Properties

Label 405.2.r.a.8.11
Level $405$
Weight $2$
Character 405.8
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 8.11
Character \(\chi\) \(=\) 405.8
Dual form 405.2.r.a.152.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.08817 - 0.761943i) q^{2} +(-0.0804885 + 0.221140i) q^{4} +(-1.23426 - 1.86457i) q^{5} +(0.827388 - 1.77434i) q^{7} +(0.768546 + 2.86825i) q^{8} +O(q^{10})\) \(q+(1.08817 - 0.761943i) q^{2} +(-0.0804885 + 0.221140i) q^{4} +(-1.23426 - 1.86457i) q^{5} +(0.827388 - 1.77434i) q^{7} +(0.768546 + 2.86825i) q^{8} +(-2.76377 - 1.08853i) q^{10} +(2.76562 - 3.29594i) q^{11} +(2.90740 - 4.15220i) q^{13} +(-0.451609 - 2.56120i) q^{14} +(2.66120 + 2.23301i) q^{16} +(0.828434 - 3.09176i) q^{17} +(-0.776109 - 0.448087i) q^{19} +(0.511675 - 0.122868i) q^{20} +(0.498142 - 5.69379i) q^{22} +(-5.07230 + 2.36525i) q^{23} +(-1.95322 + 4.60271i) q^{25} -6.73356i q^{26} +(0.325783 + 0.325783i) q^{28} +(-1.14702 + 6.50507i) q^{29} +(2.27652 + 0.828586i) q^{31} +(-1.31900 - 0.115398i) q^{32} +(-1.45427 - 3.99557i) q^{34} +(-4.32959 + 0.647269i) q^{35} +(6.96604 + 1.86654i) q^{37} +(-1.18595 + 0.103757i) q^{38} +(4.39947 - 4.97316i) q^{40} +(-8.33680 + 1.47000i) q^{41} +(0.112459 + 1.28541i) q^{43} +(0.506265 + 0.876877i) q^{44} +(-3.71732 + 6.43859i) q^{46} +(7.46943 + 3.48305i) q^{47} +(2.03580 + 2.42617i) q^{49} +(1.38157 + 6.49676i) q^{50} +(0.684206 + 0.977148i) q^{52} +(0.947342 - 0.947342i) q^{53} +(-9.55899 - 1.08866i) q^{55} +(5.72514 + 1.00950i) q^{56} +(3.70835 + 7.95258i) q^{58} +(3.72879 - 3.12883i) q^{59} +(-7.90101 + 2.87573i) q^{61} +(3.10857 - 0.832940i) q^{62} +(-7.54029 + 4.35339i) q^{64} +(-11.3305 - 0.296169i) q^{65} +(-7.90560 - 5.53556i) q^{67} +(0.617033 + 0.432051i) q^{68} +(-4.21814 + 4.00324i) q^{70} +(-4.92123 + 2.84127i) q^{71} +(4.93694 - 1.32285i) q^{73} +(9.00242 - 3.27661i) q^{74} +(0.161558 - 0.135563i) q^{76} +(-3.55988 - 7.63418i) q^{77} +(-0.410612 - 0.0724019i) q^{79} +(0.879000 - 7.71810i) q^{80} +(-7.95178 + 7.95178i) q^{82} +(5.31732 + 7.59392i) q^{83} +(-6.78729 + 2.27135i) q^{85} +(1.10179 + 1.31306i) q^{86} +(11.5791 + 5.39942i) q^{88} +(0.974450 - 1.68780i) q^{89} +(-4.96186 - 8.59420i) q^{91} +(-0.114791 - 1.31207i) q^{92} +(10.7819 - 1.90114i) q^{94} +(0.122429 + 2.00016i) q^{95} +(13.4552 - 1.17718i) q^{97} +(4.06390 + 1.08892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08817 0.761943i 0.769451 0.538775i −0.121654 0.992573i \(-0.538820\pi\)
0.891105 + 0.453797i \(0.149931\pi\)
\(3\) 0 0
\(4\) −0.0804885 + 0.221140i −0.0402443 + 0.110570i
\(5\) −1.23426 1.86457i −0.551976 0.833860i
\(6\) 0 0
\(7\) 0.827388 1.77434i 0.312723 0.670638i −0.685633 0.727947i \(-0.740474\pi\)
0.998356 + 0.0573098i \(0.0182523\pi\)
\(8\) 0.768546 + 2.86825i 0.271722 + 1.01408i
\(9\) 0 0
\(10\) −2.76377 1.08853i −0.873982 0.344223i
\(11\) 2.76562 3.29594i 0.833867 0.993764i −0.166104 0.986108i \(-0.553119\pi\)
0.999971 0.00765542i \(-0.00243682\pi\)
\(12\) 0 0
\(13\) 2.90740 4.15220i 0.806368 1.15161i −0.179446 0.983768i \(-0.557431\pi\)
0.985814 0.167844i \(-0.0536806\pi\)
\(14\) −0.451609 2.56120i −0.120698 0.684510i
\(15\) 0 0
\(16\) 2.66120 + 2.23301i 0.665301 + 0.558253i
\(17\) 0.828434 3.09176i 0.200925 0.749861i −0.789729 0.613456i \(-0.789779\pi\)
0.990653 0.136405i \(-0.0435547\pi\)
\(18\) 0 0
\(19\) −0.776109 0.448087i −0.178052 0.102798i 0.408325 0.912836i \(-0.366113\pi\)
−0.586377 + 0.810038i \(0.699446\pi\)
\(20\) 0.511675 0.122868i 0.114414 0.0274740i
\(21\) 0 0
\(22\) 0.498142 5.69379i 0.106204 1.21392i
\(23\) −5.07230 + 2.36525i −1.05765 + 0.493189i −0.872040 0.489435i \(-0.837203\pi\)
−0.185607 + 0.982624i \(0.559425\pi\)
\(24\) 0 0
\(25\) −1.95322 + 4.60271i −0.390645 + 0.920541i
\(26\) 6.73356i 1.32056i
\(27\) 0 0
\(28\) 0.325783 + 0.325783i 0.0615672 + 0.0615672i
\(29\) −1.14702 + 6.50507i −0.212996 + 1.20796i 0.671354 + 0.741137i \(0.265713\pi\)
−0.884350 + 0.466825i \(0.845398\pi\)
\(30\) 0 0
\(31\) 2.27652 + 0.828586i 0.408875 + 0.148818i 0.538266 0.842775i \(-0.319080\pi\)
−0.129390 + 0.991594i \(0.541302\pi\)
\(32\) −1.31900 0.115398i −0.233169 0.0203996i
\(33\) 0 0
\(34\) −1.45427 3.99557i −0.249405 0.685235i
\(35\) −4.32959 + 0.647269i −0.731834 + 0.109408i
\(36\) 0 0
\(37\) 6.96604 + 1.86654i 1.14521 + 0.306858i 0.781044 0.624476i \(-0.214688\pi\)
0.364166 + 0.931334i \(0.381354\pi\)
\(38\) −1.18595 + 0.103757i −0.192387 + 0.0168317i
\(39\) 0 0
\(40\) 4.39947 4.97316i 0.695617 0.786326i
\(41\) −8.33680 + 1.47000i −1.30199 + 0.229576i −0.781292 0.624166i \(-0.785439\pi\)
−0.520697 + 0.853742i \(0.674328\pi\)
\(42\) 0 0
\(43\) 0.112459 + 1.28541i 0.0171499 + 0.196024i 0.999936 + 0.0112790i \(0.00359030\pi\)
−0.982787 + 0.184745i \(0.940854\pi\)
\(44\) 0.506265 + 0.876877i 0.0763223 + 0.132194i
\(45\) 0 0
\(46\) −3.71732 + 6.43859i −0.548090 + 0.949319i
\(47\) 7.46943 + 3.48305i 1.08953 + 0.508055i 0.882516 0.470283i \(-0.155848\pi\)
0.207013 + 0.978338i \(0.433626\pi\)
\(48\) 0 0
\(49\) 2.03580 + 2.42617i 0.290829 + 0.346596i
\(50\) 1.38157 + 6.49676i 0.195383 + 0.918781i
\(51\) 0 0
\(52\) 0.684206 + 0.977148i 0.0948823 + 0.135506i
\(53\) 0.947342 0.947342i 0.130127 0.130127i −0.639043 0.769171i \(-0.720670\pi\)
0.769171 + 0.639043i \(0.220670\pi\)
\(54\) 0 0
\(55\) −9.55899 1.08866i −1.28893 0.146794i
\(56\) 5.72514 + 1.00950i 0.765054 + 0.134900i
\(57\) 0 0
\(58\) 3.70835 + 7.95258i 0.486930 + 1.04422i
\(59\) 3.72879 3.12883i 0.485447 0.407339i −0.366944 0.930243i \(-0.619596\pi\)
0.852391 + 0.522904i \(0.175151\pi\)
\(60\) 0 0
\(61\) −7.90101 + 2.87573i −1.01162 + 0.368200i −0.794055 0.607846i \(-0.792034\pi\)
−0.217566 + 0.976046i \(0.569812\pi\)
\(62\) 3.10857 0.832940i 0.394789 0.105783i
\(63\) 0 0
\(64\) −7.54029 + 4.35339i −0.942536 + 0.544173i
\(65\) −11.3305 0.296169i −1.40538 0.0367352i
\(66\) 0 0
\(67\) −7.90560 5.53556i −0.965822 0.676276i −0.0196049 0.999808i \(-0.506241\pi\)
−0.946217 + 0.323532i \(0.895130\pi\)
\(68\) 0.617033 + 0.432051i 0.0748262 + 0.0523939i
\(69\) 0 0
\(70\) −4.21814 + 4.00324i −0.504164 + 0.478478i
\(71\) −4.92123 + 2.84127i −0.584043 + 0.337197i −0.762738 0.646707i \(-0.776146\pi\)
0.178696 + 0.983904i \(0.442812\pi\)
\(72\) 0 0
\(73\) 4.93694 1.32285i 0.577825 0.154828i 0.0419419 0.999120i \(-0.486646\pi\)
0.535883 + 0.844292i \(0.319979\pi\)
\(74\) 9.00242 3.27661i 1.04651 0.380898i
\(75\) 0 0
