Properties

Label 55.2.e.a.32.2
Level $55$
Weight $2$
Character 55.32
Analytic conductor $0.439$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,2,Mod(32,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.32");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.e (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: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 32.2
Root \(1.58114 - 1.58114i\) of defining polynomial
Character \(\chi\) \(=\) 55.32
Dual form 55.2.e.a.43.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.58114 - 1.58114i) q^{2} +(-1.00000 + 1.00000i) q^{3} -3.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +3.16228i q^{6} +(-1.58114 - 1.58114i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(1.58114 - 1.58114i) q^{2} +(-1.00000 + 1.00000i) q^{3} -3.00000i q^{4} +(-2.00000 + 1.00000i) q^{5} +3.16228i q^{6} +(-1.58114 - 1.58114i) q^{8} +1.00000i q^{9} +(-1.58114 + 4.74342i) q^{10} +(1.00000 - 3.16228i) q^{11} +(3.00000 + 3.00000i) q^{12} +(-3.16228 - 3.16228i) q^{13} +(1.00000 - 3.00000i) q^{15} +1.00000 q^{16} +(-3.16228 + 3.16228i) q^{17} +(1.58114 + 1.58114i) q^{18} +6.32456 q^{19} +(3.00000 + 6.00000i) q^{20} +(-3.41886 - 6.58114i) q^{22} +(-1.00000 + 1.00000i) q^{23} +3.16228 q^{24} +(3.00000 - 4.00000i) q^{25} -10.0000 q^{26} +(-4.00000 - 4.00000i) q^{27} -6.32456 q^{29} +(-3.16228 - 6.32456i) q^{30} +2.00000 q^{31} +(4.74342 - 4.74342i) q^{32} +(2.16228 + 4.16228i) q^{33} +10.0000i q^{34} +3.00000 q^{36} +(3.00000 + 3.00000i) q^{37} +(10.0000 - 10.0000i) q^{38} +6.32456 q^{39} +(4.74342 + 1.58114i) q^{40} +6.32456i q^{41} +(-9.48683 - 3.00000i) q^{44} +(-1.00000 - 2.00000i) q^{45} +3.16228i q^{46} +(3.00000 + 3.00000i) q^{47} +(-1.00000 + 1.00000i) q^{48} +7.00000i q^{49} +(-1.58114 - 11.0680i) q^{50} -6.32456i q^{51} +(-9.48683 + 9.48683i) q^{52} +(-1.00000 + 1.00000i) q^{53} -12.6491 q^{54} +(1.16228 + 7.32456i) q^{55} +(-6.32456 + 6.32456i) q^{57} +(-10.0000 + 10.0000i) q^{58} -6.00000i q^{59} +(-9.00000 - 3.00000i) q^{60} -6.32456i q^{61} +(3.16228 - 3.16228i) q^{62} -13.0000i q^{64} +(9.48683 + 3.16228i) q^{65} +(10.0000 + 3.16228i) q^{66} +(3.00000 + 3.00000i) q^{67} +(9.48683 + 9.48683i) q^{68} -2.00000i q^{69} -8.00000 q^{71} +(1.58114 - 1.58114i) q^{72} +(3.16228 + 3.16228i) q^{73} +9.48683 q^{74} +(1.00000 + 7.00000i) q^{75} -18.9737i q^{76} +(10.0000 - 10.0000i) q^{78} -6.32456 q^{79} +(-2.00000 + 1.00000i) q^{80} +5.00000 q^{81} +(10.0000 + 10.0000i) q^{82} +(-6.32456 - 6.32456i) q^{83} +(3.16228 - 9.48683i) q^{85} +(6.32456 - 6.32456i) q^{87} +(-6.58114 + 3.41886i) q^{88} -6.00000i q^{89} +(-4.74342 - 1.58114i) q^{90} +(3.00000 + 3.00000i) q^{92} +(-2.00000 + 2.00000i) q^{93} +9.48683 q^{94} +(-12.6491 + 6.32456i) q^{95} +9.48683i q^{96} +(-7.00000 - 7.00000i) q^{97} +(11.0680 + 11.0680i) q^{98} +(3.16228 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 8 q^{5} + 4 q^{11} + 12 q^{12} + 4 q^{15} + 4 q^{16} + 12 q^{20} - 20 q^{22} - 4 q^{23} + 12 q^{25} - 40 q^{26} - 16 q^{27} + 8 q^{31} - 4 q^{33} + 12 q^{36} + 12 q^{37} + 40 q^{38} - 4 q^{45} + 12 q^{47} - 4 q^{48} - 4 q^{53} - 8 q^{55} - 40 q^{58} - 36 q^{60} + 40 q^{66} + 12 q^{67} - 32 q^{71} + 4 q^{75} + 40 q^{78} - 8 q^{80} + 20 q^{81} + 40 q^{82} - 20 q^{88} + 12 q^{92} - 8 q^{93} - 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.58114 1.58114i 1.11803 1.11803i 0.126004 0.992030i \(-0.459785\pi\)
0.992030 0.126004i \(-0.0402153\pi\)
\(3\) −1.00000 + 1.00000i −0.577350 + 0.577350i −0.934172 0.356822i \(-0.883860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(4\) 3.00000i 1.50000i
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 3.16228i 1.29099i
\(7\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(8\) −1.58114 1.58114i −0.559017 0.559017i
\(9\) 1.00000i 0.333333i
\(10\) −1.58114 + 4.74342i −0.500000 + 1.50000i
\(11\) 1.00000 3.16228i 0.301511 0.953463i
\(12\) 3.00000 + 3.00000i 0.866025 + 0.866025i
\(13\) −3.16228 3.16228i −0.877058 0.877058i 0.116171 0.993229i \(-0.462938\pi\)
−0.993229 + 0.116171i \(0.962938\pi\)
\(14\) 0 0
\(15\) 1.00000 3.00000i 0.258199 0.774597i
\(16\) 1.00000 0.250000
\(17\) −3.16228 + 3.16228i −0.766965 + 0.766965i −0.977571 0.210606i \(-0.932456\pi\)
0.210606 + 0.977571i \(0.432456\pi\)
\(18\) 1.58114 + 1.58114i 0.372678 + 0.372678i
\(19\) 6.32456 1.45095 0.725476 0.688247i \(-0.241620\pi\)
0.725476 + 0.688247i \(0.241620\pi\)
\(20\) 3.00000 + 6.00000i 0.670820 + 1.34164i
\(21\) 0 0
\(22\) −3.41886 6.58114i −0.728904 1.40310i
\(23\) −1.00000 + 1.00000i −0.208514 + 0.208514i −0.803636 0.595121i \(-0.797104\pi\)
0.595121 + 0.803636i \(0.297104\pi\)
\(24\) 3.16228 0.645497
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) −10.0000 −1.96116
\(27\) −4.00000 4.00000i −0.769800 0.769800i
\(28\) 0 0
\(29\) −6.32456 −1.17444 −0.587220 0.809427i \(-0.699778\pi\)
−0.587220 + 0.809427i \(0.699778\pi\)
\(30\) −3.16228 6.32456i −0.577350 1.15470i
