Properties

Label 729.2.g.d.676.1
Level $729$
Weight $2$
Character 729.676
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), 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: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 676.1
Character \(\chi\) \(=\) 729.676
Dual form 729.2.g.d.55.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.971435 - 2.25204i) q^{2} +(-2.75551 + 2.92067i) q^{4} +(0.232513 - 3.99210i) q^{5} +(-1.28109 + 0.303625i) q^{7} +(4.64483 + 1.69058i) q^{8} +O(q^{10})\) \(q+(-0.971435 - 2.25204i) q^{2} +(-2.75551 + 2.92067i) q^{4} +(0.232513 - 3.99210i) q^{5} +(-1.28109 + 0.303625i) q^{7} +(4.64483 + 1.69058i) q^{8} +(-9.21624 + 3.35444i) q^{10} +(-2.04879 + 1.34751i) q^{11} +(-1.30311 + 0.152312i) q^{13} +(1.92827 + 2.59012i) q^{14} +(-0.237953 - 4.08549i) q^{16} +(0.206593 + 0.173352i) q^{17} +(1.02778 - 0.862409i) q^{19} +(11.0189 + 11.6794i) q^{20} +(5.02492 + 3.30494i) q^{22} +(-5.82111 - 1.37963i) q^{23} +(-10.9166 - 1.27597i) q^{25} +(1.60890 + 2.78670i) q^{26} +(2.64328 - 4.57830i) q^{28} +(-3.30965 + 4.44563i) q^{29} +(0.369677 + 1.23481i) q^{31} +(-0.135207 + 0.0679036i) q^{32} +(0.189704 - 0.633655i) q^{34} +(0.914230 + 5.18486i) q^{35} +(-0.00841562 + 0.0477273i) q^{37} +(-2.94060 - 1.47682i) q^{38} +(7.82896 - 18.1496i) q^{40} +(1.64212 - 3.80687i) q^{41} +(5.59352 + 2.80917i) q^{43} +(1.70983 - 9.69693i) q^{44} +(2.54785 + 14.4496i) q^{46} +(2.38036 - 7.95094i) q^{47} +(-4.70641 + 2.36365i) q^{49} +(7.73125 + 25.8242i) q^{50} +(3.14588 - 4.22565i) q^{52} +(-5.79529 + 10.0377i) q^{53} +(4.90304 + 8.49231i) q^{55} +(-6.46377 - 0.755507i) q^{56} +(13.2268 + 3.13482i) q^{58} +(8.15031 + 5.36055i) q^{59} +(2.93311 + 3.10891i) q^{61} +(2.42172 - 2.03206i) q^{62} +(-5.98568 - 5.02258i) q^{64} +(0.305054 + 5.23757i) q^{65} +(-0.791752 - 1.06351i) q^{67} +(-1.07557 + 0.125716i) q^{68} +(10.7884 - 7.09563i) q^{70} +(7.40721 - 2.69600i) q^{71} +(-8.12155 - 2.95600i) q^{73} +(0.115659 - 0.0274117i) q^{74} +(-0.313243 + 5.37818i) q^{76} +(2.21556 - 2.34836i) q^{77} +(2.07109 + 4.80133i) q^{79} -16.3650 q^{80} -10.1684 q^{82} +(-2.24944 - 5.21479i) q^{83} +(0.740074 - 0.784433i) q^{85} +(0.892623 - 15.3257i) q^{86} +(-11.7944 + 2.79532i) q^{88} +(-8.61170 - 3.13440i) q^{89} +(1.62316 - 0.590783i) q^{91} +(20.0696 - 13.2000i) q^{92} +(-20.2182 + 2.36317i) q^{94} +(-3.20385 - 4.30352i) q^{95} +(-0.721447 - 12.3868i) q^{97} +(9.89500 + 8.30289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} + 45 q^{20} + 9 q^{22} - 45 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} + 36 q^{29} + 9 q^{31} - 99 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} + 18 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} - 99 q^{47} + 9 q^{49} + 126 q^{50} - 27 q^{52} + 45 q^{53} - 9 q^{55} - 225 q^{56} + 9 q^{58} + 72 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} - 81 q^{65} - 45 q^{67} + 117 q^{68} - 99 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} - 153 q^{76} + 81 q^{77} - 99 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} - 99 q^{85} + 81 q^{86} - 153 q^{88} - 81 q^{89} - 18 q^{91} + 207 q^{92} - 99 q^{94} - 171 q^{95} - 45 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{10}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.971435 2.25204i −0.686908 1.59243i −0.800795 0.598938i \(-0.795590\pi\)
0.113887 0.993494i \(-0.463670\pi\)
\(3\) 0 0
\(4\) −2.75551 + 2.92067i −1.37775 + 1.46033i
\(5\) 0.232513 3.99210i 0.103983 1.78532i −0.394971 0.918694i \(-0.629245\pi\)
0.498954 0.866629i \(-0.333718\pi\)
\(6\) 0 0
\(7\) −1.28109 + 0.303625i −0.484208 + 0.114759i −0.465468 0.885065i \(-0.654114\pi\)
−0.0187406 + 0.999824i \(0.505966\pi\)
\(8\) 4.64483 + 1.69058i 1.64220 + 0.597711i
\(9\) 0 0
\(10\) −9.21624 + 3.35444i −2.91443 + 1.06077i
\(11\) −2.04879 + 1.34751i −0.617734 + 0.406290i −0.819447 0.573154i \(-0.805720\pi\)
0.201713 + 0.979445i \(0.435349\pi\)
\(12\) 0 0
\(13\) −1.30311 + 0.152312i −0.361418 + 0.0422437i −0.294864 0.955539i \(-0.595274\pi\)
−0.0665537 + 0.997783i \(0.521200\pi\)
\(14\) 1.92827 + 2.59012i 0.515353 + 0.692239i
\(15\) 0 0
\(16\) −0.237953 4.08549i −0.0594882 1.02137i
\(17\) 0.206593 + 0.173352i 0.0501061 + 0.0420440i 0.667497 0.744613i \(-0.267366\pi\)
−0.617391 + 0.786657i \(0.711810\pi\)
\(18\) 0 0
\(19\) 1.02778 0.862409i 0.235789 0.197850i −0.517235 0.855843i \(-0.673039\pi\)
0.753024 + 0.657993i \(0.228594\pi\)
\(20\) 11.0189 + 11.6794i 2.46390 + 2.61159i
\(21\) 0 0
\(22\) 5.02492 + 3.30494i 1.07132 + 0.704616i
\(23\) −5.82111 1.37963i −1.21379 0.287673i −0.426630 0.904426i \(-0.640299\pi\)
−0.787156 + 0.616754i \(0.788447\pi\)
\(24\) 0 0
\(25\) −10.9166 1.27597i −2.18333 0.255194i
\(26\) 1.60890 + 2.78670i 0.315531 + 0.546516i
\(27\) 0 0
\(28\) 2.64328 4.57830i 0.499533 0.865216i
\(29\) −3.30965 + 4.44563i −0.614587 + 0.825533i −0.995062 0.0992581i \(-0.968353\pi\)
0.380475 + 0.924791i \(0.375760\pi\)
\(30\) 0 0
\(31\) 0.369677 + 1.23481i 0.0663960 + 0.221778i 0.984748 0.173986i \(-0.0556649\pi\)
−0.918352 + 0.395764i \(0.870480\pi\)
\(32\) −0.135207 + 0.0679036i −0.0239015 + 0.0120038i
