Properties

Label 504.2.cs.a.85.6
Level $504$
Weight $2$
Character 504.85
Analytic conductor $4.024$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(85,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.85");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.cs (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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 85.6
Character \(\chi\) \(=\) 504.85
Dual form 504.2.cs.a.421.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25626 + 0.649466i) q^{2} +(1.65525 - 0.510053i) q^{3} +(1.15639 - 1.63180i) q^{4} +(1.14688 + 0.662153i) q^{5} +(-1.74816 + 1.71579i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.392930 + 2.80100i) q^{8} +(2.47969 - 1.68853i) q^{9} +O(q^{10})\) \(q+(-1.25626 + 0.649466i) q^{2} +(1.65525 - 0.510053i) q^{3} +(1.15639 - 1.63180i) q^{4} +(1.14688 + 0.662153i) q^{5} +(-1.74816 + 1.71579i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.392930 + 2.80100i) q^{8} +(2.47969 - 1.68853i) q^{9} +(-1.87083 - 0.0869767i) q^{10} +(-2.57369 + 1.48592i) q^{11} +(1.08181 - 3.29085i) q^{12} +(5.35416 + 3.09123i) q^{13} +(-1.19058 - 0.763222i) q^{14} +(2.23611 + 0.511056i) q^{15} +(-1.32553 - 3.77399i) q^{16} -1.83600 q^{17} +(-2.01850 + 3.73171i) q^{18} +4.71301i q^{19} +(2.40674 - 1.10578i) q^{20} +(1.26934 + 1.17846i) q^{21} +(2.26818 - 3.53823i) q^{22} +(-0.697483 + 1.20808i) q^{23} +(0.778263 + 4.83677i) q^{24} +(-1.62311 - 2.81130i) q^{25} +(-8.73388 - 0.406046i) q^{26} +(3.24326 - 4.05971i) q^{27} +(1.99137 + 0.185563i) q^{28} +(1.51998 - 0.877559i) q^{29} +(-3.14105 + 0.810256i) q^{30} +(4.84568 - 8.39296i) q^{31} +(4.11629 + 3.88023i) q^{32} +(-3.50220 + 3.77229i) q^{33} +(2.30649 - 1.19242i) q^{34} +1.32431i q^{35} +(0.112148 - 5.99895i) q^{36} -6.72177i q^{37} +(-3.06094 - 5.92078i) q^{38} +(10.4392 + 2.38584i) q^{39} +(-2.30534 + 2.95224i) q^{40} +(0.988376 - 1.71192i) q^{41} +(-2.36000 - 0.656060i) q^{42} +(-5.25491 + 3.03392i) q^{43} +(-0.551463 + 5.91805i) q^{44} +(3.96198 - 0.294610i) q^{45} +(0.0916174 - 1.97065i) q^{46} +(5.91564 + 10.2462i) q^{47} +(-4.11902 - 5.57079i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(3.86489 + 2.47758i) q^{50} +(-3.03903 + 0.936457i) q^{51} +(11.2358 - 5.16226i) q^{52} -1.53947i q^{53} +(-1.43775 + 7.20645i) q^{54} -3.93563 q^{55} +(-2.62220 + 1.06021i) q^{56} +(2.40389 + 7.80121i) q^{57} +(-1.33954 + 2.08962i) q^{58} +(-5.83614 - 3.36950i) q^{59} +(3.41975 - 3.05790i) q^{60} +(-3.12079 + 1.80179i) q^{61} +(-0.636501 + 13.6909i) q^{62} +(2.70215 + 1.30321i) q^{63} +(-7.69121 - 2.20119i) q^{64} +(4.09373 + 7.09055i) q^{65} +(1.94971 - 7.01354i) q^{66} +(-0.676090 - 0.390341i) q^{67} +(-2.12313 + 2.99598i) q^{68} +(-0.538324 + 2.35542i) q^{69} +(-0.860092 - 1.66368i) q^{70} -3.54831 q^{71} +(3.75523 + 7.60909i) q^{72} +12.3283 q^{73} +(4.36556 + 8.44430i) q^{74} +(-4.12056 - 3.82553i) q^{75} +(7.69069 + 5.45007i) q^{76} +(-2.57369 - 1.48592i) q^{77} +(-14.6638 + 3.78264i) q^{78} +(-1.15576 - 2.00184i) q^{79} +(0.978727 - 5.20603i) q^{80} +(3.29774 - 8.37406i) q^{81} +(-0.129827 + 2.79253i) q^{82} +(-8.80441 + 5.08323i) q^{83} +(3.39086 - 0.708554i) q^{84} +(-2.10568 - 1.21571i) q^{85} +(4.63111 - 7.22428i) q^{86} +(2.06834 - 2.22785i) q^{87} +(-3.15079 - 7.79278i) q^{88} -8.90082 q^{89} +(-4.78595 + 2.94328i) q^{90} +6.18246i q^{91} +(1.16478 + 2.53516i) q^{92} +(3.73994 - 16.3640i) q^{93} +(-14.0861 - 9.02989i) q^{94} +(-3.12074 + 5.40528i) q^{95} +(8.79260 + 4.32321i) q^{96} +(-0.132938 - 0.230255i) q^{97} +(0.0656772 - 1.41269i) q^{98} +(-3.87294 + 8.03038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25626 + 0.649466i −0.888311 + 0.459242i
\(3\) 1.65525 0.510053i 0.955658 0.294479i
\(4\) 1.15639 1.63180i 0.578194 0.815899i
\(5\) 1.14688 + 0.662153i 0.512902 + 0.296124i 0.734026 0.679122i \(-0.237639\pi\)
−0.221124 + 0.975246i \(0.570973\pi\)
\(6\) −1.74816 + 1.71579i −0.713685 + 0.700467i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) −0.392930 + 2.80100i −0.138922 + 0.990303i
\(9\) 2.47969 1.68853i 0.826564 0.562843i
\(10\) −1.87083 0.0869767i −0.591609 0.0275044i
\(11\) −2.57369 + 1.48592i −0.775997 + 0.448022i −0.835010 0.550235i \(-0.814538\pi\)
0.0590126 + 0.998257i \(0.481205\pi\)
\(12\) 1.08181 3.29085i 0.312290 0.949987i
\(13\) 5.35416 + 3.09123i 1.48498 + 0.857352i 0.999854 0.0170931i \(-0.00544117\pi\)
0.485124 + 0.874445i \(0.338775\pi\)
\(14\) −1.19058 0.763222i −0.318197 0.203980i
\(15\) 2.23611 + 0.511056i 0.577361 + 0.131954i
\(16\) −1.32553 3.77399i −0.331383 0.943496i
\(17\) −1.83600 −0.445295 −0.222647 0.974899i \(-0.571470\pi\)
−0.222647 + 0.974899i \(0.571470\pi\)
\(18\) −2.01850 + 3.73171i −0.475765 + 0.879572i
\(19\) 4.71301i 1.08124i 0.841267 + 0.540620i \(0.181810\pi\)
−0.841267 + 0.540620i \(0.818190\pi\)
\(20\) 2.40674 1.10578i 0.538164 0.247259i
\(21\) 1.26934 + 1.17846i 0.276993 + 0.257161i
\(22\) 2.26818 3.53823i 0.483577 0.754354i
\(23\) −0.697483 + 1.20808i −0.145435 + 0.251901i −0.929535 0.368733i \(-0.879792\pi\)
0.784100 + 0.620635i \(0.213125\pi\)
\(24\) 0.778263 + 4.83677i 0.158862 + 0.987301i
\(25\) −1.62311 2.81130i −0.324621 0.562260i
\(26\) −8.73388 0.406046i −1.71285 0.0796322i
\(27\) 3.24326 4.05971i 0.624167 0.781291i
\(28\) 1.99137 + 0.185563i 0.376334 + 0.0350680i
\(29\) 1.51998 0.877559i 0.282252 0.162959i −0.352190 0.935928i \(-0.614563\pi\)
0.634443 + 0.772970i \(0.281230\pi\)
\(30\) −3.14105 + 0.810256i −0.573475 + 0.147932i
\(31\) 4.84568 8.39296i 0.870310 1.50742i 0.00863308 0.999963i \(-0.497252\pi\)
0.861677 0.507458i \(-0.169415\pi\)
\(32\) 4.11629 + 3.88023i 0.727664 + 0.685934i
\(33\) −3.50220 + 3.77229i −0.609655 + 0.656671i
\(34\) 2.30649 1.19242i 0.395561 0.204498i
\(35\) 1.32431i 0.223849i
\(36\) 0.112148 5.99895i 0.0186913 0.999825i
\(37\) 6.72177i 1.10505i −0.833496 0.552526i \(-0.813664\pi\)
0.833496 0.552526i \(-0.186336\pi\)
\(38\) −3.06094 5.92078i −0.496550 0.960477i
\(39\) 10.4392 + 2.38584i 1.67160 + 0.382040i
\(40\) −2.30534 + 2.95224i −0.364506 + 0.466790i
\(41\) 0.988376 1.71192i 0.154358 0.267357i −0.778467 0.627686i \(-0.784002\pi\)
0.932825 + 0.360329i \(0.117336\pi\)
\(42\) −2.36000 0.656060i −0.364155 0.101232i
\(43\) −5.25491 + 3.03392i −0.801366 + 0.462669i −0.843948 0.536424i \(-0.819775\pi\)
0.0425828 + 0.999093i \(0.486441\pi\)
\(44\) −0.551463 + 5.91805i −0.0831362 + 0.892179i
\(45\) 3.96198 0.294610i 0.590617 0.0439178i
\(46\) 0.0916174 1.97065i 0.0135083 0.290557i
\(47\) 5.91564 + 10.2462i 0.862885 + 1.49456i 0.869132 + 0.494580i \(0.164678\pi\)
−0.00624764 + 0.999980i \(0.501989\pi\)
\(48\) −4.11902 5.57079i −0.594529 0.804074i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 3.86489 + 2.47758i 0.546578 + 0.350383i
\(51\) −3.03903 + 0.936457i −0.425550 + 0.131130i
\(52\) 11.2358 5.16226i 1.55812 0.715876i
\(53\) 1.53947i 0.211463i −0.994395 0.105731i \(-0.966282\pi\)
0.994395 0.105731i \(-0.0337184\pi\)
\(54\) −1.43775 + 7.20645i −0.195653 + 0.980673i
\(55\) −3.93563 −0.530681
\(56\) −2.62220 + 1.06021i −0.350407 + 0.141677i
\(57\) 2.40389 + 7.80121i 0.318403 + 1.03330i
\(58\) −1.33954 + 2.08962i −0.175891 + 0.274380i
\(59\) −5.83614 3.36950i −0.759801 0.438672i 0.0694231 0.997587i \(-0.477884\pi\)
−0.829224 + 0.558916i \(0.811217\pi\)
\(60\) 3.41975 3.05790i 0.441488 0.394773i
\(61\) −3.12079 + 1.80179i −0.399577 + 0.230696i −0.686301 0.727317i \(-0.740767\pi\)
0.286725 + 0.958013i \(0.407434\pi\)
\(62\) −0.636501 + 13.6909i −0.0808357 + 1.73874i
\(63\) 2.70215 + 1.30321i 0.340440 + 0.164189i
\(64\) −7.69121 2.20119i −0.961402 0.275149i
\(65\) 4.09373 + 7.09055i 0.507765 + 0.879475i
\(66\) 1.94971 7.01354i 0.239992 0.863307i
