Properties

Label 525.2.g.f.524.10
Level $525$
Weight $2$
Character 525.524
Analytic conductor $4.192$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(524,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.524");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 32x^{14} + 386x^{12} + 2208x^{10} + 6263x^{8} + 8496x^{6} + 4790x^{4} + 704x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 524.10
Root \(0.378617i\) of defining polynomial
Character \(\chi\) \(=\) 525.524
Dual form 525.2.g.f.524.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.09941 q^{2} +(-0.323042 + 1.70166i) q^{3} -0.791288 q^{4} +(-0.355157 + 1.87083i) q^{6} +(-2.44949 - 1.00000i) q^{7} -3.06878 q^{8} +(-2.79129 - 1.09941i) q^{9} +O(q^{10})\) \(q+1.09941 q^{2} +(-0.323042 + 1.70166i) q^{3} -0.791288 q^{4} +(-0.355157 + 1.87083i) q^{6} +(-2.44949 - 1.00000i) q^{7} -3.06878 q^{8} +(-2.79129 - 1.09941i) q^{9} -3.06878i q^{11} +(0.255619 - 1.34650i) q^{12} -2.44949 q^{13} +(-2.69300 - 1.09941i) q^{14} -1.79129 q^{16} +2.69300i q^{17} +(-3.06878 - 1.20871i) q^{18} +4.38774i q^{19} +(2.49295 - 3.84515i) q^{21} -3.37386i q^{22} -5.26761 q^{23} +(0.991345 - 5.22202i) q^{24} -2.69300 q^{26} +(2.77253 - 4.39466i) q^{27} +(1.93825 + 0.791288i) q^{28} -5.26761i q^{29} -6.83723i q^{31} +4.16820 q^{32} +(5.22202 + 0.991345i) q^{33} +2.96073i q^{34} +(2.20871 + 0.869953i) q^{36} +8.58258i q^{37} +4.82395i q^{38} +(0.791288 - 4.16820i) q^{39} -10.2100 q^{41} +(2.74078 - 4.22742i) q^{42} +6.58258i q^{43} +2.42829i q^{44} -5.79129 q^{46} +2.69300i q^{47} +(0.578661 - 3.04816i) q^{48} +(5.00000 + 4.89898i) q^{49} +(-4.58258 - 0.869953i) q^{51} +1.93825 q^{52} +3.93874 q^{53} +(3.04816 - 4.83156i) q^{54} +(7.51695 + 3.06878i) q^{56} +(-7.46644 - 1.41742i) q^{57} -5.79129i q^{58} -7.51695 q^{59} +6.83723i q^{61} -7.51695i q^{62} +(5.73782 + 5.48429i) q^{63} +8.16515 q^{64} +(5.74117 + 1.08990i) q^{66} +4.16515i q^{67} -2.13094i q^{68} +(1.70166 - 8.96368i) q^{69} -3.06878i q^{71} +(8.56585 + 3.37386i) q^{72} -16.1240 q^{73} +9.43581i q^{74} -3.47197i q^{76} +(-3.06878 + 7.51695i) q^{77} +(0.869953 - 4.58258i) q^{78} -0.582576 q^{79} +(6.58258 + 6.13756i) q^{81} -11.2250 q^{82} -15.5960i q^{83} +(-1.97264 + 3.04262i) q^{84} +7.23698i q^{86} +(8.96368 + 1.70166i) q^{87} +9.41742i q^{88} +7.51695 q^{89} +(6.00000 + 2.44949i) q^{91} +4.16820 q^{92} +(11.6346 + 2.20871i) q^{93} +2.96073i q^{94} +(-1.34650 + 7.09285i) q^{96} -11.7362 q^{97} +(5.49707 + 5.38601i) q^{98} +(-3.37386 + 8.56585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 24 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 24 q^{4} - 8 q^{9} + 8 q^{16} - 24 q^{21} + 72 q^{36} - 24 q^{39} - 56 q^{46} + 80 q^{49} - 16 q^{64} + 64 q^{79} + 32 q^{81} - 120 q^{84} + 96 q^{91} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09941 0.777403 0.388702 0.921364i \(-0.372924\pi\)
0.388702 + 0.921364i \(0.372924\pi\)
\(3\) −0.323042 + 1.70166i −0.186508 + 0.982453i
\(4\) −0.791288 −0.395644
\(5\) 0 0
\(6\) −0.355157 + 1.87083i −0.144992 + 0.763763i
\(7\) −2.44949 1.00000i −0.925820 0.377964i
\(8\) −3.06878 −1.08498
\(9\) −2.79129 1.09941i −0.930429 0.366471i
\(10\) 0 0
\(11\) 3.06878i 0.925273i −0.886548 0.462636i \(-0.846904\pi\)
0.886548 0.462636i \(-0.153096\pi\)
\(12\) 0.255619 1.34650i 0.0737909 0.388702i
\(13\) −2.44949 −0.679366 −0.339683 0.940540i \(-0.610320\pi\)
−0.339683 + 0.940540i \(0.610320\pi\)
\(14\) −2.69300 1.09941i −0.719736 0.293831i
\(15\) 0 0
\(16\) −1.79129 −0.447822
\(17\) 2.69300i 0.653150i 0.945171 + 0.326575i \(0.105894\pi\)
−0.945171 + 0.326575i \(0.894106\pi\)
\(18\) −3.06878 1.20871i −0.723319 0.284896i
\(19\) 4.38774i 1.00662i 0.864107 + 0.503308i \(0.167884\pi\)
−0.864107 + 0.503308i \(0.832116\pi\)
\(20\) 0 0
\(21\) 2.49295 3.84515i 0.544006 0.839082i
\(22\) 3.37386i 0.719310i
\(23\) −5.26761 −1.09837 −0.549186 0.835700i \(-0.685062\pi\)
−0.549186 + 0.835700i \(0.685062\pi\)
\(24\) 0.991345 5.22202i 0.202358 1.06594i
\(25\) 0 0
\(26\) −2.69300 −0.528142
\(27\) 2.77253 4.39466i 0.533574 0.845753i
\(28\) 1.93825 + 0.791288i 0.366295 + 0.149539i
\(29\) 5.26761i 0.978171i −0.872236 0.489085i \(-0.837331\pi\)
0.872236 0.489085i \(-0.162669\pi\)
\(30\) 0 0
\(31\) 6.83723i 1.22800i −0.789305 0.614001i \(-0.789559\pi\)
0.789305 0.614001i \(-0.210441\pi\)
\(32\) 4.16820 0.736840
\(33\) 5.22202 + 0.991345i 0.909037 + 0.172571i
\(34\) 2.96073i 0.507761i
\(35\) 0 0
\(36\) 2.20871 + 0.869953i 0.368119 + 0.144992i
\(37\) 8.58258i 1.41097i 0.708726 + 0.705483i \(0.249270\pi\)
−0.708726 + 0.705483i \(0.750730\pi\)
\(38\) 4.82395i 0.782547i
\(39\) 0.791288 4.16820i 0.126707 0.667446i
\(40\) 0 0
\(41\) −10.2100 −1.59453 −0.797264 0.603631i \(-0.793720\pi\)
−0.797264 + 0.603631i \(0.793720\pi\)
\(42\) 2.74078 4.22742i 0.422912 0.652305i
\(43\) 6.58258i 1.00383i 0.864916 + 0.501917i \(0.167372\pi\)
−0.864916 + 0.501917i \(0.832628\pi\)
\(44\) 2.42829i 0.366079i
\(45\) 0 0
\(46\) −5.79129 −0.853879
\(47\) 2.69300i 0.392815i 0.980522 + 0.196408i \(0.0629276\pi\)
−0.980522 + 0.196408i \(0.937072\pi\)
\(48\) 0.578661 3.04816i 0.0835225 0.439964i
\(49\) 5.00000 + 4.89898i 0.714286 + 0.699854i
\(50\) 0 0
\(51\) −4.58258 0.869953i −0.641689 0.121818i
\(52\) 1.93825 0.268787
\(53\) 3.93874 0.541027 0.270513 0.962716i \(-0.412807\pi\)
0.270513 + 0.962716i \(0.412807\pi\)
\(54\) 3.04816 4.83156i 0.414802 0.657492i
\(55\) 0 0
\(56\) 7.51695 + 3.06878i 1.00449 + 0.410083i
\(57\) −7.46644 1.41742i −0.988954 0.187742i
\(58\) 5.79129i 0.760433i
\(59\) −7.51695 −0.978624 −0.489312 0.872109i \(-0.662752\pi\)
−0.489312 + 0.872109i \(0.662752\pi\)
\(60\) 0 0
\(61\) 6.83723i 0.875418i 0.899117 + 0.437709i \(0.144210\pi\)
−0.899117 + 0.437709i \(0.855790\pi\)
\(62\) 7.51695i 0.954654i
\(63\) 5.73782 + 5.48429i 0.722897 + 0.690956i
\(64\) 8.16515 1.02064
\(65\) 0 0
\(66\) 5.74117 + 1.08990i 0.706689 + 0.134157i
