Properties

Label 475.2.l.c.351.1
Level $475$
Weight $2$
Character 475.351
Analytic conductor $3.793$
Analytic rank $0$
Dimension $18$
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] = [475,2,Mod(101,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.l (of order \(9\), degree \(6\), 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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} - 156 x^{9} + 582 x^{8} - 138 x^{7} + 437 x^{6} - 132 x^{5} + 198 x^{4} - 16 x^{3} + \cdots + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 351.1
Root \(-0.566185 + 0.980662i\) of defining polynomial
Character \(\chi\) \(=\) 475.351
Dual form 475.2.l.c.226.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.370282 - 2.09998i) q^{2} +(-1.70859 + 1.43367i) q^{3} +(-2.39340 + 0.871127i) q^{4} +(3.64334 + 3.05712i) q^{6} +(0.742812 - 1.28659i) q^{7} +(0.583208 + 1.01015i) q^{8} +(0.342900 - 1.94468i) q^{9} +O(q^{10})\) \(q+(-0.370282 - 2.09998i) q^{2} +(-1.70859 + 1.43367i) q^{3} +(-2.39340 + 0.871127i) q^{4} +(3.64334 + 3.05712i) q^{6} +(0.742812 - 1.28659i) q^{7} +(0.583208 + 1.01015i) q^{8} +(0.342900 - 1.94468i) q^{9} +(-2.34068 - 4.05417i) q^{11} +(2.84042 - 4.91975i) q^{12} +(0.276562 + 0.232063i) q^{13} +(-2.97685 - 1.08349i) q^{14} +(-1.99691 + 1.67560i) q^{16} +(0.951255 + 5.39483i) q^{17} -4.21075 q^{18} +(-1.68540 + 4.01988i) q^{19} +(0.575390 + 3.26320i) q^{21} +(-7.64695 + 6.41655i) q^{22} +(-5.79545 + 2.10937i) q^{23} +(-2.44468 - 0.889790i) q^{24} +(0.384921 - 0.666703i) q^{26} +(-1.14343 - 1.98049i) q^{27} +(-0.657066 + 3.72641i) q^{28} +(-0.155581 + 0.882346i) q^{29} +(-2.40012 + 4.15713i) q^{31} +(6.04520 + 5.07252i) q^{32} +(9.81160 + 3.57113i) q^{33} +(10.9768 - 3.99522i) q^{34} +(0.873368 + 4.95311i) q^{36} -11.3982 q^{37} +(9.06572 + 2.05081i) q^{38} -0.805233 q^{39} +(-4.01104 + 3.36566i) q^{41} +(6.63958 - 2.41661i) q^{42} +(6.78295 + 2.46879i) q^{43} +(9.13387 + 7.66423i) q^{44} +(6.57558 + 11.3892i) q^{46} +(1.88678 - 10.7005i) q^{47} +(1.00962 - 5.72583i) q^{48} +(2.39646 + 4.15079i) q^{49} +(-9.35973 - 7.85374i) q^{51} +(-0.864081 - 0.314500i) q^{52} +(-6.12941 + 2.23092i) q^{53} +(-3.73558 + 3.13452i) q^{54} +1.73286 q^{56} +(-2.88354 - 9.28462i) q^{57} +1.91051 q^{58} +(-1.70300 - 9.65818i) q^{59} +(-2.20795 + 0.803626i) q^{61} +(9.61858 + 3.50088i) q^{62} +(-2.24730 - 1.88571i) q^{63} +(5.80697 - 10.0580i) q^{64} +(3.86622 - 21.9264i) q^{66} +(-1.53717 + 8.71774i) q^{67} +(-6.97632 - 12.0833i) q^{68} +(6.87787 - 11.9128i) q^{69} +(-6.02538 - 2.19306i) q^{71} +(2.16439 - 0.787775i) q^{72} +(-2.19219 + 1.83946i) q^{73} +(4.22054 + 23.9359i) q^{74} +(0.532020 - 11.0894i) q^{76} -6.95473 q^{77} +(0.298164 + 1.69097i) q^{78} +(1.58226 - 1.32767i) q^{79} +(10.3598 + 3.77066i) q^{81} +(8.55302 + 7.17684i) q^{82} +(3.08199 - 5.33816i) q^{83} +(-4.21980 - 7.30890i) q^{84} +(2.67280 - 15.1582i) q^{86} +(-0.999172 - 1.73062i) q^{87} +(2.73020 - 4.72885i) q^{88} +(-2.54338 - 2.13415i) q^{89} +(0.504004 - 0.183442i) q^{91} +(12.0333 - 10.0971i) q^{92} +(-1.85915 - 10.5438i) q^{93} -23.1693 q^{94} -17.6011 q^{96} +(-0.819060 - 4.64512i) q^{97} +(7.82919 - 6.56947i) q^{98} +(-8.68669 + 3.16170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.370282 2.09998i −0.261829 1.48491i −0.777915 0.628370i \(-0.783723\pi\)
0.516086 0.856537i \(-0.327389\pi\)
\(3\) −1.70859 + 1.43367i −0.986452 + 0.827732i −0.985050 0.172267i \(-0.944891\pi\)
−0.00140187 + 0.999999i \(0.500446\pi\)
\(4\) −2.39340 + 0.871127i −1.19670 + 0.435563i
\(5\) 0 0
\(6\) 3.64334 + 3.05712i 1.48739 + 1.24807i
\(7\) 0.742812 1.28659i 0.280757 0.486285i −0.690815 0.723032i \(-0.742748\pi\)
0.971571 + 0.236747i \(0.0760813\pi\)
\(8\) 0.583208 + 1.01015i 0.206195 + 0.357140i
\(9\) 0.342900 1.94468i 0.114300 0.648227i
\(10\) 0 0
\(11\) −2.34068 4.05417i −0.705741 1.22238i −0.966424 0.256954i \(-0.917281\pi\)
0.260683 0.965424i \(-0.416052\pi\)
\(12\) 2.84042 4.91975i 0.819958 1.42021i
\(13\) 0.276562 + 0.232063i 0.0767046 + 0.0643628i 0.680334 0.732902i \(-0.261835\pi\)
−0.603629 + 0.797265i \(0.706279\pi\)
\(14\) −2.97685 1.08349i −0.795598 0.289574i
\(15\) 0 0
\(16\) −1.99691 + 1.67560i −0.499227 + 0.418901i
\(17\) 0.951255 + 5.39483i 0.230713 + 1.30844i 0.851456 + 0.524425i \(0.175720\pi\)
−0.620743 + 0.784014i \(0.713169\pi\)
\(18\) −4.21075 −0.992484
\(19\) −1.68540 + 4.01988i −0.386658 + 0.922223i
\(20\) 0 0
\(21\) 0.575390 + 3.26320i 0.125560 + 0.712088i
\(22\) −7.64695 + 6.41655i −1.63033 + 1.36801i
\(23\) −5.79545 + 2.10937i −1.20843 + 0.439834i −0.866161 0.499766i \(-0.833419\pi\)
−0.342274 + 0.939600i \(0.611197\pi\)
\(24\) −2.44468 0.889790i −0.499018 0.181628i
\(25\) 0 0
\(26\) 0.384921 0.666703i 0.0754892 0.130751i
\(27\) −1.14343 1.98049i −0.220054 0.381145i
\(28\) −0.657066 + 3.72641i −0.124174 + 0.704225i
\(29\) −0.155581 + 0.882346i −0.0288907 + 0.163848i −0.995840 0.0911225i \(-0.970955\pi\)
0.966949 + 0.254970i \(0.0820656\pi\)
\(30\) 0 0
\(31\) −2.40012 + 4.15713i −0.431074 + 0.746642i −0.996966 0.0778374i \(-0.975199\pi\)
0.565892 + 0.824479i \(0.308532\pi\)
\(32\) 6.04520 + 5.07252i 1.06865 + 0.896704i
\(33\) 9.81160 + 3.57113i 1.70798 + 0.621654i
\(34\) 10.9768 3.99522i 1.88250 0.685175i
\(35\) 0 0
\(36\) 0.873368 + 4.95311i 0.145561 + 0.825519i
\(37\) −11.3982 −1.87385 −0.936924 0.349534i \(-0.886340\pi\)
−0.936924 + 0.349534i \(0.886340\pi\)
\(38\) 9.06572 + 2.05081i 1.47065 + 0.332686i
\(39\) −0.805233 −0.128941
\(40\) 0 0
\(41\) −4.01104 + 3.36566i −0.626419 + 0.525628i −0.899814 0.436274i \(-0.856298\pi\)
0.273395 + 0.961902i \(0.411853\pi\)
\(42\) 6.63958 2.41661i 1.02451 0.372891i
\(43\) 6.78295 + 2.46879i 1.03439 + 0.376487i 0.802751 0.596314i \(-0.203369\pi\)
0.231639 + 0.972802i \(0.425591\pi\)
\(44\) 9.13387 + 7.66423i 1.37698 + 1.15543i
\(45\) 0 0
\(46\) 6.57558 + 11.3892i 0.969516 + 1.67925i
\(47\) 1.88678 10.7005i 0.275215 1.56082i −0.463062 0.886326i \(-0.653249\pi\)
0.738278 0.674497i \(-0.235639\pi\)
\(48\) 1.00962 5.72583i 0.145726 0.826452i
\(49\) 2.39646 + 4.15079i 0.342351 + 0.592970i
\(50\) 0 0
\(51\) −9.35973 7.85374i −1.31062 1.09974i
\(52\) −0.864081 0.314500i −0.119827 0.0436133i
\(53\) −6.12941 + 2.23092i −0.841940 + 0.306441i −0.726750 0.686902i \(-0.758970\pi\)
−0.115190 + 0.993343i \(0.536748\pi\)
\(54\) −3.73558 + 3.13452i −0.508348 + 0.426555i
\(55\) 0 0
\(56\) 1.73286 0.231563
\(57\) −2.88354 9.28462i −0.381934 1.22978i
\(58\) 1.91051 0.250863
\(59\) −1.70300 9.65818i −0.221711 1.25739i −0.868873 0.495035i \(-0.835155\pi\)
0.647162 0.762353i \(-0.275956\pi\)
\(60\) 0 0
\(61\) −2.20795 + 0.803626i −0.282698 + 0.102894i −0.479478 0.877554i \(-0.659174\pi\)
0.196779 + 0.980448i \(0.436952\pi\)
\(62\) 9.61858 + 3.50088i 1.22156 + 0.444612i
\(63\) −2.24730 1.88571i −0.283133 0.237577i
\(64\) 5.80697 10.0580i 0.725871 1.25725i
\(65\) 0 0
\(66\) 3.86622 21.9264i 0.475899 2.69896i
