Properties

Label 600.2.b.i.251.11
Level $600$
Weight $2$
Character 600.251
Analytic conductor $4.791$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [600,2,Mod(251,600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("600.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.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: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.11
Root \(-0.357857i\) of defining polynomial
Character \(\chi\) \(=\) 600.251
Dual form 600.2.b.i.251.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.541196 + 1.30656i) q^{2} +(-1.64533 + 0.541196i) q^{3} +(-1.41421 + 1.41421i) q^{4} +(-1.59755 - 1.85683i) q^{6} -3.29066i q^{7} +(-2.61313 - 1.08239i) q^{8} +(2.41421 - 1.78089i) q^{9} +O(q^{10})\) \(q+(0.541196 + 1.30656i) q^{2} +(-1.64533 + 0.541196i) q^{3} +(-1.41421 + 1.41421i) q^{4} +(-1.59755 - 1.85683i) q^{6} -3.29066i q^{7} +(-2.61313 - 1.08239i) q^{8} +(2.41421 - 1.78089i) q^{9} +2.51856i q^{11} +(1.56148 - 3.09221i) q^{12} -4.65369i q^{13} +(4.29945 - 1.78089i) q^{14} -4.00000i q^{16} -3.69552i q^{17} +(3.63341 + 2.19051i) q^{18} -0.828427 q^{19} +(1.78089 + 5.41421i) q^{21} +(-3.29066 + 1.36303i) q^{22} +2.61313 q^{23} +(4.88524 + 0.366677i) q^{24} +(6.08034 - 2.51856i) q^{26} +(-3.00836 + 4.23671i) q^{27} +(4.65369 + 4.65369i) q^{28} +6.08034 q^{29} -1.17157i q^{31} +(5.22625 - 2.16478i) q^{32} +(-1.36303 - 4.14386i) q^{33} +(4.82843 - 2.00000i) q^{34} +(-0.895653 + 5.93277i) q^{36} +1.92762i q^{37} +(-0.448342 - 1.08239i) q^{38} +(2.51856 + 7.65685i) q^{39} -8.59890i q^{41} +(-6.11020 + 5.25700i) q^{42} -6.01673 q^{43} +(-3.56178 - 3.56178i) q^{44} +(1.41421 + 3.41421i) q^{46} +2.61313 q^{47} +(2.16478 + 6.58132i) q^{48} -3.82843 q^{49} +(2.00000 + 6.08034i) q^{51} +(6.58132 + 6.58132i) q^{52} +4.59220 q^{53} +(-7.16365 - 1.63772i) q^{54} +(-3.56178 + 8.59890i) q^{56} +(1.36303 - 0.448342i) q^{57} +(3.29066 + 7.94435i) q^{58} +2.51856i q^{59} -8.48528i q^{61} +(1.53073 - 0.634051i) q^{62} +(-5.86030 - 7.94435i) q^{63} +(5.65685 + 5.65685i) q^{64} +(4.67654 - 4.02353i) q^{66} -3.29066 q^{67} +(5.22625 + 5.22625i) q^{68} +(-4.29945 + 1.41421i) q^{69} -7.12356 q^{71} +(-8.23627 + 2.04057i) q^{72} -6.58132 q^{73} +(-2.51856 + 1.04322i) q^{74} +(1.17157 - 1.17157i) q^{76} +8.28772 q^{77} +(-8.64113 + 7.43452i) q^{78} -16.4853i q^{79} +(2.65685 - 8.59890i) q^{81} +(11.2350 - 4.65369i) q^{82} -9.37011i q^{83} +(-10.1754 - 5.13829i) q^{84} +(-3.25623 - 7.86123i) q^{86} +(-10.0042 + 3.29066i) q^{87} +(2.72607 - 6.58132i) q^{88} -5.03712i q^{89} -15.3137 q^{91} +(-3.69552 + 3.69552i) q^{92} +(0.634051 + 1.92762i) q^{93} +(1.41421 + 3.41421i) q^{94} +(-7.42733 + 6.39021i) q^{96} -2.72607 q^{97} +(-2.07193 - 5.00208i) q^{98} +(4.48528 + 6.08034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{9} + 32 q^{19} + 32 q^{24} + 32 q^{34} - 32 q^{36} - 16 q^{49} + 32 q^{51} - 32 q^{54} + 64 q^{66} + 64 q^{76} - 48 q^{81} - 32 q^{84} - 64 q^{91} + 64 q^{96} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).

\(n\) \(151\) \(301\) \(401\) \(577\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.541196 + 1.30656i 0.382683 + 0.923880i
\(3\) −1.64533 + 0.541196i −0.949931 + 0.312460i
\(4\) −1.41421 + 1.41421i −0.707107 + 0.707107i
\(5\) 0 0
\(6\) −1.59755 1.85683i −0.652198 0.758049i
\(7\) 3.29066i 1.24375i −0.783116 0.621876i \(-0.786371\pi\)
0.783116 0.621876i \(-0.213629\pi\)
\(8\) −2.61313 1.08239i −0.923880 0.382683i
\(9\) 2.41421 1.78089i 0.804738 0.593630i
\(10\) 0 0
\(11\) 2.51856i 0.759374i 0.925115 + 0.379687i \(0.123968\pi\)
−0.925115 + 0.379687i \(0.876032\pi\)
\(12\) 1.56148 3.09221i 0.450760 0.892645i
\(13\) 4.65369i 1.29070i −0.763886 0.645351i \(-0.776711\pi\)
0.763886 0.645351i \(-0.223289\pi\)
\(14\) 4.29945 1.78089i 1.14908 0.475963i
\(15\) 0 0
\(16\) 4.00000i 1.00000i
\(17\) 3.69552i 0.896295i −0.893960 0.448147i \(-0.852084\pi\)
0.893960 0.448147i \(-0.147916\pi\)
\(18\) 3.63341 + 2.19051i 0.856403 + 0.516308i
\(19\) −0.828427 −0.190054 −0.0950271 0.995475i \(-0.530294\pi\)
−0.0950271 + 0.995475i \(0.530294\pi\)
\(20\) 0 0
\(21\) 1.78089 + 5.41421i 0.388622 + 1.18148i
\(22\) −3.29066 + 1.36303i −0.701571 + 0.290600i
\(23\) 2.61313 0.544874 0.272437 0.962174i \(-0.412170\pi\)
0.272437 + 0.962174i \(0.412170\pi\)
\(24\) 4.88524 + 0.366677i 0.997195 + 0.0748477i
\(25\) 0 0
\(26\) 6.08034 2.51856i 1.19245 0.493930i
\(27\) −3.00836 + 4.23671i −0.578960 + 0.815356i
\(28\) 4.65369 + 4.65369i 0.879465 + 0.879465i
\(29\) 6.08034 1.12909 0.564546 0.825402i \(-0.309051\pi\)
0.564546 + 0.825402i \(0.309051\pi\)
\(30\) 0 0
\(31\) 1.17157i 0.210421i −0.994450 0.105210i \(-0.966448\pi\)
0.994450 0.105210i \(-0.0335516\pi\)
\(32\) 5.22625 2.16478i 0.923880 0.382683i
\(33\) −1.36303 4.14386i −0.237274 0.721353i
\(34\) 4.82843 2.00000i 0.828068 0.342997i
\(35\) 0 0
\(36\) −0.895653 + 5.93277i −0.149276 + 0.988796i
\(37\) 1.92762i 0.316899i 0.987367 + 0.158450i \(0.0506495\pi\)
−0.987367 + 0.158450i \(0.949350\pi\)
\(38\) −0.448342 1.08239i −0.0727306 0.175587i
\(39\) 2.51856 + 7.65685i 0.403292 + 1.22608i
\(40\) 0 0
\(41\) 8.59890i 1.34292i −0.741039 0.671461i \(-0.765667\pi\)
0.741039 0.671461i \(-0.234333\pi\)
\(42\) −6.11020 + 5.25700i −0.942824 + 0.811172i
\(43\) −6.01673 −0.917542 −0.458771 0.888554i \(-0.651710\pi\)
−0.458771 + 0.888554i \(0.651710\pi\)
\(44\) −3.56178 3.56178i −0.536959 0.536959i
\(45\) 0 0
\(46\) 1.41421 + 3.41421i 0.208514 + 0.503398i
\(47\) 2.61313 0.381164 0.190582 0.981671i \(-0.438963\pi\)
0.190582 + 0.981671i \(0.438963\pi\)
\(48\) 2.16478 + 6.58132i 0.312460 + 0.949931i
\(49\) −3.82843 −0.546918
\(50\) 0 0
\(51\) 2.00000 + 6.08034i 0.280056 + 0.851418i
\(52\) 6.58132 + 6.58132i 0.912664 + 0.912664i
\(53\) 4.59220 0.630787 0.315394 0.948961i \(-0.397863\pi\)
0.315394 + 0.948961i \(0.397863\pi\)
\(54\) −7.16365 1.63772i −0.974849 0.222866i
\(55\) 0 0
\(56\) −3.56178 + 8.59890i −0.475963 + 1.14908i
\(57\) 1.36303 0.448342i 0.180538 0.0593843i
\(58\) 3.29066 + 7.94435i 0.432085 + 1.04314i
\(59\) 2.51856i 0.327889i 0.986470 + 0.163944i \(0.0524217\pi\)
−0.986470 + 0.163944i \(0.947578\pi\)
\(60\) 0 0
\(61\) 8.48528i 1.08643i −0.839594 0.543214i \(-0.817207\pi\)
0.839594 0.543214i \(-0.182793\pi\)
\(62\) 1.53073 0.634051i 0.194403 0.0805245i
\(63\) −5.86030 7.94435i −0.738329 1.00089i
\(64\) 5.65685 + 5.65685i 0.707107 + 0.707107i
\(65\) 0 0
\(66\) 4.67654 4.02353i 0.575643 0.495263i
\(67\) −3.29066 −0.402018 −0.201009 0.979589i \(-0.564422\pi\)
