Properties

Label 360.2.bd.b.59.19
Level $360$
Weight $2$
Character 360.59
Analytic conductor $2.875$
Analytic rank $0$
Dimension $128$
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(59,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bd (of order \(6\), degree \(2\), 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: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 59.19
Character \(\chi\) \(=\) 360.59
Dual form 360.2.bd.b.299.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.814931 + 1.15581i) q^{2} +(0.679246 + 1.59331i) q^{3} +(-0.671775 - 1.88380i) q^{4} +(-1.77343 - 1.36197i) q^{5} +(-2.39509 - 0.513357i) q^{6} +(1.70997 + 2.96175i) q^{7} +(2.72476 + 0.758729i) q^{8} +(-2.07725 + 2.16449i) q^{9} +O(q^{10})\) \(q+(-0.814931 + 1.15581i) q^{2} +(0.679246 + 1.59331i) q^{3} +(-0.671775 - 1.88380i) q^{4} +(-1.77343 - 1.36197i) q^{5} +(-2.39509 - 0.513357i) q^{6} +(1.70997 + 2.96175i) q^{7} +(2.72476 + 0.758729i) q^{8} +(-2.07725 + 2.16449i) q^{9} +(3.01939 - 0.939829i) q^{10} +(-1.22829 + 0.709153i) q^{11} +(2.54518 - 2.34991i) q^{12} +(-1.52691 + 2.64468i) q^{13} +(-4.81671 - 0.437231i) q^{14} +(0.965437 - 3.75072i) q^{15} +(-3.09744 + 2.53099i) q^{16} -5.56671 q^{17} +(-0.808922 - 4.16481i) q^{18} -1.93772 q^{19} +(-1.37434 + 4.25573i) q^{20} +(-3.55748 + 4.73626i) q^{21} +(0.181328 - 1.99758i) q^{22} +(1.73462 + 1.00148i) q^{23} +(0.641898 + 4.85674i) q^{24} +(1.29009 + 4.83070i) q^{25} +(-1.81241 - 3.92004i) q^{26} +(-4.85967 - 1.83947i) q^{27} +(4.43064 - 5.21087i) q^{28} +(-2.99472 - 5.18701i) q^{29} +(3.54834 + 4.17244i) q^{30} +(3.93868 + 2.27400i) q^{31} +(-0.401131 - 5.64261i) q^{32} +(-1.96421 - 1.47535i) q^{33} +(4.53648 - 6.43403i) q^{34} +(1.00130 - 7.58136i) q^{35} +(5.47293 + 2.45908i) q^{36} +4.60997 q^{37} +(1.57911 - 2.23963i) q^{38} +(-5.25093 - 0.636440i) q^{39} +(-3.79880 - 5.05659i) q^{40} +(7.55565 + 4.36226i) q^{41} +(-2.57509 - 7.97148i) q^{42} +(3.14088 - 1.81339i) q^{43} +(2.16104 + 1.83747i) q^{44} +(6.63182 - 1.00943i) q^{45} +(-2.57112 + 1.18874i) q^{46} +(-9.41974 + 5.43849i) q^{47} +(-6.13656 - 3.21600i) q^{48} +(-2.34797 + 4.06680i) q^{49} +(-6.63469 - 2.44559i) q^{50} +(-3.78117 - 8.86947i) q^{51} +(6.00779 + 1.09976i) q^{52} +7.92349i q^{53} +(6.08636 - 4.11779i) q^{54} +(3.14413 + 0.415259i) q^{55} +(2.41209 + 9.36746i) q^{56} +(-1.31619 - 3.08739i) q^{57} +(8.43566 + 0.765737i) q^{58} +(1.71292 + 0.988953i) q^{59} +(-7.71419 + 0.700948i) q^{60} +(-0.587113 + 0.338970i) q^{61} +(-5.83805 + 2.69920i) q^{62} +(-9.96271 - 2.45108i) q^{63} +(6.84866 + 4.13471i) q^{64} +(6.30982 - 2.61055i) q^{65} +(3.30592 - 1.06794i) q^{66} +(-12.7876 - 7.38294i) q^{67} +(3.73958 + 10.4866i) q^{68} +(-0.417435 + 3.44403i) q^{69} +(7.94659 + 7.33560i) q^{70} +13.6263 q^{71} +(-7.30227 + 4.32167i) q^{72} +12.3720i q^{73} +(-3.75681 + 5.32823i) q^{74} +(-6.82050 + 5.33674i) q^{75} +(1.30171 + 3.65029i) q^{76} +(-4.20067 - 2.42526i) q^{77} +(5.01474 - 5.55040i) q^{78} +(3.19919 - 1.84706i) q^{79} +(8.94020 - 0.269911i) q^{80} +(-0.370074 - 8.99239i) q^{81} +(-11.1993 + 5.17793i) q^{82} +(3.31153 + 5.73574i) q^{83} +(11.3120 + 3.51990i) q^{84} +(9.87215 + 7.58167i) q^{85} +(-0.463676 + 5.10803i) q^{86} +(6.23034 - 8.29476i) q^{87} +(-3.88485 + 1.00034i) q^{88} +7.02054i q^{89} +(-4.23777 + 8.48771i) q^{90} -10.4438 q^{91} +(0.721324 - 3.94046i) q^{92} +(-0.947841 + 7.82012i) q^{93} +(1.39060 - 15.3194i) q^{94} +(3.43641 + 2.63912i) q^{95} +(8.71794 - 4.47185i) q^{96} +(16.1862 - 9.34508i) q^{97} +(-2.78700 - 6.02796i) q^{98} +(1.01650 - 4.13171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q - 10 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 10 q^{4} + 4 q^{9} - 48 q^{11} - 30 q^{14} + 14 q^{16} + 24 q^{19} - 24 q^{20} - 10 q^{24} + 14 q^{25} + 26 q^{30} + 8 q^{36} + 12 q^{40} - 24 q^{41} - 36 q^{46} - 52 q^{49} - 42 q^{50} - 68 q^{51} - 62 q^{54} - 54 q^{56} - 24 q^{60} + 68 q^{64} - 18 q^{65} + 44 q^{66} - 60 q^{74} + 10 q^{75} + 24 q^{76} + 36 q^{81} + 94 q^{84} - 74 q^{90} + 88 q^{91} - 26 q^{94} - 22 q^{96} - 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.814931 + 1.15581i −0.576243 + 0.817278i
\(3\) 0.679246 + 1.59331i 0.392163 + 0.919896i
\(4\) −0.671775 1.88380i −0.335888 0.941902i
\(5\) −1.77343 1.36197i −0.793101 0.609090i
\(6\) −2.39509 0.513357i −0.977792 0.209577i
\(7\) 1.70997 + 2.96175i 0.646306 + 1.11944i 0.983998 + 0.178179i \(0.0570206\pi\)
−0.337692 + 0.941257i \(0.609646\pi\)
\(8\) 2.72476 + 0.758729i 0.963349 + 0.268251i
\(9\) −2.07725 + 2.16449i −0.692416 + 0.721498i
\(10\) 3.01939 0.939829i 0.954815 0.297200i
\(11\) −1.22829 + 0.709153i −0.370343 + 0.213818i −0.673608 0.739088i \(-0.735257\pi\)
0.303265 + 0.952906i \(0.401923\pi\)
\(12\) 2.54518 2.34991i 0.734729 0.678361i
\(13\) −1.52691 + 2.64468i −0.423487 + 0.733502i −0.996278 0.0862002i \(-0.972528\pi\)
0.572791 + 0.819702i \(0.305861\pi\)
\(14\) −4.81671 0.437231i −1.28732 0.116855i
\(15\) 0.965437 3.75072i 0.249275 0.968433i
\(16\) −3.09744 + 2.53099i −0.774359 + 0.632746i
\(17\) −5.56671 −1.35012 −0.675062 0.737761i \(-0.735883\pi\)
−0.675062 + 0.737761i \(0.735883\pi\)
\(18\) −0.808922 4.16481i −0.190665 0.981655i
\(19\) −1.93772 −0.444544 −0.222272 0.974985i \(-0.571347\pi\)
−0.222272 + 0.974985i \(0.571347\pi\)
\(20\) −1.37434 + 4.25573i −0.307311 + 0.951609i
\(21\) −3.55748 + 4.73626i −0.776307 + 1.03354i
\(22\) 0.181328 1.99758i 0.0386592 0.425885i
\(23\) 1.73462 + 1.00148i 0.361693 + 0.208824i 0.669823 0.742521i \(-0.266370\pi\)
−0.308130 + 0.951344i \(0.599703\pi\)
\(24\) 0.641898 + 4.85674i 0.131027 + 0.991379i
\(25\) 1.29009 + 4.83070i 0.258018 + 0.966140i
\(26\) −1.81241 3.92004i −0.355443 0.768782i
\(27\) −4.85967 1.83947i −0.935243 0.354006i
\(28\) 4.43064 5.21087i 0.837312 0.984762i
\(29\) −2.99472 5.18701i −0.556106 0.963203i −0.997817 0.0660457i \(-0.978962\pi\)
0.441711 0.897157i \(-0.354372\pi\)
\(30\) 3.54834 + 4.17244i 0.647836 + 0.761780i
\(31\) 3.93868 + 2.27400i 0.707407 + 0.408422i 0.810100 0.586291i \(-0.199413\pi\)
−0.102693 + 0.994713i \(0.532746\pi\)
\(32\) −0.401131 5.64261i −0.0709107 0.997483i
\(33\) −1.96421 1.47535i −0.341925 0.256826i
\(34\) 4.53648 6.43403i 0.778000 1.10343i
\(35\) 1.00130 7.58136i 0.169251 1.28148i
\(36\) 5.47293 + 2.45908i 0.912155 + 0.409846i
\(37\) 4.60997 0.757875 0.378937 0.925422i \(-0.376290\pi\)
0.378937 + 0.925422i \(0.376290\pi\)
\(38\) 1.57911 2.23963i 0.256166 0.363316i
\(39\) −5.25093 0.636440i −0.840821 0.101912i
\(40\) −3.79880 5.05659i −0.600644 0.799517i
\(41\) 7.55565 + 4.36226i 1.17999 + 0.681270i 0.956013 0.293323i \(-0.0947612\pi\)
0.223981 + 0.974593i \(0.428095\pi\)
\(42\) −2.57509 7.97148i −0.397345 1.23003i
\(43\) 3.14088 1.81339i 0.478980 0.276539i −0.241012 0.970522i \(-0.577479\pi\)
0.719991 + 0.693983i \(0.244146\pi\)
\(44\) 2.16104 + 1.83747i 0.325789 + 0.277008i
\(45\) 6.63182 1.00943i 0.988614 0.150477i
\(46\) −2.57112 + 1.18874i −0.379090 + 0.175271i
\(47\) −9.41974 + 5.43849i −1.37401 + 0.793285i −0.991430 0.130637i \(-0.958298\pi\)
−0.382580 + 0.923922i \(0.624964\pi\)
\(48\) −6.13656 3.21600i −0.885736 0.464190i
\(49\) −2.34797 + 4.06680i −0.335424 + 0.580972i
\(50\) −6.63469 2.44559i −0.938286 0.345859i
\(51\) −3.78117 8.86947i −0.529469 1.24197i
\(52\) 6.00779 + 1.09976i 0.833131 + 0.152510i
\(53\) 7.92349i 1.08837i 0.838964 + 0.544187i \(0.183162\pi\)
−0.838964 + 0.544187i \(0.816838\pi\)
\(54\) 6.08636 4.11779i 0.828249 0.560360i
\(55\) 3.14413 + 0.415259i 0.423954 + 0.0559935i
\(56\) 2.41209 + 9.36746i 0.322329 + 1.25178i
\(57\) −1.31619 3.08739i −0.174334 0.408934i
\(58\) 8.43566 + 0.765737i 1.10766 + 0.100546i
\(59\) 1.71292 + 0.988953i 0.223003 + 0.128751i 0.607340 0.794442i \(-0.292237\pi\)
−0.384337 + 0.923193i \(0.625570\pi\)
\(60\) −7.71419 + 0.700948i −0.995897 + 0.0904921i
