Properties

Label 637.2.h.j.165.3
Level $637$
Weight $2$
Character 637.165
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
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] = [637,2,Mod(165,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.100088711424.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.3
Root \(-2.49541 - 1.44073i\) of defining polynomial
Character \(\chi\) \(=\) 637.165
Dual form 637.2.h.j.471.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.30278 q^{2} +(-1.08365 - 1.87694i) q^{3} +3.30278 q^{4} +(-1.08365 - 1.87694i) q^{5} +(-2.49541 - 4.32218i) q^{6} +3.00000 q^{8} +(-0.848612 + 1.46984i) q^{9} +O(q^{10})\) \(q+2.30278 q^{2} +(-1.08365 - 1.87694i) q^{3} +3.30278 q^{4} +(-1.08365 - 1.87694i) q^{5} +(-2.49541 - 4.32218i) q^{6} +3.00000 q^{8} +(-0.848612 + 1.46984i) q^{9} +(-2.49541 - 4.32218i) q^{10} +(-2.45416 - 4.25074i) q^{11} +(-3.57907 - 6.19912i) q^{12} +(-1.41176 + 3.31767i) q^{13} +(-2.34861 + 4.06792i) q^{15} +0.302776 q^{16} +7.15813 q^{17} +(-1.95416 + 3.38471i) q^{18} +(-1.08365 + 1.87694i) q^{19} +(-3.57907 - 6.19912i) q^{20} +(-5.65139 - 9.78849i) q^{22} -0.605551 q^{23} +(-3.25096 - 5.63083i) q^{24} +(0.151388 - 0.262211i) q^{25} +(-3.25096 + 7.63985i) q^{26} -2.82352 q^{27} +(1.15139 - 1.99426i) q^{29} +(-5.40833 + 9.36750i) q^{30} +(3.57907 - 6.19912i) q^{31} -5.30278 q^{32} +(-5.31893 + 9.21265i) q^{33} +16.4836 q^{34} +(-2.80278 + 4.85455i) q^{36} +8.60555 q^{37} +(-2.49541 + 4.32218i) q^{38} +(7.75694 - 0.945417i) q^{39} +(-3.25096 - 5.63083i) q^{40} +(4.99082 - 8.64436i) q^{41} +(6.25694 + 10.8373i) q^{43} +(-8.10555 - 14.0392i) q^{44} +3.67841 q^{45} -1.39445 q^{46} +(0.755550 + 1.30865i) q^{47} +(-0.328104 - 0.568293i) q^{48} +(0.348612 - 0.603814i) q^{50} +(-7.75694 - 13.4354i) q^{51} +(-4.66272 + 10.9575i) q^{52} +(-1.19722 + 2.07365i) q^{53} -6.50192 q^{54} +(-5.31893 + 9.21265i) q^{55} +4.69722 q^{57} +(2.65139 - 4.59234i) q^{58} -2.82352 q^{59} +(-7.75694 + 13.4354i) q^{60} +(-2.16731 + 3.75389i) q^{61} +(8.24179 - 14.2752i) q^{62} -12.8167 q^{64} +(7.75694 - 0.945417i) q^{65} +(-12.2483 + 21.2147i) q^{66} +(-0.500000 - 0.866025i) q^{67} +23.6417 q^{68} +(0.656208 + 1.13659i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(-2.54584 + 4.40952i) q^{72} +(2.16731 - 3.75389i) q^{73} +19.8167 q^{74} -0.656208 q^{75} +(-3.57907 + 6.19912i) q^{76} +(17.8625 - 2.17708i) q^{78} +(3.30278 + 5.72058i) q^{79} +(-0.328104 - 0.568293i) q^{80} +(5.60555 + 9.70910i) q^{81} +(11.4927 - 19.9060i) q^{82} +2.82352 q^{83} +(-7.75694 - 13.4354i) q^{85} +(14.4083 + 24.9560i) q^{86} -4.99082 q^{87} +(-7.36249 - 12.7522i) q^{88} +6.50192 q^{89} +8.47055 q^{90} -2.00000 q^{92} -15.5139 q^{93} +(1.73986 + 3.01353i) q^{94} +4.69722 q^{95} +(5.74637 + 9.95301i) q^{96} +(6.83003 + 11.8300i) q^{97} +8.33053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{2} + 12 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} - 12 q^{16} + 6 q^{18} - 38 q^{22} + 24 q^{23} - 6 q^{25} + 2 q^{29} - 28 q^{32} - 8 q^{36} + 40 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44} - 40 q^{46} + 10 q^{50} - 26 q^{51} - 24 q^{53} + 52 q^{57} + 14 q^{58} - 26 q^{60} - 16 q^{64} + 26 q^{65} - 4 q^{67} - 16 q^{71} - 42 q^{72} + 72 q^{74} + 78 q^{78} + 12 q^{79} + 16 q^{81} - 26 q^{85} + 72 q^{86} + 6 q^{88} - 16 q^{92} - 52 q^{93} + 52 q^{95} - 92 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30278 1.62831 0.814154 0.580649i \(-0.197201\pi\)
0.814154 + 0.580649i \(0.197201\pi\)
\(3\) −1.08365 1.87694i −0.625648 1.08365i −0.988415 0.151774i \(-0.951501\pi\)
0.362767 0.931880i \(-0.381832\pi\)
\(4\) 3.30278 1.65139
\(5\) −1.08365 1.87694i −0.484625 0.839395i 0.515219 0.857058i \(-0.327711\pi\)
−0.999844 + 0.0176637i \(0.994377\pi\)
\(6\) −2.49541 4.32218i −1.01875 1.76452i
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) −0.848612 + 1.46984i −0.282871 + 0.489946i
\(10\) −2.49541 4.32218i −0.789119 1.36679i
\(11\) −2.45416 4.25074i −0.739958 1.28165i −0.952514 0.304496i \(-0.901512\pi\)
0.212555 0.977149i \(-0.431821\pi\)
\(12\) −3.57907 6.19912i −1.03319 1.78953i
\(13\) −1.41176 + 3.31767i −0.391551 + 0.920156i
\(14\) 0 0
\(15\) −2.34861 + 4.06792i −0.606409 + 1.05033i
\(16\) 0.302776 0.0756939
\(17\) 7.15813 1.73610 0.868051 0.496475i \(-0.165373\pi\)
0.868051 + 0.496475i \(0.165373\pi\)
\(18\) −1.95416 + 3.38471i −0.460601 + 0.797784i
\(19\) −1.08365 + 1.87694i −0.248607 + 0.430600i −0.963140 0.269002i \(-0.913306\pi\)
0.714532 + 0.699602i \(0.246640\pi\)
\(20\) −3.57907 6.19912i −0.800304 1.38617i
\(21\) 0 0
\(22\) −5.65139 9.78849i −1.20488 2.08691i
\(23\) −0.605551 −0.126266 −0.0631331 0.998005i \(-0.520109\pi\)
−0.0631331 + 0.998005i \(0.520109\pi\)
\(24\) −3.25096 5.63083i −0.663600 1.14939i
\(25\) 0.151388 0.262211i 0.0302776 0.0524423i
\(26\) −3.25096 + 7.63985i −0.637566 + 1.49830i
\(27\) −2.82352 −0.543386
\(28\) 0 0
\(29\) 1.15139 1.99426i 0.213807 0.370325i −0.739096 0.673601i \(-0.764747\pi\)
0.952903 + 0.303275i \(0.0980802\pi\)
\(30\) −5.40833 + 9.36750i −0.987421 + 1.71026i
\(31\) 3.57907 6.19912i 0.642819 1.11340i −0.341981 0.939707i \(-0.611098\pi\)
0.984801 0.173689i \(-0.0555687\pi\)
\(32\) −5.30278 −0.937407
\(33\) −5.31893 + 9.21265i −0.925907 + 1.60372i
\(34\) 16.4836 2.82691
\(35\) 0 0
\(36\) −2.80278 + 4.85455i −0.467129 + 0.809092i
\(37\) 8.60555 1.41474 0.707372 0.706842i \(-0.249881\pi\)
0.707372 + 0.706842i \(0.249881\pi\)
\(38\) −2.49541 + 4.32218i −0.404809 + 0.701150i
\(39\) 7.75694 0.945417i 1.24210 0.151388i
\(40\) −3.25096 5.63083i −0.514022 0.890313i
\(41\) 4.99082 8.64436i 0.779436 1.35002i −0.152832 0.988252i \(-0.548839\pi\)
0.932267 0.361770i \(-0.117827\pi\)
\(42\) 0 0
\(43\) 6.25694 + 10.8373i 0.954174 + 1.65268i 0.736247 + 0.676713i \(0.236596\pi\)
0.217928 + 0.975965i \(0.430070\pi\)
\(44\) −8.10555 14.0392i −1.22196 2.11649i
\(45\) 3.67841 0.548345
\(46\) −1.39445 −0.205600
\(47\) 0.755550 + 1.30865i 0.110208 + 0.190886i 0.915854 0.401511i \(-0.131515\pi\)
−0.805646 + 0.592397i \(0.798182\pi\)
\(48\) −0.328104 0.568293i −0.0473577 0.0820260i
\(49\) 0 0
\(50\) 0.348612 0.603814i 0.0493012 0.0853922i
\(51\) −7.75694 13.4354i −1.08619 1.88133i
\(52\) −4.66272 + 10.9575i −0.646603 + 1.51953i
\(53\) −1.19722 + 2.07365i −0.164451 + 0.284838i −0.936460 0.350773i \(-0.885919\pi\)
0.772009 + 0.635612i \(0.219252\pi\)
\(54\) −6.50192 −0.884800
\(55\) −5.31893 + 9.21265i −0.717204 + 1.24223i
\(56\) 0 0
\(57\) 4.69722 0.622163
\(58\) 2.65139 4.59234i 0.348144 0.603004i
\(59\) −2.82352 −0.367590 −0.183795 0.982965i \(-0.558838\pi\)
−0.183795 + 0.982965i \(0.558838\pi\)
\(60\) −7.75694 + 13.4354i −1.00142 + 1.73450i
