Properties

Label 375.2.g.d.301.1
Level $375$
Weight $2$
Character 375.301
Analytic conductor $2.994$
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] = [375,2,Mod(76,375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(375, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("375.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.g (of order \(5\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.99439007580\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5^{2} \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 301.1
Root \(-2.53767i\) of defining polynomial
Character \(\chi\) \(=\) 375.301
Dual form 375.2.g.d.76.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.05302 + 1.49161i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.37197 - 4.22249i) q^{4} +(-0.784184 - 2.41347i) q^{6} +1.04054 q^{7} +(1.91324 + 5.88835i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-2.05302 + 1.49161i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.37197 - 4.22249i) q^{4} +(-0.784184 - 2.41347i) q^{6} +1.04054 q^{7} +(1.91324 + 5.88835i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-2.40360 + 1.74631i) q^{11} +(3.59186 + 2.60964i) q^{12} +(-4.58650 - 3.33228i) q^{13} +(-2.13624 + 1.55207i) q^{14} +(-5.52731 - 4.01583i) q^{16} +(-1.57092 - 4.83480i) q^{17} +2.53767 q^{18} +(-1.65990 - 5.10866i) q^{19} +(-0.321543 + 0.989608i) q^{21} +(2.32982 - 7.17044i) q^{22} +(-3.12312 + 2.26908i) q^{23} -6.19138 q^{24} +14.3866 q^{26} +(0.809017 - 0.587785i) q^{27} +(1.42758 - 4.39365i) q^{28} +(0.210038 - 0.646430i) q^{29} +(0.262699 + 0.808503i) q^{31} +4.95495 q^{32} +(-0.918092 - 2.82560i) q^{33} +(10.4368 + 7.58275i) q^{34} +(-3.59186 + 2.60964i) q^{36} +(1.30869 + 0.950818i) q^{37} +(11.0279 + 8.01226i) q^{38} +(4.58650 - 3.33228i) q^{39} +(-0.942740 - 0.684941i) q^{41} +(-0.815972 - 2.51130i) q^{42} +5.68601 q^{43} +(4.07613 + 12.5450i) q^{44} +(3.02725 - 9.31693i) q^{46} +(1.01555 - 3.12556i) q^{47} +(5.52731 - 4.01583i) q^{48} -5.91729 q^{49} +5.08361 q^{51} +(-20.3631 + 14.7946i) q^{52} +(3.92023 - 12.0652i) q^{53} +(-0.784184 + 2.41347i) q^{54} +(1.99080 + 6.12704i) q^{56} +5.37156 q^{57} +(0.533007 + 1.64043i) q^{58} +(-2.59846 - 1.88789i) q^{59} +(4.38562 - 3.18634i) q^{61} +(-1.74530 - 1.26803i) q^{62} +(-0.841811 - 0.611611i) q^{63} +(0.881995 - 0.640807i) q^{64} +(6.09954 + 4.43157i) q^{66} +(-0.287120 - 0.883665i) q^{67} -22.5702 q^{68} +(-1.19292 - 3.67145i) q^{69} +(-0.436821 + 1.34440i) q^{71} +(1.91324 - 5.88835i) q^{72} +(-9.16080 + 6.65571i) q^{73} -4.10501 q^{74} -23.8486 q^{76} +(-2.50103 + 1.81710i) q^{77} +(-4.44571 + 13.6825i) q^{78} +(-0.447171 + 1.37625i) q^{79} +(0.309017 + 0.951057i) q^{81} +2.95713 q^{82} +(-3.54616 - 10.9140i) q^{83} +(3.73746 + 2.71542i) q^{84} +(-11.6735 + 8.48129i) q^{86} +(0.549886 + 0.399516i) q^{87} +(-14.8816 - 10.8121i) q^{88} +(-7.33961 + 5.33254i) q^{89} +(-4.77241 - 3.46736i) q^{91} +(5.29633 + 16.3004i) q^{92} -0.850111 q^{93} +(2.57715 + 7.93164i) q^{94} +(-1.53117 + 4.71244i) q^{96} +(-1.86315 + 5.73419i) q^{97} +(12.1483 - 8.82627i) q^{98} +2.97101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{2} + 4 q^{3} - 2 q^{4} + 2 q^{6} + 16 q^{7} - 6 q^{8} - 4 q^{9} - 6 q^{11} + 2 q^{12} - 8 q^{13} + 12 q^{14} - 10 q^{16} - 8 q^{17} + 8 q^{18} + 2 q^{19} + 4 q^{21} + 4 q^{22} - 2 q^{23} - 24 q^{24} + 12 q^{26} + 4 q^{27} - 28 q^{28} - 16 q^{29} + 6 q^{31} - 4 q^{32} - 4 q^{33} + 36 q^{34} - 2 q^{36} - 24 q^{37} + 38 q^{38} + 8 q^{39} - 14 q^{41} + 18 q^{42} + 40 q^{43} - 26 q^{44} + 16 q^{46} + 10 q^{47} + 10 q^{48} - 32 q^{51} - 48 q^{52} - 12 q^{53} + 2 q^{54} + 28 q^{57} - 44 q^{58} - 12 q^{59} - 28 q^{62} - 4 q^{63} - 8 q^{64} + 16 q^{66} + 12 q^{67} - 4 q^{68} + 12 q^{69} - 8 q^{71} - 6 q^{72} + 8 q^{73} + 52 q^{74} - 32 q^{76} - 18 q^{77} - 32 q^{78} + 20 q^{79} - 4 q^{81} + 32 q^{82} - 6 q^{83} - 12 q^{84} - 36 q^{86} - 14 q^{87} - 16 q^{88} - 18 q^{89} + 26 q^{91} + 36 q^{92} + 44 q^{93} + 38 q^{94} - 26 q^{96} - 8 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05302 + 1.49161i −1.45171 + 1.05473i −0.466276 + 0.884639i \(0.654405\pi\)
−0.985429 + 0.170086i \(0.945595\pi\)
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i
\(4\) 1.37197 4.22249i 0.685985 2.11124i
\(5\) 0 0
\(6\) −0.784184 2.41347i −0.320142 0.985295i
\(7\) 1.04054 0.393285 0.196643 0.980475i \(-0.436996\pi\)
0.196643 + 0.980475i \(0.436996\pi\)
\(8\) 1.91324 + 5.88835i 0.676433 + 2.08185i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 0 0
\(11\) −2.40360 + 1.74631i −0.724711 + 0.526533i −0.887886 0.460064i \(-0.847827\pi\)
0.163175 + 0.986597i \(0.447827\pi\)
\(12\) 3.59186 + 2.60964i 1.03688 + 0.753338i
\(13\) −4.58650 3.33228i −1.27207 0.924209i −0.272782 0.962076i \(-0.587944\pi\)
−0.999283 + 0.0378663i \(0.987944\pi\)
\(14\) −2.13624 + 1.55207i −0.570934 + 0.414808i
\(15\) 0 0
\(16\) −5.52731 4.01583i −1.38183 1.00396i
\(17\) −1.57092 4.83480i −0.381005 1.17261i −0.939337 0.342995i \(-0.888559\pi\)
0.558333 0.829617i \(-0.311441\pi\)
\(18\) 2.53767 0.598135
\(19\) −1.65990 5.10866i −0.380808 1.17201i −0.939476 0.342615i \(-0.888687\pi\)
0.558668 0.829391i \(-0.311313\pi\)
\(20\) 0 0
\(21\) −0.321543 + 0.989608i −0.0701665 + 0.215950i
\(22\) 2.32982 7.17044i 0.496719 1.52874i
\(23\) −3.12312 + 2.26908i −0.651215 + 0.473135i −0.863685 0.504032i \(-0.831849\pi\)
0.212470 + 0.977168i \(0.431849\pi\)
\(24\) −6.19138 −1.26381
\(25\) 0 0
\(26\) 14.3866 2.82145
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) 1.42758 4.39365i 0.269788 0.830322i
\(29\) 0.210038 0.646430i 0.0390030 0.120039i −0.929659 0.368421i \(-0.879899\pi\)
0.968662 + 0.248382i \(0.0798987\pi\)
\(30\) 0 0
\(31\) 0.262699 + 0.808503i 0.0471821 + 0.145212i 0.971872 0.235509i \(-0.0756759\pi\)
−0.924690 + 0.380721i \(0.875676\pi\)
\(32\) 4.95495 0.875921
\(33\) −0.918092 2.82560i −0.159819 0.491873i
\(34\) 10.4368 + 7.58275i 1.78989 + 1.30043i
\(35\) 0 0
\(36\) −3.59186 + 2.60964i −0.598644 + 0.434940i
\(37\) 1.30869 + 0.950818i 0.215147 + 0.156313i 0.690139 0.723676i \(-0.257549\pi\)
−0.474992 + 0.879990i \(0.657549\pi\)
\(38\) 11.0279 + 8.01226i 1.78897 + 1.29976i
\(39\) 4.58650 3.33228i 0.734427 0.533593i
\(40\) 0 0
\(41\) −0.942740 0.684941i −0.147231 0.106970i 0.511731 0.859146i \(-0.329004\pi\)
−0.658962 + 0.752176i \(0.729004\pi\)
\(42\) −0.815972 2.51130i −0.125907 0.387502i
\(43\) 5.68601 0.867109 0.433554 0.901127i \(-0.357259\pi\)
0.433554 + 0.901127i \(0.357259\pi\)
\(44\) 4.07613 + 12.5450i 0.614500 + 1.89124i
\(45\) 0 0
\(46\) 3.02725 9.31693i 0.446344 1.37371i
\(47\) 1.01555 3.12556i 0.148134 0.455909i −0.849267 0.527964i \(-0.822956\pi\)
0.997401 + 0.0720547i \(0.0229556\pi\)
\(48\) 5.52731 4.01583i 0.797798 0.579635i
\(49\) −5.91729 −0.845327
\(50\) 0 0
\(51\) 5.08361 0.711848