\(67\) −0.676090 0.390341i −0.0825975 0.0476877i 0.458132 0.888884i \(-0.348519\pi\)
−0.540730 + 0.841196i \(0.681852\pi\)
\(68\) −2.12313 + 2.99598i −0.257467 + 0.363316i
\(69\) −0.538324 + 2.35542i −0.0648067 + 0.283559i
\(70\) −0.860092 1.66368i −0.102801 0.198847i
\(71\) −3.54831 −0.421107 −0.210553 0.977582i \(-0.567527\pi\)
−0.210553 + 0.977582i \(0.567527\pi\)
\(72\) 3.75523 + 7.60909i 0.442558 + 0.896740i
\(73\) 12.3283 1.44292 0.721459 0.692457i \(-0.243472\pi\)
0.721459 + 0.692457i \(0.243472\pi\)
\(74\) 4.36556 + 8.44430i 0.507486 + 0.981630i
\(75\) −4.12056 3.82553i −0.475801 0.441734i
\(76\) 7.69069 + 5.45007i 0.882182 + 0.625166i
\(77\) −2.57369 1.48592i −0.293299 0.169336i
\(78\) −14.6638 + 3.78264i −1.66035 + 0.428299i
\(79\) −1.15576 2.00184i −0.130033 0.225224i 0.793656 0.608367i \(-0.208175\pi\)
−0.923689 + 0.383143i \(0.874842\pi\)
\(80\) 0.978727 5.20603i 0.109425 0.582051i
\(81\) 3.29774 8.37406i 0.366415 0.930451i
\(82\) −0.129827 + 2.79253i −0.0143370 + 0.308384i
\(83\) −8.80441 + 5.08323i −0.966409 + 0.557957i −0.898140 0.439710i \(-0.855081\pi\)
−0.0682695 + 0.997667i \(0.521748\pi\)
\(84\) 3.39086 0.708554i 0.369973 0.0773096i
\(85\) −2.10568 1.21571i −0.228393 0.131863i
\(86\) 4.63111 7.22428i 0.499386 0.779014i
\(87\) 2.06834 2.22785i 0.221749 0.238850i
\(88\) −3.15079 7.79278i −0.335875 0.830713i
\(89\) −8.90082 −0.943485 −0.471743 0.881736i \(-0.656375\pi\)
−0.471743 + 0.881736i \(0.656375\pi\)
\(90\) −4.78595 + 2.94328i −0.504483 + 0.310249i
\(91\) 6.18246i 0.648097i
\(92\) 1.16478 + 2.53516i 0.121436 + 0.264308i
\(93\) 3.73994 16.3640i 0.387814 1.69687i
\(94\) −14.0861 9.02989i −1.45287 0.931362i
\(95\) −3.12074 + 5.40528i −0.320181 + 0.554570i
\(96\) 8.79260 + 4.32321i 0.897391 + 0.441236i
\(97\) −0.132938 0.230255i −0.0134978 0.0233788i 0.859198 0.511644i \(-0.170963\pi\)
−0.872695 + 0.488265i \(0.837630\pi\)
\(98\) 0.0656772 1.41269i 0.00663439 0.142703i
\(99\) −3.87294 + 8.03038i −0.389245 + 0.807084i
\(100\) −6.46442 0.602376i −0.646442 0.0602376i
\(101\) 9.68229 5.59007i 0.963424 0.556233i 0.0661989 0.997806i \(-0.478913\pi\)
0.897225 + 0.441573i \(0.145579\pi\)
\(102\) 3.20962 3.15018i 0.317800 0.311915i
\(103\) −3.56706 + 6.17833i −0.351473 + 0.608769i −0.986508 0.163714i \(-0.947652\pi\)
0.635035 + 0.772484i \(0.280986\pi\)
\(104\) −10.7623 + 13.7824i −1.05533 + 1.35147i
\(105\) 0.675467 + 2.19206i 0.0659188 + 0.213923i
\(106\) 0.999835 + 1.93398i 0.0971126 + 0.187845i
\(107\) 18.8819i 1.82538i −0.408652 0.912690i \(-0.634001\pi\)
0.408652 0.912690i \(-0.365999\pi\)
\(108\) −2.87415 9.98695i −0.276565 0.960995i
\(109\) 9.50170i 0.910098i 0.890466 + 0.455049i \(0.150378\pi\)
−0.890466 + 0.455049i \(0.849622\pi\)
\(110\) 4.94418 2.55606i 0.471410 0.243711i
\(111\) −3.42846 11.1262i −0.325415 1.05605i
\(112\) 2.60560 3.03494i 0.246206 0.286775i
\(113\) 5.84059 10.1162i 0.549437 0.951652i −0.448876 0.893594i \(-0.648176\pi\)
0.998313 0.0580586i \(-0.0184910\pi\)
\(114\) −8.08653 8.23912i −0.757373 0.771664i
\(115\) −1.59986 + 0.923682i −0.149188 + 0.0861338i
\(116\) 0.325684 3.49509i 0.0302390 0.324511i
\(117\) 18.4963 1.37537i 1.70998 0.127153i
\(118\) 9.52010 + 0.442598i 0.876396 + 0.0407445i
\(119\) −0.917999 1.59002i −0.0841528 0.145757i
\(120\) −2.31010 + 6.06254i −0.210883 + 0.553431i
\(121\) −1.08407 + 1.87767i −0.0985522 + 0.170697i
\(122\) 2.75033 4.29037i 0.249003 0.388432i
\(123\) 0.762838 3.33777i 0.0687828 0.300957i
\(124\) −8.09213 17.6127i −0.726695 1.58167i
\(125\) 10.9205i 0.976760i
\(126\) −4.24101 + 0.117782i −0.377819 + 0.0104929i
\(127\) −7.53198 −0.668355 −0.334178 0.942510i \(-0.608459\pi\)
−0.334178 + 0.942510i \(0.608459\pi\)
\(128\) 11.0918 2.22990i 0.980384 0.197098i
\(129\) −7.15071 + 7.70217i −0.629585 + 0.678139i
\(130\) −9.74787 6.24885i −0.854945 0.548061i
\(131\) −14.6741 8.47208i −1.28208 0.740209i −0.304851 0.952400i \(-0.598607\pi\)
−0.977228 + 0.212191i \(0.931940\pi\)
\(132\) 2.10571 + 10.0771i 0.183279 + 0.877100i
\(133\) −4.08159 + 2.35651i −0.353919 + 0.204335i
\(134\) 1.10286 + 0.0512729i 0.0952725 + 0.00442931i
\(135\) 6.40780 2.50847i 0.551495 0.215895i
\(136\) 0.721418 5.14263i 0.0618611 0.440977i
\(137\) −7.78721 13.4878i −0.665306 1.15234i −0.979202 0.202887i \(-0.934968\pi\)
0.313896 0.949457i \(-0.398366\pi\)
\(138\) −0.853488 3.30865i −0.0726537 0.281651i
\(139\) −16.7304 9.65929i −1.41905 0.819290i −0.422837 0.906206i \(-0.638966\pi\)
−0.996216 + 0.0869157i \(0.972299\pi\)
\(140\) 2.16100 + 1.53141i 0.182638 + 0.129428i
\(141\) 15.0180 + 13.9427i 1.26474 + 1.17419i
\(142\) 4.45760 2.30450i 0.374074 0.193390i
\(143\) −18.3733 −1.53645
\(144\) −9.65939 7.12012i −0.804949 0.593343i
\(145\) 2.32431 0.193024
\(146\) −15.4876 + 8.00681i −1.28176 + 0.662648i
\(147\) −0.385905 + 1.68851i −0.0318289 + 0.139266i
\(148\) −10.9686 7.77298i −0.901611 0.638935i
\(149\) −3.88437 2.24264i −0.318220 0.183724i 0.332379 0.943146i \(-0.392149\pi\)
−0.650599 + 0.759422i \(0.725482\pi\)
\(150\) 7.66105 + 2.12971i 0.625522 + 0.173890i
\(151\) −6.95965 12.0545i −0.566368 0.980978i −0.996921 0.0784131i \(-0.975015\pi\)
0.430553 0.902565i \(-0.358319\pi\)
\(152\) −13.2012 1.85188i −1.07076 0.150208i
\(153\) −4.55271 + 3.10014i −0.368065 + 0.250631i
\(154\) 4.19829 + 0.195182i 0.338308 + 0.0157282i
\(155\) 11.1149 6.41717i 0.892767 0.515439i
\(156\) 15.9649 14.2756i 1.27822 1.14297i
\(157\) −12.2973 7.09986i −0.981432 0.566630i −0.0787300 0.996896i \(-0.525086\pi\)
−0.902702 + 0.430266i \(0.858420\pi\)
\(158\) 2.75206 + 1.76420i 0.218942 + 0.140352i
\(159\) −0.785213 2.54821i −0.0622715 0.202086i
\(160\) 2.15160 + 7.17578i 0.170099 + 0.567295i
\(161\) −1.39497 −0.109939
\(162\) 1.29584 + 12.6618i 0.101811 + 0.994804i
\(163\) 15.8477i 1.24129i 0.784092 + 0.620645i \(0.213129\pi\)
−0.784092 + 0.620645i \(0.786871\pi\)
\(164\) −1.65056 3.59247i −0.128887 0.280525i
\(165\) −6.51445 + 2.00738i −0.507149 + 0.156274i
\(166\) 7.75926 12.1040i 0.602235 0.939454i
\(167\) 5.67624 9.83153i 0.439241 0.760787i −0.558391 0.829578i \(-0.688581\pi\)
0.997631 + 0.0687913i \(0.0219143\pi\)
\(168\) −3.79963 + 3.09238i −0.293148 + 0.238582i
\(169\) 12.6114 + 21.8435i 0.970106 + 1.68027i
\(170\) 3.43484 + 0.159689i 0.263441 + 0.0122476i
\(171\) 7.95806 + 11.6868i 0.608568 + 0.893713i
\(172\) −1.12596 + 12.0833i −0.0858540 + 0.921346i
\(173\) −2.40122 + 1.38635i −0.182562 + 0.105402i −0.588496 0.808500i \(-0.700280\pi\)
0.405934 + 0.913902i \(0.366946\pi\)
\(174\) −1.15146 + 4.14207i −0.0872921 + 0.314010i
\(175\) 1.62311 2.81130i 0.122695 0.212514i
\(176\) 9.01936 + 7.74344i 0.679860 + 0.583684i
\(177\) −11.3789 2.60061i −0.855290 0.195474i
\(178\) 11.1818 5.78078i 0.838109 0.433288i
\(179\) 25.7248i 1.92276i 0.275226 + 0.961380i \(0.411247\pi\)
−0.275226 + 0.961380i \(0.588753\pi\)
\(180\) 4.10085 6.80584i 0.305659 0.507277i
\(181\) 19.1221i 1.42133i 0.703529 + 0.710667i \(0.251607\pi\)
−0.703529 + 0.710667i \(0.748393\pi\)
\(182\) −4.01529 7.76678i −0.297633 0.575712i
\(183\) −4.24668 + 4.57418i −0.313923 + 0.338133i
\(184\) −3.10976 2.42834i −0.229255 0.179020i
\(185\) 4.45084 7.70908i 0.327232 0.566783i
\(186\) 5.92950 + 22.9864i 0.434772 + 1.68545i
\(187\) 4.72529 2.72815i 0.345548 0.199502i
\(188\) 23.5605 + 2.19544i 1.71833 + 0.160119i
\(189\) 5.13744 + 0.778895i 0.373694 + 0.0566563i
\(190\) 0.409922 8.81726i 0.0297389 0.639671i
\(191\) 13.1819 + 22.8318i 0.953811 + 1.65205i 0.737066 + 0.675820i \(0.236211\pi\)
0.216744 + 0.976228i \(0.430456\pi\)
\(192\) −13.8536 + 0.279407i −0.999797 + 0.0201645i
\(193\) 8.35398 14.4695i 0.601333 1.04154i −0.391287 0.920269i \(-0.627970\pi\)
0.992620 0.121270i \(-0.0386967\pi\)
\(194\) 0.316547 + 0.202922i 0.0227267 + 0.0145689i