\(67\) −1.53717 + 8.71774i −0.187796 + 1.06504i 0.734515 + 0.678592i \(0.237410\pi\)
−0.922311 + 0.386449i \(0.873701\pi\)
\(68\) −6.97632 12.0833i −0.846003 1.46532i
\(69\) 6.87787 11.9128i 0.827998 1.43414i
\(70\) 0 0
\(71\) −6.02538 2.19306i −0.715081 0.260268i −0.0412447 0.999149i \(-0.513132\pi\)
−0.673836 + 0.738881i \(0.735355\pi\)
\(72\) 2.16439 0.787775i 0.255076 0.0928402i
\(73\) −2.19219 + 1.83946i −0.256576 + 0.215293i −0.761998 0.647580i \(-0.775781\pi\)
0.505422 + 0.862872i \(0.331337\pi\)
\(74\) 4.22054 + 23.9359i 0.490628 + 2.78249i
\(75\) 0 0
\(76\) 0.532020 11.0894i 0.0610268 1.27204i
\(77\) −6.95473 −0.792566
\(78\) 0.298164 + 1.69097i 0.0337604 + 0.191465i
\(79\) 1.58226 1.32767i 0.178018 0.149375i −0.549425 0.835543i \(-0.685153\pi\)
0.727443 + 0.686168i \(0.240709\pi\)
\(80\) 0 0
\(81\) 10.3598 + 3.77066i 1.15109 + 0.418962i
\(82\) 8.55302 + 7.17684i 0.944523 + 0.792549i
\(83\) 3.08199 5.33816i 0.338292 0.585939i −0.645820 0.763490i \(-0.723484\pi\)
0.984112 + 0.177551i \(0.0568176\pi\)
\(84\) −4.21980 7.30890i −0.460418 0.797467i
\(85\) 0 0
\(86\) 2.67280 15.1582i 0.288215 1.63455i
\(87\) −0.999172 1.73062i −0.107122 0.185542i
\(88\) 2.73020 4.72885i 0.291040 0.504097i
\(89\) −2.54338 2.13415i −0.269598 0.226220i 0.497959 0.867201i \(-0.334083\pi\)
−0.767556 + 0.640981i \(0.778528\pi\)
\(90\) 0 0
\(91\) 0.504004 0.183442i 0.0528340 0.0192300i
\(92\) 12.0333 10.0971i 1.25456 1.05270i
\(93\) −1.85915 10.5438i −0.192785 1.09334i
\(94\) −23.1693 −2.38974
\(95\) 0 0
\(96\) −17.6011 −1.79640
\(97\) −0.819060 4.64512i −0.0831630 0.471641i −0.997738 0.0672241i \(-0.978586\pi\)
0.914575 0.404416i \(-0.132525\pi\)
\(98\) 7.82919 6.56947i 0.790867 0.663617i
\(99\) −8.68669 + 3.16170i −0.873045 + 0.317762i
\(100\) 0 0
\(101\) 6.92692 + 5.81237i 0.689254 + 0.578353i 0.918694 0.394970i \(-0.129245\pi\)
−0.229440 + 0.973323i \(0.573690\pi\)
\(102\) −13.0269 + 22.5633i −1.28986 + 2.23410i
\(103\) 3.89934 + 6.75385i 0.384213 + 0.665476i 0.991660 0.128884i \(-0.0411395\pi\)
−0.607447 + 0.794360i \(0.707806\pi\)
\(104\) −0.0731245 + 0.414709i −0.00717044 + 0.0406656i
\(105\) 0 0
\(106\) 6.95450 + 12.0455i 0.675481 + 1.16997i
\(107\) 0.259152 0.448864i 0.0250531 0.0433933i −0.853227 0.521540i \(-0.825358\pi\)
0.878280 + 0.478146i \(0.158691\pi\)
\(108\) 4.46195 + 3.74402i 0.429352 + 0.360269i
\(109\) 2.59771 + 0.945488i 0.248815 + 0.0905614i 0.463417 0.886140i \(-0.346623\pi\)
−0.214602 + 0.976702i \(0.568845\pi\)
\(110\) 0 0
\(111\) 19.4747 16.3413i 1.84846 1.55104i
\(112\) 0.672486 + 3.81386i 0.0635440 + 0.360376i
\(113\) −12.4325 −1.16955 −0.584774 0.811197i \(-0.698817\pi\)
−0.584774 + 0.811197i \(0.698817\pi\)
\(114\) −18.4297 + 9.49329i −1.72610 + 0.889128i
\(115\) 0 0
\(116\) −0.396266 2.24734i −0.0367924 0.208660i
\(117\) 0.546123 0.458251i 0.0504891 0.0423654i
\(118\) −19.6513 + 7.15250i −1.80905 + 0.658441i
\(119\) 7.64754 + 2.78348i 0.701049 + 0.255161i
\(120\) 0 0
\(121\) −5.45753 + 9.45272i −0.496139 + 0.859339i
\(122\) 2.50516 + 4.33906i 0.226806 + 0.392840i
\(123\) 2.02794 11.5010i 0.182853 1.03701i
\(124\) 2.12306 12.0405i 0.190656 1.08127i
\(125\) 0 0
\(126\) −3.12780 + 5.41751i −0.278647 + 0.482630i
\(127\) 1.04258 + 0.874829i 0.0925141 + 0.0776285i 0.687872 0.725832i \(-0.258545\pi\)
−0.595358 + 0.803461i \(0.702990\pi\)
\(128\) −8.44062 3.07213i −0.746052 0.271541i
\(129\) −15.1287 + 5.50639i −1.33201 + 0.484811i
\(130\) 0 0
\(131\) −3.39033 19.2275i −0.296214 1.67991i −0.662226 0.749305i \(-0.730388\pi\)
0.366011 0.930610i \(-0.380723\pi\)
\(132\) −26.5940 −2.31471
\(133\) 3.91999 + 5.15444i 0.339907 + 0.446946i
\(134\) 18.8762 1.63066
\(135\) 0 0
\(136\) −4.89479 + 4.10721i −0.419725 + 0.352191i
\(137\) 10.0363 3.65291i 0.857458 0.312089i 0.124381 0.992235i \(-0.460306\pi\)
0.733077 + 0.680145i \(0.238083\pi\)
\(138\) −27.5634 10.0323i −2.34635 0.854002i
\(139\) −5.50879 4.62243i −0.467250 0.392069i 0.378541 0.925585i \(-0.376426\pi\)
−0.845790 + 0.533516i \(0.820871\pi\)
\(140\) 0 0
\(141\) 12.1172 + 20.9877i 1.02046 + 1.76748i
\(142\) −2.37428 + 13.4652i −0.199245 + 1.12997i
\(143\) 0.293481 1.66442i 0.0245422 0.139185i
\(144\) 2.57378 + 4.45792i 0.214482 + 0.371493i
\(145\) 0 0
\(146\) 4.67455 + 3.92241i 0.386869 + 0.324621i
\(147\) −10.0454 3.65624i −0.828533 0.301561i
\(148\) 27.2804 9.92925i 2.24243 0.816179i
\(149\) 3.25360 2.73009i 0.266545 0.223658i −0.499713 0.866191i \(-0.666561\pi\)
0.766258 + 0.642533i \(0.222117\pi\)
\(150\) 0 0
\(151\) −19.5373 −1.58992 −0.794961 0.606660i \(-0.792509\pi\)
−0.794961 + 0.606660i \(0.792509\pi\)
\(152\) −5.04360 + 0.641923i −0.409090 + 0.0520668i
\(153\) 10.8174 0.874537
\(154\) 2.57521 + 14.6048i 0.207517 + 1.17689i
\(155\) 0 0
\(156\) 1.92725 0.701460i 0.154303 0.0561618i
\(157\) 0.269149 + 0.0979622i 0.0214804 + 0.00781823i 0.352738 0.935722i \(-0.385251\pi\)
−0.331258 + 0.943540i \(0.607473\pi\)
\(158\) −3.37396 2.83109i −0.268418 0.225230i
\(159\) 7.27421 12.5993i 0.576882 0.999190i
\(160\) 0 0
\(161\) −1.59104 + 9.02323i −0.125391 + 0.711130i
\(162\) 4.08224 23.1515i 0.320731 1.81896i
\(163\) −10.3128 17.8622i −0.807759 1.39908i −0.914413 0.404783i \(-0.867347\pi\)
0.106654 0.994296i \(-0.465986\pi\)
\(164\) 6.66811 11.5495i 0.520692 0.901864i
\(165\) 0 0
\(166\) −12.3512 4.49547i −0.958639 0.348916i
\(167\) 10.1993 3.71223i 0.789243 0.287261i 0.0842218 0.996447i \(-0.473160\pi\)
0.705021 + 0.709186i \(0.250937\pi\)
\(168\) −2.96073 + 2.48435i −0.228425 + 0.191672i
\(169\) −2.23479 12.6741i −0.171907 0.974934i
\(170\) 0 0
\(171\) 7.23946 + 4.65599i 0.553615 + 0.356052i
\(172\) −18.3850 −1.40184
\(173\) 3.04734 + 17.2823i 0.231685 + 1.31395i 0.849483 + 0.527616i \(0.176914\pi\)
−0.617798 + 0.786337i \(0.711975\pi\)
\(174\) −3.26428 + 2.73905i −0.247464 + 0.207647i
\(175\) 0 0
\(176\) 11.4673 + 4.17376i 0.864380 + 0.314609i
\(177\) 16.7564 + 14.0603i 1.25949 + 1.05684i
\(178\) −3.53989 + 6.13128i −0.265326 + 0.459559i
\(179\) −7.53220 13.0462i −0.562983 0.975116i −0.997234 0.0743239i \(-0.976320\pi\)
0.434251 0.900792i \(-0.357013\pi\)
\(180\) 0 0
\(181\) 2.59091 14.6938i 0.192581 1.09218i −0.723241 0.690596i \(-0.757348\pi\)
0.915822 0.401585i \(-0.131541\pi\)
\(182\) −0.571848 0.990471i −0.0423882 0.0734186i
\(183\) 2.62033 4.53854i 0.193700 0.335498i
\(184\) −5.51072 4.62405i −0.406256 0.340889i
\(185\) 0 0
\(186\) −21.4533 + 7.80836i −1.57303 + 0.572536i
\(187\) 19.6450 16.4841i 1.43658 1.20544i
\(188\) 4.80564 + 27.2541i 0.350487 + 1.98771i
\(189\) −3.39743 −0.247127
\(190\) 0 0
\(191\) −0.00677854 −0.000490478 −0.000245239 1.00000i \(-0.500078\pi\)
−0.000245239 1.00000i \(0.500078\pi\)
\(192\) 4.49813 + 25.5102i 0.324625 + 1.84104i
\(193\) −10.5149 + 8.82305i −0.756880 + 0.635097i −0.937313 0.348490i \(-0.886695\pi\)
0.180433 + 0.983587i \(0.442250\pi\)
\(194\) −9.45136 + 3.44001i −0.678568 + 0.246978i
\(195\) 0 0
\(196\) −9.35155 7.84688i −0.667968 0.560492i
