Properties

Label 637.2.g.l.373.3
Level $637$
Weight $2$
Character 637.373
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
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] = [637,2,Mod(263,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), degree \(2\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.3
Root \(-0.437442 + 0.757672i\) of defining polynomial
Character \(\chi\) \(=\) 637.373
Dual form 637.2.g.l.263.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.134063 + 0.232203i) q^{2} +1.14301 q^{3} +(0.964054 - 1.66979i) q^{4} +(-1.28088 + 2.21854i) q^{5} +(0.153235 + 0.265410i) q^{6} +1.05323 q^{8} -1.69353 q^{9} +O(q^{10})\) \(q+(0.134063 + 0.232203i) q^{2} +1.14301 q^{3} +(0.964054 - 1.66979i) q^{4} +(-1.28088 + 2.21854i) q^{5} +(0.153235 + 0.265410i) q^{6} +1.05323 q^{8} -1.69353 q^{9} -0.686871 q^{10} +3.94600 q^{11} +(1.10192 - 1.90859i) q^{12} +(3.15374 - 1.74755i) q^{13} +(-1.46405 + 2.53582i) q^{15} +(-1.78691 - 3.09502i) q^{16} +(0.392550 - 0.679916i) q^{17} +(-0.227039 - 0.393243i) q^{18} +7.49527 q^{19} +(2.46967 + 4.27760i) q^{20} +(0.529011 + 0.916274i) q^{22} +(3.97759 + 6.88938i) q^{23} +1.20385 q^{24} +(-0.781294 - 1.35324i) q^{25} +(0.828585 + 0.498028i) q^{26} -5.36475 q^{27} +(-1.17586 + 2.03666i) q^{29} -0.785100 q^{30} +(-1.27718 - 2.21215i) q^{31} +(1.53234 - 2.65409i) q^{32} +4.51032 q^{33} +0.210505 q^{34} +(-1.63266 + 2.82784i) q^{36} +(-3.37858 - 5.85187i) q^{37} +(1.00484 + 1.74043i) q^{38} +(3.60475 - 1.99746i) q^{39} +(-1.34905 + 2.33663i) q^{40} +(-1.21874 + 2.11091i) q^{41} +(1.12473 + 1.94809i) q^{43} +(3.80416 - 6.58900i) q^{44} +(2.16920 - 3.75717i) q^{45} +(-1.06649 + 1.84722i) q^{46} +(0.658276 - 1.14017i) q^{47} +(-2.04246 - 3.53764i) q^{48} +(0.209485 - 0.362838i) q^{50} +(0.448688 - 0.777151i) q^{51} +(0.122340 - 6.95082i) q^{52} +(-4.63977 - 8.03632i) q^{53} +(-0.719212 - 1.24571i) q^{54} +(-5.05434 + 8.75438i) q^{55} +8.56716 q^{57} -0.630558 q^{58} +(-4.48335 + 7.76540i) q^{59} +(2.82286 + 4.88933i) q^{60} -9.44547 q^{61} +(0.342445 - 0.593132i) q^{62} -6.32592 q^{64} +(-0.162546 + 9.23511i) q^{65} +(0.604665 + 1.04731i) q^{66} -1.35256 q^{67} +(-0.756879 - 1.31095i) q^{68} +(4.54642 + 7.87463i) q^{69} +(-6.15808 - 10.6661i) q^{71} -1.78367 q^{72} +(0.384295 + 0.665619i) q^{73} +(0.905882 - 1.56903i) q^{74} +(-0.893026 - 1.54677i) q^{75} +(7.22585 - 12.5155i) q^{76} +(0.947080 + 0.569251i) q^{78} +(-3.09642 + 5.36316i) q^{79} +9.15525 q^{80} -1.05136 q^{81} -0.653548 q^{82} +1.07292 q^{83} +(1.00562 + 1.74178i) q^{85} +(-0.301568 + 0.522332i) q^{86} +(-1.34402 + 2.32792i) q^{87} +4.15603 q^{88} +(3.83149 + 6.63634i) q^{89} +1.16324 q^{90} +15.3384 q^{92} +(-1.45983 - 2.52850i) q^{93} +0.353001 q^{94} +(-9.60052 + 16.6286i) q^{95} +(1.75148 - 3.03365i) q^{96} +(-1.18601 - 2.05423i) q^{97} -6.68267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23} - 22 q^{24} + 7 q^{25} - 5 q^{26} + 8 q^{27} + 3 q^{29} + 10 q^{30} - 16 q^{31} + 8 q^{32} + 32 q^{33} - 32 q^{34} - 21 q^{36} - 13 q^{37} + 17 q^{38} - 23 q^{39} + 5 q^{40} + 8 q^{41} - 11 q^{43} + 21 q^{44} + 7 q^{45} + 16 q^{46} + q^{47} - 21 q^{48} + 6 q^{50} - 20 q^{51} + 25 q^{52} - 2 q^{53} + 18 q^{54} - 9 q^{55} + 42 q^{57} + 16 q^{58} - 13 q^{59} + 20 q^{60} - 10 q^{61} - 5 q^{62} - 30 q^{64} + 19 q^{65} - 18 q^{66} + 22 q^{67} - 29 q^{68} - 23 q^{69} + 6 q^{71} - 50 q^{72} + 30 q^{73} - 3 q^{74} + 3 q^{75} + 9 q^{76} + 16 q^{78} + 7 q^{79} - 14 q^{80} + 12 q^{81} + 2 q^{82} + 54 q^{83} - q^{85} - 7 q^{86} - 16 q^{87} - 4 q^{89} + 16 q^{90} + 54 q^{92} - 7 q^{93} + 90 q^{94} - 6 q^{95} - 19 q^{96} + 35 q^{97} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.134063 + 0.232203i 0.0947966 + 0.164193i 0.909524 0.415652i \(-0.136447\pi\)
−0.814727 + 0.579845i \(0.803113\pi\)
\(3\) 1.14301 0.659917 0.329958 0.943996i \(-0.392965\pi\)
0.329958 + 0.943996i \(0.392965\pi\)
\(4\) 0.964054 1.66979i 0.482027 0.834896i
\(5\) −1.28088 + 2.21854i −0.572826 + 0.992163i 0.423448 + 0.905920i \(0.360820\pi\)
−0.996274 + 0.0862431i \(0.972514\pi\)
\(6\) 0.153235 + 0.265410i 0.0625578 + 0.108353i
\(7\) 0 0
\(8\) 1.05323 0.372371
\(9\) −1.69353 −0.564510
\(10\) −0.686871 −0.217208
\(11\) 3.94600 1.18976 0.594882 0.803813i \(-0.297199\pi\)
0.594882 + 0.803813i \(0.297199\pi\)
\(12\) 1.10192 1.90859i 0.318098 0.550961i
\(13\) 3.15374 1.74755i 0.874690 0.484682i
\(14\) 0 0
\(15\) −1.46405 + 2.53582i −0.378017 + 0.654745i
\(16\) −1.78691 3.09502i −0.446728 0.773755i
\(17\) 0.392550 0.679916i 0.0952073 0.164904i −0.814488 0.580181i \(-0.802982\pi\)
0.909695 + 0.415277i \(0.136315\pi\)
\(18\) −0.227039 0.393243i −0.0535136 0.0926883i
\(19\) 7.49527 1.71953 0.859767 0.510687i \(-0.170609\pi\)
0.859767 + 0.510687i \(0.170609\pi\)
\(20\) 2.46967 + 4.27760i 0.552235 + 0.956500i
\(21\) 0 0
\(22\) 0.529011 + 0.916274i 0.112786 + 0.195350i
\(23\) 3.97759 + 6.88938i 0.829384 + 1.43654i 0.898522 + 0.438929i \(0.144642\pi\)
−0.0691375 + 0.997607i \(0.522025\pi\)
\(24\) 1.20385 0.245734
\(25\) −0.781294 1.35324i −0.156259 0.270648i
\(26\) 0.828585 + 0.498028i 0.162499 + 0.0976714i
\(27\) −5.36475 −1.03245
\(28\) 0 0
\(29\) −1.17586 + 2.03666i −0.218353 + 0.378198i −0.954304 0.298836i \(-0.903402\pi\)
0.735952 + 0.677034i \(0.236735\pi\)
\(30\) −0.785100 −0.143339
\(31\) −1.27718 2.21215i −0.229389 0.397313i 0.728238 0.685324i \(-0.240339\pi\)
−0.957627 + 0.288011i \(0.907006\pi\)
\(32\) 1.53234 2.65409i 0.270882 0.469182i
\(33\) 4.51032 0.785145
\(34\) 0.210505 0.0361013
\(35\) 0 0
\(36\) −1.63266 + 2.82784i −0.272109 + 0.471307i
\(37\) −3.37858 5.85187i −0.555435 0.962041i −0.997870 0.0652406i \(-0.979219\pi\)
0.442435 0.896801i \(-0.354115\pi\)
\(38\) 1.00484 + 1.74043i 0.163006 + 0.282334i
\(39\) 3.60475 1.99746i 0.577223 0.319850i
\(40\) −1.34905 + 2.33663i −0.213304 + 0.369453i
\(41\) −1.21874 + 2.11091i −0.190335 + 0.329669i −0.945361 0.326025i \(-0.894291\pi\)
0.755027 + 0.655694i \(0.227624\pi\)
\(42\) 0 0
\(43\) 1.12473 + 1.94809i 0.171520 + 0.297081i 0.938951 0.344050i \(-0.111799\pi\)
−0.767432 + 0.641131i \(0.778466\pi\)
\(44\) 3.80416 6.58900i 0.573499 0.993329i
\(45\) 2.16920 3.75717i 0.323366 0.560086i
\(46\) −1.06649 + 1.84722i −0.157246 + 0.272357i
\(47\) 0.658276 1.14017i 0.0960195 0.166311i −0.814014 0.580845i \(-0.802722\pi\)
0.910034 + 0.414534i \(0.136056\pi\)
\(48\) −2.04246 3.53764i −0.294803 0.510614i
\(49\) 0 0
\(50\) 0.209485 0.362838i 0.0296256 0.0513130i
\(51\) 0.448688 0.777151i 0.0628289 0.108823i
\(52\) 0.122340 6.95082i 0.0169655 0.963905i
\(53\) −4.63977 8.03632i −0.637321 1.10387i −0.986018 0.166637i \(-0.946709\pi\)
0.348697 0.937236i \(-0.386624\pi\)
\(54\) −0.719212 1.24571i −0.0978724 0.169520i
\(55\) −5.05434 + 8.75438i −0.681528 + 1.18044i
\(56\) 0 0
\(57\) 8.56716 1.13475
\(58\) −0.630558 −0.0827963