\(61\) −0.587113 + 0.338970i −0.0751721 + 0.0434006i −0.537115 0.843509i \(-0.680486\pi\)
0.461943 + 0.886910i \(0.347153\pi\)
\(62\) −5.83805 + 2.69920i −0.741433 + 0.342798i
\(63\) −9.96271 2.45108i −1.25518 0.308807i
\(64\) 6.84866 + 4.13471i 0.856083 + 0.516839i
\(65\) 6.30982 2.61055i 0.782637 0.323799i
\(66\) 3.30592 1.06794i 0.406930 0.131454i
\(67\) −12.7876 7.38294i −1.56226 0.901970i −0.997028 0.0770368i \(-0.975454\pi\)
−0.565230 0.824933i \(-0.691213\pi\)
\(68\) 3.73958 + 10.4866i 0.453490 + 1.27169i
\(69\) −0.417435 + 3.44403i −0.0502533 + 0.414613i
\(70\) 7.94659 + 7.33560i 0.949799 + 0.876772i
\(71\) 13.6263 1.61715 0.808573 0.588396i \(-0.200240\pi\)
0.808573 + 0.588396i \(0.200240\pi\)
\(72\) −7.30227 + 4.32167i −0.860581 + 0.509313i
\(73\) 12.3720i 1.44803i 0.689782 + 0.724017i \(0.257706\pi\)
−0.689782 + 0.724017i \(0.742294\pi\)
\(74\) −3.75681 + 5.32823i −0.436720 + 0.619395i
\(75\) −6.82050 + 5.33674i −0.787563 + 0.616234i
\(76\) 1.30171 + 3.65029i 0.149317 + 0.418717i
\(77\) −4.20067 2.42526i −0.478711 0.276384i
\(78\) 5.01474 5.55040i 0.567808 0.628459i
\(79\) 3.19919 1.84706i 0.359938 0.207810i −0.309116 0.951024i \(-0.600033\pi\)
0.669053 + 0.743214i \(0.266700\pi\)
\(80\) 8.94020 0.269911i 0.999545 0.0301770i
\(81\) −0.370074 8.99239i −0.0411193 0.999154i
\(82\) −11.1993 + 5.17793i −1.23675 + 0.571807i
\(83\) 3.31153 + 5.73574i 0.363488 + 0.629580i 0.988532 0.151010i \(-0.0482525\pi\)
−0.625044 + 0.780589i \(0.714919\pi\)
\(84\) 11.3120 + 3.51990i 1.23424 + 0.384053i
\(85\) 9.87215 + 7.58167i 1.07079 + 0.822348i
\(86\) −0.463676 + 5.10803i −0.0499994 + 0.550813i
\(87\) 6.23034 8.29476i 0.667962 0.889292i
\(88\) −3.88485 + 1.00034i −0.414127 + 0.106636i
\(89\) 7.02054i 0.744176i 0.928197 + 0.372088i \(0.121358\pi\)
−0.928197 + 0.372088i \(0.878642\pi\)
\(90\) −4.23777 + 8.48771i −0.446700 + 0.894684i
\(91\) −10.4438 −1.09481
\(92\) 0.721324 3.94046i 0.0752032 0.410821i
\(93\) −0.947841 + 7.82012i −0.0982865 + 0.810909i
\(94\) 1.39060 15.3194i 0.143429 1.58007i
\(95\) 3.43641 + 2.63912i 0.352568 + 0.270768i
\(96\) 8.71794 4.47185i 0.889771 0.456406i
\(97\) 16.1862 9.34508i 1.64346 0.948849i 0.663863 0.747854i \(-0.268916\pi\)
0.979592 0.200996i \(-0.0644177\pi\)
\(98\) −2.78700 6.02796i −0.281530 0.608916i
\(99\) 1.01650 4.13171i 0.102163 0.415253i
\(100\) 8.23344 5.67542i 0.823344 0.567542i
\(101\) −1.20639 2.08954i −0.120041 0.207917i 0.799743 0.600343i \(-0.204969\pi\)
−0.919784 + 0.392426i \(0.871636\pi\)
\(102\) 13.3328 + 2.85771i 1.32014 + 0.282956i
\(103\) 7.42476 12.8601i 0.731583 1.26714i −0.224623 0.974446i \(-0.572115\pi\)
0.956206 0.292693i \(-0.0945515\pi\)
\(104\) −6.16705 + 6.04761i −0.604729 + 0.593017i
\(105\) 12.7596 3.55423i 1.24521 0.346857i
\(106\) −9.15801 6.45709i −0.889505 0.627168i
\(107\) 16.4184 1.58723 0.793614 0.608421i \(-0.208197\pi\)
0.793614 + 0.608421i \(0.208197\pi\)
\(108\) −0.200595 + 10.3904i −0.0193023 + 0.999814i
\(109\) 0.509995i 0.0488487i 0.999702 + 0.0244243i \(0.00777528\pi\)
−0.999702 + 0.0244243i \(0.992225\pi\)
\(110\) −3.04220 + 3.29559i −0.290063 + 0.314222i
\(111\) 3.13131 + 7.34510i 0.297210 + 0.697166i
\(112\) −12.7927 4.84593i −1.20879 0.457897i
\(113\) −0.626344 + 1.08486i −0.0589215 + 0.102055i −0.893982 0.448104i \(-0.852100\pi\)
0.835060 + 0.550159i \(0.185433\pi\)
\(114\) 4.64102 + 0.994745i 0.434672 + 0.0931664i
\(115\) −1.71223 4.13855i −0.159667 0.385922i
\(116\) −7.75953 + 9.12597i −0.720454 + 0.847325i
\(117\) −2.55263 8.79863i −0.235991 0.813434i
\(118\) −2.53895 + 1.17387i −0.233729 + 0.108064i
\(119\) −9.51888 16.4872i −0.872594 1.51138i
\(120\) 5.47637 9.48733i 0.499922 0.866071i
\(121\) −4.49420 + 7.78419i −0.408564 + 0.707653i
\(122\) 0.0866731 0.954825i 0.00784702 0.0864458i
\(123\) −1.81826 + 15.0015i −0.163947 + 1.35264i
\(124\) 1.63786 8.94731i 0.147084 0.803492i
\(125\) 4.29138 10.3240i 0.383833 0.923403i
\(126\) 10.9519 9.51751i 0.975672 0.847887i
\(127\) 4.29697 0.381294 0.190647 0.981659i \(-0.438941\pi\)
0.190647 + 0.981659i \(0.438941\pi\)
\(128\) −10.3601 + 4.54622i −0.915713 + 0.401833i
\(129\) 5.02271 + 3.77265i 0.442225 + 0.332163i
\(130\) −2.12478 + 9.42034i −0.186356 + 0.826219i
\(131\) 14.4106 + 8.31998i 1.25906 + 0.726920i 0.972892 0.231259i \(-0.0742845\pi\)
0.286170 + 0.958179i \(0.407618\pi\)
\(132\) −1.45977 + 4.69129i −0.127056 + 0.408324i
\(133\) −3.31344 5.73905i −0.287312 0.497639i
\(134\) 18.9543 8.76344i 1.63740 0.757045i
\(135\) 6.11297 + 9.88087i 0.526121 + 0.850410i
\(136\) −15.1680 4.22362i −1.30064 0.362172i
\(137\) −5.59760 9.69532i −0.478235 0.828327i 0.521454 0.853280i \(-0.325390\pi\)
−0.999689 + 0.0249522i \(0.992057\pi\)
\(138\) −3.64045 3.28912i −0.309896 0.279989i
\(139\) −5.43639 + 9.41611i −0.461109 + 0.798664i −0.999017 0.0443398i \(-0.985882\pi\)
0.537908 + 0.843004i \(0.319215\pi\)
\(140\) −14.9545 + 3.20671i −1.26388 + 0.271017i
\(141\) −15.0635 11.3145i −1.26858 0.952849i
\(142\) −11.1045 + 15.7494i −0.931870 + 1.32166i
\(143\) 4.33124i 0.362196i
\(144\) 0.955842 11.9619i 0.0796535 0.996823i
\(145\) −1.75362 + 13.2775i −0.145630 + 1.10264i
\(146\) −14.2996 10.0823i −1.18345 0.834420i
\(147\) −8.07451 0.978673i −0.665974 0.0807196i
\(148\) −3.09686 8.68429i −0.254561 0.713844i
\(149\) −7.28102 + 12.6111i −0.596485 + 1.03314i 0.396851 + 0.917883i \(0.370103\pi\)
−0.993336 + 0.115259i \(0.963230\pi\)
\(150\) −0.610005 12.2322i −0.0498067 0.998759i
\(151\) 1.46206 0.844120i 0.118981 0.0686935i −0.439329 0.898326i \(-0.644784\pi\)
0.558309 + 0.829633i \(0.311450\pi\)
\(152\) −5.27983 1.47021i −0.428251 0.119249i
\(153\) 11.5634 12.0491i 0.934848 0.974113i
\(154\) 6.22638 2.87874i 0.501736 0.231976i
\(155\) −3.88785 9.39712i −0.312280 0.754795i
\(156\) 2.32851 + 10.3193i 0.186430 + 0.826202i
\(157\) −7.35162 + 12.7334i −0.586723 + 1.01623i 0.407935 + 0.913011i \(0.366249\pi\)
−0.994658 + 0.103224i \(0.967084\pi\)
\(158\) −0.472284 + 5.20287i −0.0375729 + 0.413918i
\(159\) −12.6245 + 5.38200i −1.00119 + 0.426820i
\(160\) −6.97368 + 10.5531i −0.551318 + 0.834295i
\(161\) 6.85001i 0.539856i
\(162\) 10.6950 + 6.90044i 0.840282 + 0.542150i
\(163\) 11.5047i 0.901115i −0.892748 0.450557i \(-0.851225\pi\)
0.892748 0.450557i \(-0.148775\pi\)
\(164\) 3.14194 17.1638i 0.245344 1.34027i
\(165\) 1.47400 + 5.29162i 0.114751 + 0.411952i
\(166\) −9.32808 0.846745i −0.723999 0.0657202i
\(167\) 1.23207 + 0.711334i 0.0953401 + 0.0550447i 0.546912 0.837190i \(-0.315803\pi\)
−0.451572 + 0.892235i \(0.649137\pi\)
\(168\) −13.2868 + 10.2060i −1.02510 + 0.787411i
\(169\) 1.83712 + 3.18199i 0.141317 + 0.244768i
\(170\) −16.8081 + 5.23175i −1.28912 + 0.401257i
\(171\) 4.02513 4.19419i 0.307810 0.320738i
\(172\) −5.52603 4.69861i −0.421356 0.358266i
\(173\) 10.6357 6.14051i 0.808616 0.466855i −0.0378592 0.999283i \(-0.512054\pi\)
0.846475 + 0.532429i \(0.178721\pi\)
\(174\) 4.50984 + 13.9607i 0.341890 + 1.05836i
\(175\) −12.1013 + 12.0813i −0.914773 + 0.913257i
\(176\) 2.00969 5.30534i 0.151486 0.399905i
\(177\) −0.412212 + 3.40094i −0.0309838 + 0.255630i
\(178\) −8.11439 5.72126i −0.608199 0.428827i
\(179\) 6.95263i 0.519664i −0.965654 0.259832i \(-0.916333\pi\)
0.965654 0.259832i \(-0.0836672\pi\)
\(180\) −6.35666 11.8149i −0.473797 0.880634i
\(181\) 7.42538i 0.551924i 0.961169 + 0.275962i \(0.0889964\pi\)
−0.961169 + 0.275962i \(0.911004\pi\)
\(182\) 8.51100 12.0710i 0.630877 0.894765i
\(183\) −0.938877 0.705206i −0.0694038 0.0521304i
\(184\) 3.96657 + 4.04491i 0.292420 + 0.298195i
\(185\) −8.17545 6.27863i −0.601071 0.461614i
\(186\) −8.26612 7.46838i −0.606101 0.547608i
\(187\) 6.83753 3.94765i 0.500010 0.288681i
\(188\) 16.5730 + 14.0915i 1.20871 + 1.02773i
\(189\) −2.86182 17.5385i −0.208167 1.27574i
\(190\) −5.85074 + 1.82113i −0.424458 + 0.132118i
\(191\) −4.64817 8.05086i −0.336329 0.582540i 0.647410 0.762142i \(-0.275852\pi\)
