Properties

Label 525.2.b.i.251.3
Level $525$
Weight $2$
Character 525.251
Analytic conductor $4.192$
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] = [525,2,Mod(251,525)]
 
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, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.b (of order \(2\), degree \(1\), 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: \(8\)
Coefficient field: 8.0.624529833984.7
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{6} - 2x^{4} - 18x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.3
Root \(-1.70166 + 0.323042i\) of defining polynomial
Character \(\chi\) \(=\) 525.251
Dual form 525.2.b.i.251.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.09941i q^{2} +(-1.70166 + 0.323042i) q^{3} +0.791288 q^{4} +(0.355157 + 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} -3.06878i q^{8} +(2.79129 - 1.09941i) q^{9} +O(q^{10})\) \(q-1.09941i q^{2} +(-1.70166 + 0.323042i) q^{3} +0.791288 q^{4} +(0.355157 + 1.87083i) q^{6} +(1.00000 - 2.44949i) q^{7} -3.06878i q^{8} +(2.79129 - 1.09941i) q^{9} +3.06878i q^{11} +(-1.34650 + 0.255619i) q^{12} +2.44949i q^{13} +(-2.69300 - 1.09941i) q^{14} -1.79129 q^{16} +2.69300 q^{17} +(-1.20871 - 3.06878i) q^{18} -4.38774i q^{19} +(-0.910371 + 4.49124i) q^{21} +3.37386 q^{22} -5.26761i q^{23} +(0.991345 + 5.22202i) q^{24} +2.69300 q^{26} +(-4.39466 + 2.77253i) q^{27} +(0.791288 - 1.93825i) q^{28} -5.26761i q^{29} -6.83723i q^{31} -4.16820i q^{32} +(-0.991345 - 5.22202i) q^{33} -2.96073i q^{34} +(2.20871 - 0.869953i) q^{36} -8.58258 q^{37} -4.82395 q^{38} +(-0.791288 - 4.16820i) q^{39} +10.2100 q^{41} +(4.93773 + 1.00088i) q^{42} +6.58258 q^{43} +2.42829i q^{44} -5.79129 q^{46} +2.69300 q^{47} +(3.04816 - 0.578661i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(-4.58258 + 0.869953i) q^{51} +1.93825i q^{52} +3.93874i q^{53} +(3.04816 + 4.83156i) q^{54} +(-7.51695 - 3.06878i) q^{56} +(1.41742 + 7.46644i) q^{57} -5.79129 q^{58} -7.51695 q^{59} +6.83723i q^{61} -7.51695 q^{62} +(0.0982834 - 7.93665i) q^{63} -8.16515 q^{64} +(-5.74117 + 1.08990i) q^{66} -4.16515 q^{67} +2.13094 q^{68} +(1.70166 + 8.96368i) q^{69} +3.06878i q^{71} +(-3.37386 - 8.56585i) q^{72} +16.1240i q^{73} +9.43581i q^{74} -3.47197i q^{76} +(7.51695 + 3.06878i) q^{77} +(-4.58258 + 0.869953i) q^{78} +0.582576 q^{79} +(6.58258 - 6.13756i) q^{81} -11.2250i q^{82} +15.5960 q^{83} +(-0.720366 + 3.55386i) q^{84} -7.23698i q^{86} +(1.70166 + 8.96368i) q^{87} +9.41742 q^{88} +7.51695 q^{89} +(6.00000 + 2.44949i) q^{91} -4.16820i q^{92} +(2.20871 + 11.6346i) q^{93} -2.96073i q^{94} +(1.34650 + 7.09285i) q^{96} -11.7362i q^{97} +(-5.38601 + 5.49707i) q^{98} +(3.37386 + 8.56585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 12 q^{4} + 8 q^{7} + 4 q^{9} + 4 q^{16} - 28 q^{18} - 12 q^{21} - 28 q^{22} - 12 q^{28} + 36 q^{36} - 32 q^{37} + 12 q^{39} + 16 q^{43} - 28 q^{46} - 40 q^{49} + 48 q^{57} - 28 q^{58} + 4 q^{63} + 8 q^{64} + 40 q^{67} + 28 q^{72} - 32 q^{79} + 16 q^{81} + 60 q^{84} + 112 q^{88} + 48 q^{91} + 36 q^{93} - 28 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.09941i 0.777403i −0.921364 0.388702i \(-0.872924\pi\)
0.921364 0.388702i \(-0.127076\pi\)
\(3\) −1.70166 + 0.323042i −0.982453 + 0.186508i
\(4\) 0.791288 0.395644
\(5\) 0 0
\(6\) 0.355157 + 1.87083i 0.144992 + 0.763763i
\(7\) 1.00000 2.44949i 0.377964 0.925820i
\(8\) 3.06878i 1.08498i
\(9\) 2.79129 1.09941i 0.930429 0.366471i
\(10\) 0 0
\(11\) 3.06878i 0.925273i 0.886548 + 0.462636i \(0.153096\pi\)
−0.886548 + 0.462636i \(0.846904\pi\)
\(12\) −1.34650 + 0.255619i −0.388702 + 0.0737909i
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) −2.69300 1.09941i −0.719736 0.293831i
\(15\) 0 0
\(16\) −1.79129 −0.447822
\(17\) 2.69300 0.653150 0.326575 0.945171i \(-0.394106\pi\)
0.326575 + 0.945171i \(0.394106\pi\)
\(18\) −1.20871 3.06878i −0.284896 0.723319i
\(19\) 4.38774i 1.00662i −0.864107 0.503308i \(-0.832116\pi\)
0.864107 0.503308i \(-0.167884\pi\)
\(20\) 0 0
\(21\) −0.910371 + 4.49124i −0.198659 + 0.980069i
\(22\) 3.37386 0.719310
\(23\) 5.26761i 1.09837i −0.835700 0.549186i \(-0.814938\pi\)
0.835700 0.549186i \(-0.185062\pi\)
\(24\) 0.991345 + 5.22202i 0.202358 + 1.06594i
\(25\) 0 0
\(26\) 2.69300 0.528142
\(27\) −4.39466 + 2.77253i −0.845753 + 0.533574i
\(28\) 0.791288 1.93825i 0.149539 0.366295i
\(29\) 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 \(-0.210441\pi\)
\(32\) 4.16820i 0.736840i
\(33\) −0.991345 5.22202i −0.172571 0.909037i
\(34\) 2.96073i 0.507761i
\(35\) 0 0
\(36\) 2.20871 0.869953i 0.368119 0.144992i
\(37\) −8.58258 −1.41097 −0.705483 0.708726i \(-0.749270\pi\)
−0.705483 + 0.708726i \(0.749270\pi\)
\(38\) −4.82395 −0.782547
\(39\) −0.791288 4.16820i −0.126707 0.667446i
\(40\) 0 0
\(41\) 10.2100 1.59453 0.797264 0.603631i \(-0.206280\pi\)
0.797264 + 0.603631i \(0.206280\pi\)
\(42\) 4.93773 + 1.00088i 0.761909 + 0.154438i
\(43\) 6.58258 1.00383 0.501917 0.864916i \(-0.332628\pi\)
0.501917 + 0.864916i \(0.332628\pi\)
\(44\) 2.42829i 0.366079i
\(45\) 0 0
\(46\) −5.79129 −0.853879
\(47\) 2.69300 0.392815 0.196408 0.980522i \(-0.437072\pi\)
0.196408 + 0.980522i \(0.437072\pi\)
\(48\) 3.04816 0.578661i 0.439964 0.0835225i
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) 0 0
\(51\) −4.58258 + 0.869953i −0.641689 + 0.121818i
\(52\) 1.93825i 0.268787i
\(53\) 3.93874i 0.541027i 0.962716 + 0.270513i \(0.0871935\pi\)
−0.962716 + 0.270513i \(0.912807\pi\)
\(54\) 3.04816 + 4.83156i 0.414802 + 0.657492i
\(55\) 0 0
\(56\) −7.51695 3.06878i −1.00449 0.410083i
\(57\) 1.41742 + 7.46644i 0.187742 + 0.988954i
