Properties

Label 1320.2.w.a.661.1
Level $1320$
Weight $2$
Character 1320.661
Analytic conductor $10.540$
Analytic rank $0$
Dimension $2$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1320,2,Mod(661,1320)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1320, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1320.661");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1320.w (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: \(10.5402530668\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 661.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1320.661
Dual form 1320.2.w.a.661.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +1.00000i q^{3} -2.00000i q^{4} +1.00000i q^{5} +(1.00000 + 1.00000i) q^{6} -2.00000 q^{7} +(-2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +(1.00000 + 1.00000i) q^{10} -1.00000i q^{11} +2.00000 q^{12} -4.00000i q^{13} +(-2.00000 + 2.00000i) q^{14} -1.00000 q^{15} -4.00000 q^{16} +2.00000 q^{17} +(-1.00000 + 1.00000i) q^{18} -4.00000i q^{19} +2.00000 q^{20} -2.00000i q^{21} +(-1.00000 - 1.00000i) q^{22} +(2.00000 - 2.00000i) q^{24} -1.00000 q^{25} +(-4.00000 - 4.00000i) q^{26} -1.00000i q^{27} +4.00000i q^{28} -6.00000i q^{29} +(-1.00000 + 1.00000i) q^{30} -6.00000 q^{31} +(-4.00000 + 4.00000i) q^{32} +1.00000 q^{33} +(2.00000 - 2.00000i) q^{34} -2.00000i q^{35} +2.00000i q^{36} -4.00000i q^{37} +(-4.00000 - 4.00000i) q^{38} +4.00000 q^{39} +(2.00000 - 2.00000i) q^{40} +2.00000 q^{41} +(-2.00000 - 2.00000i) q^{42} -4.00000i q^{43} -2.00000 q^{44} -1.00000i q^{45} -4.00000i q^{48} -3.00000 q^{49} +(-1.00000 + 1.00000i) q^{50} +2.00000i q^{51} -8.00000 q^{52} -14.0000i q^{53} +(-1.00000 - 1.00000i) q^{54} +1.00000 q^{55} +(4.00000 + 4.00000i) q^{56} +4.00000 q^{57} +(-6.00000 - 6.00000i) q^{58} +2.00000i q^{60} +12.0000i q^{61} +(-6.00000 + 6.00000i) q^{62} +2.00000 q^{63} +8.00000i q^{64} +4.00000 q^{65} +(1.00000 - 1.00000i) q^{66} -4.00000i q^{67} -4.00000i q^{68} +(-2.00000 - 2.00000i) q^{70} -8.00000 q^{71} +(2.00000 + 2.00000i) q^{72} +10.0000 q^{73} +(-4.00000 - 4.00000i) q^{74} -1.00000i q^{75} -8.00000 q^{76} +2.00000i q^{77} +(4.00000 - 4.00000i) q^{78} +6.00000 q^{79} -4.00000i q^{80} +1.00000 q^{81} +(2.00000 - 2.00000i) q^{82} -4.00000 q^{84} +2.00000i q^{85} +(-4.00000 - 4.00000i) q^{86} +6.00000 q^{87} +(-2.00000 + 2.00000i) q^{88} +6.00000 q^{89} +(-1.00000 - 1.00000i) q^{90} +8.00000i q^{91} -6.00000i q^{93} +4.00000 q^{95} +(-4.00000 - 4.00000i) q^{96} +6.00000 q^{97} +(-3.00000 + 3.00000i) q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{12} - 4 q^{14} - 2 q^{15} - 8 q^{16} + 4 q^{17} - 2 q^{18} + 4 q^{20} - 2 q^{22} + 4 q^{24} - 2 q^{25} - 8 q^{26} - 2 q^{30} - 12 q^{31}+ \cdots - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times\).

\(n\) \(661\) \(881\) \(991\) \(1057\) \(1201\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.707107 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) 2.00000i 1.00000i
\(5\) 1.00000i 0.447214i
\(6\) 1.00000 + 1.00000i 0.408248 + 0.408248i
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) −1.00000 −0.333333
\(10\) 1.00000 + 1.00000i 0.316228 + 0.316228i
\(11\) 1.00000i 0.301511i
\(12\) 2.00000 0.577350
\(13\) 4.00000i 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) −2.00000 + 2.00000i −0.534522 + 0.534522i
\(15\) −1.00000 −0.258199
\(16\) −4.00000 −1.00000
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −1.00000 + 1.00000i −0.235702 + 0.235702i
\(19\) 4.00000i 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) 2.00000 0.447214
\(21\) 2.00000i 0.436436i
\(22\) −1.00000 1.00000i −0.213201 0.213201i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 2.00000 2.00000i 0.408248 0.408248i
\(25\) −1.00000 −0.200000
\(26\) −4.00000 4.00000i −0.784465 0.784465i
\(27\) 1.00000i 0.192450i
\(28\) 4.00000i 0.755929i
\(29\) 6.00000i 1.11417i −0.830455 0.557086i \(-0.811919\pi\)
0.830455 0.557086i \(-0.188081\pi\)
\(30\) −1.00000 + 1.00000i −0.182574 + 0.182574i
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) −4.00000 + 4.00000i −0.707107 + 0.707107i
\(33\) 1.00000 0.174078
\(34\) 2.00000 2.00000i 0.342997 0.342997i
\(35\) 2.00000i 0.338062i
\(36\) 2.00000i 0.333333i
\(37\) 4.00000i 0.657596i −0.944400 0.328798i \(-0.893356\pi\)
0.944400 0.328798i \(-0.106644\pi\)
\(38\) −4.00000 4.00000i −0.648886 0.648886i
\(39\) 4.00000 0.640513
\(40\) 2.00000 2.00000i 0.316228 0.316228i
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) −2.00000 2.00000i −0.308607 0.308607i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) −2.00000 −0.301511
\(45\) 1.00000i 0.149071i
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 4.00000i 0.577350i
\(49\) −3.00000 −0.428571
\(50\) −1.00000 + 1.00000i −0.141421 + 0.141421i
\(51\) 2.00000i 0.280056i
\(52\) −8.00000 −1.10940
\(53\) 14.0000i 1.92305i −0.274721 0.961524i \(-0.588586\pi\)
0.274721 0.961524i \(-0.411414\pi\)
\(54\) −1.00000 1.00000i −0.136083 0.136083i
\(55\) 1.00000 0.134840
\(56\) 4.00000 + 4.00000i 0.534522 + 0.534522i
\(57\) 4.00000 0.529813
\(58\) −6.00000 6.00000i −0.787839 0.787839i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 2.00000i 0.258199i
\(61\) 12.0000i 1.53644i 0.640184 + 0.768221i \(0.278858\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −6.00000 + 6.00000i −0.762001 + 0.762001i
\(63\) 2.00000 0.251976
\(64\) 8.00000i 1.00000i
\(65\) 4.00000 0.496139
\(66\) 1.00000 1.00000i 0.123091 0.123091i
