Properties

Label 845.2.e.m.191.1
Level $845$
Weight $2$
Character 845.191
Analytic conductor $6.747$
Analytic rank $0$
Dimension $8$
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] = [845,2,Mod(146,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(6))
 
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("845.146");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.e (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: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.22581504.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 191.1
Root \(1.20036 - 0.747754i\) of defining polynomial
Character \(\chi\) \(=\) 845.191
Dual form 845.2.e.m.146.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.24775 + 2.16117i) q^{2} +(1.41342 - 2.44811i) q^{3} +(-2.11378 - 3.66117i) q^{4} -1.00000 q^{5} +(3.52720 + 6.10929i) q^{6} +(-0.952606 - 1.64996i) q^{7} +5.55889 q^{8} +(-2.49551 - 4.32235i) q^{9} +O(q^{10})\) \(q+(-1.24775 + 2.16117i) q^{2} +(1.41342 - 2.44811i) q^{3} +(-2.11378 - 3.66117i) q^{4} -1.00000 q^{5} +(3.52720 + 6.10929i) q^{6} +(-0.952606 - 1.64996i) q^{7} +5.55889 q^{8} +(-2.49551 - 4.32235i) q^{9} +(1.24775 - 2.16117i) q^{10} +(-0.534695 + 0.926118i) q^{11} -11.9506 q^{12} +4.75447 q^{14} +(-1.41342 + 2.44811i) q^{15} +(-2.70857 + 4.69138i) q^{16} +(-0.318632 - 0.551886i) q^{17} +12.4551 q^{18} +(-2.86603 - 4.96410i) q^{19} +(2.11378 + 3.66117i) q^{20} -5.38573 q^{21} +(-1.33433 - 2.31114i) q^{22} +(-1.90893 + 3.30636i) q^{23} +(7.85704 - 13.6088i) q^{24} +1.00000 q^{25} -5.62828 q^{27} +(-4.02720 + 6.97531i) q^{28} +(-4.72756 + 8.18837i) q^{29} +(-3.52720 - 6.10929i) q^{30} -1.46410 q^{31} +(-1.20036 - 2.07908i) q^{32} +(1.51150 + 2.61799i) q^{33} +1.59030 q^{34} +(0.952606 + 1.64996i) q^{35} +(-10.5499 + 18.2730i) q^{36} +(-0.378725 + 0.655970i) q^{37} +14.3044 q^{38} -5.55889 q^{40} +(-0.133975 + 0.232051i) q^{41} +(6.72006 - 11.6395i) q^{42} +(-0.318632 - 0.551886i) q^{43} +4.52091 q^{44} +(2.49551 + 4.32235i) q^{45} +(-4.76374 - 8.25104i) q^{46} -9.44613 q^{47} +(7.65668 + 13.2618i) q^{48} +(1.68508 - 2.91865i) q^{49} +(-1.24775 + 2.16117i) q^{50} -1.80144 q^{51} -6.99102 q^{53} +(7.02271 - 12.1637i) q^{54} +(0.534695 - 0.926118i) q^{55} +(-5.29543 - 9.17196i) q^{56} -16.2036 q^{57} +(-11.7977 - 20.4341i) q^{58} +(-0.370518 - 0.641756i) q^{59} +11.9506 q^{60} +(-2.09928 - 3.63606i) q^{61} +(1.82684 - 3.16418i) q^{62} +(-4.75447 + 8.23499i) q^{63} -4.84325 q^{64} -7.54390 q^{66} +(-4.04739 + 7.01029i) q^{67} +(-1.34703 + 2.33313i) q^{68} +(5.39623 + 9.34654i) q^{69} -4.75447 q^{70} +(-4.88244 - 