\(76\) 0.161558 0.135563i 0.0185320 0.0155502i
\(77\) −3.55988 7.63418i −0.405686 0.869996i
\(78\) 0 0
\(79\) −0.410612 0.0724019i −0.0461974 0.00814585i 0.150502 0.988610i \(-0.451911\pi\)
−0.196699 + 0.980464i \(0.563022\pi\)
\(80\) 0.879000 7.71810i 0.0982752 0.862910i
\(81\) 0 0
\(82\) −7.95178 + 7.95178i −0.878127 + 0.878127i
\(83\) 5.31732 + 7.59392i 0.583652 + 0.833541i 0.997030 0.0770185i \(-0.0245401\pi\)
−0.413378 + 0.910560i \(0.635651\pi\)
\(84\) 0 0
\(85\) −6.78729 + 2.27135i −0.736185 + 0.246362i
\(86\) 1.10179 + 1.31306i 0.118809 + 0.141591i
\(87\) 0 0
\(88\) 11.5791 + 5.39942i 1.23434 + 0.575580i
\(89\) 0.974450 1.68780i 0.103292 0.178906i −0.809747 0.586779i \(-0.800396\pi\)
0.913039 + 0.407872i \(0.133729\pi\)
\(90\) 0 0
\(91\) −4.96186 8.59420i −0.520144 0.900917i
\(92\) −0.114791 1.31207i −0.0119678 0.136792i
\(93\) 0 0
\(94\) 10.7819 1.90114i 1.11207 0.196087i
\(95\) 0.122429 + 2.00016i 0.0125610 + 0.205212i
\(96\) 0 0
\(97\) 13.4552 1.17718i 1.36617 0.119524i 0.619644 0.784883i \(-0.287277\pi\)
0.746524 + 0.665359i \(0.231721\pi\)
\(98\) 4.06390 + 1.08892i 0.410516 + 0.109997i
\(99\) 0 0
\(100\) −0.860633 0.802402i −0.0860633 0.0802402i
\(101\) 1.45521 + 3.99814i 0.144798 + 0.397830i 0.990797 0.135354i \(-0.0432173\pi\)
−0.845999 + 0.533185i \(0.820995\pi\)
\(102\) 0 0
\(103\) −13.3028 1.16385i −1.31077 0.114677i −0.589745 0.807589i \(-0.700772\pi\)
−0.721022 + 0.692912i \(0.756327\pi\)
\(104\) 14.1440 + 5.14800i 1.38694 + 0.504803i
\(105\) 0 0
\(106\) 0.309046 1.75269i 0.0300172 0.170236i
\(107\) 10.2616 + 10.2616i 0.992026 + 0.992026i 0.999968 0.00794276i \(-0.00252829\pi\)
−0.00794276 + 0.999968i \(0.502528\pi\)
\(108\) 0 0
\(109\) 14.3459i 1.37409i −0.726615 0.687045i \(-0.758908\pi\)
0.726615 0.687045i \(-0.241092\pi\)
\(110\) −11.2313 + 6.09877i −1.07086 + 0.581495i
\(111\) 0 0
\(112\) 6.16397 2.87431i 0.582441 0.271597i
\(113\) −1.18867 + 13.5865i −0.111821 + 1.27811i 0.708295 + 0.705916i \(0.249465\pi\)
−0.820116 + 0.572198i \(0.806091\pi\)
\(114\) 0 0
\(115\) 10.6707 + 6.53832i 0.995046 + 0.609701i
\(116\) −1.34621 0.777236i −0.124993 0.0721646i
\(117\) 0 0
\(118\) 1.67356 6.24582i 0.154064 0.574974i
\(119\) −4.80039 4.02801i −0.440051 0.369247i
\(120\) 0 0
\(121\) −1.30443 7.39778i −0.118584 0.672525i
\(122\) −6.40648 + 9.14940i −0.580016 + 0.828348i
\(123\) 0 0
\(124\) −0.366468 + 0.436739i −0.0329098 + 0.0392204i
\(125\) 10.9928 2.03900i 0.983229 0.182374i
\(126\) 0 0
\(127\) 0.931838 + 3.47767i 0.0826872 + 0.308593i 0.994866 0.101199i \(-0.0322679\pi\)
−0.912179 + 0.409792i \(0.865601\pi\)
\(128\) −3.76894 + 8.08251i −0.333130 + 0.714400i
\(129\) 0 0
\(130\) −12.5552 + 8.31094i −1.10116 + 0.728918i
\(131\) −0.189922 + 0.521807i −0.0165936 + 0.0455905i −0.947713 0.319124i \(-0.896611\pi\)
0.931119 + 0.364715i \(0.118833\pi\)
\(132\) 0 0
\(133\) −1.43720 + 1.00634i −0.124621 + 0.0872607i
\(134\) −12.8204 −1.10751
\(135\) 0 0
\(136\) 9.50463 0.815015
\(137\) 4.95031 3.46624i 0.422934 0.296141i −0.342668 0.939457i \(-0.611330\pi\)
0.765601 + 0.643315i \(0.222442\pi\)
\(138\) 0 0
\(139\) −6.33390 + 17.4022i −0.537234 + 1.47604i 0.313061 + 0.949733i \(0.398646\pi\)
−0.850295 + 0.526306i \(0.823577\pi\)
\(140\) 0.205345 1.00954i 0.0173548 0.0853221i
\(141\) 0 0
\(142\) −3.19024 + 6.84148i −0.267719 + 0.574125i
\(143\) −5.64463 21.0660i −0.472027 1.76163i
\(144\) 0 0
\(145\) 13.5449 5.89023i 1.12484 0.489157i
\(146\) 4.36428 5.20115i 0.361190 0.430450i
\(147\) 0 0
\(148\) −0.973455 + 1.39024i −0.0800175 + 0.114277i
\(149\) −1.50609 8.54145i −0.123384 0.699743i −0.982255 0.187551i \(-0.939945\pi\)
0.858871 0.512192i \(-0.171166\pi\)
\(150\) 0 0
\(151\) −12.2052 10.2414i −0.993244 0.833431i −0.00721007 0.999974i \(-0.502295\pi\)
−0.986034 + 0.166543i \(0.946740\pi\)
\(152\) 0.688750 2.57045i 0.0558650 0.208491i
\(153\) 0 0
\(154\) −9.69056 5.59485i −0.780887 0.450846i
\(155\) −1.26486 5.26742i −0.101596 0.423089i
\(156\) 0 0
\(157\) 1.15698 13.2243i 0.0923367 1.05541i −0.798775 0.601630i \(-0.794518\pi\)
0.891112 0.453784i \(-0.149926\pi\)
\(158\) −0.501981 + 0.234077i −0.0399354 + 0.0186222i
\(159\) 0 0
\(160\) 1.41282 + 2.60180i 0.111693 + 0.205690i
\(161\) 10.9570i 0.863530i
\(162\) 0 0
\(163\) 5.24760 + 5.24760i 0.411024 + 0.411024i 0.882095 0.471071i \(-0.156133\pi\)
−0.471071 + 0.882095i \(0.656133\pi\)
\(164\) 0.345940 1.96192i 0.0270133 0.153200i
\(165\) 0 0
\(166\) 11.5723 + 4.21196i 0.898183 + 0.326912i
\(167\) −8.20120 0.717512i −0.634628 0.0555227i −0.234698 0.972068i \(-0.575410\pi\)
−0.399930 + 0.916546i \(0.630966\pi\)
\(168\) 0 0
\(169\) −4.34150 11.9282i −0.333962 0.917553i
\(170\) −5.65507 + 7.64314i −0.433724 + 0.586202i
\(171\) 0 0
\(172\) −0.293309 0.0785918i −0.0223646 0.00599257i
\(173\) 7.74393 0.677506i 0.588760 0.0515098i 0.211116 0.977461i \(-0.432290\pi\)
0.377643 + 0.925951i \(0.376735\pi\)
\(174\) 0 0
\(175\) 6.55069 + 7.27391i 0.495186 + 0.549856i
\(176\) 14.7198 2.59549i 1.10954 0.195643i
\(177\) 0 0
\(178\) −0.225641 2.57908i −0.0169125 0.193310i
\(179\) −2.19929 3.80928i −0.164382 0.284719i 0.772053 0.635558i \(-0.219230\pi\)
−0.936436 + 0.350839i \(0.885896\pi\)
\(180\) 0 0
\(181\) −2.85830 + 4.95072i −0.212456 + 0.367984i −0.952483 0.304593i \(-0.901479\pi\)
0.740027 + 0.672577i \(0.234813\pi\)
\(182\) −11.9476 5.57127i −0.885617 0.412970i
\(183\) 0 0
\(184\) −10.6824 12.7308i −0.787519 0.938529i
\(185\) −5.11758 15.2924i −0.376252 1.12432i
\(186\) 0 0
\(187\) −7.89911 11.2811i −0.577640 0.824956i
\(188\) −1.37145 + 1.37145i −0.100023 + 0.100023i
\(189\) 0 0
\(190\) 1.65723 + 2.08323i 0.120228 + 0.151133i
\(191\) −14.2067 2.50503i −1.02796 0.181258i −0.365860 0.930670i \(-0.619225\pi\)
−0.662104 + 0.749412i \(0.730336\pi\)
\(192\) 0 0
\(193\) 7.33254 + 15.7247i 0.527808 + 1.13189i 0.971789 + 0.235852i \(0.0757879\pi\)
−0.443981 + 0.896036i \(0.646434\pi\)
\(194\) 13.7446 11.5331i 0.986802 0.828025i
\(195\) 0 0
\(196\) −0.700384 + 0.254919i −0.0500274 + 0.0182085i
\(197\) 13.1476 3.52289i 0.936727 0.250995i 0.242006 0.970275i \(-0.422195\pi\)
0.694721 + 0.719280i \(0.255528\pi\)
\(198\) 0 0
\(199\) −7.78555 + 4.49499i −0.551903 + 0.318641i −0.749889 0.661564i \(-0.769893\pi\)
0.197986 + 0.980205i \(0.436560\pi\)
\(200\) −14.7029 2.06495i −1.03965 0.146014i
\(201\) 0 0
\(202\) 4.62987 + 3.24187i 0.325756 + 0.228097i
