Properties

Label 378.2.h.d.289.1
Level $378$
Weight $2$
Character 378.289
Analytic conductor $3.018$
Analytic rank $0$
Dimension $6$
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] = [378,2,Mod(289,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.h (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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(0.500000 - 0.224437i\) of defining polynomial
Character \(\chi\) \(=\) 378.289
Dual form 378.2.h.d.361.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.69963 q^{5} +(-1.40545 - 2.24159i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.69963 q^{5} +(-1.40545 - 2.24159i) q^{7} -1.00000 q^{8} +(-1.84981 - 3.20397i) q^{10} +1.47710 q^{11} +(-1.34981 - 2.33795i) q^{13} +(1.23855 - 2.33795i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.28799 - 5.69497i) q^{17} +(-0.444368 + 0.769668i) q^{19} +(1.84981 - 3.20397i) q^{20} +(0.738550 + 1.27921i) q^{22} -6.28799 q^{23} +8.68725 q^{25} +(1.34981 - 2.33795i) q^{26} +(2.64400 - 0.0963576i) q^{28} +(-1.25526 + 2.17417i) q^{29} +(-3.40545 + 5.89841i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.28799 - 5.69497i) q^{34} +(5.19963 + 8.29305i) q^{35} +(-1.38874 + 2.40536i) q^{37} -0.888736 q^{38} +3.69963 q^{40} +(2.05563 + 3.56046i) q^{41} +(0.00618986 - 0.0107211i) q^{43} +(-0.738550 + 1.27921i) q^{44} +(-3.14400 - 5.44556i) q^{46} +(-3.49381 - 6.05146i) q^{47} +(-3.04944 + 6.30087i) q^{49} +(4.34362 + 7.52338i) q^{50} +2.69963 q^{52} +(1.60507 + 2.78007i) q^{53} -5.46472 q^{55} +(1.40545 + 2.24159i) q^{56} -2.51052 q^{58} +(3.45489 - 5.98404i) q^{59} +(2.86652 + 4.96497i) q^{61} -6.81089 q^{62} +1.00000 q^{64} +(4.99381 + 8.64953i) q^{65} +(4.73236 - 8.19669i) q^{67} +6.57598 q^{68} +(-4.58217 + 8.64953i) q^{70} +5.46472 q^{71} +(-6.03273 - 10.4490i) q^{73} -2.77747 q^{74} +(-0.444368 - 0.769668i) q^{76} +(-2.07598 - 3.31105i) q^{77} +(-5.72617 - 9.91802i) q^{79} +(1.84981 + 3.20397i) q^{80} +(-2.05563 + 3.56046i) q^{82} +(-2.23855 + 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} +0.0123797 q^{86} -1.47710 q^{88} +(4.43818 - 7.68715i) q^{89} +(-3.34362 + 6.31159i) q^{91} +(3.14400 - 5.44556i) q^{92} +(3.49381 - 6.05146i) q^{94} +(1.64400 - 2.84748i) q^{95} +(-6.58836 + 11.4114i) q^{97} +(-6.98143 + 0.509538i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 3 q^{4} - 10 q^{5} - 2 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 3 q^{4} - 10 q^{5} - 2 q^{7} - 6 q^{8} - 5 q^{10} - 2 q^{11} - 2 q^{13} + 2 q^{14} - 3 q^{16} + 4 q^{17} - 3 q^{19} + 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} + 2 q^{26} + 4 q^{28} + 5 q^{29} - 14 q^{31} + 3 q^{32} - 4 q^{34} + 19 q^{35} - 9 q^{37} - 6 q^{38} + 10 q^{40} + 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} - 3 q^{47} + 2 q^{50} + 4 q^{52} - 9 q^{53} + 14 q^{55} + 2 q^{56} + 10 q^{58} - 4 q^{59} + 4 q^{61} - 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} - 8 q^{68} + 2 q^{70} - 14 q^{71} - 25 q^{73} - 18 q^{74} - 3 q^{76} + 35 q^{77} + 7 q^{79} + 5 q^{80} - 12 q^{82} - 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} + 9 q^{89} + 4 q^{91} + 7 q^{92} + 3 q^{94} - 2 q^{95} - 28 q^{97} + 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.69963 −1.65452 −0.827262 0.561816i \(-0.810103\pi\)
−0.827262 + 0.561816i \(0.810103\pi\)
\(6\) 0 0
\(7\) −1.40545 2.24159i −0.531209 0.847241i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.84981 3.20397i −0.584963 1.01318i
\(11\) 1.47710 0.445362 0.222681 0.974891i \(-0.428519\pi\)
0.222681 + 0.974891i \(0.428519\pi\)
\(12\) 0 0
\(13\) −1.34981 2.33795i −0.374371 0.648430i 0.615862 0.787854i \(-0.288808\pi\)
−0.990233 + 0.139425i \(0.955475\pi\)
\(14\) 1.23855 2.33795i 0.331016 0.624843i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.28799 5.69497i −0.797455 1.38123i −0.921268 0.388927i \(-0.872846\pi\)
0.123813 0.992306i \(-0.460488\pi\)
\(18\) 0 0
\(19\) −0.444368 + 0.769668i −0.101945 + 0.176574i −0.912486 0.409108i \(-0.865840\pi\)
0.810541 + 0.585682i \(0.199173\pi\)
\(20\) 1.84981 3.20397i 0.413631 0.716430i
\(21\) 0 0
\(22\) 0.738550 + 1.27921i 0.157459 + 0.272728i
\(23\) −6.28799 −1.31114 −0.655568 0.755136i \(-0.727571\pi\)
−0.655568 + 0.755136i \(0.727571\pi\)
\(24\) 0 0
\(25\) 8.68725 1.73745
\(26\) 1.34981 2.33795i 0.264720 0.458509i
\(27\) 0 0
\(28\) 2.64400 0.0963576i 0.499668 0.0182099i
\(29\) −1.25526 + 2.17417i −0.233096 + 0.403734i −0.958718 0.284360i \(-0.908219\pi\)
0.725622 + 0.688094i \(0.241552\pi\)
\(30\) 0 0
\(31\) −3.40545 + 5.89841i −0.611636 + 1.05938i 0.379329 + 0.925262i \(0.376155\pi\)
−0.990965 + 0.134123i \(0.957178\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.28799 5.69497i 0.563886 0.976679i