\(197\) 0.239890 0.415502i 0.0170915 0.0296033i −0.857353 0.514729i \(-0.827893\pi\)
0.874445 + 0.485125i \(0.161226\pi\)
\(198\) 9.85601 + 17.0711i 0.700436 + 1.21319i
\(199\) −4.65737 + 26.4133i −0.330152 + 1.87239i 0.140517 + 0.990078i \(0.455123\pi\)
−0.470670 + 0.882309i \(0.655988\pi\)
\(200\) 0 0
\(201\) −9.87200 17.0988i −0.696317 1.20606i
\(202\) 9.64092 16.6986i 0.678333 1.17491i
\(203\) 1.01965 + 0.855587i 0.0715653 + 0.0600504i
\(204\) 29.2432 + 10.6436i 2.04743 + 0.745205i
\(205\) 0 0
\(206\) 12.7391 10.6893i 0.887572 0.744761i
\(207\) 2.11480 + 11.9936i 0.146989 + 0.833614i
\(208\) −0.941116 −0.0652547
\(209\) 20.2423 2.57633i 1.40019 0.178208i
\(210\) 0 0
\(211\) 1.43107 + 8.11599i 0.0985188 + 0.558728i 0.993612 + 0.112849i \(0.0359976\pi\)
−0.895093 + 0.445879i \(0.852891\pi\)
\(212\) 12.7267 10.6790i 0.874075 0.733436i
\(213\) 13.4390 4.89139i 0.920825 0.335153i
\(214\) −1.03856 0.378006i −0.0709946 0.0258399i
\(215\) 0 0
\(216\) 1.33372 2.31007i 0.0907481 0.157180i
\(217\) 3.56567 + 6.17593i 0.242054 + 0.419249i
\(218\) 1.02362 5.80522i 0.0693281 0.393179i
\(219\) 1.10835 6.28576i 0.0748952 0.424752i
\(220\) 0 0
\(221\) −0.988862 + 1.71276i −0.0665181 + 0.115213i
\(222\) −41.5274 34.8456i −2.78713 2.33868i
\(223\) 1.61443 + 0.587605i 0.108110 + 0.0393489i 0.395509 0.918462i \(-0.370568\pi\)
−0.287399 + 0.957811i \(0.592790\pi\)
\(224\) 11.0167 4.00975i 0.736085 0.267913i
\(225\) 0 0
\(226\) 4.60352 + 26.1079i 0.306222 + 1.73667i
\(227\) −4.22601 −0.280490 −0.140245 0.990117i \(-0.544789\pi\)
−0.140245 + 0.990117i \(0.544789\pi\)
\(228\) 14.9895 + 19.7099i 0.992707 + 1.30532i
\(229\) 5.52322 0.364985 0.182492 0.983207i \(-0.441583\pi\)
0.182492 + 0.983207i \(0.441583\pi\)
\(230\) 0 0
\(231\) 11.8828 9.97082i 0.781828 0.656032i
\(232\) −0.982034 + 0.357431i −0.0644737 + 0.0234665i
\(233\) 26.4955 + 9.64357i 1.73578 + 0.631771i 0.999015 0.0443807i \(-0.0141315\pi\)
0.736762 + 0.676152i \(0.236354\pi\)
\(234\) −1.16454 0.977162i −0.0761281 0.0638791i
\(235\) 0 0
\(236\) 12.4895 + 21.6324i 0.812994 + 1.40815i
\(237\) −0.799976 + 4.53689i −0.0519640 + 0.294702i
\(238\) 3.01348 17.0903i 0.195335 1.10780i
\(239\) 5.66020 + 9.80375i 0.366128 + 0.634152i 0.988956 0.148206i \(-0.0473499\pi\)
−0.622829 + 0.782358i \(0.714017\pi\)
\(240\) 0 0
\(241\) 12.5356 + 10.5186i 0.807488 + 0.677563i 0.950007 0.312229i \(-0.101076\pi\)
−0.142519 + 0.989792i \(0.545520\pi\)
\(242\) 21.8713 + 7.96051i 1.40594 + 0.511721i
\(243\) −16.6596 + 6.06362i −1.06872 + 0.388981i
\(244\) 4.58444 3.84680i 0.293489 0.246266i
\(245\) 0 0
\(246\) −24.9028 −1.58774
\(247\) −1.39899 + 0.720627i −0.0890153 + 0.0458524i
\(248\) −5.59907 −0.355541
\(249\) 2.38734 + 13.5393i 0.151291 + 0.858015i
\(250\) 0 0
\(251\) 6.90186 2.51207i 0.435641 0.158560i −0.114884 0.993379i \(-0.536650\pi\)
0.550525 + 0.834818i \(0.314427\pi\)
\(252\) 7.02137 + 2.55557i 0.442305 + 0.160986i
\(253\) 22.1170 + 18.5584i 1.39049 + 1.16676i
\(254\) 1.45107 2.51333i 0.0910482 0.157700i
\(255\) 0 0
\(256\) 0.707484 4.01234i 0.0442178 0.250771i
\(257\) 1.04416 5.92171i 0.0651327 0.369386i −0.934768 0.355260i \(-0.884392\pi\)
0.999900 0.0141259i \(-0.00449655\pi\)
\(258\) 17.1652 + 29.7310i 1.06866 + 1.85097i
\(259\) −8.46670 + 14.6648i −0.526095 + 0.911224i
\(260\) 0 0
\(261\) 1.66253 + 0.605113i 0.102908 + 0.0374555i
\(262\) −39.1219 + 14.2392i −2.41696 + 0.879701i
\(263\) −5.65251 + 4.74302i −0.348549 + 0.292467i −0.800207 0.599724i \(-0.795277\pi\)
0.451658 + 0.892191i \(0.350833\pi\)
\(264\) 2.11484 + 11.9939i 0.130159 + 0.738171i
\(265\) 0 0
\(266\) 9.37268 10.1405i 0.574676 0.621753i
\(267\) 7.40526 0.453194
\(268\) −3.91519 22.2041i −0.239158 1.35633i
\(269\) −8.32148 + 6.98255i −0.507370 + 0.425734i −0.860203 0.509953i \(-0.829663\pi\)
0.352833 + 0.935686i \(0.385218\pi\)
\(270\) 0 0
\(271\) −2.67693 0.974323i −0.162612 0.0591859i 0.259432 0.965762i \(-0.416465\pi\)
−0.422043 + 0.906576i \(0.638687\pi\)
\(272\) −10.9392 9.17906i −0.663285 0.556562i
\(273\) −0.598137 + 1.03600i −0.0362009 + 0.0627018i
\(274\) −11.3873 19.7233i −0.687931 1.19153i
\(275\) 0 0
\(276\) −6.08393 + 34.5037i −0.366209 + 2.07688i
\(277\) −8.07213 13.9813i −0.485008 0.840058i 0.514844 0.857284i \(-0.327850\pi\)
−0.999852 + 0.0172261i \(0.994516\pi\)
\(278\) −7.66717 + 13.2799i −0.459846 + 0.796477i
\(279\) 7.26129 + 6.09294i 0.434722 + 0.364775i
\(280\) 0 0
\(281\) −3.02211 + 1.09996i −0.180284 + 0.0656179i −0.430585 0.902550i \(-0.641693\pi\)
0.250301 + 0.968168i \(0.419470\pi\)
\(282\) 39.5868 33.2173i 2.35736 1.97806i
\(283\) −2.23560 12.6787i −0.132893 0.753671i −0.976304 0.216403i \(-0.930568\pi\)
0.843412 0.537268i \(-0.180544\pi\)
\(284\) 16.3316 0.969101
\(285\) 0 0
\(286\) −3.60390 −0.213103
\(287\) 1.35077 + 7.66061i 0.0797336 + 0.452192i
\(288\) 11.9373 10.0166i 0.703415 0.590235i
\(289\) −12.2246 + 4.44938i −0.719092 + 0.261728i
\(290\) 0 0
\(291\) 8.05902 + 6.76232i 0.472428 + 0.396414i
\(292\) 3.64437 6.31224i 0.213271 0.369396i
\(293\) −15.4055 26.6831i −0.899999 1.55884i −0.827493 0.561476i \(-0.810234\pi\)
−0.0725066 0.997368i \(-0.523100\pi\)
\(294\) −3.95836 + 22.4490i −0.230856 + 1.30925i
\(295\) 0 0
\(296\) −6.64750 11.5138i −0.386378 0.669227i
\(297\) −5.35282 + 9.27136i −0.310602 + 0.537979i
\(298\) −6.93788 5.82157i −0.401900 0.337234i
\(299\) −2.09231 0.761539i −0.121001 0.0440409i
\(300\) 0 0
\(301\) 8.21478 6.89302i 0.473492 0.397307i
\(302\) 7.23432 + 41.0278i 0.416288 + 2.36089i
\(303\) −20.1683 −1.15864
\(304\) −3.37013 10.8514i −0.193290 0.622370i
\(305\) 0 0
\(306\) −4.00550 22.7163i −0.228979 1.29861i
\(307\) −12.5488 + 10.5297i −0.716196 + 0.600959i −0.926330 0.376713i \(-0.877054\pi\)
0.210134 + 0.977673i \(0.432610\pi\)
\(308\) 16.6455 6.05846i 0.948464 0.345213i
\(309\) −16.3452 5.94915i −0.929844 0.338435i
\(310\) 0 0
\(311\) −12.3873 + 21.4555i −0.702420 + 1.21663i 0.265195 + 0.964195i \(0.414564\pi\)
−0.967615 + 0.252432i \(0.918770\pi\)
\(312\) −0.469618 0.813403i −0.0265869 0.0460499i
\(313\) −1.78395 + 10.1173i −0.100835 + 0.571863i 0.891968 + 0.452099i \(0.149325\pi\)
−0.992802 + 0.119763i \(0.961786\pi\)
\(314\) 0.106057 0.601480i 0.00598515 0.0339435i
\(315\) 0 0
\(316\) −2.63041 + 4.55600i −0.147972 + 0.256295i
\(317\) −4.65473 3.90578i −0.261436 0.219371i 0.502642 0.864495i \(-0.332361\pi\)
−0.764078 + 0.645124i \(0.776806\pi\)
\(318\) −29.1517 10.6104i −1.63475 0.595000i
\(319\) 3.94135 1.43453i 0.220673 0.0803184i
\(320\) 0 0
\(321\) 0.200741 + 1.13846i 0.0112043 + 0.0635427i
\(322\) 19.5377 1.08879
\(323\) −23.2898 5.26854i −1.29588 0.293149i
\(324\) −28.0799 −1.55999
\(325\) 0 0
\(326\) −33.6916 + 28.2706i −1.86601 + 1.56577i
\(327\) −5.79393 + 2.10882i −0.320405 + 0.116618i
\(328\) −5.73908 2.08885i −0.316888 0.115338i
\(329\) −12.3656 10.3759i −0.681736 0.572044i
\(330\) 0 0
\(331\) −5.90549 10.2286i −0.324595 0.562215i 0.656835 0.754034i \(-0.271895\pi\)
