Properties

Label 840.2.j.c.589.2
Level $840$
Weight $2$
Character 840.589
Analytic conductor $6.707$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [840,2,Mod(589,840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(840, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 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("840.589");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 840.j (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: \(6.70743376979\)
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 589.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 840.589
Dual form 840.2.j.c.589.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} -1.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} -1.00000 q^{3} +2.00000i q^{4} +(2.00000 + 1.00000i) q^{5} +(-1.00000 - 1.00000i) q^{6} -1.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +1.00000 q^{9} +(1.00000 + 3.00000i) q^{10} -2.00000i q^{12} +6.00000 q^{13} +(1.00000 - 1.00000i) q^{14} +(-2.00000 - 1.00000i) q^{15} -4.00000 q^{16} +2.00000i q^{17} +(1.00000 + 1.00000i) q^{18} +4.00000i q^{19} +(-2.00000 + 4.00000i) q^{20} +1.00000i q^{21} +4.00000i q^{23} +(2.00000 - 2.00000i) q^{24} +(3.00000 + 4.00000i) q^{25} +(6.00000 + 6.00000i) q^{26} -1.00000 q^{27} +2.00000 q^{28} -6.00000i q^{29} +(-1.00000 - 3.00000i) q^{30} -8.00000 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-2.00000 + 2.00000i) q^{34} +(1.00000 - 2.00000i) q^{35} +2.00000i q^{36} +2.00000 q^{37} +(-4.00000 + 4.00000i) q^{38} -6.00000 q^{39} +(-6.00000 + 2.00000i) q^{40} -8.00000 q^{41} +(-1.00000 + 1.00000i) q^{42} +6.00000 q^{43} +(2.00000 + 1.00000i) q^{45} +(-4.00000 + 4.00000i) q^{46} +2.00000i q^{47} +4.00000 q^{48} -1.00000 q^{49} +(-1.00000 + 7.00000i) q^{50} -2.00000i q^{51} +12.0000i q^{52} +6.00000 q^{53} +(-1.00000 - 1.00000i) q^{54} +(2.00000 + 2.00000i) q^{56} -4.00000i q^{57} +(6.00000 - 6.00000i) q^{58} -6.00000i q^{59} +(2.00000 - 4.00000i) q^{60} +10.0000i q^{61} +(-8.00000 - 8.00000i) q^{62} -1.00000i q^{63} -8.00000i q^{64} +(12.0000 + 6.00000i) q^{65} +2.00000 q^{67} -4.00000 q^{68} -4.00000i q^{69} +(3.00000 - 1.00000i) q^{70} -8.00000 q^{71} +(-2.00000 + 2.00000i) q^{72} -6.00000i q^{73} +(2.00000 + 2.00000i) q^{74} +(-3.00000 - 4.00000i) q^{75} -8.00000 q^{76} +(-6.00000 - 6.00000i) q^{78} +10.0000 q^{79} +(-8.00000 - 4.00000i) q^{80} +1.00000 q^{81} +(-8.00000 - 8.00000i) q^{82} -4.00000 q^{83} -2.00000 q^{84} +(-2.00000 + 4.00000i) q^{85} +(6.00000 + 6.00000i) q^{86} +6.00000i q^{87} +(1.00000 + 3.00000i) q^{90} -6.00000i q^{91} -8.00000 q^{92} +8.00000 q^{93} +(-2.00000 + 2.00000i) q^{94} +(-4.00000 + 8.00000i) q^{95} +(4.00000 + 4.00000i) q^{96} +2.00000i q^{97} +(-1.00000 - 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 2 q^{3} + 4 q^{5} - 2 q^{6} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 2 q^{3} + 4 q^{5} - 2 q^{6} - 4 q^{8} + 2 q^{9} + 2 q^{10} + 12 q^{13} + 2 q^{14} - 4 q^{15} - 8 q^{16} + 2 q^{18} - 4 q^{20} + 4 q^{24} + 6 q^{25} + 12 q^{26} - 2 q^{27} + 4 q^{28} - 2 q^{30} - 16 q^{31} - 8 q^{32} - 4 q^{34} + 2 q^{35} + 4 q^{37} - 8 q^{38} - 12 q^{39} - 12 q^{40} - 16 q^{41} - 2 q^{42} + 12 q^{43} + 4 q^{45} - 8 q^{46} + 8 q^{48} - 2 q^{49} - 2 q^{50} + 12 q^{53} - 2 q^{54} + 4 q^{56} + 12 q^{58} + 4 q^{60} - 16 q^{62} + 24 q^{65} + 4 q^{67} - 8 q^{68} + 6 q^{70} - 16 q^{71} - 4 q^{72} + 4 q^{74} - 6 q^{75} - 16 q^{76} - 12 q^{78} + 20 q^{79} - 16 q^{80} + 2 q^{81} - 16 q^{82} - 8 q^{83} - 4 q^{84} - 4 q^{85} + 12 q^{86} + 2 q^{90} - 16 q^{92} + 16 q^{93} - 4 q^{94} - 8 q^{95} + 8 q^{96} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(281\) \(337\) \(421\) \(631\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\) \(1\)

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
\(3\) −1.00000 −0.577350
\(4\) 2.00000i 1.00000i
\(5\) 2.00000 + 1.00000i 0.894427 + 0.447214i
\(6\) −1.00000 1.00000i −0.408248 0.408248i
\(7\) 1.00000i 0.377964i
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 1.00000 0.333333
\(10\) 1.00000 + 3.00000i 0.316228 + 0.948683i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 2.00000i 0.577350i
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 1.00000 1.00000i 0.267261 0.267261i
\(15\) −2.00000 1.00000i −0.516398 0.258199i
\(16\) −4.00000 −1.00000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 1.00000 + 1.00000i 0.235702 + 0.235702i
\(19\) 4.00000i 0.917663i 0.888523 + 0.458831i \(0.151732\pi\)
−0.888523 + 0.458831i \(0.848268\pi\)
\(20\) −2.00000 + 4.00000i −0.447214 + 0.894427i
\(21\) 1.00000i 0.218218i
\(22\) 0 0
\(23\) 4.00000i 0.834058i 0.908893 + 0.417029i \(0.136929\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(24\) 2.00000 2.00000i 0.408248 0.408248i
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 6.00000 + 6.00000i 1.17670 + 1.17670i
\(27\) −1.00000 −0.192450
\(28\) 2.00000 0.377964
\(29\) 6.00000i 1.11417i −0.830455 0.557086i \(-0.811919\pi\)
0.830455 0.557086i \(-0.188081\pi\)
\(30\) −1.00000 3.00000i −0.182574 0.547723i
\(31\) −8.00000 −1.43684 −0.718421 0.695608i \(-0.755135\pi\)
−0.718421 + 0.695608i \(0.755135\pi\)
\(32\) −4.00000 4.00000i −0.707107 0.707107i
\(33\) 0 0
\(34\) −2.00000 + 2.00000i −0.342997 + 0.342997i
\(35\) 1.00000 2.00000i 0.169031 0.338062i
\(36\) 2.00000i 0.333333i
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −4.00000 + 4.00000i −0.648886 + 0.648886i
\(39\) −6.00000 −0.960769
\(40\) −6.00000 + 2.00000i −0.948683 + 0.316228i
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) −1.00000 + 1.00000i −0.154303 + 0.154303i
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 0 0
\(45\) 2.00000 + 1.00000i 0.298142 + 0.149071i
\(46\) −4.00000 + 4.00000i −0.589768 + 0.589768i
\(47\) 2.00000i 0.291730i 0.989305 + 0.145865i \(0.0465965\pi\)
−0.989305 + 0.145865i \(0.953403\pi\)
\(48\) 4.00000 0.577350
\(49\) −1.00000 −0.142857
