i
\(99\) 0 0
\(100\) 2.77366 + 9.60764i 0.277366 + 0.960764i
\(101\) −4.37300 −0.435129 −0.217565 0.976046i \(-0.569811\pi\)
−0.217565 + 0.976046i \(0.569811\pi\)
\(102\) 0 0
\(103\) 8.31768 0.819565 0.409782 0.912183i \(-0.365605\pi\)
0.409782 + 0.912183i \(0.365605\pi\)
\(104\) −4.02825 + 2.60545i −0.395002 + 0.255485i
\(105\) 0 0
\(106\) 10.6847 9.27653i 1.03779 0.901016i
\(107\) 7.41722 0.717050 0.358525 0.933520i \(-0.383280\pi\)
0.358525 + 0.933520i \(0.383280\pi\)
\(108\) 0 0
\(109\) 9.65719i 0.924991i 0.886622 + 0.462496i \(0.153046\pi\)
−0.886622 + 0.462496i \(0.846954\pi\)
\(110\) 6.88593 9.15506i 0.656548 0.872900i
\(111\) 0 0
\(112\) 11.6056 + 3.35869i 1.09662 + 0.317366i
\(113\) 0.813015 0.0764820 0.0382410 0.999269i \(-0.487825\pi\)
0.0382410 + 0.999269i \(0.487825\pi\)
\(114\) 0 0
\(115\) −3.12311 14.5845i −0.291231 1.36001i
\(116\) −1.91733 + 13.5221i −0.178019 + 1.25549i
\(117\) 0 0
\(118\) −5.19283 + 4.50846i −0.478038 + 0.415038i
\(119\) 19.9477 1.82860
\(120\) 0 0
\(121\) −2.12311 −0.193010
\(122\) 0 0
\(123\) 0 0
\(124\) 3.43845 + 0.487546i 0.308782 + 0.0437829i
\(125\) −9.01516 + 6.61262i −0.806341 + 0.591451i
\(126\) 0 0
\(127\) −15.1022 −1.34011 −0.670054 0.742313i \(-0.733729\pi\)
−0.670054 + 0.742313i \(0.733729\pi\)
\(128\) 10.8335 3.26131i 0.957552 0.288262i
\(129\) 0 0
\(130\) −4.28652 3.22408i −0.375952 0.282771i
\(131\) 6.45101i 0.563627i −0.959469 0.281814i \(-0.909064\pi\)
0.959469 0.281814i \(-0.0909360\pi\)
\(132\) 0 0
\(133\) −15.4741 −1.34177
\(134\) −14.3468 + 12.4561i −1.23938 + 1.07604i
\(135\) 0 0
\(136\) 15.6847 10.1447i 1.34495 0.869904i
\(137\) −6.60421 −0.564235 −0.282118 0.959380i \(-0.591037\pi\)
−0.282118 + 0.959380i \(0.591037\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0.946111 + 13.4747i 0.0799610 + 1.13882i
\(141\) 0 0
\(142\) −2.27678 2.62238i −0.191063 0.220066i
\(143\) 6.14441i 0.513821i
\(144\) 0 0
\(145\) −14.9309 + 3.19727i −1.23994 + 0.265519i
\(146\) 15.5747 13.5221i 1.28897 1.11910i
\(147\) 0 0
\(148\) −0.104402 + 0.736303i −0.00858181 + 0.0605238i
\(149\) 15.5747 1.27593 0.637963 0.770067i \(-0.279777\pi\)
0.637963 + 0.770067i \(0.279777\pi\)
\(150\) 0 0
\(151\) 10.6323i 0.865243i −0.901576 0.432622i \(-0.857589\pi\)
0.901576 0.432622i \(-0.142411\pi\)
\(152\) −12.1671 + 7.86962i −0.986884 + 0.638310i
\(153\) 0 0
\(154\) 11.6847 10.1447i 0.941577 0.817486i
\(155\) 0.813015 + 3.79668i 0.0653029 + 0.304957i
\(156\) 0 0
\(157\) 9.06134 0.723174 0.361587 0.932338i \(-0.382235\pi\)
0.361587 + 0.932338i \(0.382235\pi\)
\(158\) −15.0627 + 13.0776i −1.19833 + 1.04040i
\(159\) 0 0
\(160\) 7.59671 + 10.1139i 0.600572 + 0.799570i
\(161\) 20.1472i 1.58782i
\(162\) 0 0
\(163\) 10.4895i 0.821604i 0.911725 + 0.410802i \(0.134751\pi\)
−0.911725 + 0.410802i \(0.865249\pi\)
\(164\) −11.5464 1.63719i −0.901623 0.127843i
\(165\) 0 0
\(166\) 5.36932 + 6.18435i 0.416740 + 0.479999i
\(167\) 4.79741i 0.371235i −0.982622 0.185617i \(-0.940571\pi\)
0.982622 0.185617i \(-0.0594285\pi\)
\(168\) 0 0
\(169\) −10.1231 −0.778700
\(170\) 16.6903 + 12.5535i 1.28008 + 0.962809i
\(171\) 0 0
\(172\) −10.3857 1.47261i −0.791898 0.112285i
\(173\) 3.33513i 0.253565i 0.991931 + 0.126783i \(0.0404651\pi\)
−0.991931 + 0.126783i \(0.959535\pi\)
\(174\) 0 0
\(175\) −13.7779 + 6.18435i −1.04151 + 0.467493i
\(176\) 4.02825 13.9192i 0.303641 1.04920i
\(177\) 0 0
\(178\) 10.9434 9.50117i 0.820243 0.712143i
\(179\) 20.9413i 1.56523i −0.622506 0.782615i \(-0.713886\pi\)
0.622506 0.782615i \(-0.286114\pi\)
\(180\) 0 0
\(181\) 6.18435i 0.459679i −0.973229 0.229840i \(-0.926180\pi\)
0.973229 0.229840i \(-0.0738202\pi\)
\(182\) −4.74990 5.47091i −0.352086 0.405531i
\(183\) 0 0
\(184\) −10.2462 15.8415i −0.755361 1.16785i
\(185\) −0.813015 + 0.174098i −0.0597740 + 0.0127999i
\(186\) 0 0
\(187\) 23.9243i 1.74952i
\(188\) −1.04129 0.147647i −0.0759439 0.0107683i
\(189\) 0 0
\(190\) −12.9472 9.73817i −0.939289 0.706481i
\(191\) −17.4920 −1.26568 −0.632838 0.774284i \(-0.718110\pi\)
−0.632838 + 0.774284i \(0.718110\pi\)
\(192\) 0 0
\(193\) 15.7343i 1.13258i −0.824206 0.566290i \(-0.808378\pi\)
0.824206 0.566290i \(-0.191622\pi\)
\(194\) −9.97383 + 8.65938i −0.716079 + 0.621707i
\(195\) 0 0
\(196\) −0.596118 + 4.20416i −0.0425799 + 0.300297i
\(197\) 24.6929i 1.75930i 0.475623 + 0.879649i \(0.342223\pi\)
−0.475623 + 0.879649i \(0.657777\pi\)
\(198\) 0 0
\(199\) 10.6323i 0.753703i −0.926274 0.376851i \(-0.877007\pi\)
0.926274 0.376851i \(-0.122993\pi\)
\(200\) −7.68830 + 11.8697i −0.543645 + 0.839315i
\(201\) 0 0
\(202\) −4.05444 4.66988i −0.285269 0.328571i
\(203\) −20.6256 −1.44764
\(204\) 0 0
\(205\) −2.73013 12.7494i −0.190680 0.890455i
\(206\) 7.71175 + 8.88236i 0.537303 + 0.618863i
\(207\) 0 0
\(208\) −6.51713 1.88608i −0.451882 0.130776i
\(209\) 18.5589i 1.28374i
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 19.8126 + 2.80928i 1.36074 + 0.192942i
\(213\) 0 0
