Properties

Label 605.2.m.e.282.4
Level $605$
Weight $2$
Character 605.282
Analytic conductor $4.831$
Analytic rank $0$
Dimension $32$
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] = [605,2,Mod(112,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.112");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.m (of order \(20\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 55)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 282.4
Character \(\chi\) \(=\) 605.282
Dual form 605.2.m.e.118.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.40264 - 0.380541i) q^{2} +(-0.271495 - 0.532840i) q^{3} +(3.72576 - 1.21057i) q^{4} +(1.85044 + 1.25533i) q^{5} +(-0.855073 - 1.17691i) q^{6} +(-2.30033 - 1.17208i) q^{7} +(4.15610 - 2.11764i) q^{8} +(1.55315 - 2.13772i) q^{9} +O(q^{10})\) \(q+(2.40264 - 0.380541i) q^{2} +(-0.271495 - 0.532840i) q^{3} +(3.72576 - 1.21057i) q^{4} +(1.85044 + 1.25533i) q^{5} +(-0.855073 - 1.17691i) q^{6} +(-2.30033 - 1.17208i) q^{7} +(4.15610 - 2.11764i) q^{8} +(1.55315 - 2.13772i) q^{9} +(4.92366 + 2.31195i) q^{10} +(-1.65657 - 1.65657i) q^{12} +(0.439393 + 2.77422i) q^{13} +(-5.97289 - 1.94071i) q^{14} +(0.166506 - 1.32681i) q^{15} +(2.84111 - 2.06419i) q^{16} +(-0.147723 + 0.932684i) q^{17} +(2.91817 - 5.72722i) q^{18} +(1.28236 - 3.94669i) q^{19} +(8.41399 + 2.43698i) q^{20} +1.54392i q^{21} +(0.104710 - 0.104710i) q^{23} +(-2.25672 - 1.63960i) q^{24} +(1.84827 + 4.64585i) q^{25} +(2.11141 + 6.49824i) q^{26} +(-3.33271 - 0.527849i) q^{27} +(-9.98937 - 1.58216i) q^{28} +(2.14459 + 6.60038i) q^{29} +(-0.104851 - 3.25120i) q^{30} +(-7.33171 - 5.32680i) q^{31} +(-0.555921 + 0.555921i) q^{32} +2.29712i q^{34} +(-2.78528 - 5.05654i) q^{35} +(3.19879 - 9.84486i) q^{36} +(-3.44950 + 6.77002i) q^{37} +(1.57917 - 9.97047i) q^{38} +(1.35892 - 0.987312i) q^{39} +(10.3490 + 1.29873i) q^{40} +(-3.27880 - 1.06535i) q^{41} +(0.587525 + 3.70949i) q^{42} +(3.91833 + 3.91833i) q^{43} +(5.55757 - 2.00601i) q^{45} +(0.211733 - 0.291426i) q^{46} +(-0.942051 + 0.479999i) q^{47} +(-1.87123 - 0.953440i) q^{48} +(-0.196744 - 0.270795i) q^{49} +(6.20867 + 10.4590i) q^{50} +(0.537077 - 0.174507i) q^{51} +(4.99547 + 9.80416i) q^{52} +(-4.07187 + 0.644920i) q^{53} -8.20817 q^{54} -12.0424 q^{56} +(-2.45111 + 0.388217i) q^{57} +(7.66441 + 15.0422i) q^{58} +(6.16460 - 2.00300i) q^{59} +(-0.985836 - 5.14493i) q^{60} +(-5.59880 - 7.70609i) q^{61} +(-19.6426 - 10.0084i) q^{62} +(-6.07833 + 3.09706i) q^{63} +(-5.25251 + 7.22946i) q^{64} +(-2.66950 + 5.68511i) q^{65} +(2.94509 + 2.94509i) q^{67} +(0.578703 + 3.65379i) q^{68} +(-0.0842215 - 0.0273652i) q^{69} +(-8.61625 - 11.0891i) q^{70} +(-1.02426 + 0.744171i) q^{71} +(1.92811 - 12.1736i) q^{72} +(-0.804189 + 1.57831i) q^{73} +(-5.71163 + 17.5786i) q^{74} +(1.97369 - 2.24616i) q^{75} -16.2568i q^{76} +(2.88928 - 2.88928i) q^{78} +(-3.51271 - 2.55214i) q^{79} +(7.84857 - 0.253115i) q^{80} +(-1.82606 - 5.62003i) q^{81} +(-8.28320 - 1.31193i) q^{82} +(8.18939 + 1.29707i) q^{83} +(1.86903 + 5.75228i) q^{84} +(-1.44418 + 1.54044i) q^{85} +(10.9054 + 7.92326i) q^{86} +(2.93470 - 2.93470i) q^{87} +4.23092i q^{89} +(12.5895 - 6.93462i) q^{90} +(2.24084 - 6.89661i) q^{91} +(0.263364 - 0.516882i) q^{92} +(-0.847805 + 5.35283i) q^{93} +(-2.08075 + 1.51175i) q^{94} +(7.32735 - 5.69333i) q^{95} +(0.447147 + 0.145287i) q^{96} +(-2.25634 - 14.2460i) q^{97} +(-0.575755 - 0.575755i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 10 q^{2} - 4 q^{3} - 2 q^{5} + 20 q^{6} + 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 10 q^{2} - 4 q^{3} - 2 q^{5} + 20 q^{6} + 10 q^{8} + 12 q^{12} + 10 q^{13} + 14 q^{15} - 8 q^{16} + 10 q^{18} + 16 q^{20} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} - 50 q^{28} - 30 q^{30} - 28 q^{31} + 10 q^{35} + 24 q^{36} - 8 q^{37} + 10 q^{38} + 50 q^{40} - 40 q^{41} - 10 q^{42} - 28 q^{45} - 60 q^{46} - 28 q^{47} - 54 q^{48} + 50 q^{50} - 20 q^{51} + 50 q^{52} - 24 q^{53} - 80 q^{56} - 30 q^{57} - 50 q^{58} + 34 q^{60} + 60 q^{61} - 100 q^{62} + 30 q^{63} - 8 q^{67} + 30 q^{68} + 30 q^{70} + 24 q^{71} - 80 q^{72} - 50 q^{73} + 34 q^{75} + 60 q^{78} + 98 q^{80} - 12 q^{81} - 10 q^{82} - 90 q^{83} - 30 q^{85} + 100 q^{86} + 20 q^{90} + 20 q^{91} - 68 q^{92} - 8 q^{93} + 40 q^{95} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.40264 0.380541i 1.69892 0.269083i 0.769648 0.638468i \(-0.220432\pi\)
0.929276 + 0.369385i \(0.120432\pi\)
\(3\) −0.271495 0.532840i −0.156748 0.307635i 0.799255 0.600992i \(-0.205228\pi\)
−0.956003 + 0.293357i \(0.905228\pi\)
\(4\) 3.72576 1.21057i 1.86288 0.605287i
\(5\) 1.85044 + 1.25533i 0.827543 + 0.561403i
\(6\) −0.855073 1.17691i −0.349082 0.480470i
\(7\) −2.30033 1.17208i −0.869443 0.443003i −0.0384331 0.999261i \(-0.512237\pi\)
−0.831010 + 0.556258i \(0.812237\pi\)
\(8\) 4.15610 2.11764i 1.46940 0.748698i
\(9\) 1.55315 2.13772i 0.517716 0.712575i
\(10\) 4.92366 + 2.31195i 1.55700 + 0.731103i
\(11\) 0 0
\(12\) −1.65657 1.65657i −0.478210 0.478210i
\(13\) 0.439393 + 2.77422i 0.121866 + 0.769429i 0.970616 + 0.240635i \(0.0773556\pi\)
−0.848750 + 0.528794i \(0.822644\pi\)
\(14\) −5.97289 1.94071i −1.59632 0.518677i
\(15\) 0.166506 1.32681i 0.0429916 0.342580i
\(16\) 2.84111 2.06419i 0.710279 0.516048i
\(17\) −0.147723 + 0.932684i −0.0358280 + 0.226209i −0.999105 0.0423009i \(-0.986531\pi\)
0.963277 + 0.268510i \(0.0865312\pi\)
\(18\) 2.91817 5.72722i 0.687818 1.34992i
\(19\) 1.28236 3.94669i 0.294193 0.905433i −0.689298 0.724478i \(-0.742081\pi\)
0.983491 0.180955i \(-0.0579189\pi\)
\(20\) 8.41399 + 2.43698i 1.88142 + 0.544926i
\(21\) 1.54392i 0.336911i
\(22\) 0 0
\(23\) 0.104710 0.104710i 0.0218334 0.0218334i −0.696106 0.717939i \(-0.745086\pi\)
0.717939 + 0.696106i \(0.245086\pi\)
\(24\) −2.25672 1.63960i −0.460651 0.334683i
\(25\) 1.84827 + 4.64585i 0.369654 + 0.929169i
\(26\) 2.11141 + 6.49824i 0.414081 + 1.27441i
\(27\) −3.33271 0.527849i −0.641380 0.101585i
\(28\) −9.98937 1.58216i −1.88781 0.299000i
\(29\) 2.14459 + 6.60038i 0.398241 + 1.22566i 0.926409 + 0.376520i \(0.122879\pi\)
−0.528168 + 0.849140i \(0.677121\pi\)
\(30\) −0.104851 3.25120i −0.0191430 0.593586i
\(31\) −7.33171 5.32680i −1.31681 0.956722i −0.999966 0.00824590i \(-0.997375\pi\)
−0.316849 0.948476i \(-0.602625\pi\)
\(32\) −0.555921 + 0.555921i −0.0982739 + 0.0982739i
\(33\) 0 0
\(34\) 2.29712i 0.393953i
\(35\) −2.78528 5.05654i −0.470798 0.854712i
\(36\) 3.19879 9.84486i 0.533131 1.64081i
\(37\) −3.44950 + 6.77002i −0.567094 + 1.11298i 0.412305 + 0.911046i \(0.364724\pi\)
−0.979398 + 0.201938i \(0.935276\pi\)
\(38\) 1.57917 9.97047i 0.256175 1.61742i
\(39\) 1.35892 0.987312i 0.217601 0.158096i
\(40\) 10.3490 + 1.29873i 1.63631 + 0.205347i
\(41\) −3.27880 1.06535i −0.512063 0.166379i 0.0415772 0.999135i \(-0.486762\pi\)
−0.553640 + 0.832756i \(0.686762\pi\)
\(42\) 0.587525 + 3.70949i 0.0906571 + 0.572386i
\(43\) 3.91833 + 3.91833i 0.597540 + 0.597540i 0.939657 0.342117i \(-0.111144\pi\)
−0.342117 + 0.939657i \(0.611144\pi\)
\(44\) 0 0
\(45\) 5.55757 2.00601i 0.828473 0.299039i
\(46\) 0.211733 0.291426i 0.0312184 0.0429684i
\(47\) −0.942051 + 0.479999i −0.137412 + 0.0700150i −0.521345 0.853346i \(-0.674569\pi\)
0.383933 + 0.923361i \(0.374569\pi\)
\(48\) −1.87123 0.953440i −0.270089 0.137617i
\(49\) −0.196744 0.270795i −0.0281063 0.0386850i
\(50\) 6.20867 + 10.4590i 0.878038 + 1.47912i
\(51\) 0.537077 0.174507i 0.0752058 0.0244358i
\(52\) 4.99547 + 9.80416i 0.692747 + 1.35959i
\(53\) −4.07187 + 0.644920i −0.559314 + 0.0885866i −0.429690 0.902977i \(-0.641377\pi\)
−0.129624 + 0.991563i \(0.541377\pi\)
\(54\) −8.20817 −1.11699
\(55\) 0 0
\(56\) −12.0424 −1.60924
\(57\) −2.45111 + 0.388217i −0.324657 + 0.0514206i
\(58\) 7.66441 + 15.0422i 1.00639 + 1.97514i