\(50\) −1.00000 + 7.00000i −0.141421 + 0.989949i
\(51\) 2.00000i 0.280056i
\(52\) 12.0000i 1.66410i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −1.00000 1.00000i −0.136083 0.136083i
\(55\) 0 0
\(56\) 2.00000 + 2.00000i 0.267261 + 0.267261i
\(57\) 4.00000i 0.529813i
\(58\) 6.00000 6.00000i 0.787839 0.787839i
\(59\) 6.00000i 0.781133i −0.920575 0.390567i \(-0.872279\pi\)
0.920575 0.390567i \(-0.127721\pi\)
\(60\) 2.00000 4.00000i 0.258199 0.516398i
\(61\) 10.0000i 1.28037i 0.768221 + 0.640184i \(0.221142\pi\)
−0.768221 + 0.640184i \(0.778858\pi\)
\(62\) −8.00000 8.00000i −1.01600 1.01600i
\(63\) 1.00000i 0.125988i
\(64\) 8.00000i 1.00000i
\(65\) 12.0000 + 6.00000i 1.48842 + 0.744208i
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) −4.00000 −0.485071
\(69\) 4.00000i 0.481543i
\(70\) 3.00000 1.00000i 0.358569 0.119523i
\(71\) −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
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 2.00000 + 2.00000i 0.232495 + 0.232495i
\(75\) −3.00000 4.00000i −0.346410 0.461880i
\(76\) −8.00000 −0.917663
\(77\) 0 0
\(78\) −6.00000 6.00000i −0.679366 0.679366i
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) −8.00000 4.00000i −0.894427 0.447214i
\(81\) 1.00000 0.111111
\(82\) −8.00000 8.00000i −0.883452 0.883452i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) −2.00000 −0.218218
\(85\) −2.00000 + 4.00000i −0.216930 + 0.433861i
\(86\) 6.00000 + 6.00000i 0.646997 + 0.646997i
\(87\) 6.00000i 0.643268i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 1.00000 + 3.00000i 0.105409 + 0.316228i
\(91\) 6.00000i 0.628971i
\(92\) −8.00000 −0.834058
\(93\) 8.00000 0.829561
\(94\) −2.00000 + 2.00000i −0.206284 + 0.206284i
\(95\) −4.00000 + 8.00000i −0.410391 + 0.820783i
\(96\) 4.00000 + 4.00000i 0.408248 + 0.408248i
\(97\) 2.00000i 0.203069i 0.994832 + 0.101535i \(0.0323753\pi\)
−0.994832 + 0.101535i \(0.967625\pi\)
\(98\) −1.00000 1.00000i −0.101015 0.101015i
\(99\) 0 0
\(100\) −8.00000 + 6.00000i −0.800000 + 0.600000i
\(101\) 10.0000i 0.995037i 0.867453 + 0.497519i \(0.165755\pi\)
−0.867453 + 0.497519i \(0.834245\pi\)
\(102\) 2.00000 2.00000i 0.198030 0.198030i
\(103\) 16.0000i 1.57653i −0.615338 0.788263i \(-0.710980\pi\)
0.615338 0.788263i \(-0.289020\pi\)
\(104\) −12.0000 + 12.0000i −1.17670 + 1.17670i
\(105\) −1.00000 + 2.00000i −0.0975900 + 0.195180i
\(106\) 6.00000 + 6.00000i 0.582772 + 0.582772i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 2.00000i 0.192450i
\(109\) 16.0000i 1.53252i −0.642529 0.766261i \(-0.722115\pi\)
0.642529 0.766261i \(-0.277885\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 4.00000i 0.377964i
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 4.00000 4.00000i 0.374634 0.374634i
\(115\) −4.00000 + 8.00000i −0.373002 + 0.746004i
\(116\) 12.0000 1.11417
\(117\) 6.00000 0.554700
\(118\) 6.00000 6.00000i 0.552345 0.552345i
\(119\) 2.00000 0.183340
\(120\) 6.00000 2.00000i 0.547723 0.182574i
\(121\) 11.0000 1.00000
\(122\) −10.0000 + 10.0000i −0.905357 + 0.905357i
\(123\) 8.00000 0.721336
\(124\) 16.0000i 1.43684i
\(125\) 2.00000 + 11.0000i 0.178885 + 0.983870i
\(126\) 1.00000 1.00000i 0.0890871 0.0890871i
\(127\) 8.00000i 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) 8.00000 8.00000i 0.707107 0.707107i
\(129\) −6.00000 −0.528271
\(130\) 6.00000 + 18.0000i 0.526235 + 1.57870i
\(131\) 10.0000i 0.873704i −0.899533 0.436852i \(-0.856093\pi\)
0.899533 0.436852i \(-0.143907\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 2.00000 + 2.00000i 0.172774 + 0.172774i
\(135\) −2.00000 1.00000i −0.172133 0.0860663i
\(136\) −4.00000 4.00000i −0.342997 0.342997i
\(137\) 18.0000i 1.53784i −0.639343 0.768922i \(-0.720793\pi\)
0.639343 0.768922i \(-0.279207\pi\)
\(138\) 4.00000 4.00000i 0.340503 0.340503i
\(139\) 16.0000i 1.35710i −0.734553 0.678551i \(-0.762608\pi\)
0.734553 0.678551i \(-0.237392\pi\)
\(140\) 4.00000 + 2.00000i 0.338062 + 0.169031i
\(141\) 2.00000i 0.168430i
\(142\) −8.00000 8.00000i −0.671345 0.671345i
\(143\) 0 0
\(144\) −4.00000 −0.333333
\(145\) 6.00000 12.0000i 0.498273 0.996546i
\(146\) 6.00000 6.00000i 0.496564 0.496564i
\(147\) 1.00000 0.0824786
\(148\) 4.00000i 0.328798i
\(149\) 14.0000i 1.14692i 0.819232 + 0.573462i \(0.194400\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 1.00000 7.00000i 0.0816497 0.571548i
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) −8.00000 8.00000i −0.648886 0.648886i
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) −16.0000 8.00000i −1.28515 0.642575i
\(156\) 12.0000i 0.960769i
\(157\) 22.0000 1.75579 0.877896 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) 10.0000 + 10.0000i 0.795557 + 0.795557i
\(159\) −6.00000 −0.475831
\(160\) −4.00000 12.0000i −0.316228 0.948683i
\(161\) 4.00000 0.315244
\(162\) 1.00000 + 1.00000i 0.0785674 + 0.0785674i
\(163\) 6.00000 0.469956 0.234978 0.972001i \(-0.424498\pi\)
0.234978 + 0.972001i \(0.424498\pi\)
\(164\) 16.0000i 1.24939i
\(165\) 0 0
\(166\) −4.00000 4.00000i −0.310460 0.310460i
\(167\) 22.0000i 1.70241i 0.524832 + 0.851206i \(0.324128\pi\)
−0.524832 + 0.851206i \(0.675872\pi\)
\(168\) −2.00000 2.00000i −0.154303 0.154303i
\(169\) 23.0000 1.76923
\(170\) −6.00000 + 2.00000i −0.460179 + 0.153393i
\(171\) 4.00000i 0.305888i
\(172\) 12.0000i 0.914991i
\(173\) −24.0000 −1.82469 −0.912343 0.409426i \(-0.865729\pi\)
−0.912343 + 0.409426i \(0.865729\pi\)
\(174\) −6.00000 + 6.00000i −0.454859 + 0.454859i
\(175\) 4.00000 3.00000i 0.302372 0.226779i
\(176\) 0 0
\(177\) 6.00000i 0.450988i
\(178\) 0 0
\(179\) 16.0000i 1.19590i −0.801535 0.597948i \(-0.795983\pi\)
0.801535 0.597948i \(-0.204017\pi\)
\(180\) −2.00000 + 4.00000i −0.149071 + 0.298142i
\(181\) 10.0000i 0.743294i −0.928374 0.371647i \(-0.878793\pi\)
0.928374 0.371647i \(-0.121207\pi\)
\(182\) 6.00000 6.00000i 0.444750 0.444750i
\(183\) 10.0000i 0.739221i
\(184\) −8.00000 8.00000i −0.589768 0.589768i
