Properties

Label 1078.2.e.a.67.1
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1078,2,Mod(67,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1078.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not 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: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.a.177.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +2.00000 q^{6} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.00000 - 1.73205i) q^{12} -2.00000 q^{13} +4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(-1.00000 - 1.73205i) q^{19} +2.00000 q^{20} +1.00000 q^{22} +(-1.00000 + 1.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{26} -4.00000 q^{27} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-1.00000 + 1.73205i) q^{38} +(2.00000 - 3.46410i) q^{39} +(-1.00000 - 1.73205i) q^{40} -8.00000 q^{41} +12.0000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-1.00000 + 1.73205i) q^{45} +(6.00000 + 10.3923i) q^{47} +2.00000 q^{48} -1.00000 q^{50} +(1.00000 - 1.73205i) q^{52} +(1.00000 - 1.73205i) q^{53} +(2.00000 + 3.46410i) q^{54} +2.00000 q^{55} +4.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(5.00000 - 8.66025i) q^{59} +(-2.00000 + 3.46410i) q^{60} +(-5.00000 - 8.66025i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-1.00000 + 1.73205i) q^{66} +(6.00000 - 10.3923i) q^{67} +4.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(6.00000 - 10.3923i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{75} +2.00000 q^{76} -4.00000 q^{78} +(-1.00000 + 1.73205i) q^{80} +(5.50000 - 9.52628i) q^{81} +(4.00000 + 6.92820i) q^{82} +18.0000 q^{83} +(-6.00000 - 10.3923i) q^{86} +(-6.00000 + 10.3923i) q^{87} +(-0.500000 + 0.866025i) q^{88} +2.00000 q^{90} +(4.00000 + 6.92820i) q^{93} +(6.00000 - 10.3923i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{96} +12.0000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - 2 q^{3} - q^{4} - 2 q^{5} + 4 q^{6} + 2 q^{8} - q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 4 q^{13} + 8 q^{15} - q^{16} - q^{18} - 2 q^{19} + 4 q^{20} + 2 q^{22} - 2 q^{24} + q^{25} + 2 q^{26} - 8 q^{27} + 12 q^{29} - 4 q^{30} + 4 q^{31} - q^{32} - 2 q^{33} + 2 q^{36} - 2 q^{37} - 2 q^{38} + 4 q^{39} - 2 q^{40} - 16 q^{41} + 24 q^{43} - q^{44} - 2 q^{45} + 12 q^{47} + 4 q^{48} - 2 q^{50} + 2 q^{52} + 2 q^{53} + 4 q^{54} + 4 q^{55} + 8 q^{57} - 6 q^{58} + 10 q^{59} - 4 q^{60} - 10 q^{61} - 8 q^{62} + 2 q^{64} + 4 q^{65} - 2 q^{66} + 12 q^{67} + 8 q^{71} - q^{72} + 12 q^{73} - 2 q^{74} + 2 q^{75} + 4 q^{76} - 8 q^{78} - 2 q^{80} + 11 q^{81} + 8 q^{82} + 36 q^{83} - 12 q^{86} - 12 q^{87} - q^{88} + 4 q^{90} + 8 q^{93} + 12 q^{94} - 4 q^{95} - 2 q^{96} + 24 q^{97} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.00000 + 1.73205i −0.577350 + 1.00000i 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.00000 + 1.73205i −0.316228 + 0.547723i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) −1.00000 1.73205i −0.288675 0.500000i
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 4.00000 1.03280
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) −1.00000 + 1.73205i −0.204124 + 0.353553i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 1.00000 + 1.73205i 0.196116 + 0.339683i
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −2.00000 3.46410i −0.365148 0.632456i
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) −1.00000 + 1.73205i −0.162221 + 0.280976i
\(39\) 2.00000 3.46410i 0.320256 0.554700i
\(40\) −1.00000 1.73205i −0.158114 0.273861i
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 12.0000 1.82998 0.914991 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) 0 0
\(47\) 6.00000 + 10.3923i 0.875190 + 1.51587i 0.856560 + 0.516047i \(0.172597\pi\)
0.0186297 + 0.999826i \(0.494070\pi\)
\(48\) 2.00000 0.288675
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 2.00000 + 3.46410i 0.272166 + 0.471405i