\(58\) −5.79129 −0.760433
\(59\) −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 \(0.855790\pi\)
\(62\) −7.51695 −0.954654
\(63\) 0.0982834 7.93665i 0.0123825 0.999923i
\(64\) −8.16515 −1.02064
\(65\) 0 0
\(66\) −5.74117 + 1.08990i −0.706689 + 0.134157i
\(67\) −4.16515 −0.508854 −0.254427 0.967092i \(-0.581887\pi\)
−0.254427 + 0.967092i \(0.581887\pi\)
\(68\) 2.13094 0.258415
\(69\) 1.70166 + 8.96368i 0.204856 + 1.07910i
\(70\) 0 0
\(71\) 3.06878i 0.364197i 0.983280 + 0.182099i \(0.0582890\pi\)
−0.983280 + 0.182099i \(0.941711\pi\)
\(72\) −3.37386 8.56585i −0.397614 1.00950i
\(73\) 16.1240i 1.88717i 0.331136 + 0.943583i \(0.392568\pi\)
−0.331136 + 0.943583i \(0.607432\pi\)
\(74\) 9.43581i 1.09689i
\(75\) 0 0
\(76\) 3.47197i 0.398262i
\(77\) 7.51695 + 3.06878i 0.856636 + 0.349720i
\(78\) −4.58258 + 0.869953i −0.518875 + 0.0985028i
\(79\) 0.582576 0.0655449 0.0327724 0.999463i \(-0.489566\pi\)
0.0327724 + 0.999463i \(0.489566\pi\)
\(80\) 0 0
\(81\) 6.58258 6.13756i 0.731397 0.681952i
\(82\) 11.2250i 1.23959i
\(83\) 15.5960 1.71188 0.855940 0.517076i \(-0.172979\pi\)
0.855940 + 0.517076i \(0.172979\pi\)
\(84\) −0.720366 + 3.55386i −0.0785983 + 0.387758i
\(85\) 0 0
\(86\) 7.23698i 0.780384i
\(87\) 1.70166 + 8.96368i 0.182437 + 0.961007i
\(88\) 9.41742 1.00390
\(89\) 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
\(92\) 4.16820i 0.434565i
\(93\) 2.20871 + 11.6346i 0.229033 + 1.20646i
\(94\) 2.96073i 0.305376i
\(95\) 0 0
\(96\) 1.34650 + 7.09285i 0.137427 + 0.723911i
\(97\) 11.7362i 1.19163i −0.803121 0.595816i \(-0.796829\pi\)
0.803121 0.595816i \(-0.203171\pi\)
\(98\) −5.38601 + 5.49707i −0.544069 + 0.555288i
\(99\) 3.37386 + 8.56585i 0.339086 + 0.860901i
\(100\) 0 0
\(101\) −18.2890 −1.81982 −0.909910 0.414805i \(-0.863850\pi\)
−0.909910 + 0.414805i \(0.863850\pi\)
\(102\) 0.956439 + 5.03815i 0.0947016 + 0.498851i
\(103\) 4.38774i 0.432337i −0.976356 0.216168i \(-0.930644\pi\)
0.976356 0.216168i \(-0.0693561\pi\)
\(104\) 7.51695 0.737098
\(105\) 0 0
\(106\) 4.33030 0.420596
\(107\) 10.5352i 1.01848i 0.860625 + 0.509239i \(0.170073\pi\)
−0.860625 + 0.509239i \(0.829927\pi\)
\(108\) −3.47744 + 2.19387i −0.334617 + 0.211105i
\(109\) 5.00000 0.478913 0.239457 0.970907i \(-0.423031\pi\)
0.239457 + 0.970907i \(0.423031\pi\)
\(110\) 0 0
\(111\) 14.6046 2.77253i 1.38621 0.263157i
\(112\) −1.79129 + 4.38774i −0.169261 + 0.414603i
\(113\) 18.0017i 1.69345i 0.532028 + 0.846727i \(0.321430\pi\)
−0.532028 + 0.846727i \(0.678570\pi\)
\(114\) 8.20871 1.55834i 0.768816 0.145952i
\(115\) 0 0
\(116\) 4.16820i 0.387007i
\(117\) 2.69300 + 6.83723i 0.248968 + 0.632102i
\(118\) 8.26424i 0.760785i
\(119\) 2.69300 6.59649i 0.246867 0.604699i
\(120\) 0 0
\(121\) 1.58258 0.143871
\(122\) 7.51695 0.680553
\(123\) −17.3739 + 3.29824i −1.56655 + 0.297393i
\(124\) 5.41022i 0.485852i
\(125\) 0 0
\(126\) −8.72566 0.108054i −0.777344 0.00962623i
\(127\) 8.16515 0.724540 0.362270 0.932073i \(-0.382002\pi\)
0.362270 + 0.932073i \(0.382002\pi\)
\(128\) 0.640492i 0.0566120i
\(129\) −11.2013 + 2.12645i −0.986219 + 0.187223i
\(130\) 0 0
\(131\) 2.69300 0.235289 0.117644 0.993056i \(-0.462466\pi\)
0.117644 + 0.993056i \(0.462466\pi\)
\(132\) −0.784439 4.13212i −0.0682767 0.359655i
\(133\) −10.7477 4.38774i −0.931946 0.380465i
\(134\) 4.57923i 0.395585i
\(135\) 0 0
\(136\) 8.26424i 0.708653i
\(137\) 10.5352i 0.900085i 0.893007 + 0.450042i \(0.148591\pi\)
−0.893007 + 0.450042i \(0.851409\pi\)
\(138\) 9.85480 1.87083i 0.838896 0.159256i
\(139\) 2.44949i 0.207763i 0.994590 + 0.103882i \(0.0331263\pi\)
−0.994590 + 0.103882i \(0.966874\pi\)
\(140\) 0 0
\(141\) −4.58258 + 0.869953i −0.385922 + 0.0732633i
\(142\) 3.37386 0.283128
\(143\) −7.51695 −0.628599
\(144\) −5.00000 + 1.96937i −0.416667 + 0.164114i
\(145\) 0 0
\(146\) 17.7269 1.46709
\(147\) 10.0909 + 6.72118i 0.832281 + 0.554354i
\(148\) −6.79129 −0.558240
\(149\) 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 \(0.554208\pi\)
\(152\) −13.4650 −1.09216
\(153\) 7.51695 2.96073i 0.607709 0.239361i
\(154\) 3.37386 8.26424i 0.271874 0.665952i
\(155\) 0 0
\(156\) −0.626136 3.29824i −0.0501310 0.264071i
\(157\) 1.93825i 0.154689i 0.997004 + 0.0773447i \(0.0246442\pi\)
−0.997004 + 0.0773447i \(0.975356\pi\)
\(158\) 0.640492i 0.0509548i
\(159\) −1.27238 6.70239i −0.100906 0.531534i
\(160\) 0 0
\(161\) −12.9030 5.26761i −1.01690 0.415146i
\(162\) −6.74773 7.23698i −0.530152 0.568591i
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 8.07901 0.630865
\(165\) 0 0
\(166\) 17.1464i 1.33082i
\(167\) −18.2890 −1.41524 −0.707621 0.706592i \(-0.750232\pi\)
−0.707621 + 0.706592i \(0.750232\pi\)
\(168\) 13.7826 + 2.79373i 1.06335 + 0.215541i
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) −4.82395 12.2474i −0.368896 0.936586i
\(172\) 5.20871 0.397161
\(173\) 8.07901 0.614236 0.307118 0.951671i \(-0.400635\pi\)
0.307118 + 0.951671i \(0.400635\pi\)
\(174\) 9.85480 1.87083i 0.747090 0.141827i
\(175\) 0 0
\(176\) 5.49707i 0.414357i
\(177\) 12.7913 2.42829i 0.961452 0.182521i
\(178\) 8.26424i 0.619431i
\(179\) 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 \(0.849577\pi\)
\(182\) 2.69300 6.59649i 0.199619 0.488964i
\(183\) −2.20871 11.6346i −0.163273 0.860057i
\(184\) −16.1652 −1.19171
\(185\) 0 0
\(186\) 12.7913 2.42829i 0.937903 0.178051i
\(187\) 8.26424i 0.604341i
\(188\) 2.13094 0.155415
\(189\) 2.39662 + 13.5372i 0.174329 + 0.984688i
\(190\) 0 0
\(191\) 17.1317i 1.23961i 0.784757 + 0.619803i \(0.212788\pi\)
−0.784757 + 0.619803i \(0.787212\pi\)
\(192\) 13.8943 2.63769i 1.00274 0.190359i