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 4.74342 4.74342i 0.838525 0.838525i
\(33\) 2.16228 + 4.16228i 0.376404 + 0.724560i
\(34\) 10.0000i 1.71499i
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) 3.00000 + 3.00000i 0.493197 + 0.493197i 0.909312 0.416115i \(-0.136609\pi\)
−0.416115 + 0.909312i \(0.636609\pi\)
\(38\) 10.0000 10.0000i 1.62221 1.62221i
\(39\) 6.32456 1.01274
\(40\) 4.74342 + 1.58114i 0.750000 + 0.250000i
\(41\) 6.32456i 0.987730i 0.869539 + 0.493865i \(0.164416\pi\)
−0.869539 + 0.493865i \(0.835584\pi\)
\(42\) 0 0
\(43\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(44\) −9.48683 3.00000i −1.43019 0.452267i
\(45\) −1.00000 2.00000i −0.149071 0.298142i
\(46\) 3.16228i 0.466252i
\(47\) 3.00000 + 3.00000i 0.437595 + 0.437595i 0.891202 0.453607i \(-0.149863\pi\)
−0.453607 + 0.891202i \(0.649863\pi\)
\(48\) −1.00000 + 1.00000i −0.144338 + 0.144338i
\(49\) 7.00000i 1.00000i
\(50\) −1.58114 11.0680i −0.223607 1.56525i
\(51\) 6.32456i 0.885615i
\(52\) −9.48683 + 9.48683i −1.31559 + 1.31559i
\(53\) −1.00000 + 1.00000i −0.137361 + 0.137361i −0.772444 0.635083i \(-0.780966\pi\)
0.635083 + 0.772444i \(0.280966\pi\)
\(54\) −12.6491 −1.72133
\(55\) 1.16228 + 7.32456i 0.156721 + 0.987643i
\(56\) 0 0
\(57\) −6.32456 + 6.32456i −0.837708 + 0.837708i
\(58\) −10.0000 + 10.0000i −1.31306 + 1.31306i
\(59\) 6.00000i 0.781133i −0.920575 0.390567i \(-0.872279\pi\)
0.920575 0.390567i \(-0.127721\pi\)
\(60\) −9.00000 3.00000i −1.16190 0.387298i
\(61\) 6.32456i 0.809776i −0.914366 0.404888i \(-0.867310\pi\)
0.914366 0.404888i \(-0.132690\pi\)
\(62\) 3.16228 3.16228i 0.401610 0.401610i
\(63\) 0 0
\(64\) 13.0000i 1.62500i
\(65\) 9.48683 + 3.16228i 1.17670 + 0.392232i
\(66\) 10.0000 + 3.16228i 1.23091 + 0.389249i
\(67\) 3.00000 + 3.00000i 0.366508 + 0.366508i 0.866202 0.499694i \(-0.166554\pi\)
−0.499694 + 0.866202i \(0.666554\pi\)
\(68\) 9.48683 + 9.48683i 1.15045 + 1.15045i
\(69\) 2.00000i 0.240772i
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 1.58114 1.58114i 0.186339 0.186339i
\(73\) 3.16228 + 3.16228i 0.370117 + 0.370117i 0.867520 0.497403i \(-0.165713\pi\)
−0.497403 + 0.867520i \(0.665713\pi\)
\(74\) 9.48683 1.10282
\(75\) 1.00000 + 7.00000i 0.115470 + 0.808290i
\(76\) 18.9737i 2.17643i
\(77\) 0 0
\(78\) 10.0000 10.0000i 1.13228 1.13228i
\(79\) −6.32456 −0.711568 −0.355784 0.934568i \(-0.615786\pi\)
−0.355784 + 0.934568i \(0.615786\pi\)
\(80\) −2.00000 + 1.00000i −0.223607 + 0.111803i
\(81\) 5.00000 0.555556
\(82\) 10.0000 + 10.0000i 1.10432 + 1.10432i
\(83\) −6.32456 6.32456i −0.694210 0.694210i 0.268945 0.963155i \(-0.413325\pi\)
−0.963155 + 0.268945i \(0.913325\pi\)
\(84\) 0 0
\(85\) 3.16228 9.48683i 0.342997 1.02899i
\(86\) 0 0
\(87\) 6.32456 6.32456i 0.678064 0.678064i
\(88\) −6.58114 + 3.41886i −0.701552 + 0.364452i
\(89\) 6.00000i 0.635999i −0.948091 0.317999i \(-0.896989\pi\)
0.948091 0.317999i \(-0.103011\pi\)
\(90\) −4.74342 1.58114i −0.500000 0.166667i
\(91\) 0 0
\(92\) 3.00000 + 3.00000i 0.312772 + 0.312772i
\(93\) −2.00000 + 2.00000i −0.207390 + 0.207390i
\(94\) 9.48683 0.978492
\(95\) −12.6491 + 6.32456i −1.29777 + 0.648886i
\(96\) 9.48683i 0.968246i
\(97\) −7.00000 7.00000i −0.710742 0.710742i 0.255948 0.966691i \(-0.417612\pi\)
−0.966691 + 0.255948i \(0.917612\pi\)
\(98\) 11.0680 + 11.0680i 1.11803 + 1.11803i
\(99\) 3.16228 + 1.00000i 0.317821 + 0.100504i
\(100\) −12.0000 9.00000i −1.20000 0.900000i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) −10.0000 10.0000i −0.990148 0.990148i
\(103\) 9.00000 9.00000i 0.886796 0.886796i −0.107418 0.994214i \(-0.534258\pi\)
0.994214 + 0.107418i \(0.0342582\pi\)
\(104\) 10.0000i 0.980581i
\(105\) 0 0
\(106\) 3.16228i 0.307148i
\(107\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) −12.0000 + 12.0000i −1.15470 + 1.15470i
\(109\) −12.6491 −1.21157 −0.605783 0.795630i \(-0.707140\pi\)
−0.605783 + 0.795630i \(0.707140\pi\)
\(110\) 13.4189 + 9.74342i 1.27944 + 0.928998i
\(111\) −6.00000 −0.569495
\(112\) 0 0
\(113\) 9.00000 9.00000i 0.846649 0.846649i −0.143065 0.989713i \(-0.545696\pi\)
0.989713 + 0.143065i \(0.0456957\pi\)
\(114\) 20.0000i 1.87317i
\(115\) 1.00000 3.00000i 0.0932505 0.279751i
\(116\) 18.9737i 1.76166i
\(117\) 3.16228 3.16228i 0.292353 0.292353i
\(118\) −9.48683 9.48683i −0.873334 0.873334i
\(119\) 0 0
\(120\) −6.32456 + 3.16228i −0.577350 + 0.288675i
\(121\) −9.00000 6.32456i −0.818182 0.574960i
\(122\) −10.0000 10.0000i −0.905357 0.905357i
\(123\) −6.32456 6.32456i −0.570266 0.570266i
\(124\) 6.00000i 0.538816i
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) −6.32456 + 6.32456i −0.561214 + 0.561214i −0.929652 0.368439i \(-0.879892\pi\)
0.368439 + 0.929652i \(0.379892\pi\)
\(128\) −11.0680 11.0680i −0.978280 0.978280i
\(129\) 0 0
\(130\) 20.0000 10.0000i 1.75412 0.877058i
\(131\) 12.6491i 1.10516i 0.833461 + 0.552579i \(0.186356\pi\)
−0.833461 + 0.552579i \(0.813644\pi\)
\(132\) 12.4868 6.48683i 1.08684 0.564606i
