Properties

Label 1638.2.m.k.1621.1
Level $1638$
Weight $2$
Character 1638.1621
Analytic conductor $13.079$
Analytic rank $0$
Dimension $10$
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] = [1638,2,Mod(289,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.m (of order \(3\), degree \(2\), 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: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1621.1
Root \(-1.10337 + 1.91109i\) of defining polynomial
Character \(\chi\) \(=\) 1638.1621
Dual form 1638.2.m.k.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-1.10337 - 1.91109i) q^{5} +(1.19230 + 2.36187i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-1.10337 - 1.91109i) q^{5} +(1.19230 + 2.36187i) q^{7} +1.00000 q^{8} +(-1.10337 - 1.91109i) q^{10} +(-0.527733 - 0.914061i) q^{11} +(3.18376 - 1.69224i) q^{13} +(1.19230 + 2.36187i) q^{14} +1.00000 q^{16} +0.944533 q^{17} +(-1.96372 + 3.40126i) q^{19} +(-1.10337 - 1.91109i) q^{20} +(-0.527733 - 0.914061i) q^{22} +6.22771 q^{23} +(0.0651512 - 0.112845i) q^{25} +(3.18376 - 1.69224i) q^{26} +(1.19230 + 2.36187i) q^{28} +(-0.888084 + 1.53821i) q^{29} +(3.63304 - 6.29261i) q^{31} +1.00000 q^{32} +0.944533 q^{34} +(3.19819 - 4.88461i) q^{35} +2.26221 q^{37} +(-1.96372 + 3.40126i) q^{38} +(-1.10337 - 1.91109i) q^{40} +(1.63110 - 2.82515i) q^{41} +(0.537418 + 0.930835i) q^{43} +(-0.527733 - 0.914061i) q^{44} +6.22771 q^{46} +(-2.42678 - 4.20330i) q^{47} +(-4.15682 + 5.63212i) q^{49} +(0.0651512 - 0.112845i) q^{50} +(3.18376 - 1.69224i) q^{52} +(4.94074 - 8.55761i) q^{53} +(-1.16457 + 2.01709i) q^{55} +(1.19230 + 2.36187i) q^{56} +(-0.888084 + 1.53821i) q^{58} +1.01937 q^{59} +(-0.0382184 + 0.0661962i) q^{61} +(3.63304 - 6.29261i) q^{62} +1.00000 q^{64} +(-6.74690 - 4.21728i) q^{65} +(5.85308 + 10.1378i) q^{67} +0.944533 q^{68} +(3.19819 - 4.88461i) q^{70} +(4.20868 + 7.28964i) q^{71} +(6.57264 - 11.3841i) q^{73} +2.26221 q^{74} +(-1.96372 + 3.40126i) q^{76} +(1.52967 - 2.33627i) q^{77} +(3.00194 + 5.19951i) q^{79} +(-1.10337 - 1.91109i) q^{80} +(1.63110 - 2.82515i) q^{82} +1.77617 q^{83} +(-1.04217 - 1.80509i) q^{85} +(0.537418 + 0.930835i) q^{86} +(-0.527733 - 0.914061i) q^{88} -13.3353 q^{89} +(7.79286 + 5.50194i) q^{91} +6.22771 q^{92} +(-2.42678 - 4.20330i) q^{94} +8.66684 q^{95} +(-8.99467 - 15.5792i) q^{97} +(-4.15682 + 5.63212i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 10 q^{2} + 10 q^{4} + 2 q^{5} - 2 q^{7} + 10 q^{8} + 2 q^{10} - 6 q^{11} - 4 q^{13} - 2 q^{14} + 10 q^{16} + 8 q^{17} + 3 q^{19} + 2 q^{20} - 6 q^{22} + 12 q^{23} - q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} + 10 q^{32} + 8 q^{34} - 16 q^{35} - 2 q^{37} + 3 q^{38} + 2 q^{40} + 4 q^{41} + 3 q^{43} - 6 q^{44} + 12 q^{46} + 15 q^{47} + 4 q^{49} - q^{50} - 4 q^{52} + 17 q^{53} + 3 q^{55} - 2 q^{56} + 4 q^{59} + 11 q^{61} - 10 q^{62} + 10 q^{64} + 4 q^{65} - q^{67} + 8 q^{68} - 16 q^{70} - 18 q^{71} + 12 q^{73} - 2 q^{74} + 3 q^{76} - 18 q^{77} - 4 q^{79} + 2 q^{80} + 4 q^{82} + q^{85} + 3 q^{86} - 6 q^{88} + 14 q^{89} + 26 q^{91} + 12 q^{92} + 15 q^{94} + 48 q^{95} - 6 q^{97} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.10337 1.91109i −0.493442 0.854666i 0.506530 0.862223i \(-0.330928\pi\)
−0.999971 + 0.00755619i \(0.997595\pi\)
\(6\) 0 0
\(7\) 1.19230 + 2.36187i 0.450648 + 0.892702i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.10337 1.91109i −0.348916 0.604340i
\(11\) −0.527733 0.914061i −0.159118 0.275600i 0.775433 0.631430i \(-0.217532\pi\)
−0.934551 + 0.355830i \(0.884198\pi\)
\(12\) 0 0
\(13\) 3.18376 1.69224i 0.883015 0.469344i
\(14\) 1.19230 + 2.36187i 0.318657 + 0.631235i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0.944533 0.229083 0.114541 0.993418i \(-0.463460\pi\)
0.114541 + 0.993418i \(0.463460\pi\)
\(18\) 0 0
\(19\) −1.96372 + 3.40126i −0.450508 + 0.780303i −0.998418 0.0562346i \(-0.982091\pi\)
0.547909 + 0.836538i \(0.315424\pi\)
\(20\) −1.10337 1.91109i −0.246721 0.427333i
\(21\) 0 0
\(22\) −0.527733 0.914061i −0.112513 0.194879i
\(23\) 6.22771 1.29857 0.649284 0.760546i \(-0.275069\pi\)
0.649284 + 0.760546i \(0.275069\pi\)
\(24\) 0 0
\(25\) 0.0651512 0.112845i 0.0130302 0.0225690i
\(26\) 3.18376 1.69224i 0.624386 0.331876i
\(27\) 0 0
\(28\) 1.19230 + 2.36187i 0.225324 + 0.446351i
\(29\) −0.888084 + 1.53821i −0.164913 + 0.285638i −0.936624 0.350335i \(-0.886068\pi\)
0.771711 + 0.635973i \(0.219401\pi\)
\(30\) 0 0
\(31\) 3.63304 6.29261i 0.652513 1.13019i −0.329997 0.943982i \(-0.607048\pi\)
0.982511 0.186205i \(-0.0596188\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 0.944533 0.161986
\(35\) 3.19819 4.88461i 0.540593 0.825650i
\(36\) 0 0
\(37\) 2.26221 0.371904 0.185952 0.982559i \(-0.440463\pi\)
0.185952 + 0.982559i \(0.440463\pi\)
\(38\) −1.96372 + 3.40126i −0.318557 + 0.551758i
\(39\) 0 0
\(40\) −1.10337 1.91109i −0.174458 0.302170i
\(41\) 1.63110 2.82515i 0.254735 0.441215i −0.710088 0.704113i \(-0.751345\pi\)
0.964824 + 0.262898i \(0.0846783\pi\)
\(42\) 0 0
\(43\) 0.537418 + 0.930835i 0.0819554 + 0.141951i 0.904090 0.427343i \(-0.140550\pi\)
−0.822134 + 0.569293i \(0.807217\pi\)
\(44\) −0.527733 0.914061i −0.0795588 0.137800i
\(45\) 0 0
\(46\) 6.22771 0.918226
\(47\) −2.42678 4.20330i −0.353982 0.613114i 0.632961 0.774183i \(-0.281839\pi\)
−0.986943 + 0.161069i \(0.948506\pi\)
\(48\) 0 0
\(49\) −4.15682 + 5.63212i −0.593832 + 0.804589i
\(50\) 0.0651512 0.112845i 0.00921377 0.0159587i
\(51\) 0 0
\(52\) 3.18376 1.69224i 0.441508 0.234672i
\(53\) 4.94074 8.55761i 0.678663 1.17548i −0.296721 0.954964i \(-0.595893\pi\)
0.975384 0.220514i \(-0.0707734\pi\)
\(54\) 0 0
\(55\) −1.16457 + 2.01709i −0.157031 + 0.271985i
\(56\) 1.19230 + 2.36187i 0.159328 + 0.315618i
\(57\) 0 0
\(58\) −0.888084 + 1.53821i −0.116611 + 0.201976i
\(59\) 1.01937 0.132710 0.0663552 0.997796i \(-0.478863\pi\)
0.0663552 + 0.997796i \(0.478863\pi\)
\(60\) 0 0
\(61\) −0.0382184 + 0.0661962i −0.00489336 + 0.00847555i −0.868462 0.495756i \(-0.834891\pi\)
0.863568 + 0.504232i \(0.168224\pi\)