\(52\) −20.3631 + 14.7946i −2.82385 + 2.05165i
\(53\) 3.92023 12.0652i 0.538485 1.65729i −0.197511 0.980301i \(-0.563286\pi\)
0.735996 0.676986i \(-0.236714\pi\)
\(54\) −0.784184 + 2.41347i −0.106714 + 0.328432i
\(55\) 0 0
\(56\) 1.99080 + 6.12704i 0.266031 + 0.818760i
\(57\) 5.37156 0.711481
\(58\) 0.533007 + 1.64043i 0.0699873 + 0.215399i
\(59\) −2.59846 1.88789i −0.338290 0.245782i 0.405650 0.914029i \(-0.367045\pi\)
−0.743940 + 0.668246i \(0.767045\pi\)
\(60\) 0 0
\(61\) 4.38562 3.18634i 0.561521 0.407969i −0.270494 0.962722i \(-0.587187\pi\)
0.832015 + 0.554753i \(0.187187\pi\)
\(62\) −1.74530 1.26803i −0.221653 0.161040i
\(63\) −0.841811 0.611611i −0.106058 0.0770558i
\(64\) 0.881995 0.640807i 0.110249 0.0801008i
\(65\) 0 0
\(66\) 6.09954 + 4.43157i 0.750801 + 0.545489i
\(67\) −0.287120 0.883665i −0.0350773 0.107957i 0.931985 0.362497i \(-0.118076\pi\)
−0.967062 + 0.254540i \(0.918076\pi\)
\(68\) −22.5702 −2.73703
\(69\) −1.19292 3.67145i −0.143611 0.441990i
\(70\) 0 0
\(71\) −0.436821 + 1.34440i −0.0518412 + 0.159551i −0.973625 0.228153i \(-0.926731\pi\)
0.921784 + 0.387703i \(0.126731\pi\)
\(72\) 1.91324 5.88835i 0.225478 0.693949i
\(73\) −9.16080 + 6.65571i −1.07219 + 0.778992i −0.976305 0.216400i \(-0.930568\pi\)
−0.0958862 + 0.995392i \(0.530568\pi\)
\(74\) −4.10501 −0.477198
\(75\) 0 0
\(76\) −23.8486 −2.73562
\(77\) −2.50103 + 1.81710i −0.285018 + 0.207078i
\(78\) −4.44571 + 13.6825i −0.503378 + 1.54924i
\(79\) −0.447171 + 1.37625i −0.0503106 + 0.154840i −0.973055 0.230571i \(-0.925941\pi\)
0.922745 + 0.385412i \(0.125941\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 2.95713 0.326560
\(83\) −3.54616 10.9140i −0.389242 1.19796i −0.933356 0.358952i \(-0.883134\pi\)
0.544114 0.839011i \(-0.316866\pi\)
\(84\) 3.73746 + 2.71542i 0.407790 + 0.296277i
\(85\) 0 0
\(86\) −11.6735 + 8.48129i −1.25879 + 0.914561i
\(87\) 0.549886 + 0.399516i 0.0589540 + 0.0428326i
\(88\) −14.8816 10.8121i −1.58638 1.15257i
\(89\) −7.33961 + 5.33254i −0.777997 + 0.565248i −0.904377 0.426734i \(-0.859664\pi\)
0.126380 + 0.991982i \(0.459664\pi\)
\(90\) 0 0
\(91\) −4.77241 3.46736i −0.500285 0.363478i
\(92\) 5.29633 + 16.3004i 0.552181 + 1.69944i
\(93\) −0.850111 −0.0881524
\(94\) 2.57715 + 7.93164i 0.265812 + 0.818086i
\(95\) 0 0
\(96\) −1.53117 + 4.71244i −0.156274 + 0.480962i
\(97\) −1.86315 + 5.73419i −0.189174 + 0.582219i −0.999995 0.00307549i \(-0.999021\pi\)
0.810821 + 0.585294i \(0.199021\pi\)
\(98\) 12.1483 8.82627i 1.22716 0.891587i
\(99\) 2.97101 0.298597
\(100\) 0 0
\(101\) −15.3408 −1.52647 −0.763236 0.646120i \(-0.776390\pi\)
−0.763236 + 0.646120i \(0.776390\pi\)
\(102\) −10.4368 + 7.58275i −1.03339 + 0.750804i
\(103\) −3.72642 + 11.4688i −0.367175 + 1.13005i 0.581432 + 0.813595i \(0.302493\pi\)
−0.948608 + 0.316455i \(0.897507\pi\)
\(104\) 10.8466 33.3824i 1.06360 3.27341i
\(105\) 0 0
\(106\) 9.94827 + 30.6176i 0.966261 + 2.97385i
\(107\) 6.49787 0.628173 0.314086 0.949394i \(-0.398302\pi\)
0.314086 + 0.949394i \(0.398302\pi\)
\(108\) −1.37197 4.22249i −0.132018 0.406309i
\(109\) 1.86929 + 1.35812i 0.179046 + 0.130084i 0.673698 0.739006i \(-0.264705\pi\)
−0.494653 + 0.869091i \(0.664705\pi\)
\(110\) 0 0
\(111\) −1.30869 + 0.950818i −0.124215 + 0.0902476i
\(112\) −5.75136 4.17861i −0.543453 0.394841i
\(113\) 3.13317 + 2.27638i 0.294744 + 0.214144i 0.725323 0.688409i \(-0.241691\pi\)
−0.430579 + 0.902553i \(0.641691\pi\)
\(114\) −11.0279 + 8.01226i −1.03286 + 0.750417i
\(115\) 0 0
\(116\) −2.44138 1.77376i −0.226676 0.164690i
\(117\) 1.75189 + 5.39175i 0.161962 + 0.498467i
\(118\) 8.15067 0.750330
\(119\) −1.63460 5.03078i −0.149844 0.461171i
\(120\) 0 0
\(121\) −0.671530 + 2.06676i −0.0610482 + 0.187887i
\(122\) −4.25101 + 13.0832i −0.384868 + 1.18450i
\(123\) 0.942740 0.684941i 0.0850040 0.0617590i
\(124\) 3.77431 0.338943
\(125\) 0 0
\(126\) 2.64054 0.235238
\(127\) 9.46046 6.87342i 0.839480 0.609918i −0.0827456 0.996571i \(-0.526369\pi\)
0.922225 + 0.386653i \(0.126369\pi\)
\(128\) −3.91725 + 12.0561i −0.346239 + 1.06562i
\(129\) −1.75707 + 5.40772i −0.154702 + 0.476123i
\(130\) 0 0
\(131\) −2.46042 7.57241i −0.214968 0.661604i −0.999156 0.0410805i \(-0.986920\pi\)
0.784188 0.620524i \(-0.213080\pi\)
\(132\) −13.1906 −1.14810
\(133\) −1.72719 5.31574i −0.149766 0.460933i
\(134\) 1.90754 + 1.38591i 0.164787 + 0.119725i
\(135\) 0 0
\(136\) 25.4635 18.5003i 2.18348 1.58639i
\(137\) −8.94069 6.49579i −0.763854 0.554973i 0.136236 0.990676i \(-0.456500\pi\)
−0.900090 + 0.435704i \(0.856500\pi\)
\(138\) 7.92545 + 5.75818i 0.674659 + 0.490169i
\(139\) 9.92651 7.21204i 0.841956 0.611717i −0.0809604 0.996717i \(-0.525799\pi\)
0.922916 + 0.385000i \(0.125799\pi\)
\(140\) 0 0
\(141\) 2.65876 + 1.93170i 0.223908 + 0.162678i
\(142\) −1.10851 3.41164i −0.0930241 0.286299i
\(143\) 16.8433 1.40851
\(144\) 2.11124 + 6.49774i 0.175937 + 0.541479i
\(145\) 0 0
\(146\) 8.87961 27.3286i 0.734882 2.26173i
\(147\) 1.82854 5.62767i 0.150816 0.464163i
\(148\) 5.81030 4.22143i 0.477604 0.346999i
\(149\) −4.62832 −0.379167 −0.189584 0.981865i \(-0.560714\pi\)
−0.189584 + 0.981865i \(0.560714\pi\)
\(150\) 0 0
\(151\) −4.67249 −0.380242 −0.190121 0.981761i \(-0.560888\pi\)
−0.190121 + 0.981761i \(0.560888\pi\)
\(152\) 26.9058 19.5482i 2.18235 1.58557i
\(153\) −1.57092 + 4.83480i −0.127002 + 0.390871i
\(154\) 2.42426 7.46110i 0.195352 0.601232i
\(155\) 0 0
\(156\) −7.77800 23.9382i −0.622738 1.91659i
\(157\) −14.9726 −1.19494 −0.597472 0.801890i \(-0.703828\pi\)
−0.597472 + 0.801890i \(0.703828\pi\)
\(158\) −1.13477 3.49247i −0.0902777 0.277846i
\(159\) 10.2633 + 7.45672i 0.813932 + 0.591357i
\(160\) 0 0
\(161\) −3.24972 + 2.36106i −0.256113 + 0.186077i
\(162\) −2.05302 1.49161i −0.161301 0.117192i
\(163\) 9.63637 + 7.00123i 0.754779 + 0.548379i 0.897304 0.441412i \(-0.145522\pi\)
−0.142526 + 0.989791i \(0.545522\pi\)
\(164\) −4.18557 + 3.04099i −0.326838 + 0.237462i
\(165\) 0 0
\(166\) 23.5597 + 17.1171i 1.82859 + 1.32855i
\(167\) 3.27809 + 10.0889i 0.253666 + 0.780704i 0.994090 + 0.108563i \(0.0346250\pi\)
−0.740424 + 0.672141i \(0.765375\pi\)
\(168\) −6.44235 −0.497038
\(169\) 5.91461 + 18.2033i 0.454970 + 1.40025i
\(170\) 0 0
\(171\) −1.65990 + 5.10866i −0.126936 + 0.390669i
\(172\) 7.80103 24.0091i 0.594823 1.83068i
\(173\) −1.01401 + 0.736719i −0.0770935 + 0.0560117i −0.625664 0.780092i \(-0.715172\pi\)
0.548571 + 0.836104i \(0.315172\pi\)
\(174\) −1.72485 −0.130760
\(175\) 0 0
\(176\) 20.2983 1.53004
\(177\) 2.59846 1.88789i 0.195312 0.141902i
\(178\) 7.11432 21.8956i 0.533241 1.64115i
\(179\) −6.43105 + 19.7927i −0.480679 + 1.47938i 0.357464 + 0.933927i \(0.383642\pi\)
−0.838143 + 0.545451i \(0.816358\pi\)
\(180\) 0 0
\(181\) −2.14058 6.58803i −0.159108 0.489684i 0.839446 0.543443i \(-0.182880\pi\)
−0.998554 + 0.0537591i \(0.982880\pi\)