\(214\) 6.87689 + 7.92077i 0.470095 + 0.541453i
\(215\) −2.45567 11.4677i −0.167475 0.782089i
\(216\) 0 0
\(217\) 5.24477i 0.356038i
\(218\) −10.3128 + 8.95369i −0.698472 + 0.606420i
\(219\) 0 0
\(220\) 16.1609 1.13472i 1.08957 0.0765029i
\(221\) −11.2017 −0.753505
\(222\) 0 0
\(223\) 28.6714 1.91998 0.959988 0.280040i \(-0.0903477\pi\)
0.959988 + 0.280040i \(0.0903477\pi\)
\(224\) 7.17341 + 15.5075i 0.479294 + 1.03614i
\(225\) 0 0
\(226\) 0.753789 + 0.868210i 0.0501413 + 0.0577525i
\(227\) −13.2084 −0.876673 −0.438337 0.898811i \(-0.644432\pi\)
−0.438337 + 0.898811i \(0.644432\pi\)
\(228\) 0 0
\(229\) 22.0259i 1.45551i 0.685836 + 0.727756i \(0.259437\pi\)
−0.685836 + 0.727756i \(0.740563\pi\)
\(230\) 12.6791 16.8572i 0.836033 1.11153i
\(231\) 0 0
\(232\) −16.2177 + 10.4895i −1.06475 + 0.688672i
\(233\) 21.4386 1.40449 0.702246 0.711934i \(-0.252181\pi\)
0.702246 + 0.711934i \(0.252181\pi\)
\(234\) 0 0
\(235\) −0.246211 1.14978i −0.0160611 0.0750032i
\(236\) −9.62908 1.36533i −0.626800 0.0888755i
\(237\) 0 0
\(238\) 18.4945 + 21.3019i 1.19882 + 1.38080i
\(239\) 4.91134 0.317688 0.158844 0.987304i \(-0.449223\pi\)
0.158844 + 0.987304i \(0.449223\pi\)
\(240\) 0 0
\(241\) −4.00000 −0.257663 −0.128831 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) −1.96844 2.26724i −0.126536 0.145744i
\(243\) 0 0
\(244\) 0 0
\(245\) −4.64217 + 0.994066i −0.296577 + 0.0635086i
\(246\) 0 0
\(247\) 8.68951 0.552900
\(248\) 2.66732 + 4.12391i 0.169375 + 0.261869i
\(249\) 0 0
\(250\) −15.4200 3.49629i −0.975246 0.221125i
\(251\) 9.27944i 0.585713i −0.956156 0.292856i \(-0.905394\pi\)
0.956156 0.292856i \(-0.0946058\pi\)
\(252\) 0 0
\(253\) −24.1636 −1.51915
\(254\) −14.0021 16.1275i −0.878569 1.01193i
\(255\) 0 0
\(256\) 13.5270 + 8.54521i 0.845437 + 0.534076i
\(257\) 12.3954 0.773204 0.386602 0.922247i \(-0.373649\pi\)
0.386602 + 0.922247i \(0.373649\pi\)
\(258\) 0 0
\(259\) −1.12311 −0.0697864
\(260\) −0.531291 7.56674i −0.0329493 0.469270i
\(261\) 0 0
\(262\) 6.88897 5.98107i 0.425602 0.369512i
\(263\) 12.2888i 0.757761i 0.925446 + 0.378881i \(0.123691\pi\)
−0.925446 + 0.378881i \(0.876309\pi\)
\(264\) 0 0
\(265\) 4.68466 + 21.8768i 0.287776 + 1.34388i
\(266\) −14.3468 16.5246i −0.879660 1.01319i
\(267\) 0 0
\(268\) −26.6034 3.77216i −1.62506 0.230421i
\(269\) 1.91733 0.116902 0.0584508 0.998290i \(-0.481384\pi\)
0.0584508 + 0.998290i \(0.481384\pi\)
\(270\) 0 0
\(271\) 26.4738i 1.60817i 0.594514 + 0.804085i \(0.297344\pi\)
−0.594514 + 0.804085i \(0.702656\pi\)
\(272\) 25.3755 + 7.34376i 1.53862 + 0.445281i
\(273\) 0 0
\(274\) −6.12311 7.05256i −0.369910 0.426061i
\(275\) 7.41722 + 16.5246i 0.447275 + 0.996471i
\(276\) 0 0
\(277\) −11.8730 −0.713379 −0.356689 0.934223i \(-0.616095\pi\)
−0.356689 + 0.934223i \(0.616095\pi\)
\(278\) −11.1258 12.8147i −0.667283 0.768573i
\(279\) 0 0
\(280\) −13.5123 + 13.5034i −0.807513 + 0.806984i
\(281\) 8.65938i 0.516575i 0.966068 + 0.258288i \(0.0831582\pi\)
−0.966068 + 0.258288i \(0.916842\pi\)
\(282\) 0 0
\(283\) 15.7343i 0.935307i 0.883912 + 0.467654i \(0.154900\pi\)
−0.883912 + 0.467654i \(0.845100\pi\)
\(284\) 0.689494 4.86270i 0.0409139 0.288548i
\(285\) 0 0
\(286\) −6.56155 + 5.69681i −0.387993 + 0.336859i
\(287\) 17.6121i 1.03961i
\(288\) 0 0
\(289\) 26.6155 1.56562
\(290\) −17.2575 12.9802i −1.01340 0.762221i
\(291\) 0 0
\(292\) 28.8802 + 4.09499i 1.69008 + 0.239641i
\(293\) 16.9710i 0.991454i −0.868478 0.495727i \(-0.834902\pi\)
0.868478 0.495727i \(-0.165098\pi\)
\(294\) 0 0
\(295\) −2.27678 10.6323i −0.132559 0.619036i
\(296\) −0.883088 + 0.571175i −0.0513284 + 0.0331989i
\(297\) 0 0
\(298\) 14.4401 + 16.6320i 0.836492 + 0.963467i
\(299\) 11.3137i 0.654289i
\(300\) 0 0
\(301\) 15.8415i 0.913091i
\(302\) 11.3541 9.85775i 0.653355 0.567250i
\(303\) 0 0
\(304\) −19.6847 5.69681i −1.12899 0.326734i
\(305\) 0 0
\(306\) 0 0
\(307\) 18.6795i 1.06610i −0.846085 0.533048i \(-0.821046\pi\)
0.846085 0.533048i \(-0.178954\pi\)
\(308\) 21.6669 + 3.07221i 1.23459 + 0.175055i
\(309\) 0 0
\(310\) −3.30065 + 4.38831i −0.187464 + 0.249239i
\(311\) 22.4033 1.27038 0.635188 0.772358i \(-0.280923\pi\)
0.635188 + 0.772358i \(0.280923\pi\)
\(312\) 0 0
\(313\) 21.6247i 1.22230i 0.791514 + 0.611151i \(0.209293\pi\)
−0.791514 + 0.611151i \(0.790707\pi\)
\(314\) 8.40125 + 9.67651i 0.474110 + 0.546077i
\(315\) 0 0
\(316\) −27.9309 3.96039i −1.57123 0.222789i
\(317\) 0.115279i 0.00647473i 0.999995 + 0.00323737i \(0.00103049\pi\)
−0.999995 + 0.00323737i \(0.998970\pi\)
\(318\) 0 0
\(319\) 24.7374i 1.38503i
\(320\) −3.75717 + 17.4895i −0.210032 + 0.977694i
\(321\) 0 0
\(322\) 21.5150 18.6795i 1.19898 1.04097i
\(323\) −33.8340 −1.88258
\(324\) 0 0
\(325\) 7.73704 3.47284i 0.429174 0.192639i
\(326\) −11.2017 + 9.72540i −0.620403 + 0.538640i
\(327\) 0 0
\(328\) −8.95694 13.8482i −0.494564 0.764640i
\(329\) 1.58831i 0.0875664i
\(330\) 0 0
\(331\) 23.3693 1.28449 0.642247 0.766498i \(-0.278002\pi\)
0.642247 + 0.766498i \(0.278002\pi\)
