Properties

Label 261.2.k.b.136.2
Level $261$
Weight $2$
Character 261.136
Analytic conductor $2.084$
Analytic rank $0$
Dimension $18$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [261,2,Mod(82,261)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(261, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("261.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 261.k (of order \(7\), degree \(6\), 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: \(2.08409549276\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{7})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 5 x^{17} + 15 x^{16} - 32 x^{15} + 66 x^{14} - 115 x^{13} + 272 x^{12} - 387 x^{11} + 762 x^{10} + \cdots + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 87)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 136.2
Root \(0.719749 - 0.902536i\) of defining polynomial
Character \(\chi\) \(=\) 261.136
Dual form 261.2.k.b.190.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.04007 - 0.500870i) q^{2} +(-0.416111 + 0.521786i) q^{4} +(-3.10796 + 1.49671i) q^{5} +(2.81664 + 3.53195i) q^{7} +(-0.685187 + 3.00200i) q^{8} +(-2.48283 + 3.11337i) q^{10} +(-0.123323 - 0.540315i) q^{11} +(-0.614154 - 2.69078i) q^{13} +(4.69854 + 2.26270i) q^{14} +(0.493954 + 2.16416i) q^{16} +2.99688 q^{17} +(-0.173453 + 0.217503i) q^{19} +(0.512290 - 2.24449i) q^{20} +(-0.398892 - 0.500195i) q^{22} +(0.836001 + 0.402597i) q^{23} +(4.30181 - 5.39430i) q^{25} +(-1.98649 - 2.49098i) q^{26} -3.01496 q^{28} +(5.37860 + 0.265855i) q^{29} +(-8.21748 + 3.95733i) q^{31} +(-2.24199 - 2.81137i) q^{32} +(3.11696 - 1.50105i) q^{34} +(-14.0403 - 6.76146i) q^{35} +(1.52987 - 6.70278i) q^{37} +(-0.0714618 + 0.313095i) q^{38} +(-2.36360 - 10.3556i) q^{40} +2.85317 q^{41} +(10.1079 + 4.86770i) q^{43} +(0.333245 + 0.160482i) q^{44} +1.07115 q^{46} +(0.933590 + 4.09033i) q^{47} +(-2.98359 + 13.0720i) q^{49} +(1.77233 - 7.76508i) q^{50} +(1.65957 + 0.799207i) q^{52} +(-1.87299 + 0.901986i) q^{53} +(1.19198 + 1.49470i) q^{55} +(-12.5328 + 6.03550i) q^{56} +(5.72726 - 2.41747i) q^{58} +14.2670 q^{59} +(-4.50873 - 5.65377i) q^{61} +(-6.56462 + 8.23177i) q^{62} +(-7.73992 - 3.72735i) q^{64} +(5.93610 + 7.44363i) q^{65} +(2.73383 - 11.9777i) q^{67} +(-1.24704 + 1.56373i) q^{68} -17.9895 q^{70} +(-0.530060 - 2.32234i) q^{71} +(0.822693 + 0.396188i) q^{73} +(-1.76606 - 7.73761i) q^{74} +(-0.0413145 - 0.181010i) q^{76} +(1.56101 - 1.95744i) q^{77} +(-0.460193 + 2.01624i) q^{79} +(-4.77431 - 5.98680i) q^{80} +(2.96749 - 1.42907i) q^{82} +(6.83994 - 8.57702i) q^{83} +(-9.31420 + 4.48548i) q^{85} +12.9510 q^{86} +1.70652 q^{88} +(-6.13283 + 2.95341i) q^{89} +(7.77387 - 9.74812i) q^{91} +(-0.557938 + 0.268689i) q^{92} +(3.01972 + 3.78661i) q^{94} +(0.213544 - 0.935599i) q^{95} +(-2.19244 + 2.74924i) q^{97} +(3.44422 + 15.0901i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 2 q^{2} - 6 q^{4} + 7 q^{5} - 4 q^{7} + 3 q^{8} + 6 q^{10} + 6 q^{11} - 11 q^{13} + 2 q^{14} + 18 q^{16} + 32 q^{17} + 2 q^{19} - 51 q^{20} + 20 q^{22} + 6 q^{23} + 4 q^{25} + 3 q^{26} - 48 q^{28}+ \cdots + 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{6}{7}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.04007 0.500870i 0.735438 0.354169i −0.0283821 0.999597i \(-0.509036\pi\)
0.763821 + 0.645429i \(0.223321\pi\)
\(3\) 0 0
\(4\) −0.416111 + 0.521786i −0.208055 + 0.260893i
\(5\) −3.10796 + 1.49671i −1.38992 + 0.669351i −0.971090 0.238713i \(-0.923274\pi\)
−0.418831 + 0.908064i \(0.637560\pi\)
\(6\) 0 0
\(7\) 2.81664 + 3.53195i 1.06459 + 1.33495i 0.939402 + 0.342819i \(0.111382\pi\)
0.125187 + 0.992133i \(0.460047\pi\)
\(8\) −0.685187 + 3.00200i −0.242250 + 1.06137i
\(9\) 0 0
\(10\) −2.48283 + 3.11337i −0.785139 + 0.984533i
\(11\) −0.123323 0.540315i −0.0371834 0.162911i 0.952927 0.303198i \(-0.0980545\pi\)
−0.990111 + 0.140287i \(0.955197\pi\)
\(12\) 0 0
\(13\) −0.614154 2.69078i −0.170336 0.746289i −0.985861 0.167567i \(-0.946409\pi\)
0.815525 0.578722i \(-0.196448\pi\)
\(14\) 4.69854 + 2.26270i 1.25574 + 0.604731i
\(15\) 0 0
\(16\) 0.493954 + 2.16416i 0.123489 + 0.541039i
\(17\) 2.99688 0.726851 0.363426 0.931623i \(-0.381607\pi\)
0.363426 + 0.931623i \(0.381607\pi\)
\(18\) 0 0
\(19\) −0.173453 + 0.217503i −0.0397928 + 0.0498985i −0.801330 0.598223i \(-0.795874\pi\)
0.761537 + 0.648122i \(0.224445\pi\)
\(20\) 0.512290 2.24449i 0.114552 0.501883i
\(21\) 0 0
\(22\) −0.398892 0.500195i −0.0850440 0.106642i
\(23\) 0.836001 + 0.402597i 0.174318 + 0.0839472i 0.519008 0.854770i \(-0.326302\pi\)
−0.344690 + 0.938717i \(0.612016\pi\)
\(24\) 0 0
\(25\) 4.30181 5.39430i 0.860362 1.07886i
\(26\) −1.98649 2.49098i −0.389583 0.488522i
\(27\) 0 0
\(28\) −3.01496 −0.569773
\(29\) 5.37860 + 0.265855i 0.998781 + 0.0493681i
\(30\) 0 0
\(31\) −8.21748 + 3.95733i −1.47590 + 0.710757i −0.986871 0.161509i \(-0.948364\pi\)
−0.489031 + 0.872266i \(0.662650\pi\)
\(32\) −2.24199 2.81137i −0.396332 0.496985i
\(33\) 0 0
\(34\) 3.11696 1.50105i 0.534554 0.257428i