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 5.00000 8.66025i 0.650945 1.12747i −0.331949 0.943297i \(-0.607706\pi\)
0.982894 0.184172i \(-0.0589603\pi\)
\(60\) −2.00000 + 3.46410i −0.258199 + 0.447214i
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 + 3.46410i 0.248069 + 0.429669i
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) 6.00000 10.3923i 0.733017 1.26962i −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 6.00000 10.3923i 0.702247 1.21633i −0.265429 0.964130i \(-0.585514\pi\)
0.967676 0.252197i \(-0.0811531\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 1.00000 + 1.73205i 0.115470 + 0.200000i
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −1.00000 + 1.73205i −0.111803 + 0.193649i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 4.00000 + 6.92820i 0.441726 + 0.765092i
\(83\) 18.0000 1.97576 0.987878 0.155230i \(-0.0496119\pi\)
0.987878 + 0.155230i \(0.0496119\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −6.00000 10.3923i −0.646997 1.12063i
\(87\) −6.00000 + 10.3923i −0.643268 + 1.11417i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 2.00000 0.210819
\(91\) 0 0
\(92\) 0 0
\(93\) 4.00000 + 6.92820i 0.414781 + 0.718421i
\(94\) 6.00000 10.3923i 0.618853 1.07188i
\(95\) −2.00000 + 3.46410i −0.205196 + 0.355409i
\(96\) −1.00000 1.73205i −0.102062 0.176777i
\(97\) 12.0000 1.21842 0.609208 0.793011i \(-0.291488\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(98\) 0 0
\(99\) 1.00000 0.100504
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 6.00000 + 10.3923i 0.591198 + 1.02398i 0.994071 + 0.108729i \(0.0346780\pi\)
−0.402874 + 0.915255i \(0.631989\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) 0 0
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) −10.0000 −0.920575
\(119\) 0 0
\(120\) 4.00000 0.365148
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −5.00000 + 8.66025i −0.452679 + 0.784063i
\(123\) 8.00000 13.8564i 0.721336 1.24939i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −12.0000 + 20.7846i −1.05654 + 1.82998i
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) −1.00000 1.73205i −0.0873704 0.151330i 0.819028 0.573753i \(-0.194513\pi\)
−0.906399 + 0.422423i \(0.861180\pi\)
\(132\) 2.00000 0.174078
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 4.00000 + 6.92820i 0.344265 + 0.596285i
\(136\) 0 0
\(137\) −11.0000 + 19.0526i −0.939793 + 1.62777i −0.173939 + 0.984757i \(0.555649\pi\)
−0.765855 + 0.643013i \(0.777684\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) −24.0000 −2.02116
\(142\) −2.00000 3.46410i −0.167836 0.290701i
\(143\) 1.00000 1.73205i 0.0836242 0.144841i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −6.00000 10.3923i −0.498273 0.863034i
\(146\) −12.0000 −0.993127
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 7.00000 + 12.1244i 0.573462 + 0.993266i 0.996207 + 0.0870170i \(0.0277334\pi\)
−0.422744 + 0.906249i \(0.638933\pi\)
\(150\) 1.00000 1.73205i 0.0816497 0.141421i
\(151\) 2.00000 3.46410i 0.162758 0.281905i −0.773099 0.634285i \(-0.781294\pi\)
0.935857 + 0.352381i \(0.114628\pi\)
\(152\) −1.00000 1.73205i −0.0811107 0.140488i
\(153\) 0 0
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i \(0.355351\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) 0 0
\(159\) 2.00000 + 3.46410i 0.158610 + 0.274721i
\(160\) 2.00000 0.158114
\(161\) 0 0
\(162\) −11.0000 −0.864242
\(163\) −6.00000 10.3923i −0.469956 0.813988i 0.529454 0.848339i \(-0.322397\pi\)
−0.999410 + 0.0343508i \(0.989064\pi\)
\(164\) 4.00000 6.92820i 0.312348 0.541002i
\(165\) −2.00000 + 3.46410i −0.155700 + 0.269680i
\(166\) −9.00000 15.5885i −0.698535 1.20990i
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −1.00000 + 1.73205i −0.0764719 + 0.132453i
\(172\) −6.00000 + 10.3923i −0.457496 + 0.792406i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 12.0000 0.909718