\(185\) 4.00000 + 2.00000i 0.294086 + 0.147043i
\(186\) 8.00000 + 8.00000i 0.586588 + 0.586588i
\(187\) 0 0
\(188\) −4.00000 −0.291730
\(189\) 1.00000i 0.0727393i
\(190\) −12.0000 + 4.00000i −0.870572 + 0.290191i
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 8.00000i 0.577350i
\(193\) 16.0000i 1.15171i −0.817554 0.575853i \(-0.804670\pi\)
0.817554 0.575853i \(-0.195330\pi\)
\(194\) −2.00000 + 2.00000i −0.143592 + 0.143592i
\(195\) −12.0000 6.00000i −0.859338 0.429669i
\(196\) 2.00000i 0.142857i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) −14.0000 2.00000i −0.989949 0.141421i
\(201\) −2.00000 −0.141069
\(202\) −10.0000 + 10.0000i −0.703598 + 0.703598i
\(203\) −6.00000 −0.421117
\(204\) 4.00000 0.280056
\(205\) −16.0000 8.00000i −1.11749 0.558744i
\(206\) 16.0000 16.0000i 1.11477 1.11477i
\(207\) 4.00000i 0.278019i
\(208\) −24.0000 −1.66410
\(209\) 0 0
\(210\) −3.00000 + 1.00000i −0.207020 + 0.0690066i
\(211\) 20.0000i 1.37686i −0.725304 0.688428i \(-0.758301\pi\)
0.725304 0.688428i \(-0.241699\pi\)
\(212\) 12.0000i 0.824163i
\(213\) 8.00000 0.548151
\(214\) 12.0000 + 12.0000i 0.820303 + 0.820303i
\(215\) 12.0000 + 6.00000i 0.818393 + 0.409197i
\(216\) 2.00000 2.00000i 0.136083 0.136083i
\(217\) 8.00000i 0.543075i
\(218\) 16.0000 16.0000i 1.08366 1.08366i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) 12.0000i 0.807207i
\(222\) −2.00000 2.00000i −0.134231 0.134231i
\(223\) 4.00000i 0.267860i 0.990991 + 0.133930i \(0.0427597\pi\)
−0.990991 + 0.133930i \(0.957240\pi\)
\(224\) −4.00000 + 4.00000i −0.267261 + 0.267261i
\(225\) 3.00000 + 4.00000i 0.200000 + 0.266667i
\(226\) 6.00000 6.00000i 0.399114 0.399114i
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 8.00000 0.529813
\(229\) 14.0000i 0.925146i 0.886581 + 0.462573i \(0.153074\pi\)
−0.886581 + 0.462573i \(0.846926\pi\)
\(230\) −12.0000 + 4.00000i −0.791257 + 0.263752i
\(231\) 0 0
\(232\) 12.0000 + 12.0000i 0.787839 + 0.787839i
\(233\) 6.00000i 0.393073i −0.980497 0.196537i \(-0.937031\pi\)
0.980497 0.196537i \(-0.0629694\pi\)
\(234\) 6.00000 + 6.00000i 0.392232 + 0.392232i
\(235\) −2.00000 + 4.00000i −0.130466 + 0.260931i
\(236\) 12.0000 0.781133
\(237\) −10.0000 −0.649570
\(238\) 2.00000 + 2.00000i 0.129641 + 0.129641i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 8.00000 + 4.00000i 0.516398 + 0.258199i
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 11.0000 + 11.0000i 0.707107 + 0.707107i
\(243\) −1.00000 −0.0641500
\(244\) −20.0000 −1.28037
\(245\) −2.00000 1.00000i −0.127775 0.0638877i
\(246\) 8.00000 + 8.00000i 0.510061 + 0.510061i
\(247\) 24.0000i 1.52708i
\(248\) 16.0000 16.0000i 1.01600 1.01600i
\(249\) 4.00000 0.253490
\(250\) −9.00000 + 13.0000i −0.569210 + 0.822192i
\(251\) 10.0000i 0.631194i 0.948893 + 0.315597i \(0.102205\pi\)
−0.948893 + 0.315597i \(0.897795\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 8.00000 8.00000i 0.501965 0.501965i
\(255\) 2.00000 4.00000i 0.125245 0.250490i
\(256\) 16.0000 1.00000
\(257\) 18.0000i 1.12281i −0.827541 0.561405i \(-0.810261\pi\)
0.827541 0.561405i \(-0.189739\pi\)
\(258\) −6.00000 6.00000i −0.373544 0.373544i
\(259\) 2.00000i 0.124274i
\(260\) −12.0000 + 24.0000i −0.744208 + 1.48842i
\(261\) 6.00000i 0.371391i
\(262\) 10.0000 10.0000i 0.617802 0.617802i
\(263\) 24.0000i 1.47990i 0.672660 + 0.739952i \(0.265152\pi\)
−0.672660 + 0.739952i \(0.734848\pi\)
\(264\) 0 0
\(265\) 12.0000 + 6.00000i 0.737154 + 0.368577i
\(266\) 4.00000 + 4.00000i 0.245256 + 0.245256i
\(267\) 0 0
\(268\) 4.00000i 0.244339i
\(269\) 14.0000i 0.853595i 0.904347 + 0.426798i \(0.140358\pi\)
−0.904347 + 0.426798i \(0.859642\pi\)
\(270\) −1.00000 3.00000i −0.0608581 0.182574i
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 8.00000i 0.485071i
\(273\) 6.00000i 0.363137i
\(274\) 18.0000 18.0000i 1.08742 1.08742i
\(275\) 0 0
\(276\) 8.00000 0.481543
\(277\) −18.0000 −1.08152 −0.540758 0.841178i \(-0.681862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) 16.0000 16.0000i 0.959616 0.959616i
\(279\) −8.00000 −0.478947
\(280\) 2.00000 + 6.00000i 0.119523 + 0.358569i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 2.00000 2.00000i 0.119098 0.119098i
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 16.0000i 0.949425i
\(285\) 4.00000 8.00000i 0.236940 0.473879i
\(286\) 0 0
\(287\) 8.00000i 0.472225i
\(288\) −4.00000 4.00000i −0.235702 0.235702i
\(289\) 13.0000 0.764706
\(290\) 18.0000 6.00000i 1.05700 0.352332i
\(291\) 2.00000i 0.117242i
\(292\) 12.0000 0.702247
\(293\) 16.0000 0.934730 0.467365 0.884064i \(-0.345203\pi\)
0.467365 + 0.884064i \(0.345203\pi\)
\(294\) 1.00000 + 1.00000i 0.0583212 + 0.0583212i
\(295\) 6.00000 12.0000i 0.349334 0.698667i
\(296\) −4.00000 + 4.00000i −0.232495 + 0.232495i
\(297\) 0 0
\(298\) −14.0000 + 14.0000i −0.810998 + 0.810998i
\(299\) 24.0000i 1.38796i
\(300\) 8.00000 6.00000i 0.461880 0.346410i
\(301\) 6.00000i 0.345834i
\(302\) 2.00000 + 2.00000i 0.115087 + 0.115087i
\(303\) 10.0000i 0.574485i
\(304\) 16.0000i 0.917663i
\(305\) −10.0000 + 20.0000i −0.572598 + 1.14520i
\(306\) −2.00000 + 2.00000i −0.114332 + 0.114332i
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) 0 0
\(309\) 16.0000i 0.910208i
\(310\) −8.00000 24.0000i −0.454369 1.36311i
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 12.0000 12.0000i 0.679366 0.679366i
\(313\) 14.0000i 0.791327i 0.918396 + 0.395663i \(0.129485\pi\)
−0.918396 + 0.395663i \(0.870515\pi\)
\(314\) 22.0000 + 22.0000i 1.24153 + 1.24153i
\(315\) 1.00000 2.00000i 0.0563436 0.112687i
\(316\) 20.0000i 1.12509i
\(317\) −18.0000 −1.01098 −0.505490 0.862832i \(-0.668688\pi\)
−0.505490 + 0.862832i \(0.668688\pi\)
\(318\) −6.00000 6.00000i −0.336463 0.336463i
\(319\) 0 0
\(320\) 8.00000 16.0000i 0.447214 0.894427i
\(321\) −12.0000 −0.669775
\(322\) 4.00000 + 4.00000i 0.222911 + 0.222911i
\(323\) −8.00000 −0.445132
