Properties

Label 666.2.bs.b.17.2
Level $666$
Weight $2$
Character 666.17
Analytic conductor $5.318$
Analytic rank $0$
Dimension $96$
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] = [666,2,Mod(17,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("666.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.bs (of order \(36\), degree \(12\), 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: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 17.2
Character \(\chi\) \(=\) 666.17
Dual form 666.2.bs.b.431.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-1.60885 + 0.140756i) q^{5} +(1.53998 + 1.29220i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\) \(q+(-0.573576 + 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-1.60885 + 0.140756i) q^{5} +(1.53998 + 1.29220i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.807495 - 1.39862i) q^{10} +(-2.64381 - 4.57920i) q^{11} +(4.54133 + 2.11766i) q^{13} +(-1.94180 + 0.520305i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(5.07820 - 2.36800i) q^{17} +(-0.363361 + 0.254428i) q^{19} +(0.682525 + 1.46368i) q^{20} +(5.26749 + 0.460846i) q^{22} +(1.51364 + 5.64898i) q^{23} +(-2.35547 + 0.415332i) q^{25} +(-4.33948 + 2.50540i) q^{26} +(0.687564 - 1.88907i) q^{28} +(-1.91829 + 7.15914i) q^{29} +(5.12102 - 5.12102i) q^{31} +(-0.0871557 - 0.996195i) q^{32} +(-0.972981 + 5.51805i) q^{34} +(-2.65948 - 1.86218i) q^{35} +(6.05499 - 0.580588i) q^{37} -0.443582i q^{38} +(-1.59046 - 0.280440i) q^{40} +(6.41507 - 2.33489i) q^{41} +(7.63098 + 7.63098i) q^{43} +(-3.39881 + 4.05054i) q^{44} +(-5.49556 - 2.00022i) q^{46} +(4.34681 + 2.50963i) q^{47} +(-0.513770 - 2.91374i) q^{49} +(1.01082 - 2.16771i) q^{50} +(0.436720 - 4.99173i) q^{52} +(7.64299 + 9.10856i) q^{53} +(4.89802 + 6.99510i) q^{55} +(1.15306 + 1.64674i) q^{56} +(-4.76414 - 5.67769i) q^{58} +(0.615917 - 7.03996i) q^{59} +(-2.86510 + 6.14423i) q^{61} +(1.25760 + 7.13219i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-7.60437 - 2.76776i) q^{65} +(-3.96674 + 4.72738i) q^{67} +(-3.96204 - 3.96204i) q^{68} +(3.05082 - 1.11041i) q^{70} +(-1.49231 - 0.263135i) q^{71} -8.32062i q^{73} +(-2.99741 + 5.29297i) q^{74} +(0.363361 + 0.254428i) q^{76} +(1.84583 - 10.4682i) q^{77} +(-1.28011 - 14.6317i) q^{79} +(1.14197 - 1.14197i) q^{80} +(-1.76690 + 6.59415i) q^{82} +(-4.01232 + 11.0238i) q^{83} +(-7.83673 + 4.52454i) q^{85} +(-10.6279 + 1.87398i) q^{86} +(-1.36853 - 5.10744i) q^{88} +(-0.608784 - 0.0532617i) q^{89} +(4.25713 + 9.12944i) q^{91} +(4.79061 - 3.35442i) q^{92} +(-4.54900 + 2.12123i) q^{94} +(0.548780 - 0.460481i) q^{95} +(-10.0241 + 2.68596i) q^{97} +(2.68148 + 1.25039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{36}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.573576 + 0.819152i −0.405580 + 0.579228i
\(3\) 0 0
\(4\) −0.342020 0.939693i −0.171010 0.469846i
\(5\) −1.60885 + 0.140756i −0.719498 + 0.0629479i −0.441023 0.897496i \(-0.645384\pi\)
−0.278474 + 0.960444i \(0.589829\pi\)
\(6\) 0 0
\(7\) 1.53998 + 1.29220i 0.582058 + 0.488405i 0.885622 0.464406i \(-0.153732\pi\)
−0.303564 + 0.952811i \(0.598177\pi\)
\(8\) 0.965926 + 0.258819i 0.341506 + 0.0915064i
\(9\) 0 0
\(10\) 0.807495 1.39862i 0.255352 0.442283i
\(11\) −2.64381 4.57920i −0.797137 1.38068i −0.921473 0.388442i \(-0.873013\pi\)
0.124336 0.992240i \(-0.460320\pi\)
\(12\) 0 0
\(13\) 4.54133 + 2.11766i 1.25954 + 0.587332i 0.933687 0.358089i \(-0.116572\pi\)
0.325851 + 0.945421i \(0.394349\pi\)
\(14\) −1.94180 + 0.520305i −0.518969 + 0.139057i
\(15\) 0 0
\(16\) −0.766044 + 0.642788i −0.191511 + 0.160697i
\(17\) 5.07820 2.36800i 1.23164 0.574325i 0.305752 0.952111i \(-0.401092\pi\)
0.925893 + 0.377786i \(0.123314\pi\)
\(18\) 0 0
\(19\) −0.363361 + 0.254428i −0.0833608 + 0.0583698i −0.614514 0.788906i \(-0.710648\pi\)
0.531153 + 0.847276i \(0.321759\pi\)
\(20\) 0.682525 + 1.46368i 0.152617 + 0.327289i
\(21\) 0 0
\(22\) 5.26749 + 0.460846i 1.12303 + 0.0982526i
\(23\) 1.51364 + 5.64898i 0.315616 + 1.17789i 0.923415 + 0.383803i \(0.125386\pi\)
−0.607800 + 0.794090i \(0.707948\pi\)
\(24\) 0 0
\(25\) −2.35547 + 0.415332i −0.471093 + 0.0830665i
\(26\) −4.33948 + 2.50540i −0.851042 + 0.491350i
\(27\) 0 0
\(28\) 0.687564 1.88907i 0.129937 0.357000i
\(29\) −1.91829 + 7.15914i −0.356217 + 1.32942i 0.522729 + 0.852499i \(0.324914\pi\)
−0.878946 + 0.476921i \(0.841753\pi\)
\(30\) 0 0
\(31\) 5.12102 5.12102i 0.919762 0.919762i −0.0772495 0.997012i \(-0.524614\pi\)
0.997012 + 0.0772495i \(0.0246138\pi\)
\(32\) −0.0871557 0.996195i −0.0154071 0.176104i
\(33\) 0 0
\(34\) −0.972981 + 5.51805i −0.166865 + 0.946338i
\(35\) −2.65948 1.86218i −0.449533 0.314767i
\(36\) 0 0
\(37\) 6.05499 0.580588i 0.995434 0.0954481i
\(38\) 0.443582i 0.0719585i
\(39\) 0 0
\(40\) −1.59046 0.280440i −0.251473 0.0443415i
\(41\) 6.41507 2.33489i 1.00186 0.364649i 0.211561 0.977365i \(-0.432145\pi\)
0.790303 + 0.612716i \(0.209923\pi\)
\(42\) 0 0
\(43\) 7.63098 + 7.63098i 1.16371 + 1.16371i 0.983656 + 0.180057i \(0.0576281\pi\)
0.180057 + 0.983656i \(0.442372\pi\)