\(67\) 4.00000i 0.488678i −0.969690 0.244339i \(-0.921429\pi\)
0.969690 0.244339i \(-0.0785709\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) −2.00000 2.00000i −0.239046 0.239046i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 2.00000 + 2.00000i 0.235702 + 0.235702i
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) −4.00000 4.00000i −0.464991 0.464991i
\(75\) 1.00000i 0.115470i
\(76\) −8.00000 −0.917663
\(77\) 2.00000i 0.227921i
\(78\) 4.00000 4.00000i 0.452911 0.452911i
\(79\) 6.00000 0.675053 0.337526 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) 4.00000i 0.447214i
\(81\) 1.00000 0.111111
\(82\) 2.00000 2.00000i 0.220863 0.220863i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −4.00000 −0.436436
\(85\) 2.00000i 0.216930i
\(86\) −4.00000 4.00000i −0.431331 0.431331i
\(87\) 6.00000 0.643268
\(88\) −2.00000 + 2.00000i −0.213201 + 0.213201i
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −1.00000 1.00000i −0.105409 0.105409i
\(91\) 8.00000i 0.838628i
\(92\) 0 0
\(93\) 6.00000i 0.622171i
\(94\) 0 0
\(95\) 4.00000 0.410391
\(96\) −4.00000 4.00000i −0.408248 0.408248i
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) −3.00000 + 3.00000i −0.303046 + 0.303046i
\(99\) 1.00000i 0.100504i
\(100\) 2.00000i 0.200000i
\(101\) 2.00000i 0.199007i −0.995037 0.0995037i \(-0.968274\pi\)
0.995037 0.0995037i \(-0.0317255\pi\)
\(102\) 2.00000 + 2.00000i 0.198030 + 0.198030i
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) −8.00000 + 8.00000i −0.784465 + 0.784465i
\(105\) 2.00000 0.195180
\(106\) −14.0000 14.0000i −1.35980 1.35980i
\(107\) 20.0000i 1.93347i 0.255774 + 0.966736i \(0.417670\pi\)
−0.255774 + 0.966736i \(0.582330\pi\)
\(108\) −2.00000 −0.192450
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 1.00000 1.00000i 0.0953463 0.0953463i
\(111\) 4.00000 0.379663
\(112\) 8.00000 0.755929
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 4.00000 4.00000i 0.374634 0.374634i
\(115\) 0 0
\(116\) −12.0000 −1.11417
\(117\) 4.00000i 0.369800i
\(118\) 0 0
\(119\) −4.00000 −0.366679
\(120\) 2.00000 + 2.00000i 0.182574 + 0.182574i
\(121\) −1.00000 −0.0909091
\(122\) 12.0000 + 12.0000i 1.08643 + 1.08643i
\(123\) 2.00000i 0.180334i
\(124\) 12.0000i 1.07763i
\(125\) 1.00000i 0.0894427i
\(126\) 2.00000 2.00000i 0.178174 0.178174i
\(127\) 6.00000 0.532414 0.266207 0.963916i \(-0.414230\pi\)
0.266207 + 0.963916i \(0.414230\pi\)
\(128\) 8.00000 + 8.00000i 0.707107 + 0.707107i
\(129\) 4.00000 0.352180
\(130\) 4.00000 4.00000i 0.350823 0.350823i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 8.00000i 0.693688i
\(134\) −4.00000 4.00000i −0.345547 0.345547i
\(135\) 1.00000 0.0860663
\(136\) −4.00000 4.00000i −0.342997 0.342997i
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) 12.0000i 1.01783i 0.860818 + 0.508913i \(0.169953\pi\)
−0.860818 + 0.508913i \(0.830047\pi\)
\(140\) −4.00000 −0.338062
\(141\) 0 0
\(142\) −8.00000 + 8.00000i −0.671345 + 0.671345i
\(143\) −4.00000 −0.334497
\(144\) 4.00000 0.333333
\(145\) 6.00000 0.498273
\(146\) 10.0000 10.0000i 0.827606 0.827606i
\(147\) 3.00000i 0.247436i
\(148\) −8.00000 −0.657596
\(149\) 2.00000i 0.163846i 0.996639 + 0.0819232i \(0.0261062\pi\)
−0.996639 + 0.0819232i \(0.973894\pi\)
\(150\) −1.00000 1.00000i −0.0816497 0.0816497i
\(151\) −22.0000 −1.79033 −0.895167 0.445730i \(-0.852944\pi\)
−0.895167 + 0.445730i \(0.852944\pi\)
\(152\) −8.00000 + 8.00000i −0.648886 + 0.648886i
\(153\) −2.00000 −0.161690
\(154\) 2.00000 + 2.00000i 0.161165 + 0.161165i
\(155\) 6.00000i 0.481932i
\(156\) 8.00000i 0.640513i
\(157\) 4.00000i 0.319235i 0.987179 + 0.159617i \(0.0510260\pi\)
−0.987179 + 0.159617i \(0.948974\pi\)
\(158\) 6.00000 6.00000i 0.477334 0.477334i
\(159\) 14.0000 1.11027
\(160\) −4.00000 4.00000i −0.316228 0.316228i
\(161\) 0 0
\(162\) 1.00000 1.00000i 0.0785674 0.0785674i
\(163\) 4.00000i 0.313304i 0.987654 + 0.156652i \(0.0500701\pi\)
−0.987654 + 0.156652i \(0.949930\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 1.00000i 0.0778499i
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) −4.00000 + 4.00000i −0.308607 + 0.308607i
\(169\) −3.00000 −0.230769
\(170\) 2.00000 + 2.00000i 0.153393 + 0.153393i
\(171\) 4.00000i 0.305888i
\(172\) −8.00000 −0.609994
\(173\) 18.0000i 1.36851i −0.729241 0.684257i \(-0.760127\pi\)
0.729241 0.684257i \(-0.239873\pi\)
\(174\) 6.00000 6.00000i 0.454859 0.454859i
\(175\) 2.00000 0.151186
\(176\) 4.00000i 0.301511i
\(177\) 0 0
\(178\) 6.00000 6.00000i 0.449719 0.449719i
\(179\) 24.0000i 1.79384i −0.442189 0.896922i \(-0.645798\pi\)
0.442189 0.896922i \(-0.354202\pi\)
\(180\) −2.00000 −0.149071
\(181\) 20.0000i 1.48659i 0.668965 + 0.743294i \(0.266738\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 8.00000 + 8.00000i 0.592999 + 0.592999i
\(183\) −12.0000 −0.887066
\(184\) 0 0
\(185\) 4.00000 0.294086
\(186\) −6.00000 6.00000i −0.439941 0.439941i
\(187\) 2.00000i 0.146254i
\(188\) 0 0
\(189\) 2.00000i 0.145479i
\(190\) 4.00000 4.00000i 0.290191 0.290191i
\(191\) 4.00000 0.289430 0.144715 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) −8.00000 −0.577350
\(193\) 18.0000 1.29567 0.647834 0.761781i \(-0.275675\pi\)
0.647834 + 0.761781i \(0.275675\pi\)
\(194\) 6.00000 6.00000i 0.430775 0.430775i
\(195\) 4.00000i 0.286446i
\(196\) 6.00000i 0.428571i
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 1.00000 + 1.00000i 0.0710669 + 0.0710669i
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 2.00000 + 2.00000i 0.141421 + 0.141421i