\(133\) 0 0
\(134\) 9.48683 0.819538
\(135\) 12.0000 + 4.00000i 1.03280 + 0.344265i
\(136\) 10.0000 0.857493
\(137\) 13.0000 + 13.0000i 1.11066 + 1.11066i 0.993061 + 0.117604i \(0.0375215\pi\)
0.117604 + 0.993061i \(0.462479\pi\)
\(138\) −3.16228 3.16228i −0.269191 0.269191i
\(139\) 12.6491 1.07288 0.536442 0.843937i \(-0.319768\pi\)
0.536442 + 0.843937i \(0.319768\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) −12.6491 + 12.6491i −1.06149 + 1.06149i
\(143\) −13.1623 + 6.83772i −1.10068 + 0.571799i
\(144\) 1.00000i 0.0833333i
\(145\) 12.6491 6.32456i 1.05045 0.525226i
\(146\) 10.0000 0.827606
\(147\) −7.00000 7.00000i −0.577350 0.577350i
\(148\) 9.00000 9.00000i 0.739795 0.739795i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 12.6491 + 9.48683i 1.03280 + 0.774597i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) −10.0000 10.0000i −0.811107 0.811107i
\(153\) −3.16228 3.16228i −0.255655 0.255655i
\(154\) 0 0
\(155\) −4.00000 + 2.00000i −0.321288 + 0.160644i
\(156\) 18.9737i 1.51911i
\(157\) −7.00000 7.00000i −0.558661 0.558661i 0.370265 0.928926i \(-0.379267\pi\)
−0.928926 + 0.370265i \(0.879267\pi\)
\(158\) −10.0000 + 10.0000i −0.795557 + 0.795557i
\(159\) 2.00000i 0.158610i
\(160\) −4.74342 + 14.2302i −0.375000 + 1.12500i
\(161\) 0 0
\(162\) 7.90569 7.90569i 0.621130 0.621130i
\(163\) −1.00000 + 1.00000i −0.0783260 + 0.0783260i −0.745184 0.666858i \(-0.767639\pi\)
0.666858 + 0.745184i \(0.267639\pi\)
\(164\) 18.9737 1.48159
\(165\) −8.48683 6.16228i −0.660699 0.479733i
\(166\) −20.0000 −1.55230
\(167\) 12.6491 12.6491i 0.978818 0.978818i −0.0209627 0.999780i \(-0.506673\pi\)
0.999780 + 0.0209627i \(0.00667312\pi\)
\(168\) 0 0
\(169\) 7.00000i 0.538462i
\(170\) −10.0000 20.0000i −0.766965 1.53393i
\(171\) 6.32456i 0.483651i
\(172\) 0 0
\(173\) 3.16228 + 3.16228i 0.240424 + 0.240424i 0.817025 0.576602i \(-0.195622\pi\)
−0.576602 + 0.817025i \(0.695622\pi\)
\(174\) 20.0000i 1.51620i
\(175\) 0 0
\(176\) 1.00000 3.16228i 0.0753778 0.238366i
\(177\) 6.00000 + 6.00000i 0.450988 + 0.450988i
\(178\) −9.48683 9.48683i −0.711068 0.711068i
\(179\) 4.00000i 0.298974i 0.988764 + 0.149487i \(0.0477622\pi\)
−0.988764 + 0.149487i \(0.952238\pi\)
\(180\) −6.00000 + 3.00000i −0.447214 + 0.223607i
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) 6.32456 + 6.32456i 0.467525 + 0.467525i
\(184\) 3.16228 0.233126
\(185\) −9.00000 3.00000i −0.661693 0.220564i
\(186\) 6.32456i 0.463739i
\(187\) 6.83772 + 13.1623i 0.500024 + 0.962521i
\(188\) 9.00000 9.00000i 0.656392 0.656392i
\(189\) 0 0
\(190\) −10.0000 + 30.0000i −0.725476 + 2.17643i
\(191\) 22.0000 1.59186 0.795932 0.605386i \(-0.206981\pi\)
0.795932 + 0.605386i \(0.206981\pi\)
\(192\) 13.0000 + 13.0000i 0.938194 + 0.938194i
\(193\) 15.8114 + 15.8114i 1.13813 + 1.13813i 0.988785 + 0.149343i \(0.0477159\pi\)
0.149343 + 0.988785i \(0.452284\pi\)
\(194\) −22.1359 −1.58927
\(195\) −12.6491 + 6.32456i −0.905822 + 0.452911i
\(196\) 21.0000 1.50000
\(197\) 3.16228 3.16228i 0.225303 0.225303i −0.585424 0.810727i \(-0.699072\pi\)
0.810727 + 0.585424i \(0.199072\pi\)
\(198\) 6.58114 3.41886i 0.467701 0.242968i
\(199\) 6.00000i 0.425329i −0.977125 0.212664i \(-0.931786\pi\)
0.977125 0.212664i \(-0.0682141\pi\)
\(200\) −11.0680 + 1.58114i −0.782624 + 0.111803i
\(201\) −6.00000 −0.423207
\(202\) 0 0
\(203\) 0 0
\(204\) −18.9737 −1.32842
\(205\) −6.32456 12.6491i −0.441726 0.883452i
\(206\) 28.4605i 1.98294i
\(207\) −1.00000 1.00000i −0.0695048 0.0695048i
\(208\) −3.16228 3.16228i −0.219265 0.219265i
\(209\) 6.32456 20.0000i 0.437479 1.38343i
\(210\) 0 0
\(211\) 25.2982i 1.74160i 0.491636 + 0.870801i \(0.336399\pi\)
−0.491636 + 0.870801i \(0.663601\pi\)
\(212\) 3.00000 + 3.00000i 0.206041 + 0.206041i
\(213\) 8.00000 8.00000i 0.548151 0.548151i
\(214\) 0 0
\(215\) 0 0
\(216\) 12.6491i 0.860663i
\(217\) 0 0
\(218\) −20.0000 + 20.0000i −1.35457 + 1.35457i
\(219\) −6.32456 −0.427374
\(220\) 21.9737 3.48683i 1.48146 0.235082i
\(221\) 20.0000 1.34535
\(222\) −9.48683 + 9.48683i −0.636715 + 0.636715i
\(223\) −11.0000 + 11.0000i −0.736614 + 0.736614i −0.971921 0.235307i \(-0.924391\pi\)
0.235307 + 0.971921i \(0.424391\pi\)
\(224\) 0 0
\(225\) 4.00000 + 3.00000i 0.266667 + 0.200000i
\(226\) 28.4605i 1.89316i
\(227\) −6.32456 + 6.32456i −0.419775 + 0.419775i −0.885126 0.465351i \(-0.845928\pi\)
0.465351 + 0.885126i \(0.345928\pi\)
\(228\) 18.9737 + 18.9737i 1.25656 + 1.25656i
\(229\) 4.00000i 0.264327i 0.991228 + 0.132164i \(0.0421925\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) −3.16228 6.32456i −0.208514 0.417029i
\(231\) 0 0
\(232\) 10.0000 + 10.0000i 0.656532 + 0.656532i
\(233\) 9.48683 + 9.48683i 0.621503 + 0.621503i 0.945916 0.324413i \(-0.105167\pi\)
−0.324413 + 0.945916i \(0.605167\pi\)
\(234\) 10.0000i 0.653720i
\(235\) −9.00000 3.00000i −0.587095 0.195698i
\(236\) −18.0000 −1.17170
\(237\) 6.32456 6.32456i 0.410824 0.410824i
\(238\) 0 0