\(61\) −2.16731 + 3.75389i −0.277495 + 0.480636i −0.970762 0.240045i \(-0.922838\pi\)
0.693266 + 0.720682i \(0.256171\pi\)
\(62\) 8.24179 14.2752i 1.04671 1.81295i
\(63\) 0 0
\(64\) −12.8167 −1.60208
\(65\) 7.75694 0.945417i 0.962130 0.117265i
\(66\) −12.2483 + 21.2147i −1.50766 + 2.61135i
\(67\) −0.500000 0.866025i −0.0610847 0.105802i 0.833866 0.551967i \(-0.186123\pi\)
−0.894951 + 0.446165i \(0.852789\pi\)
\(68\) 23.6417 2.86698
\(69\) 0.656208 + 1.13659i 0.0789982 + 0.136829i
\(70\) 0 0
\(71\) −2.00000 3.46410i −0.237356 0.411113i 0.722599 0.691268i \(-0.242948\pi\)
−0.959955 + 0.280155i \(0.909614\pi\)
\(72\) −2.54584 + 4.40952i −0.300030 + 0.519667i
\(73\) 2.16731 3.75389i 0.253664 0.439359i −0.710868 0.703326i \(-0.751698\pi\)
0.964532 + 0.263967i \(0.0850308\pi\)
\(74\) 19.8167 2.30364
\(75\) −0.656208 −0.0757724
\(76\) −3.57907 + 6.19912i −0.410547 + 0.711088i
\(77\) 0 0
\(78\) 17.8625 2.17708i 2.02253 0.246506i
\(79\) 3.30278 + 5.72058i 0.371591 + 0.643615i 0.989811 0.142391i \(-0.0454789\pi\)
−0.618219 + 0.786006i \(0.712146\pi\)
\(80\) −0.328104 0.568293i −0.0366831 0.0635371i
\(81\) 5.60555 + 9.70910i 0.622839 + 1.07879i
\(82\) 11.4927 19.9060i 1.26916 2.19825i
\(83\) 2.82352 0.309921 0.154961 0.987921i \(-0.450475\pi\)
0.154961 + 0.987921i \(0.450475\pi\)
\(84\) 0 0
\(85\) −7.75694 13.4354i −0.841358 1.45728i
\(86\) 14.4083 + 24.9560i 1.55369 + 2.69107i
\(87\) −4.99082 −0.535073
\(88\) −7.36249 12.7522i −0.784844 1.35939i
\(89\) 6.50192 0.689203 0.344601 0.938749i \(-0.388014\pi\)
0.344601 + 0.938749i \(0.388014\pi\)
\(90\) 8.47055 0.892874
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) −15.5139 −1.60871
\(94\) 1.73986 + 3.01353i 0.179453 + 0.310822i
\(95\) 4.69722 0.481925
\(96\) 5.74637 + 9.95301i 0.586487 + 1.01583i
\(97\) 6.83003 + 11.8300i 0.693484 + 1.20115i 0.970689 + 0.240339i \(0.0772587\pi\)
−0.277205 + 0.960811i \(0.589408\pi\)
\(98\) 0 0
\(99\) 8.33053 0.837250
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 3.25096 + 5.63083i 0.323483 + 0.560289i 0.981204 0.192973i \(-0.0618129\pi\)
−0.657721 + 0.753261i \(0.728480\pi\)
\(102\) −17.8625 30.9387i −1.76865 3.06339i
\(103\) −5.74637 9.95301i −0.566207 0.980699i −0.996936 0.0782182i \(-0.975077\pi\)
0.430729 0.902481i \(-0.358256\pi\)
\(104\) −4.23527 + 9.95301i −0.415303 + 0.975973i
\(105\) 0 0
\(106\) −2.75694 + 4.77516i −0.267778 + 0.463804i
\(107\) 5.69722 0.550771 0.275386 0.961334i \(-0.411194\pi\)
0.275386 + 0.961334i \(0.411194\pi\)
\(108\) −9.32544 −0.897341
\(109\) −4.10555 + 7.11102i −0.393240 + 0.681113i −0.992875 0.119162i \(-0.961979\pi\)
0.599634 + 0.800274i \(0.295313\pi\)
\(110\) −12.2483 + 21.2147i −1.16783 + 2.02274i
\(111\) −9.32544 16.1521i −0.885132 1.53309i
\(112\) 0 0
\(113\) −3.40833 5.90340i −0.320628 0.555345i 0.659989 0.751275i \(-0.270561\pi\)
−0.980618 + 0.195930i \(0.937227\pi\)
\(114\) 10.8167 1.01307
\(115\) 0.656208 + 1.13659i 0.0611917 + 0.105987i
\(116\) 3.80278 6.58660i 0.353079 0.611551i
\(117\) −3.67841 4.89047i −0.340069 0.452124i
\(118\) −6.50192 −0.598551
\(119\) 0 0
\(120\) −7.04584 + 12.2037i −0.643194 + 1.11404i
\(121\) −6.54584 + 11.3377i −0.595076 + 1.03070i
\(122\) −4.99082 + 8.64436i −0.451848 + 0.782624i
\(123\) −21.6333 −1.95061
\(124\) 11.8209 20.4743i 1.06154 1.83865i
\(125\) −11.4927 −1.02794
\(126\) 0 0
\(127\) −3.95416 + 6.84881i −0.350875 + 0.607734i −0.986403 0.164344i \(-0.947449\pi\)
0.635528 + 0.772078i \(0.280783\pi\)
\(128\) −18.9083 −1.67128
\(129\) 13.5607 23.4878i 1.19395 2.06799i
\(130\) 17.8625 2.17708i 1.56664 0.190943i
\(131\) 5.31893 + 9.21265i 0.464717 + 0.804913i 0.999189 0.0402730i \(-0.0128228\pi\)
−0.534472 + 0.845186i \(0.679489\pi\)
\(132\) −17.5672 + 30.4273i −1.52903 + 2.64836i
\(133\) 0 0
\(134\) −1.15139 1.99426i −0.0994648 0.172278i
\(135\) 3.05971 + 5.29958i 0.263338 + 0.456115i
\(136\) 21.4744 1.84141
\(137\) 6.30278 0.538482 0.269241 0.963073i \(-0.413227\pi\)
0.269241 + 0.963073i \(0.413227\pi\)
\(138\) 1.51110 + 2.61730i 0.128633 + 0.222800i
\(139\) 5.31893 + 9.21265i 0.451146 + 0.781407i 0.998457 0.0555216i \(-0.0176822\pi\)
−0.547312 + 0.836929i \(0.684349\pi\)
\(140\) 0 0
\(141\) 1.63751 2.83625i 0.137903 0.238855i
\(142\) −4.60555 7.97705i −0.386489 0.669419i
\(143\) 17.5672 2.14110i 1.46905 0.179047i
\(144\) −0.256939 + 0.445032i −0.0214116 + 0.0370860i
\(145\) −4.99082 −0.414465
\(146\) 4.99082 8.64436i 0.413044 0.715412i
\(147\) 0 0
\(148\) 28.4222 2.33629
\(149\) 8.75694 15.1675i 0.717396 1.24257i −0.244632 0.969616i \(-0.578667\pi\)
0.962028 0.272951i \(-0.0879997\pi\)
\(150\) −1.51110 −0.123381
\(151\) −4.10555 + 7.11102i −0.334105 + 0.578687i −0.983313 0.181924i \(-0.941767\pi\)
0.649207 + 0.760611i \(0.275101\pi\)
\(152\) −3.25096 + 5.63083i −0.263688 + 0.456721i
\(153\) −6.07448 + 10.5213i −0.491092 + 0.850597i
\(154\) 0 0
\(155\) −15.5139 −1.24610
\(156\) 25.6194 3.12250i 2.05120 0.250000i
\(157\) 0.328104 0.568293i 0.0261856 0.0453547i −0.852636 0.522506i \(-0.824997\pi\)
0.878821 + 0.477151i \(0.158331\pi\)
\(158\) 7.60555 + 13.1732i 0.605065 + 1.04800i
\(159\) 5.18951 0.411555
\(160\) 5.74637 + 9.95301i 0.454291 + 0.786855i
\(161\) 0 0
\(162\) 12.9083 + 22.3579i 1.01417 + 1.75660i
\(163\) 1.39445 2.41526i 0.109222 0.189177i −0.806234 0.591597i \(-0.798498\pi\)
0.915455 + 0.402420i \(0.131831\pi\)
\(164\) 16.4836 28.5504i 1.28715 2.22941i
\(165\) 23.0555 1.79487
\(166\) 6.50192 0.504647
\(167\) −5.74637 + 9.95301i −0.444668 + 0.770187i −0.998029 0.0627542i \(-0.980012\pi\)
0.553361 + 0.832941i \(0.313345\pi\)
\(168\) 0 0
\(169\) −9.01388 9.36750i −0.693375 0.720577i
\(170\) −17.8625 30.9387i −1.36999 2.37289i
\(171\) −1.83920 3.18559i −0.140647 0.243609i
\(172\) 20.6653 + 35.7933i 1.57571 + 2.72921i
\(173\) −5.09017 + 8.81643i −0.386998 + 0.670300i −0.992044 0.125890i \(-0.959821\pi\)
0.605046 + 0.796190i \(0.293155\pi\)
\(174\) −11.4927 −0.871263
\(175\) 0 0
\(176\) −0.743061 1.28702i −0.0560103 0.0970127i
\(177\) 3.05971 + 5.29958i 0.229982 + 0.398341i
\(178\) 14.9725 1.12223
\(179\) −10.8028 18.7110i −0.807437 1.39852i −0.914633 0.404285i \(-0.867521\pi\)
0.107196 0.994238i \(-0.465813\pi\)
\(180\) 12.1490 0.905530
\(181\) −24.2979 −1.80605 −0.903025 0.429588i \(-0.858659\pi\)
−0.903025 + 0.429588i \(0.858659\pi\)
\(182\) 0 0
\(183\) 9.39445 0.694458
\(184\) −1.81665 −0.133925
\(185\) −9.32544 16.1521i −0.685620 1.18753i
\(186\) −35.7250 −2.61948
\(187\) −17.5672 30.4273i −1.28464 2.22507i
\(188\) 2.49541 + 4.32218i 0.181997 + 0.315227i
\(189\) 0 0
\(190\) 10.8167 0.784723
\(191\) −7.84861 + 13.5942i −0.567906 + 0.983641i 0.428867 + 0.903368i \(0.358913\pi\)
−0.996773 + 0.0802739i \(0.974421\pi\)
\(192\) 13.8888 + 24.0561i 1.00234 + 1.73610i