\(195\) 10.3927 + 9.64860i 0.744237 + 0.690951i
\(196\) 0.834985 + 1.81736i 0.0596418 + 0.129811i
\(197\) 0.543701i 0.0387371i −0.999812 0.0193685i \(-0.993834\pi\)
0.999812 0.0193685i \(-0.00616558\pi\)
\(198\) −0.350031 12.6036i −0.0248756 0.895699i
\(199\) −15.8980 −1.12698 −0.563491 0.826122i \(-0.690542\pi\)
−0.563491 + 0.826122i \(0.690542\pi\)
\(200\) 8.51223 3.44168i 0.601905 0.243363i
\(201\) −1.31819 0.301269i −0.0929780 0.0212499i
\(202\) −8.53293 + 13.3109i −0.600375 + 0.936553i
\(203\) 1.51998 + 0.877559i 0.106681 + 0.0615925i
\(204\) −1.98619 + 6.04200i −0.139061 + 0.423024i
\(205\) 2.26710 1.30891i 0.158341 0.0914184i
\(206\) 0.468549 10.0783i 0.0326453 0.702188i
\(207\) 0.310329 + 4.17338i 0.0215694 + 0.290070i
\(208\) 4.56914 24.3041i 0.316813 1.68518i
\(209\) −7.00317 12.1298i −0.484419 0.839039i
\(210\) −2.27223 2.31510i −0.156799 0.159757i
\(211\) −9.68441 5.59130i −0.666703 0.384921i 0.128124 0.991758i \(-0.459105\pi\)
−0.794826 + 0.606837i \(0.792438\pi\)
\(212\) −2.51211 1.78023i −0.172532 0.122267i
\(213\) −5.87333 + 1.80983i −0.402434 + 0.124007i
\(214\) 12.2631 + 23.7206i 0.838291 + 1.62151i
\(215\) −8.03569 −0.548029
\(216\) 10.0969 + 10.6796i 0.687005 + 0.726652i
\(217\) 9.69136 0.657892
\(218\) −6.17103 11.9366i −0.417955 0.808450i
\(219\) 20.4064 6.28809i 1.37894 0.424910i
\(220\) −4.55112 + 6.42216i −0.306836 + 0.432982i
\(221\) −9.83024 5.67549i −0.661253 0.381775i
\(222\) 11.5331 + 11.7507i 0.774053 + 0.788659i
\(223\) −6.25767 10.8386i −0.419044 0.725806i 0.576799 0.816886i \(-0.304302\pi\)
−0.995844 + 0.0910797i \(0.970968\pi\)
\(224\) −1.30223 + 5.50492i −0.0870089 + 0.367813i
\(225\) −8.77177 4.23050i −0.584784 0.282033i
\(226\) −0.767187 + 16.5019i −0.0510325 + 1.09769i
\(227\) 12.7359 7.35306i 0.845310 0.488040i −0.0137557 0.999905i \(-0.504379\pi\)
0.859066 + 0.511865i \(0.171045\pi\)
\(228\) 15.5098 + 5.09856i 1.02716 + 0.337661i
\(229\) 23.5034 + 13.5697i 1.55315 + 0.896710i 0.997883 + 0.0650356i \(0.0207161\pi\)
0.555264 + 0.831674i \(0.312617\pi\)
\(230\) 1.40995 2.19944i 0.0929692 0.145027i
\(231\) −5.01800 1.14685i −0.330160 0.0754571i
\(232\) 1.86080 + 4.60227i 0.122167 + 0.302154i
\(233\) −7.00103 −0.458653 −0.229326 0.973350i \(-0.573652\pi\)
−0.229326 + 0.973350i \(0.573652\pi\)
\(234\) −22.3429 + 13.7405i −1.46060 + 0.898247i
\(235\) 15.6682i 1.02208i
\(236\) −12.2472 + 5.62696i −0.797224 + 0.366284i
\(237\) −2.93411 2.72403i −0.190591 0.176945i
\(238\) 2.18591 + 1.40127i 0.141692 + 0.0908311i
\(239\) −7.08490 + 12.2714i −0.458284 + 0.793771i −0.998870 0.0475173i \(-0.984869\pi\)
0.540586 + 0.841289i \(0.318202\pi\)
\(240\) −1.03531 9.11647i −0.0668292 0.588465i
\(241\) 0.458251 + 0.793714i 0.0295185 + 0.0511276i 0.880407 0.474218i \(-0.157269\pi\)
−0.850889 + 0.525346i \(0.823936\pi\)
\(242\) 0.142398 3.06292i 0.00915367 0.196892i
\(243\) 1.18736 15.5432i 0.0761691 0.997095i
\(244\) −0.668690 + 7.17608i −0.0428085 + 0.459401i
\(245\) −1.14688 + 0.662153i −0.0732717 + 0.0423034i
\(246\) 1.20944 + 4.68855i 0.0771113 + 0.298931i
\(247\) −14.5690 + 25.2342i −0.927003 + 1.60562i
\(248\) 21.6047 + 16.8706i 1.37190 + 1.07128i
\(249\) −11.9808 + 12.9047i −0.759250 + 0.817803i
\(250\) 7.09250 + 13.7190i 0.448569 + 0.867667i
\(251\) 11.2597i 0.710705i −0.934732 0.355353i \(-0.884361\pi\)
0.934732 0.355353i \(-0.115639\pi\)
\(252\) 5.25132 2.90235i 0.330802 0.182831i
\(253\) 4.14562i 0.260633i
\(254\) 9.46214 4.89176i 0.593708 0.306937i
\(255\) −4.10549 0.938299i −0.257096 0.0587585i
\(256\) −12.4859 + 10.0051i −0.780371 + 0.625317i
\(257\) 9.32244 16.1469i 0.581518 1.00722i −0.413782 0.910376i \(-0.635792\pi\)
0.995300 0.0968426i \(-0.0308743\pi\)
\(258\) 3.98087 14.3201i 0.247838 0.891530i
\(259\) 5.82122 3.36088i 0.361713 0.208835i
\(260\) 16.3043 + 1.51929i 1.01115 + 0.0942222i
\(261\) 2.28729 4.74260i 0.141580 0.293559i
\(262\) 23.9368 + 1.11284i 1.47882 + 0.0687517i
\(263\) 7.01018 + 12.1420i 0.432266 + 0.748707i 0.997068 0.0765196i \(-0.0243808\pi\)
−0.564802 + 0.825226i \(0.691047\pi\)
\(264\) −9.19007 11.2919i −0.565609 0.694969i
\(265\) 1.01937 1.76560i 0.0626192 0.108460i
\(266\) 3.59708 5.61124i 0.220551 0.344047i
\(267\) −14.7331 + 4.53989i −0.901649 + 0.277837i
\(268\) −1.41878 + 0.651857i −0.0866658 + 0.0398185i
\(269\) 9.69756i 0.591271i −0.955301 0.295635i \(-0.904469\pi\)
0.955301 0.295635i \(-0.0955313\pi\)
\(270\) −6.42070 + 7.31294i −0.390751 + 0.445052i
\(271\) 13.0316 0.791611 0.395805 0.918334i \(-0.370466\pi\)
0.395805 + 0.918334i \(0.370466\pi\)
\(272\) 2.43367 + 6.92903i 0.147563 + 0.420134i
\(273\) 3.15338 + 10.2335i 0.190851 + 0.619359i
\(274\) 18.5427 + 11.8867i 1.12020 + 0.718104i
\(275\) 8.35475 + 4.82362i 0.503810 + 0.290875i
\(276\) 3.22106 + 3.60222i 0.193885 + 0.216828i
\(277\) 7.92057 4.57294i 0.475901 0.274761i −0.242806 0.970075i \(-0.578068\pi\)
0.718707 + 0.695314i \(0.244734\pi\)
\(278\) 27.2911 + 1.26879i 1.63681 + 0.0760969i
\(279\) −2.15597 28.9940i −0.129075 1.73583i
\(280\) −3.70938 0.520359i −0.221678 0.0310974i
\(281\) 7.48789 + 12.9694i 0.446690 + 0.773690i 0.998168 0.0604991i \(-0.0192692\pi\)
−0.551478 + 0.834190i \(0.685936\pi\)
\(282\) −27.9218 7.76203i −1.66272 0.462222i
\(283\) −4.95482 2.86067i −0.294533 0.170049i 0.345451 0.938437i \(-0.387726\pi\)
−0.639985 + 0.768388i \(0.721059\pi\)
\(284\) −4.10322 + 5.79012i −0.243481 + 0.343581i
\(285\) −2.40862 + 10.5388i −0.142674 + 0.624266i
\(286\) 23.0817 11.9328i 1.36485 0.705603i
\(287\) 1.97675 0.116684
\(288\) 16.7590 + 2.67129i 0.987534 + 0.157407i
\(289\) −13.6291 −0.801712
\(290\) −2.91995 + 1.50956i −0.171465 + 0.0886445i
\(291\) −0.337487 0.313323i −0.0197838 0.0183673i
\(292\) 14.2563 20.1173i 0.834287 1.17728i
\(293\) −5.20239 3.00360i −0.303927 0.175472i 0.340279 0.940325i \(-0.389479\pi\)
−0.644206 + 0.764852i \(0.722812\pi\)
\(294\) −0.611834 2.37185i −0.0356829 0.138329i
\(295\) −4.46225 7.72885i −0.259802 0.449991i
\(296\) 18.8277 + 2.64118i 1.09434 + 0.153516i
\(297\) −2.31475 + 15.2677i −0.134316 + 0.885920i
\(298\) 6.33630 + 0.294580i 0.367052 + 0.0170646i
\(299\) −7.46888 + 4.31216i −0.431936 + 0.249379i
\(300\) −11.0075 + 2.30012i −0.635516 + 0.132797i
\(301\) −5.25491 3.03392i −0.302888 0.174872i
\(302\) 16.5721 + 10.6235i 0.953617 + 0.611315i
\(303\) 13.1754 14.1914i 0.756905 0.815277i
\(304\) 17.7868 6.24725i 1.02015 0.358304i
\(305\) −4.77225 −0.273258
\(306\) 3.70596 6.85141i 0.211856 0.391669i
\(307\) 20.6804i 1.18030i 0.807295 + 0.590148i \(0.200930\pi\)
−0.807295 + 0.590148i \(0.799070\pi\)
\(308\) −5.40091 + 2.48144i −0.307746 + 0.141393i
\(309\) −2.75309 + 12.0461i −0.156618 + 0.685276i
\(310\) −9.79544 + 15.2804i −0.556344 + 0.867866i
\(311\) 5.09193 8.81949i 0.288737 0.500107i −0.684771 0.728758i \(-0.740098\pi\)
0.973509 + 0.228651i \(0.0734313\pi\)
\(312\) −10.7846 + 28.3026i −0.610558 + 1.60232i
\(313\) 4.79130 + 8.29877i 0.270820 + 0.469074i 0.969072 0.246778i \(-0.0793718\pi\)
−0.698252 + 0.715852i \(0.746038\pi\)
\(314\) 20.0598 + 0.932597i 1.13204 + 0.0526295i
\(315\) 2.23613 + 3.28387i 0.125992 + 0.185025i
\(316\) −4.60310 0.428932i −0.258945 0.0241293i
\(317\) −19.2474 + 11.1125i −1.08104 + 0.624140i −0.931177 0.364566i \(-0.881217\pi\)
−0.149865 + 0.988706i \(0.547884\pi\)
\(318\) 2.64141 + 2.69125i 0.148123 + 0.150918i
\(319\) −2.60797 + 4.51713i −0.146018 + 0.252911i
\(320\) −7.36340 7.61727i −0.411626 0.425819i
\(321\) −9.63077 31.2542i −0.537537 1.74444i
\(322\) 1.75244 0.905983i 0.0976599 0.0504885i
\(323\) 8.65309i 0.481471i
\(324\) −9.85131 15.0649i −0.547295 0.836940i
\(325\) 20.0696i 1.11326i
\(326\) −10.2926 19.9089i −0.570052 1.10265i
\(327\) 4.84637 + 15.7277i 0.268005 + 0.869742i
\(328\) 4.40672 + 3.44110i 0.243320 + 0.190003i
