Properties

Label 450.2.l.c.19.2
Level $450$
Weight $2$
Character 450.19
Analytic conductor $3.593$
Analytic rank $0$
Dimension $16$
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] = [450,2,Mod(19,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.l (of order \(10\), degree \(4\), 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: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + 6259 x^{8} - 11958 x^{7} - 15752 x^{6} + 14670 x^{5} + 18271 x^{4} + \cdots + 11105 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 19.2
Root \(2.32349 + 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 450.19
Dual form 450.2.l.c.379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.47959 + 1.67655i) q^{5} -3.23143i q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})\) \(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.47959 + 1.67655i) q^{5} -3.23143i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-1.92526 - 1.13727i) q^{10} +(-1.63788 - 5.04087i) q^{11} +(5.61543 + 1.82456i) q^{13} +(0.998566 + 3.07327i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.602300 - 0.828995i) q^{17} +(-3.64639 - 2.64926i) q^{19} +(2.18246 + 0.486675i) q^{20} +(3.11543 + 4.28802i) q^{22} +(1.83390 - 0.595870i) q^{23} +(-0.621629 + 4.96121i) q^{25} -5.90441 q^{26} +(-1.89939 - 2.61428i) q^{28} +(0.210961 - 0.153272i) q^{29} +(1.81386 + 1.31784i) q^{31} +1.00000i q^{32} +(-0.316648 + 0.974542i) q^{34} +(5.41765 - 4.78119i) q^{35} +(9.08596 + 2.95221i) q^{37} +(4.28659 + 1.39280i) q^{38} +(-2.22604 + 0.211563i) q^{40} +(3.07816 - 9.47359i) q^{41} -5.30164i q^{43} +(-4.28802 - 3.11543i) q^{44} +(-1.56001 + 1.13341i) q^{46} +(6.18830 + 8.51747i) q^{47} -3.44213 q^{49} +(-0.941893 - 4.91048i) q^{50} +(5.61543 - 1.82456i) q^{52} +(-1.35841 - 1.86970i) q^{53} +(6.02788 - 10.2044i) q^{55} +(2.61428 + 1.89939i) q^{56} +(-0.153272 + 0.210961i) q^{58} +(-2.00615 + 6.17428i) q^{59} +(-1.21905 - 3.75186i) q^{61} +(-2.13232 - 0.692831i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(5.24956 + 12.1141i) q^{65} +(-5.46176 + 7.51747i) q^{67} -1.02469i q^{68} +(-3.67502 + 6.22132i) q^{70} +(6.90715 - 5.01834i) q^{71} +(-3.76068 + 1.22192i) q^{73} -9.55354 q^{74} -4.50718 q^{76} +(-16.2892 + 5.29269i) q^{77} +(-10.8177 + 7.85950i) q^{79} +(2.05171 - 0.889091i) q^{80} +9.96112i q^{82} +(-4.40074 + 6.05709i) q^{83} +(2.28101 - 0.216787i) q^{85} +(1.63830 + 5.04216i) q^{86} +(5.04087 + 1.63788i) q^{88} +(-0.226687 - 0.697671i) q^{89} +(5.89595 - 18.1459i) q^{91} +(1.13341 - 1.56001i) q^{92} +(-8.51747 - 6.18830i) q^{94} +(-0.953552 - 10.0332i) q^{95} +(-10.1432 - 13.9610i) q^{97} +(3.27366 - 1.06368i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} - 4 q^{5} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 2 q^{14} - 4 q^{16} + 30 q^{17} + 4 q^{20} - 20 q^{22} + 10 q^{23} + 24 q^{25} - 4 q^{26} + 10 q^{29} - 18 q^{31} + 12 q^{34} + 34 q^{35} + 20 q^{37} - 10 q^{38} - 2 q^{40} - 22 q^{41} - 8 q^{44} - 6 q^{46} + 50 q^{47} - 52 q^{49} - 12 q^{50} + 20 q^{52} - 30 q^{53} + 18 q^{55} + 2 q^{56} - 30 q^{58} - 20 q^{59} + 12 q^{61} - 50 q^{62} + 4 q^{64} + 8 q^{65} - 50 q^{67} - 12 q^{70} + 28 q^{71} + 20 q^{73} - 12 q^{74} + 20 q^{76} - 100 q^{77} - 20 q^{79} - 4 q^{80} + 30 q^{83} - 4 q^{85} + 6 q^{86} - 70 q^{89} + 12 q^{91} + 30 q^{92} + 2 q^{94} + 30 q^{95} - 10 q^{97} - 60 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.951057 + 0.309017i −0.672499 + 0.218508i
\(3\) 0 0
\(4\) 0.809017 0.587785i 0.404508 0.293893i
\(5\) 1.47959 + 1.67655i 0.661693 + 0.749775i
\(6\) 0 0
\(7\) 3.23143i 1.22136i −0.791876 0.610682i \(-0.790895\pi\)
0.791876 0.610682i \(-0.209105\pi\)
\(8\) −0.587785 + 0.809017i −0.207813 + 0.286031i
\(9\) 0 0
\(10\) −1.92526 1.13727i −0.608819 0.359638i
\(11\) −1.63788 5.04087i −0.493839 1.51988i −0.818758 0.574138i \(-0.805337\pi\)
0.324920 0.945742i \(-0.394663\pi\)
\(12\) 0 0
\(13\) 5.61543 + 1.82456i 1.55744 + 0.506043i 0.956122 0.292967i \(-0.0946427\pi\)
0.601318 + 0.799010i \(0.294643\pi\)
\(14\) 0.998566 + 3.07327i 0.266878 + 0.821366i
\(15\) 0 0
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 0.602300 0.828995i 0.146079 0.201061i −0.729707 0.683760i \(-0.760344\pi\)
0.875786 + 0.482699i \(0.160344\pi\)
\(18\) 0 0
\(19\) −3.64639 2.64926i −0.836539 0.607781i 0.0848627 0.996393i \(-0.472955\pi\)
−0.921402 + 0.388611i \(0.872955\pi\)
\(20\) 2.18246 + 0.486675i 0.488014 + 0.108824i
\(21\) 0 0
\(22\) 3.11543 + 4.28802i 0.664212 + 0.914209i
\(23\) 1.83390 0.595870i 0.382394 0.124247i −0.111511 0.993763i \(-0.535569\pi\)
0.493905 + 0.869516i \(0.335569\pi\)
\(24\) 0 0
\(25\) −0.621629 + 4.96121i −0.124326 + 0.992241i
\(26\) −5.90441 −1.15795
\(27\) 0 0
\(28\) −1.89939 2.61428i −0.358950 0.494053i
\(29\) 0.210961 0.153272i 0.0391744 0.0284619i −0.568026 0.823011i \(-0.692293\pi\)
0.607200 + 0.794549i \(0.292293\pi\)
\(30\) 0 0
\(31\) 1.81386 + 1.31784i 0.325778 + 0.236692i 0.738637 0.674103i \(-0.235470\pi\)
−0.412859 + 0.910795i \(0.635470\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −0.316648 + 0.974542i −0.0543046 + 0.167133i
\(35\) 5.41765 4.78119i 0.915749 0.808168i
\(36\) 0 0
\(37\) 9.08596 + 2.95221i 1.49372 + 0.485340i 0.938180 0.346149i \(-0.112511\pi\)
0.555542 + 0.831488i \(0.312511\pi\)
\(38\) 4.28659 + 1.39280i 0.695376 + 0.225941i
\(39\) 0 0
\(40\) −2.22604 + 0.211563i −0.351967 + 0.0334510i
\(41\) 3.07816 9.47359i 0.480727 1.47953i −0.357348 0.933971i \(-0.616319\pi\)
0.838075 0.545555i \(-0.183681\pi\)
\(42\) 0 0
\(43\) 5.30164i 0.808492i −0.914650 0.404246i \(-0.867534\pi\)
0.914650 0.404246i \(-0.132466\pi\)
\(44\) −4.28802 3.11543i −0.646444 0.469669i
\(45\) 0 0
\(46\) −1.56001 + 1.13341i −0.230010 + 0.167112i
\(47\) 6.18830 + 8.51747i 0.902657 + 1.24240i 0.969613 + 0.244644i \(0.0786712\pi\)
−0.0669561 + 0.997756i \(0.521329\pi\)
\(48\) 0 0
\(49\) −3.44213 −0.491732
\(50\) −0.941893 4.91048i −0.133204 0.694447i
\(51\) 0 0
\(52\) 5.61543 1.82456i 0.778720 0.253021i
\(53\) −1.35841 1.86970i −0.186593 0.256823i 0.705465 0.708745i \(-0.250738\pi\)
−0.892057 + 0.451923i \(0.850738\pi\)
\(54\) 0 0
\(55\) 6.02788 10.2044i 0.812799 1.37596i
\(56\) 2.61428 + 1.89939i 0.349348 + 0.253816i
\(57\) 0 0
\(58\) −0.153272 + 0.210961i −0.0201256 + 0.0277005i