\(201\) 4.00000 0.282138
\(202\) −2.00000 2.00000i −0.140720 0.140720i
\(203\) 12.0000i 0.842235i
\(204\) 4.00000 0.280056
\(205\) 2.00000i 0.139686i
\(206\) −10.0000 + 10.0000i −0.696733 + 0.696733i
\(207\) 0 0
\(208\) 16.0000i 1.10940i
\(209\) −4.00000 −0.276686
\(210\) 2.00000 2.00000i 0.138013 0.138013i
\(211\) 20.0000i 1.37686i 0.725304 + 0.688428i \(0.241699\pi\)
−0.725304 + 0.688428i \(0.758301\pi\)
\(212\) −28.0000 −1.92305
\(213\) 8.00000i 0.548151i
\(214\) 20.0000 + 20.0000i 1.36717 + 1.36717i
\(215\) 4.00000 0.272798
\(216\) −2.00000 + 2.00000i −0.136083 + 0.136083i
\(217\) 12.0000 0.814613
\(218\) 0 0
\(219\) 10.0000i 0.675737i
\(220\) 2.00000i 0.134840i
\(221\) 8.00000i 0.538138i
\(222\) 4.00000 4.00000i 0.268462 0.268462i
\(223\) 10.0000 0.669650 0.334825 0.942280i \(-0.391323\pi\)
0.334825 + 0.942280i \(0.391323\pi\)
\(224\) 8.00000 8.00000i 0.534522 0.534522i
\(225\) 1.00000 0.0666667
\(226\) −2.00000 + 2.00000i −0.133038 + 0.133038i
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 8.00000i 0.529813i
\(229\) 20.0000i 1.32164i 0.750546 + 0.660819i \(0.229791\pi\)
−0.750546 + 0.660819i \(0.770209\pi\)
\(230\) 0 0
\(231\) −2.00000 −0.131590
\(232\) −12.0000 + 12.0000i −0.787839 + 0.787839i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 4.00000 + 4.00000i 0.261488 + 0.261488i
\(235\) 0 0
\(236\) 0 0
\(237\) 6.00000i 0.389742i
\(238\) −4.00000 + 4.00000i −0.259281 + 0.259281i
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 4.00000 0.258199
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) −1.00000 + 1.00000i −0.0642824 + 0.0642824i
\(243\) 1.00000i 0.0641500i
\(244\) 24.0000 1.53644
\(245\) 3.00000i 0.191663i
\(246\) 2.00000 + 2.00000i 0.127515 + 0.127515i
\(247\) −16.0000 −1.01806
\(248\) 12.0000 + 12.0000i 0.762001 + 0.762001i
\(249\) 0 0
\(250\) −1.00000 1.00000i −0.0632456 0.0632456i
\(251\) 4.00000i 0.252478i −0.992000 0.126239i \(-0.959709\pi\)
0.992000 0.126239i \(-0.0402906\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 0 0
\(254\) 6.00000 6.00000i 0.376473 0.376473i
\(255\) −2.00000 −0.125245
\(256\) 16.0000 1.00000
\(257\) 22.0000 1.37232 0.686161 0.727450i \(-0.259294\pi\)
0.686161 + 0.727450i \(0.259294\pi\)
\(258\) 4.00000 4.00000i 0.249029 0.249029i
\(259\) 8.00000i 0.497096i
\(260\) 8.00000i 0.496139i
\(261\) 6.00000i 0.371391i
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) −2.00000 2.00000i −0.123091 0.123091i
\(265\) 14.0000 0.860013
\(266\) 8.00000 + 8.00000i 0.490511 + 0.490511i
\(267\) 6.00000i 0.367194i
\(268\) −8.00000 −0.488678
\(269\) 18.0000i 1.09748i −0.835993 0.548740i \(-0.815108\pi\)
0.835993 0.548740i \(-0.184892\pi\)
\(270\) 1.00000 1.00000i 0.0608581 0.0608581i
\(271\) −22.0000 −1.33640 −0.668202 0.743980i \(-0.732936\pi\)
−0.668202 + 0.743980i \(0.732936\pi\)
\(272\) −8.00000 −0.485071
\(273\) −8.00000 −0.484182
\(274\) 6.00000 6.00000i 0.362473 0.362473i
\(275\) 1.00000i 0.0603023i
\(276\) 0 0
\(277\) 12.0000i 0.721010i 0.932757 + 0.360505i \(0.117396\pi\)
−0.932757 + 0.360505i \(0.882604\pi\)
\(278\) 12.0000 + 12.0000i 0.719712 + 0.719712i
\(279\) 6.00000 0.359211
\(280\) −4.00000 + 4.00000i −0.239046 + 0.239046i
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 0 0
\(283\) 4.00000i 0.237775i 0.992908 + 0.118888i \(0.0379328\pi\)
−0.992908 + 0.118888i \(0.962067\pi\)
\(284\) 16.0000i 0.949425i
\(285\) 4.00000i 0.236940i
\(286\) −4.00000 + 4.00000i −0.236525 + 0.236525i
\(287\) −4.00000 −0.236113
\(288\) 4.00000 4.00000i 0.235702 0.235702i
\(289\) −13.0000 −0.764706
\(290\) 6.00000 6.00000i 0.352332 0.352332i
\(291\) 6.00000i 0.351726i
\(292\) 20.0000i 1.17041i
\(293\) 14.0000i 0.817889i 0.912559 + 0.408944i \(0.134103\pi\)
−0.912559 + 0.408944i \(0.865897\pi\)
\(294\) −3.00000 3.00000i −0.174964 0.174964i
\(295\) 0 0
\(296\) −8.00000 + 8.00000i −0.464991 + 0.464991i
\(297\) −1.00000 −0.0580259
\(298\) 2.00000 + 2.00000i 0.115857 + 0.115857i
\(299\) 0 0
\(300\) −2.00000 −0.115470
\(301\) 8.00000i 0.461112i
\(302\) −22.0000 + 22.0000i −1.26596 + 1.26596i
\(303\) 2.00000 0.114897
\(304\) 16.0000i 0.917663i
\(305\) −12.0000 −0.687118
\(306\) −2.00000 + 2.00000i −0.114332 + 0.114332i
\(307\) 20.0000i 1.14146i −0.821138 0.570730i \(-0.806660\pi\)
0.821138 0.570730i \(-0.193340\pi\)
\(308\) 4.00000 0.227921
\(309\) 10.0000i 0.568880i
\(310\) −6.00000 6.00000i −0.340777 0.340777i
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) −8.00000 8.00000i −0.452911 0.452911i
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 4.00000 + 4.00000i 0.225733 + 0.225733i
\(315\) 2.00000i 0.112687i
\(316\) 12.0000i 0.675053i
\(317\) 34.0000i 1.90963i −0.297200 0.954815i \(-0.596053\pi\)
0.297200 0.954815i \(-0.403947\pi\)
\(318\) 14.0000 14.0000i 0.785081 0.785081i
\(319\) −6.00000 −0.335936
\(320\) −8.00000 −0.447214
\(321\) −20.0000 −1.11629
\(322\) 0 0
\(323\) 8.00000i 0.445132i
\(324\) 2.00000i 0.111111i
\(325\) 4.00000i 0.221880i
\(326\) 4.00000 + 4.00000i 0.221540 + 0.221540i
\(327\) 0 0
\(328\) −4.00000 4.00000i −0.220863 0.220863i
\(329\) 0 0
\(330\) 1.00000 + 1.00000i 0.0550482 + 0.0550482i
\(331\) 12.0000i 0.659580i 0.944054 + 0.329790i \(0.106978\pi\)
−0.944054 + 0.329790i \(0.893022\pi\)
\(332\) 0 0
\(333\) 4.00000i 0.219199i
\(334\) 0 0
\(335\) 4.00000 0.218543
\(336\) 8.00000i 0.436436i
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −3.00000 + 3.00000i −0.163178 + 0.163178i
\(339\) 2.00000i 0.108625i