−0.983739 + 0.179602i \(0.942519\pi\)
\(192\) −1.93593 + 13.7205i −0.139714 + 0.990192i
\(193\) 3.09360 + 1.78609i 0.222682 + 0.128566i 0.607192 0.794555i \(-0.292296\pi\)
−0.384509 + 0.923121i \(0.625629\pi\)
\(194\) −2.38950 + 26.3237i −0.171556 + 1.88993i
\(195\) 8.44532 + 8.28027i 0.604782 + 0.592962i
\(196\) 9.23836 + 1.69114i 0.659883 + 0.120796i
\(197\) 16.7200i 1.19125i −0.803263 0.595625i \(-0.796904\pi\)
0.803263 0.595625i \(-0.203096\pi\)
\(198\) 3.94708 + 4.54194i 0.280507 + 0.322782i
\(199\) 3.04703i 0.215998i 0.994151 + 0.107999i \(0.0344443\pi\)
−0.994151 + 0.107999i \(0.965556\pi\)
\(200\) −0.150004 + 14.1413i −0.0106069 + 0.999944i
\(201\) 3.07734 25.3895i 0.217059 1.79083i
\(202\) 3.39823 + 0.308470i 0.239098 + 0.0217039i
\(203\) 10.2417 17.7392i 0.718829 1.24505i
\(204\) −14.1682 + 13.0813i −0.991976 + 0.915872i
\(205\) −7.45815 18.0267i −0.520900 1.25904i
\(206\) 8.81307 + 19.0616i 0.614035 + 1.32809i
\(207\) −5.77094 + 1.67425i −0.401108 + 0.116368i
\(208\) −1.96415 12.0563i −0.136189 0.835954i
\(209\) 2.38009 1.37414i 0.164634 0.0950514i
\(210\) −6.29016 + 17.6440i −0.434063 + 1.21755i
\(211\) −1.28542 + 2.22641i −0.0884917 + 0.153272i −0.906874 0.421402i \(-0.861538\pi\)
0.818382 + 0.574675i \(0.194871\pi\)
\(212\) 14.9263 5.32280i 1.02514 0.365571i
\(213\) 9.25563 + 21.7109i 0.634185 + 1.48761i
\(214\) −13.3799 + 18.9765i −0.914630 + 1.29721i
\(215\) −8.03990 1.06186i −0.548316 0.0724186i
\(216\) −11.8458 8.69928i −0.806003 0.591911i
\(217\) 15.5538i 1.05586i
\(218\) −0.589456 0.415611i −0.0399230 0.0281487i
\(219\) −19.7124 + 8.40364i −1.33204 + 0.567866i
\(220\) −1.32988 6.20188i −0.0896605 0.418131i
\(221\) 8.49983 14.7221i 0.571761 0.990319i
\(222\) −11.0413 2.36656i −0.741044 0.158833i
\(223\) −11.9624 20.7194i −0.801059 1.38748i −0.918919 0.394445i \(-0.870937\pi\)
0.117860 0.993030i \(-0.462397\pi\)
\(224\) 16.0261 10.8367i 1.07079 0.724059i
\(225\) −13.1359 7.24218i −0.875724 0.482812i
\(226\) −0.743460 1.60802i −0.0494543 0.106964i
\(227\) 11.5037 + 19.9250i 0.763526 + 1.32247i 0.941022 + 0.338345i \(0.109867\pi\)
−0.177496 + 0.984122i \(0.556800\pi\)
\(228\) −4.93185 + 4.55348i −0.326619 + 0.301561i
\(229\) −18.4838 10.6716i −1.22144 0.705200i −0.256217 0.966619i \(-0.582476\pi\)
−0.965225 + 0.261420i \(0.915809\pi\)
\(230\) 6.17872 + 1.39362i 0.407413 + 0.0918929i
\(231\) 1.01089 8.34030i 0.0665116 0.548751i
\(232\) −4.22437 16.4055i −0.277343 1.07708i
\(233\) −29.4064 −1.92648 −0.963239 0.268646i \(-0.913424\pi\)
−0.963239 + 0.268646i \(0.913424\pi\)
\(234\) 12.2497 + 4.21993i 0.800790 + 0.275866i
\(235\) 24.1123 + 3.18461i 1.57291 + 0.207741i
\(236\) 0.712299 3.89115i 0.0463667 0.253292i
\(237\) 5.11597 + 3.84269i 0.332318 + 0.249610i
\(238\) 26.8132 + 2.43394i 1.73804 + 0.157769i
\(239\) −0.287284 + 0.497590i −0.0185828 + 0.0321864i −0.875167 0.483820i \(-0.839249\pi\)
0.856584 + 0.516007i \(0.172582\pi\)
\(240\) 6.50265 + 14.0611i 0.419744 + 0.907642i
\(241\) −11.7683 20.3833i −0.758062 1.31300i −0.943838 0.330409i \(-0.892813\pi\)
0.185776 0.982592i \(-0.440520\pi\)
\(242\) −5.33455 11.5380i −0.342918 0.741691i
\(243\) 14.0763 6.69769i 0.902992 0.429657i
\(244\) 1.03296 + 0.878294i 0.0661285 + 0.0562270i
\(245\) 9.70280 4.01432i 0.619889 0.256465i
\(246\) −15.8571 14.3268i −1.01101 0.913441i
\(247\) 2.95872 5.12465i 0.188259 0.326074i
\(248\) 9.00662 + 9.18449i 0.571921 + 0.583216i
\(249\) −6.88945 + 9.17227i −0.436601 + 0.581269i
\(250\) 8.43531 + 13.3733i 0.533496 + 0.845803i
\(251\) 3.65204i 0.230515i −0.993336 0.115257i \(-0.963231\pi\)
0.993336 0.115257i \(-0.0367693\pi\)
\(252\) 2.07536 + 20.4144i 0.130735 + 1.28598i
\(253\) −2.84082 −0.178601
\(254\) −3.50173 + 4.96646i −0.219718 + 0.311623i
\(255\) −5.37431 + 20.8792i −0.336552 + 1.30751i
\(256\) 3.18822 15.6791i 0.199264 0.979946i
\(257\) −9.92064 + 17.1831i −0.618833 + 1.07185i 0.370866 + 0.928686i \(0.379061\pi\)
−0.989699 + 0.143163i \(0.954273\pi\)
\(258\) −8.45361 + 2.73084i −0.526299 + 0.170014i
\(259\) 7.88290 + 13.6536i 0.489819 + 0.848392i
\(260\) −9.15654 10.1328i −0.567865 0.628407i
\(261\) 17.4480 + 4.29265i 1.08001 + 0.265708i
\(262\) −21.3599 + 9.87568i −1.31962 + 0.610121i
\(263\) 18.5206 10.6929i 1.14203 0.659351i 0.195097 0.980784i \(-0.437498\pi\)
0.946932 + 0.321433i \(0.104164\pi\)
\(264\) −4.23261 5.51029i −0.260499 0.339135i
\(265\) 10.7915 14.0517i 0.662918 0.863191i
\(266\) 9.33345 + 0.847233i 0.572271 + 0.0519472i
\(267\) −11.1859 + 4.76868i −0.684565 + 0.291838i
\(268\) −5.31761 + 29.0491i −0.324825 + 1.77445i
\(269\) 3.39669 0.207100 0.103550 0.994624i \(-0.466980\pi\)
0.103550 + 0.994624i \(0.466980\pi\)
\(270\) −16.4020 0.986821i −0.998195 0.0600560i
\(271\) 3.14526i 0.191061i 0.995427 + 0.0955304i \(0.0304547\pi\)
−0.995427 + 0.0955304i \(0.969545\pi\)
\(272\) 17.2425 14.0893i 1.04548 0.854287i
\(273\) −7.09393 16.6402i −0.429344 1.00711i
\(274\) 15.7676 + 1.43128i 0.952554 + 0.0864669i
\(275\) −5.01031 5.01863i −0.302133 0.302635i
\(276\) 6.76831 1.52725i 0.407404 0.0919297i
\(277\) 0.660382 + 1.14382i 0.0396785 + 0.0687252i 0.885183 0.465244i \(-0.154033\pi\)
−0.845504 + 0.533969i \(0.820700\pi\)
\(278\) −6.45291 13.9569i −0.387020 0.837079i
\(279\) −13.1037 + 3.80159i −0.784496 + 0.227595i
\(280\) 8.48051 19.8977i 0.506808 1.18911i
\(281\) 7.77791 4.49058i 0.463991 0.267885i −0.249730 0.968316i \(-0.580342\pi\)
0.713721 + 0.700430i \(0.247008\pi\)
\(282\) 25.3530 8.18999i 1.50975 0.487707i
\(283\) −0.734768 0.424219i −0.0436774 0.0252172i 0.478002 0.878359i \(-0.341361\pi\)
−0.521680 + 0.853141i \(0.674694\pi\)
\(284\) −9.15382 25.6693i −0.543179 1.52319i
\(285\) −1.87075 + 7.26786i −0.110814 + 0.430511i
\(286\) 5.00607 + 3.52966i 0.296015 + 0.208713i
\(287\) 29.8373i 1.76124i
\(288\) 13.0467 + 10.8529i 0.768782 + 0.639511i
\(289\) 13.9882 0.822837
\(290\) −13.9171 12.8471i −0.817242 0.754407i
\(291\) 25.8840 + 19.4419i 1.51735 + 1.13970i
\(292\) 23.3064 8.31121i 1.36391 0.486377i
\(293\) 8.75742 + 5.05610i 0.511614 + 0.295380i 0.733497 0.679693i \(-0.237887\pi\)
−0.221883 + 0.975073i \(0.571220\pi\)
\(294\) 7.71132 8.53501i 0.449733 0.497772i
\(295\) −1.69081 4.08677i −0.0984428 0.237941i
\(296\) 12.5611 + 3.49772i 0.730098 + 0.203301i
\(297\) 7.27354 1.18685i 0.422054 0.0688679i
\(298\) −8.64246 18.6926i −0.500644 1.08283i
\(299\) −5.29720 + 3.05834i −0.306345 + 0.176868i
\(300\) 14.6352 + 9.26339i 0.844965 + 0.534822i
\(301\) 10.7416 + 6.20166i 0.619135 + 0.357458i
\(302\) −0.215838 + 2.37776i −0.0124201 + 0.136824i
\(303\) 2.50983 3.34147i 0.144186 0.191962i
\(304\) 6.00197 4.90435i 0.344237 0.281284i
\(305\) 1.50287 + 0.198490i 0.0860539 + 0.0113655i
\(306\) 4.50303 + 23.1843i 0.257421 + 1.32536i
\(307\) 8.07245i 0.460719i −0.973106 0.230359i \(-0.926010\pi\)
0.973106 0.230359i \(-0.0739902\pi\)
\(308\) −1.74680 + 9.54246i −0.0995334 + 0.543732i
\(309\) 25.5332 + 3.09477i 1.45254 + 0.176055i
\(310\) 14.0296 + 3.16440i 0.796826 + 0.179726i
\(311\) −14.4391 + 25.0092i −0.818764 + 1.41814i 0.0878289 + 0.996136i \(0.472007\pi\)
−0.906593 + 0.422006i \(0.861326\pi\)
\(312\) −13.8246 5.71818i −0.782666 0.323728i
\(313\) −21.6842 + 12.5194i −1.22566 + 0.707636i −0.966119 0.258096i \(-0.916905\pi\)
−0.259542 + 0.965732i \(0.583572\pi\)
\(314\) −8.72626 18.8739i −0.492451 1.06511i
\(315\) 14.3299 + 17.9157i 0.807396 + 1.00944i
\(316\) −5.62863 4.78585i −0.316635 0.269225i
\(317\) −17.5636 + 10.1404i −0.986471 + 0.569539i −0.904218 0.427072i \(-0.859545\pi\)
−0.0822535 + 0.996611i \(0.526212\pi\)
\(318\) 4.06758 18.9775i 0.228099 1.06420i
\(319\) 7.35677 + 4.24743i 0.411900 + 0.237811i
\(320\) −6.51426 16.6603i −0.364158 0.931337i
\(321\) 11.1522 + 26.1596i 0.622452 + 1.46008i
\(322\) −7.91728 5.58228i −0.441213 0.311089i
\(323\) 10.7867 0.600190
\(324\) −16.6913 + 6.73801i −0.927294 + 0.374334i