\(67\) 4.16515i 0.508854i 0.967092 + 0.254427i \(0.0818869\pi\)
−0.967092 + 0.254427i \(0.918113\pi\)
\(68\) 2.13094i 0.258415i
\(69\) 1.70166 8.96368i 0.204856 1.07910i
\(70\) 0 0
\(71\) 3.06878i 0.364197i −0.983280 0.182099i \(-0.941711\pi\)
0.983280 0.182099i \(-0.0582890\pi\)
\(72\) 8.56585 + 3.37386i 1.00950 + 0.397614i
\(73\) −16.1240 −1.88717 −0.943583 0.331136i \(-0.892568\pi\)
−0.943583 + 0.331136i \(0.892568\pi\)
\(74\) 9.43581i 1.09689i
\(75\) 0 0
\(76\) 3.47197i 0.398262i
\(77\) −3.06878 + 7.51695i −0.349720 + 0.856636i
\(78\) 0.869953 4.58258i 0.0985028 0.518875i
\(79\) −0.582576 −0.0655449 −0.0327724 0.999463i \(-0.510434\pi\)
−0.0327724 + 0.999463i \(0.510434\pi\)
\(80\) 0 0
\(81\) 6.58258 + 6.13756i 0.731397 + 0.681952i
\(82\) −11.2250 −1.23959
\(83\) 15.5960i 1.71188i −0.517076 0.855940i \(-0.672979\pi\)
0.517076 0.855940i \(-0.327021\pi\)
\(84\) −1.97264 + 3.04262i −0.215233 + 0.331978i
\(85\) 0 0
\(86\) 7.23698i 0.780384i
\(87\) 8.96368 + 1.70166i 0.961007 + 0.182437i
\(88\) 9.41742i 1.00390i
\(89\) 7.51695 0.796795 0.398398 0.917213i \(-0.369566\pi\)
0.398398 + 0.917213i \(0.369566\pi\)
\(90\) 0 0
\(91\) 6.00000 + 2.44949i 0.628971 + 0.256776i
\(92\) 4.16820 0.434565
\(93\) 11.6346 + 2.20871i 1.20646 + 0.229033i
\(94\) 2.96073i 0.305376i
\(95\) 0 0
\(96\) −1.34650 + 7.09285i −0.137427 + 0.723911i
\(97\) −11.7362 −1.19163 −0.595816 0.803121i \(-0.703171\pi\)
−0.595816 + 0.803121i \(0.703171\pi\)
\(98\) 5.49707 + 5.38601i 0.555288 + 0.544069i
\(99\) −3.37386 + 8.56585i −0.339086 + 0.860901i
\(100\) 0 0
\(101\) 18.2890 1.81982 0.909910 0.414805i \(-0.136150\pi\)
0.909910 + 0.414805i \(0.136150\pi\)
\(102\) −5.03815 0.956439i −0.498851 0.0947016i
\(103\) 4.38774 0.432337 0.216168 0.976356i \(-0.430644\pi\)
0.216168 + 0.976356i \(0.430644\pi\)
\(104\) 7.51695 0.737098
\(105\) 0 0
\(106\) 4.33030 0.420596
\(107\) −10.5352 −1.01848 −0.509239 0.860625i \(-0.670073\pi\)
−0.509239 + 0.860625i \(0.670073\pi\)
\(108\) −2.19387 + 3.47744i −0.211105 + 0.334617i
\(109\) −5.00000 −0.478913 −0.239457 0.970907i \(-0.576969\pi\)
−0.239457 + 0.970907i \(0.576969\pi\)
\(110\) 0 0
\(111\) −14.6046 2.77253i −1.38621 0.263157i
\(112\) 4.38774 + 1.79129i 0.414603 + 0.169261i
\(113\) 18.0017 1.69345 0.846727 0.532028i \(-0.178570\pi\)
0.846727 + 0.532028i \(0.178570\pi\)
\(114\) −8.20871 1.55834i −0.768816 0.145952i
\(115\) 0 0
\(116\) 4.16820i 0.387007i
\(117\) 6.83723 + 2.69300i 0.632102 + 0.248968i
\(118\) −8.26424 −0.760785
\(119\) 2.69300 6.59649i 0.246867 0.604699i
\(120\) 0 0
\(121\) 1.58258 0.143871
\(122\) 7.51695i 0.680553i
\(123\) 3.29824 17.3739i 0.297393 1.56655i
\(124\) 5.41022i 0.485852i
\(125\) 0 0
\(126\) 6.30824 + 6.02951i 0.561983 + 0.537151i
\(127\) 8.16515i 0.724540i −0.932073 0.362270i \(-0.882002\pi\)
0.932073 0.362270i \(-0.117998\pi\)
\(128\) 0.640492 0.0566120
\(129\) −11.2013 2.12645i −0.986219 0.187223i
\(130\) 0 0
\(131\) −2.69300 −0.235289 −0.117644 0.993056i \(-0.537534\pi\)
−0.117644 + 0.993056i \(0.537534\pi\)
\(132\) −4.13212 0.784439i −0.359655 0.0682767i
\(133\) 4.38774 10.7477i 0.380465 0.931946i
\(134\) 4.57923i 0.395585i
\(135\) 0 0
\(136\) 8.26424i 0.708653i
\(137\) −10.5352 −0.900085 −0.450042 0.893007i \(-0.648591\pi\)
−0.450042 + 0.893007i \(0.648591\pi\)
\(138\) 1.87083 9.85480i 0.159256 0.838896i
\(139\) 2.44949i 0.207763i −0.994590 0.103882i \(-0.966874\pi\)
0.994590 0.103882i \(-0.0331263\pi\)
\(140\) 0 0
\(141\) −4.58258 0.869953i −0.385922 0.0732633i
\(142\) 3.37386i 0.283128i
\(143\) 7.51695i 0.628599i
\(144\) 5.00000 + 1.96937i 0.416667 + 0.164114i
\(145\) 0 0
\(146\) −17.7269 −1.46709
\(147\) −9.95160 + 6.92572i −0.820794 + 0.571224i
\(148\) 6.79129i 0.558240i
\(149\) 18.0017i 1.47475i 0.675482 + 0.737377i \(0.263936\pi\)
−0.675482 + 0.737377i \(0.736064\pi\)
\(150\) 0 0
\(151\) −4.16515 −0.338955 −0.169478 0.985534i \(-0.554208\pi\)
−0.169478 + 0.985534i \(0.554208\pi\)
\(152\) 13.4650i 1.09216i
\(153\) 2.96073 7.51695i 0.239361 0.607709i
\(154\) −3.37386 + 8.26424i −0.271874 + 0.665952i
\(155\) 0 0
\(156\) −0.626136 + 3.29824i −0.0501310 + 0.264071i
\(157\) 1.93825 0.154689 0.0773447 0.997004i \(-0.475356\pi\)
0.0773447 + 0.997004i \(0.475356\pi\)
\(158\) −0.640492 −0.0509548
\(159\) −1.27238 + 6.70239i −0.100906 + 0.531534i
\(160\) 0 0
\(161\) 12.9030 + 5.26761i 1.01690 + 0.415146i
\(162\) 7.23698 + 6.74773i 0.568591 + 0.530152i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 8.07901 0.630865
\(165\) 0 0
\(166\) 17.1464i 1.33082i
\(167\) 18.2890i 1.41524i −0.706592 0.707621i \(-0.749768\pi\)
0.706592 0.707621i \(-0.250232\pi\)
\(168\) −7.65031 + 11.7999i −0.590234 + 0.910385i
\(169\) −7.00000 −0.538462
\(170\) 0 0
\(171\) 4.82395 12.2474i 0.368896 0.936586i
\(172\) 5.20871i 0.397161i
\(173\) 8.07901i 0.614236i −0.951671 0.307118i \(-0.900635\pi\)
0.951671 0.307118i \(-0.0993646\pi\)
\(174\) 9.85480 + 1.87083i 0.747090 + 0.141827i
\(175\) 0 0
\(176\) 5.49707i 0.414357i
\(177\) 2.42829 12.7913i 0.182521 0.961452i
\(178\) 8.26424 0.619431
\(179\) 14.4740i 1.08183i −0.841076 0.540917i \(-0.818077\pi\)
0.841076 0.540917i \(-0.181923\pi\)
\(180\) 0 0
\(181\) 12.2474i 0.910346i 0.890403 + 0.455173i \(0.150423\pi\)
−0.890403 + 0.455173i \(0.849577\pi\)
\(182\) 6.59649 + 2.69300i 0.488964 + 0.199619i
\(183\) −11.6346 2.20871i −0.860057 0.163273i
\(184\) 16.1652 1.19171
\(185\) 0 0
\(186\) 12.7913 + 2.42829i 0.937903 + 0.178051i
\(187\) 8.26424 0.604341
\(188\) 2.13094i 0.155415i
\(189\) −11.1860 + 7.99215i −0.813658 + 0.581343i
\(190\) 0 0
\(191\) 17.1317i 1.23961i −0.784757 0.619803i \(-0.787212\pi\)
0.784757 0.619803i \(-0.212788\pi\)
\(192\) −2.63769 + 13.8943i −0.190359 + 1.00274i
\(193\) 11.0000i 0.791797i 0.918294 + 0.395899i \(0.129567\pi\)
−0.918294 + 0.395899i \(0.870433\pi\)
\(194\) −12.9030 −0.926379
\(195\) 0 0
\(196\) −3.95644 3.87650i −0.282603 0.276893i