\(340\) 4.00000 0.216930
\(341\) 6.00000i 0.324918i
\(342\) 4.00000 + 4.00000i 0.216295 + 0.216295i
\(343\) 20.0000 1.07990
\(344\) −8.00000 + 8.00000i −0.431331 + 0.431331i
\(345\) 0 0
\(346\) −18.0000 18.0000i −0.967686 0.967686i
\(347\) 16.0000i 0.858925i −0.903085 0.429463i \(-0.858703\pi\)
0.903085 0.429463i \(-0.141297\pi\)
\(348\) 12.0000i 0.643268i
\(349\) 28.0000i 1.49881i −0.662114 0.749403i \(-0.730341\pi\)
0.662114 0.749403i \(-0.269659\pi\)
\(350\) 2.00000 2.00000i 0.106904 0.106904i
\(351\) −4.00000 −0.213504
\(352\) 4.00000 + 4.00000i 0.213201 + 0.213201i
\(353\) 14.0000 0.745145 0.372572 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) 0 0
\(355\) 8.00000i 0.424596i
\(356\) 12.0000i 0.635999i
\(357\) 4.00000i 0.211702i
\(358\) −24.0000 24.0000i −1.26844 1.26844i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) −2.00000 + 2.00000i −0.105409 + 0.105409i
\(361\) 3.00000 0.157895
\(362\) 20.0000 + 20.0000i 1.05118 + 1.05118i
\(363\) 1.00000i 0.0524864i
\(364\) 16.0000 0.838628
\(365\) 10.0000i 0.523424i
\(366\) −12.0000 + 12.0000i −0.627250 + 0.627250i
\(367\) −34.0000 −1.77479 −0.887393 0.461014i \(-0.847486\pi\)
−0.887393 + 0.461014i \(0.847486\pi\)
\(368\) 0 0
\(369\) −2.00000 −0.104116
\(370\) 4.00000 4.00000i 0.207950 0.207950i
\(371\) 28.0000i 1.45369i
\(372\) −12.0000 −0.622171
\(373\) 24.0000i 1.24267i −0.783544 0.621336i \(-0.786590\pi\)
0.783544 0.621336i \(-0.213410\pi\)
\(374\) −2.00000 2.00000i −0.103418 0.103418i
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 2.00000 + 2.00000i 0.102869 + 0.102869i
\(379\) 36.0000i 1.84920i 0.380945 + 0.924598i \(0.375599\pi\)
−0.380945 + 0.924598i \(0.624401\pi\)
\(380\) 8.00000i 0.410391i
\(381\) 6.00000i 0.307389i
\(382\) 4.00000 4.00000i 0.204658 0.204658i
\(383\) 20.0000 1.02195 0.510976 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(384\) −8.00000 + 8.00000i −0.408248 + 0.408248i
\(385\) −2.00000 −0.101929
\(386\) 18.0000 18.0000i 0.916176 0.916176i
\(387\) 4.00000i 0.203331i
\(388\) 12.0000i 0.609208i
\(389\) 10.0000i 0.507020i −0.967333 0.253510i \(-0.918415\pi\)
0.967333 0.253510i \(-0.0815851\pi\)
\(390\) 4.00000 + 4.00000i 0.202548 + 0.202548i
\(391\) 0 0
\(392\) 6.00000 + 6.00000i 0.303046 + 0.303046i
\(393\) 0 0
\(394\) −18.0000 18.0000i −0.906827 0.906827i
\(395\) 6.00000i 0.301893i
\(396\) 2.00000 0.100504
\(397\) 28.0000i 1.40528i −0.711546 0.702640i \(-0.752005\pi\)
0.711546 0.702640i \(-0.247995\pi\)
\(398\) 2.00000 2.00000i 0.100251 0.100251i
\(399\) −8.00000 −0.400501
\(400\) 4.00000 0.200000
\(401\) −34.0000 −1.69788 −0.848939 0.528490i \(-0.822758\pi\)
−0.848939 + 0.528490i \(0.822758\pi\)
\(402\) 4.00000 4.00000i 0.199502 0.199502i
\(403\) 24.0000i 1.19553i
\(404\) −4.00000 −0.199007
\(405\) 1.00000i 0.0496904i
\(406\) 12.0000 + 12.0000i 0.595550 + 0.595550i
\(407\) −4.00000 −0.198273
\(408\) 4.00000 4.00000i 0.198030 0.198030i
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 2.00000 + 2.00000i 0.0987730 + 0.0987730i
\(411\) 6.00000i 0.295958i
\(412\) 20.0000i 0.985329i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 16.0000 + 16.0000i 0.784465 + 0.784465i
\(417\) −12.0000 −0.587643
\(418\) −4.00000 + 4.00000i −0.195646 + 0.195646i
\(419\) 4.00000i 0.195413i −0.995215 0.0977064i \(-0.968849\pi\)
0.995215 0.0977064i \(-0.0311506\pi\)
\(420\) 4.00000i 0.195180i
\(421\) 12.0000i 0.584844i −0.956289 0.292422i \(-0.905539\pi\)
0.956289 0.292422i \(-0.0944612\pi\)
\(422\) 20.0000 + 20.0000i 0.973585 + 0.973585i
\(423\) 0 0
\(424\) −28.0000 + 28.0000i −1.35980 + 1.35980i
\(425\) −2.00000 −0.0970143
\(426\) −8.00000 8.00000i −0.387601 0.387601i
\(427\) 24.0000i 1.16144i
\(428\) 40.0000 1.93347
\(429\) 4.00000i 0.193122i
\(430\) 4.00000 4.00000i 0.192897 0.192897i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 4.00000i 0.192450i
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 12.0000 12.0000i 0.576018 0.576018i
\(435\) 6.00000i 0.287678i
\(436\) 0 0
\(437\) 0 0
\(438\) 10.0000 + 10.0000i 0.477818 + 0.477818i
\(439\) 14.0000 0.668184 0.334092 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) −2.00000 2.00000i −0.0953463 0.0953463i
\(441\) 3.00000 0.142857
\(442\) −8.00000 8.00000i −0.380521 0.380521i
\(443\) 8.00000i 0.380091i −0.981775 0.190046i \(-0.939136\pi\)
0.981775 0.190046i \(-0.0608636\pi\)
\(444\) 8.00000i 0.379663i
\(445\) 6.00000i 0.284427i
\(446\) 10.0000 10.0000i 0.473514 0.473514i
\(447\) −2.00000 −0.0945968
\(448\) 16.0000i 0.755929i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 1.00000 1.00000i 0.0471405 0.0471405i
\(451\) 2.00000i 0.0941763i
\(452\) 4.00000i 0.188144i
\(453\) 22.0000i 1.03365i
\(454\) 0 0
\(455\) −8.00000 −0.375046
\(456\) −8.00000 8.00000i −0.374634 0.374634i
\(457\) 26.0000 1.21623 0.608114 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) 20.0000 + 20.0000i 0.934539 + 0.934539i
\(459\) 2.00000i 0.0933520i
\(460\) 0 0
\(461\) 10.0000i 0.465746i −0.972507 0.232873i \(-0.925187\pi\)
0.972507 0.232873i \(-0.0748127\pi\)
\(462\) −2.00000 + 2.00000i −0.0930484 + 0.0930484i
\(463\) 2.00000 0.0929479 0.0464739 0.998920i \(-0.485202\pi\)
0.0464739 + 0.998920i \(0.485202\pi\)
\(464\) 24.0000i 1.11417i
\(465\) 6.00000 0.278243
\(466\) −6.00000 + 6.00000i −0.277945 + 0.277945i
\(467\) 32.0000i 1.48078i −0.672176 0.740392i \(-0.734640\pi\)
0.672176 0.740392i \(-0.265360\pi\)
\(468\) 8.00000 0.369800
\(469\) 8.00000i 0.369406i
\(470\) 0 0
\(471\) −4.00000 −0.184310