\(59\) −4.48335 + 7.76540i −0.583683 + 1.01097i 0.411355 + 0.911475i \(0.365056\pi\)
−0.995038 + 0.0994935i \(0.968278\pi\)
\(60\) 2.82286 + 4.88933i 0.364429 + 0.631210i
\(61\) −9.44547 −1.20937 −0.604684 0.796465i \(-0.706701\pi\)
−0.604684 + 0.796465i \(0.706701\pi\)
\(62\) 0.342445 0.593132i 0.0434906 0.0753279i
\(63\) 0 0
\(64\) −6.32592 −0.790741
\(65\) −0.162546 + 9.23511i −0.0201613 + 1.14547i
\(66\) 0.604665 + 1.04731i 0.0744291 + 0.128915i
\(67\) −1.35256 −0.165242 −0.0826209 0.996581i \(-0.526329\pi\)
−0.0826209 + 0.996581i \(0.526329\pi\)
\(68\) −0.756879 1.31095i −0.0917851 0.158976i
\(69\) 4.54642 + 7.87463i 0.547324 + 0.947994i
\(70\) 0 0
\(71\) −6.15808 10.6661i −0.730829 1.26583i −0.956529 0.291637i \(-0.905800\pi\)
0.225700 0.974197i \(-0.427533\pi\)
\(72\) −1.78367 −0.210207
\(73\) 0.384295 + 0.665619i 0.0449783 + 0.0779048i 0.887638 0.460542i \(-0.152345\pi\)
−0.842660 + 0.538446i \(0.819011\pi\)
\(74\) 0.905882 1.56903i 0.105307 0.182396i
\(75\) −0.893026 1.54677i −0.103118 0.178605i
\(76\) 7.22585 12.5155i 0.828862 1.43563i
\(77\) 0 0
\(78\) 0.947080 + 0.569251i 0.107236 + 0.0644550i
\(79\) −3.09642 + 5.36316i −0.348375 + 0.603402i −0.985961 0.166976i \(-0.946600\pi\)
0.637586 + 0.770379i \(0.279933\pi\)
\(80\) 9.15525 1.02359
\(81\) −1.05136 −0.116818
\(82\) −0.653548 −0.0721723
\(83\) 1.07292 0.117768 0.0588841 0.998265i \(-0.481246\pi\)
0.0588841 + 0.998265i \(0.481246\pi\)
\(84\) 0 0
\(85\) 1.00562 + 1.74178i 0.109074 + 0.188922i
\(86\) −0.301568 + 0.522332i −0.0325190 + 0.0563245i
\(87\) −1.34402 + 2.32792i −0.144094 + 0.249579i
\(88\) 4.15603 0.443034
\(89\) 3.83149 + 6.63634i 0.406138 + 0.703451i 0.994453 0.105180i \(-0.0335420\pi\)
−0.588316 + 0.808631i \(0.700209\pi\)
\(90\) 1.16324 0.122616
\(91\) 0 0
\(92\) 15.3384 1.59914
\(93\) −1.45983 2.52850i −0.151378 0.262194i
\(94\) 0.353001 0.0364093
\(95\) −9.60052 + 16.6286i −0.984993 + 1.70606i
\(96\) 1.75148 3.03365i 0.178760 0.309621i
\(97\) −1.18601 2.05423i −0.120421 0.208575i 0.799513 0.600649i \(-0.205091\pi\)
−0.919934 + 0.392074i \(0.871758\pi\)
\(98\) 0 0
\(99\) −6.68267 −0.671634
\(100\) −3.01284 −0.301284
\(101\) 0.797330 0.0793373 0.0396686 0.999213i \(-0.487370\pi\)
0.0396686 + 0.999213i \(0.487370\pi\)
\(102\) 0.240609 0.0238239
\(103\) 1.08309 1.87597i 0.106720 0.184844i −0.807720 0.589567i \(-0.799299\pi\)
0.914440 + 0.404722i \(0.132632\pi\)
\(104\) 3.32160 1.84056i 0.325710 0.180482i
\(105\) 0 0
\(106\) 1.24404 2.15474i 0.120832 0.209287i
\(107\) 5.76311 + 9.98201i 0.557141 + 0.964997i 0.997733 + 0.0672896i \(0.0214351\pi\)
−0.440592 + 0.897707i \(0.645232\pi\)
\(108\) −5.17191 + 8.95801i −0.497667 + 0.861985i
\(109\) −4.03912 6.99595i −0.386877 0.670091i 0.605151 0.796111i \(-0.293113\pi\)
−0.992028 + 0.126020i \(0.959780\pi\)
\(110\) −2.71039 −0.258426
\(111\) −3.86174 6.68874i −0.366541 0.634867i
\(112\) 0 0
\(113\) −4.02067 6.96401i −0.378233 0.655119i 0.612572 0.790415i \(-0.290135\pi\)
−0.990805 + 0.135296i \(0.956802\pi\)
\(114\) 1.14854 + 1.98932i 0.107570 + 0.186317i
\(115\) −20.3792 −1.90037
\(116\) 2.26719 + 3.92690i 0.210504 + 0.364603i
\(117\) −5.34096 + 2.95952i −0.493772 + 0.273608i
\(118\) −2.40420 −0.221325
\(119\) 0 0
\(120\) −1.54198 + 2.67079i −0.140763 + 0.243808i
\(121\) 4.57093 0.415539
\(122\) −1.26628 2.19327i −0.114644 0.198569i
\(123\) −1.39303 + 2.41279i −0.125605 + 0.217554i
\(124\) −4.92510 −0.442287
\(125\) −8.80581 −0.787615
\(126\) 0 0
\(127\) −0.894023 + 1.54849i −0.0793317 + 0.137406i −0.902962 0.429721i \(-0.858612\pi\)
0.823630 + 0.567127i \(0.191945\pi\)
\(128\) −3.91275 6.77709i −0.345842 0.599015i
\(129\) 1.28558 + 2.22668i 0.113189 + 0.196049i
\(130\) −2.16621 + 1.20034i −0.189989 + 0.105277i
\(131\) −3.19545 + 5.53469i −0.279188 + 0.483568i −0.971183 0.238334i \(-0.923399\pi\)
0.691995 + 0.721902i \(0.256732\pi\)
\(132\) 4.34819 7.53129i 0.378461 0.655514i
\(133\) 0 0
\(134\) −0.181328 0.314069i −0.0156644 0.0271315i
\(135\) 6.87158 11.9019i 0.591412 1.02436i
\(136\) 0.413443 0.716105i 0.0354525 0.0614055i
\(137\) −5.01827 + 8.69190i −0.428740 + 0.742599i −0.996762 0.0804144i \(-0.974376\pi\)
0.568022 + 0.823014i \(0.307709\pi\)
\(138\) −1.21901 + 2.11139i −0.103769 + 0.179733i
\(139\) −2.77278 4.80260i −0.235184 0.407351i 0.724142 0.689651i \(-0.242236\pi\)
−0.959326 + 0.282300i \(0.908903\pi\)
\(140\) 0 0
\(141\) 0.752416 1.30322i 0.0633648 0.109751i
\(142\) 1.65114 2.85985i 0.138560 0.239993i
\(143\) 12.4447 6.89582i 1.04068 0.576658i
\(144\) 3.02619 + 5.24151i 0.252182 + 0.436793i
\(145\) −3.01228 5.21742i −0.250156 0.433283i
\(146\) −0.103039 + 0.178469i −0.00852759 + 0.0147702i
\(147\) 0 0
\(148\) −13.0285 −1.07094
\(149\) 18.4651 1.51272 0.756359 0.654157i \(-0.226976\pi\)
0.756359 + 0.654157i \(0.226976\pi\)
\(150\) 0.239443 0.414727i 0.0195504 0.0338623i
\(151\) −0.803678 1.39201i −0.0654024 0.113280i 0.831470 0.555570i \(-0.187500\pi\)
−0.896872 + 0.442289i \(0.854166\pi\)
\(152\) 7.89421 0.640305
\(153\) −0.664795 + 1.15146i −0.0537455 + 0.0930900i
\(154\) 0 0
\(155\) 6.54366 0.525600
\(156\) 0.139836 7.94485i 0.0111958 0.636097i
\(157\) −0.822967 1.42542i −0.0656799 0.113761i 0.831315 0.555801i \(-0.187588\pi\)
−0.896995 + 0.442040i \(0.854255\pi\)
\(158\) −1.66046 −0.132099
\(159\) −5.30330 9.18558i −0.420579 0.728464i
\(160\) 3.92548 + 6.79913i 0.310337 + 0.537519i
\(161\) 0 0
\(162\) −0.140949 0.244130i −0.0110740 0.0191807i
\(163\) −6.54819 −0.512894 −0.256447 0.966558i \(-0.582552\pi\)
−0.256447 + 0.966558i \(0.582552\pi\)
\(164\) 2.34986 + 4.07007i 0.183493 + 0.317819i
\(165\) −5.77716 + 10.0063i −0.449751 + 0.778992i
\(166\) 0.143838 + 0.249135i 0.0111640 + 0.0193367i
\(167\) 4.77440 8.26950i 0.369454 0.639913i −0.620026 0.784581i \(-0.712878\pi\)
0.989480 + 0.144668i \(0.0462114\pi\)
\(168\) 0 0
\(169\) 6.89216 11.0226i 0.530166 0.847894i
\(170\) −0.269631 + 0.467015i −0.0206798 + 0.0358184i
\(171\) −12.6935 −0.970694
\(172\) 4.33720 0.330709
\(173\) −11.1316 −0.846322 −0.423161 0.906054i \(-0.639080\pi\)
−0.423161 + 0.906054i \(0.639080\pi\)
\(174\) −0.720733 −0.0546386
\(175\) 0 0
\(176\) −7.05115 12.2130i −0.531501 0.920586i
\(177\) −5.12451 + 8.87592i −0.385182 + 0.667155i
\(178\) −1.02732 + 1.77937i −0.0770009 + 0.133369i
\(179\) −12.6435 −0.945017 −0.472508 0.881326i \(-0.656651\pi\)
−0.472508 + 0.881326i \(0.656651\pi\)
\(180\) −4.18246 7.24424i −0.311742 0.539954i
\(181\) −14.9158 −1.10868 −0.554341 0.832289i \(-0.687030\pi\)
−0.554341 + 0.832289i \(0.687030\pi\)
\(182\) 0 0
\(183\) −10.7963 −0.798082
\(184\) 4.18930 + 7.25607i 0.308839 + 0.534925i
\(185\) 17.3102 1.27267
\(186\) 0.391418 0.677956i 0.0287001 0.0497101i
\(187\) 1.54900 2.68295i 0.113274 0.196197i
\(188\) −1.26923 2.19837i −0.0925680 0.160332i
\(189\) 0 0
\(190\) −5.14829 −0.373496
\(191\) −14.1306 −1.02245 −0.511226 0.859447i \(-0.670808\pi\)
−0.511226 + 0.859447i \(0.670808\pi\)