\(59\) −2.00615 + 6.17428i −0.261178 + 0.803823i 0.731371 + 0.681979i \(0.238881\pi\)
−0.992549 + 0.121844i \(0.961119\pi\)
\(60\) 0 0
\(61\) −1.21905 3.75186i −0.156084 0.480376i 0.842185 0.539188i \(-0.181269\pi\)
−0.998269 + 0.0588118i \(0.981269\pi\)
\(62\) −2.13232 0.692831i −0.270804 0.0879897i
\(63\) 0 0
\(64\) −0.309017 0.951057i −0.0386271 0.118882i
\(65\) 5.24956 + 12.1141i 0.651128 + 1.50257i
\(66\) 0 0
\(67\) −5.46176 + 7.51747i −0.667260 + 0.918405i −0.999694 0.0247216i \(-0.992130\pi\)
0.332434 + 0.943126i \(0.392130\pi\)
\(68\) 1.02469i 0.124262i
\(69\) 0 0
\(70\) −3.67502 + 6.22132i −0.439249 + 0.743590i
\(71\) 6.90715 5.01834i 0.819728 0.595567i −0.0969066 0.995293i \(-0.530895\pi\)
0.916635 + 0.399726i \(0.130895\pi\)
\(72\) 0 0
\(73\) −3.76068 + 1.22192i −0.440155 + 0.143015i −0.520707 0.853735i \(-0.674332\pi\)
0.0805522 + 0.996750i \(0.474332\pi\)
\(74\) −9.55354 −1.11058
\(75\) 0 0
\(76\) −4.50718 −0.517010
\(77\) −16.2892 + 5.29269i −1.85633 + 0.603158i
\(78\) 0 0
\(79\) −10.8177 + 7.85950i −1.21708 + 0.884263i −0.995855 0.0909589i \(-0.971007\pi\)
−0.221229 + 0.975222i \(0.571007\pi\)
\(80\) 2.05171 0.889091i 0.229388 0.0994034i
\(81\) 0 0
\(82\) 9.96112i 1.10002i
\(83\) −4.40074 + 6.05709i −0.483044 + 0.664852i −0.979086 0.203446i \(-0.934786\pi\)
0.496043 + 0.868298i \(0.334786\pi\)
\(84\) 0 0
\(85\) 2.28101 0.216787i 0.247410 0.0235139i
\(86\) 1.63830 + 5.04216i 0.176662 + 0.543710i
\(87\) 0 0
\(88\) 5.04087 + 1.63788i 0.537359 + 0.174598i
\(89\) −0.226687 0.697671i −0.0240288 0.0739529i 0.938323 0.345760i \(-0.112379\pi\)
−0.962352 + 0.271807i \(0.912379\pi\)
\(90\) 0 0
\(91\) 5.89595 18.1459i 0.618063 1.90220i
\(92\) 1.13341 1.56001i 0.118166 0.162642i
\(93\) 0 0
\(94\) −8.51747 6.18830i −0.878510 0.638275i
\(95\) −0.953552 10.0332i −0.0978324 1.02938i
\(96\) 0 0
\(97\) −10.1432 13.9610i −1.02989 1.41752i −0.905031 0.425345i \(-0.860153\pi\)
−0.124857 0.992175i \(-0.539847\pi\)
\(98\) 3.27366 1.06368i 0.330689 0.107447i
\(99\) 0 0
\(100\) 2.41322 + 4.37909i 0.241322 + 0.437909i
\(101\) −11.8454 −1.17866 −0.589331 0.807892i \(-0.700609\pi\)
−0.589331 + 0.807892i \(0.700609\pi\)
\(102\) 0 0
\(103\) 4.20316 + 5.78515i 0.414150 + 0.570028i 0.964224 0.265087i \(-0.0854008\pi\)
−0.550075 + 0.835115i \(0.685401\pi\)
\(104\) −4.77677 + 3.47053i −0.468401 + 0.340313i
\(105\) 0 0
\(106\) 1.86970 + 1.35841i 0.181601 + 0.131941i
\(107\) 3.20058i 0.309412i 0.987961 + 0.154706i \(0.0494430\pi\)
−0.987961 + 0.154706i \(0.950557\pi\)
\(108\) 0 0
\(109\) −3.05789 + 9.41123i −0.292893 + 0.901432i 0.691028 + 0.722828i \(0.257158\pi\)
−0.983921 + 0.178604i \(0.942842\pi\)
\(110\) −2.57952 + 11.5677i −0.245947 + 1.10294i
\(111\) 0 0
\(112\) −3.07327 0.998566i −0.290397 0.0943556i
\(113\) 4.03794 + 1.31201i 0.379858 + 0.123423i 0.492721 0.870187i \(-0.336002\pi\)
−0.112863 + 0.993611i \(0.536002\pi\)
\(114\) 0 0
\(115\) 3.71242 + 2.19298i 0.346185 + 0.204496i
\(116\) 0.0805798 0.247999i 0.00748165 0.0230261i
\(117\) 0 0
\(118\) 6.49202i 0.597639i
\(119\) −2.67884 1.94629i −0.245569 0.178416i
\(120\) 0 0
\(121\) −13.8285 + 10.0470i −1.25714 + 0.913366i
\(122\) 2.31878 + 3.19152i 0.209932 + 0.288947i
\(123\) 0 0
\(124\) 2.24205 0.201342
\(125\) −9.23746 + 6.29836i −0.826224 + 0.563342i
\(126\) 0 0
\(127\) −8.79813 + 2.85868i −0.780708 + 0.253667i −0.672142 0.740422i \(-0.734626\pi\)
−0.108565 + 0.994089i \(0.534626\pi\)
\(128\) 0.587785 + 0.809017i 0.0519534 + 0.0715077i
\(129\) 0 0
\(130\) −8.73611 9.89903i −0.766207 0.868203i
\(131\) −3.93584 2.85956i −0.343876 0.249841i 0.402419 0.915455i \(-0.368169\pi\)
−0.746296 + 0.665615i \(0.768169\pi\)
\(132\) 0 0
\(133\) −8.56088 + 11.7830i −0.742323 + 1.02172i
\(134\) 2.87142 8.83731i 0.248053 0.763428i
\(135\) 0 0
\(136\) 0.316648 + 0.974542i 0.0271523 + 0.0835663i
\(137\) 5.72219 + 1.85925i 0.488879 + 0.158847i 0.543076 0.839684i \(-0.317260\pi\)
−0.0541963 + 0.998530i \(0.517260\pi\)
\(138\) 0 0
\(139\) 1.73890 + 5.35178i 0.147492 + 0.453932i 0.997323 0.0731222i \(-0.0232963\pi\)
−0.849831 + 0.527055i \(0.823296\pi\)
\(140\) 1.57266 7.05247i 0.132914 0.596043i
\(141\) 0 0
\(142\) −5.01834 + 6.90715i −0.421130 + 0.579635i
\(143\) 31.2951i 2.61703i
\(144\) 0 0
\(145\) 0.569103 + 0.126906i 0.0472614 + 0.0105390i
\(146\) 3.19903 2.32423i 0.264754 0.192355i
\(147\) 0 0
\(148\) 9.08596 2.95221i 0.746861 0.242670i
\(149\) −11.6556 −0.954863 −0.477432 0.878669i \(-0.658432\pi\)
−0.477432 + 0.878669i \(0.658432\pi\)
\(150\) 0 0
\(151\) 5.52354 0.449499 0.224750 0.974417i \(-0.427844\pi\)
0.224750 + 0.974417i \(0.427844\pi\)
\(152\) 4.28659 1.39280i 0.347688 0.112971i
\(153\) 0 0
\(154\) 13.8564 10.0673i 1.11658 0.811245i
\(155\) 0.474334 + 4.99089i 0.0380994 + 0.400878i
\(156\) 0 0
\(157\) 6.84307i 0.546136i 0.961995 + 0.273068i \(0.0880384\pi\)
−0.961995 + 0.273068i \(0.911962\pi\)
\(158\) 7.85950 10.8177i 0.625268 0.860608i
\(159\) 0 0
\(160\) −1.67655 + 1.47959i −0.132543 + 0.116972i
\(161\) −1.92551 5.92611i −0.151751 0.467043i
\(162\) 0 0
\(163\) −8.92773 2.90080i −0.699274 0.227208i −0.0622597 0.998060i \(-0.519831\pi\)
−0.637014 + 0.770852i \(0.719831\pi\)
\(164\) −3.07816 9.47359i −0.240364 0.739763i
\(165\) 0 0
\(166\) 2.31360 7.12054i 0.179570 0.552661i
\(167\) 4.01388 5.52464i 0.310604 0.427509i −0.624966 0.780652i \(-0.714887\pi\)
0.935569 + 0.353143i \(0.114887\pi\)
\(168\) 0 0
\(169\) 17.6868 + 12.8502i 1.36052 + 0.988478i
\(170\) −2.10238 + 0.911046i −0.161245 + 0.0698741i
\(171\) 0 0
\(172\) −3.11623 4.28912i −0.237610 0.327042i
\(173\) 17.9373 5.82820i 1.36375 0.443110i 0.466457 0.884544i \(-0.345530\pi\)
0.897294 + 0.441434i \(0.145530\pi\)
\(174\) 0 0
\(175\) 16.0318 + 2.00875i 1.21189 + 0.151847i
\(176\) −5.30029 −0.399524
\(177\) 0 0
\(178\) 0.431184 + 0.593474i 0.0323186 + 0.0444828i
\(179\) −0.761557 + 0.553303i −0.0569214 + 0.0413558i −0.615882 0.787838i \(-0.711200\pi\)
0.558961 + 0.829194i \(0.311200\pi\)
\(180\) 0 0
\(181\) −11.4118 8.29114i −0.848231 0.616276i 0.0764270 0.997075i \(-0.475649\pi\)
−0.924658 + 0.380800i \(0.875649\pi\)
\(182\) 19.0797i 1.41428i
\(183\) 0 0
\(184\) −0.595870 + 1.83390i −0.0439281 + 0.135197i
\(185\) 8.49397 + 19.6011i 0.624489 + 1.44110i
\(186\) 0 0
\(187\) −5.16535 1.67832i −0.377728 0.122731i
\(188\) 10.0129 + 3.25338i 0.730265 + 0.237277i
