Properties

Label 387.2.y.c.100.2
Level $387$
Weight $2$
Character 387.100
Analytic conductor $3.090$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [387,2,Mod(10,387)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(387, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("387.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 387.y (of order \(21\), degree \(12\), 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: \(3.09021055822\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(3\) over \(\Q(\zeta_{21})\)
Twist minimal: no (minimal twist has level 43)
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 100.2
Character \(\chi\) \(=\) 387.100
Dual form 387.2.y.c.298.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.982954 - 0.473366i) q^{2} +(-0.504856 + 0.633069i) q^{4} +(-1.29085 + 0.398175i) q^{5} +(-0.108163 + 0.187343i) q^{7} +(-0.682116 + 2.98855i) q^{8} +O(q^{10})\) \(q+(0.982954 - 0.473366i) q^{2} +(-0.504856 + 0.633069i) q^{4} +(-1.29085 + 0.398175i) q^{5} +(-0.108163 + 0.187343i) q^{7} +(-0.682116 + 2.98855i) q^{8} +(-1.08036 + 1.00243i) q^{10} +(3.76031 + 4.71528i) q^{11} +(2.10767 + 1.95563i) q^{13} +(-0.0176371 + 0.235350i) q^{14} +(0.383825 + 1.68165i) q^{16} +(-0.270054 - 0.0833006i) q^{17} +(1.12457 + 0.169502i) q^{19} +(0.399621 - 1.01822i) q^{20} +(5.92827 + 2.85490i) q^{22} +(1.44040 - 3.67008i) q^{23} +(-2.62344 + 1.78863i) q^{25} +(2.99747 + 0.924598i) q^{26} +(-0.0639946 - 0.163056i) q^{28} +(-0.515946 + 6.88482i) q^{29} +(-8.17225 - 5.57174i) q^{31} +(-2.64918 - 3.32196i) q^{32} +(-0.304882 + 0.0459536i) q^{34} +(0.0650265 - 0.284900i) q^{35} +(-3.77129 - 6.53207i) q^{37} +(1.18564 - 0.365721i) q^{38} +(-0.309453 - 4.12937i) q^{40} +(4.62195 - 2.22581i) q^{41} +(5.90092 + 2.85993i) q^{43} -4.88351 q^{44} +(-0.321443 - 4.28936i) q^{46} +(-0.288239 + 0.361440i) q^{47} +(3.47660 + 6.02165i) q^{49} +(-1.73205 + 2.99999i) q^{50} +(-2.30212 + 0.346988i) q^{52} +(6.12346 - 5.68174i) q^{53} +(-6.73151 - 4.58946i) q^{55} +(-0.486104 - 0.451039i) q^{56} +(2.75189 + 7.01170i) q^{58} +(-1.85926 - 8.14595i) q^{59} +(11.0987 - 7.56700i) q^{61} +(-10.6704 - 1.60831i) q^{62} +(-7.28468 - 3.50811i) q^{64} +(-3.49937 - 1.68521i) q^{65} +(6.22328 + 0.938008i) q^{67} +(0.189073 - 0.128908i) q^{68} +(-0.0709437 - 0.310825i) q^{70} +(0.540324 + 1.37672i) q^{71} +(0.601198 + 0.557830i) q^{73} +(-6.79906 - 4.63552i) q^{74} +(-0.675051 + 0.626356i) q^{76} +(-1.29010 + 0.194451i) q^{77} +(-3.07798 + 5.33121i) q^{79} +(-1.16505 - 2.01792i) q^{80} +(3.48954 - 4.37574i) q^{82} +(0.538458 + 7.18523i) q^{83} +0.381767 q^{85} +(7.15412 + 0.0178853i) q^{86} +(-16.6568 + 8.02150i) q^{88} +(-0.331353 - 4.42159i) q^{89} +(-0.594345 + 0.183331i) q^{91} +(1.59622 + 2.76473i) q^{92} +(-0.112232 + 0.491721i) q^{94} +(-1.51914 + 0.228974i) q^{95} +(-2.78649 - 3.49415i) q^{97} +(6.26778 + 4.27330i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + 10 q^{2} - 18 q^{4} + 17 q^{5} + 6 q^{7} - 18 q^{8} - 7 q^{10} + 4 q^{11} - 18 q^{14} - 10 q^{16} + 10 q^{17} + 10 q^{19} + 3 q^{20} - 3 q^{22} - 4 q^{23} - 2 q^{25} + 15 q^{26} + 20 q^{28} - 9 q^{29} + 40 q^{31} - 48 q^{32} - 42 q^{34} - 11 q^{35} - 19 q^{37} + 21 q^{38} - 97 q^{40} + 28 q^{41} - 8 q^{43} - 14 q^{44} - 61 q^{46} + 30 q^{47} + 6 q^{49} + 3 q^{50} - 8 q^{52} + 24 q^{53} + 14 q^{55} - 39 q^{56} + 64 q^{58} + q^{59} - 14 q^{61} - 33 q^{62} + 48 q^{64} - 38 q^{65} + 66 q^{67} - 66 q^{68} + 47 q^{70} + 33 q^{71} + 29 q^{73} + 40 q^{74} - 39 q^{76} + 27 q^{77} - 17 q^{79} - 8 q^{80} - 54 q^{82} + 23 q^{83} - 56 q^{85} + 45 q^{86} - 17 q^{88} + 19 q^{89} - 13 q^{91} + 18 q^{92} + 44 q^{94} - q^{95} - 31 q^{97} + 5 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/387\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(173\)
\(\chi(n)\) \(e\left(\frac{10}{21}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.982954 0.473366i 0.695054 0.334720i −0.0527802 0.998606i \(-0.516808\pi\)
0.747834 + 0.663886i \(0.231094\pi\)
\(3\) 0 0
\(4\) −0.504856 + 0.633069i −0.252428 + 0.316534i
\(5\) −1.29085 + 0.398175i −0.577286 + 0.178069i −0.569629 0.821902i \(-0.692913\pi\)
−0.00765630 + 0.999971i \(0.502437\pi\)
\(6\) 0 0
\(7\) −0.108163 + 0.187343i −0.0408816 + 0.0708091i −0.885742 0.464177i \(-0.846350\pi\)
0.844861 + 0.534987i \(0.179683\pi\)
\(8\) −0.682116 + 2.98855i −0.241164 + 1.05661i
\(9\) 0 0
\(10\) −1.08036 + 1.00243i −0.341641 + 0.316997i
\(11\) 3.76031 + 4.71528i 1.13378 + 1.42171i 0.892380 + 0.451285i \(0.149034\pi\)
0.241397 + 0.970426i \(0.422394\pi\)
\(12\) 0 0
\(13\) 2.10767 + 1.95563i 0.584562 + 0.542395i 0.916050 0.401065i \(-0.131360\pi\)
−0.331487 + 0.943460i \(0.607550\pi\)
\(14\) −0.0176371 + 0.235350i −0.00471370 + 0.0629000i
\(15\) 0 0
\(16\) 0.383825 + 1.68165i 0.0959562 + 0.420412i
\(17\) −0.270054 0.0833006i −0.0654977 0.0202034i 0.261833 0.965113i \(-0.415673\pi\)
−0.327331 + 0.944910i \(0.606149\pi\)
\(18\) 0 0
\(19\) 1.12457 + 0.169502i 0.257994 + 0.0388863i 0.276766 0.960937i \(-0.410737\pi\)
−0.0187716 + 0.999824i \(0.505976\pi\)
\(20\) 0.399621 1.01822i 0.0893580 0.227680i
\(21\) 0 0
\(22\) 5.92827 + 2.85490i 1.26391 + 0.608668i
\(23\) 1.44040 3.67008i 0.300344 0.765265i −0.698426 0.715682i \(-0.746116\pi\)
0.998770 0.0495821i \(-0.0157890\pi\)
\(24\) 0 0
\(25\) −2.62344 + 1.78863i −0.524688 + 0.357727i
\(26\) 2.99747 + 0.924598i 0.587853 + 0.181329i
\(27\) 0 0
\(28\) −0.0639946 0.163056i −0.0120938 0.0308146i
\(29\) −0.515946 + 6.88482i −0.0958088 + 1.27848i 0.717463 + 0.696596i \(0.245303\pi\)
−0.813272 + 0.581883i \(0.802316\pi\)
\(30\) 0 0
\(31\) −8.17225 5.57174i −1.46778 1.00071i −0.992679 0.120783i \(-0.961459\pi\)
−0.475100 0.879932i \(-0.657588\pi\)
\(32\) −2.64918 3.32196i −0.468313 0.587246i
\(33\) 0 0
\(34\) −0.304882 + 0.0459536i −0.0522869 + 0.00788098i
\(35\) 0.0650265 0.284900i 0.0109915 0.0481568i
\(36\) 0 0
\(37\) −3.77129 6.53207i −0.619996 1.07387i −0.989486 0.144630i \(-0.953801\pi\)
0.369489 0.929235i \(-0.379533\pi\)
\(38\) 1.18564 0.365721i 0.192336 0.0593277i
\(39\) 0 0
\(40\) −0.309453 4.12937i −0.0489289 0.652910i
\(41\) 4.62195 2.22581i 0.721827 0.347613i −0.0366371 0.999329i \(-0.511665\pi\)
0.758464 + 0.651715i \(0.225950\pi\)
\(42\) 0 0
\(43\) 5.90092 + 2.85993i 0.899881 + 0.436135i
\(44\) −4.88351 −0.736217
\(45\) 0 0
\(46\) −0.321443 4.28936i −0.0473942 0.632431i
\(47\) −0.288239 + 0.361440i −0.0420439 + 0.0527214i −0.802409 0.596775i \(-0.796449\pi\)
0.760365 + 0.649496i \(0.225020\pi\)
\(48\) 0 0
\(49\) 3.47660 + 6.02165i 0.496657 + 0.860236i