\(192\) −7.23059 −0.521823
\(193\) 3.89454 0.280335 0.140167 0.990128i \(-0.455236\pi\)
0.140167 + 0.990128i \(0.455236\pi\)
\(194\) 0.317999 0.550790i 0.0228310 0.0395444i
\(195\) −0.185791 + 10.5558i −0.0133048 + 0.755917i
\(196\) 0 0
\(197\) 5.85445 10.1402i 0.417112 0.722459i −0.578536 0.815657i \(-0.696376\pi\)
0.995648 + 0.0931979i \(0.0297089\pi\)
\(198\) −0.895897 1.55174i −0.0636686 0.110277i
\(199\) 1.74842 3.02835i 0.123942 0.214674i −0.797377 0.603482i \(-0.793780\pi\)
0.921319 + 0.388808i \(0.127113\pi\)
\(200\) −0.822878 1.42527i −0.0581863 0.100782i
\(201\) −1.54599 −0.109046
\(202\) 0.106892 + 0.185143i 0.00752090 + 0.0130266i
\(203\) 0 0
\(204\) −0.865120 1.49843i −0.0605705 0.104911i
\(205\) −3.12210 5.40764i −0.218057 0.377686i
\(206\) 0.580807 0.0404667
\(207\) −6.73617 11.6674i −0.468196 0.810939i
\(208\) −11.0441 6.63818i −0.765774 0.460275i
\(209\) 29.5764 2.04584
\(210\) 0 0
\(211\) −9.50258 + 16.4589i −0.654184 + 1.13308i 0.327913 + 0.944708i \(0.393655\pi\)
−0.982098 + 0.188373i \(0.939679\pi\)
\(212\) −17.8920 −1.22882
\(213\) −7.03874 12.1915i −0.482286 0.835345i
\(214\) −1.54524 + 2.67643i −0.105630 + 0.182957i
\(215\) −5.76256 −0.393004
\(216\) −5.65029 −0.384453
\(217\) 0 0
\(218\) 1.08299 1.87579i 0.0733492 0.127045i
\(219\) 0.439253 + 0.760808i 0.0296820 + 0.0514106i
\(220\) 9.74533 + 16.8794i 0.657030 + 1.13801i
\(221\) 0.0498153 2.83028i 0.00335094 0.190385i
\(222\) 1.03543 1.79342i 0.0694936 0.120366i
\(223\) −5.98311 + 10.3630i −0.400658 + 0.693961i −0.993805 0.111133i \(-0.964552\pi\)
0.593147 + 0.805094i \(0.297885\pi\)
\(224\) 0 0
\(225\) 1.32315 + 2.29175i 0.0882097 + 0.152784i
\(226\) 1.07804 1.86723i 0.0717104 0.124206i
\(227\) 7.69209 13.3231i 0.510542 0.884284i −0.489384 0.872069i \(-0.662778\pi\)
0.999925 0.0122157i \(-0.00388847\pi\)
\(228\) 8.25921 14.3054i 0.546980 0.947396i
\(229\) 4.33084 7.50123i 0.286190 0.495695i −0.686707 0.726934i \(-0.740945\pi\)
0.972897 + 0.231239i \(0.0742779\pi\)
\(230\) −2.73209 4.73212i −0.180149 0.312027i
\(231\) 0 0
\(232\) −1.23845 + 2.14506i −0.0813082 + 0.140830i
\(233\) −10.1253 + 17.5376i −0.663333 + 1.14893i 0.316402 + 0.948625i \(0.397525\pi\)
−0.979734 + 0.200301i \(0.935808\pi\)
\(234\) −1.40323 0.843426i −0.0917322 0.0551365i
\(235\) 1.68634 + 2.92083i 0.110005 + 0.190534i
\(236\) 8.64440 + 14.9725i 0.562702 + 0.974629i
\(237\) −3.53924 + 6.13014i −0.229898 + 0.398195i
\(238\) 0 0
\(239\) 16.5526 1.07070 0.535350 0.844630i \(-0.320180\pi\)
0.535350 + 0.844630i \(0.320180\pi\)
\(240\) 10.4645 0.675483
\(241\) −8.20038 + 14.2035i −0.528233 + 0.914926i 0.471225 + 0.882013i \(0.343812\pi\)
−0.999458 + 0.0329132i \(0.989522\pi\)
\(242\) 0.612791 + 1.06138i 0.0393917 + 0.0682284i
\(243\) 14.8925 0.955356
\(244\) −9.10595 + 15.7720i −0.582949 + 1.00970i
\(245\) 0 0
\(246\) −0.747011 −0.0476277
\(247\) 23.6381 13.0983i 1.50406 0.833427i
\(248\) −1.34516 2.32989i −0.0854178 0.147948i
\(249\) 1.22636 0.0777172
\(250\) −1.18053 2.04474i −0.0746632 0.129321i
\(251\) −10.2154 17.6935i −0.644788 1.11681i −0.984350 0.176222i \(-0.943612\pi\)
0.339563 0.940583i \(-0.389721\pi\)
\(252\) 0 0
\(253\) 15.6956 + 27.1855i 0.986772 + 1.70914i
\(254\) −0.479420 −0.0300815
\(255\) 1.14943 + 1.99087i 0.0719800 + 0.124673i
\(256\) −5.27682 + 9.13972i −0.329801 + 0.571232i
\(257\) 6.88895 + 11.9320i 0.429721 + 0.744299i 0.996848 0.0793315i \(-0.0252786\pi\)
−0.567127 + 0.823630i \(0.691945\pi\)
\(258\) −0.344695 + 0.597030i −0.0214598 + 0.0371695i
\(259\) 0 0
\(260\) 15.2640 + 9.17456i 0.946633 + 0.568982i
\(261\) 1.99136 3.44914i 0.123262 0.213496i
\(262\) −1.71356 −0.105864
\(263\) 25.9173 1.59813 0.799065 0.601244i \(-0.205328\pi\)
0.799065 + 0.601244i \(0.205328\pi\)
\(264\) 4.75038 0.292366
\(265\) 23.7719 1.46030
\(266\) 0 0
\(267\) 4.37943 + 7.58540i 0.268017 + 0.464219i
\(268\) −1.30394 + 2.25850i −0.0796510 + 0.137960i
\(269\) −15.0333 + 26.0384i −0.916596 + 1.58759i −0.112050 + 0.993703i \(0.535742\pi\)
−0.804547 + 0.593889i \(0.797592\pi\)
\(270\) 3.68489 0.224255
\(271\) 7.22527 + 12.5145i 0.438904 + 0.760204i 0.997605 0.0691651i \(-0.0220335\pi\)
−0.558701 + 0.829369i \(0.688700\pi\)
\(272\) −2.80581 −0.170127
\(273\) 0 0
\(274\) −2.69105 −0.162572
\(275\) −3.08299 5.33989i −0.185911 0.322008i
\(276\) 17.5320 1.05530
\(277\) 7.66274 13.2723i 0.460409 0.797452i −0.538572 0.842580i \(-0.681036\pi\)
0.998981 + 0.0451272i \(0.0143693\pi\)
\(278\) 0.743453 1.28770i 0.0445894 0.0772310i
\(279\) 2.16295 + 3.74634i 0.129492 + 0.224287i
\(280\) 0 0
\(281\) 5.29279 0.315741 0.157871 0.987460i \(-0.449537\pi\)
0.157871 + 0.987460i \(0.449537\pi\)
\(282\) 0.403483 0.0240271
\(283\) 30.7845 1.82995 0.914975 0.403511i \(-0.132210\pi\)
0.914975 + 0.403511i \(0.132210\pi\)
\(284\) −23.7469 −1.40912
\(285\) −10.9735 + 19.0066i −0.650013 + 1.12586i
\(286\) 3.26960 + 1.96522i 0.193335 + 0.116206i
\(287\) 0 0
\(288\) −2.59507 + 4.49479i −0.152916 + 0.264858i
\(289\) 8.19181 + 14.1886i 0.481871 + 0.834625i
\(290\) 0.807667 1.39892i 0.0474279 0.0821474i
\(291\) −1.35562 2.34800i −0.0794677 0.137642i
\(292\) 1.48193 0.0867231
\(293\) −8.75864 15.1704i −0.511685 0.886265i −0.999908 0.0135461i \(-0.995688\pi\)
0.488223 0.872719i \(-0.337645\pi\)
\(294\) 0 0
\(295\) −11.4853 19.8930i −0.668697 1.15822i
\(296\) −3.55840 6.16333i −0.206828 0.358237i
\(297\) −21.1693 −1.22837
\(298\) 2.47548 + 4.28765i 0.143400 + 0.248377i
\(299\) 24.5838 + 14.7763i 1.42172 + 0.854536i
\(300\) −3.44370 −0.198822
\(301\) 0 0
\(302\) 0.215486 0.373233i 0.0123998 0.0214772i
\(303\) 0.911355 0.0523560
\(304\) −13.3934 23.1980i −0.768163 1.33050i
\(305\) 12.0985 20.9552i 0.692757 1.19989i
\(306\) −0.356497 −0.0203796
\(307\) 8.63573 0.492867 0.246434 0.969160i \(-0.420741\pi\)
0.246434 + 0.969160i \(0.420741\pi\)
\(308\) 0 0
\(309\) 1.23798 2.14425i 0.0704262 0.121982i
\(310\) 0.877260 + 1.51946i 0.0498250 + 0.0862995i
\(311\) −8.21130 14.2224i −0.465620 0.806478i 0.533609 0.845731i \(-0.320835\pi\)
−0.999229 + 0.0392535i \(0.987502\pi\)
\(312\) 3.79662 2.10378i 0.214941 0.119103i
\(313\) 5.02308 8.70024i 0.283921 0.491766i −0.688426 0.725307i \(-0.741698\pi\)
0.972347 + 0.233541i \(0.0750312\pi\)
\(314\) 0.220658 0.382191i 0.0124525 0.0215683i
\(315\) 0 0
\(316\) 5.97024 + 10.3408i 0.335852 + 0.581713i
\(317\) −5.07249 + 8.78581i −0.284899 + 0.493460i −0.972585 0.232549i \(-0.925294\pi\)
0.687685 + 0.726009i \(0.258627\pi\)
\(318\) 1.42195 2.46289i 0.0797389 0.138112i
\(319\) −4.63996 + 8.03665i −0.259788 + 0.449966i
\(320\) 8.10273 14.0343i 0.452957 0.784544i
\(321\) 6.58729 + 11.4095i 0.367667 + 0.636817i
\(322\) 0 0
\(323\) 2.94227 5.09616i 0.163712 0.283558i
\(324\) −1.01357 + 1.75556i −0.0563095 + 0.0975310i
\(325\) −4.82885 2.90242i −0.267856 0.160998i
\(326\) −0.877867 1.52051i −0.0486206 0.0842133i
\(327\) −4.61674 7.99644i −0.255307 0.442204i