\(189\) 0 0
\(190\) 4.00730 + 9.24744i 0.290720 + 0.670880i
\(191\) −7.87125 + 24.2252i −0.569544 + 1.75288i 0.0845047 + 0.996423i \(0.473069\pi\)
−0.654049 + 0.756453i \(0.726931\pi\)
\(192\) 0 0
\(193\) 6.63439i 0.477554i −0.971074 0.238777i \(-0.923254\pi\)
0.971074 0.238777i \(-0.0767465\pi\)
\(194\) 13.9610 + 10.1432i 1.00234 + 0.728241i
\(195\) 0 0
\(196\) −2.78474 + 2.02323i −0.198910 + 0.144517i
\(197\) 5.98232 + 8.23396i 0.426223 + 0.586645i 0.967081 0.254468i \(-0.0819005\pi\)
−0.540858 + 0.841114i \(0.681900\pi\)
\(198\) 0 0
\(199\) 2.52238 0.178807 0.0894035 0.995995i \(-0.471504\pi\)
0.0894035 + 0.995995i \(0.471504\pi\)
\(200\) −3.64832 3.41903i −0.257975 0.241762i
\(201\) 0 0
\(202\) 11.2656 3.66043i 0.792648 0.257547i
\(203\) −0.495287 0.681704i −0.0347623 0.0478463i
\(204\) 0 0
\(205\) 20.4373 8.85635i 1.42741 0.618554i
\(206\) −5.78515 4.20316i −0.403071 0.292848i
\(207\) 0 0
\(208\) 3.47053 4.77677i 0.240638 0.331209i
\(209\) −7.38222 + 22.7201i −0.510639 + 1.57158i
\(210\) 0 0
\(211\) 4.87129 + 14.9923i 0.335353 + 1.03211i 0.966548 + 0.256487i \(0.0825650\pi\)
−0.631194 + 0.775625i \(0.717435\pi\)
\(212\) −2.19796 0.714161i −0.150957 0.0490487i
\(213\) 0 0
\(214\) −0.989034 3.04393i −0.0676090 0.208079i
\(215\) 8.88846 7.84425i 0.606188 0.534973i
\(216\) 0 0
\(217\) 4.25852 5.86135i 0.289087 0.397894i
\(218\) 9.89555i 0.670211i
\(219\) 0 0
\(220\) −1.12134 11.7986i −0.0756009 0.795464i
\(221\) 4.89473 3.55623i 0.329255 0.239218i
\(222\) 0 0
\(223\) 8.84040 2.87242i 0.591997 0.192351i 0.00232890 0.999997i \(-0.499259\pi\)
0.589668 + 0.807646i \(0.299259\pi\)
\(224\) 3.23143 0.215909
\(225\) 0 0
\(226\) −4.24575 −0.282423
\(227\) 3.46003 1.12423i 0.229650 0.0746178i −0.191931 0.981408i \(-0.561475\pi\)
0.421582 + 0.906791i \(0.361475\pi\)
\(228\) 0 0
\(229\) 8.03500 5.83777i 0.530968 0.385771i −0.289752 0.957102i \(-0.593573\pi\)
0.820720 + 0.571331i \(0.193573\pi\)
\(230\) −4.20839 0.938443i −0.277493 0.0618791i
\(231\) 0 0
\(232\) 0.260762i 0.0171198i
\(233\) −11.0441 + 15.2009i −0.723523 + 0.995844i 0.275877 + 0.961193i \(0.411032\pi\)
−0.999399 + 0.0346507i \(0.988968\pi\)
\(234\) 0 0
\(235\) −5.12380 + 22.9773i −0.334240 + 1.49888i
\(236\) 2.00615 + 6.17428i 0.130589 + 0.401912i
\(237\) 0 0
\(238\) 3.14916 + 1.02322i 0.204130 + 0.0663258i
\(239\) −3.01349 9.27457i −0.194926 0.599922i −0.999977 0.00671626i \(-0.997862\pi\)
0.805051 0.593206i \(-0.202138\pi\)
\(240\) 0 0
\(241\) 5.84694 17.9950i 0.376634 1.15916i −0.565735 0.824587i \(-0.691408\pi\)
0.942369 0.334574i \(-0.108592\pi\)
\(242\) 10.0470 13.8285i 0.645848 0.888933i
\(243\) 0 0
\(244\) −3.19152 2.31878i −0.204316 0.148444i
\(245\) −5.09293 5.77089i −0.325376 0.368689i
\(246\) 0 0
\(247\) −15.6423 21.5298i −0.995296 1.36991i
\(248\) −2.13232 + 0.692831i −0.135402 + 0.0439948i
\(249\) 0 0
\(250\) 6.83905 8.84463i 0.432539 0.559383i
\(251\) 1.98608 0.125360 0.0626801 0.998034i \(-0.480035\pi\)
0.0626801 + 0.998034i \(0.480035\pi\)
\(252\) 0 0
\(253\) −6.00740 8.26848i −0.377682 0.519835i
\(254\) 7.48413 5.43754i 0.469596 0.341182i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 19.2797i 1.20263i −0.799010 0.601317i \(-0.794643\pi\)
0.799010 0.601317i \(-0.205357\pi\)
\(258\) 0 0
\(259\) 9.53984 29.3606i 0.592777 1.82438i
\(260\) 11.3675 + 6.71493i 0.704982 + 0.416443i
\(261\) 0 0
\(262\) 4.62686 + 1.50336i 0.285848 + 0.0928778i
\(263\) −11.9164 3.87188i −0.734799 0.238751i −0.0823713 0.996602i \(-0.526249\pi\)
−0.652428 + 0.757851i \(0.726249\pi\)
\(264\) 0 0
\(265\) 1.12474 5.04383i 0.0690923 0.309840i
\(266\) 4.50072 13.8518i 0.275957 0.849308i
\(267\) 0 0
\(268\) 9.29210i 0.567605i
\(269\) −10.9160 7.93096i −0.665562 0.483559i 0.202975 0.979184i \(-0.434939\pi\)
−0.868537 + 0.495625i \(0.834939\pi\)
\(270\) 0 0
\(271\) 21.6926 15.7606i 1.31773 0.957387i 0.317773 0.948167i \(-0.397065\pi\)
0.999957 0.00922023i \(-0.00293493\pi\)
\(272\) −0.602300 0.828995i −0.0365198 0.0502652i
\(273\) 0 0
\(274\) −6.01666 −0.363480
\(275\) 26.0270 4.99230i 1.56948 0.301047i
\(276\) 0 0
\(277\) 7.76751 2.52382i 0.466704 0.151641i −0.0662188 0.997805i \(-0.521094\pi\)
0.532923 + 0.846164i \(0.321094\pi\)
\(278\) −3.30758 4.55250i −0.198376 0.273041i
\(279\) 0 0
\(280\) 0.683650 + 7.19328i 0.0408559 + 0.429881i
\(281\) 25.3561 + 18.4223i 1.51262 + 1.09898i 0.965000 + 0.262249i \(0.0844642\pi\)
0.547615 + 0.836730i \(0.315536\pi\)
\(282\) 0 0
\(283\) −9.61049 + 13.2277i −0.571284 + 0.786306i −0.992706 0.120559i \(-0.961531\pi\)
0.421422 + 0.906865i \(0.361531\pi\)
\(284\) 2.63830 8.11984i 0.156554 0.481824i
\(285\) 0 0
\(286\) 9.67071 + 29.7634i 0.571841 + 1.75995i
\(287\) −30.6132 9.94684i −1.80704 0.587143i
\(288\) 0 0
\(289\) 4.92882 + 15.1694i 0.289931 + 0.892315i
\(290\) −0.580465 + 0.0551675i −0.0340861 + 0.00323955i
\(291\) 0 0
\(292\) −2.32423 + 3.19903i −0.136015 + 0.187209i
\(293\) 28.1867i 1.64669i 0.567545 + 0.823343i \(0.307893\pi\)
−0.567545 + 0.823343i \(0.692107\pi\)
\(294\) 0 0
\(295\) −13.3198 + 5.77200i −0.775506 + 0.336059i
\(296\) −7.72898 + 5.61543i −0.449238 + 0.326390i
\(297\) 0 0
\(298\) 11.0851 3.60178i 0.642144 0.208645i
\(299\) 11.3853 0.658431
\(300\) 0 0
\(301\) −17.1319 −0.987464
\(302\) −5.25320 + 1.70687i −0.302288 + 0.0982192i
\(303\) 0 0
\(304\) −3.64639 + 2.64926i −0.209135 + 0.151945i
\(305\) 4.48648 7.59501i 0.256895 0.434889i
\(306\) 0 0
\(307\) 14.5372i 0.829680i 0.909894 + 0.414840i \(0.136163\pi\)
−0.909894 + 0.414840i \(0.863837\pi\)
\(308\) −10.0673 + 13.8564i −0.573637 + 0.789543i
\(309\) 0 0
\(310\) −1.99339 4.60004i −0.113217 0.261265i
\(311\) −4.47841 13.7831i −0.253947 0.781570i −0.994035 0.109060i \(-0.965216\pi\)
0.740088 0.672510i \(-0.234784\pi\)
\(312\) 0 0
\(313\) −29.9857 9.74294i −1.69489 0.550703i −0.707185 0.707029i \(-0.750035\pi\)
−0.987706 + 0.156325i \(0.950035\pi\)
\(314\) −2.11462 6.50814i −0.119335 0.367276i
\(315\) 0 0
\(316\) −4.13198 + 12.7169i −0.232442 + 0.715384i
\(317\) −8.80564 + 12.1199i −0.494574 + 0.680722i −0.981223 0.192875i \(-0.938219\pi\)
0.486650 + 0.873597i \(0.338219\pi\)
\(318\) 0 0
\(319\) −1.11815 0.812385i −0.0626045 0.0454848i
\(320\) 1.13727 1.92526i 0.0635755 0.107625i
\(321\) 0 0
\(322\) 3.66254 + 5.04105i 0.204105 + 0.280927i
