Properties

Label 35.2.b.a.29.1
Level $35$
Weight $2$
Character 35.29
Analytic conductor $0.279$
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] = [35,2,Mod(29,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("35.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 35.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.279476407074\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 35.29
Dual form 35.2.b.a.29.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000i q^{2} +1.00000i q^{3} -2.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +2.00000 q^{6} +1.00000i q^{7} +2.00000 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} +1.00000i q^{3} -2.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} +2.00000 q^{6} +1.00000i q^{7} +2.00000 q^{9} +(2.00000 + 4.00000i) q^{10} -3.00000 q^{11} -2.00000i q^{12} +1.00000i q^{13} +2.00000 q^{14} +(-1.00000 - 2.00000i) q^{15} -4.00000 q^{16} -7.00000i q^{17} -4.00000i q^{18} +(4.00000 - 2.00000i) q^{20} -1.00000 q^{21} +6.00000i q^{22} +6.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +2.00000 q^{26} +5.00000i q^{27} -2.00000i q^{28} +5.00000 q^{29} +(-4.00000 + 2.00000i) q^{30} +2.00000 q^{31} +8.00000i q^{32} -3.00000i q^{33} -14.0000 q^{34} +(-1.00000 - 2.00000i) q^{35} -4.00000 q^{36} -2.00000i q^{37} -1.00000 q^{39} +2.00000 q^{41} +2.00000i q^{42} -4.00000i q^{43} +6.00000 q^{44} +(-4.00000 + 2.00000i) q^{45} +12.0000 q^{46} +3.00000i q^{47} -4.00000i q^{48} -1.00000 q^{49} +(-8.00000 - 6.00000i) q^{50} +7.00000 q^{51} -2.00000i q^{52} +6.00000i q^{53} +10.0000 q^{54} +(6.00000 - 3.00000i) q^{55} -10.0000i q^{58} -10.0000 q^{59} +(2.00000 + 4.00000i) q^{60} -8.00000 q^{61} -4.00000i q^{62} +2.00000i q^{63} +8.00000 q^{64} +(-1.00000 - 2.00000i) q^{65} -6.00000 q^{66} -2.00000i q^{67} +14.0000i q^{68} -6.00000 q^{69} +(-4.00000 + 2.00000i) q^{70} -8.00000 q^{71} +6.00000i q^{73} -4.00000 q^{74} +(4.00000 + 3.00000i) q^{75} -3.00000i q^{77} +2.00000i q^{78} +5.00000 q^{79} +(8.00000 - 4.00000i) q^{80} +1.00000 q^{81} -4.00000i q^{82} -4.00000i q^{83} +2.00000 q^{84} +(7.00000 + 14.0000i) q^{85} -8.00000 q^{86} +5.00000i q^{87} +(4.00000 + 8.00000i) q^{90} -1.00000 q^{91} -12.0000i q^{92} +2.00000i q^{93} +6.00000 q^{94} -8.00000 q^{96} -7.00000i q^{97} +2.00000i q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{9} + 4 q^{10} - 6 q^{11} + 4 q^{14} - 2 q^{15} - 8 q^{16} + 8 q^{20} - 2 q^{21} + 6 q^{25} + 4 q^{26} + 10 q^{29} - 8 q^{30} + 4 q^{31} - 28 q^{34} - 2 q^{35} - 8 q^{36} - 2 q^{39} + 4 q^{41} + 12 q^{44} - 8 q^{45} + 24 q^{46} - 2 q^{49} - 16 q^{50} + 14 q^{51} + 20 q^{54} + 12 q^{55} - 20 q^{59} + 4 q^{60} - 16 q^{61} + 16 q^{64} - 2 q^{65} - 12 q^{66} - 12 q^{69} - 8 q^{70} - 16 q^{71} - 8 q^{74} + 8 q^{75} + 10 q^{79} + 16 q^{80} + 2 q^{81} + 4 q^{84} + 14 q^{85} - 16 q^{86} + 8 q^{90} - 2 q^{91} + 12 q^{94} - 16 q^{96} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(3\) 1.00000i 0.577350i 0.957427 + 0.288675i \(0.0932147\pi\)
−0.957427 + 0.288675i \(0.906785\pi\)
\(4\) −2.00000 −1.00000
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 2.00000 0.816497
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 2.00000 0.666667
\(10\) 2.00000 + 4.00000i 0.632456 + 1.26491i
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 2.00000i 0.577350i
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 2.00000 0.534522
\(15\) −1.00000 2.00000i −0.258199 0.516398i
\(16\) −4.00000 −1.00000
\(17\) 7.00000i 1.69775i −0.528594 0.848875i \(-0.677281\pi\)
0.528594 0.848875i \(-0.322719\pi\)
\(18\) 4.00000i 0.942809i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 4.00000 2.00000i 0.894427 0.447214i
\(21\) −1.00000 −0.218218
\(22\) 6.00000i 1.27920i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 2.00000 0.392232
\(27\) 5.00000i 0.962250i
\(28\) 2.00000i 0.377964i
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) −4.00000 + 2.00000i −0.730297 + 0.365148i
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 8.00000i 1.41421i
\(33\) 3.00000i 0.522233i