\(193\) −9.90833 17.1617i −0.713217 1.23533i −0.963643 0.267192i \(-0.913904\pi\)
0.250426 0.968136i \(-0.419429\pi\)
\(194\) 15.7280 + 27.2417i 1.12921 + 1.95584i
\(195\) −10.1803 13.5348i −0.729029 0.969250i
\(196\) 0 0
\(197\) 0.545837 0.945417i 0.0388892 0.0673581i −0.845926 0.533301i \(-0.820951\pi\)
0.884815 + 0.465943i \(0.154285\pi\)
\(198\) 19.1833 1.36330
\(199\) −7.15813 −0.507427 −0.253713 0.967279i \(-0.581652\pi\)
−0.253713 + 0.967279i \(0.581652\pi\)
\(200\) 0.454163 0.786634i 0.0321142 0.0556234i
\(201\) −1.08365 + 1.87694i −0.0764351 + 0.132389i
\(202\) 7.48624 + 12.9665i 0.526730 + 0.912323i
\(203\) 0 0
\(204\) −25.6194 44.3742i −1.79372 3.10681i
\(205\) −21.6333 −1.51094
\(206\) −13.2326 22.9196i −0.921960 1.59688i
\(207\) 0.513878 0.890063i 0.0357170 0.0618637i
\(208\) −0.427446 + 1.00451i −0.0296380 + 0.0696502i
\(209\) 10.6379 0.735836
\(210\) 0 0
\(211\) −7.50000 + 12.9904i −0.516321 + 0.894295i 0.483499 + 0.875345i \(0.339366\pi\)
−0.999820 + 0.0189499i \(0.993968\pi\)
\(212\) −3.95416 + 6.84881i −0.271573 + 0.470378i
\(213\) −4.33462 + 7.50778i −0.297003 + 0.514424i
\(214\) 13.1194 0.896826
\(215\) 13.5607 23.4878i 0.924833 1.60186i
\(216\) −8.47055 −0.576348
\(217\) 0 0
\(218\) −9.45416 + 16.3751i −0.640317 + 1.10906i
\(219\) −9.39445 −0.634818
\(220\) −17.5672 + 30.4273i −1.18438 + 2.05141i
\(221\) −10.1056 + 23.7483i −0.679773 + 1.59749i
\(222\) −21.4744 37.1947i −1.44127 2.49635i
\(223\) 8.99734 15.5838i 0.602506 1.04357i −0.389934 0.920843i \(-0.627502\pi\)
0.992440 0.122729i \(-0.0391645\pi\)
\(224\) 0 0
\(225\) 0.256939 + 0.445032i 0.0171293 + 0.0296688i
\(226\) −7.84861 13.5942i −0.522082 0.904272i
\(227\) −18.4522 −1.22472 −0.612358 0.790581i \(-0.709779\pi\)
−0.612358 + 0.790581i \(0.709779\pi\)
\(228\) 15.5139 1.02743
\(229\) 7.81434 + 13.5348i 0.516386 + 0.894407i 0.999819 + 0.0190256i \(0.00605640\pi\)
−0.483433 + 0.875381i \(0.660610\pi\)
\(230\) 1.51110 + 2.61730i 0.0996390 + 0.172580i
\(231\) 0 0
\(232\) 3.45416 5.98279i 0.226777 0.392789i
\(233\) 6.54584 + 11.3377i 0.428832 + 0.742759i 0.996770 0.0803127i \(-0.0255919\pi\)
−0.567938 + 0.823072i \(0.692259\pi\)
\(234\) −8.47055 11.2617i −0.553737 0.736198i
\(235\) 1.63751 2.83625i 0.106819 0.185017i
\(236\) −9.32544 −0.607034
\(237\) 7.15813 12.3982i 0.464971 0.805353i
\(238\) 0 0
\(239\) 4.39445 0.284253 0.142127 0.989848i \(-0.454606\pi\)
0.142127 + 0.989848i \(0.454606\pi\)
\(240\) −0.711103 + 1.23167i −0.0459015 + 0.0795037i
\(241\) −9.32544 −0.600704 −0.300352 0.953828i \(-0.597104\pi\)
−0.300352 + 0.953828i \(0.597104\pi\)
\(242\) −15.0736 + 26.1082i −0.968967 + 1.67830i
\(243\) 7.91368 13.7069i 0.507663 0.879298i
\(244\) −7.15813 + 12.3982i −0.458252 + 0.793717i
\(245\) 0 0
\(246\) −49.8167 −3.17619
\(247\) −4.69722 6.24500i −0.298877 0.397360i
\(248\) 10.7372 18.5974i 0.681813 1.18093i
\(249\) −3.05971 5.29958i −0.193902 0.335847i
\(250\) −26.4652 −1.67381
\(251\) −14.9725 25.9331i −0.945054 1.63688i −0.755643 0.654984i \(-0.772675\pi\)
−0.189411 0.981898i \(-0.560658\pi\)
\(252\) 0 0
\(253\) 1.48612 + 2.57404i 0.0934317 + 0.161828i
\(254\) −9.10555 + 15.7713i −0.571333 + 0.989578i
\(255\) −16.8117 + 29.1187i −1.05279 + 1.82348i
\(256\) −17.9083 −1.11927
\(257\) 6.30324 0.393185 0.196593 0.980485i \(-0.437012\pi\)
0.196593 + 0.980485i \(0.437012\pi\)
\(258\) 31.2273 54.0872i 1.94413 3.36732i
\(259\) 0 0
\(260\) 25.6194 3.12250i 1.58885 0.193649i
\(261\) 1.95416 + 3.38471i 0.120960 + 0.209508i
\(262\) 12.2483 + 21.2147i 0.756702 + 1.31065i
\(263\) −7.71110 13.3560i −0.475487 0.823568i 0.524119 0.851645i \(-0.324395\pi\)
−0.999606 + 0.0280776i \(0.991061\pi\)
\(264\) −15.9568 + 27.6380i −0.982072 + 1.70100i
\(265\) 5.18951 0.318789
\(266\) 0 0
\(267\) −7.04584 12.2037i −0.431198 0.746857i
\(268\) −1.65139 2.86029i −0.100875 0.174720i
\(269\) −0.656208 −0.0400097 −0.0200049 0.999800i \(-0.506368\pi\)
−0.0200049 + 0.999800i \(0.506368\pi\)
\(270\) 7.04584 + 12.2037i 0.428796 + 0.742696i
\(271\) 14.5149 0.881720 0.440860 0.897576i \(-0.354673\pi\)
0.440860 + 0.897576i \(0.354673\pi\)
\(272\) 2.16731 0.131412
\(273\) 0 0
\(274\) 14.5139 0.876815
\(275\) −1.48612 −0.0896165
\(276\) 2.16731 + 3.75389i 0.130457 + 0.225957i
\(277\) −0.211103 −0.0126839 −0.00634196 0.999980i \(-0.502019\pi\)
−0.00634196 + 0.999980i \(0.502019\pi\)
\(278\) 12.2483 + 21.2147i 0.734604 + 1.27237i
\(279\) 6.07448 + 10.5213i 0.363670 + 0.629894i
\(280\) 0 0
\(281\) 23.8167 1.42078 0.710391 0.703807i \(-0.248518\pi\)
0.710391 + 0.703807i \(0.248518\pi\)
\(282\) 3.77082 6.53125i 0.224549 0.388930i
\(283\) −9.32544 16.1521i −0.554340 0.960145i −0.997955 0.0639272i \(-0.979637\pi\)
0.443615 0.896218i \(-0.353696\pi\)
\(284\) −6.60555 11.4412i −0.391967 0.678907i
\(285\) −5.09017 8.81643i −0.301515 0.522240i
\(286\) 40.4534 4.93046i 2.39206 0.291544i
\(287\) 0 0
\(288\) 4.50000 7.79423i 0.265165 0.459279i
\(289\) 34.2389 2.01405
\(290\) −11.4927 −0.674877
\(291\) 14.8028 25.6392i 0.867754 1.50299i
\(292\) 7.15813 12.3982i 0.418898 0.725553i
\(293\) 14.3163 + 24.7965i 0.836365 + 1.44863i 0.892914 + 0.450227i \(0.148657\pi\)
−0.0565490 + 0.998400i \(0.518010\pi\)
\(294\) 0 0
\(295\) 3.05971 + 5.29958i 0.178143 + 0.308554i
\(296\) 25.8167 1.50056
\(297\) 6.92937 + 12.0020i 0.402083 + 0.696428i
\(298\) 20.1653 34.9273i 1.16814 2.02328i
\(299\) 0.854892 2.00902i 0.0494397 0.116185i
\(300\) −2.16731 −0.125130
\(301\) 0 0
\(302\) −9.45416 + 16.3751i −0.544026 + 0.942281i
\(303\) 7.04584 12.2037i 0.404773 0.701087i
\(304\) −0.328104 + 0.568293i −0.0188181 + 0.0325938i
\(305\) 9.39445 0.537925
\(306\) −13.9882 + 24.2282i −0.799650 + 1.38503i
\(307\) 3.67841 0.209938 0.104969 0.994476i \(-0.466526\pi\)
0.104969 + 0.994476i \(0.466526\pi\)
\(308\) 0 0
\(309\) −12.4542 + 21.5712i −0.708493 + 1.22715i
\(310\) −35.7250 −2.02904
\(311\) −5.31893 + 9.21265i −0.301609 + 0.522402i −0.976501 0.215515i \(-0.930857\pi\)
0.674892 + 0.737917i \(0.264190\pi\)
\(312\) 23.2708 2.83625i 1.31745 0.160571i
\(313\) 2.82352 + 4.89047i 0.159595 + 0.276426i 0.934723 0.355378i \(-0.115648\pi\)
−0.775128 + 0.631804i \(0.782315\pi\)
\(314\) 0.755550 1.30865i 0.0426382 0.0738514i
\(315\) 0 0
\(316\) 10.9083 + 18.8938i 0.613641 + 1.06286i
\(317\) 3.10555 + 5.37897i 0.174425 + 0.302113i 0.939962 0.341279i \(-0.110860\pi\)
−0.765537 + 0.643392i \(0.777527\pi\)
\(318\) 11.9503 0.670138
\(319\) −11.3028 −0.632834
\(320\) 13.8888 + 24.0561i 0.776409 + 1.34478i
\(321\) −6.17382 10.6934i −0.344589 0.596846i
\(322\) 0 0
\(323\) −7.75694 + 13.4354i −0.431608 + 0.747566i
\(324\) 18.5139 + 32.0670i 1.02855 + 1.78150i
\(325\) 0.656208 + 0.872434i 0.0363999 + 0.0483939i
