Properties

Label 475.2.p.a.468.1
Level $475$
Weight $2$
Character 475.468
Analytic conductor $3.793$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(107,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.p (of order \(12\), degree \(4\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 468.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 475.468
Dual form 475.2.p.a.407.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(2.73205 + 0.732051i) q^{3} +(2.00000 - 3.46410i) q^{6} +(2.00000 - 2.00000i) q^{8} +(4.33013 + 2.50000i) q^{9} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(2.73205 + 0.732051i) q^{3} +(2.00000 - 3.46410i) q^{6} +(2.00000 - 2.00000i) q^{8} +(4.33013 + 2.50000i) q^{9} -3.00000 q^{11} +(1.09808 + 4.09808i) q^{13} +(-2.00000 - 3.46410i) q^{16} +(-2.36603 - 0.633975i) q^{17} +(5.00000 - 5.00000i) q^{18} +(-4.33013 - 0.500000i) q^{19} +(-1.09808 + 4.09808i) q^{22} +(-7.09808 + 1.90192i) q^{23} +(6.92820 - 4.00000i) q^{24} +6.00000 q^{26} +(4.00000 + 4.00000i) q^{27} +(2.59808 - 4.50000i) q^{29} -8.66025i q^{31} +(-8.19615 - 2.19615i) q^{33} +(-1.73205 + 3.00000i) q^{34} +(3.00000 + 3.00000i) q^{37} +(-2.26795 + 5.73205i) q^{38} +12.0000i q^{39} +(9.00000 - 5.19615i) q^{41} +(-1.90192 + 7.09808i) q^{43} +10.3923i q^{46} +(-0.633975 - 2.36603i) q^{47} +(-2.92820 - 10.9282i) q^{48} +7.00000i q^{49} +(-6.00000 - 3.46410i) q^{51} +(-0.732051 - 2.73205i) q^{53} +(6.92820 - 4.00000i) q^{54} +(-11.4641 - 4.53590i) q^{57} +(-5.19615 - 5.19615i) q^{58} +(-2.59808 - 4.50000i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-11.8301 - 3.16987i) q^{62} -8.00000i q^{64} +(-6.00000 + 10.3923i) q^{66} +(12.2942 - 3.29423i) q^{67} -20.7846 q^{69} +(-13.5000 + 7.79423i) q^{71} +(13.6603 - 3.66025i) q^{72} +(-1.90192 + 7.09808i) q^{73} +(5.19615 - 3.00000i) q^{74} +(16.3923 + 4.39230i) q^{78} +(-2.59808 - 4.50000i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-3.80385 - 14.1962i) q^{82} +(8.66025 + 8.66025i) q^{83} +(9.00000 + 5.19615i) q^{86} +(10.3923 - 10.3923i) q^{87} +(-6.00000 + 6.00000i) q^{88} +(2.59808 - 4.50000i) q^{89} +(6.33975 - 23.6603i) q^{93} -3.46410 q^{94} +(-3.29423 + 12.2942i) q^{97} +(9.56218 + 2.56218i) q^{98} +(-12.9904 - 7.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{8} - 12 q^{11} - 6 q^{13} - 8 q^{16} - 6 q^{17} + 20 q^{18} + 6 q^{22} - 18 q^{23} + 24 q^{26} + 16 q^{27} - 12 q^{33} + 12 q^{37} - 16 q^{38} + 36 q^{41} - 18 q^{43} - 6 q^{47} + 16 q^{48} - 24 q^{51} + 4 q^{53} - 32 q^{57} + 2 q^{61} - 30 q^{62} - 24 q^{66} + 18 q^{67} - 54 q^{71} + 20 q^{72} - 18 q^{73} + 24 q^{78} + 2 q^{81} - 36 q^{82} + 36 q^{86} - 24 q^{88} + 60 q^{93} + 18 q^{97} + 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.258819 0.965926i −0.707107 0.707107i \(-0.750000\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) 2.73205 + 0.732051i 1.57735 + 0.422650i 0.938104 0.346353i \(-0.112580\pi\)
0.639246 + 0.769002i \(0.279247\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 2.00000 3.46410i 0.816497 1.41421i
\(7\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 4.33013 + 2.50000i 1.44338 + 0.833333i
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) 1.09808 + 4.09808i 0.304552 + 1.13660i 0.933331 + 0.359018i \(0.116888\pi\)
−0.628779 + 0.777584i \(0.716445\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) −2.36603 0.633975i −0.573845 0.153761i −0.0397858 0.999208i \(-0.512668\pi\)
−0.534060 + 0.845447i \(0.679334\pi\)
\(18\) 5.00000 5.00000i 1.17851 1.17851i
\(19\) −4.33013 0.500000i −0.993399 0.114708i
\(20\) 0 0
\(21\) 0 0
\(22\) −1.09808 + 4.09808i −0.234111 + 0.873713i
\(23\) −7.09808 + 1.90192i −1.48005 + 0.396579i −0.906365 0.422496i \(-0.861154\pi\)
−0.573687 + 0.819075i \(0.694487\pi\)
\(24\) 6.92820 4.00000i 1.41421 0.816497i
\(25\) 0 0
\(26\) 6.00000 1.17670
\(27\) 4.00000 + 4.00000i 0.769800 + 0.769800i
\(28\) 0 0
\(29\) 2.59808 4.50000i 0.482451 0.835629i −0.517346 0.855776i \(-0.673080\pi\)
0.999797 + 0.0201471i \(0.00641344\pi\)
\(30\) 0 0
\(31\) 8.66025i 1.55543i −0.628619 0.777714i \(-0.716379\pi\)
0.628619 0.777714i \(-0.283621\pi\)
\(32\) 0 0
\(33\) −8.19615 2.19615i −1.42677 0.382301i
\(34\) −1.73205 + 3.00000i −0.297044 + 0.514496i
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 + 3.00000i 0.493197 + 0.493197i 0.909312 0.416115i \(-0.136609\pi\)
−0.416115 + 0.909312i \(0.636609\pi\)
\(38\) −2.26795 + 5.73205i −0.367910 + 0.929861i
\(39\) 12.0000i 1.92154i
\(40\) 0 0
\(41\) 9.00000 5.19615i 1.40556 0.811503i 0.410608 0.911812i \(-0.365317\pi\)
0.994956 + 0.100309i \(0.0319833\pi\)
\(42\) 0 0
\(43\) −1.90192 + 7.09808i −0.290041 + 1.08245i 0.655036 + 0.755598i \(0.272653\pi\)
−0.945077 + 0.326849i \(0.894013\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 10.3923i 1.53226i
\(47\) −0.633975 2.36603i −0.0924747 0.345120i 0.904150 0.427216i \(-0.140505\pi\)
−0.996624 + 0.0820953i \(0.973839\pi\)
\(48\) −2.92820 10.9282i −0.422650 1.57735i
\(49\) 7.00000i 1.00000i
\(50\) 0 0
\(51\) −6.00000 3.46410i −0.840168 0.485071i
\(52\) 0 0
\(53\) −0.732051 2.73205i −0.100555 0.375276i 0.897248 0.441527i \(-0.145563\pi\)
−0.997803 + 0.0662507i \(0.978896\pi\)
\(54\) 6.92820 4.00000i 0.942809 0.544331i
\(55\) 0 0
\(56\) 0 0
\(57\) −11.4641 4.53590i −1.51846 0.600794i
\(58\) −5.19615 5.19615i −0.682288 0.682288i
\(59\) −2.59808 4.50000i −0.338241 0.585850i 0.645861 0.763455i \(-0.276498\pi\)
−0.984102 + 0.177605i \(0.943165\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −11.8301 3.16987i −1.50243 0.402574i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −6.00000 + 10.3923i −0.738549 + 1.27920i
\(67\) 12.2942 3.29423i 1.50198 0.402454i 0.588217 0.808703i \(-0.299830\pi\)
0.913762 + 0.406249i \(0.133164\pi\)