\(62\) 3.63304 6.29261i 0.461397 0.799163i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.74690 4.21728i −0.836849 0.523089i
\(66\) 0 0
\(67\) 5.85308 + 10.1378i 0.715067 + 1.23853i 0.962934 + 0.269739i \(0.0869373\pi\)
−0.247866 + 0.968794i \(0.579729\pi\)
\(68\) 0.944533 0.114541
\(69\) 0 0
\(70\) 3.19819 4.88461i 0.382257 0.583823i
\(71\) 4.20868 + 7.28964i 0.499478 + 0.865121i 1.00000 0.000602515i \(-0.000191787\pi\)
−0.500522 + 0.865724i \(0.666858\pi\)
\(72\) 0 0
\(73\) 6.57264 11.3841i 0.769269 1.33241i −0.168690 0.985669i \(-0.553954\pi\)
0.937960 0.346745i \(-0.112713\pi\)
\(74\) 2.26221 0.262976
\(75\) 0 0
\(76\) −1.96372 + 3.40126i −0.225254 + 0.390152i
\(77\) 1.52967 2.33627i 0.174322 0.266243i
\(78\) 0 0
\(79\) 3.00194 + 5.19951i 0.337744 + 0.584991i 0.984008 0.178124i \(-0.0570027\pi\)
−0.646264 + 0.763114i \(0.723669\pi\)
\(80\) −1.10337 1.91109i −0.123360 0.213667i
\(81\) 0 0
\(82\) 1.63110 2.82515i 0.180125 0.311986i
\(83\) 1.77617 0.194960 0.0974799 0.995237i \(-0.468922\pi\)
0.0974799 + 0.995237i \(0.468922\pi\)
\(84\) 0 0
\(85\) −1.04217 1.80509i −0.113039 0.195789i
\(86\) 0.537418 + 0.930835i 0.0579512 + 0.100374i
\(87\) 0 0
\(88\) −0.527733 0.914061i −0.0562566 0.0974393i
\(89\) −13.3353 −1.41354 −0.706769 0.707444i \(-0.749848\pi\)
−0.706769 + 0.707444i \(0.749848\pi\)
\(90\) 0 0
\(91\) 7.79286 + 5.50194i 0.816914 + 0.576760i
\(92\) 6.22771 0.649284
\(93\) 0 0
\(94\) −2.42678 4.20330i −0.250303 0.433537i
\(95\) 8.66684 0.889199
\(96\) 0 0
\(97\) −8.99467 15.5792i −0.913270 1.58183i −0.809415 0.587238i \(-0.800215\pi\)
−0.103855 0.994592i \(-0.533118\pi\)
\(98\) −4.15682 + 5.63212i −0.419903 + 0.568930i
\(99\) 0 0
\(100\) 0.0651512 0.112845i 0.00651512 0.0112845i
\(101\) 6.75018 + 11.6917i 0.671668 + 1.16336i 0.977431 + 0.211256i \(0.0677553\pi\)
−0.305763 + 0.952108i \(0.598911\pi\)
\(102\) 0 0
\(103\) 1.46258 + 2.53327i 0.144113 + 0.249610i 0.929041 0.369976i \(-0.120634\pi\)
−0.784929 + 0.619586i \(0.787301\pi\)
\(104\) 3.18376 1.69224i 0.312193 0.165938i
\(105\) 0 0
\(106\) 4.94074 8.55761i 0.479887 0.831188i
\(107\) −14.1092 −1.36399 −0.681993 0.731359i \(-0.738887\pi\)
−0.681993 + 0.731359i \(0.738887\pi\)
\(108\) 0 0
\(109\) 0.723832 1.25371i 0.0693306 0.120084i −0.829276 0.558839i \(-0.811247\pi\)
0.898607 + 0.438755i \(0.144580\pi\)
\(110\) −1.16457 + 2.01709i −0.111037 + 0.192322i
\(111\) 0 0
\(112\) 1.19230 + 2.36187i 0.112662 + 0.223175i
\(113\) 1.67707 + 2.90477i 0.157765 + 0.273257i 0.934062 0.357110i \(-0.116238\pi\)
−0.776297 + 0.630367i \(0.782904\pi\)
\(114\) 0 0
\(115\) −6.87146 11.9017i −0.640767 1.10984i
\(116\) −0.888084 + 1.53821i −0.0824565 + 0.142819i
\(117\) 0 0
\(118\) 1.01937 0.0938405
\(119\) 1.12617 + 2.23086i 0.103236 + 0.204503i
\(120\) 0 0
\(121\) 4.94299 8.56152i 0.449363 0.778320i
\(122\) −0.0382184 + 0.0661962i −0.00346013 + 0.00599312i
\(123\) 0 0
\(124\) 3.63304 6.29261i 0.326257 0.565093i
\(125\) −11.3212 −1.01260
\(126\) 0 0
\(127\) −4.80963 + 8.33053i −0.426786 + 0.739215i −0.996585 0.0825687i \(-0.973688\pi\)
0.569799 + 0.821784i \(0.307021\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −6.74690 4.21728i −0.591742 0.369880i
\(131\) 3.27649 + 5.67504i 0.286268 + 0.495831i 0.972916 0.231159i \(-0.0742519\pi\)
−0.686648 + 0.726990i \(0.740919\pi\)
\(132\) 0 0
\(133\) −10.3747 0.582706i −0.899599 0.0505270i
\(134\) 5.85308 + 10.1378i 0.505629 + 0.875775i
\(135\) 0 0
\(136\) 0.944533 0.0809930
\(137\) −7.12468 −0.608702 −0.304351 0.952560i \(-0.598440\pi\)
−0.304351 + 0.952560i \(0.598440\pi\)
\(138\) 0 0
\(139\) −3.09957 5.36862i −0.262902 0.455360i 0.704109 0.710091i \(-0.251346\pi\)
−0.967012 + 0.254731i \(0.918013\pi\)
\(140\) 3.19819 4.88461i 0.270297 0.412825i
\(141\) 0 0
\(142\) 4.20868 + 7.28964i 0.353184 + 0.611733i
\(143\) −3.22699 2.01709i −0.269854 0.168678i
\(144\) 0 0
\(145\) 3.91954 0.325500
\(146\) 6.57264 11.3841i 0.543956 0.942159i
\(147\) 0 0
\(148\) 2.26221 0.185952
\(149\) −10.9374 + 18.9442i −0.896028 + 1.55197i −0.0635010 + 0.997982i \(0.520227\pi\)
−0.832527 + 0.553984i \(0.813107\pi\)
\(150\) 0 0
\(151\) 7.25658 12.5688i 0.590532 1.02283i −0.403629 0.914923i \(-0.632251\pi\)
0.994161 0.107909i \(-0.0344154\pi\)
\(152\) −1.96372 + 3.40126i −0.159279 + 0.275879i
\(153\) 0 0
\(154\) 1.52967 2.33627i 0.123264 0.188262i
\(155\) −16.0343 −1.28791
\(156\) 0 0
\(157\) 2.13538 3.69859i 0.170422 0.295179i −0.768146 0.640275i \(-0.778820\pi\)
0.938567 + 0.345096i \(0.112154\pi\)
\(158\) 3.00194 + 5.19951i 0.238821 + 0.413651i
\(159\) 0 0
\(160\) −1.10337 1.91109i −0.0872290 0.151085i
\(161\) 7.42532 + 14.7090i 0.585197 + 1.15923i
\(162\) 0 0
\(163\) −3.03208 + 5.25172i −0.237491 + 0.411347i −0.959994 0.280021i \(-0.909658\pi\)
0.722503 + 0.691368i \(0.242992\pi\)
\(164\) 1.63110 2.82515i 0.127368 0.220607i
\(165\) 0 0
\(166\) 1.77617 0.137857
\(167\) 7.86930 13.6300i 0.608944 1.05472i −0.382470 0.923968i \(-0.624927\pi\)
0.991415 0.130755i \(-0.0417401\pi\)
\(168\) 0 0
\(169\) 7.27262 10.7754i 0.559432 0.828876i
\(170\) −1.04217 1.80509i −0.0799307 0.138444i
\(171\) 0 0
\(172\) 0.537418 + 0.930835i 0.0409777 + 0.0709755i
\(173\) −5.29220 + 9.16635i −0.402358 + 0.696905i −0.994010 0.109289i \(-0.965143\pi\)
0.591652 + 0.806194i \(0.298476\pi\)
\(174\) 0 0
\(175\) 0.344205 + 0.0193327i 0.0260195 + 0.00146141i
\(176\) −0.527733 0.914061i −0.0397794 0.0689000i
\(177\) 0 0
\(178\) −13.3353 −0.999522
\(179\) 7.11908 + 12.3306i 0.532105 + 0.921633i 0.999297 + 0.0374773i \(0.0119322\pi\)
−0.467192 + 0.884156i \(0.654734\pi\)
\(180\) 0 0
\(181\) −13.7312 −1.02063 −0.510314 0.859988i \(-0.670471\pi\)
−0.510314 + 0.859988i \(0.670471\pi\)
\(182\) 7.79286 + 5.50194i 0.577645 + 0.407831i
\(183\) 0 0
\(184\) 6.22771 0.459113
\(185\) −2.49605 4.32328i −0.183513 0.317854i
\(186\) 0 0
\(187\) −0.498462 0.863361i −0.0364511 0.0631352i
\(188\) −2.42678 4.20330i −0.176991 0.306557i
\(189\) 0 0
\(190\) 8.66684 0.628758
\(191\) 0.437999 0.758636i 0.0316925 0.0548930i −0.849744 0.527195i \(-0.823244\pi\)