\(325\) −14.7455 3.96415i −0.817933 0.219892i
\(326\) 13.2972 + 9.37550i 0.736461 + 0.519261i
\(327\) −0.812579 + 0.346412i −0.0449357 + 0.0191567i
\(328\) 17.2776 + 17.6188i 0.953995 + 0.972836i
\(329\) −32.2149 18.5993i −1.77606 1.02541i
\(330\) −7.31729 2.60864i −0.402804 0.143601i
\(331\) −0.794231 1.37565i −0.0436549 0.0756124i 0.843372 0.537330i \(-0.180567\pi\)
−0.887027 + 0.461717i \(0.847234\pi\)
\(332\) 8.58041 10.0914i 0.470911 0.553838i
\(333\) −9.57606 + 9.97826i −0.524765 + 0.546805i
\(334\) −1.82621 + 0.844342i −0.0999259 + 0.0462003i
\(335\) 12.6226 + 30.5095i 0.689647 + 1.66691i
\(336\) −0.968317 23.6742i −0.0528260 1.29153i
\(337\) 1.92124 + 1.10923i 0.104657 + 0.0604235i 0.551415 0.834231i \(-0.314088\pi\)
−0.446758 + 0.894655i \(0.647422\pi\)
\(338\) −5.17489 0.469744i −0.281477 0.0255507i
\(339\) −2.15396 0.261071i −0.116987 0.0141794i
\(340\) 7.65052 23.6904i 0.414908 1.28479i
\(341\) −6.45045 −0.349311
\(342\) 1.56747 + 8.07025i 0.0847588 + 0.436389i
\(343\) 7.87974 0.425466
\(344\) 9.93402 2.55798i 0.535606 0.137917i
\(345\) 5.43095 5.53921i 0.292393 0.298221i
\(346\) −1.57010 + 17.2969i −0.0844093 + 0.929886i
\(347\) −3.96899 + 6.87450i −0.213067 + 0.369042i −0.952673 0.303998i \(-0.901678\pi\)
0.739606 + 0.673040i \(0.235012\pi\)
\(348\) −19.8111 6.16452i −1.06199 0.330453i
\(349\) −16.0691 + 9.27748i −0.860157 + 0.496612i −0.864065 0.503380i \(-0.832089\pi\)
0.00390787 + 0.999992i \(0.498756\pi\)
\(350\) −4.10185 23.8322i −0.219253 1.27388i
\(351\) 12.2851 10.0436i 0.655727 0.536085i
\(352\) 4.49418 + 6.64630i 0.239541 + 0.354249i
\(353\) −7.79810 13.5067i −0.415051 0.718890i 0.580383 0.814344i \(-0.302903\pi\)
−0.995434 + 0.0954542i \(0.969570\pi\)
\(354\) −3.59490 3.24797i −0.191067 0.172628i
\(355\) −24.1653 18.5586i −1.28256 0.984988i
\(356\) 13.2253 4.71623i 0.700941 0.249960i
\(357\) 19.8035 26.3654i 1.04811 1.39540i
\(358\) 8.03589 + 5.66591i 0.424710 + 0.299453i
\(359\) 12.8977 0.680712 0.340356 0.940297i \(-0.389452\pi\)
0.340356 + 0.940297i \(0.389452\pi\)
\(360\) 18.8360 + 2.28130i 0.992745 + 0.120235i
\(361\) −15.2452 −0.802381
\(362\) −8.58230 6.05117i −0.451076 0.318043i
\(363\) −15.4553 1.87326i −0.811191 0.0983207i
\(364\) 7.01590 + 19.6741i 0.367733 + 1.03120i
\(365\) 16.8503 21.9409i 0.881984 1.14844i
\(366\) 1.58020 0.510465i 0.0825984 0.0266824i
\(367\) 10.6850 + 18.5069i 0.557751 + 0.966053i 0.997684 + 0.0680225i \(0.0216690\pi\)
−0.439933 + 0.898031i \(0.644998\pi\)
\(368\) −7.90761 + 1.28827i −0.412213 + 0.0671556i
\(369\) −25.1371 + 7.29267i −1.30858 + 0.379641i
\(370\) 13.9193 4.33258i 0.723630 0.225240i
\(371\) −23.4674 + 13.5489i −1.21837 + 0.703423i
\(372\) 15.3683 3.46782i 0.796810 0.179798i
\(373\) −13.3601 + 23.1403i −0.691759 + 1.19816i 0.279503 + 0.960145i \(0.409830\pi\)
−0.971261 + 0.238016i \(0.923503\pi\)
\(374\) −1.00940 + 11.1199i −0.0521947 + 0.574997i
\(375\) 19.3641 0.175030i 0.999959 0.00903853i
\(376\) −29.7929 + 7.67157i −1.53645 + 0.395631i
\(377\) 18.2906 0.942015
\(378\) 22.6033 + 10.9850i 1.16259 + 0.565007i
\(379\) 1.88580 0.0968670 0.0484335 0.998826i \(-0.484577\pi\)
0.0484335 + 0.998826i \(0.484577\pi\)
\(380\) 2.66308 8.24642i 0.136613 0.423032i
\(381\) 2.91870 + 6.84638i 0.149529 + 0.350751i
\(382\) 13.0932 + 1.18852i 0.669905 + 0.0608098i
\(383\) −10.6344 6.13978i −0.543393 0.313728i 0.203060 0.979166i \(-0.434911\pi\)
−0.746453 + 0.665438i \(0.768245\pi\)
\(384\) −14.2806 13.4188i −0.728753 0.684776i
\(385\) 4.14646 + 10.0222i 0.211323 + 0.510778i
\(386\) −4.58544 + 2.12006i −0.233393 + 0.107908i
\(387\) −2.59932 + 10.5653i −0.132131 + 0.537063i
\(388\) −28.4778 24.2138i −1.44574 1.22927i
\(389\) 13.8417 + 23.9746i 0.701804 + 1.21556i 0.967833 + 0.251594i \(0.0809549\pi\)
−0.266029 + 0.963965i \(0.585712\pi\)
\(390\) −16.4527 + 3.01331i −0.833117 + 0.152585i
\(391\) −9.65612 5.57496i −0.488331 0.281938i
\(392\) −9.48325 + 9.29960i −0.478977 + 0.469701i
\(393\) −3.46791 + 28.6118i −0.174933 + 1.44328i
\(394\) 19.3251 + 13.6256i 0.973583 + 0.686450i
\(395\) −8.18917 1.08158i −0.412042 0.0544202i
\(396\) −8.46620 + 0.860687i −0.425443 + 0.0432512i
\(397\) 24.6606 1.23768 0.618840 0.785517i \(-0.287603\pi\)
0.618840 + 0.785517i \(0.287603\pi\)
\(398\) −3.52177 2.48312i −0.176531 0.124467i
\(399\) 6.89342 9.17755i 0.345103 0.459452i
\(400\) −16.2224 11.6976i −0.811120 0.584880i
\(401\) −10.7234 6.19117i −0.535502 0.309172i 0.207752 0.978182i \(-0.433385\pi\)
−0.743254 + 0.669009i \(0.766719\pi\)
\(402\) 26.8375 + 24.2475i 1.33853 + 1.20935i
\(403\) −12.0280 + 6.94436i −0.599156 + 0.345923i
\(404\) −3.12585 + 3.67631i −0.155517 + 0.182903i
\(405\) −11.5910 + 16.4514i −0.575963 + 0.817475i
\(406\) 12.1568 + 26.2937i 0.603331 + 1.30493i
\(407\) −5.66238 + 3.26918i −0.280674 + 0.162047i
\(408\) −3.57326 27.0361i −0.176903 1.33849i
\(409\) 15.7011 27.1951i 0.776368 1.34471i −0.157654 0.987494i \(-0.550393\pi\)
0.934022 0.357215i \(-0.116274\pi\)
\(410\) 26.9132 + 6.07034i 1.32915 + 0.299793i
\(411\) 11.6455 15.5042i 0.574429 0.764766i
\(412\) −29.2136 5.34772i −1.43925 0.263463i
\(413\) 6.76430i 0.332850i
\(414\) 2.76782 8.03448i 0.136031 0.394873i
\(415\) 1.93913 14.6821i 0.0951883 0.720717i
\(416\) 15.5354 + 7.55487i 0.761685 + 0.370408i
\(417\) −18.6954 2.26598i −0.915517 0.110966i
\(418\) −0.351363 + 3.87075i −0.0171857 + 0.189324i
\(419\) 21.4368 + 12.3766i 1.04726 + 0.604634i 0.921880 0.387475i \(-0.126653\pi\)
0.125377 + 0.992109i \(0.459986\pi\)
\(420\) −15.2670 21.6489i −0.744955 1.05636i
\(421\) 16.5860 9.57596i 0.808354 0.466704i −0.0380297 0.999277i \(-0.512108\pi\)
0.846384 + 0.532573i \(0.178775\pi\)
\(422\) −1.52577 3.30006i −0.0742732 0.160644i
\(423\) 7.79556 31.6861i 0.379033 1.54063i
\(424\) −6.01178 + 21.5896i −0.291958 + 1.04848i
\(425\) −7.18155 26.8911i −0.348356 1.30441i
\(426\) −32.6363 6.99517i −1.58123 0.338917i
\(427\) −2.00789 1.15925i −0.0971684 0.0561002i
\(428\) −11.0295 30.9291i −0.533130 1.49501i
\(429\) 6.90099 2.94198i 0.333183 0.142040i
\(430\) 7.77927 8.42721i 0.375150 0.406396i
\(431\) −0.581760 −0.0280224 −0.0140112 0.999902i \(-0.504460\pi\)
−0.0140112 + 0.999902i \(0.504460\pi\)
\(432\) 19.7082 6.60211i 0.948210 0.317644i
\(433\) 26.6827i 1.28229i −0.767421 0.641143i \(-0.778460\pi\)
0.767421 0.641143i \(-0.221540\pi\)
\(434\) −17.9772 12.6753i −0.862934 0.608434i
\(435\) −22.3462 + 6.22464i −1.07142 + 0.298449i
\(436\) 0.960731 0.342602i 0.0460107 0.0164077i
\(437\) −3.36121 1.94060i −0.160789 0.0928313i
\(438\) 6.35126 29.6321i 0.303475 1.41588i
\(439\) −6.94231 + 4.00814i −0.331338 + 0.191298i −0.656435 0.754382i \(-0.727936\pi\)
0.325097 + 0.945681i \(0.394603\pi\)
\(440\) 8.25193 + 3.51702i 0.393395 + 0.167667i
\(441\) −3.92525 13.5299i −0.186917 0.644282i
\(442\) 10.0892 + 21.8217i 0.479893 + 1.03795i
\(443\) −0.847068 1.46716i −0.0402454 0.0697071i 0.845201 0.534448i \(-0.179481\pi\)
−0.885446 + 0.464741i \(0.846147\pi\)
\(444\) 11.7332 10.8330i 0.556833 0.514112i
\(445\) 9.56175 12.4504i 0.453271 0.590207i
\(446\) 33.6961 + 3.05873i 1.59556 + 0.144835i
\(447\) −25.0390 3.03485i −1.18430 0.143544i
\(448\) −0.534992 + 27.3542i −0.0252760 + 1.29237i
\(449\) 9.07219i 0.428143i 0.976818 + 0.214071i \(0.0686726\pi\)
−0.976818 + 0.214071i \(0.931327\pi\)
\(450\) 19.0754 9.28063i 0.899222 0.437493i
\(451\) −12.3740 −0.582671
\(452\) 2.46443 + 0.451128i 0.115917 + 0.0212193i
\(453\) 2.33804 + 1.75614i 0.109851 + 0.0825107i
\(454\) −32.4041 2.94144i −1.52080 0.138049i
\(455\) 18.5214 + 14.2242i 0.868295 + 0.666838i
\(456\) −1.24382 9.41102i −0.0582472 0.440712i
\(457\) 19.0867 11.0197i 0.892836 0.515479i 0.0179669 0.999839i \(-0.494281\pi\)
0.874869 + 0.484360i \(0.160947\pi\)
\(458\) 27.3973 12.6670i 1.28019 0.591891i
\(459\) 27.0523 + 10.2398i 1.26269 + 0.477952i
\(460\) −6.64599 + 6.00569i −0.309871 + 0.280017i
