Properties

Label 405.2.r.a.368.6
Level $405$
Weight $2$
Character 405.368
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,2,Mod(8,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([2, 27]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), 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: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 368.6
Character \(\chi\) \(=\) 405.368
Dual form 405.2.r.a.197.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.03978 - 0.0909691i) q^{2} +(-0.896746 - 0.158121i) q^{4} +(-2.23373 + 0.102160i) q^{5} +(-0.567627 - 0.397456i) q^{7} +(2.93441 + 0.786273i) q^{8} +O(q^{10})\) \(q+(-1.03978 - 0.0909691i) q^{2} +(-0.896746 - 0.158121i) q^{4} +(-2.23373 + 0.102160i) q^{5} +(-0.567627 - 0.397456i) q^{7} +(2.93441 + 0.786273i) q^{8} +(2.33189 + 0.0969768i) q^{10} +(-0.597632 + 1.64198i) q^{11} +(-0.0630233 - 0.720360i) q^{13} +(0.554051 + 0.464904i) q^{14} +(-1.26829 - 0.461619i) q^{16} +(2.95614 - 0.792096i) q^{17} +(3.38781 - 1.95596i) q^{19} +(2.01925 + 0.261588i) q^{20} +(0.770776 - 1.65293i) q^{22} +(4.63055 + 6.61310i) q^{23} +(4.97913 - 0.456395i) q^{25} +0.754750i q^{26} +(0.446171 + 0.446171i) q^{28} +(5.68683 - 4.77181i) q^{29} +(0.764639 - 4.33648i) q^{31} +(-4.22984 - 1.97241i) q^{32} +(-3.14580 + 0.554689i) q^{34} +(1.30853 + 0.829823i) q^{35} +(2.86540 + 10.6938i) q^{37} +(-3.70052 + 1.72558i) q^{38} +(-6.63502 - 1.45655i) q^{40} +(-2.71443 + 3.23493i) q^{41} +(2.74095 + 5.87799i) q^{43} +(0.795555 - 1.37794i) q^{44} +(-4.21317 - 7.29742i) q^{46} +(2.32838 - 3.32527i) q^{47} +(-2.22991 - 6.12663i) q^{49} +(-5.21872 + 0.0216046i) q^{50} +(-0.0573878 + 0.655945i) q^{52} +(5.90884 - 5.90884i) q^{53} +(1.16721 - 3.72880i) q^{55} +(-1.35314 - 1.61261i) q^{56} +(-6.34714 + 4.44432i) q^{58} +(-2.63750 + 0.959971i) q^{59} +(1.13591 + 6.44205i) q^{61} +(-1.18954 + 4.43943i) q^{62} +(6.55640 + 3.78534i) q^{64} +(0.214369 + 1.60265i) q^{65} +(11.1831 - 0.978397i) q^{67} +(-2.77616 + 0.242882i) q^{68} +(-1.28510 - 0.981870i) q^{70} +(-5.58689 - 3.22559i) q^{71} +(-2.16667 + 8.08612i) q^{73} +(-2.00658 - 11.3799i) q^{74} +(-3.34729 + 1.21831i) q^{76} +(0.991847 - 0.694499i) q^{77} +(-1.04738 - 1.24822i) q^{79} +(2.88018 + 0.901566i) q^{80} +(3.11669 - 3.11669i) q^{82} +(-0.156261 + 1.78607i) q^{83} +(-6.52232 + 2.07133i) q^{85} +(-2.31528 - 6.36117i) q^{86} +(-3.04474 + 4.34834i) q^{88} +(-2.78132 - 4.81739i) q^{89} +(-0.250538 + 0.433944i) q^{91} +(-3.10676 - 6.66246i) q^{92} +(-2.72350 + 3.24574i) q^{94} +(-7.36765 + 4.71518i) q^{95} +(-4.20036 + 1.95866i) q^{97} +(1.76129 + 6.57321i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03978 0.0909691i −0.735236 0.0643248i −0.286614 0.958046i \(-0.592530\pi\)
−0.448622 + 0.893721i \(0.648085\pi\)
\(3\) 0 0
\(4\) −0.896746 0.158121i −0.448373 0.0790603i
\(5\) −2.23373 + 0.102160i −0.998956 + 0.0456872i
\(6\) 0 0
\(7\) −0.567627 0.397456i −0.214543 0.150224i 0.461366 0.887210i \(-0.347360\pi\)
−0.675908 + 0.736986i \(0.736249\pi\)
\(8\) 2.93441 + 0.786273i 1.03747 + 0.277990i
\(9\) 0 0
\(10\) 2.33189 + 0.0969768i 0.737407 + 0.0306668i
\(11\) −0.597632 + 1.64198i −0.180193 + 0.495076i −0.996599 0.0824022i \(-0.973741\pi\)
0.816406 + 0.577478i \(0.195963\pi\)
\(12\) 0 0
\(13\) −0.0630233 0.720360i −0.0174795 0.199792i −0.999913 0.0131795i \(-0.995805\pi\)
0.982434 0.186612i \(-0.0597508\pi\)
\(14\) 0.554051 + 0.464904i 0.148076 + 0.124251i
\(15\) 0 0
\(16\) −1.26829 0.461619i −0.317072 0.115405i
\(17\) 2.95614 0.792096i 0.716970 0.192112i 0.118151 0.992996i \(-0.462303\pi\)
0.598819 + 0.800884i \(0.295637\pi\)
\(18\) 0 0
\(19\) 3.38781 1.95596i 0.777218 0.448727i −0.0582254 0.998303i \(-0.518544\pi\)
0.835443 + 0.549576i \(0.185211\pi\)
\(20\) 2.01925 + 0.261588i 0.451517 + 0.0584928i
\(21\) 0 0
\(22\) 0.770776 1.65293i 0.164330 0.352407i
\(23\) 4.63055 + 6.61310i 0.965535 + 1.37893i 0.925091 + 0.379746i \(0.123989\pi\)
0.0404446 + 0.999182i \(0.487123\pi\)
\(24\) 0 0
\(25\) 4.97913 0.456395i 0.995825 0.0912790i
\(26\) 0.754750i 0.148019i
\(27\) 0 0
\(28\) 0.446171 + 0.446171i 0.0843184 + 0.0843184i
\(29\) 5.68683 4.77181i 1.05602 0.886103i 0.0623035 0.998057i \(-0.480155\pi\)
0.993713 + 0.111954i \(0.0357109\pi\)
\(30\) 0 0
\(31\) 0.764639 4.33648i 0.137333 0.778855i −0.835873 0.548922i \(-0.815038\pi\)
0.973207 0.229933i \(-0.0738506\pi\)
\(32\) −4.22984 1.97241i −0.747738 0.348676i
\(33\) 0 0
\(34\) −3.14580 + 0.554689i −0.539500 + 0.0951284i
\(35\) 1.30853 + 0.829823i 0.221182 + 0.140266i
\(36\) 0 0
\(37\) 2.86540 + 10.6938i 0.471069 + 1.75805i 0.635939 + 0.771739i \(0.280613\pi\)
−0.164870 + 0.986315i \(0.552720\pi\)
\(38\) −3.70052 + 1.72558i −0.600303 + 0.279926i
\(39\) 0 0
\(40\) −6.63502 1.45655i −1.04909 0.230300i
\(41\) −2.71443 + 3.23493i −0.423923 + 0.505212i −0.935159 0.354229i \(-0.884743\pi\)
0.511236 + 0.859441i \(0.329188\pi\)
\(42\) 0 0
\(43\) 2.74095 + 5.87799i 0.417991 + 0.896385i 0.996725 + 0.0808685i \(0.0257694\pi\)
−0.578733 + 0.815517i \(0.696453\pi\)
\(44\) 0.795555 1.37794i 0.119934 0.207733i
\(45\) 0 0
\(46\) −4.21317 7.29742i −0.621197 1.07595i
\(47\) 2.32838 3.32527i 0.339628 0.485040i −0.612614 0.790382i \(-0.709882\pi\)
0.952243 + 0.305342i \(0.0987709\pi\)
\(48\) 0 0
\(49\) −2.22991 6.12663i −0.318559 0.875234i
\(50\) −5.21872 + 0.0216046i −0.738038 + 0.00305535i
\(51\) 0 0
\(52\) −0.0573878 + 0.655945i −0.00795825 + 0.0909632i
\(53\) 5.90884 5.90884i 0.811642 0.811642i −0.173238 0.984880i \(-0.555423\pi\)
0.984880 + 0.173238i \(0.0554230\pi\)
\(54\) 0 0
\(55\) 1.16721 3.72880i 0.157386 0.502791i
\(56\) −1.35314 1.61261i −0.180821 0.215494i
\(57\) 0 0
\(58\) −6.34714 + 4.44432i −0.833420 + 0.583567i
\(59\) −2.63750 + 0.959971i −0.343373 + 0.124978i −0.507950 0.861387i \(-0.669596\pi\)
0.164577 + 0.986364i \(0.447374\pi\)
\(60\) 0 0
\(61\) 1.13591 + 6.44205i 0.145438 + 0.824820i 0.967014 + 0.254722i \(0.0819838\pi\)
−0.821576 + 0.570098i \(0.806905\pi\)
\(62\) −1.18954 + 4.43943i −0.151072 + 0.563808i
\(63\) 0 0
\(64\) 6.55640 + 3.78534i 0.819551 + 0.473168i
\(65\) 0.214369 + 1.60265i 0.0265892 + 0.198785i
\(66\) 0 0
\(67\) 11.1831 0.978397i 1.36624 0.119530i 0.619682 0.784853i \(-0.287262\pi\)
0.746556 + 0.665323i \(0.231706\pi\)
\(68\) −2.77616 + 0.242882i −0.336659 + 0.0294538i
\(69\) 0 0
\(70\) −1.28510 0.981870i −0.153598 0.117356i
\(71\) −5.58689 3.22559i −0.663042 0.382807i 0.130393 0.991462i \(-0.458376\pi\)