\(203\) 10.5932 + 7.41743i 0.743496 + 0.520601i
\(204\) 0 0
\(205\) 13.0307 + 13.7302i 0.910101 + 0.958956i
\(206\) −15.3625 + 8.86955i −1.07036 + 0.617971i
\(207\) 0 0
\(208\) 17.0091 4.55757i 1.17937 0.316011i
\(209\) −3.62329 + 1.31877i −0.250628 + 0.0912212i
\(210\) 0 0
\(211\) −14.3607 + 12.0500i −0.988631 + 0.829559i −0.985369 0.170435i \(-0.945483\pi\)
−0.00326162 + 0.999995i \(0.501038\pi\)
\(212\) 0.133245 + 0.285746i 0.00915134 + 0.0196251i
\(213\) 0 0
\(214\) 18.9851 + 3.34758i 1.29779 + 0.228836i
\(215\) 2.25794 1.79622i 0.153990 0.122501i
\(216\) 0 0
\(217\) 3.35376 3.35376i 0.227668 0.227668i
\(218\) −10.9308 15.6108i −0.740326 1.05729i
\(219\) 0 0
\(220\) 1.01014 2.02626i 0.0681033 0.136610i
\(221\) −10.4290 12.4288i −0.701530 0.836051i
\(222\) 0 0
\(223\) −15.0323 7.00968i −1.00664 0.469403i −0.151862 0.988402i \(-0.548527\pi\)
−0.854775 + 0.518999i \(0.826305\pi\)
\(224\) −1.29608 + 2.24488i −0.0865981 + 0.149992i
\(225\) 0 0
\(226\) 9.05870 + 15.6901i 0.602576 + 1.04369i
\(227\) 1.57696 + 18.0248i 0.104667 + 1.19634i 0.848947 + 0.528478i \(0.177237\pi\)
−0.744281 + 0.667867i \(0.767207\pi\)
\(228\) 0 0
\(229\) 18.7074 3.29862i 1.23622 0.217979i 0.482924 0.875662i \(-0.339575\pi\)
0.753294 + 0.657684i \(0.228464\pi\)
\(230\) 16.5933 1.01567i 1.09413 0.0669714i
\(231\) 0 0
\(232\) −19.5397 + 1.70951i −1.28285 + 0.112235i
\(233\) 7.30551 + 1.95750i 0.478600 + 0.128240i 0.490050 0.871694i \(-0.336978\pi\)
−0.0114509 + 0.999934i \(0.503645\pi\)
\(234\) 0 0
\(235\) −2.72480 18.2262i −0.177747 1.18895i
\(236\) 0.391785 + 1.07642i 0.0255031 + 0.0700691i
\(237\) 0 0
\(238\) −8.29275 0.725521i −0.537539 0.0470286i
\(239\) −11.7518 4.27731i −0.760162 0.276676i −0.0672867 0.997734i \(-0.521434\pi\)
−0.692875 + 0.721057i \(0.743656\pi\)
\(240\) 0 0
\(241\) 2.97320 16.8619i 0.191521 1.08617i −0.725766 0.687942i \(-0.758514\pi\)
0.917287 0.398227i \(-0.130374\pi\)
\(242\) −7.05612 7.05612i −0.453585 0.453585i
\(243\) 0 0
\(244\) 1.97870i 0.126673i
\(245\) 2.01106 6.79041i 0.128482 0.433823i
\(246\) 0 0
\(247\) −4.11700 + 1.91979i −0.261958 + 0.122153i
\(248\) −0.626983 + 7.16645i −0.0398134 + 0.455070i
\(249\) 0 0
\(250\) 10.4085 10.5947i 0.658288 0.670067i
\(251\) −4.66370 2.69259i −0.294370 0.169955i 0.345541 0.938404i \(-0.387696\pi\)
−0.639911 + 0.768449i \(0.721029\pi\)
\(252\) 0 0
\(253\) −6.23233 + 23.2594i −0.391823 + 1.46231i
\(254\) 3.66378 + 3.07428i 0.229886 + 0.192897i
\(255\) 0 0
\(256\) −0.966651 5.48215i −0.0604157 0.342634i
\(257\) 7.03325 10.0445i 0.438722 0.626560i −0.537518 0.843252i \(-0.680638\pi\)
0.976240 + 0.216692i \(0.0695268\pi\)
\(258\) 0 0
\(259\) 9.07550 10.8158i 0.563924 0.672059i
\(260\) 0.977472 2.48180i 0.0606203 0.153915i
\(261\) 0 0
\(262\) 0.190920 + 0.712524i 0.0117951 + 0.0440199i
\(263\) 5.75913 12.3505i 0.355123 0.761563i −0.644873 0.764289i \(-0.723090\pi\)
0.999996 + 0.00272594i \(0.000867694\pi\)
\(264\) 0 0
\(265\) −2.93565 0.597121i −0.180335 0.0366808i
\(266\) −0.797143 + 2.19013i −0.0488760 + 0.134286i
\(267\) 0 0
\(268\) 1.86045 1.30270i 0.113645 0.0795749i
\(269\) −12.3342 −0.752028 −0.376014 0.926614i \(-0.622706\pi\)
−0.376014 + 0.926614i \(0.622706\pi\)
\(270\) 0 0
\(271\) 19.7578 1.20020 0.600099 0.799926i \(-0.295128\pi\)
0.600099 + 0.799926i \(0.295128\pi\)
\(272\) 9.10856 6.37789i 0.552288 0.386716i
\(273\) 0 0
\(274\) 2.74569 7.54371i 0.165873 0.455732i
\(275\) 9.76837 + 19.1671i 0.589055 + 1.15582i
\(276\) 0 0
\(277\) −0.856962 + 1.83776i −0.0514898 + 0.110420i −0.930370 0.366623i \(-0.880514\pi\)
0.878880 + 0.477044i \(0.158292\pi\)
\(278\) 6.36718 + 23.7626i 0.381878 + 1.42519i
\(279\) 0 0
\(280\) −5.18402 11.9209i −0.309804 0.712410i
\(281\) 16.8041 20.0263i 1.00245 1.19467i 0.0216244 0.999766i \(-0.493116\pi\)
0.980822 0.194903i \(-0.0624393\pi\)
\(282\) 0 0
\(283\) 1.33019 1.89971i 0.0790717 0.112926i −0.777668 0.628675i \(-0.783597\pi\)
0.856740 + 0.515749i \(0.172486\pi\)
\(284\) −0.232218 1.31697i −0.0137796 0.0781480i
\(285\) 0 0
\(286\) −22.1934 18.6225i −1.31232 1.10117i
\(287\) −4.28949 + 16.0086i −0.253200 + 0.944956i
\(288\) 0 0
\(289\) 5.84978 + 3.37737i 0.344105 + 0.198669i
\(290\) 10.2511 16.7300i 0.601963 0.982418i
\(291\) 0 0
\(292\) −0.104832 + 1.19823i −0.00613480 + 0.0701211i
\(293\) 10.9251 5.09445i 0.638250 0.297621i −0.0764274 0.997075i \(-0.524351\pi\)
0.714677 + 0.699454i \(0.246574\pi\)
\(294\) 0 0
\(295\) −10.4362 3.09081i −0.607619 0.179954i
\(296\) 21.4149i 1.24471i
\(297\) 0 0
\(298\) −8.14698 8.14698i −0.471942 0.471942i
\(299\) −4.92621 + 27.9379i −0.284890 + 1.61569i
\(300\) 0 0
\(301\) 2.37381 + 0.863996i 0.136824 + 0.0497999i
\(302\) −21.0846 1.84467i −1.21328 0.106149i
\(303\) 0 0
\(304\) −1.06480 2.92551i −0.0610704 0.167790i
\(305\) 15.1139 + 11.1826i 0.865418 + 0.640313i
\(306\) 0 0
\(307\) 22.6984 + 6.08202i 1.29547 + 0.347119i 0.839734 0.542998i \(-0.182711\pi\)
0.455732 + 0.890117i \(0.349378\pi\)
\(308\) 1.97476 0.172769i 0.112522 0.00984441i
\(309\) 0 0
\(310\) −5.38985 4.76809i −0.306123 0.270809i
\(311\) −3.91683 + 0.690642i −0.222103 + 0.0391627i −0.283592 0.958945i \(-0.591526\pi\)
0.0614891 + 0.998108i \(0.480415\pi\)
\(312\) 0 0
\(313\) −0.0797089 0.911077i −0.00450541 0.0514971i 0.993609 0.112875i \(-0.0360060\pi\)
−0.998115 + 0.0613781i \(0.980450\pi\)
\(314\) −8.81718 15.2718i −0.497582 0.861838i
\(315\) 0 0
\(316\) 0.0490605 0.0849753i 0.00275987 0.00478023i
\(317\) −23.8990 11.1443i −1.34230 0.625924i −0.387141 0.922021i \(-0.626537\pi\)
−0.955158 + 0.296096i \(0.904315\pi\)
\(318\) 0 0
\(319\) 18.2681 + 21.7711i 1.02282 + 1.21895i
\(320\) 17.4238 + 8.68618i 0.974021 + 0.485572i
\(321\) 0 0
\(322\) 8.34859 + 11.9230i 0.465249 + 0.664444i
\(323\) −2.02833 + 2.02833i −0.112859 + 0.112859i
\(324\) 0 0
\(325\) 13.4325 + 21.4921i 0.745103 + 1.19217i
\(326\) 9.70865 + 1.71190i 0.537712 + 0.0948132i
\(327\) 0 0
\(328\) −10.6235 22.7823i −0.586587 1.25794i
\(329\) 12.3602 10.3715i 0.681442 0.571798i
\(330\) 0 0
\(331\) −12.0746 + 4.39481i −0.663682 + 0.241561i −0.651825 0.758369i \(-0.725996\pi\)
−0.0118569 + 0.999930i \(0.503774\pi\)
\(332\) −2.10731 + 0.564651i −0.115653 + 0.0309893i
\(333\) 0 0
\(334\) −9.47099 + 5.46808i −0.518229 + 0.299200i
\(335\) −0.563892 + 21.5728i −0.0308087 + 1.17865i
\(336\) 0 0
\(337\) −6.96283 4.87543i −0.379290 0.265581i 0.368349 0.929688i \(-0.379923\pi\)