\(193\) 11.0000 0.791797 0.395899 0.918294i \(-0.370433\pi\)
0.395899 + 0.918294i \(0.370433\pi\)
\(194\) −12.9030 −0.926379
\(195\) 0 0
\(196\) −3.95644 3.87650i −0.282603 0.276893i
\(197\) 3.52770i 0.251339i −0.992072 0.125669i \(-0.959892\pi\)
0.992072 0.125669i \(-0.0401078\pi\)
\(198\) 9.41742 3.70927i 0.669267 0.263607i
\(199\) 7.85971i 0.557160i 0.960413 + 0.278580i \(0.0898637\pi\)
−0.960413 + 0.278580i \(0.910136\pi\)
\(200\) 0 0
\(201\) 7.08767 1.34552i 0.499926 0.0949056i
\(202\) 20.1072i 1.41473i
\(203\) −12.9030 5.26761i −0.905610 0.369714i
\(204\) −3.62614 + 0.688383i −0.253880 + 0.0481965i
\(205\) 0 0
\(206\) −4.82395 −0.336100
\(207\) −5.79129 14.7034i −0.402522 1.02196i
\(208\) 4.38774i 0.304235i
\(209\) 13.4650 0.931395
\(210\) 0 0
\(211\) −14.7477 −1.01528 −0.507638 0.861571i \(-0.669481\pi\)
−0.507638 + 0.861571i \(0.669481\pi\)
\(212\) 3.11667i 0.214054i
\(213\) −0.991345 5.22202i −0.0679259 0.357807i
\(214\) 11.5826 0.791769
\(215\) 0 0
\(216\) 8.50830 + 13.4863i 0.578916 + 0.917624i
\(217\) −16.7477 6.83723i −1.13691 0.464141i
\(218\) 5.49707i 0.372309i
\(219\) −5.20871 27.4375i −0.351972 1.85405i
\(220\) 0 0
\(221\) 6.59649i 0.443728i
\(222\) −3.04816 16.0565i −0.204579 1.07764i
\(223\) 2.44949i 0.164030i 0.996631 + 0.0820150i \(0.0261355\pi\)
−0.996631 + 0.0820150i \(0.973864\pi\)
\(224\) −10.2100 4.16820i −0.682181 0.278499i
\(225\) 0 0
\(226\) 19.7913 1.31650
\(227\) 2.69300 0.178741 0.0893705 0.995998i \(-0.471514\pi\)
0.0893705 + 0.995998i \(0.471514\pi\)
\(228\) 1.12159 + 5.90810i 0.0742792 + 0.391274i
\(229\) 3.87650i 0.256167i 0.991763 + 0.128083i \(0.0408825\pi\)
−0.991763 + 0.128083i \(0.959118\pi\)
\(230\) 0 0
\(231\) −13.7826 2.79373i −0.906831 0.183814i
\(232\) −16.1652 −1.06129
\(233\) 5.26761i 0.345093i −0.985001 0.172546i \(-0.944801\pi\)
0.985001 0.172546i \(-0.0551995\pi\)
\(234\) 7.51695 2.96073i 0.491398 0.193549i
\(235\) 0 0
\(236\) −5.94807 −0.387186
\(237\) −0.991345 + 0.188196i −0.0643948 + 0.0122247i
\(238\) −7.25227 2.96073i −0.470095 0.191915i
\(239\) 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 \(0.789287\pi\)
\(242\) 1.73991i 0.111845i
\(243\) −9.21861 + 12.5705i −0.591374 + 0.806397i
\(244\) 5.41022i 0.346354i
\(245\) 0 0
\(246\) 3.62614 + 19.1011i 0.231194 + 1.21784i
\(247\) 10.7477 0.683861
\(248\) −20.9820 −1.33236
\(249\) −26.5390 + 5.03815i −1.68184 + 0.319280i
\(250\) 0 0
\(251\) 17.7269 1.11891 0.559456 0.828860i \(-0.311010\pi\)
0.559456 + 0.828860i \(0.311010\pi\)
\(252\) 0.0777705 6.28017i 0.00489908 0.395614i
\(253\) 16.1652 1.01629
\(254\) 8.97689i 0.563260i
\(255\) 0 0
\(256\) −15.6261 −0.976634
\(257\) −4.82395 −0.300909 −0.150455 0.988617i \(-0.548074\pi\)
−0.150455 + 0.988617i \(0.548074\pi\)
\(258\) 2.33785 + 12.3149i 0.145548 + 0.766690i
\(259\) −8.58258 + 21.0229i −0.533295 + 1.30630i
\(260\) 0 0
\(261\) −5.79129 14.7034i −0.358472 0.910119i
\(262\) 2.96073i 0.182914i
\(263\) 28.5369i 1.75966i −0.475289 0.879830i \(-0.657656\pi\)
0.475289 0.879830i \(-0.342344\pi\)
\(264\) −16.0252 + 3.04222i −0.986286 + 0.187236i
\(265\) 0 0
\(266\) −4.82395 + 11.8162i −0.295775 + 0.724498i
\(267\) −12.7913 + 2.42829i −0.782814 + 0.148609i
\(268\) −3.29583 −0.201325
\(269\) −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 \(0.711467\pi\)
\(272\) −4.82395 −0.292495
\(273\) −11.0012 2.22995i −0.665826 0.134962i
\(274\) 11.5826 0.699729
\(275\) 0 0
\(276\) 1.34650 + 7.09285i 0.0810499 + 0.426939i
\(277\) 18.7477 1.12644 0.563221 0.826306i \(-0.309562\pi\)
0.563221 + 0.826306i \(0.309562\pi\)
\(278\) 2.69300 0.161516
\(279\) −7.51695 19.0847i −0.450028 1.14257i
\(280\) 0 0
\(281\) 15.3439i 0.915341i −0.889122 0.457670i \(-0.848684\pi\)
0.889122 0.457670i \(-0.151316\pi\)
\(282\) 0.956439 + 5.03815i 0.0569551 + 0.300017i
\(283\) 23.4724i 1.39529i −0.716443 0.697645i \(-0.754231\pi\)
0.716443 0.697645i \(-0.245769\pi\)
\(284\) 2.42829i 0.144093i
\(285\) 0 0
\(286\) 8.26424i 0.488675i
\(287\) 10.2100 25.0092i 0.602675 1.47625i
\(288\) −4.58258 11.6346i −0.270031 0.685578i
\(289\) −9.74773 −0.573396
\(290\) 0 0
\(291\) 3.79129 + 19.9710i 0.222249 + 1.17072i
\(292\) 12.7587i 0.746646i
\(293\) 2.13094 0.124491 0.0622455 0.998061i \(-0.480174\pi\)
0.0622455 + 0.998061i \(0.480174\pi\)
\(294\) 7.38937 11.0941i 0.430957 0.647018i
\(295\) 0 0
\(296\) 26.3381i 1.53087i
\(297\) −8.50830 13.4863i −0.493701 0.782552i
\(298\) 19.7913 1.14648
\(299\) 12.9030 0.746197
\(300\) 0 0
\(301\) 6.58258 16.1240i 0.379413 0.929369i
\(302\) 4.57923i 0.263505i
\(303\) 31.1216 5.90810i 1.78789 0.339412i
\(304\) 7.85971i 0.450785i
\(305\) 0 0
\(306\) −3.25507 8.26424i −0.186080 0.472435i
\(307\) 13.1632i 0.751265i −0.926769 0.375632i \(-0.877426\pi\)
0.926769 0.375632i \(-0.122574\pi\)
\(308\) 5.94807 + 2.42829i 0.338923 + 0.138365i
\(309\) 1.41742 + 7.46644i 0.0806345 + 0.424751i
\(310\) 0 0
\(311\) −12.3409 −0.699788 −0.349894 0.936789i \(-0.613782\pi\)
−0.349894 + 0.936789i \(0.613782\pi\)
\(312\) −12.7913 + 2.42829i −0.724164 + 0.137475i
\(313\) 22.9612i 1.29784i 0.760855 + 0.648921i \(0.224780\pi\)
−0.760855 + 0.648921i \(0.775220\pi\)
\(314\) 2.13094 0.120256
\(315\) 0 0
\(316\) 0.460985 0.0259324
\(317\) 1.32888i 0.0746371i 0.999303 + 0.0373185i \(0.0118816\pi\)
−0.999303 + 0.0373185i \(0.988118\pi\)
\(318\) −7.36870 + 1.39887i −0.413216 + 0.0784447i
\(319\) 16.1652 0.905075
\(320\) 0 0
\(321\) −3.40332 17.9274i −0.189955 1.00061i
\(322\) −5.79129 + 14.1857i −0.322736 + 0.790538i
\(323\) 11.8162i 0.657471i
\(324\) 5.20871 4.85658i 0.289373 0.269810i
\(325\) 0 0
\(326\) 4.39766i 0.243564i