−0.793435 + 0.608655i \(0.791709\pi\)
\(72\) 0 0
\(73\) −2.16667 + 8.08612i −0.253589 + 0.946409i 0.715280 + 0.698838i \(0.246299\pi\)
−0.968870 + 0.247571i \(0.920368\pi\)
\(74\) −2.00658 11.3799i −0.233261 1.32289i
\(75\) 0 0
\(76\) −3.34729 + 1.21831i −0.383960 + 0.139750i
\(77\) 0.991847 0.694499i 0.113032 0.0791455i
\(78\) 0 0
\(79\) −1.04738 1.24822i −0.117840 0.140436i 0.703899 0.710300i \(-0.251441\pi\)
−0.821739 + 0.569863i \(0.806996\pi\)
\(80\) 2.88018 + 0.901566i 0.322013 + 0.100798i
\(81\) 0 0
\(82\) 3.11669 3.11669i 0.344181 0.344181i
\(83\) −0.156261 + 1.78607i −0.0171518 + 0.196046i 0.982784 + 0.184756i \(0.0591494\pi\)
−0.999936 + 0.0112903i \(0.996406\pi\)
\(84\) 0 0
\(85\) −6.52232 + 2.07133i −0.707444 + 0.224667i
\(86\) −2.31528 6.36117i −0.249663 0.685942i
\(87\) 0 0
\(88\) −3.04474 + 4.34834i −0.324571 + 0.463535i
\(89\) −2.78132 4.81739i −0.294820 0.510643i 0.680123 0.733098i \(-0.261926\pi\)
−0.974943 + 0.222455i \(0.928593\pi\)
\(90\) 0 0
\(91\) −0.250538 + 0.433944i −0.0262635 + 0.0454897i
\(92\) −3.10676 6.66246i −0.323902 0.694610i
\(93\) 0 0
\(94\) −2.72350 + 3.24574i −0.280907 + 0.334772i
\(95\) −7.36765 + 4.71518i −0.755905 + 0.483767i
\(96\) 0 0
\(97\) −4.20036 + 1.95866i −0.426482 + 0.198872i −0.623995 0.781429i \(-0.714491\pi\)
0.197513 + 0.980300i \(0.436714\pi\)
\(98\) 1.76129 + 6.57321i 0.177917 + 0.663995i
\(99\) 0 0
\(100\) −4.53718 0.378032i −0.453718 0.0378032i
\(101\) −11.1359 + 1.96356i −1.10806 + 0.195381i −0.697594 0.716493i \(-0.745746\pi\)
−0.410469 + 0.911875i \(0.634635\pi\)
\(102\) 0 0
\(103\) −4.47475 2.08661i −0.440911 0.205600i 0.189470 0.981887i \(-0.439323\pi\)
−0.630380 + 0.776287i \(0.717101\pi\)
\(104\) 0.381463 2.16339i 0.0374055 0.212137i
\(105\) 0 0
\(106\) −6.68142 + 5.60638i −0.648957 + 0.544540i
\(107\) 11.1511 + 11.1511i 1.07801 + 1.07801i 0.996688 + 0.0813251i \(0.0259152\pi\)
0.0813251 + 0.996688i \(0.474085\pi\)
\(108\) 0 0
\(109\) 20.3152i 1.94584i −0.231133 0.972922i \(-0.574243\pi\)
0.231133 0.972922i \(-0.425757\pi\)
\(110\) −1.55284 + 3.77096i −0.148058 + 0.359546i
\(111\) 0 0
\(112\) 0.536441 + 0.766117i 0.0506889 + 0.0723912i
\(113\) −0.0516106 + 0.110679i −0.00485512 + 0.0104118i −0.908720 0.417405i \(-0.862940\pi\)
0.903865 + 0.427817i \(0.140717\pi\)
\(114\) 0 0
\(115\) −11.0190 14.2989i −1.02753 1.33338i
\(116\) −5.85416 + 3.37990i −0.543545 + 0.313816i
\(117\) 0 0
\(118\) 2.82975 0.758229i 0.260500 0.0698006i
\(119\) −1.99281 0.725323i −0.182681 0.0664903i
\(120\) 0 0
\(121\) 6.08755 + 5.10806i 0.553414 + 0.464369i
\(122\) −0.595068 6.80165i −0.0538749 0.615793i
\(123\) 0 0
\(124\) −1.37137 + 3.76782i −0.123153 + 0.338360i
\(125\) −11.0754 + 1.52813i −0.990615 + 0.136680i
\(126\) 0 0
\(127\) −16.0361 4.29687i −1.42298 0.381286i −0.536439 0.843939i \(-0.680231\pi\)
−0.886539 + 0.462654i \(0.846897\pi\)
\(128\) 1.17328 + 0.821539i 0.103704 + 0.0726144i
\(129\) 0 0
\(130\) −0.0771050 1.68591i −0.00676256 0.147864i
\(131\) 22.1825 + 3.91138i 1.93810 + 0.341739i 0.999989 0.00460251i \(-0.00146503\pi\)
0.938109 + 0.346341i \(0.112576\pi\)
\(132\) 0 0
\(133\) −2.70042 0.236256i −0.234156 0.0204860i
\(134\) −11.7170 −1.01220
\(135\) 0 0
\(136\) 9.29735 0.797241
\(137\) −5.19392 0.454409i −0.443747 0.0388228i −0.136907 0.990584i \(-0.543716\pi\)
−0.306840 + 0.951761i \(0.599272\pi\)
\(138\) 0 0
\(139\) 12.7974 + 2.25653i 1.08546 + 0.191396i 0.687630 0.726061i \(-0.258651\pi\)
0.397833 + 0.917458i \(0.369762\pi\)
\(140\) −1.04221 0.951046i −0.0880826 0.0803781i
\(141\) 0 0
\(142\) 5.51571 + 3.86214i 0.462868 + 0.324104i
\(143\) 1.22048 + 0.327027i 0.102062 + 0.0273474i
\(144\) 0 0
\(145\) −12.2154 + 11.2399i −1.01443 + 0.933425i
\(146\) 2.98845 8.21069i 0.247326 0.679522i
\(147\) 0 0
\(148\) −0.878625 10.0427i −0.0722225 0.825507i
\(149\) 8.70742 + 7.30639i 0.713340 + 0.598563i 0.925534 0.378664i \(-0.123617\pi\)
−0.212194 + 0.977227i \(0.568061\pi\)
\(150\) 0 0
\(151\) −8.54652 3.11068i −0.695506 0.253143i −0.0300149 0.999549i \(-0.509555\pi\)
−0.665491 + 0.746406i \(0.731778\pi\)
\(152\) 11.4792 3.07583i 0.931083 0.249483i
\(153\) 0 0
\(154\) −1.09448 + 0.631900i −0.0881959 + 0.0509199i
\(155\) −1.26498 + 9.76466i −0.101606 + 0.784316i
\(156\) 0 0
\(157\) 1.41498 3.03444i 0.112928 0.242175i −0.841718 0.539917i \(-0.818456\pi\)
0.954646 + 0.297742i \(0.0962335\pi\)
\(158\) 0.975501 + 1.39316i 0.0776067 + 0.110834i
\(159\) 0 0
\(160\) 9.64984 + 3.97371i 0.762887 + 0.314150i
\(161\) 5.59421i 0.440886i
\(162\) 0 0
\(163\) 9.97670 + 9.97670i 0.781435 + 0.781435i 0.980073 0.198638i \(-0.0636517\pi\)
−0.198638 + 0.980073i \(0.563652\pi\)
\(164\) 2.94567 2.47171i 0.230018 0.193008i
\(165\) 0 0
\(166\) 0.324953 1.84290i 0.0252213 0.143037i
\(167\) 12.6150 + 5.88249i 0.976182 + 0.455201i 0.844187 0.536049i \(-0.180084\pi\)
0.131995 + 0.991250i \(0.457862\pi\)
\(168\) 0 0
\(169\) 12.2876 2.16663i 0.945196 0.166664i
\(170\) 6.97021 1.56040i 0.534590 0.119677i
\(171\) 0 0
\(172\) −1.52851 5.70447i −0.116548 0.434962i
\(173\) 2.81939 1.31470i 0.214354 0.0999551i −0.312476 0.949926i \(-0.601158\pi\)
0.526830 + 0.849971i \(0.323380\pi\)
\(174\) 0 0
\(175\) −3.00768 1.71992i −0.227359 0.130014i
\(176\) 1.51594 1.80663i 0.114268 0.136180i
\(177\) 0 0
\(178\) 2.45373 + 5.26205i 0.183915 + 0.394407i
\(179\) −2.53650 + 4.39334i −0.189587 + 0.328374i −0.945113 0.326745i \(-0.894048\pi\)
0.755526 + 0.655119i \(0.227381\pi\)
\(180\) 0 0
\(181\) −4.66805 8.08530i −0.346974 0.600976i 0.638737 0.769425i \(-0.279457\pi\)
−0.985710 + 0.168449i \(0.946124\pi\)
\(182\) 0.299980 0.428416i 0.0222360 0.0317563i
\(183\) 0 0
\(184\) 8.38822 + 23.0464i 0.618388 + 1.69901i
\(185\) −7.49302 23.5944i −0.550898 1.73470i
\(186\) 0 0
\(187\) −0.466079 + 5.32731i −0.0340831 + 0.389572i
\(188\) −2.61375 + 2.61375i −0.190628 + 0.190628i
\(189\) 0 0
\(190\) 8.08968 4.23253i 0.586887 0.307060i
\(191\) −0.729528 0.869417i −0.0527868 0.0629088i 0.739005 0.673700i \(-0.235296\pi\)
−0.791792 + 0.610791i \(0.790852\pi\)
\(192\) 0 0
\(193\) 11.2910 7.90607i 0.812746 0.569091i −0.0916467 0.995792i \(-0.529213\pi\)
0.904393 + 0.426701i \(0.140324\pi\)
\(194\) 4.54563 1.65447i 0.326357 0.118784i
\(195\) 0 0
\(196\) 1.03092 + 5.84663i 0.0736371 + 0.417617i
\(197\) −0.517983 + 1.93314i −0.0369048 + 0.137730i −0.981920 0.189295i \(-0.939380\pi\)
0.945015 + 0.327026i \(0.106046\pi\)
\(198\) 0 0