\(324\) 2.00000i 0.111111i
\(325\) 18.0000 + 24.0000i 0.998460 + 1.33128i
\(326\) 6.00000 + 6.00000i 0.332309 + 0.332309i
\(327\) 16.0000i 0.884802i
\(328\) 16.0000 16.0000i 0.883452 0.883452i
\(329\) 2.00000 0.110264
\(330\) 0 0
\(331\) 20.0000i 1.09930i 0.835395 + 0.549650i \(0.185239\pi\)
−0.835395 + 0.549650i \(0.814761\pi\)
\(332\) 8.00000i 0.439057i
\(333\) 2.00000 0.109599
\(334\) −22.0000 + 22.0000i −1.20379 + 1.20379i
\(335\) 4.00000 + 2.00000i 0.218543 + 0.109272i
\(336\) 4.00000i 0.218218i
\(337\) 8.00000i 0.435788i −0.975972 0.217894i \(-0.930081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(338\) 23.0000 + 23.0000i 1.25104 + 1.25104i
\(339\) 6.00000i 0.325875i
\(340\) −8.00000 4.00000i −0.433861 0.216930i
\(341\) 0 0
\(342\) −4.00000 + 4.00000i −0.216295 + 0.216295i
\(343\) 1.00000i 0.0539949i
\(344\) −12.0000 + 12.0000i −0.646997 + 0.646997i
\(345\) 4.00000 8.00000i 0.215353 0.430706i
\(346\) −24.0000 24.0000i −1.29025 1.29025i
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) −12.0000 −0.643268
\(349\) 6.00000i 0.321173i −0.987022 0.160586i \(-0.948662\pi\)
0.987022 0.160586i \(-0.0513385\pi\)
\(350\) 7.00000 + 1.00000i 0.374166 + 0.0534522i
\(351\) −6.00000 −0.320256
\(352\) 0 0
\(353\) 14.0000i 0.745145i 0.928003 + 0.372572i \(0.121524\pi\)
−0.928003 + 0.372572i \(0.878476\pi\)
\(354\) −6.00000 + 6.00000i −0.318896 + 0.318896i
\(355\) −16.0000 8.00000i −0.849192 0.424596i
\(356\) 0 0
\(357\) −2.00000 −0.105851
\(358\) 16.0000 16.0000i 0.845626 0.845626i
\(359\) −20.0000 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) −6.00000 + 2.00000i −0.316228 + 0.105409i
\(361\) 3.00000 0.157895
\(362\) 10.0000 10.0000i 0.525588 0.525588i
\(363\) −11.0000 −0.577350
\(364\) 12.0000 0.628971
\(365\) 6.00000 12.0000i 0.314054 0.628109i
\(366\) 10.0000 10.0000i 0.522708 0.522708i
\(367\) 28.0000i 1.46159i −0.682598 0.730794i \(-0.739150\pi\)
0.682598 0.730794i \(-0.260850\pi\)
\(368\) 16.0000i 0.834058i
\(369\) −8.00000 −0.416463
\(370\) 2.00000 + 6.00000i 0.103975 + 0.311925i
\(371\) 6.00000i 0.311504i
\(372\) 16.0000i 0.829561i
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 0 0
\(375\) −2.00000 11.0000i −0.103280 0.568038i
\(376\) −4.00000 4.00000i −0.206284 0.206284i
\(377\) 36.0000i 1.85409i
\(378\) −1.00000 + 1.00000i −0.0514344 + 0.0514344i
\(379\) 4.00000i 0.205466i 0.994709 + 0.102733i \(0.0327588\pi\)
−0.994709 + 0.102733i \(0.967241\pi\)
\(380\) −16.0000 8.00000i −0.820783 0.410391i
\(381\) 8.00000i 0.409852i
\(382\) −8.00000 8.00000i −0.409316 0.409316i
\(383\) 26.0000i 1.32854i −0.747494 0.664269i \(-0.768743\pi\)
0.747494 0.664269i \(-0.231257\pi\)
\(384\) −8.00000 + 8.00000i −0.408248 + 0.408248i
\(385\) 0 0
\(386\) 16.0000 16.0000i 0.814379 0.814379i
\(387\) 6.00000 0.304997
\(388\) −4.00000 −0.203069
\(389\) 26.0000i 1.31825i −0.752032 0.659126i \(-0.770926\pi\)
0.752032 0.659126i \(-0.229074\pi\)
\(390\) −6.00000 18.0000i −0.303822 0.911465i
\(391\) −8.00000 −0.404577
\(392\) 2.00000 2.00000i 0.101015 0.101015i
\(393\) 10.0000i 0.504433i
\(394\) −18.0000 18.0000i −0.906827 0.906827i
\(395\) 20.0000 + 10.0000i 1.00631 + 0.503155i
\(396\) 0 0
\(397\) −38.0000 −1.90717 −0.953583 0.301131i \(-0.902636\pi\)
−0.953583 + 0.301131i \(0.902636\pi\)
\(398\) 20.0000 + 20.0000i 1.00251 + 1.00251i
\(399\) −4.00000 −0.200250
\(400\) −12.0000 16.0000i −0.600000 0.800000i
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) −2.00000 2.00000i −0.0997509 0.0997509i
\(403\) −48.0000 −2.39105
\(404\) −20.0000 −0.995037
\(405\) 2.00000 + 1.00000i 0.0993808 + 0.0496904i
\(406\) −6.00000 6.00000i −0.297775 0.297775i
\(407\) 0 0
\(408\) 4.00000 + 4.00000i 0.198030 + 0.198030i
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) −8.00000 24.0000i −0.395092 1.18528i
\(411\) 18.0000i 0.887875i
\(412\) 32.0000 1.57653
\(413\) −6.00000 −0.295241
\(414\) −4.00000 + 4.00000i −0.196589 + 0.196589i
\(415\) −8.00000 4.00000i −0.392705 0.196352i
\(416\) −24.0000 24.0000i −1.17670 1.17670i
\(417\) 16.0000i 0.783523i
\(418\) 0 0
\(419\) 34.0000i 1.66101i 0.557012 + 0.830504i \(0.311948\pi\)
−0.557012 + 0.830504i \(0.688052\pi\)
\(420\) −4.00000 2.00000i −0.195180 0.0975900i
\(421\) 20.0000i 0.974740i 0.873195 + 0.487370i \(0.162044\pi\)
−0.873195 + 0.487370i \(0.837956\pi\)
\(422\) 20.0000 20.0000i 0.973585 0.973585i
\(423\) 2.00000i 0.0972433i
\(424\) −12.0000 + 12.0000i −0.582772 + 0.582772i
\(425\) −8.00000 + 6.00000i −0.388057 + 0.291043i
\(426\) 8.00000 + 8.00000i 0.387601 + 0.387601i
\(427\) 10.0000 0.483934
\(428\) 24.0000i 1.16008i
\(429\) 0 0
\(430\) 6.00000 + 18.0000i 0.289346 + 0.868037i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 4.00000 0.192450
\(433\) 6.00000i 0.288342i −0.989553 0.144171i \(-0.953949\pi\)
0.989553 0.144171i \(-0.0460515\pi\)
\(434\) −8.00000 + 8.00000i −0.384012 + 0.384012i
\(435\) −6.00000 + 12.0000i −0.287678 + 0.575356i
\(436\) 32.0000 1.53252
\(437\) −16.0000 −0.765384
\(438\) −6.00000 + 6.00000i −0.286691 + 0.286691i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −1.00000 −0.0476190
\(442\) −12.0000 + 12.0000i −0.570782 + 0.570782i
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 4.00000i 0.189832i
\(445\) 0 0
\(446\) −4.00000 + 4.00000i −0.189405 + 0.189405i
\(447\) 14.0000i 0.662177i
\(448\) −8.00000 −0.377964
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −1.00000 + 7.00000i −0.0471405 + 0.329983i
\(451\) 0 0
\(452\) 12.0000 0.564433
\(453\) −2.00000 −0.0939682
\(454\) 12.0000 + 12.0000i 0.563188 + 0.563188i
\(455\) 6.00000 12.0000i 0.281284 0.562569i
\(456\) 8.00000 + 8.00000i 0.374634 + 0.374634i
\(457\) 12.0000i 0.561336i 0.959805 + 0.280668i \(0.0905560\pi\)
−0.959805 + 0.280668i \(0.909444\pi\)
\(458\) −14.0000 + 14.0000i −0.654177 + 0.654177i
\(459\) 2.00000i 0.0933520i
\(460\) −16.0000 8.00000i −0.746004 0.373002i
\(461\) 30.0000i 1.39724i −0.715493 0.698620i \(-0.753798\pi\)