\(327\) −8.50830 + 1.61521i −0.470510 + 0.0893213i
\(328\) 31.3321i 1.73003i
\(329\) 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 \(0.345262\pi\)
\(332\) 12.3409 0.677295
\(333\) −23.9564 + 9.43581i −1.31280 + 0.517079i
\(334\) 20.1072i 1.10021i
\(335\) 0 0
\(336\) 1.63074 8.04510i 0.0889640 0.438896i
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 7.69590i 0.418602i
\(339\) −5.81529 30.6327i −0.315843 1.66374i
\(340\) 0 0
\(341\) 20.9820 1.13624
\(342\) −13.4650 + 5.30352i −0.728105 + 0.286781i
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) 20.2005i 1.08914i
\(345\) 0 0
\(346\) 8.88218i 0.477509i
\(347\) 3.52770i 0.189377i −0.995507 0.0946886i \(-0.969814\pi\)
0.995507 0.0946886i \(-0.0301855\pi\)
\(348\) 1.34650 + 7.09285i 0.0721801 + 0.380217i
\(349\) 9.28672i 0.497107i 0.968618 + 0.248553i \(0.0799551\pi\)
−0.968618 + 0.248553i \(0.920045\pi\)
\(350\) 0 0
\(351\) −6.79129 10.7647i −0.362492 0.574576i
\(352\) 12.7913 0.681778
\(353\) 30.6299 1.63026 0.815132 0.579276i \(-0.196665\pi\)
0.815132 + 0.579276i \(0.196665\pi\)
\(354\) −2.66970 14.0629i −0.141893 0.747436i
\(355\) 0 0
\(356\) 5.94807 0.315247
\(357\) −2.45163 + 12.0949i −0.129754 + 0.640131i
\(358\) −15.9129 −0.841022
\(359\) 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
\(362\) 13.4650 0.707706
\(363\) −2.69300 + 0.511238i −0.141346 + 0.0268331i
\(364\) 4.74773 + 1.93825i 0.248849 + 0.101592i
\(365\) 0 0
\(366\) −12.7913 + 2.42829i −0.668611 + 0.126929i
\(367\) 0.915775i 0.0478031i −0.999714 0.0239015i \(-0.992391\pi\)
0.999714 0.0239015i \(-0.00760882\pi\)
\(368\) 9.43581i 0.491875i
\(369\) 28.4989 11.2250i 1.48359 0.584349i
\(370\) 0 0
\(371\) 9.64789 + 3.93874i 0.500894 + 0.204489i
\(372\) 1.74773 + 9.20635i 0.0906154 + 0.477327i
\(373\) −26.9129 −1.39350 −0.696748 0.717316i \(-0.745370\pi\)
−0.696748 + 0.717316i \(0.745370\pi\)
\(374\) 9.08583 0.469817
\(375\) 0 0
\(376\) 8.26424i 0.426196i
\(377\) 12.9030 0.664536
\(378\) 14.8830 2.63488i 0.765499 0.135524i
\(379\) 17.3303 0.890198 0.445099 0.895481i \(-0.353169\pi\)
0.445099 + 0.895481i \(0.353169\pi\)
\(380\) 0 0
\(381\) −13.8943 + 2.63769i −0.711827 + 0.135133i
\(382\) 18.8348 0.963675
\(383\) −27.9369 −1.42751 −0.713753 0.700397i \(-0.753006\pi\)
−0.713753 + 0.700397i \(0.753006\pi\)
\(384\) −0.206906 1.08990i −0.0105586 0.0556187i
\(385\) 0 0
\(386\) 12.0936i 0.615546i
\(387\) 18.3739 7.23698i 0.933996 0.367876i
\(388\) 9.28672i 0.471462i
\(389\) 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
\(392\) −15.0339 + 15.3439i −0.759327 + 0.774985i
\(393\) −4.58258 + 0.869953i −0.231160 + 0.0438833i
\(394\) −3.87841 −0.195391
\(395\) 0 0
\(396\) 2.66970 + 6.77806i 0.134157 + 0.340610i
\(397\) 8.77548i 0.440429i 0.975451 + 0.220214i \(0.0706757\pi\)
−0.975451 + 0.220214i \(0.929324\pi\)
\(398\) 8.64108 0.433138
\(399\) 19.7064 + 3.99447i 0.986554 + 0.199974i
\(400\) 0 0
\(401\) 20.2005i 1.00876i −0.863481 0.504382i \(-0.831720\pi\)
0.863481 0.504382i \(-0.168280\pi\)
\(402\) −1.47928 7.79228i −0.0737799 0.388644i
\(403\) 16.7477 0.834264
\(404\) −14.4718 −0.720001
\(405\) 0 0
\(406\) −5.79129 + 14.1857i −0.287417 + 0.704024i
\(407\) 26.3381i 1.30553i
\(408\) 2.66970 + 14.0629i 0.132170 + 0.696219i
\(409\) 31.7367i 1.56928i −0.619954 0.784639i \(-0.712849\pi\)
0.619954 0.784639i \(-0.287151\pi\)
\(410\) 0 0
\(411\) −3.40332 17.9274i −0.167873 0.884291i
\(412\) 3.47197i 0.171052i
\(413\) −7.51695 + 18.4127i −0.369885 + 0.906029i
\(414\) −16.1652 + 6.36703i −0.794474 + 0.312922i
\(415\) 0 0
\(416\) 10.2100 0.500584
\(417\) −0.791288 4.16820i −0.0387495 0.204117i
\(418\) 14.8036i 0.724070i
\(419\) −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 \(0.436240\pi\)
\(422\) 16.2139i 0.789279i
\(423\) 7.51695 2.96073i 0.365487 0.143956i
\(424\) 12.0871 0.587003
\(425\) 0 0
\(426\) −5.74117 + 1.08990i −0.278160 + 0.0528058i
\(427\) 16.7477 + 6.83723i 0.810479 + 0.330877i
\(428\) 8.33639i 0.402955i
\(429\) 12.7913 2.42829i 0.617569 0.117239i
\(430\) 0 0
\(431\) 34.2634i 1.65041i −0.564833 0.825205i \(-0.691059\pi\)
0.564833 0.825205i \(-0.308941\pi\)
\(432\) 7.87211 4.96640i 0.378747 0.238946i
\(433\) 1.02248i 0.0491371i 0.999698 + 0.0245685i \(0.00782120\pi\)
−0.999698 + 0.0245685i \(0.992179\pi\)
\(434\) −7.51695 + 18.4127i −0.360825 + 0.883838i
\(435\) 0 0
\(436\) 3.95644 0.189479
\(437\) −23.1129 −1.10564
\(438\) −30.1652 + 5.72653i −1.44135 + 0.273624i
\(439\) 26.9444i 1.28599i 0.765872 + 0.642993i \(0.222307\pi\)
−0.765872 + 0.642993i \(0.777693\pi\)
\(440\) 0 0
\(441\) −19.3424 8.17739i −0.921069 0.389400i
\(442\) 7.25227 0.344955
\(443\) 3.93874i 0.187135i 0.995613 + 0.0935675i \(0.0298271\pi\)
−0.995613 + 0.0935675i \(0.970173\pi\)
\(444\) 11.5565 2.19387i 0.548445 0.104116i
\(445\) 0 0
\(446\) 2.69300 0.127517
\(447\) −5.81529 30.6327i −0.275054 1.44888i
\(448\) −8.16515 + 20.0005i −0.385767 + 0.944933i
\(449\) 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
\(452\) 14.2445i 0.670005i
\(453\) 7.08767 1.34552i 0.333008 0.0632180i
\(454\) 2.96073i 0.138954i
\(455\) 0 0
\(456\) 22.9129 4.34977i 1.07299 0.203696i
\(457\) −34.1652 −1.59818 −0.799089 0.601213i \(-0.794685\pi\)
−0.799089 + 0.601213i \(0.794685\pi\)
\(458\) 4.26188 0.199145
\(459\) −11.8348 + 7.46644i −0.552403 + 0.348504i
\(460\) 0 0
\(461\) −33.3229 −1.55200 −0.776000 0.630732i \(-0.782755\pi\)
−0.776000 + 0.630732i \(0.782755\pi\)
\(462\) −3.07147 + 15.1528i −0.142898 + 0.704973i
\(463\) 12.7477 0.592437 0.296219 0.955120i \(-0.404274\pi\)
0.296219 + 0.955120i \(0.404274\pi\)
\(464\) 9.43581i 0.438046i
\(465\) 0 0
\(466\) −5.79129 −0.268276