\(199\) 16.0030 + 9.23931i 1.13442 + 0.654957i 0.945043 0.326947i \(-0.106020\pi\)
0.189377 + 0.981905i \(0.439353\pi\)
\(200\) 14.9697 + 2.57570i 1.05851 + 0.182130i
\(201\) 0 0
\(202\) 11.7575 1.02865i 0.827256 0.0723755i
\(203\) −5.12458 + 0.448343i −0.359675 + 0.0314675i
\(204\) 0 0
\(205\) 5.73284 7.50329i 0.400399 0.524052i
\(206\) 4.46295 + 2.57668i 0.310948 + 0.179526i
\(207\) 0 0
\(208\) −0.252600 + 0.942717i −0.0175147 + 0.0653656i
\(209\) 1.18697 + 6.73167i 0.0821047 + 0.465639i
\(210\) 0 0
\(211\) 15.7638 5.73754i 1.08522 0.394989i 0.263374 0.964694i \(-0.415165\pi\)
0.821849 + 0.569705i \(0.192943\pi\)
\(212\) −6.23304 + 4.36442i −0.428087 + 0.299750i
\(213\) 0 0
\(214\) −10.5803 12.6091i −0.723251 0.861937i
\(215\) −6.72305 12.8498i −0.458508 0.876352i
\(216\) 0 0
\(217\) −2.15759 + 2.15759i −0.146467 + 0.146467i
\(218\) −1.84806 + 21.1234i −0.125166 + 1.43066i
\(219\) 0 0
\(220\) −1.63629 + 3.15923i −0.110318 + 0.212995i
\(221\) −0.756900 2.07957i −0.0509146 0.139887i
\(222\) 0 0
\(223\) 11.5264 16.4615i 0.771868 1.10234i −0.220054 0.975488i \(-0.570623\pi\)
0.991921 0.126854i \(-0.0404879\pi\)
\(224\) 1.61703 + 2.80077i 0.108042 + 0.187134i
\(225\) 0 0
\(226\) 0.0637321 0.110387i 0.00423940 0.00734285i
\(227\) −1.96975 4.22414i −0.130737 0.280366i 0.830032 0.557715i \(-0.188322\pi\)
−0.960769 + 0.277349i \(0.910544\pi\)
\(228\) 0 0
\(229\) −15.6103 + 18.6036i −1.03156 + 1.22936i −0.0586205 + 0.998280i \(0.518670\pi\)
−0.972935 + 0.231080i \(0.925774\pi\)
\(230\) 10.1566 + 15.8701i 0.669706 + 1.04644i
\(231\) 0 0
\(232\) 20.4394 9.53106i 1.34191 0.625745i
\(233\) −1.83322 6.84167i −0.120098 0.448213i 0.879519 0.475863i \(-0.157864\pi\)
−0.999618 + 0.0276501i \(0.991198\pi\)
\(234\) 0 0
\(235\) −4.86126 + 7.66562i −0.317114 + 0.500050i
\(236\) 2.51696 0.443808i 0.163840 0.0288894i
\(237\) 0 0
\(238\) 2.00610 + 0.935462i 0.130036 + 0.0606370i
\(239\) −2.01666 + 11.4370i −0.130447 + 0.739799i 0.847476 + 0.530833i \(0.178121\pi\)
−0.977923 + 0.208966i \(0.932990\pi\)
\(240\) 0 0
\(241\) 8.02324 6.73230i 0.516822 0.433665i −0.346700 0.937976i \(-0.612698\pi\)
0.863522 + 0.504311i \(0.168253\pi\)
\(242\) −5.86505 5.86505i −0.377020 0.377020i
\(243\) 0 0
\(244\) 5.95649i 0.381325i
\(245\) 5.60692 + 13.4575i 0.358213 + 0.859766i
\(246\) 0 0
\(247\) −1.62250 2.31717i −0.103237 0.147438i
\(248\) 5.65342 12.1238i 0.358993 0.769862i
\(249\) 0 0
\(250\) 11.6550 0.581402i 0.737128 0.0367711i
\(251\) 9.75413 5.63155i 0.615675 0.355460i −0.159508 0.987197i \(-0.550991\pi\)
0.775183 + 0.631736i \(0.217657\pi\)
\(252\) 0 0
\(253\) −13.6259 + 3.65106i −0.856656 + 0.229540i
\(254\) 16.2832 + 5.92660i 1.02170 + 0.371868i
\(255\) 0 0
\(256\) −12.7442 10.6936i −0.796511 0.668352i
\(257\) −1.72895 19.7620i −0.107849 1.23272i −0.836551 0.547890i \(-0.815431\pi\)
0.728701 0.684832i \(-0.240124\pi\)
\(258\) 0 0
\(259\) 2.62385 7.20897i 0.163038 0.447944i
\(260\) 0.0611778 1.47107i 0.00379408 0.0912318i
\(261\) 0 0
\(262\) −22.7092 6.08491i −1.40298 0.375927i
\(263\) 13.8257 + 9.68085i 0.852529 + 0.596947i 0.916064 0.401033i \(-0.131349\pi\)
−0.0635351 + 0.997980i \(0.520237\pi\)
\(264\) 0 0
\(265\) −12.5951 + 13.8024i −0.773713 + 0.847876i
\(266\) 2.78635 + 0.491310i 0.170842 + 0.0301241i
\(267\) 0 0
\(268\) −10.1831 0.890909i −0.622034 0.0544209i
\(269\) −30.5994 −1.86568 −0.932838 0.360296i \(-0.882676\pi\)
−0.932838 + 0.360296i \(0.882676\pi\)
\(270\) 0 0
\(271\) −5.21670 −0.316892 −0.158446 0.987368i \(-0.550648\pi\)
−0.158446 + 0.987368i \(0.550648\pi\)
\(272\) −4.11489 0.360006i −0.249502 0.0218286i
\(273\) 0 0
\(274\) 5.35921 + 0.944973i 0.323761 + 0.0570879i
\(275\) −2.22629 + 8.44838i −0.134251 + 0.509457i
\(276\) 0 0
\(277\) −9.56033 6.69422i −0.574425 0.402216i 0.249952 0.968258i \(-0.419585\pi\)
−0.824377 + 0.566042i \(0.808474\pi\)
\(278\) −13.1012 3.51047i −0.785760 0.210544i
\(279\) 0 0
\(280\) 3.18730 + 3.46390i 0.190478 + 0.207008i
\(281\) −4.68215 + 12.8641i −0.279313 + 0.767407i 0.718127 + 0.695912i \(0.244999\pi\)
−0.997441 + 0.0714958i \(0.977223\pi\)
\(282\) 0 0
\(283\) 0.773481 + 8.84093i 0.0459787 + 0.525539i 0.983904 + 0.178700i \(0.0571892\pi\)
−0.937925 + 0.346838i \(0.887255\pi\)
\(284\) 4.49999 + 3.77594i 0.267025 + 0.224061i
\(285\) 0 0
\(286\) −1.23928 0.451062i −0.0732804 0.0266719i
\(287\) 2.82653 0.757366i 0.166845 0.0447059i
\(288\) 0 0
\(289\) −6.61106 + 3.81690i −0.388886 + 0.224524i
\(290\) 13.7238 10.5758i 0.805889 0.621035i
\(291\) 0 0
\(292\) 3.22153 6.90860i 0.188526 0.404295i
\(293\) −6.47833 9.25201i −0.378468 0.540508i 0.584053 0.811716i \(-0.301466\pi\)
−0.962521 + 0.271207i \(0.912577\pi\)
\(294\) 0 0
\(295\) 5.79340 2.41377i 0.337305 0.140535i
\(296\) 33.6331i 1.95488i
\(297\) 0 0
\(298\) −8.38915 8.38915i −0.485971 0.485971i
\(299\) 4.47198 3.75244i 0.258621 0.217009i
\(300\) 0 0
\(301\) 0.780408 4.42591i 0.0449820 0.255105i
\(302\) 8.60353 + 4.01189i 0.495078 + 0.230858i
\(303\) 0 0
\(304\) −5.19963 + 0.916835i −0.298219 + 0.0525841i
\(305\) −3.19543 14.2738i −0.182970 0.817314i
\(306\) 0 0
\(307\) 2.20847 + 8.24213i 0.126044 + 0.470403i 0.999875 0.0158274i \(-0.00503823\pi\)
−0.873831 + 0.486230i \(0.838372\pi\)
\(308\) −0.999250 + 0.465958i −0.0569376 + 0.0265504i
\(309\) 0 0
\(310\) 2.20359 10.0380i 0.125155 0.570122i
\(311\) 9.40563 11.2092i 0.533344 0.635615i −0.430338 0.902668i \(-0.641606\pi\)
0.963682 + 0.267053i \(0.0860500\pi\)
\(312\) 0 0
\(313\) −3.94117 8.45186i −0.222768 0.477727i 0.762880 0.646540i \(-0.223785\pi\)
−0.985648 + 0.168812i \(0.946007\pi\)
\(314\) −1.74731 + 3.02644i −0.0986067 + 0.170792i
\(315\) 0 0
\(316\) 0.741868 + 1.28495i 0.0417333 + 0.0722843i
\(317\) −13.5519 + 19.3542i −0.761152 + 1.08704i 0.232283 + 0.972648i \(0.425380\pi\)
−0.993436 + 0.114390i \(0.963509\pi\)
\(318\) 0 0
\(319\) 4.43659 + 12.1894i 0.248402 + 0.682478i
\(320\) −15.0320 7.78564i −0.840312 0.435231i
\(321\) 0 0
\(322\) −0.508900 + 5.81676i −0.0283599 + 0.324155i
\(323\) 8.46556 8.46556i 0.471036 0.471036i
\(324\) 0 0
\(325\) −0.642570 3.55800i −0.0356434 0.197362i
\(326\) −9.46601 11.2812i −0.524274 0.624805i
\(327\) 0 0
\(328\) −10.5088 + 7.35834i −0.580252 + 0.406297i
\(329\) −2.64330 + 0.962081i −0.145730 + 0.0530413i
\(330\) 0 0
\(331\) 4.01625 + 22.7773i 0.220753 + 1.25195i 0.870639 + 0.491922i \(0.163705\pi\)
−0.649886 + 0.760032i \(0.725183\pi\)
\(332\) 0.422540 1.57694i 0.0231899 0.0865458i
\(333\) 0 0
\(334\) −12.5818 7.26408i −0.688443 0.397473i