\(323\) −4.39244 + 1.42719i −0.244402 + 0.0794110i
\(324\) 0 0
\(325\) −12.5428 + 26.7251i −0.695747 + 1.48244i
\(326\) 9.38717 0.519907
\(327\) 0 0
\(328\) 5.85500 + 8.05872i 0.323288 + 0.444968i
\(329\) 27.5236 19.9971i 1.51742 1.10247i
\(330\) 0 0
\(331\) 17.4888 + 12.7064i 0.961273 + 0.698406i 0.953446 0.301563i \(-0.0975085\pi\)
0.00782724 + 0.999969i \(0.497508\pi\)
\(332\) 7.48698i 0.410901i
\(333\) 0 0
\(334\) −2.11022 + 6.49460i −0.115466 + 0.355369i
\(335\) −20.6846 + 1.96586i −1.13012 + 0.107407i
\(336\) 0 0
\(337\) 7.22323 + 2.34697i 0.393474 + 0.127848i 0.499070 0.866562i \(-0.333675\pi\)
−0.105596 + 0.994409i \(0.533675\pi\)
\(338\) −20.7921 6.75576i −1.13094 0.367465i
\(339\) 0 0
\(340\) 1.71795 1.51613i 0.0931689 0.0822235i
\(341\) 3.67220 11.3019i 0.198861 0.612031i
\(342\) 0 0
\(343\) 11.4970i 0.620780i
\(344\) 4.28912 + 3.11623i 0.231254 + 0.168016i
\(345\) 0 0
\(346\) −15.2584 + 11.0859i −0.820298 + 0.595981i
\(347\) 4.42781 + 6.09436i 0.237697 + 0.327162i 0.911155 0.412063i \(-0.135192\pi\)
−0.673458 + 0.739226i \(0.735192\pi\)
\(348\) 0 0
\(349\) −18.7527 −1.00381 −0.501904 0.864923i \(-0.667367\pi\)
−0.501904 + 0.864923i \(0.667367\pi\)
\(350\) −15.8679 + 3.04366i −0.848173 + 0.162690i
\(351\) 0 0
\(352\) 5.04087 1.63788i 0.268679 0.0872992i
\(353\) 2.56631 + 3.53223i 0.136591 + 0.188001i 0.871833 0.489803i \(-0.162931\pi\)
−0.735242 + 0.677805i \(0.762931\pi\)
\(354\) 0 0
\(355\) 18.6332 + 4.15509i 0.988950 + 0.220529i
\(356\) −0.593474 0.431184i −0.0314541 0.0228527i
\(357\) 0 0
\(358\) 0.553303 0.761557i 0.0292430 0.0402495i
\(359\) 0.227811 0.701130i 0.0120234 0.0370042i −0.944865 0.327461i \(-0.893807\pi\)
0.956888 + 0.290456i \(0.0938071\pi\)
\(360\) 0 0
\(361\) 0.406269 + 1.25037i 0.0213826 + 0.0658088i
\(362\) 13.4153 + 4.35891i 0.705095 + 0.229099i
\(363\) 0 0
\(364\) −5.89595 18.1459i −0.309032 0.951101i
\(365\) −7.61288 4.49703i −0.398476 0.235385i
\(366\) 0 0
\(367\) −11.0856 + 15.2581i −0.578666 + 0.796466i −0.993548 0.113410i \(-0.963823\pi\)
0.414882 + 0.909875i \(0.363823\pi\)
\(368\) 1.92827i 0.100518i
\(369\) 0 0
\(370\) −14.1353 16.0170i −0.734860 0.832683i
\(371\) −6.04179 + 4.38962i −0.313674 + 0.227898i
\(372\) 0 0
\(373\) 28.3763 9.22003i 1.46927 0.477395i 0.538383 0.842700i \(-0.319035\pi\)
0.930888 + 0.365305i \(0.119035\pi\)
\(374\) 5.43117 0.280839
\(375\) 0 0
\(376\) −10.5282 −0.542949
\(377\) 1.46429 0.475776i 0.0754147 0.0245037i
\(378\) 0 0
\(379\) 20.6159 14.9783i 1.05897 0.769384i 0.0850692 0.996375i \(-0.472889\pi\)
0.973897 + 0.226991i \(0.0728889\pi\)
\(380\) −6.66878 7.55651i −0.342101 0.387641i
\(381\) 0 0
\(382\) 25.4719i 1.30326i
\(383\) −18.5995 + 25.6000i −0.950389 + 1.30810i 0.000965638 1.00000i \(0.499693\pi\)
−0.951354 + 0.308098i \(0.900307\pi\)
\(384\) 0 0
\(385\) −32.9748 19.4786i −1.68055 0.992724i
\(386\) 2.05014 + 6.30968i 0.104349 + 0.321154i
\(387\) 0 0
\(388\) −16.4121 5.33261i −0.833197 0.270722i
\(389\) 3.72304 + 11.4583i 0.188766 + 0.580961i 0.999993 0.00377022i \(-0.00120010\pi\)
−0.811227 + 0.584731i \(0.801200\pi\)
\(390\) 0 0
\(391\) 0.610584 1.87918i 0.0308786 0.0950344i
\(392\) 2.02323 2.78474i 0.102189 0.140651i
\(393\) 0 0
\(394\) −8.23396 5.98232i −0.414821 0.301385i
\(395\) −29.1826 6.50752i −1.46833 0.327429i
\(396\) 0 0
\(397\) 15.1393 + 20.8374i 0.759819 + 1.04580i 0.997229 + 0.0743920i \(0.0237016\pi\)
−0.237410 + 0.971410i \(0.576298\pi\)
\(398\) −2.39893 + 0.779460i −0.120247 + 0.0390708i
\(399\) 0 0
\(400\) 4.52629 + 2.12430i 0.226315 + 0.106215i
\(401\) −26.3196 −1.31434 −0.657169 0.753743i \(-0.728246\pi\)
−0.657169 + 0.753743i \(0.728246\pi\)
\(402\) 0 0
\(403\) 7.78109 + 10.7098i 0.387604 + 0.533491i
\(404\) −9.58313 + 6.96255i −0.476779 + 0.346400i
\(405\) 0 0
\(406\) 0.681704 + 0.495287i 0.0338324 + 0.0245807i
\(407\) 50.6365i 2.50996i
\(408\) 0 0
\(409\) −11.3630 + 34.9716i −0.561863 + 1.72924i 0.115230 + 0.993339i \(0.463239\pi\)
−0.677093 + 0.735897i \(0.736761\pi\)
\(410\) −16.7003 + 14.7384i −0.824769 + 0.727876i
\(411\) 0 0
\(412\) 6.80085 + 2.20973i 0.335054 + 0.108866i
\(413\) 19.9517 + 6.48272i 0.981761 + 0.318994i
\(414\) 0 0
\(415\) −16.6663 + 1.58397i −0.818116 + 0.0777538i
\(416\) −1.82456 + 5.61543i −0.0894566 + 0.275319i
\(417\) 0 0
\(418\) 23.8894i 1.16847i
\(419\) 25.6657 + 18.6472i 1.25385 + 0.910975i 0.998439 0.0558572i \(-0.0177891\pi\)
0.255411 + 0.966833i \(0.417789\pi\)
\(420\) 0 0
\(421\) −7.13332 + 5.18266i −0.347657 + 0.252587i −0.747885 0.663828i \(-0.768931\pi\)
0.400229 + 0.916415i \(0.368931\pi\)
\(422\) −9.26574 12.7532i −0.451049 0.620816i
\(423\) 0 0
\(424\) 2.31107 0.112236
\(425\) 3.73841 + 3.50346i 0.181339 + 0.169943i
\(426\) 0 0
\(427\) −12.1239 + 3.93928i −0.586715 + 0.190635i
\(428\) 1.88125 + 2.58932i 0.0909339 + 0.125160i
\(429\) 0 0
\(430\) −6.02942 + 10.2070i −0.290764 + 0.492226i
\(431\) 19.0172 + 13.8168i 0.916026 + 0.665532i 0.942532 0.334117i \(-0.108438\pi\)
−0.0265058 + 0.999649i \(0.508438\pi\)
\(432\) 0 0
\(433\) −4.93923 + 6.79827i −0.237364 + 0.326704i −0.911036 0.412327i \(-0.864716\pi\)
0.673672 + 0.739031i \(0.264716\pi\)
\(434\) −2.23883 + 6.89042i −0.107468 + 0.330751i
\(435\) 0 0
\(436\) 3.05789 + 9.41123i 0.146447 + 0.450716i
\(437\) −8.26572 2.68569i −0.395403 0.128474i
\(438\) 0 0
\(439\) −11.0111 33.8885i −0.525529 1.61741i −0.763268 0.646083i \(-0.776406\pi\)
0.237739 0.971329i \(-0.423594\pi\)
\(440\) 4.71244 + 10.8747i 0.224657 + 0.518429i
\(441\) 0 0
\(442\) −3.55623 + 4.89473i −0.169152 + 0.232818i
\(443\) 6.79550i 0.322864i 0.986884 + 0.161432i \(0.0516112\pi\)
−0.986884 + 0.161432i \(0.948389\pi\)
\(444\) 0 0
\(445\) 0.834275 1.41232i 0.0395484 0.0669503i
\(446\) −7.52009 + 5.46366i −0.356087 + 0.258712i
\(447\) 0 0
\(448\) −3.07327 + 0.998566i −0.145198 + 0.0471778i
\(449\) 8.75011 0.412943 0.206472 0.978453i \(-0.433802\pi\)
0.206472 + 0.978453i \(0.433802\pi\)
\(450\) 0 0
\(451\) −52.7968 −2.48610
\(452\) 4.03794 1.31201i 0.189929 0.0617117i
\(453\) 0 0
\(454\) −2.94327 + 2.13841i −0.138135 + 0.100361i
\(455\) 39.1460 16.9636i 1.83519 0.795265i
\(456\) 0 0
\(457\) 38.1474i 1.78446i −0.451581 0.892230i \(-0.649140\pi\)
0.451581 0.892230i \(-0.350860\pi\)
\(458\) −5.83777 + 8.03500i −0.272781 + 0.375451i
\(459\) 0 0
\(460\) 4.29241 0.407951i 0.200135 0.0190208i