\(35\) 5.19963 + 8.29305i 0.878898 + 1.40178i
\(36\) 0 0
\(37\) −1.38874 + 2.40536i −0.228307 + 0.395439i −0.957306 0.289075i \(-0.906652\pi\)
0.729000 + 0.684514i \(0.239986\pi\)
\(38\) −0.888736 −0.144172
\(39\) 0 0
\(40\) 3.69963 0.584963
\(41\) 2.05563 + 3.56046i 0.321036 + 0.556050i 0.980702 0.195508i \(-0.0626357\pi\)
−0.659666 + 0.751559i \(0.729302\pi\)
\(42\) 0 0
\(43\) 0.00618986 0.0107211i 0.000943944 0.00163496i −0.865553 0.500817i \(-0.833033\pi\)
0.866497 + 0.499182i \(0.166366\pi\)
\(44\) −0.738550 + 1.27921i −0.111341 + 0.192848i
\(45\) 0 0
\(46\) −3.14400 5.44556i −0.463557 0.802904i
\(47\) −3.49381 6.05146i −0.509625 0.882696i −0.999938 0.0111494i \(-0.996451\pi\)
0.490313 0.871546i \(-0.336882\pi\)
\(48\) 0 0
\(49\) −3.04944 + 6.30087i −0.435635 + 0.900124i
\(50\) 4.34362 + 7.52338i 0.614281 + 1.06397i
\(51\) 0 0
\(52\) 2.69963 0.374371
\(53\) 1.60507 + 2.78007i 0.220474 + 0.381872i 0.954952 0.296760i \(-0.0959063\pi\)
−0.734478 + 0.678632i \(0.762573\pi\)
\(54\) 0 0
\(55\) −5.46472 −0.736863
\(56\) 1.40545 + 2.24159i 0.187811 + 0.299545i
\(57\) 0 0
\(58\) −2.51052 −0.329647
\(59\) 3.45489 5.98404i 0.449788 0.779056i −0.548584 0.836096i \(-0.684833\pi\)
0.998372 + 0.0570397i \(0.0181661\pi\)
\(60\) 0 0
\(61\) 2.86652 + 4.96497i 0.367021 + 0.635699i 0.989098 0.147257i \(-0.0470444\pi\)
−0.622077 + 0.782956i \(0.713711\pi\)
\(62\) −6.81089 −0.864984
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.99381 + 8.64953i 0.619406 + 1.07284i
\(66\) 0 0
\(67\) 4.73236 8.19669i 0.578150 1.00138i −0.417542 0.908658i \(-0.637108\pi\)
0.995692 0.0927271i \(-0.0295584\pi\)
\(68\) 6.57598 0.797455
\(69\) 0 0
\(70\) −4.58217 + 8.64953i −0.547675 + 1.03382i
\(71\) 5.46472 0.648543 0.324271 0.945964i \(-0.394881\pi\)
0.324271 + 0.945964i \(0.394881\pi\)
\(72\) 0 0
\(73\) −6.03273 10.4490i −0.706078 1.22296i −0.966301 0.257414i \(-0.917130\pi\)
0.260223 0.965548i \(-0.416204\pi\)
\(74\) −2.77747 −0.322875
\(75\) 0 0
\(76\) −0.444368 0.769668i −0.0509725 0.0882870i
\(77\) −2.07598 3.31105i −0.236580 0.377329i
\(78\) 0 0
\(79\) −5.72617 9.91802i −0.644244 1.11586i −0.984475 0.175522i \(-0.943839\pi\)
0.340231 0.940342i \(-0.389495\pi\)
\(80\) 1.84981 + 3.20397i 0.206816 + 0.358215i
\(81\) 0 0
\(82\) −2.05563 + 3.56046i −0.227007 + 0.393187i
\(83\) −2.23855 + 3.87728i −0.245713 + 0.425587i −0.962332 0.271878i \(-0.912355\pi\)
0.716619 + 0.697465i \(0.245689\pi\)
\(84\) 0 0
\(85\) 12.1643 + 21.0693i 1.31941 + 2.28528i
\(86\) 0.0123797 0.00133494
\(87\) 0 0
\(88\) −1.47710 −0.157459
\(89\) 4.43818 7.68715i 0.470446 0.814836i −0.528983 0.848633i \(-0.677426\pi\)
0.999429 + 0.0337963i \(0.0107597\pi\)
\(90\) 0 0
\(91\) −3.34362 + 6.31159i −0.350507 + 0.661634i
\(92\) 3.14400 5.44556i 0.327784 0.567739i
\(93\) 0 0
\(94\) 3.49381 6.05146i 0.360359 0.624160i
\(95\) 1.64400 2.84748i 0.168670 0.292146i
\(96\) 0 0
\(97\) −6.58836 + 11.4114i −0.668947 + 1.15865i 0.309252 + 0.950980i \(0.399921\pi\)
−0.978199 + 0.207670i \(0.933412\pi\)
\(98\) −6.98143 + 0.509538i −0.705231 + 0.0514711i
\(99\) 0 0
\(100\) −4.34362 + 7.52338i −0.434362 + 0.752338i
\(101\) −5.25457 −0.522849 −0.261425 0.965224i \(-0.584192\pi\)
−0.261425 + 0.965224i \(0.584192\pi\)
\(102\) 0 0
\(103\) 1.66621 0.164176 0.0820882 0.996625i \(-0.473841\pi\)
0.0820882 + 0.996625i \(0.473841\pi\)
\(104\) 1.34981 + 2.33795i 0.132360 + 0.229255i
\(105\) 0 0
\(106\) −1.60507 + 2.78007i −0.155899 + 0.270024i
\(107\) 5.38255 9.32284i 0.520350 0.901273i −0.479370 0.877613i \(-0.659135\pi\)
0.999720 0.0236602i \(-0.00753198\pi\)
\(108\) 0 0
\(109\) −0.0945538 0.163772i −0.00905662 0.0156865i 0.861462 0.507823i \(-0.169550\pi\)
−0.870518 + 0.492136i \(0.836216\pi\)
\(110\) −2.73236 4.73259i −0.260520 0.451234i
\(111\) 0 0
\(112\) −1.23855 + 2.33795i −0.117032 + 0.220915i
\(113\) 6.78180 + 11.7464i 0.637978 + 1.10501i 0.985876 + 0.167478i \(0.0535624\pi\)
−0.347897 + 0.937533i \(0.613104\pi\)
\(114\) 0 0
\(115\) 23.2632 2.16931
\(116\) −1.25526 2.17417i −0.116548 0.201867i
\(117\) 0 0
\(118\) 6.90978 0.636097
\(119\) −8.14468 + 15.3743i −0.746622 + 1.40936i
\(120\) 0 0
\(121\) −8.81818 −0.801652
\(122\) −2.86652 + 4.96497i −0.259523 + 0.449507i
\(123\) 0 0
\(124\) −3.40545 5.89841i −0.305818 0.529692i
\(125\) −13.6414 −1.22013
\(126\) 0 0
\(127\) −2.85669 −0.253490 −0.126745 0.991935i \(-0.540453\pi\)
−0.126745 + 0.991935i \(0.540453\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −4.99381 + 8.64953i −0.437986 + 0.758614i
\(131\) −0.155687 −0.0136024 −0.00680122 0.999977i \(-0.502165\pi\)
−0.00680122 + 0.999977i \(0.502165\pi\)
\(132\) 0 0
\(133\) 2.34981 0.0856364i 0.203755 0.00742562i
\(134\) 9.46472 0.817627
\(135\) 0 0
\(136\) 3.28799 + 5.69497i 0.281943 + 0.488340i