\(332\) −1.62603 + 11.4677i −0.0892400 + 0.629370i
\(333\) 0 0
\(334\) 5.12311 4.44793i 0.280324 0.243380i
\(335\) −6.29033 29.3751i −0.343677 1.60493i
\(336\) 0 0
\(337\) 12.2850i 0.669205i −0.942359 0.334602i \(-0.891398\pi\)
0.942359 0.334602i \(-0.108602\pi\)
\(338\) −9.38566 10.8104i −0.510513 0.588006i
\(339\) 0 0
\(340\) 2.06867 + 29.4624i 0.112189 + 1.59782i
\(341\) 6.29033 0.340640
\(342\) 0 0
\(343\) 14.7304 0.795367
\(344\) −8.05650 12.4561i −0.434377 0.671586i
\(345\) 0 0
\(346\) −3.56155 + 3.09218i −0.191470 + 0.166236i
\(347\) 5.79119 0.310887 0.155444 0.987845i \(-0.450319\pi\)
0.155444 + 0.987845i \(0.450319\pi\)
\(348\) 0 0
\(349\) 6.94568i 0.371794i −0.982569 0.185897i \(-0.940481\pi\)
0.982569 0.185897i \(-0.0595190\pi\)
\(350\) −19.3785 8.97947i −1.03582 0.479973i
\(351\) 0 0
\(352\) 18.5989 8.60345i 0.991326 0.458566i
\(353\) 33.0210 1.75753 0.878766 0.477253i \(-0.158367\pi\)
0.878766 + 0.477253i \(0.158367\pi\)
\(354\) 0 0
\(355\) 5.36932 1.14978i 0.284974 0.0610238i
\(356\) 20.2924 + 2.87731i 1.07550 + 0.152497i
\(357\) 0 0
\(358\) 22.3630 19.4158i 1.18192 1.02616i
\(359\) 19.9477 1.05280 0.526399 0.850238i \(-0.323542\pi\)
0.526399 + 0.850238i \(0.323542\pi\)
\(360\) 0 0
\(361\) 7.24621 0.381380
\(362\) 6.60421 5.73384i 0.347109 0.301364i
\(363\) 0 0
\(364\) 1.43845 10.1447i 0.0753951 0.531729i
\(365\) 6.82867 + 31.8890i 0.357429 + 1.66915i
\(366\) 0 0
\(367\) 19.9819 1.04304 0.521522 0.853238i \(-0.325364\pi\)
0.521522 + 0.853238i \(0.325364\pi\)
\(368\) 7.41722 25.6294i 0.386649 1.33602i
\(369\) 0 0
\(370\) −0.939706 0.706795i −0.0488530 0.0367445i
\(371\) 30.2208i 1.56898i
\(372\) 0 0
\(373\) −5.66906 −0.293533 −0.146766 0.989171i \(-0.546887\pi\)
−0.146766 + 0.989171i \(0.546887\pi\)
\(374\) 25.5485 22.1815i 1.32108 1.14698i
\(375\) 0 0
\(376\) −0.807764 1.24887i −0.0416573 0.0644058i
\(377\) 11.5824 0.596523
\(378\) 0 0
\(379\) 16.4924 0.847159 0.423579 0.905859i \(-0.360773\pi\)
0.423579 + 0.905859i \(0.360773\pi\)
\(380\) −1.60474 22.8550i −0.0823213 1.17243i
\(381\) 0 0
\(382\) −16.2177 18.6795i −0.829772 0.955727i
\(383\) 14.6875i 0.750498i −0.926924 0.375249i \(-0.877557\pi\)
0.926924 0.375249i \(-0.122443\pi\)
\(384\) 0 0
\(385\) 5.12311 + 23.9243i 0.261098 + 1.21929i
\(386\) 16.8025 14.5881i 0.855224 0.742515i
\(387\) 0 0
\(388\) −18.4945 2.62238i −0.938917 0.133131i
\(389\) −13.1190 −0.665159 −0.332580 0.943075i \(-0.607919\pi\)
−0.332580 + 0.943075i \(0.607919\pi\)
\(390\) 0 0
\(391\) 44.0518i 2.22779i
\(392\) −5.04227 + 3.26131i −0.254673 + 0.164721i
\(393\) 0 0
\(394\) −26.3693 + 22.8941i −1.32847 + 1.15339i
\(395\) −6.60421 30.8408i −0.332294 1.55177i
\(396\) 0 0
\(397\) 33.2249 1.66751 0.833756 0.552134i \(-0.186186\pi\)
0.833756 + 0.552134i \(0.186186\pi\)
\(398\) 11.3541 9.85775i 0.569130 0.494124i
\(399\) 0 0
\(400\) −19.8038 + 2.79478i −0.990188 + 0.139739i
\(401\) 34.4634i 1.72102i 0.509433 + 0.860510i \(0.329855\pi\)
−0.509433 + 0.860510i \(0.670145\pi\)
\(402\) 0 0
\(403\) 2.94521i 0.146712i
\(404\) 1.22783 8.65938i 0.0610870 0.430820i
\(405\) 0 0
\(406\) −19.1231 22.0259i −0.949064 1.09313i
\(407\) 1.34700i 0.0667683i
\(408\) 0 0
\(409\) −5.12311 −0.253321 −0.126661 0.991946i \(-0.540426\pi\)
−0.126661 + 0.991946i \(0.540426\pi\)
\(410\) 11.0837 14.7361i 0.547384 0.727763i
\(411\) 0 0
\(412\) −2.33541 + 16.4706i −0.115057 + 0.811448i
\(413\) 14.6875i 0.722726i
\(414\) 0 0
\(415\) −12.6624 + 2.71151i −0.621574 + 0.133103i
\(416\) −4.02825 8.70826i −0.197501 0.426958i
\(417\) 0 0
\(418\) −19.8188 + 17.2069i −0.969371 + 0.841617i
\(419\) 8.38752i 0.409757i 0.978787 + 0.204878i \(0.0656799\pi\)
−0.978787 + 0.204878i \(0.934320\pi\)
\(420\) 0 0
\(421\) 15.0802i 0.734965i 0.930030 + 0.367482i \(0.119780\pi\)
−0.930030 + 0.367482i \(0.880220\pi\)
\(422\) 3.70861 + 4.27156i 0.180532 + 0.207936i
\(423\) 0 0
\(424\) 15.3693 + 23.7623i 0.746400 + 1.15400i
\(425\) −30.1254 + 13.5221i −1.46130 + 0.655917i
\(426\) 0 0
\(427\) 0 0
\(428\) −2.08258 + 14.6875i −0.100665 + 0.709948i
\(429\) 0 0
\(430\) 9.96943 13.2547i 0.480769 0.639197i
\(431\) −19.9477 −0.960845 −0.480422 0.877037i \(-0.659517\pi\)
−0.480422 + 0.877037i \(0.659517\pi\)
\(432\) 0 0
\(433\) 10.4895i 0.504095i −0.967715 0.252047i \(-0.918896\pi\)
0.967715 0.252047i \(-0.0811039\pi\)
\(434\) −5.60083 + 4.86270i −0.268849 + 0.233417i
\(435\) 0 0
\(436\) −19.1231 2.71151i −0.915831 0.129858i
\(437\) 34.1725i 1.63469i
\(438\) 0 0
\(439\) 23.0010i 1.09778i −0.835895 0.548889i \(-0.815051\pi\)
0.835895 0.548889i \(-0.184949\pi\)
\(440\) 16.1954 + 16.2060i 0.772084 + 0.772590i
\(441\) 0 0
\(442\) −10.3857 11.9621i −0.493995 0.568981i
\(443\) −1.62603 −0.0772550 −0.0386275 0.999254i \(-0.512299\pi\)
−0.0386275 + 0.999254i \(0.512299\pi\)
\(444\) 0 0
\(445\) 4.79810 + 22.4066i 0.227452 + 1.06217i
\(446\) 26.5827 + 30.6179i 1.25873 + 1.44980i
\(447\) 0 0
\(448\) −9.90941 + 22.0382i −0.468176 + 1.04121i