\(335\) −24.8802 + 3.32794i −1.35935 + 0.181825i
\(336\) 0 0
\(337\) −12.4168 + 1.08633i −0.676384 + 0.0591760i −0.420172 0.907445i \(-0.638030\pi\)
−0.256212 + 0.966621i \(0.582475\pi\)
\(338\) −12.9735 + 1.13503i −0.705663 + 0.0617375i
\(339\) 0 0
\(340\) 6.17638 0.826146i 0.334961 0.0448040i
\(341\) 6.66344 + 3.84714i 0.360846 + 0.208334i
\(342\) 0 0
\(343\) −2.42474 + 9.04926i −0.130924 + 0.488614i
\(344\) 3.42137 + 19.4036i 0.184468 + 1.04617i
\(345\) 0 0
\(346\) −3.05115 + 1.11053i −0.164031 + 0.0597023i
\(347\) −9.36840 + 6.55983i −0.502922 + 0.352150i −0.797343 0.603526i \(-0.793762\pi\)
0.294421 + 0.955676i \(0.404873\pi\)
\(348\) 0 0
\(349\) −15.6113 18.6048i −0.835652 0.995891i −0.999955 0.00948135i \(-0.996982\pi\)
0.164303 0.986410i \(-0.447462\pi\)
\(350\) 2.97087 + 2.06195i 0.158800 + 0.110216i
\(351\) 0 0
\(352\) 5.76654 5.76654i 0.307358 0.307358i
\(353\) 2.92059 33.3825i 0.155447 1.77677i −0.373024 0.927822i \(-0.621679\pi\)
0.528472 0.848951i \(-0.322765\pi\)
\(354\) 0 0
\(355\) 12.8091 + 6.63436i 0.679839 + 0.352115i
\(356\) 1.73241 + 4.75976i 0.0918177 + 0.252267i
\(357\) 0 0
\(358\) 3.03706 4.33737i 0.160514 0.229237i
\(359\) −9.34241 16.1815i −0.493073 0.854028i 0.506895 0.862008i \(-0.330793\pi\)
−0.999968 + 0.00797981i \(0.997460\pi\)
\(360\) 0 0
\(361\) −1.84847 + 3.20165i −0.0972881 + 0.168508i
\(362\) 4.11824 + 8.83159i 0.216450 + 0.464178i
\(363\) 0 0
\(364\) 0.293285 0.349523i 0.0153723 0.0183200i
\(365\) 4.01368 18.2836i 0.210086 0.957006i
\(366\) 0 0
\(367\) −6.45312 + 3.00914i −0.336850 + 0.157076i −0.583682 0.811983i \(-0.698388\pi\)
0.246831 + 0.969058i \(0.420611\pi\)
\(368\) −2.82013 10.5249i −0.147009 0.548647i
\(369\) 0 0
\(370\) 5.64474 + 25.2147i 0.293456 + 1.31085i
\(371\) −5.70252 + 1.00551i −0.296060 + 0.0522034i
\(372\) 0 0
\(373\) −9.36399 4.36650i −0.484849 0.226089i 0.164794 0.986328i \(-0.447304\pi\)
−0.649643 + 0.760239i \(0.725082\pi\)
\(374\) 0.969241 5.49684i 0.0501183 0.284235i
\(375\) 0 0
\(376\) 9.44698 7.92696i 0.487191 0.408802i
\(377\) −3.79582 3.79582i −0.195495 0.195495i
\(378\) 0 0
\(379\) 5.45309i 0.280106i 0.990144 + 0.140053i \(0.0447273\pi\)
−0.990144 + 0.140053i \(0.955273\pi\)
\(380\) 7.35248 3.06334i 0.377174 0.157146i
\(381\) 0 0
\(382\) 0.679459 + 0.970368i 0.0347641 + 0.0496483i
\(383\) 1.88914 4.05128i 0.0965307 0.207011i −0.852113 0.523359i \(-0.824679\pi\)
0.948643 + 0.316348i \(0.102457\pi\)
\(384\) 0 0
\(385\) −2.14457 + 1.65265i −0.109298 + 0.0842270i
\(386\) −12.4594 + 7.19344i −0.634167 + 0.366137i
\(387\) 0 0
\(388\) 4.07636 1.09226i 0.206946 0.0554510i
\(389\) 9.10172 + 3.31276i 0.461476 + 0.167963i 0.562287 0.826942i \(-0.309922\pi\)
−0.100811 + 0.994906i \(0.532144\pi\)
\(390\) 0 0
\(391\) 18.9268 + 15.8814i 0.957168 + 0.803159i
\(392\) −1.72627 19.7314i −0.0871899 0.996586i
\(393\) 0 0
\(394\) 0.714445 1.96292i 0.0359932 0.0988906i
\(395\) 2.46710 + 2.68120i 0.124133 + 0.134906i
\(396\) 0 0
\(397\) −0.981728 0.263053i −0.0492715 0.0132023i 0.234099 0.972213i \(-0.424786\pi\)
−0.283371 + 0.959010i \(0.591453\pi\)
\(398\) −15.7991 11.0626i −0.791936 0.554520i
\(399\) 0 0
\(400\) −6.52565 1.71962i −0.326282 0.0859810i
\(401\) −8.07342 1.42356i −0.403168 0.0710893i −0.0316124 0.999500i \(-0.510064\pi\)
−0.371555 + 0.928411i \(0.621175\pi\)
\(402\) 0 0
\(403\) −3.17202 0.277515i −0.158009 0.0138240i
\(404\) 10.2965 0.512272
\(405\) 0 0
\(406\) 5.36923 0.266470
\(407\) −19.2715 1.68604i −0.955253 0.0835738i
\(408\) 0 0
\(409\) −28.0740 4.95021i −1.38817 0.244772i −0.570897 0.821021i \(-0.693405\pi\)
−0.817274 + 0.576249i \(0.804516\pi\)
\(410\) −6.64346 + 7.28026i −0.328097 + 0.359547i
\(411\) 0 0
\(412\) 3.68278 + 2.57871i 0.181438 + 0.127044i
\(413\) 1.87866 + 0.503386i 0.0924429 + 0.0247700i
\(414\) 0 0
\(415\) 0.166580 4.00556i 0.00817710 0.196625i
\(416\) −1.15426 + 3.17132i −0.0565925 + 0.155487i
\(417\) 0 0
\(418\) −0.621820 7.10744i −0.0304142 0.347636i
\(419\) 19.6956 + 16.5265i 0.962192 + 0.807375i 0.981308 0.192443i \(-0.0616409\pi\)
−0.0191165 + 0.999817i \(0.506085\pi\)
\(420\) 0 0
\(421\) −12.0396 4.38206i −0.586775 0.213569i 0.0315356 0.999503i \(-0.489960\pi\)
−0.618310 + 0.785934i \(0.712182\pi\)
\(422\) −16.9128 + 4.53177i −0.823303 + 0.220603i
\(423\) 0 0
\(424\) 21.9849 12.6930i 1.06768 0.616427i
\(425\) 14.3575 5.29312i 0.696441 0.256754i
\(426\) 0 0
\(427\) 1.91566 4.10815i 0.0927054 0.198807i
\(428\) −8.23645 11.7629i −0.398124 0.568580i
\(429\) 0 0
\(430\) 5.82156 + 13.9726i 0.280741 + 0.673819i
\(431\) 5.16823i 0.248945i −0.992223 0.124473i \(-0.960276\pi\)
0.992223 0.124473i \(-0.0397239\pi\)
\(432\) 0 0
\(433\) −2.74947 2.74947i −0.132131 0.132131i 0.637948 0.770079i \(-0.279783\pi\)
−0.770079 + 0.637948i \(0.779783\pi\)
\(434\) 2.43970 2.04715i 0.117109 0.0982663i
\(435\) 0 0
\(436\) −3.21225 + 18.2176i −0.153839 + 0.872464i
\(437\) 28.6224 + 13.3468i 1.36919 + 0.638465i
\(438\) 0 0
\(439\) −31.6512 + 5.58095i −1.51063 + 0.266364i −0.866742 0.498757i \(-0.833790\pi\)
−0.643886 + 0.765122i \(0.722679\pi\)
\(440\) 6.35692 10.0241i 0.303054 0.477880i
\(441\) 0 0
\(442\) 0.597834 + 2.23115i 0.0284361 + 0.106125i
\(443\) −13.9035 + 6.48333i −0.660577 + 0.308032i −0.723843 0.689965i \(-0.757626\pi\)
0.0632661 + 0.997997i \(0.479848\pi\)
\(444\) 0 0
\(445\) 6.70488 + 10.4766i 0.317842 + 0.496640i
\(446\) −13.4825 + 16.0678i −0.638413 + 0.760831i
\(447\) 0 0
\(448\) −2.21708 4.75455i −0.104747 0.224631i
\(449\) 1.37821 2.38713i 0.0650416 0.112655i −0.831671 0.555269i \(-0.812615\pi\)
0.896712 + 0.442614i \(0.145949\pi\)
\(450\) 0 0
\(451\) −3.68947 6.39034i −0.173730 0.300910i
\(452\) 0.0637823 0.0910905i 0.00300007 0.00428454i
\(453\) 0 0
\(454\) 1.66384 + 4.57137i 0.0780879 + 0.214545i
\(455\) 0.515303 0.994911i 0.0241578 0.0466421i
\(456\) 0 0
\(457\) −2.98806 + 34.1536i −0.139775 + 1.59764i 0.525335 + 0.850895i \(0.323940\pi\)
−0.665111 + 0.746745i \(0.731616\pi\)
\(458\) 17.9236 17.9236i 0.837515 0.837515i
\(459\) 0 0
\(460\) 7.62030 + 14.5648i 0.355298 + 0.679086i
\(461\) 1.95614 + 2.33124i 0.0911067 + 0.108577i 0.809672 0.586883i \(-0.199645\pi\)
−0.718565 + 0.695460i \(0.755201\pi\)
\(462\) 0 0
\(463\) 22.0633 15.4489i 1.02537 0.717970i 0.0653361 0.997863i \(-0.479188\pi\)
0.960031 + 0.279894i \(0.0902992\pi\)
\(464\) −9.41529 + 3.42689i −0.437094 + 0.159089i
\(465\) 0 0
\(466\) 1.28377 + 7.28061i 0.0594694 + 0.337268i