\(328\) −1.28360 + 2.22327i −0.0708751 + 0.122759i
\(329\) 0 0
\(330\) −3.09801 −0.170540
\(331\) 2.31916 0.127473 0.0637363 0.997967i \(-0.479698\pi\)
0.0637363 + 0.997967i \(0.479698\pi\)
\(332\) 1.03435 1.79155i 0.0567675 0.0983242i
\(333\) 5.72172 + 9.91032i 0.313549 + 0.543082i
\(334\) 2.56027 0.140092
\(335\) 1.73247 3.00072i 0.0946547 0.163947i
\(336\) 0 0
\(337\) −15.9998 −0.871565 −0.435783 0.900052i \(-0.643528\pi\)
−0.435783 + 0.900052i \(0.643528\pi\)
\(338\) 3.48347 + 0.122662i 0.189476 + 0.00667193i
\(339\) −4.59567 7.95993i −0.249602 0.432324i
\(340\) 3.87788 0.210307
\(341\) −5.03977 8.72913i −0.272919 0.472709i
\(342\) −1.70172 2.94747i −0.0920185 0.159381i
\(343\) 0 0
\(344\) 1.18459 + 2.05178i 0.0638690 + 0.110624i
\(345\) −23.2936 −1.25409
\(346\) −1.49234 2.58480i −0.0802285 0.138960i
\(347\) 11.4104 19.7634i 0.612543 1.06096i −0.378267 0.925696i \(-0.623480\pi\)
0.990810 0.135259i \(-0.0431867\pi\)
\(348\) 2.59142 + 4.48848i 0.138915 + 0.240608i
\(349\) −11.3511 + 19.6607i −0.607612 + 1.05241i 0.384021 + 0.923324i \(0.374539\pi\)
−0.991633 + 0.129090i \(0.958794\pi\)
\(350\) 0 0
\(351\) −16.9190 + 9.37515i −0.903071 + 0.500408i
\(352\) 6.04662 10.4731i 0.322286 0.558216i
\(353\) 27.2644 1.45114 0.725568 0.688150i \(-0.241577\pi\)
0.725568 + 0.688150i \(0.241577\pi\)
\(354\) −2.74802 −0.146056
\(355\) 31.5510 1.67455
\(356\) 14.7751 0.783077
\(357\) 0 0
\(358\) −1.69502 2.93585i −0.0895844 0.155165i
\(359\) 7.21309 12.4934i 0.380692 0.659378i −0.610469 0.792040i \(-0.709019\pi\)
0.991161 + 0.132662i \(0.0423524\pi\)
\(360\) 2.28466 3.95715i 0.120412 0.208560i
\(361\) 37.1791 1.95679
\(362\) −1.99965 3.46350i −0.105099 0.182037i
\(363\) 5.22461 0.274221
\(364\) 0 0
\(365\) −1.96894 −0.103059
\(366\) −1.44737 2.50693i −0.0756555 0.131039i
\(367\) 11.3917 0.594643 0.297322 0.954777i \(-0.403907\pi\)
0.297322 + 0.954777i \(0.403907\pi\)
\(368\) 14.2152 24.6214i 0.741018 1.28348i
\(369\) 2.06397 3.57489i 0.107446 0.186102i
\(370\) 2.32065 + 4.01948i 0.120645 + 0.208963i
\(371\) 0 0
\(372\) −5.62943 −0.291872
\(373\) −30.9629 −1.60320 −0.801599 0.597862i \(-0.796017\pi\)
−0.801599 + 0.597862i \(0.796017\pi\)
\(374\) 0.830653 0.0429521
\(375\) −10.0651 −0.519760
\(376\) 0.693313 1.20085i 0.0357549 0.0619293i
\(377\) −0.149219 + 8.47796i −0.00768518 + 0.436637i
\(378\) 0 0
\(379\) −5.29330 + 9.16826i −0.271898 + 0.470942i −0.969348 0.245692i \(-0.920985\pi\)
0.697450 + 0.716634i \(0.254318\pi\)
\(380\) 18.5109 + 32.0617i 0.949587 + 1.64473i
\(381\) −1.02188 + 1.76994i −0.0523523 + 0.0906768i
\(382\) −1.89438 3.28116i −0.0969249 0.167879i
\(383\) −30.7517 −1.57134 −0.785668 0.618648i \(-0.787681\pi\)
−0.785668 + 0.618648i \(0.787681\pi\)
\(384\) −4.47231 7.74627i −0.228227 0.395300i
\(385\) 0 0
\(386\) 0.522112 + 0.904324i 0.0265748 + 0.0460289i
\(387\) −1.90476 3.29915i −0.0968246 0.167705i
\(388\) −4.57351 −0.232185
\(389\) 8.18978 + 14.1851i 0.415239 + 0.719214i 0.995453 0.0952492i \(-0.0303648\pi\)
−0.580215 + 0.814463i \(0.697031\pi\)
\(390\) −2.47600 + 1.37200i −0.125377 + 0.0694738i
\(391\) 6.24561 0.315854
\(392\) 0 0
\(393\) −3.65243 + 6.32620i −0.184241 + 0.319114i
\(394\) 3.13945 0.158163
\(395\) −7.93227 13.7391i −0.399116 0.691289i
\(396\) −6.44246 + 11.1587i −0.323746 + 0.560744i
\(397\) 15.8827 0.797127 0.398564 0.917141i \(-0.369509\pi\)
0.398564 + 0.917141i \(0.369509\pi\)
\(398\) 0.937591 0.0469972
\(399\) 0 0
\(400\) −2.79221 + 4.83624i −0.139610 + 0.241812i
\(401\) −3.31787 5.74671i −0.165686 0.286977i 0.771212 0.636578i \(-0.219651\pi\)
−0.936899 + 0.349601i \(0.886317\pi\)
\(402\) −0.207259 0.358984i −0.0103372 0.0179045i
\(403\) −7.89373 4.74460i −0.393215 0.236345i
\(404\) 0.768670 1.33137i 0.0382427 0.0662384i
\(405\) 1.34667 2.33250i 0.0669164 0.115903i
\(406\) 0 0
\(407\) −13.3319 23.0915i −0.660836 1.14460i
\(408\) 0.472570 0.818515i 0.0233957 0.0405225i
\(409\) 2.93617 5.08560i 0.145184 0.251467i −0.784257 0.620436i \(-0.786956\pi\)
0.929442 + 0.368969i \(0.120289\pi\)
\(410\) 0.837115 1.44992i 0.0413421 0.0716067i
\(411\) −5.73593 + 9.93492i −0.282933 + 0.490053i
\(412\) −2.08831 3.61707i −0.102884 0.178200i
\(413\) 0 0
\(414\) 1.80614 3.12832i 0.0887667 0.153749i
\(415\) −1.37428 + 2.38032i −0.0674607 + 0.116845i
\(416\) 0.194457 11.0482i 0.00953403 0.541680i
\(417\) −3.16932 5.48942i −0.155202 0.268818i
\(418\) 3.96508 + 6.86773i 0.193939 + 0.335911i
\(419\) −15.0712 + 26.1040i −0.736274 + 1.27526i 0.217888 + 0.975974i \(0.430083\pi\)
−0.954162 + 0.299290i \(0.903250\pi\)
\(420\) 0 0
\(421\) 40.0580 1.95231 0.976153 0.217083i \(-0.0696543\pi\)
0.976153 + 0.217083i \(0.0696543\pi\)
\(422\) −5.09576 −0.248058
\(423\) −1.11481 + 1.93091i −0.0542040 + 0.0938840i
\(424\) −4.88672 8.46405i −0.237320 0.411051i
\(425\) −1.22679 −0.0595079
\(426\) 1.88726 3.26884i 0.0914382 0.158376i
\(427\) 0 0
\(428\) 22.2238 1.07423
\(429\) 14.2244 7.88199i 0.686759 0.380546i
\(430\) −0.772544 1.33809i −0.0372554 0.0645282i
\(431\) −3.91587 −0.188621 −0.0943104 0.995543i \(-0.530065\pi\)
−0.0943104 + 0.995543i \(0.530065\pi\)
\(432\) 9.58632 + 16.6040i 0.461222 + 0.798860i
\(433\) −20.3963 35.3274i −0.980182 1.69772i −0.661650 0.749813i \(-0.730144\pi\)
−0.318532 0.947912i \(-0.603190\pi\)
\(434\) 0 0
\(435\) −3.44306 5.96355i −0.165082 0.285930i
\(436\) −15.5757 −0.745941
\(437\) 29.8131 + 51.6378i 1.42615 + 2.47017i
\(438\) −0.117775 + 0.203992i −0.00562750 + 0.00974711i
\(439\) −12.7811 22.1376i −0.610010 1.05657i −0.991238 0.132087i \(-0.957832\pi\)
0.381228 0.924481i \(-0.375501\pi\)
\(440\) −5.32336 + 9.22033i −0.253781 + 0.439562i
\(441\) 0 0
\(442\) 0.663878 0.367867i 0.0315775 0.0174977i
\(443\) 13.7282 23.7779i 0.652247 1.12972i −0.330330 0.943866i \(-0.607160\pi\)
0.982576 0.185859i \(-0.0595067\pi\)
\(444\) −14.8917 −0.706730
\(445\) −19.6307 −0.930584
\(446\) −3.20844 −0.151924
\(447\) 21.1057 0.998267
\(448\) 0 0
\(449\) 7.40181 + 12.8203i 0.349313 + 0.605028i 0.986128 0.165989i \(-0.0530816\pi\)
−0.636815 + 0.771017i \(0.719748\pi\)
\(450\) −0.354769 + 0.614477i −0.0167240 + 0.0289667i
\(451\) −4.80913 + 8.32966i −0.226453 + 0.392229i
\(452\) −15.5046 −0.729275
\(453\) −0.918611 1.59108i −0.0431601 0.0747555i
\(454\) 4.12489 0.193590
\(455\) 0 0
\(456\) 9.02315 0.422548
\(457\) 0.325975 + 0.564606i 0.0152485 + 0.0264112i 0.873549 0.486736i \(-0.161813\pi\)
−0.858300 + 0.513147i \(0.828479\pi\)
\(458\) 2.32241 0.108519
\(459\) −2.10593 + 3.64758i −0.0982965 + 0.170254i
\(460\) −19.6467 + 34.0290i −0.916031 + 1.58661i
\(461\) 6.24774 + 10.8214i 0.290986 + 0.504003i 0.974043 0.226362i \(-0.0726833\pi\)
−0.683057 + 0.730365i \(0.739350\pi\)
\(462\) 0 0
\(463\) −0.309503 −0.0143838 −0.00719190 0.999974i \(-0.502289\pi\)
−0.00719190 + 0.999974i \(0.502289\pi\)
\(464\) 8.40466 0.390176
\(465\) 7.47946 0.346852
\(466\) −5.42972 −0.251527