\(472\) 0 0
\(473\) −4.00000 −0.183920
\(474\) 6.00000 + 6.00000i 0.275589 + 0.275589i
\(475\) 4.00000i 0.183533i
\(476\) 8.00000i 0.366679i
\(477\) 14.0000i 0.641016i
\(478\) 8.00000 8.00000i 0.365911 0.365911i
\(479\) −12.0000 −0.548294 −0.274147 0.961688i \(-0.588395\pi\)
−0.274147 + 0.961688i \(0.588395\pi\)
\(480\) 4.00000 4.00000i 0.182574 0.182574i
\(481\) −16.0000 −0.729537
\(482\) 10.0000 10.0000i 0.455488 0.455488i
\(483\) 0 0
\(484\) 2.00000i 0.0909091i
\(485\) 6.00000i 0.272446i
\(486\) 1.00000 + 1.00000i 0.0453609 + 0.0453609i
\(487\) −22.0000 −0.996915 −0.498458 0.866914i \(-0.666100\pi\)
−0.498458 + 0.866914i \(0.666100\pi\)
\(488\) 24.0000 24.0000i 1.08643 1.08643i
\(489\) −4.00000 −0.180886
\(490\) −3.00000 3.00000i −0.135526 0.135526i
\(491\) 40.0000i 1.80517i 0.430507 + 0.902587i \(0.358335\pi\)
−0.430507 + 0.902587i \(0.641665\pi\)
\(492\) 4.00000 0.180334
\(493\) 12.0000i 0.540453i
\(494\) −16.0000 + 16.0000i −0.719874 + 0.719874i
\(495\) −1.00000 −0.0449467
\(496\) 24.0000 1.07763
\(497\) 16.0000 0.717698
\(498\) 0 0
\(499\) 20.0000i 0.895323i 0.894203 + 0.447661i \(0.147743\pi\)
−0.894203 + 0.447661i \(0.852257\pi\)
\(500\) −2.00000 −0.0894427
\(501\) 0 0
\(502\) −4.00000 4.00000i −0.178529 0.178529i
\(503\) 28.0000 1.24846 0.624229 0.781241i \(-0.285413\pi\)
0.624229 + 0.781241i \(0.285413\pi\)
\(504\) −4.00000 4.00000i −0.178174 0.178174i
\(505\) 2.00000 0.0889988
\(506\) 0 0
\(507\) 3.00000i 0.133235i
\(508\) 12.0000i 0.532414i
\(509\) 42.0000i 1.86162i −0.365507 0.930809i \(-0.619104\pi\)
0.365507 0.930809i \(-0.380896\pi\)
\(510\) −2.00000 + 2.00000i −0.0885615 + 0.0885615i
\(511\) −20.0000 −0.884748
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) −4.00000 −0.176604
\(514\) 22.0000 22.0000i 0.970378 0.970378i
\(515\) 10.0000i 0.440653i
\(516\) 8.00000i 0.352180i
\(517\) 0 0
\(518\) 8.00000 + 8.00000i 0.351500 + 0.351500i
\(519\) 18.0000 0.790112
\(520\) −8.00000 8.00000i −0.350823 0.350823i
\(521\) 42.0000 1.84005 0.920027 0.391856i \(-0.128167\pi\)
0.920027 + 0.391856i \(0.128167\pi\)
\(522\) 6.00000 + 6.00000i 0.262613 + 0.262613i
\(523\) 36.0000i 1.57417i −0.616844 0.787085i \(-0.711589\pi\)
0.616844 0.787085i \(-0.288411\pi\)
\(524\) 0 0
\(525\) 2.00000i 0.0872872i
\(526\) 0 0
\(527\) −12.0000 −0.522728
\(528\) −4.00000 −0.174078
\(529\) −23.0000 −1.00000
\(530\) 14.0000 14.0000i 0.608121 0.608121i
\(531\) 0 0
\(532\) 16.0000 0.693688
\(533\) 8.00000i 0.346518i
\(534\) 6.00000 + 6.00000i 0.259645 + 0.259645i
\(535\) −20.0000 −0.864675
\(536\) −8.00000 + 8.00000i −0.345547 + 0.345547i
\(537\) 24.0000 1.03568
\(538\) −18.0000 18.0000i −0.776035 0.776035i
\(539\) 3.00000i 0.129219i
\(540\) 2.00000i 0.0860663i
\(541\) 16.0000i 0.687894i 0.938989 + 0.343947i \(0.111764\pi\)
−0.938989 + 0.343947i \(0.888236\pi\)
\(542\) −22.0000 + 22.0000i −0.944981 + 0.944981i
\(543\) −20.0000 −0.858282
\(544\) −8.00000 + 8.00000i −0.342997 + 0.342997i
\(545\) 0 0
\(546\) −8.00000 + 8.00000i −0.342368 + 0.342368i
\(547\) 44.0000i 1.88130i −0.339372 0.940652i \(-0.610215\pi\)
0.339372 0.940652i \(-0.389785\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 12.0000i 0.512148i
\(550\) 1.00000 + 1.00000i 0.0426401 + 0.0426401i
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) −12.0000 −0.510292
\(554\) 12.0000 + 12.0000i 0.509831 + 0.509831i
\(555\) 4.00000i 0.169791i
\(556\) 24.0000 1.01783
\(557\) 22.0000i 0.932170i 0.884740 + 0.466085i \(0.154336\pi\)
−0.884740 + 0.466085i \(0.845664\pi\)
\(558\) 6.00000 6.00000i 0.254000 0.254000i
\(559\) −16.0000 −0.676728
\(560\) 8.00000i 0.338062i
\(561\) 2.00000 0.0844401
\(562\) 22.0000 22.0000i 0.928014 0.928014i
\(563\) 16.0000i 0.674320i −0.941447 0.337160i \(-0.890534\pi\)
0.941447 0.337160i \(-0.109466\pi\)
\(564\) 0 0
\(565\) 2.00000i 0.0841406i
\(566\) 4.00000 + 4.00000i 0.168133 + 0.168133i
\(567\) −2.00000 −0.0839921
\(568\) 16.0000 + 16.0000i 0.671345 + 0.671345i
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 4.00000 + 4.00000i 0.167542 + 0.167542i
\(571\) 28.0000i 1.17176i 0.810397 + 0.585882i \(0.199252\pi\)
−0.810397 + 0.585882i \(0.800748\pi\)
\(572\) 8.00000i 0.334497i
\(573\) 4.00000i 0.167102i
\(574\) −4.00000 + 4.00000i −0.166957 + 0.166957i
\(575\) 0 0
\(576\) 8.00000i 0.333333i
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) −13.0000 + 13.0000i −0.540729 + 0.540729i
\(579\) 18.0000i 0.748054i
\(580\) 12.0000i 0.498273i
\(581\) 0 0
\(582\) 6.00000 + 6.00000i 0.248708 + 0.248708i
\(583\) −14.0000 −0.579821
\(584\) −20.0000 20.0000i −0.827606 0.827606i
\(585\) −4.00000 −0.165380
\(586\) 14.0000 + 14.0000i 0.578335 + 0.578335i
\(587\) 28.0000i 1.15568i 0.816149 + 0.577842i \(0.196105\pi\)
−0.816149 + 0.577842i \(0.803895\pi\)
\(588\) −6.00000 −0.247436
\(589\) 24.0000i 0.988903i
\(590\) 0 0
\(591\) 18.0000 0.740421
\(592\) 16.0000i 0.657596i
\(593\) 14.0000 0.574911 0.287456 0.957794i \(-0.407191\pi\)
0.287456 + 0.957794i \(0.407191\pi\)
\(594\) −1.00000 + 1.00000i −0.0410305 + 0.0410305i
\(595\) 4.00000i 0.163984i
\(596\) 4.00000 0.163846
\(597\) 2.00000i 0.0818546i
\(598\) 0 0
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) −2.00000 + 2.00000i −0.0816497 + 0.0816497i
\(601\) −38.0000 −1.55005 −0.775026 0.631929i \(-0.782263\pi\)
−0.775026 + 0.631929i \(0.782263\pi\)
\(602\) 8.00000 + 8.00000i 0.326056 + 0.326056i
\(603\) 4.00000i 0.162893i
\(604\) 44.0000i 1.79033i
\(605\) 1.00000i 0.0406558i