\(197\) 3.52770 0.251339 0.125669 0.992072i \(-0.459892\pi\)
0.125669 + 0.992072i \(0.459892\pi\)
\(198\) −3.70927 + 9.41742i −0.263607 + 0.669267i
\(199\) 7.85971i 0.557160i −0.960413 0.278580i \(-0.910136\pi\)
0.960413 0.278580i \(-0.0898637\pi\)
\(200\) 0 0
\(201\) −7.08767 1.34552i −0.499926 0.0949056i
\(202\) 20.1072 1.41473
\(203\) −5.26761 + 12.9030i −0.369714 + 0.905610i
\(204\) 3.62614 + 0.688383i 0.253880 + 0.0481965i
\(205\) 0 0
\(206\) 4.82395 0.336100
\(207\) 14.7034 + 5.79129i 1.02196 + 0.402522i
\(208\) 4.38774 0.304235
\(209\) 13.4650 0.931395
\(210\) 0 0
\(211\) −14.7477 −1.01528 −0.507638 0.861571i \(-0.669481\pi\)
−0.507638 + 0.861571i \(0.669481\pi\)
\(212\) −3.11667 −0.214054
\(213\) 5.22202 + 0.991345i 0.357807 + 0.0679259i
\(214\) −11.5826 −0.791769
\(215\) 0 0
\(216\) −8.50830 + 13.4863i −0.578916 + 0.917624i
\(217\) −6.83723 + 16.7477i −0.464141 + 1.13691i
\(218\) −5.49707 −0.372309
\(219\) 5.20871 27.4375i 0.351972 1.85405i
\(220\) 0 0
\(221\) 6.59649i 0.443728i
\(222\) −16.0565 3.04816i −1.07764 0.204579i
\(223\) −2.44949 −0.164030 −0.0820150 0.996631i \(-0.526136\pi\)
−0.0820150 + 0.996631i \(0.526136\pi\)
\(224\) −10.2100 4.16820i −0.682181 0.278499i
\(225\) 0 0
\(226\) 19.7913 1.31650
\(227\) 2.69300i 0.178741i 0.995998 + 0.0893705i \(0.0284855\pi\)
−0.995998 + 0.0893705i \(0.971514\pi\)
\(228\) 5.90810 + 1.12159i 0.391274 + 0.0742792i
\(229\) 3.87650i 0.256167i −0.991763 0.128083i \(-0.959118\pi\)
0.991763 0.128083i \(-0.0408825\pi\)
\(230\) 0 0
\(231\) −11.7999 7.65031i −0.776379 0.503354i
\(232\) 16.1652i 1.06129i
\(233\) −5.26761 −0.345093 −0.172546 0.985001i \(-0.555199\pi\)
−0.172546 + 0.985001i \(0.555199\pi\)
\(234\) 7.51695 + 2.96073i 0.491398 + 0.193549i
\(235\) 0 0
\(236\) 5.94807 0.387186
\(237\) 0.188196 0.991345i 0.0122247 0.0643948i
\(238\) 2.96073 7.25227i 0.191915 0.470095i
\(239\) 14.4740i 0.936242i −0.883664 0.468121i \(-0.844931\pi\)
0.883664 0.468121i \(-0.155069\pi\)
\(240\) 0 0
\(241\) 19.0847i 1.22935i 0.788780 + 0.614676i \(0.210713\pi\)
−0.788780 + 0.614676i \(0.789287\pi\)
\(242\) 1.73991 0.111845
\(243\) −12.5705 + 9.21861i −0.806397 + 0.591374i
\(244\) 5.41022i 0.346354i
\(245\) 0 0
\(246\) 3.62614 19.1011i 0.231194 1.21784i
\(247\) 10.7477i 0.683861i
\(248\) 20.9820i 1.33236i
\(249\) 26.5390 + 5.03815i 1.68184 + 0.319280i
\(250\) 0 0
\(251\) −17.7269 −1.11891 −0.559456 0.828860i \(-0.688990\pi\)
−0.559456 + 0.828860i \(0.688990\pi\)
\(252\) −4.54026 4.33965i −0.286010 0.273372i
\(253\) 16.1652i 1.01629i
\(254\) 8.97689i 0.563260i
\(255\) 0 0
\(256\) −15.6261 −0.976634
\(257\) 4.82395i 0.300909i −0.988617 0.150455i \(-0.951926\pi\)
0.988617 0.150455i \(-0.0480738\pi\)
\(258\) −12.3149 2.33785i −0.766690 0.145548i
\(259\) 8.58258 21.0229i 0.533295 1.30630i
\(260\) 0 0
\(261\) −5.79129 + 14.7034i −0.358472 + 0.910119i
\(262\) −2.96073 −0.182914
\(263\) −28.5369 −1.75966 −0.879830 0.475289i \(-0.842344\pi\)
−0.879830 + 0.475289i \(0.842344\pi\)
\(264\) −16.0252 3.04222i −0.986286 0.187236i
\(265\) 0 0
\(266\) 4.82395 11.8162i 0.295775 0.724498i
\(267\) −2.42829 + 12.7913i −0.148609 + 0.782814i
\(268\) 3.29583i 0.201325i
\(269\) −20.9820 −1.27929 −0.639647 0.768669i \(-0.720919\pi\)
−0.639647 + 0.768669i \(0.720919\pi\)
\(270\) 0 0
\(271\) 25.9219i 1.57464i 0.616542 + 0.787322i \(0.288533\pi\)
−0.616542 + 0.787322i \(0.711467\pi\)
\(272\) 4.82395i 0.292495i
\(273\) −6.10645 + 9.41867i −0.369579 + 0.570044i
\(274\) −11.5826 −0.699729
\(275\) 0 0
\(276\) −1.34650 + 7.09285i −0.0810499 + 0.426939i
\(277\) 18.7477i 1.12644i −0.826306 0.563221i \(-0.809562\pi\)
0.826306 0.563221i \(-0.190438\pi\)
\(278\) 2.69300i 0.161516i
\(279\) −7.51695 + 19.0847i −0.450028 + 1.14257i
\(280\) 0 0
\(281\) 15.3439i 0.915341i 0.889122 + 0.457670i \(0.151316\pi\)
−0.889122 + 0.457670i \(0.848684\pi\)
\(282\) −5.03815 0.956439i −0.300017 0.0569551i
\(283\) 23.4724 1.39529 0.697645 0.716443i \(-0.254231\pi\)
0.697645 + 0.716443i \(0.254231\pi\)
\(284\) 2.42829i 0.144093i
\(285\) 0 0
\(286\) 8.26424i 0.488675i
\(287\) 25.0092 + 10.2100i 1.47625 + 0.602675i
\(288\) −11.6346 4.58258i −0.685578 0.270031i
\(289\) 9.74773 0.573396
\(290\) 0 0
\(291\) 3.79129 19.9710i 0.222249 1.17072i
\(292\) 12.7587 0.746646
\(293\) 2.13094i 0.124491i −0.998061 0.0622455i \(-0.980174\pi\)
0.998061 0.0622455i \(-0.0198262\pi\)
\(294\) −10.9409 + 7.61424i −0.638088 + 0.444071i
\(295\) 0 0
\(296\) 26.3381i 1.53087i
\(297\) −13.4863 8.50830i −0.782552 0.493701i
\(298\) 19.7913i 1.14648i
\(299\) 12.9030 0.746197
\(300\) 0 0
\(301\) 6.58258 16.1240i 0.379413 0.929369i
\(302\) −4.57923 −0.263505
\(303\) −5.90810 + 31.1216i −0.339412 + 1.78789i
\(304\) 7.85971i 0.450785i
\(305\) 0 0
\(306\) 3.25507 8.26424i 0.186080 0.472435i
\(307\) −13.1632 −0.751265 −0.375632 0.926769i \(-0.622574\pi\)
−0.375632 + 0.926769i \(0.622574\pi\)
\(308\) 2.42829 5.94807i 0.138365 0.338923i
\(309\) −1.41742 + 7.46644i −0.0806345 + 0.424751i
\(310\) 0 0
\(311\) 12.3409 0.699788 0.349894 0.936789i \(-0.386218\pi\)
0.349894 + 0.936789i \(0.386218\pi\)
\(312\) −2.42829 + 12.7913i −0.137475 + 0.724164i
\(313\) −22.9612 −1.29784 −0.648921 0.760855i \(-0.724780\pi\)
−0.648921 + 0.760855i \(0.724780\pi\)
\(314\) 2.13094 0.120256
\(315\) 0 0
\(316\) 0.460985 0.0259324
\(317\) −1.32888 −0.0746371 −0.0373185 0.999303i \(-0.511882\pi\)
−0.0373185 + 0.999303i \(0.511882\pi\)
\(318\) −1.39887 + 7.36870i −0.0784447 + 0.413216i
\(319\) −16.1652 −0.905075
\(320\) 0 0
\(321\) 3.40332 17.9274i 0.189955 1.00061i
\(322\) 14.1857 + 5.79129i 0.790538 + 0.322736i
\(323\) −11.8162 −0.657471
\(324\) −5.20871 4.85658i −0.289373 0.269810i
\(325\) 0 0
\(326\) 4.39766i 0.243564i
\(327\) 1.61521 8.50830i 0.0893213 0.470510i
\(328\) 31.3321 1.73003
\(329\) 2.69300 6.59649i 0.148470 0.363676i
\(330\) 0 0
\(331\) 17.0000 0.934405 0.467202 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 12.3409i 0.677295i