\(461\) 4.18352 + 7.24606i 0.194846 + 0.337483i 0.946850 0.321676i \(-0.104246\pi\)
−0.752004 + 0.659158i \(0.770913\pi\)
\(462\) 8.81596 + 7.96516i 0.410156 + 0.370573i
\(463\) −13.0546 + 22.6112i −0.606698 + 1.05083i 0.385083 + 0.922882i \(0.374173\pi\)
−0.991781 + 0.127950i \(0.959160\pi\)
\(464\) 22.4042 + 8.48683i 1.04009 + 0.393991i
\(465\) 12.3317 12.5775i 0.571868 0.583267i
\(466\) 23.9642 33.9881i 1.11012 1.57447i
\(467\) −15.1252 −0.699910 −0.349955 0.936767i \(-0.613803\pi\)
−0.349955 + 0.936767i \(0.613803\pi\)
\(468\) −14.8601 + 10.7194i −0.686909 + 0.495502i
\(469\) 50.4983i 2.33180i
\(470\) −23.3306 + 25.2739i −1.07616 + 1.16580i
\(471\) −25.2817 3.06428i −1.16492 0.141195i
\(472\) 3.91694 + 3.99430i 0.180292 + 0.183853i
\(473\) −2.57194 + 4.45473i −0.118258 + 0.204829i
\(474\) −8.61057 + 2.78154i −0.395496 + 0.127760i
\(475\) −2.49984 9.36056i −0.114700 0.429492i
\(476\) −24.6641 + 29.0074i −1.13048 + 1.32955i
\(477\) −17.1503 16.4591i −0.785260 0.753608i
\(478\) −0.341001 0.737546i −0.0155970 0.0337345i
\(479\) −7.43918 12.8850i −0.339905 0.588733i 0.644510 0.764596i \(-0.277062\pi\)
−0.984415 + 0.175864i \(0.943728\pi\)
\(480\) −21.5512 3.94306i −0.983671 0.179975i
\(481\) −7.03899 + 12.1919i −0.320950 + 0.555902i
\(482\) 33.1494 + 3.00910i 1.50992 + 0.137061i
\(483\) −10.9142 + 4.65284i −0.496612 + 0.211712i
\(484\) 17.6830 + 3.23697i 0.803772 + 0.147135i
\(485\) −41.4327 5.47220i −1.88136 0.248480i
\(486\) −3.72995 + 21.7276i −0.169194 + 0.985583i
\(487\) 30.3341 1.37457 0.687284 0.726389i \(-0.258803\pi\)
0.687284 + 0.726389i \(0.258803\pi\)
\(488\) −1.85693 + 0.478153i −0.0840592 + 0.0216450i
\(489\) 18.3304 7.81450i 0.828931 0.353384i
\(490\) −3.26734 + 14.4859i −0.147603 + 0.654409i
\(491\) 5.96814 + 3.44571i 0.269338 + 0.155503i 0.628587 0.777739i \(-0.283634\pi\)
−0.359248 + 0.933242i \(0.616967\pi\)
\(492\) 29.4814 6.65239i 1.32912 0.299913i
\(493\) 16.6707 + 28.8745i 0.750812 + 1.30044i
\(494\) 3.51195 + 7.59594i 0.158010 + 0.341758i
\(495\) −7.42996 + 5.94285i −0.333952 + 0.267111i
\(496\) −17.9553 + 2.92518i −0.806215 + 0.131344i
\(497\) 23.3005 + 40.3577i 1.04517 + 1.81029i
\(498\) −4.98694 15.4376i −0.223470 0.691777i
\(499\) 5.17700 8.96683i 0.231754 0.401410i −0.726570 0.687092i \(-0.758887\pi\)
0.958324 + 0.285682i \(0.0922201\pi\)
\(500\) −22.3312 1.14874i −0.998680 0.0513732i
\(501\) −0.296496 + 2.44623i −0.0132465 + 0.109289i
\(502\) 4.22105 + 2.97616i 0.188395 + 0.132833i
\(503\) 14.2027i 0.633267i −0.948548 0.316634i \(-0.897447\pi\)
0.948548 0.316634i \(-0.102553\pi\)
\(504\) −25.2863 14.2376i −1.12634 0.634193i
\(505\) −0.706428 + 5.34871i −0.0314356 + 0.238014i
\(506\) 2.31507 3.28344i 0.102918 0.145967i
\(507\) −3.82202 + 5.08845i −0.169742 + 0.225986i
\(508\) −2.88660 8.09464i −0.128072 0.359142i
\(509\) −8.81692 + 15.2714i −0.390803 + 0.676891i −0.992556 0.121792i \(-0.961136\pi\)
0.601752 + 0.798683i \(0.294469\pi\)
\(510\) −19.7526 23.2267i −0.874660 1.02850i
\(511\) −36.6428 + 21.1557i −1.62098 + 0.935874i
\(512\) 15.5239 + 16.4624i 0.686064 + 0.727541i
\(513\) 9.41669 + 3.56438i 0.415757 + 0.157371i
\(514\) −11.7756 25.4693i −0.519401 1.12340i
\(515\) −30.6822 + 12.6941i −1.35202 + 0.559369i
\(516\) 3.73279 11.9962i 0.164327 0.528102i
\(517\) 7.71345 13.3601i 0.339237 0.587576i
\(518\) −22.2049 2.01562i −0.975627 0.0885614i
\(519\) 17.0080 + 12.7750i 0.746567 + 0.560759i
\(520\) 19.1735 2.32568i 0.840812 0.101988i
\(521\) 17.4429i 0.764187i 0.924124 + 0.382093i \(0.124797\pi\)
−0.924124 + 0.382093i \(0.875203\pi\)
\(522\) −19.1804 + 16.6683i −0.839504 + 0.729553i
\(523\) 11.8010i 0.516023i 0.966142 + 0.258012i \(0.0830673\pi\)
−0.966142 + 0.258012i \(0.916933\pi\)
\(524\) 5.99251 32.7359i 0.261784 1.43008i
\(525\) −27.4689 11.0749i −1.19884 0.483350i
\(526\) −2.73412 + 30.1202i −0.119213 + 1.31330i
\(527\) −21.9255 12.6587i −0.955088 0.551421i
\(528\) 9.81811 0.401578i 0.427278 0.0174764i
\(529\) −9.49406 16.4442i −0.412785 0.714965i
\(530\) 7.44672 + 23.9241i 0.323465 + 1.03920i
\(531\) −5.69874 + 1.65330i −0.247304 + 0.0717470i
\(532\) −8.58535 + 10.0972i −0.372222 + 0.437770i
\(533\) −23.0735 + 13.3215i −0.999425 + 0.577019i
\(534\) 3.60405 16.8148i 0.155962 0.727650i
\(535\) −29.1169 22.3614i −1.25883 0.966766i
\(536\) −29.2416 29.8191i −1.26305 1.28799i
\(537\) 11.0777 4.72255i 0.478036 0.203793i
\(538\) −2.76807 + 3.92592i −0.119340 + 0.169258i
\(539\) 6.66028i 0.286879i
\(540\) 14.5071 18.1534i 0.624286 0.781196i
\(541\) 22.5545i 0.969694i 0.874599 + 0.484847i \(0.161125\pi\)
−0.874599 + 0.484847i \(0.838875\pi\)
\(542\) −3.63531 2.56317i −0.156150 0.110097i
\(543\) −11.8309 + 5.04366i −0.507713 + 0.216444i
\(544\) 2.23298 + 31.4108i 0.0957383 + 1.34673i
\(545\) 0.694597 0.904440i 0.0297533 0.0387419i
\(546\) 25.0139 + 5.36142i 1.07050 + 0.229447i
\(547\) 30.7542 17.7559i 1.31495 0.759189i 0.332041 0.943265i \(-0.392263\pi\)
0.982912 + 0.184076i \(0.0589293\pi\)
\(548\) −14.5038 + 17.0579i −0.619570 + 0.728676i
\(549\) 0.485881 1.97493i 0.0207369 0.0842878i
\(550\) 9.88362 1.70111i 0.421439 0.0725356i
\(551\) 5.80294 + 10.0510i 0.247213 + 0.428186i
\(552\) −3.75050 + 9.06746i −0.159632 + 0.385937i
\(553\) 10.9410 + 6.31681i 0.465260 + 0.268618i
\(554\) −1.86019 0.168857i −0.0790321 0.00717404i
\(555\) 4.45064 17.2907i 0.188919 0.733951i
\(556\) 21.3901 + 3.91559i 0.907144 + 0.166058i
\(557\) 25.4514i 1.07841i 0.842174 + 0.539206i \(0.181275\pi\)
−0.842174 + 0.539206i \(0.818725\pi\)
\(558\) 6.28468 18.2433i 0.266052 0.772302i
\(559\) 11.0755i 0.468443i
\(560\) 16.0868 + 26.0171i 0.679793 + 1.09942i
\(561\) 10.9342 + 8.21285i 0.461641 + 0.346747i
\(562\) −1.14822 + 12.6493i −0.0484348 + 0.533577i
\(563\) −4.56276 + 7.90293i −0.192297 + 0.333069i −0.946011 0.324134i \(-0.894927\pi\)
0.753714 + 0.657203i \(0.228260\pi\)
\(564\) −11.1949 + 35.9775i −0.471392 + 1.51492i
\(565\) 2.58832 1.07086i 0.108891 0.0450514i
\(566\) 1.08910 0.503541i 0.0457783 0.0211654i
\(567\) 26.0004 16.4727i 1.09191 0.691790i
\(568\) 37.1285 + 10.3387i 1.55788 + 0.433801i
\(569\) 3.50968 2.02631i 0.147133 0.0849475i −0.424626 0.905369i \(-0.639594\pi\)
0.571759 + 0.820421i \(0.306261\pi\)
\(570\) −6.87571 8.08503i −0.287992 0.338645i
\(571\) 18.5259 32.0878i 0.775284 1.34283i −0.159350 0.987222i \(-0.550940\pi\)
0.934634 0.355610i \(-0.115727\pi\)
\(572\) −8.15921 + 2.90962i −0.341154 + 0.121657i
\(573\) 9.67023 12.8745i 0.403980 0.537839i
\(574\) −34.4861 24.3153i −1.43942 1.01490i
\(575\) −2.60005 + 9.67143i −0.108430 + 0.403327i
\(576\) −23.1759 + 6.23507i −0.965664 + 0.259795i
\(577\) 1.65668i 0.0689685i −0.999405 0.0344842i \(-0.989021\pi\)
0.999405 0.0344842i \(-0.0109789\pi\)
\(578\) −11.3994 + 16.1677i −0.474154 + 0.672487i
\(579\) −0.744473 + 6.14225i −0.0309392 + 0.255263i
\(580\) 26.1902 5.61602i 1.08749 0.233192i
\(581\) −11.3252 + 19.6159i −0.469849 + 0.813803i
\(582\) −43.5647 + 14.0730i −1.80582 + 0.583347i
\(583\) −5.61897 9.73234i −0.232714 0.403072i
\(584\) −9.38700 + 33.7108i −0.388437 + 1.39496i
\(585\) −7.45655 + 19.0803i −0.308290 + 0.788875i
\(586\) −12.9806 + 6.00150i −0.536222 + 0.247920i
\(587\) 4.45782 + 7.72117i 0.183994 + 0.318687i 0.943237 0.332120i \(-0.107764\pi\)
−0.759243 + 0.650807i \(0.774431\pi\)
\(588\) 3.58062 + 15.8682i 0.147662 + 0.654395i
\(589\) −7.63207 4.40638i −0.314474 0.181562i
\(590\) 6.10141 + 1.37619i 0.251191 + 0.0566567i
\(591\) 26.6401 11.3570i 1.09583 0.467164i
\(592\) −14.2791 + 11.6678i −0.586867 + 0.479543i
\(593\) 19.9947 0.821083 0.410542 0.911842i \(-0.365340\pi\)
0.410542 + 0.911842i \(0.365340\pi\)
\(594\) −4.55567 + 9.37400i −0.186921 + 0.384620i
\(595\) −5.57397 + 42.2032i −0.228510 + 1.73016i
\(596\) 28.6481 + 5.24420i 1.17347 + 0.214811i
\(597\) −4.85485 + 2.06968i −0.198696 + 0.0847065i
\(598\) 0.782005 8.61487i 0.0319785 0.352288i