\(461\) 0.392689 + 1.20857i 0.0182893 + 0.0562888i 0.959785 0.280737i \(-0.0905789\pi\)
−0.941495 + 0.337026i \(0.890579\pi\)
\(462\) 0 0
\(463\) −8.49626 2.76060i −0.394855 0.128296i 0.104858 0.994487i \(-0.466561\pi\)
−0.499713 + 0.866191i \(0.666561\pi\)
\(464\) −0.0805798 0.247999i −0.00374082 0.0115131i
\(465\) 0 0
\(466\) 5.80623 17.8697i 0.268968 0.827799i
\(467\) 3.38378 4.65737i 0.156582 0.215517i −0.723517 0.690306i \(-0.757476\pi\)
0.880100 + 0.474789i \(0.157476\pi\)
\(468\) 0 0
\(469\) 24.2922 + 17.6493i 1.12171 + 0.814968i
\(470\) −2.22737 23.4361i −0.102741 1.08103i
\(471\) 0 0
\(472\) −3.81592 5.25216i −0.175642 0.241750i
\(473\) −26.7249 + 8.68344i −1.22881 + 0.399265i
\(474\) 0 0
\(475\) 15.4102 16.4436i 0.707069 0.754486i
\(476\) −3.31122 −0.151770
\(477\) 0 0
\(478\) 5.73200 + 7.88942i 0.262175 + 0.360854i
\(479\) 3.74616 2.72175i 0.171167 0.124360i −0.498904 0.866657i \(-0.666264\pi\)
0.670070 + 0.742298i \(0.266264\pi\)
\(480\) 0 0
\(481\) 45.6351 + 33.1558i 2.08078 + 1.51177i
\(482\) 18.9211i 0.861832i
\(483\) 0 0
\(484\) −5.28204 + 16.2564i −0.240093 + 0.738929i
\(485\) 8.39840 37.6621i 0.381352 1.71015i
\(486\) 0 0
\(487\) 15.1442 + 4.92064i 0.686248 + 0.222975i 0.631329 0.775515i \(-0.282510\pi\)
0.0549192 + 0.998491i \(0.482510\pi\)
\(488\) 3.75186 + 1.21905i 0.169839 + 0.0551839i
\(489\) 0 0
\(490\) 6.62697 + 3.91464i 0.299376 + 0.176845i
\(491\) 1.97176 6.06846i 0.0889844 0.273866i −0.896655 0.442730i \(-0.854010\pi\)
0.985639 + 0.168864i \(0.0540100\pi\)
\(492\) 0 0
\(493\) 0.267201i 0.0120341i
\(494\) 21.5298 + 15.6423i 0.968671 + 0.703780i
\(495\) 0 0
\(496\) 1.81386 1.31784i 0.0814445 0.0591729i
\(497\) −16.2164 22.3200i −0.727405 1.00119i
\(498\) 0 0
\(499\) −12.9135 −0.578087 −0.289044 0.957316i \(-0.593337\pi\)
−0.289044 + 0.957316i \(0.593337\pi\)
\(500\) −3.77118 + 10.5251i −0.168652 + 0.470698i
\(501\) 0 0
\(502\) −1.88887 + 0.613732i −0.0843046 + 0.0273922i
\(503\) 0.853483 + 1.17472i 0.0380549 + 0.0523781i 0.827620 0.561288i \(-0.189694\pi\)
−0.789566 + 0.613666i \(0.789694\pi\)
\(504\) 0 0
\(505\) −17.5263 19.8594i −0.779912 0.883731i
\(506\) 8.26848 + 6.00740i 0.367579 + 0.267062i
\(507\) 0 0
\(508\) −5.43754 + 7.48413i −0.241252 + 0.332055i
\(509\) −3.83481 + 11.8023i −0.169975 + 0.523130i −0.999368 0.0355355i \(-0.988686\pi\)
0.829393 + 0.558665i \(0.188686\pi\)
\(510\) 0 0
\(511\) 3.94855 + 12.1524i 0.174673 + 0.537590i
\(512\) 0.951057 + 0.309017i 0.0420312 + 0.0136568i
\(513\) 0 0
\(514\) 5.95775 + 18.3361i 0.262785 + 0.808770i
\(515\) −3.48014 + 15.6064i −0.153353 + 0.687702i
\(516\) 0 0
\(517\) 32.7998 45.1450i 1.44253 1.98548i
\(518\) 30.8716i 1.35642i
\(519\) 0 0
\(520\) −12.8862 2.87353i −0.565096 0.126013i
\(521\) 6.42857 4.67063i 0.281641 0.204624i −0.437992 0.898979i \(-0.644310\pi\)
0.719633 + 0.694355i \(0.244310\pi\)
\(522\) 0 0
\(523\) −33.1258 + 10.7632i −1.44849 + 0.470643i −0.924533 0.381101i \(-0.875545\pi\)
−0.523957 + 0.851745i \(0.675545\pi\)
\(524\) −4.86497 −0.212527
\(525\) 0 0
\(526\) 12.5297 0.546320
\(527\) 2.18497 0.709940i 0.0951788 0.0309255i
\(528\) 0 0
\(529\) −15.5993 + 11.3335i −0.678229 + 0.492762i
\(530\) 0.488937 + 5.14453i 0.0212381 + 0.223464i
\(531\) 0 0
\(532\) 14.5646i 0.631457i
\(533\) 34.5703 47.5820i 1.49741 2.06100i
\(534\) 0 0
\(535\) −5.36593 + 4.73555i −0.231989 + 0.204736i
\(536\) −2.87142 8.83731i −0.124026 0.381714i
\(537\) 0 0
\(538\) 12.8326 + 4.16955i 0.553251 + 0.179762i
\(539\) 5.63778 + 17.3513i 0.242837 + 0.747374i
\(540\) 0 0
\(541\) 8.70571 26.7934i 0.374288 1.15194i −0.569670 0.821873i \(-0.692929\pi\)
0.943958 0.330065i \(-0.107071\pi\)
\(542\) −15.7606 + 21.6926i −0.676975 + 0.931776i
\(543\) 0 0
\(544\) 0.828995 + 0.602300i 0.0355429 + 0.0258234i
\(545\) −20.3028 + 8.79805i −0.869677 + 0.376867i
\(546\) 0 0
\(547\) 15.9747 + 21.9873i 0.683029 + 0.940108i 0.999965 0.00833839i \(-0.00265422\pi\)
−0.316937 + 0.948447i \(0.602654\pi\)
\(548\) 5.72219 1.85925i 0.244440 0.0794233i
\(549\) 0 0
\(550\) −23.2104 + 12.7907i −0.989695 + 0.545399i
\(551\) −1.17530 −0.0500695
\(552\) 0 0
\(553\) 25.3974 + 34.9565i 1.08001 + 1.48650i
\(554\) −6.60744 + 4.80058i −0.280723 + 0.203957i
\(555\) 0 0
\(556\) 4.55250 + 3.30758i 0.193069 + 0.140273i
\(557\) 6.74857i 0.285946i −0.989727 0.142973i \(-0.954334\pi\)
0.989727 0.142973i \(-0.0456663\pi\)
\(558\) 0 0
\(559\) 9.67318 29.7710i 0.409132 1.25918i
\(560\) −2.87303 6.62996i −0.121408 0.280167i
\(561\) 0 0
\(562\) −29.8078 9.68515i −1.25737 0.408543i
\(563\) −10.7542 3.49426i −0.453236 0.147265i 0.0734982 0.997295i \(-0.476584\pi\)
−0.526734 + 0.850030i \(0.676584\pi\)
\(564\) 0 0
\(565\) 3.77486 + 8.71104i 0.158809 + 0.366476i
\(566\) 5.05253 15.5501i 0.212374 0.653620i
\(567\) 0 0
\(568\) 8.53771i 0.358234i
\(569\) −20.4022 14.8231i −0.855304 0.621415i 0.0712991 0.997455i \(-0.477286\pi\)
−0.926603 + 0.376040i \(0.877286\pi\)
\(570\) 0 0
\(571\) 22.4908 16.3405i 0.941209 0.683828i −0.00750262 0.999972i \(-0.502388\pi\)
0.948711 + 0.316144i \(0.102388\pi\)
\(572\) −18.3948 25.3182i −0.769124 1.05861i
\(573\) 0 0
\(574\) 32.1886 1.34353
\(575\) 1.81623 + 9.46876i 0.0757420 + 0.394875i
\(576\) 0 0
\(577\) −10.9309 + 3.55168i −0.455061 + 0.147858i −0.527574 0.849509i \(-0.676898\pi\)
0.0725129 + 0.997367i \(0.476898\pi\)
\(578\) −9.37518 12.9038i −0.389956 0.536728i
\(579\) 0 0
\(580\) 0.535008 0.231841i 0.0222150 0.00962668i
\(581\) 19.5731 + 14.2207i 0.812027 + 0.589972i
\(582\) 0 0
\(583\) −7.19998 + 9.90993i −0.298193 + 0.410427i
\(584\) 1.22192 3.76068i 0.0505634 0.155618i
\(585\) 0 0
\(586\) −8.71017 26.8072i −0.359814 1.10739i
\(587\) 40.1613 + 13.0492i 1.65763 + 0.538598i 0.980374 0.197147i \(-0.0631676\pi\)
0.677259 + 0.735745i \(0.263168\pi\)
\(588\) 0 0
\(589\) −3.12272 9.61074i −0.128669 0.396004i
\(590\) 10.8842 9.60553i 0.448095 0.395454i
\(591\) 0 0
\(592\) 5.61543 7.72898i 0.230793 0.317659i
\(593\) 0.0131121i 0.000538451i 1.00000 0.000269225i \(8.56971e-5\pi\)
−1.00000 0.000269225i \(0.999914\pi\)
\(594\) 0 0
\(595\) −0.700532 7.37091i −0.0287190 0.302178i
\(596\) −9.42957 + 6.85098i −0.386250 + 0.280627i
\(597\) 0 0
\(598\) −10.8281 + 3.51826i −0.442794 + 0.143872i
\(599\) 2.38072 0.0972738 0.0486369 0.998817i \(-0.484512\pi\)
0.0486369 + 0.998817i \(0.484512\pi\)
