Properties

Label 80.2.q.a.29.1
Level $80$
Weight $2$
Character 80.29
Analytic conductor $0.639$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [80,2,Mod(29,80)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(80, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("80.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.q (of order \(4\), degree \(2\), 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: \(0.638803216170\)
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: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 29.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 80.29
Dual form 80.2.q.a.69.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} -2.00000i q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{6} +(2.00000 + 2.00000i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(1.00000 - 1.00000i) q^{3} -2.00000i q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{6} +(2.00000 + 2.00000i) q^{8} +1.00000i q^{9} +(1.00000 + 3.00000i) q^{10} +(-3.00000 + 3.00000i) q^{11} +(-2.00000 - 2.00000i) q^{12} +(3.00000 - 3.00000i) q^{13} +(-1.00000 - 3.00000i) q^{15} -4.00000 q^{16} +4.00000i q^{17} +(-1.00000 - 1.00000i) q^{18} +(-1.00000 - 1.00000i) q^{19} +(-4.00000 - 2.00000i) q^{20} -6.00000i q^{22} -8.00000 q^{23} +4.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +6.00000i q^{26} +(4.00000 + 4.00000i) q^{27} +(3.00000 + 3.00000i) q^{29} +(4.00000 + 2.00000i) q^{30} +(4.00000 - 4.00000i) q^{32} +6.00000i q^{33} +(-4.00000 - 4.00000i) q^{34} +2.00000 q^{36} +(3.00000 + 3.00000i) q^{37} +2.00000 q^{38} -6.00000i q^{39} +(6.00000 - 2.00000i) q^{40} +(3.00000 + 3.00000i) q^{43} +(6.00000 + 6.00000i) q^{44} +(2.00000 + 1.00000i) q^{45} +(8.00000 - 8.00000i) q^{46} +2.00000i q^{47} +(-4.00000 + 4.00000i) q^{48} -7.00000 q^{49} +(7.00000 + 1.00000i) q^{50} +(4.00000 + 4.00000i) q^{51} +(-6.00000 - 6.00000i) q^{52} +(-9.00000 - 9.00000i) q^{53} -8.00000 q^{54} +(3.00000 + 9.00000i) q^{55} -2.00000 q^{57} -6.00000 q^{58} +(9.00000 - 9.00000i) q^{59} +(-6.00000 + 2.00000i) q^{60} +(-5.00000 - 5.00000i) q^{61} +8.00000i q^{64} +(-3.00000 - 9.00000i) q^{65} +(-6.00000 - 6.00000i) q^{66} +(-3.00000 + 3.00000i) q^{67} +8.00000 q^{68} +(-8.00000 + 8.00000i) q^{69} -6.00000i q^{71} +(-2.00000 + 2.00000i) q^{72} +6.00000 q^{73} -6.00000 q^{74} +(-7.00000 - 1.00000i) q^{75} +(-2.00000 + 2.00000i) q^{76} +(6.00000 + 6.00000i) q^{78} +8.00000 q^{79} +(-4.00000 + 8.00000i) q^{80} +5.00000 q^{81} +(9.00000 - 9.00000i) q^{83} +(8.00000 + 4.00000i) q^{85} -6.00000 q^{86} +6.00000 q^{87} -12.0000 q^{88} +12.0000i q^{89} +(-3.00000 + 1.00000i) q^{90} +16.0000i q^{92} +(-2.00000 - 2.00000i) q^{94} +(-3.00000 + 1.00000i) q^{95} -8.00000i q^{96} -12.0000i q^{97} +(7.00000 - 7.00000i) q^{98} +(-3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{5} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{5} + 4 q^{8} + 2 q^{10} - 6 q^{11} - 4 q^{12} + 6 q^{13} - 2 q^{15} - 8 q^{16} - 2 q^{18} - 2 q^{19} - 8 q^{20} - 16 q^{23} + 8 q^{24} - 6 q^{25} + 8 q^{27} + 6 q^{29} + 8 q^{30} + 8 q^{32} - 8 q^{34} + 4 q^{36} + 6 q^{37} + 4 q^{38} + 12 q^{40} + 6 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 8 q^{48} - 14 q^{49} + 14 q^{50} + 8 q^{51} - 12 q^{52} - 18 q^{53} - 16 q^{54} + 6 q^{55} - 4 q^{57} - 12 q^{58} + 18 q^{59} - 12 q^{60} - 10 q^{61} - 6 q^{65} - 12 q^{66} - 6 q^{67} + 16 q^{68} - 16 q^{69} - 4 q^{72} + 12 q^{73} - 12 q^{74} - 14 q^{75} - 4 q^{76} + 12 q^{78} + 16 q^{79} - 8 q^{80} + 10 q^{81} + 18 q^{83} + 16 q^{85} - 12 q^{86} + 12 q^{87} - 24 q^{88} - 6 q^{90} - 4 q^{94} - 6 q^{95} + 14 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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 1.00000i 0.577350 0.577350i −0.356822 0.934172i \(-0.616140\pi\)
0.934172 + 0.356822i \(0.116140\pi\)
\(4\) 2.00000i 1.00000i
\(5\) 1.00000 2.00000i 0.447214 0.894427i
\(6\) 2.00000i 0.816497i
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 1.00000i 0.333333i
\(10\) 1.00000 + 3.00000i 0.316228 + 0.948683i
\(11\) −3.00000 + 3.00000i −0.904534 + 0.904534i −0.995824 0.0912903i \(-0.970901\pi\)
0.0912903 + 0.995824i \(0.470901\pi\)
\(12\) −2.00000 2.00000i −0.577350 0.577350i
\(13\) 3.00000 3.00000i 0.832050 0.832050i −0.155747 0.987797i \(-0.549778\pi\)
0.987797 + 0.155747i \(0.0497784\pi\)
\(14\) 0 0
\(15\) −1.00000 3.00000i −0.258199 0.774597i
\(16\) −4.00000 −1.00000
\(17\) 4.00000i 0.970143i 0.874475 + 0.485071i \(0.161206\pi\)
−0.874475 + 0.485071i \(0.838794\pi\)
\(18\) −1.00000 1.00000i −0.235702 0.235702i
\(19\) −1.00000 1.00000i −0.229416 0.229416i 0.583033 0.812449i \(-0.301866\pi\)
−0.812449 + 0.583033i \(0.801866\pi\)
\(20\) −4.00000 2.00000i −0.894427 0.447214i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 4.00000 0.816497
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 6.00000i 1.17670i