\(599\) 9.97441 17.2762i 0.407543 0.705886i −0.587071 0.809536i \(-0.699719\pi\)
0.994614 + 0.103650i \(0.0330523\pi\)
\(600\) −22.6334 + 9.36645i −0.924004 + 0.382384i
\(601\) 10.5877 + 18.3385i 0.431882 + 0.748041i 0.997035 0.0769445i \(-0.0245164\pi\)
−0.565154 + 0.824986i \(0.691183\pi\)
\(602\) −15.9216 + 7.36127i −0.648915 + 0.300023i
\(603\) 42.5434 12.3426i 1.73250 0.502628i
\(604\) −2.57233 2.18717i −0.104667 0.0889948i
\(605\) 18.5720 7.68373i 0.755057 0.312388i
\(606\) 1.81675 + 5.62394i 0.0738003 + 0.228457i
\(607\) −12.0385 + 20.8514i −0.488629 + 0.846330i −0.999914 0.0130807i \(-0.995836\pi\)
0.511285 + 0.859411i \(0.329170\pi\)
\(608\) 0.777282 + 10.9338i 0.0315229 + 0.443425i
\(609\) 35.2207 + 4.26893i 1.42721 + 0.172986i
\(610\) −1.45415 + 1.57527i −0.0588768 + 0.0637807i
\(611\) 33.2162i 1.34379i
\(612\) −30.4662 13.6890i −1.23152 0.553343i
\(613\) −10.2614 −0.414456 −0.207228 0.978293i \(-0.566444\pi\)
−0.207228 + 0.978293i \(0.566444\pi\)
\(614\) 9.33018 + 6.57849i 0.376536 + 0.265486i
\(615\) 23.6561 24.1277i 0.953907 0.972922i
\(616\) −9.60571 9.79542i −0.387025 0.394669i
\(617\) 4.51730 7.82419i 0.181860 0.314990i −0.760654 0.649157i \(-0.775122\pi\)
0.942514 + 0.334167i \(0.108455\pi\)
\(618\) −24.3848 + 26.9895i −0.980900 + 1.08568i
\(619\) −13.4128 23.2316i −0.539106 0.933758i −0.998952 0.0457601i \(-0.985429\pi\)
0.459847 0.887998i \(-0.347904\pi\)
\(620\) −15.0906 + 13.6367i −0.606052 + 0.547663i
\(621\) −6.58748 8.05765i −0.264346 0.323342i
\(622\) −17.1389 37.0695i −0.687209 1.48635i
\(623\) −20.7931 + 12.0049i −0.833057 + 0.480966i
\(624\) 17.8752 11.3187i 0.715582 0.453110i
\(625\) −21.6713 + 12.4641i −0.866854 + 0.498563i
\(626\) 3.20115 35.2651i 0.127944 1.40948i
\(627\) 3.80609 + 2.85882i 0.152001 + 0.114170i
\(628\) 28.9258 + 5.29505i 1.15427 + 0.211295i
\(629\) −25.6624 −1.02323
\(630\) −32.3849 + 1.96249i −1.29025 + 0.0781873i
\(631\) 46.1198i 1.83600i −0.396581 0.918000i \(-0.629803\pi\)
0.396581 0.918000i \(-0.370197\pi\)
\(632\) 10.1185 2.60547i 0.402491 0.103640i
\(633\) −4.42046 0.535783i −0.175698 0.0212955i
\(634\) 2.59285 28.5638i 0.102975 1.13441i
\(635\) −7.62036 5.85233i −0.302405 0.232243i
\(636\) 18.6195 + 20.1667i 0.738310 + 0.799660i
\(637\) −7.17025 12.4192i −0.284096 0.492068i
\(638\) −10.9045 + 5.04163i −0.431712 + 0.199600i
\(639\) −28.3053 + 29.4941i −1.11974 + 1.16677i
\(640\) 24.5647 + 6.04774i 0.971005 + 0.239058i
\(641\) −6.03309 + 3.48321i −0.238293 + 0.137578i −0.614392 0.789001i \(-0.710599\pi\)
0.376099 + 0.926579i \(0.377265\pi\)
\(642\) −39.3236 8.42852i −1.55198 0.332647i
\(643\) 21.7228 + 12.5416i 0.856663 + 0.494594i 0.862893 0.505386i \(-0.168650\pi\)
−0.00623069 + 0.999981i \(0.501983\pi\)
\(644\) 12.9041 4.60167i 0.508492 0.181331i
\(645\) −3.76919 13.5313i −0.148412 0.532794i
\(646\) −8.79044 + 12.4674i −0.345855 + 0.490522i
\(647\) 22.7094i 0.892799i −0.894834 0.446400i \(-0.852706\pi\)
0.894834 0.446400i \(-0.147294\pi\)
\(648\) 5.81442 24.7829i 0.228412 0.973565i
\(649\) −2.80528 −0.110117
\(650\) 16.5983 13.8124i 0.651041 0.541767i
\(651\) −24.7820 + 10.5649i −0.971284 + 0.414070i
\(652\) −21.6725 + 7.72854i −0.848762 + 0.302673i
\(653\) −13.1701 7.60377i −0.515387 0.297559i 0.219659 0.975577i \(-0.429506\pi\)
−0.735045 + 0.678018i \(0.762839\pi\)
\(654\) 0.261810 1.22149i 0.0102376 0.0477639i
\(655\) −14.2247 34.3817i −0.555803 1.34340i
\(656\) −34.4440 + 5.61143i −1.34481 + 0.219090i
\(657\) −26.7791 25.6997i −1.04475 1.00264i
\(658\) 47.7500 22.0770i 1.86149 0.860652i
\(659\) 6.93109 4.00167i 0.269997 0.155883i −0.358889 0.933380i \(-0.616844\pi\)
0.628886 + 0.777497i \(0.283511\pi\)
\(660\) 8.97818 6.33151i 0.349475 0.246454i
\(661\) −12.6305 7.29221i −0.491269 0.283634i 0.233832 0.972277i \(-0.424873\pi\)
−0.725101 + 0.688643i \(0.758207\pi\)
\(662\) 2.23722 + 0.203081i 0.0869522 + 0.00789298i
\(663\) 29.2304 + 3.54288i 1.13521 + 0.137594i
\(664\) 4.67127 + 18.1411i 0.181280 + 0.704011i
\(665\) −1.94025 + 14.6906i −0.0752397 + 0.569676i
\(666\) −3.72911 19.1997i −0.144500 0.743972i
\(667\) 11.9966i 0.464512i
\(668\) 0.512342 2.79883i 0.0198231 0.108290i
\(669\) 24.8870 33.1333i 0.962187 1.28101i
\(670\) −45.5496 10.2738i −1.75973 0.396912i
\(671\) 0.480763 0.832706i 0.0185596 0.0321463i
\(672\) 28.1519 + 18.1736i 1.08598 + 0.701064i
\(673\) −5.20531 + 3.00529i −0.200650 + 0.115845i −0.596959 0.802272i \(-0.703624\pi\)
0.396309 + 0.918117i \(0.370291\pi\)
\(674\) −2.84773 + 1.31664i −0.109691 + 0.0507150i
\(675\) 2.61652 25.8487i 0.100710 0.994916i
\(676\) 4.76011 5.59836i 0.183081 0.215321i
\(677\) −2.86348 + 1.65323i −0.110053 + 0.0635389i −0.554016 0.832506i \(-0.686905\pi\)
0.443963 + 0.896045i \(0.353572\pi\)
\(678\) 2.05707 2.27680i 0.0790014 0.0874400i
\(679\) 55.3556 + 31.9596i 2.12435 + 1.22650i
\(680\) 21.1468 + 28.1485i 0.810944 + 1.07945i
\(681\) −23.9327 + 31.8628i −0.917104 + 1.22099i
\(682\) 5.25667 7.45547i 0.201288 0.285485i
\(683\) 0.637340 0.0243872 0.0121936 0.999926i \(-0.496119\pi\)
0.0121936 + 0.999926i \(0.496119\pi\)
\(684\) −10.6050 4.76501i −0.405493 0.182195i
\(685\) −3.27778 + 24.8177i −0.125238 + 0.948236i
\(686\) −6.42144 + 9.10745i −0.245172 + 0.347724i
\(687\) 4.44811 36.6990i 0.169706 1.40015i
\(688\) −5.13902 + 13.5664i −0.195923 + 0.517213i
\(689\) −20.9551 12.0984i −0.798324 0.460913i
\(690\) 1.97640 + 10.7912i 0.0752403 + 0.410814i
\(691\) 2.21419 + 3.83509i 0.0842317 + 0.145894i 0.905064 0.425276i \(-0.139823\pi\)
−0.820832 + 0.571170i \(0.806490\pi\)
\(692\) −18.7123 15.9105i −0.711335 0.604826i
\(693\) 13.9753 4.05446i 0.530877 0.154016i
\(694\) −4.71113 10.1896i −0.178832 0.386793i
\(695\) 22.4655 9.29459i 0.852164 0.352564i
\(696\) 23.2697 17.8741i 0.882034 0.677517i
\(697\) −42.0601 24.2834i −1.59314 0.919800i
\(698\) 2.37221 26.1332i 0.0897895 0.989157i
\(699\) −19.9742 46.8534i −0.755493 1.77216i
\(700\) 30.8881 + 14.6806i 1.16746 + 0.554875i
\(701\) 39.0099 1.47338 0.736691 0.676230i \(-0.236387\pi\)
0.736691 + 0.676230i \(0.236387\pi\)
\(702\) 1.59693 + 22.3839i 0.0602724 + 0.844827i
\(703\) −8.93285 −0.336909
\(704\) −11.3443 0.221871i −0.427554 0.00836207i
\(705\) 11.3041 + 40.5814i 0.425737 + 1.52838i
\(706\) 21.9661 + 1.99394i 0.826703 + 0.0750430i
\(707\) 4.12579 7.14607i 0.155166 0.268756i
\(708\) 6.68362 1.50814i 0.251186 0.0566794i
\(709\) −0.866919 + 0.500516i −0.0325578 + 0.0187973i −0.516191 0.856474i \(-0.672650\pi\)
0.483633 + 0.875271i \(0.339317\pi\)
\(710\) 41.1432 12.8064i 1.54408 0.480616i
\(711\) −2.64758 + 10.7614i −0.0992921 + 0.403585i
\(712\) −5.32669 + 19.1293i −0.199626 + 0.716901i
\(713\) 4.55474 + 7.88904i 0.170576 + 0.295447i
\(714\) 14.3348 + 44.3749i 0.536465 + 1.66069i
\(715\) −5.89901 + 7.68114i −0.220610 + 0.287258i
\(716\) −13.0974 + 4.67060i −0.489472 + 0.174549i
\(717\) −0.987949 0.119745i −0.0368956 0.00447195i
\(718\) −10.5107 + 14.9072i −0.392256 + 0.556331i
\(719\) 14.8920 0.555377 0.277688 0.960671i \(-0.410432\pi\)
0.277688 + 0.960671i \(0.410432\pi\)
\(720\) −17.9868 + 19.9117i −0.670328 + 0.742065i
\(721\) 50.7843 1.89131
\(722\) 12.4238 17.6205i 0.462366 0.655768i
\(723\) 24.4832 32.5957i 0.910540 1.21225i
\(724\) 13.9880 4.98819i 0.519859 0.185384i
\(725\) 21.1934 21.1583i 0.787104 0.785799i
\(726\) 14.7601 16.3367i 0.547799 0.606312i
\(727\) 12.5597 + 21.7540i 0.465812 + 0.806810i 0.999238 0.0390367i \(-0.0124289\pi\)
−0.533426 + 0.845847i \(0.679096\pi\)
\(728\) −28.4569 7.92403i −1.05468 0.293684i
\(729\) 20.2327 + 17.8784i 0.749360 + 0.662163i
\(730\) 11.6276 + 37.3559i 0.430356 + 1.38261i
\(731\) −17.4844 + 10.0946i −0.646682 + 0.373362i
\(732\) −0.697757 + 2.24240i −0.0257898 + 0.0828815i
\(733\) 15.2704 26.4492i 0.564026 0.976922i −0.433113 0.901339i \(-0.642585\pi\)
0.997140 0.0755826i \(-0.0240817\pi\)