−0.981430 + 0.191819i \(0.938561\pi\)
\(332\) −2.72622 + 15.4611i −0.149621 + 0.848541i
\(333\) −3.90843 + 22.1658i −0.214181 + 1.21468i
\(334\) −11.5722 20.0436i −0.633203 1.09674i
\(335\) 0 0
\(336\) −6.61683 5.55218i −0.360978 0.302896i
\(337\) 14.3082 + 5.20776i 0.779417 + 0.283685i 0.700930 0.713230i \(-0.252769\pi\)
0.0784877 + 0.996915i \(0.474991\pi\)
\(338\) −25.7879 + 9.38602i −1.40268 + 0.510532i
\(339\) 21.2419 17.8241i 1.15370 0.968071i
\(340\) 0 0
\(341\) 22.4716 1.21691
\(342\) 7.09681 16.9267i 0.383752 0.915292i
\(343\) 17.5199 0.945983
\(344\) 1.46203 + 8.29159i 0.0788274 + 0.447052i
\(345\) 0 0
\(346\) 35.1641 12.7987i 1.89044 0.688062i
\(347\) −28.3603 10.3223i −1.52246 0.554131i −0.560700 0.828019i \(-0.689468\pi\)
−0.961762 + 0.273888i \(0.911690\pi\)
\(348\) 3.89900 + 3.27165i 0.209009 + 0.175379i
\(349\) 1.36886 2.37093i 0.0732732 0.126913i −0.827061 0.562112i \(-0.809989\pi\)
0.900334 + 0.435200i \(0.143322\pi\)
\(350\) 0 0
\(351\) 0.143367 0.813077i 0.00765239 0.0433989i
\(352\) 6.41502 36.3814i 0.341922 1.93914i
\(353\) −2.30462 3.99172i −0.122663 0.212458i 0.798154 0.602453i \(-0.205810\pi\)
−0.920817 + 0.389995i \(0.872477\pi\)
\(354\) 23.3216 40.3943i 1.23953 2.14693i
\(355\) 0 0
\(356\) 7.94645 + 2.89227i 0.421161 + 0.153290i
\(357\) −17.0571 + 6.20826i −0.902755 + 0.328576i
\(358\) −24.6076 + 20.6482i −1.30055 + 1.09129i
\(359\) 2.14281 + 12.1525i 0.113093 + 0.641383i 0.987677 + 0.156508i \(0.0500237\pi\)
−0.874584 + 0.484875i \(0.838865\pi\)
\(360\) 0 0
\(361\) −13.3188 13.5502i −0.700992 0.713170i
\(362\) −31.8160 −1.67221
\(363\) −4.22746 23.9751i −0.221884 1.25837i
\(364\) −1.04648 + 0.878103i −0.0548506 + 0.0460251i
\(365\) 0 0
\(366\) −10.5011 3.82208i −0.548900 0.199783i
\(367\) 1.25334 + 1.05168i 0.0654239 + 0.0548972i 0.674913 0.737897i \(-0.264181\pi\)
−0.609489 + 0.792794i \(0.708625\pi\)
\(368\) 8.03851 13.9231i 0.419036 0.725792i
\(369\) 5.16976 + 8.95428i 0.269127 + 0.466141i
\(370\) 0 0
\(371\) −1.68272 + 9.54319i −0.0873626 + 0.495458i
\(372\) 13.6347 + 23.6160i 0.706925 + 1.22443i
\(373\) −7.37936 + 12.7814i −0.382089 + 0.661797i −0.991361 0.131164i \(-0.958129\pi\)
0.609272 + 0.792961i \(0.291462\pi\)
\(374\) −41.8904 35.1502i −2.16610 1.81758i
\(375\) 0 0
\(376\) 11.9094 4.33467i 0.614181 0.223544i
\(377\) −0.247788 + 0.207919i −0.0127617 + 0.0107084i
\(378\) 1.25801 + 7.13452i 0.0647049 + 0.366960i
\(379\) −1.75865 −0.0903358 −0.0451679 0.998979i \(-0.514382\pi\)
−0.0451679 + 0.998979i \(0.514382\pi\)
\(380\) 0 0
\(381\) −3.03556 −0.155516
\(382\) 0.00250997 + 0.0142348i 0.000128421 + 0.000728314i
\(383\) 6.51031 5.46280i 0.332661 0.279136i −0.461122 0.887337i \(-0.652553\pi\)
0.793783 + 0.608201i \(0.208108\pi\)
\(384\) 18.8259 6.85209i 0.960708 0.349669i
\(385\) 0 0
\(386\) 22.4217 + 18.8140i 1.14123 + 0.957609i
\(387\) 7.12689 12.3441i 0.362280 0.627488i
\(388\) 6.00683 + 10.4041i 0.304951 + 0.528190i
\(389\) −5.89390 + 33.4260i −0.298833 + 1.69476i 0.352370 + 0.935861i \(0.385376\pi\)
−0.651203 + 0.758904i \(0.725735\pi\)
\(390\) 0 0
\(391\) −16.8927 29.2589i −0.854298 1.47969i
\(392\) −2.79527 + 4.84155i −0.141182 + 0.244535i
\(393\) 33.3586 + 27.9912i 1.68272 + 1.41197i
\(394\) −0.961370 0.349910i −0.0484331 0.0176282i
\(395\) 0 0
\(396\) 18.0365 15.1344i 0.906368 0.760533i
\(397\) −1.35048 7.65893i −0.0677785 0.384391i −0.999760 0.0218863i \(-0.993033\pi\)
0.931982 0.362505i \(-0.118078\pi\)
\(398\) 57.1918 2.86676
\(399\) −14.0874 3.18680i −0.705253 0.159540i
\(400\) 0 0
\(401\) 5.41570 + 30.7140i 0.270447 + 1.53378i 0.753062 + 0.657950i \(0.228576\pi\)
−0.482615 + 0.875833i \(0.660313\pi\)
\(402\) −32.2516 + 27.0623i −1.60857 + 1.34975i
\(403\) −1.62850 + 0.592725i −0.0811213 + 0.0295257i
\(404\) −21.6422 7.87712i −1.07674 0.391901i
\(405\) 0 0
\(406\) 1.41915 2.45805i 0.0704314 0.121991i
\(407\) 26.6794 + 46.2101i 1.32245 + 2.29055i
\(408\) 2.47476 14.0351i 0.122519 0.694839i
\(409\) −2.54836 + 14.4525i −0.126008 + 0.714629i 0.854695 + 0.519130i \(0.173744\pi\)
−0.980704 + 0.195499i \(0.937367\pi\)
\(410\) 0 0
\(411\) −11.9108 + 20.6301i −0.587515 + 1.01761i
\(412\) −15.2161 12.7679i −0.749645 0.629027i
\(413\) −13.6911 4.98316i −0.673696 0.245205i
\(414\) 24.4032 8.88204i 1.19935 0.436529i
\(415\) 0 0
\(416\) 0.494727 + 2.80574i 0.0242560 + 0.137563i
\(417\) 16.0393 0.785447
\(418\) −12.9056 41.5543i −0.631232 2.03249i
\(419\) −20.6063 −1.00668 −0.503341 0.864088i \(-0.667896\pi\)
−0.503341 + 0.864088i \(0.667896\pi\)
\(420\) 0 0
\(421\) 21.2034 17.7918i 1.03339 0.867119i 0.0421416 0.999112i \(-0.486582\pi\)
0.991251 + 0.131993i \(0.0421375\pi\)
\(422\) 16.5135 6.01041i 0.803864 0.292582i
\(423\) −20.1620 7.33837i −0.980311 0.356804i
\(424\) −5.82828 4.89051i −0.283046 0.237504i
\(425\) 0 0
\(426\) −15.2480 26.4104i −0.738769 1.27959i
\(427\) −0.606153 + 3.43766i −0.0293338 + 0.166360i
\(428\) −0.229237 + 1.30007i −0.0110806 + 0.0628410i
\(429\) 1.88479 + 3.26455i 0.0909986 + 0.157614i
\(430\) 0 0
\(431\) −16.0072 13.4317i −0.771042 0.646981i 0.169934 0.985455i \(-0.445645\pi\)
−0.940976 + 0.338475i \(0.890089\pi\)
\(432\) 5.60185 + 2.03891i 0.269519 + 0.0980969i
\(433\) 1.80980 0.658712i 0.0869732 0.0316557i −0.298167 0.954514i \(-0.596375\pi\)
0.385140 + 0.922858i \(0.374153\pi\)
\(434\) 11.6490 9.77467i 0.559170 0.469199i
\(435\) 0 0
\(436\) −7.04100 −0.337203
\(437\) 1.28825 26.8521i 0.0616252 1.28451i
\(438\) −13.6103 −0.650327
\(439\) 6.02549 + 34.1723i 0.287581 + 1.63095i 0.695918 + 0.718121i \(0.254998\pi\)
−0.408337 + 0.912831i \(0.633891\pi\)
\(440\) 0 0
\(441\) 8.89371 3.23705i 0.423510 0.154145i
\(442\) 3.96291 + 1.44238i 0.188496 + 0.0686071i
\(443\) −20.1629 16.9187i −0.957970 0.803832i 0.0226514 0.999743i \(-0.492789\pi\)
−0.980622 + 0.195911i \(0.937234\pi\)
\(444\) −32.3756 + 56.0761i −1.53648 + 2.66126i
\(445\) 0 0
\(446\) 0.636160 3.60784i 0.0301231 0.170836i
\(447\) −1.64499 + 9.32919i −0.0778053 + 0.441256i
\(448\) −8.62698 14.9424i −0.407586 0.705960i
\(449\) 6.71581 11.6321i 0.316939 0.548954i −0.662909 0.748700i \(-0.730678\pi\)
0.979848 + 0.199746i \(0.0640117\pi\)
\(450\) 0 0
\(451\) 23.0335 + 8.38351i 1.08461 + 0.394764i
\(452\) 29.7559 10.8302i 1.39960 0.509412i
\(453\) 33.3811 28.0101i 1.56838 1.31603i
\(454\) 1.56482 + 8.87452i 0.0734405 + 0.416502i
\(455\) 0 0
\(456\) 7.69712 8.32766i 0.360450 0.389978i
\(457\) −0.205882 −0.00963073 −0.00481537 0.999988i \(-0.501533\pi\)
−0.00481537 + 0.999988i \(0.501533\pi\)
\(458\) −2.04515 11.5986i −0.0955637 0.541969i
\(459\) 9.59670 8.05259i 0.447935 0.375863i
\(460\) 0 0
\(461\) −36.6739 13.3482i −1.70807 0.621688i −0.711371 0.702817i \(-0.751925\pi\)
−0.996704 + 0.0811290i \(0.974147\pi\)
\(462\) −25.3384 21.2615i −1.17885 0.989173i
\(463\) −3.71234 + 6.42997i −0.172527 + 0.298826i −0.939303 0.343089i \(-0.888527\pi\)
0.766776 + 0.641915i \(0.221860\pi\)