\(44\) −3.39881 + 4.05054i −0.512390 + 0.610643i
\(45\) 0 0
\(46\) −5.49556 2.00022i −0.810276 0.294916i
\(47\) 4.34681 + 2.50963i 0.634047 + 0.366067i 0.782318 0.622880i \(-0.214037\pi\)
−0.148271 + 0.988947i \(0.547371\pi\)
\(48\) 0 0
\(49\) −0.513770 2.91374i −0.0733957 0.416248i
\(50\) 1.01082 2.16771i 0.142952 0.306561i
\(51\) 0 0
\(52\) 0.436720 4.99173i 0.0605622 0.692229i
\(53\) 7.64299 + 9.10856i 1.04985 + 1.25116i 0.967049 + 0.254590i \(0.0819405\pi\)
0.0827960 + 0.996567i \(0.473615\pi\)
\(54\) 0 0
\(55\) 4.89802 + 6.99510i 0.660449 + 0.943219i
\(56\) 1.15306 + 1.64674i 0.154084 + 0.220055i
\(57\) 0 0
\(58\) −4.76414 5.67769i −0.625563 0.745517i
\(59\) 0.615917 7.03996i 0.0801855 0.916525i −0.844441 0.535649i \(-0.820067\pi\)
0.924626 0.380876i \(-0.124377\pi\)
\(60\) 0 0
\(61\) −2.86510 + 6.14423i −0.366839 + 0.786688i 0.633082 + 0.774085i \(0.281790\pi\)
−0.999921 + 0.0126035i \(0.995988\pi\)
\(62\) 1.25760 + 7.13219i 0.159715 + 0.905789i
\(63\) 0 0
\(64\) 0.866025 + 0.500000i 0.108253 + 0.0625000i
\(65\) −7.60437 2.76776i −0.943206 0.343299i
\(66\) 0 0
\(67\) −3.96674 + 4.72738i −0.484615 + 0.577541i −0.951839 0.306597i \(-0.900810\pi\)
0.467224 + 0.884139i \(0.345254\pi\)
\(68\) −3.96204 3.96204i −0.480468 0.480468i
\(69\) 0 0
\(70\) 3.05082 1.11041i 0.364643 0.132719i
\(71\) −1.49231 0.263135i −0.177105 0.0312284i 0.0843922 0.996433i \(-0.473105\pi\)
−0.261497 + 0.965204i \(0.584216\pi\)
\(72\) 0 0
\(73\) 8.32062i 0.973855i −0.873442 0.486928i \(-0.838118\pi\)
0.873442 0.486928i \(-0.161882\pi\)
\(74\) −2.99741 + 5.29297i −0.348442 + 0.615295i
\(75\) 0 0
\(76\) 0.363361 + 0.254428i 0.0416804 + 0.0291849i
\(77\) 1.84583 10.4682i 0.210352 1.19296i
\(78\) 0 0
\(79\) −1.28011 14.6317i −0.144023 1.64620i −0.633184 0.774002i \(-0.718252\pi\)
0.489160 0.872194i \(-0.337303\pi\)
\(80\) 1.14197 1.14197i 0.127676 0.127676i
\(81\) 0 0
\(82\) −1.76690 + 6.59415i −0.195121 + 0.728202i
\(83\) −4.01232 + 11.0238i −0.440409 + 1.21002i 0.498814 + 0.866709i \(0.333769\pi\)
−0.939224 + 0.343306i \(0.888453\pi\)
\(84\) 0 0
\(85\) −7.83673 + 4.52454i −0.850013 + 0.490755i
\(86\) −10.6279 + 1.87398i −1.14603 + 0.202077i
\(87\) 0 0
\(88\) −1.36853 5.10744i −0.145886 0.544455i
\(89\) −0.608784 0.0532617i −0.0645310 0.00564573i 0.0548445 0.998495i \(-0.482534\pi\)
−0.119376 + 0.992849i \(0.538089\pi\)
\(90\) 0 0
\(91\) 4.25713 + 9.12944i 0.446268 + 0.957026i
\(92\) 4.79061 3.35442i 0.499455 0.349722i
\(93\) 0 0
\(94\) −4.54900 + 2.12123i −0.469193 + 0.218788i
\(95\) 0.548780 0.460481i 0.0563036 0.0472443i
\(96\) 0 0
\(97\) −10.0241 + 2.68596i −1.01780 + 0.272717i −0.728883 0.684638i \(-0.759960\pi\)
−0.288912 + 0.957356i \(0.593294\pi\)
\(98\) 2.68148 + 1.25039i 0.270870 + 0.126309i
\(99\) 0 0
\(100\) 1.19590 + 2.07136i 0.119590 + 0.207136i
\(101\) −2.03594 + 3.52635i −0.202584 + 0.350885i −0.949360 0.314190i \(-0.898267\pi\)
0.746777 + 0.665075i \(0.231600\pi\)
\(102\) 0 0
\(103\) −4.60559 1.23406i −0.453802 0.121596i 0.0246758 0.999696i \(-0.492145\pi\)
−0.478478 + 0.878100i \(0.658811\pi\)
\(104\) 3.83850 + 3.22088i 0.376396 + 0.315833i
\(105\) 0 0
\(106\) −11.8451 + 1.03631i −1.15050 + 0.100656i
\(107\) −3.50758 9.63701i −0.339091 0.931645i −0.985653 0.168783i \(-0.946016\pi\)
0.646562 0.762861i \(-0.276206\pi\)
\(108\) 0 0
\(109\) −3.38772 + 4.83817i −0.324485 + 0.463412i −0.947941 0.318446i \(-0.896839\pi\)
0.623456 + 0.781858i \(0.285728\pi\)
\(110\) −8.53944 −0.814204
\(111\) 0 0
\(112\) −2.01030 −0.189956
\(113\) 11.1455 15.9174i 1.04848 1.49738i 0.191862 0.981422i \(-0.438547\pi\)
0.856614 0.515957i \(-0.172564\pi\)
\(114\) 0 0
\(115\) −3.23034 8.87528i −0.301231 0.827624i
\(116\) 7.38349 0.645972i 0.685540 0.0599770i
\(117\) 0 0
\(118\) 5.41352 + 4.54249i 0.498355 + 0.418170i
\(119\) 10.8803 + 2.91536i 0.997392 + 0.267250i
\(120\) 0 0
\(121\) −8.47941 + 14.6868i −0.770856 + 1.33516i
\(122\) −3.38971 5.87114i −0.306890 0.531548i
\(123\) 0 0
\(124\) −6.56368 3.06069i −0.589436 0.274858i
\(125\) 11.5309 3.08970i 1.03136 0.276351i
\(126\) 0 0
\(127\) 1.17105 0.982631i 0.103914 0.0871944i −0.589350 0.807878i \(-0.700616\pi\)
0.693265 + 0.720683i \(0.256172\pi\)
\(128\) −0.906308 + 0.422618i −0.0801070 + 0.0373545i
\(129\) 0 0
\(130\) 6.62891 4.64161i 0.581394 0.407096i
\(131\) 1.85023 + 3.96782i 0.161655 + 0.346670i 0.970405 0.241482i \(-0.0776334\pi\)
−0.808750 + 0.588152i \(0.799856\pi\)
\(132\) 0 0
\(133\) −0.888341 0.0777197i −0.0770289 0.00673916i
\(134\) −1.59721 5.96088i −0.137978 0.514942i
\(135\) 0 0
\(136\) 5.51805 0.972981i 0.473169 0.0834324i
\(137\) 3.32296 1.91851i 0.283899 0.163909i −0.351288 0.936267i \(-0.614256\pi\)
0.635187 + 0.772358i \(0.280923\pi\)
\(138\) 0 0
\(139\) 4.92800 13.5396i 0.417987 1.14841i −0.534854 0.844944i \(-0.679634\pi\)
0.952842 0.303467i \(-0.0981442\pi\)
\(140\) −0.840287 + 3.13599i −0.0710172 + 0.265040i
\(141\) 0 0
\(142\) 1.07150 1.07150i 0.0899186 0.0899186i
\(143\) −2.30921 26.3943i −0.193106 2.20721i
\(144\) 0 0