\(137\) 3.41164 0.291476 0.145738 0.989323i \(-0.453444\pi\)
0.145738 + 0.989323i \(0.453444\pi\)
\(138\) 0 0
\(139\) −6.75526 11.7005i −0.572974 0.992420i −0.996259 0.0864229i \(-0.972456\pi\)
0.423285 0.905997i \(-0.360877\pi\)
\(140\) −9.78180 + 0.356487i −0.826713 + 0.0301287i
\(141\) 0 0
\(142\) 2.73236 + 4.73259i 0.229295 + 0.397150i
\(143\) −1.99381 3.45338i −0.166731 0.288786i
\(144\) 0 0
\(145\) 4.64400 8.04364i 0.385663 0.667988i
\(146\) 6.03273 10.4490i 0.499272 0.864765i
\(147\) 0 0
\(148\) −1.38874 2.40536i −0.114153 0.197719i
\(149\) −0.333792 −0.0273453 −0.0136727 0.999907i \(-0.504352\pi\)
−0.0136727 + 0.999907i \(0.504352\pi\)
\(150\) 0 0
\(151\) −19.9098 −1.62023 −0.810117 0.586268i \(-0.800597\pi\)
−0.810117 + 0.586268i \(0.800597\pi\)
\(152\) 0.444368 0.769668i 0.0360430 0.0624283i
\(153\) 0 0
\(154\) 1.82946 3.45338i 0.147422 0.278281i
\(155\) 12.5989 21.8219i 1.01197 1.75278i
\(156\) 0 0
\(157\) 3.48143 6.03001i 0.277848 0.481248i −0.693001 0.720936i \(-0.743712\pi\)
0.970850 + 0.239689i \(0.0770454\pi\)
\(158\) 5.72617 9.91802i 0.455550 0.789035i
\(159\) 0 0
\(160\) −1.84981 + 3.20397i −0.146241 + 0.253296i
\(161\) 8.83743 + 14.0951i 0.696487 + 1.11085i
\(162\) 0 0
\(163\) 4.03706 6.99240i 0.316207 0.547687i −0.663486 0.748189i \(-0.730924\pi\)
0.979693 + 0.200502i \(0.0642572\pi\)
\(164\) −4.11126 −0.321036
\(165\) 0 0
\(166\) −4.47710 −0.347490
\(167\) −9.74288 16.8752i −0.753927 1.30584i −0.945906 0.324440i \(-0.894824\pi\)
0.191979 0.981399i \(-0.438509\pi\)
\(168\) 0 0
\(169\) 2.85600 4.94674i 0.219693 0.380519i
\(170\) −12.1643 + 21.0693i −0.932963 + 1.61594i
\(171\) 0 0
\(172\) 0.00618986 + 0.0107211i 0.000471972 + 0.000817480i
\(173\) 11.2818 + 19.5407i 0.857740 + 1.48565i 0.874080 + 0.485782i \(0.161465\pi\)
−0.0163405 + 0.999866i \(0.505202\pi\)
\(174\) 0 0
\(175\) −12.2095 19.4732i −0.922948 1.47204i
\(176\) −0.738550 1.27921i −0.0556703 0.0964238i
\(177\) 0 0
\(178\) 8.87636 0.665311
\(179\) −0.166896 0.289073i −0.0124744 0.0216063i 0.859721 0.510764i \(-0.170637\pi\)
−0.872195 + 0.489158i \(0.837304\pi\)
\(180\) 0 0
\(181\) 23.2422 1.72758 0.863789 0.503853i \(-0.168085\pi\)
0.863789 + 0.503853i \(0.168085\pi\)
\(182\) −7.13781 + 0.260130i −0.529089 + 0.0192821i
\(183\) 0 0
\(184\) 6.28799 0.463557
\(185\) 5.13781 8.89894i 0.377739 0.654263i
\(186\) 0 0
\(187\) −4.85669 8.41204i −0.355157 0.615149i
\(188\) 6.98762 0.509625
\(189\) 0 0
\(190\) 3.28799 0.238536
\(191\) −8.16071 14.1348i −0.590488 1.02276i −0.994167 0.107854i \(-0.965602\pi\)
0.403679 0.914901i \(-0.367731\pi\)
\(192\) 0 0
\(193\) 7.16071 12.4027i 0.515439 0.892766i −0.484400 0.874846i \(-0.660962\pi\)
0.999839 0.0179200i \(-0.00570443\pi\)
\(194\) −13.1767 −0.946034
\(195\) 0 0
\(196\) −3.93199 5.79133i −0.280856 0.413666i
\(197\) −2.42402 −0.172704 −0.0863520 0.996265i \(-0.527521\pi\)
−0.0863520 + 0.996265i \(0.527521\pi\)
\(198\) 0 0
\(199\) −3.05563 5.29251i −0.216608 0.375176i 0.737161 0.675717i \(-0.236166\pi\)
−0.953769 + 0.300541i \(0.902833\pi\)
\(200\) −8.68725 −0.614281
\(201\) 0 0
\(202\) −2.62729 4.55059i −0.184855 0.320179i
\(203\) 6.63781 0.241908i 0.465883 0.0169786i
\(204\) 0 0
\(205\) −7.60507 13.1724i −0.531161 0.919999i
\(206\) 0.833104 + 1.44298i 0.0580451 + 0.100537i
\(207\) 0 0
\(208\) −1.34981 + 2.33795i −0.0935928 + 0.162107i
\(209\) −0.656376 + 1.13688i −0.0454025 + 0.0786394i
\(210\) 0 0
\(211\) 5.72253 + 9.91171i 0.393955 + 0.682350i 0.992967 0.118390i \(-0.0377732\pi\)
−0.599012 + 0.800740i \(0.704440\pi\)
\(212\) −3.21015 −0.220474
\(213\) 0 0
\(214\) 10.7651 0.735887
\(215\) −0.0229002 + 0.0396643i −0.00156178 + 0.00270508i
\(216\) 0 0
\(217\) 18.0080 0.656281i 1.22246 0.0445513i
\(218\) 0.0945538 0.163772i 0.00640399 0.0110920i
\(219\) 0 0
\(220\) 2.73236 4.73259i 0.184216 0.319071i
\(221\) −8.87636 + 15.3743i −0.597088 + 1.03419i
\(222\) 0 0
\(223\) −3.61126 + 6.25489i −0.241828 + 0.418859i −0.961235 0.275730i \(-0.911080\pi\)
0.719407 + 0.694589i \(0.244414\pi\)
\(224\) −2.64400 + 0.0963576i −0.176659 + 0.00643816i
\(225\) 0 0
\(226\) −6.78180 + 11.7464i −0.451119 + 0.781361i
\(227\) −13.6552 −0.906328 −0.453164 0.891427i \(-0.649705\pi\)
−0.453164 + 0.891427i \(0.649705\pi\)
\(228\) 0 0
\(229\) 17.3745 1.14814 0.574070 0.818807i \(-0.305364\pi\)
0.574070 + 0.818807i \(0.305364\pi\)
\(230\) 11.6316 + 20.1466i 0.766966 + 1.32842i
\(231\) 0 0
\(232\) 1.25526 2.17417i 0.0824119 0.142742i
\(233\) −7.62110 + 13.2001i −0.499275 + 0.864769i −1.00000 0.000837426i \(-0.999733\pi\)
0.500725 + 0.865606i \(0.333067\pi\)
\(234\) 0 0
\(235\) 12.9258 + 22.3881i 0.843186 + 1.46044i
\(236\) 3.45489 + 5.98404i 0.224894 + 0.389528i
\(237\) 0 0
\(238\) −17.3869 + 0.633646i −1.12702 + 0.0410732i