−0.747638 + 0.664106i \(0.768812\pi\)
\(338\) −13.8129 9.67189i −0.751322 0.526081i
\(339\) 0 0
\(340\) 0.0440119 1.68376i 0.00238688 0.0913148i
\(341\) 9.02697 5.21173i 0.488838 0.282231i
\(342\) 0 0
\(343\) 19.2267 5.15177i 1.03814 0.278169i
\(344\) −3.60046 + 1.31046i −0.194124 + 0.0706553i
\(345\) 0 0
\(346\) 7.91047 6.63767i 0.425270 0.356844i
\(347\) 2.22359 + 4.76851i 0.119369 + 0.255987i 0.956909 0.290389i \(-0.0937847\pi\)
−0.837540 + 0.546376i \(0.816007\pi\)
\(348\) 0 0
\(349\) −20.3047 3.58026i −1.08688 0.191647i −0.398627 0.917113i \(-0.630513\pi\)
−0.688258 + 0.725466i \(0.741624\pi\)
\(350\) 12.6706 + 2.92398i 0.677270 + 0.156293i
\(351\) 0 0
\(352\) −4.02821 + 4.02821i −0.214704 + 0.214704i
\(353\) −16.5268 23.6027i −0.879631 1.25624i −0.965623 0.259948i \(-0.916295\pi\)
0.0859911 0.996296i \(-0.472594\pi\)
\(354\) 0 0
\(355\) 11.3718 + 5.66911i 0.603553 + 0.300885i
\(356\) 0.294808 + 0.351339i 0.0156248 + 0.0186209i
\(357\) 0 0
\(358\) −5.29565 2.46940i −0.279884 0.130512i
\(359\) −8.91393 + 15.4394i −0.470459 + 0.814860i −0.999429 0.0337810i \(-0.989245\pi\)
0.528970 + 0.848641i \(0.322578\pi\)
\(360\) 0 0
\(361\) −9.09844 15.7590i −0.478865 0.829419i
\(362\) 0.661859 + 7.56508i 0.0347865 + 0.397612i
\(363\) 0 0
\(364\) 2.29990 0.405534i 0.120547 0.0212558i
\(365\) −8.55998 7.57252i −0.448050 0.396364i
\(366\) 0 0
\(367\) −21.8448 + 1.91117i −1.14029 + 0.0997623i −0.641614 0.767028i \(-0.721735\pi\)
−0.498674 + 0.866790i \(0.666179\pi\)
\(368\) −18.7800 5.03210i −0.978978 0.262316i
\(369\) 0 0
\(370\) −17.2208 12.7414i −0.895264 0.662396i
\(371\) −0.897087 2.46473i −0.0465744 0.127962i
\(372\) 0 0
\(373\) −17.1932 1.50421i −0.890228 0.0778848i −0.367142 0.930165i \(-0.619664\pi\)
−0.523086 + 0.852280i \(0.675219\pi\)
\(374\) −17.1911 6.25706i −0.888932 0.323545i
\(375\) 0 0
\(376\) −4.24967 + 24.1011i −0.219160 + 1.24292i
\(377\) 23.6755 + 23.6755i 1.21935 + 1.21935i
\(378\) 0 0
\(379\) 27.1687i 1.39556i 0.716312 + 0.697780i \(0.245829\pi\)
−0.716312 + 0.697780i \(0.754171\pi\)
\(380\) −0.452170 0.133916i −0.0231959 0.00686974i
\(381\) 0 0
\(382\) −17.3680 + 8.09883i −0.888624 + 0.414372i
\(383\) 0.640436 7.32022i 0.0327248 0.374046i −0.962119 0.272629i \(-0.912107\pi\)
0.994844 0.101417i \(-0.0323376\pi\)
\(384\) 0 0
\(385\) −9.84065 + 16.0602i −0.501526 + 0.818502i
\(386\) 19.9604 + 11.5241i 1.01596 + 0.586562i
\(387\) 0 0
\(388\) −0.822667 + 3.07024i −0.0417646 + 0.155868i
\(389\) 23.9421 + 20.0898i 1.21391 + 1.01859i 0.999120 + 0.0419334i \(0.0133517\pi\)
0.214792 + 0.976660i \(0.431093\pi\)
\(390\) 0 0
\(391\) 3.11072 + 17.6418i 0.157316 + 0.892182i
\(392\) −5.39427 + 7.70382i −0.272452 + 0.389102i
\(393\) 0 0
\(394\) 11.6225 13.8512i 0.585535 0.697814i
\(395\) 0.371802 + 0.854976i 0.0187074 + 0.0430185i
\(396\) 0 0
\(397\) 4.26857 + 15.9305i 0.214234 + 0.799531i 0.986435 + 0.164153i \(0.0524890\pi\)
−0.772201 + 0.635378i \(0.780844\pi\)
\(398\) −5.04706 + 10.8234i −0.252986 + 0.542530i
\(399\) 0 0
\(400\) −15.4758 + 7.88716i −0.773792 + 0.394358i
\(401\) 0.517022 1.42051i 0.0258188 0.0709367i −0.926114 0.377245i \(-0.876872\pi\)
0.951932 + 0.306308i \(0.0990938\pi\)
\(402\) 0 0
\(403\) 10.0592 7.04354i 0.501085 0.350864i
\(404\) −1.00128 −0.0498155
\(405\) 0 0
\(406\) 17.1788 0.852571
\(407\) 25.4175 17.7975i 1.25990 0.882189i
\(408\) 0 0
\(409\) −8.02778 + 22.0561i −0.396948 + 1.09061i 0.566815 + 0.823845i \(0.308175\pi\)
−0.963763 + 0.266760i \(0.914047\pi\)
\(410\) 24.6412 + 5.01210i 1.21694 + 0.247530i
\(411\) 0 0
\(412\) 1.32810 2.84812i 0.0654308 0.140317i
\(413\) −2.46645 9.20490i −0.121366 0.452944i
\(414\) 0 0
\(415\) 7.59644 19.2873i 0.372895 0.946779i
\(416\) −4.31402 + 5.14125i −0.211512 + 0.252070i
\(417\) 0 0
\(418\) −2.93792 + 4.19579i −0.143698 + 0.205223i
\(419\) 2.76242 + 15.6665i 0.134953 + 0.765357i 0.974892 + 0.222677i \(0.0714794\pi\)
−0.839939 + 0.542680i \(0.817409\pi\)
\(420\) 0 0
\(421\) 27.8051 + 23.3312i 1.35514 + 1.13709i 0.977452 + 0.211160i \(0.0677241\pi\)
0.377685 + 0.925934i \(0.376720\pi\)
\(422\) −6.44539 + 24.0545i −0.313756 + 1.17096i
\(423\) 0 0
\(424\) 3.44529 + 1.98914i 0.167318 + 0.0966012i
\(425\) 12.6123 + 9.85193i 0.611788 + 0.477889i
\(426\) 0 0
\(427\) −1.43468 + 16.3984i −0.0694289 + 0.793576i
\(428\) −3.09519 + 1.44331i −0.149612 + 0.0697652i
\(429\) 0 0
\(430\) 1.08840 3.67501i 0.0524873 0.177225i
\(431\) 10.7570i 0.518146i −0.965858 0.259073i \(-0.916583\pi\)
0.965858 0.259073i \(-0.0834169\pi\)
\(432\) 0 0
\(433\) −25.8369 25.8369i −1.24164 1.24164i −0.959320 0.282321i \(-0.908896\pi\)
−0.282321 0.959320i \(-0.591104\pi\)
\(434\) 1.09408 6.20483i 0.0525175 0.297842i
\(435\) 0 0
\(436\) 3.17246 + 1.15468i 0.151933 + 0.0552992i
\(437\) 4.99649 + 0.437136i 0.239015 + 0.0209111i
\(438\) 0 0
\(439\) 4.76440 + 13.0901i 0.227393 + 0.624756i 0.999948 0.0101913i \(-0.00324405\pi\)
−0.772556 + 0.634947i \(0.781022\pi\)
\(440\) −4.22398 28.2543i −0.201371 1.34697i
\(441\) 0 0
\(442\) −20.8185 5.57831i −0.990237 0.265333i
\(443\) 11.3601 0.993879i 0.539734 0.0472206i 0.185970 0.982555i \(-0.440457\pi\)
0.353764 + 0.935335i \(0.384902\pi\)
\(444\) 0 0
\(445\) −4.34973 + 0.266246i −0.206197 + 0.0126213i
\(446\) −21.6986 + 3.82606i −1.02746 + 0.181169i
\(447\) 0 0
\(448\) 1.48564 + 16.9810i 0.0701900 + 0.802276i
\(449\) −0.807925 1.39937i −0.0381283 0.0660402i 0.846332 0.532657i \(-0.178806\pi\)
−0.884460 + 0.466616i \(0.845473\pi\)
\(450\) 0 0
\(451\) −18.2114 + 31.5431i −0.857541 + 1.48530i
\(452\) −2.90886 1.35642i −0.136821 0.0638008i
\(453\) 0 0
\(454\) 15.4498 + 18.4124i 0.725097 + 0.864137i
\(455\) −9.90025 + 19.8592i −0.464131 + 0.931012i
\(456\) 0 0
\(457\) −3.17737 4.53775i −0.148631 0.212267i 0.737932 0.674875i \(-0.235803\pi\)
−0.886563 + 0.462608i \(0.846914\pi\)
\(458\) 17.8434 17.8434i 0.833768 0.833768i
\(459\) 0 0
\(460\) −2.30475 + 1.83346i −0.107460 + 0.0854855i
\(461\) −14.9666 2.63902i −0.697065 0.122911i −0.186123 0.982527i \(-0.559592\pi\)
−0.510942 + 0.859615i \(0.670703\pi\)
\(462\) 0 0
\(463\) −13.9696 29.9580i −0.649224 1.39226i −0.904951 0.425516i \(-0.860093\pi\)
0.255727 0.966749i \(-0.417685\pi\)
\(464\) −17.5784 + 14.7500i −0.816056 + 0.684752i
\(465\) 0 0
\(466\) 9.44112 3.43629i 0.437352 0.159183i
\(467\) −21.9378 + 5.87822i −1.01516 + 0.272012i −0.727784 0.685806i \(-0.759450\pi\)
−0.287377 + 0.957818i \(0.592783\pi\)
