Properties

Label 729.2.g.d.55.1
Level $729$
Weight $2$
Character 729.55
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 55.1
Character \(\chi\) \(=\) 729.55
Dual form 729.2.g.d.676.1

$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{17}{27}\right)\)

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 0.113887 + 0.993494i \(0.463670\pi\)
−0.800795 + 0.598938i \(0.795590\pi\)
\(3\) 0 0
\(4\) −2.75551 2.92067i −1.37775 1.46033i
\(5\) 0.232513 + 3.99210i 0.103983 + 1.78532i 0.498954 + 0.866629i \(0.333718\pi\)
−0.394971 + 0.918694i \(0.629245\pi\)
\(6\) 0 0
\(7\) −1.28109 0.303625i −0.484208 0.114759i −0.0187406 0.999824i \(-0.505966\pi\)
−0.465468 + 0.885065i \(0.654114\pi\)
\(8\) 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 0.201713 0.979445i \(-0.435349\pi\)
−0.819447 + 0.573154i \(0.805720\pi\)
\(12\) 0 0
\(13\) −1.30311 0.152312i −0.361418 0.0422437i −0.0665537 0.997783i \(-0.521200\pi\)
−0.294864 + 0.955539i \(0.595274\pi\)
\(14\) 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 −0.617391 0.786657i \(-0.711810\pi\)
0.667497 + 0.744613i \(0.267366\pi\)
\(18\) 0 0
\(19\) 1.02778 + 0.862409i 0.235789 + 0.197850i 0.753024 0.657993i \(-0.228594\pi\)
−0.517235 + 0.855843i \(0.673039\pi\)
\(20\) 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 −0.787156 0.616754i \(-0.788447\pi\)
−0.426630 + 0.904426i \(0.640299\pi\)
\(24\) 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 0.380475 0.924791i \(-0.375760\pi\)
−0.995062 + 0.0992581i \(0.968353\pi\)
\(30\) 0 0
\(31\) 0.369677 1.23481i 0.0663960 0.221778i −0.918352 0.395764i \(-0.870480\pi\)
0.984748 + 0.173986i \(0.0556649\pi\)
\(32\) −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 0.984108 0.177570i \(-0.0568236\pi\)
−0.985492 + 0.169724i \(0.945712\pi\)
\(38\) −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 0.996994 0.0774824i \(-0.0246882\pi\)
−0.740537 + 0.672015i \(0.765429\pi\)
\(42\) 0 0
\(43\) 5.59352 2.80917i 0.853003 0.428394i 0.0321157 0.999484i \(-0.489775\pi\)
0.820888 + 0.571090i \(0.193479\pi\)
\(44\) 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 0.936154 + 0.351590i \(0.114359\pi\)
−0.588944 + 0.808174i \(0.700456\pi\)
\(48\) 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 −0.922174 0.386775i \(-0.873589\pi\)
0.126130 0.992014i \(-0.459744\pi\)
\(54\) 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 0.106041 0.994362i \(-0.466183\pi\)
0.955040 + 0.296478i \(0.0958122\pi\)
\(60\) 0 0
\(61\) 2.93311 3.10891i 0.375546 0.398055i −0.511842 0.859080i \(-0.671037\pi\)
0.887387 + 0.461025i \(0.152518\pi\)
\(62\) 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 −0.847852 0.530233i \(-0.822105\pi\)
0.751124 + 0.660161i \(0.229512\pi\)
\(68\) −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 0.741836 0.670581i \(-0.233955\pi\)
0.137238 + 0.990538i \(0.456177\pi\)
\(72\) 0 0
\(73\) −8.12155 + 2.95600i −0.950556 + 0.345974i −0.770326 0.637650i \(-0.779906\pi\)
−0.180230 + 0.983624i \(0.557684\pi\)
\(74\) 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 −0.761085 0.648653i \(-0.775333\pi\)
0.994101 + 0.108460i \(0.0345921\pi\)
\(80\) −16.3650 −1.82967
\(81\) 0 0
\(82\) −10.1684 −1.12291
\(83\) −2.24944 + 5.21479i −0.246908 + 0.572398i −0.995928 0.0901496i \(-0.971265\pi\)
0.749020 + 0.662548i \(0.230525\pi\)
\(84\) 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 −0.755385 0.655281i \(-0.772550\pi\)
−0.157453 + 0.987527i \(0.550328\pi\)
\(90\) 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 0.738729 + 0.674002i \(0.235426\pi\)
−0.811981 + 0.583684i \(0.801611\pi\)
\(98\) 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 −0.996112 0.0880941i \(-0.971922\pi\)
0.145864 + 0.989305i \(0.453404\pi\)