\(145\) 2.07854 11.7880i 0.172613 0.978937i
\(146\) 6.81586 + 4.77251i 0.564084 + 0.394976i
\(147\) 0 0
\(148\) −2.61650 5.49126i −0.215075 0.451379i
\(149\) 2.83869i 0.232555i −0.993217 0.116277i \(-0.962904\pi\)
0.993217 0.116277i \(-0.0370962\pi\)
\(150\) 0 0
\(151\) −0.603963 0.106495i −0.0491499 0.00866644i 0.149019 0.988834i \(-0.452388\pi\)
−0.198169 + 0.980168i \(0.563499\pi\)
\(152\) −0.416831 + 0.151714i −0.0338094 + 0.0123056i
\(153\) 0 0
\(154\) 7.51633 + 7.51633i 0.605683 + 0.605683i
\(155\) −7.51812 + 8.95974i −0.603870 + 0.719664i
\(156\) 0 0
\(157\) 6.70235 + 2.43946i 0.534906 + 0.194690i 0.595328 0.803483i \(-0.297022\pi\)
−0.0604216 + 0.998173i \(0.519245\pi\)
\(158\) 12.7198 + 7.34380i 1.01194 + 0.584241i
\(159\) 0 0
\(160\) 0.280440 + 1.59046i 0.0221707 + 0.125737i
\(161\) −4.96862 + 10.6552i −0.391582 + 0.839750i
\(162\) 0 0
\(163\) 0.866710 9.90654i 0.0678860 0.775940i −0.883599 0.468245i \(-0.844887\pi\)
0.951485 0.307696i \(-0.0995578\pi\)
\(164\) −4.38816 5.22961i −0.342658 0.408364i
\(165\) 0 0
\(166\) −6.72876 9.60967i −0.522253 0.745855i
\(167\) −13.7572 19.6474i −1.06457 1.52036i −0.837466 0.546489i \(-0.815964\pi\)
−0.227102 0.973871i \(-0.572925\pi\)
\(168\) 0 0
\(169\) 7.78296 + 9.27537i 0.598689 + 0.713490i
\(170\) 0.788679 9.01464i 0.0604889 0.691392i
\(171\) 0 0
\(172\) 4.56082 9.78072i 0.347760 0.745773i
\(173\) 2.14248 + 12.1506i 0.162890 + 0.923795i 0.951213 + 0.308534i \(0.0998384\pi\)
−0.788323 + 0.615261i \(0.789051\pi\)
\(174\) 0 0
\(175\) −4.16407 2.40412i −0.314774 0.181735i
\(176\) 4.96873 + 1.80847i 0.374532 + 0.136318i
\(177\) 0 0
\(178\) 0.392814 0.468137i 0.0294426 0.0350884i
\(179\) −7.15607 7.15607i −0.534870 0.534870i 0.387148 0.922018i \(-0.373460\pi\)
−0.922018 + 0.387148i \(0.873460\pi\)
\(180\) 0 0
\(181\) −22.2657 + 8.10406i −1.65500 + 0.602370i −0.989565 0.144087i \(-0.953975\pi\)
−0.665433 + 0.746457i \(0.731753\pi\)
\(182\) −9.92019 1.74920i −0.735334 0.129659i
\(183\) 0 0
\(184\) 5.84825i 0.431139i
\(185\) −9.65982 + 1.78635i −0.710204 + 0.131335i
\(186\) 0 0
\(187\) −24.2694 16.9936i −1.77475 1.24269i
\(188\) 0.871586 4.94301i 0.0635669 0.360506i
\(189\) 0 0
\(190\) 0.0624367 + 0.713655i 0.00452964 + 0.0517740i
\(191\) 3.04841 3.04841i 0.220575 0.220575i −0.588165 0.808741i \(-0.700150\pi\)
0.808741 + 0.588165i \(0.200150\pi\)
\(192\) 0 0
\(193\) −2.77230 + 10.3464i −0.199555 + 0.744748i 0.791486 + 0.611187i \(0.209308\pi\)
−0.991041 + 0.133561i \(0.957359\pi\)
\(194\) 3.54939 9.75188i 0.254832 0.700144i
\(195\) 0 0
\(196\) −2.56230 + 1.47934i −0.183021 + 0.105667i
\(197\) −4.08537 + 0.720361i −0.291070 + 0.0513236i −0.317277 0.948333i \(-0.602768\pi\)
0.0262063 + 0.999657i \(0.491657\pi\)
\(198\) 0 0
\(199\) −2.91327 10.8725i −0.206516 0.770729i −0.988982 0.148036i \(-0.952705\pi\)
0.782466 0.622694i \(-0.213962\pi\)
\(200\) −2.38270 0.208459i −0.168483 0.0147403i
\(201\) 0 0
\(202\) −1.72085 3.69038i −0.121079 0.259654i
\(203\) −12.2052 + 8.54614i −0.856634 + 0.599821i
\(204\) 0 0
\(205\) −9.99220 + 4.65944i −0.697885 + 0.325429i
\(206\) 3.65254 3.06485i 0.254485 0.213538i
\(207\) 0 0
\(208\) −4.84006 + 1.29689i −0.335598 + 0.0899232i
\(209\) 2.12573 + 0.991246i 0.147040 + 0.0685660i
\(210\) 0 0
\(211\) −1.28518 2.22600i −0.0884757 0.153244i 0.818391 0.574661i \(-0.194866\pi\)
−0.906867 + 0.421417i \(0.861533\pi\)
\(212\) 5.94519 10.2974i 0.408317 0.707226i
\(213\) 0 0
\(214\) 9.90604 + 2.65432i 0.677163 + 0.181445i
\(215\) −13.3512 11.2030i −0.910542 0.764035i
\(216\) 0 0
\(217\) 14.5036 1.26890i 0.984571 0.0861388i
\(218\) −2.02008 5.55012i −0.136817 0.375901i
\(219\) 0 0
\(220\) 4.89802 6.99510i 0.330225 0.471610i
\(221\) 28.0764 1.88862
\(222\) 0 0
\(223\) 8.99214 0.602158 0.301079 0.953599i \(-0.402653\pi\)
0.301079 + 0.953599i \(0.402653\pi\)
\(224\) 1.15306 1.64674i 0.0770422 0.110028i
\(225\) 0 0
\(226\) 6.64597 + 18.2596i 0.442083 + 1.21461i
\(227\) −15.0112 + 1.31331i −0.996331 + 0.0871677i −0.573641 0.819107i \(-0.694470\pi\)
−0.422690 + 0.906274i \(0.638914\pi\)
\(228\) 0 0
\(229\) 19.5108 + 16.3715i 1.28931 + 1.08186i 0.991888 + 0.127116i \(0.0405720\pi\)
0.297424 + 0.954745i \(0.403872\pi\)
\(230\) 9.12305 + 2.44451i 0.601556 + 0.161186i
\(231\) 0 0
\(232\) −3.70585 + 6.41871i −0.243301 + 0.421409i
\(233\) 6.34621 + 10.9920i 0.415754 + 0.720107i 0.995507 0.0946850i \(-0.0301844\pi\)
−0.579753 + 0.814792i \(0.696851\pi\)
\(234\) 0 0
\(235\) −7.34659 3.42577i −0.479238 0.223473i
\(236\) −6.82606 + 1.82904i −0.444338 + 0.119060i
\(237\) 0 0
\(238\) −8.62878 + 7.24041i −0.559321 + 0.469326i
\(239\) −15.0355 + 7.01117i −0.972565 + 0.453515i −0.842916 0.538045i \(-0.819163\pi\)
−0.129649 + 0.991560i \(0.541385\pi\)
\(240\) 0 0
\(241\) 4.85829 3.40181i 0.312950 0.219130i −0.406540 0.913633i \(-0.633265\pi\)
0.719490 + 0.694503i \(0.244376\pi\)
\(242\) −7.16711 15.3699i −0.460719 0.988015i
\(243\) 0 0
\(244\) 6.75361 + 0.590865i 0.432356 + 0.0378262i
\(245\) 1.23670 + 4.61543i 0.0790100 + 0.294869i
\(246\) 0 0
\(247\) −2.18893 + 0.385968i −0.139279 + 0.0245586i