−0.201009 + 0.979589i \(0.564422\pi\)
\(68\) 5.22625 + 5.22625i 0.633776 + 0.633776i
\(69\) −4.29945 + 1.41421i −0.517593 + 0.170251i
\(70\) 0 0
\(71\) −7.12356 −0.845412 −0.422706 0.906267i \(-0.638920\pi\)
−0.422706 + 0.906267i \(0.638920\pi\)
\(72\) −8.23627 + 2.04057i −0.970653 + 0.240483i
\(73\) −6.58132 −0.770285 −0.385142 0.922857i \(-0.625848\pi\)
−0.385142 + 0.922857i \(0.625848\pi\)
\(74\) −2.51856 + 1.04322i −0.292777 + 0.121272i
\(75\) 0 0
\(76\) 1.17157 1.17157i 0.134389 0.134389i
\(77\) 8.28772 0.944473
\(78\) −8.64113 + 7.43452i −0.978415 + 0.841793i
\(79\) 16.4853i 1.85474i −0.374147 0.927370i \(-0.622064\pi\)
0.374147 0.927370i \(-0.377936\pi\)
\(80\) 0 0
\(81\) 2.65685 8.59890i 0.295206 0.955434i
\(82\) 11.2350 4.65369i 1.24070 0.513914i
\(83\) 9.37011i 1.02850i −0.857639 0.514252i \(-0.828070\pi\)
0.857639 0.514252i \(-0.171930\pi\)
\(84\) −10.1754 5.13829i −1.11023 0.560634i
\(85\) 0 0
\(86\) −3.25623 7.86123i −0.351128 0.847699i
\(87\) −10.0042 + 3.29066i −1.07256 + 0.352796i
\(88\) 2.72607 6.58132i 0.290600 0.701571i
\(89\) 5.03712i 0.533934i −0.963706 0.266967i \(-0.913979\pi\)
0.963706 0.266967i \(-0.0860214\pi\)
\(90\) 0 0
\(91\) −15.3137 −1.60531
\(92\) −3.69552 + 3.69552i −0.385284 + 0.385284i
\(93\) 0.634051 + 1.92762i 0.0657480 + 0.199885i
\(94\) 1.41421 + 3.41421i 0.145865 + 0.352149i
\(95\) 0 0
\(96\) −7.42733 + 6.39021i −0.758049 + 0.652198i
\(97\) −2.72607 −0.276790 −0.138395 0.990377i \(-0.544194\pi\)
−0.138395 + 0.990377i \(0.544194\pi\)
\(98\) −2.07193 5.00208i −0.209297 0.505286i
\(99\) 4.48528 + 6.08034i 0.450788 + 0.611097i
\(100\) 0 0
\(101\) 13.2039 1.31384 0.656919 0.753961i \(-0.271859\pi\)
0.656919 + 0.753961i \(0.271859\pi\)
\(102\) −6.86196 + 5.90378i −0.679435 + 0.584562i
\(103\) 6.01673i 0.592846i −0.955057 0.296423i \(-0.904206\pi\)
0.955057 0.296423i \(-0.0957938\pi\)
\(104\) −5.03712 + 12.1607i −0.493930 + 1.19245i
\(105\) 0 0
\(106\) 2.48528 + 6.00000i 0.241392 + 0.582772i
\(107\) 8.47343i 0.819157i −0.912275 0.409579i \(-0.865676\pi\)
0.912275 0.409579i \(-0.134324\pi\)
\(108\) −1.73715 10.2461i −0.167157 0.985930i
\(109\) 0.485281i 0.0464815i −0.999730 0.0232408i \(-0.992602\pi\)
0.999730 0.0232408i \(-0.00739843\pi\)
\(110\) 0 0
\(111\) −1.04322 3.17157i −0.0990182 0.301032i
\(112\) −13.1626 −1.24375
\(113\) 8.92177i 0.839290i 0.907688 + 0.419645i \(0.137845\pi\)
−0.907688 + 0.419645i \(0.862155\pi\)
\(114\) 1.32346 + 1.53825i 0.123953 + 0.144070i
\(115\) 0 0
\(116\) −8.59890 + 8.59890i −0.798388 + 0.798388i
\(117\) −8.28772 11.2350i −0.766200 1.03868i
\(118\) −3.29066 + 1.36303i −0.302930 + 0.125478i
\(119\) −12.1607 −1.11477
\(120\) 0 0
\(121\) 4.65685 0.423350
\(122\) 11.0866 4.59220i 1.00373 0.415758i
\(123\) 4.65369 + 14.1480i 0.419609 + 1.27568i
\(124\) 1.65685 + 1.65685i 0.148790 + 0.148790i
\(125\) 0 0
\(126\) 7.20822 11.9563i 0.642159 1.06515i
\(127\) 3.29066i 0.291999i 0.989285 + 0.145999i \(0.0466397\pi\)
−0.989285 + 0.145999i \(0.953360\pi\)
\(128\) −4.32957 + 10.4525i −0.382683 + 0.923880i
\(129\) 9.89949 3.25623i 0.871602 0.286695i
\(130\) 0 0
\(131\) 21.8028i 1.90492i 0.304663 + 0.952460i \(0.401456\pi\)
−0.304663 + 0.952460i \(0.598544\pi\)
\(132\) 7.78793 + 3.93268i 0.677852 + 0.342296i
\(133\) 2.72607i 0.236380i
\(134\) −1.78089 4.29945i −0.153846 0.371416i
\(135\) 0 0
\(136\) −4.00000 + 9.65685i −0.342997 + 0.828068i
\(137\) 11.9832i 1.02380i 0.859046 + 0.511899i \(0.171058\pi\)
−0.859046 + 0.511899i \(0.828942\pi\)
\(138\) −4.17461 4.85214i −0.355366 0.413041i
\(139\) −14.4853 −1.22863 −0.614313 0.789063i \(-0.710567\pi\)
−0.614313 + 0.789063i \(0.710567\pi\)
\(140\) 0 0
\(141\) −4.29945 + 1.41421i −0.362079 + 0.119098i
\(142\) −3.85525 9.30739i −0.323525 0.781058i
\(143\) 11.7206 0.980126
\(144\) −7.12356 9.65685i −0.593630 0.804738i
\(145\) 0 0
\(146\) −3.56178 8.59890i −0.294775 0.711650i
\(147\) 6.29902 2.07193i 0.519535 0.170890i
\(148\) −2.72607 2.72607i −0.224082 0.224082i
\(149\) −14.6792 −1.20257 −0.601285 0.799034i \(-0.705344\pi\)
−0.601285 + 0.799034i \(0.705344\pi\)
\(150\) 0 0
\(151\) 2.82843i 0.230174i 0.993355 + 0.115087i \(0.0367147\pi\)
−0.993355 + 0.115087i \(0.963285\pi\)
\(152\) 2.16478 + 0.896683i 0.175587 + 0.0727306i
\(153\) −6.58132 8.92177i −0.532068 0.721282i
\(154\) 4.48528 + 10.8284i 0.361434 + 0.872580i
\(155\) 0 0
\(156\) −14.3902 7.26665i −1.15214 0.581797i
\(157\) 5.78287i 0.461523i −0.973010 0.230762i \(-0.925878\pi\)
0.973010 0.230762i \(-0.0741217\pi\)
\(158\) 21.5391 8.92177i 1.71356 0.709778i
\(159\) −7.55568 + 2.48528i −0.599204 + 0.197096i
\(160\) 0 0
\(161\) 8.59890i 0.677688i
\(162\) 12.6729 1.18235i 0.995676 0.0928938i
\(163\) 6.01673 0.471266 0.235633 0.971842i \(-0.424284\pi\)
0.235633 + 0.971842i \(0.424284\pi\)
\(164\) 12.1607 + 12.1607i 0.949590 + 0.949590i
\(165\) 0 0
\(166\) 12.2426 5.07107i 0.950213 0.393591i
\(167\) 17.3952 1.34608 0.673040 0.739606i \(-0.264988\pi\)
0.673040 + 0.739606i \(0.264988\pi\)
\(168\) 1.20661 16.0756i 0.0930920 1.24026i
\(169\) −8.65685 −0.665912
\(170\) 0 0
\(171\) −2.00000 + 1.47534i −0.152944 + 0.112822i
\(172\) 8.50894 8.50894i 0.648800 0.648800i
\(173\) −21.5391 −1.63758 −0.818792 0.574090i \(-0.805356\pi\)
−0.818792 + 0.574090i \(0.805356\pi\)
\(174\) −9.71366 11.2902i −0.736391 0.855906i
\(175\) 0 0
\(176\) 10.0742 0.759374
\(177\) −1.36303 4.14386i −0.102452 0.311472i
\(178\) 6.58132 2.72607i 0.493290 0.204328i
\(179\) 9.64212i 0.720686i 0.932820 + 0.360343i \(0.117340\pi\)
−0.932820 + 0.360343i \(0.882660\pi\)
\(180\) 0 0
\(181\) 10.3431i 0.768800i 0.923167 + 0.384400i \(0.125592\pi\)
−0.923167 + 0.384400i \(0.874408\pi\)
\(182\) −8.28772 20.0083i −0.614327 1.48312i
\(183\) 4.59220 + 13.9611i 0.339465 + 1.03203i
\(184\) −6.82843 2.82843i −0.503398 0.208514i
\(185\) 0 0
\(186\) −2.17541 + 1.87165i −0.159509 + 0.137236i
\(187\) 9.30739 0.680623
\(188\) −3.69552 + 3.69552i −0.269523 + 0.269523i
\(189\) 13.9416 + 9.89949i 1.01410 + 0.720082i
\(190\) 0 0
\(191\) −5.03712 −0.364473 −0.182237 0.983255i \(-0.558334\pi\)
−0.182237 + 0.983255i \(0.558334\pi\)
\(192\) −12.3689 6.24592i −0.892645 0.450760i
\(193\) 19.7439 1.42120 0.710600 0.703596i \(-0.248424\pi\)
0.710600 + 0.703596i \(0.248424\pi\)
\(194\) −1.47534 3.56178i −0.105923 0.255721i
\(195\) 0 0
\(196\) 5.41421 5.41421i 0.386730 0.386730i
\(197\) −11.9832 −0.853770 −0.426885 0.904306i \(-0.640389\pi\)
−0.426885 + 0.904306i \(0.640389\pi\)
\(198\) −5.51693 + 9.15096i −0.392071 + 0.650330i