\(102\) 0 0
\(103\) 5.22232 3.43478i 0.514571 0.338439i −0.265519 0.964106i \(-0.585543\pi\)
0.780090 + 0.625667i \(0.215173\pi\)
\(104\) −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 −0.234320 + 0.972159i \(0.575286\pi\)
−0.724755 + 0.689007i \(0.758047\pi\)
\(108\) 0 0
\(109\) −1.91684 3.32007i −0.183600 0.318005i 0.759504 0.650503i \(-0.225442\pi\)
−0.943104 + 0.332498i \(0.892109\pi\)
\(110\) 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 0.296023 0.955181i \(-0.404339\pi\)
−0.589400 + 0.807841i \(0.700636\pi\)
\(114\) 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 −0.698943 0.715177i \(-0.746346\pi\)
0.901397 0.432994i \(-0.142543\pi\)
\(128\) −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 −0.886423 0.462877i \(-0.846817\pi\)
0.994950 + 0.100369i \(0.0320025\pi\)
\(132\) 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 −0.984663 0.174465i \(-0.944180\pi\)
−0.917887 + 0.396841i \(0.870106\pi\)
\(138\) 0 0
\(139\) −9.34045 + 2.21373i −0.792247 + 0.187766i −0.606765 0.794882i \(-0.707533\pi\)
−0.185482 + 0.982648i \(0.559385\pi\)
\(140\) −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 −0.592208 0.805785i \(-0.701743\pi\)
−0.762071 + 0.647493i \(0.775818\pi\)
\(150\) 0 0
\(151\) 1.53093 + 1.00691i 0.124585 + 0.0819412i 0.610272 0.792192i \(-0.291060\pi\)
−0.485687 + 0.874133i \(0.661430\pi\)
\(152\) 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 0.925771 + 0.378085i \(0.123417\pi\)
−0.875618 + 0.483004i \(0.839546\pi\)
\(158\) 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 −0.914121 0.405441i \(-0.867118\pi\)
0.860872 0.508822i \(-0.169919\pi\)
\(168\) 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 0.815753 0.578400i \(-0.196323\pi\)
−0.207993 + 0.978130i \(0.566693\pi\)
\(174\) 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 −0.682514 0.730872i \(-0.739114\pi\)
0.601251 + 0.799060i \(0.294669\pi\)
\(180\) 0 0
\(181\) −7.58350 6.36331i −0.563677 0.472981i 0.315864 0.948804i \(-0.397706\pi\)
−0.879541 + 0.475823i \(0.842150\pi\)
\(182\) −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 −0.998147 0.0608474i \(-0.980620\pi\)
0.227981 0.973666i \(-0.426788\pi\)
\(192\) 0 0
\(193\) −7.92466 + 26.4702i −0.570430 + 1.90537i −0.184533 + 0.982826i \(0.559077\pi\)
−0.385897 + 0.922542i \(0.626108\pi\)
\(194\) −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 0.925052 + 0.379840i \(0.124021\pi\)
−0.999178 + 0.0405468i \(0.987090\pi\)
\(198\) 0 0
\(199\) 2.78863 + 15.8151i 0.197681 + 1.12110i 0.908549 + 0.417779i \(0.137191\pi\)
−0.710868 + 0.703326i \(0.751698\pi\)
\(200\) −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 0.111175 0.993801i \(-0.464539\pi\)
−0.730762 + 0.682633i \(0.760835\pi\)
\(212\) −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 −0.354676 0.934989i \(-0.615409\pi\)
0.954030 + 0.299711i \(0.0968903\pi\)
\(224\) 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 0.808372 + 0.588673i \(0.200349\pi\)
−0.871246 + 0.490846i \(0.836688\pi\)
\(228\) 0 0
\(229\) −4.02339 + 5.40434i −0.265873 + 0.357129i −0.914931 0.403609i \(-0.867756\pi\)
0.649059 + 0.760738i \(0.275163\pi\)
\(230\) 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 −0.119747 0.992804i \(-0.538208\pi\)
−0.729894 + 0.683560i \(0.760431\pi\)
\(234\) 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 0.386607 0.922244i \(-0.373647\pi\)
−0.943163 + 0.332330i \(0.892165\pi\)
\(240\) 0 0
\(241\) 5.42266 12.5711i 0.349304 0.809778i −0.649475 0.760383i \(-0.725011\pi\)
0.998779 0.0493949i \(-0.0157293\pi\)
\(242\) 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 −0.704599 0.709606i \(-0.748873\pi\)
−0.0836277 + 0.996497i \(0.526651\pi\)