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 10.0000 + 17.3205i 0.751646 + 1.30189i
\(178\) 0 0
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) −1.00000 1.73205i −0.0745356 0.129099i
\(181\) −18.0000 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(182\) 0 0
\(183\) 20.0000 1.47844
\(184\) 0 0
\(185\) −2.00000 + 3.46410i −0.147043 + 0.254686i
\(186\) 4.00000 6.92820i 0.293294 0.508001i
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) −1.00000 + 1.73205i −0.0721688 + 0.125000i
\(193\) 1.00000 1.73205i 0.0719816 0.124676i −0.827788 0.561041i \(-0.810401\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) −6.00000 10.3923i −0.430775 0.746124i
\(195\) −8.00000 −0.572892
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) −0.500000 0.866025i −0.0355335 0.0615457i
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 12.0000 + 20.7846i 0.846415 + 1.46603i
\(202\) −6.00000 −0.422159
\(203\) 0 0
\(204\) 0 0
\(205\) 8.00000 + 13.8564i 0.558744 + 0.967773i
\(206\) 6.00000 10.3923i 0.418040 0.724066i
\(207\) 0 0
\(208\) 1.00000 + 1.73205i 0.0693375 + 0.120096i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 1.00000 + 1.73205i 0.0686803 + 0.118958i
\(213\) −4.00000 + 6.92820i −0.274075 + 0.474713i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −12.0000 20.7846i −0.818393 1.41750i
\(216\) −4.00000 −0.272166
\(217\) 0 0
\(218\) −10.0000 −0.677285
\(219\) 12.0000 + 20.7846i 0.810885 + 1.40449i
\(220\) −1.00000 + 1.73205i −0.0674200 + 0.116775i
\(221\) 0 0
\(222\) −2.00000 3.46410i −0.134231 0.232495i
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 5.00000 + 8.66025i 0.332595 + 0.576072i
\(227\) 3.00000 5.19615i 0.199117 0.344881i −0.749125 0.662428i \(-0.769526\pi\)
0.948242 + 0.317547i \(0.102859\pi\)
\(228\) −2.00000 + 3.46410i −0.132453 + 0.229416i
\(229\) −15.0000 25.9808i −0.991228 1.71686i −0.610071 0.792347i \(-0.708859\pi\)
−0.381157 0.924510i \(-0.624474\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 5.00000 + 8.66025i 0.327561 + 0.567352i 0.982027 0.188739i \(-0.0604400\pi\)
−0.654466 + 0.756091i \(0.727107\pi\)
\(234\) 1.00000 1.73205i 0.0653720 0.113228i
\(235\) 12.0000 20.7846i 0.782794 1.35584i
\(236\) 5.00000 + 8.66025i 0.325472 + 0.563735i
\(237\) 0 0
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) −2.00000 3.46410i −0.129099 0.223607i
\(241\) 4.00000 6.92820i 0.257663 0.446285i −0.707953 0.706260i \(-0.750381\pi\)
0.965615 + 0.259975i \(0.0837143\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 5.00000 + 8.66025i 0.320750 + 0.555556i
\(244\) 10.0000 0.640184
\(245\) 0 0
\(246\) −16.0000 −1.02012
\(247\) 2.00000 + 3.46410i 0.127257 + 0.220416i
\(248\) 2.00000 3.46410i 0.127000 0.219971i
\(249\) −18.0000 + 31.1769i −1.14070 + 1.97576i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −2.00000 3.46410i −0.125491 0.217357i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.00000 + 13.8564i 0.499026 + 0.864339i 0.999999 0.00112398i \(-0.000357774\pi\)
−0.500973 + 0.865463i \(0.667024\pi\)
\(258\) 24.0000 1.49417
\(259\) 0 0
\(260\) −4.00000 −0.248069
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) −1.00000 + 1.73205i −0.0617802 + 0.107006i
\(263\) −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) −1.00000 1.73205i −0.0615457 0.106600i
\(265\) −4.00000 −0.245718
\(266\) 0 0
\(267\) 0 0
\(268\) 6.00000 + 10.3923i 0.366508 + 0.634811i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 4.00000 6.92820i 0.243432 0.421637i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 22.0000 1.32907
\(275\) 0.500000 + 0.866025i 0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) 7.00000 12.1244i 0.420589 0.728482i −0.575408 0.817867i \(-0.695157\pi\)
0.995997 + 0.0893846i \(0.0284900\pi\)
\(278\) −7.00000 12.1244i −0.419832 0.727171i