\(326\) 3.21110 5.56179i 0.177847 0.308039i
\(327\) 17.7960 0.984120
\(328\) 14.9725 25.9331i 0.826717 1.43192i
\(329\) 0 0
\(330\) 53.0917 2.92260
\(331\) −2.15139 + 3.72631i −0.118251 + 0.204817i −0.919075 0.394084i \(-0.871062\pi\)
0.800824 + 0.598900i \(0.204395\pi\)
\(332\) 9.32544 0.511800
\(333\) −7.30278 + 12.6488i −0.400190 + 0.693149i
\(334\) −13.2326 + 22.9196i −0.724056 + 1.25410i
\(335\) −1.08365 + 1.87694i −0.0592063 + 0.102548i
\(336\) 0 0
\(337\) 18.1194 0.987028 0.493514 0.869738i \(-0.335712\pi\)
0.493514 + 0.869738i \(0.335712\pi\)
\(338\) −20.7569 21.5712i −1.12903 1.17332i
\(339\) −7.38689 + 12.7945i −0.401201 + 0.694901i
\(340\) −25.6194 44.3742i −1.38941 2.40653i
\(341\) −35.1345 −1.90264
\(342\) −4.23527 7.33571i −0.229017 0.396670i
\(343\) 0 0
\(344\) 18.7708 + 32.5120i 1.01205 + 1.75293i
\(345\) 1.42221 2.46333i 0.0765689 0.132621i
\(346\) −11.7215 + 20.3023i −0.630152 + 1.09146i
\(347\) 15.2111 0.816575 0.408287 0.912853i \(-0.366126\pi\)
0.408287 + 0.912853i \(0.366126\pi\)
\(348\) −16.4836 −0.883612
\(349\) −5.09017 + 8.81643i −0.272470 + 0.471932i −0.969494 0.245116i \(-0.921174\pi\)
0.697023 + 0.717048i \(0.254507\pi\)
\(350\) 0 0
\(351\) 3.98612 9.36750i 0.212763 0.500000i
\(352\) 13.0139 + 22.5407i 0.693642 + 1.20142i
\(353\) 13.2326 + 22.9196i 0.704301 + 1.21988i 0.966943 + 0.254992i \(0.0820727\pi\)
−0.262642 + 0.964893i \(0.584594\pi\)
\(354\) 7.04584 + 12.2037i 0.374482 + 0.648622i
\(355\) −4.33462 + 7.50778i −0.230058 + 0.398471i
\(356\) 21.4744 1.13814
\(357\) 0 0
\(358\) −24.8764 43.0871i −1.31476 2.27723i
\(359\) 6.04584 + 10.4717i 0.319087 + 0.552675i 0.980298 0.197525i \(-0.0632904\pi\)
−0.661211 + 0.750200i \(0.729957\pi\)
\(360\) 11.0352 0.581607
\(361\) 7.15139 + 12.3866i 0.376389 + 0.651925i
\(362\) −55.9526 −2.94081
\(363\) 28.3737 1.48923
\(364\) 0 0
\(365\) −9.39445 −0.491728
\(366\) 21.6333 1.13079
\(367\) −12.8052 22.1792i −0.668424 1.15774i −0.978345 0.206982i \(-0.933636\pi\)
0.309921 0.950762i \(-0.399698\pi\)
\(368\) −0.183346 −0.00955758
\(369\) 8.47055 + 14.6714i 0.440959 + 0.763764i
\(370\) −21.4744 37.1947i −1.11640 1.93366i
\(371\) 0 0
\(372\) −51.2389 −2.65661
\(373\) 6.34861 10.9961i 0.328719 0.569357i −0.653539 0.756893i \(-0.726717\pi\)
0.982258 + 0.187535i \(0.0600499\pi\)
\(374\) −40.4534 70.0673i −2.09179 3.62309i
\(375\) 12.4542 + 21.5712i 0.643130 + 1.11393i
\(376\) 2.26665 + 3.92595i 0.116894 + 0.202466i
\(377\) 4.99082 + 6.63534i 0.257041 + 0.341737i
\(378\) 0 0
\(379\) 6.05971 10.4957i 0.311267 0.539130i −0.667370 0.744726i \(-0.732580\pi\)
0.978637 + 0.205596i \(0.0659134\pi\)
\(380\) 15.5139 0.795845
\(381\) 17.1398 0.878098
\(382\) −18.0736 + 31.3044i −0.924725 + 1.60167i
\(383\) 11.1646 19.3377i 0.570487 0.988112i −0.426029 0.904709i \(-0.640088\pi\)
0.996516 0.0834025i \(-0.0265787\pi\)
\(384\) 20.4901 + 35.4899i 1.04563 + 1.81108i
\(385\) 0 0
\(386\) −22.8167 39.5196i −1.16134 2.01149i
\(387\) −21.2389 −1.07963
\(388\) 22.5581 + 39.0717i 1.14521 + 1.98356i
\(389\) −14.5139 + 25.1388i −0.735883 + 1.27459i 0.218452 + 0.975848i \(0.429899\pi\)
−0.954335 + 0.298739i \(0.903434\pi\)
\(390\) −23.4430 31.1677i −1.18708 1.57824i
\(391\) −4.33462 −0.219211
\(392\) 0 0
\(393\) 11.5278 19.9667i 0.581498 1.00718i
\(394\) 1.25694 2.17708i 0.0633237 0.109680i
\(395\) 7.15813 12.3982i 0.360165 0.623824i
\(396\) 27.5139 1.38262
\(397\) −2.16731 + 3.75389i −0.108774 + 0.188402i −0.915274 0.402832i \(-0.868026\pi\)
0.806500 + 0.591234i \(0.201359\pi\)
\(398\) −16.4836 −0.826247
\(399\) 0 0
\(400\) 0.0458365 0.0793912i 0.00229183 0.00396956i
\(401\) −10.1194 −0.505340 −0.252670 0.967552i \(-0.581309\pi\)
−0.252670 + 0.967552i \(0.581309\pi\)
\(402\) −2.49541 + 4.32218i −0.124460 + 0.215571i
\(403\) 15.5139 + 20.6258i 0.772801 + 1.02745i
\(404\) 10.7372 + 18.5974i 0.534196 + 0.925254i
\(405\) 12.1490 21.0426i 0.603687 1.04562i
\(406\) 0 0
\(407\) −21.1194 36.5799i −1.04685 1.81320i
\(408\) −23.2708 40.3062i −1.15208 1.99546i
\(409\) 3.47972 0.172061 0.0860306 0.996292i \(-0.472582\pi\)
0.0860306 + 0.996292i \(0.472582\pi\)
\(410\) −49.8167 −2.46027
\(411\) −6.83003 11.8300i −0.336900 0.583529i
\(412\) −18.9790 32.8726i −0.935027 1.61952i
\(413\) 0 0
\(414\) 1.18335 2.04962i 0.0581583 0.100733i
\(415\) −3.05971 5.29958i −0.150195 0.260146i
\(416\) 7.48624 17.5929i 0.367043 0.862561i
\(417\) 11.5278 19.9667i 0.564517 0.977772i
\(418\) 24.4966 1.19817
\(419\) 8.56989 14.8435i 0.418667 0.725152i −0.577139 0.816646i \(-0.695831\pi\)
0.995806 + 0.0914942i \(0.0291643\pi\)
\(420\) 0 0
\(421\) 5.02776 0.245038 0.122519 0.992466i \(-0.460903\pi\)
0.122519 + 0.992466i \(0.460903\pi\)
\(422\) −17.2708 + 29.9139i −0.840730 + 1.45619i
\(423\) −2.56468 −0.124699
\(424\) −3.59167 + 6.22096i −0.174427 + 0.302117i
\(425\) 1.08365 1.87694i 0.0525649 0.0910452i
\(426\) −9.98165 + 17.2887i −0.483612 + 0.837641i
\(427\) 0 0
\(428\) 18.8167 0.909537
\(429\) −23.0555 30.6525i −1.11313 1.47992i
\(430\) 31.2273 54.0872i 1.50591 2.60832i
\(431\) 10.4680 + 18.1312i 0.504228 + 0.873348i 0.999988 + 0.00488877i \(0.00155615\pi\)
−0.495760 + 0.868459i \(0.665111\pi\)
\(432\) −0.854892 −0.0411310
\(433\) −8.56989 14.8435i −0.411843 0.713332i 0.583249 0.812294i \(-0.301781\pi\)
−0.995091 + 0.0989613i \(0.968448\pi\)
\(434\) 0 0
\(435\) 5.40833 + 9.36750i 0.259309 + 0.449137i
\(436\) −13.5597 + 23.4861i −0.649393 + 1.12478i
\(437\) 0.656208 1.13659i 0.0313907 0.0543703i
\(438\) −21.6333 −1.03368
\(439\) −3.67841 −0.175561 −0.0877804 0.996140i \(-0.527977\pi\)
−0.0877804 + 0.996140i \(0.527977\pi\)
\(440\) −15.9568 + 27.6380i −0.760710 + 1.31759i
\(441\) 0 0
\(442\) −23.2708 + 54.6871i −1.10688 + 2.60120i
\(443\) 10.1194 + 17.5274i 0.480789 + 0.832750i 0.999757 0.0220431i \(-0.00701711\pi\)
−0.518968 + 0.854793i \(0.673684\pi\)
\(444\) −30.7998 53.3469i −1.46170 2.53173i
\(445\) −7.04584 12.2037i −0.334005 0.578513i
\(446\) 20.7188 35.8861i 0.981066 1.69926i
\(447\) −37.9580 −1.79535
\(448\) 0 0
\(449\) 10.2111 + 17.6861i 0.481892 + 0.834661i 0.999784 0.0207849i \(-0.00661652\pi\)
−0.517892 + 0.855446i \(0.673283\pi\)
\(450\) 0.591673 + 1.02481i 0.0278917 + 0.0483099i
\(451\) −48.9932 −2.30700
\(452\) −11.2569 19.4976i −0.529482 0.917090i
\(453\) 17.7960 0.836129
\(454\) −42.4913 −1.99421
\(455\) 0 0
\(456\) 14.0917 0.659903
\(457\) 20.6056 0.963887 0.481944 0.876202i \(-0.339931\pi\)
0.481944 + 0.876202i \(0.339931\pi\)
\(458\) 17.9947 + 31.1677i 0.840836 + 1.45637i
\(459\) −20.2111 −0.943373
\(460\) 2.16731 + 3.75389i 0.101051 + 0.175026i
\(461\) 12.5764 + 21.7830i 0.585741 + 1.01453i 0.994783 + 0.102018i \(0.0325299\pi\)
−0.409041 + 0.912516i \(0.634137\pi\)
\(462\) 0 0