\(329\) −5.91564 + 10.2462i −0.326140 + 0.564891i
\(330\) 6.88013 6.75271i 0.378738 0.371724i
\(331\) 6.36605 3.67544i 0.349910 0.202021i −0.314736 0.949179i \(-0.601916\pi\)
0.664646 + 0.747159i \(0.268583\pi\)
\(332\) −1.88651 + 20.2452i −0.103536 + 1.11110i
\(333\) −11.3499 16.6679i −0.621971 0.913396i
\(334\) −0.745598 + 16.0375i −0.0407973 + 0.877533i
\(335\) −0.516931 0.895350i −0.0282429 0.0489182i
\(336\) 2.76494 6.35257i 0.150840 0.346561i
\(337\) −14.3414 + 24.8401i −0.781227 + 1.35313i 0.150000 + 0.988686i \(0.452073\pi\)
−0.931227 + 0.364439i \(0.881261\pi\)
\(338\) −30.0298 19.2506i −1.63341 1.04709i
\(339\) 4.50783 19.7238i 0.244832 1.07125i
\(340\) −4.41878 + 2.03020i −0.239642 + 0.110103i
\(341\) 28.8012i 1.55967i
\(342\) −17.5876 9.51322i −0.951028 0.514416i
\(343\) −1.00000 −0.0539949
\(344\) −6.43321 15.9111i −0.346855 0.857870i
\(345\) −2.17704 + 2.34494i −0.117208 + 0.126247i
\(346\) 2.11618 3.30113i 0.113767 0.177470i
\(347\) 15.7002 + 9.06450i 0.842830 + 0.486608i 0.858225 0.513274i \(-0.171567\pi\)
−0.0153954 + 0.999881i \(0.504901\pi\)
\(348\) −1.24360 5.95136i −0.0666637 0.319026i
\(349\) −5.69310 + 3.28691i −0.304744 + 0.175944i −0.644572 0.764543i \(-0.722965\pi\)
0.339828 + 0.940488i \(0.389631\pi\)
\(350\) −0.213202 + 4.58588i −0.0113961 + 0.245126i
\(351\) 29.9145 11.7107i 1.59672 0.625070i
\(352\) −16.3598 3.87003i −0.871979 0.206273i
\(353\) −11.8747 20.5676i −0.632028 1.09470i −0.987136 0.159880i \(-0.948889\pi\)
0.355108 0.934825i \(-0.384444\pi\)
\(354\) 15.9839 4.12315i 0.849534 0.219143i
\(355\) −4.06949 2.34952i −0.215986 0.124700i
\(356\) −10.2928 + 14.5243i −0.545518 + 0.769789i
\(357\) −2.33051 2.16365i −0.123344 0.114513i
\(358\) −16.7074 32.3170i −0.883011 1.70801i
\(359\) 24.2172 1.27813 0.639067 0.769151i \(-0.279321\pi\)
0.639067 + 0.769151i \(0.279321\pi\)
\(360\) −0.731578 + 11.2133i −0.0385576 + 0.590992i
\(361\) −3.21250 −0.169079
\(362\) −12.4191 24.0223i −0.652736 1.26259i
\(363\) −0.836699 + 3.66095i −0.0439153 + 0.192150i
\(364\) 10.0885 + 7.14932i 0.528782 + 0.374726i
\(365\) 14.1391 + 8.16322i 0.740075 + 0.427283i
\(366\) 2.36417 8.50444i 0.123577 0.444534i
\(367\) −4.89757 8.48284i −0.255651 0.442801i 0.709421 0.704785i \(-0.248956\pi\)
−0.965072 + 0.261984i \(0.915623\pi\)
\(368\) 5.48380 + 1.03095i 0.285863 + 0.0537419i
\(369\) −0.439755 5.91393i −0.0228927 0.307867i
\(370\) −0.584637 + 12.5753i −0.0303938 + 0.653759i
\(371\) 1.33322 0.769737i 0.0692175 0.0399627i
\(372\) −22.3779 25.0260i −1.16024 1.29754i
\(373\) 10.1979 + 5.88778i 0.528029 + 0.304858i 0.740214 0.672372i \(-0.234724\pi\)
−0.212184 + 0.977230i \(0.568058\pi\)
\(374\) −4.16437 + 6.49619i −0.215334 + 0.335910i
\(375\) −5.57004 18.0762i −0.287636 0.933449i
\(376\) −31.0240 + 12.5437i −1.59994 + 0.646891i
\(377\) 10.8509 0.558852
\(378\) −6.95984 + 2.35810i −0.357976 + 0.121287i
\(379\) 18.7618i 0.963727i −0.876246 0.481864i \(-0.839960\pi\)
0.876246 0.481864i \(-0.160040\pi\)
\(380\) 5.21154 + 11.3430i 0.267346 + 0.581884i
\(381\) −12.4673 + 3.84171i −0.638719 + 0.196817i
\(382\) −31.3884 20.1215i −1.60597 1.02950i
\(383\) 11.9105 20.6296i 0.608598 1.05412i −0.382874 0.923801i \(-0.625066\pi\)
0.991472 0.130322i \(-0.0416011\pi\)
\(384\) 17.2223 9.34844i 0.878870 0.477061i
\(385\) −1.96782 3.40836i −0.100289 0.173706i
\(386\) −1.09733 + 23.6031i −0.0558527 + 1.20137i
\(387\) −7.90768 + 16.3963i −0.401970 + 0.833468i
\(388\) −0.529457 0.0493365i −0.0268791 0.00250468i
\(389\) −15.1720 + 8.75954i −0.769249 + 0.444126i −0.832607 0.553865i \(-0.813152\pi\)
0.0633576 + 0.997991i \(0.479819\pi\)
\(390\) −19.3224 5.37147i −0.978428 0.271995i
\(391\) 1.28058 2.21803i 0.0647616 0.112170i
\(392\) −2.22927 1.74079i −0.112595 0.0879231i
\(393\) −28.6104 6.53883i −1.44321 0.329841i
\(394\) 0.353115 + 0.683031i 0.0177897 + 0.0344106i
\(395\) 3.06116i 0.154024i
\(396\) 8.62534 + 15.6061i 0.433440 + 0.784236i
\(397\) 2.00372i 0.100564i −0.998735 0.0502820i \(-0.983988\pi\)
0.998735 0.0502820i \(-0.0160120\pi\)
\(398\) 19.9721 10.3252i 1.00111 0.517557i
\(399\) −5.55410 + 5.98243i −0.278053 + 0.299496i
\(400\) −8.45833 + 9.85205i −0.422917 + 0.492602i
\(401\) 10.5608 18.2918i 0.527380 0.913448i −0.472111 0.881539i \(-0.656508\pi\)
0.999491 0.0319093i \(-0.0101588\pi\)
\(402\) 1.85166 0.477647i 0.0923522 0.0238229i
\(403\) 51.8891 29.9582i 2.58478 1.49232i
\(404\) 2.07462 22.2638i 0.103216 1.10767i
\(405\) 9.32703 7.42046i 0.463464 0.368726i
\(406\) −2.47943 0.115271i −0.123052 0.00572081i
\(407\) 9.98802 + 17.2998i 0.495088 + 0.857517i
\(408\) −1.42889 8.88029i −0.0707406 0.439640i
\(409\) −10.0084 + 17.3350i −0.494881 + 0.857159i −0.999983 0.00590065i \(-0.998122\pi\)
0.505101 + 0.863060i \(0.331455\pi\)
\(410\) −1.99798 + 3.11674i −0.0986733 + 0.153925i
\(411\) −19.7693 18.3538i −0.975147 0.905328i
\(412\) 5.95688 + 12.9653i 0.293475 + 0.638753i
\(413\) 6.73900i 0.331604i
\(414\) −3.10032 5.04131i −0.152372 0.247767i
\(415\) −13.4635 −0.660897
\(416\) 10.0446 + 33.4998i 0.492478 + 1.64246i
\(417\) −32.6197 7.45513i −1.59739 0.365079i
\(418\) 16.6757 + 10.6899i 0.815637 + 0.522862i
\(419\) −0.331640 0.191472i −0.0162017 0.00935403i 0.491877 0.870665i \(-0.336311\pi\)
−0.508079 + 0.861311i \(0.669644\pi\)
\(420\) 4.35810 + 1.43264i 0.212653 + 0.0699058i
\(421\) −31.6574 + 18.2774i −1.54289 + 0.890785i −0.544230 + 0.838936i \(0.683178\pi\)
−0.998655 + 0.0518491i \(0.983489\pi\)
\(422\) 15.7975 + 0.734441i 0.769011 + 0.0357520i
\(423\) 31.9699 + 15.4187i 1.55443 + 0.749681i
\(424\) 4.31207 + 0.604905i 0.209412 + 0.0293768i
\(425\) 2.98002 + 5.16155i 0.144552 + 0.250372i
\(426\) 6.20302 6.08814i 0.300537 0.294971i
\(427\) −3.12079 1.80179i −0.151026 0.0871948i
\(428\) −30.8114 21.8348i −1.48933 1.05542i
\(429\) −30.4123 + 9.37136i −1.46832 + 0.452453i
\(430\) 10.0949 5.21890i 0.486821 0.251678i
\(431\) −17.1552 −0.826338 −0.413169 0.910654i \(-0.635578\pi\)
−0.413169 + 0.910654i \(0.635578\pi\)
\(432\) −19.6203 6.85876i −0.943984 0.329992i
\(433\) 13.7752 0.661995 0.330997 0.943632i \(-0.392615\pi\)
0.330997 + 0.943632i \(0.392615\pi\)
\(434\) −12.1749 + 6.29421i −0.584413 + 0.302132i
\(435\) 3.84731 1.18552i 0.184465 0.0568415i
\(436\) 15.5049 + 10.9877i 0.742548 + 0.526213i
\(437\) −5.69368 3.28725i −0.272366 0.157250i
\(438\) −21.5519 + 21.1527i −1.02979 + 1.01072i
\(439\) 7.44538 + 12.8958i 0.355348 + 0.615482i 0.987178 0.159626i \(-0.0510289\pi\)
−0.631829 + 0.775108i \(0.717696\pi\)
\(440\) 1.54643 11.0237i 0.0737230 0.525535i
\(441\) 0.222463 + 2.99174i 0.0105935 + 0.142464i
\(442\) 16.0354 + 0.745500i 0.762726 + 0.0354598i
\(443\) −4.25611 + 2.45727i −0.202214 + 0.116748i −0.597688 0.801729i \(-0.703914\pi\)
0.395474 + 0.918477i \(0.370580\pi\)
\(444\) −22.1203 7.27165i −1.04978 0.345097i
\(445\) −10.2082 5.89371i −0.483915 0.279389i
\(446\) 14.9006 + 9.55198i 0.705562 + 0.452299i
\(447\) −7.57346 1.73089i −0.358212 0.0818684i
\(448\) −1.93932 7.76138i −0.0916241 0.366691i
\(449\) 29.2454 1.38018 0.690088 0.723725i \(-0.257572\pi\)
0.690088 + 0.723725i \(0.257572\pi\)
\(450\) 13.7672 0.382346i 0.648992 0.0180240i
\(451\) 5.87460i 0.276624i
\(452\) −9.75361 21.2289i −0.458771 0.998525i
\(453\) −17.6684 16.4033i −0.830132 0.770696i
\(454\) −11.2240 + 17.5089i −0.526770 + 0.821733i
\(455\) −4.09373 + 7.09055i −0.191917 + 0.332410i
\(456\) −22.7957 + 3.66797i −1.06751 + 0.171768i
\(457\) 15.9871 + 27.6905i 0.747846 + 1.29531i 0.948853 + 0.315717i \(0.102245\pi\)
−0.201007 + 0.979590i \(0.564422\pi\)
\(458\) −38.3394 1.78244i −1.79148 0.0832878i
\(459\) −5.95463 + 7.45362i −0.277938 + 0.347905i
\(460\) −0.342802 + 3.67879i −0.0159832 + 0.171524i