\(59\) 6.16460 2.00300i 0.802563 0.260768i 0.121118 0.992638i \(-0.461352\pi\)
0.681445 + 0.731870i \(0.261352\pi\)
\(60\) −0.985836 5.14493i −0.127271 0.664208i
\(61\) −5.59880 7.70609i −0.716853 0.986663i −0.999622 0.0274756i \(-0.991253\pi\)
0.282769 0.959188i \(-0.408747\pi\)
\(62\) −19.6426 10.0084i −2.49461 1.27107i
\(63\) −6.07833 + 3.09706i −0.765797 + 0.390193i
\(64\) −5.25251 + 7.22946i −0.656564 + 0.903682i
\(65\) −2.66950 + 5.68511i −0.331111 + 0.705151i
\(66\) 0 0
\(67\) 2.94509 + 2.94509i 0.359801 + 0.359801i 0.863739 0.503939i \(-0.168116\pi\)
−0.503939 + 0.863739i \(0.668116\pi\)
\(68\) 0.578703 + 3.65379i 0.0701781 + 0.443087i
\(69\) −0.0842215 0.0273652i −0.0101391 0.00329439i
\(70\) −8.61625 11.0891i −1.02984 1.32541i
\(71\) −1.02426 + 0.744171i −0.121558 + 0.0883168i −0.646903 0.762572i \(-0.723936\pi\)
0.525345 + 0.850889i \(0.323936\pi\)
\(72\) 1.92811 12.1736i 0.227230 1.43467i
\(73\) −0.804189 + 1.57831i −0.0941232 + 0.184727i −0.933268 0.359181i \(-0.883056\pi\)
0.839145 + 0.543908i \(0.183056\pi\)
\(74\) −5.71163 + 17.5786i −0.663964 + 2.04347i
\(75\) 1.97369 2.24616i 0.227903 0.259364i
\(76\) 16.2568i 1.86479i
\(77\) 0 0
\(78\) 2.88928 2.88928i 0.327147 0.327147i
\(79\) −3.51271 2.55214i −0.395211 0.287138i 0.372376 0.928082i \(-0.378543\pi\)
−0.767588 + 0.640944i \(0.778543\pi\)
\(80\) 7.84857 0.253115i 0.877497 0.0282991i
\(81\) −1.82606 5.62003i −0.202895 0.624448i
\(82\) −8.28320 1.31193i −0.914726 0.144878i
\(83\) 8.18939 + 1.29707i 0.898902 + 0.142372i 0.588750 0.808315i \(-0.299620\pi\)
0.310152 + 0.950687i \(0.399620\pi\)
\(84\) 1.86903 + 5.75228i 0.203928 + 0.627625i
\(85\) −1.44418 + 1.54044i −0.156644 + 0.167084i
\(86\) 10.9054 + 7.92326i 1.17596 + 0.854388i
\(87\) 2.93470 2.93470i 0.314632 0.314632i
\(88\) 0 0
\(89\) 4.23092i 0.448477i 0.974534 + 0.224238i \(0.0719894\pi\)
−0.974534 + 0.224238i \(0.928011\pi\)
\(90\) 12.5895 6.93462i 1.32705 0.730973i
\(91\) 2.24084 6.89661i 0.234904 0.722961i
\(92\) 0.263364 0.516882i 0.0274576 0.0538886i
\(93\) −0.847805 + 5.35283i −0.0879133 + 0.555063i
\(94\) −2.08075 + 1.51175i −0.214613 + 0.155926i
\(95\) 7.32735 5.69333i 0.751770 0.584124i
\(96\) 0.447147 + 0.145287i 0.0456367 + 0.0148283i
\(97\) −2.25634 14.2460i −0.229097 1.44646i −0.787205 0.616691i \(-0.788473\pi\)
0.558109 0.829768i \(-0.311527\pi\)
\(98\) −0.575755 0.575755i −0.0581600 0.0581600i
\(99\) 0 0
\(100\) 12.5104 + 15.0719i 1.25104 + 1.50719i
\(101\) −1.13747 + 1.56559i −0.113182 + 0.155782i −0.861850 0.507164i \(-0.830694\pi\)
0.748668 + 0.662946i \(0.230694\pi\)
\(102\) 1.22400 0.623657i 0.121194 0.0617513i
\(103\) 1.53187 + 0.780525i 0.150939 + 0.0769075i 0.527829 0.849351i \(-0.323006\pi\)
−0.376889 + 0.926258i \(0.623006\pi\)
\(104\) 7.70094 + 10.5994i 0.755139 + 1.03936i
\(105\) −1.93814 + 2.85693i −0.189143 + 0.278808i
\(106\) −9.53782 + 3.09903i −0.926395 + 0.301004i
\(107\) −1.88816 3.70571i −0.182535 0.358245i 0.781549 0.623844i \(-0.214430\pi\)
−0.964083 + 0.265600i \(0.914430\pi\)
\(108\) −13.0559 + 2.06785i −1.25630 + 0.198979i
\(109\) −3.22321 −0.308728 −0.154364 0.988014i \(-0.549333\pi\)
−0.154364 + 0.988014i \(0.549333\pi\)
\(110\) 0 0
\(111\) 4.54385 0.431284
\(112\) −8.95489 + 1.41832i −0.846157 + 0.134018i
\(113\) 5.06345 + 9.93758i 0.476329 + 0.934849i 0.996721 + 0.0809210i \(0.0257862\pi\)
−0.520391 + 0.853928i \(0.674214\pi\)
\(114\) −5.74140 + 1.86549i −0.537731 + 0.174720i
\(115\) 0.325204 0.0623134i 0.0303255 0.00581075i
\(116\) 15.9805 + 21.9953i 1.48375 + 2.04221i
\(117\) 6.61295 + 3.36947i 0.611367 + 0.311507i
\(118\) 14.0491 7.15838i 1.29333 0.658982i
\(119\) 1.43299 1.97234i 0.131362 0.180804i
\(120\) −2.11768 5.86693i −0.193317 0.535575i
\(121\) 0 0
\(122\) −16.3844 16.3844i −1.48337 1.48337i
\(123\) 0.322520 + 2.03631i 0.0290807 + 0.183608i
\(124\) −33.7647 10.9708i −3.03216 0.985209i
\(125\) −2.41198 + 10.9171i −0.215734 + 0.976452i
\(126\) −13.4255 + 9.75419i −1.19604 + 0.868972i
\(127\) −0.371538 + 2.34580i −0.0329687 + 0.208156i −0.998674 0.0514856i \(-0.983604\pi\)
0.965705 + 0.259641i \(0.0836044\pi\)
\(128\) −9.15495 + 17.9676i −0.809191 + 1.58813i
\(129\) 1.02403 3.15165i 0.0901611 0.277487i
\(130\) −4.25043 + 14.6751i −0.372788 + 1.28709i
\(131\) 3.12466i 0.273003i 0.990640 + 0.136501i \(0.0435858\pi\)
−0.990640 + 0.136501i \(0.956414\pi\)
\(132\) 0 0
\(133\) −7.57567 + 7.57567i −0.656894 + 0.656894i
\(134\) 8.19674 + 5.95528i 0.708090 + 0.514458i
\(135\) −5.50435 5.16042i −0.473739 0.444138i
\(136\) 1.36114 + 4.18915i 0.116716 + 0.359216i
\(137\) 16.3323 + 2.58679i 1.39537 + 0.221004i 0.808412 0.588617i \(-0.200327\pi\)
0.586953 + 0.809621i \(0.300327\pi\)
\(138\) −0.212768 0.0336991i −0.0181120 0.00286866i
\(139\) 1.33510 + 4.10901i 0.113242 + 0.348522i 0.991576 0.129524i \(-0.0413451\pi\)
−0.878335 + 0.478046i \(0.841345\pi\)
\(140\) −16.4986 15.4677i −1.39439 1.30726i
\(141\) 0.511525 + 0.371645i 0.0430782 + 0.0312981i
\(142\) −2.17775 + 2.17775i −0.182753 + 0.182753i
\(143\) 0 0
\(144\) 9.27951i 0.773293i
\(145\) −4.31724 + 14.9058i −0.358527 + 1.23786i
\(146\) −1.33157 + 4.09814i −0.110201 + 0.339164i
\(147\) −0.0908753 + 0.178353i −0.00749527 + 0.0147103i
\(148\) −4.65640 + 29.3994i −0.382754 + 2.41661i
\(149\) 6.83188 4.96365i 0.559689 0.406638i −0.271656 0.962394i \(-0.587571\pi\)
0.831345 + 0.555756i \(0.187571\pi\)
\(150\) 3.88733 6.14778i 0.317399 0.501964i
\(151\) −11.3483 3.68729i −0.923513 0.300068i −0.191606 0.981472i \(-0.561370\pi\)
−0.731907 + 0.681404i \(0.761370\pi\)
\(152\) −3.02806 19.1184i −0.245608 1.55071i
\(153\) 1.76439 + 1.76439i 0.142642 + 0.142642i
\(154\) 0 0
\(155\) −6.87999 19.0607i −0.552614 1.53099i
\(156\) 3.86780 5.32357i 0.309672 0.426226i
\(157\) −1.21312 + 0.618117i −0.0968177 + 0.0493311i −0.501729 0.865025i \(-0.667302\pi\)
0.404911 + 0.914356i \(0.367302\pi\)
\(158\) −9.41098 4.79514i −0.748698 0.381481i
\(159\) 1.44913 + 1.99456i 0.114924 + 0.158179i
\(160\) −1.72657 + 0.330833i −0.136497 + 0.0261546i
\(161\) −0.363594 + 0.118139i −0.0286552 + 0.00931064i
\(162\) −6.52602 12.8080i −0.512732 1.00629i
\(163\) 22.6610 3.58914i 1.77494 0.281123i 0.818812 0.574062i \(-0.194633\pi\)
0.956131 + 0.292939i \(0.0946333\pi\)
\(164\) −13.5057 −1.05462
\(165\) 0 0
\(166\) 20.1698 1.56548
\(167\) −14.1836 + 2.24646i −1.09756 + 0.173836i −0.678845 0.734282i \(-0.737519\pi\)
−0.418714 + 0.908118i \(0.637519\pi\)
\(168\) 3.26946 + 6.41668i 0.252244 + 0.495058i
\(169\) 4.86053 1.57928i 0.373887 0.121483i
\(170\) −2.88365 + 4.25069i −0.221166 + 0.326013i
\(171\) −6.44525 8.87112i −0.492880 0.678391i
\(172\) 19.3422 + 9.85535i 1.47483 + 0.751464i
\(173\) 19.8708 10.1247i 1.51075 0.769766i 0.514601 0.857430i \(-0.327940\pi\)
0.996150 + 0.0876641i \(0.0279402\pi\)
\(174\) 5.93425 8.16780i 0.449874 0.619199i
\(175\) 1.19366 12.8533i 0.0902321 0.971618i
\(176\) 0 0
\(177\) −2.74094 2.74094i −0.206022 0.206022i
\(178\) 1.61004 + 10.1654i 0.120678 + 0.761928i
\(179\) 4.15441 + 1.34985i 0.310516 + 0.100893i 0.460129 0.887852i \(-0.347803\pi\)
−0.149614 + 0.988745i \(0.547803\pi\)
\(180\) 18.2778 14.2018i 1.36234 1.05854i
\(181\) −7.63694 + 5.54857i −0.567650 + 0.412422i −0.834251 0.551385i \(-0.814099\pi\)
0.266601 + 0.963807i \(0.414099\pi\)
\(182\) 2.75950 17.4228i 0.204548 1.29147i
\(183\) −2.58606 + 5.07543i −0.191167 + 0.375187i
\(184\) 0.213446 0.656920i 0.0157355 0.0484287i
\(185\) −14.8817 + 8.19725i −1.09413 + 0.602674i
\(186\) 13.1836i 0.966665i
\(187\) 0 0
\(188\) −2.92879 + 2.92879i −0.213604 + 0.213604i
\(189\) 7.04765 + 5.12041i 0.512641 + 0.372455i
\(190\) 15.4384 16.4674i 1.12002 1.19467i
\(191\) −2.00020 6.15597i −0.144729 0.445430i 0.852247 0.523140i \(-0.175239\pi\)
−0.996976 + 0.0777092i \(0.975239\pi\)