0.881437 + 0.472302i \(0.156577\pi\)
\(192\) 0 0
\(193\) 11.3312 + 19.6263i 0.815640 + 1.41273i 0.908867 + 0.417085i \(0.136948\pi\)
−0.0932273 + 0.995645i \(0.529718\pi\)
\(194\) −8.99467 15.5792i −0.645779 1.11852i
\(195\) 0 0
\(196\) −4.15682 + 5.63212i −0.296916 + 0.402295i
\(197\) −8.44249 + 14.6228i −0.601502 + 1.04183i 0.391092 + 0.920352i \(0.372098\pi\)
−0.992594 + 0.121481i \(0.961236\pi\)
\(198\) 0 0
\(199\) −5.90084 −0.418300 −0.209150 0.977884i \(-0.567070\pi\)
−0.209150 + 0.977884i \(0.567070\pi\)
\(200\) 0.0651512 0.112845i 0.00460688 0.00797936i
\(201\) 0 0
\(202\) 6.75018 + 11.6917i 0.474941 + 0.822622i
\(203\) −4.69190 0.263526i −0.329307 0.0184959i
\(204\) 0 0
\(205\) −7.19884 −0.502789
\(206\) 1.46258 + 2.53327i 0.101903 + 0.176501i
\(207\) 0 0
\(208\) 3.18376 1.69224i 0.220754 0.117336i
\(209\) 4.14528 0.286735
\(210\) 0 0
\(211\) −11.7856 + 20.4132i −0.811353 + 1.40531i 0.100564 + 0.994931i \(0.467935\pi\)
−0.911917 + 0.410375i \(0.865398\pi\)
\(212\) 4.94074 8.55761i 0.339331 0.587739i
\(213\) 0 0
\(214\) −14.1092 −0.964484
\(215\) 1.18594 2.05411i 0.0808805 0.140089i
\(216\) 0 0
\(217\) 19.1940 + 1.07805i 1.30297 + 0.0731830i
\(218\) 0.723832 1.25371i 0.0490241 0.0849123i
\(219\) 0 0
\(220\) −1.16457 + 2.01709i −0.0785153 + 0.135992i
\(221\) 3.00716 1.59838i 0.202284 0.107519i
\(222\) 0 0
\(223\) −2.87906 + 4.98667i −0.192796 + 0.333932i −0.946176 0.323653i \(-0.895089\pi\)
0.753380 + 0.657586i \(0.228422\pi\)
\(224\) 1.19230 + 2.36187i 0.0796641 + 0.157809i
\(225\) 0 0
\(226\) 1.67707 + 2.90477i 0.111557 + 0.193222i
\(227\) −19.6805 −1.30624 −0.653121 0.757254i \(-0.726541\pi\)
−0.653121 + 0.757254i \(0.726541\pi\)
\(228\) 0 0
\(229\) 10.0430 + 17.3951i 0.663663 + 1.14950i 0.979646 + 0.200733i \(0.0643324\pi\)
−0.315983 + 0.948765i \(0.602334\pi\)
\(230\) −6.87146 11.9017i −0.453091 0.784777i
\(231\) 0 0
\(232\) −0.888084 + 1.53821i −0.0583056 + 0.100988i
\(233\) 2.82261 + 4.88890i 0.184915 + 0.320282i 0.943548 0.331236i \(-0.107466\pi\)
−0.758633 + 0.651518i \(0.774132\pi\)
\(234\) 0 0
\(235\) −5.35526 + 9.27559i −0.349339 + 0.605073i
\(236\) 1.01937 0.0663552
\(237\) 0 0
\(238\) 1.12617 + 2.23086i 0.0729988 + 0.144605i
\(239\) −8.20960 −0.531035 −0.265517 0.964106i \(-0.585543\pi\)
−0.265517 + 0.964106i \(0.585543\pi\)
\(240\) 0 0
\(241\) −21.0169 −1.35382 −0.676908 0.736068i \(-0.736681\pi\)
−0.676908 + 0.736068i \(0.736681\pi\)
\(242\) 4.94299 8.56152i 0.317748 0.550355i
\(243\) 0 0
\(244\) −0.0382184 + 0.0661962i −0.00244668 + 0.00423778i
\(245\) 15.3500 + 1.72976i 0.980677 + 0.110510i
\(246\) 0 0
\(247\) −0.496239 + 14.1519i −0.0315749 + 0.900463i
\(248\) 3.63304 6.29261i 0.230698 0.399581i
\(249\) 0 0
\(250\) −11.3212 −0.716018
\(251\) 12.0281 + 20.8333i 0.759209 + 1.31499i 0.943254 + 0.332071i \(0.107747\pi\)
−0.184045 + 0.982918i \(0.558919\pi\)
\(252\) 0 0
\(253\) −3.28657 5.69251i −0.206625 0.357885i
\(254\) −4.80963 + 8.33053i −0.301783 + 0.522704i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.59910 0.224506 0.112253 0.993680i \(-0.464193\pi\)
0.112253 + 0.993680i \(0.464193\pi\)
\(258\) 0 0
\(259\) 2.69724 + 5.34303i 0.167598 + 0.332000i
\(260\) −6.74690 4.21728i −0.418425 0.261545i
\(261\) 0 0
\(262\) 3.27649 + 5.67504i 0.202422 + 0.350605i
\(263\) −15.1196 26.1880i −0.932317 1.61482i −0.779350 0.626588i \(-0.784451\pi\)
−0.152966 0.988231i \(-0.548883\pi\)
\(264\) 0 0
\(265\) −21.8058 −1.33952
\(266\) −10.3747 0.582706i −0.636112 0.0357280i
\(267\) 0 0
\(268\) 5.85308 + 10.1378i 0.357534 + 0.619266i
\(269\) −10.4393 −0.636494 −0.318247 0.948008i \(-0.603094\pi\)
−0.318247 + 0.948008i \(0.603094\pi\)
\(270\) 0 0
\(271\) −10.6691 −0.648102 −0.324051 0.946040i \(-0.605045\pi\)
−0.324051 + 0.946040i \(0.605045\pi\)
\(272\) 0.944533 0.0572707
\(273\) 0 0
\(274\) −7.12468 −0.430417
\(275\) −0.137530 −0.00829336
\(276\) 0 0
\(277\) 19.0706 1.14584 0.572920 0.819611i \(-0.305810\pi\)
0.572920 + 0.819611i \(0.305810\pi\)
\(278\) −3.09957 5.36862i −0.185900 0.321988i
\(279\) 0 0
\(280\) 3.19819 4.88461i 0.191129 0.291911i
\(281\) −23.3309 −1.39181 −0.695903 0.718136i \(-0.744995\pi\)
−0.695903 + 0.718136i \(0.744995\pi\)
\(282\) 0 0
\(283\) −4.11466 7.12679i −0.244591 0.423644i 0.717426 0.696635i \(-0.245320\pi\)
−0.962017 + 0.272991i \(0.911987\pi\)
\(284\) 4.20868 + 7.28964i 0.249739 + 0.432561i
\(285\) 0 0
\(286\) −3.22699 2.01709i −0.190816 0.119273i
\(287\) 8.61740 + 0.484007i 0.508669 + 0.0285700i
\(288\) 0 0
\(289\) −16.1079 −0.947521
\(290\) 3.91954 0.230163
\(291\) 0 0
\(292\) 6.57264 11.3841i 0.384635 0.666207i
\(293\) −9.34471 16.1855i −0.545924 0.945568i −0.998548 0.0538667i \(-0.982845\pi\)
0.452624 0.891701i \(-0.350488\pi\)
\(294\) 0 0
\(295\) −1.12474 1.94811i −0.0654849 0.113423i
\(296\) 2.26221 0.131488
\(297\) 0 0
\(298\) −10.9374 + 18.9442i −0.633588 + 1.09741i
\(299\) 19.8275 10.5388i 1.14665 0.609475i
\(300\) 0 0
\(301\) −1.55774 + 2.37915i −0.0897868 + 0.137132i
\(302\) 7.25658 12.5688i 0.417569 0.723251i
\(303\) 0 0
\(304\) −1.96372 + 3.40126i −0.112627 + 0.195076i
\(305\) 0.168676 0.00965836
\(306\) 0 0
\(307\) 18.0495 1.03014 0.515069 0.857149i \(-0.327766\pi\)
0.515069 + 0.857149i \(0.327766\pi\)
\(308\) 1.52967 2.33627i 0.0871611 0.133122i
\(309\) 0 0
\(310\) −16.0343 −0.910690
\(311\) 8.46321 14.6587i 0.479905 0.831219i −0.519830 0.854270i \(-0.674005\pi\)
0.999734 + 0.0230506i \(0.00733790\pi\)
\(312\) 0 0
\(313\) −11.0035 19.0587i −0.621957 1.07726i −0.989121 0.147105i \(-0.953004\pi\)
0.367163 0.930156i \(-0.380329\pi\)
\(314\) 2.13538 3.69859i 0.120506 0.208723i
\(315\) 0 0
\(316\) 3.00194 + 5.19951i 0.168872 + 0.292495i
\(317\) −4.46606 7.73544i −0.250839 0.434466i 0.712918 0.701247i \(-0.247373\pi\)
−0.963757 + 0.266782i \(0.914040\pi\)
\(318\) 0 0
\(319\) 1.87469 0.104962
\(320\) −1.10337 1.91109i −0.0616802 0.106833i
\(321\) 0 0
\(322\) 7.42532 + 14.7090i 0.413797 + 0.819701i
\(323\) −1.85480 + 3.21260i −0.103204 + 0.178754i
\(324\) 0 0
\(325\) 0.0164639 0.469523i 0.000913254 0.0260445i