\(50\) −1.73205 + 2.99999i −0.244948 + 0.424263i
\(51\) 0 0
\(52\) −2.30212 + 0.346988i −0.319246 + 0.0481186i
\(53\) 6.12346 5.68174i 0.841123 0.780448i −0.136539 0.990635i \(-0.543598\pi\)
0.977661 + 0.210187i \(0.0674073\pi\)
\(54\) 0 0
\(55\) −6.73151 4.58946i −0.907676 0.618843i
\(56\) −0.486104 0.451039i −0.0649584 0.0602726i
\(57\) 0 0
\(58\) 2.75189 + 7.01170i 0.361341 + 0.920681i
\(59\) −1.85926 8.14595i −0.242055 1.06051i −0.939143 0.343527i \(-0.888378\pi\)
0.697088 0.716986i \(-0.254479\pi\)
\(60\) 0 0
\(61\) 11.0987 7.56700i 1.42105 0.968855i 0.423019 0.906121i \(-0.360971\pi\)
0.998030 0.0627337i \(-0.0199819\pi\)
\(62\) −10.6704 1.60831i −1.35514 0.204255i
\(63\) 0 0
\(64\) −7.28468 3.50811i −0.910584 0.438514i
\(65\) −3.49937 1.68521i −0.434043 0.209024i
\(66\) 0 0
\(67\) 6.22328 + 0.938008i 0.760294 + 0.114596i 0.517736 0.855541i \(-0.326775\pi\)
0.242559 + 0.970137i \(0.422013\pi\)
\(68\) 0.189073 0.128908i 0.0229285 0.0156324i
\(69\) 0 0
\(70\) −0.0709437 0.310825i −0.00847939 0.0371506i
\(71\) 0.540324 + 1.37672i 0.0641247 + 0.163387i 0.959344 0.282238i \(-0.0910768\pi\)
−0.895220 + 0.445625i \(0.852982\pi\)
\(72\) 0 0
\(73\) 0.601198 + 0.557830i 0.0703649 + 0.0652891i 0.714571 0.699563i \(-0.246622\pi\)
−0.644206 + 0.764852i \(0.722812\pi\)
\(74\) −6.79906 4.63552i −0.790375 0.538869i
\(75\) 0 0
\(76\) −0.675051 + 0.626356i −0.0774337 + 0.0718480i
\(77\) −1.29010 + 0.194451i −0.147021 + 0.0221598i
\(78\) 0 0
\(79\) −3.07798 + 5.33121i −0.346299 + 0.599808i −0.985589 0.169158i \(-0.945895\pi\)
0.639290 + 0.768966i \(0.279228\pi\)
\(80\) −1.16505 2.01792i −0.130256 0.225611i
\(81\) 0 0
\(82\) 3.48954 4.37574i 0.385355 0.483220i
\(83\) 0.538458 + 7.18523i 0.0591035 + 0.788681i 0.945473 + 0.325702i \(0.105601\pi\)
−0.886369 + 0.462979i \(0.846780\pi\)
\(84\) 0 0
\(85\) 0.381767 0.0414085
\(86\) 7.15412 + 0.0178853i 0.771449 + 0.00192862i
\(87\) 0 0
\(88\) −16.6568 + 8.02150i −1.77562 + 0.855095i
\(89\) −0.331353 4.42159i −0.0351233 0.468688i −0.986839 0.161707i \(-0.948300\pi\)
0.951716 0.306981i \(-0.0993189\pi\)
\(90\) 0 0
\(91\) −0.594345 + 0.183331i −0.0623043 + 0.0192183i
\(92\) 1.59622 + 2.76473i 0.166417 + 0.288243i
\(93\) 0 0
\(94\) −0.112232 + 0.491721i −0.0115759 + 0.0507172i
\(95\) −1.51914 + 0.228974i −0.155861 + 0.0234922i
\(96\) 0 0
\(97\) −2.78649 3.49415i −0.282925 0.354777i 0.619979 0.784618i \(-0.287141\pi\)
−0.902905 + 0.429841i \(0.858570\pi\)
\(98\) 6.26778 + 4.27330i 0.633142 + 0.431669i
\(99\) 0 0
\(100\) 0.192132 2.56382i 0.0192132 0.256382i
\(101\) 1.09407 + 2.78765i 0.108864 + 0.277382i 0.974916 0.222572i \(-0.0714454\pi\)
−0.866052 + 0.499954i \(0.833350\pi\)
\(102\) 0 0
\(103\) 8.07350 + 2.49034i 0.795505 + 0.245381i 0.665760 0.746166i \(-0.268108\pi\)
0.129746 + 0.991547i \(0.458584\pi\)
\(104\) −7.28217 + 4.96490i −0.714076 + 0.486848i
\(105\) 0 0
\(106\) 3.32954 8.48353i 0.323394 0.823994i
\(107\) 5.64595 + 2.71894i 0.545814 + 0.262850i 0.686407 0.727217i \(-0.259187\pi\)
−0.140593 + 0.990067i \(0.544901\pi\)
\(108\) 0 0
\(109\) 0.0776988 0.197973i 0.00744219 0.0189624i −0.927104 0.374803i \(-0.877710\pi\)
0.934547 + 0.355841i \(0.115805\pi\)
\(110\) −8.78926 1.32477i −0.838023 0.126312i
\(111\) 0 0
\(112\) −0.356561 0.109984i −0.0336918 0.0103925i
\(113\) −2.46387 10.7949i −0.231781 1.01550i −0.948161 0.317789i \(-0.897060\pi\)
0.716380 0.697710i \(-0.245798\pi\)
\(114\) 0 0
\(115\) −0.398009 + 5.31105i −0.0371145 + 0.495258i
\(116\) −4.09809 3.80247i −0.380498 0.353051i
\(117\) 0 0
\(118\) −5.68358 7.12699i −0.523216 0.656093i
\(119\) 0.0448155 0.0415827i 0.00410823 0.00381188i
\(120\) 0 0
\(121\) −5.64621 + 24.7377i −0.513292 + 2.24888i
\(122\) 7.32760 12.6918i 0.663410 1.14906i
\(123\) 0 0
\(124\) 7.65310 2.36067i 0.687269 0.211994i
\(125\) 6.88554 8.63419i 0.615861 0.772265i
\(126\) 0 0
\(127\) −7.04038 + 3.39047i −0.624733 + 0.300855i −0.719339 0.694659i \(-0.755555\pi\)
0.0946062 + 0.995515i \(0.469841\pi\)
\(128\) −0.323224 −0.0285692
\(129\) 0 0
\(130\) −4.23744 −0.371648
\(131\) −16.1797 + 7.79174i −1.41363 + 0.680768i −0.975876 0.218327i \(-0.929940\pi\)
−0.437753 + 0.899095i \(0.644226\pi\)
\(132\) 0 0
\(133\) −0.153391 + 0.192347i −0.0133007 + 0.0166786i
\(134\) 6.56122 2.02387i 0.566803 0.174836i
\(135\) 0 0
\(136\) 0.433156 0.750248i 0.0371428 0.0643332i
\(137\) 2.23563 9.79494i 0.191003 0.836839i −0.785072 0.619404i \(-0.787374\pi\)
0.976075 0.217434i \(-0.0697687\pi\)
\(138\) 0 0
\(139\) 9.10473 8.44795i 0.772253 0.716546i −0.192039 0.981387i \(-0.561510\pi\)
0.964292 + 0.264841i \(0.0853195\pi\)
\(140\) 0.147532 + 0.184999i 0.0124687 + 0.0156353i
\(141\) 0 0
\(142\) 1.18281 + 1.09749i 0.0992590 + 0.0920989i
\(143\) −1.29586 + 17.2920i −0.108365 + 1.44603i
\(144\) 0 0
\(145\) −2.07535 9.09271i −0.172349 0.755109i
\(146\) 0.855008 + 0.263735i 0.0707610 + 0.0218269i
\(147\) 0 0
\(148\) 6.03921 + 0.910264i 0.496420 + 0.0748232i
\(149\) 1.35074 3.44162i 0.110657 0.281948i −0.864809 0.502101i \(-0.832560\pi\)
0.975465 + 0.220153i \(0.0706557\pi\)
\(150\) 0 0
\(151\) 10.3773 + 4.99744i 0.844492 + 0.406686i 0.805530 0.592555i \(-0.201881\pi\)
0.0389621 + 0.999241i \(0.487595\pi\)
\(152\) −1.27365 + 3.24521i −0.103307 + 0.263221i
\(153\) 0 0
\(154\) −1.17606 + 0.801827i −0.0947699 + 0.0646130i
\(155\) 12.7677 + 3.93831i 1.02552 + 0.316332i
\(156\) 0 0
\(157\) −7.52520 19.1739i −0.600577 1.53024i −0.830490 0.557033i \(-0.811940\pi\)
0.229914 0.973211i \(-0.426156\pi\)
\(158\) −0.501897 + 6.69734i −0.0399287 + 0.532812i
\(159\) 0 0
\(160\) 4.74241 + 3.23332i 0.374921 + 0.255617i
\(161\) 0.531767 + 0.666815i 0.0419091 + 0.0525524i
\(162\) 0 0
\(163\) −6.83812 + 1.03068i −0.535603 + 0.0807292i −0.411274 0.911512i \(-0.634916\pi\)
−0.124329 + 0.992241i \(0.539678\pi\)
\(164\) −0.924323 + 4.04972i −0.0721775 + 0.316230i
\(165\) 0 0
\(166\) 3.93052 + 6.80786i 0.305068 + 0.528393i
\(167\) −3.39723 + 1.04791i −0.262886 + 0.0810895i −0.423396 0.905945i \(-0.639162\pi\)
0.160510 + 0.987034i \(0.448686\pi\)
\(168\) 0 0
\(169\) −0.353715 4.72000i −0.0272089 0.363077i
\(170\) 0.375260 0.180716i 0.0287811 0.0138603i
\(171\) 0 0
\(172\) −4.78964 + 2.29184i −0.365207 + 0.174751i
\(173\) 24.0563 1.82897 0.914483 0.404623i \(-0.132597\pi\)
0.914483 + 0.404623i \(0.132597\pi\)
\(174\) 0 0
\(175\) −0.0513297 0.684947i −0.00388016 0.0517771i
\(176\) −6.48614 + 8.13336i −0.488911 + 0.613075i
\(177\) 0 0
\(178\) −2.41874 4.18937i −0.181292 0.314007i
\(179\) −2.60094 + 4.50496i −0.194403 + 0.336717i −0.946705 0.322103i \(-0.895610\pi\)
0.752301 + 0.658819i \(0.228944\pi\)
\(180\) 0 0