0.715493 0.698620i \(-0.246202\pi\)
\(462\) 0 0
\(463\) 16.0000i 0.743583i −0.928316 0.371792i \(-0.878744\pi\)
0.928316 0.371792i \(-0.121256\pi\)
\(464\) 24.0000i 1.11417i
\(465\) 16.0000 + 8.00000i 0.741982 + 0.370991i
\(466\) 6.00000 6.00000i 0.277945 0.277945i
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 12.0000i 0.554700i
\(469\) 2.00000i 0.0923514i
\(470\) −6.00000 + 2.00000i −0.276759 + 0.0922531i
\(471\) −22.0000 −1.01371
\(472\) 12.0000 + 12.0000i 0.552345 + 0.552345i
\(473\) 0 0
\(474\) −10.0000 10.0000i −0.459315 0.459315i
\(475\) −16.0000 + 12.0000i −0.734130 + 0.550598i
\(476\) 4.00000i 0.183340i
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 4.00000 + 12.0000i 0.182574 + 0.547723i
\(481\) 12.0000 0.547153
\(482\) −18.0000 18.0000i −0.819878 0.819878i
\(483\) −4.00000 −0.182006
\(484\) 22.0000i 1.00000i
\(485\) −2.00000 + 4.00000i −0.0908153 + 0.181631i
\(486\) −1.00000 1.00000i −0.0453609 0.0453609i
\(487\) 32.0000i 1.45006i 0.688718 + 0.725029i \(0.258174\pi\)
−0.688718 + 0.725029i \(0.741826\pi\)
\(488\) −20.0000 20.0000i −0.905357 0.905357i
\(489\) −6.00000 −0.271329
\(490\) −1.00000 3.00000i −0.0451754 0.135526i
\(491\) 20.0000i 0.902587i −0.892375 0.451294i \(-0.850963\pi\)
0.892375 0.451294i \(-0.149037\pi\)
\(492\) 16.0000i 0.721336i
\(493\) 12.0000 0.540453
\(494\) −24.0000 + 24.0000i −1.07981 + 1.07981i
\(495\) 0 0
\(496\) 32.0000 1.43684
\(497\) 8.00000i 0.358849i
\(498\) 4.00000 + 4.00000i 0.179244 + 0.179244i
\(499\) 4.00000i 0.179065i 0.995984 + 0.0895323i \(0.0285372\pi\)
−0.995984 + 0.0895323i \(0.971463\pi\)
\(500\) −22.0000 + 4.00000i −0.983870 + 0.178885i
\(501\) 22.0000i 0.982888i
\(502\) −10.0000 + 10.0000i −0.446322 + 0.446322i
\(503\) 6.00000i 0.267527i −0.991013 0.133763i \(-0.957294\pi\)
0.991013 0.133763i \(-0.0427062\pi\)
\(504\) 2.00000 + 2.00000i 0.0890871 + 0.0890871i
\(505\) −10.0000 + 20.0000i −0.444994 + 0.889988i
\(506\) 0 0
\(507\) −23.0000 −1.02147
\(508\) 16.0000 0.709885
\(509\) 34.0000i 1.50702i 0.657434 + 0.753512i \(0.271642\pi\)
−0.657434 + 0.753512i \(0.728358\pi\)
\(510\) 6.00000 2.00000i 0.265684 0.0885615i
\(511\) −6.00000 −0.265424
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 4.00000i 0.176604i
\(514\) 18.0000 18.0000i 0.793946 0.793946i
\(515\) 16.0000 32.0000i 0.705044 1.41009i
\(516\) 12.0000i 0.528271i
\(517\) 0 0
\(518\) 2.00000 2.00000i 0.0878750 0.0878750i
\(519\) 24.0000 1.05348
\(520\) −36.0000 + 12.0000i −1.57870 + 0.526235i
\(521\) −28.0000 −1.22670 −0.613351 0.789810i \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) 6.00000 6.00000i 0.262613 0.262613i
\(523\) 16.0000 0.699631 0.349816 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) 20.0000 0.873704
\(525\) −4.00000 + 3.00000i −0.174574 + 0.130931i
\(526\) −24.0000 + 24.0000i −1.04645 + 1.04645i
\(527\) 16.0000i 0.696971i
\(528\) 0 0
\(529\) 7.00000 0.304348
\(530\) 6.00000 + 18.0000i 0.260623 + 0.781870i
\(531\) 6.00000i 0.260378i
\(532\) 8.00000i 0.346844i
\(533\) −48.0000 −2.07911
\(534\) 0 0
\(535\) 24.0000 + 12.0000i 1.03761 + 0.518805i
\(536\) −4.00000 + 4.00000i −0.172774 + 0.172774i
\(537\) 16.0000i 0.690451i
\(538\) −14.0000 + 14.0000i −0.603583 + 0.603583i
\(539\) 0 0
\(540\) 2.00000 4.00000i 0.0860663 0.172133i
\(541\) 20.0000i 0.859867i 0.902861 + 0.429934i \(0.141463\pi\)
−0.902861 + 0.429934i \(0.858537\pi\)
\(542\) −28.0000 28.0000i −1.20270 1.20270i
\(543\) 10.0000i 0.429141i
\(544\) 8.00000 8.00000i 0.342997 0.342997i
\(545\) 16.0000 32.0000i 0.685365 1.37073i
\(546\) −6.00000 + 6.00000i −0.256776 + 0.256776i
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 36.0000 1.53784
\(549\) 10.0000i 0.426790i
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) 8.00000 + 8.00000i 0.340503 + 0.340503i
\(553\) 10.0000i 0.425243i
\(554\) −18.0000 18.0000i −0.764747 0.764747i
\(555\) −4.00000 2.00000i −0.169791 0.0848953i
\(556\) 32.0000 1.35710
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) −8.00000 8.00000i −0.338667 0.338667i
\(559\) 36.0000 1.52264
\(560\) −4.00000 + 8.00000i −0.169031 + 0.338062i
\(561\) 0 0
\(562\) −18.0000 18.0000i −0.759284 0.759284i
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 4.00000 0.168430
\(565\) 6.00000 12.0000i 0.252422 0.504844i
\(566\) −4.00000 4.00000i −0.168133 0.168133i
\(567\) 1.00000i 0.0419961i
\(568\) 16.0000 16.0000i 0.671345 0.671345i
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) 12.0000 4.00000i 0.502625 0.167542i
\(571\) 20.0000i 0.836974i 0.908223 + 0.418487i \(0.137439\pi\)
−0.908223 + 0.418487i \(0.862561\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) −8.00000 + 8.00000i −0.333914 + 0.333914i
\(575\) −16.0000 + 12.0000i −0.667246 + 0.500435i
\(576\) 8.00000i 0.333333i
\(577\) 38.0000i 1.58196i −0.611842 0.790980i \(-0.709571\pi\)
0.611842 0.790980i \(-0.290429\pi\)
\(578\) 13.0000 + 13.0000i 0.540729 + 0.540729i
\(579\) 16.0000i 0.664937i
\(580\) 24.0000 + 12.0000i 0.996546 + 0.498273i
\(581\) 4.00000i 0.165948i
\(582\) 2.00000 2.00000i 0.0829027 0.0829027i
\(583\) 0 0
\(584\) 12.0000 + 12.0000i 0.496564 + 0.496564i
\(585\) 12.0000 + 6.00000i 0.496139 + 0.248069i
\(586\) 16.0000 + 16.0000i 0.660954 + 0.660954i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 2.00000i 0.0824786i
\(589\) 32.0000i 1.31854i
\(590\) 18.0000 6.00000i 0.741048 0.247016i
\(591\) 18.0000 0.740421
\(592\) −8.00000 −0.328798
\(593\) 14.0000i 0.574911i 0.957794 + 0.287456i \(0.0928094\pi\)
−0.957794 + 0.287456i \(0.907191\pi\)
\(594\) 0 0
\(595\) 4.00000 + 2.00000i 0.163984 + 0.0819920i
\(596\) −28.0000 −1.14692
\(597\) −20.0000 −0.818546
\(598\) −24.0000 + 24.0000i −0.981433 + 0.981433i
\(599\) 40.0000 1.63436 0.817178 0.576386i \(-0.195537\pi\)
0.817178 + 0.576386i \(0.195537\pi\)
\(600\) 14.0000 + 2.00000i 0.571548 + 0.0816497i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 6.00000 6.00000i 0.244542 0.244542i