\(192\) 5.27817 + 0.835981i 0.380919 + 0.0603317i
\(193\) 0.994245 + 0.157473i 0.0715674 + 0.0113352i 0.192115 0.981372i \(-0.438465\pi\)
−0.120548 + 0.992707i \(0.538465\pi\)
\(194\) −10.8424 33.3693i −0.778436 2.39578i
\(195\) 3.75401 0.121066i 0.268830 0.00866973i
\(196\) −1.06084 0.770746i −0.0757744 0.0550533i
\(197\) 17.3425 17.3425i 1.23560 1.23560i 0.273821 0.961781i \(-0.411713\pi\)
0.961781 0.273821i \(-0.0882874\pi\)
\(198\) 0 0
\(199\) 3.25580i 0.230797i −0.993319 0.115399i \(-0.963185\pi\)
0.993319 0.115399i \(-0.0368146\pi\)
\(200\) 17.5198 + 15.3946i 1.23884 + 1.08856i
\(201\) 0.769684 2.36884i 0.0542893 0.167085i
\(202\) −2.13715 + 4.19440i −0.150370 + 0.295117i
\(203\) 2.80288 17.6967i 0.196723 1.24206i
\(204\) 1.78977 1.30034i 0.125309 0.0910422i
\(205\) −4.72987 6.08736i −0.330348 0.425160i
\(206\) 3.97755 + 1.29238i 0.277129 + 0.0900447i
\(207\) −0.0612107 0.386469i −0.00425444 0.0268615i
\(208\) 6.97487 + 6.97487i 0.483621 + 0.483621i
\(209\) 0 0
\(210\) −3.56947 + 7.60173i −0.246317 + 0.524569i
\(211\) 14.6014 20.0971i 1.00520 1.38354i 0.0831208 0.996539i \(-0.473511\pi\)
0.922080 0.387000i \(-0.126489\pi\)
\(212\) −14.3901 + 7.33212i −0.988316 + 0.503572i
\(213\) 0.674606 + 0.343729i 0.0462232 + 0.0235519i
\(214\) −5.94674 8.18498i −0.406511 0.559514i
\(215\) 2.33183 + 12.1695i 0.159029 + 0.829951i
\(216\) −14.9688 + 4.86367i −1.01850 + 0.330931i
\(217\) 10.6219 + 20.8467i 0.721064 + 1.41517i
\(218\) −7.74423 + 1.22657i −0.524505 + 0.0830735i
\(219\) 1.05932 0.0715822
\(220\) 0 0
\(221\) −2.65237 −0.178418
\(222\) 10.9173 1.72912i 0.732718 0.116051i
\(223\) −8.89368 17.4548i −0.595565 1.16886i −0.970339 0.241746i \(-0.922280\pi\)
0.374774 0.927116i \(-0.377720\pi\)
\(224\) 1.93038 0.627220i 0.128979 0.0419079i
\(225\) 12.8022 + 3.26460i 0.853478 + 0.217640i
\(226\) 15.9473 + 21.9496i 1.06080 + 1.46007i
\(227\) −0.911427 0.464395i −0.0604935 0.0308230i 0.423482 0.905904i \(-0.360808\pi\)
−0.483976 + 0.875081i \(0.660808\pi\)
\(228\) −8.66228 + 4.41365i −0.573674 + 0.292301i
\(229\) −0.0598653 + 0.0823975i −0.00395601 + 0.00544498i −0.810990 0.585059i \(-0.801071\pi\)
0.807034 + 0.590504i \(0.201071\pi\)
\(230\) 0.757637 0.273470i 0.0499571 0.0180321i
\(231\) 0 0
\(232\) 22.8903 + 22.8903i 1.50282 + 1.50282i
\(233\) −3.34771 21.1366i −0.219316 1.38470i −0.814056 0.580786i \(-0.802745\pi\)
0.594740 0.803918i \(-0.297255\pi\)
\(234\) 17.1708 + 5.57912i 1.12249 + 0.364719i
\(235\) −2.34577 0.294379i −0.153021 0.0192032i
\(236\) 20.5431 14.9254i 1.33724 0.971562i
\(237\) −0.406194 + 2.56461i −0.0263851 + 0.166589i
\(238\) 2.69240 5.28413i 0.174522 0.342519i
\(239\) −2.67723 + 8.23966i −0.173175 + 0.532979i −0.999545 0.0301483i \(-0.990402\pi\)
0.826370 + 0.563128i \(0.190402\pi\)
\(240\) −2.26572 4.11331i −0.146252 0.265513i
\(241\) 10.6492i 0.685976i −0.939340 0.342988i \(-0.888561\pi\)
0.939340 0.342988i \(-0.111439\pi\)
\(242\) 0 0
\(243\) −9.65667 + 9.65667i −0.619476 + 0.619476i
\(244\) −30.1886 21.9333i −1.93263 1.40414i
\(245\) −0.0241252 0.748071i −0.00154130 0.0477925i
\(246\) 1.54980 + 4.76980i 0.0988118 + 0.304111i
\(247\) 11.5124 + 1.82339i 0.732518 + 0.116020i
\(248\) −41.7515 6.61279i −2.65123 0.419913i
\(249\) −1.53225 4.71578i −0.0971023 0.298850i
\(250\) −1.64072 + 27.1477i −0.103769 + 1.71697i
\(251\) 7.59915 + 5.52110i 0.479654 + 0.348489i 0.801192 0.598408i \(-0.204200\pi\)
−0.321538 + 0.946897i \(0.604200\pi\)
\(252\) −18.8972 + 18.8972i −1.19041 + 1.19041i
\(253\) 0 0
\(254\) 5.77750i 0.362513i
\(255\) 1.21289 + 0.351296i 0.0759543 + 0.0219990i
\(256\) −9.63584 + 29.6561i −0.602240 + 1.85350i
\(257\) 8.37149 16.4300i 0.522199 1.02487i −0.467804 0.883832i \(-0.654955\pi\)
0.990004 0.141042i \(-0.0450452\pi\)
\(258\) 1.26105 7.96198i 0.0785097 0.495691i
\(259\) 15.8700 11.5302i 0.986111 0.716451i
\(260\) −3.06368 + 24.4130i −0.190001 + 1.51403i
\(261\) 17.4407 + 5.66681i 1.07955 + 0.350767i
\(262\) 1.18906 + 7.50744i 0.0734605 + 0.463811i
\(263\) −11.8928 11.8928i −0.733342 0.733342i 0.237938 0.971280i \(-0.423528\pi\)
−0.971280 + 0.237938i \(0.923528\pi\)
\(264\) 0 0
\(265\) −8.34434 3.91817i −0.512589 0.240691i
\(266\) −15.3188 + 21.0845i −0.939254 + 1.29277i
\(267\) 2.25440 1.14868i 0.137967 0.0702978i
\(268\) 14.5380 + 7.40747i 0.888049 + 0.452483i
\(269\) −16.7264 23.0219i −1.01983 1.40367i −0.912325 0.409467i \(-0.865715\pi\)
−0.107502 0.994205i \(-0.534285\pi\)
\(270\) −15.1887 10.3040i −0.924358 0.627082i
\(271\) 28.2295 9.17232i 1.71482 0.557179i 0.723696 0.690118i \(-0.242442\pi\)
0.991124 + 0.132939i \(0.0424416\pi\)
\(272\) 1.50554 + 2.95479i 0.0912868 + 0.179160i
\(273\) −4.28317 + 0.678387i −0.259229 + 0.0410578i
\(274\) 40.2251 2.43009
\(275\) 0 0
\(276\) −0.346917 −0.0208820
\(277\) −12.2668 + 1.94287i −0.737041 + 0.116736i −0.513658 0.857995i \(-0.671710\pi\)
−0.223383 + 0.974731i \(0.571710\pi\)
\(278\) 4.77141 + 9.36443i 0.286170 + 0.561641i
\(279\) −22.7745 + 7.39987i −1.36347 + 0.443019i
\(280\) −22.2838 15.1173i −1.33171 0.903430i
\(281\) −12.8578 17.6972i −0.767032 1.05573i −0.996596 0.0824357i \(-0.973730\pi\)
0.229564 0.973294i \(-0.426270\pi\)
\(282\) 1.37044 + 0.698273i 0.0816083 + 0.0415815i
\(283\) −24.2332 + 12.3474i −1.44051 + 0.733978i −0.987514 0.157532i \(-0.949646\pi\)
−0.453000 + 0.891511i \(0.649646\pi\)
\(284\) −2.91529 + 4.01255i −0.172991 + 0.238101i
\(285\) −5.02297 2.35859i −0.297535 0.139711i
\(286\) 0 0
\(287\) 6.29366 + 6.29366i 0.371503 + 0.371503i
\(288\) 0.324978 + 2.05183i 0.0191495 + 0.120905i
\(289\) 15.3199 + 4.97773i 0.901170 + 0.292808i
\(290\) −4.70051 + 37.4562i −0.276024 + 2.19950i
\(291\) −6.97823 + 5.06998i −0.409071 + 0.297207i
\(292\) −1.08556 + 6.85394i −0.0635274 + 0.401096i
\(293\) −9.13077 + 17.9201i −0.533425 + 1.04691i 0.454321 + 0.890838i \(0.349882\pi\)
−0.987746 + 0.156068i \(0.950118\pi\)
\(294\) −0.150470 + 0.463100i −0.00877560 + 0.0270085i
\(295\) 13.9217 + 4.03220i 0.810551 + 0.234764i
\(296\) 35.4416i 2.06000i
\(297\) 0 0
\(298\) 14.5257 14.5257i 0.841450 0.841450i
\(299\) 0.336495 + 0.244478i 0.0194600 + 0.0141385i
\(300\) 4.63438 10.7580i 0.267566 0.621111i
\(301\) −4.42087 13.6060i −0.254815 0.784239i
\(302\) −28.6691 4.54074i −1.64972 0.261290i
\(303\) 1.14302 + 0.181037i 0.0656650 + 0.0104003i
\(304\) −4.50340 13.8600i −0.258288 0.794927i
\(305\) −0.686536 21.2880i −0.0393109 1.21895i
\(306\) 4.91061 + 3.56777i 0.280721 + 0.203956i
\(307\) −14.6921 + 14.6921i −0.838520 + 0.838520i −0.988664 0.150144i \(-0.952026\pi\)
0.150144 + 0.988664i \(0.452026\pi\)
\(308\) 0 0
\(309\) 1.02815i 0.0584893i
\(310\) −23.7835 43.1779i −1.35081 2.45234i
\(311\) 7.19358 22.1396i 0.407911 1.25542i −0.510530 0.859860i \(-0.670551\pi\)
0.918440 0.395560i \(-0.129449\pi\)
\(312\) 3.55703 6.98106i 0.201377 0.395225i
\(313\) 2.19289 13.8454i 0.123950 0.782587i −0.844898 0.534928i \(-0.820339\pi\)
0.968847 0.247659i \(-0.0796612\pi\)
\(314\) −2.67948 + 1.94676i −0.151212 + 0.109862i
\(315\) −15.1354 1.89940i −0.852785 0.107019i
\(316\) −16.1771 5.25626i −0.910032 0.295687i
\(317\) 4.61482 + 29.1369i 0.259194 + 1.63649i 0.682774 + 0.730630i \(0.260773\pi\)
−0.423580 + 0.905859i \(0.639227\pi\)
\(318\) 4.24076 + 4.24076i 0.237810 + 0.237810i
\(319\) 0 0
\(320\) −18.7949 + 6.78404i −1.05066 + 0.379239i
\(321\) −1.46193 + 2.01217i −0.0815967 + 0.112308i
\(322\) −0.828629 + 0.422208i −0.0461777 + 0.0235287i
\(323\) 3.49158 + 1.77905i 0.194277 + 0.0989889i
\(324\) −13.6069 18.7283i −0.755940 1.04046i
\(325\) −12.0765 + 7.16885i −0.669882 + 0.397656i
\(326\) 53.0803 17.2468i 2.93985 0.955215i
\(327\) 0.875087 + 1.71746i 0.0483924 + 0.0949755i
\(328\) −15.8830 + 2.51563i −0.876994 + 0.138902i
\(329\) 2.72962 0.150489
\(330\) 0 0