\(34\) −14.0000 −2.40098
\(35\) −1.00000 2.00000i −0.169031 0.338062i
\(36\) −4.00000 −0.666667
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 2.00000i 0.308607i
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 6.00000 0.904534
\(45\) −4.00000 + 2.00000i −0.596285 + 0.298142i
\(46\) 12.0000 1.76930
\(47\) 3.00000i 0.437595i 0.975770 + 0.218797i \(0.0702134\pi\)
−0.975770 + 0.218797i \(0.929787\pi\)
\(48\) 4.00000i 0.577350i
\(49\) −1.00000 −0.142857
\(50\) −8.00000 6.00000i −1.13137 0.848528i
\(51\) 7.00000 0.980196
\(52\) 2.00000i 0.277350i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 10.0000 1.36083
\(55\) 6.00000 3.00000i 0.809040 0.404520i
\(56\) 0 0
\(57\) 0 0
\(58\) 10.0000i 1.31306i
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 2.00000 + 4.00000i 0.258199 + 0.516398i
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 2.00000i 0.251976i
\(64\) 8.00000 1.00000
\(65\) −1.00000 2.00000i −0.124035 0.248069i
\(66\) −6.00000 −0.738549
\(67\) 2.00000i 0.244339i −0.992509 0.122169i \(-0.961015\pi\)
0.992509 0.122169i \(-0.0389851\pi\)
\(68\) 14.0000i 1.69775i
\(69\) −6.00000 −0.722315
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 6.00000i 0.702247i 0.936329 + 0.351123i \(0.114200\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) −4.00000 −0.464991
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) 0 0
\(77\) 3.00000i 0.341882i
\(78\) 2.00000i 0.226455i
\(79\) 5.00000 0.562544 0.281272 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(80\) 8.00000 4.00000i 0.894427 0.447214i
\(81\) 1.00000 0.111111
\(82\) 4.00000i 0.441726i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 2.00000 0.218218
\(85\) 7.00000 + 14.0000i 0.759257 + 1.51851i
\(86\) −8.00000 −0.862662
\(87\) 5.00000i 0.536056i
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 4.00000 + 8.00000i 0.421637 + 0.843274i
\(91\) −1.00000 −0.104828
\(92\) 12.0000i 1.25109i
\(93\) 2.00000i 0.207390i
\(94\) 6.00000 0.618853
\(95\) 0 0
\(96\) −8.00000 −0.816497
\(97\) 7.00000i 0.710742i −0.934725 0.355371i \(-0.884354\pi\)
0.934725 0.355371i \(-0.115646\pi\)
\(98\) 2.00000i 0.202031i
\(99\) −6.00000 −0.603023
\(100\) −6.00000 + 8.00000i −0.600000 + 0.800000i
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 14.0000i 1.38621i
\(103\) 19.0000i 1.87213i −0.351833 0.936063i \(-0.614441\pi\)
0.351833 0.936063i \(-0.385559\pi\)
\(104\) 0 0
\(105\) 2.00000 1.00000i 0.195180 0.0975900i
\(106\) 12.0000 1.16554
\(107\) 8.00000i 0.773389i 0.922208 + 0.386695i \(0.126383\pi\)
−0.922208 + 0.386695i \(0.873617\pi\)
\(108\) 10.0000i 0.962250i
\(109\) −5.00000 −0.478913 −0.239457 0.970907i \(-0.576969\pi\)
−0.239457 + 0.970907i \(0.576969\pi\)
\(110\) −6.00000 12.0000i −0.572078 1.14416i
\(111\) 2.00000 0.189832
\(112\) 4.00000i 0.377964i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) −6.00000 12.0000i −0.559503 1.11901i
\(116\) −10.0000 −0.928477
\(117\) 2.00000i 0.184900i
\(118\) 20.0000i 1.84115i
\(119\) 7.00000 0.641689
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 16.0000i 1.44857i
\(123\) 2.00000i 0.180334i
\(124\) −4.00000 −0.359211
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 4.00000 0.356348
\(127\) 2.00000i 0.177471i −0.996055 0.0887357i \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) 0 0
\(129\) 4.00000 0.352180
\(130\) −4.00000 + 2.00000i −0.350823 + 0.175412i
\(131\) 22.0000 1.92215 0.961074 0.276289i \(-0.0891049\pi\)
0.961074 + 0.276289i \(0.0891049\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) −5.00000 10.0000i −0.430331 0.860663i
\(136\) 0 0
\(137\) 12.0000i 1.02523i −0.858619 0.512615i \(-0.828677\pi\)
0.858619 0.512615i \(-0.171323\pi\)
\(138\) 12.0000i 1.02151i
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 2.00000 + 4.00000i 0.169031 + 0.338062i
\(141\) −3.00000 −0.252646
\(142\) 16.0000i 1.34269i
\(143\) 3.00000i 0.250873i
\(144\) −8.00000 −0.666667
\(145\) −10.0000 + 5.00000i −0.830455 + 0.415227i
\(146\) 12.0000 0.993127
\(147\) 1.00000i 0.0824786i