\(182\) 14.9698 1.10964
\(183\) 1.67516 + 5.15561i 0.123831 + 0.381113i
\(184\) −19.3364 14.0487i −1.42550 1.03569i
\(185\) 0 0
\(186\) 1.74530 1.26803i 0.127971 0.0929766i
\(187\) 12.2189 + 8.87759i 0.893538 + 0.649193i
\(188\) −11.8043 8.57633i −0.860918 0.625494i
\(189\) 0.841811 0.611611i 0.0612327 0.0444882i
\(190\) 0 0
\(191\) −6.60494 4.79877i −0.477916 0.347227i 0.322602 0.946535i \(-0.395442\pi\)
−0.800518 + 0.599308i \(0.795442\pi\)
\(192\) 0.336892 + 1.03685i 0.0243131 + 0.0748280i
\(193\) 13.9629 1.00507 0.502537 0.864556i \(-0.332400\pi\)
0.502537 + 0.864556i \(0.332400\pi\)
\(194\) −4.72807 14.5515i −0.339456 1.04474i
\(195\) 0 0
\(196\) −8.11834 + 24.9857i −0.579881 + 1.78469i
\(197\) −1.78071 + 5.48046i −0.126870 + 0.390467i −0.994237 0.107203i \(-0.965811\pi\)
0.867367 + 0.497669i \(0.165811\pi\)
\(198\) −6.09954 + 4.43157i −0.433475 + 0.314938i
\(199\) −26.5748 −1.88384 −0.941919 0.335841i \(-0.890980\pi\)
−0.941919 + 0.335841i \(0.890980\pi\)
\(200\) 0 0
\(201\) 0.929140 0.0655365
\(202\) 31.4951 22.8825i 2.21599 1.61001i
\(203\) 0.218552 0.672633i 0.0153393 0.0472096i
\(204\) 6.97456 21.4655i 0.488317 1.50289i
\(205\) 0 0
\(206\) −9.45644 29.1039i −0.658862 2.02777i
\(207\) 3.86039 0.268315
\(208\) 11.9691 + 36.8371i 0.829909 + 2.55420i
\(209\) 12.9111 + 9.38043i 0.893076 + 0.648858i
\(210\) 0 0
\(211\) 21.4061 15.5525i 1.47366 1.07068i 0.494125 0.869391i \(-0.335488\pi\)
0.979533 0.201285i \(-0.0645116\pi\)
\(212\) −45.5669 33.1063i −3.12954 2.27375i
\(213\) −1.14361 0.830884i −0.0783591 0.0569312i
\(214\) −13.3403 + 9.69227i −0.911922 + 0.662550i
\(215\) 0 0
\(216\) 5.00893 + 3.63920i 0.340815 + 0.247616i
\(217\) 0.273347 + 0.841277i 0.0185560 + 0.0571096i
\(218\) −5.86348 −0.397125
\(219\) −3.49912 10.7692i −0.236448 0.727713i
\(220\) 0 0
\(221\) −8.90591 + 27.4096i −0.599076 + 1.84377i
\(222\) 1.26852 3.90410i 0.0851374 0.262026i
\(223\) −22.2039 + 16.1321i −1.48689 + 1.08029i −0.511631 + 0.859205i \(0.670958\pi\)
−0.975255 + 0.221081i \(0.929042\pi\)
\(224\) 5.15581 0.344487
\(225\) 0 0
\(226\) −9.82792 −0.653744
\(227\) 0.105302 0.0765066i 0.00698916 0.00507792i −0.584285 0.811548i \(-0.698625\pi\)
0.591274 + 0.806470i \(0.298625\pi\)
\(228\) 7.36962 22.6813i 0.488065 1.50211i
\(229\) 0.873064 2.68702i 0.0576937 0.177563i −0.918057 0.396449i \(-0.870242\pi\)
0.975750 + 0.218886i \(0.0702423\pi\)
\(230\) 0 0
\(231\) −0.955307 2.94013i −0.0628546 0.193447i
\(232\) 4.20826 0.276286
\(233\) −2.46815 7.59617i −0.161694 0.497642i 0.837084 0.547075i \(-0.184259\pi\)
−0.998777 + 0.0494328i \(0.984259\pi\)
\(234\) −11.6390 8.45625i −0.760867 0.552802i
\(235\) 0 0
\(236\) −11.5366 + 8.38182i −0.750968 + 0.545610i
\(237\) −1.17071 0.850569i −0.0760457 0.0552504i
\(238\) 10.8598 + 7.89012i 0.703938 + 0.511441i
\(239\) 15.4214 11.2043i 0.997528 0.724747i 0.0359713 0.999353i \(-0.488548\pi\)
0.961557 + 0.274606i \(0.0885475\pi\)
\(240\) 0 0
\(241\) −17.0864 12.4140i −1.10063 0.799654i −0.119467 0.992838i \(-0.538118\pi\)
−0.981162 + 0.193184i \(0.938118\pi\)
\(242\) −1.70413 5.24476i −0.109545 0.337146i
\(243\) −1.00000 −0.0641500
\(244\) −7.43735 22.8898i −0.476127 1.46537i
\(245\) 0 0
\(246\) −0.913803 + 2.81240i −0.0582619 + 0.179312i
\(247\) −9.41036 + 28.9621i −0.598767 + 1.84281i
\(248\) −4.25815 + 3.09373i −0.270393 + 0.196452i
\(249\) 11.4756 0.727238
\(250\) 0 0
\(251\) 30.2224 1.90762 0.953811 0.300408i \(-0.0971228\pi\)
0.953811 + 0.300408i \(0.0971228\pi\)
\(252\) −3.73746 + 2.71542i −0.235438 + 0.171056i
\(253\) 3.54419 10.9079i 0.222821 0.685773i
\(254\) −9.17007 + 28.2226i −0.575381 + 1.77084i
\(255\) 0 0
\(256\) −9.26692 28.5207i −0.579183 1.78254i
\(257\) −5.10215 −0.318263 −0.159132 0.987257i \(-0.550869\pi\)
−0.159132 + 0.987257i \(0.550869\pi\)
\(258\) −4.45888 13.7230i −0.277598 0.854358i
\(259\) 1.36174 + 0.989360i 0.0846142 + 0.0614758i
\(260\) 0 0
\(261\) −0.549886 + 0.399516i −0.0340371 + 0.0247294i
\(262\) 16.3464 + 11.8763i 1.00988 + 0.733722i
\(263\) 5.19017 + 3.77088i 0.320040 + 0.232522i 0.736192 0.676772i \(-0.236622\pi\)
−0.416153 + 0.909295i \(0.636622\pi\)
\(264\) 14.8816 10.8121i 0.915898 0.665439i
\(265\) 0 0
\(266\) 11.4749 + 8.33704i 0.703574 + 0.511177i
\(267\) −2.80348 8.62823i −0.171570 0.528039i
\(268\) −4.12518 −0.251986
\(269\) −5.39518 16.6047i −0.328950 1.01240i −0.969626 0.244592i \(-0.921346\pi\)
0.640676 0.767811i \(-0.278654\pi\)
\(270\) 0 0
\(271\) −0.0294140 + 0.0905270i −0.00178677 + 0.00549912i −0.951946 0.306266i \(-0.900920\pi\)
0.950159 + 0.311765i \(0.100920\pi\)
\(272\) −10.7328 + 33.0320i −0.650769 + 2.00286i
\(273\) 4.77241 3.46736i 0.288840 0.209854i
\(274\) 28.0446 1.69424
\(275\) 0 0
\(276\) −17.1393 −1.03166
\(277\) −14.8865 + 10.8157i −0.894443 + 0.649851i −0.937033 0.349242i \(-0.886439\pi\)
0.0425895 + 0.999093i \(0.486439\pi\)
\(278\) −9.62182 + 29.6129i −0.577078 + 1.77606i
\(279\) 0.262699 0.808503i 0.0157274 0.0484038i
\(280\) 0 0
\(281\) 5.54254 + 17.0582i 0.330640 + 1.01761i 0.968830 + 0.247727i \(0.0796837\pi\)
−0.638189 + 0.769879i \(0.720316\pi\)
\(282\) −8.33982 −0.496629
\(283\) 6.87252 + 21.1514i 0.408529 + 1.25732i 0.917912 + 0.396783i \(0.129874\pi\)
−0.509383 + 0.860540i \(0.670126\pi\)
\(284\) 5.07740 + 3.68895i 0.301288 + 0.218899i
\(285\) 0 0
\(286\) −34.5796 + 25.1236i −2.04474 + 1.48559i
\(287\) −0.980955 0.712705i −0.0579039 0.0420697i
\(288\) −4.00864 2.91245i −0.236212 0.171618i
\(289\) −7.15424 + 5.19786i −0.420837 + 0.305756i
\(290\) 0 0
\(291\) −4.87779 3.54392i −0.285941 0.207749i
\(292\) 15.5353 + 47.8128i 0.909136 + 2.79803i
\(293\) 18.7316 1.09431 0.547155 0.837031i \(-0.315711\pi\)
0.547155 + 0.837031i \(0.315711\pi\)
\(294\) 4.64024 + 14.2812i 0.270624 + 0.832896i
\(295\) 0 0
\(296\) −3.09491 + 9.52517i −0.179888 + 0.553639i
\(297\) −0.918092 + 2.82560i −0.0532731 + 0.163958i
\(298\) 9.50204 6.90364i 0.550439 0.399917i
\(299\) 21.8854 1.26566
\(300\) 0 0
\(301\) 5.91650 0.341021
\(302\) 9.59272 6.96952i 0.551999 0.401051i
\(303\) 4.74058 14.5900i 0.272339 0.838174i
\(304\) −11.3407 + 34.9030i −0.650433 + 2.00183i
\(305\) 0 0
\(306\) −3.98649 12.2692i −0.227892 0.701381i
\(307\) 7.03850 0.401708 0.200854 0.979621i \(-0.435628\pi\)
0.200854 + 0.979621i \(0.435628\pi\)
\(308\) 4.24136 + 13.0536i 0.241674 + 0.743796i
\(309\) −9.75590 7.08808i −0.554994 0.403227i
\(310\) 0 0
\(311\) 23.6872 17.2098i 1.34318 0.975876i 0.343858 0.939022i \(-0.388266\pi\)
0.999321 0.0368546i \(-0.0117338\pi\)
\(312\) 28.3967 + 20.6314i 1.60765 + 1.16803i
\(313\) −12.6493 9.19024i −0.714980 0.519463i 0.169796 0.985479i \(-0.445689\pi\)
−0.884776 + 0.466016i \(0.845689\pi\)
\(314\) 30.7391 22.3333i 1.73471 1.26034i
\(315\) 0 0
\(316\) 5.19769 + 3.77635i 0.292393 + 0.212436i
\(317\) 1.92871 + 5.93596i 0.108327 + 0.333397i 0.990497 0.137535i \(-0.0439179\pi\)