\(68\) 0 0
\(69\) −20.7846 −2.50217
\(70\) 0 0
\(71\) −13.5000 + 7.79423i −1.60216 + 0.925005i −0.611100 + 0.791554i \(0.709273\pi\)
−0.991055 + 0.133451i \(0.957394\pi\)
\(72\) 13.6603 3.66025i 1.60988 0.431365i
\(73\) −1.90192 + 7.09808i −0.222603 + 0.830767i 0.760747 + 0.649048i \(0.224833\pi\)
−0.983351 + 0.181719i \(0.941834\pi\)
\(74\) 5.19615 3.00000i 0.604040 0.348743i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 16.3923 + 4.39230i 1.85606 + 0.497331i
\(79\) −2.59808 4.50000i −0.292306 0.506290i 0.682048 0.731307i \(-0.261089\pi\)
−0.974355 + 0.225018i \(0.927756\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −3.80385 14.1962i −0.420065 1.56770i
\(83\) 8.66025 + 8.66025i 0.950586 + 0.950586i 0.998835 0.0482490i \(-0.0153641\pi\)
−0.0482490 + 0.998835i \(0.515364\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 9.00000 + 5.19615i 0.970495 + 0.560316i
\(87\) 10.3923 10.3923i 1.11417 1.11417i
\(88\) −6.00000 + 6.00000i −0.639602 + 0.639602i
\(89\) 2.59808 4.50000i 0.275396 0.476999i −0.694839 0.719165i \(-0.744525\pi\)
0.970235 + 0.242166i \(0.0778579\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 6.33975 23.6603i 0.657401 2.45345i
\(94\) −3.46410 −0.357295
\(95\) 0 0
\(96\) 0 0
\(97\) −3.29423 + 12.2942i −0.334478 + 1.24829i 0.569955 + 0.821676i \(0.306960\pi\)
−0.904434 + 0.426614i \(0.859706\pi\)
\(98\) 9.56218 + 2.56218i 0.965926 + 0.258819i
\(99\) −12.9904 7.50000i −1.30558 0.753778i
\(100\) 0 0
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) −6.92820 + 6.92820i −0.685994 + 0.685994i
\(103\) −6.00000 + 6.00000i −0.591198 + 0.591198i −0.937955 0.346757i \(-0.887283\pi\)
0.346757 + 0.937955i \(0.387283\pi\)
\(104\) 10.3923 + 6.00000i 1.01905 + 0.588348i
\(105\) 0 0
\(106\) −4.00000 −0.388514
\(107\) −7.00000 7.00000i −0.676716 0.676716i 0.282540 0.959256i \(-0.408823\pi\)
−0.959256 + 0.282540i \(0.908823\pi\)
\(108\) 0 0
\(109\) 6.06218 + 10.5000i 0.580651 + 1.00572i 0.995402 + 0.0957826i \(0.0305354\pi\)
−0.414751 + 0.909935i \(0.636131\pi\)
\(110\) 0 0
\(111\) 6.00000 + 10.3923i 0.569495 + 0.986394i
\(112\) 0 0
\(113\) 4.00000 4.00000i 0.376288 0.376288i −0.493473 0.869761i \(-0.664273\pi\)
0.869761 + 0.493473i \(0.164273\pi\)
\(114\) −10.3923 + 14.0000i −0.973329 + 1.31122i
\(115\) 0 0
\(116\) 0 0
\(117\) −5.49038 + 20.4904i −0.507586 + 1.89434i
\(118\) −7.09808 + 1.90192i −0.653431 + 0.175086i
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −1.00000 1.00000i −0.0905357 0.0905357i
\(123\) 28.3923 7.60770i 2.56005 0.685963i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 12.2942 3.29423i 1.09094 0.292316i 0.331868 0.943326i \(-0.392321\pi\)
0.759069 + 0.651010i \(0.225655\pi\)
\(128\) −10.9282 2.92820i −0.965926 0.258819i
\(129\) −10.3923 + 18.0000i −0.914991 + 1.58481i
\(130\) 0 0
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 18.0000i 1.55496i
\(135\) 0 0
\(136\) −6.00000 + 3.46410i −0.514496 + 0.297044i
\(137\) 2.53590 + 9.46410i 0.216656 + 0.808573i 0.985577 + 0.169228i \(0.0541275\pi\)
−0.768920 + 0.639344i \(0.779206\pi\)
\(138\) −7.60770 + 28.3923i −0.647610 + 2.41691i
\(139\) 1.73205 + 1.00000i 0.146911 + 0.0848189i 0.571654 0.820495i \(-0.306302\pi\)
−0.424743 + 0.905314i \(0.639635\pi\)
\(140\) 0 0
\(141\) 6.92820i 0.583460i
\(142\) 5.70577 + 21.2942i 0.478818 + 1.78697i
\(143\) −3.29423 12.2942i −0.275477 1.02810i
\(144\) 20.0000i 1.66667i
\(145\) 0 0
\(146\) 9.00000 + 5.19615i 0.744845 + 0.430037i
\(147\) −5.12436 + 19.1244i −0.422650 + 1.57735i
\(148\) 0 0
\(149\) 2.59808 1.50000i 0.212843 0.122885i −0.389789 0.920904i \(-0.627452\pi\)
0.602632 + 0.798019i \(0.294119\pi\)
\(150\) 0 0
\(151\) 8.66025i 0.704761i 0.935857 + 0.352381i \(0.114628\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) −9.66025 + 7.66025i −0.783550 + 0.621329i
\(153\) −8.66025 8.66025i −0.700140 0.700140i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −14.1962 3.80385i −1.13298 0.303580i −0.356853 0.934161i \(-0.616150\pi\)
−0.776124 + 0.630581i \(0.782817\pi\)
\(158\) −7.09808 + 1.90192i −0.564693 + 0.151309i
\(159\) 8.00000i 0.634441i
\(160\) 0 0
\(161\) 0 0
\(162\) 1.36603 0.366025i 0.107325 0.0287577i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 15.0000 8.66025i 1.16423 0.672166i
\(167\) 19.1244 5.12436i 1.47989 0.396535i 0.573578 0.819151i \(-0.305555\pi\)
0.906309 + 0.422616i \(0.138888\pi\)
\(168\) 0 0
\(169\) −4.33013 + 2.50000i −0.333087 + 0.192308i
\(170\) 0 0
\(171\) −17.5000 12.9904i −1.33826 0.993399i
\(172\) 0 0
\(173\) 2.73205 + 0.732051i 0.207714 + 0.0556568i 0.361176 0.932498i \(-0.382375\pi\)
−0.153462 + 0.988155i \(0.549042\pi\)
\(174\) −10.3923 18.0000i −0.787839 1.36458i
\(175\) 0 0
\(176\) 6.00000 + 10.3923i 0.452267 + 0.783349i
\(177\) −3.80385 14.1962i −0.285915 1.06705i
\(178\) −5.19615 5.19615i −0.389468 0.389468i
\(179\) 25.9808 1.94189 0.970947 0.239296i \(-0.0769166\pi\)
0.970947 + 0.239296i \(0.0769166\pi\)
\(180\) 0 0
\(181\) −21.0000 12.1244i −1.56092 0.901196i −0.997164 0.0752530i \(-0.976024\pi\)
−0.563753 0.825943i \(-0.690643\pi\)
\(182\) 0 0
\(183\) 2.00000 2.00000i 0.147844 0.147844i
\(184\) −10.3923 + 18.0000i −0.766131 + 1.32698i
\(185\) 0 0
\(186\) −30.0000 17.3205i −2.19971 1.27000i
\(187\) 7.09808 + 1.90192i 0.519063 + 0.139082i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 5.85641 21.8564i 0.422650 1.57735i
\(193\) 16.3923 + 4.39230i 1.17994 + 0.316165i 0.794904 0.606735i \(-0.207521\pi\)
0.385040 + 0.922900i \(0.374188\pi\)
\(194\) 15.5885 + 9.00000i 1.11919 + 0.646162i
\(195\) 0 0
\(196\) 0 0
\(197\) 8.66025 8.66025i 0.617018 0.617018i −0.327748 0.944765i \(-0.606290\pi\)
0.944765 + 0.327748i \(0.106290\pi\)
\(198\) −15.0000 + 15.0000i −1.06600 + 1.06600i