\(35\) −14.0403 6.76146i −2.37325 1.14290i
\(36\) 0 0
\(37\) 1.52987 6.70278i 0.251509 1.10193i −0.678560 0.734545i \(-0.737396\pi\)
0.930069 0.367386i \(-0.119747\pi\)
\(38\) −0.0714618 + 0.313095i −0.0115926 + 0.0507907i
\(39\) 0 0
\(40\) −2.36360 10.3556i −0.373718 1.63737i
\(41\) 2.85317 0.445591 0.222795 0.974865i \(-0.428482\pi\)
0.222795 + 0.974865i \(0.428482\pi\)
\(42\) 0 0
\(43\) 10.1079 + 4.86770i 1.54144 + 0.742317i 0.995433 0.0954657i \(-0.0304340\pi\)
0.546004 + 0.837783i \(0.316148\pi\)
\(44\) 0.333245 + 0.160482i 0.0502386 + 0.0241936i
\(45\) 0 0
\(46\) 1.07115 0.157932
\(47\) 0.933590 + 4.09033i 0.136178 + 0.596635i 0.996254 + 0.0864700i \(0.0275587\pi\)
−0.860076 + 0.510165i \(0.829584\pi\)
\(48\) 0 0
\(49\) −2.98359 + 13.0720i −0.426227 + 1.86742i
\(50\) 1.77233 7.76508i 0.250645 1.09815i
\(51\) 0 0
\(52\) 1.65957 + 0.799207i 0.230141 + 0.110830i
\(53\) −1.87299 + 0.901986i −0.257275 + 0.123897i −0.558076 0.829790i \(-0.688460\pi\)
0.300801 + 0.953687i \(0.402746\pi\)
\(54\) 0 0
\(55\) 1.19198 + 1.49470i 0.160727 + 0.201545i
\(56\) −12.5328 + 6.03550i −1.67477 + 0.806527i
\(57\) 0 0
\(58\) 5.72726 2.41747i 0.752026 0.317429i
\(59\) 14.2670 1.85741 0.928703 0.370824i \(-0.120925\pi\)
0.928703 + 0.370824i \(0.120925\pi\)
\(60\) 0 0
\(61\) −4.50873 5.65377i −0.577284 0.723891i 0.404363 0.914599i \(-0.367493\pi\)
−0.981647 + 0.190707i \(0.938922\pi\)
\(62\) −6.56462 + 8.23177i −0.833708 + 1.04544i
\(63\) 0 0
\(64\) −7.73992 3.72735i −0.967490 0.465919i
\(65\) 5.93610 + 7.44363i 0.736282 + 0.923269i
\(66\) 0 0
\(67\) 2.73383 11.9777i 0.333990 1.46331i −0.477340 0.878719i \(-0.658399\pi\)
0.811330 0.584588i \(-0.198744\pi\)
\(68\) −1.24704 + 1.56373i −0.151225 + 0.189631i
\(69\) 0 0
\(70\) −17.9895 −2.15015
\(71\) −0.530060 2.32234i −0.0629065 0.275611i 0.933686 0.358092i \(-0.116573\pi\)
−0.996593 + 0.0824811i \(0.973716\pi\)
\(72\) 0 0
\(73\) 0.822693 + 0.396188i 0.0962889 + 0.0463703i 0.481408 0.876496i \(-0.340125\pi\)
−0.385119 + 0.922867i \(0.625840\pi\)
\(74\) −1.76606 7.73761i −0.205300 0.899479i
\(75\) 0 0
\(76\) −0.0413145 0.181010i −0.00473909 0.0207633i
\(77\) 1.56101 1.95744i 0.177893 0.223071i
\(78\) 0 0
\(79\) −0.460193 + 2.01624i −0.0517758 + 0.226845i −0.994196 0.107588i \(-0.965687\pi\)
0.942420 + 0.334432i \(0.108545\pi\)
\(80\) −4.77431 5.98680i −0.533784 0.669345i
\(81\) 0 0
\(82\) 2.96749 1.42907i 0.327705 0.157814i
\(83\) 6.83994 8.57702i 0.750781 0.941450i −0.248852 0.968542i \(-0.580053\pi\)
0.999633 + 0.0270916i \(0.00862459\pi\)
\(84\) 0 0
\(85\) −9.31420 + 4.48548i −1.01027 + 0.486519i
\(86\) 12.9510 1.39654
\(87\) 0 0
\(88\) 1.70652 0.181916
\(89\) −6.13283 + 2.95341i −0.650078 + 0.313061i −0.729703 0.683764i \(-0.760342\pi\)
0.0796253 + 0.996825i \(0.474628\pi\)
\(90\) 0 0
\(91\) 7.77387 9.74812i 0.814923 1.02188i
\(92\) −0.557938 + 0.268689i −0.0581691 + 0.0280128i
\(93\) 0 0
\(94\) 3.01972 + 3.78661i 0.311460 + 0.390559i
\(95\) 0.213544 0.935599i 0.0219092 0.0959904i
\(96\) 0 0
\(97\) −2.19244 + 2.74924i −0.222609 + 0.279143i −0.880577 0.473903i \(-0.842845\pi\)
0.657968 + 0.753046i \(0.271416\pi\)
\(98\) 3.44422 + 15.0901i 0.347918 + 1.52433i
\(99\) 0 0
\(100\) 1.02464 + 4.48925i 0.102464 + 0.448925i
\(101\) −11.4159 5.49760i −1.13592 0.547032i −0.231147 0.972919i \(-0.574248\pi\)
−0.904776 + 0.425887i \(0.859962\pi\)
\(102\) 0 0
\(103\) −0.448946 1.96696i −0.0442359 0.193810i 0.947982 0.318324i \(-0.103120\pi\)
−0.992218 + 0.124514i \(0.960263\pi\)
\(104\) 8.49854 0.833350
\(105\) 0 0
\(106\) −1.49626 + 1.87625i −0.145330 + 0.182238i
\(107\) −0.127292 + 0.557702i −0.0123058 + 0.0539151i −0.980708 0.195478i \(-0.937374\pi\)
0.968402 + 0.249393i \(0.0802312\pi\)
\(108\) 0 0
\(109\) 12.1384 + 15.2210i 1.16264 + 1.45791i 0.863962 + 0.503557i \(0.167976\pi\)
0.298682 + 0.954353i \(0.403453\pi\)
\(110\) 1.98839 + 0.957557i 0.189585 + 0.0912995i
\(111\) 0 0
\(112\) −6.25240 + 7.84026i −0.590797 + 0.740835i
\(113\) −1.51936 1.90522i −0.142929 0.179228i 0.705214 0.708994i \(-0.250851\pi\)
−0.848143 + 0.529767i \(0.822279\pi\)
\(114\) 0 0
\(115\) −3.20083 −0.298479
\(116\) −2.37681 + 2.69585i −0.220681 + 0.250304i
\(117\) 0 0
\(118\) 14.8386 7.14592i 1.36601 0.657835i
\(119\) 8.44114 + 10.5849i 0.773798 + 0.970312i
\(120\) 0 0
\(121\) 9.63393 4.63945i 0.875811 0.421769i
\(122\) −7.52119 3.62201i −0.680936 0.327922i
\(123\) 0 0
\(124\) 1.35450 5.93446i 0.121638 0.532930i
\(125\) −1.45811 + 6.38840i −0.130417 + 0.571396i
\(126\) 0 0
\(127\) 2.04476 + 8.95869i 0.181443 + 0.794955i 0.980944 + 0.194290i \(0.0622403\pi\)
−0.799501 + 0.600665i \(0.794903\pi\)
\(128\) −2.72519 −0.240875
\(129\) 0 0
\(130\) 9.90223 + 4.76866i 0.868483 + 0.418240i
\(131\) −11.7972 5.68123i −1.03073 0.496372i −0.159471 0.987203i \(-0.550979\pi\)
−0.871255 + 0.490831i \(0.836693\pi\)
\(132\) 0 0
\(133\) −1.25676 −0.108975
\(134\) −3.15590 13.8269i −0.272628 1.19446i
\(135\) 0 0
\(136\) −2.05343 + 8.99665i −0.176080 + 0.771456i