\(239\) −9.47524 16.4116i −0.612902 1.06158i −0.990749 0.135710i \(-0.956669\pi\)
0.377846 0.925868i \(-0.376665\pi\)
\(240\) 0 0
\(241\) −24.5054 −1.57853 −0.789267 0.614051i \(-0.789539\pi\)
−0.789267 + 0.614051i \(0.789539\pi\)
\(242\) −4.40909 7.63676i −0.283427 0.490910i
\(243\) 0 0
\(244\) −5.73305 −0.367021
\(245\) 11.2818 23.3109i 0.720768 1.48928i
\(246\) 0 0
\(247\) 2.39926 0.152661
\(248\) 3.40545 5.89841i 0.216246 0.374549i
\(249\) 0 0
\(250\) −6.82072 11.8138i −0.431380 0.747173i
\(251\) 12.1236 0.765238 0.382619 0.923906i \(-0.375022\pi\)
0.382619 + 0.923906i \(0.375022\pi\)
\(252\) 0 0
\(253\) −9.28799 −0.583931
\(254\) −1.42835 2.47397i −0.0896224 0.155231i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 8.20877 0.512049 0.256025 0.966670i \(-0.417587\pi\)
0.256025 + 0.966670i \(0.417587\pi\)
\(258\) 0 0
\(259\) 7.34362 0.267630i 0.456311 0.0166297i
\(260\) −9.98762 −0.619406
\(261\) 0 0
\(262\) −0.0778435 0.134829i −0.00480919 0.00832976i
\(263\) 5.34617 0.329659 0.164830 0.986322i \(-0.447293\pi\)
0.164830 + 0.986322i \(0.447293\pi\)
\(264\) 0 0
\(265\) −5.93818 10.2852i −0.364779 0.631816i
\(266\) 1.24907 + 1.99218i 0.0765854 + 0.122148i
\(267\) 0 0
\(268\) 4.73236 + 8.19669i 0.289075 + 0.500692i
\(269\) −9.24219 16.0079i −0.563506 0.976022i −0.997187 0.0749550i \(-0.976119\pi\)
0.433681 0.901067i \(-0.357215\pi\)
\(270\) 0 0
\(271\) −3.67742 + 6.36947i −0.223387 + 0.386918i −0.955834 0.293906i \(-0.905045\pi\)
0.732447 + 0.680824i \(0.238378\pi\)
\(272\) −3.28799 + 5.69497i −0.199364 + 0.345308i
\(273\) 0 0
\(274\) 1.70582 + 2.95456i 0.103052 + 0.178492i
\(275\) 12.8319 0.773795
\(276\) 0 0
\(277\) −9.09888 −0.546699 −0.273349 0.961915i \(-0.588132\pi\)
−0.273349 + 0.961915i \(0.588132\pi\)
\(278\) 6.75526 11.7005i 0.405154 0.701747i
\(279\) 0 0
\(280\) −5.19963 8.29305i −0.310737 0.495604i
\(281\) −6.00433 + 10.3998i −0.358188 + 0.620400i −0.987658 0.156624i \(-0.949939\pi\)
0.629470 + 0.777025i \(0.283272\pi\)
\(282\) 0 0
\(283\) −4.92147 + 8.52423i −0.292551 + 0.506713i −0.974412 0.224768i \(-0.927837\pi\)
0.681861 + 0.731481i \(0.261171\pi\)
\(284\) −2.73236 + 4.73259i −0.162136 + 0.280827i
\(285\) 0 0
\(286\) 1.99381 3.45338i 0.117896 0.204203i
\(287\) 5.09201 9.61192i 0.300572 0.567373i
\(288\) 0 0
\(289\) −13.1218 + 22.7276i −0.771870 + 1.33692i
\(290\) 9.28799 0.545410
\(291\) 0 0
\(292\) 12.0655 0.706078
\(293\) −10.7101 18.5505i −0.625694 1.08373i −0.988406 0.151832i \(-0.951483\pi\)
0.362713 0.931901i \(-0.381851\pi\)
\(294\) 0 0
\(295\) −12.7818 + 22.1387i −0.744185 + 1.28897i
\(296\) 1.38874 2.40536i 0.0807186 0.139809i
\(297\) 0 0
\(298\) −0.166896 0.289073i −0.00966804 0.0167455i
\(299\) 8.48762 + 14.7010i 0.490852 + 0.850180i
\(300\) 0 0
\(301\) −0.0327319 + 0.00119288i −0.00188664 + 6.87564e-5i
\(302\) −9.95489 17.2424i −0.572839 0.992187i
\(303\) 0 0
\(304\) 0.888736 0.0509725
\(305\) −10.6051 18.3685i −0.607245 1.05178i
\(306\) 0 0
\(307\) −5.68725 −0.324588 −0.162294 0.986742i \(-0.551889\pi\)
−0.162294 + 0.986742i \(0.551889\pi\)
\(308\) 3.90545 0.142330i 0.222533 0.00810999i
\(309\) 0 0
\(310\) 25.1978 1.43114
\(311\) −5.86033 + 10.1504i −0.332309 + 0.575576i −0.982964 0.183797i \(-0.941161\pi\)
0.650655 + 0.759373i \(0.274494\pi\)
\(312\) 0 0
\(313\) 13.3869 + 23.1868i 0.756671 + 1.31059i 0.944539 + 0.328398i \(0.106509\pi\)
−0.187868 + 0.982194i \(0.560158\pi\)
\(314\) 6.96286 0.392937
\(315\) 0 0
\(316\) 11.4523 0.644244
\(317\) 0.951246 + 1.64761i 0.0534273 + 0.0925388i 0.891502 0.453016i \(-0.149652\pi\)
−0.838075 + 0.545555i \(0.816319\pi\)
\(318\) 0 0
\(319\) −1.85414 + 3.21147i −0.103812 + 0.179808i
\(320\) −3.69963 −0.206816
\(321\) 0 0
\(322\) −7.78799 + 14.7010i −0.434008 + 0.819254i
\(323\) 5.84431 0.325186
\(324\) 0 0
\(325\) −11.7262 20.3103i −0.650451 1.12661i
\(326\) 8.07413 0.447184
\(327\) 0 0
\(328\) −2.05563 3.56046i −0.113503 0.196593i
\(329\) −8.65452 + 16.3367i −0.477139 + 0.900670i
\(330\) 0 0
\(331\) −2.78366 4.82144i −0.153004 0.265010i 0.779327 0.626618i \(-0.215561\pi\)
−0.932330 + 0.361608i \(0.882228\pi\)
\(332\) −2.23855 3.87728i −0.122856 0.212794i
\(333\) 0 0
\(334\) 9.74288 16.8752i 0.533107 0.923368i
\(335\) −17.5080 + 30.3247i −0.956563 + 1.65682i
\(336\) 0 0
\(337\) −16.8869 29.2489i −0.919887 1.59329i −0.799585 0.600553i \(-0.794947\pi\)
−0.120302 0.992737i \(-0.538386\pi\)
\(338\) 5.71201 0.310692
\(339\) 0 0
\(340\) −24.3287 −1.31941
\(341\) −5.03018 + 8.71253i −0.272400 + 0.471810i
\(342\) 0 0
\(343\) 18.4098 2.01993i 0.994035 0.109066i
\(344\) −0.00618986 + 0.0107211i −0.000333735 + 0.000578045i
\(345\) 0 0
\(346\) −11.2818 + 19.5407i −0.606513 + 1.05051i
\(347\) −15.2033 + 26.3328i −0.816154 + 1.41362i 0.0923418 + 0.995727i \(0.470565\pi\)