\(239\) −18.9737 −1.22730 −0.613652 0.789576i \(-0.710300\pi\)
−0.613652 + 0.789576i \(0.710300\pi\)
\(240\) 1.00000 3.00000i 0.0645497 0.193649i
\(241\) 6.32456i 0.407400i 0.979033 + 0.203700i \(0.0652968\pi\)
−0.979033 + 0.203700i \(0.934703\pi\)
\(242\) −24.2302 + 4.23025i −1.55758 + 0.271931i
\(243\) 7.00000 7.00000i 0.449050 0.449050i
\(244\) −18.9737 −1.21466
\(245\) −7.00000 14.0000i −0.447214 0.894427i
\(246\) −20.0000 −1.27515
\(247\) −20.0000 20.0000i −1.27257 1.27257i
\(248\) −3.16228 3.16228i −0.200805 0.200805i
\(249\) 12.6491 0.801605
\(250\) 14.2302 + 20.5548i 0.900000 + 1.30000i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 2.16228 + 4.16228i 0.135941 + 0.261680i
\(254\) 20.0000i 1.25491i
\(255\) 6.32456 + 12.6491i 0.396059 + 0.792118i
\(256\) −9.00000 −0.562500
\(257\) −7.00000 7.00000i −0.436648 0.436648i 0.454234 0.890882i \(-0.349913\pi\)
−0.890882 + 0.454234i \(0.849913\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 9.48683 28.4605i 0.588348 1.76505i
\(261\) 6.32456i 0.391480i
\(262\) 20.0000 + 20.0000i 1.23560 + 1.23560i
\(263\) −18.9737 18.9737i −1.16997 1.16997i −0.982217 0.187749i \(-0.939881\pi\)
−0.187749 0.982217i \(-0.560119\pi\)
\(264\) 3.16228 10.0000i 0.194625 0.615457i
\(265\) 1.00000 3.00000i 0.0614295 0.184289i
\(266\) 0 0
\(267\) 6.00000 + 6.00000i 0.367194 + 0.367194i
\(268\) 9.00000 9.00000i 0.549762 0.549762i
\(269\) 24.0000i 1.46331i 0.681677 + 0.731653i \(0.261251\pi\)
−0.681677 + 0.731653i \(0.738749\pi\)
\(270\) 25.2982 12.6491i 1.53960 0.769800i
\(271\) 12.6491i 0.768379i −0.923254 0.384189i \(-0.874481\pi\)
0.923254 0.384189i \(-0.125519\pi\)
\(272\) −3.16228 + 3.16228i −0.191741 + 0.191741i
\(273\) 0 0
\(274\) 41.1096 2.48352
\(275\) −9.64911 13.4868i −0.581863 0.813287i
\(276\) −6.00000 −0.361158
\(277\) 9.48683 9.48683i 0.570009 0.570009i −0.362122 0.932131i \(-0.617948\pi\)
0.932131 + 0.362122i \(0.117948\pi\)
\(278\) 20.0000 20.0000i 1.19952 1.19952i
\(279\) 2.00000i 0.119737i
\(280\) 0 0
\(281\) 18.9737i 1.13187i −0.824448 0.565937i \(-0.808515\pi\)
0.824448 0.565937i \(-0.191485\pi\)
\(282\) −9.48683 + 9.48683i −0.564933 + 0.564933i
\(283\) −6.32456 6.32456i −0.375956 0.375956i 0.493685 0.869641i \(-0.335650\pi\)
−0.869641 + 0.493685i \(0.835650\pi\)
\(284\) 24.0000i 1.42414i
\(285\) 6.32456 18.9737i 0.374634 1.12390i
\(286\) −10.0000 + 31.6228i −0.591312 + 1.86989i
\(287\) 0 0
\(288\) 4.74342 + 4.74342i 0.279508 + 0.279508i
\(289\) 3.00000i 0.176471i
\(290\) 10.0000 30.0000i 0.587220 1.76166i
\(291\) 14.0000 0.820695
\(292\) 9.48683 9.48683i 0.555175 0.555175i
\(293\) 15.8114 + 15.8114i 0.923711 + 0.923711i 0.997289 0.0735783i \(-0.0234419\pi\)
−0.0735783 + 0.997289i \(0.523442\pi\)
\(294\) −22.1359 −1.29099
\(295\) 6.00000 + 12.0000i 0.349334 + 0.698667i
\(296\) 9.48683i 0.551411i
\(297\) −16.6491 + 8.64911i −0.966079 + 0.501872i
\(298\) 0 0
\(299\) 6.32456 0.365758
\(300\) 21.0000 3.00000i 1.21244 0.173205i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 6.32456 0.362738
\(305\) 6.32456 + 12.6491i 0.362143 + 0.724286i
\(306\) −10.0000 −0.571662
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 18.0000i 1.02398i
\(310\) −3.16228 + 9.48683i −0.179605 + 0.538816i
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −10.0000 10.0000i −0.566139 0.566139i
\(313\) 9.00000 9.00000i 0.508710 0.508710i −0.405420 0.914130i \(-0.632875\pi\)
0.914130 + 0.405420i \(0.132875\pi\)
\(314\) −22.1359 −1.24920
\(315\) 0 0
\(316\) 18.9737i 1.06735i
\(317\) −17.0000 17.0000i −0.954815 0.954815i 0.0442073 0.999022i \(-0.485924\pi\)
−0.999022 + 0.0442073i \(0.985924\pi\)
\(318\) −3.16228 3.16228i −0.177332 0.177332i
\(319\) −6.32456 + 20.0000i −0.354107 + 1.11979i
\(320\) 13.0000 + 26.0000i 0.726722 + 1.45344i
\(321\) 0 0
\(322\) 0 0
\(323\) −20.0000 + 20.0000i −1.11283 + 1.11283i
\(324\) 15.0000i 0.833333i
\(325\) −22.1359 + 3.16228i −1.22788 + 0.175412i
\(326\) 3.16228i 0.175142i
\(327\) 12.6491 12.6491i 0.699497 0.699497i
\(328\) 10.0000 10.0000i 0.552158 0.552158i
\(329\) 0 0
\(330\) −23.1623 + 3.67544i −1.27504 + 0.202327i
\(331\) −18.0000 −0.989369 −0.494685 0.869072i \(-0.664716\pi\)
−0.494685 + 0.869072i \(0.664716\pi\)
\(332\) −18.9737 + 18.9737i −1.04132 + 1.04132i
\(333\) −3.00000 + 3.00000i −0.164399 + 0.164399i
\(334\) 40.0000i 2.18870i
\(335\) −9.00000 3.00000i −0.491723 0.163908i
\(336\) 0 0
\(337\) −9.48683 + 9.48683i −0.516781 + 0.516781i −0.916596 0.399815i \(-0.869074\pi\)
0.399815 + 0.916596i \(0.369074\pi\)
\(338\) 11.0680 + 11.0680i 0.602018 + 0.602018i
\(339\) 18.0000i 0.977626i
\(340\) −28.4605 9.48683i −1.54349 0.514496i
\(341\) 2.00000 6.32456i 0.108306 0.342494i
\(342\) 10.0000 + 10.0000i 0.540738 + 0.540738i
\(343\) 0 0
\(344\) 0 0
\(345\) 2.00000 + 4.00000i 0.107676 + 0.215353i
\(346\) 10.0000 0.537603
\(347\) 18.9737 18.9737i 1.01856 1.01856i 0.0187353 0.999824i \(-0.494036\pi\)
0.999824 0.0187353i \(-0.00596397\pi\)