\(331\) 2.18560 0.120131 0.0600657 0.998194i \(-0.480869\pi\)
0.0600657 + 0.998194i \(0.480869\pi\)
\(332\) 32.0819 5.08128i 1.76072 0.278871i
\(333\) 9.11485 + 17.8889i 0.499491 + 0.980306i
\(334\) −33.2232 + 10.7949i −1.81789 + 0.590670i
\(335\) 1.75265 + 9.14681i 0.0957573 + 0.499743i
\(336\) 3.18694 + 4.38645i 0.173862 + 0.239301i
\(337\) 1.60560 + 0.818095i 0.0874627 + 0.0445645i 0.497175 0.867650i \(-0.334371\pi\)
−0.409712 + 0.912215i \(0.634371\pi\)
\(338\) 11.0771 5.64408i 0.602516 0.306997i
\(339\) 3.92043 5.39601i 0.212929 0.293071i
\(340\) −3.51587 + 7.48759i −0.190675 + 0.406072i
\(341\) 0 0
\(342\) −18.8614 18.8614i −1.01991 1.01991i
\(343\) 2.96227 + 18.7031i 0.159948 + 1.00987i
\(344\) 24.5826 + 7.98736i 1.32540 + 0.430650i
\(345\) −0.121494 0.156364i −0.00654104 0.00841835i
\(346\) 43.8896 31.8877i 2.35952 1.71429i
\(347\) −3.35900 + 21.2079i −0.180321 + 1.13850i 0.716984 + 0.697090i \(0.245522\pi\)
−0.897305 + 0.441411i \(0.854478\pi\)
\(348\) 7.38132 14.4867i 0.395680 0.776566i
\(349\) 3.29300 10.1348i 0.176270 0.542505i −0.823419 0.567434i \(-0.807936\pi\)
0.999689 + 0.0249295i \(0.00793612\pi\)
\(350\) −2.02327 31.3361i −0.108148 1.67498i
\(351\) 9.47758i 0.505876i
\(352\) 0 0
\(353\) −7.73857 + 7.73857i −0.411883 + 0.411883i −0.882394 0.470511i \(-0.844069\pi\)
0.470511 + 0.882394i \(0.344069\pi\)
\(354\) −7.62853 5.54245i −0.405452 0.294578i
\(355\) −2.82952 + 0.0912516i −0.150175 + 0.00484313i
\(356\) 5.12185 + 15.7634i 0.271457 + 0.835460i
\(357\) −1.43999 0.228072i −0.0762123 0.0120708i
\(358\) 10.4952 + 1.66228i 0.554691 + 0.0878544i
\(359\) 1.01178 + 3.11394i 0.0533997 + 0.164347i 0.974200 0.225688i \(-0.0724629\pi\)
−0.920800 + 0.390035i \(0.872463\pi\)
\(360\) 18.8498 20.1061i 0.993471 1.05968i
\(361\) 1.43940 + 1.04578i 0.0757578 + 0.0550412i
\(362\) −16.2374 + 16.2374i −0.853418 + 0.853418i
\(363\) 0 0
\(364\) 28.4079i 1.48898i
\(365\) −3.46941 + 1.91104i −0.181597 + 0.100029i
\(366\) −4.28197 + 13.1785i −0.223822 + 0.688853i
\(367\) −8.27615 + 16.2428i −0.432011 + 0.847870i 0.567686 + 0.823246i \(0.307839\pi\)
−0.999697 + 0.0246243i \(0.992161\pi\)
\(368\) 0.0813513 0.513632i 0.00424073 0.0267749i
\(369\) −7.36989 + 5.35454i −0.383661 + 0.278746i
\(370\) −32.6361 + 25.3582i −1.69667 + 1.31831i
\(371\) 10.1225 + 3.28901i 0.525536 + 0.170757i
\(372\) 3.32128 + 20.9697i 0.172200 + 1.08723i
\(373\) 12.4917 + 12.4917i 0.646795 + 0.646795i 0.952217 0.305422i \(-0.0987976\pi\)
−0.305422 + 0.952217i \(0.598798\pi\)
\(374\) 0 0
\(375\) 6.47189 1.67874i 0.334207 0.0866895i
\(376\) −2.89879 + 3.98984i −0.149494 + 0.205760i
\(377\) −17.3686 + 8.84972i −0.894526 + 0.455784i
\(378\) 18.8815 + 9.62060i 0.971160 + 0.494831i
\(379\) 12.9685 + 17.8496i 0.666146 + 0.916872i 0.999665 0.0258717i \(-0.00823614\pi\)
−0.333519 + 0.942743i \(0.608236\pi\)
\(380\) 20.4078 30.0823i 1.04690 1.54319i
\(381\) 1.35080 0.438903i 0.0692038 0.0224857i
\(382\) −7.14836 14.0294i −0.365742 0.717809i
\(383\) −19.4473 + 3.08015i −0.993712 + 0.157389i −0.632056 0.774923i \(-0.717789\pi\)
−0.361656 + 0.932311i \(0.617789\pi\)
\(384\) 12.0594 0.615402
\(385\) 0 0
\(386\) 2.44874 0.124638
\(387\) 14.4621 2.29057i 0.735148 0.116436i
\(388\) −25.6524 50.3457i −1.30230 2.55591i
\(389\) 16.2827 5.29057i 0.825565 0.268242i 0.134389 0.990929i \(-0.457093\pi\)
0.691176 + 0.722686i \(0.257093\pi\)
\(390\) 8.97347 1.71943i 0.454389 0.0870669i
\(391\) 0.0821929 + 0.113129i 0.00415667 + 0.00572117i
\(392\) −1.39113 0.708818i −0.0702629 0.0358007i
\(393\) 1.66494 0.848330i 0.0839852 0.0427926i
\(394\) 35.0683 48.2673i 1.76671 2.43167i
\(395\) −3.29629 9.13221i −0.165854 0.459491i
\(396\) 0 0
\(397\) 5.24887 + 5.24887i 0.263433 + 0.263433i 0.826447 0.563014i \(-0.190358\pi\)
−0.563014 + 0.826447i \(0.690358\pi\)
\(398\) −1.23896 7.82252i −0.0621037 0.392107i
\(399\) 6.09337 + 1.97986i 0.305050 + 0.0991168i
\(400\) 14.8411 + 9.38420i 0.742053 + 0.469210i
\(401\) −9.93091 + 7.21523i −0.495926 + 0.360311i −0.807459 0.589924i \(-0.799158\pi\)
0.311533 + 0.950235i \(0.399158\pi\)
\(402\) 0.947832 5.98438i 0.0472736 0.298474i
\(403\) 11.5562 22.6803i 0.575655 1.12979i
\(404\) −2.34267 + 7.21000i −0.116552 + 0.358711i
\(405\) 3.67600 12.6919i 0.182662 0.630663i
\(406\) 43.5854i 2.16311i
\(407\) 0 0
\(408\) 1.86260 1.86260i 0.0922125 0.0922125i
\(409\) 21.6485 + 15.7286i 1.07045 + 0.777727i 0.975993 0.217802i \(-0.0698887\pi\)
0.0944563 + 0.995529i \(0.469889\pi\)
\(410\) −13.6807 12.8258i −0.675640 0.633423i
\(411\) −3.05581 9.40481i −0.150732 0.463905i
\(412\) 6.65226 + 1.05361i 0.327733 + 0.0519079i
\(413\) −16.5283 2.61782i −0.813304 0.128815i
\(414\) −0.294135 0.905254i −0.0144559 0.0444908i
\(415\) 13.5257 + 12.6806i 0.663952 + 0.622465i
\(416\) −1.78651 1.29798i −0.0875910 0.0636386i
\(417\) 1.82697 1.82697i 0.0894672 0.0894672i
\(418\) 0 0
\(419\) 14.2401i 0.695676i −0.937555 0.347838i \(-0.886916\pi\)
0.937555 0.347838i \(-0.113084\pi\)
\(420\) −3.76251 + 12.9905i −0.183592 + 0.633872i
\(421\) −2.13413 + 6.56818i −0.104011 + 0.320113i −0.989497 0.144553i \(-0.953826\pi\)
0.885486 + 0.464666i \(0.153826\pi\)
\(422\) 27.4341 53.8425i 1.33547 2.62101i
\(423\) −0.437039 + 2.75935i −0.0212496 + 0.134164i
\(424\) −15.5574 + 11.3031i −0.755532 + 0.548926i
\(425\) −4.60614 + 1.03755i −0.223430 + 0.0503288i
\(426\) 1.75164 + 0.569142i 0.0848672 + 0.0275750i
\(427\) 3.84696 + 24.2888i 0.186168 + 1.17542i
\(428\) −11.5209 11.5209i −0.556882 0.556882i
\(429\) 0 0
\(430\) 10.2335 + 28.3515i 0.493505 + 1.36723i
\(431\) 4.19638 5.77582i 0.202132 0.278211i −0.695902 0.718137i \(-0.744995\pi\)
0.898034 + 0.439926i \(0.144995\pi\)
\(432\) −10.5582 + 5.37966i −0.507981 + 0.258829i
\(433\) 14.9712 + 7.62822i 0.719471 + 0.366589i 0.775079 0.631864i \(-0.217710\pi\)
−0.0556084 + 0.998453i \(0.517710\pi\)
\(434\) 33.4538 + 46.0451i 1.60583 + 2.21024i
\(435\) 9.11451 1.74646i 0.437007 0.0837363i
\(436\) −12.0089 + 3.90194i −0.575124 + 0.186869i
\(437\) −0.278981 0.547531i −0.0133455 0.0261920i
\(438\) 2.54516 0.403114i 0.121613 0.0192616i
\(439\) 0.772934 0.0368901 0.0184451 0.999830i \(-0.494128\pi\)
0.0184451 + 0.999830i \(0.494128\pi\)
\(440\) 0 0
\(441\) −0.884459 −0.0421171
\(442\) −6.37271 + 1.00934i −0.303119 + 0.0480093i
\(443\) −8.53040 16.7419i −0.405292 0.795430i 0.594672 0.803968i \(-0.297282\pi\)
−0.999964 + 0.00853887i \(0.997282\pi\)
\(444\) 16.9293 5.50067i 0.803430 0.261050i
\(445\) −5.31122 + 7.82908i −0.251776 + 0.371134i
\(446\) −28.0106 38.5533i −1.32634 1.82555i
\(447\) −4.49965 2.29269i −0.212826 0.108440i
\(448\) 20.5560 10.4738i 0.971179 0.494840i
\(449\) 0.419317 0.577140i 0.0197888 0.0272369i −0.799008 0.601320i \(-0.794642\pi\)
0.818797 + 0.574084i \(0.194642\pi\)
\(450\) 32.0014 + 2.97190i 1.50856 + 0.140097i
\(451\) 0 0
\(452\) 30.8954 + 30.8954i 1.45320 + 1.45320i
\(453\) 1.11628 + 7.04792i 0.0524474 + 0.331140i
\(454\) −2.36655 0.768940i −0.111068 0.0360882i
\(455\) 12.8041 9.94877i 0.600266 0.466405i
\(456\) −9.36493 + 6.80402i −0.438553 + 0.318628i
\(457\) −3.02622 + 19.1068i −0.141561 + 0.893780i 0.810025 + 0.586396i \(0.199454\pi\)
−0.951586 + 0.307384i \(0.900546\pi\)
\(458\) −0.112479 + 0.220753i −0.00525581 + 0.0103151i
\(459\) 0.984632 3.03039i 0.0459587 0.141446i
\(460\) 1.13620 0.625849i 0.0529756 0.0291804i
\(461\) 36.5277i 1.70126i 0.525761 + 0.850632i \(0.323781\pi\)
−0.525761 + 0.850632i \(0.676219\pi\)
\(462\) 0 0
\(463\) −17.1422 + 17.1422i −0.796664 + 0.796664i −0.982568 0.185904i \(-0.940479\pi\)
0.185904 + 0.982568i \(0.440479\pi\)
\(464\) 19.7175 + 14.3256i 0.915361 + 0.665049i
\(465\) −8.28841 + 8.84082i −0.384366 + 0.409983i
\(466\) −16.0867 49.5097i −0.745201 2.29349i
\(467\) −14.6373 2.31832i −0.677333 0.107279i −0.191715 0.981451i \(-0.561405\pi\)