−0.908496 + 0.417893i \(0.862769\pi\)
\(348\) 0 0
\(349\) −6.29782 + 10.9082i −0.337115 + 0.583900i −0.983889 0.178782i \(-0.942784\pi\)
0.646774 + 0.762682i \(0.276118\pi\)
\(350\) 10.7596 20.3103i 0.575124 1.08563i
\(351\) 0 0
\(352\) 0.738550 1.27921i 0.0393648 0.0681819i
\(353\) 7.53156 0.400865 0.200432 0.979708i \(-0.435765\pi\)
0.200432 + 0.979708i \(0.435765\pi\)
\(354\) 0 0
\(355\) −20.2174 −1.07303
\(356\) 4.43818 + 7.68715i 0.235223 + 0.407418i
\(357\) 0 0
\(358\) 0.166896 0.289073i 0.00882074 0.0152780i
\(359\) 3.44801 5.97213i 0.181979 0.315197i −0.760575 0.649250i \(-0.775083\pi\)
0.942554 + 0.334053i \(0.108416\pi\)
\(360\) 0 0
\(361\) 9.10507 + 15.7705i 0.479214 + 0.830024i
\(362\) 11.6211 + 20.1283i 0.610791 + 1.05792i
\(363\) 0 0
\(364\) −3.79418 6.05146i −0.198869 0.317183i
\(365\) 22.3189 + 38.6574i 1.16822 + 2.02342i
\(366\) 0 0
\(367\) 23.1236 1.20704 0.603522 0.797346i \(-0.293763\pi\)
0.603522 + 0.797346i \(0.293763\pi\)
\(368\) 3.14400 + 5.44556i 0.163892 + 0.283869i
\(369\) 0 0
\(370\) 10.2756 0.534204
\(371\) 3.97593 7.50516i 0.206420 0.389648i
\(372\) 0 0
\(373\) 29.1643 1.51007 0.755036 0.655683i \(-0.227619\pi\)
0.755036 + 0.655683i \(0.227619\pi\)
\(374\) 4.85669 8.41204i 0.251134 0.434976i
\(375\) 0 0
\(376\) 3.49381 + 6.05146i 0.180180 + 0.312080i
\(377\) 6.77747 0.349058
\(378\) 0 0
\(379\) −13.5622 −0.696645 −0.348322 0.937375i \(-0.613249\pi\)
−0.348322 + 0.937375i \(0.613249\pi\)
\(380\) 1.64400 + 2.84748i 0.0843352 + 0.146073i
\(381\) 0 0
\(382\) 8.16071 14.1348i 0.417538 0.723197i
\(383\) 2.83565 0.144895 0.0724475 0.997372i \(-0.476919\pi\)
0.0724475 + 0.997372i \(0.476919\pi\)
\(384\) 0 0
\(385\) 7.68037 + 12.2497i 0.391428 + 0.624300i
\(386\) 14.3214 0.728941
\(387\) 0 0
\(388\) −6.58836 11.4114i −0.334474 0.579325i
\(389\) 18.6080 0.943464 0.471732 0.881742i \(-0.343629\pi\)
0.471732 + 0.881742i \(0.343629\pi\)
\(390\) 0 0
\(391\) 20.6749 + 35.8099i 1.04557 + 1.81099i
\(392\) 3.04944 6.30087i 0.154020 0.318242i
\(393\) 0 0
\(394\) −1.21201 2.09926i −0.0610601 0.105759i
\(395\) 21.1847 + 36.6930i 1.06592 + 1.84622i
\(396\) 0 0
\(397\) −10.2880 + 17.8193i −0.516340 + 0.894326i 0.483481 + 0.875355i \(0.339372\pi\)
−0.999820 + 0.0189712i \(0.993961\pi\)
\(398\) 3.05563 5.29251i 0.153165 0.265290i
\(399\) 0 0
\(400\) −4.34362 7.52338i −0.217181 0.376169i
\(401\) 6.75409 0.337283 0.168642 0.985677i \(-0.446062\pi\)
0.168642 + 0.985677i \(0.446062\pi\)
\(402\) 0 0
\(403\) 18.3869 0.915916
\(404\) 2.62729 4.55059i 0.130712 0.226400i
\(405\) 0 0
\(406\) 3.52840 + 5.62755i 0.175112 + 0.279291i
\(407\) −2.05130 + 3.55296i −0.101679 + 0.176114i
\(408\) 0 0
\(409\) −7.66071 + 13.2687i −0.378798 + 0.656097i −0.990888 0.134691i \(-0.956996\pi\)
0.612090 + 0.790788i \(0.290329\pi\)
\(410\) 7.60507 13.1724i 0.375588 0.650537i
\(411\) 0 0
\(412\) −0.833104 + 1.44298i −0.0410441 + 0.0710904i
\(413\) −18.2694 + 0.665809i −0.898980 + 0.0327623i
\(414\) 0 0
\(415\) 8.28180 14.3445i 0.406538 0.704144i
\(416\) −2.69963 −0.132360
\(417\) 0 0
\(418\) −1.31275 −0.0642088
\(419\) 4.32141 + 7.48491i 0.211115 + 0.365662i 0.952064 0.305900i \(-0.0989573\pi\)
−0.740949 + 0.671561i \(0.765624\pi\)
\(420\) 0 0
\(421\) 18.5636 32.1531i 0.904735 1.56705i 0.0834618 0.996511i \(-0.473402\pi\)
0.821273 0.570536i \(-0.193264\pi\)
\(422\) −5.72253 + 9.91171i −0.278568 + 0.482494i
\(423\) 0 0
\(424\) −1.60507 2.78007i −0.0779493 0.135012i
\(425\) −28.5636 49.4736i −1.38554 2.39982i
\(426\) 0 0
\(427\) 7.10067 13.4036i 0.343625 0.648644i
\(428\) 5.38255 + 9.32284i 0.260175 + 0.450637i
\(429\) 0 0
\(430\) −0.0458003 −0.00220869
\(431\) 4.71015 + 8.15822i 0.226880 + 0.392967i 0.956882 0.290478i \(-0.0938142\pi\)
−0.730002 + 0.683445i \(0.760481\pi\)
\(432\) 0 0
\(433\) −0.208771 −0.0100329 −0.00501645 0.999987i \(-0.501597\pi\)
−0.00501645 + 0.999987i \(0.501597\pi\)
\(434\) 9.57234 + 15.2672i 0.459487 + 0.732850i
\(435\) 0 0
\(436\) 0.189108 0.00905662
\(437\) 2.79418 4.83967i 0.133664 0.231513i
\(438\) 0 0
\(439\) 4.98398 + 8.63250i 0.237872 + 0.412007i 0.960104 0.279645i \(-0.0902167\pi\)
−0.722231 + 0.691652i \(0.756883\pi\)
\(440\) 5.46472 0.260520
\(441\) 0 0
\(442\) −17.7527 −0.844410
\(443\) −7.84981 13.5963i −0.372956 0.645979i 0.617063 0.786914i \(-0.288322\pi\)
−0.990019 + 0.140935i \(0.954989\pi\)
\(444\) 0 0
\(445\) −16.4196 + 28.4396i −0.778364 + 1.34817i
\(446\) −7.22253 −0.341997
\(447\) 0 0
\(448\) −1.40545 2.24159i −0.0664011 0.105905i
\(449\) −33.6253 −1.58688 −0.793439 0.608650i \(-0.791712\pi\)
−0.793439 + 0.608650i \(0.791712\pi\)
\(450\) 0 0
\(451\) 3.03637 + 5.25915i 0.142977 + 0.247644i
\(452\) −13.5636 −0.637978
\(453\) 0 0
\(454\) −6.82760 11.8258i −0.320435 0.555010i