8.45663i) q^{71} +(-13.8723 - 24.0274i) q^{72} -3.71649 q^{73} +(-0.945110 - 1.63698i) q^{74} +(1.41342 - 2.44811i) q^{75} +(-12.1163 + 20.9860i) q^{76} +2.03741 q^{77} -9.31937 q^{79} +(2.70857 - 4.69138i) q^{80} +(-0.468594 + 0.811629i) q^{81} +(-0.334335 - 0.579085i) q^{82} +5.11778 q^{83} +(11.3842 + 19.7181i) q^{84} +(0.318632 + 0.551886i) q^{85} +1.59030 q^{86} +(13.3640 + 23.1472i) q^{87} +(-2.97231 + 5.14819i) q^{88} +(6.28917 - 10.8932i) q^{89} -12.4551 q^{90} +16.1402 q^{92} +(-2.06939 + 3.58429i) q^{93} +(11.7864 - 20.4147i) q^{94} +(2.86603 + 4.96410i) q^{95} -6.78645 q^{96} +(2.11078 + 3.65597i) q^{97} +(4.20514 + 7.28351i) q^{98} +5.33734 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 4 q^{6} - 10 q^{7} + 12 q^{8} - 4 q^{9} + 2 q^{10} - 20 q^{12} + 4 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} + 40 q^{18} - 16 q^{19} + 2 q^{20} + 8 q^{21} - 12 q^{22} + 10 q^{23} + 24 q^{24} + 8 q^{25} - 4 q^{27} - 8 q^{28} - 8 q^{29} - 4 q^{30} + 16 q^{31} - 4 q^{32} - 18 q^{33} - 8 q^{34} + 10 q^{35} - 20 q^{36} + 2 q^{37} + 16 q^{38} - 12 q^{40} - 8 q^{41} + 4 q^{42} + 2 q^{43} + 24 q^{44} + 4 q^{45} - 16 q^{46} + 16 q^{47} + 28 q^{48} - 12 q^{49} - 2 q^{50} + 8 q^{51} - 24 q^{53} + 16 q^{54} - 12 q^{56} - 28 q^{57} - 22 q^{58} - 12 q^{59} + 20 q^{60} - 28 q^{61} - 4 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} - 14 q^{68} + 16 q^{69} - 4 q^{70} - 4 q^{71} - 12 q^{72} - 16 q^{73} + 10 q^{74} + 2 q^{75} - 20 q^{76} + 36 q^{77} - 16 q^{79} + 2 q^{80} + 8 q^{81} - 4 q^{82} - 24 q^{83} + 28 q^{84} - 2 q^{85} - 8 q^{86} + 22 q^{87} + 18 q^{88} + 12 q^{89} - 40 q^{90} + 44 q^{92} - 8 q^{93} + 32 q^{94} + 16 q^{95} + 8 q^{96} - 2 q^{97} + 24 q^{98} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24775 + 2.16117i −0.882295 + 1.52818i −0.0335125 + 0.999438i \(0.510669\pi\)
−0.848783 + 0.528742i \(0.822664\pi\)
\(3\) 1.41342 2.44811i 0.816038 1.41342i −0.0925423 0.995709i \(-0.529499\pi\)
0.908580 0.417710i \(-0.137167\pi\)
\(4\) −2.11378 3.66117i −1.05689 1.83059i
\(5\) −1.00000 −0.447214
\(6\) 3.52720 + 6.10929i 1.43997 + 2.49411i
\(7\) −0.952606 1.64996i −0.360051 0.623627i 0.627918 0.778280i \(-0.283907\pi\)
−0.987969 + 0.154653i \(0.950574\pi\)
\(8\) 5.55889 1.96536
\(9\) −2.49551 4.32235i −0.831836 1.44078i
\(10\) 1.24775 2.16117i 0.394574 0.683423i
\(11\) −0.534695 + 0.926118i −0.161217 + 0.279235i −0.935305 0.353842i \(-0.884875\pi\)
0.774089 + 0.633077i \(0.218208\pi\)
\(12\) −11.9506 −3.44985
\(13\) 0 0
\(14\) 4.75447 1.27069
\(15\) −1.41342 + 2.44811i −0.364943 + 0.632100i
\(16\) −2.70857 + 4.69138i −0.677142 + 1.17284i