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 12.0000 + 20.7846i 0.714590 + 1.23771i
\(283\) −1.00000 + 1.73205i −0.0594438 + 0.102960i −0.894216 0.447636i \(-0.852266\pi\)
0.834772 + 0.550596i \(0.185599\pi\)
\(284\) −2.00000 + 3.46410i −0.118678 + 0.205557i
\(285\) −4.00000 6.92820i −0.236940 0.410391i
\(286\) −2.00000 −0.118262
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) −6.00000 + 10.3923i −0.352332 + 0.610257i
\(291\) −12.0000 + 20.7846i −0.703452 + 1.21842i
\(292\) 6.00000 + 10.3923i 0.351123 + 0.608164i
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 0 0
\(295\) −20.0000 −1.16445
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 2.00000 3.46410i 0.116052 0.201008i
\(298\) 7.00000 12.1244i 0.405499 0.702345i
\(299\) 0 0
\(300\) −2.00000 −0.115470
\(301\) 0 0
\(302\) −4.00000 −0.230174
\(303\) 6.00000 + 10.3923i 0.344691 + 0.597022i
\(304\) −1.00000 + 1.73205i −0.0573539 + 0.0993399i
\(305\) −10.0000 + 17.3205i −0.572598 + 0.991769i
\(306\) 0 0
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) 0 0
\(309\) −24.0000 −1.36531
\(310\) 4.00000 + 6.92820i 0.227185 + 0.393496i
\(311\) 8.00000 13.8564i 0.453638 0.785725i −0.544970 0.838455i \(-0.683459\pi\)
0.998609 + 0.0527306i \(0.0167924\pi\)
\(312\) 2.00000 3.46410i 0.113228 0.196116i
\(313\) −2.00000 3.46410i −0.113047 0.195803i 0.803951 0.594696i \(-0.202728\pi\)
−0.916997 + 0.398894i \(0.869394\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 0 0
\(317\) −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i \(-0.847759\pi\)
0.0453045 0.998973i \(-0.485574\pi\)
\(318\) 2.00000 3.46410i 0.112154 0.194257i
\(319\) −3.00000 + 5.19615i −0.167968 + 0.290929i
\(320\) −1.00000 1.73205i −0.0559017 0.0968246i
\(321\) 24.0000 1.33955
\(322\) 0 0
\(323\) 0 0
\(324\) 5.50000 + 9.52628i 0.305556 + 0.529238i
\(325\) −1.00000 + 1.73205i −0.0554700 + 0.0960769i
\(326\) −6.00000 + 10.3923i −0.332309 + 0.575577i
\(327\) 10.0000 + 17.3205i 0.553001 + 0.957826i
\(328\) −8.00000 −0.441726
\(329\) 0 0
\(330\) 4.00000 0.220193
\(331\) −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) −9.00000 + 15.5885i −0.493939 + 0.855528i
\(333\) −1.00000 + 1.73205i −0.0547997 + 0.0949158i
\(334\) 6.00000 + 10.3923i 0.328305 + 0.568642i
\(335\) −24.0000 −1.31126
\(336\) 0 0
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 10.0000 17.3205i 0.543125 0.940721i
\(340\) 0 0
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) 2.00000 0.108148
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) −10.0000 + 17.3205i −0.536828 + 0.929814i 0.462244 + 0.886753i \(0.347044\pi\)
−0.999072 + 0.0430610i \(0.986289\pi\)
\(348\) −6.00000 10.3923i −0.321634 0.557086i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 8.00000 0.427008
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 10.0000 17.3205i 0.531494 0.920575i
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) −1.00000 + 1.73205i −0.0527046 + 0.0912871i
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 9.00000 + 15.5885i 0.473029 + 0.819311i
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) −24.0000 −1.25622
\(366\) −10.0000 17.3205i −0.522708 0.905357i
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) 0 0
\(369\) 4.00000 + 6.92820i 0.208232 + 0.360668i
\(370\) 4.00000 0.207950
\(371\) 0 0
\(372\) −8.00000 −0.414781
\(373\) 15.0000 + 25.9808i 0.776671 + 1.34523i 0.933851 + 0.357663i \(0.116426\pi\)
−0.157180 + 0.987570i \(0.550240\pi\)
\(374\) 0 0
\(375\) 12.0000 20.7846i 0.619677 1.07331i
\(376\) 6.00000 + 10.3923i 0.309426 + 0.535942i
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) −2.00000 3.46410i −0.102598 0.177705i
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) −6.00000 + 10.3923i −0.306987 + 0.531717i
\(383\) 6.00000 + 10.3923i 0.306586 + 0.531022i 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) −6.00000 10.3923i −0.304997 0.528271i