\(467\) −4.45355 + 16.6209i −0.206086 + 0.769122i 0.783030 + 0.621983i \(0.213673\pi\)
−0.989116 + 0.147138i \(0.952994\pi\)
\(468\) 0 0
\(469\) −6.73671 3.88944i −0.311073 0.179598i
\(470\) 5.75198 7.52834i 0.265319 0.347257i
\(471\) 0 0
\(472\) −8.49431 + 0.743156i −0.390982 + 0.0342065i
\(473\) −11.2896 + 0.987714i −0.519098 + 0.0454152i
\(474\) 0 0
\(475\) 15.9757 11.2851i 0.733014 0.517797i
\(476\) 1.67236 + 0.965535i 0.0766523 + 0.0442552i
\(477\) 0 0
\(478\) 3.13729 11.7085i 0.143497 0.535536i
\(479\) −6.03903 34.2490i −0.275930 1.56488i −0.735991 0.676991i \(-0.763283\pi\)
0.460061 0.887888i \(-0.347828\pi\)
\(480\) 0 0
\(481\) 7.52282 2.73808i 0.343011 0.124846i
\(482\) −8.95484 + 6.27025i −0.407882 + 0.285602i
\(483\) 0 0
\(484\) −4.65130 5.54320i −0.211423 0.251964i
\(485\) 9.18238 4.80423i 0.416951 0.218149i
\(486\) 0 0
\(487\) −10.1713 + 10.1713i −0.460908 + 0.460908i −0.898953 0.438045i \(-0.855671\pi\)
0.438045 + 0.898953i \(0.355671\pi\)
\(488\) −1.73199 + 19.7968i −0.0784036 + 0.896157i
\(489\) 0 0
\(490\) −4.60576 14.5029i −0.208067 0.655173i
\(491\) −10.0702 27.6677i −0.454462 1.24863i −0.929553 0.368688i \(-0.879807\pi\)
0.475091 0.879937i \(-0.342415\pi\)
\(492\) 0 0
\(493\) 13.0313 18.6107i 0.586902 0.838183i
\(494\) 1.47626 + 2.55695i 0.0664199 + 0.115043i
\(495\) 0 0
\(496\) −2.97158 + 5.14694i −0.133428 + 0.231104i
\(497\) 1.88923 + 4.05148i 0.0847438 + 0.181734i
\(498\) 0 0
\(499\) 11.3613 13.5399i 0.508604 0.606130i −0.449243 0.893410i \(-0.648306\pi\)
0.957847 + 0.287279i \(0.0927507\pi\)
\(500\) 10.1735 + 0.380905i 0.454971 + 0.0170346i
\(501\) 0 0
\(502\) −10.6545 + 4.96826i −0.475532 + 0.221744i
\(503\) 3.36375 + 12.5537i 0.149982 + 0.559742i 0.999483 + 0.0321541i \(0.0102367\pi\)
−0.849501 + 0.527588i \(0.823097\pi\)
\(504\) 0 0
\(505\) 24.6740 5.52370i 1.09798 0.245802i
\(506\) 14.5001 2.55677i 0.644610 0.113662i
\(507\) 0 0
\(508\) 13.7009 + 6.38885i 0.607880 + 0.283459i
\(509\) 0.0644329 0.365417i 0.00285594 0.0161968i −0.983346 0.181741i \(-0.941827\pi\)
0.986202 + 0.165544i \(0.0529380\pi\)
\(510\) 0 0
\(511\) 4.44374 3.72874i 0.196579 0.164950i
\(512\) 10.2528 + 10.2528i 0.453113 + 0.453113i
\(513\) 0 0
\(514\) 20.7055i 0.913279i
\(515\) 10.2086 + 4.20379i 0.449843 + 0.185241i
\(516\) 0 0
\(517\) 4.06851 + 5.81043i 0.178933 + 0.255542i
\(518\) −3.38403 + 7.25707i −0.148686 + 0.318857i
\(519\) 0 0
\(520\) −0.631076 + 4.87140i −0.0276745 + 0.213625i
\(521\) 2.40696 1.38966i 0.105451 0.0608820i −0.446347 0.894860i \(-0.647275\pi\)
0.551798 + 0.833978i \(0.313942\pi\)
\(522\) 0 0
\(523\) 14.6842 3.93462i 0.642096 0.172049i 0.0769434 0.997035i \(-0.475484\pi\)
0.565153 + 0.824986i \(0.308817\pi\)
\(524\) −19.2736 7.01503i −0.841973 0.306453i
\(525\) 0 0
\(526\) −13.4950 11.3237i −0.588411 0.493736i
\(527\) −1.17453 13.4249i −0.0511633 0.584799i
\(528\) 0 0
\(529\) −14.4247 + 39.6316i −0.627162 + 1.72311i
\(530\) 14.3518 13.2057i 0.623401 0.573620i
\(531\) 0 0
\(532\) 2.38424 + 0.638854i 0.103370 + 0.0276978i
\(533\) 2.50139 + 1.75149i 0.108347 + 0.0758655i
\(534\) 0 0
\(535\) −26.0477 23.7693i −1.12614 1.02764i
\(536\) 33.5852 + 5.92198i 1.45066 + 0.255790i
\(537\) 0 0
\(538\) 31.8166 + 2.78359i 1.37171 + 0.120009i
\(539\) 11.3925 0.490709
\(540\) 0 0
\(541\) −16.6575 −0.716163 −0.358081 0.933690i \(-0.616569\pi\)
−0.358081 + 0.933690i \(0.616569\pi\)
\(542\) 5.42423 + 0.474558i 0.232990 + 0.0203840i
\(543\) 0 0
\(544\) −14.0664 2.48028i −0.603090 0.106341i
\(545\) 2.07540 + 45.3788i 0.0889002 + 1.94381i
\(546\) 0 0
\(547\) 0.317541 + 0.222344i 0.0135771 + 0.00950676i 0.580345 0.814371i \(-0.302918\pi\)
−0.566768 + 0.823877i \(0.691806\pi\)
\(548\) 4.58578 + 1.22876i 0.195895 + 0.0524899i
\(549\) 0 0
\(550\) 3.08340 8.58195i 0.131477 0.365935i
\(551\) 9.93246 27.2892i 0.423137 1.16256i
\(552\) 0 0
\(553\) 0.0984086 + 1.12482i 0.00418476 + 0.0478320i
\(554\) 9.33168 + 7.83021i 0.396465 + 0.332674i
\(555\) 0 0
\(556\) −11.1192 4.04707i −0.471561 0.171634i
\(557\) −12.2853 + 3.29185i −0.520546 + 0.139480i −0.509519 0.860459i \(-0.670177\pi\)
−0.0110271 + 0.999939i \(0.503510\pi\)
\(558\) 0 0
\(559\) 4.06152 2.34492i 0.171784 0.0991797i
\(560\) −1.27653 1.65650i −0.0539433 0.0699998i
\(561\) 0 0
\(562\) 6.03864 12.9499i 0.254725 0.546259i
\(563\) 16.7779 + 23.9613i 0.707102 + 1.00985i 0.998580 + 0.0532691i \(0.0169641\pi\)
−0.291478 + 0.956578i \(0.594147\pi\)
\(564\) 0 0
\(565\) 0.103977 0.252500i 0.00437436 0.0106228i
\(566\) 9.26299i 0.389353i
\(567\) 0 0
\(568\) −13.8580 13.8580i −0.581470 0.581470i
\(569\) 3.92124 3.29031i 0.164387 0.137937i −0.556884 0.830591i \(-0.688003\pi\)
0.721270 + 0.692654i \(0.243559\pi\)
\(570\) 0 0
\(571\) 1.16063 6.58228i 0.0485710 0.275460i −0.950844 0.309671i \(-0.899781\pi\)
0.999415 + 0.0342116i \(0.0108920\pi\)
\(572\) −1.04275 0.486243i −0.0435997 0.0203309i
\(573\) 0 0
\(574\) −3.00787 + 0.530368i −0.125546 + 0.0221372i
\(575\) 26.0743 + 30.8141i 1.08737 + 1.28504i
\(576\) 0 0
\(577\) −11.9622 44.6435i −0.497992 1.85853i −0.512580 0.858640i \(-0.671310\pi\)
0.0145873 0.999894i \(-0.495357\pi\)
\(578\) 7.22128 3.36734i 0.300366 0.140063i
\(579\) 0 0
\(580\) 12.7313 8.14786i 0.528640 0.338321i
\(581\) 0.798581 0.951712i 0.0331307 0.0394837i
\(582\) 0 0
\(583\) 6.17089 + 13.2335i 0.255572 + 0.548076i
\(584\) −12.7158 + 22.0244i −0.526183 + 0.911376i
\(585\) 0 0
\(586\) 5.89440 + 10.2094i 0.243495 + 0.421746i
\(587\) −1.01832 + 1.45431i −0.0420306 + 0.0600260i −0.839617 0.543178i \(-0.817221\pi\)
0.797587 + 0.603204i \(0.206110\pi\)
\(588\) 0 0
\(589\) −5.89151 16.1868i −0.242755 0.666965i
\(590\) −6.24344 + 1.98277i −0.257039 + 0.0816293i
\(591\) 0 0
\(592\) 1.30232 14.8856i 0.0535250 0.611794i
\(593\) −27.8118 + 27.8118i −1.14209 + 1.14209i −0.154028 + 0.988066i \(0.549225\pi\)
−0.988066 + 0.154028i \(0.950775\pi\)
\(594\) 0 0
\(595\) 4.52550 + 1.41659i 0.185528 + 0.0580747i
\(596\) −6.65306 7.92880i −0.272520 0.324776i
\(597\) 0 0
\(598\) −4.99124 + 3.49490i −0.204107 + 0.142917i
\(599\) −37.7245 + 13.7306i −1.54138 + 0.561017i −0.966376 0.257133i \(-0.917222\pi\)
−0.575005 + 0.818150i \(0.695000\pi\)
\(600\) 0 0
\(601\) 3.13840 + 17.7988i 0.128018 + 0.726027i 0.979469 + 0.201593i \(0.0646119\pi\)
−0.851451 + 0.524434i \(0.824277\pi\)
\(602\) −1.21407 + 4.53099i −0.0494820 + 0.184669i
\(603\) 0 0
\(604\) 7.17219 + 4.14087i 0.291832 + 0.168490i
\(605\) −14.1198 10.7881i −0.574052 0.438601i