\(27\) 4.00000 + 4.00000i 0.769800 + 0.769800i
\(28\) 0 0
\(29\) 3.00000 + 3.00000i 0.557086 + 0.557086i 0.928477 0.371391i \(-0.121119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 4.00000 + 2.00000i 0.730297 + 0.365148i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 4.00000 4.00000i 0.707107 0.707107i
\(33\) 6.00000i 1.04447i
\(34\) −4.00000 4.00000i −0.685994 0.685994i
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) 3.00000 + 3.00000i 0.493197 + 0.493197i 0.909312 0.416115i \(-0.136609\pi\)
−0.416115 + 0.909312i \(0.636609\pi\)
\(38\) 2.00000 0.324443
\(39\) 6.00000i 0.960769i
\(40\) 6.00000 2.00000i 0.948683 0.316228i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 3.00000 + 3.00000i 0.457496 + 0.457496i 0.897833 0.440337i \(-0.145141\pi\)
−0.440337 + 0.897833i \(0.645141\pi\)
\(44\) 6.00000 + 6.00000i 0.904534 + 0.904534i
\(45\) 2.00000 + 1.00000i 0.298142 + 0.149071i
\(46\) 8.00000 8.00000i 1.17954 1.17954i
\(47\) 2.00000i 0.291730i 0.989305 + 0.145865i \(0.0465965\pi\)
−0.989305 + 0.145865i \(0.953403\pi\)
\(48\) −4.00000 + 4.00000i −0.577350 + 0.577350i
\(49\) −7.00000 −1.00000
\(50\) 7.00000 + 1.00000i 0.989949 + 0.141421i
\(51\) 4.00000 + 4.00000i 0.560112 + 0.560112i
\(52\) −6.00000 6.00000i −0.832050 0.832050i
\(53\) −9.00000 9.00000i −1.23625 1.23625i −0.961524 0.274721i \(-0.911414\pi\)
−0.274721 0.961524i \(-0.588586\pi\)
\(54\) −8.00000 −1.08866
\(55\) 3.00000 + 9.00000i 0.404520 + 1.21356i
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) −6.00000 −0.787839
\(59\) 9.00000 9.00000i 1.17170 1.17170i 0.189896 0.981804i \(-0.439185\pi\)
0.981804 0.189896i \(-0.0608151\pi\)
\(60\) −6.00000 + 2.00000i −0.774597 + 0.258199i
\(61\) −5.00000 5.00000i −0.640184 0.640184i 0.310416 0.950601i \(-0.399532\pi\)
−0.950601 + 0.310416i \(0.899532\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −3.00000 9.00000i −0.372104 1.11631i
\(66\) −6.00000 6.00000i −0.738549 0.738549i
\(67\) −3.00000 + 3.00000i −0.366508 + 0.366508i −0.866202 0.499694i \(-0.833446\pi\)
0.499694 + 0.866202i \(0.333446\pi\)
\(68\) 8.00000 0.970143
\(69\) −8.00000 + 8.00000i −0.963087 + 0.963087i
\(70\) 0 0
\(71\) 6.00000i 0.712069i −0.934473 0.356034i \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) −2.00000 + 2.00000i −0.235702 + 0.235702i
\(73\) 6.00000 0.702247 0.351123 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) −6.00000 −0.697486
\(75\) −7.00000 1.00000i −0.808290 0.115470i
\(76\) −2.00000 + 2.00000i −0.229416 + 0.229416i
\(77\) 0 0
\(78\) 6.00000 + 6.00000i 0.679366 + 0.679366i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −4.00000 + 8.00000i −0.447214 + 0.894427i
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) 9.00000 9.00000i 0.987878 0.987878i −0.0120491 0.999927i \(-0.503835\pi\)
0.999927 + 0.0120491i \(0.00383543\pi\)
\(84\) 0 0
\(85\) 8.00000 + 4.00000i 0.867722 + 0.433861i
\(86\) −6.00000 −0.646997
\(87\) 6.00000 0.643268
\(88\) −12.0000 −1.27920
\(89\) 12.0000i 1.27200i 0.771690 + 0.635999i \(0.219412\pi\)
−0.771690 + 0.635999i \(0.780588\pi\)
\(90\) −3.00000 + 1.00000i −0.316228 + 0.105409i
\(91\) 0 0
\(92\) 16.0000i 1.66812i
\(93\) 0 0
\(94\) −2.00000 2.00000i −0.206284 0.206284i
\(95\) −3.00000 + 1.00000i −0.307794 + 0.102598i
\(96\) 8.00000i 0.816497i
\(97\) 12.0000i 1.21842i −0.793011 0.609208i \(-0.791488\pi\)
0.793011 0.609208i \(-0.208512\pi\)
\(98\) 7.00000 7.00000i 0.707107 0.707107i
\(99\) −3.00000 3.00000i −0.301511 0.301511i
\(100\) −8.00000 + 6.00000i −0.800000 + 0.600000i
\(101\) 3.00000 3.00000i 0.298511 0.298511i −0.541919 0.840431i \(-0.682302\pi\)
0.840431 + 0.541919i \(0.182302\pi\)
\(102\) −8.00000 −0.792118
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 12.0000 1.17670
\(105\) 0 0
\(106\) 18.0000 1.74831
\(107\) −9.00000 9.00000i −0.870063 0.870063i 0.122416 0.992479i \(-0.460936\pi\)
−0.992479 + 0.122416i \(0.960936\pi\)
\(108\) 8.00000 8.00000i 0.769800 0.769800i
\(109\) −1.00000 1.00000i −0.0957826 0.0957826i 0.657592 0.753374i \(-0.271575\pi\)
−0.753374 + 0.657592i \(0.771575\pi\)
\(110\) −12.0000 6.00000i −1.14416 0.572078i
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) 8.00000i 0.752577i 0.926503 + 0.376288i \(0.122800\pi\)
−0.926503 + 0.376288i \(0.877200\pi\)
\(114\) 2.00000 2.00000i 0.187317 0.187317i
\(115\) −8.00000 + 16.0000i −0.746004 + 1.49201i
\(116\) 6.00000 6.00000i 0.557086 0.557086i
\(117\) 3.00000 + 3.00000i 0.277350 + 0.277350i
\(118\) 18.0000i 1.65703i
\(119\) 0 0
\(120\) 4.00000 8.00000i 0.365148 0.730297i
\(121\) 7.00000i 0.636364i
\(122\) 10.0000 0.905357
\(123\) 0 0
\(124\) 0 0
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) 6.00000i 0.532414i −0.963916 0.266207i \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) −8.00000 8.00000i −0.707107 0.707107i
\(129\) 6.00000 0.528271