\(468\) 0 0
\(469\) −16.3630 + 9.44716i −0.755571 + 0.436229i
\(470\) −16.8524 17.7571i −0.777343 0.819072i
\(471\) 0 0
\(472\) 11.8400 + 8.29047i 0.544981 + 0.381600i
\(473\) 4.54767 + 3.18431i 0.209102 + 0.146415i
\(474\) 0 0
\(475\) 3.57833 2.69699i 0.164185 0.123746i
\(476\) 1.27713 0.737352i 0.0585372 0.0337965i
\(477\) 0 0
\(478\) −16.0470 + 4.29979i −0.733974 + 0.196668i
\(479\) −21.4594 + 7.81060i −0.980507 + 0.356875i −0.782037 0.623232i \(-0.785819\pi\)
−0.198470 + 0.980107i \(0.563597\pi\)
\(480\) 0 0
\(481\) 28.0033 23.4976i 1.27684 1.07140i
\(482\) −9.61245 20.6140i −0.437835 0.938941i
\(483\) 0 0
\(484\) 1.74094 + 0.306975i 0.0791336 + 0.0139534i
\(485\) −18.8021 23.6352i −0.853758 1.07322i
\(486\) 0 0
\(487\) 13.1004 13.1004i 0.593634 0.593634i −0.344977 0.938611i \(-0.612113\pi\)
0.938611 + 0.344977i \(0.112113\pi\)
\(488\) −14.3206 20.4520i −0.648264 0.925817i
\(489\) 0 0
\(490\) −2.98553 8.92142i −0.134873 0.403029i
\(491\) 5.95862 + 7.10121i 0.268909 + 0.320473i 0.883553 0.468332i \(-0.155145\pi\)
−0.614644 + 0.788805i \(0.710700\pi\)
\(492\) 0 0
\(493\) 19.1619 + 8.93533i 0.863007 + 0.402427i
\(494\) −3.01722 + 5.22597i −0.135751 + 0.235128i
\(495\) 0 0
\(496\) 4.20804 + 7.28854i 0.188947 + 0.327265i
\(497\) 0.969617 + 11.0828i 0.0434933 + 0.497131i
\(498\) 0 0
\(499\) −20.3482 + 3.58794i −0.910911 + 0.160618i −0.609417 0.792850i \(-0.708596\pi\)
−0.301494 + 0.953468i \(0.597485\pi\)
\(500\) −0.433892 + 2.59508i −0.0194042 + 0.116055i
\(501\) 0 0
\(502\) −7.12650 + 0.623488i −0.318071 + 0.0278276i
\(503\) −4.53760 1.21585i −0.202322 0.0542119i 0.156235 0.987720i \(-0.450064\pi\)
−0.358557 + 0.933508i \(0.616731\pi\)
\(504\) 0 0
\(505\) 5.65871 7.64806i 0.251809 0.340334i
\(506\) 10.9405 + 30.0588i 0.486365 + 1.33628i
\(507\) 0 0
\(508\) −0.844055 0.0738452i −0.0374489 0.00327635i
\(509\) 30.3526 + 11.0475i 1.34536 + 0.489670i 0.911496 0.411309i \(-0.134928\pi\)
0.433862 + 0.900979i \(0.357151\pi\)
\(510\) 0 0
\(511\) 1.73758 9.85432i 0.0768661 0.435929i
\(512\) −17.8410 17.8410i −0.788469 0.788469i
\(513\) 0 0
\(514\) 16.2891i 0.718480i
\(515\) 14.2490 + 26.2405i 0.627887 + 1.15630i
\(516\) 0 0
\(517\) 32.1376 14.9860i 1.41341 0.659083i
\(518\) 1.63467 18.6844i 0.0718234 0.820945i
\(519\) 0 0
\(520\) −7.85854 32.7264i −0.344620 1.43515i
\(521\) 2.29310 + 1.32392i 0.100463 + 0.0580021i 0.549390 0.835566i \(-0.314860\pi\)
−0.448927 + 0.893568i \(0.648194\pi\)
\(522\) 0 0
\(523\) 3.37351 12.5901i 0.147513 0.550527i −0.852117 0.523351i \(-0.824682\pi\)
0.999631 0.0271764i \(-0.00865159\pi\)
\(524\) −0.100106 0.0839990i −0.00437316 0.00366951i
\(525\) 0 0
\(526\) −3.14347 17.8275i −0.137062 0.777317i
\(527\) 4.44773 6.35202i 0.193746 0.276698i
\(528\) 0 0
\(529\) 5.34967 6.37549i 0.232594 0.277195i
\(530\) −3.64945 + 1.58703i −0.158522 + 0.0689361i
\(531\) 0 0
\(532\) −0.106864 0.398822i −0.00463314 0.0172911i
\(533\) −18.1347 + 38.8899i −0.785499 + 1.68451i
\(534\) 0 0
\(535\) 6.46800 31.7989i 0.279636 1.37478i
\(536\) 9.80156 26.9296i 0.423363 1.16318i
\(537\) 0 0
\(538\) −13.4217 + 9.39794i −0.578649 + 0.405174i
\(539\) 13.6268 0.586947
\(540\) 0 0
\(541\) −42.0435 −1.80759 −0.903796 0.427963i \(-0.859231\pi\)
−0.903796 + 0.427963i \(0.859231\pi\)
\(542\) 21.4998 15.0543i 0.923494 0.646637i
\(543\) 0 0
\(544\) −1.44949 + 3.98243i −0.0621463 + 0.170745i
\(545\) −26.7489 + 17.7065i −1.14580 + 0.758465i
\(546\) 0 0
\(547\) −9.73975 + 20.8870i −0.416442 + 0.893062i 0.580451 + 0.814295i \(0.302876\pi\)
−0.996893 + 0.0787671i \(0.974902\pi\)
\(548\) 0.368084 + 1.37371i 0.0157238 + 0.0586818i
\(549\) 0 0
\(550\) 25.2338 + 13.4140i 1.07597 + 0.571977i
\(551\) 3.80505 4.53468i 0.162101 0.193184i
\(552\) 0 0
\(553\) −0.468201 + 0.668660i −0.0199099 + 0.0284343i
\(554\) 0.467751 + 2.65275i 0.0198728 + 0.112704i
\(555\) 0 0
\(556\) −3.33853 2.80136i −0.141585 0.118804i
\(557\) 9.19419 34.3132i 0.389570 1.45390i −0.441265 0.897377i \(-0.645470\pi\)
0.830835 0.556519i \(-0.187863\pi\)
\(558\) 0 0
\(559\) 5.66426 + 3.27026i 0.239572 + 0.138317i
\(560\) −12.9673 7.94551i −0.547967 0.335759i
\(561\) 0 0
\(562\) 3.02674 34.5957i 0.127675 1.45933i
\(563\) 4.24073 1.97748i 0.178725 0.0833410i −0.331196 0.943562i \(-0.607452\pi\)
0.509922 + 0.860221i \(0.329674\pi\)
\(564\) 0 0
\(565\) 26.8001 14.5529i 1.12749 0.612246i
\(566\) 3.08073i 0.129493i
\(567\) 0 0
\(568\) −11.9317 11.9317i −0.500642 0.500642i
\(569\) −1.37633 + 7.80556i −0.0576988 + 0.327226i −0.999971 0.00762185i \(-0.997574\pi\)
0.942272 + 0.334848i \(0.108685\pi\)
\(570\) 0 0
\(571\) 4.65824 + 1.69546i 0.194941 + 0.0709528i 0.437646 0.899147i \(-0.355812\pi\)
−0.242705 + 0.970100i \(0.578035\pi\)
\(572\) 5.11288 + 0.447319i 0.213780 + 0.0187033i
\(573\) 0 0
\(574\) 7.52995 + 20.6884i 0.314294 + 0.863516i
\(575\) −0.979225 27.9662i −0.0408365 1.16627i
\(576\) 0 0
\(577\) 22.0266 + 5.90200i 0.916977 + 0.245703i 0.686293 0.727325i \(-0.259237\pi\)
0.230684 + 0.973029i \(0.425904\pi\)
\(578\) 8.93890 0.782053i 0.371809 0.0325291i
\(579\) 0 0
\(580\) 0.212362 + 3.46941i 0.00881784 + 0.144060i
\(581\) 17.8737 3.15161i 0.741526 0.130751i
\(582\) 0 0
\(583\) −0.502393 5.74237i −0.0208070 0.237825i
\(584\) 7.58853 + 13.1437i 0.314015 + 0.543891i
\(585\) 0 0
\(586\) 8.00664 13.8679i 0.330751 0.572878i
\(587\) −33.9155 15.8151i −1.39984 0.652758i −0.431439 0.902142i \(-0.641994\pi\)
−0.968405 + 0.249384i \(0.919772\pi\)
\(588\) 0 0
\(589\) −1.39555 1.66315i −0.0575026 0.0685290i
\(590\) −13.7114 + 4.58847i −0.564488 + 0.188904i
\(591\) 0 0
\(592\) 14.3700 + 20.5225i 0.590604 + 0.843470i
\(593\) 5.46266 5.46266i 0.224324 0.224324i −0.585992 0.810317i \(-0.699295\pi\)
0.810317 + 0.585992i \(0.199295\pi\)
\(594\) 0 0
\(595\) −1.58558 + 13.9222i −0.0650024 + 0.570756i
\(596\) 2.01008 + 0.354432i 0.0823362 + 0.0145181i
\(597\) 0 0
\(598\) 15.9266 + 34.1546i 0.651286 + 1.39669i
\(599\) 1.79656 1.50749i 0.0734055 0.0615946i −0.605347 0.795962i \(-0.706965\pi\)
0.678752 + 0.734367i \(0.262521\pi\)
\(600\) 0 0
\(601\) 38.1639 13.8905i 1.55674 0.566607i 0.586753 0.809766i \(-0.300406\pi\)
0.969987 + 0.243159i \(0.0781836\pi\)
\(602\) 3.24142 0.868536i 0.132110 0.0353989i
\(603\) 0 0
\(604\) 3.24716 1.87475i 0.132125 0.0762824i
\(605\) −12.1837 + 11.5629i −0.495336 + 0.470101i
\(606\) 0 0
\(607\) −1.53527 1.07501i −0.0623147 0.0436332i 0.542004 0.840376i \(-0.317666\pi\)