\(388\) −6.00000 + 10.3923i −0.304604 + 0.527589i
\(389\) −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i \(-0.914918\pi\)
0.710980 + 0.703213i \(0.248252\pi\)
\(390\) 4.00000 + 6.92820i 0.202548 + 0.350823i
\(391\) 0 0
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) 3.00000 + 5.19615i 0.151138 + 0.261778i
\(395\) 0 0
\(396\) −0.500000 + 0.866025i −0.0251259 + 0.0435194i
\(397\) 17.0000 + 29.4449i 0.853206 + 1.47780i 0.878300 + 0.478110i \(0.158678\pi\)
−0.0250943 + 0.999685i \(0.507989\pi\)
\(398\) −4.00000 −0.200502
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 12.0000 20.7846i 0.598506 1.03664i
\(403\) −4.00000 + 6.92820i −0.199254 + 0.345118i
\(404\) 3.00000 + 5.19615i 0.149256 + 0.258518i
\(405\) −22.0000 −1.09319
\(406\) 0 0
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) 8.00000 13.8564i 0.395575 0.685155i −0.597600 0.801795i \(-0.703879\pi\)
0.993174 + 0.116639i \(0.0372122\pi\)
\(410\) 8.00000 13.8564i 0.395092 0.684319i
\(411\) −22.0000 38.1051i −1.08518 1.87959i
\(412\) −12.0000 −0.591198
\(413\) 0 0
\(414\) 0 0
\(415\) −18.0000 31.1769i −0.883585 1.53041i
\(416\) 1.00000 1.73205i 0.0490290 0.0849208i
\(417\) −14.0000 + 24.2487i −0.685583 + 1.18746i
\(418\) −1.00000 1.73205i −0.0489116 0.0847174i
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0 0
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 2.00000 + 3.46410i 0.0973585 + 0.168630i
\(423\) 6.00000 10.3923i 0.291730 0.505291i
\(424\) 1.00000 1.73205i 0.0485643 0.0841158i
\(425\) 0 0
\(426\) 8.00000 0.387601
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 2.00000 + 3.46410i 0.0965609 + 0.167248i
\(430\) −12.0000 + 20.7846i −0.578691 + 1.00232i
\(431\) 18.0000 31.1769i 0.867029 1.50174i 0.00201168 0.999998i \(-0.499360\pi\)
0.865018 0.501741i \(-0.167307\pi\)
\(432\) 2.00000 + 3.46410i 0.0962250 + 0.166667i
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 0 0
\(435\) 24.0000 1.15071
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) 0 0
\(438\) 12.0000 20.7846i 0.573382 0.993127i
\(439\) −8.00000 13.8564i −0.381819 0.661330i 0.609503 0.792784i \(-0.291369\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) −2.00000 + 3.46410i −0.0949158 + 0.164399i
\(445\) 0 0
\(446\) 4.00000 + 6.92820i 0.189405 + 0.328060i
\(447\) −28.0000 −1.32435
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) 4.00000 6.92820i 0.188353 0.326236i
\(452\) 5.00000 8.66025i 0.235180 0.407344i
\(453\) 4.00000 + 6.92820i 0.187936 + 0.325515i
\(454\) −6.00000 −0.281594
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −3.00000 5.19615i −0.140334 0.243066i 0.787288 0.616585i \(-0.211484\pi\)
−0.927622 + 0.373519i \(0.878151\pi\)
\(458\) −15.0000 + 25.9808i −0.700904 + 1.21400i
\(459\) 0 0
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) 8.00000 13.8564i 0.370991 0.642575i
\(466\) 5.00000 8.66025i 0.231621 0.401179i
\(467\) −11.0000 19.0526i −0.509019 0.881647i −0.999945 0.0104461i \(-0.996675\pi\)
0.490926 0.871201i \(-0.336658\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) −24.0000 −1.10704
\(471\) −14.0000 24.2487i −0.645086 1.11732i
\(472\) 5.00000 8.66025i 0.230144 0.398621i
\(473\) −6.00000 + 10.3923i −0.275880 + 0.477839i
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 2.00000 + 3.46410i 0.0914779 + 0.158444i
\(479\) −18.0000 + 31.1769i −0.822441 + 1.42451i 0.0814184 + 0.996680i \(0.474055\pi\)
−0.903859 + 0.427830i \(0.859278\pi\)
\(480\) −2.00000 + 3.46410i −0.0912871 + 0.158114i
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) −8.00000 −0.364390
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −12.0000 20.7846i −0.544892 0.943781i
\(486\) 5.00000 8.66025i 0.226805 0.392837i
\(487\) −4.00000 + 6.92820i −0.181257 + 0.313947i −0.942309 0.334744i \(-0.891350\pi\)
0.761052 + 0.648691i \(0.224683\pi\)
\(488\) −5.00000 8.66025i −0.226339 0.392031i