\(199\) 9.17157i 0.650156i 0.945687 + 0.325078i \(0.105390\pi\)
−0.945687 + 0.325078i \(0.894610\pi\)
\(200\) 0 0
\(201\) 5.41421 1.78089i 0.381889 0.125614i
\(202\) 7.14590 + 17.2517i 0.502784 + 1.21383i
\(203\) 20.0083i 1.40431i
\(204\) −11.4273 5.77048i −0.800073 0.404014i
\(205\) 0 0
\(206\) 7.86123 3.25623i 0.547718 0.226872i
\(207\) 6.30864 4.65369i 0.438481 0.323454i
\(208\) −18.6148 −1.29070
\(209\) 2.08644i 0.144322i
\(210\) 0 0
\(211\) 18.4853 1.27258 0.636290 0.771450i \(-0.280468\pi\)
0.636290 + 0.771450i \(0.280468\pi\)
\(212\) −6.49435 + 6.49435i −0.446034 + 0.446034i
\(213\) 11.7206 3.85525i 0.803083 0.264157i
\(214\) 11.0711 4.58579i 0.756803 0.313478i
\(215\) 0 0
\(216\) 12.4470 7.81484i 0.846912 0.531732i
\(217\) −3.85525 −0.261711
\(218\) 0.634051 0.262632i 0.0429433 0.0177877i
\(219\) 10.8284 3.56178i 0.731717 0.240683i
\(220\) 0 0
\(221\) −17.1978 −1.15685
\(222\) 3.57927 3.07948i 0.240225 0.206681i
\(223\) 21.9054i 1.46690i 0.679746 + 0.733448i \(0.262090\pi\)
−0.679746 + 0.733448i \(0.737910\pi\)
\(224\) −7.12356 17.1978i −0.475963 1.14908i
\(225\) 0 0
\(226\) −11.6569 + 4.82843i −0.775402 + 0.321182i
\(227\) 4.14386i 0.275038i −0.990499 0.137519i \(-0.956087\pi\)
0.990499 0.137519i \(-0.0439128\pi\)
\(228\) −1.29357 + 2.56167i −0.0856689 + 0.169651i
\(229\) 19.3137i 1.27629i −0.769918 0.638143i \(-0.779703\pi\)
0.769918 0.638143i \(-0.220297\pi\)
\(230\) 0 0
\(231\) −13.6360 + 4.48528i −0.897184 + 0.295110i
\(232\) −15.8887 6.58132i −1.04314 0.432085i
\(233\) 15.9414i 1.04436i 0.852837 + 0.522178i \(0.174880\pi\)
−0.852837 + 0.522178i \(0.825120\pi\)
\(234\) 10.1940 16.9088i 0.666400 1.10536i
\(235\) 0 0
\(236\) −3.56178 3.56178i −0.231852 0.231852i
\(237\) 8.92177 + 27.1237i 0.579531 + 1.76187i
\(238\) −6.58132 15.8887i −0.426603 1.02991i
\(239\) 22.2349 1.43826 0.719129 0.694877i \(-0.244541\pi\)
0.719129 + 0.694877i \(0.244541\pi\)
\(240\) 0 0
\(241\) −6.48528 −0.417754 −0.208877 0.977942i \(-0.566981\pi\)
−0.208877 + 0.977942i \(0.566981\pi\)
\(242\) 2.52027 + 6.08447i 0.162009 + 0.391125i
\(243\) 0.282294 + 15.5859i 0.0181092 + 0.999836i
\(244\) 12.0000 + 12.0000i 0.768221 + 0.768221i
\(245\) 0 0
\(246\) −15.9667 + 13.7372i −1.01800 + 0.875852i
\(247\) 3.85525i 0.245303i
\(248\) −1.26810 + 3.06147i −0.0805245 + 0.194403i
\(249\) 5.07107 + 15.4169i 0.321366 + 0.977007i
\(250\) 0 0
\(251\) 11.7286i 0.740301i −0.928972 0.370150i \(-0.879306\pi\)
0.928972 0.370150i \(-0.120694\pi\)
\(252\) 19.5227 + 2.94729i 1.22982 + 0.185662i
\(253\) 6.58132i 0.413764i
\(254\) −4.29945 + 1.78089i −0.269772 + 0.111743i
\(255\) 0 0
\(256\) −16.0000 −1.00000
\(257\) 16.3128i 1.01756i 0.860895 + 0.508782i \(0.169904\pi\)
−0.860895 + 0.508782i \(0.830096\pi\)
\(258\) 9.61204 + 11.1721i 0.598419 + 0.695542i
\(259\) 6.34315 0.394144
\(260\) 0 0
\(261\) 14.6792 10.8284i 0.908622 0.670263i
\(262\) −28.4867 + 11.7996i −1.75992 + 0.728981i
\(263\) −22.2500 −1.37200 −0.685998 0.727604i \(-0.740634\pi\)
−0.685998 + 0.727604i \(0.740634\pi\)
\(264\) −0.923499 + 12.3038i −0.0568375 + 0.757244i
\(265\) 0 0
\(266\) −3.56178 + 1.47534i −0.218387 + 0.0904588i
\(267\) 2.72607 + 8.28772i 0.166833 + 0.507200i
\(268\) 4.65369 4.65369i 0.284270 0.284270i
\(269\) 9.64212 0.587891 0.293945 0.955822i \(-0.405032\pi\)
0.293945 + 0.955822i \(0.405032\pi\)
\(270\) 0 0
\(271\) 14.1421i 0.859074i −0.903049 0.429537i \(-0.858677\pi\)
0.903049 0.429537i \(-0.141323\pi\)
\(272\) −14.7821 −0.896295
\(273\) 25.1961 8.28772i 1.52494 0.501596i
\(274\) −15.6569 + 6.48528i −0.945865 + 0.391790i
\(275\) 0 0
\(276\) 4.08034 8.08034i 0.245608 0.486379i
\(277\) 15.0903i 0.906685i 0.891336 + 0.453343i \(0.149769\pi\)
−0.891336 + 0.453343i \(0.850231\pi\)
\(278\) −7.83938 18.9259i −0.470175 1.13510i
\(279\) −2.08644 2.82843i −0.124912 0.169334i
\(280\) 0 0
\(281\) 3.56178i 0.212478i 0.994341 + 0.106239i \(0.0338809\pi\)
−0.994341 + 0.106239i \(0.966119\pi\)
\(282\) −4.17461 4.85214i −0.248594 0.288941i
\(283\) 18.0502 1.07297 0.536486 0.843909i \(-0.319751\pi\)
0.536486 + 0.843909i \(0.319751\pi\)
\(284\) 10.0742 10.0742i 0.597796 0.597796i
\(285\) 0 0
\(286\) 6.34315 + 15.3137i 0.375078 + 0.905519i
\(287\) −28.2960 −1.67026
\(288\) 8.76204 14.5336i 0.516308 0.856403i
\(289\) 3.34315 0.196656
\(290\) 0 0
\(291\) 4.48528 1.47534i 0.262932 0.0864859i
\(292\) 9.30739 9.30739i 0.544674 0.544674i
\(293\) 2.42742 0.141811 0.0709056 0.997483i \(-0.477411\pi\)
0.0709056 + 0.997483i \(0.477411\pi\)
\(294\) 6.11611 + 7.10875i 0.356699 + 0.414591i
\(295\) 0 0
\(296\) 2.08644 5.03712i 0.121272 0.292777i
\(297\) −10.6704 7.57675i −0.619161 0.439647i
\(298\) −7.94435 19.1794i −0.460204 1.11103i
\(299\) 12.1607i 0.703271i
\(300\) 0 0
\(301\) 19.7990i 1.14119i
\(302\) −3.69552 + 1.53073i −0.212653 + 0.0880838i
\(303\) −21.7248 + 7.14590i −1.24806 + 0.410521i
\(304\) 3.31371i 0.190054i
\(305\) 0 0
\(306\) 8.09507 13.4273i 0.462764 0.767589i
\(307\) 7.14590 0.407838 0.203919 0.978988i \(-0.434632\pi\)
0.203919 + 0.978988i \(0.434632\pi\)
\(308\) −11.7206 + 11.7206i −0.667843 + 0.667843i
\(309\) 3.25623 + 9.89949i 0.185240 + 0.563163i
\(310\) 0 0
\(311\) 34.3956 1.95040 0.975198 0.221334i \(-0.0710411\pi\)
0.975198 + 0.221334i \(0.0710411\pi\)
\(312\) 1.70640 22.7344i 0.0966061 1.28708i
\(313\) −17.0179 −0.961907 −0.480954 0.876746i \(-0.659709\pi\)
−0.480954 + 0.876746i \(0.659709\pi\)
\(314\) 7.55568 3.12967i 0.426392 0.176617i
\(315\) 0 0
\(316\) 23.3137 + 23.3137i 1.31150 + 1.31150i
\(317\) −13.2513 −0.744269 −0.372135 0.928179i \(-0.621374\pi\)
−0.372135 + 0.928179i \(0.621374\pi\)
\(318\) −7.33628 8.52695i −0.411398 0.478168i
\(319\) 15.3137i 0.857403i
\(320\) 0 0
\(321\) 4.58579 + 13.9416i 0.255954 + 0.778143i
\(322\) 11.2350 4.65369i 0.626102 0.259340i
\(323\) 3.06147i 0.170345i
\(324\) 8.40333 + 15.9180i 0.466851 + 0.884336i
\(325\) 0 0
\(326\) 3.25623 + 7.86123i 0.180346 + 0.435393i
\(327\) 0.262632 + 0.798447i 0.0145236 + 0.0441542i
\(328\) −9.30739 + 22.4700i −0.513914 + 1.24070i
\(329\) 8.59890i 0.474073i
\(330\) 0 0
\(331\) −18.4853 −1.01604 −0.508021 0.861344i \(-0.669623\pi\)
−0.508021 + 0.861344i \(0.669623\pi\)
\(332\) 13.2513 + 13.2513i 0.727262 + 0.727262i
\(333\) 3.43289 + 4.65369i 0.188121 + 0.255021i
\(334\) 9.41421 + 22.7279i 0.515123 + 1.24362i
\(335\) 0 0
\(336\) 21.6569 7.12356i 1.18148 0.388622i
\(337\) 27.9222 1.52102 0.760508 0.649328i \(-0.224950\pi\)
0.760508 + 0.649328i \(0.224950\pi\)
\(338\) −4.68506 11.3107i −0.254833 0.615222i
\(339\) −4.82843 14.6792i −0.262244 0.797267i