\(464\) −1.16778 2.02266i −0.0542129 0.0938995i
\(465\) 0 0
\(466\) 10.4404 59.2107i 0.483644 2.74288i
\(467\) 10.9627 + 18.9880i 0.507295 + 0.878660i 0.999964 + 0.00844368i \(0.00268774\pi\)
−0.492670 + 0.870216i \(0.663979\pi\)
\(468\) −0.907896 + 1.57252i −0.0419675 + 0.0726898i
\(469\) 10.0743 + 8.45336i 0.465189 + 0.390340i
\(470\) 0 0
\(471\) −0.600309 + 0.218495i −0.0276608 + 0.0100677i
\(472\) 8.76296 7.35300i 0.403348 0.338449i
\(473\) −5.86779 33.2779i −0.269801 1.53012i
\(474\) 9.82357 0.451211
\(475\) 0 0
\(476\) −20.7284 −0.950084
\(477\) 2.23666 + 12.6847i 0.102410 + 0.580795i
\(478\) 18.4918 15.5164i 0.845794 0.709705i
\(479\) 26.3861 9.60376i 1.20561 0.438807i 0.340433 0.940269i \(-0.389427\pi\)
0.865180 + 0.501462i \(0.167204\pi\)
\(480\) 0 0
\(481\) −3.15230 2.64510i −0.143733 0.120606i
\(482\) 17.4471 30.2193i 0.794694 1.37645i
\(483\) −10.2179 17.6980i −0.464932 0.805286i
\(484\) 4.82754 27.3784i 0.219434 1.24447i
\(485\) 0 0
\(486\) 18.9022 + 32.7396i 0.857422 + 1.48510i
\(487\) −7.06739 + 12.2411i −0.320254 + 0.554697i −0.980540 0.196318i \(-0.937102\pi\)
0.660286 + 0.751014i \(0.270435\pi\)
\(488\) −2.09947 1.76167i −0.0950386 0.0797468i
\(489\) 43.2289 + 15.7340i 1.95488 + 0.711517i
\(490\) 0 0
\(491\) −17.7677 + 14.9089i −0.801847 + 0.672830i −0.948647 0.316337i \(-0.897547\pi\)
0.146800 + 0.989166i \(0.453103\pi\)
\(492\) 5.16518 + 29.2932i 0.232864 + 1.32064i
\(493\) −4.90811 −0.221050
\(494\) 2.03132 + 2.67100i 0.0913933 + 0.120174i
\(495\) 0 0
\(496\) −2.17289 12.3230i −0.0975654 0.553321i
\(497\) −7.29729 + 6.12315i −0.327328 + 0.274661i
\(498\) 27.5481 10.0267i 1.23446 0.449307i
\(499\) 39.8744 + 14.5131i 1.78502 + 0.649695i 0.999525 + 0.0308294i \(0.00981485\pi\)
0.785497 + 0.618865i \(0.212407\pi\)
\(500\) 0 0
\(501\) −12.1042 + 20.9651i −0.540776 + 0.936651i
\(502\) −7.83092 13.5635i −0.349511 0.605371i
\(503\) −1.01542 + 5.75873i −0.0452753 + 0.256769i −0.999041 0.0437817i \(-0.986059\pi\)
0.953766 + 0.300551i \(0.0971705\pi\)
\(504\) 0.594196 3.36985i 0.0264676 0.150105i
\(505\) 0 0
\(506\) 30.7826 53.3170i 1.36845 2.37023i
\(507\) 21.9889 + 18.4509i 0.976562 + 0.819433i
\(508\) −3.25740 1.18560i −0.144524 0.0526023i
\(509\) −7.84135 + 2.85402i −0.347562 + 0.126502i −0.509902 0.860233i \(-0.670318\pi\)
0.162340 + 0.986735i \(0.448096\pi\)
\(510\) 0 0
\(511\) 0.738249 + 4.18682i 0.0326582 + 0.185214i
\(512\) −26.6524 −1.17788
\(513\) 9.88846 1.25855i 0.436586 0.0555664i
\(514\) −12.8221 −0.565557
\(515\) 0 0
\(516\) 31.4123 26.3580i 1.38285 1.16035i
\(517\) −47.7978 + 17.3970i −2.10215 + 0.765119i
\(518\) 33.9307 + 12.3498i 1.49083 + 0.542618i
\(519\) −29.9839 25.1595i −1.31615 1.10438i
\(520\) 0 0
\(521\) −15.4419 26.7461i −0.676521 1.17177i −0.976022 0.217673i \(-0.930154\pi\)
0.299501 0.954096i \(-0.403180\pi\)
\(522\) 0.655115 3.71534i 0.0286736 0.162616i
\(523\) −3.97753 + 22.5577i −0.173925 + 0.986380i 0.765452 + 0.643494i \(0.222516\pi\)
−0.939377 + 0.342886i \(0.888595\pi\)
\(524\) 24.8640 + 43.0657i 1.08619 + 1.88134i
\(525\) 0 0
\(526\) 12.0532 + 10.1139i 0.525547 + 0.440986i
\(527\) −24.7101 8.99375i −1.07639 0.391774i
\(528\) −25.5767 + 9.30914i −1.11308 + 0.405129i
\(529\) 11.5188 9.66540i 0.500816 0.420235i
\(530\) 0 0
\(531\) −19.3660 −0.840415
\(532\) −13.8723 8.92182i −0.601440 0.386810i
\(533\) −1.89035 −0.0818801
\(534\) −2.74204 15.5509i −0.118659 0.672951i
\(535\) 0 0
\(536\) −9.70268 + 3.53149i −0.419092 + 0.152537i
\(537\) 31.5733 + 11.4918i 1.36249 + 0.495906i
\(538\) 17.7445 + 14.8894i 0.765019 + 0.641927i
\(539\) 11.2187 19.4313i 0.483222 0.836966i
\(540\) 0 0
\(541\) −0.695195 + 3.94265i −0.0298888 + 0.169508i −0.996098 0.0882501i \(-0.971873\pi\)
0.966210 + 0.257758i \(0.0829837\pi\)
\(542\) −1.05483 + 5.98226i −0.0453090 + 0.256960i
\(543\) 16.6393 + 28.8201i 0.714061 + 1.23679i
\(544\) −21.6149 + 37.4381i −0.926731 + 1.60515i
\(545\) 0 0
\(546\) 2.39706 + 0.872460i 0.102585 + 0.0373378i
\(547\) 39.1590 14.2527i 1.67432 0.609402i 0.681804 0.731535i \(-0.261196\pi\)
0.992514 + 0.122133i \(0.0389735\pi\)
\(548\) −20.8387 + 17.4858i −0.890186 + 0.746954i
\(549\) 0.805694 + 4.56932i 0.0343862 + 0.195014i
\(550\) 0 0
\(551\) −3.28471 2.11253i −0.139933 0.0899966i
\(552\) 16.0449 0.682917
\(553\) −0.532848 3.02193i −0.0226590 0.128506i
\(554\) −26.3715 + 22.1283i −1.12042 + 0.940142i
\(555\) 0 0
\(556\) 17.2115 + 6.26446i 0.729929 + 0.265672i
\(557\) 2.43219 + 2.04085i 0.103055 + 0.0864735i 0.692859 0.721073i \(-0.256351\pi\)
−0.589804 + 0.807546i \(0.700795\pi\)
\(558\) 10.1063 17.5046i 0.427834 0.741030i
\(559\) 1.30299 + 2.25685i 0.0551107 + 0.0954546i
\(560\) 0 0
\(561\) −9.93232 + 56.3290i −0.419343 + 2.37821i
\(562\) 3.42891 + 5.93905i 0.144640 + 0.250524i
\(563\) 7.20295 12.4759i 0.303568 0.525796i −0.673373 0.739303i \(-0.735155\pi\)
0.976942 + 0.213507i \(0.0684886\pi\)
\(564\) −47.2843 39.6763i −1.99103 1.67067i
\(565\) 0 0
\(566\) −25.7972 + 9.38940i −1.08434 + 0.394666i
\(567\) 12.5467 10.5279i 0.526911 0.442131i
\(568\) −1.29874 7.36552i −0.0544939 0.309050i
\(569\) 24.9795 1.04719 0.523597 0.851966i \(-0.324590\pi\)
0.523597 + 0.851966i \(0.324590\pi\)
\(570\) 0 0
\(571\) 13.1086 0.548579 0.274289 0.961647i \(-0.411557\pi\)
0.274289 + 0.961647i \(0.411557\pi\)
\(572\) 0.747499 + 4.23928i 0.0312545 + 0.177253i
\(573\) 0.0115817 0.00971822i 0.000483833 0.000405984i
\(574\) 15.5869 5.67318i 0.650586 0.236794i
\(575\) 0 0
\(576\) −17.5683 14.7416i −0.732014 0.614233i
\(577\) 4.12748 7.14901i 0.171829 0.297617i −0.767230 0.641372i \(-0.778366\pi\)
0.939059 + 0.343755i \(0.111699\pi\)
\(578\) 13.8701 + 24.0238i 0.576921 + 0.999257i
\(579\) 5.31624 30.1499i 0.220935 1.25299i
\(580\) 0 0
\(581\) −4.57867 7.93050i −0.189955 0.329012i
\(582\) 11.2166 19.4277i 0.464943 0.805304i
\(583\) 23.3915 + 19.6278i 0.968778 + 0.812901i
\(584\) −3.13662 1.14164i −0.129794 0.0472413i
\(585\) 0 0
\(586\) −50.3295 + 42.2315i −2.07909 + 1.74457i
\(587\) 1.37287 + 7.78595i 0.0566646 + 0.321361i 0.999943 0.0106409i \(-0.00338717\pi\)
−0.943279 + 0.332002i \(0.892276\pi\)
\(588\) 27.2278 1.12286
\(589\) −12.6660 16.6546i −0.521892 0.686241i
\(590\) 0 0
\(591\) 0.185821 + 1.05384i 0.00764366 + 0.0433493i
\(592\) 22.7611 19.0988i 0.935475 0.784957i
\(593\) −3.34124 + 1.21611i −0.137208 + 0.0499398i −0.409712 0.912215i \(-0.634371\pi\)
0.272503 + 0.962155i \(0.412148\pi\)
\(594\) 21.4517 + 7.80777i 0.880173 + 0.320357i
\(595\) 0 0
\(596\) −5.40891 + 9.36850i −0.221557 + 0.383749i
\(597\) −29.9105 51.8065i −1.22415 2.12030i
\(598\) −0.824467 + 4.67579i −0.0337150 + 0.191207i
\(599\) 1.91987 10.8881i 0.0784437 0.444876i −0.920136 0.391599i \(-0.871922\pi\)
0.998580 0.0532774i \(-0.0169668\pi\)
\(600\) 0 0
\(601\) 22.7722 39.4426i 0.928898 1.60890i 0.143728 0.989617i \(-0.454091\pi\)
0.785170 0.619281i \(-0.212576\pi\)
\(602\) −17.5170 14.6985i −0.713938 0.599065i