\(463\) −13.7889 −0.640824 −0.320412 0.947278i \(-0.603821\pi\)
−0.320412 + 0.947278i \(0.603821\pi\)
\(464\) 0.348612 0.603814i 0.0161839 0.0280314i
\(465\) 16.8117 + 29.1187i 0.779623 + 1.35035i
\(466\) 15.0736 + 26.1082i 0.698271 + 1.20944i
\(467\) −6.40258 11.0896i −0.296276 0.513165i 0.679005 0.734134i \(-0.262412\pi\)
−0.975281 + 0.220968i \(0.929078\pi\)
\(468\) −12.1490 16.1521i −0.561586 0.746633i
\(469\) 0 0
\(470\) 3.77082 6.53125i 0.173935 0.301264i
\(471\) −1.42221 −0.0655318
\(472\) −8.47055 −0.389889
\(473\) 30.7111 53.1932i 1.41210 2.44583i
\(474\) 16.4836 28.5504i 0.757116 1.31136i
\(475\) 0.328104 + 0.568293i 0.0150544 + 0.0260751i
\(476\) 0 0
\(477\) −2.03196 3.51946i −0.0930370 0.161145i
\(478\) 10.1194 0.462852
\(479\) 8.24179 + 14.2752i 0.376577 + 0.652250i 0.990562 0.137068i \(-0.0437678\pi\)
−0.613985 + 0.789318i \(0.710434\pi\)
\(480\) 12.4542 21.5712i 0.568452 0.984588i
\(481\) −12.1490 + 28.5504i −0.553945 + 1.30179i
\(482\) −21.4744 −0.978132
\(483\) 0 0
\(484\) −21.6194 + 37.4460i −0.982701 + 1.70209i
\(485\) 14.8028 25.6392i 0.672159 1.16421i
\(486\) 18.2234 31.5639i 0.826632 1.43177i
\(487\) −31.3028 −1.41846 −0.709232 0.704975i \(-0.750958\pi\)
−0.709232 + 0.704975i \(0.750958\pi\)
\(488\) −6.50192 + 11.2617i −0.294328 + 0.509792i
\(489\) −6.04440 −0.273337
\(490\) 0 0
\(491\) −9.86249 + 17.0823i −0.445088 + 0.770915i −0.998058 0.0622859i \(-0.980161\pi\)
0.552970 + 0.833201i \(0.313494\pi\)
\(492\) −71.4500 −3.22121
\(493\) 8.24179 14.2752i 0.371191 0.642922i
\(494\) −10.8167 14.3808i −0.486664 0.647024i
\(495\) −9.02741 15.6359i −0.405752 0.702783i
\(496\) 1.08365 1.87694i 0.0486575 0.0842773i
\(497\) 0 0
\(498\) −7.04584 12.2037i −0.315731 0.546863i
\(499\) 4.16527 + 7.21445i 0.186463 + 0.322963i 0.944069 0.329749i \(-0.106964\pi\)
−0.757606 + 0.652713i \(0.773631\pi\)
\(500\) −37.9580 −1.69753
\(501\) 24.9083 1.11282
\(502\) −34.4782 59.7181i −1.53884 2.66535i
\(503\) 9.75289 + 16.8925i 0.434860 + 0.753199i 0.997284 0.0736495i \(-0.0234646\pi\)
−0.562424 + 0.826849i \(0.690131\pi\)
\(504\) 0 0
\(505\) 7.04584 12.2037i 0.313536 0.543060i
\(506\) 3.42221 + 5.92743i 0.152136 + 0.263507i
\(507\) −7.81434 + 27.0697i −0.347047 + 1.20221i
\(508\) −13.0597 + 22.6201i −0.579431 + 1.00360i
\(509\) 21.4744 0.951836 0.475918 0.879490i \(-0.342116\pi\)
0.475918 + 0.879490i \(0.342116\pi\)
\(510\) −38.7135 + 67.0538i −1.71426 + 2.96919i
\(511\) 0 0
\(512\) −3.42221 −0.151242
\(513\) 3.05971 5.29958i 0.135090 0.233982i
\(514\) 14.5149 0.640227
\(515\) −12.4542 + 21.5712i −0.548796 + 0.950543i
\(516\) 44.7880 77.5751i 1.97168 3.41505i
\(517\) 3.70849 6.42329i 0.163099 0.282496i
\(518\) 0 0
\(519\) 22.0639 0.968498
\(520\) 23.2708 2.83625i 1.02049 0.124378i
\(521\) 10.8365 18.7694i 0.474757 0.822304i −0.524825 0.851210i \(-0.675869\pi\)
0.999582 + 0.0289063i \(0.00920245\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) 24.2979 1.06247 0.531237 0.847223i \(-0.321727\pi\)
0.531237 + 0.847223i \(0.321727\pi\)
\(524\) 17.5672 + 30.4273i 0.767428 + 1.32922i
\(525\) 0 0
\(526\) −17.7569 30.7559i −0.774239 1.34102i
\(527\) 25.6194 44.3742i 1.11600 1.93297i
\(528\) −1.61044 + 2.78937i −0.0700855 + 0.121392i
\(529\) −22.6333 −0.984057
\(530\) 11.9503 0.519087
\(531\) 2.39607 4.15012i 0.103981 0.180100i
\(532\) 0 0
\(533\) 21.6333 + 28.7617i 0.937043 + 1.24581i
\(534\) −16.2250 28.1025i −0.702124 1.21611i
\(535\) −6.17382 10.6934i −0.266918 0.462315i
\(536\) −1.50000 2.59808i −0.0647901 0.112220i
\(537\) −23.4129 + 40.5524i −1.01034 + 1.74997i
\(538\) −1.51110 −0.0651481
\(539\) 0 0
\(540\) 10.1056 + 17.5033i 0.434874 + 0.753223i
\(541\) −13.9680 24.1934i −0.600533 1.04015i −0.992740 0.120277i \(-0.961622\pi\)
0.392207 0.919877i \(-0.371712\pi\)
\(542\) 33.4247 1.43571
\(543\) 26.3305 + 45.6058i 1.12995 + 1.95713i
\(544\) −37.9580 −1.62743
\(545\) 17.7960 0.762296
\(546\) 0 0
\(547\) 29.0000 1.23995 0.619975 0.784621i \(-0.287143\pi\)
0.619975 + 0.784621i \(0.287143\pi\)
\(548\) 20.8167 0.889243
\(549\) −3.67841 6.37119i −0.156991 0.271916i
\(550\) −3.42221 −0.145923
\(551\) 2.49541 + 4.32218i 0.106308 + 0.184131i
\(552\) 1.96862 + 3.40976i 0.0837902 + 0.145129i
\(553\) 0 0
\(554\) −0.486122 −0.0206533
\(555\) −20.2111 + 35.0067i −0.857914 + 1.48595i
\(556\) 17.5672 + 30.4273i 0.745016 + 1.29041i
\(557\) −3.04584 5.27554i −0.129056 0.223532i 0.794255 0.607585i \(-0.207861\pi\)
−0.923311 + 0.384053i \(0.874528\pi\)
\(558\) 13.9882 + 24.2282i 0.592166 + 1.02566i
\(559\) −44.7880 + 5.45877i −1.89433 + 0.230881i
\(560\) 0 0
\(561\) −38.0736 + 65.9454i −1.60747 + 2.78422i
\(562\) 54.8444 2.31347
\(563\) 1.31242 0.0553117 0.0276559 0.999618i \(-0.491196\pi\)
0.0276559 + 0.999618i \(0.491196\pi\)
\(564\) 5.40833 9.36750i 0.227732 0.394443i
\(565\) −7.38689 + 12.7945i −0.310769 + 0.538268i
\(566\) −21.4744 37.1947i −0.902636 1.56341i
\(567\) 0 0
\(568\) −6.00000 10.3923i −0.251754 0.436051i
\(569\) −34.6056 −1.45074 −0.725370 0.688359i \(-0.758331\pi\)
−0.725370 + 0.688359i \(0.758331\pi\)
\(570\) −11.7215 20.3023i −0.490960 0.850368i
\(571\) 5.36249 9.28811i 0.224413 0.388695i −0.731730 0.681595i \(-0.761287\pi\)
0.956143 + 0.292899i \(0.0946201\pi\)
\(572\) 58.0206 7.07156i 2.42596 0.295677i
\(573\) 34.0207 1.42124
\(574\) 0 0
\(575\) −0.0916731 + 0.158782i −0.00382303 + 0.00662169i
\(576\) 10.8764 18.8384i 0.453182 0.784934i
\(577\) −16.5829 + 28.7225i −0.690356 + 1.19573i 0.281366 + 0.959601i \(0.409213\pi\)
−0.971721 + 0.236131i \(0.924121\pi\)
\(578\) 78.8444 3.27950
\(579\) −21.4744 + 37.1947i −0.892445 + 1.54576i
\(580\) −16.4836 −0.684443
\(581\) 0 0
\(582\) 34.0875 59.0412i 1.41297 2.44734i
\(583\) 11.7527 0.486749
\(584\) 6.50192 11.2617i 0.269052 0.466011i
\(585\) −5.19302 + 12.2037i −0.214705 + 0.504563i
\(586\) 32.9671 + 57.1008i 1.36186 + 2.35881i
\(587\) −0.984312 + 1.70488i −0.0406269 + 0.0703679i −0.885624 0.464403i \(-0.846269\pi\)
0.844997 + 0.534771i \(0.179602\pi\)
\(588\) 0 0
\(589\) 7.75694 + 13.4354i 0.319619 + 0.553597i
\(590\) 7.04584 + 12.2037i 0.290072 + 0.502420i
\(591\) −2.36599 −0.0973239
\(592\) 2.60555 0.107087
\(593\) −3.15162 5.45877i −0.129422 0.224165i 0.794031 0.607877i \(-0.207979\pi\)
−0.923453 + 0.383712i \(0.874645\pi\)
\(594\) 15.9568 + 27.6380i 0.654715 + 1.13400i
\(595\) 0 0
\(596\) 28.9222 50.0947i 1.18470 2.05196i
\(597\) 7.75694 + 13.4354i 0.317470 + 0.549875i
\(598\) 1.96862 4.62632i 0.0805030 0.189184i
\(599\) 5.25694 9.10529i 0.214793 0.372032i −0.738416 0.674346i \(-0.764426\pi\)
0.953208 + 0.302314i \(0.0977591\pi\)
\(600\) −1.96862 −0.0803687
\(601\) −4.56338 + 7.90400i −0.186144 + 0.322411i −0.943961 0.330056i \(-0.892932\pi\)
0.757817 + 0.652467i \(0.226266\pi\)