\(340\) 0 0
\(341\) 2.95068 0.159788
\(342\) −3.01001 1.81468i −0.162763 0.0981266i
\(343\) 10.4366i 0.563521i
\(344\) 15.7225 + 6.51246i 0.847699 + 0.351128i
\(345\) 0 0
\(346\) −11.6569 28.1421i −0.626676 1.51293i
\(347\) 0.185709i 0.00996939i 0.999988 + 0.00498469i \(0.00158668\pi\)
−0.999988 + 0.00498469i \(0.998413\pi\)
\(348\) 9.49433 18.8017i 0.508949 1.00788i
\(349\) 2.34315i 0.125426i −0.998032 0.0627129i \(-0.980025\pi\)
0.998032 0.0627129i \(-0.0199752\pi\)
\(350\) 0 0
\(351\) 19.7164 + 14.0000i 1.05238 + 0.747265i
\(352\) 5.45214 + 13.1626i 0.290600 + 0.701571i
\(353\) 32.3630i 1.72251i 0.508175 + 0.861254i \(0.330320\pi\)
−0.508175 + 0.861254i \(0.669680\pi\)
\(354\) 4.67654 4.02353i 0.248556 0.213848i
\(355\) 0 0
\(356\) 7.12356 + 7.12356i 0.377548 + 0.377548i
\(357\) 20.0083 6.58132i 1.05895 0.348320i
\(358\) −12.5980 + 5.21828i −0.665827 + 0.275795i
\(359\) 9.21001 0.486086 0.243043 0.970016i \(-0.421854\pi\)
0.243043 + 0.970016i \(0.421854\pi\)
\(360\) 0 0
\(361\) −18.3137 −0.963879
\(362\) −13.5140 + 5.59767i −0.710279 + 0.294207i
\(363\) −7.66206 + 2.52027i −0.402154 + 0.132280i
\(364\) 21.6569 21.6569i 1.13513 1.13513i
\(365\) 0 0
\(366\) −15.7557 + 13.5557i −0.823566 + 0.708567i
\(367\) 2.16148i 0.112828i 0.998407 + 0.0564142i \(0.0179667\pi\)
−0.998407 + 0.0564142i \(0.982033\pi\)
\(368\) 10.4525i 0.544874i
\(369\) −15.3137 20.7596i −0.797200 1.08070i
\(370\) 0 0
\(371\) 15.1114i 0.784543i
\(372\) −3.62275 1.82939i −0.187831 0.0948493i
\(373\) 24.3976i 1.26326i 0.775269 + 0.631631i \(0.217614\pi\)
−0.775269 + 0.631631i \(0.782386\pi\)
\(374\) 5.03712 + 12.1607i 0.260463 + 0.628814i
\(375\) 0 0
\(376\) −6.82843 2.82843i −0.352149 0.145865i
\(377\) 28.2960i 1.45732i
\(378\) −5.38919 + 23.5731i −0.277190 + 1.21247i
\(379\) −20.8284 −1.06988 −0.534942 0.844889i \(-0.679667\pi\)
−0.534942 + 0.844889i \(0.679667\pi\)
\(380\) 0 0
\(381\) −1.78089 5.41421i −0.0912378 0.277379i
\(382\) −2.72607 6.58132i −0.139478 0.336729i
\(383\) 29.1158 1.48775 0.743874 0.668320i \(-0.232986\pi\)
0.743874 + 0.668320i \(0.232986\pi\)
\(384\) 1.46671 19.5410i 0.0748477 0.997195i
\(385\) 0 0
\(386\) 10.6853 + 25.7967i 0.543870 + 1.31302i
\(387\) −14.5257 + 10.7151i −0.738381 + 0.544681i
\(388\) 3.85525 3.85525i 0.195720 0.195720i
\(389\) 7.55568 0.383088 0.191544 0.981484i \(-0.438650\pi\)
0.191544 + 0.981484i \(0.438650\pi\)
\(390\) 0 0
\(391\) 9.65685i 0.488368i
\(392\) 10.0042 + 4.14386i 0.505286 + 0.209297i
\(393\) −11.7996 35.8728i −0.595211 1.80954i
\(394\) −6.48528 15.6569i −0.326724 0.788781i
\(395\) 0 0
\(396\) −14.9420 2.25576i −0.750866 0.113356i
\(397\) 27.1237i 1.36130i −0.732609 0.680650i \(-0.761697\pi\)
0.732609 0.680650i \(-0.238303\pi\)
\(398\) −11.9832 + 4.96362i −0.600665 + 0.248804i
\(399\) −1.47534 4.48528i −0.0738593 0.224545i
\(400\) 0 0
\(401\) 15.1114i 0.754625i 0.926086 + 0.377313i \(0.123152\pi\)
−0.926086 + 0.377313i \(0.876848\pi\)
\(402\) 5.25700 + 6.11020i 0.262195 + 0.304749i
\(403\) −5.45214 −0.271590
\(404\) −18.6731 + 18.6731i −0.929024 + 0.929024i
\(405\) 0 0
\(406\) 26.1421 10.8284i 1.29741 0.537406i
\(407\) −4.85483 −0.240645
\(408\) 1.35506 18.0535i 0.0670856 0.893781i
\(409\) 12.8284 0.634325 0.317162 0.948371i \(-0.397270\pi\)
0.317162 + 0.948371i \(0.397270\pi\)
\(410\) 0 0
\(411\) −6.48528 19.7164i −0.319895 0.972537i
\(412\) 8.50894 + 8.50894i 0.419205 + 0.419205i
\(413\) 8.28772 0.407812
\(414\) 9.49456 + 5.72408i 0.466632 + 0.281323i
\(415\) 0 0
\(416\) −10.0742 24.3214i −0.493930 1.19245i
\(417\) 23.8331 7.83938i 1.16711 0.383896i
\(418\) 2.72607 1.12918i 0.133336 0.0552298i
\(419\) 2.51856i 0.123040i −0.998106 0.0615199i \(-0.980405\pi\)
0.998106 0.0615199i \(-0.0195948\pi\)
\(420\) 0 0
\(421\) 34.8284i 1.69743i −0.528848 0.848717i \(-0.677376\pi\)
0.528848 0.848717i \(-0.322624\pi\)
\(422\) 10.0042 + 24.1522i 0.486995 + 1.17571i
\(423\) 6.30864 4.65369i 0.306737 0.226270i
\(424\) −12.0000 4.97056i −0.582772 0.241392i
\(425\) 0 0
\(426\) 11.3803 + 13.2273i 0.551376 + 0.640863i
\(427\) −27.9222 −1.35125
\(428\) 11.9832 + 11.9832i 0.579232 + 0.579232i
\(429\) −19.2842 + 6.34315i −0.931052 + 0.306250i
\(430\) 0 0
\(431\) −27.2720 −1.31365 −0.656824 0.754044i \(-0.728101\pi\)
−0.656824 + 0.754044i \(0.728101\pi\)
\(432\) 16.9469 + 12.0335i 0.815356 + 0.578960i
\(433\) 23.5992 1.13410 0.567052 0.823682i \(-0.308084\pi\)
0.567052 + 0.823682i \(0.308084\pi\)
\(434\) −2.08644 5.03712i −0.100152 0.241790i
\(435\) 0 0
\(436\) 0.686292 + 0.686292i 0.0328674 + 0.0328674i
\(437\) −2.16478 −0.103556
\(438\) 10.5140 + 12.2204i 0.502378 + 0.583913i
\(439\) 28.4853i 1.35953i −0.733431 0.679764i \(-0.762082\pi\)
0.733431 0.679764i \(-0.237918\pi\)
\(440\) 0 0
\(441\) −9.24264 + 6.81801i −0.440126 + 0.324667i
\(442\) −9.30739 22.4700i −0.442707 1.06879i
\(443\) 1.60766i 0.0763821i −0.999270 0.0381910i \(-0.987840\pi\)
0.999270 0.0381910i \(-0.0121595\pi\)
\(444\) 5.96062 + 3.00994i 0.282878 + 0.142846i
\(445\) 0 0
\(446\) −28.6208 + 11.8551i −1.35524 + 0.561357i
\(447\) 24.1522 7.94435i 1.14236 0.375755i
\(448\) 18.6148 18.6148i 0.879465 0.879465i
\(449\) 35.0067i 1.65207i 0.563620 + 0.826035i \(0.309408\pi\)
−0.563620 + 0.826035i \(0.690592\pi\)
\(450\) 0 0
\(451\) 21.6569 1.01978
\(452\) −12.6173 12.6173i −0.593467 0.593467i
\(453\) −1.53073 4.65369i −0.0719201 0.218650i
\(454\) 5.41421 2.24264i 0.254102 0.105252i
\(455\) 0 0
\(456\) −4.04706 0.303766i −0.189521 0.0142251i
\(457\) −18.6148 −0.870762 −0.435381 0.900246i \(-0.643386\pi\)
−0.435381 + 0.900246i \(0.643386\pi\)
\(458\) 25.2346 10.4525i 1.17913 0.488413i
\(459\) 15.6569 + 11.1175i 0.730799 + 0.518919i
\(460\) 0 0
\(461\) 3.99390 0.186014 0.0930072 0.995665i \(-0.470352\pi\)
0.0930072 + 0.995665i \(0.470352\pi\)
\(462\) −13.2401 15.3889i −0.615984 0.715957i
\(463\) 25.7607i 1.19720i −0.801048 0.598600i \(-0.795724\pi\)
0.801048 0.598600i \(-0.204276\pi\)
\(464\) 24.3214i 1.12909i
\(465\) 0 0
\(466\) −20.8284 + 8.62742i −0.964858 + 0.399657i
\(467\) 15.8645i 0.734120i 0.930197 + 0.367060i \(0.119636\pi\)
−0.930197 + 0.367060i \(0.880364\pi\)
\(468\) 27.6093 + 4.16810i 1.27624 + 0.192670i
\(469\) 10.8284i 0.500010i
\(470\) 0 0
\(471\) 3.12967 + 9.51472i 0.144207 + 0.438415i
\(472\) 2.72607 6.58132i 0.125478 0.302930i
\(473\) 15.1535i 0.696758i
\(474\) −30.6104 + 26.3361i −1.40598 + 1.20966i
\(475\) 0 0
\(476\) 17.1978 17.1978i 0.788260 0.788260i
\(477\) 11.0866 8.17821i 0.507618 0.374455i
\(478\) 12.0335 + 29.0513i 0.550397 + 1.32878i