\(181\) 2.74306 0.413450i 0.203890 0.0307315i −0.0463029 0.998927i \(-0.514744\pi\)
0.250193 + 0.968196i \(0.419506\pi\)
\(182\) −0.497431 + 0.461549i −0.0368721 + 0.0342123i
\(183\) 0 0
\(184\) 9.98568 + 6.80812i 0.736154 + 0.501902i
\(185\) 7.46908 + 6.93029i 0.549137 + 0.509525i
\(186\) 0 0
\(187\) −0.622701 1.58662i −0.0455364 0.116025i
\(188\) −0.0832974 0.364950i −0.00607509 0.0266167i
\(189\) 0 0
\(190\) −1.38486 + 0.944181i −0.100468 + 0.0684981i
\(191\) −3.41700 0.515030i −0.247245 0.0372662i 0.0242502 0.999706i \(-0.492280\pi\)
−0.271496 + 0.962440i \(0.587518\pi\)
\(192\) 0 0
\(193\) 16.4497 + 7.92174i 1.18407 + 0.570219i 0.919095 0.394035i \(-0.128921\pi\)
0.264977 + 0.964255i \(0.414636\pi\)
\(194\) −4.39300 2.11556i −0.315399 0.151888i
\(195\) 0 0
\(196\) −5.56730 0.839136i −0.397664 0.0599383i
\(197\) −8.41116 + 5.73463i −0.599270 + 0.408575i −0.824607 0.565705i \(-0.808604\pi\)
0.225337 + 0.974281i \(0.427652\pi\)
\(198\) 0 0
\(199\) −2.04642 8.96595i −0.145067 0.635579i −0.994214 0.107422i \(-0.965740\pi\)
0.849147 0.528157i \(-0.177117\pi\)
\(200\) −3.55592 9.06033i −0.251441 0.640662i
\(201\) 0 0
\(202\) 2.39500 + 2.22224i 0.168512 + 0.156356i
\(203\) −1.23402 0.841340i −0.0866111 0.0590505i
\(204\) 0 0
\(205\) −5.07998 + 4.71353i −0.354801 + 0.329207i
\(206\) 9.11472 1.37382i 0.635053 0.0957188i
\(207\) 0 0
\(208\) −2.47971 + 4.29498i −0.171937 + 0.297803i
\(209\) 3.42949 + 5.94004i 0.237222 + 0.410881i
\(210\) 0 0
\(211\) −11.8825 + 14.9002i −0.818025 + 1.02577i 0.181080 + 0.983468i \(0.442041\pi\)
−0.999105 + 0.0423025i \(0.986531\pi\)
\(212\) 0.505471 + 6.74504i 0.0347159 + 0.463251i
\(213\) 0 0
\(214\) 6.83676 0.467352
\(215\) −8.75595 1.34214i −0.597151 0.0915334i
\(216\) 0 0
\(217\) 1.92776 0.928360i 0.130865 0.0630212i
\(218\) −0.0173394 0.231379i −0.00117437 0.0156709i
\(219\) 0 0
\(220\) 6.30389 1.94449i 0.425008 0.131098i
\(221\) −0.406279 0.703696i −0.0273293 0.0473357i
\(222\) 0 0
\(223\) 1.62391 7.11481i 0.108745 0.476443i −0.891003 0.453997i \(-0.849998\pi\)
0.999748 0.0224455i \(-0.00714523\pi\)
\(224\) 0.908889 0.136993i 0.0607277 0.00915323i
\(225\) 0 0
\(226\) −7.53181 9.44459i −0.501008 0.628245i
\(227\) −12.9206 8.80914i −0.857573 0.584683i 0.0527382 0.998608i \(-0.483205\pi\)
−0.910311 + 0.413925i \(0.864158\pi\)
\(228\) 0 0
\(229\) −0.0803517 + 1.07222i −0.00530979 + 0.0708542i −0.999229 0.0392558i \(-0.987501\pi\)
0.993919 + 0.110110i \(0.0351203\pi\)
\(230\) 2.12285 + 5.40893i 0.139976 + 0.356654i
\(231\) 0 0
\(232\) −20.2237 6.23818i −1.32775 0.409556i
\(233\) 1.10140 0.750923i 0.0721552 0.0491946i −0.526705 0.850048i \(-0.676573\pi\)
0.598860 + 0.800853i \(0.295620\pi\)
\(234\) 0 0
\(235\) 0.228157 0.581334i 0.0148833 0.0379220i
\(236\) 6.09561 + 2.93549i 0.396790 + 0.191084i
\(237\) 0 0
\(238\) 0.0243678 0.0620881i 0.00157953 0.00402457i
\(239\) 14.7110 + 2.21733i 0.951579 + 0.143427i 0.606444 0.795126i \(-0.292595\pi\)
0.345134 + 0.938553i \(0.387833\pi\)
\(240\) 0 0
\(241\) 22.8421 + 7.04584i 1.47139 + 0.453862i 0.923796 0.382885i \(-0.125069\pi\)
0.547590 + 0.836747i \(0.315545\pi\)
\(242\) 6.16000 + 26.9887i 0.395980 + 1.73490i
\(243\) 0 0
\(244\) −0.812834 + 10.8465i −0.0520363 + 0.694377i
\(245\) −6.88544 6.38876i −0.439895 0.408163i
\(246\) 0 0
\(247\) 2.03874 + 2.55650i 0.129722 + 0.162666i
\(248\) 22.2258 20.6226i 1.41134 1.30953i
\(249\) 0 0
\(250\) 2.68104 11.7464i 0.169564 0.742907i
\(251\) −10.2680 + 17.7846i −0.648108 + 1.12256i 0.335466 + 0.942052i \(0.391106\pi\)
−0.983574 + 0.180504i \(0.942227\pi\)
\(252\) 0 0
\(253\) 22.7218 7.00875i 1.42851 0.440637i
\(254\) −5.31544 + 6.66535i −0.333520 + 0.418221i
\(255\) 0 0
\(256\) 14.2516 6.86323i 0.890727 0.428952i
\(257\) 22.8388 1.42464 0.712322 0.701853i \(-0.247644\pi\)
0.712322 + 0.701853i \(0.247644\pi\)
\(258\) 0 0
\(259\) 1.63165 0.101386
\(260\) 2.83353 1.36456i 0.175728 0.0846261i
\(261\) 0 0
\(262\) −12.2156 + 15.3179i −0.754681 + 0.946340i
\(263\) −5.88459 + 1.81516i −0.362860 + 0.111927i −0.470823 0.882227i \(-0.656043\pi\)
0.107964 + 0.994155i \(0.465567\pi\)
\(264\) 0 0
\(265\) −5.64215 + 9.77249i −0.346594 + 0.600319i
\(266\) −0.0597263 + 0.261678i −0.00366206 + 0.0160445i
\(267\) 0 0
\(268\) −3.73568 + 3.46621i −0.228193 + 0.211732i
\(269\) −9.36364 11.7416i −0.570911 0.715900i 0.409621 0.912256i \(-0.365661\pi\)
−0.980533 + 0.196355i \(0.937089\pi\)
\(270\) 0 0
\(271\) −2.26842 2.10479i −0.137797 0.127857i 0.608263 0.793735i \(-0.291866\pi\)
−0.746060 + 0.665878i \(0.768057\pi\)
\(272\) 0.0364288 0.486108i 0.00220882 0.0294746i
\(273\) 0 0
\(274\) −2.43907 10.6863i −0.147349 0.645580i
\(275\) −18.2989 5.64446i −1.10346 0.340373i
\(276\) 0 0
\(277\) −14.9446 2.25253i −0.897932 0.135341i −0.316172 0.948702i \(-0.602398\pi\)
−0.581760 + 0.813360i \(0.697636\pi\)
\(278\) 4.95056 12.6138i 0.296915 0.756527i
\(279\) 0 0
\(280\) 0.807080 + 0.388669i 0.0482322 + 0.0232274i
\(281\) −4.07782 + 10.3901i −0.243262 + 0.619822i −0.999402 0.0345883i \(-0.988988\pi\)
0.756139 + 0.654411i \(0.227083\pi\)
\(282\) 0 0
\(283\) −13.2949 + 9.06431i −0.790300 + 0.538818i −0.889871 0.456213i \(-0.849206\pi\)
0.0995704 + 0.995031i \(0.468253\pi\)
\(284\) −1.14435 0.352984i −0.0679045 0.0209458i
\(285\) 0 0
\(286\) 6.91169 + 17.6107i 0.408697 + 1.04134i
\(287\) −0.0829312 + 1.10664i −0.00489527 + 0.0653229i
\(288\) 0 0
\(289\) −13.9801 9.53145i −0.822357 0.560674i
\(290\) −6.34416 7.95532i −0.372542 0.467152i
\(291\) 0 0
\(292\) −0.656663 + 0.0989760i −0.0384283 + 0.00579213i
\(293\) −3.26781 + 14.3172i −0.190908 + 0.836421i 0.785219 + 0.619218i \(0.212550\pi\)
−0.976127 + 0.217203i \(0.930307\pi\)
\(294\) 0 0
\(295\) 5.64354 + 9.77490i 0.328580 + 0.569116i
\(296\) 22.0938 6.81505i 1.28418 0.396117i
\(297\) 0 0
\(298\) −0.301433 4.02235i −0.0174616 0.233008i
\(299\) 10.2132 4.91842i 0.590645 0.284440i
\(300\) 0 0
\(301\) −1.17405 + 0.796159i −0.0676709 + 0.0458898i
\(302\) 12.5660 0.723094
\(303\) 0 0
\(304\) 0.146596 + 1.95619i 0.00840786 + 0.112195i
\(305\) −11.3138 + 14.1871i −0.647828 + 0.812351i
\(306\) 0 0
\(307\) −0.0141820 0.0245640i −0.000809410 0.00140194i 0.865620 0.500701i \(-0.166924\pi\)
−0.866430 + 0.499299i \(0.833591\pi\)
\(308\) 0.528214 0.914893i 0.0300978 0.0521309i
\(309\) 0 0
\(310\) 14.4143 2.17261i 0.818677 0.123396i
\(311\) −7.53405 + 6.99057i −0.427217 + 0.396399i −0.864263 0.503040i \(-0.832215\pi\)
0.437047 + 0.899439i \(0.356024\pi\)
\(312\) 0 0
\(313\) 14.8130 + 10.0994i 0.837283 + 0.570850i 0.904298 0.426902i \(-0.140395\pi\)
−0.0670152 + 0.997752i \(0.521348\pi\)