\(137\) −1.69127 + 7.40992i −0.144495 + 0.633072i 0.849864 + 0.527002i \(0.176684\pi\)
−0.994359 + 0.106070i \(0.966173\pi\)
\(138\) 0 0
\(139\) −7.97635 3.84121i −0.676545 0.325807i 0.0638687 0.997958i \(-0.479656\pi\)
−0.740414 + 0.672151i \(0.765370\pi\)
\(140\) 9.37036 4.51253i 0.791940 0.381378i
\(141\) 0 0
\(142\) −1.71449 2.14990i −0.143877 0.180416i
\(143\) −1.37813 + 0.663673i −0.115245 + 0.0554991i
\(144\) 0 0
\(145\) −17.1144 + 7.22396i −1.42127 + 0.599917i
\(146\) 1.05409 0.0872375
\(147\) 0 0
\(148\) 2.86083 + 3.58736i 0.235159 + 0.294879i
\(149\) −4.96925 + 6.23124i −0.407097 + 0.510483i −0.942542 0.334087i \(-0.891572\pi\)
0.535446 + 0.844570i \(0.320144\pi\)
\(150\) 0 0
\(151\) 0.0950717 + 0.0457841i 0.00773683 + 0.00372586i 0.437748 0.899098i \(-0.355776\pi\)
−0.430011 + 0.902823i \(0.641490\pi\)
\(152\) −0.534096 0.669735i −0.0433209 0.0543226i
\(153\) 0 0
\(154\) 0.643129 2.81773i 0.0518248 0.227059i
\(155\) 19.6166 24.5984i 1.57564 1.97579i
\(156\) 0 0
\(157\) −13.5037 −1.07771 −0.538857 0.842397i \(-0.681144\pi\)
−0.538857 + 0.842397i \(0.681144\pi\)
\(158\) 0.531241 + 2.32752i 0.0422633 + 0.185168i
\(159\) 0 0
\(160\) 11.1758 + 5.38201i 0.883528 + 0.425485i
\(161\) 0.932758 + 4.08668i 0.0735117 + 0.322076i
\(162\) 0 0
\(163\) 0.581624 + 2.54826i 0.0455563 + 0.199595i 0.992585 0.121554i \(-0.0387879\pi\)
−0.947028 + 0.321150i \(0.895931\pi\)
\(164\) −1.18724 + 1.48875i −0.0927076 + 0.116252i
\(165\) 0 0
\(166\) 2.81803 12.3466i 0.218722 0.958282i
\(167\) 6.37129 + 7.98935i 0.493026 + 0.618235i 0.964640 0.263570i \(-0.0849001\pi\)
−0.471615 + 0.881805i \(0.656329\pi\)
\(168\) 0 0
\(169\) 4.84946 2.33538i 0.373036 0.179645i
\(170\) −7.44075 + 9.33040i −0.570679 + 0.715609i
\(171\) 0 0
\(172\) −6.74589 + 3.24865i −0.514370 + 0.247707i
\(173\) −23.0919 −1.75564 −0.877822 0.478987i \(-0.841004\pi\)
−0.877822 + 0.478987i \(0.841004\pi\)
\(174\) 0 0
\(175\) 31.1690 2.35616
\(176\) 1.10841 0.533782i 0.0835495 0.0402353i
\(177\) 0 0
\(178\) −4.89927 + 6.14350i −0.367216 + 0.460474i
\(179\) 13.3241 6.41655i 0.995891 0.479596i 0.136349 0.990661i \(-0.456463\pi\)
0.859542 + 0.511065i \(0.170749\pi\)
\(180\) 0 0
\(181\) 1.80146 + 2.25895i 0.133901 + 0.167907i 0.844261 0.535931i \(-0.180039\pi\)
−0.710360 + 0.703838i \(0.751468\pi\)
\(182\) 3.20280 14.0324i 0.237408 1.04015i
\(183\) 0 0
\(184\) −1.78141 + 2.23382i −0.131327 + 0.164679i
\(185\) 5.27739 + 23.1218i 0.388001 + 1.69994i
\(186\) 0 0
\(187\) −0.369586 1.61926i −0.0270268 0.118412i
\(188\) −2.52275 1.21489i −0.183991 0.0886052i
\(189\) 0 0
\(190\) −0.246513 1.08004i −0.0178839 0.0783546i
\(191\) 4.66376 0.337458 0.168729 0.985663i \(-0.446034\pi\)
0.168729 + 0.985663i \(0.446034\pi\)
\(192\) 0 0
\(193\) −9.09293 + 11.4022i −0.654523 + 0.820746i −0.992735 0.120324i \(-0.961607\pi\)
0.338212 + 0.941070i \(0.390178\pi\)
\(194\) −0.903278 + 3.95752i −0.0648516 + 0.284133i
\(195\) 0 0
\(196\) −5.57926 6.99618i −0.398519 0.499727i
\(197\) 2.60517 + 1.25458i 0.185611 + 0.0893855i 0.524381 0.851484i \(-0.324297\pi\)
−0.338770 + 0.940869i \(0.610011\pi\)
\(198\) 0 0
\(199\) 2.52561 3.16701i 0.179036 0.224504i −0.684213 0.729282i \(-0.739854\pi\)
0.863249 + 0.504778i \(0.168426\pi\)
\(200\) 13.2461 + 16.6101i 0.936643 + 1.17451i
\(201\) 0 0
\(202\) −14.6269 −1.02914
\(203\) 14.2106 + 19.7458i 0.997387 + 1.38588i
\(204\) 0 0
\(205\) −8.86755 + 4.27039i −0.619336 + 0.298257i
\(206\) −1.45212 1.82091i −0.101174 0.126869i
\(207\) 0 0
\(208\) 5.51991 2.65825i 0.382737 0.184316i
\(209\) 0.138911 + 0.0668958i 0.00960865 + 0.00462728i
\(210\) 0 0
\(211\) 2.93029 12.8385i 0.201730 0.883836i −0.768154 0.640266i \(-0.778824\pi\)
0.969883 0.243570i \(-0.0783186\pi\)
\(212\) 0.308728 1.35263i 0.0212036 0.0928989i
\(213\) 0 0
\(214\) 0.146944 + 0.643805i 0.0100449 + 0.0440096i
\(215\) −38.7004 −2.63935
\(216\) 0 0
\(217\) −37.1227 17.8774i −2.52006 1.21360i
\(218\) 20.2485 + 9.75115i 1.37140 + 0.660431i
\(219\) 0 0
\(220\) −1.27591 −0.0860217
\(221\) −1.84055 8.06397i −0.123809 0.542441i
\(222\) 0 0
\(223\) 3.39933 14.8934i 0.227636 0.997338i −0.723925 0.689878i \(-0.757664\pi\)
0.951561 0.307459i \(-0.0994788\pi\)
\(224\) 3.61474 15.8372i 0.241520 1.05817i
\(225\) 0 0
\(226\) −2.53450 1.22055i −0.168593 0.0811899i
\(227\) −13.2896 + 6.39993i −0.882061 + 0.424778i −0.819377 0.573255i \(-0.805680\pi\)
−0.0626842 + 0.998033i \(0.519966\pi\)
\(228\) 0 0
\(229\) 6.46791 + 8.11051i 0.427412 + 0.535957i 0.948177 0.317742i \(-0.102925\pi\)
−0.520765 + 0.853700i \(0.674353\pi\)
\(230\) −3.32908 + 1.60320i −0.219513 + 0.105712i
\(231\) 0 0
\(232\) −4.48344 + 15.9644i −0.294352 + 1.04811i
\(233\) −0.280226 −0.0183582 −0.00917911 0.999958i \(-0.502922\pi\)
−0.00917911 + 0.999958i \(0.502922\pi\)
\(234\) 0 0
\(235\) −9.02361 11.3152i −0.588635 0.738125i
\(236\) −5.93666 + 7.44433i −0.386443 + 0.484585i
\(237\) 0 0
\(238\) 14.0810 + 6.78104i 0.912734 + 0.439550i