\(606\) 0 0
\(607\) −14.2779 + 1.24916i −0.579522 + 0.0507016i −0.373149 0.927772i \(-0.621722\pi\)
−0.206374 + 0.978473i \(0.566166\pi\)
\(608\) −18.1879 + 1.59123i −0.737616 + 0.0645330i
\(609\) 0 0
\(610\) 2.02408 + 15.1323i 0.0819525 + 0.612688i
\(611\) −2.54213 1.46770i −0.102844 0.0593767i
\(612\) 0 0
\(613\) 7.34062 27.3956i 0.296485 1.10650i −0.643546 0.765408i \(-0.722537\pi\)
0.940031 0.341090i \(-0.110796\pi\)
\(614\) −1.54655 8.77091i −0.0624136 0.353965i
\(615\) 0 0
\(616\) 3.45655 1.25808i 0.139269 0.0506896i
\(617\) −19.2569 + 13.4838i −0.775255 + 0.542839i −0.892921 0.450214i \(-0.851348\pi\)
0.117666 + 0.993053i \(0.462459\pi\)
\(618\) 0 0
\(619\) 5.35313 + 6.37961i 0.215160 + 0.256418i 0.862820 0.505512i \(-0.168696\pi\)
−0.647659 + 0.761930i \(0.724252\pi\)
\(620\) 2.67836 8.55640i 0.107566 0.343633i
\(621\) 0 0
\(622\) −10.7995 + 10.7995i −0.433020 + 0.433020i
\(623\) −0.335951 + 3.83994i −0.0134596 + 0.153844i
\(624\) 0 0
\(625\) 24.5834 4.54490i 0.983336 0.181796i
\(626\) 3.32909 + 9.14661i 0.133057 + 0.365572i
\(627\) 0 0
\(628\) −1.74869 + 2.49739i −0.0697803 + 0.0996566i
\(629\) 16.9411 + 29.3428i 0.675485 + 1.16997i
\(630\) 0 0
\(631\) 10.7788 18.6694i 0.429097 0.743218i −0.567696 0.823238i \(-0.692165\pi\)
0.996793 + 0.0800204i \(0.0254985\pi\)
\(632\) −2.09201 4.48633i −0.0832158 0.178457i
\(633\) 0 0
\(634\) 15.8517 18.8913i 0.629550 0.750269i
\(635\) 36.2594 + 7.95982i 1.43891 + 0.315876i
\(636\) 0 0
\(637\) −4.27285 + 1.99246i −0.169296 + 0.0789442i
\(638\) −3.50422 13.0779i −0.138734 0.517761i
\(639\) 0 0
\(640\) −2.70472 1.71524i −0.106913 0.0678007i
\(641\) 4.89330 0.862821i 0.193274 0.0340794i −0.0761733 0.997095i \(-0.524270\pi\)
0.269447 + 0.963015i \(0.413159\pi\)
\(642\) 0 0
\(643\) −20.7326 9.66776i −0.817613 0.381259i −0.0316243 0.999500i \(-0.510068\pi\)
−0.785989 + 0.618241i \(0.787846\pi\)
\(644\) −0.884560 + 5.01659i −0.0348566 + 0.197681i
\(645\) 0 0
\(646\) −9.57243 + 8.03223i −0.376622 + 0.316024i
\(647\) 8.15287 + 8.15287i 0.320522 + 0.320522i 0.848967 0.528445i \(-0.177225\pi\)
−0.528445 + 0.848967i \(0.677225\pi\)
\(648\) 0 0
\(649\) 4.90443i 0.192516i
\(650\) 0.344464 + 3.75799i 0.0135110 + 0.147401i
\(651\) 0 0
\(652\) −7.36905 10.5241i −0.288594 0.412155i
\(653\) 15.6937 33.6553i 0.614142 1.31703i −0.315625 0.948884i \(-0.602214\pi\)
0.929767 0.368148i \(-0.120008\pi\)
\(654\) 0 0
\(655\) −49.9495 6.47082i −1.95169 0.252836i
\(656\) 4.93599 2.84980i 0.192718 0.111266i
\(657\) 0 0
\(658\) 2.83597 0.759896i 0.110558 0.0296238i
\(659\) −17.4051 6.33493i −0.678005 0.246774i −0.0200144 0.999800i \(-0.506371\pi\)
−0.657991 + 0.753026i \(0.728593\pi\)
\(660\) 0 0
\(661\) 32.6452 + 27.3925i 1.26975 + 1.06545i 0.994572 + 0.104053i \(0.0331813\pi\)
0.275178 + 0.961393i \(0.411263\pi\)
\(662\) −2.10399 24.0488i −0.0817740 0.934682i
\(663\) 0 0
\(664\) −1.86287 + 5.11819i −0.0722933 + 0.198624i
\(665\) 6.05616 + 0.251859i 0.234848 + 0.00976668i
\(666\) 0 0
\(667\) 57.8896 + 15.5115i 2.24149 + 0.600607i
\(668\) −10.3824 7.26980i −0.401705 0.281277i
\(669\) 0 0
\(670\) 26.1727 1.19701i 1.01114 0.0462444i
\(671\) −11.2566 1.98484i −0.434555 0.0766238i
\(672\) 0 0
\(673\) 9.45392 + 0.827111i 0.364422 + 0.0318828i 0.267896 0.963448i \(-0.413672\pi\)
0.0965254 + 0.995331i \(0.469227\pi\)
\(674\) 13.0095 0.501109
\(675\) 0 0
\(676\) −11.3614 −0.436977
\(677\) 10.7923 + 0.944208i 0.414783 + 0.0362888i 0.292638 0.956223i \(-0.405467\pi\)
0.122146 + 0.992512i \(0.461023\pi\)
\(678\) 0 0
\(679\) 3.16272 + 0.557672i 0.121374 + 0.0214015i
\(680\) −20.7678 + 0.949814i −0.796408 + 0.0364237i
\(681\) 0 0
\(682\) −6.57855 4.60635i −0.251906 0.176386i
\(683\) 2.18859 + 0.586431i 0.0837441 + 0.0224392i 0.300448 0.953798i \(-0.402864\pi\)
−0.216704 + 0.976237i \(0.569531\pi\)
\(684\) 0 0
\(685\) 11.6483 + 0.484420i 0.445057 + 0.0185087i
\(686\) 3.34440 9.18868i 0.127690 0.350825i
\(687\) 0 0
\(688\) −0.762924 8.72026i −0.0290862 0.332457i
\(689\) −4.62889 3.88410i −0.176347 0.147972i
\(690\) 0 0
\(691\) 7.28698 + 2.65224i 0.277210 + 0.100896i 0.476884 0.878966i \(-0.341766\pi\)
−0.199674 + 0.979862i \(0.563988\pi\)
\(692\) −2.73616 + 0.733152i −0.104013 + 0.0278703i
\(693\) 0 0
\(694\) 10.3378 5.96855i 0.392419 0.226563i
\(695\) −28.8165 3.73311i −1.09307 0.141605i
\(696\) 0 0
\(697\) −5.46187 + 11.7130i −0.206883 + 0.443662i
\(698\) 14.5398 + 20.7650i 0.550341 + 0.785969i
\(699\) 0 0
\(700\) 2.42517 + 2.01791i 0.0916629 + 0.0762699i
\(701\) 3.06270i 0.115677i 0.998326 + 0.0578383i \(0.0184208\pi\)
−0.998326 + 0.0578383i \(0.981579\pi\)
\(702\) 0 0
\(703\) 30.6241 + 30.6241i 1.15501 + 1.15501i
\(704\) −10.1338 + 8.50324i −0.381931 + 0.320478i
\(705\) 0 0
\(706\) −6.07355 + 34.4448i −0.228581 + 1.29635i
\(707\) 7.10146 + 3.31146i 0.267078 + 0.124540i
\(708\) 0 0
\(709\) 45.6222 8.04442i 1.71338 0.302114i 0.771041 0.636785i \(-0.219736\pi\)
0.942335 + 0.334671i \(0.108625\pi\)
\(710\) −12.7152 8.06351i −0.477192 0.302618i
\(711\) 0 0
\(712\) −4.37376 16.3231i −0.163914 0.611734i
\(713\) 32.2183 15.0236i 1.20658 0.562640i
\(714\) 0 0
\(715\) −2.75964 0.605807i −0.103205 0.0226559i
\(716\) 2.96927 3.53864i 0.110967 0.132245i
\(717\) 0 0
\(718\) 8.24204 + 17.6751i 0.307590 + 0.659629i
\(719\) 25.2485 43.7317i 0.941610 1.63092i 0.179211 0.983811i \(-0.442646\pi\)
0.762400 0.647106i \(-0.224021\pi\)
\(720\) 0 0
\(721\) 1.71065 + 2.96294i 0.0637080 + 0.110346i
\(722\) 2.21326 3.16086i 0.0823690 0.117635i
\(723\) 0 0
\(724\) 2.90761 + 7.98858i 0.108060 + 0.296893i
\(725\) 26.1376 26.3549i 0.970726 0.978796i
\(726\) 0 0
\(727\) −0.922993 + 10.5499i −0.0342319 + 0.391273i 0.959680 + 0.281095i \(0.0906976\pi\)
−0.993912 + 0.110178i \(0.964858\pi\)
\(728\) −1.07638 + 1.07638i −0.0398933 + 0.0398933i
\(729\) 0 0
\(730\) −5.83659 + 18.6458i −0.216022 + 0.690112i
\(731\) 12.7586 + 15.2051i 0.471893 + 0.562380i
\(732\) 0 0
\(733\) −23.8946 + 16.7312i −0.882569 + 0.617981i −0.924518 0.381139i \(-0.875532\pi\)
0.0419494 + 0.999120i \(0.486643\pi\)
\(734\) 6.98357 2.54181i 0.257768 0.0938200i
\(735\) 0 0
\(736\) −6.54274 37.1057i −0.241169 1.36774i
\(737\) −5.07689 + 18.9472i −0.187010 + 0.697929i
\(738\) 0 0
\(739\) 5.54415 + 3.20092i 0.203945 + 0.117748i 0.598494 0.801127i \(-0.295766\pi\)
−0.394549 + 0.918875i \(0.629099\pi\)
\(740\) 2.98858 + 22.3430i 0.109862 + 0.821346i
\(741\) 0 0
\(742\) 6.02085 0.526756i 0.221032 0.0193378i