\(314\) −16.4732 15.2849i −0.929637 0.862577i
\(315\) 0 0
\(316\) −1.82109 4.64006i −0.102444 0.261024i
\(317\) −4.83536 21.1851i −0.271581 1.18987i −0.908147 0.418652i \(-0.862503\pi\)
0.636566 0.771222i \(-0.280354\pi\)
\(318\) 0 0
\(319\) −34.4040 + 23.4563i −1.92625 + 1.31330i
\(320\) 10.8003 + 1.62788i 0.603753 + 0.0910012i
\(321\) 0 0
\(322\) 0.838350 + 0.403728i 0.0467194 + 0.0224989i
\(323\) −0.289575 0.139452i −0.0161124 0.00775931i
\(324\) 0 0
\(325\) −9.02726 1.36064i −0.500742 0.0754747i
\(326\) −6.23367 + 4.25005i −0.345251 + 0.235388i
\(327\) 0 0
\(328\) 3.49924 + 15.3312i 0.193213 + 0.846522i
\(329\) −0.0365366 0.0930938i −0.00201433 0.00513243i
\(330\) 0 0
\(331\) −9.69617 8.99673i −0.532950 0.494505i 0.367166 0.930155i \(-0.380328\pi\)
−0.900116 + 0.435650i \(0.856518\pi\)
\(332\) −4.82059 3.28662i −0.264564 0.180377i
\(333\) 0 0
\(334\) −2.84328 + 2.63818i −0.155577 + 0.144355i
\(335\) −8.40681 + 1.26712i −0.459313 + 0.0692303i
\(336\) 0 0
\(337\) 4.71536 8.16725i 0.256862 0.444898i −0.708537 0.705673i \(-0.750645\pi\)
0.965400 + 0.260775i \(0.0839780\pi\)
\(338\) −2.58197 4.47211i −0.140441 0.243251i
\(339\) 0 0
\(340\) −0.192737 + 0.241685i −0.0104527 + 0.0131072i
\(341\) −4.45786 59.4860i −0.241406 3.22135i
\(342\) 0 0
\(343\) −3.01843 −0.162980
\(344\) −12.5721 + 15.6844i −0.677844 + 0.845644i
\(345\) 0 0
\(346\) 23.6462 11.3874i 1.27123 0.612192i
\(347\) 1.30647 + 17.4336i 0.0701351 + 0.935887i 0.915661 + 0.401952i \(0.131668\pi\)
−0.845526 + 0.533935i \(0.820713\pi\)
\(348\) 0 0
\(349\) 8.91802 2.75084i 0.477370 0.147249i −0.0467268 0.998908i \(-0.514879\pi\)
0.524097 + 0.851658i \(0.324403\pi\)
\(350\) −0.374685 0.648974i −0.0200278 0.0346891i
\(351\) 0 0
\(352\) 5.70226 24.9832i 0.303932 1.33161i
\(353\) 10.2719 1.54824i 0.546718 0.0824045i 0.130125 0.991498i \(-0.458462\pi\)
0.416593 + 0.909093i \(0.363224\pi\)
\(354\) 0 0
\(355\) −1.24565 1.56200i −0.0661124 0.0829024i
\(356\) 2.96646 + 2.02250i 0.157222 + 0.107192i
\(357\) 0 0
\(358\) −0.424111 + 5.65937i −0.0224150 + 0.299107i
\(359\) −3.94742 10.0579i −0.208337 0.530834i 0.788065 0.615593i \(-0.211083\pi\)
−0.996402 + 0.0847587i \(0.972988\pi\)
\(360\) 0 0
\(361\) −16.9200 5.21912i −0.890524 0.274690i
\(362\) 2.50059 1.70487i 0.131428 0.0896062i
\(363\) 0 0
\(364\) 0.183997 0.468817i 0.00964407 0.0245727i
\(365\) −0.998170 0.480694i −0.0522466 0.0251606i
\(366\) 0 0
\(367\) 7.07784 18.0340i 0.369460 0.941369i −0.618377 0.785881i \(-0.712210\pi\)
0.987838 0.155488i \(-0.0496951\pi\)
\(368\) 6.72464 + 1.01358i 0.350546 + 0.0528363i
\(369\) 0 0
\(370\) 10.6223 + 3.27655i 0.552228 + 0.170340i
\(371\) 0.402106 + 1.76174i 0.0208763 + 0.0914651i
\(372\) 0 0
\(373\) 2.56665 34.2496i 0.132896 1.77338i −0.389841 0.920882i \(-0.627470\pi\)
0.522737 0.852494i \(-0.324911\pi\)
\(374\) −1.36314 1.26481i −0.0704861 0.0654016i
\(375\) 0 0
\(376\) −0.883567 1.10796i −0.0455665 0.0571386i
\(377\) −14.5516 + 13.5019i −0.749447 + 0.695385i
\(378\) 0 0
\(379\) −0.574248 + 2.51594i −0.0294971 + 0.129235i −0.987533 0.157414i \(-0.949684\pi\)
0.958036 + 0.286649i \(0.0925414\pi\)
\(380\) 0.621991 1.07732i 0.0319075 0.0552654i
\(381\) 0 0
\(382\) −3.60255 + 1.11124i −0.184323 + 0.0568560i
\(383\) −8.92040 + 11.1858i −0.455811 + 0.571569i −0.955633 0.294559i \(-0.904827\pi\)
0.499822 + 0.866128i \(0.333399\pi\)
\(384\) 0 0
\(385\) 1.58790 0.764693i 0.0809270 0.0389724i
\(386\) 19.9191 1.01386
\(387\) 0 0
\(388\) 3.61881 0.183717
\(389\) −14.2240 + 6.84991i −0.721185 + 0.347304i −0.758210 0.652010i \(-0.773926\pi\)
0.0370254 + 0.999314i \(0.488212\pi\)
\(390\) 0 0
\(391\) −0.694706 + 0.871133i −0.0351328 + 0.0440551i
\(392\) −20.3674 + 6.28252i −1.02871 + 0.317315i
\(393\) 0 0
\(394\) −5.55321 + 9.61843i −0.279766 + 0.484570i
\(395\) 1.85045 8.10736i 0.0931064 0.407926i
\(396\) 0 0
\(397\) 21.3361 19.7970i 1.07083 0.993585i 0.0708372 0.997488i \(-0.477433\pi\)
0.999992 + 0.00390325i \(0.00124245\pi\)
\(398\) −6.25571 7.84441i −0.313570 0.393205i
\(399\) 0 0
\(400\) −4.01479 3.72518i −0.200740 0.186259i
\(401\) −1.06942 + 14.2704i −0.0534043 + 0.712631i 0.904670 + 0.426112i \(0.140117\pi\)
−0.958075 + 0.286519i \(0.907502\pi\)
\(402\) 0 0
\(403\) −6.32812 27.7253i −0.315226 1.38110i
\(404\) −2.31712 0.714738i −0.115281 0.0355596i
\(405\) 0 0
\(406\) −1.61125 0.242856i −0.0799648 0.0120527i
\(407\) 16.6193 42.3453i 0.823789 2.09898i
\(408\) 0 0
\(409\) −27.4363 13.2126i −1.35664 0.653322i −0.392754 0.919644i \(-0.628478\pi\)
−0.963884 + 0.266321i \(0.914192\pi\)
\(410\) −2.76216 + 7.03787i −0.136413 + 0.347576i
\(411\) 0 0
\(412\) −5.65251 + 3.85382i −0.278479 + 0.189864i
\(413\) 1.72719 + 0.532768i 0.0849895 + 0.0262158i
\(414\) 0 0
\(415\) −3.55604 9.06065i −0.174559 0.444770i
\(416\) 0.912946 12.1824i 0.0447608 0.597292i
\(417\) 0 0
\(418\) 6.18284 + 4.21539i 0.302413 + 0.206181i
\(419\) −22.1749 27.8065i −1.08332 1.35844i −0.928858 0.370437i \(-0.879208\pi\)
−0.154459 0.987999i \(-0.549363\pi\)
\(420\) 0 0
\(421\) −16.3130 + 2.45879i −0.795047 + 0.119834i −0.533992 0.845490i \(-0.679309\pi\)
−0.261056 + 0.965324i \(0.584071\pi\)
\(422\) −4.62672 + 20.2710i −0.225225 + 0.986775i
\(423\) 0 0
\(424\) 12.8032 + 22.1759i 0.621780 + 1.07696i
\(425\) 0.857465 0.264493i 0.0415932 0.0128298i
\(426\) 0 0
\(427\) 0.217156 + 2.89774i 0.0105089 + 0.140231i
\(428\) −4.57167 + 2.20160i −0.220980 + 0.106418i
\(429\) 0 0
\(430\) −9.24202 + 2.82550i −0.445690 + 0.136258i
\(431\) 9.05750 0.436285 0.218142 0.975917i \(-0.430000\pi\)
0.218142 + 0.975917i \(0.430000\pi\)
\(432\) 0 0
\(433\) 1.29146 + 17.2334i 0.0620638 + 0.828184i 0.938194 + 0.346110i \(0.112497\pi\)
−0.876130 + 0.482074i \(0.839884\pi\)
\(434\) 1.45545 1.82507i 0.0698636 0.0876062i
\(435\) 0 0
\(436\) 0.0861040 + 0.149137i 0.00412364 + 0.00714235i
\(437\) 2.24191 3.88311i 0.107245 0.185754i
\(438\) 0 0
\(439\) −18.2692 + 2.75364i −0.871943 + 0.131424i −0.569745 0.821821i \(-0.692958\pi\)
−0.302197 + 0.953245i \(0.597720\pi\)
\(440\) 18.3075 16.9869i 0.872775 0.809817i
\(441\) 0 0
\(442\) −0.732459 0.499382i −0.0348395 0.0237532i
\(443\) −6.55737 6.08435i −0.311550 0.289076i 0.508863 0.860848i \(-0.330066\pi\)
−0.820413 + 0.571771i \(0.806256\pi\)
\(444\) 0 0
\(445\) 2.18829 + 5.57568i 0.103735 + 0.264313i
\(446\) −1.77168 7.76223i −0.0838914 0.367552i
\(447\) 0 0
\(448\) 1.44515 0.985287i 0.0682770 0.0465504i
\(449\) −20.0461 3.02146i −0.946032 0.142591i −0.342132 0.939652i \(-0.611149\pi\)
−0.603900 + 0.797060i \(0.706387\pi\)
\(450\) 0 0
\(451\) 27.8753 + 13.4240i 1.31260 + 0.632113i