\(333\) 9.43581 23.9564i 0.517079 1.31280i
\(334\) 20.1072i 1.10021i
\(335\) 0 0
\(336\) −4.46559 + 6.88778i −0.243618 + 0.375759i
\(337\) 2.00000i 0.108947i −0.998515 0.0544735i \(-0.982652\pi\)
0.998515 0.0544735i \(-0.0173480\pi\)
\(338\) −7.69590 −0.418602
\(339\) −5.81529 + 30.6327i −0.315843 + 1.66374i
\(340\) 0 0
\(341\) −20.9820 −1.13624
\(342\) 5.30352 13.4650i 0.286781 0.728105i
\(343\) −7.34847 17.0000i −0.396780 0.917914i
\(344\) 20.2005i 1.08914i
\(345\) 0 0
\(346\) 8.88218i 0.477509i
\(347\) 3.52770 0.189377 0.0946886 0.995507i \(-0.469814\pi\)
0.0946886 + 0.995507i \(0.469814\pi\)
\(348\) −7.09285 1.34650i −0.380217 0.0721801i
\(349\) 9.28672i 0.497107i −0.968618 0.248553i \(-0.920045\pi\)
0.968618 0.248553i \(-0.0799551\pi\)
\(350\) 0 0
\(351\) −6.79129 + 10.7647i −0.362492 + 0.574576i
\(352\) 12.7913i 0.681778i
\(353\) 30.6299i 1.63026i −0.579276 0.815132i \(-0.696665\pi\)
0.579276 0.815132i \(-0.303335\pi\)
\(354\) 2.66970 14.0629i 0.141893 0.747436i
\(355\) 0 0
\(356\) −5.94807 −0.315247
\(357\) 10.3550 + 6.71352i 0.548046 + 0.355317i
\(358\) 15.9129i 0.841022i
\(359\) 18.0017i 0.950091i 0.879961 + 0.475046i \(0.157568\pi\)
−0.879961 + 0.475046i \(0.842432\pi\)
\(360\) 0 0
\(361\) −0.252273 −0.0132775
\(362\) 13.4650i 0.707706i
\(363\) −0.511238 + 2.69300i −0.0268331 + 0.141346i
\(364\) −4.74773 1.93825i −0.248849 0.101592i
\(365\) 0 0
\(366\) −12.7913 2.42829i −0.668611 0.126929i
\(367\) −0.915775 −0.0478031 −0.0239015 0.999714i \(-0.507609\pi\)
−0.0239015 + 0.999714i \(0.507609\pi\)
\(368\) 9.43581 0.491875
\(369\) 28.4989 + 11.2250i 1.48359 + 0.584349i
\(370\) 0 0
\(371\) −9.64789 3.93874i −0.500894 0.204489i
\(372\) −9.20635 1.74773i −0.477327 0.0906154i
\(373\) 26.9129i 1.39350i −0.717316 0.696748i \(-0.754630\pi\)
0.717316 0.696748i \(-0.245370\pi\)
\(374\) 9.08583 0.469817
\(375\) 0 0
\(376\) 8.26424i 0.426196i
\(377\) 12.9030i 0.664536i
\(378\) −12.2980 + 8.78669i −0.632541 + 0.451938i
\(379\) −17.3303 −0.890198 −0.445099 0.895481i \(-0.646831\pi\)
−0.445099 + 0.895481i \(0.646831\pi\)
\(380\) 0 0
\(381\) 13.8943 + 2.63769i 0.711827 + 0.135133i
\(382\) 18.8348i 0.963675i
\(383\) 27.9369i 1.42751i 0.700397 + 0.713753i \(0.253006\pi\)
−0.700397 + 0.713753i \(0.746994\pi\)
\(384\) −0.206906 + 1.08990i −0.0105586 + 0.0556187i
\(385\) 0 0
\(386\) 12.0936i 0.615546i
\(387\) 7.23698 18.3739i 0.367876 0.933996i
\(388\) 9.28672 0.471462
\(389\) 13.1451i 0.666482i 0.942842 + 0.333241i \(0.108142\pi\)
−0.942842 + 0.333241i \(0.891858\pi\)
\(390\) 0 0
\(391\) 14.1857i 0.717402i
\(392\) −15.3439 15.0339i −0.774985 0.759327i
\(393\) 0.869953 4.58258i 0.0438833 0.231160i
\(394\) 3.87841 0.195391
\(395\) 0 0
\(396\) 2.66970 6.77806i 0.134157 0.340610i
\(397\) 8.77548 0.440429 0.220214 0.975451i \(-0.429324\pi\)
0.220214 + 0.975451i \(0.429324\pi\)
\(398\) 8.64108i 0.433138i
\(399\) 16.8715 + 10.9384i 0.844634 + 0.547605i
\(400\) 0 0
\(401\) 20.2005i 1.00876i 0.863481 + 0.504382i \(0.168280\pi\)
−0.863481 + 0.504382i \(0.831720\pi\)
\(402\) −7.79228 1.47928i −0.388644 0.0737799i
\(403\) 16.7477i 0.834264i
\(404\) −14.4718 −0.720001
\(405\) 0 0
\(406\) −5.79129 + 14.1857i −0.287417 + 0.704024i
\(407\) 26.3381 1.30553
\(408\) 14.0629 + 2.66970i 0.696219 + 0.132170i
\(409\) 31.7367i 1.56928i 0.619954 + 0.784639i \(0.287151\pi\)
−0.619954 + 0.784639i \(0.712849\pi\)
\(410\) 0 0
\(411\) 3.40332 17.9274i 0.167873 0.884291i
\(412\) −3.47197 −0.171052
\(413\) 18.4127 + 7.51695i 0.906029 + 0.369885i
\(414\) 16.1652 + 6.36703i 0.794474 + 0.312922i
\(415\) 0 0
\(416\) −10.2100 −0.500584
\(417\) 4.16820 + 0.791288i 0.204117 + 0.0387495i
\(418\) 14.8036 0.724070
\(419\) −20.9820 −1.02504 −0.512518 0.858676i \(-0.671287\pi\)
−0.512518 + 0.858676i \(0.671287\pi\)
\(420\) 0 0
\(421\) 8.16515 0.397945 0.198973 0.980005i \(-0.436240\pi\)
0.198973 + 0.980005i \(0.436240\pi\)
\(422\) −16.2139 −0.789279
\(423\) 2.96073 7.51695i 0.143956 0.365487i
\(424\) −12.0871 −0.587003
\(425\) 0 0
\(426\) 5.74117 + 1.08990i 0.278160 + 0.0528058i
\(427\) 6.83723 16.7477i 0.330877 0.810479i
\(428\) 8.33639 0.402955
\(429\) −12.7913 2.42829i −0.617569 0.117239i
\(430\) 0 0
\(431\) 34.2634i 1.65041i 0.564833 + 0.825205i \(0.308941\pi\)
−0.564833 + 0.825205i \(0.691059\pi\)
\(432\) −4.96640 + 7.87211i −0.238946 + 0.378747i
\(433\) −1.02248 −0.0491371 −0.0245685 0.999698i \(-0.507821\pi\)
−0.0245685 + 0.999698i \(0.507821\pi\)
\(434\) −7.51695 + 18.4127i −0.360825 + 0.883838i
\(435\) 0 0
\(436\) 3.95644 0.189479
\(437\) 23.1129i 1.10564i
\(438\) 5.72653 30.1652i 0.273624 1.44135i
\(439\) 26.9444i 1.28599i −0.765872 0.642993i \(-0.777693\pi\)
0.765872 0.642993i \(-0.222307\pi\)
\(440\) 0 0
\(441\) −8.57043 19.1715i −0.408116 0.912930i
\(442\) 7.25227i 0.344955i
\(443\) 3.93874 0.187135 0.0935675 0.995613i \(-0.470173\pi\)
0.0935675 + 0.995613i \(0.470173\pi\)
\(444\) 11.5565 + 2.19387i 0.548445 + 0.104116i
\(445\) 0 0
\(446\) −2.69300 −0.127517
\(447\) −30.6327 5.81529i −1.44888 0.275054i
\(448\) −20.0005 8.16515i −0.944933 0.385767i
\(449\) 36.4144i 1.71850i 0.511556 + 0.859250i \(0.329069\pi\)
−0.511556 + 0.859250i \(0.670931\pi\)
\(450\) 0 0
\(451\) 31.3321i 1.47537i
\(452\) −14.2445 −0.670005
\(453\) 1.34552 7.08767i 0.0632180 0.333008i
\(454\) 2.96073i 0.138954i
\(455\) 0 0
\(456\) 22.9129 + 4.34977i 1.07299 + 0.203696i
\(457\) 34.1652i 1.59818i 0.601213 + 0.799089i \(0.294685\pi\)
−0.601213 + 0.799089i \(0.705315\pi\)
\(458\) 4.26188i 0.199145i
\(459\) 11.8348 + 7.46644i 0.552403 + 0.348504i
\(460\) 0 0
\(461\) 33.3229 1.55200 0.776000 0.630732i \(-0.217245\pi\)
0.776000 + 0.630732i \(0.217245\pi\)
\(462\) −12.9730 8.41086i −0.603560 0.391309i
\(463\) 12.7477i 0.592437i 0.955120 + 0.296219i \(0.0957257\pi\)
−0.955120 + 0.296219i \(0.904274\pi\)
\(464\) 9.43581i 0.438046i
\(465\) 0 0
\(466\) −5.79129 −0.268276
\(467\) 16.1580i 0.747704i 0.927488 + 0.373852i \(0.121963\pi\)