\(130\) 12.0000 + 6.00000i 1.05247 + 0.526235i
\(131\) −9.00000 9.00000i −0.786334 0.786334i 0.194557 0.980891i \(-0.437673\pi\)
−0.980891 + 0.194557i \(0.937673\pi\)
\(132\) 12.0000 1.04447
\(133\) 0 0
\(134\) 6.00000i 0.518321i
\(135\) 12.0000 4.00000i 1.03280 0.344265i
\(136\) −8.00000 + 8.00000i −0.685994 + 0.685994i
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 16.0000i 1.36201i
\(139\) −7.00000 + 7.00000i −0.593732 + 0.593732i −0.938638 0.344905i \(-0.887911\pi\)
0.344905 + 0.938638i \(0.387911\pi\)
\(140\) 0 0
\(141\) 2.00000 + 2.00000i 0.168430 + 0.168430i
\(142\) 6.00000 + 6.00000i 0.503509 + 0.503509i
\(143\) 18.0000i 1.50524i
\(144\) 4.00000i 0.333333i
\(145\) 9.00000 3.00000i 0.747409 0.249136i
\(146\) −6.00000 + 6.00000i −0.496564 + 0.496564i
\(147\) −7.00000 + 7.00000i −0.577350 + 0.577350i
\(148\) 6.00000 6.00000i 0.493197 0.493197i
\(149\) 3.00000 3.00000i 0.245770 0.245770i −0.573462 0.819232i \(-0.694400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 8.00000 6.00000i 0.653197 0.489898i
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) 4.00000i 0.324443i
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) 0 0
\(156\) −12.0000 −0.960769
\(157\) −9.00000 + 9.00000i −0.718278 + 0.718278i −0.968252 0.249974i \(-0.919578\pi\)
0.249974 + 0.968252i \(0.419578\pi\)
\(158\) −8.00000 + 8.00000i −0.636446 + 0.636446i
\(159\) −18.0000 −1.42749
\(160\) −4.00000 12.0000i −0.316228 0.948683i
\(161\) 0 0
\(162\) −5.00000 + 5.00000i −0.392837 + 0.392837i
\(163\) 9.00000 9.00000i 0.704934 0.704934i −0.260531 0.965465i \(-0.583898\pi\)
0.965465 + 0.260531i \(0.0838976\pi\)
\(164\) 0 0
\(165\) 12.0000 + 6.00000i 0.934199 + 0.467099i
\(166\) 18.0000i 1.39707i
\(167\) 8.00000 0.619059 0.309529 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 5.00000i 0.384615i
\(170\) −12.0000 + 4.00000i −0.920358 + 0.306786i
\(171\) 1.00000 1.00000i 0.0764719 0.0764719i
\(172\) 6.00000 6.00000i 0.457496 0.457496i
\(173\) −9.00000 + 9.00000i −0.684257 + 0.684257i −0.960957 0.276699i \(-0.910759\pi\)
0.276699 + 0.960957i \(0.410759\pi\)
\(174\) −6.00000 + 6.00000i −0.454859 + 0.454859i
\(175\) 0 0
\(176\) 12.0000 12.0000i 0.904534 0.904534i
\(177\) 18.0000i 1.35296i
\(178\) −12.0000 12.0000i −0.899438 0.899438i
\(179\) 3.00000 + 3.00000i 0.224231 + 0.224231i 0.810277 0.586047i \(-0.199317\pi\)
−0.586047 + 0.810277i \(0.699317\pi\)
\(180\) 2.00000 4.00000i 0.149071 0.298142i
\(181\) −1.00000 + 1.00000i −0.0743294 + 0.0743294i −0.743294 0.668965i \(-0.766738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) −10.0000 −0.739221
\(184\) −16.0000 16.0000i −1.17954 1.17954i
\(185\) 9.00000 3.00000i 0.661693 0.220564i
\(186\) 0 0
\(187\) −12.0000 12.0000i −0.877527 0.877527i
\(188\) 4.00000 0.291730
\(189\) 0 0
\(190\) 2.00000 4.00000i 0.145095 0.290191i
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 8.00000 + 8.00000i 0.577350 + 0.577350i
\(193\) 12.0000i 0.863779i 0.901927 + 0.431889i \(0.142153\pi\)
−0.901927 + 0.431889i \(0.857847\pi\)
\(194\) 12.0000 + 12.0000i 0.861550 + 0.861550i
\(195\) −12.0000 6.00000i −0.859338 0.429669i
\(196\) 14.0000i 1.00000i
\(197\) −5.00000 5.00000i −0.356235 0.356235i 0.506188 0.862423i \(-0.331054\pi\)
−0.862423 + 0.506188i \(0.831054\pi\)
\(198\) 6.00000 0.426401
\(199\) 2.00000i 0.141776i 0.997484 + 0.0708881i \(0.0225833\pi\)
−0.997484 + 0.0708881i \(0.977417\pi\)
\(200\) 2.00000 14.0000i 0.141421 0.989949i
\(201\) 6.00000i 0.423207i
\(202\) 6.00000i 0.422159i
\(203\) 0 0
\(204\) 8.00000 8.00000i 0.560112 0.560112i
\(205\) 0 0
\(206\) 0 0
\(207\) 8.00000i 0.556038i
\(208\) −12.0000 + 12.0000i −0.832050 + 0.832050i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) 11.0000 + 11.0000i 0.757271 + 0.757271i 0.975825 0.218554i \(-0.0701339\pi\)
−0.218554 + 0.975825i \(0.570134\pi\)
\(212\) −18.0000 + 18.0000i −1.23625 + 1.23625i
\(213\) −6.00000 6.00000i −0.411113 0.411113i
\(214\) 18.0000 1.23045
\(215\) 9.00000 3.00000i 0.613795 0.204598i
\(216\) 16.0000i 1.08866i
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) 6.00000 6.00000i 0.405442 0.405442i
\(220\) 18.0000 6.00000i 1.21356 0.404520i
\(221\) 12.0000 + 12.0000i 0.807207 + 0.807207i
\(222\) −6.00000 + 6.00000i −0.402694 + 0.402694i
\(223\) 6.00000i 0.401790i −0.979613 0.200895i \(-0.935615\pi\)
0.979613 0.200895i \(-0.0643850\pi\)
\(224\) 0 0
\(225\) 4.00000 3.00000i 0.266667 0.200000i
\(226\) −8.00000 8.00000i −0.532152 0.532152i
\(227\) 9.00000 9.00000i 0.597351 0.597351i −0.342256 0.939607i \(-0.611191\pi\)
0.939607 + 0.342256i \(0.111191\pi\)
\(228\) 4.00000i 0.264906i
\(229\) 7.00000 7.00000i 0.462573 0.462573i −0.436925 0.899498i \(-0.643932\pi\)
0.899498 + 0.436925i \(0.143932\pi\)
\(230\) −8.00000 24.0000i −0.527504 1.58251i
\(231\) 0 0
\(232\) 12.0000i 0.787839i
\(233\) 22.0000 1.44127 0.720634 0.693316i \(-0.243851\pi\)