\(17\) −0.318632 0.551886i −0.0772795 0.133852i 0.824796 0.565431i \(-0.191290\pi\)
−0.902075 + 0.431579i \(0.857957\pi\)
\(18\) 12.4551 2.93570
\(19\) −2.86603 4.96410i −0.657511 1.13884i −0.981258 0.192699i \(-0.938276\pi\)
0.323747 0.946144i \(-0.395057\pi\)
\(20\) 2.11378 + 3.66117i 0.472655 + 0.818663i
\(21\) −5.38573 −1.17526
\(22\) −1.33433 2.31114i −0.284481 0.492736i
\(23\) −1.90893 + 3.30636i −0.398039 + 0.689423i −0.993484 0.113973i \(-0.963642\pi\)
0.595445 + 0.803396i \(0.296976\pi\)
\(24\) 7.85704 13.6088i 1.60381 2.77788i
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.62828 −1.08316
\(28\) −4.02720 + 6.97531i −0.761069 + 1.31821i
\(29\) −4.72756 + 8.18837i −0.877886 + 1.52054i −0.0242288 + 0.999706i \(0.507713\pi\)
−0.853657 + 0.520836i \(0.825620\pi\)
\(30\) −3.52720 6.10929i −0.643975 1.11540i
\(31\) −1.46410 −0.262960 −0.131480 0.991319i \(-0.541973\pi\)
−0.131480 + 0.991319i \(0.541973\pi\)
\(32\) −1.20036 2.07908i −0.212196 0.367534i
\(33\) 1.51150 + 2.61799i 0.263118 + 0.455733i
\(34\) 1.59030 0.272733
\(35\) 0.952606 + 1.64996i 0.161020 + 0.278895i
\(36\) −10.5499 + 18.2730i −1.75832 + 3.04550i
\(37\) −0.378725 + 0.655970i −0.0622619 + 0.107841i −0.895476 0.445110i \(-0.853165\pi\)
0.833214 + 0.552950i \(0.186498\pi\)
\(38\) 14.3044 2.32048
\(39\) 0 0
\(40\) −5.55889 −0.878938
\(41\) −0.133975 + 0.232051i −0.0209233 + 0.0362402i −0.876297 0.481770i \(-0.839994\pi\)
0.855374 + 0.518011i \(0.173327\pi\)
\(42\) 6.72006 11.6395i 1.03693 1.79601i
\(43\) −0.318632 0.551886i −0.0485909 0.0841618i 0.840707 0.541490i \(-0.182140\pi\)
−0.889298 + 0.457328i \(0.848806\pi\)
\(44\) 4.52091 0.681552
\(45\) 2.49551 + 4.32235i 0.372008 + 0.644337i
\(46\) −4.76374 8.25104i −0.702375 1.21655i
\(47\) −9.44613 −1.37786 −0.688930 0.724828i \(-0.741919\pi\)
−0.688930 + 0.724828i \(0.741919\pi\)
\(48\) 7.65668 + 13.2618i 1.10515 + 1.91417i
\(49\) 1.68508 2.91865i 0.240726 0.416950i
\(50\) −1.24775 + 2.16117i −0.176459 + 0.305636i
\(51\) −1.80144 −0.252252
\(52\) 0 0
\(53\) −6.99102 −0.960290 −0.480145 0.877189i \(-0.659416\pi\)
−0.480145 + 0.877189i \(0.659416\pi\)
\(54\) 7.02271 12.1637i 0.955669 1.65527i
\(55\) 0.534695 0.926118i 0.0720982 0.124878i
\(56\) −5.29543 9.17196i −0.707632 1.22565i
\(57\) −16.2036 −2.14622
\(58\) −11.7977 20.4341i −1.54911 2.68313i
\(59\) −0.370518 0.641756i −0.0482373 0.0835495i 0.840899 0.541193i \(-0.182027\pi\)
−0.889136 + 0.457643i \(0.848694\pi\)
\(60\) 11.9506 1.54282
\(61\) −2.09928 3.63606i −0.268785 0.465550i 0.699763 0.714375i \(-0.253289\pi\)
−0.968548 + 0.248825i \(0.919956\pi\)