\(148\) 4.00000i 0.328798i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) 6.00000 8.00000i 0.489898 0.653197i
\(151\) −13.0000 −1.05792 −0.528962 0.848645i \(-0.677419\pi\)
−0.528962 + 0.848645i \(0.677419\pi\)
\(152\) 0 0
\(153\) 14.0000i 1.13183i
\(154\) −6.00000 −0.483494
\(155\) −4.00000 + 2.00000i −0.321288 + 0.160644i
\(156\) 2.00000 0.160128
\(157\) 18.0000i 1.43656i 0.695756 + 0.718278i \(0.255069\pi\)
−0.695756 + 0.718278i \(0.744931\pi\)
\(158\) 10.0000i 0.795557i
\(159\) −6.00000 −0.475831
\(160\) −8.00000 16.0000i −0.632456 1.26491i
\(161\) −6.00000 −0.472866
\(162\) 2.00000i 0.157135i
\(163\) 14.0000i 1.09656i −0.836293 0.548282i \(-0.815282\pi\)
0.836293 0.548282i \(-0.184718\pi\)
\(164\) −4.00000 −0.312348
\(165\) 3.00000 + 6.00000i 0.233550 + 0.467099i
\(166\) −8.00000 −0.620920
\(167\) 3.00000i 0.232147i 0.993241 + 0.116073i \(0.0370308\pi\)
−0.993241 + 0.116073i \(0.962969\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 28.0000 14.0000i 2.14750 1.07375i
\(171\) 0 0
\(172\) 8.00000i 0.609994i
\(173\) 9.00000i 0.684257i −0.939653 0.342129i \(-0.888852\pi\)
0.939653 0.342129i \(-0.111148\pi\)
\(174\) 10.0000 0.758098
\(175\) 4.00000 + 3.00000i 0.302372 + 0.226779i
\(176\) 12.0000 0.904534
\(177\) 10.0000i 0.751646i
\(178\) 0 0
\(179\) 20.0000 1.49487 0.747435 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) 8.00000 4.00000i 0.596285 0.298142i
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 2.00000i 0.148250i
\(183\) 8.00000i 0.591377i
\(184\) 0 0
\(185\) 2.00000 + 4.00000i 0.147043 + 0.294086i
\(186\) 4.00000 0.293294
\(187\) 21.0000i 1.53567i
\(188\) 6.00000i 0.437595i
\(189\) −5.00000 −0.363696
\(190\) 0 0
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 8.00000i 0.577350i
\(193\) 16.0000i 1.15171i 0.817554 + 0.575853i \(0.195330\pi\)
−0.817554 + 0.575853i \(0.804670\pi\)
\(194\) −14.0000 −1.00514
\(195\) 2.00000 1.00000i 0.143223 0.0716115i
\(196\) 2.00000 0.142857
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 12.0000i 0.852803i
\(199\) 10.0000 0.708881 0.354441 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) 2.00000 0.141069
\(202\) 24.0000i 1.68863i
\(203\) 5.00000i 0.350931i
\(204\) −14.0000 −0.980196
\(205\) −4.00000 + 2.00000i −0.279372 + 0.139686i
\(206\) −38.0000 −2.64759
\(207\) 12.0000i 0.834058i
\(208\) 4.00000i 0.277350i
\(209\) 0 0
\(210\) −2.00000 4.00000i −0.138013 0.276026i
\(211\) −13.0000 −0.894957 −0.447478 0.894295i \(-0.647678\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) 12.0000i 0.824163i
\(213\) 8.00000i 0.548151i
\(214\) 16.0000 1.09374
\(215\) 4.00000 + 8.00000i 0.272798 + 0.545595i
\(216\) 0 0
\(217\) 2.00000i 0.135769i
\(218\) 10.0000i 0.677285i
\(219\) −6.00000 −0.405442
\(220\) −12.0000 + 6.00000i −0.809040 + 0.404520i
\(221\) 7.00000 0.470871
\(222\) 4.00000i 0.268462i
\(223\) 21.0000i 1.40626i 0.711059 + 0.703132i \(0.248216\pi\)
−0.711059 + 0.703132i \(0.751784\pi\)
\(224\) −8.00000 −0.534522
\(225\) 6.00000 8.00000i 0.400000 0.533333i
\(226\) 12.0000 0.798228
\(227\) 17.0000i 1.12833i −0.825662 0.564165i \(-0.809198\pi\)
0.825662 0.564165i \(-0.190802\pi\)
\(228\) 0 0
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −24.0000 + 12.0000i −1.58251 + 0.791257i
\(231\) 3.00000 0.197386
\(232\) 0 0
\(233\) 16.0000i 1.04819i 0.851658 + 0.524097i \(0.175597\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 4.00000 0.261488
\(235\) −3.00000 6.00000i −0.195698 0.391397i
\(236\) 20.0000 1.30189
\(237\) 5.00000i 0.324785i
\(238\) 14.0000i 0.907485i
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 4.00000 + 8.00000i 0.258199 + 0.516398i
\(241\) 22.0000 1.41714 0.708572 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 4.00000i 0.257130i
\(243\) 16.0000i 1.02640i
\(244\) 16.0000 1.02430
\(245\) 2.00000 1.00000i 0.127775 0.0638877i
\(246\) 4.00000 0.255031
\(247\) 0 0
\(248\) 0 0
\(249\) 4.00000 0.253490
\(250\) 22.0000 + 4.00000i 1.39140 + 0.252982i
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 4.00000i 0.251976i
\(253\) 18.0000i 1.13165i