\(199\) 6.06218 + 3.50000i 0.429736 + 0.248108i 0.699234 0.714893i \(-0.253524\pi\)
−0.269498 + 0.963001i \(0.586858\pi\)
\(200\) 0 0
\(201\) 36.0000 2.53924
\(202\) 9.00000 + 9.00000i 0.633238 + 0.633238i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 6.00000 + 10.3923i 0.418040 + 0.724066i
\(207\) −35.4904 9.50962i −2.46675 0.660964i
\(208\) 12.0000 12.0000i 0.832050 0.832050i
\(209\) 12.9904 + 1.50000i 0.898563 + 0.103757i
\(210\) 0 0
\(211\) 1.50000 0.866025i 0.103264 0.0596196i −0.447478 0.894295i \(-0.647678\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 0 0
\(213\) −42.5885 + 11.4115i −2.91811 + 0.781906i
\(214\) −12.1244 + 7.00000i −0.828804 + 0.478510i
\(215\) 0 0
\(216\) 16.0000 1.08866
\(217\) 0 0
\(218\) 16.5622 4.43782i 1.12173 0.300567i
\(219\) −10.3923 + 18.0000i −0.702247 + 1.21633i
\(220\) 0 0
\(221\) 10.3923i 0.699062i
\(222\) 16.3923 4.39230i 1.10018 0.294792i
\(223\) −4.09808 1.09808i −0.274427 0.0735326i 0.118981 0.992897i \(-0.462037\pi\)
−0.393408 + 0.919364i \(0.628704\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.00000 6.92820i −0.266076 0.460857i
\(227\) −7.00000 7.00000i −0.464606 0.464606i 0.435556 0.900162i \(-0.356552\pi\)
−0.900162 + 0.435556i \(0.856552\pi\)
\(228\) 0 0
\(229\) 11.0000i 0.726900i −0.931614 0.363450i \(-0.881599\pi\)
0.931614 0.363450i \(-0.118401\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.80385 14.1962i −0.249735 0.932023i
\(233\) 1.26795 4.73205i 0.0830661 0.310007i −0.911875 0.410468i \(-0.865365\pi\)
0.994941 + 0.100461i \(0.0320319\pi\)
\(234\) 25.9808 + 15.0000i 1.69842 + 0.980581i
\(235\) 0 0
\(236\) 0 0
\(237\) −3.80385 14.1962i −0.247086 0.922139i
\(238\) 0 0
\(239\) 21.0000i 1.35838i −0.733964 0.679189i \(-0.762332\pi\)
0.733964 0.679189i \(-0.237668\pi\)
\(240\) 0 0
\(241\) 16.5000 + 9.52628i 1.06286 + 0.613642i 0.926222 0.376980i \(-0.123037\pi\)
0.136637 + 0.990621i \(0.456371\pi\)
\(242\) −0.732051 + 2.73205i −0.0470580 + 0.175623i
\(243\) −3.66025 13.6603i −0.234805 0.876306i
\(244\) 0 0
\(245\) 0 0
\(246\) 41.5692i 2.65036i
\(247\) −2.70577 18.2942i −0.172164 1.16403i
\(248\) −17.3205 17.3205i −1.09985 1.09985i
\(249\) 17.3205 + 30.0000i 1.09764 + 1.90117i
\(250\) 0 0
\(251\) 10.5000 18.1865i 0.662754 1.14792i −0.317135 0.948380i \(-0.602721\pi\)
0.979889 0.199543i \(-0.0639459\pi\)
\(252\) 0 0
\(253\) 21.2942 5.70577i 1.33876 0.358719i
\(254\) 18.0000i 1.12942i
\(255\) 0 0
\(256\) 0 0
\(257\) −1.36603 + 0.366025i −0.0852103 + 0.0228320i −0.301172 0.953570i \(-0.597378\pi\)
0.215962 + 0.976402i \(0.430711\pi\)
\(258\) 20.7846 + 20.7846i 1.29399 + 1.29399i
\(259\) 0 0
\(260\) 0 0
\(261\) 22.5000 12.9904i 1.39272 0.804084i
\(262\) 8.19615 2.19615i 0.506360 0.135679i
\(263\) −5.07180 + 18.9282i −0.312740 + 1.16716i 0.613335 + 0.789823i \(0.289828\pi\)
−0.926075 + 0.377340i \(0.876839\pi\)
\(264\) −20.7846 + 12.0000i −1.27920 + 0.738549i
\(265\) 0 0
\(266\) 0 0
\(267\) 10.3923 10.3923i 0.635999 0.635999i
\(268\) 0 0
\(269\) −2.59808 4.50000i −0.158408 0.274370i 0.775887 0.630872i \(-0.217303\pi\)
−0.934295 + 0.356502i \(0.883969\pi\)
\(270\) 0 0
\(271\) −9.50000 16.4545i −0.577084 0.999539i −0.995812 0.0914269i \(-0.970857\pi\)
0.418728 0.908112i \(-0.362476\pi\)
\(272\) 2.53590 + 9.46410i 0.153761 + 0.573845i
\(273\) 0 0
\(274\) 13.8564 0.837096
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(278\) 2.00000 2.00000i 0.119952 0.119952i
\(279\) 21.6506 37.5000i 1.29619 2.24507i
\(280\) 0 0
\(281\) 9.00000 + 5.19615i 0.536895 + 0.309976i 0.743820 0.668380i \(-0.233012\pi\)
−0.206925 + 0.978357i \(0.566345\pi\)
\(282\) −9.46410 2.53590i −0.563579 0.151011i
\(283\) −1.90192 + 7.09808i −0.113058 + 0.421937i −0.999134 0.0416020i \(-0.986754\pi\)
0.886077 + 0.463539i \(0.153421\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −18.0000 −1.06436
\(287\) 0 0
\(288\) 0 0
\(289\) −9.52628 5.50000i −0.560369 0.323529i
\(290\) 0 0
\(291\) −18.0000 + 31.1769i −1.05518 + 1.82762i
\(292\) 0 0
\(293\) 14.0000 14.0000i 0.817889 0.817889i −0.167913 0.985802i \(-0.553703\pi\)
0.985802 + 0.167913i \(0.0537028\pi\)
\(294\) 24.2487 + 14.0000i 1.41421 + 0.816497i
\(295\) 0 0
\(296\) 12.0000 0.697486
\(297\) −12.0000 12.0000i −0.696311 0.696311i
\(298\) −1.09808 4.09808i −0.0636098 0.237395i
\(299\) −15.5885 27.0000i −0.901504 1.56145i
\(300\) 0 0
\(301\) 0 0
\(302\) 11.8301 + 3.16987i 0.680747 + 0.182406i
\(303\) −18.0000 + 18.0000i −1.03407 + 1.03407i
\(304\) 6.92820 + 16.0000i 0.397360 + 0.917663i
\(305\) 0 0
\(306\) −15.0000 + 8.66025i −0.857493 + 0.495074i
\(307\) −8.78461 + 32.7846i −0.501364 + 1.87112i −0.0103834 + 0.999946i \(0.503305\pi\)
−0.490981 + 0.871170i \(0.663361\pi\)
\(308\) 0 0
\(309\) −20.7846 + 12.0000i −1.18240 + 0.682656i
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 24.0000 + 24.0000i 1.35873 + 1.35873i
\(313\) −7.09808 + 1.90192i −0.401207 + 0.107503i −0.453779 0.891114i \(-0.649925\pi\)
0.0525725 + 0.998617i \(0.483258\pi\)
\(314\) −10.3923 + 18.0000i −0.586472 + 1.01580i
\(315\) 0 0
\(316\) 0 0
\(317\) −1.36603 + 0.366025i −0.0767236 + 0.0205580i −0.296977 0.954885i \(-0.595978\pi\)
0.220253 + 0.975443i \(0.429312\pi\)
\(318\) −10.9282 2.92820i −0.612823 0.164205i
\(319\) −7.79423 + 13.5000i −0.436393 + 0.755855i
\(320\) 0 0
\(321\) −14.0000 24.2487i −0.781404 1.35343i
\(322\) 0 0
\(323\) 9.92820 + 3.92820i 0.552420 + 0.218571i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 8.87564 + 33.1244i 0.490824 + 1.83178i
\(328\) 7.60770 28.3923i 0.420065 1.56770i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 5.49038 + 20.4904i 0.300871 + 1.12287i
\(334\) 28.0000i 1.53209i
\(335\) 0 0
\(336\) 0 0
\(337\) −3.29423 + 12.2942i −0.179448 + 0.669709i 0.816303 + 0.577624i \(0.196020\pi\)