\(455\) 12.3702 23.3505i 0.579922 1.09469i
\(456\) 0 0
\(457\) −16.3541 28.3262i −0.765015 1.32504i −0.940239 0.340516i \(-0.889398\pi\)
0.175224 0.984529i \(-0.443935\pi\)
\(458\) 8.68725 + 15.0468i 0.405928 + 0.703089i
\(459\) 0 0
\(460\) −11.6316 + 20.1466i −0.542327 + 0.939338i
\(461\) 2.07165 3.58821i 0.0964865 0.167120i −0.813742 0.581227i \(-0.802573\pi\)
0.910228 + 0.414107i \(0.135906\pi\)
\(462\) 0 0
\(463\) −8.34176 14.4484i −0.387675 0.671472i 0.604462 0.796634i \(-0.293388\pi\)
−0.992136 + 0.125162i \(0.960055\pi\)
\(464\) 2.51052 0.116548
\(465\) 0 0
\(466\) −15.2422 −0.706081
\(467\) −14.9585 + 25.9089i −0.692198 + 1.19892i 0.278918 + 0.960315i \(0.410024\pi\)
−0.971116 + 0.238608i \(0.923309\pi\)
\(468\) 0 0
\(469\) −25.0247 + 0.911998i −1.15553 + 0.0421121i
\(470\) −12.9258 + 22.3881i −0.596223 + 1.03269i
\(471\) 0 0
\(472\) −3.45489 + 5.98404i −0.159024 + 0.275438i
\(473\) 0.00914304 0.0158362i 0.000420397 0.000728149i
\(474\) 0 0
\(475\) −3.86033 + 6.68630i −0.177124 + 0.306788i
\(476\) −9.24219 14.7407i −0.423615 0.675637i
\(477\) 0 0
\(478\) 9.47524 16.4116i 0.433387 0.750649i
\(479\) 2.95930 0.135214 0.0676068 0.997712i \(-0.478464\pi\)
0.0676068 + 0.997712i \(0.478464\pi\)
\(480\) 0 0
\(481\) 7.49814 0.341886
\(482\) −12.2527 21.2223i −0.558096 0.966650i
\(483\) 0 0
\(484\) 4.40909 7.63676i 0.200413 0.347126i
\(485\) 24.3745 42.2179i 1.10679 1.91701i
\(486\) 0 0
\(487\) −14.0309 24.3022i −0.635800 1.10124i −0.986345 0.164691i \(-0.947337\pi\)
0.350546 0.936546i \(-0.385996\pi\)
\(488\) −2.86652 4.96497i −0.129761 0.224753i
\(489\) 0 0
\(490\) 25.8287 1.88510i 1.16682 0.0851602i
\(491\) −17.0734 29.5721i −0.770513 1.33457i −0.937282 0.348572i \(-0.886667\pi\)
0.166769 0.985996i \(-0.446667\pi\)
\(492\) 0 0
\(493\) 16.5091 0.743534
\(494\) 1.19963 + 2.07782i 0.0539738 + 0.0934854i
\(495\) 0 0
\(496\) 6.81089 0.305818
\(497\) −7.68037 12.2497i −0.344512 0.549472i
\(498\) 0 0
\(499\) −2.28071 −0.102099 −0.0510493 0.998696i \(-0.516257\pi\)
−0.0510493 + 0.998696i \(0.516257\pi\)
\(500\) 6.82072 11.8138i 0.305032 0.528331i
\(501\) 0 0
\(502\) 6.06182 + 10.4994i 0.270552 + 0.468610i
\(503\) −13.9890 −0.623739 −0.311869 0.950125i \(-0.600955\pi\)
−0.311869 + 0.950125i \(0.600955\pi\)
\(504\) 0 0
\(505\) 19.4400 0.865067
\(506\) −4.64400 8.04364i −0.206451 0.357583i
\(507\) 0 0
\(508\) 1.42835 2.47397i 0.0633726 0.109765i
\(509\) −25.6181 −1.13550 −0.567750 0.823201i \(-0.692186\pi\)
−0.567750 + 0.823201i \(0.692186\pi\)
\(510\) 0 0
\(511\) −14.9437 + 28.2084i −0.661069 + 1.24787i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 4.10439 + 7.10900i 0.181037 + 0.313565i
\(515\) −6.16435 −0.271634
\(516\) 0 0
\(517\) −5.16071 8.93861i −0.226968 0.393119i
\(518\) 3.90359 + 6.22595i 0.171514 + 0.273553i
\(519\) 0 0
\(520\) −4.99381 8.64953i −0.218993 0.379307i
\(521\) 20.9127 + 36.2219i 0.916203 + 1.58691i 0.805130 + 0.593099i \(0.202096\pi\)
0.111073 + 0.993812i \(0.464571\pi\)
\(522\) 0 0
\(523\) 7.88323 13.6542i 0.344710 0.597055i −0.640591 0.767882i \(-0.721311\pi\)
0.985301 + 0.170827i \(0.0546440\pi\)
\(524\) 0.0778435 0.134829i 0.00340061 0.00589003i
\(525\) 0 0
\(526\) 2.67309 + 4.62992i 0.116552 + 0.201874i
\(527\) 44.7883 1.95101
\(528\) 0 0
\(529\) 16.5388 0.719080
\(530\) 5.93818 10.2852i 0.257938 0.446762i
\(531\) 0 0
\(532\) −1.10074 + 2.07782i −0.0477233 + 0.0900848i
\(533\) 5.54944 9.61192i 0.240373 0.416338i
\(534\) 0 0
\(535\) −19.9134 + 34.4911i −0.860932 + 1.49118i
\(536\) −4.73236 + 8.19669i −0.204407 + 0.354043i
\(537\) 0 0
\(538\) 9.24219 16.0079i 0.398459 0.690152i
\(539\) −4.50433 + 9.30701i −0.194015 + 0.400881i
\(540\) 0 0
\(541\) −21.0963 + 36.5399i −0.907002 + 1.57097i −0.0887957 + 0.996050i \(0.528302\pi\)
−0.818207 + 0.574924i \(0.805031\pi\)
\(542\) −7.35483 −0.315917
\(543\) 0 0
\(544\) −6.57598 −0.281943
\(545\) 0.349814 + 0.605896i 0.0149844 + 0.0259537i
\(546\) 0 0
\(547\) 20.3356 35.2222i 0.869486 1.50599i 0.00696400 0.999976i \(-0.497783\pi\)
0.862522 0.506019i \(-0.168883\pi\)
\(548\) −1.70582 + 2.95456i −0.0728689 + 0.126213i
\(549\) 0 0
\(550\) 6.41597 + 11.1128i 0.273578 + 0.473851i
\(551\) −1.11559 1.93227i −0.0475259 0.0823173i
\(552\) 0 0
\(553\) −14.1843 + 26.7750i −0.603178 + 1.13859i
\(554\) −4.54944 7.87987i −0.193287 0.334783i
\(555\) 0 0
\(556\) 13.5105 0.572974
\(557\) −6.68794 11.5838i −0.283377 0.490823i 0.688837 0.724916i \(-0.258121\pi\)
−0.972214 + 0.234093i \(0.924788\pi\)
\(558\) 0 0
\(559\) −0.0334206 −0.00141354
\(560\) 4.58217 8.64953i 0.193632 0.365509i
\(561\) 0 0
\(562\) −12.0087 −0.506555
\(563\) −16.3807 + 28.3722i −0.690364 + 1.19574i 0.281355 + 0.959604i \(0.409216\pi\)
−0.971719 + 0.236141i \(0.924117\pi\)
\(564\) 0 0