\(467\) 16.1580 0.747704 0.373852 0.927488i \(-0.378037\pi\)
0.373852 + 0.927488i \(0.378037\pi\)
\(468\) 2.13094 + 5.41022i 0.0985028 + 0.250087i
\(469\) −4.16515 + 10.2025i −0.192329 + 0.471107i
\(470\) 0 0
\(471\) −0.626136 3.29824i −0.0288508 0.151975i
\(472\) 23.0679i 1.06179i
\(473\) 20.2005i 0.928820i
\(474\) 0.206906 + 1.08990i 0.00950350 + 0.0500607i
\(475\) 0 0
\(476\) 2.13094 5.21972i 0.0976716 0.239245i
\(477\) 4.33030 + 10.9941i 0.198271 + 0.503387i
\(478\) −15.9129 −0.727838
\(479\) −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
\(482\) 20.9820 0.955703
\(483\) 23.6581 + 4.79548i 1.07648 + 0.218202i
\(484\) 1.25227 0.0569215
\(485\) 0 0
\(486\) 13.8202 + 10.1351i 0.626896 + 0.459736i
\(487\) −21.8348 −0.989431 −0.494716 0.869055i \(-0.664728\pi\)
−0.494716 + 0.869055i \(0.664728\pi\)
\(488\) 20.9820 0.949809
\(489\) 6.80664 1.29217i 0.307807 0.0584338i
\(490\) 0 0
\(491\) 26.3381i 1.18862i 0.804236 + 0.594310i \(0.202575\pi\)
−0.804236 + 0.594310i \(0.797425\pi\)
\(492\) −13.7477 + 2.60986i −0.619795 + 0.117662i
\(493\) 14.1857i 0.638892i
\(494\) 11.8162i 0.531636i
\(495\) 0 0
\(496\) 12.2474i 0.549927i
\(497\) 7.51695 + 3.06878i 0.337181 + 0.137654i
\(498\) 5.53901 + 29.1774i 0.248209 + 1.30747i
\(499\) 3.25227 0.145592 0.0727959 0.997347i \(-0.476808\pi\)
0.0727959 + 0.997347i \(0.476808\pi\)
\(500\) 0 0
\(501\) 31.1216 5.90810i 1.39041 0.263955i
\(502\) 19.4892i 0.869846i
\(503\) −5.38601 −0.240150 −0.120075 0.992765i \(-0.538314\pi\)
−0.120075 + 0.992765i \(0.538314\pi\)
\(504\) −24.3558 0.301610i −1.08490 0.0134348i
\(505\) 0 0
\(506\) 17.7722i 0.790071i
\(507\) −11.9116 + 2.26129i −0.529013 + 0.100428i
\(508\) 6.46099 0.286660
\(509\) 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
\(512\) 18.4606i 0.815850i
\(513\) 12.1652 + 19.2826i 0.537105 + 0.851350i
\(514\) 5.30352i 0.233928i
\(515\) 0 0
\(516\) −8.86345 + 1.68263i −0.390192 + 0.0740738i
\(517\) 8.26424i 0.363461i
\(518\) 23.1129 + 9.43581i 1.01552 + 0.414586i
\(519\) −13.7477 + 2.60986i −0.603458 + 0.114560i
\(520\) 0 0
\(521\) 16.1580 0.707896 0.353948 0.935265i \(-0.384839\pi\)
0.353948 + 0.935265i \(0.384839\pi\)
\(522\) −16.1652 + 6.36703i −0.707529 + 0.278677i
\(523\) 14.6969i 0.642652i 0.946969 + 0.321326i \(0.104129\pi\)
−0.946969 + 0.321326i \(0.895871\pi\)
\(524\) 2.13094 0.0930906
\(525\) 0 0
\(526\) −31.3739 −1.36797
\(527\) 18.4127i 0.802070i
\(528\) 1.77578 + 9.35414i 0.0772811 + 0.407087i
\(529\) −4.74773 −0.206423
\(530\) 0 0
\(531\) −20.9820 + 8.26424i −0.910540 + 0.358638i
\(532\) −8.50455 3.47197i −0.368719 0.150529i
\(533\) 25.0092i 1.08327i
\(534\) 2.66970 + 14.0629i 0.115529 + 0.608562i
\(535\) 0 0
\(536\) 12.7819i 0.552096i
\(537\) 4.67569 + 24.6297i 0.201771 + 1.06285i
\(538\) 23.0679i 0.994527i
\(539\) 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 \(0.559066\pi\)
\(542\) 28.4989 1.22413
\(543\) −3.95644 20.8410i −0.169787 0.894372i
\(544\) 11.2250i 0.481267i
\(545\) 0 0
\(546\) −2.45163 + 12.0949i −0.104920 + 0.517615i
\(547\) 4.66970 0.199662 0.0998309 0.995004i \(-0.468170\pi\)
0.0998309 + 0.995004i \(0.468170\pi\)
\(548\) 8.33639i 0.356113i
\(549\) 7.51695 + 19.0847i 0.320816 + 0.814514i
\(550\) 0 0
\(551\) −23.1129 −0.984643
\(552\) 27.5076 5.22202i 1.17080 0.222264i
\(553\) 0.582576 1.42701i 0.0247736 0.0606828i
\(554\) 20.6115i 0.875700i
\(555\) 0 0
\(556\) 1.93825i 0.0822002i
\(557\) 6.18546i 0.262086i 0.991377 + 0.131043i \(0.0418326\pi\)
−0.991377 + 0.131043i \(0.958167\pi\)
\(558\) −20.9820 + 8.26424i −0.888238 + 0.349853i
\(559\) 16.1240i 0.681970i
\(560\) 0 0
\(561\) −2.66970 14.0629i −0.112715 0.593737i
\(562\) −16.8693 −0.711589
\(563\) 9.64789 0.406610 0.203305 0.979115i \(-0.434832\pi\)
0.203305 + 0.979115i \(0.434832\pi\)
\(564\) −3.62614 + 0.688383i −0.152688 + 0.0289862i
\(565\) 0 0
\(566\) −25.8059 −1.08470
\(567\) −8.45133 22.2615i −0.354922 0.934896i
\(568\) 9.41742 0.395146
\(569\) 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 \(0.713863\pi\)
\(572\) −5.94807 −0.248701
\(573\) −5.53426 29.1523i −0.231197 1.21786i
\(574\) −27.4955 11.2250i −1.14764 0.468521i
\(575\) 0 0
\(576\) −22.7913 + 8.97689i −0.949637 + 0.374037i
\(577\) 23.9837i 0.998453i −0.866472 0.499226i \(-0.833618\pi\)
0.866472 0.499226i \(-0.166382\pi\)
\(578\) 10.7168i 0.445760i
\(579\) −18.7183 + 3.55346i −0.777904 + 0.147677i
\(580\) 0 0
\(581\) 15.5960 38.2022i 0.647030 1.58489i
\(582\) 21.9564 4.16820i 0.910124 0.172777i
\(583\) −12.0871 −0.500597
\(584\) 49.4809 2.04753
\(585\) 0 0
\(586\) 2.34279i 0.0967797i
\(587\) −3.25507 −0.134351 −0.0671755 0.997741i \(-0.521399\pi\)
−0.0671755 + 0.997741i \(0.521399\pi\)
\(588\) 7.98478 + 5.31839i 0.329287 + 0.219327i
\(589\) −30.0000 −1.23613
\(590\) 0 0
\(591\) 1.13960 + 6.00295i 0.0468767 + 0.246928i
\(592\) 15.3739 0.631862
\(593\) −5.38601 −0.221177 −0.110588 0.993866i \(-0.535274\pi\)
−0.110588 + 0.993866i \(0.535274\pi\)
\(594\) −14.8270 + 9.35414i −0.608359 + 0.383805i
\(595\) 0 0
\(596\) 14.2445i 0.583477i
\(597\) −2.53901 13.3745i −0.103915 0.547384i
\(598\) 14.1857i 0.580096i
\(599\) 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 \(-0.0185390\pi\)
\(602\) −17.7269 7.23698i −0.722495 0.294957i
\(603\) −11.6261 + 4.57923i −0.473453 + 0.186481i
\(604\) −3.29583 −0.134106
\(605\) 0 0
\(606\) −6.49545 34.2155i −0.263860 1.38991i
\(607\) 21.0229i 0.853294i 0.904418 + 0.426647i \(0.140305\pi\)
−0.904418 + 0.426647i \(0.859695\pi\)
\(608\) −18.2890 −0.741716
\(609\) 23.6581 + 4.79548i 0.958675 + 0.194323i
\(610\) 0 0
\(611\) 6.59649i 0.266865i
\(612\) 5.94807 2.34279i 0.240437 0.0947016i