0.720634 + 0.693316i \(0.243851\pi\)
\(234\) −6.00000 −0.392232
\(235\) 4.00000 + 2.00000i 0.260931 + 0.130466i
\(236\) −18.0000 18.0000i −1.17170 1.17170i
\(237\) 8.00000 8.00000i 0.519656 0.519656i
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 4.00000 + 12.0000i 0.258199 + 0.774597i
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 7.00000 + 7.00000i 0.449977 + 0.449977i
\(243\) −7.00000 + 7.00000i −0.449050 + 0.449050i
\(244\) −10.0000 + 10.0000i −0.640184 + 0.640184i
\(245\) −7.00000 + 14.0000i −0.447214 + 0.894427i
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) 0 0
\(249\) 18.0000i 1.14070i
\(250\) 9.00000 13.0000i 0.569210 0.822192i
\(251\) 9.00000 9.00000i 0.568075 0.568075i −0.363514 0.931589i \(-0.618423\pi\)
0.931589 + 0.363514i \(0.118423\pi\)
\(252\) 0 0
\(253\) 24.0000 24.0000i 1.50887 1.50887i
\(254\) 6.00000 + 6.00000i 0.376473 + 0.376473i
\(255\) 12.0000 4.00000i 0.751469 0.250490i
\(256\) 16.0000 1.00000
\(257\) 8.00000i 0.499026i 0.968371 + 0.249513i \(0.0802706\pi\)
−0.968371 + 0.249513i \(0.919729\pi\)
\(258\) −6.00000 + 6.00000i −0.373544 + 0.373544i
\(259\) 0 0
\(260\) −18.0000 + 6.00000i −1.11631 + 0.372104i
\(261\) −3.00000 + 3.00000i −0.185695 + 0.185695i
\(262\) 18.0000 1.11204
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) −12.0000 + 12.0000i −0.738549 + 0.738549i
\(265\) −27.0000 + 9.00000i −1.65860 + 0.552866i
\(266\) 0 0
\(267\) 12.0000 + 12.0000i 0.734388 + 0.734388i
\(268\) 6.00000 + 6.00000i 0.366508 + 0.366508i
\(269\) −9.00000 9.00000i −0.548740 0.548740i 0.377337 0.926076i \(-0.376840\pi\)
−0.926076 + 0.377337i \(0.876840\pi\)
\(270\) −8.00000 + 16.0000i −0.486864 + 0.973729i
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 16.0000i 0.970143i
\(273\) 0 0
\(274\) −2.00000 + 2.00000i −0.120824 + 0.120824i
\(275\) 21.0000 + 3.00000i 1.26635 + 0.180907i
\(276\) 16.0000 + 16.0000i 0.963087 + 0.963087i
\(277\) 3.00000 + 3.00000i 0.180253 + 0.180253i 0.791466 0.611213i \(-0.209318\pi\)
−0.611213 + 0.791466i \(0.709318\pi\)
\(278\) 14.0000i 0.839664i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000i 0.715860i 0.933748 + 0.357930i \(0.116517\pi\)
−0.933748 + 0.357930i \(0.883483\pi\)
\(282\) −4.00000 −0.238197
\(283\) 15.0000 + 15.0000i 0.891657 + 0.891657i 0.994679 0.103022i \(-0.0328511\pi\)
−0.103022 + 0.994679i \(0.532851\pi\)
\(284\) −12.0000 −0.712069
\(285\) −2.00000 + 4.00000i −0.118470 + 0.236940i
\(286\) −18.0000 18.0000i −1.06436 1.06436i
\(287\) 0 0
\(288\) 4.00000 + 4.00000i 0.235702 + 0.235702i
\(289\) 1.00000 0.0588235
\(290\) −6.00000 + 12.0000i −0.352332 + 0.704664i
\(291\) −12.0000 12.0000i −0.703452 0.703452i
\(292\) 12.0000i 0.702247i
\(293\) −9.00000 9.00000i −0.525786 0.525786i 0.393527 0.919313i \(-0.371255\pi\)
−0.919313 + 0.393527i \(0.871255\pi\)
\(294\) 14.0000i 0.816497i
\(295\) −9.00000 27.0000i −0.524000 1.57200i
\(296\) 12.0000i 0.697486i
\(297\) −24.0000 −1.39262
\(298\) 6.00000i 0.347571i
\(299\) −24.0000 + 24.0000i −1.38796 + 1.38796i
\(300\) −2.00000 + 14.0000i −0.115470 + 0.808290i
\(301\) 0 0
\(302\) −18.0000 18.0000i −1.03578 1.03578i
\(303\) 6.00000i 0.344691i
\(304\) 4.00000 + 4.00000i 0.229416 + 0.229416i
\(305\) −15.0000 + 5.00000i −0.858898 + 0.286299i
\(306\) 4.00000 4.00000i 0.228665 0.228665i
\(307\) −3.00000 + 3.00000i −0.171219 + 0.171219i −0.787515 0.616296i \(-0.788633\pi\)
0.616296 + 0.787515i \(0.288633\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 6.00000i 0.340229i −0.985424 0.170114i \(-0.945586\pi\)
0.985424 0.170114i \(-0.0544137\pi\)
\(312\) 12.0000 12.0000i 0.679366 0.679366i
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 18.0000i 1.01580i
\(315\) 0 0
\(316\) 16.0000i 0.900070i
\(317\) 7.00000 7.00000i 0.393159 0.393159i −0.482653 0.875812i \(-0.660327\pi\)
0.875812 + 0.482653i \(0.160327\pi\)
\(318\) 18.0000 18.0000i 1.00939 1.00939i
\(319\) −18.0000 −1.00781
\(320\) 16.0000 + 8.00000i 0.894427 + 0.447214i
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) 4.00000 4.00000i 0.222566 0.222566i
\(324\) 10.0000i 0.555556i
\(325\) −21.0000 3.00000i −1.16487 0.166410i
\(326\) 18.0000i 0.996928i
\(327\) −2.00000 −0.110600
\(328\) 0 0
\(329\) 0 0
\(330\) −18.0000 + 6.00000i −0.990867 + 0.330289i
\(331\) 5.00000 5.00000i 0.274825 0.274825i −0.556214 0.831039i \(-0.687747\pi\)
0.831039 + 0.556214i \(0.187747\pi\)
\(332\) −18.0000 18.0000i −0.987878 0.987878i
\(333\) −3.00000 + 3.00000i −0.164399 + 0.164399i
\(334\) −8.00000 + 8.00000i −0.437741 + 0.437741i
\(335\) 3.00000 + 9.00000i 0.163908 + 0.491723i
\(336\) 0 0
\(337\) 24.0000i 1.30736i 0.756770 + 0.653682i \(0.226776\pi\)
−0.756770 + 0.653682i \(0.773224\pi\)
\(338\) 5.00000 + 5.00000i 0.271964 + 0.271964i
\(339\) 8.00000 + 8.00000i 0.434500 + 0.434500i
\(340\) 8.00000 16.0000i 0.433861 0.867722i
\(341\) 0 0
\(342\) 2.00000i 0.108148i
\(343\) 0 0