\(565\) −25.0901 43.4574i −1.05555 1.82827i
\(566\) −9.84294 −0.413729
\(567\) 0 0
\(568\) −5.46472 −0.229295
\(569\) −8.36398 14.4868i −0.350636 0.607320i 0.635725 0.771916i \(-0.280701\pi\)
−0.986361 + 0.164596i \(0.947368\pi\)
\(570\) 0 0
\(571\) 13.7367 23.7926i 0.574863 0.995691i −0.421194 0.906971i \(-0.638389\pi\)
0.996057 0.0887207i \(-0.0282778\pi\)
\(572\) 3.98762 0.166731
\(573\) 0 0
\(574\) 10.8702 0.396151i 0.453712 0.0165350i
\(575\) −54.6253 −2.27803
\(576\) 0 0
\(577\) 1.41714 + 2.45455i 0.0589962 + 0.102184i 0.894015 0.448037i \(-0.147877\pi\)
−0.835019 + 0.550221i \(0.814543\pi\)
\(578\) −26.2436 −1.09159
\(579\) 0 0
\(580\) 4.64400 + 8.04364i 0.192831 + 0.333994i
\(581\) 11.8374 0.431403i 0.491100 0.0178976i
\(582\) 0 0
\(583\) 2.37085 + 4.10644i 0.0981908 + 0.170071i
\(584\) 6.03273 + 10.4490i 0.249636 + 0.432383i
\(585\) 0 0
\(586\) 10.7101 18.5505i 0.442432 0.766315i
\(587\) 2.34795 4.06678i 0.0969105 0.167854i −0.813494 0.581573i \(-0.802437\pi\)
0.910404 + 0.413720i \(0.135771\pi\)
\(588\) 0 0
\(589\) −3.02654 5.24212i −0.124706 0.215998i
\(590\) −25.5636 −1.05244
\(591\) 0 0
\(592\) 2.77747 0.114153
\(593\) −0.636024 + 1.10163i −0.0261184 + 0.0452383i −0.878789 0.477210i \(-0.841648\pi\)
0.852671 + 0.522449i \(0.174981\pi\)
\(594\) 0 0
\(595\) 30.1323 56.8792i 1.23530 2.33182i
\(596\) 0.166896 0.289073i 0.00683634 0.0118409i
\(597\) 0 0
\(598\) −8.48762 + 14.7010i −0.347085 + 0.601168i
\(599\) 21.9258 37.9766i 0.895864 1.55168i 0.0631320 0.998005i \(-0.479891\pi\)
0.832732 0.553676i \(-0.186776\pi\)
\(600\) 0 0
\(601\) −6.71634 + 11.6330i −0.273965 + 0.474522i −0.969874 0.243609i \(-0.921669\pi\)
0.695908 + 0.718131i \(0.255002\pi\)
\(602\) −0.0173990 0.0277502i −0.000709131 0.00113101i
\(603\) 0 0
\(604\) 9.95489 17.2424i 0.405059 0.701582i
\(605\) 32.6240 1.32635
\(606\) 0 0
\(607\) −4.58465 −0.186085 −0.0930425 0.995662i \(-0.529659\pi\)
−0.0930425 + 0.995662i \(0.529659\pi\)
\(608\) 0.444368 + 0.769668i 0.0180215 + 0.0312142i
\(609\) 0 0
\(610\) 10.6051 18.3685i 0.429387 0.743720i
\(611\) −9.43199 + 16.3367i −0.381577 + 0.660911i
\(612\) 0 0
\(613\) −11.0538 19.1457i −0.446458 0.773287i 0.551695 0.834046i \(-0.313981\pi\)
−0.998152 + 0.0607587i \(0.980648\pi\)
\(614\) −2.84362 4.92530i −0.114759 0.198769i
\(615\) 0 0
\(616\) 2.07598 + 3.31105i 0.0836438 + 0.133406i
\(617\) −6.00433 10.3998i −0.241725 0.418680i 0.719481 0.694513i \(-0.244380\pi\)
−0.961206 + 0.275832i \(0.911047\pi\)
\(618\) 0 0
\(619\) −17.5636 −0.705941 −0.352970 0.935634i \(-0.614828\pi\)
−0.352970 + 0.935634i \(0.614828\pi\)
\(620\) 12.5989 + 21.8219i 0.505983 + 0.876389i
\(621\) 0 0
\(622\) −11.7207 −0.469956
\(623\) −23.4691 + 0.855304i −0.940268 + 0.0342670i
\(624\) 0 0
\(625\) 7.03204 0.281282
\(626\) −13.3869 + 23.1868i −0.535047 + 0.926729i
\(627\) 0 0
\(628\) 3.48143 + 6.03001i 0.138924 + 0.240624i
\(629\) 18.2646 0.728258
\(630\) 0 0
\(631\) −44.9381 −1.78896 −0.894479 0.447110i \(-0.852453\pi\)
−0.894479 + 0.447110i \(0.852453\pi\)
\(632\) 5.72617 + 9.91802i 0.227775 + 0.394518i
\(633\) 0 0
\(634\) −0.951246 + 1.64761i −0.0377788 + 0.0654348i
\(635\) 10.5687 0.419406
\(636\) 0 0
\(637\) 18.8473 1.37556i 0.746756 0.0545018i
\(638\) −3.70829 −0.146813
\(639\) 0 0
\(640\) −1.84981 3.20397i −0.0731203 0.126648i
\(641\) 28.9839 1.14480 0.572398 0.819976i \(-0.306013\pi\)
0.572398 + 0.819976i \(0.306013\pi\)
\(642\) 0 0
\(643\) 6.03087 + 10.4458i 0.237834 + 0.411941i 0.960093 0.279682i \(-0.0902291\pi\)
−0.722258 + 0.691623i \(0.756896\pi\)
\(644\) −16.6254 + 0.605896i −0.655134 + 0.0238756i
\(645\) 0 0
\(646\) 2.92216 + 5.06132i 0.114971 + 0.199135i
\(647\) −18.8825 32.7055i −0.742349 1.28579i −0.951423 0.307887i \(-0.900378\pi\)
0.209073 0.977900i \(-0.432955\pi\)
\(648\) 0 0
\(649\) 5.10322 8.83903i 0.200319 0.346962i
\(650\) 11.7262 20.3103i 0.459938 0.796636i
\(651\) 0 0
\(652\) 4.03706 + 6.99240i 0.158104 + 0.273843i
\(653\) −37.4079 −1.46388 −0.731942 0.681366i \(-0.761386\pi\)
−0.731942 + 0.681366i \(0.761386\pi\)
\(654\) 0 0
\(655\) 0.575984 0.0225056
\(656\) 2.05563 3.56046i 0.0802589 0.139013i
\(657\) 0 0
\(658\) −18.4752 + 0.673310i −0.720240 + 0.0262484i
\(659\) −14.9356 + 25.8693i −0.581810 + 1.00772i 0.413455 + 0.910524i \(0.364322\pi\)
−0.995265 + 0.0971993i \(0.969012\pi\)
\(660\) 0 0
\(661\) −2.80401 + 4.85669i −0.109063 + 0.188904i −0.915391 0.402566i \(-0.868119\pi\)
0.806328 + 0.591469i \(0.201452\pi\)
\(662\) 2.78366 4.82144i 0.108190 0.187391i
\(663\) 0 0
\(664\) 2.23855 3.87728i 0.0868726 0.150468i
\(665\) −8.69344 + 0.316823i −0.337117 + 0.0122859i
\(666\) 0 0
\(667\) 7.89307 13.6712i 0.305621 0.529351i
\(668\) 19.4858 0.753927
\(669\) 0 0
\(670\) −35.0159 −1.35278
\(671\) 4.23414 + 7.33375i 0.163457 + 0.283116i