\(254\) −4.00000 −0.250982
\(255\) −14.0000 + 7.00000i −0.876714 + 0.438357i
\(256\) 16.0000 1.00000
\(257\) 22.0000i 1.37232i −0.727450 0.686161i \(-0.759294\pi\)
0.727450 0.686161i \(-0.240706\pi\)
\(258\) 8.00000i 0.498058i
\(259\) 2.00000 0.124274
\(260\) 2.00000 + 4.00000i 0.124035 + 0.248069i
\(261\) 10.0000 0.618984
\(262\) 44.0000i 2.71833i
\(263\) 24.0000i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(264\) 0 0
\(265\) −6.00000 12.0000i −0.368577 0.737154i
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000i 0.244339i
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) −20.0000 + 10.0000i −1.21716 + 0.608581i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 28.0000i 1.69775i
\(273\) 1.00000i 0.0605228i
\(274\) −24.0000 −1.44989
\(275\) −9.00000 + 12.0000i −0.542720 + 0.723627i
\(276\) 12.0000 0.722315
\(277\) 2.00000i 0.120168i −0.998193 0.0600842i \(-0.980863\pi\)
0.998193 0.0600842i \(-0.0191369\pi\)
\(278\) 20.0000i 1.19952i
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 7.00000 0.417585 0.208792 0.977960i \(-0.433047\pi\)
0.208792 + 0.977960i \(0.433047\pi\)
\(282\) 6.00000i 0.357295i
\(283\) 11.0000i 0.653882i 0.945045 + 0.326941i \(0.106018\pi\)
−0.945045 + 0.326941i \(0.893982\pi\)
\(284\) 16.0000 0.949425
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 2.00000i 0.118056i
\(288\) 16.0000i 0.942809i
\(289\) −32.0000 −1.88235
\(290\) 10.0000 + 20.0000i 0.587220 + 1.17444i
\(291\) 7.00000 0.410347
\(292\) 12.0000i 0.702247i
\(293\) 9.00000i 0.525786i −0.964825 0.262893i \(-0.915323\pi\)
0.964825 0.262893i \(-0.0846766\pi\)
\(294\) −2.00000 −0.116642
\(295\) 20.0000 10.0000i 1.16445 0.582223i
\(296\) 0 0
\(297\) 15.0000i 0.870388i
\(298\) 20.0000i 1.15857i
\(299\) −6.00000 −0.346989
\(300\) −8.00000 6.00000i −0.461880 0.346410i
\(301\) 4.00000 0.230556
\(302\) 26.0000i 1.49613i
\(303\) 12.0000i 0.689382i
\(304\) 0 0
\(305\) 16.0000 8.00000i 0.916157 0.458079i
\(306\) −28.0000 −1.60065
\(307\) 7.00000i 0.399511i −0.979846 0.199756i \(-0.935985\pi\)
0.979846 0.199756i \(-0.0640148\pi\)
\(308\) 6.00000i 0.341882i
\(309\) 19.0000 1.08087
\(310\) 4.00000 + 8.00000i 0.227185 + 0.454369i
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) 21.0000i 1.18699i 0.804838 + 0.593495i \(0.202252\pi\)
−0.804838 + 0.593495i \(0.797748\pi\)
\(314\) 36.0000 2.03160
\(315\) −2.00000 4.00000i −0.112687 0.225374i
\(316\) −10.0000 −0.562544
\(317\) 12.0000i 0.673987i −0.941507 0.336994i \(-0.890590\pi\)
0.941507 0.336994i \(-0.109410\pi\)
\(318\) 12.0000i 0.672927i
\(319\) −15.0000 −0.839839
\(320\) −16.0000 + 8.00000i −0.894427 + 0.447214i
\(321\) −8.00000 −0.446516
\(322\) 12.0000i 0.668734i
\(323\) 0 0
\(324\) −2.00000 −0.111111
\(325\) 4.00000 + 3.00000i 0.221880 + 0.166410i
\(326\) −28.0000 −1.55078
\(327\) 5.00000i 0.276501i
\(328\) 0 0
\(329\) −3.00000 −0.165395
\(330\) 12.0000 6.00000i 0.660578 0.330289i
\(331\) 12.0000 0.659580 0.329790 0.944054i \(-0.393022\pi\)
0.329790 + 0.944054i \(0.393022\pi\)
\(332\) 8.00000i 0.439057i
\(333\) 4.00000i 0.219199i
\(334\) 6.00000 0.328305
\(335\) 2.00000 + 4.00000i 0.109272 + 0.218543i
\(336\) 4.00000 0.218218
\(337\) 18.0000i 0.980522i 0.871576 + 0.490261i \(0.163099\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) 24.0000i 1.30543i
\(339\) −6.00000 −0.325875
\(340\) −14.0000 28.0000i −0.759257 1.51851i
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 12.0000 6.00000i 0.646058 0.323029i
\(346\) −18.0000 −0.967686
\(347\) 18.0000i 0.966291i 0.875540 + 0.483145i \(0.160506\pi\)
−0.875540 + 0.483145i \(0.839494\pi\)
\(348\) 10.0000i 0.536056i
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) 6.00000 8.00000i 0.320713 0.427618i
\(351\) −5.00000 −0.266880
\(352\) 24.0000i 1.27920i
\(353\) 11.0000i 0.585471i 0.956193 + 0.292735i \(0.0945655\pi\)
−0.956193 + 0.292735i \(0.905434\pi\)
\(354\) −20.0000 −1.06299
\(355\) 16.0000 8.00000i 0.849192 0.424596i
\(356\) 0 0
\(357\) 7.00000i 0.370479i
\(358\) 40.0000i 2.11407i
\(359\) 20.0000 1.05556 0.527780 0.849381i \(-0.323025\pi\)