\(743\) −29.7334 + 2.60134i −1.09081 + 0.0954338i −0.618339 0.785911i \(-0.712194\pi\)
−0.472473 + 0.881345i \(0.656639\pi\)
\(744\) 0 0
\(745\) −20.1965 15.4310i −0.739941 0.565347i
\(746\) 9.33928 + 5.39204i 0.341935 + 0.197416i
\(747\) 0 0
\(748\) 1.26031 4.70355i 0.0460816 0.171979i
\(749\) −1.89758 10.7617i −0.0693359 0.393224i
\(750\) 0 0
\(751\) −9.53000 + 3.46864i −0.347755 + 0.126572i −0.509991 0.860180i \(-0.670351\pi\)
0.162237 + 0.986752i \(0.448129\pi\)
\(752\) −4.48806 + 3.14257i −0.163663 + 0.114598i
\(753\) 0 0
\(754\) 3.60152 + 4.29213i 0.131160 + 0.156310i
\(755\) 19.4084 + 6.07531i 0.706345 + 0.221103i
\(756\) 0 0
\(757\) 6.39851 6.39851i 0.232558 0.232558i −0.581202 0.813760i \(-0.697417\pi\)
0.813760 + 0.581202i \(0.197417\pi\)
\(758\) 0.496062 5.67002i 0.0180178 0.205944i
\(759\) 0 0
\(760\) −25.3271 + 8.04329i −0.918712 + 0.291761i
\(761\) −9.16585 25.1830i −0.332262 0.912882i −0.987522 0.157479i \(-0.949663\pi\)
0.655260 0.755403i \(-0.272559\pi\)
\(762\) 0 0
\(763\) −8.07441 + 11.5315i −0.292313 + 0.417467i
\(764\) 0.516728 + 0.895000i 0.0186946 + 0.0323800i
\(765\) 0 0
\(766\) −2.33284 + 4.04059i −0.0842888 + 0.145993i
\(767\) 0.857749 + 1.83945i 0.0309715 + 0.0664186i
\(768\) 0 0
\(769\) −8.41448 + 10.0280i −0.303434 + 0.361619i −0.896117 0.443817i \(-0.853624\pi\)
0.592684 + 0.805435i \(0.298068\pi\)
\(770\) 2.38023 1.52331i 0.0857774 0.0548962i
\(771\) 0 0
\(772\) −11.3753 + 5.30439i −0.409406 + 0.190909i
\(773\) 3.35520 + 12.5218i 0.120678 + 0.450377i 0.999649 0.0264987i \(-0.00843577\pi\)
−0.878971 + 0.476876i \(0.841769\pi\)
\(774\) 0 0
\(775\) 1.82808 21.9409i 0.0656667 0.788139i
\(776\) −13.8656 + 2.44488i −0.497747 + 0.0877662i
\(777\) 0 0
\(778\) −9.16244 4.27252i −0.328489 0.153177i
\(779\) −2.86861 + 16.2687i −0.102778 + 0.582886i
\(780\) 0 0
\(781\) 8.63526 7.24584i 0.308994 0.259277i
\(782\) −18.2350 18.2350i −0.652082 0.652082i
\(783\) 0 0
\(784\) 8.79971i 0.314275i
\(785\) −2.85070 + 6.92269i −0.101746 + 0.247081i
\(786\) 0 0
\(787\) −7.17412 10.2457i −0.255730 0.365220i 0.670673 0.741753i \(-0.266005\pi\)
−0.926403 + 0.376533i \(0.877116\pi\)
\(788\) 0.770169 1.65163i 0.0274361 0.0588370i
\(789\) 0 0
\(790\) −2.32133 3.01229i −0.0825893 0.107172i
\(791\) 0.0732857 0.0423115i 0.00260574 0.00150443i
\(792\) 0 0
\(793\) 4.56900 1.22426i 0.162250 0.0434748i
\(794\) 0.996853 + 0.362825i 0.0353770 + 0.0128762i
\(795\) 0 0
\(796\) −12.8897 10.8157i −0.456862 0.383353i
\(797\) −0.571540 6.53273i −0.0202450 0.231401i −0.999575 0.0291347i \(-0.990725\pi\)
0.979331 0.202267i \(-0.0648307\pi\)
\(798\) 0 0
\(799\) 4.24908 11.6743i 0.150322 0.413006i
\(800\) −21.9611 7.89039i −0.776443 0.278967i
\(801\) 0 0
\(802\) 8.26509 + 2.21462i 0.291851 + 0.0782011i
\(803\) −11.9824 8.39015i −0.422849 0.296082i
\(804\) 0 0
\(805\) 0.571503 + 12.4960i 0.0201429 + 0.440425i
\(806\) 3.27296 + 0.577111i 0.115285 + 0.0203279i
\(807\) 0 0
\(808\) −34.2212 2.99397i −1.20390 0.105327i
\(809\) 21.1375 0.743156 0.371578 0.928402i \(-0.378817\pi\)
0.371578 + 0.928402i \(0.378817\pi\)
\(810\) 0 0
\(811\) −48.6371 −1.70788 −0.853940 0.520371i \(-0.825794\pi\)
−0.853940 + 0.520371i \(0.825794\pi\)
\(812\) 4.66634 + 0.408252i 0.163756 + 0.0143268i
\(813\) 0 0
\(814\) 19.8848 + 3.50622i 0.696961 + 0.122893i
\(815\) −23.3045 21.2661i −0.816321 0.744918i
\(816\) 0 0
\(817\) 20.7829 + 14.5524i 0.727103 + 0.509123i
\(818\) 28.7405 + 7.70100i 1.00489 + 0.269259i
\(819\) 0 0
\(820\) −6.32732 + 5.82206i −0.220960 + 0.203315i
\(821\) −8.00089 + 21.9823i −0.279233 + 0.767186i 0.718217 + 0.695819i \(0.244958\pi\)
−0.997450 + 0.0713672i \(0.977264\pi\)
\(822\) 0 0
\(823\) −0.292711 3.34570i −0.0102033 0.116624i 0.989385 0.145318i \(-0.0464206\pi\)
−0.999588 + 0.0286943i \(0.990865\pi\)
\(824\) −11.4901 9.64136i −0.400277 0.335873i
\(825\) 0 0
\(826\) −1.90760 0.694311i −0.0663740 0.0241582i
\(827\) 20.9358 5.60974i 0.728010 0.195070i 0.124267 0.992249i \(-0.460342\pi\)
0.603743 + 0.797179i \(0.293675\pi\)
\(828\) 0 0
\(829\) −4.62453 + 2.66997i −0.160617 + 0.0927320i −0.578154 0.815928i \(-0.696227\pi\)
0.417537 + 0.908660i \(0.362893\pi\)
\(830\) −0.537589 + 4.14975i −0.0186600 + 0.144040i
\(831\) 0 0
\(832\) 2.31360 4.96154i 0.0802097 0.172010i
\(833\) −11.4448 16.3449i −0.396540 0.566317i
\(834\) 0 0
\(835\) −28.7796 11.8512i −0.995959 0.410127i
\(836\) 6.22428i 0.215271i
\(837\) 0 0
\(838\) −18.9757 18.9757i −0.655504 0.655504i
\(839\) −0.256169 + 0.214952i −0.00884395 + 0.00742095i −0.647199 0.762321i \(-0.724060\pi\)
0.638355 + 0.769742i \(0.279615\pi\)
\(840\) 0 0
\(841\) 4.53398 25.7135i 0.156344 0.886673i
\(842\) 12.1199 + 5.65161i 0.417680 + 0.194767i
\(843\) 0 0
\(844\) −15.0433 + 2.65254i −0.517813 + 0.0913043i
\(845\) −27.2258 + 6.09496i −0.936595 + 0.209673i
\(846\) 0 0
\(847\) −1.42522 5.31901i −0.0489713 0.182763i
\(848\) −10.2217 + 4.76648i −0.351016 + 0.163682i
\(849\) 0 0
\(850\) −15.4102 + 4.19759i −0.528565 + 0.143976i
\(851\) −57.4510 + 68.4675i −1.96940 + 2.34703i
\(852\) 0 0
\(853\) 7.30797 + 15.6720i 0.250220 + 0.536598i 0.990794 0.135376i \(-0.0432242\pi\)
−0.740574 + 0.671974i \(0.765446\pi\)
\(854\) −2.36558 + 4.09731i −0.0809486 + 0.140207i
\(855\) 0 0
\(856\) 23.9540 + 41.4895i 0.818731 + 1.41808i
\(857\) 6.28056 8.96957i 0.214540 0.306395i −0.697429 0.716654i \(-0.745673\pi\)
0.911969 + 0.410259i \(0.134562\pi\)
\(858\) 0 0
\(859\) −9.19021 25.2499i −0.313566 0.861515i −0.991930 0.126789i \(-0.959533\pi\)
0.678364 0.734726i \(-0.262689\pi\)
\(860\) 3.99704 + 12.5861i 0.136298 + 0.429183i
\(861\) 0 0
\(862\) −0.470149 + 5.37383i −0.0160133 + 0.183033i
\(863\) −14.0569 + 14.0569i −0.478502 + 0.478502i −0.904652 0.426150i \(-0.859869\pi\)
0.426150 + 0.904652i \(0.359869\pi\)
\(864\) 0 0
\(865\) −6.16346 + 3.22473i −0.209564 + 0.109644i
\(866\) 2.60873 + 3.10897i 0.0886484 + 0.105647i
\(867\) 0 0
\(868\) 2.27597 1.59365i 0.0772515 0.0540921i
\(869\) 2.67551 0.973806i 0.0907605 0.0330341i
\(870\) 0 0
\(871\) −1.40960 7.99422i −0.0477623 0.270874i
\(872\) 15.9733 59.6132i 0.540924 2.01876i
\(873\) 0 0
\(874\) −28.5469 16.4815i −0.965612 0.557496i
\(875\) 6.89407 + 3.53459i 0.233062 + 0.119491i
\(876\) 0 0
\(877\) −31.0262 + 2.71444i −1.04768 + 0.0916602i −0.597974 0.801516i \(-0.704027\pi\)
−0.449708 + 0.893176i \(0.648472\pi\)
\(878\) 33.4180 2.92369i 1.12780 0.0986699i
\(879\) 0 0
\(880\) −3.20164 + 4.19039i −0.107927 + 0.141258i