\(252\) 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 −0.860324 0.509747i \(-0.829739\pi\)
0.735076 + 0.677984i \(0.237146\pi\)
\(258\) 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 0.0381328 0.999273i \(-0.487859\pi\)
0.995365 0.0961708i \(-0.0306595\pi\)
\(264\) 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 −0.853023 0.521874i \(-0.825233\pi\)
0.878467 + 0.477802i \(0.158567\pi\)
\(270\) 0 0
\(271\) 14.1085 + 24.4366i 0.857029 + 1.48442i 0.874750 + 0.484575i \(0.161026\pi\)
−0.0177208 + 0.999843i \(0.505641\pi\)
\(272\) 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 0.798465 + 0.602042i \(0.205646\pi\)
−0.336280 + 0.941762i \(0.609169\pi\)
\(278\) 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 −0.0136939 0.999906i \(-0.504359\pi\)
0.793871 + 0.608087i \(0.208063\pi\)
\(282\) 0 0
\(283\) 0.462413 + 1.07199i 0.0274876 + 0.0637234i 0.931407 0.363980i \(-0.118582\pi\)
−0.903919 + 0.427703i \(0.859323\pi\)
\(284\) −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 0.695538 + 0.718490i \(0.255166\pi\)
−0.975930 + 0.218085i \(0.930019\pi\)
\(294\) 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 −0.968691 0.248268i \(-0.920139\pi\)
0.0762844 + 0.997086i \(0.475694\pi\)
\(308\) 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 −0.0728501 0.997343i \(-0.523209\pi\)
−0.300889 + 0.953659i \(0.597284\pi\)
\(312\) 0 0
\(313\) 7.66936 + 5.04422i 0.433498 + 0.285116i 0.747444 0.664325i \(-0.231281\pi\)
−0.313946 + 0.949441i \(0.601651\pi\)
\(314\) −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 0.231984 0.972719i \(-0.425478\pi\)
−0.229247 + 0.973368i \(0.573626\pi\)
\(318\) 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 −0.296164 0.955137i \(-0.595708\pi\)
−0.693327 + 0.720623i \(0.743856\pi\)
\(332\) 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 0.214251 0.976779i \(-0.431269\pi\)
−0.0167846 + 0.999859i \(0.505343\pi\)
\(338\) 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 −0.122123 0.992515i \(-0.538970\pi\)
0.336307 + 0.941752i \(0.390822\pi\)
\(348\) 0 0
\(349\) −7.51393 + 0.878252i −0.402211 + 0.0470118i −0.314794 0.949160i \(-0.601935\pi\)
−0.0874174 + 0.996172i \(0.527861\pi\)
\(350\) −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 0.833513 0.552500i \(-0.186326\pi\)
−0.768343 + 0.640038i \(0.778919\pi\)
\(354\) 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 0.903479 + 0.428631i \(0.141004\pi\)
−0.995594 + 0.0937737i \(0.970107\pi\)
\(360\) 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 0.519363 0.854554i \(-0.326169\pi\)
0.995599 + 0.0937115i \(0.0298731\pi\)
\(368\) −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 0.762469 0.647024i \(-0.223987\pi\)
−0.0636783 + 0.997970i \(0.520283\pi\)
\(374\) 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 −0.829851 0.557985i \(-0.811575\pi\)
0.898155 + 0.439680i \(0.144908\pi\)
\(380\) 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 −0.515902 0.856648i \(-0.672543\pi\)
0.582250 + 0.813010i \(0.302173\pi\)
\(384\) 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 −0.988543 0.150943i \(-0.951769\pi\)
0.999382 0.0351591i \(-0.0111938\pi\)
\(390\) 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 0.818965 0.573844i \(-0.194548\pi\)
0.996223 0.0868301i \(-0.0276737\pi\)
\(398\) −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 0.346454 0.938067i \(-0.387386\pi\)
−0.956625 + 0.291324i \(0.905904\pi\)
\(402\) 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 0.959395 0.282066i \(-0.0910198\pi\)
−0.337373 + 0.941371i \(0.609538\pi\)
\(410\) −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 −0.946074 0.323952i \(-0.894988\pi\)
0.581680 + 0.813418i \(0.302396\pi\)
\(420\) 0 0