\(62\) 1.82684 3.16418i 0.232009 0.401851i
\(63\) −4.75447 + 8.23499i −0.599007 + 1.03751i
\(64\) −4.84325 −0.605406
\(65\) 0 0
\(66\) −7.54390 −0.928589
\(67\) −4.04739 + 7.01029i −0.494468 + 0.856443i −0.999980 0.00637624i \(-0.997970\pi\)
0.505512 + 0.862820i \(0.331304\pi\)
\(68\) −1.34703 + 2.33313i −0.163352 + 0.282934i
\(69\) 5.39623 + 9.34654i 0.649629 + 1.12519i
\(70\) −4.75447 −0.568268
\(71\) −4.88244 8.45663i −0.579439 1.00362i −0.995544 0.0943010i \(-0.969938\pi\)
0.416105 0.909317i \(-0.363395\pi\)
\(72\) −13.8723 24.0274i −1.63486 2.83166i
\(73\) −3.71649 −0.434982 −0.217491 0.976062i \(-0.569787\pi\)
−0.217491 + 0.976062i \(0.569787\pi\)
\(74\) −0.945110 1.63698i −0.109867 0.190295i
\(75\) 1.41342 2.44811i 0.163208 0.282684i
\(76\) −12.1163 + 20.9860i −1.38983 + 2.40726i
\(77\) 2.03741 0.232185
\(78\) 0 0
\(79\) −9.31937 −1.04851 −0.524255 0.851561i \(-0.675656\pi\)
−0.524255 + 0.851561i \(0.675656\pi\)
\(80\) 2.70857 4.69138i 0.302827 0.524512i
\(81\) −0.468594 + 0.811629i −0.0520660 + 0.0901809i
\(82\) −0.334335 0.579085i −0.0369211 0.0639492i
\(83\) 5.11778 0.561749 0.280875 0.959744i \(-0.409376\pi\)
0.280875 + 0.959744i \(0.409376\pi\)
\(84\) 11.3842 + 19.7181i 1.24212 + 2.15142i
\(85\) 0.318632 + 0.551886i 0.0345605 + 0.0598605i
\(86\) 1.59030 0.171486
\(87\) 13.3640 + 23.1472i 1.43278 + 2.48164i
\(88\) −2.97231 + 5.14819i −0.316849 + 0.548799i
\(89\) 6.28917 10.8932i 0.666650 1.15467i −0.312185 0.950021i \(-0.601061\pi\)
0.978835 0.204651i \(-0.0656059\pi\)
\(90\) −12.4551 −1.31288
\(91\) 0 0
\(92\) 16.1402 1.68273
\(93\) −2.06939 + 3.58429i −0.214586 + 0.371673i
\(94\) 11.7864 20.4147i 1.21568 2.10562i
\(95\) 2.86603 + 4.96410i 0.294048 + 0.509306i
\(96\) −6.78645 −0.692639
\(97\) 2.11078 + 3.65597i 0.214317 + 0.371208i 0.953061 0.302778i \(-0.0979142\pi\)
−0.738744 + 0.673986i \(0.764581\pi\)
\(98\) 4.20514 + 7.28351i 0.424783 + 0.735746i
\(99\) 5.33734 0.536423
\(100\) −2.11378 3.66117i −0.211378 0.366117i
\(101\) 7.62379 13.2048i 0.758595 1.31393i −0.184972 0.982744i \(-0.559219\pi\)
0.943567 0.331181i \(-0.107447\pi\)
\(102\) 2.24775 3.89322i 0.222561 0.385487i
\(103\) −13.5269 −1.33285 −0.666423 0.745574i \(-0.732176\pi\)
−0.666423 + 0.745574i \(0.732176\pi\)
\(104\) 0 0
\(105\) 5.38573 0.525593
\(106\) 8.72307 15.1088i 0.847259 1.46750i
\(107\) 3.68137 6.37632i 0.355891 0.616422i −0.631379 0.775475i \(-0.717511\pi\)
0.987270 + 0.159053i \(0.0508440\pi\)
\(108\) 11.8969 + 20.6061i 1.14478 + 1.98282i
\(109\) 10.0760 0.965103 0.482551 0.875868i \(-0.339710\pi\)
0.482551 + 0.875868i \(0.339710\pi\)