\(672\) 0 0
\(673\) −4.72253 + 8.17966i −0.182040 + 0.315303i −0.942575 0.333994i \(-0.891603\pi\)
0.760535 + 0.649297i \(0.224937\pi\)
\(674\) 16.8869 29.2489i 0.650458 1.12663i
\(675\) 0 0
\(676\) 2.85600 + 4.94674i 0.109846 + 0.190259i
\(677\) 5.53087 + 9.57975i 0.212569 + 0.368180i 0.952518 0.304483i \(-0.0984837\pi\)
−0.739949 + 0.672663i \(0.765150\pi\)
\(678\) 0 0
\(679\) 34.8392 1.26968i 1.33701 0.0487258i
\(680\) −12.1643 21.0693i −0.466481 0.807970i
\(681\) 0 0
\(682\) −10.0604 −0.385231
\(683\) 4.41961 + 7.65499i 0.169112 + 0.292910i 0.938108 0.346343i \(-0.112577\pi\)
−0.768996 + 0.639253i \(0.779243\pi\)
\(684\) 0 0
\(685\) −12.6218 −0.482254
\(686\) 10.9542 + 14.9334i 0.418233 + 0.570159i
\(687\) 0 0
\(688\) −0.0123797 −0.000471972
\(689\) 4.33310 7.50516i 0.165078 0.285924i
\(690\) 0 0
\(691\) −12.5309 21.7041i −0.476697 0.825663i 0.522947 0.852365i \(-0.324833\pi\)
−0.999643 + 0.0267023i \(0.991499\pi\)
\(692\) −22.5636 −0.857740
\(693\) 0 0
\(694\) −30.4065 −1.15422
\(695\) 24.9920 + 43.2873i 0.947999 + 1.64198i
\(696\) 0 0
\(697\) 13.5178 23.4135i 0.512023 0.886850i
\(698\) −12.5956 −0.476752
\(699\) 0 0
\(700\) 22.9691 0.837082i 0.868149 0.0316387i
\(701\) 43.4858 1.64243 0.821217 0.570616i \(-0.193295\pi\)
0.821217 + 0.570616i \(0.193295\pi\)
\(702\) 0 0
\(703\) −1.23422 2.13773i −0.0465495 0.0806260i
\(704\) 1.47710 0.0556703
\(705\) 0 0
\(706\) 3.76578 + 6.52252i 0.141727 + 0.245478i
\(707\) 7.38502 + 11.7786i 0.277742 + 0.442979i
\(708\) 0 0
\(709\) 11.3702 + 19.6937i 0.427016 + 0.739613i 0.996606 0.0823158i \(-0.0262316\pi\)
−0.569591 + 0.821928i \(0.692898\pi\)
\(710\) −10.1087 17.5088i −0.379373 0.657094i
\(711\) 0 0
\(712\) −4.43818 + 7.68715i −0.166328 + 0.288088i
\(713\) 21.4134 37.0891i 0.801939 1.38900i
\(714\) 0 0
\(715\) 7.37636 + 12.7762i 0.275860 + 0.477804i
\(716\) 0.333792 0.0124744
\(717\) 0 0
\(718\) 6.89602 0.257357
\(719\) −6.06182 + 10.4994i −0.226068 + 0.391561i −0.956639 0.291275i \(-0.905920\pi\)
0.730571 + 0.682836i \(0.239254\pi\)
\(720\) 0 0
\(721\) −2.34176 3.73495i −0.0872119 0.139097i
\(722\) −9.10507 + 15.7705i −0.338856 + 0.586915i
\(723\) 0 0
\(724\) −11.6211 + 20.1283i −0.431895 + 0.748063i
\(725\) −10.9048 + 18.8876i −0.404993 + 0.701468i
\(726\) 0 0
\(727\) 23.0908 39.9945i 0.856392 1.48331i −0.0189562 0.999820i \(-0.506034\pi\)
0.875348 0.483494i \(-0.160632\pi\)
\(728\) 3.34362 6.31159i 0.123923 0.233923i
\(729\) 0 0
\(730\) −22.3189 + 38.6574i −0.826058 + 1.43077i
\(731\) −0.0814088 −0.00301101
\(732\) 0 0
\(733\) −36.0297 −1.33079 −0.665394 0.746493i \(-0.731736\pi\)
−0.665394 + 0.746493i \(0.731736\pi\)
\(734\) 11.5618 + 20.0257i 0.426755 + 0.739161i
\(735\) 0 0
\(736\) −3.14400 + 5.44556i −0.115889 + 0.200726i
\(737\) 6.99017 12.1073i 0.257486 0.445979i
\(738\) 0 0
\(739\) 23.2119 + 40.2042i 0.853865 + 1.47894i 0.877694 + 0.479221i \(0.159081\pi\)
−0.0238296 + 0.999716i \(0.507586\pi\)
\(740\) 5.13781 + 8.89894i 0.188870 + 0.327132i
\(741\) 0 0
\(742\) 8.48762 0.309322i 0.311590 0.0113556i
\(743\) −0.598884 1.03730i −0.0219709 0.0380548i 0.854831 0.518907i \(-0.173661\pi\)
−0.876802 + 0.480852i \(0.840327\pi\)
\(744\) 0 0
\(745\) 1.23491 0.0452435
\(746\) 14.5822 + 25.2571i 0.533891 + 0.924727i
\(747\) 0 0
\(748\) 9.71339 0.355157
\(749\) −28.4629 + 1.03730i −1.04001 + 0.0379021i
\(750\) 0 0
\(751\) 48.1199 1.75592 0.877961 0.478733i \(-0.158904\pi\)
0.877961 + 0.478733i \(0.158904\pi\)
\(752\) −3.49381 + 6.05146i −0.127406 + 0.220674i
\(753\) 0 0
\(754\) 3.38874 + 5.86946i 0.123410 + 0.213753i
\(755\) 73.6588 2.68072
\(756\) 0 0
\(757\) 49.6006 1.80276 0.901382 0.433025i \(-0.142554\pi\)
0.901382 + 0.433025i \(0.142554\pi\)
\(758\) −6.78111 11.7452i −0.246301 0.426606i
\(759\) 0 0
\(760\) −1.64400 + 2.84748i −0.0596340 + 0.103289i
\(761\) 37.5402 1.36083 0.680416 0.732826i \(-0.261799\pi\)
0.680416 + 0.732826i \(0.261799\pi\)
\(762\) 0 0
\(763\) −0.234219 + 0.442124i −0.00847931 + 0.0160060i
\(764\) 16.3214 0.590488
\(765\) 0 0
\(766\) 1.41783 + 2.45575i 0.0512281 + 0.0887297i
\(767\) −18.6538 −0.673551
\(768\) 0 0
\(769\) −13.4592 23.3121i −0.485352 0.840654i 0.514506 0.857486i \(-0.327975\pi\)
−0.999858 + 0.0168324i \(0.994642\pi\)
\(770\) −6.76833 + 12.7762i −0.243914 + 0.460423i
\(771\) 0 0
\(772\) 7.16071 + 12.4027i 0.257719 + 0.446383i
\(773\) −25.1130 43.4971i −0.903254 1.56448i −0.823245 0.567687i \(-0.807838\pi\)
−0.0800089 0.996794i \(-0.525495\pi\)
\(774\) 0 0
\(775\) −29.5840 + 51.2409i −1.06269 + 1.84063i
\(776\) 6.58836 11.4114i 0.236508 0.409645i
\(777\) 0 0
\(778\) 9.30401 + 16.1150i 0.333565 + 0.577752i
\(779\) −3.65383 −0.130912
\(780\) 0 0
\(781\) 8.07194 0.288837
\(782\) −20.6749 + 35.8099i −0.739332 + 1.28056i