\(421\) −1.25709 + 21.5834i −0.0612668 + 1.05191i 0.817889 + 0.575376i \(0.195144\pi\)
−0.879156 + 0.476534i \(0.841893\pi\)
\(422\) 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 −0.199986 0.979799i \(-0.564090\pi\)
0.948524 0.316707i \(-0.102577\pi\)
\(432\) 0 0
\(433\) −6.64480 11.5091i −0.319329 0.553093i 0.661019 0.750369i \(-0.270124\pi\)
−0.980348 + 0.197275i \(0.936791\pi\)
\(434\) −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 0.966319 0.257348i \(-0.0828487\pi\)
−0.948763 + 0.315990i \(0.897663\pi\)
\(440\) 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 −0.663939 + 0.747787i \(0.731116\pi\)
−0.996294 + 0.0860134i \(0.972587\pi\)
\(444\) 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 −0.977298 0.211871i \(-0.932044\pi\)
0.845895 0.533349i \(-0.179067\pi\)
\(450\) 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 0.744844 0.667239i \(-0.232524\pi\)
−0.852832 + 0.522186i \(0.825117\pi\)
\(458\) −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 0.390159 0.920748i \(-0.372420\pi\)
0.591981 + 0.805952i \(0.298346\pi\)
\(462\) 0 0
\(463\) 18.7929 4.45400i 0.873381 0.206995i 0.230603 0.973048i \(-0.425930\pi\)
0.642778 + 0.766053i \(0.277782\pi\)
\(464\) 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 0.566848 0.823822i \(-0.308162\pi\)
−0.712874 + 0.701292i \(0.752607\pi\)
\(468\) 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 0.813043 0.582204i \(-0.197809\pi\)
0.465269 + 0.885169i \(0.345958\pi\)
\(480\) 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 0.807108 + 0.590404i \(0.201032\pi\)
−0.733108 + 0.680112i \(0.761931\pi\)
\(492\) 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 0.0895954 0.995978i \(-0.471443\pi\)
−0.142508 + 0.989794i \(0.545517\pi\)
\(500\) −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 −0.534629 0.845087i \(-0.679549\pi\)
0.739411 + 0.673255i \(0.235104\pi\)
\(504\) 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 0.350514 0.936558i \(-0.386007\pi\)
0.733557 + 0.679628i \(0.237859\pi\)
\(510\) 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 0.536488 + 0.843908i \(0.319750\pi\)
−0.792768 + 0.609524i \(0.791361\pi\)
\(522\) 0 0
\(523\) 4.18478 + 23.7331i 0.182988 + 1.03778i 0.928513 + 0.371299i \(0.121087\pi\)
−0.745526 + 0.666477i \(0.767801\pi\)
\(524\) −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 −0.999918 0.0128282i \(-0.995917\pi\)
0.511068 + 0.859540i \(0.329250\pi\)
\(542\) −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 −0.733062 0.680162i \(-0.761909\pi\)
0.721635 + 0.692274i \(0.243391\pi\)
\(548\) 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 0.723118 0.690725i \(-0.242708\pi\)
0.109951 + 0.993937i \(0.464931\pi\)
\(558\) 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 0.896162 0.443728i \(-0.146344\pi\)
−0.495084 + 0.868845i \(0.664863\pi\)
\(564\) 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 −0.977815 0.209471i \(-0.932826\pi\)
0.823381 + 0.567489i \(0.192085\pi\)
\(570\) 0 0
\(571\) −24.7267 26.2088i −1.03478 1.09680i −0.995227 0.0975862i \(-0.968888\pi\)
−0.0395538 0.999217i \(-0.512594\pi\)
\(572\) −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 0.506115 0.862466i \(-0.331081\pi\)
−0.166675 + 0.986012i \(0.553303\pi\)
\(578\) −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 −0.845085 0.534632i \(-0.820450\pi\)
0.582864 + 0.812569i \(0.301932\pi\)
\(588\) 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 −0.194884 0.980826i \(-0.562433\pi\)
0.946862 0.321639i \(-0.104234\pi\)
\(594\) 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 0.839157 0.543889i \(-0.183049\pi\)
0.0648441 + 0.997895i \(0.479345\pi\)
\(600\) 0 0
\(601\) −6.33556 21.1622i −0.258433 0.863226i −0.984467 0.175568i \(-0.943824\pi\)