−0.604319 + 0.796743i \(0.706555\pi\)
\(608\) 0.971981 + 0.680588i 0.0394190 + 0.0276015i
\(609\) 0 0
\(610\) 24.9669 + 0.652611i 1.01088 + 0.0264234i
\(611\) 36.1789 20.8879i 1.46364 0.845035i
\(612\) 0 0
\(613\) −17.5910 + 4.71349i −0.710494 + 0.190376i −0.595926 0.803039i \(-0.703215\pi\)
−0.114568 + 0.993415i \(0.536548\pi\)
\(614\) 29.3338 10.6766i 1.18382 0.430874i
\(615\) 0 0
\(616\) 19.1608 16.0778i 0.772012 0.647795i
\(617\) 7.87526 + 16.8885i 0.317046 + 0.679907i 0.998657 0.0518073i \(-0.0164982\pi\)
−0.681611 + 0.731715i \(0.738720\pi\)
\(618\) 0 0
\(619\) −28.0130 4.93945i −1.12594 0.198533i −0.420492 0.907296i \(-0.638142\pi\)
−0.705447 + 0.708763i \(0.749254\pi\)
\(620\) 1.26665 + 0.144256i 0.0508697 + 0.00579345i
\(621\) 0 0
\(622\) −3.73594 + 3.73594i −0.149797 + 0.149797i
\(623\) −2.18848 3.12547i −0.0876795 0.125219i
\(624\) 0 0
\(625\) −17.3698 17.9802i −0.694793 0.719210i
\(626\) −0.780926 0.930671i −0.0312121 0.0371971i
\(627\) 0 0
\(628\) 2.83130 + 1.32026i 0.112981 + 0.0526840i
\(629\) 11.5418 19.9910i 0.460202 0.797093i
\(630\) 0 0
\(631\) −16.2016 28.0619i −0.644974 1.11713i −0.984307 0.176462i \(-0.943535\pi\)
0.339333 0.940666i \(-0.389799\pi\)
\(632\) −0.107907 1.23338i −0.00429231 0.0490613i
\(633\) 0 0
\(634\) −34.4974 + 6.08282i −1.37007 + 0.241580i
\(635\) 5.33422 6.02981i 0.211682 0.239286i
\(636\) 0 0
\(637\) 15.9928 1.39919i 0.633659 0.0554380i
\(638\) 36.4671 + 9.77134i 1.44375 + 0.386851i
\(639\) 0 0
\(640\) 19.7222 2.94845i 0.779589 0.116548i
\(641\) 7.10695 + 19.5262i 0.280708 + 0.771238i 0.997279 + 0.0737239i \(0.0234884\pi\)
−0.716571 + 0.697514i \(0.754289\pi\)
\(642\) 0 0
\(643\) 39.3334 + 3.44122i 1.55116 + 0.135709i 0.830277 0.557351i \(-0.188182\pi\)
0.720880 + 0.693060i \(0.243738\pi\)
\(644\) −2.42303 0.881910i −0.0954807 0.0347521i
\(645\) 0 0
\(646\) −0.661691 + 3.75263i −0.0260339 + 0.147645i
\(647\) −27.7872 27.7872i −1.09243 1.09243i −0.995269 0.0971593i \(-0.969024\pi\)
−0.0971593 0.995269i \(-0.530976\pi\)
\(648\) 0 0
\(649\) 20.9430i 0.822086i
\(650\) 30.9926 + 13.1522i 1.21563 + 0.515870i
\(651\) 0 0
\(652\) −1.58283 + 0.738085i −0.0619884 + 0.0289056i
\(653\) 1.47726 16.8852i 0.0578098 0.660770i −0.910909 0.412608i \(-0.864618\pi\)
0.968719 0.248162i \(-0.0798264\pi\)
\(654\) 0 0
\(655\) 1.20736 0.289921i 0.0471754 0.0113281i
\(656\) −25.4684 14.7042i −0.994375 0.574103i
\(657\) 0 0
\(658\) 5.54754 20.7037i 0.216266 0.807115i
\(659\) −36.7210 30.8125i −1.43045 1.20029i −0.945449 0.325770i \(-0.894376\pi\)
−0.484997 0.874516i \(-0.661179\pi\)
\(660\) 0 0
\(661\) −0.726513 4.12026i −0.0282581 0.160259i 0.967413 0.253202i \(-0.0814838\pi\)
−0.995671 + 0.0929427i \(0.970373\pi\)
\(662\) −9.79064 + 13.9825i −0.380524 + 0.543445i
\(663\) 0 0
\(664\) −17.6947 + 21.0877i −0.686687 + 0.818361i
\(665\) 3.65026 + 1.43768i 0.141551 + 0.0557508i
\(666\) 0 0
\(667\) −9.56811 35.7087i −0.370479 1.38264i
\(668\) 0.818774 1.75587i 0.0316793 0.0679365i
\(669\) 0 0
\(670\) 15.8237 + 23.9045i 0.611321 + 0.923511i
\(671\) −12.3730 + 33.9945i −0.477653 + 1.31234i
\(672\) 0 0
\(673\) −19.5570 + 13.6940i −0.753867 + 0.527863i −0.886178 0.463345i \(-0.846649\pi\)
0.132311 + 0.991208i \(0.457760\pi\)
\(674\) −11.2915 −0.434933
\(675\) 0 0
\(676\) 2.98725 0.114894
\(677\) 18.1236 12.6903i 0.696547 0.487727i −0.170880 0.985292i \(-0.554661\pi\)
0.867427 + 0.497565i \(0.165772\pi\)
\(678\) 0 0
\(679\) 9.04396 24.8481i 0.347075 0.953581i
\(680\) −11.7311 17.7220i −0.449869 0.679608i
\(681\) 0 0
\(682\) 5.85182 12.5493i 0.224078 0.480537i
\(683\) −6.53337 24.3829i −0.249993 0.932985i −0.970808 0.239858i \(-0.922899\pi\)
0.720815 0.693127i \(-0.243768\pi\)
\(684\) 0 0
\(685\) −12.5730 4.95195i −0.480389 0.189204i
\(686\) 16.9965 20.2556i 0.648929 0.773363i
\(687\) 0 0
\(688\) −2.57107 + 3.67187i −0.0980212 + 0.139989i
\(689\) −1.17925 6.68785i −0.0449258 0.254787i
\(690\) 0 0
\(691\) 25.5999 + 21.4808i 0.973865 + 0.817170i 0.983153 0.182787i \(-0.0585118\pi\)
−0.00928734 + 0.999957i \(0.502956\pi\)
\(692\) −0.473473 + 1.76703i −0.0179988 + 0.0671723i
\(693\) 0 0
\(694\) 6.05298 + 3.49469i 0.229768 + 0.132657i
\(695\) 40.2653 9.66884i 1.52735 0.366760i
\(696\) 0 0
\(697\) −2.36159 + 26.9931i −0.0894517 + 1.02244i
\(698\) −24.8229 + 11.5751i −0.939559 + 0.438124i
\(699\) 0 0
\(700\) −2.13581 + 0.863157i −0.0807261 + 0.0326243i
\(701\) 12.4042i 0.468499i 0.972177 + 0.234249i \(0.0752632\pi\)
−0.972177 + 0.234249i \(0.924737\pi\)
\(702\) 0 0
\(703\) −4.57003 4.57003i −0.172362 0.172362i
\(704\) −6.50508 + 36.8922i −0.245170 + 1.39043i
\(705\) 0 0
\(706\) −35.9678 13.0912i −1.35367 0.492694i
\(707\) 8.29809 + 0.725989i 0.312082 + 0.0273036i
\(708\) 0 0
\(709\) −4.29127 11.7902i −0.161162 0.442789i 0.832659 0.553786i \(-0.186818\pi\)
−0.993821 + 0.110998i \(0.964595\pi\)
\(710\) 16.6940 2.49573i 0.626514 0.0936631i
\(711\) 0 0
\(712\) 5.58994 + 1.49782i 0.209492 + 0.0561332i
\(713\) −13.5070 + 1.18171i −0.505842 + 0.0442554i
\(714\) 0 0
\(715\) −32.3121 + 36.5257i −1.20840 + 1.36598i
\(716\) 1.01940 0.179748i 0.0380969 0.00671750i
\(717\) 0 0
\(718\) 2.06408 + 23.5926i 0.0770308 + 0.880466i
\(719\) −9.10268 15.7663i −0.339473 0.587984i 0.644861 0.764300i \(-0.276915\pi\)
−0.984334 + 0.176316i \(0.943582\pi\)
\(720\) 0 0
\(721\) −13.0717 + 22.6408i −0.486815 + 0.843188i
\(722\) −21.9081 10.2159i −0.815334 0.380196i
\(723\) 0 0
\(724\) −0.864744 1.03056i −0.0321380 0.0383005i
\(725\) −27.7006 17.9853i −1.02877 0.667956i
\(726\) 0 0
\(727\) −5.64377 8.06014i −0.209316 0.298934i 0.700742 0.713414i \(-0.252852\pi\)
−0.910058 + 0.414480i \(0.863963\pi\)
\(728\) 20.8369 20.8369i 0.772267 0.772267i
\(729\) 0 0
\(730\) −15.0845 1.71795i −0.558304 0.0635841i
\(731\) 4.06735 + 0.717184i 0.150436 + 0.0265260i
\(732\) 0 0
\(733\) −15.6224 33.5024i −0.577027 1.23744i −0.950767 0.309905i \(-0.899703\pi\)
0.373740 0.927533i \(-0.378075\pi\)
\(734\) −22.3146 + 18.7242i −0.823646 + 0.691121i
\(735\) 0 0
\(736\) 6.96332 2.53444i 0.256671 0.0934207i
\(737\) −40.1088 + 10.7471i −1.47743 + 0.395875i
\(738\) 0 0
\(739\) −7.02338 + 4.05495i −0.258359 + 0.149164i −0.623586 0.781755i \(-0.714325\pi\)
0.365227 + 0.930919i \(0.380991\pi\)
\(740\) 3.79368 + 0.0991631i 0.139459 + 0.00364531i
\(741\) 0 0
\(742\) −2.85416 1.99851i −0.104780 0.0733675i