\(467\) 12.2387 21.1980i 0.566338 0.980926i −0.430586 0.902549i \(-0.641693\pi\)
0.996924 0.0783762i \(-0.0249735\pi\)
\(468\) −0.207187 + 11.7714i −0.00957722 + 0.544134i
\(469\) 0 0
\(470\) −0.452151 + 0.783149i −0.0208562 + 0.0361240i
\(471\) −0.940659 1.62927i −0.0433433 0.0750727i
\(472\) −4.72198 + 8.17871i −0.217347 + 0.376456i
\(473\) 4.43818 + 7.68716i 0.204068 + 0.353456i
\(474\) −1.89792 −0.0871742
\(475\) −5.85601 10.1429i −0.268692 0.465389i
\(476\) 0 0
\(477\) 7.85759 + 13.6097i 0.359774 + 0.623147i
\(478\) 2.21909 + 3.84357i 0.101499 + 0.175801i
\(479\) −8.13850 −0.371858 −0.185929 0.982563i \(-0.559529\pi\)
−0.185929 + 0.982563i \(0.559529\pi\)
\(480\) 4.48686 + 7.77147i 0.204796 + 0.354718i
\(481\) −20.8816 12.5511i −0.952118 0.572279i
\(482\) −4.39746 −0.200299
\(483\) 0 0
\(484\) 4.40662 7.63250i 0.200301 0.346932i
\(485\) 6.07653 0.275921
\(486\) 1.99653 + 3.45809i 0.0905645 + 0.156862i
\(487\) −2.30480 + 3.99203i −0.104440 + 0.180896i −0.913509 0.406817i \(-0.866638\pi\)
0.809069 + 0.587714i \(0.199972\pi\)
\(488\) −9.94821 −0.450334
\(489\) −7.48464 −0.338467
\(490\) 0 0
\(491\) −6.50947 + 11.2747i −0.293768 + 0.508822i −0.974698 0.223527i \(-0.928243\pi\)
0.680929 + 0.732349i \(0.261576\pi\)
\(492\) 2.68591 + 4.65213i 0.121090 + 0.209734i
\(493\) 0.923171 + 1.59898i 0.0415775 + 0.0720144i
\(494\) 6.21047 + 3.73286i 0.279422 + 0.167949i
\(495\) 8.55969 14.8258i 0.384729 0.666371i
\(496\) −4.56443 + 7.90582i −0.204949 + 0.354982i
\(497\) 0 0
\(498\) 0.164409 + 0.284764i 0.00736733 + 0.0127606i
\(499\) 16.1603 27.9905i 0.723436 1.25303i −0.236178 0.971710i \(-0.575895\pi\)
0.959614 0.281319i \(-0.0907717\pi\)
\(500\) −8.48928 + 14.7039i −0.379652 + 0.657577i
\(501\) 5.45718 9.45211i 0.243809 0.422289i
\(502\) 2.73900 4.74408i 0.122247 0.211739i
\(503\) −15.9126 27.5615i −0.709509 1.22891i −0.965039 0.262105i \(-0.915583\pi\)
0.255531 0.966801i \(-0.417750\pi\)
\(504\) 0 0
\(505\) −1.02128 + 1.76891i −0.0454465 + 0.0787156i
\(506\) −4.20838 + 7.28912i −0.187085 + 0.324041i
\(507\) 7.87780 12.5990i 0.349866 0.559539i
\(508\) 1.72377 + 2.98566i 0.0764801 + 0.132467i
\(509\) 1.12788 + 1.95354i 0.0499922 + 0.0865891i 0.889939 0.456080i \(-0.150747\pi\)
−0.839946 + 0.542669i \(0.817414\pi\)
\(510\) −0.308191 + 0.533802i −0.0136469 + 0.0236372i
\(511\) 0 0
\(512\) −18.4807 −0.816739
\(513\) −40.2102 −1.77533
\(514\) −1.84710 + 3.19927i −0.0814722 + 0.141114i
\(515\) 2.77461 + 4.80576i 0.122264 + 0.211767i
\(516\) 4.95746 0.218240
\(517\) 2.59756 4.49911i 0.114241 0.197870i
\(518\) 0 0
\(519\) −12.7236 −0.558502
\(520\) −0.171197 + 9.72665i −0.00750749 + 0.426542i
\(521\) 5.38562 + 9.32817i 0.235948 + 0.408675i 0.959548 0.281546i \(-0.0908471\pi\)
−0.723600 + 0.690220i \(0.757514\pi\)
\(522\) 1.06787 0.0467393
\(523\) 3.70397 + 6.41546i 0.161963 + 0.280528i 0.935573 0.353134i \(-0.114884\pi\)
−0.773610 + 0.633663i \(0.781551\pi\)
\(524\) 6.16118 + 10.6715i 0.269152 + 0.466186i
\(525\) 0 0
\(526\) 3.47454 + 6.01809i 0.151497 + 0.262401i
\(527\) −2.00543 −0.0873580
\(528\) −8.05953 13.9595i −0.350746 0.607510i
\(529\) −20.1424 + 34.8877i −0.875757 + 1.51686i
\(530\) 3.18692 + 5.51991i 0.138431 + 0.239770i
\(531\) 7.59270 13.1509i 0.329495 0.570702i
\(532\) 0 0
\(533\) −0.154660 + 8.78707i −0.00669906 + 0.380610i
\(534\) −1.17424 + 2.03384i −0.0508142 + 0.0880127i
\(535\) −29.5274 −1.27658
\(536\) −1.42455 −0.0615313
\(537\) −14.4516 −0.623632
\(538\) −8.06161 −0.347561
\(539\) 0 0
\(540\) −13.2492 22.9482i −0.570153 0.987534i
\(541\) −16.2741 + 28.1875i −0.699676 + 1.21188i 0.268902 + 0.963168i \(0.413339\pi\)
−0.968579 + 0.248708i \(0.919994\pi\)
\(542\) −1.93728 + 3.35546i −0.0832132 + 0.144129i
\(543\) −17.0489 −0.731638
\(544\) −1.20304 2.08373i −0.0515799 0.0893391i
\(545\) 20.6944 0.886453
\(546\) 0 0
\(547\) −13.4997 −0.577206 −0.288603 0.957449i \(-0.593191\pi\)
−0.288603 + 0.957449i \(0.593191\pi\)
\(548\) 9.67577 + 16.7589i 0.413329 + 0.715906i
\(549\) 15.9962 0.682701
\(550\) 0.826627 1.43176i 0.0352475 0.0610504i
\(551\) −8.81342 + 15.2653i −0.375464 + 0.650323i
\(552\) 4.78840 + 8.29376i 0.203808 + 0.353006i
\(553\) 0 0
\(554\) 4.10915 0.174581
\(555\) 19.7857 0.839856
\(556\) −10.6925 −0.453461
\(557\) −29.7703 −1.26141 −0.630703 0.776024i \(-0.717233\pi\)
−0.630703 + 0.776024i \(0.717233\pi\)
\(558\) −0.579941 + 1.00449i −0.0245509 + 0.0425233i
\(559\) 6.95148 + 4.17825i 0.294016 + 0.176721i
\(560\) 0 0
\(561\) 1.77052 3.06664i 0.0747516 0.129474i
\(562\) 0.709566 + 1.22900i 0.0299312 + 0.0518424i
\(563\) 7.06629 12.2392i 0.297809 0.515819i −0.677826 0.735223i \(-0.737078\pi\)
0.975634 + 0.219403i \(0.0704110\pi\)
\(564\) −1.45074 2.51275i −0.0610872 0.105806i
\(565\) 20.6000 0.866647
\(566\) 4.12705 + 7.14826i 0.173473 + 0.300464i
\(567\) 0 0
\(568\) −6.48584 11.2338i −0.272140 0.471360i
\(569\) 12.1270 + 21.0046i 0.508391 + 0.880558i 0.999953 + 0.00971585i \(0.00309270\pi\)
−0.491562 + 0.870842i \(0.663574\pi\)
\(570\) −5.88454 −0.246476
\(571\) −0.604159 1.04643i −0.0252832 0.0437919i 0.853107 0.521736i \(-0.174715\pi\)
−0.878390 + 0.477944i \(0.841382\pi\)
\(572\) 0.482755 27.4279i 0.0201850 1.14682i
\(573\) −16.1514 −0.674732
\(574\) 0 0
\(575\) 6.21533 10.7653i 0.259197 0.448943i
\(576\) 10.7131 0.446381
\(577\) −7.30518 12.6529i −0.304119 0.526749i 0.672946 0.739692i \(-0.265029\pi\)
−0.977065 + 0.212943i \(0.931695\pi\)
\(578\) −2.19643 + 3.80433i −0.0913595 + 0.158239i
\(579\) 4.45149 0.184998
\(580\) −11.6160 −0.482328
\(581\) 0 0
\(582\) 0.363475 0.629558i 0.0150665 0.0260960i
\(583\) −18.3085 31.7113i −0.758262 1.31335i
\(584\) 0.404749 + 0.701046i 0.0167486 + 0.0290095i
\(585\) 0.275276 15.6399i 0.0113813 0.646632i
\(586\) 2.34841 4.06757i 0.0970120 0.168030i
\(587\) 10.7548 18.6278i 0.443897 0.768852i −0.554078 0.832465i \(-0.686929\pi\)
0.997975 + 0.0636132i \(0.0202624\pi\)
\(588\) 0 0
\(589\) −9.57284 16.5806i −0.394442 0.683193i
\(590\) 3.07949 5.33383i 0.126780 0.219590i
\(591\) 6.69168 11.5903i 0.275259 0.476763i
\(592\) −12.0744 + 20.9135i −0.496256 + 0.859541i
\(593\) −1.32429 + 2.29373i −0.0543820 + 0.0941923i −0.891935 0.452164i \(-0.850652\pi\)
0.837553 + 0.546356i \(0.183986\pi\)
\(594\) −2.83801 4.91558i −0.116445 0.201689i
\(595\) 0 0
\(596\) 17.8013 30.8328i 0.729171 1.26296i
\(597\) 1.99846 3.46143i 0.0817915 0.141667i
\(598\) −0.135340 + 7.68939i −0.00553445 + 0.314443i
\(599\) 20.1250 + 34.8576i 0.822287 + 1.42424i 0.903975 + 0.427584i \(0.140635\pi\)
−0.0816889 + 0.996658i \(0.526031\pi\)
\(600\) −0.940558 1.62909i −0.0383981 0.0665075i
\(601\) 19.1725 33.2077i 0.782061 1.35457i −0.148679 0.988886i \(-0.547502\pi\)
0.930739 0.365683i \(-0.119165\pi\)
\(602\) 0 0
\(603\) 2.29060 0.0932806
\(604\) −3.09916 −0.126103
\(605\) −5.85480 + 10.1408i −0.238031 + 0.412283i
\(606\) 0.122179 + 0.211620i 0.00496317 + 0.00859646i