\(600\) 0 0
\(601\) −19.6020 −0.799581 −0.399790 0.916607i \(-0.630917\pi\)
−0.399790 + 0.916607i \(0.630917\pi\)
\(602\) 16.2934 5.29404i 0.664068 0.215769i
\(603\) 0 0
\(604\) 4.46864 3.24666i 0.181826 0.132105i
\(605\) −37.3049 8.31875i −1.51666 0.338205i
\(606\) 0 0
\(607\) 10.7155i 0.434930i −0.976068 0.217465i \(-0.930221\pi\)
0.976068 0.217465i \(-0.0697788\pi\)
\(608\) 2.64926 3.64639i 0.107442 0.147881i
\(609\) 0 0
\(610\) −1.91990 + 8.60968i −0.0777346 + 0.348596i
\(611\) 19.2093 + 59.1202i 0.777126 + 2.39175i
\(612\) 0 0
\(613\) 1.10735 + 0.359801i 0.0447256 + 0.0145322i 0.331294 0.943527i \(-0.392515\pi\)
−0.286569 + 0.958060i \(0.592515\pi\)
\(614\) −4.49223 13.8257i −0.181292 0.557959i
\(615\) 0 0
\(616\) 5.29269 16.2892i 0.213248 0.656311i
\(617\) 13.3095 18.3190i 0.535821 0.737495i −0.452182 0.891926i \(-0.649354\pi\)
0.988004 + 0.154431i \(0.0493544\pi\)
\(618\) 0 0
\(619\) 20.0413 + 14.5609i 0.805529 + 0.585251i 0.912531 0.409008i \(-0.134125\pi\)
−0.107002 + 0.994259i \(0.534125\pi\)
\(620\) 3.31731 + 3.75890i 0.133227 + 0.150961i
\(621\) 0 0
\(622\) 8.51844 + 11.7246i 0.341559 + 0.470115i
\(623\) −2.25447 + 0.732522i −0.0903235 + 0.0293479i
\(624\) 0 0
\(625\) −24.2272 6.16806i −0.969086 0.246722i
\(626\) 31.5288 1.26014
\(627\) 0 0
\(628\) 4.02225 + 5.53616i 0.160505 + 0.220917i
\(629\) 7.91983 5.75410i 0.315784 0.229431i
\(630\) 0 0
\(631\) 26.4156 + 19.1920i 1.05159 + 0.764023i 0.972514 0.232845i \(-0.0748036\pi\)
0.0790740 + 0.996869i \(0.474804\pi\)
\(632\) 13.3714i 0.531885i
\(633\) 0 0
\(634\) 4.62940 14.2478i 0.183857 0.565853i
\(635\) −17.8103 10.5208i −0.706782 0.417505i
\(636\) 0 0
\(637\) −19.3290 6.28038i −0.765844 0.248838i
\(638\) 1.31447 + 0.427096i 0.0520402 + 0.0169089i
\(639\) 0 0
\(640\) −0.486675 + 2.18246i −0.0192375 + 0.0862694i
\(641\) 8.29842 25.5399i 0.327768 1.00877i −0.642408 0.766363i \(-0.722064\pi\)
0.970176 0.242403i \(-0.0779356\pi\)
\(642\) 0 0
\(643\) 17.1051i 0.674559i 0.941405 + 0.337279i \(0.109507\pi\)
−0.941405 + 0.337279i \(0.890493\pi\)
\(644\) −5.04105 3.66254i −0.198645 0.144324i
\(645\) 0 0
\(646\) 3.73643 2.71468i 0.147008 0.106808i
\(647\) 26.9285 + 37.0639i 1.05867 + 1.45713i 0.881043 + 0.473036i \(0.156842\pi\)
0.177626 + 0.984098i \(0.443158\pi\)
\(648\) 0 0
\(649\) 34.4096 1.35069
\(650\) 3.67035 29.2930i 0.143963 1.14897i
\(651\) 0 0
\(652\) −8.92773 + 2.90080i −0.349637 + 0.113604i
\(653\) −6.73337 9.26769i −0.263497 0.362673i 0.656684 0.754166i \(-0.271959\pi\)
−0.920181 + 0.391493i \(0.871959\pi\)
\(654\) 0 0
\(655\) −1.02925 10.8296i −0.0402160 0.423148i
\(656\) −8.05872 5.85500i −0.314640 0.228599i
\(657\) 0 0
\(658\) −19.9971 + 27.5236i −0.779566 + 1.07298i
\(659\) 12.3601 38.0405i 0.481482 1.48185i −0.355531 0.934664i \(-0.615700\pi\)
0.837013 0.547183i \(-0.184300\pi\)
\(660\) 0 0
\(661\) −1.75871 5.41276i −0.0684060 0.210532i 0.911010 0.412384i \(-0.135304\pi\)
−0.979416 + 0.201852i \(0.935304\pi\)
\(662\) −20.5594 6.68014i −0.799062 0.259631i
\(663\) 0 0
\(664\) −2.31360 7.12054i −0.0897852 0.276331i
\(665\) −32.4214 + 3.08134i −1.25725 + 0.119489i
\(666\) 0 0
\(667\) 0.295550 0.406790i 0.0114438 0.0157510i
\(668\) 6.82883i 0.264215i
\(669\) 0 0
\(670\) 19.0647 8.26153i 0.736534 0.319171i
\(671\) −16.9160 + 12.2902i −0.653034 + 0.474457i
\(672\) 0 0
\(673\) 46.0813 14.9727i 1.77630 0.577156i 0.777633 0.628719i \(-0.216420\pi\)
0.998670 + 0.0515628i \(0.0164202\pi\)
\(674\) −7.59495 −0.292547
\(675\) 0 0
\(676\) 21.8621 0.840849
\(677\) 17.6033 5.71966i 0.676550 0.219824i 0.0494656 0.998776i \(-0.484248\pi\)
0.627084 + 0.778951i \(0.284248\pi\)
\(678\) 0 0
\(679\) −45.1138 + 32.7771i −1.73131 + 1.25787i
\(680\) −1.16536 + 1.97280i −0.0446894 + 0.0756533i
\(681\) 0 0
\(682\) 11.8835i 0.455043i
\(683\) −21.1745 + 29.1442i −0.810219 + 1.11517i 0.181070 + 0.983470i \(0.442044\pi\)
−0.991289 + 0.131701i \(0.957956\pi\)
\(684\) 0 0
\(685\) 5.34936 + 12.3445i 0.204389 + 0.471657i
\(686\) 3.55277 + 10.9343i 0.135645 + 0.417474i
\(687\) 0 0
\(688\) −5.04216 1.63830i −0.192231 0.0624595i
\(689\) −4.21670 12.9777i −0.160643 0.494410i
\(690\) 0 0
\(691\) −4.47133 + 13.7613i −0.170097 + 0.523506i −0.999376 0.0353301i \(-0.988752\pi\)
0.829278 + 0.558836i \(0.188752\pi\)
\(692\) 11.0859 15.2584i 0.421422 0.580038i
\(693\) 0 0
\(694\) −6.09436 4.42781i −0.231339 0.168077i
\(695\) −6.39967 + 10.8338i −0.242753 + 0.410949i
\(696\) 0 0
\(697\) −5.99958 8.25772i −0.227250 0.312783i
\(698\) 17.8349 5.79489i 0.675059 0.219340i
\(699\) 0 0
\(700\) 14.1507 7.79813i 0.534846 0.294742i
\(701\) −8.31284 −0.313972 −0.156986 0.987601i \(-0.550178\pi\)
−0.156986 + 0.987601i \(0.550178\pi\)
\(702\) 0 0
\(703\) −25.3098 34.8359i −0.954576 1.31386i
\(704\) −4.28802 + 3.11543i −0.161611 + 0.117417i
\(705\) 0 0
\(706\) −3.53223 2.56631i −0.132937 0.0965845i
\(707\) 38.2776i 1.43958i
\(708\) 0 0
\(709\) 2.77255 8.53302i 0.104125 0.320464i −0.885399 0.464832i \(-0.846115\pi\)
0.989524 + 0.144368i \(0.0461148\pi\)
\(710\) −19.0053 + 1.80626i −0.713254 + 0.0677878i
\(711\) 0 0
\(712\) 0.697671 + 0.226687i 0.0261463 + 0.00849545i
\(713\) 4.11169 + 1.33597i 0.153984 + 0.0500324i
\(714\) 0 0
\(715\) 52.4677 46.3039i 1.96218 1.73167i
\(716\) −0.290889 + 0.895264i −0.0108710 + 0.0334576i
\(717\) 0 0
\(718\) 0.737212i 0.0275125i
\(719\) −22.7445 16.5249i −0.848228 0.616274i 0.0764289 0.997075i \(-0.475648\pi\)
−0.924657 + 0.380801i \(0.875648\pi\)
\(720\) 0 0
\(721\) 18.6943 13.5822i 0.696212 0.505828i
\(722\) −0.772769 1.06363i −0.0287595 0.0395840i
\(723\) 0 0
\(724\) −14.1057 −0.524235
\(725\) 0.629274 + 1.14190i 0.0233707 + 0.0424090i
\(726\) 0 0
\(727\) 23.6592 7.68734i 0.877471 0.285108i 0.164564 0.986366i \(-0.447378\pi\)
0.712907 + 0.701259i \(0.247378\pi\)
\(728\) 11.2148 + 15.4358i 0.415647 + 0.572088i
\(729\) 0 0
\(730\) 8.62994 + 1.92442i 0.319408 + 0.0712260i
\(731\) −4.39503 3.19318i −0.162556 0.118104i
\(732\) 0 0
\(733\) −3.97108 + 5.46572i −0.146675 + 0.201881i −0.876033 0.482252i \(-0.839819\pi\)
0.729358 + 0.684133i \(0.239819\pi\)
\(734\) 5.82807 17.9370i 0.215118 0.662065i
\(735\) 0 0
\(736\) 0.595870 + 1.83390i 0.0219640 + 0.0675984i
\(737\) 46.8403 + 15.2193i 1.72538 + 0.560611i
\(738\) 0 0
\(739\) 1.57339 + 4.84241i 0.0578783 + 0.178131i 0.975816 0.218593i \(-0.0701469\pi\)