\(110\) 1.33433 + 2.31114i 0.127224 + 0.220358i
\(111\) 1.07059 + 1.85432i 0.101616 + 0.176004i
\(112\) 10.3208 0.975223
\(113\) 3.34403 + 5.79203i 0.314580 + 0.544868i 0.979348 0.202181i \(-0.0648030\pi\)
−0.664768 + 0.747050i \(0.731470\pi\)
\(114\) 20.2181 35.0187i 1.89360 3.27981i
\(115\) 1.90893 3.30636i 0.178008 0.308320i
\(116\) 39.9721 3.71131
\(117\) 0 0
\(118\) 1.84926 0.170238
\(119\) −0.607061 + 1.05146i −0.0556492 + 0.0963872i
\(120\) −7.85704 + 13.6088i −0.717246 + 1.24231i
\(121\) 4.92820 + 8.53590i 0.448018 + 0.775991i
\(122\) 10.4775 0.948592
\(123\) 0.378725 + 0.655970i 0.0341484 + 0.0591468i
\(124\) 3.09479 + 5.36033i 0.277920 + 0.481372i
\(125\) −1.00000 −0.0894427
\(126\) −11.8648 20.5505i −1.05700 1.83078i
\(127\) −0.744750 + 1.28994i −0.0660859 + 0.114464i −0.897175 0.441675i \(-0.854384\pi\)
0.831089 + 0.556139i \(0.187718\pi\)
\(128\) 8.44391 14.6253i 0.746343 1.29270i
\(129\) −1.80144 −0.158608
\(130\) 0 0
\(131\) 4.12676 0.360557 0.180278 0.983616i \(-0.442300\pi\)
0.180278 + 0.983616i \(0.442300\pi\)
\(132\) 6.38994 11.0677i 0.556172 0.963319i
\(133\) −5.46039 + 9.45767i −0.473476 + 0.820084i
\(134\) −10.1003 17.4942i −0.872533 1.51127i
\(135\) 5.62828 0.484405
\(136\) −1.77124 3.06787i −0.151882 0.263068i
\(137\) 10.0548 + 17.4155i 0.859041 + 1.48790i 0.872844 + 0.487999i \(0.162273\pi\)
−0.0138029 + 0.999905i \(0.504394\pi\)
\(138\) −26.9327 −2.29266
\(139\) −10.4126 18.0352i −0.883189 1.52973i −0.847776 0.530355i \(-0.822059\pi\)
−0.0354130 0.999373i \(-0.511275\pi\)
\(140\) 4.02720 6.97531i 0.340360 0.589521i
\(141\) −13.3513 + 23.1252i −1.12439 + 1.94749i
\(142\) 24.3683 2.04494
\(143\) 0 0
\(144\) 27.0370 2.25308
\(145\) 4.72756 8.18837i 0.392602 0.680007i
\(146\) 4.63726 8.03198i 0.383783 0.664731i
\(147\) −4.76346 8.25055i −0.392883 0.680494i
\(148\) 3.20216 0.263216
\(149\) −6.68388 11.5768i −0.547565 0.948410i −0.998441 0.0558233i \(-0.982222\pi\)
0.450876 0.892587i \(-0.351112\pi\)
\(150\) 3.52720 + 6.10929i 0.287995 + 0.498821i
\(151\) 18.2984 1.48910 0.744550 0.667567i \(-0.232664\pi\)
0.744550 + 0.667567i \(0.232664\pi\)
\(152\) −15.9319 27.5949i −1.29225 2.23824i
\(153\) −1.59030 + 2.75447i −0.128568 + 0.222686i
\(154\) −2.54219 + 4.40320i −0.204856 + 0.354820i
\(155\) 1.46410 0.117599
\(156\) 0 0
\(157\) 2.42229 0.193320 0.0966599 0.995317i \(-0.469184\pi\)
0.0966599 + 0.995317i \(0.469184\pi\)
\(158\) 11.6283 20.1408i 0.925096 1.60231i
\(159\) −9.88124 + 17.1148i −0.783633 + 1.35729i
\(160\) 1.20036 + 2.07908i 0.0948968 + 0.164366i
\(161\) 7.27382 0.573258