\(344\) 12.0000i 0.646997i
\(345\) 8.00000 + 24.0000i 0.430706 + 1.29212i
\(346\) 18.0000i 0.967686i
\(347\) 19.0000 + 19.0000i 1.01997 + 1.01997i 0.999796 + 0.0201770i \(0.00642298\pi\)
0.0201770 + 0.999796i \(0.493577\pi\)
\(348\) 12.0000i 0.643268i
\(349\) −5.00000 5.00000i −0.267644 0.267644i 0.560506 0.828150i \(-0.310607\pi\)
−0.828150 + 0.560506i \(0.810607\pi\)
\(350\) 0 0
\(351\) 24.0000 1.28103
\(352\) 24.0000i 1.27920i
\(353\) 16.0000i 0.851594i 0.904819 + 0.425797i \(0.140006\pi\)
−0.904819 + 0.425797i \(0.859994\pi\)
\(354\) 18.0000 + 18.0000i 0.956689 + 0.956689i
\(355\) −12.0000 6.00000i −0.636894 0.318447i
\(356\) 24.0000 1.27200
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) 18.0000i 0.950004i 0.879985 + 0.475002i \(0.157553\pi\)
−0.879985 + 0.475002i \(0.842447\pi\)
\(360\) 2.00000 + 6.00000i 0.105409 + 0.316228i
\(361\) 17.0000i 0.894737i
\(362\) 2.00000i 0.105118i
\(363\) −7.00000 7.00000i −0.367405 0.367405i
\(364\) 0 0
\(365\) 6.00000 12.0000i 0.314054 0.628109i
\(366\) 10.0000 10.0000i 0.522708 0.522708i
\(367\) 18.0000i 0.939592i 0.882775 + 0.469796i \(0.155673\pi\)
−0.882775 + 0.469796i \(0.844327\pi\)
\(368\) 32.0000 1.66812
\(369\) 0 0
\(370\) −6.00000 + 12.0000i −0.311925 + 0.623850i
\(371\) 0 0
\(372\) 0 0
\(373\) 3.00000 + 3.00000i 0.155334 + 0.155334i 0.780496 0.625161i \(-0.214967\pi\)
−0.625161 + 0.780496i \(0.714967\pi\)
\(374\) 24.0000 1.24101
\(375\) −9.00000 + 13.0000i −0.464758 + 0.671317i
\(376\) −4.00000 + 4.00000i −0.206284 + 0.206284i
\(377\) 18.0000 0.927047
\(378\) 0 0
\(379\) 1.00000 1.00000i 0.0513665 0.0513665i −0.680957 0.732323i \(-0.738436\pi\)
0.732323 + 0.680957i \(0.238436\pi\)
\(380\) 2.00000 + 6.00000i 0.102598 + 0.307794i
\(381\) −6.00000 6.00000i −0.307389 0.307389i
\(382\) 24.0000 24.0000i 1.22795 1.22795i
\(383\) 10.0000i 0.510976i 0.966812 + 0.255488i \(0.0822362\pi\)
−0.966812 + 0.255488i \(0.917764\pi\)
\(384\) −16.0000 −0.816497
\(385\) 0 0
\(386\) −12.0000 12.0000i −0.610784 0.610784i
\(387\) −3.00000 + 3.00000i −0.152499 + 0.152499i
\(388\) −24.0000 −1.21842
\(389\) 15.0000 15.0000i 0.760530 0.760530i −0.215888 0.976418i \(-0.569265\pi\)
0.976418 + 0.215888i \(0.0692646\pi\)
\(390\) 18.0000 6.00000i 0.911465 0.303822i
\(391\) 32.0000i 1.61831i
\(392\) −14.0000 14.0000i −0.707107 0.707107i
\(393\) −18.0000 −0.907980
\(394\) 10.0000 0.503793
\(395\) 8.00000 16.0000i 0.402524 0.805047i
\(396\) −6.00000 + 6.00000i −0.301511 + 0.301511i
\(397\) −9.00000 + 9.00000i −0.451697 + 0.451697i −0.895918 0.444220i \(-0.853481\pi\)
0.444220 + 0.895918i \(0.353481\pi\)
\(398\) −2.00000 2.00000i −0.100251 0.100251i
\(399\) 0 0
\(400\) 12.0000 + 16.0000i 0.600000 + 0.800000i
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) −6.00000 6.00000i −0.299253 0.299253i
\(403\) 0 0
\(404\) −6.00000 6.00000i −0.298511 0.298511i
\(405\) 5.00000 10.0000i 0.248452 0.496904i
\(406\) 0 0
\(407\) −18.0000 −0.892227
\(408\) 16.0000i 0.792118i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 2.00000 2.00000i 0.0986527 0.0986527i
\(412\) 0 0
\(413\) 0 0
\(414\) 8.00000 + 8.00000i 0.393179 + 0.393179i
\(415\) −9.00000 27.0000i −0.441793 1.32538i
\(416\) 24.0000i 1.17670i
\(417\) 14.0000i 0.685583i
\(418\) −6.00000 + 6.00000i −0.293470 + 0.293470i
\(419\) 15.0000 + 15.0000i 0.732798 + 0.732798i 0.971173 0.238375i \(-0.0766148\pi\)
−0.238375 + 0.971173i \(0.576615\pi\)
\(420\) 0 0
\(421\) −5.00000 + 5.00000i −0.243685 + 0.243685i −0.818373 0.574688i \(-0.805124\pi\)
0.574688 + 0.818373i \(0.305124\pi\)
\(422\) −22.0000 −1.07094
\(423\) −2.00000 −0.0972433
\(424\) 36.0000i 1.74831i
\(425\) 16.0000 12.0000i 0.776114 0.582086i
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) −18.0000 + 18.0000i −0.870063 + 0.870063i
\(429\) 18.0000 + 18.0000i 0.869048 + 0.869048i
\(430\) −6.00000 + 12.0000i −0.289346 + 0.578691i
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) −16.0000 16.0000i −0.769800 0.769800i
\(433\) 36.0000i 1.73005i −0.501729 0.865025i \(-0.667303\pi\)
0.501729 0.865025i \(-0.332697\pi\)
\(434\) 0 0
\(435\) 6.00000 12.0000i 0.287678 0.575356i
\(436\) −2.00000 + 2.00000i −0.0957826 + 0.0957826i
\(437\) 8.00000 + 8.00000i 0.382692 + 0.382692i
\(438\) 12.0000i 0.573382i
\(439\) 10.0000i 0.477274i 0.971109 + 0.238637i \(0.0767006\pi\)
−0.971109 + 0.238637i \(0.923299\pi\)
\(440\) −12.0000 + 24.0000i −0.572078 + 1.14416i
\(441\) 7.00000i 0.333333i
\(442\) −24.0000 −1.14156
\(443\) −9.00000 9.00000i −0.427603 0.427603i 0.460208 0.887811i \(-0.347775\pi\)
−0.887811 + 0.460208i \(0.847775\pi\)
\(444\) 12.0000i 0.569495i
\(445\) 24.0000 + 12.0000i 1.13771 + 0.568855i
\(446\) 6.00000 + 6.00000i 0.284108 + 0.284108i
\(447\) 6.00000i 0.283790i
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) −1.00000 + 7.00000i −0.0471405 + 0.329983i
\(451\) 0 0
\(452\) 16.0000 0.752577