−0.927488 + 0.373852i \(0.878037\pi\)
\(468\) −5.41022 2.13094i −0.250087 0.0985028i
\(469\) 4.16515 10.2025i 0.192329 0.471107i
\(470\) 0 0
\(471\) −0.626136 + 3.29824i −0.0288508 + 0.151975i
\(472\) 23.0679 1.06179
\(473\) 20.2005 0.928820
\(474\) 0.206906 1.08990i 0.00950350 0.0500607i
\(475\) 0 0
\(476\) −2.13094 + 5.21972i −0.0976716 + 0.239245i
\(477\) −10.9941 4.33030i −0.503387 0.198271i
\(478\) 15.9129i 0.727838i
\(479\) −7.51695 −0.343458 −0.171729 0.985144i \(-0.554935\pi\)
−0.171729 + 0.985144i \(0.554935\pi\)
\(480\) 0 0
\(481\) 21.0229i 0.958563i
\(482\) 20.9820i 0.955703i
\(483\) −13.1319 + 20.2548i −0.597521 + 0.921624i
\(484\) −1.25227 −0.0569215
\(485\) 0 0
\(486\) −13.8202 + 10.1351i −0.626896 + 0.459736i
\(487\) 21.8348i 0.989431i 0.869055 + 0.494716i \(0.164728\pi\)
−0.869055 + 0.494716i \(0.835272\pi\)
\(488\) 20.9820i 0.949809i
\(489\) 6.80664 + 1.29217i 0.307807 + 0.0584338i
\(490\) 0 0
\(491\) 26.3381i 1.18862i −0.804236 0.594310i \(-0.797425\pi\)
0.804236 0.594310i \(-0.202575\pi\)
\(492\) −2.60986 + 13.7477i −0.117662 + 0.619795i
\(493\) 14.1857 0.638892
\(494\) 11.8162i 0.531636i
\(495\) 0 0
\(496\) 12.2474i 0.549927i
\(497\) −3.06878 + 7.51695i −0.137654 + 0.337181i
\(498\) 29.1774 + 5.53901i 1.30747 + 0.248209i
\(499\) −3.25227 −0.145592 −0.0727959 0.997347i \(-0.523192\pi\)
−0.0727959 + 0.997347i \(0.523192\pi\)
\(500\) 0 0
\(501\) 31.1216 + 5.90810i 1.39041 + 0.263955i
\(502\) −19.4892 −0.869846
\(503\) 5.38601i 0.240150i 0.992765 + 0.120075i \(0.0383135\pi\)
−0.992765 + 0.120075i \(0.961686\pi\)
\(504\) −17.6081 16.8301i −0.784328 0.749672i
\(505\) 0 0
\(506\) 17.7722i 0.790071i
\(507\) 2.26129 11.9116i 0.100428 0.529013i
\(508\) 6.46099i 0.286660i
\(509\) 22.5509 0.999549 0.499774 0.866156i \(-0.333416\pi\)
0.499774 + 0.866156i \(0.333416\pi\)
\(510\) 0 0
\(511\) 39.4955 + 16.1240i 1.74718 + 0.713282i
\(512\) −18.4606 −0.815850
\(513\) 19.2826 + 12.1652i 0.851350 + 0.537105i
\(514\) 5.30352i 0.233928i
\(515\) 0 0
\(516\) 8.86345 + 1.68263i 0.390192 + 0.0740738i
\(517\) 8.26424 0.363461
\(518\) 9.43581 23.1129i 0.414586 1.01552i
\(519\) 13.7477 + 2.60986i 0.603458 + 0.114560i
\(520\) 0 0
\(521\) −16.1580 −0.707896 −0.353948 0.935265i \(-0.615161\pi\)
−0.353948 + 0.935265i \(0.615161\pi\)
\(522\) −6.36703 + 16.1652i −0.278677 + 0.707529i
\(523\) −14.6969 −0.642652 −0.321326 0.946969i \(-0.604129\pi\)
−0.321326 + 0.946969i \(0.604129\pi\)
\(524\) 2.13094 0.0930906
\(525\) 0 0
\(526\) −31.3739 −1.36797
\(527\) 18.4127 0.802070
\(528\) −9.35414 1.77578i −0.407087 0.0772811i
\(529\) 4.74773 0.206423
\(530\) 0 0
\(531\) 20.9820 + 8.26424i 0.910540 + 0.358638i
\(532\) −3.47197 + 8.50455i −0.150529 + 0.368719i
\(533\) 25.0092 1.08327
\(534\) −2.66970 + 14.0629i −0.115529 + 0.608562i
\(535\) 0 0
\(536\) 12.7819i 0.552096i
\(537\) 24.6297 + 4.67569i 1.06285 + 0.201771i
\(538\) −23.0679 −0.994527
\(539\) 15.0339 15.3439i 0.647556 0.660909i
\(540\) 0 0
\(541\) −8.58258 −0.368994 −0.184497 0.982833i \(-0.559066\pi\)
−0.184497 + 0.982833i \(0.559066\pi\)
\(542\) 28.4989i 1.22413i
\(543\) −20.8410 3.95644i −0.894372 0.169787i
\(544\) 11.2250i 0.481267i
\(545\) 0 0
\(546\) −6.71352 + 10.3550i −0.287312 + 0.443154i
\(547\) 4.66970i 0.199662i −0.995004 0.0998309i \(-0.968170\pi\)
0.995004 0.0998309i \(-0.0318302\pi\)
\(548\) 8.33639 0.356113
\(549\) 7.51695 19.0847i 0.320816 0.814514i
\(550\) 0 0
\(551\) 23.1129 0.984643
\(552\) −5.22202 + 27.5076i −0.222264 + 1.17080i
\(553\) 1.42701 + 0.582576i 0.0606828 + 0.0247736i
\(554\) 20.6115i 0.875700i
\(555\) 0 0
\(556\) 1.93825i 0.0822002i
\(557\) −6.18546 −0.262086 −0.131043 0.991377i \(-0.541833\pi\)
−0.131043 + 0.991377i \(0.541833\pi\)
\(558\) −8.26424 + 20.9820i −0.349853 + 0.888238i
\(559\) 16.1240i 0.681970i
\(560\) 0 0
\(561\) −2.66970 + 14.0629i −0.112715 + 0.593737i
\(562\) 16.8693i 0.711589i
\(563\) 9.64789i 0.406610i −0.979115 0.203305i \(-0.934832\pi\)
0.979115 0.203305i \(-0.0651683\pi\)
\(564\) 3.62614 + 0.688383i 0.152688 + 0.0289862i
\(565\) 0 0
\(566\) 25.8059 1.08470
\(567\) −9.98639 21.6165i −0.419389 0.907807i
\(568\) 9.41742i 0.395146i
\(569\) 0.411031i 0.0172313i −0.999963 0.00861566i \(-0.997258\pi\)
0.999963 0.00861566i \(-0.00274248\pi\)
\(570\) 0 0
\(571\) −29.7477 −1.24490 −0.622452 0.782658i \(-0.713863\pi\)
−0.622452 + 0.782658i \(0.713863\pi\)
\(572\) 5.94807i 0.248701i
\(573\) 29.1523 + 5.53426i 1.21786 + 0.231197i
\(574\) 27.4955 + 11.2250i 1.14764 + 0.468521i
\(575\) 0 0
\(576\) −22.7913 8.97689i −0.949637 0.374037i
\(577\) −23.9837 −0.998453 −0.499226 0.866472i \(-0.666382\pi\)
−0.499226 + 0.866472i \(0.666382\pi\)
\(578\) 10.7168 0.445760
\(579\) −18.7183 3.55346i −0.777904 0.147677i
\(580\) 0 0
\(581\) −15.5960 + 38.2022i −0.647030 + 1.58489i
\(582\) 4.16820 21.9564i 0.172777 0.910124i
\(583\) 12.0871i 0.500597i
\(584\) 49.4809 2.04753
\(585\) 0 0
\(586\) 2.34279i 0.0967797i
\(587\) 3.25507i 0.134351i −0.997741 0.0671755i \(-0.978601\pi\)
0.997741 0.0671755i \(-0.0213987\pi\)
\(588\) 7.87458 5.48024i 0.324742 0.226001i
\(589\) 30.0000 1.23613
\(590\) 0 0
\(591\) −1.13960 + 6.00295i −0.0468767 + 0.246928i
\(592\) 15.3739i 0.631862i
\(593\) 5.38601i 0.221177i 0.993866 + 0.110588i \(0.0352735\pi\)
−0.993866 + 0.110588i \(0.964726\pi\)
\(594\) −14.8270 9.35414i −0.608359 0.383805i
\(595\) 0 0
\(596\) 14.2445i 0.583477i
\(597\) 13.3745 + 2.53901i 0.547384 + 0.103915i
\(598\) 14.1857 0.580096
\(599\) 36.4144i 1.48785i 0.668263 + 0.743925i \(0.267038\pi\)
−0.668263 + 0.743925i \(0.732962\pi\)
\(600\) 0 0
\(601\) 2.85403i 0.116418i −0.998304 0.0582091i \(-0.981461\pi\)
0.998304 0.0582091i \(-0.0185390\pi\)
\(602\) 7.23698 17.7269i 0.294957 0.722495i
\(603\) 4.57923 11.6261i 0.186481 0.473453i
\(604\) 3.29583 0.134106
\(605\) 0 0
\(606\) −6.49545 + 34.2155i −0.263860 + 1.38991i
\(607\) 21.0229 0.853294 0.426647 0.904418i \(-0.359695\pi\)