−0.882170 + 0.470932i \(0.843918\pi\)
\(318\) −32.1933 −1.80531
\(319\) 0.624024 + 1.92055i 0.0349386 + 0.107530i
\(320\) 0 0
\(321\) −2.00795 + 6.17984i −0.112073 + 0.344925i
\(322\) 3.14997 9.69460i 0.175541 0.540259i
\(323\) −22.0918 + 16.0506i −1.22922 + 0.893080i
\(324\) 4.43979 0.246655
\(325\) 0 0
\(326\) −30.2268 −1.67411
\(327\) −1.86929 + 1.35812i −0.103372 + 0.0751042i
\(328\) 2.22948 6.86164i 0.123103 0.378871i
\(329\) 1.05672 3.25225i 0.0582589 0.179302i
\(330\) 0 0
\(331\) 6.63073 + 20.4073i 0.364458 + 1.12169i 0.950320 + 0.311275i \(0.100756\pi\)
−0.585862 + 0.810411i \(0.699244\pi\)
\(332\) −50.9493 −2.79621
\(333\) −0.499875 1.53846i −0.0273930 0.0843068i
\(334\) −21.7787 15.8231i −1.19168 0.865804i
\(335\) 0 0
\(336\) 5.75136 4.17861i 0.313763 0.227962i
\(337\) −28.1142 20.4262i −1.53148 1.11269i −0.955409 0.295287i \(-0.904585\pi\)
−0.576072 0.817399i \(-0.695415\pi\)
\(338\) −39.2950 28.5495i −2.13736 1.55289i
\(339\) −3.13317 + 2.27638i −0.170170 + 0.123636i
\(340\) 0 0
\(341\) −2.04332 1.48456i −0.110652 0.0803935i
\(342\) −4.21229 12.9641i −0.227775 0.701019i
\(343\) −13.4409 −0.725740
\(344\) 10.8787 + 33.4812i 0.586541 + 1.80519i
\(345\) 0 0
\(346\) 0.982882 3.02500i 0.0528401 0.162625i
\(347\) 8.87623 27.3182i 0.476501 1.46652i −0.367421 0.930055i \(-0.619759\pi\)
0.843922 0.536465i \(-0.180241\pi\)
\(348\) 2.44138 1.77376i 0.130871 0.0950837i
\(349\) −12.2834 −0.657515 −0.328758 0.944414i \(-0.606630\pi\)
−0.328758 + 0.944414i \(0.606630\pi\)
\(350\) 0 0
\(351\) −5.66922 −0.302601
\(352\) −11.9097 + 8.65291i −0.634789 + 0.461201i
\(353\) −8.33663 + 25.6575i −0.443714 + 1.36561i 0.440174 + 0.897913i \(0.354917\pi\)
−0.883888 + 0.467699i \(0.845083\pi\)
\(354\) −2.51870 + 7.75175i −0.133867 + 0.412001i
\(355\) 0 0
\(356\) 12.4469 + 38.3075i 0.659682 + 2.03029i
\(357\) 5.28968 0.279960
\(358\) −16.3199 50.2275i −0.862533 2.65461i
\(359\) −13.2875 9.65393i −0.701287 0.509515i 0.179064 0.983837i \(-0.442693\pi\)
−0.880351 + 0.474322i \(0.842693\pi\)
\(360\) 0 0
\(361\) −7.97178 + 5.79184i −0.419567 + 0.304834i
\(362\) 14.2214 + 10.3325i 0.747460 + 0.543062i
\(363\) −1.75809 1.27733i −0.0922758 0.0670423i
\(364\) −21.1885 + 15.3943i −1.11058 + 0.806883i
\(365\) 0 0
\(366\) −11.1293 8.08589i −0.581737 0.422656i
\(367\) −9.23816 28.4321i −0.482228 1.48415i −0.835956 0.548797i \(-0.815086\pi\)
0.353727 0.935349i \(-0.384914\pi\)
\(368\) 26.3747 1.37487
\(369\) 0.360095 + 1.10826i 0.0187458 + 0.0576936i
\(370\) 0 0
\(371\) 4.07914 12.5543i 0.211778 0.651787i
\(372\) −1.16633 + 3.58958i −0.0604712 + 0.186111i
\(373\) 20.0885 14.5951i 1.04014 0.755706i 0.0698276 0.997559i \(-0.477755\pi\)
0.970313 + 0.241853i \(0.0777551\pi\)
\(374\) −38.3276 −1.98187
\(375\) 0 0
\(376\) 20.3474 1.04934
\(377\) −3.11742 + 2.26494i −0.160556 + 0.116650i
\(378\) −0.815972 + 2.51130i −0.0419690 + 0.129167i
\(379\) 5.99389 18.4473i 0.307885 0.947574i −0.670699 0.741729i \(-0.734006\pi\)
0.978585 0.205845i \(-0.0659941\pi\)
\(380\) 0 0
\(381\) 3.61357 + 11.1214i 0.185129 + 0.569768i
\(382\) 20.7179 1.06002
\(383\) −3.47670 10.7002i −0.177651 0.546754i 0.822094 0.569353i \(-0.192806\pi\)
−0.999745 + 0.0225986i \(0.992806\pi\)
\(384\) −10.2555 7.45106i −0.523349 0.380235i
\(385\) 0 0
\(386\) −28.6662 + 20.8272i −1.45907 + 1.06008i
\(387\) −4.60008 3.34215i −0.233835 0.169891i
\(388\) 21.6564 + 15.7343i 1.09944 + 0.798786i
\(389\) −12.0558 + 8.75903i −0.611252 + 0.444100i −0.849855 0.527017i \(-0.823310\pi\)
0.238603 + 0.971117i \(0.423310\pi\)
\(390\) 0 0
\(391\) 15.8767 + 11.5351i 0.802920 + 0.583356i
\(392\) −11.3212 34.8431i −0.571807 1.75984i
\(393\) 7.96210 0.401635
\(394\) −4.51886 13.9076i −0.227657 0.700656i
\(395\) 0 0
\(396\) 4.07613 12.5450i 0.204833 0.630412i
\(397\) 7.44626 22.9172i 0.373717 1.15018i −0.570623 0.821212i \(-0.693298\pi\)
0.944340 0.328971i \(-0.106702\pi\)
\(398\) 54.5586 39.6392i 2.73478 1.98693i
\(399\) 5.58930 0.279815
\(400\) 0 0
\(401\) 13.4580 0.672059 0.336030 0.941851i \(-0.390916\pi\)
0.336030 + 0.941851i \(0.390916\pi\)
\(402\) −1.90754 + 1.38591i −0.0951397 + 0.0691230i
\(403\) 1.48930 4.58358i 0.0741872 0.228325i
\(404\) −21.0472 + 64.7765i −1.04714 + 3.22275i
\(405\) 0 0
\(406\) 0.554613 + 1.70692i 0.0275250 + 0.0847132i
\(407\) −4.80598 −0.238224
\(408\) 9.72618 + 29.9341i 0.481518 + 1.48196i
\(409\) 28.6988 + 20.8509i 1.41906 + 1.03101i 0.991925 + 0.126825i \(0.0404788\pi\)
0.427140 + 0.904186i \(0.359521\pi\)
\(410\) 0 0
\(411\) 8.94069 6.49579i 0.441012 0.320414i
\(412\) 43.3141 + 31.4696i 2.13393 + 1.55039i
\(413\) −2.70379 1.96441i −0.133045 0.0966625i
\(414\) −7.92545 + 5.75818i −0.389515 + 0.282999i
\(415\) 0 0
\(416\) −22.7259 16.5113i −1.11423 0.809534i
\(417\) 3.79159 + 11.6693i 0.185675 + 0.571449i
\(418\) −40.4986 −1.98085
\(419\) 4.88617 + 15.0381i 0.238705 + 0.734659i 0.996608 + 0.0822916i \(0.0262239\pi\)
−0.757903 + 0.652367i \(0.773776\pi\)
\(420\) 0 0
\(421\) 3.70244 11.3949i 0.180446 0.555355i −0.819394 0.573230i \(-0.805690\pi\)
0.999840 + 0.0178752i \(0.00569015\pi\)
\(422\) −20.7491 + 63.8590i −1.01005 + 3.10861i
\(423\) −2.65876 + 1.93170i −0.129273 + 0.0939225i
\(424\) 78.5447 3.81447
\(425\) 0 0
\(426\) 3.58721 0.173801
\(427\) 4.56340 3.31550i 0.220838 0.160448i
\(428\) 8.91488 27.4372i 0.430917 1.32623i
\(429\) −5.20486 + 16.0189i −0.251293 + 0.773401i
\(430\) 0 0
\(431\) 4.52486 + 13.9261i 0.217955 + 0.670797i 0.998931 + 0.0462350i \(0.0147223\pi\)
−0.780976 + 0.624562i \(0.785278\pi\)
\(432\) −6.83213 −0.328711
\(433\) −1.32041 4.06380i −0.0634547 0.195294i 0.914303 0.405031i \(-0.132739\pi\)
−0.977758 + 0.209737i \(0.932739\pi\)
\(434\) −1.81604 1.31943i −0.0871728 0.0633347i
\(435\) 0 0
\(436\) 8.29926 6.02976i 0.397462 0.288773i
\(437\) 16.7760 + 12.1885i 0.802506 + 0.583055i
\(438\) 23.2471 + 16.8900i 1.11079 + 0.807037i
\(439\) 16.4289 11.9363i 0.784111 0.569690i −0.122099 0.992518i \(-0.538963\pi\)
0.906210 + 0.422828i \(0.138963\pi\)
\(440\) 0 0
\(441\) 4.78718 + 3.47809i 0.227961 + 0.165623i
\(442\) −22.6003 69.5565i −1.07499 3.30847i
\(443\) −19.0543 −0.905299 −0.452649 0.891689i \(-0.649521\pi\)
−0.452649 + 0.891689i \(0.649521\pi\)
\(444\) 2.21934 + 6.83041i 0.105325 + 0.324157i
\(445\) 0 0
\(446\) 21.5224 66.2391i 1.01912 3.13651i
\(447\) 1.43023 4.40180i 0.0676476 0.208198i
\(448\) 0.917747 0.666782i 0.0433595 0.0315025i
\(449\) 29.4793 1.39122 0.695608 0.718421i \(-0.255135\pi\)
0.695608 + 0.718421i \(0.255135\pi\)
\(450\) 0 0
\(451\) 3.46209 0.163023
\(452\) 13.9106 10.1066i 0.654299 0.475376i
\(453\) 1.44388 4.44380i 0.0678394 0.208788i
\(454\) −0.102070 + 0.314139i −0.00479038 + 0.0147433i
\(455\) 0 0
\(456\) 10.2771 + 31.6296i 0.481269 + 1.48119i
\(457\) −28.3015 −1.32389 −0.661945 0.749553i \(-0.730269\pi\)