\(734\) −30.0979 2.73210i −1.11093 0.100844i
\(735\) 12.9866 + 12.7328i 0.479019 + 0.469657i
\(736\) 4.95517 10.1895i 0.182650 0.375591i
\(737\) 20.9426 0.771429
\(738\) 12.0560 34.9966i 0.443789 1.28824i
\(739\) 10.1478 0.373292 0.186646 0.982427i \(-0.440238\pi\)
0.186646 + 0.982427i \(0.440238\pi\)
\(740\) −6.33565 + 19.6188i −0.232903 + 0.721201i
\(741\) 10.1748 + 1.23324i 0.373782 + 0.0453044i
\(742\) 3.46439 38.1651i 0.127182 1.40109i
\(743\) −11.6247 6.71153i −0.426469 0.246222i 0.271372 0.962475i \(-0.412523\pi\)
−0.697841 + 0.716252i \(0.745856\pi\)
\(744\) −8.51599 + 20.5888i −0.312211 + 0.754823i
\(745\) 30.0883 12.4484i 1.10235 0.456072i
\(746\) −15.8582 34.2994i −0.580610 1.25579i
\(747\) −19.2939 4.74677i −0.705926 0.173675i
\(748\) −12.0299 10.2286i −0.439856 0.373996i
\(749\) 28.0749 + 48.6272i 1.02584 + 1.77680i
\(750\) −15.5781 + 22.5238i −0.568833 + 0.822453i
\(751\) −16.6827 9.63177i −0.608761 0.351468i 0.163719 0.986507i \(-0.447651\pi\)
−0.772480 + 0.635039i \(0.780984\pi\)
\(752\) 15.4123 40.6866i 0.562029 1.48369i
\(753\) 5.81882 2.48063i 0.212050 0.0903994i
\(754\) −14.9056 + 21.1404i −0.542830 + 0.769888i
\(755\) −3.74252 0.494291i −0.136204 0.0179891i
\(756\) −31.1167 + 17.1731i −1.13170 + 0.624578i
\(757\) 23.7562 0.863433 0.431717 0.902009i \(-0.357908\pi\)
0.431717 + 0.902009i \(0.357908\pi\)
\(758\) −1.53680 + 2.17962i −0.0558189 + 0.0791673i
\(759\) −1.92962 4.52630i −0.0700407 0.164294i
\(760\) 7.36103 + 9.79827i 0.267013 + 0.355420i
\(761\) 11.7336 + 6.77437i 0.425341 + 0.245571i 0.697360 0.716721i \(-0.254358\pi\)
−0.272019 + 0.962292i \(0.587691\pi\)
\(762\) −10.2916 2.20588i −0.372826 0.0799106i
\(763\) −1.51048 + 0.872075i −0.0546830 + 0.0315712i
\(764\) −12.0437 + 14.1646i −0.435727 + 0.512457i
\(765\) −36.9174 + 5.61919i −1.33475 + 0.203162i
\(766\) 15.7627 7.28782i 0.569530 0.263320i
\(767\) −5.23092 + 3.02007i −0.188878 + 0.109049i
\(768\) 27.1472 5.57018i 0.979592 0.200996i
\(769\) 5.93118 10.2731i 0.213884 0.370458i −0.739043 0.673658i \(-0.764722\pi\)
0.952927 + 0.303201i \(0.0980553\pi\)
\(770\) −14.9628 3.37489i −0.539221 0.121623i
\(771\) −34.1164 4.13509i −1.22867 0.148922i
\(772\) 1.28644 7.02759i 0.0463000 0.252928i
\(773\) 18.9610i 0.681980i −0.940067 0.340990i \(-0.889238\pi\)
0.940067 0.340990i \(-0.110762\pi\)
\(774\) −10.0931 11.6143i −0.362790 0.417467i
\(775\) −5.90375 + 21.9602i −0.212069 + 0.788835i
\(776\) 51.1938 13.1822i 1.83775 0.473215i
\(777\) −16.3999 + 21.8340i −0.588343 + 0.783291i
\(778\) −38.9900 3.53927i −1.39786 0.126889i
\(779\) −14.6408 8.45285i −0.524560 0.302855i
\(780\) 9.92505 21.4718i 0.355374 0.768814i
\(781\) −16.7371 + 9.66315i −0.598899 + 0.345775i
\(782\) 14.3126 6.61739i 0.511819 0.236637i
\(783\) 5.01200 + 30.7158i 0.179114 + 1.09769i
\(784\) −3.02033 18.5393i −0.107869 0.662119i
\(785\) 30.3800 12.5691i 1.08431 0.448609i
\(786\) −30.2436 27.3249i −1.07875 0.974647i
\(787\) 33.6917 + 19.4519i 1.20098 + 0.693386i 0.960773 0.277336i \(-0.0894515\pi\)
0.240207 + 0.970722i \(0.422785\pi\)
\(788\) −31.4972 + 11.2321i −1.12204 + 0.400126i
\(789\) 29.6171 + 22.2459i 1.05440 + 0.791975i
\(790\) 7.92370 8.58368i 0.281913 0.305394i
\(791\) −4.28411 −0.152325
\(792\) 5.90458 10.4867i 0.209810 0.372628i
\(793\) 2.07030i 0.0735184i
\(794\) −20.0967 + 28.5029i −0.713205 + 1.01153i
\(795\) 29.7188 + 7.64963i 1.05402 + 0.271304i
\(796\) 5.74000 2.04692i 0.203449 0.0725511i
\(797\) −9.04532 5.22232i −0.320402 0.184984i 0.331170 0.943571i \(-0.392557\pi\)
−0.651572 + 0.758587i \(0.725890\pi\)
\(798\) 4.98981 + 15.4465i 0.176637 + 0.546801i
\(799\) 52.4369 30.2745i 1.85509 1.07103i
\(800\) 26.7403 9.21722i 0.945412 0.325878i
\(801\) −15.1959 14.5834i −0.536922 0.515280i
\(802\) 15.8946 7.34882i 0.561260 0.259496i
\(803\) −8.77365 15.1964i −0.309615 0.536270i
\(804\) −49.8960 + 11.2589i −1.75970 + 0.397071i
\(805\) 9.32949 12.1480i 0.328821 0.428161i
\(806\) 1.77564 19.5612i 0.0625443 0.689013i
\(807\) 2.30719 + 5.41197i 0.0812169 + 0.190510i
\(808\) −1.70175 6.60882i −0.0598673 0.232497i
\(809\) 19.8027i 0.696226i 0.937453 + 0.348113i \(0.113177\pi\)
−0.937453 + 0.348113i \(0.886823\pi\)
\(810\) −9.56870 26.8037i −0.336210 0.941787i
\(811\) 15.5879 0.547364 0.273682 0.961820i \(-0.411758\pi\)
0.273682 + 0.961820i \(0.411758\pi\)
\(812\) −40.2974 7.37667i −1.41416 0.258870i
\(813\) −5.01136 + 2.13640i −0.175756 + 0.0749270i
\(814\) 0.835915 9.20877i 0.0292988 0.322767i
\(815\) −15.6690 + 20.4027i −0.548860 + 0.714675i
\(816\) 34.1604 + 17.9025i 1.19585 + 0.626714i
\(817\) −6.08615 + 3.51384i −0.212928 + 0.122934i
\(818\) 18.6369 + 40.3095i 0.651625 + 1.40939i
\(819\) 21.6944 22.6056i 0.758065 0.789904i
\(820\) −28.9486 + 26.1596i −1.01093 + 0.913532i
\(821\) −20.0595 34.7441i −0.700082 1.21258i −0.968437 0.249258i \(-0.919813\pi\)
0.268355 0.963320i \(-0.413520\pi\)
\(822\) 8.42959 + 26.0948i 0.294016 + 0.910159i
\(823\) 7.61400 13.1878i 0.265407 0.459699i −0.702263 0.711918i \(-0.747827\pi\)
0.967670 + 0.252219i \(0.0811603\pi\)
\(824\) 29.9880 29.4072i 1.04468 1.02445i
\(825\) 4.59298 11.3918i 0.159907 0.396613i
\(826\) −7.81822 5.51244i −0.272031 0.191802i
\(827\) −38.9725 −1.35521 −0.677603 0.735428i \(-0.736981\pi\)
−0.677603 + 0.735428i \(0.736981\pi\)
\(828\) 7.03073 + 9.74661i 0.244335 + 0.338718i
\(829\) 55.7978i 1.93794i 0.247180 + 0.968969i \(0.420496\pi\)
−0.247180 + 0.968969i \(0.579504\pi\)
\(830\) 15.3894 + 14.2062i 0.534175 + 0.493104i
\(831\) −1.37389 + 1.82912i −0.0476596 + 0.0634516i
\(832\) −21.3922 + 11.7992i −0.741642 + 0.409063i
\(833\) 13.0705 22.6387i 0.452864 0.784384i
\(834\) 17.8545 19.7616i 0.618250 0.684289i
\(835\) −1.21617 2.93953i −0.0420872 0.101727i
\(836\) −4.18750 3.56050i −0.144828 0.123142i
\(837\) −14.9577 18.2959i −0.517014 0.632400i
\(838\) −31.7744 + 14.6908i −1.09763 + 0.507484i
\(839\) −11.2520 19.4891i −0.388464 0.672839i 0.603779 0.797151i \(-0.293661\pi\)
−0.992243 + 0.124313i \(0.960327\pi\)
\(840\) 37.4635 0.00338368i 1.29261 0.000116748i
\(841\) −3.43670 + 5.95253i −0.118507 + 0.205260i
\(842\) −2.44853 + 26.9740i −0.0843820 + 0.929585i
\(843\) 12.4380 + 9.34238i 0.428387 + 0.321769i
\(844\) 5.05762 + 0.925828i 0.174091 + 0.0318683i
\(845\) 1.07576 8.14512i 0.0370073 0.280201i
\(846\) 30.2701 + 34.8321i 1.04071 + 1.19755i
\(847\) −30.7397 −1.05623
\(848\) −20.0542 24.5425i −0.688665 0.842793i
\(849\) 0.176822 1.45886i 0.00606850 0.0500679i
\(850\) 36.9334 + 13.6139i 1.26680 + 0.466953i
\(851\) 7.99655 + 4.61681i 0.274118 + 0.158262i
\(852\) 34.6814 32.0206i 1.18816 1.09701i
\(853\) 7.72252 + 13.3758i 0.264414 + 0.457978i 0.967410 0.253215i \(-0.0814881\pi\)
−0.702996 + 0.711194i \(0.748155\pi\)
\(854\) 2.97616 1.37601i 0.101842 0.0470863i
\(855\) −12.8506 + 1.95599i −0.439482 + 0.0668935i
\(856\) 44.7363 + 12.4571i 1.52906 + 0.425776i
\(857\) 6.56783 + 11.3758i 0.224353 + 0.388591i 0.956125 0.292959i \(-0.0946398\pi\)
−0.731772 + 0.681549i \(0.761307\pi\)
\(858\) −2.22347 + 10.3737i −0.0759082 + 0.354153i
\(859\) −21.3607 + 36.9978i −0.728818 + 1.26235i 0.228565 + 0.973529i \(0.426597\pi\)
−0.957383 + 0.288821i \(0.906737\pi\)
\(860\) 3.40066 + 15.8589i 0.115961 + 0.540785i
\(861\) −47.5399 + 20.2668i −1.62015 + 0.690692i
\(862\) 0.474094 0.672402i 0.0161477 0.0229021i
\(863\) 20.6871i 0.704196i −0.935963 0.352098i \(-0.885468\pi\)
0.935963 0.352098i \(-0.114532\pi\)
\(864\) −8.43005 + 28.1591i −0.286796 + 0.957992i
\(865\) −27.2248 3.59570i −0.925670 0.122257i
\(866\) 30.8400 + 21.7445i 1.04798 + 0.738909i
\(867\) 9.50145 + 22.2875i 0.322686 + 0.756924i
\(868\) 29.3004 10.4487i 0.994519 0.354651i
\(869\) −2.61969 + 4.53744i −0.0888670 + 0.153922i
\(870\) 11.0162 30.9006i 0.373483 1.04763i
\(871\) 39.0510 22.5461i 1.32319 0.763946i
\(872\) −0.386948 + 1.38962i −0.0131037 + 0.0470583i
\(873\) −13.3953 + 54.4469i −0.453362 + 1.84275i