\(452\) 8.07782 + 3.89007i 0.379949 + 0.182974i
\(453\) 0 0
\(454\) −16.8703 2.54279i −0.791764 0.119339i
\(455\) 0.694213 0.473306i 0.0325452 0.0221889i
\(456\) 0 0
\(457\) 2.39474 + 10.4921i 0.112021 + 0.490797i 0.999549 + 0.0300423i \(0.00956421\pi\)
−0.887527 + 0.460755i \(0.847579\pi\)
\(458\) 0.428570 + 1.09198i 0.0200257 + 0.0510248i
\(459\) 0 0
\(460\) −3.16133 2.93328i −0.147398 0.136765i
\(461\) 7.03749 + 4.79808i 0.327769 + 0.223469i 0.716012 0.698088i \(-0.245966\pi\)
−0.388243 + 0.921557i \(0.626918\pi\)
\(462\) 0 0
\(463\) 1.66719 1.54693i 0.0774811 0.0718919i −0.640482 0.767973i \(-0.721265\pi\)
0.717963 + 0.696082i \(0.245075\pi\)
\(464\) −11.7759 + 1.77493i −0.546681 + 0.0823989i
\(465\) 0 0
\(466\) 0.727166 1.25949i 0.0336853 0.0583447i
\(467\) −15.1256 26.1983i −0.699930 1.21231i −0.968490 0.249052i \(-0.919881\pi\)
0.268560 0.963263i \(-0.413452\pi\)
\(468\) 0 0
\(469\) −0.848855 + 1.06443i −0.0391965 + 0.0491509i
\(470\) −0.0509160 0.679426i −0.00234858 0.0313396i
\(471\) 0 0
\(472\) 25.6128 1.17892
\(473\) 8.70393 + 38.5787i 0.400207 + 1.77385i
\(474\) 0 0
\(475\) −3.25342 + 1.56676i −0.149277 + 0.0718881i
\(476\) 0.00369937 + 0.0493646i 0.000169560 + 0.00226262i
\(477\) 0 0
\(478\) 15.5099 4.78417i 0.709406 0.218823i
\(479\) 6.78977 + 11.7602i 0.310233 + 0.537338i 0.978413 0.206661i \(-0.0662598\pi\)
−0.668180 + 0.744000i \(0.732926\pi\)
\(480\) 0 0
\(481\) 4.82568 21.1427i 0.220032 0.964024i
\(482\) 25.7880 3.88691i 1.17461 0.177044i
\(483\) 0 0
\(484\) −12.8101 16.0634i −0.582279 0.730154i
\(485\) 4.98822 + 3.40091i 0.226504 + 0.154428i
\(486\) 0 0
\(487\) −2.78410 + 37.1512i −0.126159 + 1.68348i 0.471605 + 0.881810i \(0.343675\pi\)
−0.597765 + 0.801672i \(0.703944\pi\)
\(488\) 15.0437 + 38.3307i 0.680996 + 1.73515i
\(489\) 0 0
\(490\) −9.79229 3.02052i −0.442371 0.136453i
\(491\) −16.9652 + 11.5667i −0.765629 + 0.521997i −0.882023 0.471206i \(-0.843819\pi\)
0.116394 + 0.993203i \(0.462866\pi\)
\(492\) 0 0
\(493\) 0.712843 1.81629i 0.0321048 0.0818018i
\(494\) 3.21414 + 1.54785i 0.144611 + 0.0696411i
\(495\) 0 0
\(496\) 6.23299 15.8814i 0.279870 0.713096i
\(497\) −0.316363 0.0476840i −0.0141908 0.00213892i
\(498\) 0 0
\(499\) 6.66084 + 2.05460i 0.298180 + 0.0919763i 0.440235 0.897882i \(-0.354895\pi\)
−0.142056 + 0.989859i \(0.545371\pi\)
\(500\) 1.98984 + 8.71804i 0.0889882 + 0.389883i
\(501\) 0 0
\(502\) −1.67430 + 22.3420i −0.0747277 + 0.997172i
\(503\) 9.51112 + 8.82503i 0.424080 + 0.393488i 0.863136 0.504971i \(-0.168497\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(504\) 0 0
\(505\) −2.52226 3.16281i −0.112239 0.140743i
\(506\) 19.0168 17.6450i 0.845400 0.784417i
\(507\) 0 0
\(508\) 1.40798 6.16874i 0.0624688 0.273694i
\(509\) 14.9031 25.8129i 0.660568 1.14414i −0.319898 0.947452i \(-0.603649\pi\)
0.980467 0.196686i \(-0.0630179\pi\)
\(510\) 0 0
\(511\) −0.169533 + 0.0522939i −0.00749969 + 0.00231335i
\(512\) 11.1629 13.9979i 0.493337 0.618625i
\(513\) 0 0
\(514\) 22.4495 10.8111i 0.990204 0.476857i
\(515\) −11.4133 −0.502929
\(516\) 0 0
\(517\) −2.78816 −0.122623
\(518\) 1.60384 0.772368i 0.0704686 0.0339359i
\(519\) 0 0
\(520\) 7.42329 9.30852i 0.325533 0.408205i
\(521\) 29.7906 9.18917i 1.30515 0.402585i 0.437256 0.899337i \(-0.355950\pi\)
0.867892 + 0.496752i \(0.165474\pi\)
\(522\) 0 0
\(523\) −6.95091 + 12.0393i −0.303942 + 0.526443i −0.977025 0.213124i \(-0.931636\pi\)
0.673083 + 0.739567i \(0.264970\pi\)
\(524\) 3.23571 14.1766i 0.141353 0.619307i
\(525\) 0 0
\(526\) −4.92505 + 4.56978i −0.214742 + 0.199252i
\(527\) 1.74282 + 2.18542i 0.0759183 + 0.0951986i
\(528\) 0 0
\(529\) 5.46546 + 5.07120i 0.237629 + 0.220487i
\(530\) −0.920012 + 12.2767i −0.0399628 + 0.533266i
\(531\) 0 0
\(532\) −0.0443282 0.194215i −0.00192187 0.00842027i
\(533\) 14.0944 + 4.34755i 0.610496 + 0.188313i
\(534\) 0 0
\(535\) −8.37069 1.26168i −0.361896 0.0545471i
\(536\) −7.04828 + 17.9587i −0.304439 + 0.775699i
\(537\) 0 0
\(538\) −14.7621 7.10906i −0.636440 0.306493i
\(539\) −15.3207 + 39.0365i −0.659908 + 1.68142i
\(540\) 0 0
\(541\) −17.1344 + 11.6820i −0.736664 + 0.502249i −0.872580 0.488472i \(-0.837555\pi\)
0.135916 + 0.990720i \(0.456602\pi\)
\(542\) −3.22609 0.995118i −0.138573 0.0427440i
\(543\) 0 0
\(544\) 0.438699 + 1.11779i 0.0188091 + 0.0479247i
\(545\) −0.0214696 + 0.286491i −0.000919655 + 0.0122719i
\(546\) 0 0
\(547\) 16.9135 + 11.5314i 0.723169 + 0.493049i 0.868098 0.496394i \(-0.165343\pi\)
−0.144928 + 0.989442i \(0.546295\pi\)
\(548\) 5.07220 + 6.36034i 0.216674 + 0.271700i
\(549\) 0 0
\(550\) −20.6589 + 3.11382i −0.880896 + 0.132774i
\(551\) −1.74721 + 7.65501i −0.0744335 + 0.326114i
\(552\) 0 0
\(553\) −0.665844 1.15328i −0.0283146 0.0490423i
\(554\) −15.7561 + 4.86011i −0.669413 + 0.206486i
\(555\) 0 0
\(556\) 0.751563 + 10.0289i 0.0318734 + 0.425321i
\(557\) −15.3932 + 7.41296i −0.652229 + 0.314097i −0.730578 0.682829i \(-0.760749\pi\)
0.0783489 + 0.996926i \(0.475035\pi\)
\(558\) 0 0
\(559\) 6.84422 + 17.5678i 0.289480 + 0.743039i
\(560\) 0.504059 0.0213004
\(561\) 0 0
\(562\) 0.910015 + 12.1433i 0.0383867 + 0.512235i
\(563\) 7.02348 8.80717i 0.296004 0.371178i −0.611483 0.791258i \(-0.709427\pi\)
0.907487 + 0.420080i \(0.137998\pi\)
\(564\) 0 0
\(565\) 7.47874 + 12.9536i 0.314633 + 0.544960i
\(566\) −8.77755 + 15.2032i −0.368948 + 0.639037i
\(567\) 0 0
\(568\) −4.48296 + 0.675698i −0.188101 + 0.0283517i
\(569\) −5.89078 + 5.46585i −0.246955 + 0.229140i −0.793931 0.608007i \(-0.791969\pi\)
0.546977 + 0.837148i \(0.315779\pi\)
\(570\) 0 0
\(571\) −24.0538 16.3996i −1.00662 0.686302i −0.0565700 0.998399i \(-0.518016\pi\)
−0.950050 + 0.312096i \(0.898969\pi\)
\(572\) −10.2928 9.55035i −0.430365 0.399320i
\(573\) 0 0
\(574\) 0.442328 + 1.12703i 0.0184624 + 0.0470414i
\(575\) 2.78562 + 12.2046i 0.116168 + 0.508967i
\(576\) 0 0
\(577\) −5.93710 + 4.04784i −0.247165 + 0.168514i −0.680565 0.732687i \(-0.738266\pi\)
0.433401 + 0.901201i \(0.357313\pi\)
\(578\) −18.2536 2.75129i −0.759251 0.114439i
\(579\) 0 0
\(580\) 6.80407 + 3.27667i 0.282523 + 0.136056i
\(581\) −1.40434 0.676297i −0.0582620 0.0280575i
\(582\) 0 0
\(583\) 49.8172 + 7.50873i 2.06322 + 0.310980i
\(584\) −2.07719 + 1.41620i −0.0859547 + 0.0586029i
\(585\) 0 0
\(586\) 3.56517 + 15.6200i 0.147276 + 0.645258i
\(587\) 10.8541 + 27.6558i 0.447997 + 1.14148i 0.959378 + 0.282123i \(0.0910387\pi\)
−0.511381 + 0.859354i \(0.670866\pi\)
\(588\) 0 0
\(589\) −8.24584 7.65102i −0.339764 0.315255i
\(590\) 10.1744 + 6.93682i 0.418875 + 0.285584i
\(591\) 0 0
\(592\) 9.53712 8.84915i 0.391973 0.363698i