−0.485617 + 0.874172i \(0.661405\pi\)
\(468\) 28.7173 + 4.54837i 1.32746 + 0.210249i
\(469\) −3.32281 10.2266i −0.153433 0.472219i
\(470\) −5.74807 + 0.185374i −0.265139 + 0.00855068i
\(471\) 0.658714 + 0.478584i 0.0303519 + 0.0220520i
\(472\) 21.3791 21.3791i 0.984051 0.984051i
\(473\) 0 0
\(474\) 6.31640i 0.290122i
\(475\) 20.7059 1.33691i 0.950050 0.0613417i
\(476\) 2.95131 9.08320i 0.135273 0.416328i
\(477\) −4.94555 + 9.70618i −0.226441 + 0.444416i
\(478\) −3.29689 + 20.8157i −0.150796 + 0.952090i
\(479\) 22.3176 16.2146i 1.01971 0.740866i 0.0534905 0.998568i \(-0.482965\pi\)
0.966224 + 0.257702i \(0.0829653\pi\)
\(480\) 0.645035 + 0.830163i 0.0294417 + 0.0378916i
\(481\) −20.2972 6.59495i −0.925471 0.300704i
\(482\) −4.05246 25.5862i −0.184585 1.16542i
\(483\) 0.161663 + 0.161663i 0.00735592 + 0.00735592i
\(484\) 0 0
\(485\) 13.7082 29.1938i 0.622459 1.32562i
\(486\) −19.5268 + 26.8763i −0.885752 + 1.21913i
\(487\) −34.6563 + 17.6583i −1.57043 + 0.800174i −0.999779 0.0210198i \(-0.993309\pi\)
−0.570650 + 0.821193i \(0.693309\pi\)
\(488\) −39.5879 20.1710i −1.79206 0.913099i
\(489\) −8.06478 11.1002i −0.364702 0.501969i
\(490\) −0.342636 1.78817i −0.0154787 0.0807811i
\(491\) −17.8811 + 5.80992i −0.806962 + 0.262198i −0.683311 0.730128i \(-0.739461\pi\)
−0.123652 + 0.992326i \(0.539461\pi\)
\(492\) 3.66674 + 7.19639i 0.165310 + 0.324438i
\(493\) −6.47287 + 1.02520i −0.291523 + 0.0461728i
\(494\) 28.3541 1.27571
\(495\) 0 0
\(496\) −31.8258 −1.42902
\(497\) 3.22837 0.511323i 0.144812 0.0229360i
\(498\) −5.47599 10.7472i −0.245385 0.481595i
\(499\) 4.98327 1.61916i 0.223082 0.0724837i −0.195343 0.980735i \(-0.562582\pi\)
0.418425 + 0.908251i \(0.362582\pi\)
\(500\) 4.22946 + 43.5943i 0.189147 + 1.94960i
\(501\) 5.04778 + 6.94768i 0.225518 + 0.310399i
\(502\) 20.3590 + 10.3734i 0.908668 + 0.462990i
\(503\) −11.7545 + 5.98921i −0.524106 + 0.267046i −0.695965 0.718076i \(-0.745023\pi\)
0.171858 + 0.985122i \(0.445023\pi\)
\(504\) −18.7037 + 25.7434i −0.833127 + 1.14670i
\(505\) −4.07015 + 1.46913i −0.181119 + 0.0653754i
\(506\) 0 0
\(507\) −2.16111 2.16111i −0.0959784 0.0959784i
\(508\) 1.45550 + 9.18967i 0.0645774 + 0.407726i
\(509\) 5.32193 + 1.72920i 0.235890 + 0.0766454i 0.424577 0.905392i \(-0.360423\pi\)
−0.188686 + 0.982037i \(0.560423\pi\)
\(510\) 3.04783 + 0.382483i 0.134960 + 0.0169367i
\(511\) 3.69980 2.68806i 0.163669 0.118913i
\(512\) −5.55696 + 35.0853i −0.245585 + 1.55056i
\(513\) −6.35698 + 12.4763i −0.280667 + 0.550841i
\(514\) 13.8614 42.6611i 0.611401 1.88170i
\(515\) 1.85481 + 3.36732i 0.0817327 + 0.148382i
\(516\) 12.9820i 0.571500i
\(517\) 0 0
\(518\) 33.7421 33.7421i 1.48254 1.48254i
\(519\) −10.7897 7.83915i −0.473614 0.344101i
\(520\) 0.944304 + 29.2809i 0.0414105 + 1.28405i
\(521\) 5.89515 + 18.1434i 0.258271 + 0.794877i 0.993168 + 0.116697i \(0.0372308\pi\)
−0.734896 + 0.678179i \(0.762769\pi\)
\(522\) 44.0601 + 6.97844i 1.92846 + 0.305438i
\(523\) 34.6664 + 5.49061i 1.51585 + 0.240088i 0.858233 0.513261i \(-0.171563\pi\)
0.657621 + 0.753349i \(0.271563\pi\)
\(524\) 3.78263 + 11.6417i 0.165245 + 0.508572i
\(525\) −7.17282 + 2.85358i −0.313047 + 0.124540i
\(526\) −33.0999 24.0485i −1.44322 1.04856i
\(527\) 6.05128 6.05128i 0.263598 0.263598i
\(528\) 0 0
\(529\) 22.9781i 0.999047i
\(530\) −21.5395 6.23859i −0.935616 0.270987i
\(531\) 5.29267 16.2892i 0.229682 0.706890i
\(532\) −19.0542 + 37.3961i −0.826106 + 1.62132i
\(533\) 1.51482 9.56421i 0.0656143 0.414272i
\(534\) 4.97940 3.61775i 0.215480 0.156555i
\(535\) 1.15799 9.22747i 0.0500642 0.398938i
\(536\) 18.4767 + 6.00346i 0.798074 + 0.259310i
\(537\) −0.408650 2.58011i −0.0176345 0.111340i
\(538\) −48.9484 48.9484i −2.11031 2.11031i
\(539\) 0 0
\(540\) −26.7550 12.5631i −1.15135 0.540628i
\(541\) 1.49345 2.05556i 0.0642084 0.0883752i −0.775705 0.631095i \(-0.782606\pi\)
0.839914 + 0.542720i \(0.182606\pi\)
\(542\) 64.3350 32.7803i 2.76342 1.40803i
\(543\) 5.02989 + 2.56286i 0.215853 + 0.109983i
\(544\) −0.436376 0.600621i −0.0187095 0.0257514i
\(545\) −5.96437 4.04621i −0.255486 0.173321i
\(546\) −10.0328 + 3.25984i −0.429363 + 0.139508i
\(547\) −6.73017 13.2087i −0.287761 0.564764i 0.701195 0.712969i \(-0.252650\pi\)
−0.988957 + 0.148206i \(0.952650\pi\)
\(548\) 63.9819 10.1337i 2.73317 0.432892i
\(549\) −25.1693 −1.07420
\(550\) 0 0
\(551\) 28.7998 1.22691
\(552\) −0.407982 + 0.0646180i −0.0173649 + 0.00275033i
\(553\) 5.08910 + 9.98792i 0.216411 + 0.424730i
\(554\) −28.7334 + 9.33604i −1.22076 + 0.396650i
\(555\) 8.40814 + 5.70406i 0.356906 + 0.242124i
\(556\) 9.94853 + 13.6930i 0.421912 + 0.580712i
\(557\) −11.3704 5.79353i −0.481781 0.245480i 0.196194 0.980565i \(-0.437142\pi\)
−0.677974 + 0.735086i \(0.737142\pi\)
\(558\) −51.9029 + 26.4459i −2.19723 + 1.11954i
\(559\) −9.14861 + 12.5920i −0.386945 + 0.532584i
\(560\) −18.3510 8.61687i −0.775470 0.364129i
\(561\) 0 0
\(562\) −37.6272 37.6272i −1.58721 1.58721i
\(563\) −5.24553 33.1190i −0.221073 1.39580i −0.809439 0.587204i \(-0.800229\pi\)
0.588367 0.808594i \(-0.299771\pi\)
\(564\) 2.35572 + 0.765421i 0.0991939 + 0.0322300i
\(565\) −3.10537 + 24.7452i −0.130644 + 1.04104i
\(566\) −53.5250 + 38.8882i −2.24982 + 1.63459i
\(567\) −2.38657 + 15.0682i −0.100226 + 0.632805i
\(568\) −2.68105 + 5.26186i −0.112494 + 0.220783i
\(569\) 2.57065 7.91165i 0.107767 0.331674i −0.882603 0.470120i \(-0.844211\pi\)
0.990370 + 0.138446i \(0.0442107\pi\)
\(570\) −12.9659 3.75539i −0.543084 0.157296i
\(571\) 45.2601i 1.89408i 0.321118 + 0.947039i \(0.395941\pi\)
−0.321118 + 0.947039i \(0.604059\pi\)
\(572\) 0 0
\(573\) −2.73710 + 2.73710i −0.114344 + 0.114344i
\(574\) 17.5164 + 12.7264i 0.731121 + 0.531190i
\(575\) 0.679996 + 0.292933i 0.0283578 + 0.0122161i
\(576\) 7.29667 + 22.4568i 0.304028 + 0.935701i
\(577\) −22.6517 3.58768i −0.943005 0.149357i −0.334044 0.942558i \(-0.608413\pi\)
−0.608961 + 0.793200i \(0.708413\pi\)
\(578\) 38.7024 + 6.12986i 1.60981 + 0.254969i
\(579\) −0.186025 0.572526i −0.00773094 0.0237934i
\(580\) 1.95956 + 60.7618i 0.0813663 + 2.52300i
\(581\) −17.3180 12.5823i −0.718472 0.522001i
\(582\) −14.8369 + 14.8369i −0.615007 + 0.615007i
\(583\) 0 0
\(584\) 8.26259i 0.341908i
\(585\) 8.00707 + 14.5365i 0.331052 + 0.601009i
\(586\) −15.1186 + 46.5303i −0.624545 + 1.92215i
\(587\) −4.58380 + 8.99622i −0.189194 + 0.371314i −0.966046 0.258369i \(-0.916815\pi\)
0.776853 + 0.629683i \(0.216815\pi\)
\(588\) −0.122671 + 0.774512i −0.00505885 + 0.0319403i
\(589\) −30.4251 + 22.1051i −1.25365 + 0.910827i
\(590\) 34.9832 + 4.39017i 1.44024 + 0.180740i
\(591\) −13.9492 4.53236i −0.573792 0.186436i
\(592\) 4.17419 + 26.3548i 0.171558 + 1.08318i
\(593\) 9.47168 + 9.47168i 0.388955 + 0.388955i 0.874315 0.485359i \(-0.161311\pi\)
−0.485359 + 0.874315i \(0.661311\pi\)
\(594\) 0 0
\(595\) 5.12760 1.85082i 0.210211 0.0758761i
\(596\) 19.4451 26.7639i 0.796503 1.09629i
\(597\) −1.73482 + 0.883934i −0.0710014 + 0.0361770i
\(598\) 0.901512 + 0.459343i 0.0368656 + 0.0187839i
\(599\) −23.5167 32.3680i −0.960866 1.32252i −0.946528 0.322622i \(-0.895436\pi\)
−0.0143383 0.999897i \(-0.504564\pi\)
\(600\) 3.44632 13.5148i 0.140695 0.551740i
\(601\) −34.5805 + 11.2359i −1.41057 + 0.458322i −0.912593 0.408869i \(-0.865923\pi\)
−0.497976 + 0.867191i \(0.665923\pi\)
\(602\) −15.7994 31.0081i −0.643937 1.26380i
\(603\) 10.8700 1.72163i 0.442659 0.0701103i
\(604\) −46.7449 −1.90202
\(605\) 0 0
\(606\) 2.81517 0.114358
\(607\) −24.6231 + 3.89991i −0.999420 + 0.158293i −0.634646 0.772803i \(-0.718854\pi\)
−0.364774 + 0.931096i \(0.618854\pi\)
\(608\) 1.48116 + 2.90694i 0.0600689 + 0.117892i
\(609\) −10.1905 + 3.31108i −0.412938 + 0.134172i
\(610\) −9.75047 50.8863i −0.394785 2.06033i