\(348\) −18.9737 18.9737i −1.01710 1.01710i
\(349\) −31.6228 −1.69273 −0.846364 0.532605i \(-0.821213\pi\)
−0.846364 + 0.532605i \(0.821213\pi\)
\(350\) 0 0
\(351\) 25.2982i 1.35032i
\(352\) −10.2566 19.7434i −0.546678 1.05233i
\(353\) −21.0000 + 21.0000i −1.11772 + 1.11772i −0.125642 + 0.992076i \(0.540099\pi\)
−0.992076 + 0.125642i \(0.959901\pi\)
\(354\) 18.9737 1.00844
\(355\) 16.0000 8.00000i 0.849192 0.424596i
\(356\) −18.0000 −0.953998
\(357\) 0 0
\(358\) 6.32456 + 6.32456i 0.334263 + 0.334263i
\(359\) 18.9737 1.00139 0.500696 0.865623i \(-0.333077\pi\)
0.500696 + 0.865623i \(0.333077\pi\)
\(360\) −1.58114 + 4.74342i −0.0833333 + 0.250000i
\(361\) 21.0000 1.10526
\(362\) −12.6491 + 12.6491i −0.664822 + 0.664822i
\(363\) 15.3246 2.67544i 0.804331 0.140424i
\(364\) 0 0
\(365\) −9.48683 3.16228i −0.496564 0.165521i
\(366\) 20.0000 1.04542
\(367\) 3.00000 + 3.00000i 0.156599 + 0.156599i 0.781058 0.624459i \(-0.214680\pi\)
−0.624459 + 0.781058i \(0.714680\pi\)
\(368\) −1.00000 + 1.00000i −0.0521286 + 0.0521286i
\(369\) −6.32456 −0.329243
\(370\) −18.9737 + 9.48683i −0.986394 + 0.493197i
\(371\) 0 0
\(372\) 6.00000 + 6.00000i 0.311086 + 0.311086i
\(373\) 3.16228 + 3.16228i 0.163737 + 0.163737i 0.784220 0.620483i \(-0.213063\pi\)
−0.620483 + 0.784220i \(0.713063\pi\)
\(374\) 31.6228 + 10.0000i 1.63517 + 0.517088i
\(375\) −9.00000 13.0000i −0.464758 0.671317i
\(376\) 9.48683i 0.489246i
\(377\) 20.0000 + 20.0000i 1.03005 + 1.03005i
\(378\) 0 0
\(379\) 26.0000i 1.33553i −0.744372 0.667765i \(-0.767251\pi\)
0.744372 0.667765i \(-0.232749\pi\)
\(380\) 18.9737 + 37.9473i 0.973329 + 1.94666i
\(381\) 12.6491i 0.648034i
\(382\) 34.7851 34.7851i 1.77976 1.77976i
\(383\) 19.0000 19.0000i 0.970855 0.970855i −0.0287325 0.999587i \(-0.509147\pi\)
0.999587 + 0.0287325i \(0.00914709\pi\)
\(384\) 22.1359 1.12962
\(385\) 0 0
\(386\) 50.0000 2.54493
\(387\) 0 0
\(388\) −21.0000 + 21.0000i −1.06611 + 1.06611i
\(389\) 16.0000i 0.811232i −0.914044 0.405616i \(-0.867057\pi\)
0.914044 0.405616i \(-0.132943\pi\)
\(390\) −10.0000 + 30.0000i −0.506370 + 1.51911i
\(391\) 6.32456i 0.319847i
\(392\) 11.0680 11.0680i 0.559017 0.559017i
\(393\) −12.6491 12.6491i −0.638063 0.638063i
\(394\) 10.0000i 0.503793i
\(395\) 12.6491 6.32456i 0.636446 0.318223i
\(396\) 3.00000 9.48683i 0.150756 0.476731i
\(397\) 13.0000 + 13.0000i 0.652451 + 0.652451i 0.953583 0.301131i \(-0.0973643\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(398\) −9.48683 9.48683i −0.475532 0.475532i
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) 12.0000 0.599251 0.299626 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) −9.48683 + 9.48683i −0.473160 + 0.473160i
\(403\) −6.32456 6.32456i −0.315049 0.315049i
\(404\) 0 0
\(405\) −10.0000 + 5.00000i −0.496904 + 0.248452i
\(406\) 0 0
\(407\) 12.4868 6.48683i 0.618949 0.321540i
\(408\) −10.0000 + 10.0000i −0.495074 + 0.495074i
\(409\) −12.6491 −0.625458 −0.312729 0.949842i \(-0.601243\pi\)
−0.312729 + 0.949842i \(0.601243\pi\)
\(410\) −30.0000 10.0000i −1.48159 0.493865i
\(411\) −26.0000 −1.28249
\(412\) −27.0000 27.0000i −1.33019 1.33019i
\(413\) 0 0
\(414\) −3.16228 −0.155417
\(415\) 18.9737 + 6.32456i 0.931381 + 0.310460i
\(416\) −30.0000 −1.47087
\(417\) −12.6491 + 12.6491i −0.619430 + 0.619430i
\(418\) −21.6228 41.6228i −1.05760 2.03584i
\(419\) 36.0000i 1.75872i −0.476162 0.879358i \(-0.657972\pi\)
0.476162 0.879358i \(-0.342028\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 40.0000 + 40.0000i 1.94717 + 1.94717i
\(423\) −3.00000 + 3.00000i −0.145865 + 0.145865i
\(424\) 3.16228 0.153574
\(425\) 3.16228 + 22.1359i 0.153393 + 1.07375i
\(426\) 25.2982i 1.22570i
\(427\) 0 0
\(428\) 0 0
\(429\) 6.32456 20.0000i 0.305352 0.965609i
\(430\) 0 0
\(431\) 18.9737i 0.913929i −0.889485 0.456965i \(-0.848937\pi\)
0.889485 0.456965i \(-0.151063\pi\)
\(432\) −4.00000 4.00000i −0.192450 0.192450i
\(433\) −1.00000 + 1.00000i −0.0480569 + 0.0480569i −0.730727 0.682670i \(-0.760819\pi\)
0.682670 + 0.730727i \(0.260819\pi\)
\(434\) 0 0
\(435\) −6.32456 + 18.9737i −0.303239 + 0.909718i
\(436\) 37.9473i 1.81735i
\(437\) −6.32456 + 6.32456i −0.302545 + 0.302545i
\(438\) −10.0000 + 10.0000i −0.477818 + 0.477818i
\(439\) 12.6491 0.603709 0.301855 0.953354i \(-0.402394\pi\)
0.301855 + 0.953354i \(0.402394\pi\)
\(440\) 9.74342 13.4189i 0.464499 0.639719i
\(441\) −7.00000 −0.333333
\(442\) 31.6228 31.6228i 1.50414 1.50414i
\(443\) −11.0000 + 11.0000i −0.522626 + 0.522626i −0.918364 0.395738i \(-0.870489\pi\)
0.395738 + 0.918364i \(0.370489\pi\)
\(444\) 18.0000i 0.854242i
\(445\) 6.00000 + 12.0000i 0.284427 + 0.568855i
\(446\) 34.7851i 1.64712i
\(447\) 0 0
\(448\) 0 0
\(449\) 6.00000i 0.283158i −0.989927 0.141579i \(-0.954782\pi\)
0.989927 0.141579i \(-0.0452178\pi\)
\(450\) 11.0680 1.58114i 0.521749 0.0745356i
\(451\) 20.0000 + 6.32456i 0.941763 + 0.297812i
\(452\) −27.0000 27.0000i −1.26997 1.26997i
\(453\) 0 0
\(454\) 20.0000i 0.938647i