0.527780 + 0.849381i \(0.323025\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 36.0000i 1.89212i
\(363\) 2.00000i 0.104973i
\(364\) 2.00000 0.104828
\(365\) −6.00000 12.0000i −0.314054 0.628109i
\(366\) −16.0000 −0.836333
\(367\) 3.00000i 0.156599i 0.996930 + 0.0782994i \(0.0249490\pi\)
−0.996930 + 0.0782994i \(0.975051\pi\)
\(368\) 24.0000i 1.25109i
\(369\) 4.00000 0.208232
\(370\) 8.00000 4.00000i 0.415900 0.207950i
\(371\) −6.00000 −0.311504
\(372\) 4.00000i 0.207390i
\(373\) 24.0000i 1.24267i −0.783544 0.621336i \(-0.786590\pi\)
0.783544 0.621336i \(-0.213410\pi\)
\(374\) 42.0000 2.17177
\(375\) −11.0000 2.00000i −0.568038 0.103280i
\(376\) 0 0
\(377\) 5.00000i 0.257513i
\(378\) 10.0000i 0.514344i
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 6.00000i 0.306987i
\(383\) 16.0000i 0.817562i 0.912633 + 0.408781i \(0.134046\pi\)
−0.912633 + 0.408781i \(0.865954\pi\)
\(384\) 0 0
\(385\) 3.00000 + 6.00000i 0.152894 + 0.305788i
\(386\) 32.0000 1.62876
\(387\) 8.00000i 0.406663i
\(388\) 14.0000i 0.710742i
\(389\) −5.00000 −0.253510 −0.126755 0.991934i \(-0.540456\pi\)
−0.126755 + 0.991934i \(0.540456\pi\)
\(390\) −2.00000 4.00000i −0.101274 0.202548i
\(391\) 42.0000 2.12403
\(392\) 0 0
\(393\) 22.0000i 1.10975i
\(394\) −4.00000 −0.201517
\(395\) −10.0000 + 5.00000i −0.503155 + 0.251577i
\(396\) 12.0000 0.603023
\(397\) 7.00000i 0.351320i −0.984451 0.175660i \(-0.943794\pi\)
0.984451 0.175660i \(-0.0562059\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 0 0
\(400\) −12.0000 + 16.0000i −0.600000 + 0.800000i
\(401\) −3.00000 −0.149813 −0.0749064 0.997191i \(-0.523866\pi\)
−0.0749064 + 0.997191i \(0.523866\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 2.00000i 0.0996271i
\(404\) −24.0000 −1.19404
\(405\) −2.00000 + 1.00000i −0.0993808 + 0.0496904i
\(406\) 10.0000 0.496292
\(407\) 6.00000i 0.297409i
\(408\) 0 0
\(409\) −20.0000 −0.988936 −0.494468 0.869196i \(-0.664637\pi\)
−0.494468 + 0.869196i \(0.664637\pi\)
\(410\) 4.00000 + 8.00000i 0.197546 + 0.395092i
\(411\) 12.0000 0.591916
\(412\) 38.0000i 1.87213i
\(413\) 10.0000i 0.492068i
\(414\) 24.0000 1.17954
\(415\) 4.00000 + 8.00000i 0.196352 + 0.392705i
\(416\) −8.00000 −0.392232
\(417\) 10.0000i 0.489702i
\(418\) 0 0
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) −4.00000 + 2.00000i −0.195180 + 0.0975900i
\(421\) −3.00000 −0.146211 −0.0731055 0.997324i \(-0.523291\pi\)
−0.0731055 + 0.997324i \(0.523291\pi\)
\(422\) 26.0000i 1.26566i
\(423\) 6.00000i 0.291730i
\(424\) 0 0
\(425\) −28.0000 21.0000i −1.35820 1.01865i
\(426\) −16.0000 −0.775203
\(427\) 8.00000i 0.387147i
\(428\) 16.0000i 0.773389i
\(429\) 3.00000 0.144841
\(430\) 16.0000 8.00000i 0.771589 0.385794i
\(431\) −23.0000 −1.10787 −0.553936 0.832560i \(-0.686875\pi\)
−0.553936 + 0.832560i \(0.686875\pi\)
\(432\) 20.0000i 0.962250i
\(433\) 26.0000i 1.24948i 0.780833 + 0.624740i \(0.214795\pi\)
−0.780833 + 0.624740i \(0.785205\pi\)
\(434\) 4.00000 0.192006
\(435\) −5.00000 10.0000i −0.239732 0.479463i
\(436\) 10.0000 0.478913
\(437\) 0 0
\(438\) 12.0000i 0.573382i
\(439\) −30.0000 −1.43182 −0.715911 0.698192i \(-0.753988\pi\)
−0.715911 + 0.698192i \(0.753988\pi\)
\(440\) 0 0
\(441\) −2.00000 −0.0952381
\(442\) 14.0000i 0.665912i
\(443\) 4.00000i 0.190046i −0.995475 0.0950229i \(-0.969708\pi\)
0.995475 0.0950229i \(-0.0302924\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) 42.0000 1.98876
\(447\) 10.0000i 0.472984i
\(448\) 8.00000i 0.377964i
\(449\) 5.00000 0.235965 0.117982 0.993016i \(-0.462357\pi\)
0.117982 + 0.993016i \(0.462357\pi\)
\(450\) −16.0000 12.0000i −0.754247 0.565685i
\(451\) −6.00000 −0.282529
\(452\) 12.0000i 0.564433i
\(453\) 13.0000i 0.610793i
\(454\) −34.0000 −1.59570
\(455\) 2.00000 1.00000i 0.0937614 0.0468807i
\(456\) 0 0
\(457\) 38.0000i 1.77757i 0.458329 + 0.888783i \(0.348448\pi\)
−0.458329 + 0.888783i \(0.651552\pi\)
\(458\) 20.0000i 0.934539i
\(459\) 35.0000 1.63366
\(460\) 12.0000 + 24.0000i 0.559503 + 1.11901i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 6.00000i 0.279145i