\(453\) 18.0000 + 18.0000i 0.845714 + 0.845714i
\(454\) 18.0000i 0.844782i
\(455\) 0 0
\(456\) −4.00000 4.00000i −0.187317 0.187317i
\(457\) 18.0000 0.842004 0.421002 0.907060i \(-0.361678\pi\)
0.421002 + 0.907060i \(0.361678\pi\)
\(458\) 14.0000i 0.654177i
\(459\) −16.0000 + 16.0000i −0.746816 + 0.746816i
\(460\) 32.0000 + 16.0000i 1.49201 + 0.746004i
\(461\) 3.00000 + 3.00000i 0.139724 + 0.139724i 0.773509 0.633785i \(-0.218500\pi\)
−0.633785 + 0.773509i \(0.718500\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i −0.716965 0.697109i \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) −12.0000 12.0000i −0.557086 0.557086i
\(465\) 0 0
\(466\) −22.0000 + 22.0000i −1.01913 + 1.01913i
\(467\) 5.00000 5.00000i 0.231372 0.231372i −0.581893 0.813265i \(-0.697688\pi\)
0.813265 + 0.581893i \(0.197688\pi\)
\(468\) 6.00000 6.00000i 0.277350 0.277350i
\(469\) 0 0
\(470\) −6.00000 + 2.00000i −0.276759 + 0.0922531i
\(471\) 18.0000i 0.829396i
\(472\) 36.0000 1.65703
\(473\) −18.0000 −0.827641
\(474\) 16.0000i 0.734904i
\(475\) −1.00000 + 7.00000i −0.0458831 + 0.321182i
\(476\) 0 0
\(477\) 9.00000 9.00000i 0.412082 0.412082i
\(478\) −24.0000 + 24.0000i −1.09773 + 1.09773i
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) −16.0000 8.00000i −0.730297 0.365148i
\(481\) 18.0000 0.820729
\(482\) 18.0000 18.0000i 0.819878 0.819878i
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) −24.0000 12.0000i −1.08978 0.544892i
\(486\) 14.0000i 0.635053i
\(487\) 24.0000 1.08754 0.543772 0.839233i \(-0.316996\pi\)
0.543772 + 0.839233i \(0.316996\pi\)
\(488\) 20.0000i 0.905357i
\(489\) 18.0000i 0.813988i
\(490\) −7.00000 21.0000i −0.316228 0.948683i
\(491\) −15.0000 + 15.0000i −0.676941 + 0.676941i −0.959307 0.282366i \(-0.908881\pi\)
0.282366 + 0.959307i \(0.408881\pi\)
\(492\) 0 0
\(493\) −12.0000 + 12.0000i −0.540453 + 0.540453i
\(494\) 6.00000 6.00000i 0.269953 0.269953i
\(495\) −9.00000 + 3.00000i −0.404520 + 0.134840i
\(496\) 0 0
\(497\) 0 0
\(498\) 18.0000 + 18.0000i 0.806599 + 0.806599i
\(499\) −29.0000 29.0000i −1.29822 1.29822i −0.929568 0.368650i \(-0.879820\pi\)
−0.368650 0.929568i \(-0.620180\pi\)
\(500\) 4.00000 + 22.0000i 0.178885 + 0.983870i
\(501\) 8.00000 8.00000i 0.357414 0.357414i
\(502\) 18.0000i 0.803379i
\(503\) 32.0000 1.42681 0.713405 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) −3.00000 9.00000i −0.133498 0.400495i
\(506\) 48.0000i 2.13386i
\(507\) −5.00000 5.00000i −0.222058 0.222058i
\(508\) −12.0000 −0.532414
\(509\) −9.00000 9.00000i −0.398918 0.398918i 0.478933 0.877851i \(-0.341024\pi\)
−0.877851 + 0.478933i \(0.841024\pi\)
\(510\) −8.00000 + 16.0000i −0.354246 + 0.708492i
\(511\) 0 0
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) 8.00000i 0.353209i
\(514\) −8.00000 8.00000i −0.352865 0.352865i
\(515\) 0 0
\(516\) 12.0000i 0.528271i
\(517\) −6.00000 6.00000i −0.263880 0.263880i
\(518\) 0 0
\(519\) 18.0000i 0.790112i
\(520\) 12.0000 24.0000i 0.526235 1.05247i
\(521\) 24.0000i 1.05146i 0.850652 + 0.525730i \(0.176208\pi\)
−0.850652 + 0.525730i \(0.823792\pi\)
\(522\) 6.00000i 0.262613i
\(523\) −9.00000 9.00000i −0.393543 0.393543i 0.482405 0.875948i \(-0.339763\pi\)
−0.875948 + 0.482405i \(0.839763\pi\)
\(524\) −18.0000 + 18.0000i −0.786334 + 0.786334i
\(525\) 0 0
\(526\) 16.0000 16.0000i 0.697633 0.697633i
\(527\) 0 0
\(528\) 24.0000i 1.04447i
\(529\) 41.0000 1.78261
\(530\) 18.0000 36.0000i 0.781870 1.56374i
\(531\) 9.00000 + 9.00000i 0.390567 + 0.390567i
\(532\) 0 0
\(533\) 0 0
\(534\) −24.0000 −1.03858
\(535\) −27.0000 + 9.00000i −1.16731 + 0.389104i
\(536\) −12.0000 −0.518321
\(537\) 6.00000 0.258919
\(538\) 18.0000 0.776035
\(539\) 21.0000 21.0000i 0.904534 0.904534i
\(540\) −8.00000 24.0000i −0.344265 1.03280i
\(541\) −1.00000 1.00000i −0.0429934 0.0429934i 0.685283 0.728277i \(-0.259678\pi\)
−0.728277 + 0.685283i \(0.759678\pi\)
\(542\) −16.0000 + 16.0000i −0.687259 + 0.687259i
\(543\) 2.00000i 0.0858282i
\(544\) 16.0000 + 16.0000i 0.685994 + 0.685994i
\(545\) −3.00000 + 1.00000i −0.128506 + 0.0428353i
\(546\) 0 0
\(547\) −3.00000 + 3.00000i −0.128271 + 0.128271i −0.768328 0.640057i \(-0.778911\pi\)
0.640057 + 0.768328i \(0.278911\pi\)
\(548\) 4.00000i 0.170872i
\(549\) 5.00000 5.00000i 0.213395 0.213395i
\(550\) −24.0000 + 18.0000i −1.02336 + 0.767523i
\(551\) 6.00000i 0.255609i
\(552\) −32.0000 −1.36201
\(553\) 0 0
\(554\) −6.00000 −0.254916
\(555\) 6.00000 12.0000i 0.254686 0.509372i
\(556\) 14.0000 + 14.0000i 0.593732 + 0.593732i
\(557\) −9.00000 + 9.00000i −0.381342 + 0.381342i −0.871586 0.490243i \(-0.836908\pi\)
0.490243 + 0.871586i \(0.336908\pi\)
\(558\) 0 0
\(559\) 18.0000 0.761319
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) −12.0000 12.0000i −0.506189 0.506189i
\(563\) −19.0000 + 19.0000i −0.800755 + 0.800755i −0.983213 0.182459i \(-0.941594\pi\)