\(326\) −3.03208 + 5.25172i −0.167932 + 0.290866i
\(327\) 0 0
\(328\) 1.63110 2.82515i 0.0900626 0.155993i
\(329\) 7.03418 10.7433i 0.387807 0.592299i
\(330\) 0 0
\(331\) −2.16425 + 3.74859i −0.118958 + 0.206041i −0.919355 0.393429i \(-0.871289\pi\)
0.800397 + 0.599470i \(0.204622\pi\)
\(332\) 1.77617 0.0974799
\(333\) 0 0
\(334\) 7.86930 13.6300i 0.430589 0.745802i
\(335\) 12.9162 22.3715i 0.705688 1.22229i
\(336\) 0 0
\(337\) −0.416096 −0.0226662 −0.0113331 0.999936i \(-0.503608\pi\)
−0.0113331 + 0.999936i \(0.503608\pi\)
\(338\) 7.27262 10.7754i 0.395578 0.586104i
\(339\) 0 0
\(340\) −1.04217 1.80509i −0.0565196 0.0978947i
\(341\) −7.66911 −0.415306
\(342\) 0 0
\(343\) −18.2585 3.10266i −0.985867 0.167528i
\(344\) 0.537418 + 0.930835i 0.0289756 + 0.0501872i
\(345\) 0 0
\(346\) −5.29220 + 9.16635i −0.284510 + 0.492786i
\(347\) −21.7452 −1.16734 −0.583671 0.811990i \(-0.698384\pi\)
−0.583671 + 0.811990i \(0.698384\pi\)
\(348\) 0 0
\(349\) 15.8128 27.3885i 0.846438 1.46607i −0.0379278 0.999280i \(-0.512076\pi\)
0.884366 0.466794i \(-0.154591\pi\)
\(350\) 0.344205 + 0.0193327i 0.0183985 + 0.00103338i
\(351\) 0 0
\(352\) −0.527733 0.914061i −0.0281283 0.0487196i
\(353\) 13.8944 + 24.0658i 0.739523 + 1.28089i 0.952710 + 0.303880i \(0.0982821\pi\)
−0.213188 + 0.977011i \(0.568385\pi\)
\(354\) 0 0
\(355\) 9.28745 16.0863i 0.492927 0.853774i
\(356\) −13.3353 −0.706769
\(357\) 0 0
\(358\) 7.11908 + 12.3306i 0.376255 + 0.651693i
\(359\) −4.17747 7.23559i −0.220478 0.381880i 0.734475 0.678636i \(-0.237428\pi\)
−0.954953 + 0.296756i \(0.904095\pi\)
\(360\) 0 0
\(361\) 1.78761 + 3.09623i 0.0940847 + 0.162959i
\(362\) −13.7312 −0.721693
\(363\) 0 0
\(364\) 7.79286 + 5.50194i 0.408457 + 0.288380i
\(365\) −29.0082 −1.51836
\(366\) 0 0
\(367\) 10.3905 + 17.9969i 0.542379 + 0.939429i 0.998767 + 0.0496476i \(0.0158098\pi\)
−0.456387 + 0.889781i \(0.650857\pi\)
\(368\) 6.22771 0.324642
\(369\) 0 0
\(370\) −2.49605 4.32328i −0.129763 0.224757i
\(371\) 26.1028 + 1.46609i 1.35519 + 0.0761158i
\(372\) 0 0
\(373\) −7.72840 + 13.3860i −0.400161 + 0.693100i −0.993745 0.111672i \(-0.964379\pi\)
0.593584 + 0.804772i \(0.297713\pi\)
\(374\) −0.498462 0.863361i −0.0257748 0.0446433i
\(375\) 0 0
\(376\) −2.42678 4.20330i −0.125151 0.216769i
\(377\) −0.224422 + 6.40013i −0.0115583 + 0.329623i
\(378\) 0 0
\(379\) 12.1123 20.9792i 0.622169 1.07763i −0.366912 0.930256i \(-0.619585\pi\)
0.989081 0.147372i \(-0.0470816\pi\)
\(380\) 8.66684 0.444599
\(381\) 0 0
\(382\) 0.437999 0.758636i 0.0224100 0.0388152i
\(383\) 7.49967 12.9898i 0.383215 0.663749i −0.608304 0.793704i \(-0.708150\pi\)
0.991520 + 0.129955i \(0.0414834\pi\)
\(384\) 0 0
\(385\) −6.15263 0.345570i −0.313567 0.0176119i
\(386\) 11.3312 + 19.6263i 0.576745 + 0.998951i
\(387\) 0 0
\(388\) −8.99467 15.5792i −0.456635 0.790915i
\(389\) −4.37986 + 7.58613i −0.222068 + 0.384632i −0.955436 0.295200i \(-0.904614\pi\)
0.733368 + 0.679832i \(0.237947\pi\)
\(390\) 0 0
\(391\) 5.88228 0.297480
\(392\) −4.15682 + 5.63212i −0.209951 + 0.284465i
\(393\) 0 0
\(394\) −8.44249 + 14.6228i −0.425326 + 0.736687i
\(395\) 6.62449 11.4740i 0.333315 0.577318i
\(396\) 0 0
\(397\) −17.4400 + 30.2070i −0.875289 + 1.51604i −0.0188334 + 0.999823i \(0.505995\pi\)
−0.856455 + 0.516222i \(0.827338\pi\)
\(398\) −5.90084 −0.295783
\(399\) 0 0
\(400\) 0.0651512 0.112845i 0.00325756 0.00564226i
\(401\) 12.9474 0.646565 0.323282 0.946303i \(-0.395214\pi\)
0.323282 + 0.946303i \(0.395214\pi\)
\(402\) 0 0
\(403\) 0.918082 26.1821i 0.0457329 1.30423i
\(404\) 6.75018 + 11.6917i 0.335834 + 0.581682i
\(405\) 0 0
\(406\) −4.69190 0.263526i −0.232855 0.0130786i
\(407\) −1.19384 2.06779i −0.0591765 0.102497i
\(408\) 0 0
\(409\) −34.1242 −1.68733 −0.843666 0.536869i \(-0.819607\pi\)
−0.843666 + 0.536869i \(0.819607\pi\)
\(410\) −7.19884 −0.355525
\(411\) 0 0
\(412\) 1.46258 + 2.53327i 0.0720563 + 0.124805i
\(413\) 1.21540 + 2.40761i 0.0598058 + 0.118471i
\(414\) 0 0
\(415\) −1.95977 3.39442i −0.0962013 0.166626i
\(416\) 3.18376 1.69224i 0.156097 0.0829691i
\(417\) 0 0
\(418\) 4.14528 0.202752
\(419\) −11.0690 + 19.1720i −0.540754 + 0.936613i 0.458107 + 0.888897i \(0.348528\pi\)
−0.998861 + 0.0477160i \(0.984806\pi\)
\(420\) 0 0
\(421\) −31.1012 −1.51578 −0.757890 0.652382i \(-0.773770\pi\)
−0.757890 + 0.652382i \(0.773770\pi\)
\(422\) −11.7856 + 20.4132i −0.573713 + 0.993701i
\(423\) 0 0
\(424\) 4.94074 8.55761i 0.239943 0.415594i
\(425\) 0.0615374 0.106586i 0.00298500 0.00517018i
\(426\) 0 0
\(427\) −0.201914 0.0113408i −0.00977133 0.000548818i
\(428\) −14.1092 −0.681993
\(429\) 0 0
\(430\) 1.18594 2.05411i 0.0571911 0.0990580i
\(431\) 5.65730 + 9.79873i 0.272502 + 0.471988i 0.969502 0.245083i \(-0.0788154\pi\)
−0.697000 + 0.717072i \(0.745482\pi\)
\(432\) 0 0
\(433\) −19.0285 32.9583i −0.914450 1.58387i −0.807704 0.589588i \(-0.799290\pi\)
−0.106746 0.994286i \(-0.534043\pi\)
\(434\) 19.1940 + 1.07805i 0.921341 + 0.0517482i
\(435\) 0 0
\(436\) 0.723832 1.25371i 0.0346653 0.0600420i
\(437\) −12.2295 + 21.1821i −0.585015 + 1.01328i
\(438\) 0 0
\(439\) −2.96609 −0.141564 −0.0707818 0.997492i \(-0.522549\pi\)
−0.0707818 + 0.997492i \(0.522549\pi\)
\(440\) −1.16457 + 2.01709i −0.0555187 + 0.0961612i
\(441\) 0 0
\(442\) 3.00716 1.59838i 0.143036 0.0760272i
\(443\) 10.1253 + 17.5375i 0.481067 + 0.833233i 0.999764 0.0217253i \(-0.00691593\pi\)
−0.518697 + 0.854958i \(0.673583\pi\)
\(444\) 0 0
\(445\) 14.7138 + 25.4850i 0.697499 + 1.20810i
\(446\) −2.87906 + 4.98667i −0.136327 + 0.236126i
\(447\) 0 0
\(448\) 1.19230 + 2.36187i 0.0563311 + 0.111588i
\(449\) −5.97830 10.3547i −0.282133 0.488669i 0.689777 0.724022i \(-0.257709\pi\)
−0.971910 + 0.235353i \(0.924375\pi\)
\(450\) 0 0
\(451\) −3.44315 −0.162132
\(452\) 1.67707 + 2.90477i 0.0788826 + 0.136629i
\(453\) 0 0
\(454\) −19.6805 −0.923652
\(455\) 1.91631 20.9635i 0.0898379 0.982786i
\(456\) 0 0
\(457\) 23.0842 1.07983 0.539916 0.841719i \(-0.318456\pi\)
0.539916 + 0.841719i \(0.318456\pi\)
\(458\) 10.0430 + 17.3951i 0.469281 + 0.812818i