\(449\) 9.89949i 0.467186i −0.972334 0.233593i \(-0.924952\pi\)
0.972334 0.233593i \(-0.0750483\pi\)
\(450\) 0 0
\(451\) −21.1231 −0.994648
\(452\) −0.228275 + 1.60993i −0.0107372 + 0.0757246i
\(453\) 0 0
\(454\) −12.2462 14.1051i −0.574743 0.661986i
\(455\) 11.2017 2.39871i 0.525142 0.112453i
\(456\) 0 0
\(457\) 19.8293i 0.927575i 0.885946 + 0.463788i \(0.153510\pi\)
−0.885946 + 0.463788i \(0.846490\pi\)
\(458\) −23.5212 + 20.4214i −1.09907 + 0.954228i
\(459\) 0 0
\(460\) 29.7571 2.08936i 1.38743 0.0974170i
\(461\) 15.5747 0.725384 0.362692 0.931909i \(-0.381858\pi\)
0.362692 + 0.931909i \(0.381858\pi\)
\(462\) 0 0
\(463\) −17.7509 −0.824952 −0.412476 0.910968i \(-0.635336\pi\)
−0.412476 + 0.910968i \(0.635336\pi\)
\(464\) −26.2380 7.59336i −1.21807 0.352513i
\(465\) 0 0
\(466\) 19.8769 + 22.8941i 0.920779 + 1.06055i
\(467\) 28.0429 1.29767 0.648834 0.760930i \(-0.275257\pi\)
0.648834 + 0.760930i \(0.275257\pi\)
\(468\) 0 0
\(469\) 40.5790i 1.87376i
\(470\) 0.999559 1.32894i 0.0461062 0.0612996i
\(471\) 0 0
\(472\) −7.46960 11.5487i −0.343816 0.531570i
\(473\) −18.9996 −0.873603
\(474\) 0 0
\(475\) 23.3693 10.4895i 1.07226 0.481293i
\(476\) −5.60083 + 39.5002i −0.256714 + 1.81049i
\(477\) 0 0
\(478\) 4.55356 + 5.24477i 0.208275 + 0.239890i
\(479\) −37.4396 −1.71066 −0.855331 0.518083i \(-0.826646\pi\)
−0.855331 + 0.518083i \(0.826646\pi\)
\(480\) 0 0
\(481\) 0.630683 0.0287567
\(482\) −3.70861 4.27156i −0.168923 0.194564i
\(483\) 0 0
\(484\) 0.596118 4.20416i 0.0270963 0.191098i
\(485\) −4.37300 20.4214i −0.198568 0.927286i
\(486\) 0 0
\(487\) −4.50778 −0.204267 −0.102134 0.994771i \(-0.532567\pi\)
−0.102134 + 0.994771i \(0.532567\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −5.36555 4.03567i −0.242391 0.182313i
\(491\) 10.5196i 0.474741i −0.971419 0.237370i \(-0.923714\pi\)
0.971419 0.237370i \(-0.0762855\pi\)
\(492\) 0 0
\(493\) −45.0979 −2.03111
\(494\) 8.05650 + 9.27944i 0.362479 + 0.417502i
\(495\) 0 0
\(496\) −1.93087 + 6.67190i −0.0866986 + 0.299577i
\(497\) 7.41722 0.332708
\(498\) 0 0
\(499\) 25.1231 1.12466 0.562332 0.826911i \(-0.309904\pi\)
0.562332 + 0.826911i \(0.309904\pi\)
\(500\) −10.5630 19.7084i −0.472393 0.881388i
\(501\) 0 0
\(502\) 9.90941 8.60345i 0.442279 0.383991i
\(503\) 16.5604i 0.738391i 0.929352 + 0.369195i \(0.120367\pi\)
−0.929352 + 0.369195i \(0.879633\pi\)
\(504\) 0 0
\(505\) 9.56155 2.04750i 0.425484 0.0911123i
\(506\) −22.4033 25.8040i −0.995949 1.14713i
\(507\) 0 0
\(508\) 4.24035 29.9054i 0.188135 1.32684i
\(509\) −4.37300 −0.193830 −0.0969148 0.995293i \(-0.530897\pi\)
−0.0969148 + 0.995293i \(0.530897\pi\)
\(510\) 0 0
\(511\) 44.0518i 1.94874i
\(512\) 3.41624 + 22.3680i 0.150978 + 0.988537i
\(513\) 0 0
\(514\) 11.4924 + 13.2369i 0.506909 + 0.583855i
\(515\) −18.1866 + 3.89445i −0.801397 + 0.171610i
\(516\) 0 0
\(517\) −1.90495 −0.0837794
\(518\) −1.04129 1.19935i −0.0457517 0.0526965i
\(519\) 0 0
\(520\) 7.58786 7.58289i 0.332750 0.332532i
\(521\) 14.3162i 0.627206i −0.949554 0.313603i \(-0.898464\pi\)
0.949554 0.313603i \(-0.101536\pi\)
\(522\) 0 0
\(523\) 18.6795i 0.816798i 0.912803 + 0.408399i \(0.133913\pi\)
−0.912803 + 0.408399i \(0.866087\pi\)
\(524\) 12.7742 + 1.81129i 0.558045 + 0.0791266i
\(525\) 0 0
\(526\) −13.1231 + 11.3936i −0.572195 + 0.496785i
\(527\) 11.4677i 0.499540i
\(528\) 0 0
\(529\) −21.4924 −0.934453
\(530\) −19.0186 + 25.2858i −0.826115 + 1.09835i
\(531\) 0 0
\(532\) 4.34475 30.6417i 0.188369 1.32848i
\(533\) 9.89012i 0.428389i
\(534\) 0 0
\(535\) −16.2177 + 3.47284i −0.701154 + 0.150144i
\(536\) −20.6372 31.9069i −0.891389 1.37817i
\(537\) 0 0
\(538\) 1.77766 + 2.04750i 0.0766402 + 0.0882738i
\(539\) 7.69113i 0.331280i
\(540\) 0 0
\(541\) 37.8674i 1.62805i 0.580831 + 0.814024i \(0.302728\pi\)
−0.580831 + 0.814024i \(0.697272\pi\)
\(542\) −28.2711 + 24.5453i −1.21435 + 1.05431i
\(543\) 0 0
\(544\) 15.6847 + 33.9071i 0.672474 + 1.45375i
\(545\) −4.52162 21.1154i −0.193685 0.904486i
\(546\) 0 0
\(547\) 32.1143i 1.37311i −0.727079 0.686553i \(-0.759123\pi\)
0.727079 0.686553i \(-0.240877\pi\)
\(548\) 1.85431 13.0776i 0.0792120 0.558647i
\(549\) 0 0
\(550\) −10.7696 + 23.2416i −0.459215 + 0.991025i
\(551\) 34.9840 1.49037
\(552\) 0 0
\(553\) 42.6038i 1.81170i
\(554\) −11.0081 12.6790i −0.467688 0.538681i
\(555\) 0 0
\(556\) 3.36932 23.7623i 0.142891 1.00775i
\(557\) 9.18425i 0.389149i −0.980888 0.194575i \(-0.937667\pi\)
0.980888 0.194575i \(-0.0623326\pi\)
\(558\) 0 0
\(559\) 8.89586i 0.376255i
\(560\) −26.9481 1.90989i −1.13877 0.0807076i
\(561\) 0 0
\(562\) −9.24726 + 8.02857i −0.390072 + 0.338665i
\(563\) −5.79119 −0.244070 −0.122035 0.992526i \(-0.538942\pi\)
−0.122035 + 0.992526i \(0.538942\pi\)
\(564\) 0 0
\(565\) −1.77766 + 0.380664i −0.0747865 + 0.0160147i
\(566\) −16.8025 + 14.5881i −0.706262 + 0.613183i
\(567\) 0 0
\(568\) 5.83209 3.77216i 0.244709 0.158276i
\(569\) 6.72287i 0.281837i −0.990021 0.140919i \(-0.954994\pi\)