\(33\) 0 0
\(34\) 0.189704 0.633655i 0.0325339 0.108671i
\(35\) 0.914230 + 5.18486i 0.154533 + 0.876401i
\(36\) 0 0
\(37\) −0.00841562 + 0.0477273i −0.00138352 + 0.00784632i −0.985492 0.169724i \(-0.945712\pi\)
0.984108 + 0.177570i \(0.0568236\pi\)
\(38\) −2.94060 1.47682i −0.477028 0.239572i
\(39\) 0 0
\(40\) 7.82896 18.1496i 1.23787 2.86970i
\(41\) 1.64212 3.80687i 0.256456 0.594533i −0.740537 0.672015i \(-0.765429\pi\)
0.996994 + 0.0774824i \(0.0246882\pi\)
\(42\) 0 0
\(43\) 5.59352 + 2.80917i 0.853003 + 0.428394i 0.820888 0.571090i \(-0.193479\pi\)
0.0321157 + 0.999484i \(0.489775\pi\)
\(44\) 1.70983 9.69693i 0.257767 1.46187i
\(45\) 0 0
\(46\) 2.54785 + 14.4496i 0.375660 + 2.13048i
\(47\) 2.38036 7.95094i 0.347210 1.15976i −0.588944 0.808174i \(-0.700456\pi\)
0.936154 0.351590i \(-0.114359\pi\)
\(48\) 0 0
\(49\) −4.70641 + 2.36365i −0.672345 + 0.337664i
\(50\) 7.73125 + 25.8242i 1.09336 + 3.65209i
\(51\) 0 0
\(52\) 3.14588 4.22565i 0.436256 0.585993i
\(53\) −5.79529 + 10.0377i −0.796044 + 1.37879i 0.126130 + 0.992014i \(0.459744\pi\)
−0.922174 + 0.386775i \(0.873589\pi\)
\(54\) 0 0
\(55\) 4.90304 + 8.49231i 0.661125 + 1.14510i
\(56\) −6.46377 0.755507i −0.863758 0.100959i
\(57\) 0 0
\(58\) 13.2268 + 3.13482i 1.73677 + 0.411622i
\(59\) 8.15031 + 5.36055i 1.06108 + 0.697884i 0.955040 0.296478i \(-0.0958122\pi\)
0.106041 + 0.994362i \(0.466183\pi\)
\(60\) 0 0
\(61\) 2.93311 + 3.10891i 0.375546 + 0.398055i 0.887387 0.461025i \(-0.152518\pi\)
−0.511842 + 0.859080i \(0.671037\pi\)
\(62\) 2.42172 2.03206i 0.307558 0.258072i
\(63\) 0 0
\(64\) −5.98568 5.02258i −0.748210 0.627823i
\(65\) 0.305054 + 5.23757i 0.0378372 + 0.649640i
\(66\) 0 0
\(67\) −0.791752 1.06351i −0.0967278 0.129928i 0.751124 0.660161i \(-0.229512\pi\)
−0.847852 + 0.530233i \(0.822105\pi\)
\(68\) −1.07557 + 0.125716i −0.130432 + 0.0152453i
\(69\) 0 0
\(70\) 10.7884 7.09563i 1.28946 0.848090i
\(71\) 7.40721 2.69600i 0.879074 0.319957i 0.137238 0.990538i \(-0.456177\pi\)
0.741836 + 0.670581i \(0.233955\pi\)
\(72\) 0 0
\(73\) −8.12155 2.95600i −0.950556 0.345974i −0.180230 0.983624i \(-0.557684\pi\)
−0.770326 + 0.637650i \(0.779906\pi\)
\(74\) 0.115659 0.0274117i 0.0134451 0.00318654i
\(75\) 0 0
\(76\) −0.313243 + 5.37818i −0.0359315 + 0.616919i
\(77\) 2.21556 2.34836i 0.252486 0.267620i
\(78\) 0 0
\(79\) 2.07109 + 4.80133i 0.233016 + 0.540192i 0.994101 0.108460i \(-0.0345921\pi\)
−0.761085 + 0.648653i \(0.775333\pi\)
\(80\) −16.3650 −1.82967
\(81\) 0 0
\(82\) −10.1684 −1.12291
\(83\) −2.24944 5.21479i −0.246908 0.572398i 0.749020 0.662548i \(-0.230525\pi\)
−0.995928 + 0.0901496i \(0.971265\pi\)
\(84\) 0 0
\(85\) 0.740074 0.784433i 0.0802723 0.0850837i
\(86\) 0.892623 15.3257i 0.0962540 1.65262i
\(87\) 0 0
\(88\) −11.7944 + 2.79532i −1.25729 + 0.297982i
\(89\) −8.61170 3.13440i −0.912838 0.332246i −0.157453 0.987527i \(-0.550328\pi\)
−0.755385 + 0.655281i \(0.772550\pi\)
\(90\) 0 0
\(91\) 1.62316 0.590783i 0.170154 0.0619309i
\(92\) 20.0696 13.2000i 2.09240 1.37619i
\(93\) 0 0
\(94\) −20.2182 + 2.36317i −2.08535 + 0.243742i
\(95\) −3.20385 4.30352i −0.328708 0.441532i
\(96\) 0 0
\(97\) −0.721447 12.3868i −0.0732518 1.25769i −0.811981 0.583684i \(-0.801611\pi\)
0.738729 0.674002i \(-0.235426\pi\)
\(98\) 9.89500 + 8.30289i 0.999546 + 0.838719i
\(99\) 0 0
\(100\) 33.8076 28.3679i 3.38076 2.83679i
\(101\) −8.54489 9.05705i −0.850248 0.901211i 0.145864 0.989305i \(-0.453404\pi\)
−0.996112 + 0.0880941i \(0.971922\pi\)
\(102\) 0 0
\(103\) 5.22232 + 3.43478i 0.514571 + 0.338439i 0.780090 0.625667i \(-0.215173\pi\)
−0.265519 + 0.964106i \(0.585543\pi\)
\(104\) −6.31023 1.49555i −0.618769 0.146651i
\(105\) 0 0
\(106\) 28.2351 + 3.30021i 2.74244 + 0.320545i
\(107\) −9.92075 17.1832i −0.959075 1.66117i −0.724755 0.689007i \(-0.758047\pi\)
−0.234320 0.972159i \(-0.575286\pi\)
\(108\) 0 0
\(109\) −1.91684 + 3.32007i −0.183600 + 0.318005i −0.943104 0.332498i \(-0.892109\pi\)
0.759504 + 0.650503i \(0.225442\pi\)
\(110\) 14.3620 19.2915i 1.36937 1.83938i
\(111\) 0 0
\(112\) 1.54530 + 5.16165i 0.146017 + 0.487730i
\(113\) −3.11864 + 1.56624i −0.293377 + 0.147339i −0.589400 0.807841i \(-0.700636\pi\)
0.296023 + 0.955181i \(0.404339\pi\)
\(114\) 0 0
\(115\) −6.86111 + 22.9177i −0.639802 + 2.13709i
\(116\) −3.86445 21.9164i −0.358805 2.03488i
\(117\) 0 0
\(118\) 4.15466 23.5622i 0.382467 2.16908i
\(119\) −0.317299 0.159353i −0.0290867 0.0146079i
\(120\) 0 0
\(121\) −1.97511 + 4.57883i −0.179556 + 0.416257i
\(122\) 4.15207 9.62557i 0.375910 0.871458i
\(123\) 0 0
\(124\) −4.62511 2.32282i −0.415347 0.208595i
\(125\) −4.16009 + 23.5930i −0.372090 + 2.11022i
\(126\) 0 0
\(127\) 2.28154 + 12.9392i 0.202454 + 1.14817i 0.901397 + 0.432994i \(0.142543\pi\)
−0.698943 + 0.715177i \(0.746346\pi\)
\(128\) −5.58314 + 18.6490i −0.493484 + 1.64835i
\(129\) 0 0
\(130\) 11.4989 5.77495i 1.00852 0.506496i
\(131\) 1.24215 + 4.14908i 0.108528 + 0.362507i 0.994950 0.100369i \(-0.0320025\pi\)
−0.886423 + 0.462877i \(0.846817\pi\)
\(132\) 0 0
\(133\) −1.05483 + 1.41689i −0.0914656 + 0.122860i
\(134\) −1.62592 + 2.81618i −0.140458 + 0.243281i
\(135\) 0 0