0.182459 + 0.983213i \(0.441594\pi\)
\(564\) 4.00000 4.00000i 0.168430 0.168430i
\(565\) 16.0000 + 8.00000i 0.673125 + 0.336563i
\(566\) −30.0000 −1.26099
\(567\) 0 0
\(568\) 12.0000 12.0000i 0.503509 0.503509i
\(569\) 24.0000i 1.00613i −0.864248 0.503066i \(-0.832205\pi\)
0.864248 0.503066i \(-0.167795\pi\)
\(570\) −2.00000 6.00000i −0.0837708 0.251312i
\(571\) −11.0000 + 11.0000i −0.460336 + 0.460336i −0.898765 0.438430i \(-0.855535\pi\)
0.438430 + 0.898765i \(0.355535\pi\)
\(572\) 36.0000 1.50524
\(573\) −24.0000 + 24.0000i −1.00261 + 1.00261i
\(574\) 0 0
\(575\) 24.0000 + 32.0000i 1.00087 + 1.33449i
\(576\) −8.00000 −0.333333
\(577\) 24.0000i 0.999133i −0.866276 0.499567i \(-0.833493\pi\)
0.866276 0.499567i \(-0.166507\pi\)
\(578\) −1.00000 + 1.00000i −0.0415945 + 0.0415945i
\(579\) 12.0000 + 12.0000i 0.498703 + 0.498703i
\(580\) −6.00000 18.0000i −0.249136 0.747409i
\(581\) 0 0
\(582\) 24.0000 0.994832
\(583\) 54.0000 2.23645
\(584\) 12.0000 + 12.0000i 0.496564 + 0.496564i
\(585\) 9.00000 3.00000i 0.372104 0.124035i
\(586\) 18.0000 0.743573
\(587\) −9.00000 9.00000i −0.371470 0.371470i 0.496543 0.868012i \(-0.334603\pi\)
−0.868012 + 0.496543i \(0.834603\pi\)
\(588\) 14.0000 + 14.0000i 0.577350 + 0.577350i
\(589\) 0 0
\(590\) 36.0000 + 18.0000i 1.48210 + 0.741048i
\(591\) −10.0000 −0.411345
\(592\) −12.0000 12.0000i −0.493197 0.493197i
\(593\) 32.0000i 1.31408i −0.753855 0.657041i \(-0.771808\pi\)
0.753855 0.657041i \(-0.228192\pi\)
\(594\) 24.0000 24.0000i 0.984732 0.984732i
\(595\) 0 0
\(596\) −6.00000 6.00000i −0.245770 0.245770i
\(597\) 2.00000 + 2.00000i 0.0818546 + 0.0818546i
\(598\) 48.0000i 1.96287i
\(599\) 30.0000i 1.22577i −0.790173 0.612883i \(-0.790010\pi\)
0.790173 0.612883i \(-0.209990\pi\)
\(600\) −12.0000 16.0000i −0.489898 0.653197i
\(601\) 36.0000i 1.46847i 0.678895 + 0.734235i \(0.262459\pi\)
−0.678895 + 0.734235i \(0.737541\pi\)
\(602\) 0 0
\(603\) −3.00000 3.00000i −0.122169 0.122169i
\(604\) 36.0000 1.46482
\(605\) −14.0000 7.00000i −0.569181 0.284590i
\(606\) 6.00000 + 6.00000i 0.243733 + 0.243733i
\(607\) 42.0000i 1.70473i 0.522949 + 0.852364i \(0.324832\pi\)
−0.522949 + 0.852364i \(0.675168\pi\)
\(608\) −8.00000 −0.324443
\(609\) 0 0
\(610\) 10.0000 20.0000i 0.404888 0.809776i
\(611\) 6.00000 + 6.00000i 0.242734 + 0.242734i
\(612\) 8.00000i 0.323381i
\(613\) 27.0000 + 27.0000i 1.09052 + 1.09052i 0.995473 + 0.0950469i \(0.0303001\pi\)
0.0950469 + 0.995473i \(0.469700\pi\)
\(614\) 6.00000i 0.242140i
\(615\) 0 0
\(616\) 0 0
\(617\) −10.0000 −0.402585 −0.201292 0.979531i \(-0.564514\pi\)
−0.201292 + 0.979531i \(0.564514\pi\)
\(618\) 0 0
\(619\) 13.0000 13.0000i 0.522514 0.522514i −0.395816 0.918330i \(-0.629538\pi\)
0.918330 + 0.395816i \(0.129538\pi\)
\(620\) 0 0
\(621\) −32.0000 32.0000i −1.28412 1.28412i
\(622\) 6.00000 + 6.00000i 0.240578 + 0.240578i
\(623\) 0 0
\(624\) 24.0000i 0.960769i
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 6.00000 6.00000i 0.239808 0.239808i
\(627\) 6.00000 6.00000i 0.239617 0.239617i
\(628\) 18.0000 + 18.0000i 0.718278 + 0.718278i
\(629\) −12.0000 + 12.0000i −0.478471 + 0.478471i
\(630\) 0 0
\(631\) 2.00000i 0.0796187i 0.999207 + 0.0398094i \(0.0126751\pi\)
−0.999207 + 0.0398094i \(0.987325\pi\)
\(632\) 16.0000 + 16.0000i 0.636446 + 0.636446i
\(633\) 22.0000 0.874421
\(634\) 14.0000i 0.556011i
\(635\) −12.0000 6.00000i −0.476205 0.238103i
\(636\) 36.0000i 1.42749i
\(637\) −21.0000 + 21.0000i −0.832050 + 0.832050i
\(638\) 18.0000 18.0000i 0.712627 0.712627i
\(639\) 6.00000 0.237356
\(640\) −24.0000 + 8.00000i −0.948683 + 0.316228i
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 18.0000 18.0000i 0.710403 0.710403i
\(643\) −27.0000 + 27.0000i −1.06478 + 1.06478i −0.0670247 + 0.997751i \(0.521351\pi\)
−0.997751 + 0.0670247i \(0.978649\pi\)
\(644\) 0 0
\(645\) 6.00000 12.0000i 0.236250 0.472500i
\(646\) 8.00000i 0.314756i
\(647\) −32.0000 −1.25805 −0.629025 0.777385i \(-0.716546\pi\)
−0.629025 + 0.777385i \(0.716546\pi\)
\(648\) 10.0000 + 10.0000i 0.392837 + 0.392837i
\(649\) 54.0000i 2.11969i
\(650\) 24.0000 18.0000i 0.941357 0.706018i
\(651\) 0 0
\(652\) −18.0000 18.0000i −0.704934 0.704934i
\(653\) −9.00000 + 9.00000i −0.352197 + 0.352197i −0.860927 0.508729i \(-0.830115\pi\)
0.508729 + 0.860927i \(0.330115\pi\)
\(654\) 2.00000 2.00000i 0.0782062 0.0782062i
\(655\) −27.0000 + 9.00000i −1.05498 + 0.351659i
\(656\) 0 0
\(657\) 6.00000i 0.234082i
\(658\) 0 0
\(659\) −21.0000 21.0000i −0.818044 0.818044i 0.167781 0.985824i \(-0.446340\pi\)
−0.985824 + 0.167781i \(0.946340\pi\)
\(660\) 12.0000 24.0000i 0.467099 0.934199i
\(661\) −29.0000 + 29.0000i −1.12797 + 1.12797i −0.137462 + 0.990507i \(0.543895\pi\)
−0.990507 + 0.137462i \(0.956105\pi\)
\(662\) 10.0000i 0.388661i
\(663\) 24.0000 0.932083
\(664\) 36.0000 1.39707
\(665\) 0 0
\(666\) 6.00000i 0.232495i