\(239\) −4.01459 5.03414i −0.259682 0.325631i 0.634849 0.772636i \(-0.281062\pi\)
−0.894532 + 0.447005i \(0.852491\pi\)
\(240\) 0 0
\(241\) 3.43240 15.0383i 0.221101 0.968705i −0.735551 0.677470i \(-0.763077\pi\)
0.956651 0.291235i \(-0.0940663\pi\)
\(242\) 7.69617 9.65069i 0.494728 0.620370i
\(243\) 0 0
\(244\) 4.82619 0.308965
\(245\) −10.2921 45.0927i −0.657539 2.88087i
\(246\) 0 0
\(247\) 0.691779 + 0.333143i 0.0440169 + 0.0211974i
\(248\) −6.24939 27.3804i −0.396837 1.73866i
\(249\) 0 0
\(250\) 1.68322 + 7.37469i 0.106456 + 0.466416i
\(251\) 2.05218 2.57336i 0.129533 0.162429i −0.712836 0.701331i \(-0.752589\pi\)
0.842368 + 0.538902i \(0.181161\pi\)
\(252\) 0 0
\(253\) 0.114431 0.501353i 0.00719419 0.0315198i
\(254\) 6.61383 + 8.29347i 0.414988 + 0.520379i
\(255\) 0 0
\(256\) 12.6455 6.08973i 0.790341 0.380608i
\(257\) 0.246680 0.309326i 0.0153874 0.0192953i −0.774078 0.633090i \(-0.781786\pi\)
0.789466 + 0.613795i \(0.210358\pi\)
\(258\) 0 0
\(259\) 27.9830 13.4759i 1.73878 0.837351i
\(260\) −6.35406 −0.394062
\(261\) 0 0
\(262\) −15.1154 −0.933835
\(263\) −7.33709 + 3.53336i −0.452425 + 0.217876i −0.646198 0.763170i \(-0.723642\pi\)
0.193773 + 0.981046i \(0.437927\pi\)
\(264\) 0 0
\(265\) 4.47117 5.60667i 0.274662 0.344415i
\(266\) −1.30712 + 0.629474i −0.0801445 + 0.0385955i
\(267\) 0 0
\(268\) 5.11222 + 6.41052i 0.312278 + 0.391585i
\(269\) 1.99769 8.75246i 0.121801 0.533647i −0.876804 0.480848i \(-0.840329\pi\)
0.998605 0.0527984i \(-0.0168141\pi\)
\(270\) 0 0
\(271\) 3.14213 3.94011i 0.190871 0.239344i −0.677183 0.735815i \(-0.736799\pi\)
0.868054 + 0.496470i \(0.165371\pi\)
\(272\) 1.48032 + 6.48573i 0.0897579 + 0.393255i
\(273\) 0 0
\(274\) 1.95238 + 8.55391i 0.117947 + 0.516761i
\(275\) −3.44513 1.65909i −0.207749 0.100047i
\(276\) 0 0
\(277\) −0.452859 1.98410i −0.0272097 0.119213i 0.959499 0.281711i \(-0.0909020\pi\)
−0.986709 + 0.162498i \(0.948045\pi\)
\(278\) −10.2199 −0.612948
\(279\) 0 0
\(280\) 29.9181 37.5162i 1.78795 2.24202i
\(281\) 5.30139 23.2269i 0.316255 1.38560i −0.527811 0.849362i \(-0.676987\pi\)
0.844065 0.536240i \(-0.180156\pi\)
\(282\) 0 0
\(283\) −9.34352 11.7164i −0.555414 0.696468i 0.422288 0.906462i \(-0.361227\pi\)
−0.977703 + 0.209994i \(0.932656\pi\)
\(284\) 1.43233 + 0.689774i 0.0849932 + 0.0409306i
\(285\) 0 0
\(286\) −1.10093 + 1.38053i −0.0650996 + 0.0816323i
\(287\) 8.03636 + 10.0773i 0.474371 + 0.594843i
\(288\) 0 0
\(289\) −8.01868 −0.471687
\(290\) −14.1818 + 16.0855i −0.832786 + 0.944572i
\(291\) 0 0
\(292\) −0.549057 + 0.264412i −0.0321311 + 0.0154735i
\(293\) −18.9354 23.7443i −1.10622 1.38715i −0.913957 0.405810i \(-0.866989\pi\)
−0.192261 0.981344i \(-0.561582\pi\)
\(294\) 0 0
\(295\) −44.3413 + 21.3536i −2.58165 + 1.24326i
\(296\) 19.0735 + 9.18532i 1.10863 + 0.533886i
\(297\) 0 0
\(298\) −2.04731 + 8.96985i −0.118598 + 0.519610i
\(299\) 0.569868 2.49675i 0.0329563 0.144391i
\(300\) 0 0
\(301\) 11.2778 + 49.4111i 0.650039 + 2.84801i
\(302\) 0.121813 0.00700954
\(303\) 0 0
\(304\) −0.556387 0.267942i −0.0319110 0.0153675i
\(305\) 22.4750 + 10.8234i 1.28692 + 0.619746i
\(306\) 0 0
\(307\) 2.10479 0.120127 0.0600635 0.998195i \(-0.480870\pi\)
0.0600635 + 0.998195i \(0.480870\pi\)
\(308\) 0.371814 + 1.62903i 0.0211861 + 0.0928223i
\(309\) 0 0
\(310\) 8.08196 35.4094i 0.459025 2.01112i
\(311\) 3.75530 16.4530i 0.212943 0.932965i −0.749611 0.661878i \(-0.769760\pi\)
0.962555 0.271087i \(-0.0873832\pi\)
\(312\) 0 0
\(313\) −13.3609 6.43428i −0.755203 0.363687i 0.0163375 0.999867i \(-0.494799\pi\)
−0.771541 + 0.636180i \(0.780514\pi\)
\(314\) −14.0448 + 6.76361i −0.792593 + 0.381693i
\(315\) 0 0
\(316\) −0.860555 1.07910i −0.0484100 0.0607042i
\(317\) −4.96094 + 2.38906i −0.278634 + 0.134183i −0.567982 0.823041i \(-0.692276\pi\)
0.289348 + 0.957224i \(0.406561\pi\)
\(318\) 0 0
\(319\) −0.519661 2.93892i −0.0290954 0.164548i
\(320\) 29.6341 1.65660
\(321\) 0 0
\(322\) 3.01703 + 3.78323i 0.168132 + 0.210831i
\(323\) −0.519818 + 0.651831i −0.0289234 + 0.0362688i
\(324\) 0 0
\(325\) −17.1569 8.26231i −0.951691 0.458310i
\(326\) 1.88127 + 2.35904i 0.104194 + 0.130655i
\(327\) 0 0
\(328\) −1.95496 + 8.56523i −0.107944 + 0.472936i
\(329\) −11.8172 + 14.8184i −0.651506 + 0.816963i
\(330\) 0 0
\(331\) −5.88833 −0.323652 −0.161826 0.986819i \(-0.551738\pi\)
−0.161826 + 0.986819i \(0.551738\pi\)
\(332\) 1.62920 + 7.13798i 0.0894138 + 0.391747i
\(333\) 0 0
\(334\) 10.6282 + 5.11827i 0.581549 + 0.280059i
\(335\) 9.43054 + 41.3179i 0.515246 + 2.25744i
\(336\) 0 0
\(337\) −3.87848 16.9927i −0.211274 0.925652i −0.963703 0.266978i \(-0.913975\pi\)
0.752428 0.658674i \(-0.228882\pi\)
\(338\) 3.87405 4.85790i 0.210720 0.264235i
\(339\) 0 0
\(340\) 1.53527 6.72648i 0.0832619 0.364794i
\(341\) 3.15161 + 3.95199i 0.170669 + 0.214012i
\(342\) 0 0
\(343\) −26.0821 + 12.5605i −1.40830 + 0.678201i
\(344\) −21.5386 + 27.0086i −1.16128 + 1.45620i
\(345\) 0 0
\(346\) −24.0171 + 11.5660i −1.29117 + 0.621794i
\(347\) 2.81562 0.151150 0.0755751 0.997140i \(-0.475921\pi\)