\(461\) 5.15400 2.97566i 0.240046 0.138590i −0.375152 0.926963i \(-0.622410\pi\)
0.615198 + 0.788373i \(0.289076\pi\)
\(462\) 7.04876 1.81827i 0.327938 0.0845938i
\(463\) 3.97874 6.89138i 0.184908 0.320270i −0.758638 0.651513i \(-0.774135\pi\)
0.943545 + 0.331243i \(0.107468\pi\)
\(464\) −5.32667 4.57314i −0.247284 0.212303i
\(465\) 15.1247 16.2912i 0.701393 0.755485i
\(466\) 8.79513 4.54693i 0.407427 0.210633i
\(467\) 6.61242i 0.305986i −0.988227 0.152993i \(-0.951109\pi\)
0.988227 0.152993i \(-0.0488912\pi\)
\(468\) 19.1446 31.7727i 0.884959 1.46869i
\(469\) 0.780681i 0.0360485i
\(470\) −10.1760 19.6834i −0.469383 0.907928i
\(471\) −23.9764 5.47974i −1.10477 0.252493i
\(472\) 11.7312 15.0231i 0.539971 0.691493i
\(473\) 9.01634 15.6168i 0.414572 0.718059i
\(474\) 5.45518 + 1.51650i 0.250565 + 0.0696549i
\(475\) 13.2497 7.64972i 0.607938 0.350993i
\(476\) −3.65616 0.340693i −0.167580 0.0156156i
\(477\) −2.59945 3.81742i −0.119020 0.174788i
\(478\) 0.930632 20.0175i 0.0425661 0.915579i
\(479\) 4.39372 + 7.61015i 0.200754 + 0.347717i 0.948772 0.315962i \(-0.102327\pi\)
−0.748017 + 0.663679i \(0.768994\pi\)
\(480\) 7.22146 + 10.7803i 0.329613 + 0.492050i
\(481\) 20.7785 35.9895i 0.947419 1.64098i
\(482\) −1.09117 0.699495i −0.0497016 0.0318611i
\(483\) −2.30902 + 0.711507i −0.105064 + 0.0323747i
\(484\) 1.81037 + 3.94031i 0.0822895 + 0.179105i
\(485\) 0.352100i 0.0159881i
\(486\) 8.60312 + 20.2974i 0.390246 + 0.920711i
\(487\) 29.8389 1.35213 0.676066 0.736841i \(-0.263683\pi\)
0.676066 + 0.736841i \(0.263683\pi\)
\(488\) −3.82057 9.44932i −0.172949 0.427751i
\(489\) 8.08318 + 26.2319i 0.365534 + 1.18625i
\(490\) 1.01074 1.57670i 0.0456606 0.0712280i
\(491\) 3.90406 + 2.25401i 0.176188 + 0.101722i 0.585500 0.810672i \(-0.300898\pi\)
−0.409313 + 0.912394i \(0.634231\pi\)
\(492\) −4.56443 5.10456i −0.205781 0.230131i
\(493\) −2.79067 + 1.61120i −0.125686 + 0.0725646i
\(494\) 1.91370 41.1629i 0.0861015 1.85201i
\(495\) −9.75915 + 6.64543i −0.438641 + 0.298690i
\(496\) −38.0980 7.16239i −1.71065 0.321601i
\(497\) −1.77415 3.07292i −0.0795817 0.137839i
\(498\) 6.66980 23.9928i 0.298881 1.07514i
\(499\) 20.6652 + 11.9310i 0.925100 + 0.534107i 0.885259 0.465099i \(-0.153981\pi\)
0.0398414 + 0.999206i \(0.487315\pi\)
\(500\) −17.8201 12.6284i −0.796938 0.564757i
\(501\) 4.38098 19.1688i 0.195728 0.856399i
\(502\) 7.31278 + 14.1451i 0.326385 + 0.631327i
\(503\) 7.53637 0.336030 0.168015 0.985784i \(-0.446264\pi\)
0.168015 + 0.985784i \(0.446264\pi\)
\(504\) −4.71205 + 7.05667i −0.209892 + 0.314329i
\(505\) 14.8059 0.658856
\(506\) 2.69244 + 5.20799i 0.119694 + 0.231523i
\(507\) 32.0163 + 29.7240i 1.42190 + 1.32009i
\(508\) −8.70990 + 12.2907i −0.386439 + 0.545311i
\(509\) 10.1793 + 5.87705i 0.451192 + 0.260496i 0.708333 0.705878i \(-0.249447\pi\)
−0.257142 + 0.966374i \(0.582781\pi\)
\(510\) 5.76697 1.48763i 0.255366 0.0658733i
\(511\) 6.16415 + 10.6766i 0.272686 + 0.472306i
\(512\) 9.18765 20.6782i 0.406041 0.913855i
\(513\) 19.1335 + 15.2855i 0.844763 + 0.674874i
\(514\) −1.22454 + 26.3394i −0.0540123 + 1.16178i
\(515\) −8.18201 + 4.72388i −0.360542 + 0.208159i
\(516\) 4.29940 + 20.5752i 0.189270 + 0.905774i
\(517\) −30.4501 17.5804i −1.33919 0.773183i
\(518\) −5.13020 + 8.00284i −0.225408 + 0.351624i
\(519\) −3.26751 + 3.51950i −0.143428 + 0.154489i
\(520\) −21.4692 + 8.68046i −0.941487 + 0.380663i
\(521\) −4.50583 −0.197404 −0.0987021 0.995117i \(-0.531469\pi\)
−0.0987021 + 0.995117i \(0.531469\pi\)
\(522\) 0.206722 + 7.44346i 0.00904796 + 0.325791i
\(523\) 33.3777i 1.45950i −0.683712 0.729752i \(-0.739635\pi\)
0.683712 0.729752i \(-0.260365\pi\)
\(524\) −30.7937 + 14.1481i −1.34523 + 0.618063i
\(525\) 1.25273 5.48127i 0.0546736 0.239222i
\(526\) −16.6924 10.7006i −0.727824 0.466570i
\(527\) −8.89666 + 15.4095i −0.387545 + 0.671247i
\(528\) 18.8788 + 8.21696i 0.821596 + 0.357597i
\(529\) 10.5270 + 18.2334i 0.457697 + 0.792755i
\(530\) −0.133898 + 2.88010i −0.00581617 + 0.125103i
\(531\) −20.1613 + 1.49918i −0.874928 + 0.0650589i
\(532\) −0.874559 + 9.38537i −0.0379169 + 0.406907i
\(533\) 10.5839 6.11059i 0.458438 0.264679i
\(534\) 15.5601 15.2719i 0.673351 0.660880i
\(535\) 12.5027 21.6553i 0.540539 0.936241i
\(536\) 1.35900 1.74035i 0.0586999 0.0751717i
\(537\) 13.1210 + 42.5809i 0.566213 + 1.83750i
\(538\) 6.29823 + 12.1827i 0.271536 + 0.525232i
\(539\) 2.97184i 0.128006i
\(540\) 3.31658 13.3570i 0.142723 0.574794i
\(541\) 3.39295i 0.145874i −0.997337 0.0729372i \(-0.976763\pi\)
0.997337 0.0729372i \(-0.0232373\pi\)
\(542\) −16.3710 + 8.46355i −0.703197 + 0.363541i
\(543\) 9.75328 + 31.6518i 0.418553 + 1.35831i
\(544\) −7.55750 7.12409i −0.324025 0.305443i
\(545\) −6.29158 + 10.8973i −0.269502 + 0.466791i
\(546\) −10.6078 10.8079i −0.453971 0.462537i
\(547\) 11.7045 6.75759i 0.500448 0.288934i −0.228451 0.973555i \(-0.573366\pi\)
0.728898 + 0.684622i \(0.240033\pi\)
\(548\) −31.0145 2.89003i −1.32487 0.123456i
\(549\) −4.69623 + 9.73744i −0.200430 + 0.415584i
\(550\) −13.6285 0.633603i −0.581122 0.0270169i
\(551\) 4.13595 + 7.16367i 0.176197 + 0.305183i
\(552\) −6.38601 2.43336i −0.271807 0.103571i
\(553\) 1.15576 2.00184i 0.0491479 0.0851267i
\(554\) −6.98034 + 10.8889i −0.296566 + 0.462627i
\(555\) 3.43520 15.0306i 0.145816 0.638014i
\(556\) −35.1088 + 16.1307i −1.48895 + 0.684095i
\(557\) 22.8232i 0.967049i 0.875331 + 0.483525i \(0.160644\pi\)
−0.875331 + 0.483525i \(0.839356\pi\)
\(558\) 21.5391 + 35.0239i 0.911823 + 1.48268i
\(559\) −37.5142 −1.58668
\(560\) 4.99791 1.75541i 0.211200 0.0741796i
\(561\) 6.43003 6.92592i 0.271476 0.292412i
\(562\) −17.8299 11.4299i −0.752111 0.482139i
\(563\) 14.1072 + 8.14479i 0.594547 + 0.343262i 0.766894 0.641774i \(-0.221801\pi\)
−0.172346 + 0.985036i \(0.555135\pi\)
\(564\) 40.1182 8.38310i 1.68928 0.352992i
\(565\) 13.3970 7.73474i 0.563614 0.325403i
\(566\) 8.08245 + 0.375761i 0.339731 + 0.0157944i
\(567\) 8.90102 1.33111i 0.373808 0.0559012i
\(568\) 1.39424 9.93881i 0.0585008 0.417023i
\(569\) 23.6682 + 40.9945i 0.992221 + 1.71858i 0.603921 + 0.797044i \(0.293604\pi\)
0.388300 + 0.921533i \(0.373062\pi\)
\(570\) −3.81875 14.8038i −0.159950 0.620064i
\(571\) 15.5387 + 8.97129i 0.650276 + 0.375437i 0.788562 0.614955i \(-0.210826\pi\)
−0.138286 + 0.990392i \(0.544159\pi\)
\(572\) −21.2467 + 29.9815i −0.888367 + 1.25359i
\(573\) 33.4648 + 31.0688i 1.39801 + 1.29792i
\(574\) −2.48332 + 1.28383i −0.103652 + 0.0535861i
\(575\) 4.52836 0.188846
\(576\) −22.7886 + 7.52856i −0.949526 + 0.313690i
\(577\) 13.7786 0.573611 0.286806 0.957989i \(-0.407407\pi\)
0.286806 + 0.957989i \(0.407407\pi\)
\(578\) 17.1217 8.85164i 0.712170 0.368180i
\(579\) 6.44768 28.2116i 0.267957 1.17243i
\(580\) 2.68781 3.79281i 0.111605 0.157488i
\(581\) −8.80441 5.08323i −0.365268 0.210888i
\(582\) 0.627465 + 0.174430i 0.0260092 + 0.00723036i
\(583\) 2.28754 + 3.96213i 0.0947401 + 0.164095i
\(584\) −4.84415 + 34.5316i −0.200453 + 1.42893i
\(585\) 22.1238 + 10.6700i 0.914707 + 0.441150i
\(586\) 8.48630 + 0.394536i 0.350566 + 0.0162981i
\(587\) 38.1036 21.9991i 1.57270 0.908002i 0.576869 0.816837i \(-0.304274\pi\)
0.995836 0.0911651i \(-0.0290591\pi\)
\(588\) 2.30906 + 2.58230i 0.0952239 + 0.106492i
\(589\) 39.5561 + 22.8378i 1.62988 + 0.941013i
\(590\) 10.6254 + 6.81138i 0.437440 + 0.280420i
\(591\) −0.277316 0.899960i −0.0114073 0.0370194i
\(592\) −25.3679 + 8.90992i −1.04261 + 0.366195i
\(593\) −41.4353 −1.70154 −0.850772 0.525535i \(-0.823865\pi\)
−0.850772 + 0.525535i \(0.823865\pi\)
\(594\) −7.00790 20.6836i −0.287537 0.848657i
\(595\) 2.43142i 0.0996787i
\(596\) −8.15137 + 3.74514i −0.333893 + 0.153407i
\(597\) −26.3152 + 8.10885i −1.07701 + 0.331873i
\(598\) 6.58227 10.2680i 0.269169 0.419889i