\(603\) 2.00000 0.0814463
\(604\) 4.00000i 0.162758i
\(605\) 22.0000 + 11.0000i 0.894427 + 0.447214i
\(606\) 10.0000 10.0000i 0.406222 0.406222i
\(607\) 8.00000i 0.324710i −0.986732 0.162355i \(-0.948091\pi\)
0.986732 0.162355i \(-0.0519090\pi\)
\(608\) 16.0000 16.0000i 0.648886 0.648886i
\(609\) 6.00000 0.243132
\(610\) −30.0000 + 10.0000i −1.21466 + 0.404888i
\(611\) 12.0000i 0.485468i
\(612\) −4.00000 −0.161690
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) −28.0000 28.0000i −1.12999 1.12999i
\(615\) 16.0000 + 8.00000i 0.645182 + 0.322591i
\(616\) 0 0
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) −16.0000 + 16.0000i −0.643614 + 0.643614i
\(619\) 44.0000i 1.76851i 0.467005 + 0.884255i \(0.345333\pi\)
−0.467005 + 0.884255i \(0.654667\pi\)
\(620\) 16.0000 32.0000i 0.642575 1.28515i
\(621\) 4.00000i 0.160514i
\(622\) −8.00000 8.00000i −0.320771 0.320771i
\(623\) 0 0
\(624\) 24.0000 0.960769
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −14.0000 + 14.0000i −0.559553 + 0.559553i
\(627\) 0 0
\(628\) 44.0000i 1.75579i
\(629\) 4.00000i 0.159490i
\(630\) 3.00000 1.00000i 0.119523 0.0398410i
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) −20.0000 + 20.0000i −0.795557 + 0.795557i
\(633\) 20.0000i 0.794929i
\(634\) −18.0000 18.0000i −0.714871 0.714871i
\(635\) 8.00000 16.0000i 0.317470 0.634941i
\(636\) 12.0000i 0.475831i
\(637\) −6.00000 −0.237729
\(638\) 0 0
\(639\) −8.00000 −0.316475
\(640\) 24.0000 8.00000i 0.948683 0.316228i
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) −12.0000 12.0000i −0.473602 0.473602i
\(643\) 16.0000 0.630978 0.315489 0.948929i \(-0.397831\pi\)
0.315489 + 0.948929i \(0.397831\pi\)
\(644\) 8.00000i 0.315244i
\(645\) −12.0000 6.00000i −0.472500 0.236250i
\(646\) −8.00000 8.00000i −0.314756 0.314756i
\(647\) 42.0000i 1.65119i 0.564263 + 0.825595i \(0.309160\pi\)
−0.564263 + 0.825595i \(0.690840\pi\)
\(648\) −2.00000 + 2.00000i −0.0785674 + 0.0785674i
\(649\) 0 0
\(650\) −6.00000 + 42.0000i −0.235339 + 1.64738i
\(651\) 8.00000i 0.313545i
\(652\) 12.0000i 0.469956i
\(653\) −14.0000 −0.547862 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) −16.0000 + 16.0000i −0.625650 + 0.625650i
\(655\) 10.0000 20.0000i 0.390732 0.781465i
\(656\) 32.0000 1.24939
\(657\) 6.00000i 0.234082i
\(658\) 2.00000 + 2.00000i 0.0779681 + 0.0779681i
\(659\) 36.0000i 1.40236i −0.712984 0.701180i \(-0.752657\pi\)
0.712984 0.701180i \(-0.247343\pi\)
\(660\) 0 0
\(661\) 30.0000i 1.16686i 0.812162 + 0.583432i \(0.198291\pi\)
−0.812162 + 0.583432i \(0.801709\pi\)
\(662\) −20.0000 + 20.0000i −0.777322 + 0.777322i
\(663\) 12.0000i 0.466041i
\(664\) 8.00000 8.00000i 0.310460 0.310460i
\(665\) 8.00000 + 4.00000i 0.310227 + 0.155113i
\(666\) 2.00000 + 2.00000i 0.0774984 + 0.0774984i
\(667\) 24.0000 0.929284
\(668\) −44.0000 −1.70241
\(669\) 4.00000i 0.154649i
\(670\) 2.00000 + 6.00000i 0.0772667 + 0.231800i
\(671\) 0 0
\(672\) 4.00000 4.00000i 0.154303 0.154303i
\(673\) 44.0000i 1.69608i 0.529936 + 0.848038i \(0.322216\pi\)
−0.529936 + 0.848038i \(0.677784\pi\)
\(674\) 8.00000 8.00000i 0.308148 0.308148i
\(675\) −3.00000 4.00000i −0.115470 0.153960i
\(676\) 46.0000i 1.76923i
\(677\) 32.0000 1.22986 0.614930 0.788582i \(-0.289184\pi\)
0.614930 + 0.788582i \(0.289184\pi\)
\(678\) −6.00000 + 6.00000i −0.230429 + 0.230429i
\(679\) 2.00000 0.0767530
\(680\) −4.00000 12.0000i −0.153393 0.460179i
\(681\) −12.0000 −0.459841
\(682\) 0 0
\(683\) −44.0000 −1.68361 −0.841807 0.539779i \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) −8.00000 −0.305888
\(685\) 18.0000 36.0000i 0.687745 1.37549i
\(686\) −1.00000 + 1.00000i −0.0381802 + 0.0381802i
\(687\) 14.0000i 0.534133i
\(688\) −24.0000 −0.914991
\(689\) 36.0000 1.37149
\(690\) 12.0000 4.00000i 0.456832 0.152277i
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 48.0000i 1.82469i
\(693\) 0 0
\(694\) 12.0000 + 12.0000i 0.455514 + 0.455514i
\(695\) 16.0000 32.0000i 0.606915 1.21383i
\(696\) −12.0000 12.0000i −0.454859 0.454859i
\(697\) 16.0000i 0.606043i
\(698\) 6.00000 6.00000i 0.227103 0.227103i
\(699\) 6.00000i 0.226941i
\(700\) 6.00000 + 8.00000i 0.226779 + 0.302372i
\(701\) 50.0000i 1.88847i −0.329267 0.944237i \(-0.606802\pi\)
0.329267 0.944237i \(-0.393198\pi\)
\(702\) −6.00000 6.00000i −0.226455 0.226455i
\(703\) 8.00000i 0.301726i
\(704\) 0 0
\(705\) 2.00000 4.00000i 0.0753244 0.150649i
\(706\) −14.0000 + 14.0000i −0.526897 + 0.526897i
\(707\) 10.0000 0.376089
\(708\) −12.0000 −0.450988
\(709\) 16.0000i 0.600893i −0.953799 0.300446i \(-0.902864\pi\)
0.953799 0.300446i \(-0.0971356\pi\)
\(710\) −8.00000 24.0000i −0.300235 0.900704i
\(711\) 10.0000 0.375029
\(712\) 0 0
\(713\) 32.0000i 1.19841i
\(714\) −2.00000 2.00000i −0.0748481 0.0748481i
\(715\) 0 0
\(716\) 32.0000 1.19590
\(717\) 0 0
\(718\) −20.0000 20.0000i −0.746393 0.746393i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) −8.00000 4.00000i −0.298142 0.149071i
\(721\) −16.0000 −0.595871
\(722\) 3.00000 + 3.00000i 0.111648 + 0.111648i
\(723\) 18.0000 0.669427
\(724\) 20.0000 0.743294
\(725\) 24.0000 18.0000i 0.891338 0.668503i
\(726\) −11.0000 11.0000i −0.408248 0.408248i
\(727\) 52.0000i 1.92857i 0.264861 + 0.964287i \(0.414674\pi\)
−0.264861 + 0.964287i \(0.585326\pi\)
\(728\) 12.0000 + 12.0000i 0.444750 + 0.444750i
\(729\) 1.00000 0.0370370
\(730\) 18.0000 6.00000i 0.666210 0.222070i
\(731\) 12.0000i 0.443836i
\(732\) 20.0000 0.739221
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 28.0000 28.0000i 1.03350 1.03350i
\(735\) 2.00000 + 1.00000i 0.0737711 + 0.0368856i
\(736\) 16.0000 16.0000i 0.589768 0.589768i
\(737\) 0 0
\(738\) −8.00000 8.00000i −0.294484 0.294484i
\(739\) 4.00000i 0.147142i 0.997290 + 0.0735712i \(0.0234396\pi\)
−0.997290 + 0.0735712i \(0.976560\pi\)
\(740\) −4.00000 + 8.00000i −0.147043 + 0.294086i
\(741\) 24.0000i 0.881662i