\(613\) 36.5826 1.47756 0.738778 0.673949i \(-0.235403\pi\)
0.738778 + 0.673949i \(0.235403\pi\)
\(614\) −14.4718 −0.584036
\(615\) 0 0
\(616\) 9.41742 23.0679i 0.379439 0.929432i
\(617\) 1.32888i 0.0534985i 0.999642 + 0.0267493i \(0.00851557\pi\)
−0.999642 + 0.0267493i \(0.991484\pi\)
\(618\) 8.20871 1.55834i 0.330203 0.0626855i
\(619\) 13.2699i 0.533363i 0.963785 + 0.266682i \(0.0859272\pi\)
−0.963785 + 0.266682i \(0.914073\pi\)
\(620\) 0 0
\(621\) 14.6046 + 23.1494i 0.586063 + 0.928953i
\(622\) 13.5678i 0.544018i
\(623\) 7.51695 18.4127i 0.301160 0.737689i
\(624\) 1.41742 + 7.46644i 0.0567424 + 0.298897i
\(625\) 0 0
\(626\) 25.2439 1.00895
\(627\) −22.9129 + 4.34977i −0.915052 + 0.173713i
\(628\) 1.53371i 0.0612019i
\(629\) −23.1129 −0.921572
\(630\) 0 0
\(631\) 33.7477 1.34348 0.671738 0.740789i \(-0.265548\pi\)
0.671738 + 0.740789i \(0.265548\pi\)
\(632\) 1.78780i 0.0711148i
\(633\) 25.0956 4.76413i 0.997461 0.189357i
\(634\) 1.46099 0.0580231
\(635\) 0 0
\(636\) −1.00682 5.30352i −0.0399229 0.210298i
\(637\) 12.0000 12.2474i 0.475457 0.485262i
\(638\) 17.7722i 0.703608i
\(639\) 3.37386 + 8.56585i 0.133468 + 0.338860i
\(640\) 0 0
\(641\) 1.78780i 0.0706138i −0.999377 0.0353069i \(-0.988759\pi\)
0.999377 0.0353069i \(-0.0112409\pi\)
\(642\) −19.7096 + 3.74166i −0.777876 + 0.147671i
\(643\) 20.6184i 0.813110i −0.913626 0.406555i \(-0.866730\pi\)
0.913626 0.406555i \(-0.133270\pi\)
\(644\) −10.2100 4.16820i −0.402329 0.164250i
\(645\) 0 0
\(646\) −12.9909 −0.511120
\(647\) −40.8398 −1.60558 −0.802790 0.596263i \(-0.796652\pi\)
−0.802790 + 0.596263i \(0.796652\pi\)
\(648\) −18.8348 20.2005i −0.739903 0.793550i
\(649\) 23.0679i 0.905494i
\(650\) 0 0
\(651\) 30.7076 + 6.22442i 1.20353 + 0.243954i
\(652\) −3.16515 −0.123957
\(653\) 14.4740i 0.566410i −0.959059 0.283205i \(-0.908602\pi\)
0.959059 0.283205i \(-0.0913976\pi\)
\(654\) 1.77578 + 9.35414i 0.0694387 + 0.365776i
\(655\) 0 0
\(656\) −18.2890 −0.714064
\(657\) 17.7269 + 45.0066i 0.691592 + 1.75587i
\(658\) −7.25227 2.96073i −0.282723 0.115421i
\(659\) 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 \(-0.321908\pi\)
\(662\) 18.6900i 0.726409i
\(663\) −2.13094 11.2250i −0.0827589 0.435942i
\(664\) 47.8606i 1.85735i
\(665\) 0 0
\(666\) 10.3739 + 26.3381i 0.401979 + 1.02058i
\(667\) −27.7477 −1.07440
\(668\) −14.4718 −0.559932
\(669\) −0.791288 4.16820i −0.0305930 0.161152i
\(670\) 0 0
\(671\) −20.9820 −0.810000
\(672\) 18.7204 + 3.79461i 0.722154 + 0.146380i
\(673\) −7.49545 −0.288929 −0.144464 0.989510i \(-0.546146\pi\)
−0.144464 + 0.989510i \(0.546146\pi\)
\(674\) 2.19883i 0.0846957i
\(675\) 0 0
\(676\) 5.53901 0.213039
\(677\) −10.7720 −0.414002 −0.207001 0.978341i \(-0.566370\pi\)
−0.207001 + 0.978341i \(0.566370\pi\)
\(678\) −33.6780 + 6.39342i −1.29340 + 0.245538i
\(679\) −28.7477 11.7362i −1.10324 0.450394i
\(680\) 0 0
\(681\) −4.58258 + 0.869953i −0.175605 + 0.0333367i
\(682\) 23.0679i 0.883315i
\(683\) 10.1242i 0.387391i −0.981062 0.193696i \(-0.937953\pi\)
0.981062 0.193696i \(-0.0620474\pi\)
\(684\) −3.81713 9.69126i −0.145952 0.370554i
\(685\) 0 0
\(686\) 8.07901 + 18.6900i 0.308458 + 0.713589i
\(687\) −1.25227 6.59649i −0.0477772 0.251672i
\(688\) −11.7913 −0.449539
\(689\) −9.64789 −0.367555
\(690\) 0 0
\(691\) 6.83723i 0.260101i 0.991507 + 0.130050i \(0.0415139\pi\)
−0.991507 + 0.130050i \(0.958486\pi\)
\(692\) 6.39283 0.243019
\(693\) 24.3558 + 0.301610i 0.925202 + 0.0114572i
\(694\) −3.87841 −0.147222
\(695\) 0 0
\(696\) 27.5076 5.22202i 1.04267 0.197940i
\(697\) 27.4955 1.04146
\(698\) 10.2100 0.386452
\(699\) 1.70166 + 8.96368i 0.0643627 + 0.339037i
\(700\) 0 0
\(701\) 17.1317i 0.647056i 0.946219 + 0.323528i \(0.104869\pi\)
−0.946219 + 0.323528i \(0.895131\pi\)
\(702\) −11.8348 + 7.46644i −0.446678 + 0.281803i
\(703\) 37.6581i 1.42030i
\(704\) 25.0571i 0.944374i
\(705\) 0 0
\(706\) 33.6749i 1.26737i
\(707\) −18.2890 + 44.7986i −0.687827 + 1.68483i
\(708\) 10.1216 1.92148i 0.380393 0.0722135i
\(709\) 23.4955 0.882390 0.441195 0.897411i \(-0.354555\pi\)
0.441195 + 0.897411i \(0.354555\pi\)
\(710\) 0 0
\(711\) 1.62614 0.640492i 0.0609849 0.0240203i
\(712\) 23.0679i 0.864506i
\(713\) −36.0159 −1.34881
\(714\) 13.2973 + 2.69536i 0.497640 + 0.100871i
\(715\) 0 0
\(716\) 11.4531i 0.428021i
\(717\) 4.67569 + 24.6297i 0.174617 + 0.919815i
\(718\) 19.7913 0.738604
\(719\) −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
\(722\) 0.277352i 0.0103220i
\(723\) −6.16515 32.4756i −0.229284 1.20778i
\(724\) 9.69126i 0.360173i
\(725\) 0 0
\(726\) 0.562063 + 2.96073i 0.0208601 + 0.109883i
\(727\) 11.3317i 0.420269i 0.977673 + 0.210134i \(0.0673901\pi\)
−0.977673 + 0.210134i \(0.932610\pi\)
\(728\) 7.51695 18.4127i 0.278597 0.682420i
\(729\) 11.6261 24.3687i 0.430598 0.902544i
\(730\) 0 0
\(731\) 17.7269 0.655653
\(732\) −1.74773 9.20635i −0.0645979 0.340276i
\(733\) 12.6520i 0.467312i −0.972319 0.233656i \(-0.924931\pi\)
0.972319 0.233656i \(-0.0750689\pi\)
\(734\) −1.00682 −0.0371623
\(735\) 0 0
\(736\) −21.9564 −0.809325
\(737\) 12.7819i 0.470829i
\(738\) −12.3409 31.3321i −0.454275 1.15335i
\(739\) 50.8258 1.86966 0.934828 0.355101i \(-0.115554\pi\)
0.934828 + 0.355101i \(0.115554\pi\)
\(740\) 0 0
\(741\) −18.2890 + 3.47197i −0.671862 + 0.127546i
\(742\) 4.33030 10.6070i 0.158970 0.389396i
\(743\) 14.4740i 0.530998i −0.964111 0.265499i \(-0.914463\pi\)
0.964111 0.265499i \(-0.0855367\pi\)
\(744\) 35.7042 6.77806i 1.30898 0.248496i
\(745\) 0 0
\(746\) 29.5884i 1.08331i
\(747\) 43.5328 17.1464i 1.59278 0.627355i
\(748\) 6.53940i 0.239104i