\(479\) −19.2842 −0.881120 −0.440560 0.897723i \(-0.645220\pi\)
−0.440560 + 0.897723i \(0.645220\pi\)
\(480\) 0 0
\(481\) 8.97056 0.409022
\(482\) −3.50981 8.47343i −0.159867 0.385954i
\(483\) 4.65369 + 14.1480i 0.211750 + 0.643757i
\(484\) −6.58579 + 6.58579i −0.299354 + 0.299354i
\(485\) 0 0
\(486\) −20.2112 + 8.80386i −0.916798 + 0.399351i
\(487\) 8.74280i 0.396174i 0.980184 + 0.198087i \(0.0634729\pi\)
−0.980184 + 0.198087i \(0.936527\pi\)
\(488\) −9.18440 + 22.1731i −0.415758 + 1.00373i
\(489\) −9.89949 + 3.25623i −0.447671 + 0.147252i
\(490\) 0 0
\(491\) 36.9142i 1.66591i −0.553338 0.832957i \(-0.686646\pi\)
0.553338 0.832957i \(-0.313354\pi\)
\(492\) −26.5896 13.4270i −1.19875 0.605336i
\(493\) 22.4700i 1.01200i
\(494\) −5.03712 + 2.08644i −0.226631 + 0.0938735i
\(495\) 0 0
\(496\) −4.68629 −0.210421
\(497\) 23.4412i 1.05148i
\(498\) −17.3987 + 14.9692i −0.779656 + 0.670788i
\(499\) 37.1127 1.66139 0.830696 0.556726i \(-0.187943\pi\)
0.830696 + 0.556726i \(0.187943\pi\)
\(500\) 0 0
\(501\) −28.6208 + 9.41421i −1.27868 + 0.420596i
\(502\) 15.3241 6.34746i 0.683949 0.283301i
\(503\) 9.63274 0.429503 0.214751 0.976669i \(-0.431106\pi\)
0.214751 + 0.976669i \(0.431106\pi\)
\(504\) 6.71481 + 27.1027i 0.299101 + 1.20725i
\(505\) 0 0
\(506\) −8.59890 + 3.56178i −0.382268 + 0.158341i
\(507\) 14.2434 4.68506i 0.632570 0.208071i
\(508\) −4.65369 4.65369i −0.206474 0.206474i
\(509\) −13.2039 −0.585253 −0.292626 0.956227i \(-0.594529\pi\)
−0.292626 + 0.956227i \(0.594529\pi\)
\(510\) 0 0
\(511\) 21.6569i 0.958043i
\(512\) −8.65914 20.9050i −0.382683 0.923880i
\(513\) 2.49221 3.50981i 0.110034 0.154962i
\(514\) −21.3137 + 8.82843i −0.940107 + 0.389405i
\(515\) 0 0
\(516\) −9.39500 + 18.6050i −0.413592 + 0.819040i
\(517\) 6.58132i 0.289446i
\(518\) 3.43289 + 8.28772i 0.150832 + 0.364141i
\(519\) 35.4388 11.6569i 1.55559 0.511679i
\(520\) 0 0
\(521\) 34.3956i 1.50690i 0.657506 + 0.753450i \(0.271612\pi\)
−0.657506 + 0.753450i \(0.728388\pi\)
\(522\) 22.0924 + 13.3191i 0.966957 + 0.582959i
\(523\) −12.5980 −0.550874 −0.275437 0.961319i \(-0.588823\pi\)
−0.275437 + 0.961319i \(0.588823\pi\)
\(524\) −30.8338 30.8338i −1.34698 1.34698i
\(525\) 0 0
\(526\) −12.0416 29.0711i −0.525040 1.26756i
\(527\) −4.32957 −0.188599
\(528\) −16.5754 + 5.45214i −0.721353 + 0.237274i
\(529\) −16.1716 −0.703112
\(530\) 0 0
\(531\) 4.48528 + 6.08034i 0.194645 + 0.263864i
\(532\) −3.85525 3.85525i −0.167146 0.167146i
\(533\) −40.0166 −1.73331
\(534\) −9.35309 + 8.04706i −0.404748 + 0.348230i
\(535\) 0 0
\(536\) 8.59890 + 3.56178i 0.371416 + 0.153846i
\(537\) −5.21828 15.8645i −0.225185 0.684602i
\(538\) 5.21828 + 12.5980i 0.224976 + 0.543140i
\(539\) 9.64212i 0.415316i
\(540\) 0 0
\(541\) 16.0000i 0.687894i −0.938989 0.343947i \(-0.888236\pi\)
0.938989 0.343947i \(-0.111764\pi\)
\(542\) 18.4776 7.65367i 0.793680 0.328753i
\(543\) −5.59767 17.0179i −0.240219 0.730307i
\(544\) −8.00000 19.3137i −0.342997 0.828068i
\(545\) 0 0
\(546\) 24.4645 + 28.4350i 1.04698 + 1.21691i
\(547\) −11.0011 −0.470375 −0.235188 0.971950i \(-0.575570\pi\)
−0.235188 + 0.971950i \(0.575570\pi\)
\(548\) −16.9469 16.9469i −0.723934 0.723934i
\(549\) −15.1114 20.4853i −0.644937 0.874291i
\(550\) 0 0
\(551\) −5.03712 −0.214589
\(552\) 12.7657 + 0.958174i 0.543346 + 0.0407826i
\(553\) −54.2474 −2.30683
\(554\) −19.7164 + 8.16679i −0.837668 + 0.346973i
\(555\) 0 0
\(556\) 20.4853 20.4853i 0.868769 0.868769i
\(557\) 4.96362 0.210315 0.105158 0.994456i \(-0.466465\pi\)
0.105158 + 0.994456i \(0.466465\pi\)
\(558\) 2.56634 4.25680i 0.108642 0.180205i
\(559\) 28.0000i 1.18427i
\(560\) 0 0
\(561\) −15.3137 + 5.03712i −0.646545 + 0.212667i
\(562\) −4.65369 + 1.92762i −0.196304 + 0.0813119i
\(563\) 21.9874i 0.926658i −0.886186 0.463329i \(-0.846655\pi\)
0.886186 0.463329i \(-0.153345\pi\)
\(564\) 4.08034 8.08034i 0.171813 0.340244i
\(565\) 0 0
\(566\) 9.76869 + 23.5837i 0.410609 + 0.991297i
\(567\) −28.2960 8.74280i −1.18832 0.367163i
\(568\) 18.6148 + 7.71049i 0.781058 + 0.323525i
\(569\) 15.7225i 0.659120i 0.944135 + 0.329560i \(0.106900\pi\)
−0.944135 + 0.329560i \(0.893100\pi\)
\(570\) 0 0
\(571\) 21.1127 0.883539 0.441769 0.897129i \(-0.354351\pi\)
0.441769 + 0.897129i \(0.354351\pi\)
\(572\) −16.5754 + 16.5754i −0.693054 + 0.693054i
\(573\) 8.28772 2.72607i 0.346224 0.113883i
\(574\) −15.3137 36.9706i −0.639182 1.54312i
\(575\) 0 0
\(576\) 23.7311 + 3.58261i 0.988796 + 0.149276i
\(577\) 3.85525 0.160496 0.0802480 0.996775i \(-0.474429\pi\)
0.0802480 + 0.996775i \(0.474429\pi\)
\(578\) 1.80930 + 4.36803i 0.0752569 + 0.181686i
\(579\) −32.4853 + 10.6853i −1.35004 + 0.444068i
\(580\) 0 0
\(581\) −30.8338 −1.27920
\(582\) 4.35504 + 5.06186i 0.180522 + 0.209821i
\(583\) 11.5657i 0.479004i
\(584\) 17.1978 + 7.12356i 0.711650 + 0.294775i
\(585\) 0 0
\(586\) 1.31371 + 3.17157i 0.0542688 + 0.131016i
\(587\) 7.20533i 0.297396i −0.988883 0.148698i \(-0.952492\pi\)
0.988883 0.148698i \(-0.0475082\pi\)
\(588\) −5.97801 + 11.8383i −0.246529 + 0.488204i
\(589\) 0.970563i 0.0399913i
\(590\) 0 0
\(591\) 19.7164 6.48528i 0.811023 0.266769i
\(592\) 7.71049 0.316899
\(593\) 1.00547i 0.0412897i 0.999787 + 0.0206448i \(0.00657192\pi\)
−0.999787 + 0.0206448i \(0.993428\pi\)
\(594\) 4.12471 18.0421i 0.169239 0.740276i
\(595\) 0 0
\(596\) 20.7596 20.7596i 0.850346 0.850346i
\(597\) −4.96362 15.0903i −0.203147 0.617603i
\(598\) 15.8887 6.58132i 0.649737 0.269130i
\(599\) −32.3092 −1.32012 −0.660058 0.751214i \(-0.729468\pi\)
−0.660058 + 0.751214i \(0.729468\pi\)
\(600\) 0 0
\(601\) 13.5147 0.551277 0.275638 0.961261i \(-0.411111\pi\)
0.275638 + 0.961261i \(0.411111\pi\)
\(602\) −25.8686 + 10.7151i −1.05433 + 0.436716i
\(603\) −7.94435 + 5.86030i −0.323519 + 0.238650i
\(604\) −4.00000 4.00000i −0.162758 0.162758i
\(605\) 0 0
\(606\) −21.0939 24.5174i −0.856882 0.995953i
\(607\) 4.88755i 0.198380i −0.995069 0.0991898i \(-0.968375\pi\)
0.995069 0.0991898i \(-0.0316251\pi\)
\(608\) −4.32957 + 1.79337i −0.175587 + 0.0727306i
\(609\) 10.8284 + 32.9203i 0.438790 + 1.33400i
\(610\) 0 0
\(611\) 12.1607i 0.491969i
\(612\) 21.9247 + 3.30990i 0.886252 + 0.133795i
\(613\) 23.2685i 0.939804i −0.882718 0.469902i \(-0.844289\pi\)
0.882718 0.469902i \(-0.155711\pi\)
\(614\) 3.86733 + 9.33657i 0.156073 + 0.376793i
\(615\) 0 0
\(616\) −21.6569 8.97056i −0.872580 0.361434i
\(617\) 8.55035i 0.344224i 0.985077 + 0.172112i \(0.0550591\pi\)
−0.985077 + 0.172112i \(0.944941\pi\)
\(618\) −11.1721 + 9.61204i −0.449406 + 0.386653i