0.990021 0.140919i \(-0.0450056\pi\)
\(570\) 0 0
\(571\) −23.8617 −0.998583 −0.499291 0.866434i \(-0.666406\pi\)
−0.499291 + 0.866434i \(0.666406\pi\)
\(572\) −12.1671 1.72521i −0.508733 0.0721345i
\(573\) 0 0
\(574\) 18.8078 16.3291i 0.785021 0.681563i
\(575\) 13.6573 + 30.4268i 0.569550 + 1.26888i
\(576\) 0 0
\(577\) 5.24477i 0.218342i −0.994023 0.109171i \(-0.965180\pi\)
0.994023 0.109171i \(-0.0348197\pi\)
\(578\) 24.6767 + 28.4224i 1.02641 + 1.18222i
\(579\) 0 0
\(580\) −2.13898 30.4637i −0.0888163 1.26494i
\(581\) −17.4920 −0.725690
\(582\) 0 0
\(583\) 36.2454 1.50113
\(584\) 22.4033 + 34.6375i 0.927056 + 1.43331i
\(585\) 0 0
\(586\) 18.1231 15.7347i 0.748659 0.649993i
\(587\) −7.41722 −0.306141 −0.153071 0.988215i \(-0.548916\pi\)
−0.153071 + 0.988215i \(0.548916\pi\)
\(588\) 0 0
\(589\) 8.89586i 0.366548i
\(590\) 9.24318 12.2891i 0.380536 0.505934i
\(591\) 0 0
\(592\) −1.42871 0.413473i −0.0587196 0.0169936i
\(593\) −23.9778 −0.984649 −0.492325 0.870412i \(-0.663853\pi\)
−0.492325 + 0.870412i \(0.663853\pi\)
\(594\) 0 0
\(595\) −43.6155 + 9.33976i −1.78806 + 0.382893i
\(596\) −4.37300 + 30.8408i −0.179125 + 1.26329i
\(597\) 0 0
\(598\) −12.0818 + 10.4895i −0.494061 + 0.428949i
\(599\) −29.7703 −1.21638 −0.608191 0.793790i \(-0.708105\pi\)
−0.608191 + 0.793790i \(0.708105\pi\)
\(600\) 0 0
\(601\) 1.36932 0.0558556 0.0279278 0.999610i \(-0.491109\pi\)
0.0279278 + 0.999610i \(0.491109\pi\)
\(602\) 16.9170 14.6875i 0.689486 0.598619i
\(603\) 0 0
\(604\) 21.0540 + 2.98529i 0.856674 + 0.121470i
\(605\) 4.64217 0.994066i 0.188731 0.0404145i
\(606\) 0 0
\(607\) −43.4018 −1.76162 −0.880812 0.473467i \(-0.843002\pi\)
−0.880812 + 0.473467i \(0.843002\pi\)
\(608\) −12.1671 26.3029i −0.493442 1.06672i
\(609\) 0 0
\(610\) 0 0
\(611\) 0.891921i 0.0360832i
\(612\) 0 0
\(613\) 22.6305 0.914036 0.457018 0.889457i \(-0.348917\pi\)
0.457018 + 0.889457i \(0.348917\pi\)
\(614\) 19.9477 17.3188i 0.805022 0.698928i
\(615\) 0 0
\(616\) 16.8078 + 25.9863i 0.677204 + 1.04702i
\(617\) −12.3954 −0.499020 −0.249510 0.968372i \(-0.580270\pi\)
−0.249510 + 0.968372i \(0.580270\pi\)
\(618\) 0 0
\(619\) −30.7386 −1.23549 −0.617745 0.786378i \(-0.711954\pi\)
−0.617745 + 0.786378i \(0.711954\pi\)
\(620\) −7.74644 + 0.543908i −0.311104 + 0.0218439i
\(621\) 0 0
\(622\) 20.7713 + 23.9243i 0.832853 + 0.959276i
\(623\) 30.9526i 1.24009i
\(624\) 0 0
\(625\) 16.6155 18.6795i 0.664621 0.747181i
\(626\) −23.0928 + 20.0494i −0.922975 + 0.801336i
\(627\) 0 0
\(628\) −2.54421 + 17.9432i −0.101525 + 0.716012i
\(629\) −2.45567 −0.0979139
\(630\) 0 0
\(631\) 10.6323i 0.423265i −0.977349 0.211632i \(-0.932122\pi\)
0.977349 0.211632i \(-0.0678779\pi\)
\(632\) −21.6669 33.4990i −0.861864 1.33252i
\(633\) 0 0
\(634\) −0.123106 + 0.106882i −0.00488915 + 0.00424481i
\(635\) 33.0210 7.07107i 1.31040 0.280607i
\(636\) 0 0
\(637\) 3.60109 0.142680
\(638\) −26.4168 + 22.9354i −1.04585 + 0.908019i
\(639\) 0 0
\(640\) −22.1604 + 12.2032i −0.875965 + 0.482374i
\(641\) 7.07107i 0.279290i −0.990202 0.139645i \(-0.955404\pi\)
0.990202 0.139645i \(-0.0445962\pi\)
\(642\) 0 0
\(643\) 37.3590i 1.47330i 0.676276 + 0.736648i \(0.263593\pi\)
−0.676276 + 0.736648i \(0.736407\pi\)
\(644\) 39.8953 + 5.65685i 1.57210 + 0.222911i
\(645\) 0 0
\(646\) −31.3693 36.1310i −1.23421 1.42156i
\(647\) 4.27156i 0.167932i 0.996469 + 0.0839661i \(0.0267588\pi\)
−0.996469 + 0.0839661i \(0.973241\pi\)
\(648\) 0 0
\(649\) −17.6155 −0.691470
\(650\) 10.8820 + 5.04245i 0.426828 + 0.197781i
\(651\) 0 0
\(652\) −20.7713 2.94521i −0.813467 0.115343i
\(653\) 10.5312i 0.412120i −0.978539 0.206060i \(-0.933936\pi\)
0.978539 0.206060i \(-0.0660641\pi\)
\(654\) 0 0
\(655\) 3.02045 + 14.1051i 0.118019 + 0.551133i
\(656\) 6.48392 22.4044i 0.253155 0.874746i
\(657\) 0 0
\(658\) 1.69614 1.47261i 0.0661225 0.0574082i
\(659\) 27.4901i 1.07086i −0.844579 0.535431i \(-0.820149\pi\)
0.844579 0.535431i \(-0.179851\pi\)
\(660\) 0 0
\(661\) 33.6333i 1.30818i −0.756416 0.654091i \(-0.773051\pi\)
0.756416 0.654091i \(-0.226949\pi\)
\(662\) 21.6669 + 24.9559i 0.842109 + 0.969937i
\(663\) 0 0
\(664\) −13.7538 + 8.89586i −0.533751 + 0.345226i
\(665\) 33.8340 7.24517i 1.31203 0.280955i
\(666\) 0 0
\(667\) 45.5490i 1.76366i
\(668\) 9.49980 + 1.34700i 0.367558 + 0.0521170i
\(669\) 0 0
\(670\) 25.5372 33.9525i 0.986589 1.31170i
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 13.1190 11.3900i 0.505325 0.438728i
\(675\) 0 0
\(676\) 2.84233 20.0457i 0.109320 0.770989i
\(677\) 44.7037i 1.71810i −0.511889 0.859052i \(-0.671054\pi\)
0.511889 0.859052i \(-0.328946\pi\)
\(678\) 0 0
\(679\) 28.2102i 1.08261i
\(680\) −29.5446 + 29.5252i −1.13298 + 1.13224i
\(681\) 0 0
\(682\) 5.83209 + 6.71737i 0.223322 + 0.257222i
\(683\) 32.2080 1.23241 0.616203 0.787588i \(-0.288670\pi\)
0.616203 + 0.787588i \(0.288670\pi\)
\(684\) 0 0
\(685\) 14.4401 3.09218i 0.551727 0.118146i
\(686\) 13.6573 + 15.7304i 0.521439 + 0.600591i