\(455\) 0 0
\(456\) 20.0000 0.936586
\(457\) −15.8114 + 15.8114i −0.739626 + 0.739626i −0.972505 0.232880i \(-0.925185\pi\)
0.232880 + 0.972505i \(0.425185\pi\)
\(458\) 6.32456 + 6.32456i 0.295527 + 0.295527i
\(459\) 25.2982 1.18082
\(460\) −9.00000 3.00000i −0.419627 0.139876i
\(461\) 25.2982i 1.17826i 0.808040 + 0.589128i \(0.200529\pi\)
−0.808040 + 0.589128i \(0.799471\pi\)
\(462\) 0 0
\(463\) 9.00000 9.00000i 0.418265 0.418265i −0.466340 0.884606i \(-0.654428\pi\)
0.884606 + 0.466340i \(0.154428\pi\)
\(464\) −6.32456 −0.293610
\(465\) 2.00000 6.00000i 0.0927478 0.278243i
\(466\) 30.0000 1.38972
\(467\) −7.00000 7.00000i −0.323921 0.323921i 0.526348 0.850269i \(-0.323561\pi\)
−0.850269 + 0.526348i \(0.823561\pi\)
\(468\) −9.48683 9.48683i −0.438529 0.438529i
\(469\) 0 0
\(470\) −18.9737 + 9.48683i −0.875190 + 0.437595i
\(471\) 14.0000 0.645086
\(472\) −9.48683 + 9.48683i −0.436667 + 0.436667i
\(473\) 0 0
\(474\) 20.0000i 0.918630i
\(475\) 18.9737 25.2982i 0.870572 1.16076i
\(476\) 0 0
\(477\) −1.00000 1.00000i −0.0457869 0.0457869i
\(478\) −30.0000 + 30.0000i −1.37217 + 1.37217i
\(479\) −6.32456 −0.288976 −0.144488 0.989507i \(-0.546154\pi\)
−0.144488 + 0.989507i \(0.546154\pi\)
\(480\) −9.48683 18.9737i −0.433013 0.866025i
\(481\) 18.9737i 0.865125i
\(482\) 10.0000 + 10.0000i 0.455488 + 0.455488i
\(483\) 0 0
\(484\) −18.9737 + 27.0000i −0.862439 + 1.22727i
\(485\) 21.0000 + 7.00000i 0.953561 + 0.317854i
\(486\) 22.1359i 1.00411i
\(487\) 3.00000 + 3.00000i 0.135943 + 0.135943i 0.771804 0.635861i \(-0.219355\pi\)
−0.635861 + 0.771804i \(0.719355\pi\)
\(488\) −10.0000 + 10.0000i −0.452679 + 0.452679i
\(489\) 2.00000i 0.0904431i
\(490\) −33.2039 11.0680i −1.50000 0.500000i
\(491\) 6.32456i 0.285423i 0.989764 + 0.142712i \(0.0455821\pi\)
−0.989764 + 0.142712i \(0.954418\pi\)
\(492\) −18.9737 + 18.9737i −0.855399 + 0.855399i
\(493\) 20.0000 20.0000i 0.900755 0.900755i
\(494\) −63.2456 −2.84555
\(495\) −7.32456 + 1.16228i −0.329214 + 0.0522405i
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 20.0000 20.0000i 0.896221 0.896221i
\(499\) 34.0000i 1.52205i 0.648723 + 0.761025i \(0.275303\pi\)
−0.648723 + 0.761025i \(0.724697\pi\)
\(500\) 33.0000 + 6.00000i 1.47580 + 0.268328i
\(501\) 25.2982i 1.13024i
\(502\) 18.9737 18.9737i 0.846836 0.846836i
\(503\) 6.32456 + 6.32456i 0.281998 + 0.281998i 0.833905 0.551907i \(-0.186100\pi\)
−0.551907 + 0.833905i \(0.686100\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 10.0000 + 3.16228i 0.444554 + 0.140580i
\(507\) −7.00000 7.00000i −0.310881 0.310881i
\(508\) 18.9737 + 18.9737i 0.841820 + 0.841820i
\(509\) 4.00000i 0.177297i 0.996063 + 0.0886484i \(0.0282548\pi\)
−0.996063 + 0.0886484i \(0.971745\pi\)
\(510\) 30.0000 + 10.0000i 1.32842 + 0.442807i
\(511\) 0 0
\(512\) 7.90569 7.90569i 0.349386 0.349386i
\(513\) −25.2982 25.2982i −1.11694 1.11694i
\(514\) −22.1359 −0.976375
\(515\) −9.00000 + 27.0000i −0.396587 + 1.18976i
\(516\) 0 0
\(517\) 12.4868 6.48683i 0.549170 0.285291i
\(518\) 0 0
\(519\) −6.32456 −0.277617
\(520\) −10.0000 20.0000i −0.438529 0.877058i
\(521\) −28.0000 −1.22670 −0.613351 0.789810i \(-0.710179\pi\)
−0.613351 + 0.789810i \(0.710179\pi\)
\(522\) −10.0000 10.0000i −0.437688 0.437688i
\(523\) 18.9737 + 18.9737i 0.829660 + 0.829660i 0.987470 0.157809i \(-0.0504431\pi\)
−0.157809 + 0.987470i \(0.550443\pi\)
\(524\) 37.9473 1.65774
\(525\) 0 0
\(526\) −60.0000 −2.61612
\(527\) −6.32456 + 6.32456i −0.275502 + 0.275502i
\(528\) 2.16228 + 4.16228i 0.0941011 + 0.181140i
\(529\) 21.0000i 0.913043i
\(530\) −3.16228 6.32456i −0.137361 0.274721i
\(531\) 6.00000 0.260378
\(532\) 0 0
\(533\) 20.0000 20.0000i 0.866296 0.866296i
\(534\) 18.9737 0.821071
\(535\) 0 0
\(536\) 9.48683i 0.409769i
\(537\) −4.00000 4.00000i −0.172613 0.172613i
\(538\) 37.9473 + 37.9473i 1.63603 + 1.63603i
\(539\) 22.1359 + 7.00000i 0.953463 + 0.301511i
\(540\) 12.0000 36.0000i 0.516398 1.54919i
\(541\) 37.9473i 1.63148i 0.578416 + 0.815742i \(0.303671\pi\)
−0.578416 + 0.815742i \(0.696329\pi\)
\(542\) −20.0000 20.0000i −0.859074 0.859074i
\(543\) 8.00000 8.00000i 0.343313 0.343313i
\(544\) 30.0000i 1.28624i
\(545\) 25.2982 12.6491i 1.08366 0.541828i
\(546\) 0 0
\(547\) −12.6491 + 12.6491i −0.540837 + 0.540837i −0.923774 0.382937i \(-0.874912\pi\)
0.382937 + 0.923774i \(0.374912\pi\)
\(548\) 39.0000 39.0000i 1.66600 1.66600i
\(549\) 6.32456 0.269925
\(550\) −36.5811 6.06797i −1.55983 0.258739i
\(551\) −40.0000 −1.70406
\(552\) −3.16228 + 3.16228i −0.134595 + 0.134595i
\(553\) 0 0
\(554\) 30.0000i 1.27458i
\(555\) 12.0000 6.00000i 0.509372 0.254686i
\(556\) 37.9473i 1.60933i
\(557\) −15.8114 + 15.8114i −0.669950 + 0.669950i −0.957704 0.287754i \(-0.907091\pi\)
0.287754 + 0.957704i \(0.407091\pi\)
\(558\) 3.16228 + 3.16228i 0.133870 + 0.133870i
\(559\) 0 0
\(560\) 0 0
\(561\) −20.0000 6.32456i −0.844401 0.267023i
\(562\) −30.0000 30.0000i −1.26547 1.26547i