\(619\) 2.48528 0.0998919 0.0499459 0.998752i \(-0.484095\pi\)
0.0499459 + 0.998752i \(0.484095\pi\)
\(620\) 0 0
\(621\) −7.86123 + 11.0711i −0.315460 + 0.444267i
\(622\) 18.6148 + 44.9400i 0.746384 + 1.80193i
\(623\) −16.5754 −0.664081
\(624\) 30.6274 10.0742i 1.22608 0.403292i
\(625\) 0 0
\(626\) −9.21001 22.2349i −0.368106 0.888686i
\(627\) 1.12918 + 3.43289i 0.0450949 + 0.137096i
\(628\) 8.17821 + 8.17821i 0.326346 + 0.326346i
\(629\) 7.12356 0.284035
\(630\) 0 0
\(631\) 2.14214i 0.0852771i −0.999091 0.0426385i \(-0.986424\pi\)
0.999091 0.0426385i \(-0.0135764\pi\)
\(632\) −17.8435 + 43.0781i −0.709778 + 1.71356i
\(633\) −30.4144 + 10.0042i −1.20886 + 0.397630i
\(634\) −7.17157 17.3137i −0.284820 0.687615i
\(635\) 0 0
\(636\) 7.17063 14.2001i 0.284334 0.563069i
\(637\) 17.8163i 0.705908i
\(638\) −20.0083 + 8.28772i −0.792137 + 0.328114i
\(639\) −17.1978 + 12.6863i −0.680335 + 0.501862i
\(640\) 0 0
\(641\) 35.0067i 1.38268i 0.722529 + 0.691341i \(0.242980\pi\)
−0.722529 + 0.691341i \(0.757020\pi\)
\(642\) −15.7337 + 13.5367i −0.620961 + 0.534253i
\(643\) −35.0681 −1.38295 −0.691475 0.722401i \(-0.743039\pi\)
−0.691475 + 0.722401i \(0.743039\pi\)
\(644\) 12.1607 + 12.1607i 0.479198 + 0.479198i
\(645\) 0 0
\(646\) −4.00000 + 1.65685i −0.157378 + 0.0651881i
\(647\) 28.3730 1.11546 0.557728 0.830024i \(-0.311673\pi\)
0.557728 + 0.830024i \(0.311673\pi\)
\(648\) −16.2501 + 19.5943i −0.638363 + 0.769735i
\(649\) −6.34315 −0.248990
\(650\) 0 0
\(651\) 6.34315 2.08644i 0.248607 0.0817742i
\(652\) −8.50894 + 8.50894i −0.333236 + 0.333236i
\(653\) 24.2291 0.948158 0.474079 0.880482i \(-0.342781\pi\)
0.474079 + 0.880482i \(0.342781\pi\)
\(654\) −0.901086 + 0.775262i −0.0352353 + 0.0303152i
\(655\) 0 0
\(656\) −34.3956 −1.34292
\(657\) −15.8887 + 11.7206i −0.619877 + 0.457264i
\(658\) 11.2350 4.65369i 0.437986 0.181420i
\(659\) 14.6792i 0.571822i −0.958256 0.285911i \(-0.907704\pi\)
0.958256 0.285911i \(-0.0922962\pi\)
\(660\) 0 0
\(661\) 44.7696i 1.74133i 0.491873 + 0.870667i \(0.336312\pi\)
−0.491873 + 0.870667i \(0.663688\pi\)
\(662\) −10.0042 24.1522i −0.388823 0.938701i
\(663\) 28.2960 9.30739i 1.09893 0.361469i
\(664\) −10.1421 + 24.4853i −0.393591 + 0.950213i
\(665\) 0 0
\(666\) −4.22248 + 7.00384i −0.163618 + 0.271393i
\(667\) 15.8887 0.615213
\(668\) −24.6005 + 24.6005i −0.951823 + 0.951823i
\(669\) −11.8551 36.0416i −0.458346 1.39345i
\(670\) 0 0
\(671\) 21.3707 0.825006
\(672\) 21.0280 + 24.4408i 0.811172 + 0.942824i
\(673\) 47.6661 1.83739 0.918697 0.394964i \(-0.129243\pi\)
0.918697 + 0.394964i \(0.129243\pi\)
\(674\) 15.1114 + 36.4821i 0.582068 + 1.40524i
\(675\) 0 0
\(676\) 12.2426 12.2426i 0.470871 0.470871i
\(677\) −1.00547 −0.0386433 −0.0193217 0.999813i \(-0.506151\pi\)
−0.0193217 + 0.999813i \(0.506151\pi\)
\(678\) 16.5662 14.2530i 0.636222 0.547383i
\(679\) 8.97056i 0.344259i
\(680\) 0 0
\(681\) 2.24264 + 6.81801i 0.0859382 + 0.261267i
\(682\) 1.59689 + 3.85525i 0.0611483 + 0.147625i
\(683\) 14.9678i 0.572726i −0.958121 0.286363i \(-0.907554\pi\)
0.958121 0.286363i \(-0.0924464\pi\)
\(684\) 0.741983 4.91487i 0.0283704 0.187925i
\(685\) 0 0
\(686\) 13.6360 5.64823i 0.520626 0.215650i
\(687\) 10.4525 + 31.7774i 0.398788 + 1.21238i
\(688\) 24.0669i 0.917542i
\(689\) 21.3707i 0.814159i
\(690\) 0 0
\(691\) −7.17157 −0.272819 −0.136410 0.990653i \(-0.543556\pi\)
−0.136410 + 0.990653i \(0.543556\pi\)
\(692\) 30.4608 30.4608i 1.15795 1.15795i
\(693\) 20.0083 14.7595i 0.760053 0.560668i
\(694\) −0.242641 + 0.100505i −0.00921051 + 0.00381512i
\(695\) 0 0
\(696\) 29.7039 + 2.22952i 1.12592 + 0.0845099i
\(697\) −31.7774 −1.20365
\(698\) 3.06147 1.26810i 0.115878 0.0479983i
\(699\) −8.62742 26.2288i −0.326319 0.992065i
\(700\) 0 0
\(701\) 26.8399 1.01373 0.506865 0.862025i \(-0.330804\pi\)
0.506865 + 0.862025i \(0.330804\pi\)
\(702\) −7.62146 + 33.3374i −0.287654 + 1.25824i
\(703\) 1.59689i 0.0602280i
\(704\) −14.2471 + 14.2471i −0.536959 + 0.536959i
\(705\) 0 0
\(706\) −42.2843 + 17.5147i −1.59139 + 0.659175i
\(707\) 43.4495i 1.63409i
\(708\) 7.78793 + 3.93268i 0.292688 + 0.147799i
\(709\) 36.2843i 1.36268i 0.731965 + 0.681342i \(0.238603\pi\)
−0.731965 + 0.681342i \(0.761397\pi\)
\(710\) 0 0
\(711\) −29.3585 39.7990i −1.10103 1.49258i
\(712\) −5.45214 + 13.1626i −0.204328 + 0.493290i
\(713\) 3.06147i 0.114653i
\(714\) 19.4273 + 22.5804i 0.727050 + 0.845048i
\(715\) 0 0
\(716\) −13.6360 13.6360i −0.509602 0.509602i
\(717\) −36.5838 + 12.0335i −1.36625 + 0.449398i
\(718\) 4.98442 + 12.0335i 0.186017 + 0.449085i
\(719\) 2.95068 0.110042 0.0550208 0.998485i \(-0.482477\pi\)
0.0550208 + 0.998485i \(0.482477\pi\)
\(720\) 0 0
\(721\) −19.7990 −0.737353
\(722\) −9.91131 23.9280i −0.368861 0.890508i
\(723\) 10.6704 3.50981i 0.396837 0.130531i
\(724\) −14.6274 14.6274i −0.543624 0.543624i
\(725\) 0 0
\(726\) −7.43957 8.64700i −0.276108 0.320920i
\(727\) 47.1015i 1.74690i −0.486915 0.873449i \(-0.661878\pi\)
0.486915 0.873449i \(-0.338122\pi\)
\(728\) 40.0166 + 16.5754i 1.48312 + 0.614327i
\(729\) −8.89949 25.4912i −0.329611 0.944117i
\(730\) 0 0
\(731\) 22.2349i 0.822388i
\(732\) −26.2383 13.2496i −0.969795 0.489719i
\(733\) 9.63811i 0.355992i −0.984031 0.177996i \(-0.943039\pi\)
0.984031 0.177996i \(-0.0569614\pi\)
\(734\) −2.82411 + 1.16979i −0.104240 + 0.0431776i
\(735\) 0 0
\(736\) 13.6569 5.65685i 0.503398 0.208514i
\(737\) 8.28772i 0.305282i
\(738\) 18.8360 31.2433i 0.693362 1.15008i
\(739\) 27.1716 0.999522 0.499761 0.866163i \(-0.333421\pi\)
0.499761 + 0.866163i \(0.333421\pi\)
\(740\) 0 0
\(741\) −2.08644 6.34315i −0.0766474 0.233021i
\(742\) 19.7439 8.17821i 0.724823 0.300232i
\(743\) −15.2304 −0.558750 −0.279375 0.960182i \(-0.590127\pi\)
−0.279375 + 0.960182i \(0.590127\pi\)
\(744\) 0.429589 5.72341i 0.0157495 0.209830i
\(745\) 0 0
\(746\) −31.8771 + 13.2039i −1.16710 + 0.483429i
\(747\) −16.6871 22.6215i −0.610551 0.827676i
\(748\) −13.1626 + 13.1626i −0.481273 + 0.481273i
\(749\) −27.8832 −1.01883
\(750\) 0 0
\(751\) 35.1127i 1.28128i 0.767841 + 0.640640i \(0.221331\pi\)
−0.767841 + 0.640640i \(0.778669\pi\)
\(752\) 10.4525i 0.381164i
\(753\) 6.34746 + 19.2974i 0.231314 + 0.703235i
\(754\) 36.9706 15.3137i 1.34639 0.557692i
\(755\) 0 0
\(756\) −33.7164 + 5.71637i −1.22625 + 0.207902i
\(757\) 12.8319i 0.466383i 0.972431 + 0.233192i \(0.0749170\pi\)
−0.972431 + 0.233192i \(0.925083\pi\)
\(758\) −11.2723 27.2137i −0.409427 0.988444i
\(759\) −3.56178 10.8284i −0.129284 0.393047i
\(760\) 0 0
\(761\) 17.1978i 0.623420i −0.950177 0.311710i \(-0.899098\pi\)