\(687\) 0 0
\(688\) 5.83209 20.1521i 0.222346 0.768292i
\(689\) 16.9706i 0.646527i
\(690\) 0 0
\(691\) −14.8769 −0.565944 −0.282972 0.959128i \(-0.591320\pi\)
−0.282972 + 0.959128i \(0.591320\pi\)
\(692\) −6.60421 0.936426i −0.251054 0.0355976i
\(693\) 0 0
\(694\) 5.36932 + 6.18435i 0.203816 + 0.234755i
\(695\) 26.2380 5.61856i 0.995263 0.213124i
\(696\) 0 0
\(697\) 38.5088i 1.45862i
\(698\) 7.41722 6.43971i 0.280746 0.243746i
\(699\) 0 0
\(700\) −8.37769 29.0194i −0.316647 1.09683i
\(701\) 9.28434 0.350665 0.175332 0.984509i \(-0.443900\pi\)
0.175332 + 0.984509i \(0.443900\pi\)
\(702\) 0 0
\(703\) 1.90495 0.0718464
\(704\) 26.4316 + 11.8849i 0.996178 + 0.447928i
\(705\) 0 0
\(706\) 30.6155 + 35.2628i 1.15223 + 1.32713i
\(707\) 13.2084 0.496753
\(708\) 0 0
\(709\) 15.0802i 0.566349i 0.959068 + 0.283175i \(0.0913876\pi\)
−0.959068 + 0.283175i \(0.908612\pi\)
\(710\) 6.20601 + 4.66782i 0.232907 + 0.175180i
\(711\) 0 0
\(712\) 15.7415 + 24.3378i 0.589938 + 0.912096i
\(713\) 11.5824 0.433764
\(714\) 0 0
\(715\) −2.87689 13.4347i −0.107590 0.502431i
\(716\) 41.4679 + 5.87983i 1.54973 + 0.219740i
\(717\) 0 0
\(718\) 18.4945 + 21.3019i 0.690209 + 0.794980i
\(719\) −47.2623 −1.76259 −0.881294 0.472569i \(-0.843327\pi\)
−0.881294 + 0.472569i \(0.843327\pi\)
\(720\) 0 0
\(721\) −25.1231 −0.935633
\(722\) 6.71834 + 7.73815i 0.250031 + 0.287984i
\(723\) 0 0
\(724\) 12.2462 + 1.73642i 0.455127 + 0.0645335i
\(725\) 31.1493 13.9817i 1.15686 0.519266i
\(726\) 0 0
\(727\) 5.66906 0.210254 0.105127 0.994459i \(-0.466475\pi\)
0.105127 + 0.994459i \(0.466475\pi\)
\(728\) 12.1671 7.86962i 0.450943 0.291667i
\(729\) 0 0
\(730\) −27.7228 + 36.8583i −1.02607 + 1.36419i
\(731\) 34.6375i 1.28111i
\(732\) 0 0
\(733\) 23.9548 0.884790 0.442395 0.896820i \(-0.354129\pi\)
0.442395 + 0.896820i \(0.354129\pi\)
\(734\) 18.5262 + 21.3384i 0.683816 + 0.787615i
\(735\) 0 0
\(736\) 34.2462 15.8415i 1.26233 0.583927i
\(737\) −48.6685 −1.79273
\(738\) 0 0
\(739\) −5.61553 −0.206571 −0.103285 0.994652i \(-0.532935\pi\)
−0.103285 + 0.994652i \(0.532935\pi\)
\(740\) −0.116472 1.65881i −0.00428158 0.0609790i
\(741\) 0 0
\(742\) −32.2725 + 28.0193i −1.18476 + 1.02862i
\(743\) 14.6875i 0.538833i −0.963024 0.269417i \(-0.913169\pi\)
0.963024 0.269417i \(-0.0868308\pi\)
\(744\) 0 0
\(745\) −34.0540 + 7.29226i −1.24764 + 0.267168i
\(746\) −5.25608 6.05393i −0.192439 0.221650i
\(747\) 0 0
\(748\) 47.3747 + 6.71737i 1.73219 + 0.245611i
\(749\) −22.4033 −0.818600
\(750\) 0 0
\(751\) 8.68210i 0.316814i −0.987374 0.158407i \(-0.949364\pi\)
0.987374 0.158407i \(-0.0506359\pi\)
\(752\) 0.584739 2.02050i 0.0213233 0.0736800i
\(753\) 0 0
\(754\) 10.7386 + 12.3687i 0.391078 + 0.450442i
\(755\) 4.97818 + 23.2475i 0.181174 + 0.846062i
\(756\) 0 0
\(757\) 1.69614 0.0616473 0.0308236 0.999525i \(-0.490187\pi\)
0.0308236 + 0.999525i \(0.490187\pi\)
\(758\) 15.2910 + 17.6121i 0.555394 + 0.639700i
\(759\) 0 0
\(760\) 22.9187 22.9037i 0.831350 0.830805i
\(761\) 32.3314i 1.17201i −0.810307 0.586006i \(-0.800700\pi\)
0.810307 0.586006i \(-0.199300\pi\)
\(762\) 0 0
\(763\) 29.1690i 1.05599i
\(764\) 4.91134 34.6375i 0.177686 1.25314i
\(765\) 0 0
\(766\) 15.6847 13.6176i 0.566710 0.492023i
\(767\) 8.24782i 0.297812i
\(768\) 0 0
\(769\) −15.6155 −0.563110 −0.281555 0.959545i \(-0.590850\pi\)
−0.281555 + 0.959545i \(0.590850\pi\)
\(770\) −20.7986 + 27.6524i −0.749529 + 0.996522i
\(771\) 0 0
\(772\) 31.1570 + 4.41782i 1.12136 + 0.159001i
\(773\) 16.1498i 0.580868i −0.956895 0.290434i \(-0.906200\pi\)
0.956895 0.290434i \(-0.0937997\pi\)
\(774\) 0 0
\(775\) −3.55531 7.92077i −0.127711 0.284523i
\(776\) −14.3468 22.1815i −0.515021 0.796268i
\(777\) 0 0
\(778\) −12.1633 14.0096i −0.436076 0.502270i
\(779\) 29.8726i 1.07030i
\(780\) 0 0
\(781\) 8.89586i 0.318319i
\(782\) 47.0425 40.8427i 1.68223 1.46053i
\(783\) 0 0
\(784\) −8.15767 2.36086i −0.291345 0.0843163i
\(785\) −19.8126 + 4.24264i −0.707143 + 0.151426i
\(786\) 0 0
\(787\) 8.18998i 0.291941i 0.989289 + 0.145971i \(0.0466305\pi\)
−0.989289 + 0.145971i \(0.953369\pi\)
\(788\) −48.8968 6.93319i −1.74187 0.246985i
\(789\) 0 0
\(790\) 26.8115 35.6467i 0.953910 1.26825i
\(791\) −2.45567 −0.0873135
\(792\) 0 0
\(793\) 0 0
\(794\) 30.8046 + 35.4806i 1.09321 + 1.25916i
\(795\) 0 0
\(796\) 21.0540 + 2.98529i 0.746238 + 0.105811i
\(797\) 24.1671i 0.856042i −0.903769 0.428021i \(-0.859211\pi\)
0.903769 0.428021i \(-0.140789\pi\)
\(798\) 0 0
\(799\) 3.47284i 0.122860i
\(800\) −21.3456 18.5570i −0.754682 0.656091i
\(801\) 0 0
\(802\) −36.8031 + 31.9528i −1.29956 + 1.12829i
\(803\) 52.8336 1.86446
\(804\) 0 0
\(805\) 9.43318 + 44.0518i 0.332476 + 1.55262i
\(806\) 3.14516 2.73066i 0.110784 0.0961835i
\(807\) 0 0
\(808\) 10.3857 6.71737i 0.365366 0.236316i
\(809\) 37.6400i 1.32335i 0.749789 + 0.661677i \(0.230155\pi\)
−0.749789 + 0.661677i \(0.769845\pi\)
\(810\) 0 0
\(811\) 49.4773 1.73738 0.868691 0.495354i \(-0.164962\pi\)