\(611\) −1.74555 2.40254i −0.0706174 0.0971965i
\(612\) 8.70960 + 4.43777i 0.352065 + 0.179386i
\(613\) 10.4167 5.30759i 0.420728 0.214372i −0.230792 0.973003i \(-0.574132\pi\)
0.651520 + 0.758632i \(0.274132\pi\)
\(614\) −29.7088 + 40.8907i −1.19895 + 1.65021i
\(615\) −1.95945 + 4.17295i −0.0790126 + 0.168270i
\(616\) 0 0
\(617\) 6.18386 + 6.18386i 0.248953 + 0.248953i 0.820541 0.571588i \(-0.193672\pi\)
−0.571588 + 0.820541i \(0.693672\pi\)
\(618\) −0.391253 2.47027i −0.0157385 0.0993689i
\(619\) 1.04489 + 0.339504i 0.0419975 + 0.0136458i 0.329940 0.944002i \(-0.392971\pi\)
−0.287943 + 0.957648i \(0.592971\pi\)
\(620\) −48.7076 62.6869i −1.95614 2.51757i
\(621\) −0.404237 + 0.293695i −0.0162215 + 0.0117856i
\(622\) 8.85859 55.9309i 0.355197 2.24263i
\(623\) 4.95896 9.73251i 0.198677 0.389925i
\(624\) 1.82284 5.61013i 0.0729721 0.224585i
\(625\) −18.1678 + 17.1736i −0.726712 + 0.686942i
\(626\) 34.1000i 1.36291i
\(627\) 0 0
\(628\) −3.77153 + 3.77153i −0.150501 + 0.150501i
\(629\) −5.80472 4.21737i −0.231449 0.168158i
\(630\) −37.0878 + 1.19608i −1.47762 + 0.0476529i
\(631\) −1.00765 3.10124i −0.0401140 0.123458i 0.928994 0.370095i \(-0.120675\pi\)
−0.969108 + 0.246636i \(0.920675\pi\)
\(632\) −20.0037 3.16827i −0.795703 0.126027i
\(633\) −14.6727 2.32393i −0.583188 0.0923680i
\(634\) 22.1755 + 68.2493i 0.880703 + 2.71053i
\(635\) −3.63227 + 3.87436i −0.144142 + 0.153749i
\(636\) 7.81368 + 5.67697i 0.309833 + 0.225107i
\(637\) 0.664797 0.664797i 0.0263402 0.0263402i
\(638\) 0 0
\(639\) 3.34540i 0.132342i
\(640\) −39.4960 + 21.7555i −1.56122 + 0.859960i
\(641\) −2.75407 + 8.47616i −0.108779 + 0.334788i −0.990599 0.136799i \(-0.956319\pi\)
0.881820 + 0.471587i \(0.156319\pi\)
\(642\) −2.74677 + 5.39084i −0.108406 + 0.212760i
\(643\) −5.80382 + 36.6439i −0.228880 + 1.44509i 0.558950 + 0.829202i \(0.311204\pi\)
−0.787830 + 0.615893i \(0.788796\pi\)
\(644\) −1.21165 + 0.880315i −0.0477457 + 0.0346893i
\(645\) 5.85129 4.54644i 0.230394 0.179016i
\(646\) 9.06602 + 2.94573i 0.356698 + 0.115898i
\(647\) −3.44966 21.7803i −0.135620 0.856273i −0.957882 0.287163i \(-0.907288\pi\)
0.822262 0.569110i \(-0.192712\pi\)
\(648\) −19.4905 19.4905i −0.765657 0.765657i
\(649\) 0 0
\(650\) −26.2874 + 21.8198i −1.03108 + 0.855842i
\(651\) 8.22416 11.3196i 0.322330 0.443649i
\(652\) 80.0844 40.8051i 3.13635 1.59805i
\(653\) −43.2861 22.0554i −1.69392 0.863093i −0.987936 0.154861i \(-0.950507\pi\)
−0.705980 0.708232i \(-0.749493\pi\)
\(654\) 2.75608 + 3.79342i 0.107771 + 0.148335i
\(655\) −3.92249 + 5.78200i −0.153265 + 0.225921i
\(656\) −11.5145 + 3.74130i −0.449567 + 0.146073i
\(657\) 2.12497 + 4.17048i 0.0829028 + 0.162706i
\(658\) 6.55831 1.03873i 0.255669 0.0404941i
\(659\) −47.3029 −1.84266 −0.921329 0.388783i \(-0.872896\pi\)
−0.921329 + 0.388783i \(0.872896\pi\)
\(660\) 0 0
\(661\) −26.7159 −1.03913 −0.519564 0.854432i \(-0.673906\pi\)
−0.519564 + 0.854432i \(0.673906\pi\)
\(662\) 5.25121 0.831711i 0.204094 0.0323254i
\(663\) 0.720107 + 1.41329i 0.0279666 + 0.0548876i
\(664\) 36.7826 11.9514i 1.42744 0.463804i
\(665\) −23.5283 + 4.50833i −0.912389 + 0.174826i
\(666\) 28.7072 + 39.5121i 1.11238 + 1.53106i
\(667\) 0.915682 + 0.466563i 0.0354553 + 0.0180654i
\(668\) −50.1252 + 25.5401i −1.93940 + 0.988175i
\(669\) −6.88603 + 9.47781i −0.266229 + 0.366433i
\(670\) 7.69172 + 21.3095i 0.297157 + 0.823260i
\(671\) 0 0
\(672\) −0.858297 0.858297i −0.0331095 0.0331095i
\(673\) 2.07046 + 13.0723i 0.0798102 + 0.503902i 0.994918 + 0.100692i \(0.0321056\pi\)
−0.915107 + 0.403210i \(0.867894\pi\)
\(674\) 4.16900 + 1.35459i 0.160584 + 0.0521769i
\(675\) −3.70744 16.4589i −0.142699 0.633502i
\(676\) 16.1973 11.7681i 0.622975 0.452618i
\(677\) 5.37982 33.9668i 0.206763 1.30545i −0.637885 0.770131i \(-0.720191\pi\)
0.844649 0.535321i \(-0.179809\pi\)
\(678\) 7.36599 14.4566i 0.282889 0.555201i
\(679\) −11.5070 + 35.4150i −0.441600 + 1.35910i
\(680\) −2.74008 + 9.46045i −0.105077 + 0.362792i
\(681\) 0.611726i 0.0234414i
\(682\) 0 0
\(683\) 27.9495 27.9495i 1.06946 1.06946i 0.0720555 0.997401i \(-0.477044\pi\)
0.997401 0.0720555i \(-0.0229559\pi\)
\(684\) −34.7526 25.2493i −1.32880 0.965429i
\(685\) 26.9747 + 25.2892i 1.03065 + 0.966252i
\(686\) 14.2346 + 43.8095i 0.543478 + 1.67265i
\(687\) 0.0601578 + 0.00952805i 0.00229516 + 0.000363518i
\(688\) 19.2206 + 3.04425i 0.732779 + 0.116061i
\(689\) −3.57830 11.0129i −0.136322 0.419557i
\(690\) −0.351411 0.329453i −0.0133780 0.0125421i
\(691\) −2.64892 1.92455i −0.100770 0.0732134i 0.536259 0.844053i \(-0.319837\pi\)
−0.637029 + 0.770840i \(0.719837\pi\)
\(692\) 61.7773 61.7773i 2.34842 2.34842i
\(693\) 0 0
\(694\) 52.2333i 1.98275i
\(695\) −2.68766 + 9.27949i −0.101949 + 0.351991i
\(696\) 5.98226 18.4115i 0.226757 0.697886i
\(697\) 1.47799 2.90071i 0.0559827 0.109872i
\(698\) 4.05519 25.6035i 0.153491 0.969106i
\(699\) −10.3535 + 7.52228i −0.391606 + 0.284519i
\(700\) −11.1126 49.3334i −0.420016 1.86463i
\(701\) 5.55696 + 1.80557i 0.209883 + 0.0681953i 0.412072 0.911151i \(-0.364805\pi\)
−0.202188 + 0.979347i \(0.564805\pi\)
\(702\) −3.60661 22.7712i −0.136123 0.859445i
\(703\) 22.2957 + 22.2957i 0.840897 + 0.840897i
\(704\) 0 0
\(705\) 0.480009 + 1.32984i 0.0180782 + 0.0500847i
\(706\) −15.6482 + 21.5379i −0.588927 + 0.810588i
\(707\) 4.45154 2.26817i 0.167417 0.0853034i
\(708\) −13.5302 6.89398i −0.508496 0.259092i
\(709\) 23.5016 + 32.3472i 0.882623 + 1.21483i 0.975688 + 0.219166i \(0.0703337\pi\)
−0.0930647 + 0.995660i \(0.529666\pi\)
\(710\) −6.76360 + 1.29599i −0.253834 + 0.0486378i
\(711\) −10.9115 + 3.54537i −0.409214 + 0.132962i
\(712\) 8.95956 + 17.5841i 0.335774 + 0.658993i
\(713\) −1.32547 + 0.209933i −0.0496391 + 0.00786207i
\(714\) −3.54657 −0.132727
\(715\) 0 0
\(716\) 17.1125 0.639523
\(717\) 5.11727 0.810496i 0.191108 0.0302685i
\(718\) 3.61592 + 7.09665i 0.134945 + 0.264845i
\(719\) 19.2106 6.24190i 0.716434 0.232784i 0.0719577 0.997408i \(-0.477075\pi\)
0.644477 + 0.764624i \(0.277075\pi\)
\(720\) 11.6489 17.1712i 0.434129 0.639933i
\(721\) −2.60896 3.59093i −0.0971629 0.133733i
\(722\) 3.85632 + 1.96489i 0.143517 + 0.0731258i
\(723\) −5.67432 + 2.89121i −0.211030 + 0.107525i
\(724\) −21.7365 + 29.9177i −0.807831 + 1.11188i
\(725\) −26.7006 + 22.1627i −0.991634 + 0.823103i
\(726\) 0 0
\(727\) 26.5141 + 26.5141i 0.983354 + 0.983354i 0.999864 0.0165102i \(-0.00525558\pi\)
−0.0165102 + 0.999864i \(0.505256\pi\)
\(728\) −5.29135 33.4083i −0.196111 1.23819i
\(729\) −9.09289 2.95446i −0.336774 0.109424i
\(730\) −7.60852 + 5.91181i −0.281604 + 0.218806i
\(731\) −4.23339 + 3.07574i −0.156578 + 0.113760i
\(732\) −3.49087 + 22.0405i −0.129026 + 0.814639i
\(733\) −14.4811 + 28.4208i −0.534873 + 1.04975i 0.452563 + 0.891732i \(0.350510\pi\)
−0.987437 + 0.158015i \(0.949490\pi\)
\(734\) −13.7035 + 42.1752i −0.505807 + 1.55671i
\(735\) −0.392052 + 0.215953i −0.0144611 + 0.00796553i
\(736\) 0.116420i 0.00429131i
\(737\) 0 0
\(738\) −15.6696 + 15.6696i −0.576805 + 0.576805i
\(739\) 31.6871 + 23.0220i 1.16563 + 0.846879i 0.990479 0.137662i \(-0.0439589\pi\)
0.175150 + 0.984542i \(0.443959\pi\)
\(740\) −45.5224 + 48.5565i −1.67344 + 1.78497i
\(741\) −2.15400 6.62932i −0.0791290 0.243534i
\(742\) 25.5724 + 4.05027i 0.938793 + 0.148690i
\(743\) 6.70139 + 1.06140i 0.245850 + 0.0389389i 0.278143 0.960540i \(-0.410281\pi\)
−0.0322930 + 0.999478i \(0.510281\pi\)
\(744\) 7.81179 + 24.0422i 0.286394 + 0.881430i
\(745\) 18.8730 0.608652i 0.691455 0.0222993i
\(746\) 34.7666 + 25.2594i 1.27290 + 0.924814i
\(747\) 15.4921 15.4921i 0.566826 0.566826i
\(748\) 0 0
\(749\) 10.7374i 0.392337i
\(750\) 14.9108 6.49622i 0.544465 0.237208i
\(751\) −6.82703 + 21.0114i −0.249122 + 0.766718i 0.745809 + 0.666160i \(0.232063\pi\)