\(463\) 36.0000i 1.67306i 0.547920 + 0.836531i \(0.315420\pi\)
−0.547920 + 0.836531i \(0.684580\pi\)
\(464\) −20.0000 −0.928477
\(465\) −2.00000 4.00000i −0.0927478 0.185496i
\(466\) 32.0000 1.48237
\(467\) 27.0000i 1.24941i −0.780860 0.624705i \(-0.785219\pi\)
0.780860 0.624705i \(-0.214781\pi\)
\(468\) 4.00000i 0.184900i
\(469\) 2.00000 0.0923514
\(470\) −12.0000 + 6.00000i −0.553519 + 0.276759i
\(471\) −18.0000 −0.829396
\(472\) 0 0
\(473\) 12.0000i 0.551761i
\(474\) 10.0000 0.459315
\(475\) 0 0
\(476\) −14.0000 −0.641689
\(477\) 12.0000i 0.549442i
\(478\) 30.0000i 1.37217i
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 16.0000 8.00000i 0.730297 0.365148i
\(481\) 2.00000 0.0911922
\(482\) 44.0000i 2.00415i
\(483\) 6.00000i 0.273009i
\(484\) 4.00000 0.181818
\(485\) 7.00000 + 14.0000i 0.317854 + 0.635707i
\(486\) 32.0000 1.45155
\(487\) 42.0000i 1.90320i −0.307337 0.951601i \(-0.599438\pi\)
0.307337 0.951601i \(-0.400562\pi\)
\(488\) 0 0
\(489\) 14.0000 0.633102
\(490\) −2.00000 4.00000i −0.0903508 0.180702i
\(491\) 7.00000 0.315906 0.157953 0.987447i \(-0.449511\pi\)
0.157953 + 0.987447i \(0.449511\pi\)
\(492\) 4.00000i 0.180334i
\(493\) 35.0000i 1.57632i
\(494\) 0 0
\(495\) 12.0000 6.00000i 0.539360 0.269680i
\(496\) −8.00000 −0.359211
\(497\) 8.00000i 0.358849i
\(498\) 8.00000i 0.358489i
\(499\) 35.0000 1.56682 0.783408 0.621508i \(-0.213480\pi\)
0.783408 + 0.621508i \(0.213480\pi\)
\(500\) 4.00000 22.0000i 0.178885 0.983870i
\(501\) −3.00000 −0.134030
\(502\) 36.0000i 1.60676i
\(503\) 9.00000i 0.401290i −0.979664 0.200645i \(-0.935696\pi\)
0.979664 0.200645i \(-0.0643038\pi\)
\(504\) 0 0
\(505\) −24.0000 + 12.0000i −1.06799 + 0.533993i
\(506\) −36.0000 −1.60040
\(507\) 12.0000i 0.532939i
\(508\) 4.00000i 0.177471i
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 14.0000 + 28.0000i 0.619930 + 1.23986i
\(511\) −6.00000 −0.265424
\(512\) 32.0000i 1.41421i
\(513\) 0 0
\(514\) −44.0000 −1.94076
\(515\) 19.0000 + 38.0000i 0.837240 + 1.67448i
\(516\) −8.00000 −0.352180
\(517\) 9.00000i 0.395820i
\(518\) 4.00000i 0.175750i
\(519\) 9.00000 0.395056
\(520\) 0 0
\(521\) −28.0000 −1.22670 −0.613351 0.789810i \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) 20.0000i 0.875376i
\(523\) 4.00000i 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) −44.0000 −1.92215
\(525\) −3.00000 + 4.00000i −0.130931 + 0.174574i
\(526\) −48.0000 −2.09290
\(527\) 14.0000i 0.609850i
\(528\) 12.0000i 0.522233i
\(529\) −13.0000 −0.565217
\(530\) −24.0000 + 12.0000i −1.04249 + 0.521247i
\(531\) −20.0000 −0.867926
\(532\) 0 0
\(533\) 2.00000i 0.0866296i
\(534\) 0 0
\(535\) −8.00000 16.0000i −0.345870 0.691740i
\(536\) 0 0
\(537\) 20.0000i 0.863064i
\(538\) 20.0000i 0.862261i
\(539\) 3.00000 0.129219
\(540\) 10.0000 + 20.0000i 0.430331 + 0.860663i
\(541\) 27.0000 1.16082 0.580410 0.814324i \(-0.302892\pi\)
0.580410 + 0.814324i \(0.302892\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 18.0000i 0.772454i
\(544\) 56.0000 2.40098
\(545\) 10.0000 5.00000i 0.428353 0.214176i
\(546\) −2.00000 −0.0855921
\(547\) 32.0000i 1.36822i −0.729378 0.684111i \(-0.760191\pi\)
0.729378 0.684111i \(-0.239809\pi\)
\(548\) 24.0000i 1.02523i
\(549\) −16.0000 −0.682863
\(550\) 24.0000 + 18.0000i 1.02336 + 0.767523i
\(551\) 0 0
\(552\) 0 0
\(553\) 5.00000i 0.212622i
\(554\) −4.00000 −0.169944
\(555\) −4.00000 + 2.00000i −0.169791 + 0.0848953i
\(556\) −20.0000 −0.848189
\(557\) 28.0000i 1.18640i 0.805056 + 0.593199i \(0.202135\pi\)
−0.805056 + 0.593199i \(0.797865\pi\)
\(558\) 8.00000i 0.338667i
\(559\) 4.00000 0.169182
\(560\) 4.00000 + 8.00000i 0.169031 + 0.338062i
\(561\) −21.0000 −0.886621
\(562\) 14.0000i 0.590554i
\(563\) 24.0000i 1.01148i −0.862686 0.505740i \(-0.831220\pi\)
0.862686 0.505740i \(-0.168780\pi\)
\(564\) 6.00000 0.252646
\(565\) −6.00000 12.0000i −0.252422 0.504844i
\(566\) 22.0000 0.924729
\(567\) 1.00000i 0.0419961i
\(568\) 0 0
\(569\) 30.0000 1.25767 0.628833 0.777541i \(-0.283533\pi\)