−0.995751 + 0.0920854i \(0.970647\pi\)
\(338\) 1.83013 + 6.83013i 0.0995458 + 0.371510i
\(339\) 13.8564 8.00000i 0.752577 0.434500i
\(340\) 0 0
\(341\) 25.9808i 1.40694i
\(342\) −24.1506 + 19.1506i −1.30592 + 1.03555i
\(343\) 0 0
\(344\) 10.3923 + 18.0000i 0.560316 + 0.970495i
\(345\) 0 0
\(346\) 2.00000 3.46410i 0.107521 0.186231i
\(347\) 9.46410 + 2.53590i 0.508060 + 0.136134i 0.503738 0.863857i \(-0.331958\pi\)
0.00432163 + 0.999991i \(0.498624\pi\)
\(348\) 0 0
\(349\) 4.00000i 0.214115i 0.994253 + 0.107058i \(0.0341429\pi\)
−0.994253 + 0.107058i \(0.965857\pi\)
\(350\) 0 0
\(351\) −12.0000 + 20.7846i −0.640513 + 1.10940i
\(352\) 0 0
\(353\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(354\) −20.7846 −1.10469
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 9.50962 35.4904i 0.502599 1.87572i
\(359\) −10.3923 + 6.00000i −0.548485 + 0.316668i −0.748511 0.663123i \(-0.769231\pi\)
0.200026 + 0.979791i \(0.435897\pi\)
\(360\) 0 0
\(361\) 18.5000 + 4.33013i 0.973684 + 0.227901i
\(362\) −24.2487 + 24.2487i −1.27448 + 1.27448i
\(363\) −5.46410 1.46410i −0.286791 0.0768454i
\(364\) 0 0
\(365\) 0 0
\(366\) −2.00000 3.46410i −0.104542 0.181071i
\(367\) −3.80385 14.1962i −0.198559 0.741033i −0.991317 0.131496i \(-0.958022\pi\)
0.792757 0.609537i \(-0.208645\pi\)
\(368\) 20.7846 + 20.7846i 1.08347 + 1.08347i
\(369\) 51.9615 2.70501
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −6.00000 + 6.00000i −0.310668 + 0.310668i −0.845168 0.534500i \(-0.820500\pi\)
0.534500 + 0.845168i \(0.320500\pi\)
\(374\) 5.19615 9.00000i 0.268687 0.465379i
\(375\) 0 0
\(376\) −6.00000 3.46410i −0.309426 0.178647i
\(377\) 21.2942 + 5.70577i 1.09671 + 0.293862i
\(378\) 0 0
\(379\) −25.9808 −1.33454 −0.667271 0.744815i \(-0.732538\pi\)
−0.667271 + 0.744815i \(0.732538\pi\)
\(380\) 0 0
\(381\) 36.0000 1.84434
\(382\) −1.09808 + 4.09808i −0.0561825 + 0.209676i
\(383\) −31.4186 8.41858i −1.60541 0.430170i −0.658743 0.752368i \(-0.728911\pi\)
−0.946672 + 0.322199i \(0.895578\pi\)
\(384\) −27.7128 16.0000i −1.41421 0.816497i
\(385\) 0 0
\(386\) 12.0000 20.7846i 0.610784 1.05791i
\(387\) −25.9808 + 25.9808i −1.32068 + 1.32068i
\(388\) 0 0
\(389\) −2.59808 1.50000i −0.131728 0.0760530i 0.432688 0.901544i \(-0.357565\pi\)
−0.564416 + 0.825491i \(0.690898\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 14.0000 + 14.0000i 0.707107 + 0.707107i
\(393\) 4.39230 + 16.3923i 0.221562 + 0.826882i
\(394\) −8.66025 15.0000i −0.436297 0.755689i
\(395\) 0 0
\(396\) 0 0
\(397\) −14.1962 3.80385i −0.712484 0.190910i −0.115669 0.993288i \(-0.536901\pi\)
−0.596816 + 0.802378i \(0.703568\pi\)
\(398\) 7.00000 7.00000i 0.350878 0.350878i
\(399\) 0 0
\(400\) 0 0
\(401\) −13.5000 + 7.79423i −0.674158 + 0.389225i −0.797650 0.603120i \(-0.793924\pi\)
0.123492 + 0.992346i \(0.460591\pi\)
\(402\) 13.1769 49.1769i 0.657205 2.45272i
\(403\) 35.4904 9.50962i 1.76790 0.473708i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9.00000 9.00000i −0.446113 0.446113i
\(408\) −18.9282 + 5.07180i −0.937086 + 0.251091i
\(409\) 2.59808 4.50000i 0.128467 0.222511i −0.794616 0.607112i \(-0.792328\pi\)
0.923083 + 0.384602i \(0.125661\pi\)
\(410\) 0 0
\(411\) 27.7128i 1.36697i
\(412\) 0 0
\(413\) 0 0
\(414\) −25.9808 + 45.0000i −1.27688 + 2.21163i
\(415\) 0 0
\(416\) 0 0
\(417\) 4.00000 + 4.00000i 0.195881 + 0.195881i
\(418\) 6.80385 17.1962i 0.332787 0.841091i
\(419\) 9.00000i 0.439679i 0.975536 + 0.219839i \(0.0705533\pi\)
−0.975536 + 0.219839i \(0.929447\pi\)
\(420\) 0 0
\(421\) 31.5000 18.1865i 1.53522 0.886357i 0.536107 0.844150i \(-0.319894\pi\)
0.999109 0.0422075i \(-0.0134391\pi\)
\(422\) −0.633975 2.36603i −0.0308614 0.115176i
\(423\) 3.16987 11.8301i 0.154124 0.575200i
\(424\) −6.92820 4.00000i −0.336463 0.194257i
\(425\) 0 0
\(426\) 62.3538i 3.02105i
\(427\) 0 0
\(428\) 0 0
\(429\) 36.0000i 1.73810i
\(430\) 0 0
\(431\) −13.5000 7.79423i −0.650272 0.375435i 0.138288 0.990392i \(-0.455840\pi\)
−0.788560 + 0.614957i \(0.789173\pi\)
\(432\) 5.85641 21.8564i 0.281766 1.05157i
\(433\) 6.58846 + 24.5885i 0.316621 + 1.18165i 0.922471 + 0.386067i \(0.126167\pi\)
−0.605850 + 0.795579i \(0.707167\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 31.6865 4.68653i 1.51577 0.224187i
\(438\) 20.7846 + 20.7846i 0.993127 + 0.993127i
\(439\) 6.06218 + 10.5000i 0.289332 + 0.501138i 0.973650 0.228046i \(-0.0732335\pi\)
−0.684318 + 0.729183i \(0.739900\pi\)
\(440\) 0 0
\(441\) −17.5000 + 30.3109i −0.833333 + 1.44338i
\(442\) −14.1962 3.80385i −0.675242 0.180931i
\(443\) 4.73205 1.26795i 0.224827 0.0602421i −0.144647 0.989483i \(-0.546205\pi\)
0.369474 + 0.929241i \(0.379538\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −3.00000 + 5.19615i −0.142054 + 0.246045i
\(447\) 8.19615 2.19615i 0.387665 0.103874i
\(448\) 0 0
\(449\) 25.9808 1.22611 0.613054 0.790041i \(-0.289941\pi\)
0.613054 + 0.790041i \(0.289941\pi\)
\(450\) 0 0
\(451\) −27.0000 + 15.5885i −1.27138 + 0.734032i
\(452\) 0 0
\(453\) −6.33975 + 23.6603i −0.297867 + 1.11166i
\(454\) −12.1244 + 7.00000i −0.569024 + 0.328526i
\(455\) 0 0
\(456\) −32.0000 + 13.8564i −1.49854 + 0.648886i
\(457\) 25.9808 25.9808i 1.21533 1.21533i 0.246079 0.969250i \(-0.420858\pi\)
0.969250 0.246079i \(-0.0791423\pi\)
\(458\) −15.0263 4.02628i −0.702132 0.188136i
\(459\) −6.92820 12.0000i −0.323381 0.560112i
\(460\) 0 0
\(461\) −4.50000 7.79423i −0.209586 0.363013i 0.741998 0.670402i \(-0.233878\pi\)
−0.951584 + 0.307388i \(0.900545\pi\)
\(462\) 0 0
\(463\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) −20.7846 −0.964901
\(465\) 0 0
\(466\) −6.00000 3.46410i −0.277945 0.160471i
\(467\) 8.66025 8.66025i 0.400749 0.400749i −0.477748 0.878497i \(-0.658547\pi\)