\(248\) 6.27194 3.62111i 0.398269 0.229941i
\(249\) 0 0
\(250\) −4.08293 + 11.2178i −0.258227 + 0.709474i
\(251\) 3.60918 13.4696i 0.227809 0.850195i −0.753450 0.657505i \(-0.771612\pi\)
0.981260 0.192691i \(-0.0617214\pi\)
\(252\) 0 0
\(253\) 21.8661 21.8661i 1.37471 1.37471i
\(254\) 0.133235 + 1.52289i 0.00835992 + 0.0955543i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) 14.2192 + 9.95637i 0.886967 + 0.621061i 0.925729 0.378187i \(-0.123452\pi\)
−0.0387618 + 0.999248i \(0.512341\pi\)
\(258\) 0 0
\(259\) 10.0748 + 6.93015i 0.626018 + 0.430618i
\(260\) 8.09240i 0.501869i
\(261\) 0 0
\(262\) −4.31150 0.760233i −0.266365 0.0469674i
\(263\) −17.1405 + 6.23863i −1.05693 + 0.384690i −0.811273 0.584667i \(-0.801225\pi\)
−0.245655 + 0.969357i \(0.579003\pi\)
\(264\) 0 0
\(265\) −13.5785 13.5785i −0.834119 0.834119i
\(266\) 0.573196 0.683108i 0.0351449 0.0418840i
\(267\) 0 0
\(268\) 5.79899 + 2.11066i 0.354230 + 0.128929i
\(269\) 18.3513 + 10.5952i 1.11890 + 0.645998i 0.941120 0.338072i \(-0.109775\pi\)
0.177781 + 0.984070i \(0.443108\pi\)
\(270\) 0 0
\(271\) −1.33346 7.56242i −0.0810018 0.459384i −0.998148 0.0608331i \(-0.980624\pi\)
0.917146 0.398551i \(-0.130487\pi\)
\(272\) −2.36800 + 5.07820i −0.143581 + 0.307911i
\(273\) 0 0
\(274\) −0.334418 + 3.82242i −0.0202029 + 0.230921i
\(275\) 8.12929 + 9.68811i 0.490215 + 0.584215i
\(276\) 0 0
\(277\) −13.1625 18.7980i −0.790858 1.12946i −0.988800 0.149249i \(-0.952314\pi\)
0.197941 0.980214i \(-0.436574\pi\)
\(278\) 8.26438 + 11.8028i 0.495665 + 0.707882i
\(279\) 0 0
\(280\) −2.08689 2.48706i −0.124715 0.148630i
\(281\) −1.50538 + 17.2066i −0.0898037 + 1.02646i 0.808912 + 0.587930i \(0.200057\pi\)
−0.898716 + 0.438532i \(0.855499\pi\)
\(282\) 0 0
\(283\) −11.9844 + 25.7006i −0.712398 + 1.52774i 0.131546 + 0.991310i \(0.458006\pi\)
−0.843944 + 0.536432i \(0.819772\pi\)
\(284\) 0.263135 + 1.49231i 0.0156142 + 0.0885525i
\(285\) 0 0
\(286\) 22.9455 + 13.2476i 1.35680 + 0.783346i
\(287\) 12.8962 + 4.69384i 0.761240 + 0.277069i
\(288\) 0 0
\(289\) 9.25330 11.0276i 0.544311 0.648685i
\(290\) 8.46394 + 8.46394i 0.497020 + 0.497020i
\(291\) 0 0
\(292\) −7.81883 + 2.84582i −0.457562 + 0.166539i
\(293\) −7.60493 1.34096i −0.444285 0.0783394i −0.0529698 0.998596i \(-0.516869\pi\)
−0.391315 + 0.920257i \(0.627980\pi\)
\(294\) 0 0
\(295\) 11.4129i 0.664485i
\(296\) 5.99894 + 1.00634i 0.348681 + 0.0584924i
\(297\) 0 0
\(298\) 2.32532 + 1.62821i 0.134702 + 0.0943195i
\(299\) −5.08866 + 28.8592i −0.294285 + 1.66897i
\(300\) 0 0
\(301\) 1.89083 + 21.6123i 0.108986 + 1.24571i
\(302\) 0.433655 0.433655i 0.0249540 0.0249540i
\(303\) 0 0
\(304\) 0.114807 0.428467i 0.00658466 0.0245743i
\(305\) 3.74467 10.2884i 0.214419 0.589112i
\(306\) 0 0
\(307\) −21.0086 + 12.1293i −1.19902 + 0.692256i −0.960337 0.278841i \(-0.910050\pi\)
−0.238685 + 0.971097i \(0.576716\pi\)
\(308\) −10.4682 + 1.84583i −0.596481 + 0.105176i
\(309\) 0 0
\(310\) −3.02718 11.2976i −0.171932 0.641659i
\(311\) −1.90821 0.166946i −0.108204 0.00946667i 0.0329249 0.999458i \(-0.489518\pi\)
−0.141129 + 0.989991i \(0.545073\pi\)
\(312\) 0 0
\(313\) 7.60147 + 16.3014i 0.429661 + 0.921410i 0.995307 + 0.0967626i \(0.0308488\pi\)
−0.565647 + 0.824648i \(0.691373\pi\)
\(314\) −5.84260 + 4.09103i −0.329717 + 0.230870i
\(315\) 0 0
\(316\) −13.3115 + 6.20725i −0.748830 + 0.349185i
\(317\) −14.1675 + 11.8879i −0.795725 + 0.667693i −0.947155 0.320775i \(-0.896057\pi\)
0.151430 + 0.988468i \(0.451612\pi\)
\(318\) 0 0
\(319\) 37.8548 10.1432i 2.11946 0.567908i
\(320\) −1.46368 0.682525i −0.0818221 0.0381543i
\(321\) 0 0
\(322\) −5.87838 10.1816i −0.327589 0.567401i
\(323\) −1.24273 + 2.15248i −0.0691476 + 0.119767i
\(324\) 0 0
\(325\) −11.5765 3.10191i −0.642148 0.172063i
\(326\) 7.61784 + 6.39213i 0.421913 + 0.354027i
\(327\) 0 0
\(328\) 6.80079 0.594992i 0.375511 0.0328529i
\(329\) 3.45106 + 9.48172i 0.190263 + 0.522744i
\(330\) 0 0
\(331\) 7.39020 10.5543i 0.406202 0.580117i −0.562977 0.826472i \(-0.690344\pi\)
0.969180 + 0.246356i \(0.0792331\pi\)
\(332\) 11.7312 0.643836
\(333\) 0 0
\(334\) 23.9850 1.31240
\(335\) 5.71647 8.16397i 0.312324 0.446045i
\(336\) 0 0
\(337\) 1.77550 + 4.87816i 0.0967179 + 0.265730i 0.978611 0.205719i \(-0.0659533\pi\)
−0.881893 + 0.471449i \(0.843731\pi\)
\(338\) −12.0621 + 1.05529i −0.656090 + 0.0574004i
\(339\) 0 0
\(340\) 6.93200 + 5.81663i 0.375940 + 0.315451i
\(341\) −36.9892 9.91122i −2.00308 0.536723i
\(342\) 0 0
\(343\) 10.0100 17.3378i 0.540488 0.936153i
\(344\) 5.39591 + 9.34600i 0.290928 + 0.503902i
\(345\) 0 0
\(346\) −11.1821 5.21430i −0.601153 0.280322i
\(347\) 3.93518 1.05443i 0.211252 0.0566047i −0.151641 0.988436i \(-0.548456\pi\)
0.362893 + 0.931831i \(0.381789\pi\)
\(348\) 0 0
\(349\) 10.4267 8.74905i 0.558129 0.468326i −0.319554 0.947568i \(-0.603533\pi\)
0.877683 + 0.479242i \(0.159088\pi\)
\(350\) 4.35775 2.03205i 0.232932 0.108618i
\(351\) 0 0
\(352\) −4.33136 + 3.03285i −0.230862 + 0.161651i
\(353\) −0.684424 1.46775i −0.0364282 0.0781205i 0.887252 0.461286i \(-0.152612\pi\)