\(136\) 0.666523 + 1.15445i 0.0571539 + 0.0989935i
\(137\) −22.2688 2.60285i −1.90255 0.222376i −0.917887 0.396841i \(-0.870106\pi\)
−0.984663 + 0.174465i \(0.944180\pi\)
\(138\) 0 0
\(139\) −9.34045 2.21373i −0.792247 0.187766i −0.185482 0.982648i \(-0.559385\pi\)
−0.606765 + 0.794882i \(0.707533\pi\)
\(140\) −17.6624 11.6168i −1.49275 0.981795i
\(141\) 0 0
\(142\) −13.2671 14.0623i −1.11335 1.18008i
\(143\) 2.46456 2.06801i 0.206097 0.172936i
\(144\) 0 0
\(145\) 16.9779 + 14.2461i 1.40994 + 1.18308i
\(146\) 1.23252 + 21.1616i 0.102004 + 1.75135i
\(147\) 0 0
\(148\) −0.116206 0.156092i −0.00955211 0.0128307i
\(149\) −16.5311 + 1.93221i −1.35428 + 0.158293i −0.762071 0.647493i \(-0.775818\pi\)
−0.592208 + 0.805785i \(0.701743\pi\)
\(150\) 0 0
\(151\) 1.53093 1.00691i 0.124585 0.0819412i −0.485687 0.874133i \(-0.661430\pi\)
0.610272 + 0.792192i \(0.291060\pi\)
\(152\) 6.23183 2.26820i 0.505468 0.183975i
\(153\) 0 0
\(154\) −7.44086 2.70825i −0.599601 0.218237i
\(155\) 5.01543 1.18868i 0.402849 0.0954770i
\(156\) 0 0
\(157\) 0.628412 10.7894i 0.0501528 0.861090i −0.875618 0.483004i \(-0.839546\pi\)
0.925771 0.378085i \(-0.123417\pi\)
\(158\) 8.80086 9.32836i 0.700159 0.742125i
\(159\) 0 0
\(160\) 0.239641 + 0.555549i 0.0189453 + 0.0439200i
\(161\) 7.87629 0.620738
\(162\) 0 0
\(163\) 3.76716 0.295067 0.147533 0.989057i \(-0.452867\pi\)
0.147533 + 0.989057i \(0.452867\pi\)
\(164\) 6.59372 + 15.2860i 0.514883 + 1.19363i
\(165\) 0 0
\(166\) −9.55873 + 10.1317i −0.741901 + 0.786369i
\(167\) −0.688138 + 11.8149i −0.0532498 + 0.914263i 0.860872 + 0.508822i \(0.169919\pi\)
−0.914121 + 0.405441i \(0.867118\pi\)
\(168\) 0 0
\(169\) −10.9747 + 2.60105i −0.844206 + 0.200081i
\(170\) −2.48551 0.904650i −0.190630 0.0693835i
\(171\) 0 0
\(172\) −23.6176 + 8.59612i −1.80083 + 0.655448i
\(173\) 7.99384 5.25763i 0.607761 0.399730i −0.207993 0.978130i \(-0.566693\pi\)
0.815753 + 0.578400i \(0.196323\pi\)
\(174\) 0 0
\(175\) 14.3726 1.67992i 1.08647 0.126990i
\(176\) 5.99277 + 8.04968i 0.451722 + 0.606768i
\(177\) 0 0
\(178\) 1.30691 + 22.4387i 0.0979569 + 1.68185i
\(179\) −1.08723 0.912294i −0.0812633 0.0681880i 0.601251 0.799060i \(-0.294669\pi\)
−0.682514 + 0.730872i \(0.739114\pi\)
\(180\) 0 0
\(181\) −7.58350 + 6.36331i −0.563677 + 0.472981i −0.879541 0.475823i \(-0.842150\pi\)
0.315864 + 0.948804i \(0.397706\pi\)
\(182\) −2.90726 3.08152i −0.215501 0.228417i
\(183\) 0 0
\(184\) −24.7057 16.2492i −1.82133 1.19791i
\(185\) 0.188576 + 0.0446932i 0.0138644 + 0.00328591i
\(186\) 0 0
\(187\) −0.656860 0.0767759i −0.0480343 0.00561441i
\(188\) 16.6630 + 28.8611i 1.21527 + 2.10491i
\(189\) 0 0
\(190\) −6.57936 + 11.3958i −0.477317 + 0.826737i
\(191\) −10.6439 + 14.2973i −0.770166 + 1.03451i 0.227981 + 0.973666i \(0.426788\pi\)
−0.998147 + 0.0608474i \(0.980620\pi\)
\(192\) 0 0
\(193\) −7.92466 26.4702i −0.570430 1.90537i −0.385897 0.922542i \(-0.626108\pi\)
−0.184533 0.982826i \(-0.559077\pi\)
\(194\) −27.1946 + 13.6577i −1.95246 + 0.980563i
\(195\) 0 0
\(196\) 6.06513 20.2589i 0.433223 1.44707i
\(197\) −1.04040 5.90042i −0.0741256 0.420387i −0.999178 0.0405468i \(-0.987090\pi\)
0.925052 0.379840i \(-0.124021\pi\)
\(198\) 0 0
\(199\) 2.78863 15.8151i 0.197681 1.12110i −0.710868 0.703326i \(-0.751698\pi\)
0.908549 0.417779i \(-0.137191\pi\)
\(200\) −48.5488 24.3821i −3.43292 1.72408i
\(201\) 0 0
\(202\) −12.0960 + 28.0418i −0.851074 + 1.97301i
\(203\) 2.89017 6.70017i 0.202850 0.470260i
\(204\) 0 0
\(205\) −14.8156 7.44067i −1.03477 0.519679i
\(206\) 2.66210 15.0975i 0.185478 1.05190i
\(207\) 0 0
\(208\) 0.932348 + 5.28761i 0.0646467 + 0.366630i
\(209\) −0.943600 + 3.15184i −0.0652701 + 0.218017i
\(210\) 0 0
\(211\) −9.00002 + 4.51998i −0.619587 + 0.311168i −0.730762 0.682633i \(-0.760835\pi\)
0.111175 + 0.993801i \(0.464539\pi\)
\(212\) −13.3479 44.5852i −0.916740 3.06212i
\(213\) 0 0
\(214\) −29.0600 + 39.0343i −1.98650 + 2.66833i
\(215\) 12.5151 21.6767i 0.853520 1.47834i
\(216\) 0 0
\(217\) −0.848510 1.46966i −0.0576006 0.0997672i
\(218\) 9.33901 + 1.09157i 0.632518 + 0.0739307i
\(219\) 0 0
\(220\) −38.3136 9.08049i −2.58310 0.612206i
\(221\) −0.295617 0.194430i −0.0198853 0.0130788i
\(222\) 0 0
\(223\) 8.95026 + 9.48672i 0.599354 + 0.635278i 0.954030 0.299711i \(-0.0968903\pi\)
−0.354676 + 0.934989i \(0.615409\pi\)
\(224\) 0.152596 0.128043i 0.0101957 0.00855525i
\(225\) 0 0
\(226\) 6.55678 + 5.50179i 0.436151 + 0.365974i
\(227\) −0.947304 16.2646i −0.0628748 1.07952i −0.871246 0.490846i \(-0.836688\pi\)
0.808372 0.588673i \(-0.200349\pi\)
\(228\) 0 0
\(229\) −4.02339 5.40434i −0.265873 0.357129i 0.649059 0.760738i \(-0.275163\pi\)
−0.914931 + 0.403609i \(0.867756\pi\)
\(230\) 58.2767 6.81156i 3.84265 0.449141i
\(231\) 0 0
\(232\) −22.8885 + 15.0540i −1.50270 + 0.988343i
\(233\) −12.9692 + 4.72040i −0.849641 + 0.309244i −0.729894 0.683560i \(-0.760431\pi\)
−0.119747 + 0.992804i \(0.538208\pi\)
\(234\) 0 0
\(235\) −31.1875 11.3513i −2.03445 0.740479i
\(236\) −38.1147 + 9.03334i −2.48105 + 0.588020i
\(237\) 0 0
\(238\) −0.0506351 + 0.869371i −0.00328218 + 0.0563529i
\(239\) −8.60415 + 9.11986i −0.556556 + 0.589915i −0.943163 0.332330i \(-0.892165\pi\)