\(459\) 0 0
\(460\) −6.87146 11.9017i −0.320384 0.554921i
\(461\) 9.46131 + 16.3875i 0.440657 + 0.763240i 0.997738 0.0672176i \(-0.0214122\pi\)
−0.557081 + 0.830458i \(0.688079\pi\)
\(462\) 0 0
\(463\) −32.7770 −1.52328 −0.761638 0.648002i \(-0.775605\pi\)
−0.761638 + 0.648002i \(0.775605\pi\)
\(464\) −0.888084 + 1.53821i −0.0412283 + 0.0714094i
\(465\) 0 0
\(466\) 2.82261 + 4.88890i 0.130755 + 0.226474i
\(467\) 10.7307 + 18.5861i 0.496557 + 0.860061i 0.999992 0.00397163i \(-0.00126421\pi\)
−0.503436 + 0.864033i \(0.667931\pi\)
\(468\) 0 0
\(469\) −16.9655 + 25.9116i −0.783396 + 1.19648i
\(470\) −5.35526 + 9.27559i −0.247020 + 0.427851i
\(471\) 0 0
\(472\) 1.01937 0.0469202
\(473\) 0.567227 0.982465i 0.0260811 0.0451738i
\(474\) 0 0
\(475\) 0.255877 + 0.443193i 0.0117405 + 0.0203351i
\(476\) 1.12617 + 2.23086i 0.0516179 + 0.102251i
\(477\) 0 0
\(478\) −8.20960 −0.375498
\(479\) −15.9460 27.6194i −0.728593 1.26196i −0.957478 0.288507i \(-0.906841\pi\)
0.228884 0.973454i \(-0.426492\pi\)
\(480\) 0 0
\(481\) 7.20231 3.82821i 0.328397 0.174551i
\(482\) −21.0169 −0.957293
\(483\) 0 0
\(484\) 4.94299 8.56152i 0.224682 0.389160i
\(485\) −19.8489 + 34.3793i −0.901291 + 1.56108i
\(486\) 0 0
\(487\) 0.744679 0.0337446 0.0168723 0.999858i \(-0.494629\pi\)
0.0168723 + 0.999858i \(0.494629\pi\)
\(488\) −0.0382184 + 0.0661962i −0.00173007 + 0.00299656i
\(489\) 0 0
\(490\) 15.3500 + 1.72976i 0.693443 + 0.0781426i
\(491\) 20.5033 35.5127i 0.925301 1.60267i 0.134224 0.990951i \(-0.457146\pi\)
0.791077 0.611717i \(-0.209521\pi\)
\(492\) 0 0
\(493\) −0.838824 + 1.45289i −0.0377788 + 0.0654347i
\(494\) −0.496239 + 14.1519i −0.0223268 + 0.636724i
\(495\) 0 0
\(496\) 3.63304 6.29261i 0.163128 0.282547i
\(497\) −12.1991 + 18.6318i −0.547206 + 0.835750i
\(498\) 0 0
\(499\) 5.61372 + 9.72324i 0.251305 + 0.435272i 0.963885 0.266318i \(-0.0858071\pi\)
−0.712581 + 0.701590i \(0.752474\pi\)
\(500\) −11.3212 −0.506301
\(501\) 0 0
\(502\) 12.0281 + 20.8333i 0.536842 + 0.929837i
\(503\) 19.4719 + 33.7264i 0.868211 + 1.50379i 0.863823 + 0.503796i \(0.168064\pi\)
0.00438828 + 0.999990i \(0.498603\pi\)
\(504\) 0 0
\(505\) 14.8959 25.8004i 0.662859 1.14810i
\(506\) −3.28657 5.69251i −0.146106 0.253063i
\(507\) 0 0
\(508\) −4.80963 + 8.33053i −0.213393 + 0.369608i
\(509\) 21.6152 0.958079 0.479039 0.877793i \(-0.340985\pi\)
0.479039 + 0.877793i \(0.340985\pi\)
\(510\) 0 0
\(511\) 34.7244 + 1.95034i 1.53612 + 0.0862779i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 3.59910 0.158749
\(515\) 3.22754 5.59026i 0.142222 0.246336i
\(516\) 0 0
\(517\) −2.56138 + 4.43644i −0.112649 + 0.195115i
\(518\) 2.69724 + 5.34303i 0.118510 + 0.234759i
\(519\) 0 0
\(520\) −6.74690 4.21728i −0.295871 0.184940i
\(521\) −3.75964 + 6.51188i −0.164713 + 0.285291i −0.936553 0.350525i \(-0.886003\pi\)
0.771840 + 0.635816i \(0.219336\pi\)
\(522\) 0 0
\(523\) 33.6196 1.47008 0.735041 0.678023i \(-0.237163\pi\)
0.735041 + 0.678023i \(0.237163\pi\)
\(524\) 3.27649 + 5.67504i 0.143134 + 0.247915i
\(525\) 0 0
\(526\) −15.1196 26.1880i −0.659247 1.14185i
\(527\) 3.43153 5.94358i 0.149480 0.258906i
\(528\) 0 0
\(529\) 15.7844 0.686276
\(530\) −21.8058 −0.947185
\(531\) 0 0
\(532\) −10.3747 0.582706i −0.449799 0.0252635i
\(533\) 0.412185 11.7548i 0.0178537 0.509158i
\(534\) 0 0
\(535\) 15.5676 + 26.9640i 0.673048 + 1.16575i
\(536\) 5.85308 + 10.1378i 0.252814 + 0.437888i
\(537\) 0 0
\(538\) −10.4393 −0.450069
\(539\) 7.34180 + 0.827332i 0.316234 + 0.0356357i
\(540\) 0 0
\(541\) 3.62006 + 6.27013i 0.155639 + 0.269574i 0.933291 0.359120i \(-0.116923\pi\)
−0.777653 + 0.628694i \(0.783590\pi\)
\(542\) −10.6691 −0.458278
\(543\) 0 0
\(544\) 0.944533 0.0404965
\(545\) −3.19462 −0.136842
\(546\) 0 0
\(547\) 13.7236 0.586779 0.293390 0.955993i \(-0.405217\pi\)
0.293390 + 0.955993i \(0.405217\pi\)
\(548\) −7.12468 −0.304351
\(549\) 0 0
\(550\) −0.137530 −0.00586429
\(551\) −3.48790 6.04121i −0.148589 0.257364i
\(552\) 0 0
\(553\) −8.70132 + 13.2896i −0.370018 + 0.565130i
\(554\) 19.0706 0.810232
\(555\) 0 0
\(556\) −3.09957 5.36862i −0.131451 0.227680i
\(557\) −11.6122 20.1129i −0.492024 0.852210i 0.507934 0.861396i \(-0.330409\pi\)
−0.999958 + 0.00918575i \(0.997076\pi\)
\(558\) 0 0
\(559\) 3.28621 + 2.05411i 0.138992 + 0.0868796i
\(560\) 3.19819 4.88461i 0.135148 0.206413i
\(561\) 0 0
\(562\) −23.3309 −0.984155
\(563\) 15.6123 0.657981 0.328990 0.944333i \(-0.393292\pi\)
0.328990 + 0.944333i \(0.393292\pi\)
\(564\) 0 0
\(565\) 3.70085 6.41006i 0.155696 0.269673i
\(566\) −4.11466 7.12679i −0.172952 0.299561i
\(567\) 0 0
\(568\) 4.20868 + 7.28964i 0.176592 + 0.305867i
\(569\) 13.3032 0.557698 0.278849 0.960335i \(-0.410047\pi\)
0.278849 + 0.960335i \(0.410047\pi\)
\(570\) 0 0
\(571\) 15.4972 26.8420i 0.648539 1.12330i −0.334933 0.942242i \(-0.608714\pi\)
0.983472 0.181061i \(-0.0579530\pi\)
\(572\) −3.22699 2.01709i −0.134927 0.0843390i
\(573\) 0 0
\(574\) 8.61740 + 0.484007i 0.359684 + 0.0202020i
\(575\) 0.405743 0.702767i 0.0169206 0.0293074i
\(576\) 0 0
\(577\) −22.8416 + 39.5629i −0.950910 + 1.64702i −0.207449 + 0.978246i \(0.566516\pi\)
−0.743462 + 0.668779i \(0.766817\pi\)
\(578\) −16.1079 −0.669999
\(579\) 0 0
\(580\) 3.91954 0.162750
\(581\) 2.11773 + 4.19507i 0.0878583 + 0.174041i
\(582\) 0 0
\(583\) −10.4296 −0.431949
\(584\) 6.57264 11.3841i 0.271978 0.471079i
\(585\) 0 0
\(586\) −9.34471 16.1855i −0.386027 0.668618i
\(587\) 1.75183 3.03426i 0.0723057 0.125237i −0.827606 0.561310i \(-0.810298\pi\)
0.899911 + 0.436073i \(0.143631\pi\)
\(588\) 0 0
\(589\) 14.2686 + 24.7139i 0.587925 + 1.01832i
\(590\) −1.12474 1.94811i −0.0463048 0.0802023i
\(591\) 0 0
\(592\) 2.26221 0.0929761
\(593\) 6.29875 + 10.9098i 0.258659 + 0.448010i 0.965883 0.258979i \(-0.0833862\pi\)
−0.707224 + 0.706989i \(0.750053\pi\)
\(594\) 0 0
\(595\) 3.02080 4.61368i 0.123841 0.189142i
\(596\) −10.9374 + 18.9442i −0.448014 + 0.775983i
\(597\) 0 0
\(598\) 19.8275 10.5388i 0.810807 0.430964i
\(599\) 15.2844 26.4733i 0.624503 1.08167i −0.364134 0.931347i \(-0.618635\pi\)