0.0755751 + 0.997140i \(0.475921\pi\)
\(348\) 0 0
\(349\) 23.4949 1.25765 0.628826 0.777546i \(-0.283536\pi\)
0.628826 + 0.777546i \(0.283536\pi\)
\(350\) 32.4179 15.6116i 1.73281 0.834477i
\(351\) 0 0
\(352\) −1.24254 + 1.55809i −0.0662274 + 0.0830465i
\(353\) 14.5563 7.00993i 0.774752 0.373101i −0.00435584 0.999991i \(-0.501387\pi\)
0.779108 + 0.626889i \(0.215672\pi\)
\(354\) 0 0
\(355\) 5.12329 + 6.42440i 0.271916 + 0.340972i
\(356\) 1.01088 4.42897i 0.0535767 0.234735i
\(357\) 0 0
\(358\) 10.6441 13.3473i 0.562559 0.705426i
\(359\) −1.92263 8.42361i −0.101473 0.444581i −0.999984 0.00563099i \(-0.998208\pi\)
0.898511 0.438950i \(-0.144650\pi\)
\(360\) 0 0
\(361\) 4.21068 + 18.4482i 0.221615 + 0.970957i
\(362\) 3.00508 + 1.44717i 0.157943 + 0.0760615i
\(363\) 0 0
\(364\) 1.85165 + 8.11260i 0.0970527 + 0.425216i
\(365\) −3.14988 −0.164872
\(366\) 0 0
\(367\) 8.38364 10.5127i 0.437622 0.548761i −0.513293 0.858214i \(-0.671574\pi\)
0.950915 + 0.309453i \(0.100146\pi\)
\(368\) −0.458336 + 2.00810i −0.0238924 + 0.104679i
\(369\) 0 0
\(370\) 17.0698 + 21.4049i 0.887418 + 1.11279i
\(371\) −8.46131 4.07475i −0.439289 0.211551i
\(372\) 0 0
\(373\) −1.99095 + 2.49657i −0.103088 + 0.129268i −0.830699 0.556722i \(-0.812059\pi\)
0.727611 + 0.685989i \(0.240630\pi\)
\(374\) −1.19543 1.49903i −0.0618144 0.0775128i
\(375\) 0 0
\(376\) −12.9188 −0.666238
\(377\) −2.58793 14.6359i −0.133285 0.753788i
\(378\) 0 0
\(379\) 14.8677 7.15991i 0.763703 0.367780i −0.0111367 0.999938i \(-0.503545\pi\)
0.774839 + 0.632158i \(0.217831\pi\)
\(380\) 0.399325 + 0.500737i 0.0204849 + 0.0256873i
\(381\) 0 0
\(382\) 4.85062 2.33594i 0.248179 0.119517i
\(383\) 1.42189 + 0.684747i 0.0726553 + 0.0349889i 0.469859 0.882742i \(-0.344305\pi\)
−0.397203 + 0.917731i \(0.630019\pi\)
\(384\) 0 0
\(385\) −1.92182 + 8.42003i −0.0979449 + 0.429125i
\(386\) −3.74625 + 16.4134i −0.190679 + 0.835420i
\(387\) 0 0
\(388\) −0.522215 2.28797i −0.0265114 0.116154i
\(389\) 14.0108 0.710375 0.355188 0.934795i \(-0.384417\pi\)
0.355188 + 0.934795i \(0.384417\pi\)
\(390\) 0 0
\(391\) 2.50540 + 1.20654i 0.126703 + 0.0610171i
\(392\) −37.1977 17.9135i −1.87877 0.904766i
\(393\) 0 0
\(394\) 3.33794 0.168163
\(395\) −1.58747 6.95517i −0.0798744 0.349952i
\(396\) 0 0
\(397\) −5.32177 + 23.3162i −0.267092 + 1.17021i 0.646286 + 0.763095i \(0.276321\pi\)
−0.913378 + 0.407112i \(0.866536\pi\)
\(398\) 1.04054 4.55891i 0.0521576 0.228517i
\(399\) 0 0
\(400\) 13.7990 + 6.64525i 0.689950 + 0.332262i
\(401\) −32.3263 + 15.5675i −1.61430 + 0.777406i −0.999933 0.0116132i \(-0.996303\pi\)
−0.614368 + 0.789019i \(0.710589\pi\)
\(402\) 0 0
\(403\) 15.6951 + 19.6810i 0.781829 + 0.980383i
\(404\) 7.61885 3.66904i 0.379052 0.182542i
\(405\) 0 0
\(406\) 24.6700 + 13.4193i 1.22435 + 0.665987i
\(407\) −3.81028 −0.188869
\(408\) 0 0
\(409\) 9.36367 + 11.7417i 0.463004 + 0.580588i 0.957442 0.288624i \(-0.0931978\pi\)
−0.494439 + 0.869212i \(0.664626\pi\)
\(410\) −7.08394 + 8.88298i −0.349851 + 0.438699i
\(411\) 0 0
\(412\) 1.21314 + 0.584219i 0.0597673 + 0.0287824i
\(413\) 40.1850 + 50.3904i 1.97737 + 2.47955i
\(414\) 0 0
\(415\) −8.42092 + 36.8945i −0.413367 + 1.81108i
\(416\) −6.18786 + 7.75934i −0.303385 + 0.380433i
\(417\) 0 0
\(418\) 0.177983 0.00870541
\(419\) 8.22309 + 36.0277i 0.401724 + 1.76007i 0.620415 + 0.784274i \(0.286964\pi\)
−0.218691 + 0.975794i \(0.570179\pi\)
\(420\) 0 0
\(421\) −1.15916 0.558222i −0.0564940 0.0272061i 0.405423 0.914129i \(-0.367124\pi\)
−0.461917 + 0.886923i \(0.652838\pi\)
\(422\) −3.38269 14.8206i −0.164667 0.721453i
\(423\) 0 0
\(424\) −1.42441 6.24075i −0.0691755 0.303078i
\(425\) 12.8920 16.1661i 0.625355 0.784170i
\(426\) 0 0
\(427\) 7.26938 31.8492i 0.351790 1.54129i
\(428\) −0.238034 0.298485i −0.0115058 0.0144278i
\(429\) 0 0
\(430\) −40.2510 + 19.3839i −1.94108 + 0.934774i
\(431\) 15.7634 19.7667i 0.759298 0.952130i −0.240531 0.970642i \(-0.577321\pi\)
0.999829 + 0.0185118i \(0.00589284\pi\)
\(432\) 0 0
\(433\) 9.33295 4.49451i 0.448513 0.215993i −0.195972 0.980610i \(-0.562786\pi\)
0.644485 + 0.764617i \(0.277072\pi\)
\(434\) −47.5644 −2.28316
\(435\) 0 0
\(436\) −12.9930 −0.622253
\(437\) −0.232572 + 0.112001i −0.0111254 + 0.00535773i
\(438\) 0 0
\(439\) −8.35161 + 10.4726i −0.398601 + 0.499829i −0.940113 0.340864i \(-0.889281\pi\)
0.541512 + 0.840693i \(0.317852\pi\)
\(440\) −5.30381 + 2.55418i −0.252849 + 0.121766i
\(441\) 0 0
\(442\) −5.95329 7.46519i −0.283169 0.355083i
\(443\) 6.85215 30.0213i 0.325556 1.42635i −0.501951 0.864896i \(-0.667384\pi\)
0.827506 0.561456i \(-0.189759\pi\)
\(444\) 0 0
\(445\) 14.6402 18.3582i 0.694010 0.870261i
\(446\) −3.92414 17.1928i −0.185813 0.814102i
\(447\) 0 0
\(448\) −8.63573 37.8356i −0.408000 1.78756i
\(449\) 5.54036 + 2.66810i 0.261466 + 0.125915i 0.560025 0.828476i \(-0.310792\pi\)
−0.298559 + 0.954391i \(0.596506\pi\)
\(450\) 0 0
\(451\) −0.351863 1.54161i −0.0165686 0.0725917i
\(452\) 1.62634 0.0764965