−0.923680 + 0.383165i \(0.874834\pi\)
\(354\) 0 0
\(355\) 2.43794 + 0.213292i 0.129392 + 0.0113204i
\(356\) 0.158167 + 0.590287i 0.00838283 + 0.0312851i
\(357\) 0 0
\(358\) 9.96647 1.75736i 0.526744 0.0928792i
\(359\) 2.36755 1.36690i 0.124954 0.0721424i −0.436220 0.899840i \(-0.643683\pi\)
0.561174 + 0.827698i \(0.310350\pi\)
\(360\) 0 0
\(361\) −6.43109 + 17.6693i −0.338478 + 0.929961i
\(362\) 6.13264 22.8873i 0.322324 1.20293i
\(363\) 0 0
\(364\) 7.12285 7.12285i 0.373339 0.373339i
\(365\) 1.17118 + 13.3866i 0.0613021 + 0.700687i
\(366\) 0 0
\(367\) 0.766502 4.34705i 0.0400111 0.226914i −0.958245 0.285949i \(-0.907691\pi\)
0.998256 + 0.0590349i \(0.0188023\pi\)
\(368\) −4.79061 3.35442i −0.249728 0.174861i
\(369\) 0 0
\(370\) 4.07735 8.93747i 0.211972 0.464637i
\(371\) 23.9033i 1.24100i
\(372\) 0 0
\(373\) −35.6634 6.28842i −1.84658 0.325602i −0.862879 0.505410i \(-0.831341\pi\)
−0.983702 + 0.179808i \(0.942452\pi\)
\(374\) 27.8407 10.1332i 1.43961 0.523974i
\(375\) 0 0
\(376\) 3.54915 + 3.54915i 0.183034 + 0.183034i
\(377\) −23.8722 + 28.4498i −1.22948 + 1.46524i
\(378\) 0 0
\(379\) 8.36262 + 3.04374i 0.429559 + 0.156347i 0.547746 0.836645i \(-0.315486\pi\)
−0.118187 + 0.992991i \(0.537708\pi\)
\(380\) −0.620404 0.358190i −0.0318261 0.0183748i
\(381\) 0 0
\(382\) 0.748615 + 4.24561i 0.0383025 + 0.217224i
\(383\) 5.29342 11.3518i 0.270481 0.580049i −0.723409 0.690419i \(-0.757426\pi\)
0.993890 + 0.110371i \(0.0352038\pi\)
\(384\) 0 0
\(385\) −1.49619 + 17.1015i −0.0762529 + 0.871575i
\(386\) −6.88513 8.20537i −0.350444 0.417643i
\(387\) 0 0
\(388\) 5.95242 + 8.50094i 0.302189 + 0.431570i
\(389\) −6.09399 8.70312i −0.308978 0.441266i 0.634391 0.773012i \(-0.281251\pi\)
−0.943369 + 0.331747i \(0.892362\pi\)
\(390\) 0 0
\(391\) 21.0634 + 25.1023i 1.06522 + 1.26948i
\(392\) 0.257866 2.94743i 0.0130242 0.148868i
\(393\) 0 0
\(394\) 1.75319 3.75972i 0.0883243 0.189412i
\(395\) 4.11899 + 23.3600i 0.207249 + 1.17537i
\(396\) 0 0
\(397\) 4.58110 + 2.64490i 0.229919 + 0.132744i 0.610535 0.791990i \(-0.290955\pi\)
−0.380616 + 0.924733i \(0.624288\pi\)
\(398\) 10.5772 + 3.84978i 0.530187 + 0.192972i
\(399\) 0 0
\(400\) 1.53742 1.83223i 0.0768711 0.0916114i
\(401\) 13.9354 + 13.9354i 0.695899 + 0.695899i 0.963523 0.267624i \(-0.0862387\pi\)
−0.267624 + 0.963523i \(0.586239\pi\)
\(402\) 0 0
\(403\) 34.1008 12.4117i 1.69868 0.618270i
\(404\) 4.01002 + 0.707074i 0.199506 + 0.0351783i
\(405\) 0 0
\(406\) 14.8997i 0.739462i
\(407\) −18.6668 26.1921i −0.925281 1.29829i
\(408\) 0 0
\(409\) 15.7440 + 11.0240i 0.778489 + 0.545104i 0.893928 0.448211i \(-0.147939\pi\)
−0.115439 + 0.993315i \(0.536827\pi\)
\(410\) 1.91450 10.8577i 0.0945505 0.536222i
\(411\) 0 0
\(412\) 0.415563 + 4.74991i 0.0204733 + 0.234011i
\(413\) 10.0455 10.0455i 0.494308 0.494308i
\(414\) 0 0
\(415\) 4.90355 18.3003i 0.240706 0.898326i
\(416\) 1.71380 4.70861i 0.0840257 0.230859i
\(417\) 0 0
\(418\) −2.03125 + 1.17274i −0.0993518 + 0.0573608i
\(419\) −3.04843 + 0.537521i −0.148926 + 0.0262596i −0.247614 0.968859i \(-0.579646\pi\)
0.0986883 + 0.995118i \(0.468535\pi\)
\(420\) 0 0
\(421\) −8.45077 31.5387i −0.411865 1.53710i −0.791033 0.611774i \(-0.790456\pi\)
0.379167 0.925328i \(-0.376211\pi\)
\(422\) 2.56059 + 0.224022i 0.124647 + 0.0109052i
\(423\) 0 0
\(424\) 5.02509 + 10.7763i 0.244040 + 0.523345i
\(425\) −10.9780 + 7.68690i −0.532513 + 0.372869i
\(426\) 0 0
\(427\) −12.3518 + 5.75972i −0.597744 + 0.278733i
\(428\) −7.85616 + 6.59210i −0.379742 + 0.318641i
\(429\) 0 0
\(430\) 16.8348 4.51088i 0.811848 0.217534i
\(431\) 30.9774 + 14.4450i 1.49213 + 0.695791i 0.986012 0.166674i \(-0.0533027\pi\)
0.506117 + 0.862465i \(0.331081\pi\)
\(432\) 0 0
\(433\) −0.983226 1.70300i −0.0472508 0.0818408i 0.841433 0.540362i \(-0.181713\pi\)
−0.888684 + 0.458521i \(0.848379\pi\)
\(434\) −7.27952 + 12.6085i −0.349428 + 0.605227i
\(435\) 0 0
\(436\) 5.70506 + 1.52867i 0.273223 + 0.0732098i
\(437\) −1.98726 1.66751i −0.0950634 0.0797677i
\(438\) 0 0
\(439\) −36.2043 + 3.16747i −1.72794 + 0.151175i −0.907359 0.420357i \(-0.861905\pi\)
−0.820579 + 0.571532i \(0.806349\pi\)
\(440\) 2.92066 + 8.02445i 0.139237 + 0.382551i
\(441\) 0 0
\(442\) −16.1040 + 22.9988i −0.765987 + 1.09394i
\(443\) 2.18977 0.104039 0.0520196 0.998646i \(-0.483434\pi\)
0.0520196 + 0.998646i \(0.483434\pi\)
\(444\) 0 0
\(445\) 0.986937 0.0467853
\(446\) −5.15768 + 7.36593i −0.244223 + 0.348787i
\(447\) 0 0
\(448\) 0.687564 + 1.88907i 0.0324843 + 0.0892500i
\(449\) −18.5664 + 1.62435i −0.876200 + 0.0766576i −0.516376 0.856362i \(-0.672719\pi\)
−0.359825 + 0.933020i \(0.617164\pi\)
\(450\) 0 0
\(451\) −27.6521 23.2029i −1.30209 1.09258i
\(452\) −18.7694 5.02924i −0.882838 0.236556i
\(453\) 0 0
\(454\) 7.53429 13.0498i 0.353602 0.612456i
\(455\) −8.13409 14.0886i −0.381332 0.660486i
\(456\) 0 0
\(457\) −18.1151 8.44721i −0.847388 0.395144i −0.0501015 0.998744i \(-0.515954\pi\)
−0.797287 + 0.603600i \(0.793732\pi\)
\(458\) −24.6017 + 6.59201i −1.14956 + 0.308025i