−0.917938 + 0.396724i \(0.870147\pi\)
\(740\) 18.3930 + 10.8650i 0.676140 + 0.399405i
\(741\) 0 0
\(742\) 4.38962 6.04179i 0.161148 0.221801i
\(743\) 16.0999i 0.590647i −0.955397 0.295324i \(-0.904573\pi\)
0.955397 0.295324i \(-0.0954274\pi\)
\(744\) 0 0
\(745\) −17.2455 19.5412i −0.631826 0.715933i
\(746\) −24.1383 + 17.5375i −0.883768 + 0.642095i
\(747\) 0 0
\(748\) −5.16535 + 1.67832i −0.188864 + 0.0613656i
\(749\) 10.3424 0.377905
\(750\) 0 0
\(751\) −25.4366 −0.928196 −0.464098 0.885784i \(-0.653622\pi\)
−0.464098 + 0.885784i \(0.653622\pi\)
\(752\) 10.0129 3.25338i 0.365132 0.118639i
\(753\) 0 0
\(754\) −1.24560 + 0.904981i −0.0453620 + 0.0329575i
\(755\) 8.17257 + 9.26048i 0.297430 + 0.337024i
\(756\) 0 0
\(757\) 12.4947i 0.454129i 0.973880 + 0.227064i \(0.0729128\pi\)
−0.973880 + 0.227064i \(0.927087\pi\)
\(758\) −14.9783 + 20.6159i −0.544037 + 0.748802i
\(759\) 0 0
\(760\) 8.67748 + 5.12590i 0.314765 + 0.185936i
\(761\) 3.58120 + 11.0218i 0.129818 + 0.399540i 0.994748 0.102353i \(-0.0326371\pi\)
−0.864930 + 0.501893i \(0.832637\pi\)
\(762\) 0 0
\(763\) 30.4117 + 9.88136i 1.10098 + 0.357729i
\(764\) 7.87125 + 24.2252i 0.284772 + 0.876438i
\(765\) 0 0
\(766\) 9.77832 30.0946i 0.353305 1.08736i
\(767\) −22.5307 + 31.0109i −0.813538 + 1.11974i
\(768\) 0 0
\(769\) −19.2155 13.9609i −0.692927 0.503441i 0.184694 0.982796i \(-0.440871\pi\)
−0.877621 + 0.479355i \(0.840871\pi\)
\(770\) 37.3801 + 8.33553i 1.34709 + 0.300391i
\(771\) 0 0
\(772\) −3.89960 5.36734i −0.140350 0.193175i
\(773\) −11.5030 + 3.73754i −0.413732 + 0.134430i −0.508485 0.861071i \(-0.669794\pi\)
0.0947521 + 0.995501i \(0.469794\pi\)
\(774\) 0 0
\(775\) −7.66564 + 8.17971i −0.275358 + 0.293824i
\(776\) 17.2567 0.619479
\(777\) 0 0
\(778\) −7.08164 9.74704i −0.253889 0.349448i
\(779\) −36.3221 + 26.3896i −1.30138 + 0.945504i
\(780\) 0 0
\(781\) −36.6099 26.5986i −1.31000 0.951774i
\(782\) 1.97589i 0.0706577i
\(783\) 0 0
\(784\) −1.06368 + 3.27366i −0.0379884 + 0.116916i
\(785\) −11.4727 + 10.1249i −0.409479 + 0.361374i
\(786\) 0 0
\(787\) −19.3085 6.27371i −0.688274 0.223634i −0.0560597 0.998427i \(-0.517854\pi\)
−0.632214 + 0.774794i \(0.717854\pi\)
\(788\) 9.67960 + 3.14509i 0.344821 + 0.112039i
\(789\) 0 0
\(790\) 29.7652 2.82889i 1.05900 0.100647i
\(791\) 4.23966 13.0483i 0.150745 0.463945i
\(792\) 0 0
\(793\) 23.2925i 0.827142i
\(794\) −20.8374 15.1393i −0.739493 0.537273i
\(795\) 0 0
\(796\) 2.04065 1.48262i 0.0723290 0.0525501i
\(797\) −18.6343 25.6479i −0.660059 0.908493i 0.339424 0.940633i \(-0.389768\pi\)
−0.999483 + 0.0321399i \(0.989768\pi\)
\(798\) 0 0
\(799\) 10.7881 0.381657
\(800\) −4.96121 0.621629i −0.175405 0.0219779i
\(801\) 0 0
\(802\) 25.0314 8.13321i 0.883891 0.287194i
\(803\) 12.3191 + 16.9558i 0.434731 + 0.598356i
\(804\) 0 0
\(805\) 7.08645 11.9964i 0.249764 0.422818i
\(806\) −10.7098 7.78109i −0.377235 0.274077i
\(807\) 0 0
\(808\) 6.96255 9.58313i 0.244942 0.337133i
\(809\) 2.69637 8.29856i 0.0947992 0.291762i −0.892402 0.451241i \(-0.850981\pi\)
0.987201 + 0.159479i \(0.0509815\pi\)
\(810\) 0 0
\(811\) 4.69774 + 14.4581i 0.164960 + 0.507694i 0.999033 0.0439592i \(-0.0139972\pi\)
−0.834074 + 0.551653i \(0.813997\pi\)
\(812\) −0.801391 0.260388i −0.0281233 0.00913782i
\(813\) 0 0
\(814\) 15.6475 + 48.1582i 0.548446 + 1.68794i
\(815\) −8.34605 19.2598i −0.292349 0.674640i
\(816\) 0 0
\(817\) −14.0454 + 19.3318i −0.491387 + 0.676336i
\(818\) 36.7714i 1.28568i
\(819\) 0 0
\(820\) 11.3285 19.1777i 0.395609 0.669714i
\(821\) 13.3160 9.67465i 0.464732 0.337648i −0.330653 0.943753i \(-0.607269\pi\)
0.795385 + 0.606105i \(0.207269\pi\)
\(822\) 0 0
\(823\) −21.8728 + 7.10692i −0.762439 + 0.247732i −0.664325 0.747444i \(-0.731281\pi\)
−0.0981141 + 0.995175i \(0.531281\pi\)
\(824\) −7.15084 −0.249111
\(825\) 0 0
\(826\) −20.9785 −0.729936
\(827\) −23.5214 + 7.64257i −0.817919 + 0.265758i −0.687948 0.725760i \(-0.741488\pi\)
−0.129971 + 0.991518i \(0.541488\pi\)
\(828\) 0 0
\(829\) 16.8789 12.2632i 0.586227 0.425919i −0.254736 0.967011i \(-0.581989\pi\)
0.840964 + 0.541091i \(0.181989\pi\)
\(830\) 15.3611 6.65661i 0.533192 0.231054i
\(831\) 0 0
\(832\) 5.90441i 0.204699i
\(833\) −2.07319 + 2.85350i −0.0718319 + 0.0988681i
\(834\) 0 0
\(835\) 15.2012 1.44473i 0.526060 0.0499968i
\(836\) 7.38222 + 22.7201i 0.255319 + 0.785792i
\(837\) 0 0
\(838\) −30.1718 9.80341i −1.04227 0.338653i
\(839\) −7.29166 22.4414i −0.251736 0.774764i −0.994455 0.105161i \(-0.966464\pi\)
0.742719 0.669603i \(-0.233536\pi\)
\(840\) 0 0
\(841\) −8.94048 + 27.5160i −0.308292 + 0.948827i
\(842\) 5.18266 7.13332i 0.178606 0.245830i
\(843\) 0 0
\(844\) 12.7532 + 9.26574i 0.438983 + 0.318940i
\(845\) 4.62520 + 48.6658i 0.159112 + 1.67415i
\(846\) 0 0
\(847\) 32.4663 + 44.6860i 1.11555 + 1.53543i
\(848\) −2.19796 + 0.714161i −0.0754783 + 0.0245244i
\(849\) 0 0
\(850\) −4.63807 2.17676i −0.159084 0.0746622i
\(851\) 18.4218 0.631493
\(852\) 0 0
\(853\) 15.4957 + 21.3280i 0.530563 + 0.730257i 0.987216 0.159388i \(-0.0509520\pi\)
−0.456653 + 0.889645i \(0.650952\pi\)
\(854\) 10.3132 7.49296i 0.352910 0.256404i
\(855\) 0 0
\(856\) −2.58932 1.88125i −0.0885013 0.0643000i
\(857\) 16.0891i 0.549593i −0.961502 0.274797i \(-0.911389\pi\)
0.961502 0.274797i \(-0.0886105\pi\)
\(858\) 0 0
\(859\) −3.26846 + 10.0593i −0.111519 + 0.343219i −0.991205 0.132335i \(-0.957752\pi\)
0.879686 + 0.475554i \(0.157752\pi\)
\(860\) 2.58018 11.5706i 0.0879833 0.394555i
\(861\) 0 0
\(862\) −22.3560 7.26392i −0.761450 0.247410i
\(863\) −39.7177 12.9051i −1.35201 0.439293i −0.458640 0.888622i \(-0.651663\pi\)
−0.893366 + 0.449329i \(0.851663\pi\)
\(864\) 0 0
\(865\) 36.3112 + 21.4495i 1.23462 + 0.729304i
\(866\) 2.59671 7.99185i 0.0882397 0.271574i
\(867\) 0 0
\(868\) 7.24502i 0.245912i
\(869\) 57.3368 + 41.6576i 1.94502 + 1.41314i
\(870\) 0 0
\(871\) −44.3862 + 32.2485i −1.50397 + 1.09270i
\(872\) −5.81646 8.00567i −0.196970 0.271106i
\(873\) 0 0
\(874\) 8.69109 0.293980
\(875\) 20.3527 + 29.8502i 0.688047 + 1.00912i
\(876\) 0 0
\(877\) −30.2690 + 9.83498i −1.02211 + 0.332104i −0.771667 0.636027i \(-0.780577\pi\)
−0.250444 + 0.968131i \(0.580577\pi\)
\(878\) 20.9443 + 28.8273i 0.706835 + 0.972875i
\(879\) 0 0
\(880\) −7.84225 8.88619i −0.264362 0.299553i