\(874\) 4.98211 2.30346i 0.168522 0.0779156i
\(875\) 37.9151 4.94363i 1.28176 0.167125i
\(876\) 29.0731 + 31.4889i 0.982290 + 1.06391i
\(877\) −11.2431 + 19.4737i −0.379653 + 0.657579i −0.991012 0.133775i \(-0.957290\pi\)
0.611359 + 0.791354i \(0.290623\pi\)
\(878\) 1.02487 11.2903i 0.0345875 0.381030i
\(879\) −2.10747 + 17.3876i −0.0710831 + 0.586469i
\(880\) −10.7897 + 6.67150i −0.363722 + 0.224896i
\(881\) 4.92044i 0.165774i −0.996559 0.0828870i \(-0.973586\pi\)
0.996559 0.0828870i \(-0.0264140\pi\)
\(882\) 18.8368 + 6.48912i 0.634267 + 0.218500i
\(883\) 12.2664i 0.412796i 0.978468 + 0.206398i \(0.0661742\pi\)
−0.978468 + 0.206398i \(0.933826\pi\)
\(884\) −33.4436 6.12205i −1.12483 0.205907i
\(885\) 5.36300 5.46990i 0.180275 0.183869i
\(886\) 2.38606 + 0.216592i 0.0801612 + 0.00727654i
\(887\) 25.0638 + 14.4706i 0.841560 + 0.485875i 0.857794 0.513994i \(-0.171834\pi\)
−0.0162345 + 0.999868i \(0.505168\pi\)
\(888\) 2.95913 + 22.3895i 0.0993020 + 0.751341i
\(889\) 7.34767 + 12.7265i 0.246433 + 0.426834i
\(890\) 6.59811 + 21.1978i 0.221169 + 0.710551i
\(891\) 6.83154 + 10.7828i 0.228865 + 0.361238i
\(892\) −30.9953 + 36.4536i −1.03780 + 1.22056i
\(893\) 18.2528 10.5383i 0.610808 0.352650i
\(894\) 23.9127 26.4670i 0.799761 0.885188i
\(895\) −9.46925 + 12.3300i −0.316522 + 0.412146i
\(896\) −31.1802 22.9102i −1.04166 0.765375i
\(897\) −8.47098 6.36270i −0.282838 0.212444i
\(898\) −10.4857 7.39321i −0.349912 0.246714i
\(899\) 27.2399i 0.908503i
\(900\) −4.81850 + 29.6105i −0.160617 + 0.987017i
\(901\) 44.1077i 1.46944i
\(902\) 10.0840 14.3020i 0.335760 0.476204i
\(903\) −2.58496 + 21.3271i −0.0860220 + 0.709722i
\(904\) −2.52975 + 2.48076i −0.0841384 + 0.0825089i
\(905\) 10.1131 13.1684i 0.336172 0.437732i
\(906\) −3.93510 + 1.27119i −0.130735 + 0.0422323i
\(907\) −20.5974 + 11.8919i −0.683927 + 0.394865i −0.801333 0.598219i \(-0.795875\pi\)
0.117406 + 0.993084i \(0.462542\pi\)
\(908\) 29.8068 35.0558i 0.989175 1.16337i
\(909\) 7.02877 + 1.72925i 0.233130 + 0.0573557i
\(910\) −31.5340 + 9.81541i −1.04534 + 0.325378i
\(911\) −11.6298 20.1434i −0.385313 0.667382i 0.606499 0.795084i \(-0.292573\pi\)
−0.991813 + 0.127702i \(0.959240\pi\)
\(912\) 11.8909 + 6.23172i 0.393749 + 0.206353i
\(913\) −8.13504 4.69677i −0.269231 0.155440i
\(914\) −2.81769 + 31.0407i −0.0932008 + 1.02674i
\(915\) 0.704561 + 2.52935i 0.0232921 + 0.0836178i
\(916\) −7.68629 + 41.9887i −0.253962 + 1.38735i
\(917\) 56.9075i 1.87925i
\(918\) −33.8810 + 22.9225i −1.11824 + 0.756557i
\(919\) 33.3802i 1.10111i 0.834798 + 0.550556i \(0.185584\pi\)
−0.834798 + 0.550556i \(0.814416\pi\)
\(920\) −1.52539 12.5757i −0.0502907 0.414608i
\(921\) 12.8619 5.48318i 0.423813 0.180677i
\(922\) −11.7843 1.06971i −0.388096 0.0352289i
\(923\) −20.8061 + 36.0372i −0.684841 + 1.18618i
\(924\) −16.3906 + 3.69849i −0.539210 + 0.121671i
\(925\) 5.94728 + 22.2694i 0.195545 + 0.732213i
\(926\) −15.4956 33.5151i −0.509216 1.10138i
\(927\) 12.4125 + 42.7844i 0.407679 + 1.40522i
\(928\) −28.0670 + 18.9787i −0.921345 + 0.623007i
\(929\) 24.5035 14.1471i 0.803934 0.464152i −0.0409108 0.999163i \(-0.513026\pi\)
0.844845 + 0.535011i \(0.179693\pi\)
\(930\) 4.48767 + 24.5028i 0.147157 + 0.803479i
\(931\) 4.54971 7.88033i 0.149111 0.258267i
\(932\) 19.7545 + 55.3959i 0.647080 + 1.81455i
\(933\) −49.6550 6.01845i −1.62563 0.197035i
\(934\) 12.3260 17.4818i 0.403318 0.572021i
\(935\) −17.5024 2.31162i −0.572391 0.0755982i
\(936\) −0.279532 25.9109i −0.00913677 0.846925i
\(937\) 52.5703i 1.71740i −0.512480 0.858699i \(-0.671273\pi\)
0.512480 0.858699i \(-0.328727\pi\)
\(938\) 58.3663 + 41.1527i 1.90573 + 1.34368i
\(939\) −34.6761 26.0458i −1.13161 0.849972i
\(940\) −10.1988 47.5621i −0.332649 1.55131i
\(941\) 18.9477 32.8183i 0.617676 1.06985i −0.372232 0.928140i \(-0.621408\pi\)
0.989909 0.141707i \(-0.0452591\pi\)
\(942\) 24.1446 26.7236i 0.786673 0.870702i
\(943\) 8.73746 + 15.1337i 0.284531 + 0.492822i
\(944\) −7.80867 + 1.27215i −0.254151 + 0.0414049i
\(945\) −18.8117 + 35.0010i −0.611944 + 1.13858i
\(946\) −3.05285 6.60296i −0.0992567 0.214681i
\(947\) −29.3171 50.7788i −0.952679 1.65009i −0.739593 0.673054i \(-0.764982\pi\)
−0.213085 0.977034i \(-0.568351\pi\)
\(948\) 3.80210 12.2189i 0.123486 0.396852i
\(949\) −32.7200 18.8909i −1.06214 0.613224i
\(950\) 12.8562 + 4.73888i 0.417110 + 0.153750i
\(951\) −28.0867 21.0964i −0.910774 0.684098i
\(952\) −13.4274 52.1459i −0.435184 1.69006i
\(953\) 47.0453 1.52395 0.761973 0.647609i \(-0.224231\pi\)
0.761973 + 0.647609i \(0.224231\pi\)
\(954\) 32.9998 6.40948i 1.06841 0.207515i
\(955\) −2.72182 + 20.6083i −0.0880762 + 0.666868i
\(956\) 1.13035 + 0.206918i 0.0365582 + 0.00669219i
\(957\) −1.77040 + 14.6066i −0.0572290 + 0.472165i
\(958\) 20.9550 + 1.90217i 0.677026 + 0.0614562i
\(959\) 19.1434 33.1574i 0.618173 1.07071i
\(960\) 22.1201 21.6956i 0.713924 0.700224i
\(961\) −5.15788 8.93370i −0.166383 0.288184i
\(962\) −8.35517 18.0713i −0.269381 0.582641i
\(963\) −34.1051 + 35.5376i −1.09902 + 1.14518i
\(964\) −30.4924 + 35.8621i −0.982095 + 1.15504i
\(965\) −3.05368 7.38088i −0.0983013 0.237599i
\(966\) 3.51650 16.4064i 0.113142 0.527867i
\(967\) 17.7621 30.7649i 0.571191 0.989331i −0.425254 0.905074i \(-0.639815\pi\)
0.996444 0.0842568i \(-0.0268516\pi\)
\(968\) −18.1517 + 17.8002i −0.583418 + 0.572120i
\(969\) 7.32685 + 17.1866i 0.235372 + 0.552112i
\(970\) 40.0896 43.4287i 1.28720 1.39441i
\(971\) 25.3826i 0.814566i −0.913302 0.407283i \(-0.866476\pi\)
0.913302 0.407283i \(-0.133524\pi\)
\(972\) −22.0732 22.0176i −0.707999 0.706214i
\(973\) −37.1842 −1.19207
\(974\) −24.7202 + 35.0603i −0.792086 + 1.12340i
\(975\) −3.69971 26.1867i −0.118486 0.838646i
\(976\) 0.960617 2.53591i 0.0307486 0.0811725i
\(977\) 4.17627 7.23351i 0.133611 0.231421i −0.791455 0.611227i \(-0.790676\pi\)
0.925066 + 0.379807i \(0.124009\pi\)
\(978\) −5.90600 + 27.5547i −0.188853 + 0.881103i
\(979\) −4.97864 8.62326i −0.159118 0.275601i
\(980\) −14.0803 15.5815i −0.449778 0.497731i
\(981\) −1.10388 1.05939i −0.0352442 0.0338236i
\(982\) −8.84619 + 4.09000i −0.282293 + 0.130517i
\(983\) 19.8624 11.4676i 0.633514 0.365759i −0.148598 0.988898i \(-0.547476\pi\)
0.782112 + 0.623138i \(0.214143\pi\)
\(984\) −16.3364 + 39.4960i −0.520786 + 1.25909i
\(985\) −22.7721 + 29.6517i −0.725579 + 0.944781i
\(986\) −46.9589 4.26264i −1.49548 0.135750i
\(987\) 7.75249 63.9616i 0.246765 2.03592i
\(988\) −11.6414 2.13103i −0.370363 0.0677972i
\(989\) 7.26431 0.230992
\(990\) −0.813878 13.4306i −0.0258667 0.426853i
\(991\) 25.1720i 0.799616i 0.916599 + 0.399808i \(0.130923\pi\)
−0.916599 + 0.399808i \(0.869077\pi\)
\(992\) 11.2514 23.1366i 0.357231 0.734588i
\(993\) 1.65235 2.19986i 0.0524357 0.0698103i
\(994\) −65.6340 5.95785i −2.08179 0.188972i
\(995\) 4.14995 5.40368i 0.131562 0.171308i
\(996\) 21.9069 + 6.81667i 0.694147 + 0.215994i
\(997\) −11.1711 19.3489i −0.353792 0.612785i 0.633119 0.774055i \(-0.281775\pi\)
−0.986910 + 0.161269i \(0.948441\pi\)
\(998\) 6.14502 + 13.2910i 0.194517 + 0.420718i
\(999\) −22.4029 8.47990i −0.708797 0.268292i
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.bd.b.59.19 yes 128
5.4 even 2 inner 360.2.bd.b.59.46 yes 128
8.3 odd 2 inner 360.2.bd.b.59.63 yes 128
9.2 odd 6 inner 360.2.bd.b.299.2 yes 128
40.19 odd 2 inner 360.2.bd.b.59.2 128
45.29 odd 6 inner 360.2.bd.b.299.63 yes 128
72.11 even 6 inner 360.2.bd.b.299.46 yes 128
360.299 even 6 inner 360.2.bd.b.299.19 yes 128
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bd.b.59.2 128 40.19 odd 2 inner
360.2.bd.b.59.19 yes 128 1.1 even 1 trivial
360.2.bd.b.59.46 yes 128 5.4 even 2 inner
360.2.bd.b.59.63 yes 128 8.3 odd 2 inner
360.2.bd.b.299.2 yes 128 9.2 odd 6 inner
360.2.bd.b.299.19 yes 128 360.299 even 6 inner
360.2.bd.b.299.46 yes 128 72.11 even 6 inner
360.2.bd.b.299.63 yes 128 45.29 odd 6 inner