0.950177 0.311710i \(-0.100902\pi\)
\(762\) 6.11020 5.25700i 0.221349 0.190441i
\(763\) −1.59689 −0.0578115
\(764\) 7.12356 7.12356i 0.257722 0.257722i
\(765\) 0 0
\(766\) 15.7574 + 38.0416i 0.569337 + 1.37450i
\(767\) 11.7206 0.423207
\(768\) 26.3253 8.65914i 0.949931 0.312460i
\(769\) 49.5980 1.78855 0.894274 0.447519i \(-0.147692\pi\)
0.894274 + 0.447519i \(0.147692\pi\)
\(770\) 0 0
\(771\) −8.82843 26.8399i −0.317948 0.966616i
\(772\) −27.9222 + 27.9222i −1.00494 + 1.00494i
\(773\) 18.8490 0.677952 0.338976 0.940795i \(-0.389919\pi\)
0.338976 + 0.940795i \(0.389919\pi\)
\(774\) −21.8612 13.1797i −0.785786 0.473735i
\(775\) 0 0
\(776\) 7.12356 + 2.95068i 0.255721 + 0.105923i
\(777\) −10.4366 + 3.43289i −0.374410 + 0.123154i
\(778\) 4.08910 + 9.87197i 0.146602 + 0.353927i
\(779\) 7.12356i 0.255228i
\(780\) 0 0
\(781\) 17.9411i 0.641984i
\(782\) 12.6173 5.22625i 0.451193 0.186890i
\(783\) −18.2919 + 25.7607i −0.653699 + 0.920611i
\(784\) 15.3137i 0.546918i
\(785\) 0 0
\(786\) 40.4842 34.8311i 1.44402 1.24239i
\(787\) 48.2307 1.71924 0.859619 0.510935i \(-0.170701\pi\)
0.859619 + 0.510935i \(0.170701\pi\)
\(788\) 16.9469 16.9469i 0.603707 0.603707i
\(789\) 36.6086 12.0416i 1.30330 0.428693i
\(790\) 0 0
\(791\) 29.3585 1.04387
\(792\) −5.13929 20.7435i −0.182617 0.737089i
\(793\) −39.4879 −1.40226
\(794\) 35.4388 14.6792i 1.25768 0.520947i
\(795\) 0 0
\(796\) −12.9706 12.9706i −0.459729 0.459729i
\(797\) −8.92177 −0.316025 −0.158013 0.987437i \(-0.550509\pi\)
−0.158013 + 0.987437i \(0.550509\pi\)
\(798\) 5.06186 4.35504i 0.179188 0.154167i
\(799\) 9.65685i 0.341635i
\(800\) 0 0
\(801\) −8.97056 12.1607i −0.316959 0.429677i
\(802\) −19.7439 + 8.17821i −0.697183 + 0.288783i
\(803\) 16.5754i 0.584935i
\(804\) −5.13829 + 10.1754i −0.181214 + 0.358859i
\(805\) 0 0
\(806\) −2.95068 7.12356i −0.103933 0.250917i
\(807\) −15.8645 + 5.21828i −0.558456 + 0.183692i
\(808\) −34.5035 14.2918i −1.21383 0.502784i
\(809\) 4.17289i 0.146711i −0.997306 0.0733555i \(-0.976629\pi\)
0.997306 0.0733555i \(-0.0233708\pi\)
\(810\) 0 0
\(811\) −14.4853 −0.508647 −0.254324 0.967119i \(-0.581853\pi\)
−0.254324 + 0.967119i \(0.581853\pi\)
\(812\) 28.2960 + 28.2960i 0.992996 + 0.992996i
\(813\) 7.65367 + 23.2685i 0.268426 + 0.816061i
\(814\) −2.62742 6.34315i −0.0920909 0.222327i
\(815\) 0 0
\(816\) 24.3214 8.00000i 0.851418 0.280056i
\(817\) 4.98442 0.174383
\(818\) 6.94269 + 16.7611i 0.242746 + 0.586040i
\(819\) −36.9706 + 27.2720i −1.29186 + 0.952962i
\(820\) 0 0
\(821\) −23.8893 −0.833741 −0.416870 0.908966i \(-0.636873\pi\)
−0.416870 + 0.908966i \(0.636873\pi\)
\(822\) 22.2509 19.1438i 0.776088 0.667718i
\(823\) 23.5023i 0.819239i 0.912256 + 0.409620i \(0.134339\pi\)
−0.912256 + 0.409620i \(0.865661\pi\)
\(824\) −6.51246 + 15.7225i −0.226872 + 0.547718i
\(825\) 0 0
\(826\) 4.48528 + 10.8284i 0.156063 + 0.376769i
\(827\) 35.5014i 1.23450i 0.786766 + 0.617252i \(0.211754\pi\)
−0.786766 + 0.617252i \(0.788246\pi\)
\(828\) −2.34045 + 15.5031i −0.0813364 + 0.538769i
\(829\) 5.17157i 0.179616i 0.995959 + 0.0898081i \(0.0286254\pi\)
−0.995959 + 0.0898081i \(0.971375\pi\)
\(830\) 0 0
\(831\) −8.16679 24.8284i −0.283303 0.861289i
\(832\) 26.3253 26.3253i 0.912664 0.912664i
\(833\) 14.1480i 0.490200i
\(834\) 23.1410 + 26.8967i 0.801307 + 0.931358i
\(835\) 0 0
\(836\) 2.95068 + 2.95068i 0.102051 + 0.102051i
\(837\) 4.96362 + 3.52452i 0.171568 + 0.121825i
\(838\) 3.29066 1.36303i 0.113674 0.0470853i
\(839\) 53.6799 1.85323 0.926617 0.376006i \(-0.122703\pi\)
0.926617 + 0.376006i \(0.122703\pi\)
\(840\) 0 0
\(841\) 7.97056 0.274847
\(842\) 45.5055 18.8490i 1.56822 0.649580i
\(843\) −1.92762 5.86030i −0.0663908 0.201840i
\(844\) −26.1421 + 26.1421i −0.899849 + 0.899849i
\(845\) 0 0
\(846\) 9.49456 + 5.72408i 0.326430 + 0.196798i
\(847\) 15.3241i 0.526543i
\(848\) 18.3688i 0.630787i
\(849\) −29.6985 + 9.76869i −1.01925 + 0.335261i
\(850\) 0 0
\(851\) 5.03712i 0.172670i
\(852\) −11.1233 + 22.0276i −0.381078 + 0.754652i
\(853\) 36.4311i 1.24738i −0.781673 0.623688i \(-0.785633\pi\)
0.781673 0.623688i \(-0.214367\pi\)
\(854\) −15.1114 36.4821i −0.517100 1.24839i
\(855\) 0 0
\(856\) −9.17157 + 22.1421i −0.313478 + 0.756803i
\(857\) 28.5587i 0.975546i 0.872971 + 0.487773i \(0.162191\pi\)
−0.872971 + 0.487773i \(0.837809\pi\)
\(858\) −18.7243 21.7632i −0.639236 0.742983i
\(859\) −3.85786 −0.131629 −0.0658143 0.997832i \(-0.520965\pi\)
−0.0658143 + 0.997832i \(0.520965\pi\)
\(860\) 0 0
\(861\) 46.5563 15.3137i 1.58663 0.521890i
\(862\) −14.7595 35.6326i −0.502711 1.21365i
\(863\) 20.0852 0.683710 0.341855 0.939753i \(-0.388945\pi\)
0.341855 + 0.939753i \(0.388945\pi\)
\(864\) −6.55089 + 28.6546i −0.222866 + 0.974849i
\(865\) 0 0
\(866\) 12.7718 + 30.8338i 0.434003 + 1.04778i
\(867\) −5.50057 + 1.80930i −0.186809 + 0.0614470i
\(868\) 5.45214 5.45214i 0.185058 0.185058i
\(869\) 41.5192 1.40844
\(870\) 0 0
\(871\) 15.3137i 0.518885i
\(872\) −0.525265 + 1.26810i −0.0177877 + 0.0429433i
\(873\) −6.58132 + 4.85483i −0.222744 + 0.164311i
\(874\) −1.17157 2.82843i −0.0396290 0.0956730i
\(875\) 0 0
\(876\) −10.2766 + 20.3508i −0.347214 + 0.687591i
\(877\) 35.3019i 1.19206i −0.802962 0.596031i \(-0.796744\pi\)
0.802962 0.596031i \(-0.203256\pi\)
\(878\) 37.2178 15.4161i 1.25604 0.520269i
\(879\) −3.99390 + 1.31371i −0.134711 + 0.0443103i
\(880\) 0 0
\(881\) 42.9945i 1.44852i −0.689526 0.724261i \(-0.742181\pi\)
0.689526 0.724261i \(-0.257819\pi\)
\(882\) −13.9102 8.38621i −0.468382 0.282378i
\(883\) 37.7941 1.27187 0.635937 0.771741i \(-0.280614\pi\)
0.635937 + 0.771741i \(0.280614\pi\)
\(884\) 24.3214 24.3214i 0.818016 0.818016i
\(885\) 0 0
\(886\) 2.10051 0.870058i 0.0705678 0.0292302i
\(887\) 12.5404 0.421064 0.210532 0.977587i \(-0.432480\pi\)
0.210532 + 0.977587i \(0.432480\pi\)
\(888\) −0.706816 + 9.41689i −0.0237192 + 0.316010i
\(889\) 10.8284 0.363174
\(890\) 0 0
\(891\) 21.6569 + 6.69145i 0.725532 + 0.224172i
\(892\) −30.9790 30.9790i −1.03725 1.03725i
\(893\) −2.16478 −0.0724417
\(894\) 23.4509 + 27.2569i 0.784314 + 0.911607i
\(895\) 0 0
\(896\) 34.3956 + 14.2471i 1.14908 + 0.475963i
\(897\) 6.58132 + 20.0083i 0.219744 + 0.668059i
\(898\) −45.7385 + 18.9455i −1.52631 + 0.632219i
\(899\) 7.12356i 0.237584i
\(900\) 0 0
\(901\) 16.9706i 0.565371i
\(902\) 11.7206 + 28.2960i 0.390253 + 0.942155i
\(903\) −10.7151 32.5758i −0.356577 1.08406i
\(904\) 9.65685 23.3137i 0.321182 0.775402i
\(905\) 0 0
\(906\) 5.25192 4.51856i 0.174483 0.150119i