\(603\) 16.4261 + 5.97863i 0.668924 + 0.243468i
\(604\) 46.7606 17.0195i 1.90266 0.692512i
\(605\) 0 0
\(606\) 7.46795 + 42.3529i 0.303365 + 1.72047i
\(607\) −36.4498 −1.47945 −0.739727 0.672907i \(-0.765045\pi\)
−0.739727 + 0.672907i \(0.765045\pi\)
\(608\) −30.5795 + 15.7517i −1.24016 + 0.638817i
\(609\) −2.96879 −0.120301
\(610\) 0 0
\(611\) 3.00500 2.52149i 0.121569 0.102009i
\(612\) −25.8904 + 9.42334i −1.04656 + 0.380916i
\(613\) 6.33713 + 2.30653i 0.255954 + 0.0931597i 0.466811 0.884357i \(-0.345403\pi\)
−0.210856 + 0.977517i \(0.567625\pi\)
\(614\) 26.7586 + 22.4531i 1.07989 + 0.906135i
\(615\) 0 0
\(616\) −4.05606 7.02529i −0.163423 0.283057i
\(617\) −4.38423 + 24.8642i −0.176503 + 1.00100i 0.759893 + 0.650049i \(0.225252\pi\)
−0.936395 + 0.350947i \(0.885860\pi\)
\(618\) −6.44075 + 36.5273i −0.259085 + 1.46934i
\(619\) −11.1611 19.3317i −0.448604 0.777006i 0.549691 0.835368i \(-0.314745\pi\)
−0.998295 + 0.0583624i \(0.981412\pi\)
\(620\) 0 0
\(621\) 10.8043 + 9.06588i 0.433562 + 0.363801i
\(622\) 49.6427 + 18.0685i 1.99049 + 0.724480i
\(623\) −4.63503 + 1.68701i −0.185699 + 0.0675887i
\(624\) 1.60798 1.34925i 0.0643706 0.0540133i
\(625\) 0 0
\(626\) 21.9066 0.875564
\(627\) −30.8920 + 33.4226i −1.23371 + 1.33477i
\(628\) −0.729519 −0.0291110
\(629\) −10.8426 61.4912i −0.432321 2.45182i
\(630\) 0 0
\(631\) −3.32590 + 1.21053i −0.132402 + 0.0481904i −0.407371 0.913263i \(-0.633555\pi\)
0.274969 + 0.961453i \(0.411332\pi\)
\(632\) 2.26393 + 0.824003i 0.0900543 + 0.0327771i
\(633\) −14.0808 11.8152i −0.559661 0.469611i
\(634\) −6.47848 + 11.2211i −0.257293 + 0.445645i
\(635\) 0 0
\(636\) −6.43451 + 36.4919i −0.255145 + 1.44700i
\(637\) −0.300476 + 1.70408i −0.0119053 + 0.0675182i
\(638\) −4.47189 7.74555i −0.177044 0.306649i
\(639\) −6.33090 + 10.9654i −0.250447 + 0.433786i
\(640\) 0 0
\(641\) −24.7767 9.01799i −0.978622 0.356189i −0.197318 0.980340i \(-0.563223\pi\)
−0.781304 + 0.624150i \(0.785445\pi\)
\(642\) 2.31641 0.843104i 0.0914213 0.0332746i
\(643\) 11.2983 9.48043i 0.445563 0.373872i −0.392223 0.919870i \(-0.628294\pi\)
0.837786 + 0.545998i \(0.183850\pi\)
\(644\) −4.05238 22.9822i −0.159686 0.905626i
\(645\) 0 0
\(646\) −2.43999 + 50.8589i −0.0960000 + 2.00102i
\(647\) −5.04555 −0.198361 −0.0991804 0.995069i \(-0.531622\pi\)
−0.0991804 + 0.995069i \(0.531622\pi\)
\(648\) 2.23300 + 12.6640i 0.0877207 + 0.497489i
\(649\) −35.1697 + 29.5109i −1.38053 + 1.15840i
\(650\) 0 0
\(651\) −14.9465 5.44009i −0.585800 0.213214i
\(652\) 40.2429 + 33.7678i 1.57603 + 1.32245i
\(653\) −22.3362 + 38.6875i −0.874084 + 1.51396i −0.0163488 + 0.999866i \(0.505204\pi\)
−0.857735 + 0.514092i \(0.828129\pi\)
\(654\) 6.57385 + 11.3862i 0.257058 + 0.445237i
\(655\) 0 0
\(656\) 2.37016 13.4418i 0.0925391 0.524815i
\(657\) 2.82547 + 4.89386i 0.110232 + 0.190927i
\(658\) −17.2105 + 29.8094i −0.670934 + 1.16209i
\(659\) 22.5147 + 18.8921i 0.877049 + 0.735931i 0.965570 0.260143i \(-0.0837697\pi\)
−0.0885212 + 0.996074i \(0.528214\pi\)
\(660\) 0 0
\(661\) 19.0049 6.91721i 0.739204 0.269048i 0.0551486 0.998478i \(-0.482437\pi\)
0.684056 + 0.729430i \(0.260215\pi\)
\(662\) −19.2931 + 16.1889i −0.749849 + 0.629198i
\(663\) −0.765982 4.34410i −0.0297483 0.168711i
\(664\) 7.18975 0.279016
\(665\) 0 0
\(666\) 47.9949 1.85976
\(667\) −0.959531 5.44177i −0.0371532 0.210706i
\(668\) −21.1771 + 17.7697i −0.819367 + 0.687531i
\(669\) −3.60083 + 1.31059i −0.139216 + 0.0506705i
\(670\) 0 0
\(671\) 8.42612 + 7.07036i 0.325287 + 0.272948i
\(672\) −13.0743 + 22.6454i −0.504352 + 0.873564i
\(673\) −13.8331 23.9597i −0.533227 0.923577i −0.999247 0.0388026i \(-0.987646\pi\)
0.466019 0.884774i \(-0.345688\pi\)
\(674\) 5.63809 31.9752i 0.217171 1.23164i
\(675\) 0 0
\(676\) 16.3895 + 28.3875i 0.630367 + 1.09183i
\(677\) 15.8370 27.4305i 0.608665 1.05424i −0.382796 0.923833i \(-0.625039\pi\)
0.991461 0.130405i \(-0.0416279\pi\)
\(678\) −45.2956 38.0075i −1.73957 1.45967i
\(679\) −6.58477 2.39666i −0.252700 0.0919754i
\(680\) 0 0
\(681\) 7.22050 6.05872i 0.276690 0.232171i
\(682\) −8.32083 47.1898i −0.318621 1.80699i
\(683\) 4.75181 0.181823 0.0909114 0.995859i \(-0.471022\pi\)
0.0909114 + 0.995859i \(0.471022\pi\)
\(684\) −21.3829 4.83716i −0.817595 0.184953i
\(685\) 0 0
\(686\) −6.48729 36.7913i −0.247686 1.40470i
\(687\) −9.43690 + 7.91850i −0.360040 + 0.302110i
\(688\) −17.6816 + 6.43559i −0.674106 + 0.245355i
\(689\) −2.21288 0.805423i −0.0843040 0.0306842i
\(690\) 0 0
\(691\) 0.211770 0.366797i 0.00805613 0.0139536i −0.861969 0.506961i \(-0.830769\pi\)
0.870025 + 0.493007i \(0.164102\pi\)
\(692\) −22.3486 38.7090i −0.849568 1.47149i
\(693\) −2.38478 + 13.5247i −0.0905902 + 0.513763i
\(694\) −11.1753 + 63.3781i −0.424208 + 2.40580i
\(695\) 0 0
\(696\) 1.16545 2.01862i 0.0441762 0.0765155i
\(697\) −21.9727 18.4373i −0.832275 0.698362i
\(698\) −5.48575 1.99665i −0.207639 0.0755743i
\(699\) −59.0955 + 21.5090i −2.23520 + 0.813545i
\(700\) 0 0
\(701\) 1.37980 + 7.82526i 0.0521145 + 0.295556i 0.999714 0.0239040i \(-0.00760962\pi\)
−0.947600 + 0.319460i \(0.896499\pi\)
\(702\) −1.76053 −0.0664469
\(703\) 19.2105 45.8193i 0.724538 1.72811i
\(704\) −54.3689 −2.04911
\(705\) 0 0
\(706\) −7.52915 + 6.31771i −0.283363 + 0.237770i
\(707\) 12.6235 4.59459i 0.474757 0.172797i
\(708\) −52.3530 19.0549i −1.96755 0.716129i
\(709\) 8.99170 + 7.54493i 0.337690 + 0.283356i 0.795825 0.605527i \(-0.207038\pi\)
−0.458134 + 0.888883i \(0.651482\pi\)
\(710\) 0 0
\(711\) −2.03935 3.53225i −0.0764815 0.132470i
\(712\) 0.672483 3.81384i 0.0252024 0.142930i
\(713\) 5.14084 29.1552i 0.192526 1.09187i
\(714\) 19.3531 + 33.5206i 0.724272 + 1.25448i
\(715\) 0 0
\(716\) 29.3924 + 24.6632i 1.09845 + 0.921707i
\(717\) −23.7263 8.63567i −0.886075 0.322505i
\(718\) 24.7264 8.99969i 0.922783 0.335865i
\(719\) −38.6452 + 32.4272i −1.44122 + 1.20933i −0.502536 + 0.864556i \(0.667600\pi\)
−0.938686 + 0.344773i \(0.887956\pi\)
\(720\) 0 0
\(721\) 11.5859 0.431481
\(722\) −23.5234 + 32.9866i −0.875450 + 1.22764i
\(723\) −36.4983 −1.35739
\(724\) 6.59907 + 37.4252i 0.245252 + 1.39090i
\(725\) 0 0
\(726\) −48.7818 + 17.7551i −1.81046 + 0.658954i
\(727\) 24.4935 + 8.91490i 0.908414 + 0.330636i 0.753619 0.657311i \(-0.228306\pi\)
0.154794 + 0.987947i \(0.450529\pi\)
\(728\) 0.479243 + 0.402132i 0.0177619 + 0.0149040i
\(729\) 3.23417 5.60174i 0.119784 0.207472i
\(730\) 0 0
\(731\) −6.86641 + 38.9413i −0.253963 + 1.44030i
\(732\) −2.31785 + 13.1452i −0.0856702 + 0.485860i
\(733\) 8.54306 + 14.7970i 0.315545 + 0.546540i 0.979553 0.201185i \(-0.0644793\pi\)
−0.664008 + 0.747725i \(0.731146\pi\)
\(734\) 1.74441 3.02141i 0.0643873 0.111522i
\(735\) 0 0
\(736\) −45.7345 16.6460i −1.68580 0.613580i
\(737\) 38.9412 14.1734i 1.43442 0.522086i
\(738\) 16.8895 14.1720i 0.621711 0.521677i
\(739\) −4.27432 24.2409i −0.157233 0.891715i −0.956715 0.291025i \(-0.906004\pi\)
0.799482 0.600690i \(-0.205107\pi\)
\(740\) 0 0