\(489\) 24.0000 1.08532
\(490\) 0 0
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 8.00000 + 13.8564i 0.360668 + 0.624695i
\(493\) 0 0
\(494\) 2.00000 3.46410i 0.0899843 0.155857i
\(495\) −1.00000 1.73205i −0.0449467 0.0778499i
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 36.0000 1.61320
\(499\) −10.0000 17.3205i −0.447661 0.775372i 0.550572 0.834788i \(-0.314410\pi\)
−0.998233 + 0.0594153i \(0.981076\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) −9.00000 15.5885i −0.401690 0.695747i
\(503\) 8.00000 0.356702 0.178351 0.983967i \(-0.442924\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) 9.00000 15.5885i 0.399704 0.692308i
\(508\) −2.00000 + 3.46410i −0.0887357 + 0.153695i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 4.00000 + 6.92820i 0.176604 + 0.305888i
\(514\) 8.00000 13.8564i 0.352865 0.611180i
\(515\) 12.0000 20.7846i 0.528783 0.915879i
\(516\) −12.0000 20.7846i −0.528271 0.914991i
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) 12.0000 0.526742
\(520\) 2.00000 + 3.46410i 0.0877058 + 0.151911i
\(521\) −2.00000 + 3.46410i −0.0876216 + 0.151765i −0.906505 0.422194i \(-0.861260\pi\)
0.818884 + 0.573959i \(0.194593\pi\)
\(522\) −3.00000 + 5.19615i −0.131306 + 0.227429i
\(523\) −17.0000 29.4449i −0.743358 1.28753i −0.950958 0.309320i \(-0.899899\pi\)
0.207600 0.978214i \(-0.433435\pi\)
\(524\) 2.00000 0.0873704
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) 0 0
\(528\) −1.00000 + 1.73205i −0.0435194 + 0.0753778i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 2.00000 + 3.46410i 0.0868744 + 0.150471i
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 16.0000 0.693037
\(534\) 0 0
\(535\) −12.0000 + 20.7846i −0.518805 + 0.898597i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −12.0000 20.7846i −0.517838 0.896922i
\(538\) 6.00000 0.258678
\(539\) 0 0
\(540\) −8.00000 −0.344265
\(541\) −17.0000 29.4449i −0.730887 1.26593i −0.956504 0.291718i \(-0.905773\pi\)
0.225617 0.974216i \(-0.427560\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 18.0000 31.1769i 0.772454 1.33793i
\(544\) 0 0
\(545\) −20.0000 −0.856706
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −11.0000 19.0526i −0.469897 0.813885i
\(549\) −5.00000 + 8.66025i −0.213395 + 0.369611i
\(550\) 0.500000 0.866025i 0.0213201 0.0369274i
\(551\) −6.00000 10.3923i −0.255609 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) −14.0000 −0.594803
\(555\) −4.00000 6.92820i −0.169791 0.294086i
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) −17.0000 + 29.4449i −0.720313 + 1.24762i 0.240561 + 0.970634i \(0.422669\pi\)
−0.960874 + 0.276985i \(0.910665\pi\)
\(558\) 2.00000 + 3.46410i 0.0846668 + 0.146647i
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) 5.00000 + 8.66025i 0.210912 + 0.365311i
\(563\) −11.0000 + 19.0526i −0.463595 + 0.802970i −0.999137 0.0415389i \(-0.986774\pi\)
0.535542 + 0.844508i \(0.320107\pi\)
\(564\) 12.0000 20.7846i 0.505291 0.875190i
\(565\) 10.0000 + 17.3205i 0.420703 + 0.728679i
\(566\) 2.00000 0.0840663
\(567\) 0 0
\(568\) 4.00000 0.167836
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) −4.00000 + 6.92820i −0.167542 + 0.290191i
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) 1.00000 + 1.73205i 0.0418121 + 0.0724207i
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −16.0000 + 27.7128i −0.666089 + 1.15370i 0.312900 + 0.949786i \(0.398699\pi\)
−0.978989 + 0.203913i \(0.934634\pi\)
\(578\) 8.50000 14.7224i 0.353553 0.612372i
\(579\) 2.00000 + 3.46410i 0.0831172 + 0.143963i
\(580\) 12.0000 0.498273
\(581\) 0 0
\(582\) 24.0000 0.994832
\(583\) 1.00000 + 1.73205i 0.0414158 + 0.0717342i
\(584\) 6.00000 10.3923i 0.248282 0.430037i
\(585\) 2.00000 3.46410i 0.0826898 0.143223i
\(586\) −13.0000 22.5167i −0.537025 0.930155i
\(587\) 42.0000 1.73353 0.866763 0.498721i \(-0.166197\pi\)