−0.661945 + 0.749553i \(0.730269\pi\)
\(458\) 2.21555 + 6.81877i 0.103526 + 0.318620i
\(459\) −4.11273 2.98807i −0.191966 0.139471i
\(460\) 0 0
\(461\) 13.3953 9.73223i 0.623879 0.453275i −0.230395 0.973097i \(-0.574002\pi\)
0.854274 + 0.519822i \(0.174002\pi\)
\(462\) 6.34679 + 4.61121i 0.295279 + 0.214533i
\(463\) 7.45051 + 5.41311i 0.346254 + 0.251569i 0.747296 0.664491i \(-0.231352\pi\)
−0.401042 + 0.916060i \(0.631352\pi\)
\(464\) −3.75689 + 2.72954i −0.174409 + 0.126716i
\(465\) 0 0
\(466\) 16.3977 + 11.9136i 0.759607 + 0.551887i
\(467\) −3.27938 10.0929i −0.151752 0.467043i 0.846066 0.533079i \(-0.178965\pi\)
−0.997817 + 0.0660353i \(0.978965\pi\)
\(468\) 25.1701 1.16349
\(469\) −0.298759 0.919485i −0.0137954 0.0424579i
\(470\) 0 0
\(471\) 4.62679 14.2398i 0.213191 0.656135i
\(472\) 6.14508 18.9126i 0.282850 0.870524i
\(473\) −13.6669 + 9.92956i −0.628403 + 0.456562i
\(474\) 3.67220 0.168670
\(475\) 0 0
\(476\) −23.4850 −1.07644
\(477\) −10.2633 + 7.45672i −0.469924 + 0.341420i
\(478\) −14.9480 + 46.0054i −0.683708 + 2.10424i
\(479\) 10.3849 31.9613i 0.474496 1.46035i −0.372140 0.928177i \(-0.621376\pi\)
0.846636 0.532172i \(-0.178624\pi\)
\(480\) 0 0
\(481\) −2.83390 8.72184i −0.129215 0.397682i
\(482\) 53.5954 2.44120
\(483\) −1.24128 3.82027i −0.0564802 0.173828i
\(484\) 7.80554 + 5.67106i 0.354797 + 0.257775i
\(485\) 0 0
\(486\) 2.05302 1.49161i 0.0931269 0.0676607i
\(487\) 23.6626 + 17.1919i 1.07226 + 0.779039i 0.976316 0.216348i \(-0.0694147\pi\)
0.0959389 + 0.995387i \(0.469415\pi\)
\(488\) 27.1531 + 19.7279i 1.22916 + 0.893038i
\(489\) −9.63637 + 7.00123i −0.435772 + 0.316607i
\(490\) 0 0
\(491\) −11.2898 8.20251i −0.509501 0.370174i 0.303133 0.952948i \(-0.401967\pi\)
−0.812634 + 0.582774i \(0.801967\pi\)
\(492\) −1.59874 4.92043i −0.0720769 0.221830i
\(493\) −3.45531 −0.155619
\(494\) −23.8804 73.4964i −1.07443 3.30676i
\(495\) 0 0
\(496\) 1.79479 5.52380i 0.0805885 0.248026i
\(497\) −0.454528 + 1.39889i −0.0203884 + 0.0627490i
\(498\) −23.5597 + 17.1171i −1.05573 + 0.767036i
\(499\) −35.7533 −1.60054 −0.800268 0.599642i \(-0.795310\pi\)
−0.800268 + 0.599642i \(0.795310\pi\)
\(500\) 0 0
\(501\) −10.6081 −0.473936
\(502\) −62.0472 + 45.0800i −2.76930 + 2.01202i
\(503\) 3.59828 11.0744i 0.160439 0.493782i −0.838232 0.545314i \(-0.816410\pi\)
0.998671 + 0.0515323i \(0.0164105\pi\)
\(504\) 1.99080 6.12704i 0.0886771 0.272920i
\(505\) 0 0
\(506\) 8.99399 + 27.6807i 0.399832 + 1.23056i
\(507\) −19.1401 −0.850040
\(508\) −16.0435 49.3768i −0.711815 2.19074i
\(509\) 6.90384 + 5.01594i 0.306007 + 0.222327i 0.730181 0.683253i \(-0.239436\pi\)
−0.424174 + 0.905581i \(0.639436\pi\)
\(510\) 0 0
\(511\) −9.53214 + 6.92551i −0.421677 + 0.306366i
\(512\) 41.0558 + 29.8288i 1.81443 + 1.31826i
\(513\) −4.34568 3.15732i −0.191867 0.139399i
\(514\) 10.4748 7.61040i 0.462025 0.335681i
\(515\) 0 0
\(516\) 20.4234 + 14.8384i 0.899089 + 0.653226i
\(517\) 3.01722 + 9.28605i 0.132697 + 0.408400i
\(518\) −4.27141 −0.187675
\(519\) −0.387316 1.19204i −0.0170013 0.0523246i
\(520\) 0 0
\(521\) 0.390998 1.20337i 0.0171299 0.0527205i −0.942126 0.335259i \(-0.891176\pi\)
0.959256 + 0.282538i \(0.0911763\pi\)
\(522\) 0.533007 1.64043i 0.0233291 0.0717996i
\(523\) 22.0218 15.9998i 0.962946 0.699621i 0.00911285 0.999958i \(-0.497099\pi\)
0.953833 + 0.300337i \(0.0970993\pi\)
\(524\) −35.3500 −1.54427
\(525\) 0 0
\(526\) −16.2802 −0.709850
\(527\) 3.49628 2.54019i 0.152300 0.110653i
\(528\) −6.27252 + 19.3048i −0.272976 + 0.840135i
\(529\) −2.50224 + 7.70110i −0.108793 + 0.334831i
\(530\) 0 0
\(531\) 0.992522 + 3.05467i 0.0430718 + 0.132561i
\(532\) −24.8153 −1.07588
\(533\) 2.04146 + 6.28296i 0.0884253 + 0.272145i
\(534\) 18.6255 + 13.5322i 0.806005 + 0.585597i
\(535\) 0 0
\(536\) 4.65400 3.38133i 0.201022 0.146051i
\(537\) −16.8367 12.2326i −0.726557 0.527875i
\(538\) 35.8440 + 26.0422i 1.54535 + 1.12276i
\(539\) 14.2228 10.3334i 0.612618 0.445093i
\(540\) 0 0
\(541\) −24.5804 17.8587i −1.05679 0.767805i −0.0833007 0.996524i \(-0.526546\pi\)
−0.973492 + 0.228719i \(0.926546\pi\)
\(542\) −0.0746431 0.229728i −0.00320620 0.00986766i
\(543\) 6.92706 0.297269
\(544\) −7.78385 23.9562i −0.333730 1.02711i
\(545\) 0 0
\(546\) −4.62592 + 14.2371i −0.197971 + 0.609293i
\(547\) −3.51564 + 10.8200i −0.150318 + 0.462631i −0.997656 0.0684223i \(-0.978203\pi\)
0.847339 + 0.531053i \(0.178203\pi\)
\(548\) −39.6947 + 28.8399i −1.69568 + 1.23198i
\(549\) −5.42093 −0.231360
\(550\) 0 0
\(551\) −3.65103 −0.155539
\(552\) 19.3364 14.0487i 0.823012 0.597954i
\(553\) −0.465297 + 1.43204i −0.0197864 + 0.0608964i
\(554\) 14.4296 44.4096i 0.613053 1.88678i
\(555\) 0 0
\(556\) −16.8339 51.8093i −0.713914 2.19720i
\(557\) 45.7532 1.93862 0.969312 0.245833i \(-0.0790616\pi\)
0.969312 + 0.245833i \(0.0790616\pi\)
\(558\) 0.666643 + 2.05172i 0.0282213 + 0.0868561i
\(559\) −26.0789 18.9474i −1.10302 0.801390i
\(560\) 0 0
\(561\) −12.2189 + 8.87759i −0.515884 + 0.374812i
\(562\) −36.8231 26.7535i −1.55329 1.12853i
\(563\) 7.23495 + 5.25650i 0.304917 + 0.221535i 0.729712 0.683754i \(-0.239654\pi\)
−0.424796 + 0.905289i \(0.639654\pi\)
\(564\) 11.8043 8.57633i 0.497051 0.361129i
\(565\) 0 0
\(566\) −45.6591 33.1733i −1.91919 1.39438i
\(567\) 0.321543 + 0.989608i 0.0135035 + 0.0415596i
\(568\) −8.75203 −0.367227
\(569\) −0.707365 2.17704i −0.0296543 0.0912665i 0.935134 0.354294i \(-0.115279\pi\)
−0.964788 + 0.263028i \(0.915279\pi\)
\(570\) 0 0
\(571\) −9.50522 + 29.2541i −0.397781 + 1.22424i 0.528993 + 0.848626i \(0.322570\pi\)
−0.926774 + 0.375618i \(0.877430\pi\)
\(572\) 23.1085 71.1206i 0.966214 2.97370i
\(573\) 6.60494 4.79877i 0.275925 0.200471i
\(574\) 3.07700 0.128431
\(575\) 0 0
\(576\) −1.09021 −0.0454252
\(577\) 5.33326 3.87484i 0.222027 0.161312i −0.471212 0.882020i \(-0.656183\pi\)
0.693238 + 0.720708i \(0.256183\pi\)
\(578\) 6.93464 21.3426i 0.288443 0.887736i
\(579\) −4.31479 + 13.2795i −0.179316 + 0.551879i
\(580\) 0 0
\(581\) −3.68991 11.3564i −0.153083 0.471141i
\(582\) 15.3004 0.634220
\(583\) 11.6470 + 35.8459i 0.482371 + 1.48458i
\(584\) −56.7180 41.2081i −2.34701 1.70520i
\(585\) 0 0
\(586\) −38.4563 + 27.9401i −1.58861 + 1.15420i
\(587\) 4.48010 + 3.25499i 0.184914 + 0.134348i 0.676391 0.736543i \(-0.263543\pi\)
−0.491477 + 0.870890i \(0.663543\pi\)
\(588\) −21.2541 15.4420i −0.876503 0.636817i
\(589\) 3.69431 2.68408i 0.152222 0.110595i
\(590\) 0 0
\(591\) −4.66196 3.38711i −0.191767 0.139327i
\(592\) −3.41521 10.5109i −0.140364 0.431997i
\(593\) −1.88122 −0.0772524 −0.0386262 0.999254i \(-0.512298\pi\)
−0.0386262 + 0.999254i \(0.512298\pi\)
\(594\) −2.32982 7.17044i −0.0955935 0.294207i
\(595\) 0 0
\(596\) −6.34992 + 19.5430i −0.260103 + 0.800514i
\(597\) 8.21206 25.2741i 0.336097 1.03440i
\(598\) −44.9311 + 32.6444i −1.83737 + 1.33493i
\(599\) 17.8272 0.728400 0.364200 0.931321i \(-0.381342\pi\)