0.386607 + 0.922244i \(0.373647\pi\)
\(240\) 0 0
\(241\) 5.42266 + 12.5711i 0.349304 + 0.809778i 0.998779 + 0.0493949i \(0.0157293\pi\)
−0.649475 + 0.760383i \(0.725011\pi\)
\(242\) 12.2304 0.786199
\(243\) 0 0
\(244\) −17.1623 −1.09870
\(245\) 8.34163 + 19.3381i 0.532927 + 1.23546i
\(246\) 0 0
\(247\) −1.20796 + 1.28036i −0.0768604 + 0.0814672i
\(248\) −0.370454 + 6.36044i −0.0235238 + 0.403889i
\(249\) 0 0
\(250\) 57.1737 13.5504i 3.61598 0.857003i
\(251\) −12.4879 4.54521i −0.788226 0.286891i −0.0836277 0.996497i \(-0.526651\pi\)
−0.704599 + 0.709606i \(0.748873\pi\)
\(252\) 0 0
\(253\) 13.7853 5.01745i 0.866676 0.315444i
\(254\) 26.9233 17.7077i 1.68932 1.11108i
\(255\) 0 0
\(256\) 31.9000 3.72858i 1.99375 0.233036i
\(257\) −2.00787 2.69704i −0.125248 0.168237i 0.735076 0.677984i \(-0.237146\pi\)
−0.860324 + 0.509747i \(0.829739\pi\)
\(258\) 0 0
\(259\) −0.00371001 0.0636984i −0.000230529 0.00395803i
\(260\) −16.1378 13.5412i −1.00082 0.839790i
\(261\) 0 0
\(262\) 8.13723 6.82794i 0.502720 0.421832i
\(263\) 16.7605 + 17.7651i 1.03350 + 1.09544i 0.995365 + 0.0961708i \(0.0306595\pi\)
0.0381328 + 0.999273i \(0.487859\pi\)
\(264\) 0 0
\(265\) 38.7242 + 25.4693i 2.37881 + 1.56457i
\(266\) 4.21558 + 0.999112i 0.258474 + 0.0612595i
\(267\) 0 0
\(268\) 5.28783 + 0.618059i 0.323006 + 0.0377539i
\(269\) 0.417322 + 0.722824i 0.0254446 + 0.0440713i 0.878467 0.477802i \(-0.158567\pi\)
−0.853023 + 0.521874i \(0.825233\pi\)
\(270\) 0 0
\(271\) 14.1085 24.4366i 0.857029 1.48442i −0.0177208 0.999843i \(-0.505641\pi\)
0.874750 0.484575i \(-0.161026\pi\)
\(272\) 0.659069 0.885283i 0.0399619 0.0536782i
\(273\) 0 0
\(274\) 15.7710 + 52.6787i 0.952758 + 3.18243i
\(275\) 24.0853 12.0961i 1.45240 0.729422i
\(276\) 0 0
\(277\) 7.69228 25.6940i 0.462185 1.54380i −0.336280 0.941762i \(-0.609169\pi\)
0.798465 0.602042i \(-0.205646\pi\)
\(278\) 4.08824 + 23.1856i 0.245196 + 1.39058i
\(279\) 0 0
\(280\) −4.51897 + 25.6284i −0.270060 + 1.53159i
\(281\) 13.0781 + 6.56809i 0.780177 + 0.391819i 0.793871 0.608087i \(-0.208063\pi\)
−0.0136939 + 0.999906i \(0.504359\pi\)
\(282\) 0 0
\(283\) 0.462413 1.07199i 0.0274876 0.0637234i −0.903919 0.427703i \(-0.859323\pi\)
0.931407 + 0.363980i \(0.118582\pi\)
\(284\) −12.5365 + 29.0629i −0.743905 + 1.72456i
\(285\) 0 0
\(286\) −7.05141 3.54135i −0.416959 0.209405i
\(287\) −0.947854 + 5.37555i −0.0559500 + 0.317308i
\(288\) 0 0
\(289\) −2.93939 16.6701i −0.172905 0.980594i
\(290\) 15.5899 52.0740i 0.915473 3.05789i
\(291\) 0 0
\(292\) 31.0125 15.5751i 1.81487 0.911463i
\(293\) −4.79954 16.0316i −0.280392 0.936575i −0.975930 0.218085i \(-0.930019\pi\)
0.695538 0.718490i \(-0.255166\pi\)
\(294\) 0 0
\(295\) 23.2949 31.2905i 1.35628 1.82180i
\(296\) −0.119776 + 0.207458i −0.00696184 + 0.0120583i
\(297\) 0 0
\(298\) 20.4103 + 35.3516i 1.18234 + 2.04786i
\(299\) 7.79569 + 0.911186i 0.450837 + 0.0526952i
\(300\) 0 0
\(301\) −8.01876 1.90048i −0.462194 0.109542i
\(302\) −3.75480 2.46957i −0.216064 0.142108i
\(303\) 0 0
\(304\) −3.76793 3.99377i −0.216105 0.229058i
\(305\) 13.0931 10.9864i 0.749707 0.629079i
\(306\) 0 0
\(307\) −15.6362 13.1204i −0.892407 0.748818i 0.0762844 0.997086i \(-0.475694\pi\)
−0.968691 + 0.248268i \(0.920139\pi\)
\(308\) 0.753776 + 12.9418i 0.0429504 + 0.737429i
\(309\) 0 0
\(310\) −7.54912 10.1402i −0.428761 0.575926i
\(311\) −6.59097 + 0.770374i −0.373740 + 0.0436839i −0.300889 0.953659i \(-0.597284\pi\)
−0.0728501 + 0.997343i \(0.523209\pi\)
\(312\) 0 0
\(313\) 7.66936 5.04422i 0.433498 0.285116i −0.313946 0.949441i \(-0.601651\pi\)
0.747444 + 0.664325i \(0.231281\pi\)
\(314\) −24.9087 + 9.06601i −1.40568 + 0.511625i
\(315\) 0 0
\(316\) −19.7300 7.18114i −1.10990 0.403971i
\(317\) 0.0487426 0.0115522i 0.00273766 0.000648836i −0.229247 0.973368i \(-0.573626\pi\)
0.231984 + 0.972719i \(0.425478\pi\)
\(318\) 0 0
\(319\) 0.790245 13.5680i 0.0442452 0.759661i
\(320\) −21.4424 + 22.7276i −1.19867 + 1.27051i
\(321\) 0 0
\(322\) −7.65130 17.7377i −0.426390 0.988483i
\(323\) 0.361832 0.0201329
\(324\) 0 0
\(325\) 14.4199 0.799874
\(326\) −3.65955 8.48379i −0.202684 0.469874i
\(327\) 0 0
\(328\) 14.0632 14.9061i 0.776510 0.823053i
\(329\) −0.635356 + 10.9086i −0.0350283 + 0.601413i
\(330\) 0 0
\(331\) −18.0022 + 4.26660i −0.989491 + 0.234514i −0.693327 0.720623i \(-0.743856\pi\)
−0.296164 + 0.955137i \(0.595708\pi\)
\(332\) 21.4290 + 7.79954i 1.17607 + 0.428055i
\(333\) 0 0
\(334\) 27.2761 9.92767i 1.49248 0.543218i
\(335\) −4.42972 + 2.91347i −0.242022 + 0.159180i
\(336\) 0 0
\(337\) 3.62501 0.423702i 0.197467 0.0230805i −0.0167846 0.999859i \(-0.505343\pi\)
0.214251 + 0.976779i \(0.431269\pi\)
\(338\) 16.5188 + 22.1887i 0.898507 + 1.20690i
\(339\) 0 0
\(340\) 0.251787 + 4.32302i 0.0136551 + 0.234449i
\(341\) −2.42131 2.03172i −0.131121 0.110024i
\(342\) 0 0
\(343\) 12.3716 10.3810i 0.668005 0.560523i
\(344\) 21.2318 + 22.5044i 1.14474 + 1.21336i
\(345\) 0 0
\(346\) −19.6059 12.8950i −1.05402 0.693239i
\(347\) 3.98981 + 0.945603i 0.214184 + 0.0507626i 0.336307 0.941752i \(-0.390822\pi\)
−0.122123 + 0.992515i \(0.538970\pi\)