\(593\) 31.8484 4.80037i 1.30786 0.197127i 0.542130 0.840295i \(-0.317618\pi\)
0.765726 + 0.643167i \(0.222380\pi\)
\(594\) 0 0
\(595\) −0.0412930 + 0.0715215i −0.00169285 + 0.00293210i
\(596\) 1.49686 + 2.59263i 0.0613136 + 0.106198i
\(597\) 0 0
\(598\) 7.71091 9.66917i 0.315322 0.395402i
\(599\) 1.13778 + 15.1826i 0.0464885 + 0.620346i 0.970983 + 0.239150i \(0.0768687\pi\)
−0.924494 + 0.381196i \(0.875512\pi\)
\(600\) 0 0
\(601\) −14.8489 −0.605699 −0.302849 0.953038i \(-0.597938\pi\)
−0.302849 + 0.953038i \(0.597938\pi\)
\(602\) −0.777159 + 1.33834i −0.0316747 + 0.0545467i
\(603\) 0 0
\(604\) −8.40276 + 4.04656i −0.341904 + 0.164652i
\(605\) −2.56150 34.1808i −0.104140 1.38965i
\(606\) 0 0
\(607\) −8.93135 + 2.75496i −0.362512 + 0.111820i −0.470660 0.882315i \(-0.655984\pi\)
0.108148 + 0.994135i \(0.465508\pi\)
\(608\) −2.41611 4.18482i −0.0979860 0.169717i
\(609\) 0 0
\(610\) −4.40529 + 19.3009i −0.178365 + 0.781469i
\(611\) −1.31435 + 0.198107i −0.0531731 + 0.00801455i
\(612\) 0 0
\(613\) 19.2070 + 24.0849i 0.775765 + 0.972779i 0.999998 0.00175653i \(-0.000559122\pi\)
−0.224233 + 0.974536i \(0.571988\pi\)
\(614\) −0.0255680 0.0174320i −0.00103184 0.000703497i
\(615\) 0 0
\(616\) 0.298872 3.98817i 0.0120419 0.160688i
\(617\) 1.40309 + 3.57502i 0.0564864 + 0.143925i 0.956331 0.292285i \(-0.0944156\pi\)
−0.899845 + 0.436210i \(0.856320\pi\)
\(618\) 0 0
\(619\) 32.6404 + 10.0682i 1.31193 + 0.404676i 0.870300 0.492521i \(-0.163925\pi\)
0.441629 + 0.897198i \(0.354401\pi\)
\(620\) −8.93905 + 6.09454i −0.359001 + 0.244763i
\(621\) 0 0
\(622\) −4.09653 + 10.4378i −0.164256 + 0.418517i
\(623\) 0.864195 + 0.416175i 0.0346233 + 0.0166737i
\(624\) 0 0
\(625\) 0.349803 0.891285i 0.0139921 0.0356514i
\(626\) 19.3412 + 2.91522i 0.773031 + 0.116516i
\(627\) 0 0
\(628\) 15.9375 + 4.91608i 0.635977 + 0.196173i
\(629\) 0.474327 + 2.07816i 0.0189126 + 0.0828617i
\(630\) 0 0
\(631\) −0.687936 + 9.17986i −0.0273863 + 0.365445i 0.966627 + 0.256187i \(0.0824663\pi\)
−0.994013 + 0.109257i \(0.965153\pi\)
\(632\) −13.8330 12.8352i −0.550248 0.510556i
\(633\) 0 0
\(634\) −14.7812 18.5351i −0.587038 0.736123i
\(635\) 7.73808 7.17989i 0.307076 0.284925i
\(636\) 0 0
\(637\) −4.44860 + 19.4906i −0.176260 + 0.772246i
\(638\) −22.7142 + 39.3421i −0.899263 + 1.55757i
\(639\) 0 0
\(640\) 0.417233 0.128699i 0.0164926 0.00508729i
\(641\) −2.10948 + 2.64521i −0.0833196 + 0.104479i −0.821744 0.569857i \(-0.806999\pi\)
0.738424 + 0.674336i \(0.235570\pi\)
\(642\) 0 0
\(643\) −10.1874 + 4.90598i −0.401751 + 0.193473i −0.623838 0.781554i \(-0.714427\pi\)
0.222087 + 0.975027i \(0.428713\pi\)
\(644\) −0.690605 −0.0272137
\(645\) 0 0
\(646\) −0.350651 −0.0137962
\(647\) −20.4890 + 9.86700i −0.805507 + 0.387912i −0.790873 0.611981i \(-0.790373\pi\)
−0.0146350 + 0.999893i \(0.504659\pi\)
\(648\) 0 0
\(649\) 31.4191 39.3983i 1.23331 1.54652i
\(650\) −9.51746 + 2.93575i −0.373306 + 0.115150i
\(651\) 0 0
\(652\) 2.79977 4.84935i 0.109648 0.189915i
\(653\) 5.74350 25.1639i 0.224760 0.984739i −0.729081 0.684428i \(-0.760052\pi\)
0.953841 0.300312i \(-0.0970907\pi\)
\(654\) 0 0
\(655\) 17.7831 16.5003i 0.694844 0.644721i
\(656\) 5.51705 + 6.91816i 0.215404 + 0.270109i
\(657\) 0 0
\(658\) −0.0799813 0.0742118i −0.00311799 0.00289308i
\(659\) −0.761704 + 10.1642i −0.0296718 + 0.395942i 0.962519 + 0.271214i \(0.0874251\pi\)
−0.992191 + 0.124729i \(0.960194\pi\)
\(660\) 0 0
\(661\) 2.96298 + 12.9817i 0.115247 + 0.504928i 0.999295 + 0.0375336i \(0.0119501\pi\)
−0.884049 + 0.467395i \(0.845193\pi\)
\(662\) −13.7896 4.25354i −0.535949 0.165318i
\(663\) 0 0
\(664\) −21.8407 3.29195i −0.847583 0.127753i
\(665\) 0.121418 0.309367i 0.00470838 0.0119967i
\(666\) 0 0
\(667\) 24.5247 + 11.8105i 0.949600 + 0.457303i
\(668\) 1.05171 2.67972i 0.0406920 0.103682i
\(669\) 0 0
\(670\) −7.66370 + 5.22502i −0.296075 + 0.201860i
\(671\) 77.4153 + 23.8795i 2.98858 + 0.921856i
\(672\) 0 0
\(673\) −2.30694 5.87798i −0.0889259 0.226579i 0.879491 0.475915i \(-0.157883\pi\)
−0.968417 + 0.249336i \(0.919788\pi\)
\(674\) 0.768890 10.2601i 0.0296165 0.395205i
\(675\) 0 0
\(676\) 3.16666 + 2.15899i 0.121795 + 0.0830382i
\(677\) 16.2431 + 20.3682i 0.624273 + 0.782814i 0.988939 0.148325i \(-0.0473881\pi\)
−0.364666 + 0.931139i \(0.618817\pi\)
\(678\) 0 0
\(679\) 0.955999 0.144094i 0.0366879 0.00552981i
\(680\) −0.260410 + 1.14093i −0.00998625 + 0.0437526i
\(681\) 0 0
\(682\) −32.5405 56.3618i −1.24604 2.15820i
\(683\) 47.0692 14.5189i 1.80105 0.555551i 0.801930 0.597418i \(-0.203807\pi\)
0.999123 + 0.0418665i \(0.0133304\pi\)
\(684\) 0 0
\(685\) 1.01423 + 13.5340i 0.0387518 + 0.517107i
\(686\) −2.96698 + 1.42882i −0.113280 + 0.0545527i
\(687\) 0 0
\(688\) −2.54447 + 11.0210i −0.0970070 + 0.420171i
\(689\) 24.0176 0.914999
\(690\) 0 0
\(691\) −3.68891 49.2251i −0.140333 1.87261i −0.413311 0.910590i \(-0.635628\pi\)
0.272978 0.962020i \(-0.411991\pi\)
\(692\) −12.1450 + 15.2293i −0.461682 + 0.578931i
\(693\) 0 0
\(694\) 9.53670 + 16.5180i 0.362008 + 0.627016i
\(695\) −8.38908 + 14.5303i −0.318216 + 0.551166i
\(696\) 0 0
\(697\) −1.43359 + 0.216078i −0.0543009 + 0.00818455i
\(698\) 7.46385 6.92544i 0.282511 0.262132i
\(699\) 0 0
\(700\) 0.459533 + 0.313304i 0.0173687 + 0.0118418i
\(701\) −12.8277 11.9024i −0.484495 0.449546i 0.399712 0.916641i \(-0.369110\pi\)
−0.884207 + 0.467095i \(0.845301\pi\)
\(702\) 0 0
\(703\) −3.13388 7.98500i −0.118197 0.301160i
\(704\) −10.8509 47.5409i −0.408959 1.79177i
\(705\) 0 0
\(706\) 9.36392 6.38421i 0.352416 0.240273i
\(707\) −0.640585 0.0965527i −0.0240917 0.00363124i
\(708\) 0 0
\(709\) −28.7314 13.8363i −1.07903 0.519634i −0.192025 0.981390i \(-0.561505\pi\)
−0.887007 + 0.461756i \(0.847220\pi\)
\(710\) −1.96382 0.945725i −0.0737008 0.0354924i
\(711\) 0 0
\(712\) 13.4402 + 2.02578i 0.503691 + 0.0759192i
\(713\) −32.2201 + 21.9673i −1.20665 + 0.822680i
\(714\) 0 0
\(715\) −5.21249 22.8374i −0.194936 0.854071i
\(716\) −1.53885 3.92093i −0.0575096 0.146532i
\(717\) 0 0
\(718\) −8.64119 8.01785i −0.322486 0.299224i
\(719\) −35.7184 24.3524i −1.33207 0.908190i −0.332677 0.943041i \(-0.607952\pi\)
−0.999393 + 0.0348509i \(0.988904\pi\)
\(720\) 0 0
\(721\) −1.33980 + 1.24315i −0.0498968 + 0.0462974i
\(722\) −19.1021 + 2.87918i −0.710906 + 0.107152i
\(723\) 0 0
\(724\) −1.12311 + 1.94528i −0.0417400 + 0.0722958i
\(725\) −10.9609 18.9848i −0.407076 0.705077i
\(726\) 0 0
\(727\) −2.61281 + 3.27636i −0.0969039 + 0.121514i −0.827919 0.560848i \(-0.810475\pi\)
0.731015 + 0.682361i \(0.239047\pi\)
\(728\) −0.142481 1.90128i −0.00528071 0.0704662i
\(729\) 0 0
\(730\) −1.20870 −0.0447360