\(599\) 6.60491 11.4400i 0.269869 0.467427i −0.698959 0.715162i \(-0.746353\pi\)
0.968828 + 0.247735i \(0.0796862\pi\)
\(600\) 12.3344 10.0385i 0.503550 0.409821i
\(601\) −19.9741 34.5961i −0.814760 1.41121i −0.909500 0.415704i \(-0.863535\pi\)
0.0947400 0.995502i \(-0.469798\pi\)
\(602\) 8.57197 + 0.398519i 0.349367 + 0.0162424i
\(603\) −2.33560 + 0.173673i −0.0951128 + 0.00707251i
\(604\) −27.7185 2.58290i −1.12785 0.105097i
\(605\) −2.48661 + 1.43565i −0.101095 + 0.0583673i
\(606\) −7.33485 + 26.3851i −0.297958 + 1.07182i
\(607\) 3.45338 5.98143i 0.140168 0.242779i −0.787392 0.616453i \(-0.788569\pi\)
0.927560 + 0.373674i \(0.121902\pi\)
\(608\) −18.2876 + 19.4001i −0.741659 + 0.786779i
\(609\) 2.96354 + 0.677308i 0.120089 + 0.0274459i
\(610\) 5.99519 3.09941i 0.242738 0.125492i
\(611\) 73.1464i 2.95918i
\(612\) −0.205903 + 11.0141i −0.00832313 + 0.445217i
\(613\) 45.9169i 1.85456i −0.374363 0.927282i \(-0.622139\pi\)
0.374363 0.927282i \(-0.377861\pi\)
\(614\) −13.4312 25.9801i −0.542041 1.04847i
\(615\) 3.08500 3.32292i 0.124399 0.133993i
\(616\) 5.17335 6.62505i 0.208440 0.266931i
\(617\) 11.9943 20.7748i 0.482874 0.836362i −0.516933 0.856026i \(-0.672926\pi\)
0.999807 + 0.0196640i \(0.00625965\pi\)
\(618\) −4.36490 16.9210i −0.175582 0.680664i
\(619\) −33.1469 + 19.1374i −1.33229 + 0.769196i −0.985650 0.168803i \(-0.946010\pi\)
−0.346637 + 0.937999i \(0.612677\pi\)
\(620\) 2.38157 25.5579i 0.0956462 1.02643i
\(621\) 2.64232 + 6.74969i 0.106033 + 0.270856i
\(622\) −0.668847 + 14.3866i −0.0268183 + 0.576851i
\(623\) −4.45041 7.70834i −0.178302 0.308828i
\(624\) −4.83331 42.5597i −0.193487 1.70375i
\(625\) −0.884475 + 1.53196i −0.0353790 + 0.0612782i
\(626\) −11.4089 7.31364i −0.455991 0.292312i
\(627\) −17.7788 16.5059i −0.710019 0.659183i
\(628\) −25.8060 + 11.8565i −1.02977 + 0.473127i
\(629\) 12.3412i 0.492074i
\(630\) −4.94193 2.67311i −0.196891 0.106499i
\(631\) −13.9601 −0.555742 −0.277871 0.960618i \(-0.589629\pi\)
−0.277871 + 0.960618i \(0.589629\pi\)
\(632\) 6.06127 2.45070i 0.241105 0.0974838i
\(633\) −18.8820 4.31542i −0.750491 0.171523i
\(634\) 16.9626 26.4607i 0.673671 1.05089i
\(635\) −8.63830 4.98733i −0.342801 0.197916i
\(636\) −5.06618 1.66541i −0.200887 0.0660378i
\(637\) −5.35416 + 3.09123i −0.212140 + 0.122479i
\(638\) 0.342568 7.36848i 0.0135624 0.291721i
\(639\) −8.79871 + 5.99142i −0.348071 + 0.237017i
\(640\) 14.1975 + 4.78702i 0.561206 + 0.189224i
\(641\) −11.8317 20.4931i −0.467323 0.809427i 0.531980 0.846757i \(-0.321448\pi\)
−0.999303 + 0.0373296i \(0.988115\pi\)
\(642\) 32.3973 + 33.0086i 1.27862 + 1.30275i
\(643\) −17.3058 9.99151i −0.682474 0.394027i 0.118313 0.992976i \(-0.462252\pi\)
−0.800787 + 0.598950i \(0.795585\pi\)
\(644\) −1.61312 + 2.27630i −0.0635660 + 0.0896990i
\(645\) −13.3011 + 4.09863i −0.523728 + 0.161383i
\(646\) 5.61988 + 10.8705i 0.221111 + 0.427696i
\(647\) −31.2787 −1.22969 −0.614846 0.788647i \(-0.710782\pi\)
−0.614846 + 0.788647i \(0.710782\pi\)
\(648\) 22.1600 + 12.5274i 0.870526 + 0.492122i
\(649\) 20.0273 0.786138
\(650\) 13.0345 + 25.2126i 0.511255 + 0.988921i
\(651\) 16.0416 4.94311i 0.628720 0.193736i
\(652\) 25.8603 + 18.3261i 1.01277 + 0.717707i
\(653\) 5.78411 + 3.33946i 0.226350 + 0.130683i 0.608887 0.793257i \(-0.291616\pi\)
−0.382537 + 0.923940i \(0.624950\pi\)
\(654\) −16.3029 16.6105i −0.637494 0.649523i
\(655\) −11.2196 19.4330i −0.438387 0.759309i
\(656\) −7.77087 1.46092i −0.303402 0.0570392i
\(657\) 30.5704 20.8167i 1.19266 0.812136i
\(658\) 0.777045 16.7139i 0.0302924 0.651576i
\(659\) −8.11343 + 4.68429i −0.316055 + 0.182474i −0.649633 0.760248i \(-0.725077\pi\)
0.333578 + 0.942722i \(0.391744\pi\)
\(660\) −4.25759 + 12.9516i −0.165726 + 0.504139i
\(661\) −8.14781 4.70414i −0.316913 0.182970i 0.333103 0.942891i \(-0.391904\pi\)
−0.650016 + 0.759921i \(0.725238\pi\)
\(662\) −5.61036 + 8.75185i −0.218053 + 0.340150i
\(663\) −19.1663 4.38040i −0.744357 0.170121i
\(664\) −10.7786 26.6585i −0.418291 1.03455i
\(665\) −6.24148 −0.242034
\(666\) 25.0837 + 13.5679i 0.971973 + 0.525745i
\(667\) 2.44833i 0.0947997i
\(668\) −9.47914 20.6315i −0.366759 0.798259i
\(669\) −15.8863 14.7488i −0.614198 0.570223i
\(670\) 1.23090 + 0.789066i 0.0475538 + 0.0304843i
\(671\) 5.35464 9.27451i 0.206714 0.358039i
\(672\) 0.652290 + 9.77622i 0.0251626 + 0.377126i
\(673\) −7.48291 12.9608i −0.288445 0.499601i 0.684994 0.728549i \(-0.259805\pi\)
−0.973439 + 0.228947i \(0.926472\pi\)
\(674\) 1.88381 40.5199i 0.0725616 1.56077i
\(675\) −16.6772 2.52846i −0.641907 0.0973204i
\(676\) 50.2279 + 4.68040i 1.93184 + 0.180015i
\(677\) 6.47998 3.74122i 0.249046 0.143787i −0.370281 0.928920i \(-0.620739\pi\)
0.619327 + 0.785133i \(0.287405\pi\)
\(678\) 7.14695 + 27.7060i 0.274477 + 1.06404i
\(679\) 0.132938 0.230255i 0.00510168 0.00883636i
\(680\) 4.23259 5.42031i 0.162313 0.207859i
\(681\) 17.3306 18.6671i 0.664109 0.715326i
\(682\) −18.7054 36.1819i −0.716266 1.38547i
\(683\) 1.96860i 0.0753264i −0.999290 0.0376632i \(-0.988009\pi\)
0.999290 0.0376632i \(-0.0119914\pi\)
\(684\) 28.2731 + 0.528553i 1.08105 + 0.0202097i
\(685\) 20.6253i 0.788053i
\(686\) 1.25626 0.649466i 0.0479643 0.0247967i
\(687\) 45.8252 + 10.4732i 1.74834 + 0.399578i
\(688\) 18.4155 + 15.8104i 0.702085 + 0.602765i
\(689\) 4.75886 8.24259i 0.181298 0.314018i
\(690\) 1.21198 4.35977i 0.0461393 0.165974i
\(691\) −3.05236 + 1.76228i −0.116117 + 0.0670402i −0.556934 0.830557i \(-0.688022\pi\)
0.440817 + 0.897597i \(0.354689\pi\)
\(692\) −0.514508 + 5.52147i −0.0195587 + 0.209895i
\(693\) −8.89098 + 0.661126i −0.337741 + 0.0251141i
\(694\) −25.6106 1.19066i −0.972166 0.0451969i
\(695\) −12.7919 22.1562i −0.485223 0.840431i
\(696\) 5.42749 + 6.66880i 0.205728 + 0.252780i
\(697\) −1.81466 + 3.14308i −0.0687350 + 0.119053i
\(698\) 5.01729 7.82669i 0.189907 0.296245i
\(699\) −11.5884 + 3.57090i −0.438315 + 0.135064i
\(700\) −2.71054 5.89954i −0.102449 0.222982i
\(701\) 27.2753i 1.03017i −0.857138 0.515086i \(-0.827760\pi\)
0.857138 0.515086i \(-0.172240\pi\)
\(702\) −29.9747 + 34.1401i −1.13132 + 1.28853i
\(703\) 31.6798 1.19483
\(704\) 23.0656 5.76335i 0.869318 0.217214i
\(705\) 7.99164 + 25.9348i 0.300982 + 0.976762i
\(706\) 28.2758 + 18.1261i 1.06417 + 0.682185i
\(707\) 9.68229 + 5.59007i 0.364140 + 0.210236i
\(708\) −17.4021 + 15.5607i −0.654011 + 0.584808i
\(709\) −5.07687 + 2.93113i −0.190666 + 0.110081i −0.592294 0.805722i \(-0.701778\pi\)
0.401628 + 0.915803i \(0.368444\pi\)
\(710\) 6.63829 + 0.308620i 0.249130 + 0.0115823i
\(711\) −6.24609 3.01240i −0.234246 0.112974i
\(712\) 3.49740 24.9312i 0.131071 0.934337i
\(713\) 6.75956 + 11.7079i 0.253148 + 0.438464i
\(714\) 4.33295 + 1.20452i 0.162157 + 0.0450782i
\(715\) −21.0720 12.1659i −0.788049 0.454980i
\(716\) 41.9776 + 29.7478i 1.56878 + 1.11173i
\(717\) −5.46819 + 23.9259i −0.204213 + 0.893529i
\(718\) −30.4231 + 15.7282i −1.13538 + 0.586973i
\(719\) −9.78534 −0.364932 −0.182466 0.983212i \(-0.558408\pi\)
−0.182466 + 0.983212i \(0.558408\pi\)
\(720\) −6.36358 14.5619i −0.237157 0.542692i
\(721\) −7.13412 −0.265689
\(722\) 4.03574 2.08641i 0.150195 0.0776481i
\(723\) 1.16336 + 1.08006i 0.0432657 + 0.0401679i
\(724\) 31.2034 + 22.1126i 1.15966 + 0.821807i
\(725\) −4.93416 2.84874i −0.183250 0.105800i
\(726\) −1.32655 5.14251i −0.0492327 0.190857i
\(727\) 16.2446 + 28.1365i 0.602480 + 1.04353i 0.992444 + 0.122696i \(0.0391540\pi\)
−0.389964 + 0.920830i \(0.627513\pi\)
\(728\) −17.3171 2.42927i −0.641813 0.0900348i
\(729\) −5.96247 26.3334i −0.220832 0.975312i
\(730\) −23.0642 1.07227i −0.853643 0.0396867i
\(731\) 9.64800 5.57027i 0.356844 0.206024i
\(732\) 2.55333 + 12.2193i 0.0943739 + 0.451637i
\(733\) 38.4902 + 22.2224i 1.42167 + 0.820801i 0.996442 0.0842848i \(-0.0268605\pi\)