−0.994931 + 0.100559i \(0.967937\pi\)
\(752\) −1.68567 + 3.30830i −0.0614699 + 0.120641i
\(753\) 0.878729 5.54808i 0.0320227 0.202183i
\(754\) −38.3627 + 27.8722i −1.39709 + 1.01504i
\(755\) −16.3706 21.0691i −0.595788 0.766782i
\(756\) 32.4565 + 10.5458i 1.18043 + 0.383546i
\(757\) −5.23341 33.0425i −0.190212 1.20095i −0.879299 0.476271i \(-0.841988\pi\)
0.689087 0.724678i \(-0.258012\pi\)
\(758\) 37.9511 + 37.9511i 1.37845 + 1.37845i
\(759\) 0 0
\(760\) 18.3967 39.1787i 0.667320 1.42116i
\(761\) 15.3149 21.0791i 0.555163 0.764117i −0.435538 0.900170i \(-0.643442\pi\)
0.990701 + 0.136054i \(0.0434419\pi\)
\(762\) 3.07848 1.56856i 0.111522 0.0568231i
\(763\) 7.41445 + 3.77785i 0.268421 + 0.136767i
\(764\) −14.9045 20.5143i −0.539227 0.742182i
\(765\) 1.05000 + 5.47979i 0.0379628 + 0.198122i
\(766\) −45.5528 + 14.8010i −1.64589 + 0.534782i
\(767\) 8.26544 + 16.2218i 0.298448 + 0.585736i
\(768\) 18.4180 2.91713i 0.664603 0.105263i
\(769\) 51.2907 1.84959 0.924794 0.380468i \(-0.124237\pi\)
0.924794 + 0.380468i \(0.124237\pi\)
\(770\) 0 0
\(771\) −11.0274 −0.397141
\(772\) 3.89496 0.616901i 0.140183 0.0222027i
\(773\) −7.49740 14.7145i −0.269663 0.529243i 0.715973 0.698128i \(-0.245983\pi\)
−0.985636 + 0.168885i \(0.945983\pi\)
\(774\) 33.8755 11.0068i 1.21763 0.395632i
\(775\) 11.1965 43.9074i 0.402191 1.57720i
\(776\) −39.5453 54.4295i −1.41960 1.95391i
\(777\) −10.4524 5.32574i −0.374976 0.191060i
\(778\) 37.1082 18.9076i 1.33039 0.677869i
\(779\) −8.40920 + 11.5743i −0.301291 + 0.414691i
\(780\) 13.8400 4.99557i 0.495551 0.178870i
\(781\) 0 0
\(782\) 0.240530 + 0.240530i 0.00860135 + 0.00860135i
\(783\) −3.66330 23.1292i −0.130916 0.826569i
\(784\) −1.11795 0.363243i −0.0399267 0.0129730i
\(785\) −3.02076 0.379085i −0.107815 0.0135301i
\(786\) 3.67744 2.67181i 0.131170 0.0953004i
\(787\) 0.692641 4.37316i 0.0246900 0.155886i −0.972263 0.233890i \(-0.924854\pi\)
0.996953 + 0.0780034i \(0.0248545\pi\)
\(788\) 43.6197 85.6084i 1.55389 3.04967i
\(789\) −3.10812 + 9.56580i −0.110652 + 0.340551i
\(790\) −11.3950 20.6871i −0.405415 0.736012i
\(791\) 28.7945i 1.02381i
\(792\) 0 0
\(793\) 18.9183 18.9183i 0.671808 0.671808i
\(794\) 14.6086 + 10.6137i 0.518438 + 0.376667i
\(795\) 0.177695 + 5.50996i 0.00630220 + 0.195418i
\(796\) −3.94138 12.1303i −0.139699 0.429948i
\(797\) 18.9850 + 3.00692i 0.672482 + 0.106511i 0.483331 0.875437i \(-0.339427\pi\)
0.189150 + 0.981948i \(0.439427\pi\)
\(798\) 15.3936 + 2.43811i 0.544928 + 0.0863081i
\(799\) −0.308525 0.949542i −0.0109148 0.0335924i
\(800\) −3.61022 1.55523i −0.127640 0.0549858i
\(801\) 9.04454 + 6.57125i 0.319573 + 0.232184i
\(802\) −21.1147 + 21.1147i −0.745587 + 0.745587i
\(803\) 0 0
\(804\) 9.75751i 0.344121i
\(805\) −0.821113 0.237823i −0.0289404 0.00838216i
\(806\) 19.1346 58.8903i 0.673988 2.07432i
\(807\) −7.72585 + 15.1628i −0.271963 + 0.533757i
\(808\) −1.41207 + 8.91548i −0.0496765 + 0.313645i
\(809\) 24.9923 18.1580i 0.878683 0.638401i −0.0542197 0.998529i \(-0.517267\pi\)
0.932903 + 0.360128i \(0.117267\pi\)
\(810\) 4.00235 31.8928i 0.140628 1.12060i
\(811\) −23.8090 7.73601i −0.836047 0.271648i −0.140456 0.990087i \(-0.544857\pi\)
−0.695590 + 0.718439i \(0.744857\pi\)
\(812\) −10.9803 69.3267i −0.385332 2.43289i
\(813\) −12.5516 12.5516i −0.440202 0.440202i
\(814\) 0 0
\(815\) 46.4383 + 21.8056i 1.62666 + 0.763816i
\(816\) 1.16568 1.60442i 0.0408070 0.0561660i
\(817\) 20.4891 10.4397i 0.716825 0.365240i
\(818\) 57.9990 + 29.5519i 2.02789 + 1.03326i
\(819\) −11.2627 15.5018i −0.393550 0.541675i
\(820\) −24.9916 16.9542i −0.872744 0.592067i
\(821\) 21.6750 7.04264i 0.756463 0.245790i 0.0947032 0.995506i \(-0.469810\pi\)
0.661760 + 0.749716i \(0.269810\pi\)
\(822\) −10.9209 21.4335i −0.380911 0.747580i
\(823\) 17.4278 2.76029i 0.607495 0.0962177i 0.154894 0.987931i \(-0.450496\pi\)
0.452601 + 0.891713i \(0.350496\pi\)
\(824\) 8.01946 0.279371
\(825\) 0 0
\(826\) −40.7077 −1.41640
\(827\) −16.4544 + 2.60613i −0.572177 + 0.0906239i −0.435817 0.900035i \(-0.643540\pi\)
−0.136360 + 0.990659i \(0.543540\pi\)
\(828\) −0.695907 1.36579i −0.0241844 0.0474646i
\(829\) 39.7855 12.9271i 1.38181 0.448976i 0.478544 0.878064i \(-0.341165\pi\)
0.903263 + 0.429087i \(0.141165\pi\)
\(830\) 37.3230 + 25.3198i 1.29550 + 0.878863i
\(831\) 4.36562 + 6.00876i 0.151442 + 0.208441i
\(832\) −22.3640 11.3950i −0.775332 0.395051i
\(833\) 0.281630 0.143498i 0.00975790 0.00497190i
\(834\) 3.69432 5.08480i 0.127924 0.176072i
\(835\) −29.0660 13.6482i −1.00587 0.472316i
\(836\) 0 0
\(837\) 21.6227 + 21.6227i 0.747390 + 0.747390i
\(838\) −5.41895 34.2139i −0.187195 1.18190i
\(839\) −49.3818 16.0451i −1.70485 0.553939i −0.715388 0.698728i \(-0.753750\pi\)
−0.989463 + 0.144788i \(0.953750\pi\)
\(840\) −2.00513 + 15.9780i −0.0691836 + 0.551292i
\(841\) −15.5042 + 11.2645i −0.534629 + 0.388431i
\(842\) −2.62809 + 16.5931i −0.0905699 + 0.571836i
\(843\) −5.93896 + 11.6559i −0.204549 + 0.401449i
\(844\) 30.0723 92.5530i 1.03513 3.18581i
\(845\) 10.9767 + 3.17922i 0.377608 + 0.109369i
\(846\) 6.79605i 0.233653i
\(847\) 0 0
\(848\) −10.2374 + 10.2374i −0.351554 + 0.351554i
\(849\) 13.1584 + 9.56013i 0.451595 + 0.328103i
\(850\) −10.6721 + 4.24570i −0.366049 + 0.145626i
\(851\) 0.347690 + 1.07008i 0.0119187 + 0.0366819i
\(852\) 2.92953 + 0.463992i 0.100364 + 0.0158961i
\(853\) −13.8327 2.19089i −0.473623 0.0750145i −0.0849401 0.996386i \(-0.527070\pi\)
−0.388683 + 0.921372i \(0.627070\pi\)
\(854\) 18.4857 + 56.8933i 0.632569 + 1.94685i
\(855\) −0.790328 24.5064i −0.0270287 0.838102i
\(856\) −15.6947 11.4029i −0.536434 0.389742i
\(857\) −10.2364 + 10.2364i −0.349669 + 0.349669i −0.859986 0.510317i \(-0.829528\pi\)
0.510317 + 0.859986i \(0.329528\pi\)
\(858\) 0 0
\(859\) 56.0426i 1.91215i −0.293125 0.956074i \(-0.594695\pi\)
0.293125 0.956074i \(-0.405305\pi\)
\(860\) 23.4199 + 42.5177i 0.798611 + 1.44984i
\(861\) 1.64481 5.06221i 0.0560550 0.172520i
\(862\) 7.88446 15.4741i 0.268546 0.527050i
\(863\) −2.69640 + 17.0244i −0.0917867 + 0.579518i 0.898335 + 0.439310i \(0.144777\pi\)
−0.990122 + 0.140208i \(0.955223\pi\)
\(864\) 2.14616 1.55928i 0.0730140 0.0530478i
\(865\) 49.4797 + 6.20938i 1.68236 + 0.211125i
\(866\) 38.8733 + 12.6307i 1.32097 + 0.429209i
\(867\) −1.50694 9.51447i −0.0511785 0.323128i
\(868\) 64.8114 + 64.8114i 2.19984 + 2.19984i
\(869\) 0 0
\(870\) 21.2343 7.66456i 0.719910 0.259853i
\(871\) −6.87628 + 9.46438i −0.232994 + 0.320688i
\(872\) −13.3960 + 6.82560i −0.453645 + 0.231144i
\(873\) −33.9584 17.3027i −1.14932 0.585606i
\(874\) −0.878650 1.20936i −0.0297208 0.0409071i
\(875\) 18.3440 22.2858i 0.620140 0.753399i
\(876\) 3.94677 1.28238i 0.133349 0.0433278i
\(877\) −3.20066 6.28165i −0.108079 0.212116i 0.830633 0.556821i \(-0.187979\pi\)
−0.938711 + 0.344705i \(0.887979\pi\)
\(878\) 1.85708 0.294133i 0.0626735 0.00992651i
\(879\) 12.0275 0.405678
\(880\) 0 0
\(881\) −46.6330 −1.57111 −0.785553 0.618794i \(-0.787622\pi\)
−0.785553 + 0.618794i \(0.787622\pi\)
\(882\) −2.12504 + 0.336573i −0.0715537 + 0.0113330i
\(883\) −4.99714 9.80743i −0.168167 0.330046i 0.791508 0.611159i \(-0.209296\pi\)
−0.959675 + 0.281113i \(0.909296\pi\)
\(884\) −9.88212 + 3.21090i −0.332372 + 0.107994i
\(885\) −1.63115 8.51274i −0.0548306 0.286153i
\(886\) −26.8665 36.9785i −0.902597 1.24232i
\(887\) 34.7292 + 17.6954i 1.16609 + 0.594154i 0.926343 0.376680i \(-0.122934\pi\)
0.239750 + 0.970835i \(0.422934\pi\)
\(888\) 18.8847 9.62223i 0.633729 0.322901i
\(889\) 3.60411 4.96064i 0.120878 0.166374i
\(890\) −9.78168 + 20.8316i −0.327883 + 0.698277i
\(891\) 0 0
\(892\) −54.2662 54.2662i −1.81697 1.81697i
\(893\) 0.686361 + 4.33351i 0.0229682 + 0.145016i
\(894\) −11.6835 3.79620i −0.390755 0.126964i
\(895\) 5.99299 + 7.71300i 0.200323 + 0.257817i