\(743\) −25.5056 17.8592i −0.935709 0.655190i 0.00296531 0.999996i \(-0.499056\pi\)
−0.938674 + 0.344805i \(0.887945\pi\)
\(744\) 0 0
\(745\) −14.0672 + 13.3505i −0.515383 + 0.489126i
\(746\) −19.8552 + 11.4634i −0.726949 + 0.419704i
\(747\) 0 0
\(748\) 3.13050 0.838814i 0.114462 0.0306701i
\(749\) 26.6979 9.71724i 0.975519 0.355060i
\(750\) 0 0
\(751\) −13.4156 + 11.2570i −0.489541 + 0.410774i −0.853862 0.520500i \(-0.825746\pi\)
0.364321 + 0.931273i \(0.381301\pi\)
\(752\) 12.1000 + 25.9484i 0.441240 + 0.946243i
\(753\) 0 0
\(754\) 43.8023 + 7.72353i 1.59519 + 0.281274i
\(755\) −4.03140 + 35.3979i −0.146718 + 1.28826i
\(756\) 0 0
\(757\) −20.1777 + 20.1777i −0.733371 + 0.733371i −0.971286 0.237915i \(-0.923536\pi\)
0.237915 + 0.971286i \(0.423536\pi\)
\(758\) 20.7010 + 29.5641i 0.751893 + 1.07381i
\(759\) 0 0
\(760\) −5.64287 + 1.88837i −0.204688 + 0.0684985i
\(761\) −23.7584 28.3141i −0.861240 1.02639i −0.999353 0.0359689i \(-0.988548\pi\)
0.138113 0.990416i \(-0.455896\pi\)
\(762\) 0 0
\(763\) −25.4545 11.8696i −0.921516 0.429710i
\(764\) 1.69744 2.94006i 0.0614113 0.106368i
\(765\) 0 0
\(766\) −4.88069 8.45360i −0.176346 0.305441i
\(767\) −2.15042 24.5794i −0.0776472 0.887512i
\(768\) 0 0
\(769\) 8.53754 1.50540i 0.307872 0.0542861i −0.0175779 0.999845i \(-0.505595\pi\)
0.325450 + 0.945559i \(0.394484\pi\)
\(770\) 1.52866 + 24.9742i 0.0550891 + 0.900007i
\(771\) 0 0
\(772\) −4.06755 + 0.355865i −0.146394 + 0.0128078i
\(773\) −11.3983 3.05417i −0.409969 0.109851i 0.0479396 0.998850i \(-0.484734\pi\)
−0.457908 + 0.889000i \(0.651401\pi\)
\(774\) 0 0
\(775\) −8.26030 + 8.85975i −0.296719 + 0.318252i
\(776\) 13.7174 + 37.6882i 0.492425 + 1.35293i
\(777\) 0 0
\(778\) 41.3603 + 3.61856i 1.48284 + 0.129732i
\(779\) 7.12895 + 2.59472i 0.255421 + 0.0929657i
\(780\) 0 0
\(781\) −4.24560 + 24.0780i −0.151919 + 0.861578i
\(782\) 16.8270 + 16.8270i 0.601733 + 0.601733i
\(783\) 0 0
\(784\) 11.0025i 0.392947i
\(785\) −26.0856 + 14.1649i −0.931035 + 0.505567i
\(786\) 0 0
\(787\) 17.0214 7.93722i 0.606748 0.282931i −0.0948643 0.995490i \(-0.530242\pi\)
0.701612 + 0.712559i \(0.252464\pi\)
\(788\) −0.279178 + 3.19101i −0.00994529 + 0.113675i
\(789\) 0 0
\(790\) 1.05603 + 0.647065i 0.0375717 + 0.0230215i
\(791\) 23.1237 + 13.3505i 0.822183 + 0.474687i
\(792\) 0 0
\(793\) −11.0308 + 41.1675i −0.391715 + 1.46190i
\(794\) 16.7831 + 14.0827i 0.595610 + 0.499776i
\(795\) 0 0
\(796\) −0.367376 2.08349i −0.0130213 0.0738475i
\(797\) −12.3706 + 17.6670i −0.438188 + 0.625797i −0.976131 0.217184i \(-0.930313\pi\)
0.537943 + 0.842981i \(0.319202\pi\)
\(798\) 0 0
\(799\) 16.9567 20.2082i 0.599884 0.714914i
\(800\) 3.10745 5.84558i 0.109865 0.206673i
\(801\) 0 0
\(802\) −0.519739 1.93969i −0.0183526 0.0684929i
\(803\) 9.29368 19.9304i 0.327967 0.703327i
\(804\) 0 0
\(805\) 20.4300 13.5237i 0.720063 0.476648i
\(806\) 5.57934 15.3291i 0.196524 0.539945i
\(807\) 0 0
\(808\) −10.3493 + 7.24665i −0.364087 + 0.254936i
\(809\) 4.46938 0.157135 0.0785676 0.996909i \(-0.474965\pi\)
0.0785676 + 0.996909i \(0.474965\pi\)
\(810\) 0 0
\(811\) 37.9099 1.33120 0.665598 0.746311i \(-0.268177\pi\)
0.665598 + 0.746311i \(0.268177\pi\)
\(812\) −2.49292 + 1.74556i −0.0874845 + 0.0612573i
\(813\) 0 0
\(814\) 14.0978 38.7333i 0.494127 1.35760i
\(815\) 3.30762 16.2614i 0.115861 0.569612i
\(816\) 0 0
\(817\) 0.488696 1.04801i 0.0170973 0.0366653i
\(818\) 8.06996 + 30.1175i 0.282159 + 1.05303i
\(819\) 0 0
\(820\) −4.08511 + 1.77649i −0.142658 + 0.0620376i
\(821\) −23.1674 + 27.6099i −0.808549 + 0.963591i −0.999839 0.0179428i \(-0.994288\pi\)
0.191290 + 0.981533i \(0.438733\pi\)
\(822\) 0 0
\(823\) 1.52711 2.18095i 0.0532319 0.0760230i −0.791654 0.610970i \(-0.790780\pi\)
0.844886 + 0.534947i \(0.179668\pi\)
\(824\) −6.88563 39.0504i −0.239872 1.36038i
\(825\) 0 0
\(826\) −9.69752 8.13719i −0.337420 0.283129i
\(827\) −10.6874 + 39.8859i −0.371637 + 1.38697i 0.486560 + 0.873647i \(0.338252\pi\)
−0.858197 + 0.513321i \(0.828415\pi\)
\(828\) 0 0
\(829\) 19.6326 + 11.3349i 0.681869 + 0.393677i 0.800559 0.599254i \(-0.204536\pi\)
−0.118690 + 0.992931i \(0.537869\pi\)
\(830\) −6.42966 26.7759i −0.223177 0.929406i
\(831\) 0 0
\(832\) −3.84651 + 43.9658i −0.133354 + 1.52424i
\(833\) 9.18766 4.28428i 0.318334 0.148441i
\(834\) 0 0
\(835\) 8.78453 + 16.1773i 0.304001 + 0.559838i
\(836\) 0.907402i 0.0313832i
\(837\) 0 0
\(838\) 14.9429 + 14.9429i 0.516195 + 0.516195i
\(839\) 1.44230 8.17971i 0.0497938 0.282395i −0.949736 0.313052i \(-0.898649\pi\)
0.999530 + 0.0306567i \(0.00975985\pi\)
\(840\) 0 0
\(841\) −13.7493 5.00432i −0.474112 0.172563i
\(842\) 48.0337 + 4.20240i 1.65535 + 0.144824i
\(843\) 0 0
\(844\) −1.50888 4.14562i −0.0519379 0.142698i
\(845\) −16.8824 + 22.8175i −0.580771 + 0.784945i
\(846\) 0 0
\(847\) −14.2054 3.80634i −0.488105 0.130787i
\(848\) 4.63650 0.405641i 0.159218 0.0139298i
\(849\) 0 0
\(850\) 21.2310 + 1.11067i 0.728216 + 0.0380957i
\(851\) −39.7487 + 7.00876i −1.36257 + 0.240257i
\(852\) 0 0
\(853\) −0.534954 6.11455i −0.0183165 0.209358i −0.999838 0.0180058i \(-0.994268\pi\)
0.981521 0.191352i \(-0.0612873\pi\)
\(854\) 10.9335 + 18.9374i 0.374137 + 0.648024i
\(855\) 0 0
\(856\) −21.5463 + 37.3193i −0.736439 + 1.27555i
\(857\) 31.3187 + 14.6042i 1.06983 + 0.498869i 0.876072 0.482181i \(-0.160155\pi\)
0.193756 + 0.981050i \(0.437933\pi\)
\(858\) 0 0
\(859\) −14.4078 17.1705i −0.491587 0.585850i 0.462034 0.886862i \(-0.347120\pi\)
−0.953620 + 0.301012i \(0.902676\pi\)
\(860\) 0.215478 + 0.643896i 0.00734775 + 0.0219567i
\(861\) 0 0
\(862\) −8.19621 11.7054i −0.279164 0.398688i
\(863\) −34.4337 + 34.4337i −1.17214 + 1.17214i −0.190436 + 0.981700i \(0.560990\pi\)
−0.981700 + 0.190436i \(0.939010\pi\)
\(864\) 0 0
\(865\) −10.8212 13.6029i −0.367933 0.462511i
\(866\) −47.8011 8.42862i −1.62435 0.286416i
\(867\) 0 0
\(868\) 0.471713 + 1.01159i 0.0160110 + 0.0343357i
\(869\) −1.37423 + 1.15312i −0.0466175 + 0.0391168i
\(870\) 0 0
\(871\) −45.9694 + 16.7315i −1.55762 + 0.566926i
\(872\) 41.1477 11.0255i 1.39344 0.373370i
\(873\) 0 0
\(874\) 5.77009 3.33137i 0.195176 0.112685i
\(875\) 5.47747 21.1921i 0.185172 0.716423i
\(876\) 0 0
\(877\) 11.3525 + 7.94910i 0.383347 + 0.268422i 0.749327 0.662201i \(-0.230377\pi\)
−0.365980 + 0.930623i \(0.619266\pi\)
\(878\) 15.1584 + 10.6140i 0.511571 + 0.358206i
\(879\) 0 0
\(880\) −23.0074 24.2425i −0.775580 0.817214i