\(741\) 1.35714 3.23694i 0.0498559 0.118912i
\(742\) 20.6636 0.758583
\(743\) 1.33186 + 7.55333i 0.0488610 + 0.277105i 0.999443 0.0333687i \(-0.0106236\pi\)
−0.950582 + 0.310473i \(0.899512\pi\)
\(744\) 9.56649 8.02724i 0.350724 0.294293i
\(745\) 0 0
\(746\) 29.5731 + 10.7637i 1.08275 + 0.394089i
\(747\) −9.32420 7.82393i −0.341155 0.286263i
\(748\) −32.6586 + 56.5664i −1.19412 + 2.06827i
\(749\) −0.385002 0.666843i −0.0140677 0.0243659i
\(750\) 0 0
\(751\) 3.65755 20.7430i 0.133466 0.756923i −0.842450 0.538775i \(-0.818887\pi\)
0.975916 0.218148i \(-0.0700017\pi\)
\(752\) 14.1620 + 24.5293i 0.516436 + 0.894493i
\(753\) −8.19092 + 14.1871i −0.298494 + 0.517006i
\(754\) 0.528376 + 0.443360i 0.0192423 + 0.0161462i
\(755\) 0 0
\(756\) 8.13141 2.95959i 0.295737 0.107639i
\(757\) −3.29957 + 2.76867i −0.119925 + 0.100629i −0.700778 0.713379i \(-0.747164\pi\)
0.580853 + 0.814009i \(0.302719\pi\)
\(758\) 0.651197 + 3.69312i 0.0236525 + 0.134140i
\(759\) −64.3955 −2.33741
\(760\) 0 0
\(761\) −1.11318 −0.0403529 −0.0201764 0.999796i \(-0.506423\pi\)
−0.0201764 + 0.999796i \(0.506423\pi\)
\(762\) 1.12401 + 6.37459i 0.0407187 + 0.230927i
\(763\) 3.14606 2.63986i 0.113895 0.0955694i
\(764\) 0.0162238 0.00590497i 0.000586956 0.000213634i
\(765\) 0 0
\(766\) −13.8824 11.6487i −0.501591 0.420885i
\(767\) 1.77032 3.06629i 0.0639227 0.110717i
\(768\) 4.54359 + 7.86973i 0.163953 + 0.283975i
\(769\) 1.71410 9.72113i 0.0618119 0.350553i −0.938178 0.346152i \(-0.887488\pi\)
0.999990 0.00440066i \(-0.00140078\pi\)
\(770\) 0 0
\(771\) 6.70576 + 11.6147i 0.241502 + 0.418294i
\(772\) 17.4804 30.2769i 0.629133 1.08969i
\(773\) 13.0788 + 10.9744i 0.470410 + 0.394721i 0.846944 0.531682i \(-0.178440\pi\)
−0.376534 + 0.926403i \(0.622884\pi\)
\(774\) −28.5613 10.3955i −1.02662 0.373658i
\(775\) 0 0
\(776\) 4.21457 3.53644i 0.151294 0.126951i
\(777\) −6.55839 37.1945i −0.235281 1.33434i
\(778\) 72.3761 2.59481
\(779\) −6.76933 21.7964i −0.242537 0.780936i
\(780\) 0 0
\(781\) 5.21243 + 29.5611i 0.186515 + 1.05778i
\(782\) −55.1880 + 46.3082i −1.97352 + 1.65598i
\(783\) 1.92537 0.700778i 0.0688072 0.0250438i
\(784\) −11.7406 4.27323i −0.419307 0.152615i
\(785\) 0 0
\(786\) 46.4287 80.4169i 1.65606 2.86838i
\(787\) −5.82825 10.0948i −0.207755 0.359842i 0.743252 0.669011i \(-0.233282\pi\)
−0.951007 + 0.309170i \(0.899949\pi\)
\(788\) −0.212198 + 1.20344i −0.00755925 + 0.0428707i
\(789\) 2.85786 16.2077i 0.101742 0.577010i
\(790\) 0 0
\(791\) −9.23498 + 15.9955i −0.328358 + 0.568733i
\(792\) −8.25992 6.93090i −0.293503 0.246279i
\(793\) −0.797127 0.290130i −0.0283068 0.0103028i
\(794\) −15.5835 + 5.67194i −0.553038 + 0.201289i
\(795\) 0 0
\(796\) −11.8624 67.2747i −0.420450 2.38449i
\(797\) 29.8609 1.05773 0.528864 0.848707i \(-0.322618\pi\)
0.528864 + 0.848707i \(0.322618\pi\)
\(798\) −1.47589 + 30.7632i −0.0522458 + 1.08901i
\(799\) 59.5220 2.10574
\(800\) 0 0
\(801\) −5.02237 + 4.21427i −0.177457 + 0.148904i
\(802\) 62.4932 22.7457i 2.20671 0.803178i
\(803\) 12.5887 + 4.58191i 0.444245 + 0.161692i
\(804\) 38.5229 + 32.3245i 1.35860 + 1.14000i
\(805\) 0 0
\(806\) 1.84771 + 3.20033i 0.0650829 + 0.112727i
\(807\) 4.20726 23.8606i 0.148103 0.839932i
\(808\) −1.83151 + 10.3870i −0.0644323 + 0.365414i
\(809\) 19.1756 + 33.2132i 0.674180 + 1.16771i 0.976708 + 0.214573i \(0.0688360\pi\)
−0.302528 + 0.953140i \(0.597831\pi\)
\(810\) 0 0
\(811\) 8.55127 + 7.17537i 0.300276 + 0.251961i 0.780459 0.625207i \(-0.214985\pi\)
−0.480183 + 0.877168i \(0.659430\pi\)
\(812\) −3.18575 1.15952i −0.111798 0.0406911i
\(813\) 5.97062 2.17313i 0.209399 0.0762150i
\(814\) 87.1612 73.1369i 3.05500 2.56345i
\(815\) 0 0
\(816\) 31.8503 1.11498
\(817\) −21.3562 + 23.1057i −0.747160 + 0.808367i
\(818\) 31.2935 1.09415
\(819\) −0.183914 1.04303i −0.00642649 0.0364464i
\(820\) 0 0
\(821\) −7.18934 + 2.61671i −0.250910 + 0.0913236i −0.464413 0.885619i \(-0.653735\pi\)
0.213504 + 0.976942i \(0.431513\pi\)
\(822\) 47.7330 + 17.3734i 1.66488 + 0.605966i
\(823\) −25.4494 21.3546i −0.887110 0.744373i 0.0805185 0.996753i \(-0.474342\pi\)
−0.967628 + 0.252380i \(0.918787\pi\)
\(824\) −4.54825 + 7.87779i −0.158446 + 0.274436i
\(825\) 0 0
\(826\) −5.39493 + 30.5962i −0.187714 + 1.06458i
\(827\) 0.591681 3.35559i 0.0205748 0.116685i −0.972791 0.231686i \(-0.925576\pi\)
0.993365 + 0.115001i \(0.0366870\pi\)
\(828\) −15.5095 26.8633i −0.538993 0.933563i
\(829\) −2.21217 + 3.83160i −0.0768320 + 0.133077i −0.901881 0.431984i \(-0.857814\pi\)
0.825049 + 0.565060i \(0.191147\pi\)
\(830\) 0 0
\(831\) 33.8366 + 12.3155i 1.17378 + 0.427221i
\(832\) 3.94007 1.43407i 0.136597 0.0497174i
\(833\) −20.1132 + 16.8770i −0.696880 + 0.584752i
\(834\) −5.93906 33.6821i −0.205653 1.16632i
\(835\) 0 0
\(836\) −46.2035 + 23.7998i −1.59798 + 0.823132i
\(837\) 10.9775 0.379438
\(838\) 7.63013 + 43.2726i 0.263579 + 1.49483i
\(839\) −18.2406 + 15.3057i −0.629736 + 0.528411i −0.900847 0.434137i \(-0.857053\pi\)
0.271111 + 0.962548i \(0.412609\pi\)
\(840\) 0 0
\(841\) 26.4968 + 9.64403i 0.913681 + 0.332553i
\(842\) −45.2136 37.9387i −1.55816 1.30745i
\(843\) 3.58655 6.21208i 0.123527 0.213956i
\(844\) −10.4952 18.1782i −0.361259 0.625719i
\(845\) 0 0
\(846\) −7.94477 + 45.0570i −0.273147 + 1.54909i
\(847\) 8.10785 + 14.0432i 0.278589 + 0.482530i
\(848\) 8.50173 14.7254i 0.291951 0.505673i
\(849\) 21.9968 + 18.4575i 0.754929 + 0.633461i
\(850\) 0 0
\(851\) 66.0575 24.0430i 2.26442 0.824183i
\(852\) −27.9039 + 23.4141i −0.955971 + 0.802155i
\(853\) 0.769903 + 4.36634i 0.0263610 + 0.149501i 0.995147 0.0983970i \(-0.0313715\pi\)
−0.968786 + 0.247898i \(0.920260\pi\)
\(854\) 7.44345 0.254710
\(855\) 0 0
\(856\) 0.604557 0.0206633
\(857\) −4.68808 26.5874i −0.160142 0.908208i −0.953933 0.300019i \(-0.903007\pi\)
0.793792 0.608190i \(-0.208104\pi\)
\(858\) 6.15758 5.16682i 0.210216 0.176392i
\(859\) 12.8850 4.68976i 0.439631 0.160013i −0.112715 0.993627i \(-0.535955\pi\)
0.552346 + 0.833615i \(0.313733\pi\)
\(860\) 0 0
\(861\) −13.2907 11.1522i −0.452947 0.380067i
\(862\) −22.2790 + 38.5883i −0.758825 + 1.31432i
\(863\) 26.2240 + 45.4213i 0.892676 + 1.54616i 0.836655 + 0.547730i \(0.184508\pi\)
0.0560208 + 0.998430i \(0.482159\pi\)
\(864\) 3.13378 17.7725i 0.106613 0.604634i
\(865\) 0 0
\(866\) −2.05341 3.55662i −0.0697778 0.120859i
\(867\) 14.5078 25.1282i 0.492709 0.853398i
\(868\) −13.9141 11.6753i −0.472276 0.396286i
\(869\) −9.08617 3.30710i −0.308227 0.112186i
\(870\) 0 0
\(871\) −2.44819 + 2.05428i −0.0829538 + 0.0696065i
\(872\) 0.559923 + 3.17548i 0.0189614 + 0.107535i
\(873\) −9.31414 −0.315236
\(874\) −56.8658 + 7.23758i −1.92352 + 0.244815i
\(875\) 0 0
\(876\) 2.82297 + 16.0098i 0.0953792 + 0.540923i
\(877\) 31.2742 26.2422i 1.05606 0.886136i 0.0623382 0.998055i \(-0.480144\pi\)
0.993717 + 0.111919i \(0.0356998\pi\)
\(878\) 69.5298 25.3068i 2.34652 0.854062i
\(879\) 64.5765 + 23.5039i 2.17811 + 0.792768i
\(880\) 0 0