0.866763 + 0.498721i \(0.166197\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 10.0000 + 17.3205i 0.411693 + 0.713074i
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 10.0000 + 17.3205i 0.410651 + 0.711268i 0.994961 0.100262i \(-0.0319682\pi\)
−0.584310 + 0.811530i \(0.698635\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −14.0000 −0.573462
\(597\) 4.00000 + 6.92820i 0.163709 + 0.283552i
\(598\) 0 0
\(599\) −14.0000 + 24.2487i −0.572024 + 0.990775i 0.424333 + 0.905506i \(0.360508\pi\)
−0.996358 + 0.0852695i \(0.972825\pi\)
\(600\) 1.00000 + 1.73205i 0.0408248 + 0.0707107i
\(601\) −4.00000 −0.163163 −0.0815817 0.996667i \(-0.525997\pi\)
−0.0815817 + 0.996667i \(0.525997\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 2.00000 + 3.46410i 0.0813788 + 0.140952i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 6.00000 10.3923i 0.243733 0.422159i
\(607\) 16.0000 + 27.7128i 0.649420 + 1.12483i 0.983262 + 0.182199i \(0.0583216\pi\)
−0.333842 + 0.942629i \(0.608345\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 20.0000 0.809776
\(611\) −12.0000 20.7846i −0.485468 0.840855i
\(612\) 0 0
\(613\) 21.0000 36.3731i 0.848182 1.46909i −0.0346469 0.999400i \(-0.511031\pi\)
0.882829 0.469695i \(-0.155636\pi\)
\(614\) 7.00000 + 12.1244i 0.282497 + 0.489299i
\(615\) −32.0000 −1.29036
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 12.0000 + 20.7846i 0.482711 + 0.836080i
\(619\) −7.00000 + 12.1244i −0.281354 + 0.487319i −0.971718 0.236143i \(-0.924117\pi\)
0.690365 + 0.723462i \(0.257450\pi\)
\(620\) 4.00000 6.92820i 0.160644 0.278243i
\(621\) 0 0
\(622\) −16.0000 −0.641542
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) −2.00000 + 3.46410i −0.0799361 + 0.138453i
\(627\) −2.00000 + 3.46410i −0.0798723 + 0.138343i
\(628\) −7.00000 12.1244i −0.279330 0.483814i
\(629\) 0 0
\(630\) 0 0
\(631\) −28.0000 −1.11466 −0.557331 0.830290i \(-0.688175\pi\)
−0.557331 + 0.830290i \(0.688175\pi\)
\(632\) 0 0
\(633\) 4.00000 6.92820i 0.158986 0.275371i
\(634\) −15.0000 + 25.9808i −0.595726 + 1.03183i
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) −4.00000 −0.158610
\(637\) 0 0
\(638\) 6.00000 0.237542
\(639\) −2.00000 3.46410i −0.0791188 0.137038i
\(640\) −1.00000 + 1.73205i −0.0395285 + 0.0684653i
\(641\) −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) −12.0000 20.7846i −0.473602 0.820303i
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) 0 0
\(645\) 48.0000 1.89000
\(646\) 0 0
\(647\) −22.0000 + 38.1051i −0.864909 + 1.49807i 0.00222801 + 0.999998i \(0.499291\pi\)
−0.867137 + 0.498069i \(0.834043\pi\)
\(648\) 5.50000 9.52628i 0.216060 0.374228i
\(649\) 5.00000 + 8.66025i 0.196267 + 0.339945i
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 10.0000 17.3205i 0.391031 0.677285i
\(655\) −2.00000 + 3.46410i −0.0781465 + 0.135354i
\(656\) 4.00000 + 6.92820i 0.156174 + 0.270501i
\(657\) −12.0000 −0.468165
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) −2.00000 3.46410i −0.0778499 0.134840i
\(661\) 3.00000 5.19615i 0.116686 0.202107i −0.801766 0.597638i \(-0.796106\pi\)
0.918453 + 0.395531i \(0.129439\pi\)
\(662\) −6.00000 + 10.3923i −0.233197 + 0.403908i
\(663\) 0 0
\(664\) 18.0000 0.698535
\(665\) 0 0
\(666\) 2.00000 0.0774984
\(667\) 0 0
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) 12.0000 + 20.7846i 0.463600 + 0.802980i
\(671\) 10.0000 0.386046
\(672\) 0 0
\(673\) 6.00000 0.231283 0.115642 0.993291i \(-0.463108\pi\)
0.115642 + 0.993291i \(0.463108\pi\)
\(674\) −17.0000 29.4449i −0.654816 1.13417i
\(675\) −2.00000 + 3.46410i −0.0769800 + 0.133333i
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) 21.0000 + 36.3731i 0.807096 + 1.39793i 0.914867 + 0.403755i \(0.132295\pi\)
−0.107772 + 0.994176i \(0.534372\pi\)
\(678\) −20.0000 −0.768095
\(679\) 0 0
\(680\) 0 0
\(681\) 6.00000 + 10.3923i 0.229920 + 0.398234i
\(682\) 2.00000 3.46410i 0.0765840 0.132647i