0.878497 + 0.477748i \(0.158547\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −36.0000 20.7846i −1.65879 0.957704i
\(472\) −14.1962 3.80385i −0.653431 0.175086i
\(473\) 5.70577 21.2942i 0.262352 0.979110i
\(474\) −20.7846 −0.954669
\(475\) 0 0
\(476\) 0 0
\(477\) 3.66025 13.6603i 0.167592 0.625460i
\(478\) −28.6865 7.68653i −1.31209 0.351574i
\(479\) −2.59808 1.50000i −0.118709 0.0685367i 0.439470 0.898257i \(-0.355166\pi\)
−0.558179 + 0.829721i \(0.688500\pi\)
\(480\) 0 0
\(481\) −9.00000 + 15.5885i −0.410365 + 0.710772i
\(482\) 19.0526 19.0526i 0.867820 0.867820i
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) −20.0000 −0.907218
\(487\) −27.0000 27.0000i −1.22349 1.22349i −0.966384 0.257103i \(-0.917232\pi\)
−0.257103 0.966384i \(-0.582768\pi\)
\(488\) −0.732051 2.73205i −0.0331384 0.123674i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.5000 + 18.1865i 0.473858 + 0.820747i 0.999552 0.0299272i \(-0.00952753\pi\)
−0.525694 + 0.850674i \(0.676194\pi\)
\(492\) 0 0
\(493\) −9.00000 + 9.00000i −0.405340 + 0.405340i
\(494\) −25.9808 3.00000i −1.16893 0.134976i
\(495\) 0 0
\(496\) −30.0000 + 17.3205i −1.34704 + 0.777714i
\(497\) 0 0
\(498\) 47.3205 12.6795i 2.12048 0.568182i
\(499\) 32.9090 19.0000i 1.47321 0.850557i 0.473662 0.880707i \(-0.342932\pi\)
0.999545 + 0.0301498i \(0.00959843\pi\)
\(500\) 0 0
\(501\) 56.0000 2.50190
\(502\) −21.0000 21.0000i −0.937276 0.937276i
\(503\) −30.7583 + 8.24167i −1.37145 + 0.367478i −0.868007 0.496553i \(-0.834599\pi\)
−0.503440 + 0.864030i \(0.667932\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 31.1769i 1.38598i
\(507\) −13.6603 + 3.66025i −0.606673 + 0.162558i
\(508\) 0 0
\(509\) −10.3923 + 18.0000i −0.460631 + 0.797836i −0.998992 0.0448779i \(-0.985710\pi\)
0.538362 + 0.842714i \(0.319043\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) −15.3205 19.3205i −0.676417 0.853021i
\(514\) 2.00000i 0.0882162i
\(515\) 0 0
\(516\) 0 0
\(517\) 1.90192 + 7.09808i 0.0836465 + 0.312173i
\(518\) 0 0
\(519\) 6.92820 + 4.00000i 0.304114 + 0.175581i
\(520\) 0 0
\(521\) 25.9808i 1.13824i 0.822255 + 0.569119i \(0.192716\pi\)
−0.822255 + 0.569119i \(0.807284\pi\)
\(522\) −9.50962 35.4904i −0.416225 1.55337i
\(523\) −4.39230 16.3923i −0.192062 0.716785i −0.993008 0.118049i \(-0.962336\pi\)
0.800946 0.598737i \(-0.204331\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 24.0000 + 13.8564i 1.04645 + 0.604168i
\(527\) −5.49038 + 20.4904i −0.239165 + 0.892575i
\(528\) 8.78461 + 32.7846i 0.382301 + 1.42677i
\(529\) 26.8468 15.5000i 1.16725 0.673913i
\(530\) 0 0
\(531\) 25.9808i 1.12747i
\(532\) 0 0
\(533\) 31.1769 + 31.1769i 1.35042 + 1.35042i
\(534\) −10.3923 18.0000i −0.449719 0.778936i
\(535\) 0 0
\(536\) 18.0000 31.1769i 0.777482 1.34664i
\(537\) 70.9808 + 19.0192i 3.06305 + 0.820741i
\(538\) −7.09808 + 1.90192i −0.306020 + 0.0819978i
\(539\) 21.0000i 0.904534i
\(540\) 0 0
\(541\) −9.50000 + 16.4545i −0.408437 + 0.707433i −0.994715 0.102677i \(-0.967259\pi\)
0.586278 + 0.810110i \(0.300593\pi\)
\(542\) −25.9545 + 6.95448i −1.11484 + 0.298721i
\(543\) −48.4974 48.4974i −2.08122 2.08122i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −28.6865 + 7.68653i −1.22655 + 0.328652i −0.813234 0.581936i \(-0.802295\pi\)
−0.413313 + 0.910589i \(0.635629\pi\)
\(548\) 0 0
\(549\) 4.33013 2.50000i 0.184805 0.106697i
\(550\) 0 0
\(551\) −13.5000 + 18.1865i −0.575119 + 0.774772i
\(552\) −41.5692 + 41.5692i −1.76930 + 1.76930i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.70577 + 21.2942i 0.241761 + 0.902265i 0.974984 + 0.222276i \(0.0713488\pi\)
−0.733222 + 0.679989i \(0.761985\pi\)
\(558\) −43.3013 43.3013i −1.83309 1.83309i
\(559\) −31.1769 −1.31864
\(560\) 0 0
\(561\) 18.0000 + 10.3923i 0.759961 + 0.438763i
\(562\) 10.3923 10.3923i 0.438373 0.438373i
\(563\) 14.0000 14.0000i 0.590030 0.590030i −0.347610 0.937639i \(-0.613007\pi\)
0.937639 + 0.347610i \(0.113007\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 9.00000 + 5.19615i 0.378298 + 0.218411i
\(567\) 0 0
\(568\) −11.4115 + 42.5885i −0.478818 + 1.78697i
\(569\) −25.9808 −1.08917 −0.544585 0.838706i \(-0.683313\pi\)
−0.544585 + 0.838706i \(0.683313\pi\)
\(570\) 0 0
\(571\) 7.00000 0.292941 0.146470 0.989215i \(-0.453209\pi\)
0.146470 + 0.989215i \(0.453209\pi\)
\(572\) 0 0
\(573\) −8.19615 2.19615i −0.342399 0.0917456i
\(574\) 0 0
\(575\) 0 0
\(576\) 20.0000 34.6410i 0.833333 1.44338i
\(577\) 25.9808 25.9808i 1.08159 1.08159i 0.0852322 0.996361i \(-0.472837\pi\)
0.996361 0.0852322i \(-0.0271632\pi\)
\(578\) −11.0000 + 11.0000i −0.457540 + 0.457540i
\(579\) 41.5692 + 24.0000i 1.72756 + 0.997406i
\(580\) 0 0
\(581\) 0 0
\(582\) 36.0000 + 36.0000i 1.49225 + 1.49225i
\(583\) 2.19615 + 8.19615i 0.0909553 + 0.339450i
\(584\) 10.3923 + 18.0000i 0.430037 + 0.744845i
\(585\) 0 0
\(586\) −14.0000 24.2487i −0.578335 1.00171i
\(587\) 9.46410 + 2.53590i 0.390625 + 0.104668i 0.448785 0.893640i \(-0.351857\pi\)
−0.0581602 + 0.998307i \(0.518523\pi\)
\(588\) 0 0
\(589\) −4.33013 + 37.5000i −0.178420 + 1.54516i
\(590\) 0 0
\(591\) 30.0000 17.3205i 1.23404 0.712470i
\(592\) 4.39230 16.3923i 0.180523 0.673720i
\(593\) −18.9282 + 5.07180i −0.777288 + 0.208274i −0.625589 0.780153i \(-0.715141\pi\)
−0.151699 + 0.988427i \(0.548475\pi\)
\(594\) −20.7846 + 12.0000i −0.852803 + 0.492366i
\(595\) 0 0
\(596\) 0 0
\(597\) 14.0000 + 14.0000i 0.572982 + 0.572982i
\(598\) −42.5885 + 11.4115i −1.74157 + 0.466653i
\(599\) 15.5885 27.0000i 0.636927 1.10319i −0.349176 0.937057i \(-0.613539\pi\)
0.986103 0.166133i \(-0.0531281\pi\)
\(600\) 0 0
\(601\) 25.9808i 1.05978i −0.848067 0.529889i \(-0.822234\pi\)
0.848067 0.529889i \(-0.177766\pi\)
\(602\) 0 0
\(603\) 61.4711 + 16.4711i 2.50330 + 0.670757i
\(604\) 0 0
\(605\) 0 0
\(606\) 18.0000 + 31.1769i 0.731200 + 1.26648i