\(607\) −42.5547 −1.72724 −0.863620 0.504143i \(-0.831808\pi\)
−0.863620 + 0.504143i \(0.831808\pi\)
\(608\) 11.4853 19.8931i 0.465791 0.806773i
\(609\) 0 0
\(610\) 6.48782 0.262684
\(611\) 0.0835364 4.74616i 0.00337952 0.192009i
\(612\) 1.28180 + 2.22014i 0.0518136 + 0.0897438i
\(613\) 15.2652 0.616556 0.308278 0.951296i \(-0.400247\pi\)
0.308278 + 0.951296i \(0.400247\pi\)
\(614\) 1.15773 + 2.00524i 0.0467221 + 0.0809251i
\(615\) −3.56859 6.18098i −0.143899 0.249241i
\(616\) 0 0
\(617\) −6.99061 12.1081i −0.281431 0.487453i 0.690306 0.723517i \(-0.257476\pi\)
−0.971737 + 0.236064i \(0.924142\pi\)
\(618\) 0.663868 0.0267047
\(619\) −4.25792 7.37494i −0.171140 0.296424i 0.767678 0.640835i \(-0.221412\pi\)
−0.938819 + 0.344411i \(0.888079\pi\)
\(620\) 6.30845 10.9265i 0.253353 0.438821i
\(621\) −21.3388 36.9598i −0.856295 1.48315i
\(622\) 2.20166 3.81338i 0.0882784 0.152903i
\(623\) 0 0
\(624\) −12.6236 7.58750i −0.505347 0.303743i
\(625\) 15.1856 26.3023i 0.607425 1.05209i
\(626\) 2.69363 0.107659
\(627\) 33.8060 1.35008
\(628\) −3.17354 −0.126638
\(629\) −5.30504 −0.211526
\(630\) 0 0
\(631\) −18.4146 31.8950i −0.733074 1.26972i −0.955563 0.294786i \(-0.904752\pi\)
0.222490 0.974935i \(-0.428582\pi\)
\(632\) −3.26123 + 5.64861i −0.129725 + 0.224690i
\(633\) −10.8615 + 18.8127i −0.431707 + 0.747739i
\(634\) −2.72013 −0.108030
\(635\) −2.29027 3.96686i −0.0908865 0.157420i
\(636\) −20.4507 −0.810922
\(637\) 0 0
\(638\) −2.48818 −0.0985081
\(639\) 10.4289 + 18.0634i 0.412561 + 0.714576i
\(640\) 20.0470 0.792428
\(641\) −12.9374 + 22.4082i −0.510996 + 0.885070i 0.488923 + 0.872327i \(0.337390\pi\)
−0.999919 + 0.0127435i \(0.995944\pi\)
\(642\) −1.76622 + 3.05918i −0.0697071 + 0.120736i
\(643\) 20.2626 + 35.0958i 0.799078 + 1.38404i 0.920217 + 0.391408i \(0.128012\pi\)
−0.121139 + 0.992636i \(0.538655\pi\)
\(644\) 0 0
\(645\) −6.58666 −0.259350
\(646\) 1.57779 0.0620774
\(647\) −1.78400 −0.0701364 −0.0350682 0.999385i \(-0.511165\pi\)
−0.0350682 + 0.999385i \(0.511165\pi\)
\(648\) −1.10732 −0.0434997
\(649\) −17.6913 + 30.6423i −0.694445 + 1.20281i
\(650\) 0.0265840 1.51038i 0.00104271 0.0592420i
\(651\) 0 0
\(652\) −6.31281 + 10.9341i −0.247229 + 0.428213i
\(653\) −6.20210 10.7424i −0.242707 0.420381i 0.718778 0.695240i \(-0.244702\pi\)
−0.961484 + 0.274860i \(0.911369\pi\)
\(654\) 1.23787 2.14405i 0.0484044 0.0838389i
\(655\) −8.18597 14.1785i −0.319852 0.554000i
\(656\) 8.71109 0.340111
\(657\) −0.650815 1.12725i −0.0253907 0.0439780i
\(658\) 0 0
\(659\) 0.564336 + 0.977458i 0.0219834 + 0.0380764i 0.876808 0.480841i \(-0.159669\pi\)
−0.854824 + 0.518917i \(0.826335\pi\)
\(660\) 11.1390 + 19.2933i 0.433585 + 0.750991i
\(661\) 28.9254 1.12507 0.562534 0.826774i \(-0.309826\pi\)
0.562534 + 0.826774i \(0.309826\pi\)
\(662\) 0.310913 + 0.538517i 0.0120840 + 0.0209301i
\(663\) 0.0569393 3.23503i 0.00221134 0.125638i
\(664\) 1.13003 0.0438535
\(665\) 0 0
\(666\) −1.53414 + 2.65721i −0.0594467 + 0.102965i
\(667\) −18.7084 −0.724393
\(668\) −9.20556 15.9445i −0.356174 0.616911i
\(669\) −6.83874 + 11.8451i −0.264401 + 0.457956i
\(670\) 0.929036 0.0358918
\(671\) −37.2718 −1.43886
\(672\) 0 0
\(673\) 3.54980 6.14843i 0.136835 0.237005i −0.789462 0.613799i \(-0.789640\pi\)
0.926297 + 0.376795i \(0.122974\pi\)
\(674\) −2.14498 3.71521i −0.0826214 0.143104i
\(675\) 4.19145 + 7.25980i 0.161329 + 0.279430i
\(676\) −11.7610 22.1349i −0.452348 0.851341i
\(677\) −25.2010 + 43.6494i −0.968552 + 1.67758i −0.268800 + 0.963196i \(0.586627\pi\)
−0.699752 + 0.714386i \(0.746706\pi\)
\(678\) 1.23221 2.13426i 0.0473229 0.0819657i
\(679\) 0 0
\(680\) 1.05914 + 1.83449i 0.0406162 + 0.0703493i
\(681\) 8.79213 15.2284i 0.336915 0.583554i
\(682\) 1.35129 2.34050i 0.0517435 0.0896224i
\(683\) −13.7641 + 23.8401i −0.526669 + 0.912217i 0.472848 + 0.881144i \(0.343226\pi\)
−0.999517 + 0.0310735i \(0.990107\pi\)
\(684\) −12.2372 + 21.1954i −0.467901 + 0.810428i
\(685\) −12.8556 22.2665i −0.491186 0.850760i
\(686\) 0 0
\(687\) 4.95019 8.57398i 0.188861 0.327118i
\(688\) 4.01958 6.96212i 0.153245 0.265428i
\(689\) −28.6765 17.2362i −1.09249 0.656649i
\(690\) −3.12280 5.40885i −0.118883 0.205912i
\(691\) −12.1669 21.0737i −0.462851 0.801682i 0.536251 0.844059i \(-0.319840\pi\)
−0.999102 + 0.0423772i \(0.986507\pi\)
\(692\) −10.7315 + 18.5875i −0.407950 + 0.706591i
\(693\) 0 0
\(694\) 6.11884 0.232268
\(695\) 14.2064 0.538879
\(696\) −1.41556 + 2.45182i −0.0536566 + 0.0929360i
\(697\) 0.956829 + 1.65728i 0.0362425 + 0.0627738i
\(698\) −6.08704 −0.230398
\(699\) −11.5733 + 20.0456i −0.437744 + 0.758195i
\(700\) 0 0
\(701\) −20.5588 −0.776495 −0.388248 0.921555i \(-0.626919\pi\)
−0.388248 + 0.921555i \(0.626919\pi\)
\(702\) −4.44515 2.67180i −0.167771 0.100840i
\(703\) −25.3234 43.8613i −0.955088 1.65426i
\(704\) −24.9621 −0.940795
\(705\) 1.92751 + 3.33854i 0.0725940 + 0.125737i
\(706\) 3.65513 + 6.33088i 0.137563 + 0.238266i
\(707\) 0 0
\(708\) 9.88062 + 17.1137i 0.371336 + 0.643174i
\(709\) 40.9089 1.53637 0.768183 0.640230i \(-0.221161\pi\)
0.768183 + 0.640230i \(0.221161\pi\)
\(710\) 4.22981 + 7.32624i 0.158742 + 0.274949i
\(711\) 5.24388 9.08267i 0.196661 0.340627i
\(712\) 4.03543 + 6.98956i 0.151234 + 0.261945i
\(713\) 10.1602 17.5980i 0.380503 0.659051i
\(714\) 0 0
\(715\) −0.641405 + 36.4418i −0.0239872 + 1.36284i
\(716\) −12.1890 + 21.1119i −0.455524 + 0.788990i
\(717\) 18.9198 0.706572
\(718\) 3.86802 0.144353
\(719\) 1.19947 0.0447326 0.0223663 0.999750i \(-0.492880\pi\)
0.0223663 + 0.999750i \(0.492880\pi\)
\(720\) −15.5047 −0.577826
\(721\) 0 0
\(722\) 4.98433 + 8.63311i 0.185497 + 0.321291i
\(723\) −9.37311 + 16.2347i −0.348590 + 0.603775i
\(724\) −14.3796 + 24.9063i −0.534415 + 0.925634i
\(725\) 3.67478 0.136478
\(726\) 0.700425 + 1.21317i 0.0259952 + 0.0450250i
\(727\) 2.06230 0.0764865 0.0382433 0.999268i \(-0.487824\pi\)
0.0382433 + 0.999268i \(0.487824\pi\)
\(728\) 0 0
\(729\) 20.1764 0.747273
\(730\) −0.263961 0.457194i −0.00976964 0.0169215i
\(731\) 1.76605 0.0653197
\(732\) −10.4082 + 18.0275i −0.384697 + 0.666315i
\(733\) 15.0310 26.0345i 0.555184 0.961606i −0.442706 0.896667i \(-0.645981\pi\)
0.997889 0.0649392i \(-0.0206853\pi\)
\(734\) 1.52720 + 2.64520i 0.0563702 + 0.0976360i
\(735\) 0 0
\(736\) 24.3801 0.898662
\(737\) −5.33721 −0.196599
\(738\) 1.10680 0.0407420
\(739\) 44.2548 1.62794 0.813969 0.580908i \(-0.197303\pi\)
0.813969 + 0.580908i \(0.197303\pi\)
\(740\) 16.6880 28.9044i 0.613461 1.06255i
\(741\) 27.0186 14.9715i 0.992553 0.549992i
\(742\) 0 0
\(743\) 4.31326 7.47078i 0.158238 0.274076i −0.775995 0.630739i \(-0.782752\pi\)
0.934233 + 0.356662i \(0.116085\pi\)
\(744\) −1.53753 2.66308i −0.0563686 0.0976334i
\(745\) −23.6515 + 40.9656i −0.866524 + 1.50086i
\(746\) −4.15097 7.18969i −0.151978 0.263233i
\(747\) −1.81702 −0.0664814
\(748\) −2.98665 5.17302i −0.109203 0.189144i