0.425228 + 0.905086i \(0.360194\pi\)
\(734\) 11.6619 + 7.47587i 0.430450 + 0.275939i
\(735\) −1.56064 + 1.68100i −0.0575652 + 0.0620046i
\(736\) −7.55865 + 2.26640i −0.278616 + 0.0835406i
\(737\) 2.32006 0.0854606
\(738\) 4.39334 + 7.14384i 0.161721 + 0.262968i
\(739\) 10.6660i 0.392356i 0.980568 + 0.196178i \(0.0628530\pi\)
−0.980568 + 0.196178i \(0.937147\pi\)
\(740\) −7.43277 16.1776i −0.273234 0.594699i
\(741\) −11.2445 + 49.1999i −0.413077 + 1.80740i
\(742\) −1.17496 + 1.83287i −0.0431341 + 0.0672869i
\(743\) −23.2659 + 40.2977i −0.853543 + 1.47838i 0.0244480 + 0.999701i \(0.492217\pi\)
−0.877991 + 0.478678i \(0.841116\pi\)
\(744\) 44.3660 + 16.9055i 1.62654 + 0.619785i
\(745\) −2.96994 5.14409i −0.108810 0.188465i
\(746\) −16.6352 0.773386i −0.609058 0.0283157i
\(747\) −13.2490 + 27.4713i −0.484757 + 1.00512i
\(748\) 1.01249 10.8655i 0.0370201 0.397283i
\(749\) 16.3522 9.44094i 0.597496 0.344964i
\(750\) 18.7373 + 19.0908i 0.684189 + 0.697099i
\(751\) −6.17353 + 10.6929i −0.225275 + 0.390188i −0.956402 0.292054i \(-0.905661\pi\)
0.731127 + 0.682242i \(0.238995\pi\)
\(752\) 30.8276 35.9072i 1.12417 1.30940i
\(753\) −5.74304 18.6376i −0.209288 0.679191i
\(754\) −13.6316 + 7.04731i −0.496434 + 0.256648i
\(755\) 18.4334i 0.670861i
\(756\) 7.21188 7.48257i 0.262294 0.272138i
\(757\) 40.5489i 1.47378i −0.676015 0.736888i \(-0.736294\pi\)
0.676015 0.736888i \(-0.263706\pi\)
\(758\) 12.1851 + 23.5697i 0.442584 + 0.856090i
\(759\) −2.11449 6.86203i −0.0767511 0.249076i
\(760\) −13.9140 10.8651i −0.504712 0.394118i
\(761\) −17.2534 + 29.8838i −0.625436 + 1.08329i 0.363020 + 0.931781i \(0.381746\pi\)
−0.988456 + 0.151506i \(0.951588\pi\)
\(762\) 13.1671 12.9233i 0.476995 0.468161i
\(763\) −8.22871 + 4.75085i −0.297899 + 0.171992i
\(764\) 52.5003 + 4.89215i 1.89939 + 0.176992i
\(765\) −7.27419 + 0.540903i −0.262999 + 0.0195564i
\(766\) −1.56450 + 33.6516i −0.0565275 + 1.21588i
\(767\) −20.8318 36.0817i −0.752192 1.30283i
\(768\) −15.5642 + 22.9294i −0.561624 + 0.827392i
\(769\) −1.10561 + 1.91497i −0.0398692 + 0.0690555i −0.885271 0.465075i \(-0.846027\pi\)
0.845402 + 0.534130i \(0.179361\pi\)
\(770\) 4.68570 + 3.00376i 0.168861 + 0.108248i
\(771\) 7.19515 31.4821i 0.259127 1.13380i
\(772\) −13.9509 30.3644i −0.502104 1.09284i
\(773\) 17.9298i 0.644890i 0.946588 + 0.322445i \(0.104505\pi\)
−0.946588 + 0.322445i \(0.895495\pi\)
\(774\) −0.714684 25.7338i −0.0256888 0.924981i
\(775\) −31.4602 −1.13008
\(776\) 0.697179 0.281884i 0.0250273 0.0101191i
\(777\) 7.92134 8.53223i 0.284176 0.306092i
\(778\) 13.3709 20.8579i 0.479371 0.747794i
\(779\) 8.06829 + 4.65823i 0.289076 + 0.166898i
\(780\) 27.7626 5.80126i 0.994060 0.207719i
\(781\) 9.13225 5.27251i 0.326778 0.188665i
\(782\) −0.168209 + 3.61811i −0.00601516 + 0.129383i
\(783\) 1.36705 9.01681i 0.0488544 0.322235i
\(784\) 3.93113 + 0.739049i 0.140398 + 0.0263946i
\(785\) −9.40239 16.2854i −0.335586 0.581251i
\(786\) 40.1890 10.3670i 1.43349 0.369779i
\(787\) −0.0369277 0.0213202i −0.00131633 0.000759984i 0.499342 0.866405i \(-0.333575\pi\)
−0.500658 + 0.865645i \(0.666909\pi\)
\(788\) −0.887210 0.628729i −0.0316055 0.0223976i
\(789\) 17.7966 + 16.5224i 0.633577 + 0.588214i
\(790\) 1.98812 + 3.84562i 0.0707341 + 0.136821i
\(791\) 11.6812 0.415335
\(792\) −20.9713 14.0035i −0.745183 0.497592i
\(793\) −22.2790 −0.791150
\(794\) 1.30135 + 2.51720i 0.0461832 + 0.0893321i
\(795\) 0.786758 3.44243i 0.0279034 0.122090i
\(796\) −18.3843 + 25.9424i −0.651615 + 0.919504i
\(797\) 27.9380 + 16.1300i 0.989615 + 0.571354i 0.905159 0.425073i \(-0.139752\pi\)
0.0844556 + 0.996427i \(0.473085\pi\)
\(798\) 3.09202 11.1227i 0.109456 0.393739i
\(799\) −10.8611 18.8120i −0.384238 0.665520i
\(800\) 4.22732 17.8702i 0.149458 0.631805i
\(801\) −22.0713 + 15.0293i −0.779851 + 0.531034i
\(802\) −1.38720 + 29.8381i −0.0489838 + 1.05362i
\(803\) −31.7292 + 18.3189i −1.11970 + 0.646459i
\(804\) −2.01595 + 1.80264i −0.0710971 + 0.0635741i
\(805\) −1.59986 0.923682i −0.0563878 0.0325555i
\(806\) −45.7295 + 71.3355i −1.61075 + 2.51269i
\(807\) −4.94627 16.0519i −0.174117 0.565052i
\(808\) 11.8533 + 29.3166i 0.416999 + 1.03135i
\(809\) 36.1200 1.26991 0.634956 0.772549i \(-0.281018\pi\)
0.634956 + 0.772549i \(0.281018\pi\)
\(810\) −6.89786 + 15.3796i −0.242366 + 0.540385i
\(811\) 14.9254i 0.524102i 0.965054 + 0.262051i \(0.0843989\pi\)
−0.965054 + 0.262051i \(0.915601\pi\)
\(812\) 3.18968 1.46550i 0.111936 0.0514288i
\(813\) 21.5705 6.64679i 0.756509 0.233113i
\(814\) −23.7832 15.2462i −0.833600 0.534378i
\(815\) −10.4936 + 18.1755i −0.367576 + 0.636660i
\(816\) 7.56251 + 10.2280i 0.264741 + 0.358050i
\(817\) −14.2989 24.7664i −0.500256 0.866468i
\(818\) 1.31464 28.2774i 0.0459653 0.988694i
\(819\) 10.4393 + 15.3306i 0.364777 + 0.535694i
\(820\) 0.485771 5.21307i 0.0169638 0.182048i
\(821\) 41.4573 23.9354i 1.44687 0.835351i 0.448577 0.893744i \(-0.351931\pi\)
0.998294 + 0.0583926i \(0.0185975\pi\)
\(822\) 36.7556 + 10.2178i 1.28200 + 0.356385i
\(823\) 10.4875 18.1649i 0.365572 0.633189i −0.623296 0.781986i \(-0.714207\pi\)
0.988868 + 0.148797i \(0.0475402\pi\)
\(824\) −15.9039 12.4190i −0.554039 0.432636i
\(825\) 16.2895 + 3.72291i 0.567127 + 0.129615i
\(826\) 4.37675 + 8.46595i 0.152287 + 0.294568i
\(827\) 3.66717i 0.127520i 0.997965 + 0.0637600i \(0.0203092\pi\)
−0.997965 + 0.0637600i \(0.979691\pi\)
\(828\) 7.16897 + 4.31965i 0.249139 + 0.150118i
\(829\) 3.47918i 0.120837i 0.998173 + 0.0604185i \(0.0192435\pi\)
−0.998173 + 0.0604185i \(0.980756\pi\)
\(830\) 16.9137 8.74408i 0.587083 0.303512i
\(831\) 10.7781 11.6093i 0.373887 0.402721i
\(832\) −34.3756 35.5608i −1.19176 1.23285i
\(833\) 0.917999 1.59002i 0.0318068 0.0550910i
\(834\) 45.8207 11.8198i 1.58664 0.409285i
\(835\) 13.0200 7.51708i 0.450574 0.260139i
\(836\) −27.8918 2.59905i −0.964660 0.0898901i
\(837\) −18.3572 46.8926i −0.634516 1.62085i
\(838\) 0.540981 + 0.0251507i 0.0186879 + 0.000868816i
\(839\) 11.3173 + 19.6022i 0.390717 + 0.676742i 0.992544 0.121884i \(-0.0388936\pi\)
−0.601827 + 0.798627i \(0.705560\pi\)
\(840\) −6.40536 + 1.03066i −0.221006 + 0.0355611i
\(841\) −12.9598 + 22.4470i −0.446889 + 0.774035i
\(842\) 27.8994 43.5215i 0.961477 1.49985i
\(843\) 19.0094 + 17.6484i 0.654719 + 0.607842i
\(844\) −20.3228 + 9.33730i −0.699540 + 0.321403i
\(845\) 33.4027i 1.14909i
\(846\) −50.1765 + 1.39352i −1.72510 + 0.0479100i
\(847\) −2.16815 −0.0744984
\(848\) −5.80995 + 2.04062i −0.199514 + 0.0700752i
\(849\) −9.66054 2.20789i −0.331549 0.0757746i
\(850\) −7.09593 4.54883i −0.243388 0.156024i
\(851\) 8.12041 + 4.68832i 0.278364 + 0.160714i
\(852\) −3.83858 + 11.6769i −0.131508 + 0.400046i
\(853\) −15.3908 + 8.88587i −0.526970 + 0.304246i −0.739782 0.672847i \(-0.765071\pi\)
0.212812 + 0.977093i \(0.431738\pi\)
\(854\) 5.09074 + 0.236673i 0.174201 + 0.00809878i
\(855\) 1.38850 + 18.6729i 0.0474857 + 0.638599i
\(856\) 52.8882 + 7.41925i 1.80768 + 0.253585i
\(857\) 21.0571 + 36.4720i 0.719298 + 1.24586i 0.961278 + 0.275579i \(0.0888696\pi\)
−0.241981 + 0.970281i \(0.577797\pi\)
\(858\) 32.1195 31.5247i 1.09654 1.07623i
\(859\) −22.4831 12.9806i −0.767113 0.442893i 0.0647307 0.997903i \(-0.479381\pi\)
−0.831844 + 0.555010i \(0.812715\pi\)
\(860\) −9.29237 + 13.1126i −0.316867 + 0.447137i
\(861\) 3.27201 1.00825i 0.111510 0.0343610i
\(862\) 21.5514 11.1417i 0.734045 0.379489i
\(863\) 46.0325 1.56696 0.783482 0.621415i \(-0.213442\pi\)
0.783482 + 0.621415i \(0.213442\pi\)
\(864\) 29.1028 4.12633i 0.990098 0.140381i
\(865\) −3.67190 −0.124848
\(866\) −17.3053 + 8.94653i −0.588057 + 0.304016i
\(867\) −22.5596 + 6.95157i −0.766163 + 0.236088i
\(868\) 11.2070 15.8143i 0.380390 0.536774i