0.364200 + 0.931321i \(0.381342\pi\)
\(600\) 0 0
\(601\) 33.0994 1.35015 0.675077 0.737747i \(-0.264110\pi\)
0.675077 + 0.737747i \(0.264110\pi\)
\(602\) −12.1467 + 8.82509i −0.495062 + 0.359684i
\(603\) −0.287120 + 0.883665i −0.0116924 + 0.0359856i
\(604\) −6.41052 + 19.7295i −0.260840 + 0.802784i
\(605\) 0 0
\(606\) 12.0300 + 37.0247i 0.488687 + 1.50402i
\(607\) −23.4603 −0.952226 −0.476113 0.879384i \(-0.657955\pi\)
−0.476113 + 0.879384i \(0.657955\pi\)
\(608\) −8.22475 25.3132i −0.333558 1.02658i
\(609\) 0.572176 + 0.415710i 0.0231857 + 0.0168454i
\(610\) 0 0
\(611\) −15.0731 + 10.9512i −0.609792 + 0.443039i
\(612\) 18.2596 + 13.2664i 0.738102 + 0.536263i
\(613\) −38.2083 27.7600i −1.54322 1.12121i −0.948277 0.317445i \(-0.897175\pi\)
−0.594942 0.803769i \(-0.702825\pi\)
\(614\) −14.4502 + 10.4987i −0.583162 + 0.423692i
\(615\) 0 0
\(616\) −15.4848 11.2504i −0.623901 0.453290i
\(617\) 5.02765 + 15.4735i 0.202406 + 0.622941i 0.999810 + 0.0194952i \(0.00620592\pi\)
−0.797404 + 0.603446i \(0.793794\pi\)
\(618\) 30.6017 1.23098
\(619\) 10.9577 + 33.7244i 0.440428 + 1.35550i 0.887421 + 0.460960i \(0.152495\pi\)
−0.446993 + 0.894537i \(0.647505\pi\)
\(620\) 0 0
\(621\) −1.19292 + 3.67145i −0.0478704 + 0.147330i
\(622\) −22.9601 + 70.6640i −0.920617 + 2.83337i
\(623\) −7.63712 + 5.54869i −0.305975 + 0.222304i
\(624\) −38.7329 −1.55056
\(625\) 0 0
\(626\) 39.6775 1.58583
\(627\) −12.9111 + 9.38043i −0.515618 + 0.374618i
\(628\) −20.5420 + 63.2217i −0.819714 + 2.52282i
\(629\) 2.54117 7.82091i 0.101323 0.311840i
\(630\) 0 0
\(631\) −9.03453 27.8054i −0.359659 1.10692i −0.953258 0.302156i \(-0.902294\pi\)
0.593599 0.804761i \(-0.297706\pi\)
\(632\) −8.95939 −0.356385
\(633\) 8.17641 + 25.1644i 0.324983 + 1.00020i
\(634\) −12.8138 9.30978i −0.508901 0.369738i
\(635\) 0 0
\(636\) 45.5669 33.1063i 1.80684 1.31275i
\(637\) 27.1396 + 19.7181i 1.07531 + 0.781259i
\(638\) −4.14583 3.01213i −0.164135 0.119251i
\(639\) 1.14361 0.830884i 0.0452406 0.0328692i
\(640\) 0 0
\(641\) 12.7145 + 9.23764i 0.502194 + 0.364865i 0.809854 0.586631i \(-0.199546\pi\)
−0.307661 + 0.951496i \(0.599546\pi\)
\(642\) −5.09553 15.6824i −0.201104 0.618936i
\(643\) 8.08055 0.318666 0.159333 0.987225i \(-0.449066\pi\)
0.159333 + 0.987225i \(0.449066\pi\)
\(644\) 5.51102 + 16.9612i 0.217165 + 0.668364i
\(645\) 0 0
\(646\) 21.4137 65.9045i 0.842510 2.59298i
\(647\) −3.40516 + 10.4800i −0.133870 + 0.412011i −0.995413 0.0956751i \(-0.969499\pi\)
0.861542 + 0.507686i \(0.169499\pi\)
\(648\) −5.00893 + 3.63920i −0.196769 + 0.142961i
\(649\) 9.54248 0.374575
\(650\) 0 0
\(651\) −0.884570 −0.0346691
\(652\) 42.7834 31.0840i 1.67553 1.21734i
\(653\) 9.60613 29.5646i 0.375917 1.15695i −0.566941 0.823758i \(-0.691873\pi\)
0.942858 0.333195i \(-0.108127\pi\)
\(654\) 1.81191 5.57650i 0.0708515 0.218058i
\(655\) 0 0
\(656\) 2.46021 + 7.57176i 0.0960552 + 0.295628i
\(657\) 11.3234 0.441767
\(658\) 2.68161 + 8.25315i 0.104540 + 0.321741i
\(659\) −26.2325 19.0590i −1.02187 0.742435i −0.0552080 0.998475i \(-0.517582\pi\)
−0.966666 + 0.256040i \(0.917582\pi\)
\(660\) 0 0
\(661\) −12.6268 + 9.17394i −0.491128 + 0.356825i −0.805618 0.592436i \(-0.798166\pi\)
0.314490 + 0.949261i \(0.398166\pi\)
\(662\) −44.0527 32.0061i −1.71216 1.24395i
\(663\) −23.3160 16.9400i −0.905517 0.657897i
\(664\) 57.4806 41.7621i 2.23068 1.62068i
\(665\) 0 0
\(666\) 3.32102 + 2.41287i 0.128687 + 0.0934966i
\(667\) 0.810827 + 2.49547i 0.0313953 + 0.0966249i
\(668\) 47.0978 1.82227
\(669\) −8.48115 26.1023i −0.327900 1.00917i
\(670\) 0 0
\(671\) −4.97691 + 15.3173i −0.192131 + 0.591320i
\(672\) −1.59323 + 4.90346i −0.0614602 + 0.189155i
\(673\) 25.1014 18.2373i 0.967589 0.702995i 0.0126883 0.999919i \(-0.495961\pi\)
0.954901 + 0.296925i \(0.0959611\pi\)
\(674\) 88.1870 3.39684
\(675\) 0 0
\(676\) 84.9778 3.26838
\(677\) −18.6796 + 13.5716i −0.717917 + 0.521597i −0.885718 0.464224i \(-0.846333\pi\)
0.167801 + 0.985821i \(0.446333\pi\)
\(678\) 3.03700 9.34691i 0.116635 0.358966i
\(679\) −1.93868 + 5.96663i −0.0743995 + 0.228978i
\(680\) 0 0
\(681\) 0.0402219 + 0.123790i 0.00154131 + 0.00474365i
\(682\) 6.40936 0.245427
\(683\) 12.7791 + 39.3301i 0.488979 + 1.50492i 0.826134 + 0.563474i \(0.190536\pi\)
−0.337154 + 0.941449i \(0.609464\pi\)
\(684\) 19.2939 + 14.0178i 0.737721 + 0.535986i
\(685\) 0 0
\(686\) 27.5944 20.0485i 1.05356 0.765457i
\(687\) 2.28571 + 1.66067i 0.0872053 + 0.0633584i
\(688\) −31.4283 22.8340i −1.19819 0.870539i
\(689\) −58.1849 + 42.2738i −2.21667 + 1.61050i
\(690\) 0 0
\(691\) −3.61557 2.62686i −0.137543 0.0999306i 0.516886 0.856054i \(-0.327091\pi\)
−0.654429 + 0.756123i \(0.727091\pi\)
\(692\) 1.71960 + 5.29239i 0.0653694 + 0.201186i
\(693\) 3.09144 0.117434
\(694\) 22.5250 + 69.3248i 0.855037 + 2.63153i
\(695\) 0 0
\(696\) −1.30042 + 4.00229i −0.0492924 + 0.151707i
\(697\) −1.83058 + 5.63395i −0.0693382 + 0.213401i
\(698\) 25.2181 18.3220i 0.954518 0.693498i
\(699\) 7.98709 0.302099
\(700\) 0 0
\(701\) −25.2265 −0.952791 −0.476396 0.879231i \(-0.658057\pi\)
−0.476396 + 0.879231i \(0.658057\pi\)
\(702\) 11.6390 8.45625i 0.439287 0.319161i
\(703\) 2.68511 8.26391i 0.101271 0.311679i
\(704\) −1.00091 + 3.08048i −0.0377231 + 0.116100i
\(705\) 0 0
\(706\) −21.1556 65.1104i −0.796203 2.45046i
\(707\) −15.9627 −0.600339
\(708\) −4.40658 13.5621i −0.165610 0.509694i
\(709\) −1.26199 0.916889i −0.0473950 0.0344345i 0.563836 0.825887i \(-0.309325\pi\)
−0.611231 + 0.791453i \(0.709325\pi\)
\(710\) 0 0
\(711\) 1.17071 0.850569i 0.0439050 0.0318988i
\(712\) −45.4423 33.0158i −1.70302 1.23732i
\(713\) −2.65500 1.92897i −0.0994304 0.0722404i
\(714\) −10.8598 + 7.89012i −0.406419 + 0.295280i
\(715\) 0 0
\(716\) 74.7514 + 54.3100i 2.79359 + 2.02966i
\(717\) 5.89045 + 18.1290i 0.219983 + 0.677038i
\(718\) 41.6794 1.55546
\(719\) 8.94304 + 27.5238i 0.333519 + 1.02647i 0.967447 + 0.253074i \(0.0814416\pi\)
−0.633928 + 0.773392i \(0.718558\pi\)
\(720\) 0 0
\(721\) −3.87748 + 11.9336i −0.144405 + 0.444432i
\(722\) 7.72709 23.7815i 0.287572 0.885057i
\(723\) 17.0864 12.4140i 0.635448 0.461680i
\(724\) −30.7547 −1.14299
\(725\) 0 0
\(726\) 5.51466 0.204668
\(727\) 29.9008 21.7242i 1.10896 0.805707i 0.126461 0.991972i \(-0.459638\pi\)
0.982500 + 0.186265i \(0.0596382\pi\)
\(728\) 11.2863 34.7355i 0.418297 1.28739i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 0 0
\(731\) −8.93229 27.4907i −0.330372 1.01678i
\(732\) 24.0678 0.889570
\(733\) −1.28601 3.95793i −0.0474998 0.146189i 0.924494 0.381198i \(-0.124488\pi\)
−0.971993 + 0.235008i \(0.924488\pi\)
\(734\) 61.3757 + 44.5921i 2.26542 + 1.64592i
\(735\) 0 0
\(736\) −15.4749 + 11.2432i −0.570413 + 0.414429i
\(737\) 2.23328 + 1.62257i 0.0822638 + 0.0597682i
\(738\) −2.39237 1.73816i −0.0880642 0.0639824i