\(602\) 0 0
\(603\) 1.69722 0.0691163
\(604\) −13.5597 + 23.4861i −0.551737 + 0.955636i
\(605\) 28.3737 1.15355
\(606\) 16.2250 28.1025i 0.659095 1.14159i
\(607\) −19.4064 + 33.6129i −0.787683 + 1.36431i 0.139701 + 0.990194i \(0.455386\pi\)
−0.927383 + 0.374113i \(0.877947\pi\)
\(608\) 5.74637 9.95301i 0.233046 0.403648i
\(609\) 0 0
\(610\) 21.6333 0.875907
\(611\) −5.40833 + 0.659168i −0.218797 + 0.0266671i
\(612\) −20.0626 + 34.7495i −0.810984 + 1.40467i
\(613\) −15.9542 27.6334i −0.644383 1.11610i −0.984444 0.175700i \(-0.943781\pi\)
0.340061 0.940403i \(-0.389552\pi\)
\(614\) 8.47055 0.341844
\(615\) 23.4430 + 40.6045i 0.945314 + 1.63733i
\(616\) 0 0
\(617\) −7.92221 13.7217i −0.318936 0.552413i 0.661330 0.750095i \(-0.269992\pi\)
−0.980266 + 0.197681i \(0.936659\pi\)
\(618\) −28.6791 + 49.6737i −1.15364 + 1.99817i
\(619\) 14.9725 25.9331i 0.601794 1.04234i −0.390755 0.920495i \(-0.627786\pi\)
0.992549 0.121844i \(-0.0388807\pi\)
\(620\) −51.2389 −2.05780
\(621\) 1.70978 0.0686113
\(622\) −12.2483 + 21.2147i −0.491112 + 0.850631i
\(623\) 0 0
\(624\) 2.34861 0.286249i 0.0940197 0.0114591i
\(625\) 11.6972 + 20.2602i 0.467889 + 0.810407i
\(626\) 6.50192 + 11.2617i 0.259869 + 0.450107i
\(627\) −11.5278 19.9667i −0.460374 0.797392i
\(628\) 1.08365 1.87694i 0.0432425 0.0748982i
\(629\) 61.5997 2.45614
\(630\) 0 0
\(631\) −11.4542 19.8392i −0.455983 0.789786i 0.542761 0.839887i \(-0.317379\pi\)
−0.998744 + 0.0501013i \(0.984046\pi\)
\(632\) 9.90833 + 17.1617i 0.394132 + 0.682657i
\(633\) 32.5096 1.29214
\(634\) 7.15139 + 12.3866i 0.284018 + 0.491933i
\(635\) 17.1398 0.680171
\(636\) 17.1398 0.679637
\(637\) 0 0
\(638\) −26.0278 −1.03045
\(639\) 6.78890 0.268565
\(640\) 20.4901 + 35.4899i 0.809942 + 1.40286i
\(641\) −14.5139 −0.573264 −0.286632 0.958041i \(-0.592536\pi\)
−0.286632 + 0.958041i \(0.592536\pi\)
\(642\) −14.2169 24.6244i −0.561097 0.971849i
\(643\) −8.56989 14.8435i −0.337963 0.585370i 0.646086 0.763265i \(-0.276405\pi\)
−0.984050 + 0.177895i \(0.943071\pi\)
\(644\) 0 0
\(645\) −58.7805 −2.31448
\(646\) −17.8625 + 30.9387i −0.702790 + 1.21727i
\(647\) 16.4836 + 28.5504i 0.648036 + 1.12243i 0.983591 + 0.180411i \(0.0577428\pi\)
−0.335555 + 0.942021i \(0.608924\pi\)
\(648\) 16.8167 + 29.1273i 0.660621 + 1.14423i
\(649\) 6.92937 + 12.0020i 0.272002 + 0.471121i
\(650\) 1.51110 + 2.00902i 0.0592702 + 0.0788002i
\(651\) 0 0
\(652\) 4.60555 7.97705i 0.180367 0.312405i
\(653\) −46.7527 −1.82958 −0.914788 0.403934i \(-0.867642\pi\)
−0.914788 + 0.403934i \(0.867642\pi\)
\(654\) 40.9802 1.60245
\(655\) 11.5278 19.9667i 0.450427 0.780162i
\(656\) 1.51110 2.61730i 0.0589985 0.102188i
\(657\) 3.67841 + 6.37119i 0.143508 + 0.248564i
\(658\) 0 0
\(659\) 9.81665 + 17.0029i 0.382403 + 0.662341i 0.991405 0.130828i \(-0.0417634\pi\)
−0.609003 + 0.793168i \(0.708430\pi\)
\(660\) 76.1472 2.96403
\(661\) 11.4927 + 19.9060i 0.447016 + 0.774255i 0.998190 0.0601356i \(-0.0191533\pi\)
−0.551174 + 0.834390i \(0.685820\pi\)
\(662\) −4.95416 + 8.58086i −0.192549 + 0.333505i
\(663\) 55.5252 6.76742i 2.15642 0.262825i
\(664\) 8.47055 0.328721
\(665\) 0 0
\(666\) −16.8167 + 29.1273i −0.651632 + 1.12866i
\(667\) −0.697224 + 1.20763i −0.0269966 + 0.0467595i
\(668\) −18.9790 + 32.8726i −0.734319 + 1.27188i
\(669\) −39.0000 −1.50783
\(670\) −2.49541 + 4.32218i −0.0964062 + 0.166980i
\(671\) 21.2757 0.821340
\(672\) 0 0
\(673\) 1.10555 1.91487i 0.0426159 0.0738129i −0.843931 0.536452i \(-0.819764\pi\)
0.886547 + 0.462639i \(0.153098\pi\)
\(674\) 41.7250 1.60719
\(675\) −0.427446 + 0.740358i −0.0164524 + 0.0284964i
\(676\) −29.7708 30.9387i −1.14503 1.18995i
\(677\) 13.2326 + 22.9196i 0.508571 + 0.880870i 0.999951 + 0.00992485i \(0.00315923\pi\)
−0.491380 + 0.870945i \(0.663507\pi\)
\(678\) −17.0104 + 29.4628i −0.653279 + 1.13151i
\(679\) 0 0
\(680\) −23.2708 40.3062i −0.892395 1.54567i
\(681\) 19.9958 + 34.6337i 0.766241 + 1.32717i
\(682\) −80.9068 −3.09808
\(683\) −3.60555 −0.137963 −0.0689813 0.997618i \(-0.521975\pi\)
−0.0689813 + 0.997618i \(0.521975\pi\)
\(684\) −6.07448 10.5213i −0.232263 0.402292i
\(685\) −6.83003 11.8300i −0.260962 0.451999i
\(686\) 0 0
\(687\) 16.9361 29.3342i 0.646152 1.11917i
\(688\) 1.89445 + 3.28128i 0.0722252 + 0.125098i
\(689\) −5.18951 6.89949i −0.197705 0.262850i
\(690\) 3.27502 5.67250i 0.124678 0.215948i
\(691\) −37.7593 −1.43643 −0.718215 0.695821i \(-0.755041\pi\)
−0.718215 + 0.695821i \(0.755041\pi\)
\(692\) −16.8117 + 29.1187i −0.639084 + 1.10693i
\(693\) 0 0
\(694\) 35.0278 1.32964
\(695\) 11.5278 19.9667i 0.437273 0.757379i
\(696\) −14.9725 −0.567530
\(697\) 35.7250 61.8775i 1.35318 2.34378i
\(698\) −11.7215 + 20.3023i −0.443666 + 0.768452i
\(699\) 14.1868 24.5723i 0.536596 0.929411i
\(700\) 0 0
\(701\) 9.02776 0.340974 0.170487 0.985360i \(-0.445466\pi\)
0.170487 + 0.985360i \(0.445466\pi\)
\(702\) 9.17914 21.5712i 0.346444 0.814154i
\(703\) −9.32544 + 16.1521i −0.351716 + 0.609189i
\(704\) 31.4542 + 54.4802i 1.18547 + 2.05330i
\(705\) −7.09798 −0.267325
\(706\) 30.4717 + 52.7786i 1.14682 + 1.98635i
\(707\) 0 0
\(708\) 10.1056 + 17.5033i 0.379790 + 0.657815i
\(709\) −16.3625 + 28.3407i −0.614506 + 1.06436i 0.375965 + 0.926634i \(0.377311\pi\)
−0.990471 + 0.137722i \(0.956022\pi\)
\(710\) −9.98165 + 17.2887i −0.374605 + 0.648834i
\(711\) −11.2111 −0.420449
\(712\) 19.5058 0.731010
\(713\) −2.16731 + 3.75389i −0.0811663 + 0.140584i
\(714\) 0 0
\(715\) −23.0555 30.6525i −0.862227 1.14634i
\(716\) −35.6791 61.7981i −1.33339 2.30950i
\(717\) −4.76206 8.24813i −0.177842 0.308032i
\(718\) 13.9222 + 24.1140i 0.519572 + 0.899925i
\(719\) 11.3934 19.7340i 0.424902 0.735952i −0.571509 0.820596i \(-0.693642\pi\)
0.996411 + 0.0846433i \(0.0269751\pi\)
\(720\) 1.11373 0.0415064
\(721\) 0 0
\(722\) 16.4680 + 28.5235i 0.612877 + 1.06153i
\(723\) 10.1056 + 17.5033i 0.375829 + 0.650956i
\(724\) −80.2506 −2.98249
\(725\) −0.348612 0.603814i −0.0129471 0.0224251i
\(726\) 65.3382 2.42493
\(727\) 37.1031 1.37608 0.688038 0.725674i \(-0.258472\pi\)
0.688038 + 0.725674i \(0.258472\pi\)
\(728\) 0 0
\(729\) −0.669468 −0.0247951
\(730\) −21.6333 −0.800685
\(731\) 44.7880 + 77.5751i 1.65654 + 2.86922i
\(732\) 31.0278 1.14682
\(733\) 3.35030 + 5.80290i 0.123746 + 0.214335i 0.921242 0.388990i \(-0.127176\pi\)
−0.797496 + 0.603324i \(0.793842\pi\)
\(734\) −29.4874 51.0737i −1.08840 1.88517i
\(735\) 0 0
\(736\) 3.21110 0.118363
\(737\) −2.45416 + 4.25074i −0.0904003 + 0.156578i
\(738\) 19.5058 + 33.7850i 0.718017 + 1.24364i
\(739\) 16.6056 + 28.7617i 0.610845 + 1.05801i 0.991098 + 0.133132i \(0.0425035\pi\)
−0.380253 + 0.924882i \(0.624163\pi\)
\(740\) −30.7998 53.3469i −1.13222 1.96107i
\(741\) −6.63134 + 15.5838i −0.243609 + 0.572487i