0.426647 + 0.904418i \(0.359695\pi\)
\(608\) 18.2890i 0.741716i
\(609\) −20.2548 13.1319i −0.820765 0.532130i
\(610\) 0 0
\(611\) 6.59649i 0.266865i
\(612\) −2.34279 + 5.94807i −0.0947016 + 0.240437i
\(613\) 36.5826i 1.47756i 0.673949 + 0.738778i \(0.264597\pi\)
−0.673949 + 0.738778i \(0.735403\pi\)
\(614\) −14.4718 −0.584036
\(615\) 0 0
\(616\) 9.41742 23.0679i 0.379439 0.929432i
\(617\) −1.32888 −0.0534985 −0.0267493 0.999642i \(-0.508516\pi\)
−0.0267493 + 0.999642i \(0.508516\pi\)
\(618\) −1.55834 + 8.20871i −0.0626855 + 0.330203i
\(619\) 13.2699i 0.533363i −0.963785 0.266682i \(-0.914073\pi\)
0.963785 0.266682i \(-0.0859272\pi\)
\(620\) 0 0
\(621\) −14.6046 + 23.1494i −0.586063 + 0.928953i
\(622\) 13.5678 0.544018
\(623\) −18.4127 7.51695i −0.737689 0.301160i
\(624\) −1.41742 + 7.46644i −0.0567424 + 0.298897i
\(625\) 0 0
\(626\) −25.2439 −1.00895
\(627\) −4.34977 + 22.9129i −0.173713 + 0.915052i
\(628\) −1.53371 −0.0612019
\(629\) −23.1129 −0.921572
\(630\) 0 0
\(631\) 33.7477 1.34348 0.671738 0.740789i \(-0.265548\pi\)
0.671738 + 0.740789i \(0.265548\pi\)
\(632\) 1.78780 0.0711148
\(633\) 4.76413 25.0956i 0.189357 0.997461i
\(634\) −1.46099 −0.0580231
\(635\) 0 0
\(636\) 1.00682 5.30352i 0.0399229 0.210298i
\(637\) −12.2474 12.0000i −0.485262 0.475457i
\(638\) −17.7722 −0.703608
\(639\) −3.37386 + 8.56585i −0.133468 + 0.338860i
\(640\) 0 0
\(641\) 1.78780i 0.0706138i 0.999377 + 0.0353069i \(0.0112409\pi\)
−0.999377 + 0.0353069i \(0.988759\pi\)
\(642\) 3.74166 19.7096i 0.147671 0.777876i
\(643\) 20.6184 0.813110 0.406555 0.913626i \(-0.366730\pi\)
0.406555 + 0.913626i \(0.366730\pi\)
\(644\) −10.2100 4.16820i −0.402329 0.164250i
\(645\) 0 0
\(646\) −12.9909 −0.511120
\(647\) 40.8398i 1.60558i −0.596263 0.802790i \(-0.703348\pi\)
0.596263 0.802790i \(-0.296652\pi\)
\(648\) −20.2005 18.8348i −0.793550 0.739903i
\(649\) 23.0679i 0.905494i
\(650\) 0 0
\(651\) −26.2902 17.0449i −1.03039 0.668041i
\(652\) 3.16515i 0.123957i
\(653\) −14.4740 −0.566410 −0.283205 0.959059i \(-0.591398\pi\)
−0.283205 + 0.959059i \(0.591398\pi\)
\(654\) 1.77578 9.35414i 0.0694387 0.365776i
\(655\) 0 0
\(656\) 18.2890 0.714064
\(657\) 45.0066 + 17.7269i 1.75587 + 0.691592i
\(658\) 2.96073 7.25227i 0.115421 0.282723i
\(659\) 14.4740i 0.563825i −0.959440 0.281913i \(-0.909031\pi\)
0.959440 0.281913i \(-0.0909688\pi\)
\(660\) 0 0
\(661\) 43.5796i 1.69505i −0.530756 0.847525i \(-0.678092\pi\)
0.530756 0.847525i \(-0.321908\pi\)
\(662\) 18.6900 0.726409
\(663\) 11.2250 + 2.13094i 0.435942 + 0.0827589i
\(664\) 47.8606i 1.85735i
\(665\) 0 0
\(666\) 10.3739 26.3381i 0.401979 1.02058i
\(667\) 27.7477i 1.07440i
\(668\) 14.4718i 0.559932i
\(669\) 0.791288 4.16820i 0.0305930 0.161152i
\(670\) 0 0
\(671\) 20.9820 0.810000
\(672\) 10.3911 16.0274i 0.400845 0.618269i
\(673\) 7.49545i 0.288929i −0.989510 0.144464i \(-0.953854\pi\)
0.989510 0.144464i \(-0.0461459\pi\)
\(674\) 2.19883i 0.0846957i
\(675\) 0 0
\(676\) 5.53901 0.213039
\(677\) 10.7720i 0.414002i −0.978341 0.207001i \(-0.933630\pi\)
0.978341 0.207001i \(-0.0663704\pi\)
\(678\) −6.39342 + 33.6780i −0.245538 + 1.29340i
\(679\) 28.7477 + 11.7362i 1.10324 + 0.450394i
\(680\) 0 0
\(681\) −4.58258 0.869953i −0.175605 0.0333367i
\(682\) −23.0679 −0.883315
\(683\) −10.1242 −0.387391 −0.193696 0.981062i \(-0.562047\pi\)
−0.193696 + 0.981062i \(0.562047\pi\)
\(684\) −3.81713 + 9.69126i −0.145952 + 0.370554i
\(685\) 0 0
\(686\) −8.07901 18.6900i −0.308458 0.713589i
\(687\) 6.59649 + 1.25227i 0.251672 + 0.0477772i
\(688\) 11.7913i 0.449539i
\(689\) −9.64789 −0.367555
\(690\) 0 0
\(691\) 6.83723i 0.260101i 0.991507 + 0.130050i \(0.0415139\pi\)
−0.991507 + 0.130050i \(0.958486\pi\)
\(692\) 6.39283i 0.243019i
\(693\) 16.8301 17.6081i 0.639323 0.668877i
\(694\) 3.87841 0.147222
\(695\) 0 0
\(696\) −27.5076 5.22202i −1.04267 0.197940i
\(697\) 27.4955i 1.04146i
\(698\) 10.2100i 0.386452i
\(699\) 1.70166 8.96368i 0.0643627 0.339037i
\(700\) 0 0
\(701\) 17.1317i 0.647056i −0.946219 0.323528i \(-0.895131\pi\)
0.946219 0.323528i \(-0.104869\pi\)
\(702\) −7.46644 + 11.8348i −0.281803 + 0.446678i
\(703\) −37.6581 −1.42030
\(704\) 25.0571i 0.944374i
\(705\) 0 0
\(706\) 33.6749i 1.26737i
\(707\) −44.7986 18.2890i −1.68483 0.687827i
\(708\) −1.92148 + 10.1216i −0.0722135 + 0.380393i
\(709\) −23.4955 −0.882390 −0.441195 0.897411i \(-0.645445\pi\)
−0.441195 + 0.897411i \(0.645445\pi\)
\(710\) 0 0
\(711\) 1.62614 + 0.640492i 0.0609849 + 0.0240203i
\(712\) −23.0679 −0.864506
\(713\) 36.0159i 1.34881i
\(714\) 11.3845 + 7.38094i 0.426053 + 0.276225i
\(715\) 0 0
\(716\) 11.4531i 0.428021i
\(717\) 24.6297 + 4.67569i 0.919815 + 0.174617i
\(718\) 19.7913i 0.738604i
\(719\) −5.94807 −0.221826 −0.110913 0.993830i \(-0.535377\pi\)
−0.110913 + 0.993830i \(0.535377\pi\)
\(720\) 0 0
\(721\) −10.7477 4.38774i −0.400266 0.163408i
\(722\) −0.277352 −0.0103220
\(723\) −32.4756 6.16515i −1.20778 0.229284i
\(724\) 9.69126i 0.360173i
\(725\) 0 0
\(726\) −0.562063 + 2.96073i −0.0208601 + 0.109883i
\(727\) 11.3317 0.420269 0.210134 0.977673i \(-0.432610\pi\)
0.210134 + 0.977673i \(0.432610\pi\)
\(728\) −18.4127 7.51695i −0.682420 0.278597i
\(729\) −11.6261 24.3687i −0.430598 0.902544i
\(730\) 0 0
\(731\) −17.7269 −0.655653
\(732\) 9.20635 + 1.74773i 0.340276 + 0.0645979i
\(733\) 12.6520 0.467312 0.233656 0.972319i \(-0.424931\pi\)
0.233656 + 0.972319i \(0.424931\pi\)
\(734\) −1.00682 −0.0371623
\(735\) 0 0
\(736\) −21.9564 −0.809325
\(737\) 12.7819 0.470829
\(738\) 31.3321 + 12.3409i 1.15335 + 0.454275i
\(739\) −50.8258 −1.86966 −0.934828 0.355101i \(-0.884446\pi\)
−0.934828 + 0.355101i \(0.884446\pi\)
\(740\) 0 0
\(741\) 18.2890 + 3.47197i 0.671862 + 0.127546i
\(742\) −10.6070 4.33030i −0.389396 0.158970i
\(743\) −14.4740 −0.530998 −0.265499 0.964111i \(-0.585537\pi\)
−0.265499 + 0.964111i \(0.585537\pi\)
\(744\) −35.7042 6.77806i −1.30898 0.248496i
\(745\) 0 0