\(881\) 10.7039 + 6.17988i 0.360623 + 0.208206i 0.669354 0.742944i \(-0.266571\pi\)
−0.308731 + 0.951149i \(0.599904\pi\)
\(882\) 0 0
\(883\) −9.26338 + 34.5714i −0.311738 + 1.16342i 0.615251 + 0.788331i \(0.289055\pi\)
−0.926989 + 0.375089i \(0.877612\pi\)
\(884\) 0.349925 + 1.98452i 0.0117693 + 0.0667468i
\(885\) 0 0
\(886\) 15.0464 5.47645i 0.505494 0.183985i
\(887\) −1.91991 + 1.34433i −0.0644642 + 0.0451383i −0.605364 0.795949i \(-0.706973\pi\)
0.540900 + 0.841087i \(0.318084\pi\)
\(888\) 0 0
\(889\) 7.39472 + 8.81269i 0.248011 + 0.295568i
\(890\) −6.01856 11.5033i −0.201742 0.385593i
\(891\) 0 0
\(892\) −12.9392 + 12.9392i −0.433236 + 0.433236i
\(893\) 1.38403 15.8196i 0.0463149 0.529382i
\(894\) 0 0
\(895\) 5.21703 10.0727i 0.174386 0.336693i
\(896\) −0.339458 0.932655i −0.0113405 0.0311578i
\(897\) 0 0
\(898\) −1.65019 + 2.35671i −0.0550675 + 0.0786446i
\(899\) −16.3445 28.3095i −0.545120 0.944175i
\(900\) 0 0
\(901\) 12.7870 22.1478i 0.425997 0.737849i
\(902\) 3.25491 + 6.98019i 0.108377 + 0.232415i
\(903\) 0 0
\(904\) −0.238471 + 0.284198i −0.00793142 + 0.00945230i
\(905\) 11.2532 + 17.5835i 0.374068 + 0.584496i
\(906\) 0 0
\(907\) 50.7113 23.6471i 1.68384 0.785188i 0.685472 0.728099i \(-0.259596\pi\)
0.998369 0.0570890i \(-0.0181819\pi\)
\(908\) 1.09844 + 4.09944i 0.0364530 + 0.136045i
\(909\) 0 0
\(910\) −0.626309 + 0.987613i −0.0207619 + 0.0327391i
\(911\) 26.4465 4.66323i 0.876211 0.154500i 0.282587 0.959242i \(-0.408808\pi\)
0.593625 + 0.804742i \(0.297696\pi\)
\(912\) 0 0
\(913\) −2.83930 1.32399i −0.0939671 0.0438176i
\(914\) 6.21385 35.2405i 0.205536 1.16565i
\(915\) 0 0
\(916\) 16.9401 14.2144i 0.559715 0.469657i
\(917\) −11.0368 11.0368i −0.364467 0.364467i
\(918\) 0 0
\(919\) 30.8687i 1.01826i 0.860688 + 0.509132i \(0.170033\pi\)
−0.860688 + 0.509132i \(0.829967\pi\)
\(920\) −21.0915 50.6227i −0.695365 1.66898i
\(921\) 0 0
\(922\) −1.82189 2.60193i −0.0600008 0.0856900i
\(923\) −1.97148 + 4.22786i −0.0648921 + 0.139162i
\(924\) 0 0
\(925\) 19.1478 + 51.9382i 0.629576 + 1.70772i
\(926\) −24.3463 + 14.0564i −0.800070 + 0.461921i
\(927\) 0 0
\(928\) −33.4663 + 8.96728i −1.09859 + 0.294365i
\(929\) 14.1178 + 5.13847i 0.463191 + 0.168588i 0.563065 0.826412i \(-0.309622\pi\)
−0.0998747 + 0.995000i \(0.531844\pi\)
\(930\) 0 0
\(931\) −19.5380 16.3943i −0.640331 0.537301i
\(932\) 0.562125 + 6.42512i 0.0184130 + 0.210462i
\(933\) 0 0
\(934\) 6.14270 16.8769i 0.200995 0.552230i
\(935\) 0.496860 11.9474i 0.0162491 0.390722i
\(936\) 0 0
\(937\) 44.9601 + 12.0470i 1.46878 + 0.393559i 0.902514 0.430660i \(-0.141719\pi\)
0.566270 + 0.824220i \(0.308386\pi\)
\(938\) 6.65089 + 4.65700i 0.217159 + 0.152057i
\(939\) 0 0
\(940\) 5.57141 6.10545i 0.181719 0.199138i
\(941\) 13.0261 + 2.29686i 0.424640 + 0.0748755i 0.381884 0.924210i \(-0.375275\pi\)
0.0427555 + 0.999086i \(0.486386\pi\)
\(942\) 0 0
\(943\) −33.9623 2.97131i −1.10596 0.0967593i
\(944\) 3.78825 0.123297
\(945\) 0 0
\(946\) 11.8286 0.384581
\(947\) 33.5777 + 2.93767i 1.09113 + 0.0954614i 0.618488 0.785794i \(-0.287745\pi\)
0.472640 + 0.881255i \(0.343301\pi\)
\(948\) 0 0
\(949\) 5.96147 + 1.05117i 0.193517 + 0.0341223i
\(950\) −17.6378 + 10.2808i −0.572246 + 0.333552i
\(951\) 0 0
\(952\) −5.27742 3.69529i −0.171042 0.119765i
\(953\) −37.8969 10.1544i −1.22760 0.328935i −0.413956 0.910297i \(-0.635853\pi\)
−0.813645 + 0.581362i \(0.802520\pi\)
\(954\) 0 0
\(955\) 1.71839 + 1.86752i 0.0556058 + 0.0604314i
\(956\) 3.61686 9.93723i 0.116977 0.321393i
\(957\) 0 0
\(958\) 3.16367 + 36.1609i 0.102213 + 1.16830i
\(959\) 2.76760 + 2.32229i 0.0893705 + 0.0749908i
\(960\) 0 0
\(961\) 10.9101 + 3.97094i 0.351938 + 0.128095i
\(962\) −8.07116 + 2.16266i −0.260225 + 0.0697270i
\(963\) 0 0
\(964\) −8.25932 + 4.76852i −0.266015 + 0.153584i
\(965\) −24.4135 + 18.8135i −0.785897 + 0.605629i
\(966\) 0 0
\(967\) −10.7806 + 23.1190i −0.346680 + 0.743457i −0.999906 0.0137056i \(-0.995637\pi\)
0.653226 + 0.757163i \(0.273415\pi\)
\(968\) 13.8471 + 19.7756i 0.445061 + 0.635613i
\(969\) 0 0
\(970\) −9.98470 + 4.16003i −0.320590 + 0.133571i
\(971\) 23.0327i 0.739156i −0.929200 0.369578i \(-0.879502\pi\)
0.929200 0.369578i \(-0.120498\pi\)
\(972\) 0 0
\(973\) −6.36728 6.36728i −0.204126 0.204126i
\(974\) 11.5013 9.65070i 0.368524 0.309228i
\(975\) 0 0
\(976\) 1.53312 8.69473i 0.0490738 0.278312i
\(977\) 0.251362 + 0.117212i 0.00804177 + 0.00374994i 0.426635 0.904424i \(-0.359699\pi\)
−0.418593 + 0.908174i \(0.637477\pi\)
\(978\) 0 0
\(979\) 9.57227 1.68785i 0.305931 0.0539439i
\(980\) −2.90009 12.9545i −0.0926399 0.413816i
\(981\) 0 0
\(982\) 7.95391 + 29.6844i 0.253820 + 0.947268i
\(983\) −7.55984 + 3.52521i −0.241122 + 0.112437i −0.539423 0.842035i \(-0.681358\pi\)
0.298302 + 0.954472i \(0.403580\pi\)
\(984\) 0 0
\(985\) 0.959547 4.37104i 0.0305737 0.139273i
\(986\) −15.2427 + 18.1656i −0.485427 + 0.578510i
\(987\) 0 0
\(988\) 1.08858 + 2.33447i 0.0346324 + 0.0742694i
\(989\) −26.1797 + 45.3445i −0.832465 + 1.44187i
\(990\) 0 0
\(991\) −3.48806 6.04150i −0.110802 0.191914i 0.805292 0.592878i \(-0.202009\pi\)
−0.916094 + 0.400964i \(0.868675\pi\)
\(992\) −11.7876 + 16.8345i −0.374257 + 0.534494i
\(993\) 0 0
\(994\) −1.59583 4.38451i −0.0506167 0.139068i
\(995\) −36.6902 19.0033i −1.16316 0.602445i
\(996\) 0 0
\(997\) 4.81022 54.9810i 0.152341 1.74127i −0.407980 0.912991i \(-0.633767\pi\)
0.560321 0.828276i \(-0.310678\pi\)
\(998\) −13.0450 + 13.0450i −0.412933 + 0.412933i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 405.2.r.a.368.6 192
3.2 odd 2 135.2.q.a.113.11 yes 192
5.2 odd 4 inner 405.2.r.a.287.11 192
15.2 even 4 135.2.q.a.32.6 192
15.8 even 4 675.2.ba.b.32.11 192
15.14 odd 2 675.2.ba.b.518.6 192
27.11 odd 18 inner 405.2.r.a.278.11 192
27.16 even 9 135.2.q.a.38.6 yes 192
135.43 odd 36 675.2.ba.b.632.6 192
135.92 even 36 inner 405.2.r.a.197.6 192
135.97 odd 36 135.2.q.a.92.11 yes 192
135.124 even 18 675.2.ba.b.443.11 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.q.a.32.6 192 15.2 even 4
135.2.q.a.38.6 yes 192 27.16 even 9
135.2.q.a.92.11 yes 192 135.97 odd 36
135.2.q.a.113.11 yes 192 3.2 odd 2
405.2.r.a.197.6 192 135.92 even 36 inner
405.2.r.a.278.11 192 27.11 odd 18 inner
405.2.r.a.287.11 192 5.2 odd 4 inner
405.2.r.a.368.6 192 1.1 even 1 trivial
675.2.ba.b.32.11 192 15.8 even 4
675.2.ba.b.443.11 192 135.124 even 18
675.2.ba.b.518.6 192 15.14 odd 2
675.2.ba.b.632.6 192 135.43 odd 36