\(667\) −24.0000 24.0000i −0.929284 0.929284i
\(668\) 16.0000i 0.619059i
\(669\) −6.00000 6.00000i −0.231973 0.231973i
\(670\) −12.0000 6.00000i −0.463600 0.231800i
\(671\) 30.0000 1.15814
\(672\) 0 0
\(673\) 12.0000i 0.462566i −0.972887 0.231283i \(-0.925708\pi\)
0.972887 0.231283i \(-0.0742923\pi\)
\(674\) −24.0000 24.0000i −0.924445 0.924445i
\(675\) 4.00000 28.0000i 0.153960 1.07772i
\(676\) −10.0000 −0.384615
\(677\) −9.00000 9.00000i −0.345898 0.345898i 0.512681 0.858579i \(-0.328652\pi\)
−0.858579 + 0.512681i \(0.828652\pi\)
\(678\) −16.0000 −0.614476
\(679\) 0 0
\(680\) 8.00000 + 24.0000i 0.306786 + 0.920358i
\(681\) 18.0000i 0.689761i
\(682\) 0 0
\(683\) −13.0000 13.0000i −0.497431 0.497431i 0.413206 0.910637i \(-0.364409\pi\)
−0.910637 + 0.413206i \(0.864409\pi\)
\(684\) −2.00000 2.00000i −0.0764719 0.0764719i
\(685\) 2.00000 4.00000i 0.0764161 0.152832i
\(686\) 0 0
\(687\) 14.0000i 0.534133i
\(688\) −12.0000 12.0000i −0.457496 0.457496i
\(689\) −54.0000 −2.05724
\(690\) −32.0000 16.0000i −1.21822 0.609110i
\(691\) −5.00000 5.00000i −0.190209 0.190209i 0.605577 0.795786i \(-0.292942\pi\)
−0.795786 + 0.605577i \(0.792942\pi\)
\(692\) 18.0000 + 18.0000i 0.684257 + 0.684257i
\(693\) 0 0
\(694\) −38.0000 −1.44246
\(695\) 7.00000 + 21.0000i 0.265525 + 0.796575i
\(696\) 12.0000 + 12.0000i 0.454859 + 0.454859i
\(697\) 0 0
\(698\) 10.0000 0.378506
\(699\) 22.0000 22.0000i 0.832116 0.832116i
\(700\) 0 0
\(701\) 3.00000 + 3.00000i 0.113308 + 0.113308i 0.761488 0.648179i \(-0.224469\pi\)
−0.648179 + 0.761488i \(0.724469\pi\)
\(702\) −24.0000 + 24.0000i −0.905822 + 0.905822i
\(703\) 6.00000i 0.226294i
\(704\) −24.0000 24.0000i −0.904534 0.904534i
\(705\) 6.00000 2.00000i 0.225973 0.0753244i
\(706\) −16.0000 16.0000i −0.602168 0.602168i
\(707\) 0 0
\(708\) −36.0000 −1.35296
\(709\) −13.0000 + 13.0000i −0.488225 + 0.488225i −0.907746 0.419521i \(-0.862198\pi\)
0.419521 + 0.907746i \(0.362198\pi\)
\(710\) 18.0000 6.00000i 0.675528 0.225176i
\(711\) 8.00000i 0.300023i
\(712\) −24.0000 + 24.0000i −0.899438 + 0.899438i
\(713\) 0 0
\(714\) 0 0
\(715\) 36.0000 + 18.0000i 1.34632 + 0.673162i
\(716\) 6.00000 6.00000i 0.224231 0.224231i
\(717\) 24.0000 24.0000i 0.896296 0.896296i
\(718\) −18.0000 18.0000i −0.671754 0.671754i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) −8.00000 4.00000i −0.298142 0.149071i
\(721\) 0 0
\(722\) 17.0000 + 17.0000i 0.632674 + 0.632674i
\(723\) −18.0000 + 18.0000i −0.669427 + 0.669427i
\(724\) 2.00000 + 2.00000i 0.0743294 + 0.0743294i
\(725\) 3.00000 21.0000i 0.111417 0.779920i
\(726\) 14.0000 0.519589
\(727\) 24.0000 0.890111 0.445055 0.895503i \(-0.353184\pi\)
0.445055 + 0.895503i \(0.353184\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 6.00000 + 18.0000i 0.222070 + 0.666210i
\(731\) −12.0000 + 12.0000i −0.443836 + 0.443836i
\(732\) 20.0000i 0.739221i
\(733\) 3.00000 3.00000i 0.110808 0.110808i −0.649529 0.760337i \(-0.725034\pi\)
0.760337 + 0.649529i \(0.225034\pi\)
\(734\) −18.0000 18.0000i −0.664392 0.664392i
\(735\) 7.00000 + 21.0000i 0.258199 + 0.774597i
\(736\) −32.0000 + 32.0000i −1.17954 + 1.17954i
\(737\) 18.0000i 0.663039i
\(738\) 0 0
\(739\) 19.0000 + 19.0000i 0.698926 + 0.698926i 0.964179 0.265253i \(-0.0854554\pi\)
−0.265253 + 0.964179i \(0.585455\pi\)
\(740\) −6.00000 18.0000i −0.220564 0.661693i
\(741\) −6.00000 + 6.00000i −0.220416 + 0.220416i
\(742\) 0 0
\(743\) −8.00000 −0.293492 −0.146746 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 0 0
\(745\) −3.00000 9.00000i −0.109911 0.329734i
\(746\) −6.00000 −0.219676
\(747\) 9.00000 + 9.00000i 0.329293 + 0.329293i
\(748\) −24.0000 + 24.0000i −0.877527 + 0.877527i
\(749\) 0 0
\(750\) −4.00000 22.0000i −0.146059 0.803326i
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 18.0000i 0.655956i
\(754\) −18.0000 + 18.0000i −0.655521 + 0.655521i
\(755\) 36.0000 + 18.0000i 1.31017 + 0.655087i
\(756\) 0 0
\(757\) −33.0000 33.0000i −1.19941 1.19941i −0.974345 0.225061i \(-0.927742\pi\)
−0.225061 0.974345i \(-0.572258\pi\)
\(758\) 2.00000i 0.0726433i
\(759\) 48.0000i 1.74229i
\(760\) −8.00000 4.00000i −0.290191 0.145095i
\(761\) 48.0000i 1.74000i −0.493053 0.869999i \(-0.664119\pi\)
0.493053 0.869999i \(-0.335881\pi\)
\(762\) 12.0000 0.434714
\(763\) 0 0
\(764\) 48.0000i 1.73658i
\(765\) −4.00000 + 8.00000i −0.144620 + 0.289241i
\(766\) −10.0000 10.0000i −0.361315 0.361315i
\(767\) 54.0000i 1.94983i
\(768\) 16.0000 16.0000i 0.577350 0.577350i
\(769\) −18.0000 −0.649097 −0.324548 0.945869i \(-0.605212\pi\)
−0.324548 + 0.945869i \(0.605212\pi\)
\(770\) 0 0
\(771\) 8.00000 + 8.00000i 0.288113 + 0.288113i
\(772\) 24.0000 0.863779
\(773\) 23.0000 + 23.0000i 0.827253 + 0.827253i 0.987136 0.159883i \(-0.0511118\pi\)
−0.159883 + 0.987136i \(0.551112\pi\)
\(774\) 6.00000i 0.215666i
\(775\) 0 0
\(776\) 24.0000 24.0000i 0.861550 0.861550i
\(777\) 0 0
\(778\)