\(742\) 6.00000 6.00000i 0.220267 0.220267i
\(743\) 24.0000i 0.880475i 0.897881 + 0.440237i \(0.145106\pi\)
−0.897881 + 0.440237i \(0.854894\pi\)
\(744\) −16.0000 + 16.0000i −0.586588 + 0.586588i
\(745\) −14.0000 + 28.0000i −0.512920 + 1.02584i
\(746\) 26.0000 + 26.0000i 0.951928 + 0.951928i
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) 12.0000i 0.438470i
\(750\) 9.00000 13.0000i 0.328634 0.474693i
\(751\) −38.0000 −1.38664 −0.693320 0.720630i \(-0.743853\pi\)
−0.693320 + 0.720630i \(0.743853\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 10.0000i 0.364420i
\(754\) 36.0000 36.0000i 1.31104 1.31104i
\(755\) 4.00000 + 2.00000i 0.145575 + 0.0727875i
\(756\) −2.00000 −0.0727393
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) −4.00000 + 4.00000i −0.145287 + 0.145287i
\(759\) 0 0
\(760\) −8.00000 24.0000i −0.290191 0.870572i
\(761\) −8.00000 −0.290000 −0.145000 0.989432i \(-0.546318\pi\)
−0.145000 + 0.989432i \(0.546318\pi\)
\(762\) −8.00000 + 8.00000i −0.289809 + 0.289809i
\(763\) −16.0000 −0.579239
\(764\) 16.0000i 0.578860i
\(765\) −2.00000 + 4.00000i −0.0723102 + 0.144620i
\(766\) 26.0000 26.0000i 0.939418 0.939418i
\(767\) 36.0000i 1.29988i
\(768\) −16.0000 −0.577350
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) 18.0000i 0.648254i
\(772\) 32.0000 1.15171
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 6.00000 + 6.00000i 0.215666 + 0.215666i
\(775\) −24.0000 32.0000i −0.862105 1.14947i
\(776\) −4.00000 4.00000i −0.143592 0.143592i
\(777\) 2.00000i 0.0717496i
\(778\) 26.0000 26.0000i 0.932145 0.932145i
\(779\) 32.0000i 1.14652i
\(780\) 12.0000 24.0000i 0.429669 0.859338i
\(781\) 0 0
\(782\) −8.00000 8.00000i −0.286079 0.286079i
\(783\) 6.00000i 0.214423i
\(784\) 4.00000 0.142857
\(785\) 44.0000 + 22.0000i 1.57043 + 0.785214i
\(786\) −10.0000 + 10.0000i −0.356688 + 0.356688i
\(787\) 52.0000 1.85360 0.926800 0.375555i \(-0.122548\pi\)
0.926800 + 0.375555i \(0.122548\pi\)
\(788\) 36.0000i 1.28245i
\(789\) 24.0000i 0.854423i
\(790\) 10.0000 + 30.0000i 0.355784 + 1.06735i
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) 60.0000i 2.13066i
\(794\) −38.0000 38.0000i −1.34857 1.34857i
\(795\) −12.0000 6.00000i −0.425596 0.212798i
\(796\) 40.0000i 1.41776i
\(797\) −8.00000 −0.283375 −0.141687 0.989911i \(-0.545253\pi\)
−0.141687 + 0.989911i \(0.545253\pi\)
\(798\) −4.00000 4.00000i −0.141598 0.141598i
\(799\) −4.00000 −0.141510
\(800\) 4.00000 28.0000i 0.141421 0.989949i
\(801\) 0 0
\(802\) 2.00000 + 2.00000i 0.0706225 + 0.0706225i
\(803\) 0 0
\(804\) 4.00000i 0.141069i
\(805\) 8.00000 + 4.00000i 0.281963 + 0.140981i
\(806\) −48.0000 48.0000i −1.69073 1.69073i
\(807\) 14.0000i 0.492823i
\(808\) −20.0000 20.0000i −0.703598 0.703598i
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 1.00000 + 3.00000i 0.0351364 + 0.105409i
\(811\) 20.0000i 0.702295i −0.936320 0.351147i \(-0.885792\pi\)
0.936320 0.351147i \(-0.114208\pi\)
\(812\) 12.0000i 0.421117i
\(813\) 28.0000 0.982003
\(814\) 0 0
\(815\) 12.0000 + 6.00000i 0.420342 + 0.210171i
\(816\) 8.00000i 0.280056i
\(817\) 24.0000i 0.839654i
\(818\) 10.0000 + 10.0000i 0.349642 + 0.349642i
\(819\) 6.00000i 0.209657i
\(820\) 16.0000 32.0000i 0.558744 1.11749i
\(821\) 10.0000i 0.349002i 0.984657 + 0.174501i \(0.0558313\pi\)
−0.984657 + 0.174501i \(0.944169\pi\)
\(822\) −18.0000 + 18.0000i −0.627822 + 0.627822i
\(823\) 16.0000i 0.557725i −0.960331 0.278862i \(-0.910043\pi\)
0.960331 0.278862i \(-0.0899574\pi\)
\(824\) 32.0000 + 32.0000i 1.11477 + 1.11477i
\(825\) 0 0
\(826\) −6.00000 6.00000i −0.208767 0.208767i
\(827\) 52.0000 1.80822 0.904109 0.427303i \(-0.140536\pi\)
0.904109 + 0.427303i \(0.140536\pi\)
\(828\) −8.00000 −0.278019
\(829\) 46.0000i 1.59765i −0.601566 0.798823i \(-0.705456\pi\)
0.601566 0.798823i \(-0.294544\pi\)
\(830\) −4.00000 12.0000i −0.138842 0.416526i
\(831\) 18.0000 0.624413
\(832\) 48.0000i 1.66410i
\(833\) 2.00000i 0.0692959i
\(834\) −16.0000 + 16.0000i −0.554035 + 0.554035i
\(835\) −22.0000 + 44.0000i −0.761341 + 1.52268i
\(836\) 0 0
\(837\) 8.00000 0.276520
\(838\) −34.0000 + 34.0000i −1.17451 + 1.17451i
\(839\) 40.0000 1.38095 0.690477 0.723355i \(-0.257401\pi\)
0.690477 + 0.723355i \(0.257401\pi\)
\(840\) −2.00000 6.00000i −0.0690066 0.207020i
\(841\) −7.00000 −0.241379
\(842\) −20.0000 + 20.0000i −0.689246 + 0.689246i
\(843\) 18.0000 0.619953
\(844\) 40.0000 1.37686
\(845\) 46.0000 + 23.0000i 1.58245 + 0.791224i
\(846\) −2.00000 + 2.00000i −0.0687614 + 0.0687614i
\(847\) 11.0000i 0.377964i
\(848\) −24.0000 −0.824163
\(849\) 4.00000 0.137280
\(850\) −14.0000 2.00000i −0.480196 0.0685994i
\(851\) 8.00000i 0.274236i
\(852\) 16.0000i 0.548151i
\(853\) 26.0000 0.890223 0.445112 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 10.0000 + 10.0000i 0.342193 + 0.342193i
\(855\) −4.00000 + 8.00000i −0.136797 + 0.273594i
\(856\) −24.0000 + 24.0000i −0.820303 + 0.820303i
\(857\) 18.0000i 0.614868i −0.951569 0.307434i \(-0.900530\pi\)
0.951569 0.307434i \(-0.0994704\pi\)
\(858\) 0 0
\(859\) 36.0000i 1.22830i −0.789188 0.614152i \(-0.789498\pi\)
0.789188 0.614152i \(-0.210502\pi\)
\(860\) −12.0000 + 24.0000i −0.409197 + 0.818393i
\(861\) 8.00000i 0.272639i
\(862\) 12.0000 + 12.0000i 0.408722 + 0.408722i
\(863\) 36.0000i 1.22545i −0.790295 0.612727i \(-0.790072\pi\)
0.790295 0.612727i \(-0.209928\pi\)
\(864\) 4.00000 + 4.00000i 0.136083 + 0.136083i
\(865\) −48.0000 24.0000i −1.63205 0.816024i
\(866\) 6.00000 6.00000i 0.203888 0.203888i
\(867\) −13.0000 −0.441503
\(868\) −16.0000 −0.543075
\(869\) 0 0
\(870\) −18.0000 + 6.00000i −0.610257 + 0.203419i
\(871\) 12.0000 0.406604
\(872\) 32.0000 + 32.0000i 1.08366 + 1.08366i
\(873\) 2.00000i 0.0676897i
\(874\) −16.0000 16.0000i −0.541208 0.541208i
\(875\) 11.0000 2.00000i 0.371868 0.0676123i
\(876\) −12.0000 −0.405442
\(877\) −18.0000 −0.607817 −0.303908 0.952701i \(-0.598292\pi\)
−0.303908 + 0.952701i \(0.598292\pi\)