\(683\) −2.00000 + 3.46410i −0.0765279 + 0.132550i −0.901750 0.432259i \(-0.857717\pi\)
0.825222 + 0.564809i \(0.191050\pi\)
\(684\) −1.00000 1.73205i −0.0382360 0.0662266i
\(685\) 44.0000 1.68115
\(686\) 0 0
\(687\) 60.0000 2.28914
\(688\) −6.00000 10.3923i −0.228748 0.396203i
\(689\) −2.00000 + 3.46410i −0.0761939 + 0.131972i
\(690\) 0 0
\(691\) 25.0000 + 43.3013i 0.951045 + 1.64726i 0.743170 + 0.669102i \(0.233321\pi\)
0.207875 + 0.978155i \(0.433345\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 20.0000 0.759190
\(695\) −14.0000 24.2487i −0.531050 0.919806i
\(696\) −6.00000 + 10.3923i −0.227429 + 0.393919i
\(697\) 0 0
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) −20.0000 −0.756469
\(700\) 0 0
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) −4.00000 6.92820i −0.150970 0.261488i
\(703\) −2.00000 + 3.46410i −0.0754314 + 0.130651i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 24.0000 + 41.5692i 0.903892 + 1.56559i
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) −20.0000 −0.751646
\(709\) 7.00000 + 12.1244i 0.262891 + 0.455340i 0.967009 0.254743i \(-0.0819909\pi\)
−0.704118 + 0.710083i \(0.748658\pi\)
\(710\) −4.00000 + 6.92820i −0.150117 + 0.260011i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 4.00000 6.92820i 0.149383 0.258738i
\(718\) −10.0000 + 17.3205i −0.373197 + 0.646396i
\(719\) −14.0000 24.2487i −0.522112 0.904324i −0.999669 0.0257237i \(-0.991811\pi\)
0.477557 0.878601i \(-0.341522\pi\)
\(720\) 2.00000 0.0745356
\(721\) 0 0
\(722\) −15.0000 −0.558242
\(723\) 8.00000 + 13.8564i 0.297523 + 0.515325i
\(724\) 9.00000 15.5885i 0.334482 0.579340i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −12.0000 −0.445055 −0.222528 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 12.0000 + 20.7846i 0.444140 + 0.769273i
\(731\) 0 0
\(732\) −10.0000 + 17.3205i −0.369611 + 0.640184i
\(733\) 3.00000 + 5.19615i 0.110808 + 0.191924i 0.916096 0.400959i \(-0.131323\pi\)
−0.805289 + 0.592883i \(0.797990\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) 0 0
\(737\) 6.00000 + 10.3923i 0.221013 + 0.382805i
\(738\) 4.00000 6.92820i 0.147242 0.255031i
\(739\) 2.00000 3.46410i 0.0735712 0.127429i −0.826893 0.562360i \(-0.809894\pi\)
0.900464 + 0.434930i \(0.143227\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 4.00000 + 6.92820i 0.146647 + 0.254000i
\(745\) 14.0000 24.2487i 0.512920 0.888404i
\(746\) 15.0000 25.9808i 0.549189 0.951223i
\(747\) −9.00000 15.5885i −0.329293 0.570352i
\(748\) 0 0
\(749\) 0 0
\(750\) −24.0000 −0.876356
\(751\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(752\) 6.00000 10.3923i 0.218797 0.378968i
\(753\) −18.0000 + 31.1769i −0.655956 + 1.13615i
\(754\) 6.00000 + 10.3923i 0.218507 + 0.378465i
\(755\) −8.00000 −0.291150
\(756\) 0 0
\(757\) −30.0000 −1.09037 −0.545184 0.838316i \(-0.683540\pi\)
−0.545184 + 0.838316i \(0.683540\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) 0 0
\(760\) −2.00000 + 3.46410i −0.0725476 + 0.125656i
\(761\) 4.00000 + 6.92820i 0.145000 + 0.251147i 0.929373 0.369142i \(-0.120348\pi\)
−0.784373 + 0.620289i \(0.787015\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) 12.0000 0.434145
\(765\) 0 0
\(766\) 6.00000 10.3923i 0.216789 0.375489i
\(767\) −10.0000 + 17.3205i −0.361079 + 0.625407i
\(768\) −1.00000 1.73205i −0.0360844 0.0625000i
\(769\) 40.0000 1.44244 0.721218 0.692708i \(-0.243582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(770\) 0 0
\(771\) −32.0000 −1.15245
\(772\) 1.00000 + 1.73205i 0.0359908 + 0.0623379i
\(773\) 7.00000 12.1244i 0.251773 0.436083i −0.712241 0.701935i \(-0.752320\pi\)
0.964014 + 0.265852i \(0.0856532\pi\)
\(774\) −6.00000 + 10.3923i −0.215666 + 0.373544i
\(775\) −2.00000 3.46410i −0.0718421 0.124434i
\(776\) 12.0000 0.430775
\(777\) 0 0
\(778\) 10.0000 0.358517
\(779\) 8.00000 + 13.8564i 0.286630 + 0.496457i