0.868691 + 0.495354i \(0.164962\pi\)
\(812\) 5.79119 40.8427i 0.203231 1.43330i
\(813\) 0 0
\(814\) −1.43845 + 1.24887i −0.0504175 + 0.0437730i
\(815\) −4.91134 22.9354i −0.172037 0.803390i
\(816\) 0 0
\(817\) 26.8695i 0.940045i
\(818\) −4.74990 5.47091i −0.166076 0.191286i
\(819\) 0 0
\(820\) 26.0128 1.82646i 0.908405 0.0637827i
\(821\) 37.9780 1.32544 0.662720 0.748867i \(-0.269402\pi\)
0.662720 + 0.748867i \(0.269402\pi\)
\(822\) 0 0
\(823\) −32.0636 −1.11767 −0.558834 0.829279i \(-0.688751\pi\)
−0.558834 + 0.829279i \(0.688751\pi\)
\(824\) −19.7541 + 12.7768i −0.688165 + 0.445101i
\(825\) 0 0
\(826\) 15.6847 13.6176i 0.545739 0.473816i
\(827\) −4.16516 −0.144837 −0.0724184 0.997374i \(-0.523072\pi\)
−0.0724184 + 0.997374i \(0.523072\pi\)
\(828\) 0 0
\(829\) 6.18435i 0.214791i −0.994216 0.107396i \(-0.965749\pi\)
0.994216 0.107396i \(-0.0342512\pi\)
\(830\) −14.6356 11.0081i −0.508009 0.382096i
\(831\) 0 0
\(832\) 5.56466 12.3756i 0.192920 0.429047i
\(833\) −14.0214 −0.485814
\(834\) 0 0
\(835\) 2.24621 + 10.4895i 0.0777333 + 0.363005i
\(836\) −36.7502 5.21089i −1.27103 0.180223i
\(837\) 0 0
\(838\) −8.95694 + 7.77651i −0.309412 + 0.268635i
\(839\) 15.0363 0.519111 0.259556 0.965728i \(-0.416424\pi\)
0.259556 + 0.965728i \(0.416424\pi\)
\(840\) 0 0
\(841\) 17.6307 0.607955
\(842\) −16.1040 + 13.9817i −0.554981 + 0.481840i
\(843\) 0 0
\(844\) −1.12311 + 7.92077i −0.0386589 + 0.272644i
\(845\) 22.1342 4.73977i 0.761438 0.163053i
\(846\) 0 0
\(847\) 6.41273 0.220344
\(848\) −11.1258 + 38.4440i −0.382063 + 1.32017i
\(849\) 0 0
\(850\) −42.3710 19.6336i −1.45331 0.673427i
\(851\) 2.48023i 0.0850213i
\(852\) 0 0
\(853\) 22.3044 0.763689 0.381844 0.924227i \(-0.375289\pi\)
0.381844 + 0.924227i \(0.375289\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −17.6155 + 11.3936i −0.602086 + 0.389426i
\(857\) −10.7694 −0.367875 −0.183937 0.982938i \(-0.558884\pi\)
−0.183937 + 0.982938i \(0.558884\pi\)
\(858\) 0 0
\(859\) −50.2462 −1.71438 −0.857189 0.515001i \(-0.827791\pi\)
−0.857189 + 0.515001i \(0.827791\pi\)
\(860\) 23.3977 1.64285i 0.797855 0.0560206i
\(861\) 0 0
\(862\) −18.4945 21.3019i −0.629926 0.725545i
\(863\) 6.43971i 0.219210i −0.993975 0.109605i \(-0.965041\pi\)
0.993975 0.109605i \(-0.0349586\pi\)
\(864\) 0 0
\(865\) −1.56155 7.29226i −0.0530944 0.247944i
\(866\) 11.2017 9.72540i 0.380648 0.330482i
\(867\) 0 0
\(868\) −10.3857 1.47261i −0.352512 0.0499835i
\(869\) −51.0970 −1.73335
\(870\) 0 0
\(871\) 22.7872i 0.772116i
\(872\) −14.8344 22.9354i −0.502358 0.776689i
\(873\) 0 0
\(874\) −36.4924 + 31.6831i −1.23437 + 1.07170i
\(875\) 27.2298 19.9731i 0.920536 0.675214i
\(876\) 0 0
\(877\) −0.789443 −0.0266576 −0.0133288 0.999911i \(-0.504243\pi\)
−0.0133288 + 0.999911i \(0.504243\pi\)
\(878\) 24.5625 21.3254i 0.828945 0.719698i
\(879\) 0 0
\(880\) −2.29063 + 32.3203i −0.0772172 + 1.08952i
\(881\) 5.83095i 0.196450i −0.995164 0.0982249i \(-0.968684\pi\)
0.995164 0.0982249i \(-0.0313164\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 3.14516 22.1815i 0.105783 0.746043i
\(885\) 0 0
\(886\) −1.50758 1.73642i −0.0506481 0.0583362i
\(887\) 18.1379i 0.609012i 0.952510 + 0.304506i \(0.0984914\pi\)
−0.952510 + 0.304506i \(0.901509\pi\)
\(888\) 0 0
\(889\) 45.6155 1.52990
\(890\) −19.4792 + 25.8981i −0.652943 + 0.868108i
\(891\) 0 0
\(892\) −8.05024 + 56.7748i −0.269542 + 1.90096i
\(893\) 2.69400i 0.0901513i
\(894\) 0 0
\(895\) 9.80501 + 45.7882i 0.327745 + 1.53053i
\(896\) −32.7219 + 9.85061i −1.09316 + 0.329086i
\(897\) 0 0
\(898\) 10.5716 9.17834i 0.352778 0.306285i
\(899\) 11.8574i 0.395468i
\(900\) 0 0
\(901\) 66.0777i 2.20137i
\(902\) −19.5843 22.5571i −0.652087 0.751071i
\(903\) 0 0
\(904\) −1.93087 + 1.24887i −0.0642198 + 0.0415369i
\(905\) 2.89560 + 13.5221i 0.0962528 + 0.449489i
\(906\) 0 0
\(907\) 32.1143i 1.06634i 0.846009 + 0.533168i \(0.178999\pi\)
−0.846009 + 0.533168i \(0.821001\pi\)
\(908\) 3.70861 26.1552i 0.123075 0.867991i
\(909\) 0 0
\(910\) 12.9472 + 9.73817i 0.429196 + 0.322817i
\(911\) −12.5807 −0.416816 −0.208408 0.978042i \(-0.566828\pi\)
−0.208408 + 0.978042i \(0.566828\pi\)
\(912\) 0 0
\(913\) 20.9791i 0.694306i
\(914\) −21.1755 + 18.3848i −0.700423 + 0.608114i
\(915\) 0 0
\(916\) −43.6155 6.18435i −1.44110 0.204337i
\(917\) 19.4849i 0.643449i
\(918\) 0 0
\(919\) 49.2611i 1.62497i −0.582981 0.812486i \(-0.698114\pi\)
0.582981 0.812486i \(-0.301886\pi\)
\(920\) 29.8205 + 29.8401i 0.983154 + 0.983799i
\(921\) 0 0
\(922\) 14.4401 + 16.6320i 0.475559 + 0.547746i
\(923\) −4.16516 −0.137098
\(924\) 0 0
\(925\) 1.69614 0.761329i 0.0557688 0.0250323i
\(926\) −16.4577 18.9560i −0.540835 0.622931i
\(927\) 0 0
\(928\) −16.2177 35.0595i −0.532373 1.15088i
\(929\) 8.65938i 0.284105i −0.989859 0.142053i \(-0.954630\pi\)
0.989859 0.142053i \(-0.0453702\pi\)
\(930\) 0 0
\(931\) 10.8769 0.356476
\(932\) −6.01947 + 42.4527i −0.197174 + 1.39058i
\(933\) 0 0
\(934\) 26.0000 + 29.9467i 0.850746 + 0.979885i