\(749\) 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 \(0.565817\pi\)
\(752\) −4.82395 −0.175911
\(753\) −30.1652 + 5.72653i −1.09928 + 0.208686i
\(754\) 14.1857i 0.516613i
\(755\) 0 0
\(756\) 1.89642 + 10.7118i 0.0689721 + 0.389586i
\(757\) 33.7477 1.22658 0.613291 0.789857i \(-0.289845\pi\)
0.613291 + 0.789857i \(0.289845\pi\)
\(758\) 19.0532i 0.692043i
\(759\) −27.5076 + 5.22202i −0.998462 + 0.189547i
\(760\) 0 0
\(761\) 4.26188 0.154493 0.0772466 0.997012i \(-0.475387\pi\)
0.0772466 + 0.997012i \(0.475387\pi\)
\(762\) 2.89991 + 15.2756i 0.105053 + 0.553377i
\(763\) 5.00000 12.2474i 0.181012 0.443387i
\(764\) 13.5561i 0.490443i
\(765\) 0 0
\(766\) 30.7142i 1.10975i
\(767\) 18.4127i 0.664844i
\(768\) 26.5904 5.04790i 0.959497 0.182150i
\(769\) 30.3097i 1.09299i −0.837461 0.546497i \(-0.815961\pi\)
0.837461 0.546497i \(-0.184039\pi\)
\(770\) 0 0
\(771\) 8.20871 1.55834i 0.295630 0.0561221i
\(772\) 8.70417 0.313270
\(773\) 15.5960 0.560948 0.280474 0.959862i \(-0.409508\pi\)
0.280474 + 0.959862i \(0.409508\pi\)
\(774\) −7.95644 20.2005i −0.285988 0.726092i
\(775\) 0 0
\(776\) −36.0159 −1.29289
\(777\) 7.81333 38.5464i 0.280302 1.38284i
\(778\) 14.4519 0.518125
\(779\) 44.7986i 1.60508i
\(780\) 0 0
\(781\) −9.41742 −0.336982
\(782\) −15.5960 −0.557711
\(783\) 14.6046 + 23.1494i 0.521926 + 0.827291i
\(784\) 8.95644 + 8.77548i 0.319873 + 0.313410i
\(785\) 0 0
\(786\) 0.956439 + 5.03815i 0.0341151 + 0.179705i
\(787\) 6.32599i 0.225497i −0.993624 0.112749i \(-0.964035\pi\)
0.993624 0.112749i \(-0.0359655\pi\)
\(788\) 2.79143i 0.0994406i
\(789\) 9.21861 + 48.5601i 0.328191 + 1.72878i
\(790\) 0 0
\(791\) 44.0949 + 18.0017i 1.56783 + 0.640065i
\(792\) 26.2867 10.3537i 0.934059 0.367901i
\(793\) −16.7477 −0.594729
\(794\) 9.64789 0.342391
\(795\) 0 0
\(796\) 6.21929i 0.220437i
\(797\) 17.7269 0.627919 0.313960 0.949436i \(-0.398344\pi\)
0.313960 + 0.949436i \(0.398344\pi\)
\(798\) 4.39158 21.6655i 0.155460 0.766950i
\(799\) 7.25227 0.256567
\(800\) 0 0
\(801\) 20.9820 8.26424i 0.741362 0.292003i
\(802\) −22.2087 −0.784217
\(803\) −49.4809 −1.74614
\(804\) 5.60839 1.06469i 0.197793 0.0375488i
\(805\) 0 0
\(806\) 18.4127i 0.648559i
\(807\) 35.7042 6.77806i 1.25685 0.238599i
\(808\) 56.1249i 1.97447i
\(809\) 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 \(0.922824\pi\)
\(812\) −10.2100 4.16820i −0.358299 0.146275i
\(813\) −8.37386 44.1103i −0.293684 1.54701i
\(814\) −28.9564 −1.01492
\(815\) 0 0
\(816\) 8.20871 1.55834i 0.287362 0.0545527i
\(817\) 28.8826i 1.01048i
\(818\) −34.8917 −1.21996
\(819\) 19.4407 + 0.240744i 0.679314 + 0.00841228i
\(820\) 0 0
\(821\) 17.1317i 0.597901i 0.954269 + 0.298950i \(0.0966365\pi\)
−0.954269 + 0.298950i \(0.903363\pi\)
\(822\) −19.7096 + 3.74166i −0.687451 + 0.130505i
\(823\) −2.25227 −0.0785093 −0.0392546 0.999229i \(-0.512498\pi\)
−0.0392546 + 0.999229i \(0.512498\pi\)
\(824\) −13.4650 −0.469076
\(825\) 0 0
\(826\) 20.2432 + 8.26424i 0.704350 + 0.287550i
\(827\) 14.8850i 0.517602i 0.965931 + 0.258801i \(0.0833273\pi\)
−0.965931 + 0.258801i \(0.916673\pi\)
\(828\) −4.58258 11.6346i −0.159256 0.404332i
\(829\) 15.2082i 0.528202i −0.964495 0.264101i \(-0.914925\pi\)
0.964495 0.264101i \(-0.0850752\pi\)
\(830\) 0 0
\(831\) −31.9022 + 6.05630i −1.10668 + 0.210091i
\(832\) 20.0005i 0.693391i
\(833\) −13.4650 13.1930i −0.466535 0.457109i
\(834\) −4.58258 + 0.869953i −0.158682 + 0.0301240i
\(835\) 0 0
\(836\) 10.6547 0.368501
\(837\) 18.9564 + 30.0473i 0.655230 + 1.03859i
\(838\) 23.0679i 0.796867i
\(839\) −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
\(842\) 8.97689i 0.309364i
\(843\) 4.95673 + 26.1101i 0.170719 + 0.899280i
\(844\) −11.6697 −0.401688
\(845\) 0 0
\(846\) −3.25507 8.26424i −0.111912 0.284131i
\(847\) 1.58258 3.87650i 0.0543779 0.133198i
\(848\) 7.05541i 0.242284i
\(849\) 7.58258 + 39.9421i 0.260233 + 1.37081i
\(850\) 0 0
\(851\) 45.2097i 1.54977i
\(852\) −0.784439 4.13212i −0.0268745 0.141564i
\(853\) 17.5510i 0.600934i 0.953792 + 0.300467i \(0.0971425\pi\)
−0.953792 + 0.300467i \(0.902858\pi\)
\(854\) 7.51695 18.4127i 0.257225 0.630069i
\(855\) 0 0
\(856\) 32.3303 1.10503
\(857\) −46.7879 −1.59824 −0.799122 0.601169i \(-0.794702\pi\)
−0.799122 + 0.601169i \(0.794702\pi\)
\(858\) −2.66970 14.0629i −0.0911420 0.480100i
\(859\) 47.9673i 1.63662i −0.574774 0.818312i \(-0.694910\pi\)
0.574774 0.818312i \(-0.305090\pi\)
\(860\) 0 0
\(861\) −9.29485 + 45.8553i −0.316768 + 1.56275i
\(862\) −37.6697 −1.28303
\(863\) 22.8582i 0.778104i 0.921216 + 0.389052i \(0.127197\pi\)
−0.921216 + 0.389052i \(0.872803\pi\)
\(864\) 11.5565 + 18.3178i 0.393159 + 0.623185i
\(865\) 0 0
\(866\) 1.12413 0.0381993
\(867\) 16.5873 3.14892i 0.563335 0.106943i
\(868\) −13.2523 5.41022i −0.449811 0.183635i
\(869\) 1.78780i 0.0606469i
\(870\) 0 0
\(871\) 10.2025i 0.345698i
\(872\) 15.3439i 0.519610i
\(873\) −12.9030 32.7591i −0.436699 1.10873i
\(874\) 25.4107i 0.859529i
\(875\) 0 0
\(876\) −4.12159 21.7109i −0.139256 0.733545i
\(877\) −31.4955 −1.06353 −0.531763 0.846893i \(-0.678470\pi\)
−0.531763 + 0.846893i \(0.678470\pi\)
\(878\) 29.6230 0.999729
\(879\) −3.62614 + 0.688383i −0.122307 + 0.0232186i
\(880\) 0 0
\(881\) −34.8917 −1.17553 −0.587766 0.809031i \(-0.699993\pi\)
−0.587766 + 0.809031i \(0.699993\pi\)
\(882\) −8.99034 + 21.2654i −0.302721 + 0.716042i
\(883\) 15.4174 0.518838 0.259419 0.965765i \(-0.416469\pi\)
0.259419 + 0.965765i \(0.416469\pi\)
\(884\) 5.21972i 0.175558i
\(885\) 0 0
\(886\) 4.33030 0.145479
\(887\) 40.2778 1.35239 0.676197 0.736721i \(-0.263627\pi\)
0.676197 + 0.736721i \(0.263627\pi\)