\(348\) 0 0
\(349\) −7.51393 0.878252i −0.402211 0.0470118i −0.0874174 0.996172i \(-0.527861\pi\)
−0.314794 + 0.949160i \(0.601935\pi\)
\(350\) −17.7453 30.7358i −0.948528 1.64290i
\(351\) 0 0
\(352\) 0.185511 0.321314i 0.00988775 0.0171261i
\(353\) 1.22443 1.64470i 0.0651699 0.0875384i −0.768343 0.640038i \(-0.778919\pi\)
0.833513 + 0.552500i \(0.186326\pi\)
\(354\) 0 0
\(355\) −9.04045 30.1972i −0.479817 1.60270i
\(356\) 32.8842 16.5150i 1.74286 0.875296i
\(357\) 0 0
\(358\) −0.998349 + 3.33472i −0.0527644 + 0.176245i
\(359\) −1.74531 9.89817i −0.0921141 0.522405i −0.995594 0.0937737i \(-0.970107\pi\)
0.903479 0.428631i \(-0.141004\pi\)
\(360\) 0 0
\(361\) −2.98674 + 16.9386i −0.157197 + 0.891506i
\(362\) 21.6973 + 10.8968i 1.14038 + 0.572722i
\(363\) 0 0
\(364\) −2.74716 + 6.36863i −0.143990 + 0.333807i
\(365\) −13.6890 + 31.7348i −0.716517 + 1.66107i
\(366\) 0 0
\(367\) 29.0225 + 14.5756i 1.51496 + 0.760842i 0.995599 0.0937115i \(-0.0298731\pi\)
0.519363 + 0.854554i \(0.326169\pi\)
\(368\) −4.25131 + 24.1104i −0.221615 + 1.25684i
\(369\) 0 0
\(370\) −0.0825380 0.468096i −0.00429095 0.0243352i
\(371\) 4.37661 14.6189i 0.227222 0.758975i
\(372\) 0 0
\(373\) 13.4959 6.77789i 0.698791 0.350946i −0.0636783 0.997970i \(-0.520283\pi\)
0.762469 + 0.647024i \(0.223987\pi\)
\(374\) 0.465194 + 1.55386i 0.0240546 + 0.0803480i
\(375\) 0 0
\(376\) 24.4981 32.9066i 1.26339 1.69703i
\(377\) 3.63572 6.29725i 0.187249 0.324325i
\(378\) 0 0
\(379\) 1.32973 + 2.30316i 0.0683037 + 0.118305i 0.898155 0.439680i \(-0.144908\pi\)
−0.829851 + 0.557985i \(0.811575\pi\)
\(380\) 21.3974 + 2.50100i 1.09766 + 0.128298i
\(381\) 0 0
\(382\) 42.5378 + 10.0817i 2.17643 + 0.515822i
\(383\) 1.29846 + 0.854009i 0.0663481 + 0.0436378i 0.582250 0.813010i \(-0.302173\pi\)
−0.515902 + 0.856648i \(0.672543\pi\)
\(384\) 0 0
\(385\) −8.85973 9.39076i −0.451534 0.478598i
\(386\) −51.9137 + 43.5607i −2.64234 + 2.21718i
\(387\) 0 0
\(388\) 38.1656 + 32.0247i 1.93757 + 1.62581i
\(389\) 0.213782 + 3.67050i 0.0108392 + 0.186102i 0.999382 + 0.0351591i \(0.0111938\pi\)
−0.988543 + 0.150943i \(0.951769\pi\)
\(390\) 0 0
\(391\) −0.963439 1.29412i −0.0487232 0.0654466i
\(392\) −25.8564 + 3.02218i −1.30595 + 0.152643i
\(393\) 0 0
\(394\) −12.2773 + 8.07490i −0.618521 + 0.406807i
\(395\) 19.6490 7.15164i 0.988647 0.359838i
\(396\) 0 0
\(397\) 36.1674 + 13.1638i 1.81519 + 0.660674i 0.996223 + 0.0868301i \(0.0276737\pi\)
0.818965 + 0.573844i \(0.194548\pi\)
\(398\) −38.3252 + 9.08325i −1.92107 + 0.455302i
\(399\) 0 0
\(400\) −2.61533 + 44.9034i −0.130766 + 2.24517i
\(401\) −12.2187 + 12.9510i −0.610171 + 0.646743i −0.956625 0.291324i \(-0.905904\pi\)
0.346454 + 0.938067i \(0.387386\pi\)
\(402\) 0 0
\(403\) −0.669806 1.55279i −0.0333654 0.0773498i
\(404\) 49.9982 2.48750
\(405\) 0 0
\(406\) −17.8966 −0.888196
\(407\) −0.0470713 0.109124i −0.00233324 0.00540905i
\(408\) 0 0
\(409\) 12.5796 13.3336i 0.622022 0.659305i −0.337373 0.941371i \(-0.609538\pi\)
0.959395 + 0.282066i \(0.0910198\pi\)
\(410\) −2.36430 + 40.5934i −0.116764 + 2.00477i
\(411\) 0 0
\(412\) −24.4220 + 5.78812i −1.20319 + 0.285160i
\(413\) −12.0689 4.39273i −0.593873 0.216152i
\(414\) 0 0
\(415\) −21.3410 + 7.76749i −1.04759 + 0.381291i
\(416\) 0.165848 0.109080i 0.00813134 0.00534807i
\(417\) 0 0
\(418\) 8.01472 0.936786i 0.392013 0.0458197i
\(419\) −7.45896 10.0191i −0.364394 0.489466i 0.581680 0.813418i \(-0.302396\pi\)
−0.946074 + 0.323952i \(0.894988\pi\)
\(420\) 0 0
\(421\) −1.25709 21.5834i −0.0612668 1.05191i −0.879156 0.476534i \(-0.841893\pi\)
0.817889 0.575376i \(-0.195144\pi\)
\(422\) 18.9221 + 15.8775i 0.921114 + 0.772906i
\(423\) 0 0
\(424\) −43.8878 + 36.8262i −2.13138 + 1.78844i
\(425\) −2.03410 2.15602i −0.0986685 0.104583i
\(426\) 0 0
\(427\) −4.70153 3.09224i −0.227523 0.149644i
\(428\) 77.5233 + 18.3734i 3.74723 + 0.888110i
\(429\) 0 0
\(430\) −60.9744 7.12688i −2.94045 0.343689i
\(431\) 15.5400 + 26.9162i 0.748538 + 1.29651i 0.948524 + 0.316707i \(0.102577\pi\)
−0.199986 + 0.979799i \(0.564090\pi\)
\(432\) 0 0
\(433\) −6.64480 + 11.5091i −0.319329 + 0.553093i −0.980348 0.197275i \(-0.936791\pi\)
0.661019 + 0.750369i \(0.270124\pi\)
\(434\) −2.48546 + 3.33856i −0.119306 + 0.160256i
\(435\) 0 0
\(436\) −4.41495 14.7469i −0.211438 0.706251i
\(437\) −7.17262 + 3.60223i −0.343113 + 0.172318i
\(438\) 0 0
\(439\) 0.367842 1.22868i 0.0175562 0.0586417i −0.948763 0.315990i \(-0.897663\pi\)
0.966319 + 0.257348i \(0.0828487\pi\)
\(440\) 8.41685 + 47.7343i 0.401258 + 2.27564i
\(441\) 0 0
\(442\) −0.150692 + 0.854617i −0.00716769 + 0.0406500i
\(443\) −34.9439 17.5495i −1.66023 0.833800i −0.996294 0.0860134i \(-0.972587\pi\)
−0.663939 0.747787i \(-0.731116\pi\)
\(444\) 0 0
\(445\) −14.5152 + 33.6500i −0.688086 + 1.59516i
\(446\) 12.6699 29.3721i 0.599936 1.39081i
\(447\) 0 0
\(448\) 9.19320 + 4.61700i 0.434338 + 0.218133i
\(449\) −2.78437 + 15.7909i −0.131403 + 0.745221i 0.845895 + 0.533349i \(0.179067\pi\)
−0.977298 + 0.211871i \(0.932044\pi\)
\(450\) 0 0
\(451\) 1.76543 + 10.0123i 0.0831310 + 0.471459i
\(452\) 4.01897 13.4243i 0.189036 0.631426i
\(453\) 0 0