\(607\) 3.00000 + 3.00000i 0.121766 + 0.121766i 0.765364 0.643598i \(-0.222559\pi\)
−0.643598 + 0.765364i \(0.722559\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.00000 5.19615i 0.364101 0.210214i
\(612\) 0 0
\(613\) 7.60770 28.3923i 0.307272 1.14675i −0.623700 0.781664i \(-0.714371\pi\)
0.930972 0.365091i \(-0.118962\pi\)
\(614\) 41.5692 + 24.0000i 1.67760 + 0.968561i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.633975 2.36603i −0.0255229 0.0952526i 0.951990 0.306131i \(-0.0990344\pi\)
−0.977512 + 0.210878i \(0.932368\pi\)
\(618\) 8.78461 + 32.7846i 0.353369 + 1.31879i
\(619\) 14.0000i 0.562708i 0.959604 + 0.281354i \(0.0907834\pi\)
−0.959604 + 0.281354i \(0.909217\pi\)
\(620\) 0 0
\(621\) −36.0000 20.7846i −1.44463 0.834058i
\(622\) −6.58846 + 24.5885i −0.264173 + 0.985907i
\(623\) 0 0
\(624\) 41.5692 24.0000i 1.66410 0.960769i
\(625\) 0 0
\(626\) 10.3923i 0.415360i
\(627\) 34.3923 + 13.6077i 1.37350 + 0.543439i
\(628\) 0 0
\(629\) −5.19615 9.00000i −0.207184 0.358854i
\(630\) 0 0
\(631\) 0.500000 0.866025i 0.0199047 0.0344759i −0.855901 0.517139i \(-0.826997\pi\)
0.875806 + 0.482663i \(0.160330\pi\)
\(632\) −14.1962 3.80385i −0.564693 0.151309i
\(633\) 4.73205 1.26795i 0.188082 0.0503965i
\(634\) 2.00000i 0.0794301i
\(635\) 0 0
\(636\) 0 0
\(637\) −28.6865 + 7.68653i −1.13660 + 0.304552i
\(638\) 15.5885 + 15.5885i 0.617153 + 0.617153i
\(639\) −77.9423 −3.08335
\(640\) 0 0
\(641\) −13.5000 + 7.79423i −0.533218 + 0.307854i −0.742326 0.670039i \(-0.766277\pi\)
0.209108 + 0.977893i \(0.432944\pi\)
\(642\) −38.2487 + 10.2487i −1.50956 + 0.404484i
\(643\) −1.90192 + 7.09808i −0.0750046 + 0.279921i −0.993234 0.116127i \(-0.962952\pi\)
0.918230 + 0.396048i \(0.129619\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 9.00000 12.1244i 0.354100 0.477026i
\(647\) −8.66025 + 8.66025i −0.340470 + 0.340470i −0.856544 0.516074i \(-0.827393\pi\)
0.516074 + 0.856544i \(0.327393\pi\)
\(648\) 2.73205 + 0.732051i 0.107325 + 0.0287577i
\(649\) 7.79423 + 13.5000i 0.305950 + 0.529921i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −25.9808 25.9808i −1.01671 1.01671i −0.999858 0.0168477i \(-0.994637\pi\)
−0.0168477 0.999858i \(-0.505363\pi\)
\(654\) 48.4974 1.89640
\(655\) 0 0
\(656\) −36.0000 20.7846i −1.40556 0.811503i
\(657\) −25.9808 + 25.9808i −1.01361 + 1.01361i
\(658\) 0 0
\(659\) −10.3923 + 18.0000i −0.404827 + 0.701180i −0.994301 0.106606i \(-0.966001\pi\)
0.589475 + 0.807787i \(0.299335\pi\)
\(660\) 0 0
\(661\) 16.5000 + 9.52628i 0.641776 + 0.370529i 0.785298 0.619118i \(-0.212510\pi\)
−0.143523 + 0.989647i \(0.545843\pi\)
\(662\) 0 0
\(663\) 7.60770 28.3923i 0.295458 1.10267i
\(664\) 34.6410 1.34433
\(665\) 0 0
\(666\) 30.0000 1.16248
\(667\) −9.88269 + 36.8827i −0.382659 + 1.42810i
\(668\) 0 0
\(669\) −10.3923 6.00000i −0.401790 0.231973i
\(670\) 0 0
\(671\) −1.50000 + 2.59808i −0.0579069 + 0.100298i
\(672\) 0 0
\(673\) 24.0000 24.0000i 0.925132 0.925132i −0.0722542 0.997386i \(-0.523019\pi\)
0.997386 + 0.0722542i \(0.0230193\pi\)
\(674\) 15.5885 + 9.00000i 0.600445 + 0.346667i
\(675\) 0 0
\(676\) 0 0
\(677\) 8.00000 + 8.00000i 0.307465 + 0.307465i 0.843925 0.536460i \(-0.180239\pi\)
−0.536460 + 0.843925i \(0.680239\pi\)
\(678\) −5.85641 21.8564i −0.224914 0.839390i
\(679\) 0 0
\(680\) 0 0
\(681\) −14.0000 24.2487i −0.536481 0.929213i
\(682\) 35.4904 + 9.50962i 1.35900 + 0.364142i
\(683\) −11.0000 + 11.0000i −0.420903 + 0.420903i −0.885515 0.464611i \(-0.846194\pi\)
0.464611 + 0.885515i \(0.346194\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 8.05256 30.0526i 0.307224 1.14658i
\(688\) 28.3923 7.60770i 1.08245 0.290041i
\(689\) 10.3923 6.00000i 0.395915 0.228582i
\(690\) 0 0
\(691\) −13.0000 −0.494543 −0.247272 0.968946i \(-0.579534\pi\)
−0.247272 + 0.968946i \(0.579534\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 6.92820 12.0000i 0.262991 0.455514i
\(695\) 0 0
\(696\) 41.5692i 1.57568i
\(697\) −24.5885 + 6.58846i −0.931354 + 0.249556i
\(698\) 5.46410 + 1.46410i 0.206819 + 0.0554171i
\(699\) 6.92820 12.0000i 0.262049 0.453882i
\(700\) 0 0
\(701\) −12.0000 20.7846i −0.453234 0.785024i 0.545351 0.838208i \(-0.316396\pi\)
−0.998585 + 0.0531839i \(0.983063\pi\)
\(702\) 24.0000 + 24.0000i 0.905822 + 0.905822i
\(703\) −11.4904 14.4904i −0.433368 0.546515i
\(704\) 24.0000i 0.904534i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −11.2583 6.50000i −0.422815 0.244113i 0.273466 0.961882i \(-0.411830\pi\)
−0.696281 + 0.717769i \(0.745163\pi\)
\(710\) 0 0
\(711\) 25.9808i 0.974355i
\(712\) −3.80385 14.1962i −0.142555 0.532023i
\(713\) 16.4711 + 61.4711i 0.616849 + 2.30211i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 15.3731 57.3731i 0.574118 2.14264i
\(718\) 4.39230 + 16.3923i 0.163919 + 0.611755i
\(719\) −23.3827 + 13.5000i −0.872027 + 0.503465i −0.868021 0.496527i \(-0.834608\pi\)
−0.00400572 + 0.999992i \(0.501275\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 12.6865 23.6865i 0.472144 0.881521i
\(723\) 38.1051 + 38.1051i 1.41714 + 1.41714i
\(724\) 0 0
\(725\) 0 0
\(726\) −4.00000 + 6.92820i −0.148454 + 0.257130i
\(727\) −14.1962 3.80385i −0.526506 0.141077i −0.0142317 0.999899i \(-0.504530\pi\)
−0.512274 + 0.858822i \(0.671197\pi\)
\(728\) 0 0
\(729\) 43.0000i 1.59259i
\(730\) 0 0
\(731\) 9.00000 15.5885i 0.332877 0.576560i
\(732\) 0 0
\(733\) 25.9808 + 25.9808i 0.959621 + 0.959621i 0.999216 0.0395945i \(-0.0126066\pi\)
−0.0395945 + 0.999216i \(0.512607\pi\)
\(734\) −20.7846 −0.767174
\(735\) 0 0
\(736\) 0 0
\(737\) −36.8827 + 9.88269i −1.35859 + 0.364033i
\(738\) 19.0192 70.9808i 0.700108 2.61284i
\(739\) 45.8993 26.5000i 1.68843 0.974818i 0.732717 0.680534i \(-0.238252\pi\)
0.955718 0.294285i \(-0.0950814\pi\)
\(740\) 0 0