\(907\) 7.61362 0.252806 0.126403 0.991979i \(-0.459657\pi\)
0.126403 + 0.991979i \(0.459657\pi\)
\(908\) 5.86030 + 5.86030i 0.194481 + 0.194481i
\(909\) 31.8771 23.5147i 1.05730 0.779934i
\(910\) 0 0
\(911\) 2.95068 0.0977603 0.0488801 0.998805i \(-0.484435\pi\)
0.0488801 + 0.998805i \(0.484435\pi\)
\(912\) −1.79337 5.45214i −0.0593843 0.180538i
\(913\) 23.5992 0.781019
\(914\) −10.0742 24.3214i −0.333226 0.804479i
\(915\) 0 0
\(916\) 27.3137 + 27.3137i 0.902470 + 0.902470i
\(917\) 71.7456 2.36925
\(918\) −6.05224 + 26.4734i −0.199754 + 0.873752i
\(919\) 6.14214i 0.202610i 0.994855 + 0.101305i \(0.0323019\pi\)
−0.994855 + 0.101305i \(0.967698\pi\)
\(920\) 0 0
\(921\) −11.7574 + 3.86733i −0.387418 + 0.127433i
\(922\) 2.16148 + 5.21828i 0.0711846 + 0.171855i
\(923\) 33.1509i 1.09117i
\(924\) 12.9411 25.6274i 0.425731 0.843079i
\(925\) 0 0
\(926\) 33.6579 13.9416i 1.10607 0.458149i
\(927\) −10.7151 14.5257i −0.351931 0.477085i
\(928\) 31.7774 13.1626i 1.04314 0.432085i
\(929\) 26.6609i 0.874717i −0.899287 0.437359i \(-0.855914\pi\)
0.899287 0.437359i \(-0.144086\pi\)
\(930\) 0 0
\(931\) 3.17157 0.103944
\(932\) −22.5445 22.5445i −0.738471 0.738471i
\(933\) −56.5921 + 18.6148i −1.85274 + 0.609420i
\(934\) −20.7279 + 8.58579i −0.678238 + 0.280936i
\(935\) 0 0
\(936\) 9.49617 + 38.3291i 0.310392 + 1.25282i
\(937\) 8.17821 0.267170 0.133585 0.991037i \(-0.457351\pi\)
0.133585 + 0.991037i \(0.457351\pi\)
\(938\) −14.1480 + 5.86030i −0.461949 + 0.191346i
\(939\) 28.0000 9.21001i 0.913745 0.300557i
\(940\) 0 0
\(941\) 23.2781 0.758846 0.379423 0.925223i \(-0.376123\pi\)
0.379423 + 0.925223i \(0.376123\pi\)
\(942\) −10.7378 + 9.23843i −0.349857 + 0.301004i
\(943\) 22.4700i 0.731724i
\(944\) 10.0742 0.327889
\(945\) 0 0
\(946\) 19.7990 8.20101i 0.643721 0.266638i
\(947\) 21.6160i 0.702425i −0.936296 0.351213i \(-0.885769\pi\)
0.936296 0.351213i \(-0.114231\pi\)
\(948\) −50.9760 25.7414i −1.65562 0.836043i
\(949\) 30.6274i 0.994208i
\(950\) 0 0
\(951\) 21.8028 7.17157i 0.707005 0.232554i
\(952\) 31.7774 + 13.1626i 1.02991 + 0.426603i
\(953\) 44.0836i 1.42801i −0.700142 0.714004i \(-0.746880\pi\)
0.700142 0.714004i \(-0.253120\pi\)
\(954\) 16.6853 + 10.0593i 0.540208 + 0.325681i
\(955\) 0 0
\(956\) −31.4449 + 31.4449i −1.01700 + 1.01700i
\(957\) −8.28772 25.1961i −0.267904 0.814474i
\(958\) −10.4366 25.1961i −0.337190 0.814049i
\(959\) 39.4327 1.27335
\(960\) 0 0
\(961\) 29.6274 0.955723
\(962\) 4.85483 + 11.7206i 0.156526 + 0.377887i
\(963\) −15.0903 20.4567i −0.486277 0.659207i
\(964\) 9.17157 9.17157i 0.295396 0.295396i
\(965\) 0 0
\(966\) −15.9667 + 13.7372i −0.513721 + 0.441987i
\(967\) 55.2797i 1.77768i 0.458222 + 0.888838i \(0.348487\pi\)
−0.458222 + 0.888838i \(0.651513\pi\)
\(968\) −12.1689 5.04054i −0.391125 0.162009i
\(969\) −1.65685 5.03712i −0.0532258 0.161816i
\(970\) 0 0
\(971\) 13.8150i 0.443345i 0.975121 + 0.221672i \(0.0711516\pi\)
−0.975121 + 0.221672i \(0.928848\pi\)
\(972\) −22.4410 21.6426i −0.719796 0.694186i
\(973\) 47.6661i 1.52811i
\(974\) −11.4230 + 4.73157i −0.366017 + 0.151609i
\(975\) 0 0
\(976\) −33.9411 −1.08643
\(977\) 33.2597i 1.06407i −0.846722 0.532035i \(-0.821427\pi\)
0.846722 0.532035i \(-0.178573\pi\)
\(978\) −9.61204 11.1721i −0.307359 0.357243i
\(979\) 12.6863 0.405456
\(980\) 0 0
\(981\) −0.864233 1.17157i −0.0275928 0.0374054i
\(982\) 48.2307 19.9778i 1.53910 0.637517i
\(983\) 10.0042 0.319083 0.159542 0.987191i \(-0.448998\pi\)
0.159542 + 0.987191i \(0.448998\pi\)
\(984\) 3.15302 42.0077i 0.100515 1.33916i
\(985\) 0 0
\(986\) 29.3585 12.1607i 0.934965 0.387275i
\(987\) 4.65369 + 14.1480i 0.148129 + 0.450336i
\(988\) −5.45214 5.45214i −0.173456 0.173456i
\(989\) −15.7225 −0.499945
\(990\) 0 0
\(991\) 19.7990i 0.628936i −0.949268 0.314468i \(-0.898174\pi\)
0.949268 0.314468i \(-0.101826\pi\)
\(992\) −2.53620 6.12293i −0.0805245 0.194403i
\(993\) 30.4144 10.0042i 0.965171 0.317472i
\(994\) −30.6274 + 12.6863i −0.971443 + 0.402385i
\(995\) 0 0
\(996\) −28.9744 14.6312i −0.918088 0.463608i
\(997\) 8.50894i 0.269481i −0.990881 0.134740i \(-0.956980\pi\)
0.990881 0.134740i \(-0.0430200\pi\)
\(998\) 20.0852 + 48.4901i 0.635787 + 1.53493i
\(999\) −8.16679 5.79899i −0.258386 0.183472i
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 600.2.b.i.251.11 16
3.2 odd 2 inner 600.2.b.i.251.5 16
4.3 odd 2 2400.2.b.i.2351.14 16
5.2 odd 4 120.2.m.b.59.4 yes 16
5.3 odd 4 120.2.m.b.59.13 yes 16
5.4 even 2 inner 600.2.b.i.251.6 16
8.3 odd 2 inner 600.2.b.i.251.7 16
8.5 even 2 2400.2.b.i.2351.13 16
12.11 even 2 2400.2.b.i.2351.16 16
15.2 even 4 120.2.m.b.59.14 yes 16
15.8 even 4 120.2.m.b.59.3 yes 16
15.14 odd 2 inner 600.2.b.i.251.12 16
20.3 even 4 480.2.m.b.239.12 16
20.7 even 4 480.2.m.b.239.6 16
20.19 odd 2 2400.2.b.i.2351.3 16
24.5 odd 2 2400.2.b.i.2351.15 16
24.11 even 2 inner 600.2.b.i.251.9 16
40.3 even 4 120.2.m.b.59.15 yes 16
40.13 odd 4 480.2.m.b.239.11 16
40.19 odd 2 inner 600.2.b.i.251.10 16
40.27 even 4 120.2.m.b.59.2 yes 16
40.29 even 2 2400.2.b.i.2351.4 16
40.37 odd 4 480.2.m.b.239.5 16
60.23 odd 4 480.2.m.b.239.7 16
60.47 odd 4 480.2.m.b.239.9 16
60.59 even 2 2400.2.b.i.2351.1 16
120.29 odd 2 2400.2.b.i.2351.2 16
120.53 even 4 480.2.m.b.239.8 16
120.59 even 2 inner 600.2.b.i.251.8 16
120.77 even 4 480.2.m.b.239.10 16
120.83 odd 4 120.2.m.b.59.1 16
120.107 odd 4 120.2.m.b.59.16 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.2.m.b.59.1 16 120.83 odd 4
120.2.m.b.59.2 yes 16 40.27 even 4
120.2.m.b.59.3 yes 16 15.8 even 4
120.2.m.b.59.4 yes 16 5.2 odd 4
120.2.m.b.59.13 yes 16 5.3 odd 4
120.2.m.b.59.14 yes 16 15.2 even 4
120.2.m.b.59.15 yes 16 40.3 even 4
120.2.m.b.59.16 yes 16 120.107 odd 4
480.2.m.b.239.5 16 40.37 odd 4
480.2.m.b.239.6 16 20.7 even 4
480.2.m.b.239.7 16 60.23 odd 4
480.2.m.b.239.8 16 120.53 even 4
480.2.m.b.239.9 16 60.47 odd 4
480.2.m.b.239.10 16 120.77 even 4
480.2.m.b.239.11 16 40.13 odd 4
480.2.m.b.239.12 16 20.3 even 4
600.2.b.i.251.5 16 3.2 odd 2 inner
600.2.b.i.251.6 16 5.4 even 2 inner
600.2.b.i.251.7 16 8.3 odd 2 inner
600.2.b.i.251.8 16 120.59 even 2 inner
600.2.b.i.251.9 16 24.11 even 2 inner
600.2.b.i.251.10 16 40.19 odd 2 inner
600.2.b.i.251.11 16 1.1 even 1 trivial
600.2.b.i.251.12 16 15.14 odd 2 inner
2400.2.b.i.2351.1 16 60.59 even 2
2400.2.b.i.2351.2 16 120.29 odd 2
2400.2.b.i.2351.3 16 20.19 odd 2
2400.2.b.i.2351.4 16 40.29 even 2
2400.2.b.i.2351.13 16 8.5 even 2
2400.2.b.i.2351.14 16 4.3 odd 2
2400.2.b.i.2351.15 16 24.5 odd 2
2400.2.b.i.2351.16 16 12.11 even 2