0.988637 0.150324i \(-0.0480318\pi\)
\(600\) 0 0
\(601\) 7.11682 12.3267i 0.290301 0.502817i −0.683580 0.729876i \(-0.739578\pi\)
0.973881 + 0.227059i \(0.0729112\pi\)
\(602\) −1.55774 + 2.37915i −0.0634888 + 0.0969668i
\(603\) 0 0
\(604\) 7.25658 12.5688i 0.295266 0.511416i
\(605\) −21.8158 −0.886938
\(606\) 0 0
\(607\) −1.20981 + 2.09546i −0.0491049 + 0.0850521i −0.889533 0.456871i \(-0.848970\pi\)
0.840428 + 0.541923i \(0.182304\pi\)
\(608\) −1.96372 + 3.40126i −0.0796394 + 0.137939i
\(609\) 0 0
\(610\) 0.168676 0.00682949
\(611\) −14.8393 9.27559i −0.600333 0.375250i
\(612\) 0 0
\(613\) −0.269478 0.466750i −0.0108841 0.0188518i 0.860532 0.509396i \(-0.170131\pi\)
−0.871416 + 0.490544i \(0.836798\pi\)
\(614\) 18.0495 0.728418
\(615\) 0 0
\(616\) 1.52967 2.33627i 0.0616322 0.0941312i
\(617\) −22.1866 38.4283i −0.893198 1.54706i −0.836020 0.548700i \(-0.815123\pi\)
−0.0571781 0.998364i \(-0.518210\pi\)
\(618\) 0 0
\(619\) 9.10976 15.7786i 0.366152 0.634194i −0.622808 0.782375i \(-0.714008\pi\)
0.988960 + 0.148180i \(0.0473416\pi\)
\(620\) −16.0343 −0.643955
\(621\) 0 0
\(622\) 8.46321 14.6587i 0.339344 0.587761i
\(623\) −15.8997 31.4962i −0.637009 1.26187i
\(624\) 0 0
\(625\) 12.1658 + 21.0717i 0.486630 + 0.842868i
\(626\) −11.0035 19.0587i −0.439790 0.761739i
\(627\) 0 0
\(628\) 2.13538 3.69859i 0.0852110 0.147590i
\(629\) 2.13673 0.0851969
\(630\) 0 0
\(631\) −1.76140 3.05083i −0.0701200 0.121451i 0.828834 0.559495i \(-0.189005\pi\)
−0.898954 + 0.438044i \(0.855672\pi\)
\(632\) 3.00194 + 5.19951i 0.119411 + 0.206825i
\(633\) 0 0
\(634\) −4.46606 7.73544i −0.177370 0.307214i
\(635\) 21.2272 0.842376
\(636\) 0 0
\(637\) −3.70339 + 24.9657i −0.146734 + 0.989176i
\(638\) 1.87469 0.0742195
\(639\) 0 0
\(640\) −1.10337 1.91109i −0.0436145 0.0755426i
\(641\) 27.2176 1.07503 0.537515 0.843254i \(-0.319363\pi\)
0.537515 + 0.843254i \(0.319363\pi\)
\(642\) 0 0
\(643\) −20.1450 34.8922i −0.794442 1.37601i −0.923193 0.384338i \(-0.874430\pi\)
0.128750 0.991677i \(-0.458903\pi\)
\(644\) 7.42532 + 14.7090i 0.292599 + 0.579616i
\(645\) 0 0
\(646\) −1.85480 + 3.21260i −0.0729761 + 0.126398i
\(647\) −15.5929 27.0077i −0.613020 1.06178i −0.990728 0.135857i \(-0.956621\pi\)
0.377709 0.925925i \(-0.376712\pi\)
\(648\) 0 0
\(649\) −0.537955 0.931765i −0.0211166 0.0365750i
\(650\) 0.0164639 0.469523i 0.000645768 0.0184162i
\(651\) 0 0
\(652\) −3.03208 + 5.25172i −0.118746 + 0.205673i
\(653\) −0.465996 −0.0182358 −0.00911792 0.999958i \(-0.502902\pi\)
−0.00911792 + 0.999958i \(0.502902\pi\)
\(654\) 0 0
\(655\) 7.23035 12.5233i 0.282513 0.489327i
\(656\) 1.63110 2.82515i 0.0636839 0.110304i
\(657\) 0 0
\(658\) 7.03418 10.7433i 0.274221 0.418819i
\(659\) 22.1490 + 38.3632i 0.862803 + 1.49442i 0.869212 + 0.494439i \(0.164627\pi\)
−0.00640903 + 0.999979i \(0.502040\pi\)
\(660\) 0 0
\(661\) −15.9918 27.6986i −0.622008 1.07735i −0.989111 0.147169i \(-0.952984\pi\)
0.367103 0.930180i \(-0.380350\pi\)
\(662\) −2.16425 + 3.74859i −0.0841160 + 0.145693i
\(663\) 0 0
\(664\) 1.77617 0.0689287
\(665\) 10.3335 + 20.4699i 0.400716 + 0.793789i
\(666\) 0 0
\(667\) −5.53073 + 9.57950i −0.214151 + 0.370920i
\(668\) 7.86930 13.6300i 0.304472 0.527361i
\(669\) 0 0
\(670\) 12.9162 22.3715i 0.498997 0.864288i
\(671\) 0.0806765 0.00311448
\(672\) 0 0
\(673\) 2.49379 4.31938i 0.0961286 0.166500i −0.813950 0.580934i \(-0.802687\pi\)
0.910079 + 0.414435i \(0.136021\pi\)
\(674\) −0.416096 −0.0160274
\(675\) 0 0
\(676\) 7.27262 10.7754i 0.279716 0.414438i
\(677\) 17.6543 + 30.5782i 0.678511 + 1.17522i 0.975429 + 0.220312i \(0.0707076\pi\)
−0.296919 + 0.954903i \(0.595959\pi\)
\(678\) 0 0
\(679\) 26.0717 39.8194i 1.00054 1.52813i
\(680\) −1.04217 1.80509i −0.0399654 0.0692220i
\(681\) 0 0
\(682\) −7.66911 −0.293665
\(683\) 35.6076 1.36249 0.681243 0.732057i \(-0.261440\pi\)
0.681243 + 0.732057i \(0.261440\pi\)
\(684\) 0 0
\(685\) 7.86115 + 13.6159i 0.300359 + 0.520237i
\(686\) −18.2585 3.10266i −0.697113 0.118460i
\(687\) 0 0
\(688\) 0.537418 + 0.930835i 0.0204889 + 0.0354877i
\(689\) 1.24854 35.6063i 0.0475656 1.35649i
\(690\) 0 0
\(691\) −17.0171 −0.647361 −0.323680 0.946166i \(-0.604920\pi\)
−0.323680 + 0.946166i \(0.604920\pi\)
\(692\) −5.29220 + 9.16635i −0.201179 + 0.348452i
\(693\) 0 0
\(694\) −21.7452 −0.825435
\(695\) −6.83995 + 11.8471i −0.259454 + 0.449388i
\(696\) 0 0
\(697\) 1.54063 2.66845i 0.0583555 0.101075i
\(698\) 15.8128 27.3885i 0.598522 1.03667i
\(699\) 0 0
\(700\) 0.344205 + 0.0193327i 0.0130097 + 0.000730707i
\(701\) 24.2469 0.915792 0.457896 0.889006i \(-0.348603\pi\)
0.457896 + 0.889006i \(0.348603\pi\)
\(702\) 0 0
\(703\) −4.44234 + 7.69436i −0.167546 + 0.290198i
\(704\) −0.527733 0.914061i −0.0198897 0.0344500i
\(705\) 0 0
\(706\) 13.8944 + 24.0658i 0.522922 + 0.905727i
\(707\) −19.5659 + 29.8830i −0.735850 + 1.12387i
\(708\) 0 0
\(709\) −3.13933 + 5.43748i −0.117900 + 0.204209i −0.918935 0.394408i \(-0.870950\pi\)
0.801035 + 0.598617i \(0.204283\pi\)
\(710\) 9.28745 16.0863i 0.348552 0.603710i
\(711\) 0 0
\(712\) −13.3353 −0.499761
\(713\) 22.6255 39.1886i 0.847333 1.46762i
\(714\) 0 0
\(715\) −0.294291 + 8.39268i −0.0110059 + 0.313868i
\(716\) 7.11908 + 12.3306i 0.266053 + 0.460816i
\(717\) 0 0
\(718\) −4.17747 7.23559i −0.155902 0.270030i
\(719\) −9.96438 + 17.2588i −0.371609 + 0.643645i −0.989813 0.142372i \(-0.954527\pi\)
0.618204 + 0.786017i \(0.287860\pi\)
\(720\) 0 0
\(721\) −4.23940 + 6.47485i −0.157883 + 0.241136i
\(722\) 1.78761 + 3.09623i 0.0665279 + 0.115230i
\(723\) 0 0
\(724\) −13.7312 −0.510314
\(725\) 0.115719 + 0.200432i 0.00429771 + 0.00744385i
\(726\) 0 0
\(727\) 10.1916 0.377984 0.188992 0.981979i \(-0.439478\pi\)
0.188992 + 0.981979i \(0.439478\pi\)
\(728\) 7.79286 + 5.50194i 0.288823 + 0.203915i
\(729\) 0 0
\(730\) −29.0082 −1.07364
\(731\) 0.507609 + 0.879204i 0.0187746 + 0.0325185i
\(732\) 0 0
\(733\) 14.7321 + 25.5168i 0.544144 + 0.942485i 0.998660 + 0.0517467i \(0.0164788\pi\)
−0.454516 + 0.890738i \(0.650188\pi\)
\(734\) 10.3905 + 17.9969i 0.383520 + 0.664276i