\(741\) 6.00000 51.9615i 0.220416 1.90885i
\(742\) 0 0
\(743\) −31.4186 8.41858i −1.15264 0.308848i −0.368615 0.929582i \(-0.620168\pi\)
−0.784021 + 0.620734i \(0.786835\pi\)
\(744\) −34.6410 60.0000i −1.27000 2.19971i
\(745\) 0 0
\(746\) 6.00000 + 10.3923i 0.219676 + 0.380489i
\(747\) 15.8494 + 59.1506i 0.579898 + 2.16421i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 46.5000 + 26.8468i 1.69681 + 0.979653i 0.948753 + 0.316017i \(0.102346\pi\)
0.748056 + 0.663636i \(0.230988\pi\)
\(752\) −6.92820 + 6.92820i −0.252646 + 0.252646i
\(753\) 42.0000 42.0000i 1.53057 1.53057i
\(754\) 15.5885 27.0000i 0.567698 0.983282i
\(755\) 0 0
\(756\) 0 0
\(757\) 21.2942 + 5.70577i 0.773952 + 0.207380i 0.624117 0.781331i \(-0.285459\pi\)
0.149835 + 0.988711i \(0.452126\pi\)
\(758\) −9.50962 + 35.4904i −0.345405 + 1.28907i
\(759\) 62.3538 2.26330
\(760\) 0 0
\(761\) −48.0000 −1.74000 −0.869999 0.493053i \(-0.835881\pi\)
−0.869999 + 0.493053i \(0.835881\pi\)
\(762\) 13.1769 49.1769i 0.477349 1.78149i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −23.0000 + 39.8372i −0.831024 + 1.43938i
\(767\) 15.5885 15.5885i 0.562867 0.562867i
\(768\) 0 0
\(769\) 6.06218 + 3.50000i 0.218608 + 0.126213i 0.605305 0.795993i \(-0.293051\pi\)
−0.386698 + 0.922207i \(0.626384\pi\)
\(770\) 0 0
\(771\) −4.00000 −0.144056
\(772\) 0 0
\(773\) 8.41858 + 31.4186i 0.302795 + 1.13005i 0.934826 + 0.355105i \(0.115555\pi\)
−0.632031 + 0.774943i \(0.717778\pi\)
\(774\) 25.9808 + 45.0000i 0.933859 + 1.61749i
\(775\) 0 0
\(776\) 18.0000 + 31.1769i 0.646162 + 1.11919i
\(777\) 0 0
\(778\) −3.00000 + 3.00000i −0.107555 + 0.107555i
\(779\) −41.5692 + 18.0000i −1.48937 + 0.644917i
\(780\) 0 0
\(781\) 40.5000 23.3827i 1.44920 0.836698i
\(782\) 6.58846 24.5885i 0.235603 0.879281i
\(783\) 28.3923 7.60770i 1.01466 0.271877i
\(784\) 24.2487 14.0000i 0.866025 0.500000i
\(785\) 0 0
\(786\) 24.0000 0.856052
\(787\) −27.0000 27.0000i −0.962446 0.962446i 0.0368739 0.999320i \(-0.488260\pi\)
−0.999320 + 0.0368739i \(0.988260\pi\)
\(788\) 0 0
\(789\) −27.7128 + 48.0000i −0.986602 + 1.70885i
\(790\) 0 0
\(791\) 0 0
\(792\) −40.9808 + 10.9808i −1.45619 + 0.390184i
\(793\) 4.09808 + 1.09808i 0.145527 + 0.0389938i
\(794\) −10.3923 + 18.0000i −0.368809 + 0.638796i
\(795\) 0 0
\(796\) 0 0
\(797\) −32.0000 32.0000i −1.13350 1.13350i −0.989591 0.143907i \(-0.954033\pi\)
−0.143907 0.989591i \(-0.545967\pi\)
\(798\) 0 0
\(799\) 6.00000i 0.212265i
\(800\) 0 0
\(801\) 22.5000 12.9904i 0.794998 0.458993i
\(802\) 5.70577 + 21.2942i 0.201478 + 0.751925i
\(803\) 5.70577 21.2942i 0.201352 0.751457i
\(804\) 0 0
\(805\) 0 0
\(806\) 51.9615i 1.83027i
\(807\) −3.80385 14.1962i −0.133902 0.499728i
\(808\) 6.58846 + 24.5885i 0.231781 + 0.865019i
\(809\) 39.0000i 1.37117i 0.727994 + 0.685583i \(0.240453\pi\)
−0.727994 + 0.685583i \(0.759547\pi\)
\(810\) 0 0
\(811\) 1.50000 + 0.866025i 0.0526721 + 0.0304103i 0.526105 0.850420i \(-0.323652\pi\)
−0.473433 + 0.880830i \(0.656985\pi\)
\(812\) 0 0
\(813\) −13.9090 51.9090i −0.487809 1.82053i
\(814\) −15.5885 + 9.00000i −0.546375 + 0.315450i
\(815\) 0 0
\(816\) 27.7128i 0.970143i
\(817\) 11.7846 29.7846i 0.412291 1.04203i
\(818\) −5.19615 5.19615i −0.181679 0.181679i
\(819\) 0 0
\(820\) 0 0
\(821\) 10.5000 18.1865i 0.366453 0.634714i −0.622556 0.782576i \(-0.713906\pi\)
0.989008 + 0.147861i \(0.0472389\pi\)
\(822\) 37.8564 + 10.1436i 1.32039 + 0.353798i
\(823\) −7.09808 + 1.90192i −0.247423 + 0.0662969i −0.380399 0.924822i \(-0.624213\pi\)
0.132976 + 0.991119i \(0.457547\pi\)
\(824\) 24.0000i 0.836080i
\(825\) 0 0
\(826\) 0 0
\(827\) −15.0263 + 4.02628i −0.522515 + 0.140007i −0.510430 0.859920i \(-0.670514\pi\)
−0.0120853 + 0.999927i \(0.503847\pi\)
\(828\) 0 0
\(829\) −17.3205 −0.601566 −0.300783 0.953693i \(-0.597248\pi\)
−0.300783 + 0.953693i \(0.597248\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 32.7846 8.78461i 1.13660 0.304552i
\(833\) 4.43782 16.5622i 0.153761 0.573845i
\(834\) 6.92820 4.00000i 0.239904 0.138509i
\(835\) 0 0
\(836\) 0 0
\(837\) 34.6410 34.6410i 1.19737 1.19737i
\(838\) 12.2942 + 3.29423i 0.424697 + 0.113797i
\(839\) 10.3923 + 18.0000i 0.358782 + 0.621429i 0.987758 0.155996i \(-0.0498587\pi\)
−0.628975 + 0.777425i \(0.716525\pi\)
\(840\) 0 0
\(841\) 1.00000 + 1.73205i 0.0344828 + 0.0597259i
\(842\) −13.3135 49.6865i −0.458812 1.71231i
\(843\) 20.7846 + 20.7846i 0.715860 + 0.715860i
\(844\) 0 0
\(845\) 0 0
\(846\) −15.0000 8.66025i −0.515711 0.297746i
\(847\) 0 0
\(848\) −8.00000 + 8.00000i −0.274721 + 0.274721i
\(849\) −10.3923 + 18.0000i −0.356663 + 0.617758i
\(850\) 0 0
\(851\) −27.0000 15.5885i −0.925548 0.534365i
\(852\) 0 0
\(853\) −11.4115 + 42.5885i −0.390724 + 1.45820i 0.438219 + 0.898868i \(0.355609\pi\)
−0.828943 + 0.559333i \(0.811057\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −28.0000 −0.957020
\(857\) −6.95448 + 25.9545i −0.237561 + 0.886588i 0.739417 + 0.673247i \(0.235101\pi\)
−0.976978 + 0.213341i \(0.931566\pi\)
\(858\) −49.1769 13.1769i −1.67887 0.449852i
\(859\) 40.7032 + 23.5000i 1.38878 + 0.801810i 0.993177 0.116614i \(-0.0372041\pi\)
0.395598 + 0.918424i \(0.370537\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −15.5885 + 15.5885i −0.530945 + 0.530945i
\(863\) 14.0000 14.0000i 0.476566 0.476566i −0.427466 0.904031i \(-0.640594\pi\)
0.904031 + 0.427466i \(0.140594\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 36.0000 1.22333
\(867\) −22.0000 22.0000i −0.747159 0.747159i
\(868\) 0 0
\(869\) 7.79423 + 13.5000i 0.264401 + 0.457956i
\(870\) 0 0
\(871\) 27.0000 + 46.7654i 0.914860 + 1.58458i
\(872\) 33.1244 + 8.87564i 1.12173 + 0.300567i
\(873\) −45.0000 + 45.0000i −1.52302 + 1.52302i
\(874\) 5.19615 45.0000i 0.175762 1.52215i
\(875\) 0 0
\(876\) 0 0