\(742\) 0 0
\(743\) 20.6514 35.7693i 0.757626 1.31225i −0.186432 0.982468i \(-0.559692\pi\)
0.944058 0.329779i \(-0.106974\pi\)
\(744\) −46.5416 −1.70630
\(745\) −37.9580 −1.39067
\(746\) 14.6194 25.3216i 0.535255 0.927089i
\(747\) −2.39607 + 4.15012i −0.0876676 + 0.151845i
\(748\) −58.0206 100.495i −2.12144 3.67445i
\(749\) 0 0
\(750\) 28.6791 + 49.6737i 1.04721 + 1.81383i
\(751\) −11.6056 −0.423493 −0.211746 0.977325i \(-0.567915\pi\)
−0.211746 + 0.977325i \(0.567915\pi\)
\(752\) 0.228762 + 0.396228i 0.00834210 + 0.0144489i
\(753\) −32.4500 + 56.2050i −1.18254 + 2.04822i
\(754\) 11.4927 + 15.2797i 0.418541 + 0.556454i
\(755\) 17.7960 0.647662
\(756\) 0 0
\(757\) −3.11943 + 5.40301i −0.113378 + 0.196376i −0.917130 0.398588i \(-0.869500\pi\)
0.803752 + 0.594964i \(0.202834\pi\)
\(758\) 13.9542 24.1693i 0.506838 0.877869i
\(759\) 3.22088 5.57873i 0.116911 0.202495i
\(760\) 14.0917 0.511159
\(761\) 21.1463 36.6265i 0.766553 1.32771i −0.172869 0.984945i \(-0.555304\pi\)
0.939422 0.342763i \(-0.111363\pi\)
\(762\) 39.4691 1.42981
\(763\) 0 0
\(764\) −25.9222 + 44.8986i −0.937832 + 1.62437i
\(765\) 26.3305 0.951982
\(766\) 25.7097 44.5305i 0.928928 1.60895i
\(767\) 3.98612 9.36750i 0.143931 0.338241i
\(768\) 19.4064 + 33.6129i 0.700269 + 1.21290i
\(769\) −23.5424 + 40.7766i −0.848959 + 1.47044i 0.0331785 + 0.999449i \(0.489437\pi\)
−0.882138 + 0.470991i \(0.843896\pi\)
\(770\) 0 0
\(771\) −6.83053 11.8308i −0.245996 0.426077i
\(772\) −32.7250 56.6813i −1.17780 2.04001i
\(773\) 28.4338 1.02269 0.511347 0.859374i \(-0.329147\pi\)
0.511347 + 0.859374i \(0.329147\pi\)
\(774\) −48.9083 −1.75797
\(775\) −1.08365 1.87694i −0.0389260 0.0674218i
\(776\) 20.4901 + 35.4899i 0.735551 + 1.27401i
\(777\) 0 0
\(778\) −33.4222 + 57.8890i −1.19824 + 2.07542i
\(779\) 10.8167 + 18.7350i 0.387547 + 0.671251i
\(780\) −33.6234 44.7025i −1.20391 1.60061i
\(781\) −9.81665 + 17.0029i −0.351267 + 0.608413i
\(782\) −9.98165 −0.356943
\(783\) −3.25096 + 5.63083i −0.116180 + 0.201230i
\(784\) 0 0
\(785\) −1.42221 −0.0507607
\(786\) 26.5458 45.9787i 0.946859 1.64001i
\(787\) −31.2574 −1.11420 −0.557102 0.830444i \(-0.688087\pi\)
−0.557102 + 0.830444i \(0.688087\pi\)
\(788\) 1.80278 3.12250i 0.0642212 0.111234i
\(789\) −16.7123 + 28.9466i −0.594975 + 1.03053i
\(790\) 16.4836 28.5504i 0.586459 1.01578i
\(791\) 0 0
\(792\) 24.9916 0.888038
\(793\) −9.39445 12.4900i −0.333607 0.443533i
\(794\) −4.99082 + 8.64436i −0.177118 + 0.306777i
\(795\) −5.62363 9.74042i −0.199450 0.345457i
\(796\) −23.6417 −0.837958
\(797\) −13.0038 22.5233i −0.460620 0.797817i 0.538372 0.842707i \(-0.319040\pi\)
−0.998992 + 0.0448902i \(0.985706\pi\)
\(798\) 0 0
\(799\) 5.40833 + 9.36750i 0.191333 + 0.331398i
\(800\) −0.802776 + 1.39045i −0.0283824 + 0.0491598i
\(801\) −5.51761 + 9.55678i −0.194955 + 0.337672i
\(802\) −23.3028 −0.822850
\(803\) −21.2757 −0.750804
\(804\) −3.57907 + 6.19912i −0.126224 + 0.218626i
\(805\) 0 0
\(806\) 35.7250 + 47.4967i 1.25836 + 1.67300i
\(807\) 0.711103 + 1.23167i 0.0250320 + 0.0433567i
\(808\) 9.75289 + 16.8925i 0.343105 + 0.594276i
\(809\) −10.0139 17.3445i −0.352069 0.609802i 0.634543 0.772888i \(-0.281188\pi\)
−0.986612 + 0.163086i \(0.947855\pi\)
\(810\) 27.9763 48.4564i 0.982988 1.70258i
\(811\) 0.854892 0.0300193 0.0150097 0.999887i \(-0.495222\pi\)
0.0150097 + 0.999887i \(0.495222\pi\)
\(812\) 0 0
\(813\) −15.7292 27.2437i −0.551647 0.955480i
\(814\) −48.6333 84.2354i −1.70460 2.95245i
\(815\) −6.04440 −0.211726
\(816\) −2.34861 4.06792i −0.0822179 0.142406i
\(817\) −27.1214 −0.948859
\(818\) 8.01302 0.280169
\(819\) 0 0
\(820\) −71.4500 −2.49514
\(821\) −55.8444 −1.94898 −0.974492 0.224424i \(-0.927950\pi\)
−0.974492 + 0.224424i \(0.927950\pi\)
\(822\) −15.7280 27.2417i −0.548578 0.950165i
\(823\) 42.2666 1.47332 0.736661 0.676262i \(-0.236401\pi\)
0.736661 + 0.676262i \(0.236401\pi\)
\(824\) −17.2391 29.8590i −0.600553 1.04019i
\(825\) 1.61044 + 2.78937i 0.0560684 + 0.0971133i
\(826\) 0 0
\(827\) −16.7527 −0.582550 −0.291275 0.956639i \(-0.594079\pi\)
−0.291275 + 0.956639i \(0.594079\pi\)
\(828\) 1.69722 2.93968i 0.0589826 0.102161i
\(829\) −25.3816 43.9622i −0.881538 1.52687i −0.849631 0.527378i \(-0.823175\pi\)
−0.0319077 0.999491i \(-0.510158\pi\)
\(830\) −7.04584 12.2037i −0.244565 0.423598i
\(831\) 0.228762 + 0.396228i 0.00793567 + 0.0137450i
\(832\) 18.0940 42.5214i 0.627297 1.47417i
\(833\) 0 0
\(834\) 26.5458 45.9787i 0.919207 1.59211i
\(835\) 24.9083 0.861988
\(836\) 35.1345 1.21515
\(837\) −10.1056 + 17.5033i −0.349299 + 0.605004i
\(838\) 19.7345 34.1812i 0.681718 1.18077i
\(839\) −6.73069 11.6579i −0.232369 0.402475i 0.726136 0.687551i \(-0.241314\pi\)
−0.958505 + 0.285076i \(0.907981\pi\)
\(840\) 0 0
\(841\) 11.8486 + 20.5224i 0.408573 + 0.707669i
\(842\) 11.5778 0.398997
\(843\) −25.8090 44.7025i −0.888910 1.53964i
\(844\) −24.7708 + 42.9043i −0.852647 + 1.47683i
\(845\) −7.81434 + 27.0697i −0.268821 + 0.931225i
\(846\) −5.90587 −0.203048
\(847\) 0 0
\(848\) −0.362490 + 0.627852i −0.0124480 + 0.0215605i
\(849\) −20.2111 + 35.0067i −0.693643 + 1.20143i
\(850\) 2.49541 4.32218i 0.0855919 0.148250i
\(851\) −5.21110 −0.178634
\(852\) −14.3163 + 24.7965i −0.490467 + 0.849514i
\(853\) 12.8052 0.438440 0.219220 0.975675i \(-0.429649\pi\)
0.219220 + 0.975675i \(0.429649\pi\)
\(854\) 0 0
\(855\) −3.98612 + 6.90417i −0.136322 + 0.236117i
\(856\) 17.0917 0.584181
\(857\) −1.64052 + 2.84146i −0.0560391 + 0.0970626i −0.892684 0.450683i \(-0.851180\pi\)
0.836645 + 0.547746i \(0.184514\pi\)
\(858\) −53.0917 70.5858i −1.81252 2.40976i
\(859\) −1.51110 2.61730i −0.0515581 0.0893012i 0.839095 0.543986i \(-0.183085\pi\)
−0.890653 + 0.454684i \(0.849752\pi\)
\(860\) 44.7880 77.5751i 1.52726 2.64529i
\(861\) 0 0
\(862\) 24.1056 + 41.7520i 0.821038 + 1.42208i
\(863\) −4.90833 8.50147i −0.167081 0.289393i 0.770311 0.637668i \(-0.220101\pi\)
−0.937392 + 0.348275i \(0.886768\pi\)
\(864\) 14.9725 0.509374
\(865\) 22.0639 0.750196
\(866\) −19.7345 34.1812i −0.670607 1.16153i
\(867\) −37.1031 64.2644i −1.26009 2.18253i
\(868\) 0 0
\(869\) 16.2111 28.0785i 0.549924 0.952496i
\(870\) 12.4542 + 21.5712i 0.422236 + 0.731334i
\(871\) 3.57907 0.436217i 0.121272 0.0147806i
\(872\) −12.3167 + 21.3331i −0.417095 + 0.722429i
\(873\) −23.1842 −0.784666
\(874\) 1.51110 2.61730i 0.0511137 0.0885316i
\(875\) 0 0
\(876\) −31.0278 −1.04833
\(877\) 22.8028 39.4956i 0.769995 1.33367i −0.167570 0.985860i \(-0.553592\pi\)
0.937565 0.347810i \(-0.113075\pi\)
\(878\) −8.47055 −0.285867
\(879\) 31.0278 53.7417i 1.04654 1.81266i
\(880\) −1.61044 + 2.78937i −0.0542880 + 0.0940295i
\(881\) −9.42478 + 16.3242i −0.317529 + 0.549976i −0.979972 0.199136i \(-0.936186\pi\)