\(739\) −15.3371 + 11.1431i −0.564184 + 0.409904i −0.832988 0.553291i \(-0.813372\pi\)
0.268804 + 0.963195i \(0.413372\pi\)
\(740\) 0 0
\(741\) −24.6366 17.8996i −0.905050 0.657557i
\(742\) 10.3515 + 31.8587i 0.380016 + 1.16957i
\(743\) −11.7060 −0.429452 −0.214726 0.976674i \(-0.568886\pi\)
−0.214726 + 0.976674i \(0.568886\pi\)
\(744\) −1.62647 5.00575i −0.0596292 0.183520i
\(745\) 0 0
\(746\) −19.4718 + 59.9281i −0.712915 + 2.19413i
\(747\) −3.54616 + 10.9140i −0.129747 + 0.399321i
\(748\) 54.2495 39.4146i 1.98356 1.44114i
\(749\) 6.76126 0.247051
\(750\) 0 0
\(751\) −4.95672 −0.180873 −0.0904367 0.995902i \(-0.528826\pi\)
−0.0904367 + 0.995902i \(0.528826\pi\)
\(752\) −18.1650 + 13.1976i −0.662408 + 0.481268i
\(753\) −9.33924 + 28.7432i −0.340341 + 1.04746i
\(754\) 3.02174 9.29995i 0.110045 0.338684i
\(755\) 0 0
\(756\) −1.42758 4.39365i −0.0519207 0.159795i
\(757\) 18.6020 0.676101 0.338051 0.941128i \(-0.390232\pi\)
0.338051 + 0.941128i \(0.390232\pi\)
\(758\) 15.2105 + 46.8132i 0.552472 + 1.70033i
\(759\) 9.27881 + 6.74145i 0.336799 + 0.244699i
\(760\) 0 0
\(761\) 9.18925 6.67638i 0.333110 0.242019i −0.408639 0.912696i \(-0.633997\pi\)
0.741749 + 0.670677i \(0.233997\pi\)
\(762\) −24.0075 17.4425i −0.869702 0.631875i
\(763\) 1.94507 + 1.41317i 0.0704161 + 0.0511603i
\(764\) −29.3245 + 21.3055i −1.06092 + 0.770806i
\(765\) 0 0
\(766\) 23.0982 + 16.7818i 0.834572 + 0.606352i
\(767\) 5.62682 + 17.3176i 0.203173 + 0.625302i
\(768\) 29.9884 1.08211
\(769\) 2.24803 + 6.91872i 0.0810660 + 0.249495i 0.983373 0.181599i \(-0.0581274\pi\)
−0.902307 + 0.431095i \(0.858127\pi\)
\(770\) 0 0
\(771\) 1.57665 4.85243i 0.0567817 0.174756i
\(772\) 19.1567 58.9584i 0.689466 2.12196i
\(773\) −7.54237 + 5.47985i −0.271280 + 0.197097i −0.715105 0.699017i \(-0.753621\pi\)
0.443825 + 0.896114i \(0.353621\pi\)
\(774\) 14.4292 0.518648
\(775\) 0 0
\(776\) −37.3296 −1.34005
\(777\) −1.36174 + 0.989360i −0.0488520 + 0.0354931i
\(778\) 11.6857 35.9649i 0.418953 1.28941i
\(779\) −1.93427 + 5.95307i −0.0693024 + 0.213291i
\(780\) 0 0
\(781\) −1.29780 3.99421i −0.0464389 0.142924i
\(782\) −49.8011 −1.78088
\(783\) −0.210038 0.646430i −0.00750614 0.0231015i
\(784\) 32.7067 + 23.7628i 1.16810 + 0.848671i
\(785\) 0 0
\(786\) −16.3464 + 11.8763i −0.583055 + 0.423615i
\(787\) 12.0266 + 8.73787i 0.428704 + 0.311471i 0.781130 0.624368i \(-0.214643\pi\)
−0.352427 + 0.935839i \(0.614643\pi\)
\(788\) 20.6981 + 15.0381i 0.737339 + 0.535708i
\(789\) −5.19017 + 3.77088i −0.184775 + 0.134247i
\(790\) 0 0
\(791\) 3.26017 + 2.36865i 0.115918 + 0.0842196i
\(792\) 5.68426 + 17.4943i 0.201981 + 0.621634i
\(793\) −30.7324 −1.09134
\(794\) 18.8962 + 58.1565i 0.670600 + 2.06390i
\(795\) 0 0
\(796\) −36.4598 + 112.212i −1.29228 + 3.97724i
\(797\) 2.95898 9.10680i 0.104812 0.322580i −0.884874 0.465831i \(-0.845756\pi\)
0.989686 + 0.143251i \(0.0457556\pi\)
\(798\) −11.4749 + 8.33704i −0.406209 + 0.295128i
\(799\) −16.7068 −0.591044
\(800\) 0 0
\(801\) 9.07225 0.320552
\(802\) −27.6295 + 20.0740i −0.975632 + 0.708838i
\(803\) 10.3959 31.9953i 0.366863 1.12909i
\(804\) 1.27475 3.92328i 0.0449570 0.138364i
\(805\) 0 0
\(806\) 3.77935 + 11.6316i 0.133122 + 0.409707i
\(807\) 17.4592 0.614592
\(808\) −29.3508 90.3323i −1.03256 3.17788i
\(809\) −33.2859 24.1836i −1.17027 0.850250i −0.179228 0.983808i \(-0.557360\pi\)
−0.991041 + 0.133557i \(0.957360\pi\)
\(810\) 0 0
\(811\) −35.1435 + 25.5333i −1.23406 + 0.896594i −0.997187 0.0749479i \(-0.976121\pi\)
−0.236868 + 0.971542i \(0.576121\pi\)
\(812\) −2.54034 1.84566i −0.0891484 0.0647701i
\(813\) −0.0770069 0.0559488i −0.00270075 0.00196221i
\(814\) 9.86679 7.16864i 0.345831 0.251261i
\(815\) 0 0
\(816\) −28.0987 20.4149i −0.983651 0.714665i
\(817\) −9.43823 29.0479i −0.330202 1.01626i
\(818\) −90.0206 −3.14750
\(819\) 1.82290 + 5.61031i 0.0636973 + 0.196040i
\(820\) 0 0
\(821\) 5.39595 16.6070i 0.188320 0.579589i −0.811670 0.584116i \(-0.801441\pi\)
0.999990 + 0.00452746i \(0.00144114\pi\)
\(822\) −8.66625 + 26.6720i −0.302270 + 0.930292i
\(823\) −1.79970 + 1.30756i −0.0627337 + 0.0455787i −0.618710 0.785619i \(-0.712344\pi\)
0.555976 + 0.831198i \(0.312344\pi\)
\(824\) −74.6616 −2.60096
\(825\) 0 0
\(826\) 8.48106 0.295094
\(827\) 25.4476 18.4888i 0.884900 0.642918i −0.0496432 0.998767i \(-0.515808\pi\)
0.934543 + 0.355849i \(0.115808\pi\)
\(828\) 5.29633 16.3004i 0.184060 0.566479i
\(829\) 16.4690 50.6862i 0.571990 1.76041i −0.0742155 0.997242i \(-0.523645\pi\)
0.646206 0.763163i \(-0.276355\pi\)
\(830\) 0 0
\(831\) −5.68614 17.5001i −0.197250 0.607073i
\(832\) −6.18061 −0.214274
\(833\) 9.29560 + 28.6089i 0.322073 + 0.991240i
\(834\) −25.1903 18.3018i −0.872267 0.633739i
\(835\) 0 0
\(836\) 57.3223 41.6471i 1.98253 1.44040i
\(837\) 0.687754 + 0.499683i 0.0237723 + 0.0172716i
\(838\) −32.4623 23.5853i −1.12139 0.814739i
\(839\) 6.77415 4.92171i 0.233870 0.169916i −0.464678 0.885480i \(-0.653830\pi\)
0.698548 + 0.715563i \(0.253830\pi\)
\(840\) 0 0
\(841\) 23.0877 + 16.7742i 0.796129 + 0.578421i
\(842\) 9.39558 + 28.9166i 0.323793 + 0.996532i
\(843\) −17.9361 −0.617750
\(844\) −36.3015 111.725i −1.24955 3.84572i
\(845\) 0 0
\(846\) 2.57715 7.93164i 0.0886041 0.272695i
\(847\) −0.698751 + 2.15054i −0.0240094 + 0.0738933i
\(848\) −70.1202 + 50.9453i −2.40794 + 1.74947i
\(849\) −22.2399 −0.763273
\(850\) 0 0
\(851\) −6.24467 −0.214064
\(852\) −5.07740 + 3.68895i −0.173949 + 0.126381i
\(853\) 0.378146 1.16381i 0.0129475 0.0398482i −0.944374 0.328873i \(-0.893331\pi\)
0.957322 + 0.289025i \(0.0933311\pi\)
\(854\) −4.42332 + 13.6136i −0.151363 + 0.465847i
\(855\) 0 0
\(856\) 12.4320 + 38.2618i 0.424917 + 1.30776i
\(857\) 14.3684 0.490816 0.245408 0.969420i \(-0.421078\pi\)
0.245408 + 0.969420i \(0.421078\pi\)
\(858\) −13.2082 40.6508i −0.450922 1.38780i
\(859\) 8.34015 + 6.05947i 0.284562 + 0.206747i 0.720905 0.693034i \(-0.243726\pi\)
−0.436343 + 0.899781i \(0.643726\pi\)
\(860\) 0 0
\(861\) 0.980955 0.712705i 0.0334308 0.0242889i
\(862\) −30.0619 21.8413i −1.02391 0.743916i
\(863\) 24.4909 + 17.7937i 0.833679 + 0.605703i 0.920598 0.390512i \(-0.127702\pi\)
−0.0869190 + 0.996215i \(0.527702\pi\)
\(864\) 4.00864 2.91245i 0.136377 0.0990835i
\(865\) 0 0
\(866\) 8.77241 + 6.37353i 0.298099 + 0.216581i
\(867\) −2.73268 8.41031i −0.0928065 0.285629i
\(868\) 3.92730 0.133301
\(869\) −1.32855 4.08885i −0.0450679 0.138705i
\(870\) 0 0
\(871\) −1.62775 + 5.00969i −0.0551541 + 0.169747i
\(872\) −4.42068 + 13.6055i −0.149703 + 0.460739i
\(873\) 4.87779 3.54392i 0.165088 0.119944i
\(874\) −52.6220 −1.77996
\(875\) 0 0
\(876\) −50.2734 −1.69858
\(877\) 24.7839 18.0065i 0.836892 0.608037i −0.0846091 0.996414i \(-0.526964\pi\)
0.921501 + 0.388377i \(0.126964\pi\)
\(878\) −15.9247 + 49.0111i −0.537431 + 1.65404i
\(879\) −5.78837 + 17.8148i −0.195237 + 0.600877i
\(880\) 0 0