\(878\) 0 0
\(879\) −16.0000 −0.539667
\(880\) 0 0
\(881\) −28.0000 −0.943344 −0.471672 0.881774i \(-0.656349\pi\)
−0.471672 + 0.881774i \(0.656349\pi\)
\(882\) −1.00000 1.00000i −0.0336718 0.0336718i
\(883\) 26.0000 0.874970 0.437485 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) −24.0000 −0.807207
\(885\) −6.00000 + 12.0000i −0.201688 + 0.403376i
\(886\) 36.0000 + 36.0000i 1.20944 + 1.20944i
\(887\) 42.0000i 1.41022i 0.709097 + 0.705111i \(0.249103\pi\)
−0.709097 + 0.705111i \(0.750897\pi\)
\(888\) 4.00000 4.00000i 0.134231 0.134231i
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) −8.00000 −0.267860
\(893\) −8.00000 −0.267710
\(894\) 14.0000 14.0000i 0.468230 0.468230i
\(895\) 16.0000 32.0000i 0.534821 1.06964i
\(896\) −8.00000 8.00000i −0.267261 0.267261i
\(897\) 24.0000i 0.801337i
\(898\) −30.0000 30.0000i −1.00111 1.00111i
\(899\) 48.0000i 1.60089i
\(900\) −8.00000 + 6.00000i −0.266667 + 0.200000i
\(901\) 12.0000i 0.399778i
\(902\) 0 0
\(903\) 6.00000i 0.199667i
\(904\) 12.0000 + 12.0000i 0.399114 + 0.399114i
\(905\) 10.0000 20.0000i 0.332411 0.664822i
\(906\) −2.00000 2.00000i −0.0664455 0.0664455i
\(907\) −18.0000 −0.597680 −0.298840 0.954303i \(-0.596600\pi\)
−0.298840 + 0.954303i \(0.596600\pi\)
\(908\) 24.0000i 0.796468i
\(909\) 10.0000i 0.331679i
\(910\) 18.0000 6.00000i 0.596694 0.198898i
\(911\) −28.0000 −0.927681 −0.463841 0.885919i \(-0.653529\pi\)
−0.463841 + 0.885919i \(0.653529\pi\)
\(912\) 16.0000i 0.529813i
\(913\) 0 0
\(914\) −12.0000 + 12.0000i −0.396925 + 0.396925i
\(915\) 10.0000 20.0000i 0.330590 0.661180i
\(916\) −28.0000 −0.925146
\(917\) −10.0000 −0.330229
\(918\) 2.00000 2.00000i 0.0660098 0.0660098i
\(919\) 50.0000 1.64935 0.824674 0.565608i \(-0.191359\pi\)
0.824674 + 0.565608i \(0.191359\pi\)
\(920\) −8.00000 24.0000i −0.263752 0.791257i
\(921\) 28.0000 0.922631
\(922\) 30.0000 30.0000i 0.987997 0.987997i
\(923\) −48.0000 −1.57994
\(924\) 0 0
\(925\) 6.00000 + 8.00000i 0.197279 + 0.263038i
\(926\) 16.0000 16.0000i 0.525793 0.525793i
\(927\) 16.0000i 0.525509i
\(928\) −24.0000 + 24.0000i −0.787839 + 0.787839i
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 8.00000 + 24.0000i 0.262330 + 0.786991i
\(931\) 4.00000i 0.131095i
\(932\) 12.0000 0.393073
\(933\) 8.00000 0.261908
\(934\) 12.0000 + 12.0000i 0.392652 + 0.392652i
\(935\) 0 0
\(936\) −12.0000 + 12.0000i −0.392232 + 0.392232i
\(937\) 38.0000i 1.24141i −0.784046 0.620703i \(-0.786847\pi\)
0.784046 0.620703i \(-0.213153\pi\)
\(938\) 2.00000 2.00000i 0.0653023 0.0653023i
\(939\) 14.0000i 0.456873i
\(940\) −8.00000 4.00000i −0.260931 0.130466i
\(941\) 50.0000i 1.62995i −0.579494 0.814977i \(-0.696750\pi\)
0.579494 0.814977i \(-0.303250\pi\)
\(942\) −22.0000 22.0000i −0.716799 0.716799i
\(943\) 32.0000i 1.04206i
\(944\) 24.0000i 0.781133i
\(945\) −1.00000 + 2.00000i −0.0325300 + 0.0650600i
\(946\) 0 0
\(947\) 12.0000 0.389948 0.194974 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 20.0000i 0.649570i
\(949\) 36.0000i 1.16861i
\(950\) −28.0000 4.00000i −0.908440 0.129777i
\(951\) 18.0000 0.583690
\(952\) −4.00000 + 4.00000i −0.129641 + 0.129641i
\(953\) 34.0000i 1.10137i 0.834714 + 0.550684i \(0.185633\pi\)
−0.834714 + 0.550684i \(0.814367\pi\)
\(954\) 6.00000 + 6.00000i 0.194257 + 0.194257i
\(955\) −16.0000 8.00000i −0.517748 0.258874i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −18.0000 −0.581250
\(960\) −8.00000 + 16.0000i −0.258199 + 0.516398i
\(961\) 33.0000 1.06452
\(962\) 12.0000 + 12.0000i 0.386896 + 0.386896i
\(963\) 12.0000 0.386695
\(964\) 36.0000i 1.15948i
\(965\) 16.0000 32.0000i 0.515058 1.03012i
\(966\) −4.00000 4.00000i −0.128698 0.128698i
\(967\) 8.00000i 0.257263i −0.991692 0.128631i \(-0.958942\pi\)
0.991692 0.128631i \(-0.0410584\pi\)
\(968\) −22.0000 + 22.0000i −0.707107 + 0.707107i
\(969\) 8.00000 0.256997
\(970\) −6.00000 + 2.00000i −0.192648 + 0.0642161i
\(971\) 10.0000i 0.320915i 0.987043 + 0.160458i \(0.0512970\pi\)
−0.987043 + 0.160458i \(0.948703\pi\)
\(972\) 2.00000i 0.0641500i
\(973\) −16.0000 −0.512936
\(974\) −32.0000 + 32.0000i −1.02535 + 1.02535i
\(975\) −18.0000 24.0000i −0.576461 0.768615i
\(976\) 40.0000i 1.28037i
\(977\) 18.0000i 0.575871i −0.957650 0.287936i \(-0.907031\pi\)
0.957650 0.287936i \(-0.0929689\pi\)
\(978\) −6.00000 6.00000i −0.191859 0.191859i
\(979\) 0 0
\(980\) 2.00000 4.00000i 0.0638877 0.127775i
\(981\) 16.0000i 0.510841i
\(982\) 20.0000 20.0000i 0.638226 0.638226i
\(983\) 14.0000i 0.446531i 0.974758 + 0.223265i \(0.0716716\pi\)
−0.974758 + 0.223265i \(0.928328\pi\)
\(984\) −16.0000 + 16.0000i −0.510061 + 0.510061i
\(985\) −36.0000 18.0000i −1.14706 0.573528i
\(986\) 12.0000 + 12.0000i 0.382158 + 0.382158i
\(987\) −2.00000 −0.0636607
\(988\) −48.0000 −1.52708
\(989\) 24.0000i 0.763156i
\(990\) 0 0
\(991\) 22.0000 0.698853 0.349427 0.936964i \(-0.386376\pi\)
0.349427 + 0.936964i \(0.386376\pi\)
\(992\) 32.0000 + 32.0000i 1.01600 + 1.01600i
\(993\) 20.0000i 0.634681i
\(994\) −8.00000 + 8.00000i −0.253745 + 0.253745i
\(995\) 40.0000 + 20.0000i 1.26809 + 0.634043i
\(996\) 8.00000i 0.253490i
\(997\) 2.00000 0.0633406 0.0316703 0.999498i \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) −4.00000 + 4.00000i −0.126618 + 0.126618i
\(999\) −2.00000 −0.0632772
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 840.2.j.c.589.2 yes 2
4.3 odd 2 3360.2.j.d.1009.2 2
5.4 even 2 840.2.j.b.589.1 2
8.3 odd 2 3360.2.j.a.1009.1 2
8.5 even 2 840.2.j.b.589.2 yes 2
20.19 odd 2 3360.2.j.a.1009.2 2
40.19 odd 2 3360.2.j.d.1009.1 2
40.29 even 2 inner 840.2.j.c.589.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
840.2.j.b.589.1 2 5.4 even 2
840.2.j.b.589.2 yes 2 8.5 even 2
840.2.j.c.589.1 yes 2 40.29 even 2 inner
840.2.j.c.589.2 yes 2 1.1 even 1 trivial
3360.2.j.a.1009.1 2 8.3 odd 2
3360.2.j.a.1009.2 2 20.19 odd 2
3360.2.j.d.1009.1 2 40.19 odd 2
3360.2.j.d.1009.2 2 4.3 odd 2