0.662443 + 0.749112i \(0.269520\pi\)
\(882\) 0 0
\(883\) −24.3944 −0.820939 −0.410469 0.911874i \(-0.634635\pi\)
−0.410469 + 0.911874i \(0.634635\pi\)
\(884\) −33.3764 + 78.4354i −1.12257 + 2.63807i
\(885\) 6.63134 11.4858i 0.222910 0.386092i
\(886\) 23.3028 + 40.3616i 0.782872 + 1.35597i
\(887\) 34.6769 1.16434 0.582169 0.813068i \(-0.302204\pi\)
0.582169 + 0.813068i \(0.302204\pi\)
\(888\) −27.9763 48.4564i −0.938824 1.62609i
\(889\) 0 0
\(890\) −16.2250 28.1025i −0.543863 0.941998i
\(891\) 27.5139 47.6554i 0.921750 1.59652i
\(892\) 29.7162 51.4699i 0.994971 1.72334i
\(893\) −3.27502 −0.109594
\(894\) −87.4087 −2.92338
\(895\) −23.4129 + 40.5524i −0.782608 + 1.35552i
\(896\) 0 0
\(897\) −4.69722 + 0.572498i −0.156836 + 0.0191152i
\(898\) 23.5139 + 40.7272i 0.784668 + 1.35909i
\(899\) −8.24179 14.2752i −0.274879 0.476104i
\(900\) 0.848612 + 1.46984i 0.0282871 + 0.0489946i
\(901\) −8.56989 + 14.8435i −0.285504 + 0.494508i
\(902\) −112.820 −3.75651
\(903\) 0 0
\(904\) −10.2250 17.7102i −0.340078 0.589032i
\(905\) 26.3305 + 45.6058i 0.875256 + 1.51599i
\(906\) 40.9802 1.36147
\(907\) 19.4222 + 33.6402i 0.644904 + 1.11701i 0.984324 + 0.176371i \(0.0564359\pi\)
−0.339420 + 0.940635i \(0.610231\pi\)
\(908\) −60.9435 −2.02248
\(909\) −11.0352 −0.366015
\(910\) 0 0
\(911\) 35.9361 1.19062 0.595308 0.803498i \(-0.297030\pi\)
0.595308 + 0.803498i \(0.297030\pi\)
\(912\) 1.42221 0.0470939
\(913\) −6.92937 12.0020i −0.229329 0.397209i
\(914\) 47.4500 1.56951
\(915\) −10.1803 17.6329i −0.336551 0.582924i
\(916\) 25.8090 + 44.7025i 0.852754 + 1.47701i
\(917\) 0 0
\(918\) −46.5416 −1.53610
\(919\) −26.7250 + 46.2890i −0.881576 + 1.52693i −0.0319871 + 0.999488i \(0.510184\pi\)
−0.849589 + 0.527446i \(0.823150\pi\)
\(920\) 1.96862 + 3.40976i 0.0649036 + 0.112416i
\(921\) −3.98612 6.90417i −0.131347 0.227500i
\(922\) 28.9606 + 50.1613i 0.953768 + 1.65197i
\(923\) 14.3163 1.74487i 0.471226 0.0574330i
\(924\) 0 0
\(925\) 1.30278 2.25647i 0.0428350 0.0741924i
\(926\) −31.7527 −1.04346
\(927\) 19.5058 0.640654
\(928\) −6.10555 + 10.5751i −0.200425 + 0.347145i
\(929\) 8.56989 14.8435i 0.281169 0.486999i −0.690504 0.723329i \(-0.742611\pi\)
0.971673 + 0.236330i \(0.0759445\pi\)
\(930\) 38.7135 + 67.0538i 1.26947 + 2.19878i
\(931\) 0 0
\(932\) 21.6194 + 37.4460i 0.708168 + 1.22658i
\(933\) 23.0555 0.754804
\(934\) −14.7437 25.5369i −0.482429 0.835591i
\(935\) −38.0736 + 65.9454i −1.24514 + 2.15665i
\(936\) −11.0352 14.6714i −0.360698 0.479550i
\(937\) −19.7646 −0.645682 −0.322841 0.946453i \(-0.604638\pi\)
−0.322841 + 0.946453i \(0.604638\pi\)
\(938\) 0 0
\(939\) 6.11943 10.5992i 0.199700 0.345891i
\(940\) 5.40833 9.36750i 0.176400 0.305534i
\(941\) 2.72417 4.71841i 0.0888055 0.153816i −0.818201 0.574932i \(-0.805028\pi\)
0.907006 + 0.421117i \(0.138362\pi\)
\(942\) −3.27502 −0.106706
\(943\) −3.02220 + 5.23460i −0.0984164 + 0.170462i
\(944\) −0.854892 −0.0278244
\(945\) 0 0
\(946\) 70.7208 122.492i 2.29933 3.98256i
\(947\) 27.8806 0.905997 0.452998 0.891511i \(-0.350354\pi\)
0.452998 + 0.891511i \(0.350354\pi\)
\(948\) 23.6417 40.9486i 0.767847 1.32995i
\(949\) 9.39445 + 12.4900i 0.304957 + 0.405442i
\(950\) 0.755550 + 1.30865i 0.0245133 + 0.0424582i
\(951\) 6.73069 11.6579i 0.218257 0.378033i
\(952\) 0 0
\(953\) −17.1972 29.7865i −0.557073 0.964878i −0.997739 0.0672073i \(-0.978591\pi\)
0.440666 0.897671i \(-0.354742\pi\)
\(954\) −4.67914 8.10452i −0.151493 0.262393i
\(955\) 34.0207 1.10088
\(956\) 14.5139 0.469412
\(957\) 12.2483 + 21.2147i 0.395931 + 0.685773i
\(958\) 18.9790 + 32.8726i 0.613183 + 1.06206i
\(959\) 0 0
\(960\) 30.1013 52.1371i 0.971517 1.68272i
\(961\) −10.1194 17.5274i −0.326433 0.565399i
\(962\) −27.9763 + 65.7451i −0.901993 + 2.11971i
\(963\) −4.83473 + 8.37400i −0.155797 + 0.269849i
\(964\) −30.7998 −0.991996
\(965\) −21.4744 + 37.1947i −0.691285 + 1.19734i
\(966\) 0 0
\(967\) −42.4500 −1.36510 −0.682549 0.730839i \(-0.739129\pi\)
−0.682549 + 0.730839i \(0.739129\pi\)
\(968\) −19.6375 + 34.0132i −0.631173 + 1.09322i
\(969\) 33.6234 1.08014
\(970\) 34.0875 59.0412i 1.09448 1.89570i
\(971\) 15.7280 27.2417i 0.504736 0.874229i −0.495249 0.868751i \(-0.664923\pi\)
0.999985 0.00547764i \(-0.00174359\pi\)
\(972\) 26.1371 45.2708i 0.838348 1.45206i
\(973\) 0 0
\(974\) −72.0833 −2.30970
\(975\) 0.926407 2.17708i 0.0296688 0.0697224i
\(976\) −0.656208 + 1.13659i −0.0210047 + 0.0363812i
\(977\) 1.98612 + 3.44006i 0.0635417 + 0.110057i 0.896046 0.443961i \(-0.146427\pi\)
−0.832504 + 0.554018i \(0.813094\pi\)
\(978\) −13.9189 −0.445077
\(979\) −15.9568 27.6380i −0.509981 0.883313i
\(980\) 0 0
\(981\) −6.96804 12.0690i −0.222472 0.385334i
\(982\) −22.7111 + 39.3368i −0.724740 + 1.25529i
\(983\) −14.6444 + 25.3648i −0.467083 + 0.809011i −0.999293 0.0376012i \(-0.988028\pi\)
0.532210 + 0.846612i \(0.321362\pi\)
\(984\) −64.8999 −2.06893
\(985\) −2.36599 −0.0753868
\(986\) 18.9790 32.8726i 0.604414 1.04688i
\(987\) 0 0
\(988\) −15.5139 20.6258i −0.493562 0.656195i
\(989\) −3.78890 6.56256i −0.120480 0.208677i
\(990\) −20.7881 36.0061i −0.660690 1.14435i
\(991\) 3.33473 + 5.77593i 0.105931 + 0.183478i 0.914118 0.405448i \(-0.132884\pi\)
−0.808187 + 0.588926i \(0.799551\pi\)
\(992\) −18.9790 + 32.8726i −0.602583 + 1.04371i
\(993\) 9.32544 0.295934
\(994\) 0 0
\(995\) 7.75694 + 13.4354i 0.245912 + 0.425931i
\(996\) −10.1056 17.5033i −0.320207 0.554614i
\(997\) 52.7318 1.67003 0.835016 0.550226i \(-0.185458\pi\)
0.835016 + 0.550226i \(0.185458\pi\)
\(998\) 9.59167 + 16.6133i 0.303619 + 0.525884i
\(999\) −24.2979 −0.768752
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 637.2.h.j.165.3 8
7.2 even 3 637.2.g.i.373.2 8
7.3 odd 6 637.2.f.h.295.2 yes 8
7.4 even 3 637.2.f.h.295.1 8
7.5 odd 6 637.2.g.i.373.1 8
7.6 odd 2 inner 637.2.h.j.165.4 8
13.3 even 3 637.2.g.i.263.2 8
91.3 odd 6 637.2.f.h.393.2 yes 8
91.4 even 6 8281.2.a.bo.1.2 4
91.16 even 3 inner 637.2.h.j.471.3 8
91.17 odd 6 8281.2.a.bo.1.1 4
91.55 odd 6 637.2.g.i.263.1 8
91.68 odd 6 inner 637.2.h.j.471.4 8
91.74 even 3 8281.2.a.bu.1.4 4
91.81 even 3 637.2.f.h.393.1 yes 8
91.87 odd 6 8281.2.a.bu.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.h.295.1 8 7.4 even 3
637.2.f.h.295.2 yes 8 7.3 odd 6
637.2.f.h.393.1 yes 8 91.81 even 3
637.2.f.h.393.2 yes 8 91.3 odd 6
637.2.g.i.263.1 8 91.55 odd 6
637.2.g.i.263.2 8 13.3 even 3
637.2.g.i.373.1 8 7.5 odd 6
637.2.g.i.373.2 8 7.2 even 3
637.2.h.j.165.3 8 1.1 even 1 trivial
637.2.h.j.165.4 8 7.6 odd 2 inner
637.2.h.j.471.3 8 91.16 even 3 inner
637.2.h.j.471.4 8 91.68 odd 6 inner
8281.2.a.bo.1.1 4 91.17 odd 6
8281.2.a.bo.1.2 4 91.4 even 6
8281.2.a.bu.1.3 4 91.87 odd 6
8281.2.a.bu.1.4 4 91.74 even 3