\(735\) 0 0
\(736\) 6.22771 0.229556
\(737\) 6.17773 10.7001i 0.227560 0.394145i
\(738\) 0 0
\(739\) −16.3475 28.3148i −0.601354 1.04158i −0.992616 0.121296i \(-0.961295\pi\)
0.391263 0.920279i \(-0.372038\pi\)
\(740\) −2.49605 4.32328i −0.0917566 0.158927i
\(741\) 0 0
\(742\) 26.1028 + 1.46609i 0.958263 + 0.0538220i
\(743\) 10.7085 18.5477i 0.392857 0.680448i −0.599968 0.800024i \(-0.704820\pi\)
0.992825 + 0.119576i \(0.0381535\pi\)
\(744\) 0 0
\(745\) 48.2720 1.76855
\(746\) −7.72840 + 13.3860i −0.282957 + 0.490096i
\(747\) 0 0
\(748\) −0.498462 0.863361i −0.0182256 0.0315676i
\(749\) −16.8224 33.3240i −0.614678 1.21763i
\(750\) 0 0
\(751\) −31.4156 −1.14637 −0.573185 0.819426i \(-0.694292\pi\)
−0.573185 + 0.819426i \(0.694292\pi\)
\(752\) −2.42678 4.20330i −0.0884954 0.153279i
\(753\) 0 0
\(754\) −0.224422 + 6.40013i −0.00817296 + 0.233079i
\(755\) −32.0268 −1.16557
\(756\) 0 0
\(757\) −9.28891 + 16.0889i −0.337611 + 0.584760i −0.983983 0.178263i \(-0.942952\pi\)
0.646372 + 0.763023i \(0.276286\pi\)
\(758\) 12.1123 20.9792i 0.439940 0.761998i
\(759\) 0 0
\(760\) 8.66684 0.314379
\(761\) 12.9141 22.3679i 0.468137 0.810838i −0.531200 0.847247i \(-0.678259\pi\)
0.999337 + 0.0364091i \(0.0115919\pi\)
\(762\) 0 0
\(763\) 3.82413 + 0.214787i 0.138443 + 0.00777581i
\(764\) 0.437999 0.758636i 0.0158462 0.0274465i
\(765\) 0 0
\(766\) 7.49967 12.9898i 0.270974 0.469341i
\(767\) 3.24542 1.72502i 0.117185 0.0622869i
\(768\) 0 0
\(769\) −9.92009 + 17.1821i −0.357727 + 0.619602i −0.987581 0.157112i \(-0.949782\pi\)
0.629853 + 0.776714i \(0.283115\pi\)
\(770\) −6.15263 0.345570i −0.221725 0.0124535i
\(771\) 0 0
\(772\) 11.3312 + 19.6263i 0.407820 + 0.706365i
\(773\) −43.0325 −1.54777 −0.773885 0.633326i \(-0.781689\pi\)
−0.773885 + 0.633326i \(0.781689\pi\)
\(774\) 0 0
\(775\) −0.473394 0.819942i −0.0170048 0.0294532i
\(776\) −8.99467 15.5792i −0.322890 0.559261i
\(777\) 0 0
\(778\) −4.37986 + 7.58613i −0.157025 + 0.271976i
\(779\) 6.40606 + 11.0956i 0.229521 + 0.397542i
\(780\) 0 0
\(781\) 4.44212 7.69398i 0.158952 0.275312i
\(782\) 5.88228 0.210350
\(783\) 0 0
\(784\) −4.15682 + 5.63212i −0.148458 + 0.201147i
\(785\) −9.42445 −0.336373
\(786\) 0 0
\(787\) −9.28254 −0.330887 −0.165443 0.986219i \(-0.552906\pi\)
−0.165443 + 0.986219i \(0.552906\pi\)
\(788\) −8.44249 + 14.6228i −0.300751 + 0.520916i
\(789\) 0 0
\(790\) 6.62449 11.4740i 0.235689 0.408225i
\(791\) −4.86110 + 7.42437i −0.172841 + 0.263980i
\(792\) 0 0
\(793\) −0.00965792 + 0.275427i −0.000342963 + 0.00978072i
\(794\) −17.4400 + 30.2070i −0.618922 + 1.07201i
\(795\) 0 0
\(796\) −5.90084 −0.209150
\(797\) −19.2169 33.2847i −0.680698 1.17900i −0.974768 0.223219i \(-0.928343\pi\)
0.294071 0.955784i \(-0.404990\pi\)
\(798\) 0 0
\(799\) −2.29217 3.97016i −0.0810912 0.140454i
\(800\) 0.0651512 0.112845i 0.00230344 0.00398968i
\(801\) 0 0
\(802\) 12.9474 0.457190
\(803\) −13.8744 −0.489617
\(804\) 0 0
\(805\) 19.9174 30.4200i 0.701997 1.07216i
\(806\) 0.918082 26.1821i 0.0323381 0.922227i
\(807\) 0 0
\(808\) 6.75018 + 11.6917i 0.237471 + 0.411311i
\(809\) 15.7351 + 27.2540i 0.553217 + 0.958200i 0.998040 + 0.0625814i \(0.0199333\pi\)
−0.444823 + 0.895619i \(0.646733\pi\)
\(810\) 0 0
\(811\) 50.9386 1.78870 0.894348 0.447373i \(-0.147640\pi\)
0.894348 + 0.447373i \(0.147640\pi\)
\(812\) −4.69190 0.263526i −0.164654 0.00924796i
\(813\) 0 0
\(814\) −1.19384 2.06779i −0.0418441 0.0724762i
\(815\) 13.3820 0.468752
\(816\) 0 0
\(817\) −4.22135 −0.147686
\(818\) −34.1242 −1.19312
\(819\) 0 0
\(820\) −7.19884 −0.251394
\(821\) −40.3254 −1.40736 −0.703682 0.710515i \(-0.748462\pi\)
−0.703682 + 0.710515i \(0.748462\pi\)
\(822\) 0 0
\(823\) 21.4715 0.748450 0.374225 0.927338i \(-0.377909\pi\)
0.374225 + 0.927338i \(0.377909\pi\)
\(824\) 1.46258 + 2.53327i 0.0509515 + 0.0882505i
\(825\) 0 0
\(826\) 1.21540 + 2.40761i 0.0422891 + 0.0837715i
\(827\) 48.0554 1.67105 0.835525 0.549452i \(-0.185164\pi\)
0.835525 + 0.549452i \(0.185164\pi\)
\(828\) 0 0
\(829\) −4.41512 7.64722i −0.153344 0.265599i 0.779111 0.626886i \(-0.215671\pi\)
−0.932455 + 0.361287i \(0.882337\pi\)
\(830\) −1.95977 3.39442i −0.0680246 0.117822i
\(831\) 0 0
\(832\) 3.18376 1.69224i 0.110377 0.0586680i
\(833\) −3.92626 + 5.31973i −0.136037 + 0.184318i
\(834\) 0 0
\(835\) −34.7310 −1.20191
\(836\) 4.14528 0.143368
\(837\) 0 0
\(838\) −11.0690 + 19.1720i −0.382371 + 0.662285i
\(839\) 10.3799 + 17.9786i 0.358355 + 0.620689i 0.987686 0.156448i \(-0.0500043\pi\)
−0.629331 + 0.777137i \(0.716671\pi\)
\(840\) 0 0
\(841\) 12.9226 + 22.3826i 0.445607 + 0.771815i
\(842\) −31.1012 −1.07182
\(843\) 0 0
\(844\) −11.7856 + 20.4132i −0.405677 + 0.702653i
\(845\) −28.6171 2.00940i −0.984460 0.0691256i
\(846\) 0 0
\(847\) 26.1147 + 1.46676i 0.897312 + 0.0503986i
\(848\) 4.94074 8.55761i 0.169666 0.293869i
\(849\) 0 0
\(850\) 0.0615374 0.106586i 0.00211072 0.00365587i
\(851\) 14.0884 0.482943
\(852\) 0 0
\(853\) 9.67377 0.331224 0.165612 0.986191i \(-0.447040\pi\)
0.165612 + 0.986191i \(0.447040\pi\)
\(854\) −0.201914 0.0113408i −0.00690937 0.000388073i
\(855\) 0 0
\(856\) −14.1092 −0.482242
\(857\) −5.94275 + 10.2931i −0.203000 + 0.351607i −0.949494 0.313786i \(-0.898403\pi\)
0.746493 + 0.665393i \(0.231736\pi\)
\(858\) 0 0
\(859\) −12.4094 21.4937i −0.423404 0.733357i 0.572866 0.819649i \(-0.305832\pi\)
−0.996270 + 0.0862919i \(0.972498\pi\)
\(860\) 1.18594 2.05411i 0.0404402 0.0700446i
\(861\) 0 0
\(862\) 5.65730 + 9.79873i 0.192688 + 0.333746i
\(863\) 19.3325 + 33.4848i 0.658084 + 1.13984i 0.981111 + 0.193446i \(0.0619663\pi\)
−0.323027 + 0.946390i \(0.604700\pi\)
\(864\) 0 0
\(865\) 23.3570 0.794162
\(866\) −19.0285 32.9583i −0.646614 1.11997i
\(867\) 0 0
\(868\) 19.1940 + 1.07805i 0.651487 + 0.0365915i
\(869\) 3.16845 5.48791i 0.107482 0.186165i
\(870\) 0 0
\(871\) 35.7905 + 22.3715i 1.21271 + 0.758031i
\(872\) 0.723832 1.25371i 0.0245121 0.0424561i
\(873\) 0 0
\(874\) −12.2295 + 21.1821i −0.413668 + 0.716494i
\(875\) −13.4984 26.7393i −0.456328 0.903952i
\(876\) 0 0