\(454\) −35.7082 + 17.9333i −1.67587 + 0.841654i
\(455\) −1.98106 6.61720i −0.0928735 0.310219i
\(456\) 0 0
\(457\) −2.30852 + 3.10088i −0.107988 + 0.145053i −0.852832 0.522186i \(-0.825117\pi\)
0.744844 + 0.667239i \(0.232524\pi\)
\(458\) −8.26234 + 14.3108i −0.386074 + 0.668699i
\(459\) 0 0
\(460\) −48.0292 83.1890i −2.23937 3.87871i
\(461\) 21.0874 + 2.46477i 0.982140 + 0.114796i 0.591981 0.805952i \(-0.298346\pi\)
0.390159 + 0.920748i \(0.372420\pi\)
\(462\) 0 0
\(463\) 18.7929 + 4.45400i 0.873381 + 0.206995i 0.642778 0.766053i \(-0.277782\pi\)
0.230603 + 0.973048i \(0.425930\pi\)
\(464\) 18.9501 + 12.4637i 0.879738 + 0.578613i
\(465\) 0 0
\(466\) 23.2293 + 24.6216i 1.07607 + 1.14057i
\(467\) −3.15564 + 2.64790i −0.146026 + 0.122530i −0.712874 0.701292i \(-0.752607\pi\)
0.566848 + 0.823822i \(0.308162\pi\)
\(468\) 0 0
\(469\) 1.33722 + 1.12206i 0.0617469 + 0.0518118i
\(470\) 4.73300 + 81.2625i 0.218317 + 3.74836i
\(471\) 0 0
\(472\) 28.7944 + 38.6776i 1.32537 + 1.78028i
\(473\) −15.2453 + 1.78193i −0.700982 + 0.0819330i
\(474\) 0 0
\(475\) −12.3203 + 8.10318i −0.565293 + 0.371799i
\(476\) 1.33974 0.487625i 0.0614068 0.0223503i
\(477\) 0 0
\(478\) 28.8966 + 10.5175i 1.32170 + 0.481060i
\(479\) 27.9772 6.63072i 1.27831 0.302966i 0.465269 0.885169i \(-0.345958\pi\)
0.813043 + 0.582204i \(0.197809\pi\)
\(480\) 0 0
\(481\) 0.00369705 0.0634758i 0.000168571 0.00289425i
\(482\) 23.0429 24.4241i 1.04958 1.11249i
\(483\) 0 0
\(484\) −7.93080 18.3857i −0.360491 0.835712i
\(485\) −49.6170 −2.25299
\(486\) 0 0
\(487\) 8.88765 0.402738 0.201369 0.979515i \(-0.435461\pi\)
0.201369 + 0.979515i \(0.435461\pi\)
\(488\) 8.36792 + 19.3990i 0.378798 + 0.878153i
\(489\) 0 0
\(490\) 35.4467 37.5713i 1.60132 1.69730i
\(491\) 1.63971 28.1528i 0.0739991 1.27052i −0.733108 0.680112i \(-0.761931\pi\)
0.807108 0.590404i \(-0.201032\pi\)
\(492\) 0 0
\(493\) −1.45441 + 0.344701i −0.0655033 + 0.0155246i
\(494\) 4.05686 + 1.47658i 0.182527 + 0.0664344i
\(495\) 0 0
\(496\) 4.95683 1.80414i 0.222568 0.0810082i
\(497\) −8.67076 + 5.70285i −0.388937 + 0.255808i
\(498\) 0 0
\(499\) −1.18198 + 0.138153i −0.0529126 + 0.00618460i −0.142508 0.989794i \(-0.545517\pi\)
0.0895954 + 0.995978i \(0.471443\pi\)
\(500\) −57.4443 77.1611i −2.56899 3.45075i
\(501\) 0 0
\(502\) 1.89515 + 32.5385i 0.0845848 + 1.45226i
\(503\) 4.59276 + 3.85379i 0.204781 + 0.171832i 0.739411 0.673255i \(-0.235104\pi\)
−0.534629 + 0.845087i \(0.679549\pi\)
\(504\) 0 0
\(505\) −38.1435 + 32.0062i −1.69736 + 1.42426i
\(506\) −24.6910 26.1710i −1.09765 1.16344i
\(507\) 0 0
\(508\) −44.0780 28.9906i −1.95565 1.28625i
\(509\) 24.4578 + 5.79659i 1.08407 + 0.256929i 0.733557 0.679628i \(-0.237859\pi\)
0.350514 + 0.936558i \(0.386007\pi\)
\(510\) 0 0
\(511\) 11.3020 + 1.32101i 0.499971 + 0.0584382i
\(512\) −19.9189 34.5006i −0.880300 1.52473i
\(513\) 0 0
\(514\) −4.12333 + 7.14181i −0.181872 + 0.315012i
\(515\) 14.9262 20.0494i 0.657729 0.883483i
\(516\) 0 0
\(517\) 5.83713 + 19.4974i 0.256717 + 0.857494i
\(518\) −0.139847 + 0.0702339i −0.00614454 + 0.00308590i
\(519\) 0 0
\(520\) −7.43761 + 24.8433i −0.326161 + 1.08945i
\(521\) −5.84968 33.1752i −0.256279 1.45343i −0.792768 0.609524i \(-0.791361\pi\)
0.536488 0.843908i \(-0.319750\pi\)
\(522\) 0 0
\(523\) 4.18478 23.7331i 0.182988 1.03778i −0.745526 0.666477i \(-0.767801\pi\)
0.928513 0.371299i \(-0.121087\pi\)
\(524\) −15.5409 7.80492i −0.678906 0.340960i
\(525\) 0 0
\(526\) 23.7260 55.0030i 1.03450 2.39824i
\(527\) −0.137684 + 0.319187i −0.00599759 + 0.0139040i
\(528\) 0 0
\(529\) 11.4284 + 5.73957i 0.496888 + 0.249547i
\(530\) 19.7398 111.950i 0.857443 4.86280i
\(531\) 0 0
\(532\) −1.23166 6.98506i −0.0533990 0.302841i
\(533\) −1.56004 + 5.21089i −0.0675727 + 0.225709i
\(534\) 0 0
\(535\) −70.9040 + 35.6093i −3.06545 + 1.53952i
\(536\) −1.87961 6.27833i −0.0811867 0.271183i
\(537\) 0 0
\(538\) 1.22243 1.64200i 0.0527025 0.0707918i
\(539\) 6.45742 11.1846i 0.278141 0.481754i
\(540\) 0 0
\(541\) −11.3703 19.6940i −0.488849 0.846712i 0.511068 0.859540i \(-0.329250\pi\)
−0.999918 + 0.0128282i \(0.995917\pi\)
\(542\) −68.7376 8.03428i −2.95253 0.345102i
\(543\) 0 0
\(544\) −0.0397040 0.00941003i −0.00170230 0.000403452i
\(545\) 12.8084 + 8.42419i 0.548650 + 0.360853i
\(546\) 0 0
\(547\) −0.267245 0.283263i −0.0114266 0.0121115i 0.721635 0.692274i \(-0.243391\pi\)
−0.733062 + 0.680162i \(0.761909\pi\)
\(548\) 68.9639 57.8676i 2.94599 2.47198i
\(549\) 0 0
\(550\) −50.6382 42.4905i −2.15922 1.81180i
\(551\) 0.432364 + 7.42340i 0.0184193 + 0.316247i
\(552\) 0 0
\(553\) −4.11107 5.52213i −0.174821 0.234825i
\(554\) −65.3365 + 7.63674i −2.77588 + 0.324454i
\(555\) 0 0
\(556\) 32.2033 21.1804i 1.36572 0.898250i
\(557\) 19.6611 7.15607i 0.833069 0.303212i 0.109951 0.993937i \(-0.464931\pi\)
0.723118 + 0.690725i \(0.242708\pi\)
\(558\) 0 0
\(559\) −7.71685 2.80870i −0.326388 0.118795i
\(560\) 20.9652 4.96883i 0.885939 0.209971i
\(561\) 0 0
\(562\) 2.08703 35.8330i 0.0880361 1.51152i
\(563\) 9.51661 10.0870i 0.401077 0.425117i −0.495084 0.868845i \(-0.664863\pi\)
0.896162 + 0.443728i \(0.146344\pi\)
\(564\) 0 0