\(563\) −18.9737 18.9737i −0.799645 0.799645i 0.183395 0.983039i \(-0.441291\pi\)
−0.983039 + 0.183395i \(0.941291\pi\)
\(564\) 18.0000i 0.757937i
\(565\) −9.00000 + 27.0000i −0.378633 + 1.13590i
\(566\) −20.0000 −0.840663
\(567\) 0 0
\(568\) 12.6491 + 12.6491i 0.530745 + 0.530745i
\(569\) 37.9473 1.59083 0.795417 0.606062i \(-0.207252\pi\)
0.795417 + 0.606062i \(0.207252\pi\)
\(570\) −20.0000 40.0000i −0.837708 1.67542i
\(571\) 44.2719i 1.85272i −0.376638 0.926360i \(-0.622920\pi\)
0.376638 0.926360i \(-0.377080\pi\)
\(572\) 20.5132 + 39.4868i 0.857699 + 1.65103i
\(573\) −22.0000 + 22.0000i −0.919063 + 0.919063i
\(574\) 0 0
\(575\) 1.00000 + 7.00000i 0.0417029 + 0.291920i
\(576\) 13.0000 0.541667
\(577\) 23.0000 + 23.0000i 0.957503 + 0.957503i 0.999133 0.0416305i \(-0.0132552\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −4.74342 4.74342i −0.197300 0.197300i
\(579\) −31.6228 −1.31420
\(580\) −18.9737 37.9473i −0.787839 1.57568i
\(581\) 0 0
\(582\) 22.1359 22.1359i 0.917564 0.917564i
\(583\) 2.16228 + 4.16228i 0.0895524 + 0.172384i
\(584\) 10.0000i 0.413803i
\(585\) −3.16228 + 9.48683i −0.130744 + 0.392232i
\(586\) 50.0000 2.06548
\(587\) −7.00000 7.00000i −0.288921 0.288921i 0.547733 0.836653i \(-0.315491\pi\)
−0.836653 + 0.547733i \(0.815491\pi\)
\(588\) −21.0000 + 21.0000i −0.866025 + 0.866025i
\(589\) 12.6491 0.521198
\(590\) 28.4605 + 9.48683i 1.17170 + 0.390567i
\(591\) 6.32456i 0.260157i
\(592\) 3.00000 + 3.00000i 0.123299 + 0.123299i
\(593\) −15.8114 15.8114i −0.649296 0.649296i 0.303527 0.952823i \(-0.401836\pi\)
−0.952823 + 0.303527i \(0.901836\pi\)
\(594\) −12.6491 + 40.0000i −0.518999 + 1.64122i
\(595\) 0 0
\(596\) 0 0
\(597\) 6.00000 + 6.00000i 0.245564 + 0.245564i
\(598\) 10.0000 10.0000i 0.408930 0.408930i
\(599\) 16.0000i 0.653742i −0.945069 0.326871i \(-0.894006\pi\)
0.945069 0.326871i \(-0.105994\pi\)
\(600\) 9.48683 12.6491i 0.387298 0.516398i
\(601\) 31.6228i 1.28992i −0.764216 0.644960i \(-0.776874\pi\)
0.764216 0.644960i \(-0.223126\pi\)
\(602\) 0 0
\(603\) −3.00000 + 3.00000i −0.122169 + 0.122169i
\(604\) 0 0
\(605\) 24.3246 + 3.64911i 0.988934 + 0.148357i
\(606\) 0 0
\(607\) −31.6228 + 31.6228i −1.28353 + 1.28353i −0.344883 + 0.938646i \(0.612082\pi\)
−0.938646 + 0.344883i \(0.887918\pi\)
\(608\) 30.0000 30.0000i 1.21666 1.21666i
\(609\) 0 0
\(610\) 30.0000 + 10.0000i 1.21466 + 0.404888i
\(611\) 18.9737i 0.767592i
\(612\) −9.48683 + 9.48683i −0.383482 + 0.383482i
\(613\) 28.4605 + 28.4605i 1.14951 + 1.14951i 0.986649 + 0.162859i \(0.0520717\pi\)
0.162859 + 0.986649i \(0.447928\pi\)
\(614\) 0 0
\(615\) 18.9737 + 6.32456i 0.765092 + 0.255031i
\(616\) 0 0
\(617\) −17.0000 17.0000i −0.684394 0.684394i 0.276593 0.960987i \(-0.410795\pi\)
−0.960987 + 0.276593i \(0.910795\pi\)
\(618\) 28.4605 + 28.4605i 1.14485 + 1.14485i
\(619\) 36.0000i 1.44696i −0.690344 0.723481i \(-0.742541\pi\)
0.690344 0.723481i \(-0.257459\pi\)
\(620\) 6.00000 + 12.0000i 0.240966 + 0.481932i
\(621\) 8.00000 0.321029
\(622\) −12.6491 + 12.6491i −0.507183 + 0.507183i
\(623\) 0 0
\(624\) 6.32456 0.253185
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 28.4605i 1.13751i
\(627\) 13.6754 + 26.3246i 0.546145 + 1.05130i
\(628\) −21.0000 + 21.0000i −0.837991 + 0.837991i
\(629\) −18.9737 −0.756530
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 10.0000 + 10.0000i 0.397779 + 0.397779i
\(633\) −25.2982 25.2982i −1.00551 1.00551i
\(634\) −53.7587 −2.13503
\(635\) 6.32456 18.9737i 0.250982 0.752947i
\(636\) −6.00000 −0.237915
\(637\) 22.1359 22.1359i 0.877058 0.877058i
\(638\) 21.6228 + 41.6228i 0.856054 + 1.64786i
\(639\) 8.00000i 0.316475i
\(640\) 33.2039 + 11.0680i 1.31250 + 0.437500i
\(641\) −8.00000 −0.315981 −0.157991 0.987441i \(-0.550502\pi\)
−0.157991 + 0.987441i \(0.550502\pi\)
\(642\) 0 0
\(643\) −11.0000 + 11.0000i −0.433798 + 0.433798i −0.889918 0.456120i \(-0.849239\pi\)
0.456120 + 0.889918i \(0.349239\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 63.2456i 2.48836i
\(647\) 13.0000 + 13.0000i 0.511083 + 0.511083i 0.914858 0.403775i \(-0.132302\pi\)
−0.403775 + 0.914858i \(0.632302\pi\)
\(648\) −7.90569 7.90569i −0.310565 0.310565i
\(649\) −18.9737 6.00000i −0.744782 0.235521i
\(650\) −30.0000 + 40.0000i −1.17670 + 1.56893i
\(651\) 0 0
\(652\) 3.00000 + 3.00000i 0.117489 + 0.117489i
\(653\) −1.00000 + 1.00000i −0.0391330 + 0.0391330i −0.726403 0.687270i \(-0.758809\pi\)
0.687270 + 0.726403i \(0.258809\pi\)
\(654\) 40.0000i 1.56412i
\(655\) −12.6491 25.2982i −0.494242 0.988483i
\(656\) 6.32456i 0.246932i
\(657\) −3.16228 + 3.16228i −0.123372 + 0.123372i
\(658\) 0 0
\(659\) −12.6491 −0.492739 −0.246370 0.969176i \(-0.579238\pi\)
−0.246370 + 0.969176i \(0.579238\pi\)
\(660\) −18.4868 + 25.4605i −0.719599 + 0.991049i
\(661\) 42.0000 1.63361 0.816805 0.576913i \(-0.195743\pi\)
0.816805 + 0.576913i \(0.195743\pi\)
\(662\) −28.4605 + 28.4605i −1.10615 + 1.10615i
\(663\) −20.0000 + 20.0000i −0.776736 + 0.776736i
\(664\) 20.0000i 0.776151i