\(877\) −27.8476 + 48.2335i −0.940347 + 1.62873i −0.175537 + 0.984473i \(0.556166\pi\)
−0.764810 + 0.644256i \(0.777167\pi\)
\(878\) −2.96609 −0.100101
\(879\) 0 0
\(880\) −1.16457 + 2.01709i −0.0392577 + 0.0679962i
\(881\) 1.98870 3.44454i 0.0670011 0.116049i −0.830579 0.556901i \(-0.811990\pi\)
0.897580 + 0.440852i \(0.145324\pi\)
\(882\) 0 0
\(883\) −10.3816 −0.349370 −0.174685 0.984624i \(-0.555891\pi\)
−0.174685 + 0.984624i \(0.555891\pi\)
\(884\) 3.00716 1.59838i 0.101142 0.0537594i
\(885\) 0 0
\(886\) 10.1253 + 17.5375i 0.340166 + 0.589185i
\(887\) 1.35095 0.0453604 0.0226802 0.999743i \(-0.492780\pi\)
0.0226802 + 0.999743i \(0.492780\pi\)
\(888\) 0 0
\(889\) −25.4101 1.42719i −0.852229 0.0478664i
\(890\) 14.7138 + 25.4850i 0.493206 + 0.854258i
\(891\) 0 0
\(892\) −2.87906 + 4.98667i −0.0963979 + 0.166966i
\(893\) 19.0620 0.637887
\(894\) 0 0
\(895\) 15.7100 27.2104i 0.525126 0.909545i
\(896\) 1.19230 + 2.36187i 0.0398321 + 0.0789044i
\(897\) 0 0
\(898\) −5.97830 10.3547i −0.199498 0.345541i
\(899\) 6.45289 + 11.1767i 0.215216 + 0.372765i
\(900\) 0 0
\(901\) 4.66669 8.08294i 0.155470 0.269282i
\(902\) −3.44315 −0.114644
\(903\) 0 0
\(904\) 1.67707 + 2.90477i 0.0557784 + 0.0966111i
\(905\) 15.1505 + 26.2415i 0.503621 + 0.872297i
\(906\) 0 0
\(907\) −13.3731 23.1628i −0.444045 0.769109i 0.553940 0.832557i \(-0.313124\pi\)
−0.997985 + 0.0634476i \(0.979790\pi\)
\(908\) −19.6805 −0.653121
\(909\) 0 0
\(910\) 1.91631 20.9635i 0.0635250 0.694935i
\(911\) 13.3116 0.441034 0.220517 0.975383i \(-0.429226\pi\)
0.220517 + 0.975383i \(0.429226\pi\)
\(912\) 0 0
\(913\) −0.937343 1.62353i −0.0310215 0.0537309i
\(914\) 23.0842 0.763557
\(915\) 0 0
\(916\) 10.0430 + 17.3951i 0.331831 + 0.574749i
\(917\) −9.49712 + 14.5050i −0.313623 + 0.478997i
\(918\) 0 0
\(919\) −16.4317 + 28.4606i −0.542032 + 0.938827i 0.456755 + 0.889592i \(0.349012\pi\)
−0.998787 + 0.0492346i \(0.984322\pi\)
\(920\) −6.87146 11.9017i −0.226545 0.392388i
\(921\) 0 0
\(922\) 9.46131 + 16.3875i 0.311592 + 0.539692i
\(923\) 25.7353 + 16.0863i 0.847087 + 0.529488i
\(924\) 0 0
\(925\) 0.147385 0.255279i 0.00484600 0.00839352i
\(926\) −32.7770 −1.07712
\(927\) 0 0
\(928\) −0.888084 + 1.53821i −0.0291528 + 0.0504941i
\(929\) 22.3652 38.7377i 0.733780 1.27094i −0.221477 0.975166i \(-0.571088\pi\)
0.955257 0.295779i \(-0.0955790\pi\)
\(930\) 0 0
\(931\) −10.9935 25.1984i −0.360297 0.825843i
\(932\) 2.82261 + 4.88890i 0.0924575 + 0.160141i
\(933\) 0 0
\(934\) 10.7307 + 18.5861i 0.351118 + 0.608155i
\(935\) −1.09997 + 1.90521i −0.0359730 + 0.0623071i
\(936\) 0 0
\(937\) 26.6286 0.869917 0.434958 0.900451i \(-0.356763\pi\)
0.434958 + 0.900451i \(0.356763\pi\)
\(938\) −16.9655 + 25.9116i −0.553945 + 0.846042i
\(939\) 0 0
\(940\) −5.35526 + 9.27559i −0.174669 + 0.302536i
\(941\) 5.48027 9.49210i 0.178652 0.309434i −0.762767 0.646673i \(-0.776160\pi\)
0.941419 + 0.337239i \(0.109493\pi\)
\(942\) 0 0
\(943\) 10.1580 17.5942i 0.330791 0.572947i
\(944\) 1.01937 0.0331776
\(945\) 0 0
\(946\) 0.567227 0.982465i 0.0184421 0.0319427i
\(947\) 53.7000 1.74501 0.872507 0.488602i \(-0.162493\pi\)
0.872507 + 0.488602i \(0.162493\pi\)
\(948\) 0 0
\(949\) 1.66093 47.3669i 0.0539160 1.53759i
\(950\) 0.255877 + 0.443193i 0.00830176 + 0.0143791i
\(951\) 0 0
\(952\) 1.12617 + 2.23086i 0.0364994 + 0.0723026i
\(953\) −15.5264 26.8924i −0.502948 0.871131i −0.999994 0.00340721i \(-0.998915\pi\)
0.497046 0.867724i \(-0.334418\pi\)
\(954\) 0 0
\(955\) −1.93310 −0.0625536
\(956\) −8.20960 −0.265517
\(957\) 0 0
\(958\) −15.9460 27.6194i −0.515193 0.892341i
\(959\) −8.49478 16.8275i −0.274311 0.543389i
\(960\) 0 0
\(961\) −10.8980 18.8759i −0.351548 0.608898i
\(962\) 7.20231 3.82821i 0.232212 0.123426i
\(963\) 0 0
\(964\) −21.0169 −0.676908
\(965\) 25.0051 43.3101i 0.804942 1.39420i
\(966\) 0 0
\(967\) −49.7062 −1.59844 −0.799221 0.601037i \(-0.794754\pi\)
−0.799221 + 0.601037i \(0.794754\pi\)
\(968\) 4.94299 8.56152i 0.158874 0.275178i
\(969\) 0 0
\(970\) −19.8489 + 34.3793i −0.637309 + 1.10385i
\(971\) −25.5570 + 44.2660i −0.820163 + 1.42056i 0.0853971 + 0.996347i \(0.472784\pi\)
−0.905560 + 0.424217i \(0.860549\pi\)
\(972\) 0 0
\(973\) 8.98433 13.7218i 0.288024 0.439901i
\(974\) 0.744679 0.0238610
\(975\) 0 0
\(976\) −0.0382184 + 0.0661962i −0.00122334 + 0.00211889i
\(977\) −2.31793 4.01477i −0.0741571 0.128444i 0.826562 0.562845i \(-0.190293\pi\)
−0.900719 + 0.434401i \(0.856960\pi\)
\(978\) 0 0
\(979\) 7.03748 + 12.1893i 0.224919 + 0.389571i
\(980\) 15.3500 + 1.72976i 0.490338 + 0.0552552i
\(981\) 0 0
\(982\) 20.5033 35.5127i 0.654286 1.13326i
\(983\) −5.80348 + 10.0519i −0.185102 + 0.320607i −0.943611 0.331056i \(-0.892595\pi\)
0.758509 + 0.651663i \(0.225928\pi\)
\(984\) 0 0
\(985\) 37.2607 1.18723
\(986\) −0.838824 + 1.45289i −0.0267136 + 0.0462693i
\(987\) 0 0
\(988\) −0.496239 + 14.1519i −0.0157875 + 0.450232i
\(989\) 3.34688 + 5.79697i 0.106425 + 0.184333i
\(990\) 0 0
\(991\) 23.7478 + 41.1323i 0.754373 + 1.30661i 0.945686 + 0.325083i \(0.105392\pi\)
−0.191313 + 0.981529i \(0.561274\pi\)
\(992\) 3.63304 6.29261i 0.115349 0.199791i
\(993\) 0 0
\(994\) −12.1991 + 18.6318i −0.386933 + 0.590965i
\(995\) 6.51081 + 11.2771i 0.206407 + 0.357507i
\(996\) 0 0
\(997\) 1.47510 0.0467168 0.0233584 0.999727i \(-0.492564\pi\)
0.0233584 + 0.999727i \(0.492564\pi\)
\(998\) 5.61372 + 9.72324i 0.177699 + 0.307784i
\(999\) 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 1638.2.m.k.1621.1 10
3.2 odd 2 546.2.j.e.529.5 yes 10
7.2 even 3 1638.2.p.j.919.1 10
13.3 even 3 1638.2.p.j.991.1 10
21.2 odd 6 546.2.k.e.373.5 yes 10
39.29 odd 6 546.2.k.e.445.5 yes 10
91.16 even 3 inner 1638.2.m.k.289.1 10
273.107 odd 6 546.2.j.e.289.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.j.e.289.5 10 273.107 odd 6
546.2.j.e.529.5 yes 10 3.2 odd 2
546.2.k.e.373.5 yes 10 21.2 odd 6
546.2.k.e.445.5 yes 10 39.29 odd 6
1638.2.m.k.289.1 10 91.16 even 3 inner
1638.2.m.k.1621.1 10 1.1 even 1 trivial
1638.2.p.j.919.1 10 7.2 even 3
1638.2.p.j.991.1 10 13.3 even 3