\(565\) 5.52746 + 12.8141i 0.232542 + 0.539093i
\(566\) −2.86338 −0.120357
\(567\) 0 0
\(568\) 38.9631 1.63485
\(569\) −3.68383 8.54007i −0.154434 0.358019i 0.823381 0.567489i \(-0.192085\pi\)
−0.977815 + 0.209471i \(0.932826\pi\)
\(570\) 0 0
\(571\) −24.7267 + 26.2088i −1.03478 + 1.09680i −0.0395538 + 0.999217i \(0.512594\pi\)
−0.995227 + 0.0975862i \(0.968888\pi\)
\(572\) −0.751142 + 12.8966i −0.0314068 + 0.539234i
\(573\) 0 0
\(574\) 13.0267 3.08739i 0.543725 0.128865i
\(575\) 61.7866 + 22.4885i 2.57668 + 0.937834i
\(576\) 0 0
\(577\) 8.15363 2.96768i 0.339440 0.123546i −0.166675 0.986012i \(-0.553303\pi\)
0.506115 + 0.862466i \(0.331081\pi\)
\(578\) −34.6863 + 22.8135i −1.44276 + 0.948918i
\(579\) 0 0
\(580\) −88.3909 + 10.3314i −3.67023 + 0.428989i
\(581\) 4.46509 + 5.99766i 0.185243 + 0.248825i
\(582\) 0 0
\(583\) −1.65262 28.3745i −0.0684447 1.17515i
\(584\) −32.7259 27.4603i −1.35421 1.13631i
\(585\) 0 0
\(586\) −31.4413 + 26.3824i −1.29883 + 1.08985i
\(587\) −6.35311 6.73390i −0.262221 0.277938i 0.582864 0.812569i \(-0.301932\pi\)
−0.845085 + 0.534632i \(0.820450\pi\)
\(588\) 0 0
\(589\) 1.44486 + 0.950296i 0.0595342 + 0.0391563i
\(590\) −93.0969 22.0644i −3.83274 0.908375i
\(591\) 0 0
\(592\) 0.196992 + 0.0230251i 0.00809633 + 0.000946325i
\(593\) 18.3119 + 31.7171i 0.751979 + 1.30247i 0.946862 + 0.321639i \(0.104234\pi\)
−0.194884 + 0.980826i \(0.562433\pi\)
\(594\) 0 0
\(595\) −0.709932 + 1.22964i −0.0291044 + 0.0504102i
\(596\) 39.9082 53.6060i 1.63470 2.19579i
\(597\) 0 0
\(598\) −5.52098 18.4414i −0.225770 0.754123i
\(599\) 22.1250 11.1116i 0.904001 0.454007i 0.0648441 0.997895i \(-0.479345\pi\)
0.839157 + 0.543889i \(0.183049\pi\)
\(600\) 0 0
\(601\) −6.33556 + 21.1622i −0.258433 + 0.863226i 0.726034 + 0.687658i \(0.241361\pi\)
−0.984467 + 0.175568i \(0.943824\pi\)
\(602\) 3.50974 + 19.9047i 0.143046 + 0.811257i
\(603\) 0 0
\(604\) −1.27765 + 7.24590i −0.0519867 + 0.294831i
\(605\) 17.8199 + 8.94950i 0.724482 + 0.363849i
\(606\) 0 0
\(607\) −3.79033 + 8.78698i −0.153845 + 0.356653i −0.977656 0.210212i \(-0.932585\pi\)
0.823811 + 0.566865i \(0.191844\pi\)
\(608\) −0.0804024 + 0.186394i −0.00326075 + 0.00755927i
\(609\) 0 0
\(610\) −37.4609 18.8135i −1.51675 0.761738i
\(611\) −1.89085 + 10.7235i −0.0764954 + 0.433827i
\(612\) 0 0
\(613\) −2.38544 13.5285i −0.0963469 0.546410i −0.994326 0.106373i \(-0.966076\pi\)
0.897979 0.440037i \(-0.145035\pi\)
\(614\) −14.3580 + 47.9590i −0.579441 + 1.93547i
\(615\) 0 0
\(616\) 14.2610 7.16214i 0.574592 0.288571i
\(617\) 3.90172 + 13.0327i 0.157077 + 0.524675i 0.999909 0.0135025i \(-0.00429810\pi\)
−0.842831 + 0.538178i \(0.819113\pi\)
\(618\) 0 0
\(619\) −8.51625 + 11.4393i −0.342297 + 0.459785i −0.939622 0.342215i \(-0.888823\pi\)
0.597325 + 0.801999i \(0.296230\pi\)
\(620\) −10.3483 + 17.9238i −0.415599 + 0.719839i
\(621\) 0 0
\(622\) 8.13761 + 14.0947i 0.326288 + 0.565148i
\(623\) 11.9841 + 1.40074i 0.480132 + 0.0561194i
\(624\) 0 0
\(625\) 39.7451 + 9.41976i 1.58980 + 0.376790i
\(626\) −18.8101 12.3716i −0.751801 0.494467i
\(627\) 0 0
\(628\) 29.7807 + 31.5657i 1.18838 + 1.25961i
\(629\) −0.0100122 + 0.00840126i −0.000399214 + 0.000334980i
\(630\) 0 0
\(631\) −6.09157 5.11144i −0.242502 0.203483i 0.513434 0.858129i \(-0.328373\pi\)
−0.755935 + 0.654646i \(0.772818\pi\)
\(632\) 1.50284 + 25.8027i 0.0597797 + 1.02638i
\(633\) 0 0
\(634\) −0.0733662 0.0985479i −0.00291374 0.00391384i
\(635\) 52.1852 6.09958i 2.07091 0.242054i
\(636\) 0 0
\(637\) 5.77297 3.79694i 0.228733 0.150440i
\(638\) −31.3233 + 11.4007i −1.24010 + 0.451360i
\(639\) 0 0
\(640\) 73.1505 + 26.6246i 2.89153 + 1.05243i
\(641\) 4.09023 0.969403i 0.161555 0.0382891i −0.149043 0.988831i \(-0.547619\pi\)
0.310597 + 0.950542i \(0.399471\pi\)
\(642\) 0 0
\(643\) −1.11571 + 19.1561i −0.0439995 + 0.755442i 0.902092 + 0.431543i \(0.142031\pi\)
−0.946092 + 0.323899i \(0.895006\pi\)
\(644\) −21.7032 + 23.0040i −0.855225 + 0.906486i
\(645\) 0 0
\(646\) −0.351496 0.814859i −0.0138294 0.0320602i
\(647\) −33.3755 −1.31213 −0.656063 0.754706i \(-0.727779\pi\)
−0.656063 + 0.754706i \(0.727779\pi\)
\(648\) 0 0
\(649\) −23.9217 −0.939009
\(650\) −14.0080 32.4742i −0.549440 1.27374i
\(651\) 0 0
\(652\) −10.3804 + 11.0026i −0.406530 + 0.430896i
\(653\) −0.709166 + 12.1759i −0.0277518 + 0.476480i 0.955588 + 0.294705i \(0.0952214\pi\)
−0.983340 + 0.181775i \(0.941816\pi\)
\(654\) 0 0
\(655\) 16.8524 3.99409i 0.658477 0.156062i
\(656\) −15.9437 5.80302i −0.622496 0.226570i
\(657\) 0 0
\(658\) 25.1839 9.16619i 0.981770 0.357335i
\(659\) 19.5651 12.8682i 0.762148 0.501272i −0.107947 0.994157i \(-0.534428\pi\)
0.870095 + 0.492884i \(0.164057\pi\)
\(660\) 0 0
\(661\) 33.4396 3.90853i 1.30065 0.152024i 0.562577 0.826745i \(-0.309810\pi\)
0.738073 + 0.674721i \(0.235736\pi\)
\(662\) 27.0965 + 36.3969i 1.05314 + 1.41461i
\(663\) 0 0
\(664\) −1.63225 28.0247i −0.0633437 1.08757i
\(665\) 5.41109 + 4.54045i 0.209833 + 0.176071i
\(666\) 0 0
\(667\) 25.3992 21.3124i 0.983460 0.825221i
\(668\) −32.6112 34.5658i −1.26176 1.33739i
\(669\) 0 0
\(670\) 10.8644 + 7.14565i 0.419730 + 0.276061i