\(749\) 0 0
\(750\) −1.34936 2.33715i −0.0492715 0.0853408i
\(751\) −2.86105 4.95549i −0.104401 0.180828i 0.809092 0.587682i \(-0.199959\pi\)
−0.913493 + 0.406853i \(0.866626\pi\)
\(752\) −4.70512 −0.171578
\(753\) −11.6763 20.2239i −0.425506 0.736998i
\(754\) −1.98862 + 1.10193i −0.0724211 + 0.0401299i
\(755\) 4.11765 0.149857
\(756\) 0 0
\(757\) 17.3611 30.0703i 0.631000 1.09292i −0.356347 0.934354i \(-0.615978\pi\)
0.987348 0.158571i \(-0.0506887\pi\)
\(758\) −2.83853 −0.103100
\(759\) 17.9402 + 31.0733i 0.651187 + 1.12789i
\(760\) −10.1115 + 17.5137i −0.366783 + 0.635287i
\(761\) 53.1735 1.92754 0.963768 0.266741i \(-0.0859467\pi\)
0.963768 + 0.266741i \(0.0859467\pi\)
\(762\) −0.547981 −0.0198513
\(763\) 0 0
\(764\) −13.6226 + 23.5951i −0.492849 + 0.853640i
\(765\) −1.70304 2.94976i −0.0615736 0.106649i
\(766\) −4.12265 7.14063i −0.148957 0.258002i
\(767\) −0.568946 + 32.3249i −0.0205434 + 1.16719i
\(768\) −6.03145 + 10.4468i −0.217641 + 0.376966i
\(769\) 2.45578 4.25354i 0.0885578 0.153387i −0.818344 0.574729i \(-0.805108\pi\)
0.906902 + 0.421342i \(0.138441\pi\)
\(770\) 0 0
\(771\) 7.87414 + 13.6384i 0.283580 + 0.491175i
\(772\) 3.75455 6.50306i 0.135129 0.234050i
\(773\) −11.4903 + 19.9018i −0.413279 + 0.715819i −0.995246 0.0973926i \(-0.968950\pi\)
0.581967 + 0.813212i \(0.302283\pi\)
\(774\) 0.510715 0.884585i 0.0183573 0.0317957i
\(775\) −1.99571 + 3.45667i −0.0716881 + 0.124167i
\(776\) −1.24913 2.16356i −0.0448413 0.0776674i
\(777\) 0 0
\(778\) −2.19589 + 3.80339i −0.0787264 + 0.136358i
\(779\) −9.13476 + 15.8219i −0.327287 + 0.566877i
\(780\) 17.4469 + 10.4866i 0.624699 + 0.375481i
\(781\) −24.2998 42.0885i −0.869515 1.50604i
\(782\) 0.837302 + 1.45025i 0.0299419 + 0.0518608i
\(783\) 6.30821 10.9261i 0.225437 0.390469i
\(784\) 0 0
\(785\) 4.21648 0.150493
\(786\) −1.95862 −0.0698616
\(787\) −1.59387 + 2.76067i −0.0568154 + 0.0984071i −0.893034 0.449989i \(-0.851428\pi\)
0.836219 + 0.548396i \(0.184761\pi\)
\(788\) −11.2880 19.5514i −0.402119 0.696490i
\(789\) 29.6237 1.05463
\(790\) 2.12684 3.68380i 0.0756696 0.131064i
\(791\) 0 0
\(792\) −7.03836 −0.250097
\(793\) −29.7886 + 16.5064i −1.05782 + 0.586159i
\(794\) 2.12927 + 3.68800i 0.0755650 + 0.130882i
\(795\) 27.1715 0.963674
\(796\) −3.37114 5.83899i −0.119487 0.206958i
\(797\) 27.3255 + 47.3291i 0.967918 + 1.67648i 0.701562 + 0.712608i \(0.252486\pi\)
0.266355 + 0.963875i \(0.414180\pi\)
\(798\) 0 0
\(799\) −0.516813 0.895146i −0.0182835 0.0316680i
\(800\) −4.78884 −0.169311
\(801\) −6.48875 11.2388i −0.229269 0.397105i
\(802\) 0.889604 1.54084i 0.0314130 0.0544089i
\(803\) 1.51643 + 2.62653i 0.0535136 + 0.0926883i
\(804\) −1.49042 + 2.58148i −0.0525630 + 0.0910418i
\(805\) 0 0
\(806\) 0.0434569 2.46902i 0.00153070 0.0869677i
\(807\) −17.1832 + 29.7622i −0.604877 + 1.04768i
\(808\) 0.839768 0.0295429
\(809\) −20.2995 −0.713694 −0.356847 0.934163i \(-0.616148\pi\)
−0.356847 + 0.934163i \(0.616148\pi\)
\(810\) 0.722151 0.0253738
\(811\) −2.43587 −0.0855350 −0.0427675 0.999085i \(-0.513617\pi\)
−0.0427675 + 0.999085i \(0.513617\pi\)
\(812\) 0 0
\(813\) 8.25855 + 14.3042i 0.289640 + 0.501671i
\(814\) 3.57461 6.19141i 0.125290 0.217009i
\(815\) 8.38742 14.5274i 0.293799 0.508874i
\(816\) −3.20706 −0.112270
\(817\) 8.43015 + 14.6015i 0.294934 + 0.510840i
\(818\) 1.57452 0.0550519
\(819\) 0 0
\(820\) −12.0395 −0.420438
\(821\) −22.6762 39.2763i −0.791405 1.37075i −0.925097 0.379731i \(-0.876017\pi\)
0.133692 0.991023i \(-0.457317\pi\)
\(822\) −3.07589 −0.107284
\(823\) 1.37871 2.38800i 0.0480588 0.0832403i −0.840995 0.541042i \(-0.818030\pi\)
0.889054 + 0.457802i \(0.151363\pi\)
\(824\) 1.14074 1.97581i 0.0397394 0.0688307i
\(825\) −3.52388 6.10354i −0.122686 0.212498i
\(826\) 0 0
\(827\) −8.64504 −0.300618 −0.150309 0.988639i \(-0.548027\pi\)
−0.150309 + 0.988639i \(0.548027\pi\)
\(828\) −25.9761 −0.902733
\(829\) 29.5741 1.02715 0.513576 0.858044i \(-0.328320\pi\)
0.513576 + 0.858044i \(0.328320\pi\)
\(830\) −0.736958 −0.0255802
\(831\) 8.75858 15.1703i 0.303832 0.526252i
\(832\) −19.9503 + 11.0548i −0.691653 + 0.383258i
\(833\) 0 0
\(834\) 0.849774 1.47185i 0.0294253 0.0509660i
\(835\) 12.2308 + 21.1844i 0.423266 + 0.733117i
\(836\) 28.5132 49.3863i 0.986150 1.70806i
\(837\) 6.85177 + 11.8676i 0.236832 + 0.410204i
\(838\) −8.08191 −0.279185
\(839\) 12.6236 + 21.8648i 0.435817 + 0.754857i 0.997362 0.0725895i \(-0.0231263\pi\)
−0.561545 + 0.827446i \(0.689793\pi\)
\(840\) 0 0
\(841\) 11.7347 + 20.3251i 0.404644 + 0.700865i
\(842\) 5.37028 + 9.30159i 0.185072 + 0.320554i
\(843\) 6.04971 0.208363
\(844\) 18.3220 + 31.7346i 0.630669 + 1.09235i
\(845\) 15.6262 + 29.4092i 0.537556 + 1.01171i
\(846\) −0.597818 −0.0205534
\(847\) 0 0
\(848\) −16.5817 + 28.7204i −0.569418 + 0.986261i
\(849\) 35.1870 1.20761
\(850\) −0.164466 0.284864i −0.00564115 0.00977076i
\(851\) 26.8772 46.5526i 0.921338 1.59580i
\(852\) −27.1429 −0.929901
\(853\) 35.1368 1.20306 0.601531 0.798850i \(-0.294558\pi\)
0.601531 + 0.798850i \(0.294558\pi\)
\(854\) 0 0
\(855\) 16.2588 28.1610i 0.556039 0.963087i
\(856\) 6.06986 + 10.5133i 0.207463 + 0.359337i
\(857\) −0.671345 1.16280i −0.0229327 0.0397206i 0.854331 0.519729i \(-0.173967\pi\)
−0.877264 + 0.480008i \(0.840634\pi\)
\(858\) 3.73718 + 2.24626i 0.127585 + 0.0766862i
\(859\) 2.38386 4.12897i 0.0813363 0.140879i −0.822488 0.568783i \(-0.807415\pi\)
0.903824 + 0.427904i \(0.140748\pi\)
\(860\) −5.55542 + 9.62228i −0.189438 + 0.328117i
\(861\) 0 0
\(862\) −0.524972 0.909278i −0.0178806 0.0309701i
\(863\) 13.3052 23.0453i 0.452915 0.784472i −0.545650 0.838013i \(-0.683717\pi\)
0.998566 + 0.0535407i \(0.0170507\pi\)
\(864\) −8.22062 + 14.2385i −0.279671 + 0.484405i
\(865\) 14.2583 24.6960i 0.484795 0.839690i
\(866\) 5.46875 9.47216i 0.185836 0.321877i
\(867\) 9.36331 + 16.2177i 0.317995 + 0.550783i
\(868\) 0 0
\(869\) −12.2185 + 21.1630i −0.414484 + 0.717907i
\(870\) 0.923171 1.59898i 0.0312984 0.0542105i
\(871\) −4.26563 + 2.36366i −0.144535 + 0.0800897i
\(872\) −4.25410 7.36831i −0.144062 0.249523i
\(873\) 2.00854 + 3.47890i 0.0679788 + 0.117743i
\(874\) −7.99364 + 13.8454i −0.270389 + 0.468328i
\(875\) 0 0
\(876\) 1.69385 0.0572300
\(877\) 8.03696 0.271389 0.135695 0.990751i \(-0.456673\pi\)
0.135695 + 0.990751i \(0.456673\pi\)
\(878\) 3.42694 5.93564i 0.115654 0.200318i
\(879\) −10.0112 17.3399i −0.337670 0.584861i
\(880\) 36.1266 1.21783
\(881\) −27.3349 + 47.3454i −0.920935 + 1.59511i −0.122964 + 0.992411i \(0.539240\pi\)
−0.797971 + 0.602695i \(0.794093\pi\)
\(882\) 0 0
\(883\) −8.45085 −0.284394 −0.142197 0.989838i \(-0.545417\pi\)
−0.142197 + 0.989838i \(0.545417\pi\)
\(884\) −4.67795 2.81172i −0.157337 0.0945685i
\(885\) −13.1277 22.7379i −0.441284 0.764327i
\(886\) 7.36176 0.247323
\(887\) −5.17784 8.96829i −0.173855 0.301126i 0.765909 0.642948i \(-0.222289\pi\)