0.628833 + 0.777541i \(0.283533\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 6.00000i 0.250873i
\(573\) 3.00000i 0.125327i
\(574\) 4.00000 0.166957
\(575\) 24.0000 + 18.0000i 1.00087 + 0.750652i
\(576\) 16.0000 0.666667
\(577\) 43.0000i 1.79011i 0.445952 + 0.895057i \(0.352865\pi\)
−0.445952 + 0.895057i \(0.647135\pi\)
\(578\) 64.0000i 2.66205i
\(579\) −16.0000 −0.664937
\(580\) 20.0000 10.0000i 0.830455 0.415227i
\(581\) 4.00000 0.165948
\(582\) 14.0000i 0.580319i
\(583\) 18.0000i 0.745484i
\(584\) 0 0
\(585\) −2.00000 4.00000i −0.0826898 0.165380i
\(586\) −18.0000 −0.743573
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 2.00000i 0.0824786i
\(589\) 0 0
\(590\) −20.0000 40.0000i −0.823387 1.64677i
\(591\) 2.00000 0.0822690
\(592\) 8.00000i 0.328798i
\(593\) 41.0000i 1.68367i 0.539736 + 0.841834i \(0.318524\pi\)
−0.539736 + 0.841834i \(0.681476\pi\)
\(594\) −30.0000 −1.23091
\(595\) −14.0000 + 7.00000i −0.573944 + 0.286972i
\(596\) 20.0000 0.819232
\(597\) 10.0000i 0.409273i
\(598\) 12.0000i 0.490716i
\(599\) −25.0000 −1.02147 −0.510736 0.859738i \(-0.670627\pi\)
−0.510736 + 0.859738i \(0.670627\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 4.00000i 0.162893i
\(604\) 26.0000 1.05792
\(605\) 4.00000 2.00000i 0.162623 0.0813116i
\(606\) 24.0000 0.974933
\(607\) 27.0000i 1.09590i −0.836512 0.547948i \(-0.815409\pi\)
0.836512 0.547948i \(-0.184591\pi\)
\(608\) 0 0
\(609\) −5.00000 −0.202610
\(610\) −16.0000 32.0000i −0.647821 1.29564i
\(611\) −3.00000 −0.121367
\(612\) 28.0000i 1.13183i
\(613\) 44.0000i 1.77714i −0.458738 0.888572i \(-0.651698\pi\)
0.458738 0.888572i \(-0.348302\pi\)
\(614\) −14.0000 −0.564994
\(615\) −2.00000 4.00000i −0.0806478 0.161296i
\(616\) 0 0
\(617\) 22.0000i 0.885687i −0.896599 0.442843i \(-0.853970\pi\)
0.896599 0.442843i \(-0.146030\pi\)
\(618\) 38.0000i 1.52858i
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 8.00000 4.00000i 0.321288 0.160644i
\(621\) −30.0000 −1.20386
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) 4.00000 0.160128
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 42.0000 1.67866
\(627\) 0 0
\(628\) 36.0000i 1.43656i
\(629\) −14.0000 −0.558217
\(630\) −8.00000 + 4.00000i −0.318728 + 0.159364i
\(631\) 37.0000 1.47295 0.736473 0.676467i \(-0.236490\pi\)
0.736473 + 0.676467i \(0.236490\pi\)
\(632\) 0 0
\(633\) 13.0000i 0.516704i
\(634\) −24.0000 −0.953162
\(635\) 2.00000 + 4.00000i 0.0793676 + 0.158735i
\(636\) 12.0000 0.475831
\(637\) 1.00000i 0.0396214i
\(638\) 30.0000i 1.18771i
\(639\) −16.0000 −0.632950
\(640\) 0 0
\(641\) 22.0000 0.868948 0.434474 0.900684i \(-0.356934\pi\)
0.434474 + 0.900684i \(0.356934\pi\)
\(642\) 16.0000i 0.631470i
\(643\) 1.00000i 0.0394362i 0.999806 + 0.0197181i \(0.00627687\pi\)
−0.999806 + 0.0197181i \(0.993723\pi\)
\(644\) 12.0000 0.472866
\(645\) −8.00000 + 4.00000i −0.315000 + 0.157500i
\(646\) 0 0
\(647\) 8.00000i 0.314512i 0.987558 + 0.157256i \(0.0502649\pi\)
−0.987558 + 0.157256i \(0.949735\pi\)
\(648\) 0 0
\(649\) 30.0000 1.17760
\(650\) 6.00000 8.00000i 0.235339 0.313786i
\(651\) −2.00000 −0.0783862
\(652\) 28.0000i 1.09656i
\(653\) 4.00000i 0.156532i −0.996933 0.0782660i \(-0.975062\pi\)
0.996933 0.0782660i \(-0.0249384\pi\)
\(654\) −10.0000 −0.391031
\(655\) −44.0000 + 22.0000i −1.71922 + 0.859611i
\(656\) −8.00000 −0.312348
\(657\) 12.0000i 0.468165i
\(658\) 6.00000i 0.233904i
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) −6.00000 12.0000i −0.233550 0.467099i
\(661\) 12.0000 0.466746 0.233373 0.972387i \(-0.425024\pi\)
0.233373 + 0.972387i \(0.425024\pi\)
\(662\) 24.0000i 0.932786i
\(663\) 7.00000i 0.271857i
\(664\) 0 0
\(665\) 0 0
\(666\) −8.00000 −0.309994
\(667\) 30.0000i 1.16160i
\(668\) 6.00000i 0.232147i
\(669\) −21.0000 −0.811907
\(670\) 8.00000 4.00000i 0.309067 0.154533i
\(671\) 24.0000 0.926510
\(672\) 8.00000i 0.308607i
\(673\) 24.0000i 0.925132i −0.886585 0.462566i \(-0.846929\pi\)
0.886585 0.462566i \(-0.153071\pi\)
\(674\) 36.0000 1.38667
\(675\) 20.0000 + 15.0000i 0.769800 + 0.577350i
\(676\) −24.0000 −0.923077
\(677\) 43.0000i 1.65262i 0.563212 + 0.826312i \(0.309565\pi\)