\(453\) 0 0
\(454\) −10.6165 + 13.3127i −0.498259 + 0.624797i
\(455\) −9.57071 + 41.9320i −0.448682 + 1.96580i
\(456\) 0 0
\(457\) −10.6275 13.3265i −0.497134 0.623386i 0.468446 0.883492i \(-0.344814\pi\)
−0.965580 + 0.260106i \(0.916242\pi\)
\(458\) 10.7894 + 5.19589i 0.504154 + 0.242788i
\(459\) 0 0
\(460\) 1.33190 1.67015i 0.0621001 0.0778711i
\(461\) 10.3278 + 12.9506i 0.481012 + 0.603170i 0.961829 0.273651i \(-0.0882313\pi\)
−0.480817 + 0.876821i \(0.659660\pi\)
\(462\) 0 0
\(463\) 28.9072 1.34343 0.671715 0.740809i \(-0.265558\pi\)
0.671715 + 0.740809i \(0.265558\pi\)
\(464\) 2.08143 + 11.7714i 0.0966280 + 0.546476i
\(465\) 0 0
\(466\) −0.291454 + 0.140357i −0.0135013 + 0.00650190i
\(467\) −14.1479 17.7409i −0.654688 0.820953i 0.338065 0.941123i \(-0.390228\pi\)
−0.992753 + 0.120170i \(0.961656\pi\)
\(468\) 0 0
\(469\) 50.0048 24.0810i 2.30901 1.11196i
\(470\) −15.0526 7.24896i −0.694326 0.334370i
\(471\) 0 0
\(472\) −9.77556 + 42.8295i −0.449957 + 1.97139i
\(473\) 1.38355 6.06173i 0.0636158 0.278719i
\(474\) 0 0
\(475\) 0.427114 + 1.87131i 0.0195973 + 0.0858616i
\(476\) −9.03548 −0.414140
\(477\) 0 0
\(478\) −6.69689 3.22505i −0.306309 0.147511i
\(479\) 5.87751 + 2.83046i 0.268550 + 0.129327i 0.563313 0.826243i \(-0.309526\pi\)
−0.294763 + 0.955570i \(0.595241\pi\)
\(480\) 0 0
\(481\) −18.9753 −0.865200
\(482\) −3.96232 17.3601i −0.180479 0.790730i
\(483\) 0 0
\(484\) −1.58798 + 6.95738i −0.0721807 + 0.316244i
\(485\) 2.69920 11.8260i 0.122564 0.536990i
\(486\) 0 0
\(487\) 21.1411 + 10.1810i 0.957996 + 0.461346i 0.846482 0.532417i \(-0.178716\pi\)
0.111513 + 0.993763i \(0.464430\pi\)
\(488\) 20.0619 9.66132i 0.908161 0.437347i
\(489\) 0 0
\(490\) −33.2900 41.7444i −1.50389 1.88582i
\(491\) −27.0162 + 13.0103i −1.21923 + 0.587148i −0.929096 0.369839i \(-0.879413\pi\)
−0.290130 + 0.956987i \(0.593699\pi\)
\(492\) 0 0
\(493\) 16.1190 + 0.796738i 0.725965 + 0.0358833i
\(494\) 0.886358 0.0398791
\(495\) 0 0
\(496\) −12.6233 15.8292i −0.566805 0.710750i
\(497\) 6.70942 8.41334i 0.300958 0.377390i
\(498\) 0 0
\(499\) −13.9764 6.73068i −0.625669 0.301307i 0.0940543 0.995567i \(-0.470017\pi\)
−0.719724 + 0.694261i \(0.755732\pi\)
\(500\) −2.72664 3.41910i −0.121939 0.152907i
\(501\) 0 0
\(502\) 0.845492 3.70434i 0.0377361 0.165333i
\(503\) 9.15733 11.4829i 0.408305 0.511999i −0.534579 0.845118i \(-0.679530\pi\)
0.942885 + 0.333120i \(0.108101\pi\)
\(504\) 0 0
\(505\) 43.7085 1.94500
\(506\) −0.132097 0.578755i −0.00587244 0.0257288i
\(507\) 0 0
\(508\) −5.52537 2.66088i −0.245149 0.118057i
\(509\) 7.27387 + 31.8689i 0.322408 + 1.41256i 0.833254 + 0.552891i \(0.186475\pi\)
−0.510845 + 0.859673i \(0.670667\pi\)
\(510\) 0 0
\(511\) 0.917911 + 4.02163i 0.0406060 + 0.177906i
\(512\) 13.5002 16.9287i 0.596631 0.748151i
\(513\) 0 0
\(514\) 0.101631 0.445275i 0.00448275 0.0196402i
\(515\) 4.33928 + 5.44129i 0.191212 + 0.239772i
\(516\) 0 0
\(517\) 2.09493 1.00886i 0.0921349 0.0443698i
\(518\) 22.3545 28.0317i 0.982201 1.23164i
\(519\) 0 0
\(520\) −26.4131 + 12.7199i −1.15829 + 0.557804i
\(521\) 33.5048 1.46787 0.733937 0.679218i \(-0.237681\pi\)
0.733937 + 0.679218i \(0.237681\pi\)
\(522\) 0 0
\(523\) −23.3879 −1.02268 −0.511341 0.859378i \(-0.670851\pi\)
−0.511341 + 0.859378i \(0.670851\pi\)
\(524\) 7.87333 3.79160i 0.343948 0.165637i
\(525\) 0 0
\(526\) −5.86132 + 7.34986i −0.255566 + 0.320469i
\(527\) −24.6268 + 11.8597i −1.07276 + 0.516615i
\(528\) 0 0
\(529\) −13.8035 17.3090i −0.600150 0.752564i
\(530\) 1.84210 8.07079i 0.0800159 0.350573i
\(531\) 0 0
\(532\) 0.522952 0.655761i 0.0226729 0.0284309i
\(533\) −1.75229 7.67727i −0.0759000 0.332540i
\(534\) 0 0
\(535\) −0.439103 1.92384i −0.0189841 0.0831747i
\(536\) 34.0838 + 16.4139i 1.47220 + 0.708972i
\(537\) 0 0
\(538\) −2.30611 10.1037i −0.0994234 0.435602i
\(539\) 7.43091 0.320072
\(540\) 0 0
\(541\) −9.10698 + 11.4198i −0.391540 + 0.490975i −0.938061 0.346470i \(-0.887380\pi\)
0.546521 + 0.837445i \(0.315952\pi\)
\(542\) 1.29455 5.67177i 0.0556055 0.243624i
\(543\) 0 0
\(544\) −6.71900 8.42536i −0.288075 0.361234i
\(545\) −60.5071 29.1387i −2.59184 1.24816i
\(546\) 0 0
\(547\) 7.68546 9.63726i 0.328607 0.412060i −0.589893 0.807481i \(-0.700830\pi\)
0.918500 + 0.395422i \(0.129402\pi\)
\(548\) −3.16264 3.96583i −0.135101 0.169412i
\(549\) 0 0
\(550\) −4.41415 −0.188220
\(551\) −0.990756 + 1.12375i −0.0422076 + 0.0478732i
\(552\) 0 0
\(553\) −8.41746 + 4.05363i −0.357947 + 0.172378i
\(554\) −1.46478 1.83678i −0.0622326 0.0780372i
\(555\) 0 0
\(556\) 5.32333 2.56358i 0.225760 0.108720i
\(557\) −22.4253 10.7994i −0.950190 0.457587i −0.106437 0.994319i \(-0.533944\pi\)
−0.843753 + 0.536732i \(0.819659\pi\)
\(558\) 0 0
\(559\) 6.89013 30.1876i 0.291421 1.27680i
\(560\) 7.69758 33.7253i 0.325282 1.42515i
\(561\) 0 0
\(562\) −6.11986 26.8129i −0.258151 1.13103i
\(563\) −16.2217 −0.683662 −0.341831 0.939762i \(-0.611047\pi\)
−0.341831 + 0.939762i \(0.611047\pi\)
\(564\) 0 0