\(606\) 2.00000 2.00000i 0.0812444 0.0812444i
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 16.0000 + 16.0000i 0.648886 + 0.648886i
\(609\) −12.0000 −0.486265
\(610\) −12.0000 + 12.0000i −0.485866 + 0.485866i
\(611\) 0 0
\(612\) 4.00000i 0.161690i
\(613\) 8.00000i 0.323117i 0.986863 + 0.161558i \(0.0516520\pi\)
−0.986863 + 0.161558i \(0.948348\pi\)
\(614\) −20.0000 20.0000i −0.807134 0.807134i
\(615\) −2.00000 −0.0806478
\(616\) 4.00000 4.00000i 0.161165 0.161165i
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) −10.0000 10.0000i −0.402259 0.402259i
\(619\) 44.0000i 1.76851i −0.467005 0.884255i \(-0.654667\pi\)
0.467005 0.884255i \(-0.345333\pi\)
\(620\) −12.0000 −0.481932
\(621\) 0 0
\(622\) 20.0000 20.0000i 0.801927 0.801927i
\(623\) −12.0000 −0.480770
\(624\) −16.0000 −0.640513
\(625\) 1.00000 0.0400000
\(626\) 6.00000 6.00000i 0.239808 0.239808i
\(627\) 4.00000i 0.159745i
\(628\) 8.00000 0.319235
\(629\) 8.00000i 0.318981i
\(630\) 2.00000 + 2.00000i 0.0796819 + 0.0796819i
\(631\) 30.0000 1.19428 0.597141 0.802137i \(-0.296303\pi\)
0.597141 + 0.802137i \(0.296303\pi\)
\(632\) −12.0000 12.0000i −0.477334 0.477334i
\(633\) −20.0000 −0.794929
\(634\) −34.0000 34.0000i −1.35031 1.35031i
\(635\) 6.00000i 0.238103i
\(636\) 28.0000i 1.11027i
\(637\) 12.0000i 0.475457i
\(638\) −6.00000 + 6.00000i −0.237542 + 0.237542i
\(639\) 8.00000 0.316475
\(640\) −8.00000 + 8.00000i −0.316228 + 0.316228i
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −20.0000 + 20.0000i −0.789337 + 0.789337i
\(643\) 28.0000i 1.10421i 0.833774 + 0.552106i \(0.186176\pi\)
−0.833774 + 0.552106i \(0.813824\pi\)
\(644\) 0 0
\(645\) 4.00000i 0.157500i
\(646\) −8.00000 8.00000i −0.314756 0.314756i
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) −2.00000 2.00000i −0.0785674 0.0785674i
\(649\) 0 0
\(650\) 4.00000 + 4.00000i 0.156893 + 0.156893i
\(651\) 12.0000i 0.470317i
\(652\) 8.00000 0.313304
\(653\) 26.0000i 1.01746i 0.860927 + 0.508729i \(0.169885\pi\)
−0.860927 + 0.508729i \(0.830115\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −8.00000 −0.312348
\(657\) −10.0000 −0.390137
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 2.00000 0.0778499
\(661\) 8.00000i 0.311164i 0.987823 + 0.155582i \(0.0497253\pi\)
−0.987823 + 0.155582i \(0.950275\pi\)
\(662\) 12.0000 + 12.0000i 0.466393 + 0.466393i
\(663\) 8.00000 0.310694
\(664\) 0 0
\(665\) −8.00000 −0.310227
\(666\) 4.00000 + 4.00000i 0.154997 + 0.154997i
\(667\) 0 0
\(668\) 0 0
\(669\) 10.0000i 0.386622i
\(670\) 4.00000 4.00000i 0.154533 0.154533i
\(671\) 12.0000 0.463255
\(672\) 8.00000 + 8.00000i 0.308607 + 0.308607i
\(673\) 6.00000 0.231283 0.115642 0.993291i \(-0.463108\pi\)
0.115642 + 0.993291i \(0.463108\pi\)
\(674\) −2.00000 + 2.00000i −0.0770371 + 0.0770371i
\(675\) 1.00000i 0.0384900i
\(676\) 6.00000i 0.230769i
\(677\) 18.0000i 0.691796i 0.938272 + 0.345898i \(0.112426\pi\)
−0.938272 + 0.345898i \(0.887574\pi\)
\(678\) −2.00000 2.00000i −0.0768095 0.0768095i
\(679\) −12.0000 −0.460518
\(680\) 4.00000 4.00000i 0.153393 0.153393i
\(681\) 0 0
\(682\) 6.00000 + 6.00000i 0.229752 + 0.229752i
\(683\) 8.00000i 0.306111i 0.988218 + 0.153056i \(0.0489114\pi\)
−0.988218 + 0.153056i \(0.951089\pi\)
\(684\) 8.00000 0.305888
\(685\) 6.00000i 0.229248i
\(686\) 20.0000 20.0000i 0.763604 0.763604i
\(687\) −20.0000 −0.763048
\(688\) 16.0000i 0.609994i
\(689\) −56.0000 −2.13343
\(690\) 0 0
\(691\) 36.0000i 1.36950i −0.728776 0.684752i \(-0.759910\pi\)
0.728776 0.684752i \(-0.240090\pi\)
\(692\) −36.0000 −1.36851
\(693\) 2.00000i 0.0759737i
\(694\) −16.0000 16.0000i −0.607352 0.607352i
\(695\) −12.0000 −0.455186
\(696\) −12.0000 12.0000i −0.454859 0.454859i
\(697\) 4.00000 0.151511
\(698\) −28.0000 28.0000i −1.05982 1.05982i
\(699\) 6.00000i 0.226941i
\(700\) 4.00000i 0.151186i
\(701\) 34.0000i 1.28416i 0.766637 + 0.642081i \(0.221929\pi\)
−0.766637 + 0.642081i \(0.778071\pi\)
\(702\) −4.00000 + 4.00000i −0.150970 + 0.150970i
\(703\) −16.0000 −0.603451
\(704\) 8.00000 0.301511
\(705\) 0 0
\(706\) 14.0000 14.0000i 0.526897 0.526897i
\(707\) 4.00000i 0.150435i
\(708\) 0 0
\(709\) 52.0000i 1.95290i 0.215742 + 0.976450i \(0.430783\pi\)
−0.215742 + 0.976450i \(0.569217\pi\)
\(710\) −8.00000 8.00000i −0.300235 0.300235i
\(711\) −6.00000 −0.225018
\(712\) −12.0000 12.0000i −0.449719 0.449719i
\(713\) 0 0
\(714\) −4.00000 4.00000i −0.149696 0.149696i
\(715\) 4.00000i 0.149592i
\(716\) −48.0000 −1.79384
\(717\) 8.00000i 0.298765i
\(718\) −12.0000 + 12.0000i −0.447836 + 0.447836i
\(719\) 48.0000 1.79010 0.895049 0.445968i \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) 4.00000i 0.149071i
\(721\) 20.0000 0.744839
\(722\) 3.00000 3.00000i 0.111648 0.111648i
\(723\) 10.0000i 0.371904i
\(724\) 40.0000 1.48659
\(725\) 6.00000i 0.222834i
\(726\) −1.00000 1.00000i −0.0371135 0.0371135i
\(727\) −6.00000 −0.222528 −0.111264 0.993791i \(-0.535490\pi\)
−0.111264 + 0.993791i \(0.535490\pi\)
\(728\) 16.0000 16.0000i 0.592999 0.592999i
\(729\) −1.00000 −0.0370370
\(730\) 10.0000 + 10.0000i 0.370117 + 0.370117i
\(731\) 8.00000i 0.295891i
\(732\) 24.0000i 0.887066i
\(733\) 20.0000i 0.738717i 0.929287 + 0.369358i \(0.120423\pi\)
−0.929287 + 0.369358i \(0.879577\pi\)
\(734\) −34.0000 + 34.0000i −1.25496 + 1.25496i
\(735\) 3.00000 0.110657
\(736\) 0 0
\(737\) −4.00000 −0.147342
\(738\) −2.00000 + 2.00000i −0.0736210 + 0.0736210i
\(739\) 28.0000i 1.03000i −0.857191 0.514998i \(-0.827793\pi\)
0.857191 0.514998i \(-0.172207\pi\)