\(881\) 4.70359 + 14.4762i 0.158468 + 0.487714i 0.998496 0.0548293i \(-0.0174615\pi\)
−0.840028 + 0.542543i \(0.817461\pi\)
\(882\) −15.0161 −0.505620
\(883\) −12.4220 38.2310i −0.418034 1.28658i −0.909509 0.415684i \(-0.863542\pi\)
0.491475 0.870892i \(-0.336458\pi\)
\(884\) 103.518 + 75.2102i 3.48169 + 2.52959i
\(885\) 0 0
\(886\) 39.1189 28.4216i 1.31423 0.954842i
\(887\) −25.7617 18.7169i −0.864992 0.628453i 0.0642465 0.997934i \(-0.479536\pi\)
−0.929238 + 0.369481i \(0.879536\pi\)
\(888\) −8.10259 5.88688i −0.271905 0.197551i
\(889\) 9.84394 7.15204i 0.330155 0.239872i
\(890\) 0 0
\(891\) −2.40360 1.74631i −0.0805235 0.0585037i
\(892\) 37.6545 + 115.889i 1.26077 + 3.88024i
\(893\) −17.6531 −0.590739
\(894\) 3.62946 + 11.1703i 0.121387 + 0.373591i
\(895\) 0 0
\(896\) −4.07604 + 12.5448i −0.136171 + 0.419091i
\(897\) −6.76296 + 20.8142i −0.225809 + 0.694967i
\(898\) −60.5217 + 43.9716i −2.01964 + 1.46735i
\(899\) 0.577817 0.0192713
\(900\) 0 0
\(901\) −64.4914 −2.14852
\(902\) −7.10774 + 5.16407i −0.236662 + 0.171945i
\(903\) −1.82830 + 5.62692i −0.0608419 + 0.187252i
\(904\) −7.40962 + 22.8045i −0.246440 + 0.758465i
\(905\) 0 0
\(906\) 3.66409 + 11.2769i 0.121731 + 0.374651i
\(907\) 28.8507 0.957970 0.478985 0.877823i \(-0.341005\pi\)
0.478985 + 0.877823i \(0.341005\pi\)
\(908\) −0.178577 0.549602i −0.00592627 0.0182392i
\(909\) 12.4110 + 9.01712i 0.411647 + 0.299079i
\(910\) 0 0
\(911\) −39.1370 + 28.4347i −1.29667 + 0.942084i −0.999917 0.0128711i \(-0.995903\pi\)
−0.296750 + 0.954955i \(0.595903\pi\)
\(912\) −29.6903 21.5713i −0.983143 0.714296i
\(913\) 27.5827 + 20.0400i 0.912855 + 0.663228i
\(914\) 58.1036 42.2148i 1.92190 1.39634i
\(915\) 0 0
\(916\) −10.1481 7.37301i −0.335302 0.243611i
\(917\) −2.56016 7.87936i −0.0845439 0.260199i
\(918\) 12.9006 0.425782
\(919\) −2.58963 7.97006i −0.0854240 0.262908i 0.899216 0.437505i \(-0.144138\pi\)
−0.984640 + 0.174597i \(0.944138\pi\)
\(920\) 0 0
\(921\) −2.17501 + 6.69401i −0.0716692 + 0.220575i
\(922\) −12.9841 + 39.9609i −0.427608 + 1.31604i
\(923\) 6.48340 4.71046i 0.213404 0.155047i
\(924\) −13.7253 −0.451530
\(925\) 0 0
\(926\) −23.3703 −0.767995
\(927\) 9.75590 7.08808i 0.320426 0.232803i
\(928\) 1.04073 3.20303i 0.0341636 0.105145i
\(929\) 4.42283 13.6121i 0.145108 0.446597i −0.851917 0.523677i \(-0.824560\pi\)
0.997025 + 0.0770801i \(0.0245597\pi\)
\(930\) 0 0
\(931\) 9.82212 + 30.2294i 0.321907 + 0.990728i
\(932\) −35.4610 −1.16156
\(933\) 9.04771 + 27.8460i 0.296209 + 0.911637i
\(934\) 21.7873 + 15.8294i 0.712901 + 0.517953i
\(935\) 0 0
\(936\) −28.3967 + 20.6314i −0.928177 + 0.674360i
\(937\) −17.7372 12.8869i −0.579451 0.420996i 0.259075 0.965857i \(-0.416582\pi\)
−0.838526 + 0.544862i \(0.816582\pi\)
\(938\) 1.98487 + 1.44209i 0.0648082 + 0.0470859i
\(939\) 12.6493 9.19024i 0.412794 0.299912i
\(940\) 0 0
\(941\) −18.1167 13.1625i −0.590586 0.429086i 0.251939 0.967743i \(-0.418932\pi\)
−0.842525 + 0.538657i \(0.818932\pi\)
\(942\) 11.7413 + 36.1360i 0.382552 + 1.17737i
\(943\) 4.49847 0.146490
\(944\) 6.78104 + 20.8699i 0.220704 + 0.679257i
\(945\) 0 0
\(946\) 13.2474 40.7712i 0.430709 1.32559i
\(947\) −13.4619 + 41.4316i −0.437454 + 1.34635i 0.453096 + 0.891462i \(0.350319\pi\)
−0.890550 + 0.454884i \(0.849681\pi\)
\(948\) −5.19769 + 3.77635i −0.168813 + 0.122650i
\(949\) 64.1947 2.08385
\(950\) 0 0
\(951\) −6.24144 −0.202393
\(952\) 26.4957 19.2502i 0.858729 0.623903i
\(953\) −0.732893 + 2.25561i −0.0237407 + 0.0730664i −0.962225 0.272256i \(-0.912230\pi\)
0.938484 + 0.345322i \(0.112230\pi\)
\(954\) 9.94827 30.6176i 0.322087 0.991282i
\(955\) 0 0
\(956\) −26.1524 80.4887i −0.845828 2.60319i
\(957\) −2.01938 −0.0652774
\(958\) 26.3534 + 81.1073i 0.851439 + 2.62046i
\(959\) −9.30310 6.75910i −0.300413 0.218263i
\(960\) 0 0
\(961\) 24.4949 17.7966i 0.790157 0.574082i
\(962\) 18.8276 + 13.6791i 0.607027 + 0.441031i
\(963\) −5.25689 3.81935i −0.169401 0.123077i
\(964\) −75.8598 + 55.1154i −2.44328 + 1.77515i
\(965\) 0 0
\(966\) 8.24672 + 5.99159i 0.265334 + 0.192776i
\(967\) 6.11413 + 18.8174i 0.196617 + 0.605125i 0.999954 + 0.00960036i \(0.00305594\pi\)
−0.803337 + 0.595525i \(0.796944\pi\)
\(968\) −13.4546 −0.432447
\(969\) −8.43831 25.9704i −0.271077 0.834291i
\(970\) 0 0
\(971\) 15.2604 46.9668i 0.489731 1.50724i −0.335279 0.942119i \(-0.608831\pi\)
0.825010 0.565118i \(-0.191169\pi\)
\(972\) −1.37197 + 4.22249i −0.0440059 + 0.135436i
\(973\) 10.3289 7.50438i 0.331129 0.240579i
\(974\) −74.2234 −2.37827
\(975\) 0 0
\(976\) −37.0365 −1.18551
\(977\) −38.6429 + 28.0757i −1.23630 + 0.898221i −0.997346 0.0728110i \(-0.976803\pi\)
−0.238949 + 0.971032i \(0.576803\pi\)
\(978\) 9.34058 28.7474i 0.298679 0.919239i
\(979\) 8.32916 25.6345i 0.266201 0.819283i
\(980\) 0 0
\(981\) −0.714006 2.19749i −0.0227965 0.0701603i
\(982\) 35.4131 1.13008
\(983\) −16.0467 49.3867i −0.511810 1.57519i −0.789011 0.614379i \(-0.789407\pi\)
0.277201 0.960812i \(-0.410593\pi\)
\(984\) 5.83686 + 4.24073i 0.186072 + 0.135190i
\(985\) 0 0
\(986\) 7.09383 5.15397i 0.225914 0.164136i
\(987\) 2.76653 + 2.01000i 0.0880596 + 0.0639791i
\(988\) 109.381 + 79.4703i 3.47989 + 2.52829i
\(989\) −17.7581 + 12.9020i −0.564674 + 0.410260i
\(990\) 0 0
\(991\) 13.2509 + 9.62734i 0.420929 + 0.305823i 0.778011 0.628250i \(-0.216229\pi\)
−0.357083 + 0.934073i \(0.616229\pi\)
\(992\) 1.30166 + 4.00610i 0.0413277 + 0.127194i
\(993\) −21.4575 −0.680933
\(994\) −1.15344 3.54994i −0.0365850 0.112597i
\(995\) 0 0
\(996\) 15.7442 48.4557i 0.498874 1.53538i
\(997\) 6.87610 21.1625i 0.217768 0.670222i −0.781177 0.624309i \(-0.785380\pi\)
0.998945 0.0459126i \(-0.0146196\pi\)
\(998\) 73.4022 53.3299i 2.32351 1.68813i
\(999\) 1.61763 0.0511795
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 375.2.g.d.301.1 16
5.2 odd 4 375.2.i.c.199.1 16
5.3 odd 4 75.2.i.a.64.4 yes 16
5.4 even 2 375.2.g.e.301.4 16
15.8 even 4 225.2.m.b.64.1 16
25.3 odd 20 1875.2.b.h.1249.1 16
25.4 even 10 1875.2.a.m.1.1 8
25.9 even 10 375.2.g.e.76.4 16
25.12 odd 20 75.2.i.a.34.4 16
25.13 odd 20 375.2.i.c.49.1 16
25.16 even 5 inner 375.2.g.d.76.1 16
25.21 even 5 1875.2.a.p.1.8 8
25.22 odd 20 1875.2.b.h.1249.16 16
75.29 odd 10 5625.2.a.bd.1.8 8
75.62 even 20 225.2.m.b.109.1 16
75.71 odd 10 5625.2.a.t.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.i.a.34.4 16 25.12 odd 20
75.2.i.a.64.4 yes 16 5.3 odd 4
225.2.m.b.64.1 16 15.8 even 4
225.2.m.b.109.1 16 75.62 even 20
375.2.g.d.76.1 16 25.16 even 5 inner
375.2.g.d.301.1 16 1.1 even 1 trivial
375.2.g.e.76.4 16 25.9 even 10
375.2.g.e.301.4 16 5.4 even 2
375.2.i.c.49.1 16 25.13 odd 20
375.2.i.c.199.1 16 5.2 odd 4
1875.2.a.m.1.1 8 25.4 even 10
1875.2.a.p.1.8 8 25.21 even 5
1875.2.b.h.1249.1 16 25.3 odd 20
1875.2.b.h.1249.16 16 25.22 odd 20
5625.2.a.t.1.1 8 75.71 odd 10
5625.2.a.bd.1.8 8 75.29 odd 10