\(746\) 29.5884i 1.08331i
\(747\) −17.1464 + 43.5328i −0.627355 + 1.59278i
\(748\) −6.53940 −0.239104
\(749\) 25.8059 + 10.5352i 0.942928 + 0.384949i
\(750\) 0 0
\(751\) −11.2523 −0.410601 −0.205301 0.978699i \(-0.565817\pi\)
−0.205301 + 0.978699i \(0.565817\pi\)
\(752\) 4.82395i 0.175911i
\(753\) 5.72653 30.1652i 0.208686 1.09928i
\(754\) 14.1857i 0.516613i
\(755\) 0 0
\(756\) 8.85131 6.32409i 0.321919 0.230005i
\(757\) 33.7477i 1.22658i −0.789857 0.613291i \(-0.789845\pi\)
0.789857 0.613291i \(-0.210155\pi\)
\(758\) −19.0532 −0.692043
\(759\) −27.5076 5.22202i −0.998462 0.189547i
\(760\) 0 0
\(761\) −4.26188 −0.154493 −0.0772466 0.997012i \(-0.524613\pi\)
−0.0772466 + 0.997012i \(0.524613\pi\)
\(762\) 15.2756 + 2.89991i 0.553377 + 0.105053i
\(763\) 12.2474 + 5.00000i 0.443387 + 0.181012i
\(764\) 13.5561i 0.490443i
\(765\) 0 0
\(766\) 30.7142i 1.10975i
\(767\) 18.4127 0.664844
\(768\) 5.04790 26.5904i 0.182150 0.959497i
\(769\) 30.3097i 1.09299i 0.837461 + 0.546497i \(0.184039\pi\)
−0.837461 + 0.546497i \(0.815961\pi\)
\(770\) 0 0
\(771\) 8.20871 + 1.55834i 0.295630 + 0.0561221i
\(772\) 8.70417i 0.313270i
\(773\) 15.5960i 0.560948i −0.959862 0.280474i \(-0.909508\pi\)
0.959862 0.280474i \(-0.0904916\pi\)
\(774\) 7.95644 20.2005i 0.285988 0.726092i
\(775\) 0 0
\(776\) 36.0159 1.29289
\(777\) 33.0013 + 21.3959i 1.18392 + 0.767574i
\(778\) 14.4519i 0.518125i
\(779\) 44.7986i 1.60508i
\(780\) 0 0
\(781\) −9.41742 −0.336982
\(782\) 15.5960i 0.557711i
\(783\) −23.1494 14.6046i −0.827291 0.521926i
\(784\) −8.95644 8.77548i −0.319873 0.313410i
\(785\) 0 0
\(786\) 0.956439 5.03815i 0.0341151 0.179705i
\(787\) −6.32599 −0.225497 −0.112749 0.993624i \(-0.535965\pi\)
−0.112749 + 0.993624i \(0.535965\pi\)
\(788\) −2.79143 −0.0994406
\(789\) 9.21861 48.5601i 0.328191 1.72878i
\(790\) 0 0
\(791\) −44.0949 18.0017i −1.56783 0.640065i
\(792\) 10.3537 26.2867i 0.367901 0.934059i
\(793\) 16.7477i 0.594729i
\(794\) 9.64789 0.342391
\(795\) 0 0
\(796\) 6.21929i 0.220437i
\(797\) 17.7269i 0.627919i 0.949436 + 0.313960i \(0.101656\pi\)
−0.949436 + 0.313960i \(0.898344\pi\)
\(798\) 18.5488 + 12.0258i 0.656621 + 0.425710i
\(799\) −7.25227 −0.256567
\(800\) 0 0
\(801\) −20.9820 8.26424i −0.741362 0.292003i
\(802\) 22.2087i 0.784217i
\(803\) 49.4809i 1.74614i
\(804\) 5.60839 + 1.06469i 0.197793 + 0.0375488i
\(805\) 0 0
\(806\) 18.4127i 0.648559i
\(807\) 6.77806 35.7042i 0.238599 1.25685i
\(808\) −56.1249 −1.97447
\(809\) 28.5369i 1.00330i −0.865070 0.501652i \(-0.832726\pi\)
0.865070 0.501652i \(-0.167274\pi\)
\(810\) 0 0
\(811\) 13.6745i 0.480175i 0.970751 + 0.240088i \(0.0771762\pi\)
−0.970751 + 0.240088i \(0.922824\pi\)
\(812\) 4.16820 10.2100i 0.146275 0.358299i
\(813\) −44.1103 8.37386i −1.54701 0.293684i
\(814\) 28.9564 1.01492
\(815\) 0 0
\(816\) 8.20871 + 1.55834i 0.287362 + 0.0545527i
\(817\) −28.8826 −1.01048
\(818\) 34.8917i 1.21996i
\(819\) −14.0547 13.4337i −0.491112 0.469412i
\(820\) 0 0
\(821\) 17.1317i 0.597901i −0.954269 0.298950i \(-0.903363\pi\)
0.954269 0.298950i \(-0.0966365\pi\)
\(822\) 3.74166 19.7096i 0.130505 0.687451i
\(823\) 2.25227i 0.0785093i −0.999229 0.0392546i \(-0.987502\pi\)
0.999229 0.0392546i \(-0.0124984\pi\)
\(824\) −13.4650 −0.469076
\(825\) 0 0
\(826\) 20.2432 + 8.26424i 0.704350 + 0.287550i
\(827\) −14.8850 −0.517602 −0.258801 0.965931i \(-0.583327\pi\)
−0.258801 + 0.965931i \(0.583327\pi\)
\(828\) −11.6346 4.58258i −0.404332 0.159256i
\(829\) 15.2082i 0.528202i 0.964495 + 0.264101i \(0.0850752\pi\)
−0.964495 + 0.264101i \(0.914925\pi\)
\(830\) 0 0
\(831\) 31.9022 + 6.05630i 1.10668 + 0.210091i
\(832\) −20.0005 −0.693391
\(833\) −13.1930 + 13.4650i −0.457109 + 0.466535i
\(834\) 4.58258 + 0.869953i 0.158682 + 0.0301240i
\(835\) 0 0
\(836\) −10.6547 −0.368501
\(837\) −30.0473 18.9564i −1.03859 0.655230i
\(838\) −23.0679 −0.796867
\(839\) −7.51695 −0.259514 −0.129757 0.991546i \(-0.541420\pi\)
−0.129757 + 0.991546i \(0.541420\pi\)
\(840\) 0 0
\(841\) 1.25227 0.0431818
\(842\) 8.97689 0.309364
\(843\) −26.1101 4.95673i −0.899280 0.170719i
\(844\) 11.6697 0.401688
\(845\) 0 0
\(846\) 3.25507 8.26424i 0.111912 0.284131i
\(847\) −3.87650 1.58258i −0.133198 0.0543779i
\(848\) −7.05541 −0.242284
\(849\) −7.58258 + 39.9421i −0.260233 + 1.37081i
\(850\) 0 0
\(851\) 45.2097i 1.54977i
\(852\) −4.13212 0.784439i −0.141564 0.0268745i
\(853\) −17.5510 −0.600934 −0.300467 0.953792i \(-0.597142\pi\)
−0.300467 + 0.953792i \(0.597142\pi\)
\(854\) 7.51695 18.4127i 0.257225 0.630069i
\(855\) 0 0
\(856\) 32.3303 1.10503
\(857\) 46.7879i 1.59824i −0.601169 0.799122i \(-0.705298\pi\)
0.601169 0.799122i \(-0.294702\pi\)
\(858\) −14.0629 2.66970i −0.480100 0.0911420i
\(859\) 47.9673i 1.63662i 0.574774 + 0.818312i \(0.305090\pi\)
−0.574774 + 0.818312i \(0.694910\pi\)
\(860\) 0 0
\(861\) −25.4529 + 39.2589i −0.867432 + 1.33794i
\(862\) 37.6697i 1.28303i
\(863\) 22.8582 0.778104 0.389052 0.921216i \(-0.372803\pi\)
0.389052 + 0.921216i \(0.372803\pi\)
\(864\) 11.5565 18.3178i 0.393159 0.623185i
\(865\) 0 0
\(866\) −1.12413 −0.0381993
\(867\) −3.14892 + 16.5873i −0.106943 + 0.563335i
\(868\) 5.41022 13.2523i 0.183635 0.449811i
\(869\) 1.78780i 0.0606469i
\(870\) 0 0
\(871\) 10.2025i 0.345698i
\(872\) 15.3439 0.519610
\(873\) 32.7591 + 12.9030i 1.10873 + 0.436699i
\(874\) 25.4107i 0.859529i
\(875\) 0 0
\(876\) −4.12159 + 21.7109i −0.139256 + 0.733545i
\(877\) 31.4955i 1.06353i 0.846893 + 0.531763i \(0.178470\pi\)
−0.846893 + 0.531763i \(0.821530\pi\)
\(878\) 29.6230i 0.999729i
\(879\) 3.62614 + 0.688383i 0.122307 + 0.0232186i
\(880\) 0 0
\(881\) 34.8917 1.17553 0.587766 0.809031i \(-0.300007\pi\)
0.587766 + 0.809031i \(0.300007\pi\)
\(882\) −9.42246 21.0775i −0.317271 0.709715i
\(883\) 15.4174i 0.518838i 0.965765 + 0.259419i \(0.0835310\pi\)
−0.965765 + 0.259419i \(0.916469\pi\)
\(884\) 5.21972i 0.175558i
\(885\) 0 0
\(886\) 4.33030 0.145479