\(565\) 7.57368 + 3.64729i 0.318627 + 0.153443i
\(566\) −15.5863 7.50596i −0.655140 0.315499i
\(567\) 0 0
\(568\) 7.33486 0.307764
\(569\) −9.97556 43.7058i −0.418197 1.83224i −0.542575 0.840007i \(-0.682551\pi\)
0.124378 0.992235i \(-0.460307\pi\)
\(570\) 0 0
\(571\) 3.78155 16.5681i 0.158253 0.693352i −0.832081 0.554653i \(-0.812851\pi\)
0.990335 0.138699i \(-0.0442920\pi\)
\(572\) 0.227160 0.995251i 0.00949802 0.0416135i
\(573\) 0 0
\(574\) 13.4058 + 6.45587i 0.559545 + 0.269463i
\(575\) 5.76804 2.77774i 0.240544 0.115840i
\(576\) 0 0
\(577\) −3.45830 4.33657i −0.143971 0.180534i 0.704618 0.709587i \(-0.251119\pi\)
−0.848589 + 0.529053i \(0.822547\pi\)
\(578\) −8.33997 + 4.01632i −0.346897 + 0.167057i
\(579\) 0 0
\(580\) 3.35211 11.9360i 0.139189 0.495616i
\(581\) 49.5592 2.05606
\(582\) 0 0
\(583\) 0.718340 + 0.900769i 0.0297506 + 0.0373061i
\(584\) −1.75305 + 2.19826i −0.0725419 + 0.0909647i
\(585\) 0 0
\(586\) −31.5869 15.2114i −1.30484 0.628379i
\(587\) 11.9358 + 14.9671i 0.492644 + 0.617756i 0.964552 0.263891i \(-0.0850060\pi\)
−0.471908 + 0.881648i \(0.656435\pi\)
\(588\) 0 0
\(589\) 0.564613 2.47373i 0.0232645 0.101928i
\(590\) −35.4225 + 44.4184i −1.45832 + 1.82868i
\(591\) 0 0
\(592\) 15.2616 0.627246
\(593\) 7.05758 + 30.9213i 0.289820 + 1.26978i 0.884772 + 0.466024i \(0.154314\pi\)
−0.594952 + 0.803761i \(0.702829\pi\)
\(594\) 0 0
\(595\) −42.0772 20.2633i −1.72500 0.830715i
\(596\) −1.18362 5.18577i −0.0484829 0.212418i
\(597\) 0 0
\(598\) −0.657848 2.88222i −0.0269014 0.117863i
\(599\) 29.4026 36.8696i 1.20136 1.50645i 0.391129 0.920336i \(-0.372085\pi\)
0.810227 0.586117i \(-0.199344\pi\)
\(600\) 0 0
\(601\) −3.29442 + 14.4338i −0.134382 + 0.588766i 0.862230 + 0.506517i \(0.169067\pi\)
−0.996612 + 0.0822488i \(0.973790\pi\)
\(602\) 36.4781 + 45.7421i 1.48674 + 1.86431i
\(603\) 0 0
\(604\) −0.0634499 + 0.0305559i −0.00258174 + 0.00124330i
\(605\) −22.9979 + 28.8385i −0.934998 + 1.17245i
\(606\) 0 0
\(607\) −10.5442 + 5.07781i −0.427975 + 0.206102i −0.635456 0.772137i \(-0.719188\pi\)
0.207481 + 0.978239i \(0.433474\pi\)
\(608\) 1.00036 0.0405700
\(609\) 0 0
\(610\) 28.7967 1.16594
\(611\) 10.4328 5.02418i 0.422066 0.203256i
\(612\) 0 0
\(613\) −28.6483 + 35.9238i −1.15709 + 1.45095i −0.287091 + 0.957903i \(0.592688\pi\)
−0.870003 + 0.493046i \(0.835883\pi\)
\(614\) 2.18913 1.05423i 0.0883460 0.0425452i
\(615\) 0 0
\(616\) 4.80666 + 6.02736i 0.193666 + 0.242849i
\(617\) −9.15351 + 40.1041i −0.368506 + 1.61453i 0.362378 + 0.932031i \(0.381965\pi\)
−0.730885 + 0.682501i \(0.760892\pi\)
\(618\) 0 0
\(619\) −1.85196 + 2.32229i −0.0744367 + 0.0933407i −0.817656 0.575708i \(-0.804727\pi\)
0.743219 + 0.669048i \(0.233298\pi\)
\(620\) 4.67245 + 20.4713i 0.187650 + 0.822149i
\(621\) 0 0
\(622\) −4.33507 18.9932i −0.173820 0.761557i
\(623\) −27.7053 13.3421i −1.10999 0.534542i
\(624\) 0 0
\(625\) 2.64663 + 11.5956i 0.105865 + 0.463825i
\(626\) −17.1190 −0.684212
\(627\) 0 0
\(628\) 5.61905 7.04606i 0.224224 0.281168i
\(629\) 4.58483 20.0875i 0.182809 0.800940i
\(630\) 0 0
\(631\) 13.4129 + 16.8192i 0.533959 + 0.669563i 0.973507 0.228656i \(-0.0734330\pi\)
−0.439549 + 0.898219i \(0.644862\pi\)
\(632\) −5.73743 2.76300i −0.228223 0.109906i
\(633\) 0 0
\(634\) −3.96310 + 4.96957i −0.157395 + 0.197367i
\(635\) −19.7636 24.7828i −0.784296 0.983476i
\(636\) 0 0
\(637\) 37.0062 1.46624
\(638\) −2.01250 2.79639i −0.0796756 0.110710i
\(639\) 0 0
\(640\) 8.46978 4.07883i 0.334797 0.161230i
\(641\) 20.0815 + 25.1814i 0.793172 + 0.994606i 0.999869 + 0.0162011i \(0.00515721\pi\)
−0.206697 + 0.978405i \(0.566271\pi\)
\(642\) 0 0
\(643\) −35.1799 + 16.9417i −1.38736 + 0.668117i −0.970555 0.240880i \(-0.922564\pi\)
−0.416803 + 0.908997i \(0.636850\pi\)
\(644\) −2.52051 1.21381i −0.0993218 0.0478309i
\(645\) 0 0
\(646\) −0.214163 + 0.938308i −0.00842612 + 0.0369173i
\(647\) −0.917446 + 4.01959i −0.0360685 + 0.158027i −0.989755 0.142776i \(-0.954397\pi\)
0.953687 + 0.300802i \(0.0972544\pi\)
\(648\) 0 0
\(649\) −1.75945 7.70867i −0.0690646 0.302592i
\(650\) −21.9826 −0.862229
\(651\) 0 0
\(652\) −1.57167 0.756875i −0.0615512 0.0296415i
\(653\) −13.7671 6.62990i −0.538749 0.259448i 0.144663 0.989481i \(-0.453790\pi\)
−0.683412 + 0.730033i \(0.739505\pi\)
\(654\) 0 0
\(655\) 45.1684 1.76488
\(656\) 1.40934 + 6.17471i 0.0550254 + 0.241082i
\(657\) 0 0
\(658\) −4.86866 + 21.3310i −0.189800 + 0.831569i
\(659\) −7.68022 + 33.6492i −0.299179 + 1.31079i 0.572175 + 0.820132i \(0.306100\pi\)
−0.871353 + 0.490656i \(0.836757\pi\)
\(660\) 0 0
\(661\) −10.7766 5.18973i −0.419160 0.201857i 0.212401 0.977182i \(-0.431872\pi\)
−0.631562 + 0.775325i \(0.717586\pi\)
\(662\) −6.12425 + 2.94928i −0.238026 + 0.114627i
\(663\) 0 0
\(664\) 21.0616 + 26.4104i 0.817347 + 1.02492i
\(665\) 3.90597 1.88101i 0.151467 0.0729426i
\(666\) 0 0
\(667\) 4.38948 + 2.38766i 0.169961 + 0.0924506i
\(668\) −6.81990 −0.263870
\(669\) 0 0
\(670\) 30.5033 + 38.2499i 1.17845 + 1.47772i