\(935\) 11.2017 + 52.3104i 0.366334 + 1.71073i
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 43.3338 37.6229i 1.41490 1.22843i
\(939\) 0 0
\(940\) 2.34591 0.164716i 0.0765151 0.00537243i
\(941\) 4.37300 0.142556 0.0712778 0.997457i \(-0.477292\pi\)
0.0712778 + 0.997457i \(0.477292\pi\)
\(942\) 0 0
\(943\) −38.8940 −1.26656
\(944\) 5.40724 18.6841i 0.175991 0.608115i
\(945\) 0 0
\(946\) −17.6155 20.2895i −0.572730 0.659668i
\(947\) −22.2517 −0.723082 −0.361541 0.932356i \(-0.617749\pi\)
−0.361541 + 0.932356i \(0.617749\pi\)
\(948\) 0 0
\(949\) 24.7374i 0.803010i
\(950\) 32.8686 + 15.2305i 1.06640 + 0.494141i
\(951\) 0 0
\(952\) −47.3747 + 30.6417i −1.53542 + 0.993102i
\(953\) −0.813015 −0.0263361 −0.0131681 0.999913i \(-0.504192\pi\)
−0.0131681 + 0.999913i \(0.504192\pi\)
\(954\) 0 0
\(955\) 38.2462 8.18998i 1.23762 0.265022i
\(956\) −1.37899 + 9.72540i −0.0445997 + 0.314542i
\(957\) 0 0
\(958\) −34.7123 39.9814i −1.12150 1.29174i
\(959\) 19.9477 0.644143
\(960\) 0 0
\(961\) 27.9848 0.902737
\(962\) 0.584739 + 0.673500i 0.0188528 + 0.0217145i
\(963\) 0 0
\(964\) 1.12311 7.92077i 0.0361728 0.255111i
\(965\) 7.36701 + 34.4030i 0.237152 + 1.10747i
\(966\) 0 0
\(967\) −23.7917 −0.765091 −0.382546 0.923937i \(-0.624952\pi\)
−0.382546 + 0.923937i \(0.624952\pi\)
\(968\) 5.04227 3.26131i 0.162065 0.104822i
\(969\) 0 0
\(970\) 17.7533 23.6036i 0.570025 0.757866i
\(971\) 32.6032i 1.04629i 0.852244 + 0.523144i \(0.175241\pi\)
−0.852244 + 0.523144i \(0.824759\pi\)
\(972\) 0 0
\(973\) 36.2454 1.16197
\(974\) −4.17940 4.81382i −0.133917 0.154245i
\(975\) 0 0
\(976\) 0 0
\(977\) 2.43904 0.0780319 0.0390160 0.999239i \(-0.487578\pi\)
0.0390160 + 0.999239i \(0.487578\pi\)
\(978\) 0 0
\(979\) 37.1231 1.18646
\(980\) −0.665032 9.47150i −0.0212437 0.302556i
\(981\) 0 0
\(982\) 11.2337 9.75323i 0.358482 0.311238i
\(983\) 12.5841i 0.401371i 0.979656 + 0.200685i \(0.0643169\pi\)
−0.979656 + 0.200685i \(0.935683\pi\)
\(984\) 0 0
\(985\) −11.5616 53.9910i −0.368382 1.72030i
\(986\) −41.8126 48.1596i −1.33159 1.53371i
\(987\) 0 0
\(988\) −2.43981 + 17.2069i −0.0776207 + 0.547425i
\(989\) −34.9840 −1.11243
\(990\) 0 0
\(991\) 10.6323i 0.337746i 0.985638 + 0.168873i \(0.0540127\pi\)
−0.985638 + 0.168873i \(0.945987\pi\)
\(992\) −8.91506 + 4.12391i −0.283053 + 0.130934i
\(993\) 0 0
\(994\) 6.87689 + 7.92077i 0.218122 + 0.251232i
\(995\) 4.97818 + 23.2475i 0.157819 + 0.736995i
\(996\) 0 0
\(997\) −32.4813 −1.02869 −0.514346 0.857583i \(-0.671965\pi\)
−0.514346 + 0.857583i \(0.671965\pi\)
\(998\) 23.2930 + 26.8287i 0.737325 + 0.849248i
\(999\) 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 360.2.m.c.179.11 yes 16
3.2 odd 2 inner 360.2.m.c.179.6 yes 16
4.3 odd 2 1440.2.m.c.719.4 16
5.2 odd 4 1800.2.b.g.251.3 16
5.3 odd 4 1800.2.b.g.251.14 16
5.4 even 2 inner 360.2.m.c.179.5 16
8.3 odd 2 inner 360.2.m.c.179.10 yes 16
8.5 even 2 1440.2.m.c.719.13 16
12.11 even 2 1440.2.m.c.719.14 16
15.2 even 4 1800.2.b.g.251.13 16
15.8 even 4 1800.2.b.g.251.4 16
15.14 odd 2 inner 360.2.m.c.179.12 yes 16
20.3 even 4 7200.2.b.i.4751.2 16
20.7 even 4 7200.2.b.i.4751.13 16
20.19 odd 2 1440.2.m.c.719.1 16
24.5 odd 2 1440.2.m.c.719.3 16
24.11 even 2 inner 360.2.m.c.179.7 yes 16
40.3 even 4 1800.2.b.g.251.1 16
40.13 odd 4 7200.2.b.i.4751.14 16
40.19 odd 2 inner 360.2.m.c.179.8 yes 16
40.27 even 4 1800.2.b.g.251.16 16
40.29 even 2 1440.2.m.c.719.16 16
40.37 odd 4 7200.2.b.i.4751.1 16
60.23 odd 4 7200.2.b.i.4751.3 16
60.47 odd 4 7200.2.b.i.4751.16 16
60.59 even 2 1440.2.m.c.719.15 16
120.29 odd 2 1440.2.m.c.719.2 16
120.53 even 4 7200.2.b.i.4751.15 16
120.59 even 2 inner 360.2.m.c.179.9 yes 16
120.77 even 4 7200.2.b.i.4751.4 16
120.83 odd 4 1800.2.b.g.251.15 16
120.107 odd 4 1800.2.b.g.251.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.m.c.179.5 16 5.4 even 2 inner
360.2.m.c.179.6 yes 16 3.2 odd 2 inner
360.2.m.c.179.7 yes 16 24.11 even 2 inner
360.2.m.c.179.8 yes 16 40.19 odd 2 inner
360.2.m.c.179.9 yes 16 120.59 even 2 inner
360.2.m.c.179.10 yes 16 8.3 odd 2 inner
360.2.m.c.179.11 yes 16 1.1 even 1 trivial
360.2.m.c.179.12 yes 16 15.14 odd 2 inner
1440.2.m.c.719.1 16 20.19 odd 2
1440.2.m.c.719.2 16 120.29 odd 2
1440.2.m.c.719.3 16 24.5 odd 2
1440.2.m.c.719.4 16 4.3 odd 2
1440.2.m.c.719.13 16 8.5 even 2
1440.2.m.c.719.14 16 12.11 even 2
1440.2.m.c.719.15 16 60.59 even 2
1440.2.m.c.719.16 16 40.29 even 2
1800.2.b.g.251.1 16 40.3 even 4
1800.2.b.g.251.2 16 120.107 odd 4
1800.2.b.g.251.3 16 5.2 odd 4
1800.2.b.g.251.4 16 15.8 even 4
1800.2.b.g.251.13 16 15.2 even 4
1800.2.b.g.251.14 16 5.3 odd 4
1800.2.b.g.251.15 16 120.83 odd 4
1800.2.b.g.251.16 16 40.27 even 4
7200.2.b.i.4751.1 16 40.37 odd 4
7200.2.b.i.4751.2 16 20.3 even 4
7200.2.b.i.4751.3 16 60.23 odd 4
7200.2.b.i.4751.4 16 120.77 even 4
7200.2.b.i.4751.13 16 20.7 even 4
7200.2.b.i.4751.14 16 40.13 odd 4
7200.2.b.i.4751.15 16 120.53 even 4
7200.2.b.i.4751.16 16 60.47 odd 4