\(881\) −40.1535 29.1732i −1.35280 0.982870i −0.998866 0.0476012i \(-0.984842\pi\)
−0.353938 0.935269i \(-0.615158\pi\)
\(882\) 0 0
\(883\) −2.97477 + 4.09442i −0.100109 + 0.137788i −0.856133 0.516756i \(-0.827139\pi\)
0.756024 + 0.654544i \(0.227139\pi\)
\(884\) 1.86962 5.75410i 0.0628821 0.193531i
\(885\) 0 0
\(886\) −2.09992 6.46290i −0.0705483 0.217125i
\(887\) 10.5132 + 3.41594i 0.352998 + 0.114696i 0.480148 0.877187i \(-0.340583\pi\)
−0.127150 + 0.991884i \(0.540583\pi\)
\(888\) 0 0
\(889\) 9.23763 + 28.4305i 0.309820 + 0.953529i
\(890\) −0.357012 + 1.60100i −0.0119671 + 0.0536656i
\(891\) 0 0
\(892\) 5.46366 7.52009i 0.182937 0.251791i
\(893\) 47.4524i 1.58793i
\(894\) 0 0
\(895\) −2.05443 0.458125i −0.0686721 0.0153134i
\(896\) 2.61428 1.89939i 0.0873370 0.0634540i
\(897\) 0 0
\(898\) −8.32185 + 2.70393i −0.277704 + 0.0902314i
\(899\) 0.584641 0.0194989
\(900\) 0 0
\(901\) −2.36814 −0.0788942
\(902\) 50.2127 16.3151i 1.67190 0.543234i
\(903\) 0 0
\(904\) −3.43488 + 2.49559i −0.114242 + 0.0830020i
\(905\) −2.98425 31.3999i −0.0991997 1.04377i
\(906\) 0 0
\(907\) 7.57086i 0.251386i 0.992069 + 0.125693i \(0.0401155\pi\)
−0.992069 + 0.125693i \(0.959885\pi\)
\(908\) 2.13841 2.94327i 0.0709658 0.0976760i
\(909\) 0 0
\(910\) −31.9880 + 28.2301i −1.06039 + 0.935819i
\(911\) −11.0530 34.0177i −0.366203 1.12706i −0.949224 0.314601i \(-0.898129\pi\)
0.583021 0.812457i \(-0.301871\pi\)
\(912\) 0 0
\(913\) 37.7409 + 12.2628i 1.24904 + 0.405838i
\(914\) 11.7882 + 36.2803i 0.389919 + 1.20005i
\(915\) 0 0
\(916\) 3.06910 9.44571i 0.101406 0.312095i
\(917\) −9.24046 + 12.7184i −0.305147 + 0.419998i
\(918\) 0 0
\(919\) −40.1464 29.1680i −1.32431 0.962165i −0.999868 0.0162579i \(-0.994825\pi\)
−0.324438 0.945907i \(-0.605175\pi\)
\(920\) −3.95626 + 1.71441i −0.130434 + 0.0565225i
\(921\) 0 0
\(922\) −0.746939 1.02807i −0.0245991 0.0338578i
\(923\) 47.9429 15.5776i 1.57806 0.512743i
\(924\) 0 0
\(925\) −20.2946 + 43.2421i −0.667282 + 1.42179i
\(926\) 8.93349 0.293573
\(927\) 0 0
\(928\) 0.153272 + 0.210961i 0.00503140 + 0.00692512i
\(929\) 13.1559 9.55836i 0.431633 0.313599i −0.350669 0.936500i \(-0.614046\pi\)
0.782301 + 0.622900i \(0.214046\pi\)
\(930\) 0 0
\(931\) 12.5513 + 9.11908i 0.411353 + 0.298866i
\(932\) 18.7893i 0.615465i
\(933\) 0 0
\(934\) −1.77896 + 5.47507i −0.0582092 + 0.179150i
\(935\) −4.82881 11.1432i −0.157919 0.364421i
\(936\) 0 0
\(937\) −0.541982 0.176101i −0.0177058 0.00575296i 0.300151 0.953892i \(-0.402963\pi\)
−0.317857 + 0.948139i \(0.602963\pi\)
\(938\) −28.5571 9.27878i −0.932424 0.302963i
\(939\) 0 0
\(940\) 9.36050 + 21.6008i 0.305306 + 0.704539i
\(941\) −2.16169 + 6.65300i −0.0704691 + 0.216882i −0.980089 0.198561i \(-0.936373\pi\)
0.909619 + 0.415443i \(0.136373\pi\)
\(942\) 0 0
\(943\) 19.2078i 0.625491i
\(944\) 5.25216 + 3.81592i 0.170943 + 0.124198i
\(945\) 0 0
\(946\) 22.7335 16.5169i 0.739131 0.537010i
\(947\) −20.2563 27.8804i −0.658241 0.905991i 0.341181 0.939998i \(-0.389173\pi\)
−0.999422 + 0.0340070i \(0.989173\pi\)
\(948\) 0 0
\(949\) −23.3473 −0.757886
\(950\) −9.57462 + 20.4008i −0.310642 + 0.661891i
\(951\) 0 0
\(952\) 3.14916 1.02322i 0.102065 0.0331629i
\(953\) 24.7083 + 34.0081i 0.800382 + 1.10163i 0.992737 + 0.120305i \(0.0383874\pi\)
−0.192355 + 0.981325i \(0.561613\pi\)
\(954\) 0 0
\(955\) −52.2610 + 22.6469i −1.69113 + 0.732835i
\(956\) −7.88942 5.73200i −0.255162 0.185386i
\(957\) 0 0
\(958\) −2.72175 + 3.74616i −0.0879356 + 0.121033i
\(959\) 6.00804 18.4908i 0.194010 0.597100i
\(960\) 0 0
\(961\) −8.02616 24.7020i −0.258909 0.796839i
\(962\) −53.6472 17.4310i −1.72966 0.561999i
\(963\) 0 0
\(964\) −5.84694 17.9950i −0.188317 0.579580i
\(965\) 11.1229 9.81618i 0.358058 0.315994i
\(966\) 0 0
\(967\) 7.03499 9.68283i 0.226230 0.311379i −0.680780 0.732488i \(-0.738359\pi\)
0.907010 + 0.421109i \(0.138359\pi\)
\(968\) 17.0930i 0.549391i
\(969\) 0 0
\(970\) 3.65087 + 38.4140i 0.117222 + 1.23340i
\(971\) 1.09374 0.794651i 0.0350999 0.0255016i −0.570097 0.821577i \(-0.693094\pi\)
0.605197 + 0.796076i \(0.293094\pi\)
\(972\) 0 0
\(973\) 17.2939 5.61913i 0.554417 0.180141i
\(974\) −15.9235 −0.510223
\(975\) 0 0
\(976\) −3.94494 −0.126274
\(977\) −17.6371 + 5.73065i −0.564262 + 0.183340i −0.577238 0.816576i \(-0.695869\pi\)
0.0129761 + 0.999916i \(0.495869\pi\)
\(978\) 0 0
\(979\) −3.14558 + 2.28540i −0.100533 + 0.0730417i
\(980\) −7.51232 1.67520i −0.239972 0.0535122i
\(981\) 0 0
\(982\) 6.38076i 0.203618i
\(983\) 9.62915 13.2534i 0.307122 0.422718i −0.627359 0.778730i \(-0.715864\pi\)
0.934481 + 0.356013i \(0.115864\pi\)
\(984\) 0 0
\(985\) −4.95325 + 22.2125i −0.157824 + 0.707750i
\(986\) 0.0825696 + 0.254123i 0.00262955 + 0.00809293i
\(987\) 0 0
\(988\) −25.3098 8.22365i −0.805211 0.261629i
\(989\) −3.15909 9.72267i −0.100453 0.309163i
\(990\) 0 0
\(991\) 6.12790 18.8597i 0.194659 0.599099i −0.805321 0.592839i \(-0.798007\pi\)
0.999980 0.00626045i \(-0.00199278\pi\)
\(992\) −1.31784 + 1.81386i −0.0418416 + 0.0575900i
\(993\) 0 0
\(994\) 22.3200 + 16.2164i 0.707946 + 0.514353i
\(995\) 3.73209 + 4.22890i 0.118315 + 0.134065i
\(996\) 0 0
\(997\) −6.15262 8.46835i −0.194855 0.268195i 0.700398 0.713752i \(-0.253006\pi\)
−0.895254 + 0.445557i \(0.853006\pi\)
\(998\) 12.2815 3.99049i 0.388763 0.126317i
\(999\) 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 450.2.l.c.19.2 16
3.2 odd 2 150.2.h.b.19.3 16
15.2 even 4 750.2.g.f.151.4 16
15.8 even 4 750.2.g.g.151.1 16
15.14 odd 2 750.2.h.d.349.2 16
25.4 even 10 inner 450.2.l.c.379.2 16
75.2 even 20 3750.2.a.v.1.7 8
75.11 odd 10 3750.2.c.k.1249.2 16
75.14 odd 10 3750.2.c.k.1249.15 16
75.23 even 20 3750.2.a.u.1.2 8
75.29 odd 10 150.2.h.b.79.3 yes 16
75.47 even 20 750.2.g.f.601.4 16
75.53 even 20 750.2.g.g.601.1 16
75.71 odd 10 750.2.h.d.649.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.2.h.b.19.3 16 3.2 odd 2
150.2.h.b.79.3 yes 16 75.29 odd 10
450.2.l.c.19.2 16 1.1 even 1 trivial
450.2.l.c.379.2 16 25.4 even 10 inner
750.2.g.f.151.4 16 15.2 even 4
750.2.g.f.601.4 16 75.47 even 20
750.2.g.g.151.1 16 15.8 even 4
750.2.g.g.601.1 16 75.53 even 20
750.2.h.d.349.2 16 15.14 odd 2
750.2.h.d.649.1 16 75.71 odd 10
3750.2.a.u.1.2 8 75.23 even 20
3750.2.a.v.1.7 8 75.2 even 20
3750.2.c.k.1249.2 16 75.11 odd 10
3750.2.c.k.1249.15 16 75.14 odd 10