\(459\) 0 0
\(460\) −7.23519 + 6.07105i −0.337343 + 0.283064i
\(461\) −5.36047 + 2.49963i −0.249662 + 0.116419i −0.543421 0.839460i \(-0.682871\pi\)
0.293759 + 0.955879i \(0.405094\pi\)
\(462\) 0 0
\(463\) 13.4573 9.42294i 0.625416 0.437921i −0.217430 0.976076i \(-0.569767\pi\)
0.842846 + 0.538155i \(0.180878\pi\)
\(464\) −3.13232 6.71727i −0.145414 0.311842i
\(465\) 0 0
\(466\) −12.6441 1.10622i −0.585728 0.0512445i
\(467\) 1.64833 + 6.15166i 0.0762757 + 0.284665i 0.993520 0.113661i \(-0.0362579\pi\)
−0.917244 + 0.398326i \(0.869591\pi\)
\(468\) 0 0
\(469\) −12.2174 + 2.15426i −0.564148 + 0.0994745i
\(470\) 7.02006 4.05303i 0.323811 0.186952i
\(471\) 0 0
\(472\) 2.41701 6.64067i 0.111252 0.305662i
\(473\) 14.7690 55.1186i 0.679079 2.53436i
\(474\) 0 0
\(475\) 0.750213 0.750213i 0.0344221 0.0344221i
\(476\) −0.981729 11.2212i −0.0449975 0.514323i
\(477\) 0 0
\(478\) 2.88079 16.3378i 0.131764 0.747273i
\(479\) −14.9805 10.4895i −0.684478 0.479276i 0.178879 0.983871i \(-0.442753\pi\)
−0.863356 + 0.504595i \(0.831642\pi\)
\(480\) 0 0
\(481\) 28.7272 + 10.1857i 1.30985 + 0.464430i
\(482\) 5.93088i 0.270144i
\(483\) 0 0
\(484\) 16.7012 + 2.94487i 0.759145 + 0.133858i
\(485\) 15.7492 5.73224i 0.715134 0.260288i
\(486\) 0 0
\(487\) 26.0608 + 26.0608i 1.18093 + 1.18093i 0.979504 + 0.201423i \(0.0645566\pi\)
0.201423 + 0.979504i \(0.435443\pi\)
\(488\) −4.35772 + 5.19333i −0.197265 + 0.235091i
\(489\) 0 0
\(490\) −4.49009 1.63426i −0.202841 0.0738282i
\(491\) −13.1272 7.57897i −0.592421 0.342034i 0.173633 0.984810i \(-0.444449\pi\)
−0.766054 + 0.642776i \(0.777783\pi\)
\(492\) 0 0
\(493\) 7.21144 + 40.8981i 0.324787 + 1.84196i
\(494\) 0.939354 2.01445i 0.0422636 0.0906345i
\(495\) 0 0
\(496\) −0.631201 + 7.21466i −0.0283417 + 0.323948i
\(497\) −1.95811 2.33359i −0.0878333 0.104676i
\(498\) 0 0
\(499\) −15.9973 22.8465i −0.716136 1.02275i −0.997995 0.0632929i \(-0.979840\pi\)
0.281859 0.959456i \(-0.409049\pi\)
\(500\) −6.84718 9.77879i −0.306215 0.437321i
\(501\) 0 0
\(502\) 8.96354 + 10.6823i 0.400062 + 0.476776i
\(503\) −0.167644 + 1.91618i −0.00747490 + 0.0854385i −0.999016 0.0443563i \(-0.985876\pi\)
0.991541 + 0.129795i \(0.0414319\pi\)
\(504\) 0 0
\(505\) 2.77916 5.95992i 0.123671 0.265213i
\(506\) 5.36977 + 30.4535i 0.238715 + 1.35382i
\(507\) 0 0
\(508\) −1.32390 0.764351i −0.0587384 0.0339126i
\(509\) −1.24147 0.451859i −0.0550273 0.0200283i 0.314360 0.949304i \(-0.398210\pi\)
−0.369387 + 0.929276i \(0.620432\pi\)
\(510\) 0 0
\(511\) 10.7519 12.8136i 0.475636 0.566840i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) −16.3116 + 5.93692i −0.719472 + 0.261866i
\(515\) 7.58338 + 1.33715i 0.334164 + 0.0589221i
\(516\) 0 0
\(517\) 26.5399i 1.16722i
\(518\) −11.4555 + 4.27783i −0.503326 + 0.187957i
\(519\) 0 0
\(520\) −6.62891 4.64161i −0.290697 0.203548i
\(521\) 2.36376 13.4055i 0.103558 0.587308i −0.888228 0.459402i \(-0.848064\pi\)
0.991786 0.127905i \(-0.0408253\pi\)
\(522\) 0 0
\(523\) 3.09092 + 35.3294i 0.135156 + 1.54485i 0.696679 + 0.717383i \(0.254660\pi\)
−0.561522 + 0.827462i \(0.689784\pi\)
\(524\) 3.09572 3.09572i 0.135237 0.135237i
\(525\) 0 0
\(526\) 4.72100 17.6190i 0.205845 0.768225i
\(527\) 13.8790 38.1322i 0.604578 1.66106i
\(528\) 0 0
\(529\) −9.70126 + 5.60103i −0.421794 + 0.243523i
\(530\) 18.9111 3.33454i 0.821446 0.144843i
\(531\) 0 0
\(532\) 0.230798 + 0.861349i 0.0100064 + 0.0373442i
\(533\) 34.0774 + 2.98139i 1.47606 + 0.129138i
\(534\) 0 0
\(535\) 6.99962 + 15.0107i 0.302620 + 0.648971i
\(536\) −5.05512 + 3.53963i −0.218348 + 0.152889i
\(537\) 0 0
\(538\) −19.2049 + 8.95541i −0.827984 + 0.386095i
\(539\) −11.9843 + 10.0560i −0.516200 + 0.433143i
\(540\) 0 0
\(541\) 30.1363 8.07499i 1.29566 0.347171i 0.455852 0.890055i \(-0.349334\pi\)
0.839807 + 0.542884i \(0.182668\pi\)
\(542\) 6.95961 + 3.24532i 0.298941 + 0.139398i
\(543\) 0 0
\(544\) −2.80159 4.85249i −0.120117 0.208049i
\(545\) 4.76932 8.26070i 0.204295 0.353850i
\(546\) 0 0
\(547\) −16.0232 4.29339i −0.685101 0.183572i −0.100553 0.994932i \(-0.532061\pi\)
−0.584547 + 0.811360i \(0.698728\pi\)
\(548\) −2.93933 2.46639i −0.125562 0.105359i
\(549\) 0 0
\(550\) −12.5988 + 1.10225i −0.537215 + 0.0470002i
\(551\) −1.12446 3.08942i −0.0479035 0.131614i
\(552\) 0 0
\(553\) 16.9357 24.1867i 0.720180 1.02852i
\(554\) 22.9481 0.974972
\(555\) 0 0
\(556\) −14.4085 −0.611057
\(557\) 10.3351 14.7600i 0.437910 0.625401i −0.538163 0.842841i \(-0.680882\pi\)
0.976074 + 0.217440i \(0.0697705\pi\)
\(558\) 0 0
\(559\) 18.4950 + 50.8146i 0.782255 + 2.14923i
\(560\) 3.23427 0.282962i 0.136673 0.0119573i
\(561\) 0 0
\(562\) −13.2314 11.1025i −0.558132 0.468329i
\(563\) 25.8416 + 6.92423i 1.08909 + 0.291822i 0.758316 0.651887i \(-0.226022\pi\)
0.330777 + 0.943709i \(0.392689\pi\)
\(564\) 0 0
\(565\) −15.6909 + 27.1774i −0.660119 + 1.14336i
\(566\) −14.1787 24.5583i −0.595977 1.03226i
\(567\) 0 0
\(568\) −1.37336 0.640408i −0.0576249 0.0268709i
\(569\) 7.98458 2.13946i 0.334731 0.0896909i −0.0875387 0.996161i \(-0.527900\pi\)