−0.939764 + 0.341823i \(0.888956\pi\)
\(888\) −4.06729 7.04475i −0.136489 0.236406i
\(889\) 0 0
\(890\) −2.63174 4.55831i −0.0882162 0.152795i
\(891\) −4.14868 −0.138986
\(892\) 11.5361 + 19.9811i 0.386256 + 0.669016i
\(893\) 4.93396 8.54587i 0.165109 0.285977i
\(894\) 2.82949 + 4.90082i 0.0946323 + 0.163908i
\(895\) 16.1947 28.0501i 0.541330 0.937611i
\(896\) 0 0
\(897\) 28.0995 + 16.8895i 0.938215 + 0.563923i
\(898\) −1.98461 + 3.43745i −0.0662274 + 0.114709i
\(899\) 6.00718 0.200351
\(900\) 5.10234 0.170078
\(901\) −7.28536 −0.242711
\(902\) −2.57890 −0.0858680
\(903\) 0 0
\(904\) −4.23468 7.33467i −0.140843 0.243948i
\(905\) 19.1053 33.0914i 0.635082 1.09999i
\(906\) 0.246303 0.426609i 0.00818287 0.0141731i
\(907\) 18.4804 0.613631 0.306815 0.951769i \(-0.400737\pi\)
0.306815 + 0.951769i \(0.400737\pi\)
\(908\) −14.8312 25.6884i −0.492190 0.852498i
\(909\) −1.35030 −0.0447867
\(910\) 0 0
\(911\) −26.6282 −0.882230 −0.441115 0.897451i \(-0.645417\pi\)
−0.441115 + 0.897451i \(0.645417\pi\)
\(912\) −15.3088 26.5155i −0.506924 0.878017i
\(913\) 4.23374 0.140116
\(914\) −0.0874022 + 0.151385i −0.00289101 + 0.00500737i
\(915\) 13.8287 23.9520i 0.457162 0.791828i
\(916\) −8.35033 14.4632i −0.275903 0.477877i
\(917\) 0 0
\(918\) −1.12931 −0.0372727
\(919\) −11.1493 −0.367783 −0.183891 0.982947i \(-0.558869\pi\)
−0.183891 + 0.982947i \(0.558869\pi\)
\(920\) −21.4639 −0.707644
\(921\) 9.87072 0.325251
\(922\) −1.67518 + 2.90149i −0.0551690 + 0.0955555i
\(923\) −38.0605 22.8766i −1.25278 0.752993i
\(924\) 0 0
\(925\) −5.27933 + 9.14406i −0.173583 + 0.300655i
\(926\) −0.0414927 0.0718675i −0.00136354 0.00236171i
\(927\) −1.83424 + 3.17700i −0.0602445 + 0.104347i
\(928\) 3.60365 + 6.24170i 0.118296 + 0.204894i
\(929\) −7.74510 −0.254108 −0.127054 0.991896i \(-0.540552\pi\)
−0.127054 + 0.991896i \(0.540552\pi\)
\(930\) 1.00272 + 1.73676i 0.0328804 + 0.0569505i
\(931\) 0 0
\(932\) 19.5227 + 33.8144i 0.639489 + 1.10763i
\(933\) −9.38559 16.2563i −0.307270 0.532208i
\(934\) 6.56299 0.214748
\(935\) 3.96817 + 6.87306i 0.129773 + 0.224773i
\(936\) −5.62523 + 3.11704i −0.183866 + 0.101884i
\(937\) −36.4239 −1.18992 −0.594959 0.803756i \(-0.702832\pi\)
−0.594959 + 0.803756i \(0.702832\pi\)
\(938\) 0 0
\(939\) 5.74143 9.94445i 0.187364 0.324525i
\(940\) 6.50291 0.212101
\(941\) −9.89466 17.1381i −0.322557 0.558685i 0.658458 0.752617i \(-0.271209\pi\)
−0.981015 + 0.193933i \(0.937876\pi\)
\(942\) 0.252214 0.436848i 0.00821759 0.0142333i
\(943\) −19.3905 −0.631442
\(944\) 32.0454 1.04299
\(945\) 0 0
\(946\) −1.18999 + 2.06112i −0.0386899 + 0.0670129i
\(947\) −4.97398 8.61519i −0.161633 0.279956i 0.773822 0.633403i \(-0.218343\pi\)
−0.935454 + 0.353448i \(0.885009\pi\)
\(948\) 6.82403 + 11.8196i 0.221634 + 0.383882i
\(949\) 2.37517 + 1.42762i 0.0771012 + 0.0463424i
\(950\) 1.57014 2.71957i 0.0509422 0.0882345i
\(951\) −5.79790 + 10.0423i −0.188010 + 0.325643i
\(952\) 0 0
\(953\) −0.0105567 0.0182847i −0.000341965 0.000592300i 0.865854 0.500296i \(-0.166776\pi\)
−0.866196 + 0.499704i \(0.833442\pi\)
\(954\) −2.10682 + 3.64912i −0.0682108 + 0.118144i
\(955\) 18.0995 31.3493i 0.585686 1.01444i
\(956\) 15.9576 27.6394i 0.516106 0.893922i
\(957\) −5.30352 + 9.18596i −0.171438 + 0.296940i
\(958\) −1.09107 1.88979i −0.0352508 0.0610562i
\(959\) 0 0
\(960\) 9.26150 16.0414i 0.298914 0.517733i
\(961\) 12.2376 21.1962i 0.394761 0.683747i
\(962\) 0.114958 6.53140i 0.00370640 0.210581i
\(963\) −9.76001 16.9048i −0.314512 0.544751i
\(964\) 15.8112 + 27.3858i 0.509245 + 0.882039i
\(965\) −4.98842 + 8.64020i −0.160583 + 0.278138i
\(966\) 0 0
\(967\) −19.8102 −0.637053 −0.318526 0.947914i \(-0.603188\pi\)
−0.318526 + 0.947914i \(0.603188\pi\)
\(968\) 4.81422 0.154735
\(969\) 3.36304 5.82495i 0.108036 0.187124i
\(970\) 0.814635 + 1.41099i 0.0261563 + 0.0453041i
\(971\) 3.61774 0.116099 0.0580493 0.998314i \(-0.481512\pi\)
0.0580493 + 0.998314i \(0.481512\pi\)
\(972\) 14.3572 24.8674i 0.460508 0.797622i
\(973\) 0 0
\(974\) −1.23595 −0.0396024
\(975\) −5.51942 3.31750i −0.176763 0.106245i
\(976\) 16.8782 + 29.2339i 0.540258 + 0.935755i
\(977\) 2.16169 0.0691586 0.0345793 0.999402i \(-0.488991\pi\)
0.0345793 + 0.999402i \(0.488991\pi\)
\(978\) −1.00341 1.73796i −0.0320855 0.0555737i
\(979\) 15.1191 + 26.1870i 0.483208 + 0.836941i
\(980\) 0 0
\(981\) 6.84036 + 11.8479i 0.218396 + 0.378273i
\(982\) −3.49071 −0.111393
\(983\) −15.0545 26.0752i −0.480165 0.831671i 0.519576 0.854424i \(-0.326090\pi\)
−0.999741 + 0.0227535i \(0.992757\pi\)
\(984\) −1.46717 + 2.54121i −0.0467717 + 0.0810109i
\(985\) 14.9977 + 25.9767i 0.477865 + 0.827687i
\(986\) −0.247525 + 0.428727i −0.00788281 + 0.0136534i
\(987\) 0 0
\(988\) 0.916973 52.0983i 0.0291728 1.65747i
\(989\) −8.94742 + 15.4974i −0.284511 + 0.492788i
\(990\) 4.59014 0.145884
\(991\) −27.1460 −0.862323 −0.431161 0.902275i \(-0.641896\pi\)
−0.431161 + 0.902275i \(0.641896\pi\)
\(992\) −7.82832 −0.248549
\(993\) 2.65082 0.0841213
\(994\) 0 0
\(995\) 4.47902 + 7.75790i 0.141995 + 0.245942i
\(996\) 1.18227 2.04776i 0.0374618 0.0648858i
\(997\) 25.4005 43.9949i 0.804441 1.39333i −0.112227 0.993683i \(-0.535798\pi\)
0.916668 0.399650i \(-0.130868\pi\)
\(998\) 8.66599 0.274317
\(999\) 18.1252 + 31.3938i 0.573456 + 0.993256i
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 637.2.g.l.373.3 12
7.2 even 3 637.2.f.j.295.3 12
7.3 odd 6 91.2.h.b.74.4 yes 12
7.4 even 3 637.2.h.l.165.4 12
7.5 odd 6 637.2.f.k.295.3 12
7.6 odd 2 91.2.g.b.9.3 12
13.3 even 3 637.2.h.l.471.4 12
21.17 even 6 819.2.s.d.802.3 12
21.20 even 2 819.2.n.d.100.4 12
91.3 odd 6 91.2.g.b.81.3 yes 12
91.9 even 3 8281.2.a.ca.1.4 6
91.16 even 3 637.2.f.j.393.3 12
91.17 odd 6 1183.2.e.g.508.4 12
91.30 even 6 8281.2.a.cf.1.3 6
91.48 odd 6 1183.2.e.h.170.3 12
91.55 odd 6 91.2.h.b.16.4 yes 12
91.61 odd 6 8281.2.a.bz.1.4 6
91.68 odd 6 637.2.f.k.393.3 12
91.69 odd 6 1183.2.e.g.170.4 12
91.81 even 3 inner 637.2.g.l.263.3 12
91.82 odd 6 8281.2.a.ce.1.3 6
91.87 odd 6 1183.2.e.h.508.3 12
273.146 even 6 819.2.s.d.289.3 12
273.185 even 6 819.2.n.d.172.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.3 12 7.6 odd 2
91.2.g.b.81.3 yes 12 91.3 odd 6
91.2.h.b.16.4 yes 12 91.55 odd 6
91.2.h.b.74.4 yes 12 7.3 odd 6
637.2.f.j.295.3 12 7.2 even 3
637.2.f.j.393.3 12 91.16 even 3
637.2.f.k.295.3 12 7.5 odd 6
637.2.f.k.393.3 12 91.68 odd 6
637.2.g.l.263.3 12 91.81 even 3 inner
637.2.g.l.373.3 12 1.1 even 1 trivial
637.2.h.l.165.4 12 7.4 even 3
637.2.h.l.471.4 12 13.3 even 3
819.2.n.d.100.4 12 21.20 even 2
819.2.n.d.172.4 12 273.185 even 6
819.2.s.d.289.3 12 273.146 even 6
819.2.s.d.802.3 12 21.17 even 6
1183.2.e.g.170.4 12 91.69 odd 6
1183.2.e.g.508.4 12 91.17 odd 6
1183.2.e.h.170.3 12 91.48 odd 6
1183.2.e.h.508.3 12 91.87 odd 6
8281.2.a.bz.1.4 6 91.61 odd 6
8281.2.a.ca.1.4 6 91.9 even 3
8281.2.a.ce.1.3 6 91.82 odd 6
8281.2.a.cf.1.3 6 91.30 even 6