−0.563212 + 0.826312i \(0.690435\pi\)
\(678\) 12.0000i 0.460857i
\(679\) 7.00000 0.268635
\(680\) 0 0
\(681\) 17.0000 0.651441
\(682\) 12.0000i 0.459504i
\(683\) 16.0000i 0.612223i 0.951996 + 0.306111i \(0.0990280\pi\)
−0.951996 + 0.306111i \(0.900972\pi\)
\(684\) 0 0
\(685\) 12.0000 + 24.0000i 0.458496 + 0.916993i
\(686\) −2.00000 −0.0763604
\(687\) 10.0000i 0.381524i
\(688\) 16.0000i 0.609994i
\(689\) −6.00000 −0.228582
\(690\) −12.0000 24.0000i −0.456832 0.913664i
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 6.00000i 0.227921i
\(694\) 36.0000 1.36654
\(695\) −20.0000 + 10.0000i −0.758643 + 0.379322i
\(696\) 0 0
\(697\) 14.0000i 0.530288i
\(698\) 40.0000i 1.51402i
\(699\) −16.0000 −0.605176
\(700\) −8.00000 6.00000i −0.302372 0.226779i
\(701\) −13.0000 −0.491003 −0.245502 0.969396i \(-0.578953\pi\)
−0.245502 + 0.969396i \(0.578953\pi\)
\(702\) 10.0000i 0.377426i
\(703\) 0 0
\(704\) −24.0000 −0.904534
\(705\) 6.00000 3.00000i 0.225973 0.112987i
\(706\) 22.0000 0.827981
\(707\) 12.0000i 0.451306i
\(708\) 20.0000i 0.751646i
\(709\) −35.0000 −1.31445 −0.657226 0.753693i \(-0.728270\pi\)
−0.657226 + 0.753693i \(0.728270\pi\)
\(710\) −16.0000 32.0000i −0.600469 1.20094i
\(711\) 10.0000 0.375029
\(712\) 0 0
\(713\) 12.0000i 0.449404i
\(714\) 14.0000 0.523937
\(715\) 3.00000 + 6.00000i 0.112194 + 0.224387i
\(716\) −40.0000 −1.49487
\(717\) 15.0000i 0.560185i
\(718\) 40.0000i 1.49279i
\(719\) −30.0000 −1.11881 −0.559406 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 16.0000 8.00000i 0.596285 0.298142i
\(721\) 19.0000 0.707597
\(722\) 38.0000i 1.41421i
\(723\) 22.0000i 0.818189i
\(724\) 36.0000 1.33793
\(725\) 15.0000 20.0000i 0.557086 0.742781i
\(726\) −4.00000 −0.148454
\(727\) 28.0000i 1.03846i 0.854634 + 0.519231i \(0.173782\pi\)
−0.854634 + 0.519231i \(0.826218\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) −24.0000 + 12.0000i −0.888280 + 0.444140i
\(731\) −28.0000 −1.03562
\(732\) 16.0000i 0.591377i
\(733\) 1.00000i 0.0369358i 0.999829 + 0.0184679i \(0.00587886\pi\)
−0.999829 + 0.0184679i \(0.994121\pi\)
\(734\) 6.00000 0.221464
\(735\) 1.00000 + 2.00000i 0.0368856 + 0.0737711i
\(736\) −48.0000 −1.76930
\(737\) 6.00000i 0.221013i
\(738\) 8.00000i 0.294484i
\(739\) 35.0000 1.28750 0.643748 0.765238i \(-0.277379\pi\)
0.643748 + 0.765238i \(0.277379\pi\)
\(740\) −4.00000 8.00000i −0.147043 0.294086i
\(741\) 0 0
\(742\) 12.0000i 0.440534i
\(743\) 14.0000i 0.513610i −0.966463 0.256805i \(-0.917330\pi\)
0.966463 0.256805i \(-0.0826698\pi\)
\(744\) 0 0
\(745\) 20.0000 10.0000i 0.732743 0.366372i
\(746\) −48.0000 −1.75740
\(747\) 8.00000i 0.292705i
\(748\) 42.0000i 1.53567i
\(749\) −8.00000 −0.292314
\(750\) −4.00000 + 22.0000i −0.146059 + 0.803326i
\(751\) −33.0000 −1.20419 −0.602094 0.798426i \(-0.705667\pi\)
−0.602094 + 0.798426i \(0.705667\pi\)
\(752\) 12.0000i 0.437595i
\(753\) 18.0000i 0.655956i
\(754\) 10.0000 0.364179
\(755\) 26.0000 13.0000i 0.946237 0.473118i
\(756\) 10.0000 0.363696
\(757\) 32.0000i 1.16306i −0.813525 0.581530i \(-0.802454\pi\)
0.813525 0.581530i \(-0.197546\pi\)
\(758\) 40.0000i 1.45287i
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) 2.00000 0.0724999 0.0362500 0.999343i \(-0.488459\pi\)
0.0362500 + 0.999343i \(0.488459\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 5.00000i 0.181012i
\(764\) 6.00000 0.217072
\(765\) 14.0000 + 28.0000i 0.506171 + 1.01234i
\(766\) 32.0000 1.15621
\(767\) 10.0000i 0.361079i
\(768\) 16.0000i 0.577350i
\(769\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(770\) 12.0000 6.00000i 0.432450 0.216225i
\(771\) 22.0000 0.792311
\(772\) 32.0000i 1.15171i
\(773\) 21.0000i 0.755318i 0.925945 + 0.377659i \(0.123271\pi\)
−0.925945 + 0.377659i \(0.876729\pi\)
\(774\) −16.0000 −0.575108
\(775\) 6.00000 8.00000i 0.215526 0.287368i
\(776\) 0 0
\(777\) 2.00000i 0.0717496i
\(778\) 10.0000i 0.358517i
\(779\) 0 0
\(780\) −4.00000 + 2.00000i −0.143223 + 0.0716115i
\(781\) 24.0000 0.858788
\(782\) 84.0000i 3.00383i
\(783\) 25.0000i 0.893427i