\(869\) 5.94914 + 3.43474i 0.201811 + 0.116515i
\(870\) −4.06328 + 3.98803i −0.137758 + 0.135207i
\(871\) −2.41326 4.17989i −0.0817703 0.141630i
\(872\) −26.6143 3.73350i −0.901273 0.126432i
\(873\) −0.718436 0.346492i −0.0243154 0.0117270i
\(874\) 9.28771 + 0.431794i 0.314162 + 0.0146057i
\(875\) 9.45744 5.46026i 0.319720 0.184590i
\(876\) 13.3368 40.5706i 0.450609 1.37075i
\(877\) −16.3218 9.42340i −0.551148 0.318205i 0.198437 0.980114i \(-0.436414\pi\)
−0.749585 + 0.661908i \(0.769747\pi\)
\(878\) −17.7287 11.3649i −0.598315 0.383548i
\(879\) −10.1432 2.31821i −0.342123 0.0781913i
\(880\) 5.21680 + 14.8530i 0.175858 + 0.500695i
\(881\) −54.5049 −1.83632 −0.918159 0.396213i \(-0.870324\pi\)
−0.918159 + 0.396213i \(0.870324\pi\)
\(882\) −2.22251 3.61393i −0.0748356 0.121687i
\(883\) 6.26574i 0.210859i −0.994427 0.105429i \(-0.966378\pi\)
0.994427 0.105429i \(-0.0336217\pi\)
\(884\) −20.6288 + 9.47789i −0.693822 + 0.318776i
\(885\) −11.3283 10.5172i −0.380795 0.353531i
\(886\) 3.75088 5.85117i 0.126013 0.196574i
\(887\) 3.88225 6.72425i 0.130353 0.225778i −0.793460 0.608623i \(-0.791722\pi\)
0.923813 + 0.382845i \(0.125056\pi\)
\(888\) 32.5116 5.23131i 1.09102 0.175551i
\(889\) −3.76599 6.52289i −0.126307 0.218771i
\(890\) 16.6519 + 0.774164i 0.558174 + 0.0259500i
\(891\) 3.95584 + 26.4524i 0.132526 + 0.886190i
\(892\) −24.9227 2.32238i −0.834474 0.0777590i
\(893\) −48.2904 + 27.8805i −1.61598 + 0.932985i
\(894\) 10.6384 2.74425i 0.355801 0.0917814i
\(895\) −17.0337 + 29.5033i −0.569375 + 0.986187i
\(896\) 7.47704 + 8.49081i 0.249790 + 0.283658i
\(897\) −10.1634 + 10.9472i −0.339347 + 0.365517i
\(898\) −36.7399 + 18.9939i −1.22603 + 0.633835i
\(899\) 17.0095i 0.567298i
\(900\) −17.0469 + 9.42165i −0.568230 + 0.314055i
\(901\) 2.82647i 0.0941634i
\(902\) −3.81535 7.38003i −0.127037 0.245728i
\(903\) −10.2456 2.34161i −0.340953 0.0779239i
\(904\) 26.0406 + 20.3345i 0.866096 + 0.676314i
\(905\) −12.6618 + 21.9308i −0.420891 + 0.729004i
\(906\) 32.8495 + 9.13189i 1.09135 + 0.303387i
\(907\) 14.6059 8.43273i 0.484981 0.280004i −0.237509 0.971385i \(-0.576331\pi\)
0.722490 + 0.691381i \(0.242998\pi\)
\(908\) 2.72891 29.2854i 0.0905620 0.971870i
\(909\) 14.5701 30.2105i 0.483260 1.00202i
\(910\) 0.537730 11.5663i 0.0178256 0.383420i
\(911\) −16.8269 29.1450i −0.557499 0.965617i −0.997704 0.0677195i \(-0.978428\pi\)
0.440205 0.897897i \(-0.354906\pi\)
\(912\) 26.2552 19.4130i 0.869397 0.642828i
\(913\) 15.1066 26.1653i 0.499954 0.865946i
\(914\) −38.0680 24.4034i −1.25918 0.807194i
\(915\) −7.89925 + 2.43410i −0.261141 + 0.0804689i
\(916\) 49.3220 22.6609i 1.62965 0.748739i
\(917\) 16.9442i 0.559545i
\(918\) 2.63970 13.2310i 0.0871232 0.436689i
\(919\) 20.7288 0.683781 0.341890 0.939740i \(-0.388933\pi\)
0.341890 + 0.939740i \(0.388933\pi\)
\(920\) −1.95860 4.84416i −0.0645731 0.159707i
\(921\) 10.5481 + 34.2313i 0.347573 + 1.12796i
\(922\) −4.54218 + 7.08555i −0.149589 + 0.233350i
\(923\) −18.9982 10.9686i −0.625334 0.361037i
\(924\) −7.67418 + 6.86216i −0.252462 + 0.225748i
\(925\) −18.8969 + 10.9101i −0.621327 + 0.358723i
\(926\) −0.522625 + 11.2414i −0.0171745 + 0.369417i
\(927\) 1.58708 + 21.3434i 0.0521266 + 0.701011i
\(928\) 9.66179 + 2.28557i 0.317164 + 0.0750274i
\(929\) 12.6456 + 21.9028i 0.414888 + 0.718608i 0.995417 0.0956322i \(-0.0304873\pi\)
−0.580528 + 0.814240i \(0.697154\pi\)
\(930\) −8.42009 + 30.2890i −0.276106 + 0.993215i
\(931\) −4.08159 2.35651i −0.133769 0.0772314i
\(932\) −8.09591 + 11.4243i −0.265190 + 0.374215i
\(933\) 3.93000 17.1956i 0.128663 0.562959i
\(934\) 4.29454 + 8.30693i 0.140522 + 0.271811i
\(935\) 7.22581 0.236309
\(936\) −3.41533 + 52.3486i −0.111634 + 1.71107i
\(937\) −43.1018 −1.40807 −0.704037 0.710164i \(-0.748621\pi\)
−0.704037 + 0.710164i \(0.748621\pi\)
\(938\) 0.507026 + 0.980740i 0.0165550 + 0.0320223i
\(939\) 12.1636 + 11.2927i 0.396944 + 0.368523i
\(940\) 25.5674 + 18.1186i 0.833917 + 0.590963i
\(941\) 11.4234 + 6.59531i 0.372393 + 0.215001i 0.674503 0.738272i \(-0.264358\pi\)
−0.302110 + 0.953273i \(0.597691\pi\)
\(942\) 33.6795 8.68787i 1.09734 0.283066i
\(943\) 1.37875 + 2.38807i 0.0448983 + 0.0777662i
\(944\) −4.98045 + 26.4919i −0.162100 + 0.862238i
\(945\) 5.37630 + 4.29508i 0.174891 + 0.139719i
\(946\) −1.18434 + 25.4745i −0.0385061 + 0.828249i
\(947\) −6.29295 + 3.63324i −0.204494 + 0.118064i −0.598750 0.800936i \(-0.704336\pi\)
0.394256 + 0.919001i \(0.371002\pi\)
\(948\) −7.83805 + 1.63784i −0.254568 + 0.0531945i
\(949\) 66.0077 + 38.1096i 2.14270 + 1.23709i
\(950\) −11.6769 + 18.2153i −0.378848 + 0.590982i
\(951\) −26.1913 + 28.2111i −0.849310 + 0.914809i
\(952\) 4.81436 1.94655i 0.156034 0.0630880i
\(953\) −39.9962 −1.29560 −0.647802 0.761809i \(-0.724312\pi\)
−0.647802 + 0.761809i \(0.724312\pi\)
\(954\) 5.74487 + 3.10743i 0.185997 + 0.100607i
\(955\) 34.9138i 1.12979i
\(956\) 11.8316 + 25.7516i 0.382660 + 0.832867i
\(957\) −2.01285 + 8.80717i −0.0650663 + 0.284695i
\(958\) −10.4622 6.70677i −0.338018 0.216686i
\(959\) 7.78721 13.4878i 0.251462 0.435545i
\(960\) −16.0735 8.85275i −0.518769 0.285721i
\(961\) −31.4612 54.4924i −1.01488 1.75782i
\(962\) −2.72935 + 58.7071i −0.0879977 + 1.89279i
\(963\) −31.8826 46.8212i −1.02740 1.50879i
\(964\) 1.82510 + 0.170069i 0.0587824 + 0.00547754i
\(965\) 19.1621 11.0632i 0.616849 0.356138i
\(966\) 2.43863 2.39347i 0.0784616 0.0770085i
\(967\) 25.3681 43.9389i 0.815784 1.41298i −0.0929804 0.995668i \(-0.529639\pi\)
0.908764 0.417311i \(-0.137027\pi\)
\(968\) −4.83339 3.77428i −0.155351 0.121310i
\(969\) −4.41353 14.3230i −0.141783 0.460121i
\(970\) 0.228677 + 0.442330i 0.00734238 + 0.0142024i
\(971\) 5.37369i 0.172450i 0.996276 + 0.0862249i \(0.0274804\pi\)
−0.996276 + 0.0862249i \(0.972520\pi\)
\(972\) −23.9903 19.9115i −0.769488 0.638661i
\(973\) 19.3186i 0.619325i
\(974\) −37.4855 + 19.3794i −1.20111 + 0.620955i
\(975\) −10.2365 33.2201i −0.327832 1.06389i
\(976\) 10.9366 + 9.38950i 0.350073 + 0.300551i
\(977\) −25.8542 + 44.7807i −0.827148 + 1.43266i 0.0731187 + 0.997323i \(0.476705\pi\)
−0.900267 + 0.435339i \(0.856629\pi\)
\(978\) −27.1913 27.7044i −0.869483 0.885889i
\(979\) 22.9080 13.2259i 0.732142 0.422702i
\(980\) −0.245742 + 2.63719i −0.00784993 + 0.0842419i
\(981\) 16.0439 + 23.5613i 0.512242 + 0.752254i
\(982\) −6.36842 0.296074i −0.203225 0.00944810i
\(983\) 9.94753 + 17.2296i 0.317277 + 0.549540i 0.979919 0.199397i \(-0.0638982\pi\)
−0.662642 + 0.748936i \(0.730565\pi\)
\(984\) 9.04936 + 3.44822i 0.288483 + 0.109925i
\(985\) 0.360013 0.623561i 0.0114710 0.0198683i
\(986\) 2.45940 3.83653i 0.0783233 0.122180i
\(987\) −4.56575 + 19.9773i −0.145329 + 0.635884i
\(988\) 24.3298 + 52.9543i 0.774033 + 1.68470i
\(989\) 8.46444i 0.269154i
\(990\) 7.94407 14.6866i 0.252479 0.466772i
\(991\) −15.7154 −0.499217 −0.249609 0.968347i \(-0.580302\pi\)
−0.249609 + 0.968347i \(0.580302\pi\)
\(992\) 52.5128 15.7455i 1.66728 0.499921i
\(993\) 8.66272 9.33079i 0.274903 0.296104i
\(994\) 4.22456 + 2.70815i 0.133995 + 0.0858972i
\(995\) −18.2332 10.5269i −0.578031 0.333726i
\(996\) 7.20348 + 34.4730i 0.228251 + 1.09232i
\(997\) −17.7281 + 10.2353i −0.561455 + 0.324156i −0.753729 0.657185i \(-0.771747\pi\)
0.192275 + 0.981341i \(0.438414\pi\)
\(998\) −33.7097 1.56719i −1.06706 0.0496086i
\(999\) −27.2884 21.8005i −0.863368 0.689737i
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 504.2.cs.a.85.6 72
8.5 even 2 inner 504.2.cs.a.85.30 yes 72
9.7 even 3 inner 504.2.cs.a.421.30 yes 72
72.61 even 6 inner 504.2.cs.a.421.6 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.cs.a.85.6 72 1.1 even 1 trivial
504.2.cs.a.85.30 yes 72 8.5 even 2 inner
504.2.cs.a.421.6 yes 72 72.61 even 6 inner
504.2.cs.a.421.30 yes 72 9.7 even 3 inner