0.726034 0.687658i \(-0.241361\pi\)
\(602\) 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 0.823811 0.566865i \(-0.191844\pi\)
−0.977656 + 0.210212i \(0.932585\pi\)
\(608\) −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 0.897979 + 0.440037i \(0.145035\pi\)
−0.994326 + 0.106373i \(0.966076\pi\)
\(614\) −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 −0.842831 0.538178i \(-0.819113\pi\)
0.999909 + 0.0135025i \(0.00429810\pi\)
\(618\) 0 0
\(619\) −8.51625 11.4393i −0.342297 0.459785i 0.597325 0.801999i \(-0.296230\pi\)
−0.939622 + 0.342215i \(0.888823\pi\)
\(620\) −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 −0.755935 0.654646i \(-0.772818\pi\)
0.513434 + 0.858129i \(0.328373\pi\)
\(632\) 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 0.310597 0.950542i \(-0.399471\pi\)
−0.149043 + 0.988831i \(0.547619\pi\)
\(642\) 0 0
\(643\) −1.11571 19.1561i −0.0439995 0.755442i −0.946092 0.323899i \(-0.895006\pi\)
0.902092 0.431543i \(-0.142031\pi\)
\(644\) −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 −0.983340 0.181775i \(-0.941816\pi\)
0.955588 0.294705i \(-0.0952214\pi\)
\(654\) 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 0.870095 0.492884i \(-0.164057\pi\)
−0.107947 + 0.994157i \(0.534428\pi\)
\(660\) 0 0
\(661\) 33.4396 + 3.90853i 1.30065 + 0.152024i 0.738073 0.674721i \(-0.235736\pi\)
0.562577 + 0.826745i \(0.309810\pi\)
\(662\) 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 0.124847 0.992176i \(-0.460156\pi\)
0.350293 + 0.936640i \(0.386082\pi\)
\(674\) −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 0.599103 0.800672i \(-0.295524\pi\)
−0.938860 + 0.344299i \(0.888117\pi\)
\(678\) 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 −0.500612 0.865672i \(-0.666892\pi\)
0.766499 0.642246i \(-0.221997\pi\)
\(684\) 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 −0.966584 0.256351i \(-0.917480\pi\)
−0.371578 + 0.928402i \(0.621183\pi\)
\(692\) −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 0.817726 0.575607i \(-0.195234\pi\)
−0.907354 + 0.420368i \(0.861901\pi\)
\(702\) 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 −0.732047 0.681254i \(-0.761435\pi\)
0.722667 + 0.691197i \(0.242916\pi\)
\(710\) −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 0.0416792 0.999131i \(-0.486729\pi\)
−0.610301 + 0.792170i \(0.708951\pi\)
\(720\) 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 −0.994035 0.109057i \(-0.965217\pi\)
0.761474 + 0.648196i \(0.224476\pi\)
\(728\) 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 −0.969399 0.245491i \(-0.921051\pi\)
−0.188710 0.982033i \(-0.560431\pi\)
\(734\) 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 0.302574 0.953126i \(-0.402154\pi\)
−0.380873 + 0.924628i \(0.624376\pi\)
\(740\) −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 −0.831020 0.556242i \(-0.812243\pi\)
0.771213 + 0.636577i \(0.219650\pi\)
\(744\) 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 0.318021 0.948084i \(-0.396982\pi\)
0.996507 + 0.0835052i \(0.0266115\pi\)
\(752\) −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 0.966764 + 0.255672i \(0.0822968\pi\)
−0.261963 + 0.965078i \(0.584370\pi\)
\(758\) 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 −0.423608 0.905845i \(-0.639237\pi\)
−0.979561 + 0.201147i \(0.935533\pi\)
\(762\) 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 0.756912 + 0.653517i \(0.226707\pi\)
−0.0440729 + 0.999028i \(0.514033\pi\)
\(770\) −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 0.999995 0.00321947i \(-0.00102479\pi\)
−0.940789 + 0.338993i \(0.889914\pi\)
\(774\) 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
\(782\) −1.97850 3.42686i −0.0707509 0.122544i
\(783\) 0 0