\(740\) 8.00000i 0.294086i
\(741\) 16.0000i 0.587775i
\(742\) 28.0000 + 28.0000i 1.02791 + 1.02791i
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) −12.0000 + 12.0000i −0.439941 + 0.439941i
\(745\) −2.00000 −0.0732743
\(746\) −24.0000 24.0000i −0.878702 0.878702i
\(747\) 0 0
\(748\) −4.00000 −0.146254
\(749\) 40.0000i 1.46157i
\(750\) 1.00000 1.00000i 0.0365148 0.0365148i
\(751\) 10.0000 0.364905 0.182453 0.983215i \(-0.441596\pi\)
0.182453 + 0.983215i \(0.441596\pi\)
\(752\) 0 0
\(753\) 4.00000 0.145768
\(754\) −24.0000 + 24.0000i −0.874028 + 0.874028i
\(755\) 22.0000i 0.800662i
\(756\) 4.00000 0.145479
\(757\) 16.0000i 0.581530i −0.956795 0.290765i \(-0.906090\pi\)
0.956795 0.290765i \(-0.0939098\pi\)
\(758\) 36.0000 + 36.0000i 1.30758 + 1.30758i
\(759\) 0 0
\(760\) −8.00000 8.00000i −0.290191 0.290191i
\(761\) −22.0000 −0.797499 −0.398750 0.917060i \(-0.630556\pi\)
−0.398750 + 0.917060i \(0.630556\pi\)
\(762\) 6.00000 + 6.00000i 0.217357 + 0.217357i
\(763\) 0 0
\(764\) 8.00000i 0.289430i
\(765\) 2.00000i 0.0723102i
\(766\) 20.0000 20.0000i 0.722629 0.722629i
\(767\) 0 0
\(768\) 16.0000i 0.577350i
\(769\) 18.0000 0.649097 0.324548 0.945869i \(-0.394788\pi\)
0.324548 + 0.945869i \(0.394788\pi\)
\(770\) −2.00000 + 2.00000i −0.0720750 + 0.0720750i
\(771\) 22.0000i 0.792311i
\(772\) 36.0000i 1.29567i
\(773\) 46.0000i 1.65451i −0.561830 0.827253i \(-0.689903\pi\)
0.561830 0.827253i \(-0.310097\pi\)
\(774\) 4.00000 + 4.00000i 0.143777 + 0.143777i
\(775\) 6.00000 0.215526
\(776\) −12.0000 12.0000i −0.430775 0.430775i
\(777\) −8.00000 −0.286998
\(778\) −10.0000 10.0000i −0.358517 0.358517i
\(779\) 8.00000i 0.286630i
\(780\) 8.00000 0.286446
\(781\) 8.00000i 0.286263i
\(782\) 0 0
\(783\) −6.00000 −0.214423
\(784\) 12.0000 0.428571
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) 52.0000i 1.85360i −0.375555 0.926800i \(-0.622548\pi\)
0.375555 0.926800i \(-0.377452\pi\)
\(788\) −36.0000 −1.28245
\(789\) 0 0
\(790\) 6.00000 + 6.00000i 0.213470 + 0.213470i
\(791\) 4.00000 0.142224
\(792\) 2.00000 2.00000i 0.0710669 0.0710669i
\(793\) 48.0000 1.70453
\(794\) −28.0000 28.0000i −0.993683 0.993683i
\(795\) 14.0000i 0.496529i
\(796\) 4.00000i 0.141776i
\(797\) 14.0000i 0.495905i −0.968772 0.247953i \(-0.920242\pi\)
0.968772 0.247953i \(-0.0797578\pi\)
\(798\) −8.00000 + 8.00000i −0.283197 + 0.283197i
\(799\) 0 0
\(800\) 4.00000 4.00000i 0.141421 0.141421i
\(801\) −6.00000 −0.212000
\(802\) −34.0000 + 34.0000i −1.20058 + 1.20058i
\(803\) 10.0000i 0.352892i
\(804\) 8.00000i 0.282138i
\(805\) 0 0
\(806\) 24.0000 + 24.0000i 0.845364 + 0.845364i
\(807\) 18.0000 0.633630
\(808\) −4.00000 + 4.00000i −0.140720 + 0.140720i
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 1.00000 + 1.00000i 0.0351364 + 0.0351364i
\(811\) 4.00000i 0.140459i −0.997531 0.0702295i \(-0.977627\pi\)
0.997531 0.0702295i \(-0.0223732\pi\)
\(812\) 24.0000 0.842235
\(813\) 22.0000i 0.771574i
\(814\) −4.00000 + 4.00000i −0.140200 + 0.140200i
\(815\) −4.00000 −0.140114
\(816\) 8.00000i 0.280056i
\(817\) −16.0000 −0.559769
\(818\) 10.0000 10.0000i 0.349642 0.349642i
\(819\) 8.00000i 0.279543i
\(820\) 4.00000 0.139686
\(821\) 54.0000i 1.88461i 0.334751 + 0.942306i \(0.391348\pi\)
−0.334751 + 0.942306i \(0.608652\pi\)
\(822\) 6.00000 + 6.00000i 0.209274 + 0.209274i
\(823\) 10.0000 0.348578 0.174289 0.984695i \(-0.444237\pi\)
0.174289 + 0.984695i \(0.444237\pi\)
\(824\) 20.0000 + 20.0000i 0.696733 + 0.696733i
\(825\) −1.00000 −0.0348155
\(826\) 0 0
\(827\) 20.0000i 0.695468i −0.937593 0.347734i \(-0.886951\pi\)
0.937593 0.347734i \(-0.113049\pi\)
\(828\) 0 0
\(829\) 28.0000i 0.972480i −0.873825 0.486240i \(-0.838368\pi\)
0.873825 0.486240i \(-0.161632\pi\)
\(830\) 0 0
\(831\) −12.0000 −0.416275
\(832\) 32.0000 1.10940
\(833\) −6.00000 −0.207888
\(834\) −12.0000 + 12.0000i −0.415526 + 0.415526i
\(835\) 0 0
\(836\) 8.00000i 0.276686i
\(837\) 6.00000i 0.207390i
\(838\) −4.00000 4.00000i −0.138178 0.138178i
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) −4.00000 4.00000i −0.138013 0.138013i
\(841\) −7.00000 −0.241379
\(842\) −12.0000 12.0000i −0.413547 0.413547i
\(843\) 22.0000i 0.757720i
\(844\) 40.0000 1.37686
\(845\) 3.00000i 0.103203i
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) 56.0000i 1.92305i
\(849\) −4.00000 −0.137280
\(850\) −2.00000 + 2.00000i −0.0685994 + 0.0685994i
\(851\) 0 0
\(852\) −16.0000 −0.548151
\(853\) 16.0000i 0.547830i −0.961754 0.273915i \(-0.911681\pi\)
0.961754 0.273915i \(-0.0883186\pi\)
\(854\) −24.0000 24.0000i −0.821263 0.821263i
\(855\) −4.00000 −0.136797
\(856\) 40.0000 40.0000i 1.36717 1.36717i
\(857\) 38.0000 1.29806 0.649028 0.760765i \(-0.275176\pi\)
0.649028 + 0.760765i \(0.275176\pi\)
\(858\) −4.00000 4.00000i −0.136558 0.136558i
\(859\) 20.0000i 0.682391i −0.939992 0.341196i \(-0.889168\pi\)
0.939992 0.341196i \(-0.110832\pi\)
\(860\) 8.00000i 0.272798i
\(861\) 4.00000i 0.136320i
\(862\) 12.0000 12.0000i 0.408722 0.408722i
\(863\) 28.0000 0.953131 0.476566 0.879139i \(-0.341881\pi\)
0.476566 + 0.879139i \(0.341881\pi\)
\(864\) 4.00000 + 4.00000i 0.136083 + 0.136083i
\(865\) 18.0000 0.612018
\(866\) −2.00000 + 2.00000i −0.0679628 + 0.0679628i
\(867\) 13.0000i 0.441503i
\(868\) 24.0000i 0.814613i
\(869\) 6.00000i 0.203536i
\(870\) 6.00000 + 6.00000i 0.203419 + 0.203419i
\(871\) −16.0000 −0.542139
\(872\) 0 0
\(873\) −6.00000 −0.203069
\(874\) 0 0
\(875\) 2.00000i 0.0676123i
\(876\) 20.0000 0.675737