\(896\) 42.1188 30.6011i 1.40709 1.02231i
\(897\) 0.0389107 0.245673i 0.00129919 0.00820277i
\(898\) 0.787843 1.54623i 0.0262906 0.0515983i
\(899\) 19.4354 59.8159i 0.648206 1.99497i
\(900\) 51.6499 3.33487i 1.72166 0.111162i
\(901\) 3.89303i 0.129696i
\(902\) 0 0
\(903\) −6.04959 + 6.04959i −0.201318 + 0.201318i
\(904\) 42.0884 + 30.5790i 1.39984 + 1.01704i
\(905\) −21.0970 + 0.680376i −0.701289 + 0.0226165i
\(906\) 5.36404 + 16.5088i 0.178208 + 0.548469i
\(907\) −27.7688 4.39815i −0.922049 0.146038i −0.322677 0.946509i \(-0.604583\pi\)
−0.599372 + 0.800471i \(0.704583\pi\)
\(908\) −3.95795 0.626877i −0.131349 0.0208037i
\(909\) 1.58014 + 4.86318i 0.0524100 + 0.161301i
\(910\) 26.9778 28.7758i 0.894305 0.953909i
\(911\) 23.8530 + 17.3302i 0.790285 + 0.574175i 0.908048 0.418866i \(-0.137572\pi\)
−0.117763 + 0.993042i \(0.537572\pi\)
\(912\) −6.16252 + 6.16252i −0.204061 + 0.204061i
\(913\) 0 0
\(914\) 47.0585i 1.55656i
\(915\) −11.1567 + 6.14542i −0.368830 + 0.203161i
\(916\) −0.123296 + 0.379465i −0.00407380 + 0.0125379i
\(917\) 3.66234 7.18775i 0.120941 0.237360i
\(918\) 1.21253 7.65563i 0.0400195 0.252673i
\(919\) −32.9943 + 23.9718i −1.08838 + 0.790755i −0.979125 0.203258i \(-0.934847\pi\)
−0.109256 + 0.994014i \(0.534847\pi\)
\(920\) 1.21962 0.947645i 0.0402098 0.0312429i
\(921\) 11.8173 + 3.83968i 0.389394 + 0.126522i
\(922\) 13.9003 + 87.7630i 0.457782 + 2.89032i
\(923\) −2.51454 2.51454i −0.0827672 0.0827672i
\(924\) 0 0
\(925\) −37.8281 3.51301i −1.24378 0.115507i
\(926\) −34.6632 + 47.7098i −1.13910 + 1.56784i
\(927\) 4.04776 2.06244i 0.132946 0.0677394i
\(928\) −4.86151 2.47706i −0.159587 0.0813136i
\(929\) 30.1380 + 41.4814i 0.988795 + 1.36096i 0.931954 + 0.362577i \(0.118103\pi\)
0.0568413 + 0.998383i \(0.481897\pi\)
\(930\) −16.5498 + 24.3954i −0.542689 + 0.799957i
\(931\) −1.32104 + 0.429233i −0.0432954 + 0.0140675i
\(932\) −38.0602 74.6973i −1.24670 2.44679i
\(933\) −13.7499 + 2.17776i −0.450150 + 0.0712968i
\(934\) −36.0504 −1.17960
\(935\) 0 0
\(936\) 34.6194 1.13157
\(937\) 3.04254 0.481891i 0.0993955 0.0157427i −0.106539 0.994309i \(-0.533977\pi\)
0.205934 + 0.978566i \(0.433977\pi\)
\(938\) −11.8752 23.3063i −0.387738 0.760978i
\(939\) −7.97272 + 2.59049i −0.260180 + 0.0845376i
\(940\) −9.09615 + 1.74294i −0.296684 + 0.0568485i
\(941\) 16.7138 + 23.0045i 0.544854 + 0.749927i 0.989303 0.145877i \(-0.0466005\pi\)
−0.444449 + 0.895804i \(0.646601\pi\)
\(942\) 1.76477 + 0.899198i 0.0574995 + 0.0292974i
\(943\) −0.454874 + 0.231770i −0.0148127 + 0.00754747i
\(944\) 13.3798 18.4157i 0.435474 0.599379i
\(945\) 6.61343 + 18.3222i 0.215135 + 0.596021i
\(946\) 0 0
\(947\) −40.6526 40.6526i −1.32103 1.32103i −0.912941 0.408091i \(-0.866195\pi\)
−0.408091 0.912941i \(-0.633805\pi\)
\(948\) 1.59126 + 10.0468i 0.0516818 + 0.326306i
\(949\) −4.73193 1.53750i −0.153605 0.0499092i
\(950\) 49.2400 11.0916i 1.59756 0.359858i
\(951\) 14.2724 10.3695i 0.462813 0.336253i
\(952\) 1.77894 11.2318i 0.0576557 0.364024i
\(953\) 8.68746 17.0501i 0.281414 0.552307i −0.706424 0.707788i \(-0.749693\pi\)
0.987839 + 0.155482i \(0.0496930\pi\)
\(954\) −8.18878 + 25.2025i −0.265122 + 0.815960i
\(955\) 4.02656 13.9022i 0.130296 0.449864i
\(956\) 33.9400i 1.09770i
\(957\) 0 0
\(958\) 47.4507 47.4507i 1.53306 1.53306i
\(959\) −34.5378 25.0932i −1.11528 0.810302i
\(960\) 8.71752 + 8.17281i 0.281357 + 0.263776i
\(961\) 15.7997 + 48.6264i 0.509667 + 1.56859i
\(962\) −51.2765 8.12140i −1.65322 0.261844i
\(963\) −10.8544 1.71916i −0.349777 0.0553993i
\(964\) −12.8917 39.6764i −0.415212 1.27789i
\(965\) 1.64211 + 1.53951i 0.0528615 + 0.0495584i
\(966\) 0.449938 + 0.326899i 0.0144765 + 0.0105178i
\(967\) 12.6930 12.6930i 0.408178 0.408178i −0.472925 0.881103i \(-0.656802\pi\)
0.881103 + 0.472925i \(0.156802\pi\)
\(968\) 0 0
\(969\) 2.34346i 0.0752826i
\(970\) 21.8265 75.3588i 0.700808 2.41962i
\(971\) −1.07721 + 3.31533i −0.0345695 + 0.106394i −0.966852 0.255336i \(-0.917814\pi\)
0.932283 + 0.361730i \(0.117814\pi\)
\(972\) −24.2884 + 47.6686i −0.779050 + 1.52897i
\(973\) 1.74491 11.0169i 0.0559392 0.353186i
\(974\) −76.5471 + 55.6147i −2.45273 + 1.78201i
\(975\) 7.09855 + 4.48851i 0.227336 + 0.143747i
\(976\) −31.8137 10.3369i −1.01833 0.330876i
\(977\) 4.04170 + 25.5183i 0.129305 + 0.816402i 0.964042 + 0.265752i \(0.0856201\pi\)
−0.834736 + 0.550650i \(0.814380\pi\)
\(978\) −23.6009 23.6009i −0.754672 0.754672i
\(979\) 0 0
\(980\) −0.995480 2.75793i −0.0317994 0.0880989i
\(981\) −5.00613 + 6.89034i −0.159833 + 0.219992i
\(982\) −40.7509 + 20.7636i −1.30042 + 0.662595i
\(983\) 27.8228 + 14.1764i 0.887409 + 0.452158i 0.837400 0.546591i \(-0.184075\pi\)
0.0500096 + 0.998749i \(0.484075\pi\)
\(984\) 5.65260 + 7.78013i 0.180198 + 0.248022i
\(985\) 53.8619 10.3206i 1.71618 0.328843i
\(986\) −15.1619 + 4.92639i −0.482852 + 0.156888i
\(987\) −0.741080 1.45445i −0.0235888 0.0462957i
\(988\) 45.1000 7.14313i 1.43482 0.227253i
\(989\) 0.820573 0.0260927
\(990\) 0 0
\(991\) −19.5868 −0.622196 −0.311098 0.950378i \(-0.600697\pi\)
−0.311098 + 0.950378i \(0.600697\pi\)
\(992\) 7.03714 1.11457i 0.223429 0.0353877i
\(993\) −0.593380 1.16457i −0.0188303 0.0369566i
\(994\) 7.56203 2.45705i 0.239853 0.0779330i
\(995\) 4.08712 6.02466i 0.129570 0.190995i
\(996\) −11.4176 15.7150i −0.361780 0.497948i
\(997\) −25.2279 12.8543i −0.798976 0.407098i 0.00631392 0.999980i \(-0.497990\pi\)
−0.805290 + 0.592882i \(0.797990\pi\)
\(998\) 11.3569 5.78661i 0.359495 0.183172i
\(999\) 15.0697 20.7417i 0.476784 0.656237i
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 605.2.m.e.282.4 32
5.3 odd 4 inner 605.2.m.e.403.1 32
11.2 odd 10 605.2.m.d.457.4 32
11.3 even 5 55.2.l.a.52.4 yes 32
11.4 even 5 605.2.m.d.112.4 32
11.5 even 5 605.2.e.b.362.2 32
11.6 odd 10 605.2.e.b.362.15 32
11.7 odd 10 605.2.m.c.112.1 32
11.8 odd 10 inner 605.2.m.e.602.1 32
11.9 even 5 605.2.m.c.457.1 32
11.10 odd 2 55.2.l.a.7.1 32
33.14 odd 10 495.2.bj.a.217.1 32
33.32 even 2 495.2.bj.a.172.4 32
44.3 odd 10 880.2.cm.a.657.2 32
44.43 even 2 880.2.cm.a.337.3 32
55.3 odd 20 55.2.l.a.8.1 yes 32
55.8 even 20 inner 605.2.m.e.118.4 32
55.13 even 20 605.2.m.d.578.4 32
55.14 even 10 275.2.bm.b.107.1 32
55.18 even 20 605.2.m.c.233.1 32
55.28 even 20 605.2.e.b.483.2 32
55.32 even 4 275.2.bm.b.18.1 32
55.38 odd 20 605.2.e.b.483.15 32
55.43 even 4 55.2.l.a.18.4 yes 32
55.47 odd 20 275.2.bm.b.118.4 32
55.48 odd 20 605.2.m.d.233.4 32
55.53 odd 20 605.2.m.c.578.1 32
55.54 odd 2 275.2.bm.b.7.4 32
165.98 odd 4 495.2.bj.a.73.1 32
165.113 even 20 495.2.bj.a.118.4 32
220.3 even 20 880.2.cm.a.833.3 32
220.43 odd 4 880.2.cm.a.513.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.2.l.a.7.1 32 11.10 odd 2
55.2.l.a.8.1 yes 32 55.3 odd 20
55.2.l.a.18.4 yes 32 55.43 even 4
55.2.l.a.52.4 yes 32 11.3 even 5
275.2.bm.b.7.4 32 55.54 odd 2
275.2.bm.b.18.1 32 55.32 even 4
275.2.bm.b.107.1 32 55.14 even 10
275.2.bm.b.118.4 32 55.47 odd 20
495.2.bj.a.73.1 32 165.98 odd 4
495.2.bj.a.118.4 32 165.113 even 20
495.2.bj.a.172.4 32 33.32 even 2
495.2.bj.a.217.1 32 33.14 odd 10
605.2.e.b.362.2 32 11.5 even 5
605.2.e.b.362.15 32 11.6 odd 10
605.2.e.b.483.2 32 55.28 even 20
605.2.e.b.483.15 32 55.38 odd 20
605.2.m.c.112.1 32 11.7 odd 10
605.2.m.c.233.1 32 55.18 even 20
605.2.m.c.457.1 32 11.9 even 5
605.2.m.c.578.1 32 55.53 odd 20
605.2.m.d.112.4 32 11.4 even 5
605.2.m.d.233.4 32 55.48 odd 20
605.2.m.d.457.4 32 11.2 odd 10
605.2.m.d.578.4 32 55.13 even 20
605.2.m.e.118.4 32 55.8 even 20 inner
605.2.m.e.282.4 32 1.1 even 1 trivial
605.2.m.e.403.1 32 5.3 odd 4 inner
605.2.m.e.602.1 32 11.8 odd 10 inner
880.2.cm.a.337.3 32 44.43 even 2
880.2.cm.a.513.2 32 220.43 odd 4
880.2.cm.a.657.2 32 44.3 odd 10
880.2.cm.a.833.3 32 220.3 even 20