\(162\) −1.16938 2.02543i −0.0918752 0.159132i
\(163\) −7.99144 13.8416i −0.625938 1.08416i −0.988359 0.152142i \(-0.951383\pi\)
0.362421 0.932015i \(-0.381950\pi\)
\(164\) 1.13277 0.0884545
\(165\) −1.51150 2.61799i −0.117670 0.203810i
\(166\) −6.38573 + 11.0604i −0.495629 + 0.858454i
\(167\) 7.19658 12.4648i 0.556888 0.964558i −0.440866 0.897573i \(-0.645329\pi\)
0.997754 0.0669853i \(-0.0213381\pi\)
\(168\) −29.9387 −2.30982
\(169\) 0 0
\(170\) −1.59030 −0.121970
\(171\) −14.3044 + 24.7759i −1.09388 + 1.89466i
\(172\) −1.34703 + 2.33313i −0.102710 + 0.177900i
\(173\) 12.1745 + 21.0868i 0.925608 + 1.60320i 0.790581 + 0.612358i \(0.209779\pi\)
0.135027 + 0.990842i \(0.456888\pi\)
\(174\) −66.7001 −5.05653
\(175\) −0.952606 1.64996i −0.0720103 0.124725i
\(176\) −2.89651 5.01691i −0.218333 0.378164i
\(177\) −2.09479 −0.157454
\(178\) 15.6947 + 27.1840i 1.17636 + 2.03752i
\(179\) −1.89414 + 3.28075i −0.141575 + 0.245215i −0.928090 0.372356i \(-0.878550\pi\)
0.786515 + 0.617571i \(0.211883\pi\)
\(180\) 10.5499 18.2730i 0.786343 1.36199i
\(181\) −8.48794 −0.630904 −0.315452 0.948942i \(-0.602156\pi\)
−0.315452 + 0.948942i \(0.602156\pi\)
\(182\) 0 0
\(183\) −11.8687 −0.877356
\(184\) −10.6115 + 18.3797i −0.782291 + 1.35497i
\(185\) 0.378725 0.655970i 0.0278444 0.0482279i
\(186\) −5.16418 8.94462i −0.378656 0.655851i
\(187\) 0.681482 0.0498349
\(188\) 19.9670 + 34.5839i 1.45625 + 2.52229i
\(189\) 5.36153 + 9.28645i 0.389994 + 0.675490i
\(190\) −14.3044 −1.03775
\(191\) 2.72155 + 4.71386i 0.196924 + 0.341083i 0.947530 0.319668i \(-0.103571\pi\)
−0.750605 + 0.660751i \(0.770238\pi\)
\(192\) −6.84555 + 11.8568i −0.494035 + 0.855693i
\(193\) −6.07880 + 10.5288i −0.437562 + 0.757879i −0.997501 0.0706548i \(-0.977491\pi\)
0.559939 + 0.828534i \(0.310824\pi\)
\(194\) −10.5349 −0.756363
\(195\) 0 0
\(196\) −14.2476 −1.01768
\(197\) 2.18915 3.79172i 0.155970 0.270149i −0.777442 0.628955i \(-0.783483\pi\)
0.933412 + 0.358807i \(0.116816\pi\)
\(198\) −6.65968 + 11.5349i −0.473283 + 0.819751i
\(199\) −10.4186 18.0456i −0.738558 1.27922i −0.953144 0.302516i \(-0.902174\pi\)
0.214586 0.976705i \(-0.431160\pi\)
\(200\) 5.55889 0.393073
\(201\) 11.4413 + 19.8170i 0.807009 + 1.39778i
\(202\) 19.0252 + 32.9526i 1.33861 + 2.31854i
\(203\) 18.0140 1.26434
\(204\) 3.80785 + 6.59538i 0.266603 + 0.461769i
\(205\) 0.133975 0.232051i 0.00935719 0.0162071i
\(206\) 16.8783 29.2340i 1.17596 2.03683i
\(207\) 19.0550 1.32441
\(208\) 0 0
\(209\) 6.12979 0.424007
\(210\) −6.72006 + 11.6395i −0.463728 + 0.803201i
\(211\) 5.32684 9.22635i 0.366715 0.635168i −0.622335 0.782751i \(-0.713816\pi\)