\(881\) 20.3929 11.7738i 0.687054 0.396671i −0.115453 0.993313i \(-0.536832\pi\)
0.802507 + 0.596642i \(0.203499\pi\)
\(882\) 0 0
\(883\) −15.8795 + 4.25489i −0.534386 + 0.143188i −0.515913 0.856641i \(-0.672547\pi\)
−0.0184733 + 0.999829i \(0.505881\pi\)
\(884\) 3.58792 1.30590i 0.120675 0.0439221i
\(885\) 0 0
\(886\) 11.6044 9.73725i 0.389857 0.327129i
\(887\) 4.33234 + 9.29073i 0.145466 + 0.311952i 0.965518 0.260336i \(-0.0838335\pi\)
−0.820052 + 0.572289i \(0.806056\pi\)
\(888\) 0 0
\(889\) 6.94156 + 1.22398i 0.232812 + 0.0410511i
\(890\) −4.53038 + 3.60397i −0.151859 + 0.120805i
\(891\) 0 0
\(892\) 2.76005 2.76005i 0.0924133 0.0924133i
\(893\) −4.23638 6.05018i −0.141765 0.202461i
\(894\) 0 0
\(895\) −4.38817 + 8.80234i −0.146680 + 0.294230i
\(896\) 11.2227 + 13.3748i 0.374926 + 0.446819i
\(897\) 0 0
\(898\) −1.94540 0.907153i −0.0649187 0.0302721i
\(899\) −8.00123 + 13.8585i −0.266856 + 0.462208i
\(900\) 0 0
\(901\) −2.14414 3.71376i −0.0714317 0.123723i
\(902\) 4.21697 + 48.2002i 0.140410 + 1.60489i
\(903\) 0 0
\(904\) −39.8832 + 7.03248i −1.32649 + 0.233897i
\(905\) 12.7588 0.780964i 0.424118 0.0259601i
\(906\) 0 0
\(907\) −13.4551 + 1.17717i −0.446769 + 0.0390872i −0.308321 0.951283i \(-0.599767\pi\)
−0.138448 + 0.990370i \(0.544211\pi\)
\(908\) −4.11293 1.10206i −0.136492 0.0365730i
\(909\) 0 0
\(910\) 4.35842 + 29.1535i 0.144480 + 0.966430i
\(911\) −4.95701 13.6193i −0.164233 0.451227i 0.830090 0.557629i \(-0.188289\pi\)
−0.994323 + 0.106403i \(0.966067\pi\)
\(912\) 0 0
\(913\) 39.7348 + 3.47635i 1.31503 + 0.115050i
\(914\) −6.91502 2.51686i −0.228729 0.0832504i
\(915\) 0 0
\(916\) −0.776272 + 4.40246i −0.0256488 + 0.145461i
\(917\) 0.768724 + 0.768724i 0.0253855 + 0.0253855i
\(918\) 0 0
\(919\) 11.7599i 0.387925i 0.981009 + 0.193962i \(0.0621340\pi\)
−0.981009 + 0.193962i \(0.937866\pi\)
\(920\) −10.5526 + 35.6312i −0.347910 + 1.17473i
\(921\) 0 0
\(922\) −18.2970 + 8.53202i −0.602579 + 0.280987i
\(923\) −2.51046 + 28.6946i −0.0826327 + 0.944496i
\(924\) 0 0
\(925\) −22.1974 + 28.4169i −0.729846 + 0.934340i
\(926\) −38.0276 21.9552i −1.24966 0.721494i
\(927\) 0 0
\(928\) 2.26359 8.44784i 0.0743061 0.277314i
\(929\) −36.0388 30.2401i −1.18239 0.992146i −0.999960 0.00892776i \(-0.997158\pi\)
−0.182433 0.983218i \(-0.558397\pi\)
\(930\) 0 0
\(931\) −0.492867 2.79519i −0.0161531 0.0916086i
\(932\) −1.02089 + 1.45799i −0.0334405 + 0.0477579i
\(933\) 0 0
\(934\) −19.3932 + 23.1119i −0.634563 + 0.756243i
\(935\) −11.2848 + 28.6522i −0.369054 + 0.937027i
\(936\) 0 0
\(937\) −9.80740 36.6017i −0.320394 1.19573i −0.918862 0.394580i \(-0.870890\pi\)
0.598468 0.801147i \(-0.295776\pi\)
\(938\) −10.6074 + 22.7477i −0.346346 + 0.742740i
\(939\) 0 0
\(940\) 4.24987 + 0.864439i 0.138616 + 0.0281949i
\(941\) 3.79401 10.4240i 0.123681 0.339811i −0.862364 0.506289i \(-0.831017\pi\)
0.986045 + 0.166477i \(0.0532392\pi\)
\(942\) 0 0
\(943\) 38.8098 27.1749i 1.26382 0.884937i
\(944\) 16.9098 0.550367
\(945\) 0 0
\(946\) 7.37489 0.239778
\(947\) 13.0294 9.12331i 0.423400 0.296468i −0.342391 0.939558i \(-0.611237\pi\)
0.765791 + 0.643090i \(0.222348\pi\)
\(948\) 0 0
\(949\) 8.86092 24.3452i 0.287638 0.790278i
\(950\) 1.83887 5.66126i 0.0596607 0.183675i
\(951\) 0 0
\(952\) 7.86402 16.8644i 0.254874 0.546580i
\(953\) 9.45180 + 35.2746i 0.306174 + 1.14266i 0.931930 + 0.362638i \(0.118124\pi\)
−0.625756 + 0.780019i \(0.715210\pi\)
\(954\) 0 0
\(955\) 12.8639 + 29.5813i 0.416268 + 0.957227i
\(956\) 1.89177 2.25453i 0.0611843 0.0729167i
\(957\) 0 0
\(958\) −17.4002 + 24.8501i −0.562176 + 0.802871i
\(959\) −2.05447 11.6515i −0.0663422 0.376245i
\(960\) 0 0
\(961\) −19.2514 16.1538i −0.621012 0.521091i
\(962\) 12.5685 46.9062i 0.405224 1.51232i
\(963\) 0 0
\(964\) 3.48953 + 2.01468i 0.112390 + 0.0648886i
\(965\) 20.2695 33.0803i 0.652499 1.06489i
\(966\) 0 0
\(967\) −0.170714 + 1.95128i −0.00548981 + 0.0627488i −0.998445 0.0557381i \(-0.982249\pi\)
0.992956 + 0.118487i \(0.0378044\pi\)
\(968\) 20.2162 9.42696i 0.649773 0.302994i
\(969\) 0 0
\(970\) −38.4685 11.3929i −1.23515 0.365805i
\(971\) 27.5442i 0.883934i −0.897031 0.441967i \(-0.854281\pi\)
0.897031 0.441967i \(-0.145719\pi\)
\(972\) 0 0
\(973\) 25.6369 + 25.6369i 0.821881 + 0.821881i
\(974\) 4.27366 24.2371i 0.136937 0.776607i
\(975\) 0 0
\(976\) −27.4477 9.99016i −0.878581 0.319777i
\(977\) 32.5167 + 2.84484i 1.04030 + 0.0910146i 0.594483 0.804108i \(-0.297357\pi\)
0.445819 + 0.895123i \(0.352912\pi\)
\(978\) 0 0
\(979\) −2.86792 7.87954i −0.0916591 0.251831i
\(980\) 1.33977 + 0.991278i 0.0427973 + 0.0316652i
\(981\) 0 0
\(982\) 11.8947 + 3.18718i 0.379575 + 0.101707i
\(983\) 31.9076 2.79155i 1.01769 0.0890367i 0.433919 0.900952i \(-0.357130\pi\)
0.583775 + 0.811915i \(0.301575\pi\)
\(984\) 0 0
\(985\) −22.7961 20.1664i −0.726346 0.642556i
\(986\) 27.6596 4.87713i 0.880860 0.155319i
\(987\) 0 0
\(988\) −0.0931716 1.06496i −0.00296418 0.0338808i
\(989\) −3.61075 6.25401i −0.114815 0.198866i
\(990\) 0 0
\(991\) 24.5859 42.5840i 0.780995 1.35272i −0.150367 0.988630i \(-0.548046\pi\)
0.931362 0.364094i \(-0.118621\pi\)
\(992\) −2.90712 1.35561i −0.0923012 0.0430407i
\(993\) 0 0
\(994\) 9.49956 + 11.3211i 0.301308 + 0.359084i
\(995\) 17.9906 + 8.96871i 0.570339 + 0.284327i
\(996\) 0 0
\(997\) −18.0163 25.7299i −0.570581 0.814874i 0.425347 0.905031i \(-0.360152\pi\)
−0.995928 + 0.0901563i \(0.971263\pi\)
\(998\) −19.4085 + 19.4085i −0.614364 + 0.614364i
\(999\) 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.8.11 192
3.2 odd 2 135.2.q.a.83.6 yes 192
5.2 odd 4 inner 405.2.r.a.332.11 192
15.2 even 4 135.2.q.a.2.6 192
15.8 even 4 675.2.ba.b.407.11 192
15.14 odd 2 675.2.ba.b.218.11 192
27.13 even 9 135.2.q.a.68.6 yes 192
27.14 odd 18 inner 405.2.r.a.233.11 192
135.13 odd 36 675.2.ba.b.257.11 192
135.67 odd 36 135.2.q.a.122.6 yes 192
135.94 even 18 675.2.ba.b.68.11 192
135.122 even 36 inner 405.2.r.a.152.11 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.q.a.2.6 192 15.2 even 4
135.2.q.a.68.6 yes 192 27.13 even 9
135.2.q.a.83.6 yes 192 3.2 odd 2
135.2.q.a.122.6 yes 192 135.67 odd 36
405.2.r.a.8.11 192 1.1 even 1 trivial
405.2.r.a.152.11 192 135.122 even 36 inner
405.2.r.a.233.11 192 27.14 odd 18 inner
405.2.r.a.332.11 192 5.2 odd 4 inner
675.2.ba.b.68.11 192 135.94 even 18
675.2.ba.b.218.11 192 15.14 odd 2
675.2.ba.b.257.11 192 135.13 odd 36
675.2.ba.b.407.11 192 15.8 even 4