\(877\) 56.0000i 1.89099i 0.325643 + 0.945493i \(0.394419\pi\)
−0.325643 + 0.945493i \(0.605581\pi\)
\(878\) 14.0000 14.0000i 0.472477 0.472477i
\(879\) −14.0000 −0.472208
\(880\) −4.00000 −0.134840
\(881\) −38.0000 −1.28025 −0.640126 0.768270i \(-0.721118\pi\)
−0.640126 + 0.768270i \(0.721118\pi\)
\(882\) 3.00000 3.00000i 0.101015 0.101015i
\(883\) 36.0000i 1.21150i −0.795656 0.605748i \(-0.792874\pi\)
0.795656 0.605748i \(-0.207126\pi\)
\(884\) −16.0000 −0.538138
\(885\) 0 0
\(886\) −8.00000 8.00000i −0.268765 0.268765i
\(887\) 24.0000 0.805841 0.402921 0.915235i \(-0.367995\pi\)
0.402921 + 0.915235i \(0.367995\pi\)
\(888\) −8.00000 8.00000i −0.268462 0.268462i
\(889\) −12.0000 −0.402467
\(890\) 6.00000 + 6.00000i 0.201120 + 0.201120i
\(891\) 1.00000i 0.0335013i
\(892\) 20.0000i 0.669650i
\(893\) 0 0
\(894\) −2.00000 + 2.00000i −0.0668900 + 0.0668900i
\(895\) 24.0000 0.802232
\(896\) −16.0000 16.0000i −0.534522 0.534522i
\(897\) 0 0
\(898\) 6.00000 6.00000i 0.200223 0.200223i
\(899\) 36.0000i 1.20067i
\(900\) 2.00000i 0.0666667i
\(901\) 28.0000i 0.932815i
\(902\) −2.00000 2.00000i −0.0665927 0.0665927i
\(903\) −8.00000 −0.266223
\(904\) 4.00000 + 4.00000i 0.133038 + 0.133038i
\(905\) −20.0000 −0.664822
\(906\) −22.0000 22.0000i −0.730901 0.730901i
\(907\) 20.0000i 0.664089i 0.943264 + 0.332045i \(0.107738\pi\)
−0.943264 + 0.332045i \(0.892262\pi\)
\(908\) 0 0
\(909\) 2.00000i 0.0663358i
\(910\) −8.00000 + 8.00000i −0.265197 + 0.265197i
\(911\) 20.0000 0.662630 0.331315 0.943520i \(-0.392508\pi\)
0.331315 + 0.943520i \(0.392508\pi\)
\(912\) −16.0000 −0.529813
\(913\) 0 0
\(914\) 26.0000 26.0000i 0.860004 0.860004i
\(915\) 12.0000i 0.396708i
\(916\) 40.0000 1.32164
\(917\) 0 0
\(918\) −2.00000 2.00000i −0.0660098 0.0660098i
\(919\) 10.0000 0.329870 0.164935 0.986304i \(-0.447259\pi\)
0.164935 + 0.986304i \(0.447259\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) −10.0000 10.0000i −0.329332 0.329332i
\(923\) 32.0000i 1.05329i
\(924\) 4.00000i 0.131590i
\(925\) 4.00000i 0.131519i
\(926\) 2.00000 2.00000i 0.0657241 0.0657241i
\(927\) 10.0000 0.328443
\(928\) 24.0000 + 24.0000i 0.787839 + 0.787839i
\(929\) 6.00000 0.196854 0.0984268 0.995144i \(-0.468619\pi\)
0.0984268 + 0.995144i \(0.468619\pi\)
\(930\) 6.00000 6.00000i 0.196748 0.196748i
\(931\) 12.0000i 0.393284i
\(932\) 12.0000i 0.393073i
\(933\) 20.0000i 0.654771i
\(934\) −32.0000 32.0000i −1.04707 1.04707i
\(935\) 2.00000 0.0654070
\(936\) 8.00000 8.00000i 0.261488 0.261488i
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) 8.00000 + 8.00000i 0.261209 + 0.261209i
\(939\) 6.00000i 0.195803i
\(940\) 0 0
\(941\) 6.00000i 0.195594i 0.995206 + 0.0977972i \(0.0311797\pi\)
−0.995206 + 0.0977972i \(0.968820\pi\)
\(942\) −4.00000 + 4.00000i −0.130327 + 0.130327i
\(943\) 0 0
\(944\) 0 0
\(945\) −2.00000 −0.0650600
\(946\) −4.00000 + 4.00000i −0.130051 + 0.130051i
\(947\) 52.0000i 1.68977i −0.534946 0.844886i \(-0.679668\pi\)
0.534946 0.844886i \(-0.320332\pi\)
\(948\) 12.0000 0.389742
\(949\) 40.0000i 1.29845i
\(950\) 4.00000 + 4.00000i 0.129777 + 0.129777i
\(951\) 34.0000 1.10253
\(952\) 8.00000 + 8.00000i 0.259281 + 0.259281i
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) 14.0000 + 14.0000i 0.453267 + 0.453267i
\(955\) 4.00000i 0.129437i
\(956\) 16.0000i 0.517477i
\(957\) 6.00000i 0.193952i
\(958\) −12.0000 + 12.0000i −0.387702 + 0.387702i
\(959\) −12.0000 −0.387500
\(960\) 8.00000i 0.258199i
\(961\) 5.00000 0.161290
\(962\) −16.0000 + 16.0000i −0.515861 + 0.515861i
\(963\) 20.0000i 0.644491i
\(964\) 20.0000i 0.644157i
\(965\) 18.0000i 0.579441i
\(966\) 0 0
\(967\) 18.0000 0.578841 0.289420 0.957202i \(-0.406537\pi\)
0.289420 + 0.957202i \(0.406537\pi\)
\(968\) 2.00000 + 2.00000i 0.0642824 + 0.0642824i
\(969\) 8.00000 0.256997
\(970\) 6.00000 + 6.00000i 0.192648 + 0.192648i
\(971\) 12.0000i 0.385098i 0.981287 + 0.192549i \(0.0616755\pi\)
−0.981287 + 0.192549i \(0.938325\pi\)
\(972\) 2.00000 0.0641500
\(973\) 24.0000i 0.769405i
\(974\) −22.0000 + 22.0000i −0.704925 + 0.704925i
\(975\) −4.00000 −0.128103
\(976\) 48.0000i 1.53644i
\(977\) 58.0000 1.85558 0.927792 0.373097i \(-0.121704\pi\)
0.927792 + 0.373097i \(0.121704\pi\)
\(978\) −4.00000 + 4.00000i −0.127906 + 0.127906i
\(979\) 6.00000i 0.191761i
\(980\) −6.00000 −0.191663
\(981\) 0 0
\(982\) 40.0000 + 40.0000i 1.27645 + 1.27645i
\(983\) 4.00000 0.127580 0.0637901 0.997963i \(-0.479681\pi\)
0.0637901 + 0.997963i \(0.479681\pi\)
\(984\) 4.00000 4.00000i 0.127515 0.127515i
\(985\) 18.0000 0.573528
\(986\) −12.0000 12.0000i −0.382158 0.382158i
\(987\) 0 0
\(988\) 32.0000i 1.01806i
\(989\) 0 0
\(990\) −1.00000 + 1.00000i −0.0317821 + 0.0317821i
\(991\) −14.0000 −0.444725 −0.222362 0.974964i \(-0.571377\pi\)
−0.222362 + 0.974964i \(0.571377\pi\)
\(992\) 24.0000 24.0000i 0.762001 0.762001i
\(993\) −12.0000 −0.380808
\(994\) 16.0000 16.0000i 0.507489 0.507489i
\(995\) 2.00000i 0.0634043i
\(996\) 0 0
\(997\) 40.0000i 1.26681i 0.773819 + 0.633406i \(0.218344\pi\)
−0.773819 + 0.633406i \(0.781656\pi\)
\(998\) 20.0000 + 20.0000i 0.633089 + 0.633089i
\(999\) −4.00000 −0.126554
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 1320.2.w.a.661.1 2
4.3 odd 2 5280.2.w.b.2641.1 2
8.3 odd 2 5280.2.w.b.2641.2 2
8.5 even 2 inner 1320.2.w.a.661.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1320.2.w.a.661.1 2 1.1 even 1 trivial
1320.2.w.a.661.2 yes 2 8.5 even 2 inner
5280.2.w.b.2641.1 2 4.3 odd 2
5280.2.w.b.2641.2 2 8.3 odd 2