\(731\) −1.35533 1.26388i −0.0501288 0.0467464i
\(732\) 0 0
\(733\) −44.3364 + 21.3513i −1.63760 + 0.788629i −0.637773 + 0.770224i \(0.720144\pi\)
−0.999831 + 0.0184045i \(0.994141\pi\)
\(734\) −1.57951 21.0771i −0.0583007 0.777968i
\(735\) 0 0
\(736\) −16.0077 + 4.93774i −0.590053 + 0.182007i
\(737\) 18.9785 + 32.8717i 0.699082 + 1.21085i
\(738\) 0 0
\(739\) 0.558133 2.44534i 0.0205313 0.0899533i −0.963624 0.267261i \(-0.913882\pi\)
0.984156 + 0.177307i \(0.0567387\pi\)
\(740\) −8.15815 + 1.22964i −0.299900 + 0.0452026i
\(741\) 0 0
\(742\) 1.22920 + 1.54137i 0.0451254 + 0.0565854i
\(743\) −14.7210 10.0366i −0.540059 0.368206i 0.262357 0.964971i \(-0.415500\pi\)
−0.802416 + 0.596765i \(0.796453\pi\)
\(744\) 0 0
\(745\) −0.373233 + 4.98044i −0.0136742 + 0.182469i
\(746\) −13.6897 34.8807i −0.501215 1.27707i
\(747\) 0 0
\(748\) 1.31881 + 0.406800i 0.0482205 + 0.0148741i
\(749\) −1.12006 + 0.763641i −0.0409260 + 0.0279028i
\(750\) 0 0
\(751\) 14.1468 36.0454i 0.516223 1.31532i −0.400684 0.916216i \(-0.631228\pi\)
0.916908 0.399099i \(-0.130677\pi\)
\(752\) −0.718447 0.345986i −0.0261991 0.0126168i
\(753\) 0 0
\(754\) −7.91223 + 20.1600i −0.288146 + 0.734185i
\(755\) −15.3854 2.31897i −0.559932 0.0843961i
\(756\) 0 0
\(757\) 29.5522 + 9.11563i 1.07409 + 0.331313i 0.780846 0.624724i \(-0.214788\pi\)
0.293246 + 0.956037i \(0.405265\pi\)
\(758\) 0.626503 + 2.74489i 0.0227556 + 0.0996988i
\(759\) 0 0
\(760\) 0.351933 4.69621i 0.0127659 0.170350i
\(761\) −31.4994 29.2271i −1.14185 1.05948i −0.997551 0.0699487i \(-0.977716\pi\)
−0.144300 0.989534i \(-0.546093\pi\)
\(762\) 0 0
\(763\) 0.0286848 + 0.0359696i 0.00103846 + 0.00130219i
\(764\) 2.05114 1.90318i 0.0742077 0.0688546i
\(765\) 0 0
\(766\) −3.47336 + 15.2178i −0.125498 + 0.549841i
\(767\) 12.0118 20.8050i 0.433720 0.751225i
\(768\) 0 0
\(769\) 11.0134 3.39717i 0.397152 0.122505i −0.0897448 0.995965i \(-0.528605\pi\)
0.486896 + 0.873460i \(0.338129\pi\)
\(770\) 1.19886 1.50332i 0.0432038 0.0541758i
\(771\) 0 0
\(772\) −13.3197 + 6.41443i −0.479387 + 0.230861i
\(773\) 24.2393 0.871828 0.435914 0.899988i \(-0.356425\pi\)
0.435914 + 0.899988i \(0.356425\pi\)
\(774\) 0 0
\(775\) 31.4052 1.12811
\(776\) 12.3431 5.94414i 0.443093 0.213382i
\(777\) 0 0
\(778\) −10.7390 + 13.4663i −0.385013 + 0.482790i
\(779\) 5.57498 1.71965i 0.199744 0.0616130i
\(780\) 0 0
\(781\) −4.45985 + 7.72469i −0.159586 + 0.276411i
\(782\) −0.270499 + 1.18513i −0.00967303 + 0.0423803i
\(783\) 0 0
\(784\) −8.79188 + 8.15768i −0.313996 + 0.291346i
\(785\) 17.3485 + 21.7543i 0.619194 + 0.776444i
\(786\) 0 0
\(787\) −7.37365 6.84175i −0.262842 0.243882i 0.537732 0.843116i \(-0.319281\pi\)
−0.800574 + 0.599234i \(0.795472\pi\)
\(788\) 0.616004 8.22000i 0.0219442 0.292825i
\(789\) 0 0
\(790\) −2.01884 8.84511i −0.0718271 0.314695i
\(791\) 2.28885 + 0.706017i 0.0813821 + 0.0251031i
\(792\) 0 0
\(793\) 38.1907 + 5.75633i 1.35619 + 0.204413i
\(794\) 11.6012 29.5594i 0.411711 1.04902i
\(795\) 0 0
\(796\) 6.70921 + 3.23098i 0.237802 + 0.114519i
\(797\) 14.9088 37.9869i 0.528096 1.34557i −0.379294 0.925276i \(-0.623833\pi\)
0.907390 0.420290i \(-0.138072\pi\)
\(798\) 0 0
\(799\) 0.107948 0.0735978i 0.00381893 0.00260370i
\(800\) 12.8917 + 3.97657i 0.455792 + 0.140593i
\(801\) 0 0
\(802\) 5.70394 + 14.5334i 0.201413 + 0.513192i
\(803\) −0.369635 + 4.93243i −0.0130441 + 0.174062i
\(804\) 0 0
\(805\) −0.951940 0.649022i −0.0335515 0.0228750i
\(806\) −19.3445 24.2572i −0.681380 0.854423i
\(807\) 0 0
\(808\) −9.07731 + 1.36818i −0.319339 + 0.0481326i
\(809\) −10.4359 + 45.7228i −0.366908 + 1.60753i 0.368313 + 0.929702i \(0.379935\pi\)
−0.735221 + 0.677827i \(0.762922\pi\)
\(810\) 0 0
\(811\) −17.1357 29.6798i −0.601714 1.04220i −0.992562 0.121744i \(-0.961151\pi\)
0.390847 0.920456i \(-0.372182\pi\)
\(812\) 1.15563 0.356464i 0.0405546 0.0125094i
\(813\) 0 0
\(814\) −3.70880 49.4905i −0.129993 1.73464i
\(815\) 8.41660 4.05322i 0.294821 0.141978i
\(816\) 0 0
\(817\) 6.15123 + 4.21640i 0.215204 + 0.147513i
\(818\) −33.2230 −1.16162
\(819\) 0 0
\(820\) −0.419334 5.59563i −0.0146438 0.195408i
\(821\) 11.5042 14.4258i 0.401500 0.503465i −0.539447 0.842020i \(-0.681367\pi\)
0.940947 + 0.338555i \(0.109938\pi\)
\(822\) 0 0
\(823\) −4.59427 7.95750i −0.160146 0.277381i 0.774775 0.632237i \(-0.217863\pi\)
−0.934921 + 0.354856i \(0.884530\pi\)
\(824\) −12.9496 + 22.4293i −0.451120 + 0.781362i
\(825\) 0 0
\(826\) 1.94994 0.293907i 0.0678472 0.0102263i
\(827\) 26.9067 24.9658i 0.935637 0.868145i −0.0558380 0.998440i \(-0.517783\pi\)
0.991475 + 0.130295i \(0.0415925\pi\)
\(828\) 0 0
\(829\) 3.75599 + 2.56079i 0.130451 + 0.0889400i 0.626788 0.779190i \(-0.284369\pi\)
−0.496336 + 0.868130i \(0.665322\pi\)
\(830\) −7.78443 7.22290i −0.270202 0.250710i
\(831\) 0 0
\(832\) −8.49311 21.6401i −0.294446 0.750235i
\(833\) −0.437263 1.91577i −0.0151503 0.0663776i
\(834\) 0 0
\(835\) 3.96807 2.70538i 0.137321 0.0936236i
\(836\) −5.49185 0.827763i −0.189940 0.0286288i
\(837\) 0 0
\(838\) −34.9596 16.8357i −1.20766 0.581578i
\(839\) −21.6424 10.4224i −0.747177 0.359822i 0.0212370 0.999774i \(-0.493240\pi\)
−0.768414 + 0.639953i \(0.778954\pi\)
\(840\) 0 0
\(841\) −18.4585 2.78217i −0.636500 0.0959369i
\(842\) −14.8710 + 10.1389i −0.512490 + 0.349410i
\(843\) 0 0
\(844\) −3.43390 15.0449i −0.118200 0.517866i
\(845\) 2.33598 + 5.95197i 0.0803601 + 0.204754i
\(846\) 0 0
\(847\) −4.02372 3.73347i −0.138257 0.128284i
\(848\) 11.9050 + 8.11671i 0.408820 + 0.278729i
\(849\) 0 0
\(850\) 0.717647 0.665879i 0.0246151 0.0228395i
\(851\) −29.4054 + 4.43215i −1.00800 + 0.151932i
\(852\) 0 0
\(853\) 24.8630 43.0639i 0.851292 1.47448i −0.0287512 0.999587i \(-0.509153\pi\)
0.880043 0.474894i \(-0.157514\pi\)
\(854\) 1.58515 + 2.74555i 0.0542426 + 0.0939509i
\(855\) 0 0
\(856\) −11.9769 + 15.0185i −0.409361 + 0.513323i
\(857\) 2.63975 + 35.2251i 0.0901723 + 1.20327i 0.840356 + 0.542036i \(0.182346\pi\)
−0.750183 + 0.661230i \(0.770035\pi\)
\(858\) 0 0
\(859\) 8.58814 0.293024 0.146512 0.989209i \(-0.453195\pi\)
0.146512 + 0.989209i \(0.453195\pi\)
\(860\) 5.27016 4.86553i 0.179711 0.165913i
\(861\) 0 0
\(862\) 8.90311 4.28751i 0.303241 0.146033i
\(863\) −2.53059 33.7684i −0.0861424 1.14949i −0.857984 0.513676i \(-0.828283\pi\)
0.771842 0.635814i \(-0.219336\pi\)
\(864\) 0 0
\(865\) −31.0531 + 9.57861i −1.05584 + 0.325682i
\(866\) 9.42715 + 16.3283i 0.320348 + 0.554858i
\(867\) 0 0
\(868\) −0.385524 + 1.68909i −0.0130856 + 0.0573315i
\(869\) −36.7123 + 5.53349i −1.24538 + 0.187711i
\(870\) 0 0
\(871\) 11.2822 + 14.1474i 0.382283 + 0.479368i