0.422270 + 0.906470i \(0.361233\pi\)
\(570\) 0 0
\(571\) −5.51840 + 4.63049i −0.230938 + 0.193780i −0.750912 0.660402i \(-0.770386\pi\)
0.519974 + 0.854182i \(0.325941\pi\)
\(572\) −24.0128 + 11.1973i −1.00402 + 0.468184i
\(573\) 0 0
\(574\) −11.2419 + 7.87169i −0.469229 + 0.328558i
\(575\) −5.91153 12.6773i −0.246528 0.528681i
\(576\) 0 0
\(577\) −39.9468 3.49489i −1.66301 0.145494i −0.783504 0.621387i \(-0.786570\pi\)
−0.879504 + 0.475892i \(0.842125\pi\)
\(578\) 3.72585 + 13.9051i 0.154975 + 0.578374i
\(579\) 0 0
\(580\) −11.7880 + 2.07854i −0.489469 + 0.0863065i
\(581\) −20.4238 + 11.7917i −0.847321 + 0.489201i
\(582\) 0 0
\(583\) 21.5034 59.0801i 0.890579 2.44685i
\(584\) 2.15354 8.03711i 0.0891140 0.332578i
\(585\) 0 0
\(586\) 5.46046 5.46046i 0.225569 0.225569i
\(587\) −2.16060 24.6958i −0.0891776 1.01930i −0.900544 0.434766i \(-0.856831\pi\)
0.811366 0.584539i \(-0.198724\pi\)
\(588\) 0 0
\(589\) −0.557848 + 3.16371i −0.0229857 + 0.130358i
\(590\) −9.34890 6.54617i −0.384888 0.269502i
\(591\) 0 0
\(592\) −4.26520 + 4.33683i −0.175299 + 0.178243i
\(593\) 5.96828i 0.245088i 0.992463 + 0.122544i \(0.0391052\pi\)
−0.992463 + 0.122544i \(0.960895\pi\)
\(594\) 0 0
\(595\) −17.9150 3.15890i −0.734444 0.129502i
\(596\) −2.66750 + 0.970890i −0.109265 + 0.0397692i
\(597\) 0 0
\(598\) −20.7214 20.7214i −0.847360 0.847360i
\(599\) −23.8933 + 28.4749i −0.976252 + 1.16345i 0.0102905 + 0.999947i \(0.496724\pi\)
−0.986543 + 0.163505i \(0.947720\pi\)
\(600\) 0 0
\(601\) −42.7015 15.5421i −1.74183 0.633974i −0.742474 0.669875i \(-0.766348\pi\)
−0.999355 + 0.0359013i \(0.988570\pi\)
\(602\) −18.7883 10.8474i −0.765753 0.442108i
\(603\) 0 0
\(604\) 0.106495 + 0.603963i 0.00433322 + 0.0245749i
\(605\) 11.5748 24.8223i 0.470583 1.00917i
\(606\) 0 0
\(607\) −1.76803 + 20.2086i −0.0717620 + 0.820243i 0.871976 + 0.489549i \(0.162839\pi\)
−0.943738 + 0.330695i \(0.892717\pi\)
\(608\) 0.285129 + 0.339804i 0.0115635 + 0.0137809i
\(609\) 0 0
\(610\) 6.27991 + 8.96864i 0.254266 + 0.363130i
\(611\) 14.4257 + 20.6021i 0.583603 + 0.833472i
\(612\) 0 0
\(613\) −8.10272 9.65644i −0.327266 0.390020i 0.577174 0.816621i \(-0.304155\pi\)
−0.904440 + 0.426601i \(0.859711\pi\)
\(614\) 2.11428 24.1663i 0.0853253 0.975272i
\(615\) 0 0
\(616\) 4.49230 9.63378i 0.181000 0.388156i
\(617\) −5.34176 30.2946i −0.215051 1.21962i −0.880818 0.473456i \(-0.843006\pi\)
0.665767 0.746160i \(-0.268105\pi\)
\(618\) 0 0
\(619\) 4.52235 + 2.61098i 0.181768 + 0.104944i 0.588123 0.808771i \(-0.299867\pi\)
−0.406355 + 0.913715i \(0.633200\pi\)
\(620\) 10.9908 + 4.00031i 0.441399 + 0.160656i
\(621\) 0 0
\(622\) 1.23126 1.46736i 0.0493689 0.0588356i
\(623\) −0.868691 0.868691i −0.0348034 0.0348034i
\(624\) 0 0
\(625\) −6.87879 + 2.50367i −0.275151 + 0.100147i
\(626\) −17.7134 3.12334i −0.707968 0.124834i
\(627\) 0 0
\(628\) 7.13250i 0.284618i
\(629\) 29.3736 17.2866i 1.17120 0.689261i
\(630\) 0 0
\(631\) −12.1428 8.50250i −0.483399 0.338479i 0.306341 0.951922i \(-0.400895\pi\)
−0.789739 + 0.613443i \(0.789784\pi\)
\(632\) 2.55047 14.4645i 0.101452 0.575365i
\(633\) 0 0
\(634\) −1.61189 18.4240i −0.0640162 0.731709i
\(635\) −1.74573 + 1.74573i −0.0692773 + 0.0692773i
\(636\) 0 0
\(637\) 3.83709 14.3202i 0.152031 0.567388i
\(638\) −13.4038 + 36.8267i −0.530662 + 1.45798i
\(639\) 0 0
\(640\) 1.39862 0.807495i 0.0552854 0.0319191i
\(641\) −13.0347 + 2.29837i −0.514839 + 0.0907801i −0.425031 0.905179i \(-0.639737\pi\)
−0.0898087 + 0.995959i \(0.528626\pi\)
\(642\) 0 0
\(643\) −1.97118 7.35655i −0.0777358 0.290114i 0.916104 0.400941i \(-0.131317\pi\)
−0.993840 + 0.110827i \(0.964650\pi\)
\(644\) 11.7120 + 1.02467i 0.461518 + 0.0403776i
\(645\) 0 0
\(646\) −1.05040 2.25260i −0.0413276 0.0886273i
\(647\) 21.2126 14.8532i 0.833952 0.583939i −0.0767281 0.997052i \(-0.524447\pi\)
0.910680 + 0.413113i \(0.135558\pi\)
\(648\) 0 0
\(649\) −33.8658 + 15.7919i −1.32935 + 0.619885i
\(650\) 9.18093 7.70372i 0.360106 0.302165i
\(651\) 0 0
\(652\) −9.60554 + 2.57380i −0.376182 + 0.100798i
\(653\) 3.17955 + 1.48265i 0.124425 + 0.0580205i 0.483834 0.875160i \(-0.339244\pi\)
−0.359409 + 0.933180i \(0.617022\pi\)
\(654\) 0 0
\(655\) −3.53522 6.12319i −0.138133 0.239253i
\(656\) −3.41338 + 5.91216i −0.133270 + 0.230831i
\(657\) 0 0
\(658\) −9.74642 2.61154i −0.379955 0.101809i
\(659\) −29.4951 24.7493i −1.14896 0.964096i −0.149270 0.988797i \(-0.547692\pi\)
−0.999695 + 0.0247007i \(0.992137\pi\)
\(660\) 0 0
\(661\) 29.0548 2.54197i 1.13010 0.0988711i 0.493272 0.869875i \(-0.335801\pi\)
0.636830 + 0.771004i \(0.280245\pi\)
\(662\) 4.40673 + 12.1074i 0.171272 + 0.470567i
\(663\) 0 0
\(664\) −6.72876 + 9.60967i −0.261127 + 0.372928i
\(665\) 1.44014 0.0558463
\(666\) 0 0
\(667\) −43.3454 −1.67834
\(668\) −13.7572 + 19.6474i −0.532284 + 0.760180i
\(669\) 0 0
\(670\) 3.40870 + 9.36532i 0.131689 + 0.361814i
\(671\) 35.7105 3.12426i 1.37859 0.120611i
\(672\) 0 0
\(673\) 31.4280 + 26.3713i 1.21146 + 1.01654i 0.999227 + 0.0393187i \(0.0125188\pi\)
0.212235 + 0.977219i \(0.431926\pi\)