\(877\) −3.29423 + 12.2942i −0.111238 + 0.415147i −0.998978 0.0451990i \(-0.985608\pi\)
0.887740 + 0.460346i \(0.152274\pi\)
\(878\) 16.5622 4.43782i 0.558946 0.149769i
\(879\) 48.4974 28.0000i 1.63578 0.944417i
\(880\) 0 0
\(881\) −33.0000 −1.11180 −0.555899 0.831250i \(-0.687626\pi\)
−0.555899 + 0.831250i \(0.687626\pi\)
\(882\) 35.0000 + 35.0000i 1.17851 + 1.17851i
\(883\) −42.5885 + 11.4115i −1.43322 + 0.384029i −0.890152 0.455663i \(-0.849402\pi\)
−0.543063 + 0.839692i \(0.682736\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 6.92820i 0.232758i
\(887\) 19.1244 5.12436i 0.642133 0.172059i 0.0769636 0.997034i \(-0.475477\pi\)
0.565169 + 0.824975i \(0.308811\pi\)
\(888\) 32.7846 + 8.78461i 1.10018 + 0.294792i
\(889\) 0 0
\(890\) 0 0
\(891\) −1.50000 2.59808i −0.0502519 0.0870388i
\(892\) 0 0
\(893\) 1.56218 + 10.5622i 0.0522763 + 0.353450i
\(894\) 12.0000i 0.401340i
\(895\) 0 0
\(896\) 0 0
\(897\) −22.8231 85.1769i −0.762041 2.84397i
\(898\) 9.50962 35.4904i 0.317340 1.18433i
\(899\) −38.9711 22.5000i −1.29976 0.750417i
\(900\) 0 0
\(901\) 6.92820i 0.230812i
\(902\) 11.4115 + 42.5885i 0.379963 + 1.41804i
\(903\) 0 0
\(904\) 16.0000i 0.532152i
\(905\) 0 0
\(906\) 30.0000 + 17.3205i 0.996683 + 0.575435i
\(907\) 2.19615 8.19615i 0.0729220 0.272149i −0.919832 0.392312i \(-0.871675\pi\)
0.992754 + 0.120164i \(0.0383419\pi\)
\(908\) 0 0
\(909\) −38.9711 + 22.5000i −1.29259 + 0.746278i
\(910\) 0 0
\(911\) 25.9808i 0.860781i −0.902643 0.430391i \(-0.858376\pi\)
0.902643 0.430391i \(-0.141624\pi\)
\(912\) 7.21539 + 48.7846i 0.238925 + 1.61542i
\(913\) −25.9808 25.9808i −0.859838 0.859838i
\(914\) −25.9808 45.0000i −0.859367 1.48847i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) −18.9282 + 5.07180i −0.624724 + 0.167394i
\(919\) 46.0000i 1.51740i −0.651440 0.758700i \(-0.725835\pi\)
0.651440 0.758700i \(-0.274165\pi\)
\(920\) 0 0
\(921\) −48.0000 + 83.1384i −1.58165 + 2.73950i
\(922\) −12.2942 + 3.29423i −0.404889 + 0.108490i
\(923\) −46.7654 46.7654i −1.53930 1.53930i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −40.9808 + 10.9808i −1.34598 + 0.360656i
\(928\) 0 0
\(929\) 2.59808 1.50000i 0.0852401 0.0492134i −0.456774 0.889583i \(-0.650995\pi\)
0.542014 + 0.840369i \(0.317662\pi\)
\(930\) 0 0
\(931\) 3.50000 30.3109i 0.114708 0.993399i
\(932\) 0 0
\(933\) −49.1769 13.1769i −1.60998 0.431393i
\(934\) −8.66025 15.0000i −0.283372 0.490815i
\(935\) 0 0
\(936\) 30.0000 + 51.9615i 0.980581 + 1.69842i
\(937\) 15.2154 + 56.7846i 0.497065 + 1.85507i 0.518142 + 0.855294i \(0.326624\pi\)
−0.0210771 + 0.999778i \(0.506710\pi\)
\(938\) 0 0
\(939\) −20.7846 −0.678280
\(940\) 0 0
\(941\) −13.5000 7.79423i −0.440087 0.254085i 0.263547 0.964646i \(-0.415107\pi\)
−0.703635 + 0.710562i \(0.748441\pi\)
\(942\) −41.5692 + 41.5692i −1.35440 + 1.35440i
\(943\) −54.0000 + 54.0000i −1.75848 + 1.75848i
\(944\) −10.3923 + 18.0000i −0.338241 + 0.585850i
\(945\) 0 0
\(946\) −27.0000 15.5885i −0.877846 0.506824i
\(947\) −49.6865 13.3135i −1.61460 0.432630i −0.665188 0.746676i \(-0.731649\pi\)
−0.949408 + 0.314047i \(0.898315\pi\)
\(948\) 0 0
\(949\) −31.1769 −1.01205
\(950\) 0 0
\(951\) −4.00000 −0.129709
\(952\) 0 0
\(953\) 2.73205 + 0.732051i 0.0884998 + 0.0237135i 0.302797 0.953055i \(-0.402080\pi\)
−0.214297 + 0.976768i \(0.568746\pi\)
\(954\) −17.3205 10.0000i −0.560772 0.323762i
\(955\) 0 0
\(956\) 0 0
\(957\) −31.1769 + 31.1769i −1.00781 + 1.00781i
\(958\) −3.00000 + 3.00000i −0.0969256 + 0.0969256i
\(959\) 0 0
\(960\) 0 0
\(961\) −44.0000 −1.41935
\(962\) 18.0000 + 18.0000i 0.580343 + 0.580343i
\(963\) −12.8109 47.8109i −0.412825 1.54068i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 21.2942 + 5.70577i 0.684776 + 0.183485i 0.584402 0.811464i \(-0.301329\pi\)
0.100374 + 0.994950i \(0.467996\pi\)
\(968\) −4.00000 + 4.00000i −0.128565 + 0.128565i
\(969\) 24.2487 + 18.0000i 0.778981 + 0.578243i
\(970\) 0 0
\(971\) −36.0000 + 20.7846i −1.15529 + 0.667010i −0.950172 0.311726i \(-0.899093\pi\)
−0.205123 + 0.978736i \(0.565759\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −46.7654 + 27.0000i −1.49846 + 0.865136i
\(975\) 0 0
\(976\) −4.00000 −0.128037
\(977\) −32.0000 32.0000i −1.02377 1.02377i −0.999711 0.0240602i \(-0.992341\pi\)
−0.0240602 0.999711i \(-0.507659\pi\)
\(978\) 0 0
\(979\) −7.79423 + 13.5000i −0.249105 + 0.431462i
\(980\) 0 0
\(981\) 60.6218i 1.93550i
\(982\) 28.6865 7.68653i 0.915424 0.245287i
\(983\) −10.9282 2.92820i −0.348556 0.0933952i 0.0802937 0.996771i \(-0.474414\pi\)
−0.428849 + 0.903376i \(0.641081\pi\)
\(984\) 41.5692 72.0000i 1.32518 2.29528i
\(985\) 0 0
\(986\) 9.00000 + 15.5885i 0.286618 + 0.496438i
\(987\) 0 0
\(988\) 0 0
\(989\) 54.0000i 1.71710i
\(990\) 0 0
\(991\) −21.0000 + 12.1244i −0.667087 + 0.385143i −0.794972 0.606646i \(-0.792514\pi\)
0.127885 + 0.991789i \(0.459181\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 5.70577 + 21.2942i 0.180704 + 0.674395i 0.995510 + 0.0946612i \(0.0301768\pi\)
−0.814806 + 0.579734i \(0.803157\pi\)
\(998\) −13.9090 51.9090i −0.440281 1.64315i
\(999\) 24.0000i 0.759326i
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 475.2.p.a.468.1 yes 4
5.2 odd 4 475.2.p.c.107.1 yes 4
5.3 odd 4 inner 475.2.p.a.107.1 4
5.4 even 2 475.2.p.c.468.1 yes 4
19.8 odd 6 475.2.p.c.293.1 yes 4
95.8 even 12 475.2.p.c.407.1 yes 4
95.27 even 12 inner 475.2.p.a.407.1 yes 4
95.84 odd 6 inner 475.2.p.a.293.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
475.2.p.a.107.1 4 5.3 odd 4 inner
475.2.p.a.293.1 yes 4 95.84 odd 6 inner
475.2.p.a.407.1 yes 4 95.27 even 12 inner
475.2.p.a.468.1 yes 4 1.1 even 1 trivial
475.2.p.c.107.1 yes 4 5.2 odd 4
475.2.p.c.293.1 yes 4 19.8 odd 6
475.2.p.c.407.1 yes 4 95.8 even 12
475.2.p.c.468.1 yes 4 5.4 even 2