\(887\) 40.2778i 1.35239i 0.736721 + 0.676197i \(0.236373\pi\)
−0.736721 + 0.676197i \(0.763627\pi\)
\(888\) 44.8184 + 8.50830i 1.50401 + 0.285520i
\(889\) −8.16515 + 20.0005i −0.273850 + 0.670794i
\(890\) 0 0
\(891\) 18.8348 20.2005i 0.630991 0.676742i
\(892\) 1.93825 0.0648975
\(893\) −11.8162 −0.395414
\(894\) −33.6780 6.39342i −1.12636 0.213828i
\(895\) 0 0
\(896\) −1.56888 0.640492i −0.0524126 0.0213973i
\(897\) −4.16820 + 21.9564i −0.139172 + 0.733104i
\(898\) 40.0345i 1.33597i
\(899\) −36.0159 −1.20120
\(900\) 0 0
\(901\) 10.6070i 0.353371i
\(902\) 34.4470i 1.14696i
\(903\) 25.3110 + 16.4100i 0.842298 + 0.546091i
\(904\) −55.2432 −1.83736
\(905\) 0 0
\(906\) 1.47928 7.79228i 0.0491459 0.258881i
\(907\) 1.49545i 0.0496557i 0.999692 + 0.0248279i \(0.00790377\pi\)
−0.999692 + 0.0248279i \(0.992096\pi\)
\(908\) 2.13094i 0.0707178i
\(909\) −51.0498 20.1072i −1.69321 0.666912i
\(910\) 0 0
\(911\) 10.4873i 0.347461i 0.984793 + 0.173730i \(0.0555821\pi\)
−0.984793 + 0.173730i \(0.944418\pi\)
\(912\) 13.3745 + 2.53901i 0.442875 + 0.0840752i
\(913\) −47.8606 −1.58396
\(914\) 37.5617i 1.24243i
\(915\) 0 0
\(916\) 3.06743i 0.101351i
\(917\) 6.59649 + 2.69300i 0.217835 + 0.0889308i
\(918\) 13.0114 + 8.20871i 0.429440 + 0.270928i
\(919\) 24.0780 0.794261 0.397130 0.917762i \(-0.370006\pi\)
0.397130 + 0.917762i \(0.370006\pi\)
\(920\) 0 0
\(921\) 4.25227 22.3993i 0.140117 0.738083i
\(922\) 36.6356 1.20653
\(923\) 7.51695i 0.247423i
\(924\) 9.33715 + 6.05360i 0.307170 + 0.199149i
\(925\) 0 0
\(926\) 14.0150i 0.460563i
\(927\) −12.2474 4.82395i −0.402259 0.158439i
\(928\) 21.9564i 0.720755i
\(929\) 7.51695 0.246623 0.123312 0.992368i \(-0.460649\pi\)
0.123312 + 0.992368i \(0.460649\pi\)
\(930\) 0 0
\(931\) −21.4955 + 21.9387i −0.704485 + 0.719012i
\(932\) 4.16820 0.136534
\(933\) −3.98663 + 21.0000i −0.130516 + 0.687509i
\(934\) 17.7644i 0.581268i
\(935\) 0 0
\(936\) −20.9820 8.26424i −0.685817 0.270125i
\(937\) −36.2311 −1.18362 −0.591809 0.806078i \(-0.701586\pi\)
−0.591809 + 0.806078i \(0.701586\pi\)
\(938\) 4.57923 11.2168i 0.149517 0.366241i
\(939\) 7.41742 39.0721i 0.242058 1.27507i
\(940\) 0 0
\(941\) −25.2439 −0.822926 −0.411463 0.911426i \(-0.634982\pi\)
−0.411463 + 0.911426i \(0.634982\pi\)
\(942\) −0.688383 + 3.62614i −0.0224287 + 0.118146i
\(943\) 53.7821 1.75139
\(944\) 13.4650 0.438249
\(945\) 0 0
\(946\) 22.2087 0.722068
\(947\) −28.9479 −0.940681 −0.470340 0.882485i \(-0.655869\pi\)
−0.470340 + 0.882485i \(0.655869\pi\)
\(948\) −0.148917 + 0.784439i −0.00483662 + 0.0254774i
\(949\) 39.4955 1.28208
\(950\) 0 0
\(951\) 0.429283 2.26129i 0.0139204 0.0733275i
\(952\) −8.26424 + 20.2432i −0.267846 + 0.656085i
\(953\) −5.26761 −0.170635 −0.0853173 0.996354i \(-0.527190\pi\)
−0.0853173 + 0.996354i \(0.527190\pi\)
\(954\) −12.0871 4.76080i −0.391335 0.154137i
\(955\) 0 0
\(956\) 11.4531i 0.370419i
\(957\) 5.22202 27.5076i 0.168804 0.889194i
\(958\) −8.26424 −0.267006
\(959\) 25.8059 + 10.5352i 0.833317 + 0.340200i
\(960\) 0 0
\(961\) −15.7477 −0.507991
\(962\) 23.1129i 0.745190i
\(963\) 29.4068 + 11.5826i 0.947622 + 0.373243i
\(964\) 15.1015i 0.486386i
\(965\) 0 0
\(966\) −14.4374 + 22.2684i −0.464515 + 0.716474i
\(967\) 14.7477i 0.474255i 0.971479 + 0.237127i \(0.0762059\pi\)
−0.971479 + 0.237127i \(0.923794\pi\)
\(968\) −4.85658 −0.156096
\(969\) 3.81713 20.1072i 0.122624 0.645935i
\(970\) 0 0
\(971\) 27.3748 0.878499 0.439250 0.898365i \(-0.355244\pi\)
0.439250 + 0.898365i \(0.355244\pi\)
\(972\) 9.94688 7.29457i 0.319046 0.233974i
\(973\) −2.44949 + 6.00000i −0.0785270 + 0.192351i
\(974\) 24.0055i 0.769187i
\(975\) 0 0
\(976\) 12.2474i 0.392031i
\(977\) −1.32888 −0.0425145 −0.0212572 0.999774i \(-0.506767\pi\)
−0.0212572 + 0.999774i \(0.506767\pi\)
\(978\) 7.48331 + 1.42063i 0.239290 + 0.0454267i
\(979\) 23.0679i 0.737253i
\(980\) 0 0
\(981\) 13.9564 + 5.49707i 0.445595 + 0.175508i
\(982\) 28.9564i 0.924037i
\(983\) 15.5960i 0.497434i −0.968576 0.248717i \(-0.919991\pi\)
0.968576 0.248717i \(-0.0800089\pi\)
\(984\) −10.1216 + 53.3166i −0.322665 + 1.69967i
\(985\) 0 0
\(986\) 15.5960 0.496677
\(987\) 10.3550 + 6.71352i 0.329604 + 0.213694i
\(988\) 8.50455i 0.270566i
\(989\) 34.6744i 1.10258i
\(990\) 0 0
\(991\) −42.0780 −1.33665 −0.668326 0.743868i \(-0.732989\pi\)
−0.668326 + 0.743868i \(0.732989\pi\)
\(992\) 28.4989i 0.904842i
\(993\) −5.49171 + 28.9282i −0.174274 + 0.918009i
\(994\) −3.37386 + 8.26424i −0.107012 + 0.262126i
\(995\) 0 0
\(996\) −21.0000 3.98663i −0.665410 0.126321i
\(997\) 25.0061 0.791952 0.395976 0.918261i \(-0.370406\pi\)
0.395976 + 0.918261i \(0.370406\pi\)
\(998\) −3.57560 −0.113184
\(999\) 37.7175 + 23.7955i 1.19333 + 0.752855i
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 525.2.g.f.524.10 16
3.2 odd 2 inner 525.2.g.f.524.5 16
5.2 odd 4 525.2.b.i.251.6 yes 8
5.3 odd 4 525.2.b.h.251.3 8
5.4 even 2 inner 525.2.g.f.524.7 16
7.6 odd 2 inner 525.2.g.f.524.11 16
15.2 even 4 525.2.b.i.251.3 yes 8
15.8 even 4 525.2.b.h.251.6 yes 8
15.14 odd 2 inner 525.2.g.f.524.12 16
21.20 even 2 inner 525.2.g.f.524.8 16
35.13 even 4 525.2.b.h.251.4 yes 8
35.27 even 4 525.2.b.i.251.5 yes 8
35.34 odd 2 inner 525.2.g.f.524.6 16
105.62 odd 4 525.2.b.i.251.4 yes 8
105.83 odd 4 525.2.b.h.251.5 yes 8
105.104 even 2 inner 525.2.g.f.524.9 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.b.h.251.3 8 5.3 odd 4
525.2.b.h.251.4 yes 8 35.13 even 4
525.2.b.h.251.5 yes 8 105.83 odd 4
525.2.b.h.251.6 yes 8 15.8 even 4
525.2.b.i.251.3 yes 8 15.2 even 4
525.2.b.i.251.4 yes 8 105.62 odd 4
525.2.b.i.251.5 yes 8 35.27 even 4
525.2.b.i.251.6 yes 8 5.2 odd 4
525.2.g.f.524.5 16 3.2 odd 2 inner
525.2.g.f.524.6 16 35.34 odd 2 inner
525.2.g.f.524.7 16 5.4 even 2 inner
525.2.g.f.524.8 16 21.20 even 2 inner
525.2.g.f.524.9 16 105.104 even 2 inner
525.2.g.f.524.10 16 1.1 even 1 trivial
525.2.g.f.524.11 16 7.6 odd 2 inner
525.2.g.f.524.12 16 15.14 odd 2 inner