\(665\) 0 0
\(666\) 9.48683i 0.367607i
\(667\) 6.32456 6.32456i 0.244888 0.244888i
\(668\) −37.9473 37.9473i −1.46823 1.46823i
\(669\) 22.0000i 0.850569i
\(670\) −18.9737 + 9.48683i −0.733017 + 0.366508i
\(671\) −20.0000 6.32456i −0.772091 0.244157i
\(672\) 0 0
\(673\) −28.4605 28.4605i −1.09707 1.09707i −0.994752 0.102320i \(-0.967373\pi\)
−0.102320 0.994752i \(-0.532627\pi\)
\(674\) 30.0000i 1.15556i
\(675\) −28.0000 + 4.00000i −1.07772 + 0.153960i
\(676\) 21.0000 0.807692
\(677\) 9.48683 9.48683i 0.364609 0.364609i −0.500898 0.865506i \(-0.666997\pi\)
0.865506 + 0.500898i \(0.166997\pi\)
\(678\) 28.4605 + 28.4605i 1.09302 + 1.09302i
\(679\) 0 0
\(680\) −20.0000 + 10.0000i −0.766965 + 0.383482i
\(681\) 12.6491i 0.484715i
\(682\) −6.83772 13.1623i −0.261830 0.504010i
\(683\) 29.0000 29.0000i 1.10965 1.10965i 0.116459 0.993196i \(-0.462846\pi\)
0.993196 0.116459i \(-0.0371542\pi\)
\(684\) 18.9737 0.725476
\(685\) −39.0000 13.0000i −1.49011 0.496704i
\(686\) 0 0
\(687\) −4.00000 4.00000i −0.152610 0.152610i
\(688\) 0 0
\(689\) 6.32456 0.240946
\(690\) 9.48683 + 3.16228i 0.361158 + 0.120386i
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 9.48683 9.48683i 0.360635 0.360635i
\(693\) 0 0
\(694\) 60.0000i 2.27757i
\(695\) −25.2982 + 12.6491i −0.959616 + 0.479808i
\(696\) −20.0000 −0.758098
\(697\) −20.0000 20.0000i −0.757554 0.757554i
\(698\) −50.0000 + 50.0000i −1.89253 + 1.89253i
\(699\) −18.9737 −0.717650
\(700\) 0 0
\(701\) 31.6228i 1.19438i 0.802101 + 0.597188i \(0.203715\pi\)
−0.802101 + 0.597188i \(0.796285\pi\)
\(702\) 40.0000 + 40.0000i 1.50970 + 1.50970i
\(703\) 18.9737 + 18.9737i 0.715605 + 0.715605i
\(704\) −41.1096 13.0000i −1.54938 0.489956i
\(705\) 12.0000 6.00000i 0.451946 0.225973i
\(706\) 66.4078i 2.49929i
\(707\) 0 0
\(708\) 18.0000 18.0000i 0.676481 0.676481i
\(709\) 6.00000i 0.225335i −0.993633 0.112667i \(-0.964061\pi\)
0.993633 0.112667i \(-0.0359394\pi\)
\(710\) 12.6491 37.9473i 0.474713 1.42414i
\(711\) 6.32456i 0.237189i
\(712\) −9.48683 + 9.48683i −0.355534 + 0.355534i
\(713\) −2.00000 + 2.00000i −0.0749006 + 0.0749006i
\(714\) 0 0
\(715\) 19.4868 26.8377i 0.728766 1.00367i
\(716\) 12.0000 0.448461
\(717\) 18.9737 18.9737i 0.708585 0.708585i
\(718\) 30.0000 30.0000i 1.11959 1.11959i
\(719\) 24.0000i 0.895049i 0.894272 + 0.447524i \(0.147694\pi\)
−0.894272 + 0.447524i \(0.852306\pi\)
\(720\) −1.00000 2.00000i −0.0372678 0.0745356i
\(721\) 0 0
\(722\) 33.2039 33.2039i 1.23572 1.23572i
\(723\) −6.32456 6.32456i −0.235213 0.235213i
\(724\) 24.0000i 0.891953i
\(725\) −18.9737 + 25.2982i −0.704664 + 0.939552i
\(726\) 20.0000 28.4605i 0.742270 1.05627i
\(727\) 23.0000 + 23.0000i 0.853023 + 0.853023i 0.990504 0.137482i \(-0.0439008\pi\)
−0.137482 + 0.990504i \(0.543901\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) −20.0000 + 10.0000i −0.740233 + 0.370117i
\(731\) 0 0
\(732\) 18.9737 18.9737i 0.701287 0.701287i
\(733\) 9.48683 + 9.48683i 0.350404 + 0.350404i 0.860260 0.509856i \(-0.170301\pi\)
−0.509856 + 0.860260i \(0.670301\pi\)
\(734\) 9.48683 0.350165
\(735\) 21.0000 + 7.00000i 0.774597 + 0.258199i
\(736\) 9.48683i 0.349689i
\(737\) 12.4868 6.48683i 0.459958 0.238946i
\(738\) −10.0000 + 10.0000i −0.368105 + 0.368105i
\(739\) 12.6491 0.465305 0.232653 0.972560i \(-0.425260\pi\)
0.232653 + 0.972560i \(0.425260\pi\)
\(740\) −9.00000 + 27.0000i −0.330847 + 0.992540i
\(741\) 40.0000 1.46944
\(742\) 0 0
\(743\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(744\) 6.32456 0.231869
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) 6.32456 6.32456i 0.231403 0.231403i
\(748\) 39.4868 20.5132i 1.44378 0.750036i
\(749\) 0 0
\(750\) −34.7851 6.32456i −1.27017 0.230940i
\(751\) −8.00000 −0.291924 −0.145962 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 3.00000 + 3.00000i 0.109399 + 0.109399i
\(753\) −12.0000 + 12.0000i −0.437304 + 0.437304i
\(754\) 63.2456 2.30327
\(755\) 0 0
\(756\) 0 0
\(757\) −27.0000 27.0000i −0.981332 0.981332i 0.0184972 0.999829i \(-0.494112\pi\)
−0.999829 + 0.0184972i \(0.994112\pi\)
\(758\) −41.1096 41.1096i −1.49317 1.49317i
\(759\) −6.32456 2.00000i −0.229567 0.0725954i
\(760\) 30.0000 + 10.0000i 1.08821 + 0.362738i
\(761\) 37.9473i 1.37559i −0.725905 0.687795i \(-0.758579\pi\)
0.725905 0.687795i \(-0.241421\pi\)
\(762\) −20.0000 20.0000i −0.724524 0.724524i
\(763\) 0 0
\(764\) 66.0000i 2.38780i
\(765\) 9.48683 + 3.16228i 0.342997 + 0.114332i
\(766\) 60.0833i 2.17090i
\(767\) −18.9737 + 18.9737i −0.685099 + 0.685099i
\(768\) 9.00000 9.00000i 0.324760 0.324760i
\(769\) 6.32456 0.228069 0.114035 0.993477i \(-0.463623\pi\)
0.114035 + 0.993477i \(0.463623\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) 47.4342 47.4342i 1.70719 1.70719i
\(773\) −11.0000 + 11.0000i −0.395643 + 0.395643i −0.876693 0.481050i \(-0.840255\pi\)
0.481050 + 0.876693i \(0.340255\pi\)
\(774\) 0 0
\(775\) 6.00000 8.00000i 0.215526 0.287368i
\(776\) 22.1359i 0.794634i