\(872\) 0.538653 + 0.367247i 0.0182411 + 0.0124366i
\(873\) 0 0
\(874\) 0.365568 4.87817i 0.0123655 0.165006i
\(875\) 0.872799 + 2.22386i 0.0295060 + 0.0751800i
\(876\) 0 0
\(877\) −17.2010 5.30581i −0.580837 0.179164i −0.00960602 0.999954i \(-0.503058\pi\)
−0.571231 + 0.820789i \(0.693534\pi\)
\(878\) −16.6543 + 11.3547i −0.562057 + 0.383204i
\(879\) 0 0
\(880\) 5.13414 13.0816i 0.173072 0.440980i
\(881\) −23.6192 11.3744i −0.795750 0.383213i −0.00859074 0.999963i \(-0.502735\pi\)
−0.787159 + 0.616750i \(0.788449\pi\)
\(882\) 0 0
\(883\) −18.1802 + 46.3225i −0.611814 + 1.55888i 0.203016 + 0.979176i \(0.434926\pi\)
−0.814829 + 0.579701i \(0.803169\pi\)
\(884\) 0.650600 + 0.0980622i 0.0218821 + 0.00329819i
\(885\) 0 0
\(886\) −9.32572 2.87660i −0.313304 0.0966414i
\(887\) −1.90844 8.36143i −0.0640792 0.280749i 0.932730 0.360577i \(-0.117420\pi\)
−0.996809 + 0.0798277i \(0.974563\pi\)
\(888\) 0 0
\(889\) 0.126325 1.68569i 0.00423680 0.0565362i
\(890\) 4.79033 + 4.44478i 0.160572 + 0.148989i
\(891\) 0 0
\(892\) 3.68432 + 4.62000i 0.123360 + 0.154689i
\(893\) −0.385409 + 0.357607i −0.0128972 + 0.0119669i
\(894\) 0 0
\(895\) 1.56366 6.85086i 0.0522675 0.228999i
\(896\) 0.0349607 0.0605537i 0.00116796 0.00202296i
\(897\) 0 0
\(898\) −21.1346 + 6.51917i −0.705271 + 0.217547i
\(899\) 42.5769 53.3898i 1.42002 1.78065i
\(900\) 0 0
\(901\) −2.12696 + 1.02429i −0.0708592 + 0.0341240i
\(902\) 33.7546 1.12391
\(903\) 0 0
\(904\) 33.9417 1.12888
\(905\) −3.37626 + 1.62592i −0.112231 + 0.0540474i
\(906\) 0 0
\(907\) −17.5664 + 22.0275i −0.583282 + 0.731412i −0.982669 0.185370i \(-0.940652\pi\)
0.399387 + 0.916782i \(0.369223\pi\)
\(908\) 12.0998 3.73231i 0.401548 0.123861i
\(909\) 0 0
\(910\) 0.458332 0.793855i 0.0151936 0.0263160i
\(911\) −5.43767 + 23.8240i −0.180158 + 0.789324i 0.801395 + 0.598135i \(0.204091\pi\)
−0.981553 + 0.191189i \(0.938766\pi\)
\(912\) 0 0
\(913\) −31.8556 + 29.5577i −1.05427 + 0.978217i
\(914\) 7.32050 + 9.17962i 0.242141 + 0.303635i
\(915\) 0 0
\(916\) −0.638222 0.592184i −0.0210875 0.0195663i
\(917\) 0.290311 3.87394i 0.00958692 0.127929i
\(918\) 0 0
\(919\) 3.55017 + 15.5543i 0.117109 + 0.513089i 0.999123 + 0.0418659i \(0.0133302\pi\)
−0.882014 + 0.471223i \(0.843813\pi\)
\(920\) −15.6008 4.81222i −0.514345 0.158654i
\(921\) 0 0
\(922\) 9.18878 + 1.38499i 0.302616 + 0.0456121i
\(923\) −1.55354 + 3.95835i −0.0511353 + 0.130291i
\(924\) 0 0
\(925\) 21.5772 + 10.3910i 0.709455 + 0.341656i
\(926\) 0.906512 2.30975i 0.0297898 0.0759032i
\(927\) 0 0
\(928\) 24.2380 16.5252i 0.795650 0.542465i
\(929\) 5.97357 + 1.84260i 0.195987 + 0.0604539i 0.391195 0.920308i \(-0.372062\pi\)
−0.195208 + 0.980762i \(0.562538\pi\)
\(930\) 0 0
\(931\) 2.88900 + 7.36105i 0.0946832 + 0.241249i
\(932\) −0.0806629 + 1.07637i −0.00264220 + 0.0352577i
\(933\) 0 0
\(934\) −27.2692 18.5918i −0.892275 0.608343i
\(935\) 1.43556 + 1.80014i 0.0469480 + 0.0588709i
\(936\) 0 0
\(937\) 53.4604 8.05785i 1.74647 0.263239i 0.803309 0.595563i \(-0.203071\pi\)
0.943165 + 0.332324i \(0.107833\pi\)
\(938\) −0.330521 + 1.44811i −0.0107919 + 0.0472823i
\(939\) 0 0
\(940\) 0.252838 + 0.437929i 0.00824667 + 0.0142837i
\(941\) −29.8574 + 9.20978i −0.973322 + 0.300230i −0.740326 0.672248i \(-0.765329\pi\)
−0.232996 + 0.972478i \(0.574853\pi\)
\(942\) 0 0
\(943\) −1.51146 20.1690i −0.0492198 0.656792i
\(944\) 12.9850 6.25324i 0.422625 0.203526i
\(945\) 0 0
\(946\) 26.8174 + 33.8010i 0.871909 + 1.09896i
\(947\) 38.7946 1.26066 0.630328 0.776329i \(-0.282920\pi\)
0.630328 + 0.776329i \(0.282920\pi\)
\(948\) 0 0
\(949\) 0.176216 + 2.35144i 0.00572022 + 0.0763311i
\(950\) −2.45631 + 3.08012i −0.0796932 + 0.0999321i
\(951\) 0 0
\(952\) 0.0937025 + 0.162298i 0.00303692 + 0.00526009i
\(953\) −14.6148 + 25.3136i −0.473420 + 0.819987i −0.999537 0.0304252i \(-0.990314\pi\)
0.526118 + 0.850412i \(0.323647\pi\)
\(954\) 0 0
\(955\) 4.61591 0.695736i 0.149367 0.0225135i
\(956\) −8.83068 + 8.19367i −0.285605 + 0.265002i
\(957\) 0 0
\(958\) 12.2409 + 8.34572i 0.395486 + 0.269638i
\(959\) 1.59320 + 1.47828i 0.0514472 + 0.0477361i
\(960\) 0 0
\(961\) 24.4157 + 62.2103i 0.787604 + 2.00678i
\(962\) −5.26480 23.0666i −0.169744 0.743698i
\(963\) 0 0
\(964\) −15.9924 + 10.9035i −0.515082 + 0.351177i
\(965\) −24.3883 3.67594i −0.785087 0.118333i
\(966\) 0 0
\(967\) −22.9889 11.0709i −0.739274 0.356015i 0.0260504 0.999661i \(-0.491707\pi\)
−0.765324 + 0.643645i \(0.777421\pi\)
\(968\) −70.0783 33.7479i −2.25240 1.08470i
\(969\) 0 0
\(970\) 6.51307 + 0.981688i 0.209122 + 0.0315201i
\(971\) −17.1865 + 11.7176i −0.551542 + 0.376035i −0.806788 0.590841i \(-0.798796\pi\)
0.255246 + 0.966876i \(0.417844\pi\)
\(972\) 0 0
\(973\) 0.597875 + 2.61946i 0.0191670 + 0.0839761i
\(974\) 14.8495 + 37.8358i 0.475808 + 1.21234i
\(975\) 0 0
\(976\) 16.9850 + 15.7598i 0.543676 + 0.504458i
\(977\) 15.5522 + 10.6033i 0.497559 + 0.339230i 0.785958 0.618280i \(-0.212170\pi\)
−0.288398 + 0.957510i \(0.593123\pi\)
\(978\) 0 0
\(979\) 19.6031 18.1890i 0.626517 0.581323i
\(980\) 7.52068 1.13356i 0.240239 0.0362102i
\(981\) 0 0
\(982\) −11.2007 + 19.4003i −0.357430 + 0.619087i
\(983\) −11.1156 19.2529i −0.354534 0.614071i 0.632504 0.774557i \(-0.282027\pi\)
−0.987038 + 0.160486i \(0.948694\pi\)
\(984\) 0 0
\(985\) 8.57416 10.7517i 0.273195 0.342576i
\(986\) −0.159080 2.12277i −0.00506613 0.0676028i
\(987\) 0 0
\(988\) −2.64771 −0.0842348
\(989\) 18.9958 17.5374i 0.604033 0.557657i
\(990\) 0 0
\(991\) −13.8081 + 6.64964i −0.438630 + 0.211233i −0.640148 0.768252i \(-0.721127\pi\)
0.201518 + 0.979485i \(0.435413\pi\)
\(992\) 3.14060 + 41.9084i 0.0997143 + 1.33059i
\(993\) 0 0
\(994\) −0.333542 + 0.102884i −0.0105793 + 0.00326328i
\(995\) 6.21163 + 10.7589i 0.196922 + 0.341079i
\(996\) 0 0
\(997\) −1.57862 + 6.91637i −0.0499953 + 0.219044i −0.993754 0.111591i \(-0.964405\pi\)
0.943759 + 0.330634i \(0.107263\pi\)
\(998\) 7.51987 1.13344i 0.238037 0.0358784i
\(999\) 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 387.2.y.c.100.2 36
3.2 odd 2 43.2.g.a.14.2 36
12.11 even 2 688.2.bg.c.401.1 36
43.40 even 21 inner 387.2.y.c.298.2 36
129.56 odd 42 1849.2.a.n.1.13 18
129.83 odd 42 43.2.g.a.40.2 yes 36
129.116 even 42 1849.2.a.o.1.6 18
516.83 even 42 688.2.bg.c.513.1 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.2.g.a.14.2 36 3.2 odd 2
43.2.g.a.40.2 yes 36 129.83 odd 42
387.2.y.c.100.2 36 1.1 even 1 trivial
387.2.y.c.298.2 36 43.40 even 21 inner
688.2.bg.c.401.1 36 12.11 even 2
688.2.bg.c.513.1 36 516.83 even 42
1849.2.a.n.1.13 18 129.56 odd 42
1849.2.a.o.1.6 18 129.116 even 42