\(674\) −5.01434 1.34359i −0.193145 0.0517531i
\(675\) 0 0
\(676\) 6.05407 10.4860i 0.232849 0.403306i
\(677\) −8.58666 14.8725i −0.330012 0.571598i 0.652502 0.757787i \(-0.273719\pi\)
−0.982514 + 0.186190i \(0.940386\pi\)
\(678\) 0 0
\(679\) −18.9077 8.81683i −0.725613 0.338359i
\(680\) −8.74074 + 2.34207i −0.335192 + 0.0898144i
\(681\) 0 0
\(682\) 29.3349 24.6149i 1.12329 0.942554i
\(683\) −38.9760 + 18.1748i −1.49138 + 0.695440i −0.985890 0.167394i \(-0.946465\pi\)
−0.505487 + 0.862834i \(0.668687\pi\)
\(684\) 0 0
\(685\) −5.07608 + 3.55431i −0.193947 + 0.135803i
\(686\) 8.46080 + 18.1443i 0.323035 + 0.692751i
\(687\) 0 0
\(688\) −10.7508 0.940570i −0.409869 0.0358589i
\(689\) 15.4205 + 57.5502i 0.587475 + 2.19249i
\(690\) 0 0
\(691\) 35.7513 6.30392i 1.36004 0.239813i 0.554419 0.832238i \(-0.312940\pi\)
0.805626 + 0.592425i \(0.201829\pi\)
\(692\) 10.6851 6.16904i 0.406186 0.234512i
\(693\) 0 0
\(694\) −1.39339 + 3.82831i −0.0528924 + 0.145321i
\(695\) −6.02262 + 22.4767i −0.228451 + 0.852590i
\(696\) 0 0
\(697\) 27.0480 27.0480i 1.02451 1.02451i
\(698\) 1.18629 + 13.5593i 0.0449016 + 0.513227i
\(699\) 0 0
\(700\) −0.834944 + 4.73520i −0.0315579 + 0.178974i
\(701\) −11.9407 8.36099i −0.450995 0.315790i 0.325918 0.945398i \(-0.394327\pi\)
−0.776913 + 0.629608i \(0.783216\pi\)
\(702\) 0 0
\(703\) −2.05243 + 1.75152i −0.0774089 + 0.0660600i
\(704\) 5.28761i 0.199284i
\(705\) 0 0
\(706\) 1.59488 + 0.281221i 0.0600241 + 0.0105839i
\(707\) −7.69205 + 2.79968i −0.289289 + 0.105293i
\(708\) 0 0
\(709\) 7.98129 + 7.98129i 0.299744 + 0.299744i 0.840913 0.541170i \(-0.182018\pi\)
−0.541170 + 0.840913i \(0.682018\pi\)
\(710\) −1.57306 + 1.87470i −0.0590360 + 0.0703564i
\(711\) 0 0
\(712\) −0.574255 0.209012i −0.0215211 0.00783305i
\(713\) 36.6799 + 21.1772i 1.37367 + 0.793091i
\(714\) 0 0
\(715\) 7.43031 + 42.1394i 0.277878 + 1.57592i
\(716\) −4.27699 + 9.17203i −0.159839 + 0.342775i
\(717\) 0 0
\(718\) −0.238267 + 2.72340i −0.00889205 + 0.101637i
\(719\) −16.3215 19.4512i −0.608690 0.725408i 0.370392 0.928876i \(-0.379223\pi\)
−0.979082 + 0.203467i \(0.934779\pi\)
\(720\) 0 0
\(721\) −5.49786 7.85176i −0.204751 0.292415i
\(722\) −10.7851 15.4027i −0.401380 0.573229i
\(723\) 0 0
\(724\) 15.2307 + 18.1512i 0.566043 + 0.674583i
\(725\) 1.54504 17.6599i 0.0573812 0.655871i
\(726\) 0 0
\(727\) −3.73661 + 8.01319i −0.138583 + 0.297193i −0.963335 0.268303i \(-0.913537\pi\)
0.824751 + 0.565496i \(0.191315\pi\)
\(728\) 1.74920 + 9.92019i 0.0648296 + 0.367667i
\(729\) 0 0
\(730\) −11.6374 6.71887i −0.430720 0.248676i
\(731\) 56.8218 + 20.6814i 2.10163 + 0.764931i
\(732\) 0 0
\(733\) −24.2840 + 28.9405i −0.896948 + 1.06894i 0.100311 + 0.994956i \(0.468016\pi\)
−0.997259 + 0.0739853i \(0.976428\pi\)
\(734\) 3.12125 + 3.12125i 0.115207 + 0.115207i
\(735\) 0 0
\(736\) 5.49556 2.00022i 0.202569 0.0737291i
\(737\) 32.1349 + 5.66626i 1.18371 + 0.208719i
\(738\) 0 0
\(739\) 50.6865i 1.86453i −0.361773 0.932266i \(-0.617829\pi\)
0.361773 0.932266i \(-0.382171\pi\)
\(740\) 4.98248 + 8.46630i 0.183159 + 0.311227i
\(741\) 0 0
\(742\) −19.5804 13.7103i −0.718819 0.503322i
\(743\) 5.53715 31.4028i 0.203139 1.15206i −0.697204 0.716873i \(-0.745573\pi\)
0.900342 0.435183i \(-0.143316\pi\)
\(744\) 0 0
\(745\) 0.399562 + 4.56702i 0.0146388 + 0.167323i
\(746\) 25.6069 25.6069i 0.937534 0.937534i
\(747\) 0 0
\(748\) −7.66814 + 28.6179i −0.280375 + 1.04637i
\(749\) 7.05130 19.3733i 0.257649 0.707885i
\(750\) 0 0
\(751\) −31.0917 + 17.9508i −1.13455 + 0.655034i −0.945076 0.326851i \(-0.894012\pi\)
−0.189476 + 0.981885i \(0.560679\pi\)
\(752\) −4.94301 + 0.871586i −0.180253 + 0.0317835i
\(753\) 0 0
\(754\) −9.61216 35.8731i −0.350054 1.30642i
\(755\) 0.986674 + 0.0863228i 0.0359087 + 0.00314161i
\(756\) 0 0
\(757\) −16.9967 36.4495i −0.617754 1.32478i −0.927452 0.373943i \(-0.878006\pi\)
0.309697 0.950835i \(-0.399772\pi\)
\(758\) −7.28989 + 5.10443i −0.264781 + 0.185401i
\(759\) 0 0
\(760\) 0.649262 0.302756i 0.0235512 0.0109821i
\(761\) 0.414396 0.347720i 0.0150219 0.0126048i −0.635246 0.772310i \(-0.719101\pi\)
0.650268 + 0.759705i \(0.274657\pi\)
\(762\) 0 0
\(763\) −11.4689 + 3.07308i −0.415202 + 0.111253i
\(764\) −3.90719 1.82195i −0.141357 0.0659159i
\(765\) 0 0
\(766\) 6.26265 + 10.8472i 0.226279 + 0.391926i
\(767\) 17.7053 30.6665i 0.639301 1.10730i
\(768\) 0 0
\(769\) 38.3997 + 10.2892i 1.38473 + 0.371037i 0.872836 0.488013i \(-0.162278\pi\)
0.511891 + 0.859050i \(0.328945\pi\)
\(770\) −13.1506 11.0346i −0.473914 0.397661i
\(771\) 0 0
\(772\) 10.6706 0.933556i 0.384043 0.0335994i
\(773\) −3.27444 8.99645i −0.117773 0.323580i 0.866773 0.498703i \(-0.166190\pi\)
−0.984547 + 0.175123i \(0.943968\pi\)
\(774\) 0 0
\(775\) −9.93547 + 14.1893i −0.356893 + 0.509695i
\(776\) −10.3777 −0.372539
\(777\) 0 0
\(778\) 10.6246 0.380909
\(779\) −1.73692 + 2.48058i −0.0622317 + 0.0888761i
\(780\) 0 0
\(781\) 2.74044 + 7.52929i 0.0980605 + 0.269419i
\(782\) −32.6441 + 2.85599i −1.16735 + 0.102130i
\(783\) 0 0
\(784\) 2.26648 + 1.90181i 0.0809459 + 0.0679216i