\(671\) −10.1986 2.41712i −0.393713 0.0933118i
\(672\) 0 0
\(673\) 12.3262 + 1.44072i 0.475140 + 0.0555358i 0.350293 0.936640i \(-0.386082\pi\)
0.124847 + 0.992176i \(0.460156\pi\)
\(674\) −4.47565 7.75205i −0.172396 0.298598i
\(675\) 0 0
\(676\) 22.6440 39.2206i 0.870925 1.50849i
\(677\) −8.84021 + 11.8745i −0.339757 + 0.456373i −0.938860 0.344299i \(-0.888117\pi\)
0.599103 + 0.800672i \(0.295524\pi\)
\(678\) 0 0
\(679\) 4.68517 + 15.6496i 0.179800 + 0.600575i
\(680\) 4.76367 2.39240i 0.182678 0.0917445i
\(681\) 0 0
\(682\) −2.22337 + 7.42657i −0.0851372 + 0.284378i
\(683\) 6.94875 + 39.4083i 0.265887 + 1.50792i 0.766499 + 0.642246i \(0.221997\pi\)
−0.500612 + 0.865672i \(0.666892\pi\)
\(684\) 0 0
\(685\) −15.5686 + 88.2941i −0.594847 + 3.37354i
\(686\) −35.3967 17.7769i −1.35145 0.678725i
\(687\) 0 0
\(688\) 10.1458 23.5207i 0.386807 0.896719i
\(689\) 6.02304 13.9630i 0.229460 0.531947i
\(690\) 0 0
\(691\) −35.1761 17.6661i −1.33816 0.672050i −0.371578 0.928402i \(-0.621183\pi\)
−0.966584 + 0.256351i \(0.917480\pi\)
\(692\) −6.67130 + 37.8348i −0.253605 + 1.43826i
\(693\) 0 0
\(694\) −1.74631 9.90380i −0.0662889 0.375943i
\(695\) −11.0092 + 36.7733i −0.417603 + 1.39489i
\(696\) 0 0
\(697\) 0.999178 0.501806i 0.0378466 0.0190073i
\(698\) 5.32143 + 17.7748i 0.201419 + 0.672787i
\(699\) 0 0
\(700\) −34.6975 + 46.6068i −1.31144 + 1.76157i
\(701\) −2.37301 + 4.11018i −0.0896274 + 0.155239i −0.907354 0.420368i \(-0.861901\pi\)
0.817726 + 0.575607i \(0.195234\pi\)
\(702\) 0 0
\(703\) 0.0325111 + 0.0563108i 0.00122618 + 0.00212380i
\(704\) 19.0314 + 2.22445i 0.717273 + 0.0838372i
\(705\) 0 0
\(706\) −4.89337 1.15975i −0.184165 0.0436478i
\(707\) 13.6968 + 9.00850i 0.515120 + 0.338800i
\(708\) 0 0
\(709\) −0.249769 0.264740i −0.00938029 0.00994253i 0.722667 0.691197i \(-0.242916\pi\)
−0.732047 + 0.681254i \(0.761435\pi\)
\(710\) −59.2231 + 49.6940i −2.22260 + 1.86498i
\(711\) 0 0
\(712\) −34.7009 29.1175i −1.30047 1.09123i
\(713\) −0.448356 7.69797i −0.0167911 0.288291i
\(714\) 0 0
\(715\) −7.68268 10.3196i −0.287316 0.385932i
\(716\) 5.66038 0.661604i 0.211538 0.0247253i
\(717\) 0 0
\(718\) −20.5956 + 13.5459i −0.768621 + 0.505530i
\(719\) −15.2471 + 5.54950i −0.568622 + 0.206961i −0.610301 0.792170i \(-0.708951\pi\)
0.0416792 + 0.999131i \(0.486729\pi\)
\(720\) 0 0
\(721\) −7.73318 2.81465i −0.287998 0.104823i
\(722\) 41.0478 9.72852i 1.52764 0.362058i
\(723\) 0 0
\(724\) 2.31127 39.6830i 0.0858978 1.47481i
\(725\) 41.8027 44.3083i 1.55251 1.64557i
\(726\) 0 0
\(727\) −6.27054 14.5368i −0.232562 0.539138i 0.761474 0.648196i \(-0.224476\pi\)
−0.994035 + 0.109057i \(0.965217\pi\)
\(728\) 8.53809 0.316443
\(729\) 0 0
\(730\) 84.7659 3.13733
\(731\) 0.668605 + 1.55000i 0.0247293 + 0.0573289i
\(732\) 0 0
\(733\) −31.3546 + 33.2339i −1.15811 + 1.22752i −0.188710 + 0.982033i \(0.560431\pi\)
−0.969399 + 0.245491i \(0.921051\pi\)
\(734\) 4.63146 79.5191i 0.170950 2.93510i
\(735\) 0 0
\(736\) 0.880738 0.208739i 0.0324644 0.00769421i
\(737\) 3.05522 + 1.11201i 0.112541 + 0.0409614i
\(738\) 0 0
\(739\) −2.12852 + 0.774717i −0.0782987 + 0.0284984i −0.380873 0.924628i \(-0.624376\pi\)
0.302574 + 0.953126i \(0.402154\pi\)
\(740\) −0.650156 + 0.427614i −0.0239002 + 0.0157194i
\(741\) 0 0
\(742\) −37.1739 + 4.34500i −1.36470 + 0.159510i
\(743\) −1.63022 2.18977i −0.0598071 0.0803349i 0.771213 0.636577i \(-0.219650\pi\)
−0.831020 + 0.556242i \(0.812243\pi\)
\(744\) 0 0
\(745\) 3.86987 + 66.4430i 0.141781 + 2.43428i
\(746\) −28.3745 23.8090i −1.03886 0.871709i
\(747\) 0 0
\(748\) 2.03422 1.70691i 0.0743785 0.0624109i
\(749\) 17.9267 + 19.0012i 0.655027 + 0.694288i
\(750\) 0 0
\(751\) 36.0238 + 23.6932i 1.31453 + 0.864579i 0.996507 0.0835052i \(-0.0266115\pi\)
0.318021 + 0.948084i \(0.396982\pi\)
\(752\) −33.0499 7.83297i −1.20521 0.285639i
\(753\) 0 0
\(754\) −17.7135 2.07041i −0.645088 0.0754000i
\(755\) −3.66372 6.34576i −0.133337 0.230946i
\(756\) 0 0
\(757\) 19.3916 33.5873i 0.704800 1.22075i −0.261963 0.965078i \(-0.584370\pi\)
0.966764 0.255672i \(-0.0822968\pi\)
\(758\) 3.89506 5.23198i 0.141475 0.190034i
\(759\) 0 0
\(760\) −7.60591 25.4055i −0.275895 0.921554i
\(761\) −38.7081 + 19.4400i −1.40317 + 0.704698i −0.979561 0.201147i \(-0.935533\pi\)
−0.423608 + 0.905845i \(0.639237\pi\)
\(762\) 0 0
\(763\) 1.44760 4.83532i 0.0524067 0.175050i
\(764\) −12.4282 70.4836i −0.449635 2.55001i
\(765\) 0 0
\(766\) 0.661895 3.75379i 0.0239152 0.135630i
\(767\) −11.4372 5.74400i −0.412975 0.207404i
\(768\) 0 0
\(769\) 19.7676 45.8265i 0.712839 1.65255i −0.0440729 0.999028i \(-0.514033\pi\)
0.756912 0.653517i \(-0.226707\pi\)
\(770\) −12.5417 + 29.0750i −0.451972 + 1.04779i
\(771\) 0 0
\(772\) 99.1473 + 49.7936i 3.56839 + 1.79211i
\(773\) 1.64610 9.33547i 0.0592059 0.335774i −0.940789 0.338993i \(-0.889914\pi\)
0.999995 + 0.00321947i \(0.00102479\pi\)
\(774\) 0 0
\(775\) −2.46005 13.9516i −0.0883676 0.501157i
\(776\) 17.5898 58.7541i 0.631438 2.10915i
\(777\) 0 0
\(778\) 8.05843 4.04710i 0.288909 0.145095i
\(779\) −1.59534 5.32880i −0.0571589 0.190924i
\(780\) 0 0
\(781\) −11.5429 + 15.5049i −0.413039 + 0.554808i
\(782\)