\(881\) 23.8807 41.3627i 0.804563 1.39354i −0.112023 0.993706i \(-0.535733\pi\)
0.916586 0.399838i \(-0.130934\pi\)
\(882\) −10.0909 17.4780i −0.339778 0.588513i
\(883\) −5.57488 + 31.6167i −0.187610 + 1.06399i 0.734946 + 0.678125i \(0.237207\pi\)
−0.922556 + 0.385863i \(0.873904\pi\)
\(884\) 0.874713 4.96074i 0.0294198 0.166848i
\(885\) 0 0
\(886\) −28.0629 + 48.6064i −0.942792 + 1.63296i
\(887\) 6.75510 + 5.66820i 0.226814 + 0.190319i 0.749112 0.662444i \(-0.230481\pi\)
−0.522298 + 0.852763i \(0.674925\pi\)
\(888\) 27.8649 + 10.1420i 0.935084 + 0.340343i
\(889\) 1.89999 0.691539i 0.0637235 0.0231935i
\(890\) 0 0
\(891\) −8.96205 50.8263i −0.300240 1.70275i
\(892\) −4.37586 −0.146515
\(893\) 39.8346 + 25.6192i 1.33301 + 0.857314i
\(894\) 20.2002 0.675595
\(895\) 0 0
\(896\) −10.2224 + 8.57759i −0.341505 + 0.286557i
\(897\) 4.66669 1.69854i 0.155816 0.0567125i
\(898\) −26.9139 9.79587i −0.898130 0.326892i
\(899\) −3.29461 2.76451i −0.109881 0.0922014i
\(900\) 0 0
\(901\) −17.8661 30.9450i −0.595206 1.03093i
\(902\) 9.07627 51.4741i 0.302207 1.71390i
\(903\) −4.15332 + 23.5546i −0.138214 + 0.783849i
\(904\) −7.25071 12.5586i −0.241155 0.417693i
\(905\) 0 0
\(906\) −71.1810 59.7279i −2.36483 1.98433i
\(907\) 9.71693 + 3.53667i 0.322645 + 0.117433i 0.498265 0.867025i \(-0.333971\pi\)
−0.175620 + 0.984458i \(0.556193\pi\)
\(908\) 10.1145 3.68139i 0.335663 0.122171i
\(909\) 13.6785 11.4776i 0.453686 0.380688i
\(910\) 0 0
\(911\) 5.25941 0.174252 0.0871260 0.996197i \(-0.472232\pi\)
0.0871260 + 0.996197i \(0.472232\pi\)
\(912\) 21.3155 + 13.7089i 0.705827 + 0.453946i
\(913\) −28.8557 −0.954985
\(914\) 0.0762343 + 0.432346i 0.00252161 + 0.0143007i
\(915\) 0 0
\(916\) −13.2193 + 4.81143i −0.436778 + 0.158974i
\(917\) −27.2563 9.92047i −0.900081 0.327603i
\(918\) −20.4637 17.1711i −0.675403 0.566731i
\(919\) −0.101184 + 0.175255i −0.00333774 + 0.00578114i −0.867689 0.497107i \(-0.834396\pi\)
0.864352 + 0.502888i \(0.167729\pi\)
\(920\) 0 0
\(921\) 6.34453 35.9816i 0.209060 1.18564i
\(922\) −14.4512 + 81.9569i −0.475925 + 2.69911i
\(923\) −1.15746 2.00479i −0.0380984 0.0659883i
\(924\) −19.7544 + 34.2155i −0.649871 + 1.12561i
\(925\) 0 0
\(926\) 14.8774 + 5.41492i 0.488901 + 0.177945i
\(927\) 14.4712 5.26707i 0.475296 0.172993i
\(928\) −5.41624 + 4.54477i −0.177797 + 0.149189i
\(929\) 3.23698 + 18.3578i 0.106202 + 0.602301i 0.990733 + 0.135821i \(0.0433671\pi\)
−0.884532 + 0.466480i \(0.845522\pi\)
\(930\) 0 0
\(931\) −20.7247 + 2.63773i −0.679223 + 0.0864480i
\(932\) −71.8151 −2.35238
\(933\) −9.59533 54.4178i −0.314137 1.78156i
\(934\) 35.8150 30.0524i 1.17190 0.983344i
\(935\) 0 0
\(936\) 0.781404 + 0.284408i 0.0255410 + 0.00929615i
\(937\) 38.6935 + 32.4677i 1.26406 + 1.06067i 0.995237 + 0.0974836i \(0.0310794\pi\)
0.268824 + 0.963189i \(0.413365\pi\)
\(938\) 14.0215 24.2859i 0.457818 0.792964i
\(939\) −11.4568 19.8438i −0.373880 0.647579i
\(940\) 0 0
\(941\) −2.87903 + 16.3278i −0.0938538 + 0.532271i 0.901239 + 0.433323i \(0.142659\pi\)
−0.995093 + 0.0989484i \(0.968452\pi\)
\(942\) 0.681118 + 1.17973i 0.0221920 + 0.0384377i
\(943\) 16.1463 27.9663i 0.525797 0.910708i
\(944\) 19.5840 + 16.4329i 0.637405 + 0.534847i
\(945\) 0 0
\(946\) −67.7100 + 24.6444i −2.20144 + 0.801259i
\(947\) −28.6765 + 24.0625i −0.931862 + 0.781925i −0.976151 0.217094i \(-0.930342\pi\)
0.0442887 + 0.999019i \(0.485898\pi\)
\(948\) −2.03754 11.5555i −0.0661763 0.375304i
\(949\) −1.03315 −0.0335374
\(950\) 0 0
\(951\) 13.5526 0.439474
\(952\) 1.64839 + 9.34847i 0.0534245 + 0.302986i
\(953\) −32.5326 + 27.2981i −1.05384 + 0.884273i −0.993492 0.113905i \(-0.963664\pi\)
−0.0603438 + 0.998178i \(0.519220\pi\)
\(954\) 25.8095 9.39387i 0.835612 0.304138i
\(955\) 0 0
\(956\) −22.0874 18.5336i −0.714359 0.599418i
\(957\) −4.67748 + 8.10162i −0.151201 + 0.261888i
\(958\) −29.9380 51.8541i −0.967252 1.67533i
\(959\) 2.75529 15.6260i 0.0889728 0.504590i
\(960\) 0 0
\(961\) 3.97887 + 6.89160i 0.128351 + 0.222310i
\(962\) −4.38740 + 7.59919i −0.141455 + 0.245008i
\(963\) −0.784034 0.657883i −0.0252652 0.0212000i
\(964\) −39.1657 14.2552i −1.26144 0.459128i
\(965\) 0 0
\(966\) −33.3818 + 28.0107i −1.07404 + 0.901228i
\(967\) −2.81797 15.9815i −0.0906197 0.513930i −0.996002 0.0893324i \(-0.971527\pi\)
0.905382 0.424598i \(-0.139584\pi\)
\(968\) −12.7315 −0.409206
\(969\) 47.3460 24.3882i 1.52097 0.783463i
\(970\) 0 0
\(971\) −3.05833 17.3447i −0.0981465 0.556617i −0.993738 0.111738i \(-0.964358\pi\)
0.895591 0.444878i \(-0.146753\pi\)
\(972\) 34.5910 29.0253i 1.10951 0.930988i
\(973\) −10.0392 + 3.65396i −0.321841 + 0.117140i
\(974\) 28.3229 + 10.3087i 0.907524 + 0.330312i
\(975\) 0 0
\(976\) 3.06250 5.30441i 0.0980283 0.169790i
\(977\) 0.0604375 + 0.104681i 0.00193357 + 0.00334903i 0.866991 0.498325i \(-0.166051\pi\)
−0.865057 + 0.501674i \(0.832718\pi\)
\(978\) 17.0342 96.6056i 0.544693 3.08911i
\(979\) −2.69898 + 15.3067i −0.0862597 + 0.489203i
\(980\) 0 0
\(981\) 2.72943 4.72751i 0.0871439 0.150938i
\(982\) 37.8874 + 31.7913i 1.20904 + 1.01450i
\(983\) 21.3108 + 7.75648i 0.679708 + 0.247393i 0.658722 0.752386i \(-0.271097\pi\)
0.0209857 + 0.999780i \(0.493320\pi\)
\(984\) 12.8004 4.65898i 0.408063 0.148523i
\(985\) 0 0
\(986\) 1.81738 + 10.3069i 0.0578773 + 0.328239i
\(987\) 36.0033 1.14600
\(988\) 2.72058 2.94344i 0.0865530 0.0936434i
\(989\) −44.5179 −1.41559
\(990\) 0 0
\(991\) −41.1874 + 34.5603i −1.30836 + 1.09784i −0.319725 + 0.947510i \(0.603591\pi\)
−0.988635 + 0.150334i \(0.951965\pi\)
\(992\) −35.5963 + 12.9560i −1.13018 + 0.411353i
\(993\) 24.7545 + 9.00991i 0.785561 + 0.285921i
\(994\) 15.5605 + 13.0568i 0.493550 + 0.414137i
\(995\) 0 0
\(996\) −17.5083 30.3252i −0.554770 0.960890i
\(997\) −6.38045 + 36.1853i −0.202071 + 1.14600i 0.699912 + 0.714229i \(0.253223\pi\)
−0.901983 + 0.431772i \(0.857889\pi\)
\(998\) 15.7123 89.1091i 0.497365 2.82070i
\(999\) 13.0331 + 22.5739i 0.412348 + 0.714207i
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 475.2.l.c.351.1 18
5.2 odd 4 475.2.u.b.199.5 36
5.3 odd 4 475.2.u.b.199.2 36
5.4 even 2 95.2.k.a.66.3 yes 18
15.14 odd 2 855.2.bs.c.541.1 18
19.6 even 9 9025.2.a.cc.1.3 9
19.13 odd 18 9025.2.a.cf.1.7 9
19.17 even 9 inner 475.2.l.c.226.1 18
95.17 odd 36 475.2.u.b.74.2 36
95.44 even 18 1805.2.a.v.1.7 9
95.74 even 18 95.2.k.a.36.3 18
95.89 odd 18 1805.2.a.s.1.3 9
95.93 odd 36 475.2.u.b.74.5 36
285.74 odd 18 855.2.bs.c.226.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.k.a.36.3 18 95.74 even 18
95.2.k.a.66.3 yes 18 5.4 even 2
475.2.l.c.226.1 18 19.17 even 9 inner
475.2.l.c.351.1 18 1.1 even 1 trivial
475.2.u.b.74.2 36 95.17 odd 36
475.2.u.b.74.5 36 95.93 odd 36
475.2.u.b.199.2 36 5.3 odd 4
475.2.u.b.199.5 36 5.2 odd 4
855.2.bs.c.226.1 18 285.74 odd 18
855.2.bs.c.541.1 18 15.14 odd 2
1805.2.a.s.1.3 9 95.89 odd 18
1805.2.a.v.1.7 9 95.44 even 18
9025.2.a.cc.1.3 9 19.6 even 9
9025.2.a.cf.1.7 9 19.13 odd 18