\(888\) −8.50830 44.8184i −0.285520 1.50401i
\(889\) 8.16515 20.0005i 0.273850 0.670794i
\(890\) 0 0
\(891\) 18.8348 + 20.2005i 0.630991 + 0.676742i
\(892\) 1.93825i 0.0648975i
\(893\) 11.8162i 0.395414i
\(894\) −33.6780 + 6.39342i −1.12636 + 0.213828i
\(895\) 0 0
\(896\) 1.56888 + 0.640492i 0.0524126 + 0.0213973i
\(897\) −21.9564 + 4.16820i −0.733104 + 0.139172i
\(898\) 40.0345 1.33597
\(899\) −36.0159 −1.20120
\(900\) 0 0
\(901\) 10.6070i 0.353371i
\(902\) 34.4470 1.14696
\(903\) −5.99259 + 29.5639i −0.199421 + 0.983826i
\(904\) 55.2432 1.83736
\(905\) 0 0
\(906\) −1.47928 7.79228i −0.0491459 0.258881i
\(907\) −1.49545 −0.0496557 −0.0248279 0.999692i \(-0.507904\pi\)
−0.0248279 + 0.999692i \(0.507904\pi\)
\(908\) 2.13094 0.0707178
\(909\) −51.0498 + 20.1072i −1.69321 + 0.666912i
\(910\) 0 0
\(911\) 10.4873i 0.347461i −0.984793 0.173730i \(-0.944418\pi\)
0.984793 0.173730i \(-0.0555821\pi\)
\(912\) −2.53901 13.3745i −0.0840752 0.442875i
\(913\) 47.8606i 1.58396i
\(914\) 37.5617i 1.24243i
\(915\) 0 0
\(916\) 3.06743i 0.101351i
\(917\) 2.69300 6.59649i 0.0889308 0.217835i
\(918\) 8.20871 + 13.0114i 0.270928 + 0.429440i
\(919\) −24.0780 −0.794261 −0.397130 0.917762i \(-0.629994\pi\)
−0.397130 + 0.917762i \(0.629994\pi\)
\(920\) 0 0
\(921\) 4.25227 + 22.3993i 0.140117 + 0.738083i
\(922\) 36.6356i 1.20653i
\(923\) −7.51695 −0.247423
\(924\) −10.9060 2.21065i −0.358782 0.0727249i
\(925\) 0 0
\(926\) 14.0150i 0.460563i
\(927\) −4.82395 12.2474i −0.158439 0.402259i
\(928\) −21.9564 −0.720755
\(929\) 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
\(932\) 4.16820i 0.136534i
\(933\) 21.0000 3.98663i 0.687509 0.130516i
\(934\) 17.7644i 0.581268i
\(935\) 0 0
\(936\) 20.9820 8.26424i 0.685817 0.270125i
\(937\) 36.2311i 1.18362i −0.806078 0.591809i \(-0.798414\pi\)
0.806078 0.591809i \(-0.201586\pi\)
\(938\) 11.2168 + 4.57923i 0.366241 + 0.149517i
\(939\) −7.41742 39.0721i −0.242058 1.27507i
\(940\) 0 0
\(941\) 25.2439 0.822926 0.411463 0.911426i \(-0.365018\pi\)
0.411463 + 0.911426i \(0.365018\pi\)
\(942\) −3.62614 + 0.688383i −0.118146 + 0.0224287i
\(943\) 53.7821i 1.75139i
\(944\) 13.4650 0.438249
\(945\) 0 0
\(946\) 22.2087 0.722068
\(947\) 28.9479i 0.940681i 0.882485 + 0.470340i \(0.155869\pi\)
−0.882485 + 0.470340i \(0.844131\pi\)
\(948\) −0.784439 + 0.148917i −0.0254774 + 0.00483662i
\(949\) −39.4955 −1.28208
\(950\) 0 0
\(951\) −0.429283 2.26129i −0.0139204 0.0733275i
\(952\) −20.2432 8.26424i −0.656085 0.267846i
\(953\) 5.26761i 0.170635i −0.996354 0.0853173i \(-0.972810\pi\)
0.996354 0.0853173i \(-0.0271904\pi\)
\(954\) 12.0871 4.76080i 0.391335 0.154137i
\(955\) 0 0
\(956\) 11.4531i 0.370419i
\(957\) −27.5076 + 5.22202i −0.889194 + 0.168804i
\(958\) 8.26424i 0.267006i
\(959\) 25.8059 + 10.5352i 0.833317 + 0.340200i
\(960\) 0 0
\(961\) −15.7477 −0.507991
\(962\) −23.1129 −0.745190
\(963\) 11.5826 + 29.4068i 0.373243 + 0.947622i
\(964\) 15.1015i 0.486386i
\(965\) 0 0
\(966\) 5.27222 26.0101i 0.169631 0.836860i
\(967\) −14.7477 −0.474255 −0.237127 0.971479i \(-0.576206\pi\)
−0.237127 + 0.971479i \(0.576206\pi\)
\(968\) 4.85658i 0.156096i
\(969\) 3.81713 + 20.1072i 0.122624 + 0.645935i
\(970\) 0 0
\(971\) −27.3748 −0.878499 −0.439250 0.898365i \(-0.644756\pi\)
−0.439250 + 0.898365i \(0.644756\pi\)
\(972\) −7.29457 + 9.94688i −0.233974 + 0.319046i
\(973\) 6.00000 + 2.44949i 0.192351 + 0.0785270i
\(974\) 24.0055i 0.769187i
\(975\) 0 0
\(976\) 12.2474i 0.392031i
\(977\) 1.32888i 0.0425145i 0.999774 + 0.0212572i \(0.00676690\pi\)
−0.999774 + 0.0212572i \(0.993233\pi\)
\(978\) −1.42063 7.48331i −0.0454267 0.239290i
\(979\) 23.0679i 0.737253i
\(980\) 0 0
\(981\) 13.9564 5.49707i 0.445595 0.175508i
\(982\) 28.9564 0.924037
\(983\) 15.5960 0.497434 0.248717 0.968576i \(-0.419991\pi\)
0.248717 + 0.968576i \(0.419991\pi\)
\(984\) 10.1216 + 53.3166i 0.322665 + 1.69967i
\(985\) 0 0
\(986\) −15.5960 −0.496677
\(987\) −2.45163 + 12.0949i −0.0780364 + 0.384986i
\(988\) 8.50455 0.270566
\(989\) 34.6744i 1.10258i
\(990\) 0 0
\(991\) −42.0780 −1.33665 −0.668326 0.743868i \(-0.732989\pi\)
−0.668326 + 0.743868i \(0.732989\pi\)
\(992\) −28.4989 −0.904842
\(993\) −28.9282 + 5.49171i −0.918009 + 0.174274i
\(994\) 3.37386 8.26424i 0.107012 0.262126i
\(995\) 0 0
\(996\) −21.0000 + 3.98663i −0.665410 + 0.126321i
\(997\) 25.0061i 0.791952i 0.918261 + 0.395976i \(0.129594\pi\)
−0.918261 + 0.395976i \(0.870406\pi\)
\(998\) 3.57560i 0.113184i
\(999\) 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.b.i.251.3 yes 8
3.2 odd 2 inner 525.2.b.i.251.6 yes 8
5.2 odd 4 525.2.g.f.524.12 16
5.3 odd 4 525.2.g.f.524.5 16
5.4 even 2 525.2.b.h.251.6 yes 8
7.6 odd 2 inner 525.2.b.i.251.4 yes 8
15.2 even 4 525.2.g.f.524.7 16
15.8 even 4 525.2.g.f.524.10 16
15.14 odd 2 525.2.b.h.251.3 8
21.20 even 2 inner 525.2.b.i.251.5 yes 8
35.13 even 4 525.2.g.f.524.8 16
35.27 even 4 525.2.g.f.524.9 16
35.34 odd 2 525.2.b.h.251.5 yes 8
105.62 odd 4 525.2.g.f.524.6 16
105.83 odd 4 525.2.g.f.524.11 16
105.104 even 2 525.2.b.h.251.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.b.h.251.3 8 15.14 odd 2
525.2.b.h.251.4 yes 8 105.104 even 2
525.2.b.h.251.5 yes 8 35.34 odd 2
525.2.b.h.251.6 yes 8 5.4 even 2
525.2.b.i.251.3 yes 8 1.1 even 1 trivial
525.2.b.i.251.4 yes 8 7.6 odd 2 inner
525.2.b.i.251.5 yes 8 21.20 even 2 inner
525.2.b.i.251.6 yes 8 3.2 odd 2 inner
525.2.g.f.524.5 16 5.3 odd 4
525.2.g.f.524.6 16 105.62 odd 4
525.2.g.f.524.7 16 15.2 even 4
525.2.g.f.524.8 16 35.13 even 4
525.2.g.f.524.9 16 35.27 even 4
525.2.g.f.524.10 16 15.8 even 4
525.2.g.f.524.11 16 105.83 odd 4
525.2.g.f.524.12 16 5.2 odd 4