\(671\) −2.49878 + 3.13338i −0.0964645 + 0.120963i
\(672\) 0 0
\(673\) 15.9364 + 7.67456i 0.614303 + 0.295833i 0.715043 0.699080i \(-0.246407\pi\)
−0.100741 + 0.994913i \(0.532121\pi\)
\(674\) −12.5450 15.7310i −0.483216 0.605934i
\(675\) 0 0
\(676\) −0.799345 + 3.50216i −0.0307440 + 0.134698i
\(677\) −18.5642 + 23.2788i −0.713480 + 0.894675i −0.997949 0.0640097i \(-0.979611\pi\)
0.284469 + 0.958685i \(0.408183\pi\)
\(678\) 0 0
\(679\) −15.8855 −0.609629
\(680\) −7.08344 31.0346i −0.271638 1.19012i
\(681\) 0 0
\(682\) 5.25732 + 2.53179i 0.201313 + 0.0969473i
\(683\) −3.77624 16.5448i −0.144494 0.633069i −0.994359 0.106068i \(-0.966174\pi\)
0.849865 0.527000i \(-0.176683\pi\)
\(684\) 0 0
\(685\) −5.83414 25.5611i −0.222911 0.976638i
\(686\) −20.8360 + 26.1275i −0.795520 + 0.997551i
\(687\) 0 0
\(688\) −5.54162 + 24.2794i −0.211272 + 0.925645i
\(689\) 3.57735 + 4.48586i 0.136286 + 0.170898i
\(690\) 0 0
\(691\) 22.2454 10.7128i 0.846254 0.407534i 0.0400683 0.999197i \(-0.487242\pi\)
0.806186 + 0.591662i \(0.201528\pi\)
\(692\) 9.60878 12.0490i 0.365271 0.458036i
\(693\) 0 0
\(694\) 2.92843 1.41026i 0.111162 0.0535327i
\(695\) 30.5394 1.15842
\(696\) 0 0
\(697\) 8.55063 0.323878
\(698\) 24.4363 11.7679i 0.924926 0.445421i
\(699\) 0 0
\(700\) −12.9698 + 16.2636i −0.490211 + 0.614705i
\(701\) 22.7891 10.9746i 0.860732 0.414507i 0.0491820 0.998790i \(-0.484339\pi\)
0.811550 + 0.584283i \(0.198624\pi\)
\(702\) 0 0
\(703\) 1.19251 + 1.49537i 0.0449765 + 0.0563988i
\(704\) −1.05943 + 4.64166i −0.0399287 + 0.174939i
\(705\) 0 0
\(706\) 11.6284 14.5816i 0.437642 0.548786i
\(707\) −12.7372 55.8051i −0.479030 2.09877i
\(708\) 0 0
\(709\) −0.443854 1.94465i −0.0166693 0.0730329i 0.965909 0.258881i \(-0.0833538\pi\)
−0.982578 + 0.185848i \(0.940497\pi\)
\(710\) 8.54635 + 4.11571i 0.320739 + 0.154460i
\(711\) 0 0
\(712\) −4.66401 20.4344i −0.174791 0.765811i
\(713\) −8.46302 −0.316943
\(714\) 0 0
\(715\) 3.28984 4.12533i 0.123033 0.154279i
\(716\) −2.19624 + 9.62234i −0.0820772 + 0.359604i
\(717\) 0 0
\(718\) −6.21880 7.79813i −0.232084 0.291024i
\(719\) 5.69960 + 2.74478i 0.212559 + 0.102363i 0.537134 0.843497i \(-0.319507\pi\)
−0.324575 + 0.945860i \(0.605221\pi\)
\(720\) 0 0
\(721\) 5.68269 7.12586i 0.211634 0.265381i
\(722\) 13.6195 + 17.0783i 0.506866 + 0.635590i
\(723\) 0 0
\(724\) −1.92830 −0.0716646
\(725\) 24.5718 27.8701i 0.912574 1.03507i
\(726\) 0 0
\(727\) −16.3885 + 7.89230i −0.607817 + 0.292709i −0.712363 0.701811i \(-0.752375\pi\)
0.104547 + 0.994520i \(0.466661\pi\)
\(728\) 23.9373 + 30.0164i 0.887175 + 1.11248i
\(729\) 0 0
\(730\) −3.27608 + 1.57768i −0.121253 + 0.0583925i
\(731\) 30.2921 + 14.5879i 1.12040 + 0.539554i
\(732\) 0 0
\(733\) 8.06036 35.3148i 0.297716 1.30438i −0.575802 0.817589i \(-0.695310\pi\)
0.873518 0.486791i \(-0.161833\pi\)
\(734\) 3.45403 15.1331i 0.127490 0.558572i
\(735\) 0 0
\(736\) −0.742460 3.25293i −0.0273674 0.119905i
\(737\) −6.80886 −0.250808
\(738\) 0 0
\(739\) 3.75343 + 1.80755i 0.138072 + 0.0664920i 0.501644 0.865074i \(-0.332729\pi\)
−0.363572 + 0.931566i \(0.618443\pi\)
\(740\) −14.2606 6.86754i −0.524230 0.252456i
\(741\) 0 0
\(742\) −10.8412 −0.397995
\(743\) 5.47368 + 23.9818i 0.200810 + 0.879806i 0.970445 + 0.241322i \(0.0775809\pi\)
−0.769635 + 0.638484i \(0.779562\pi\)
\(744\) 0 0
\(745\) 6.11783 26.8040i 0.224140 0.982022i
\(746\) −0.820264 + 3.59381i −0.0300320 + 0.131579i
\(747\) 0 0
\(748\) 0.998697 + 0.480947i 0.0365160 + 0.0175852i
\(749\) −2.32831 + 1.12126i −0.0850747 + 0.0409698i
\(750\) 0 0
\(751\) 16.3234 + 20.4689i 0.595651 + 0.746922i 0.984693 0.174297i \(-0.0557654\pi\)
−0.389042 + 0.921220i \(0.627194\pi\)
\(752\) −8.39095 + 4.04087i −0.305987 + 0.147355i
\(753\) 0 0
\(754\) −10.0223 13.9261i −0.364991 0.507160i
\(755\) −0.364005 −0.0132475
\(756\) 0 0
\(757\) −32.5871 40.8630i −1.18440 1.48519i −0.836767 0.547559i \(-0.815557\pi\)
−0.347632 0.937631i \(-0.613014\pi\)
\(758\) 11.8772 14.8936i 0.431400 0.540959i
\(759\) 0 0
\(760\) 2.66235 + 1.28212i 0.0965735 + 0.0465074i
\(761\) −3.05680 3.83310i −0.110809 0.138950i 0.723334 0.690498i \(-0.242609\pi\)
−0.834143 + 0.551548i \(0.814037\pi\)
\(762\) 0 0
\(763\) −19.5706 + 85.7442i −0.708502 + 3.10415i
\(764\) −1.94064 + 2.43348i −0.0702099 + 0.0880404i
\(765\) 0 0
\(766\) 1.82183 0.0658255
\(767\) −8.76214 38.3894i −0.316382 1.38616i
\(768\) 0 0
\(769\) −26.1703 12.6029i −0.943725 0.454474i −0.102243 0.994759i \(-0.532602\pi\)
−0.841482 + 0.540285i \(0.818316\pi\)
\(770\) 2.21852 + 9.71998i 0.0799500 + 0.350284i
\(771\) 0 0
\(772\) −2.16583 9.48913i −0.0779500 0.341521i
\(773\) −33.3981 + 41.8799i −1.20125 + 1.50632i −0.390829 + 0.920463i \(0.627812\pi\)
−0.810418 + 0.585853i \(0.800760\pi\)
\(774\) 0 0
\(775\) −14.0030 + 61.3512i −0.503003 + 2.20380i
\(776\) −6.75097 8.46545i −0.242346 0.303892i
\(777\) 0 0
\(778\) 14.5722 7.01758i 0.522437 0.251593i
\(779\) −0.494891 + 0.620573i −0.0177313 + 0.0222343i
\(780\) 0 0
\(781\) −1.18943 + 0.572798i −0.0425611 +