0.989050 + 0.147583i \(0.0471492\pi\)
\(212\) 14.7775 + 25.5953i 1.01492 + 1.75789i
\(213\) −27.6037 −1.89138
\(214\) 9.18688 + 15.9121i 0.628002 + 1.08773i
\(215\) 0.318632 + 0.551886i 0.0217305 + 0.0376383i
\(216\) −31.2870 −2.12881
\(217\) 1.39471 + 2.41571i 0.0946792 + 0.163989i
\(218\) −12.5723 + 21.7759i −0.851505 + 1.47485i
\(219\) −5.25296 + 9.09839i −0.354962 + 0.614812i
\(220\) −4.52091 −0.304799
\(221\) 0 0
\(222\) −5.34335 −0.358622
\(223\) −10.6697 + 18.4804i −0.714494 + 1.23754i 0.248661 + 0.968591i \(0.420010\pi\)
−0.963155 + 0.268949i \(0.913324\pi\)
\(224\) −2.28694 + 3.96110i −0.152803 + 0.264662i
\(225\) −2.49551 4.32235i −0.166367 0.288156i
\(226\) −16.6901 −1.11021
\(227\) −7.84283 13.5842i −0.520547 0.901613i −0.999715 0.0238900i \(-0.992395\pi\)
0.479168 0.877723i \(-0.340938\pi\)
\(228\) 34.2508 + 59.3241i 2.26831 + 3.92884i
\(229\) −7.62085 −0.503600 −0.251800 0.967779i \(-0.581023\pi\)
−0.251800 + 0.967779i \(0.581023\pi\)
\(230\) 4.76374 + 8.25104i 0.314112 + 0.544058i
\(231\) 2.87972 4.98782i 0.189472 0.328175i
\(232\) −26.2800 + 45.5182i −1.72536 + 2.98842i
\(233\) −19.0550 −1.24833 −0.624166 0.781292i \(-0.714561\pi\)
−0.624166 + 0.781292i \(0.714561\pi\)
\(234\) 0 0
\(235\) 9.44613 0.616198
\(236\) −1.56639 + 2.71306i −0.101963 + 0.176605i
\(237\) −13.1722 + 22.8149i −0.855625 + 1.48199i
\(238\) −1.51493 2.62393i −0.0981980 0.170084i
\(239\) 12.7535 0.824954 0.412477 0.910968i \(-0.364664\pi\)
0.412477 + 0.910968i \(0.364664\pi\)
\(240\) −7.65668 13.2618i −0.494237 0.856043i
\(241\) −12.9644 22.4550i −0.835111 1.44646i −0.893940 0.448187i \(-0.852070\pi\)
0.0588285 0.998268i \(-0.481263\pi\)
\(242\) −24.5967 −1.58114
\(243\) −7.11778 12.3284i −0.456606 0.790864i
\(244\) −8.87483 + 15.3717i −0.568153 + 0.984069i
\(245\) −1.68508 + 2.91865i −0.107656 + 0.186466i
\(246\) −1.89022 −0.120516
\(247\) 0 0
\(248\) −8.13878 −0.516813
\(249\) 7.23357 12.5289i 0.458409 0.793987i
\(250\) 1.24775 2.16117i 0.0789149 0.136685i
\(251\) −3.80593 6.59207i −0.240228 0.416088i 0.720551 0.693402i \(-0.243889\pi\)
−0.960779 + 0.277314i \(0.910556\pi\)
\(252\) 40.1996 2.53234
\(253\) −2.04139 3.53578i −0.128341 0.222293i
\(254\) −1.85853 3.21907i −0.116614 0.201982i
\(255\) 1.80144 0.112811
\(256\) 16.2286 + 28.1087i 1.01429 + 1.75680i
\(257\) −0.167891 + 0.290796i −0.0104728 + 0.0181394i −0.871214 0.490903i \(-0.836667\pi\)
0.860742 + 0.509042i \(0.170000\pi\)
\(258\) 2.24775 3.89322i 0.139939 0.242382i
\(259\) 1.44310 0.0896700
\(260\) 0 0
\(261\) 47.1906 2.92103
\(262\) −5.14918 + 8.91865i −0.318118 + 0.550996i
\(263\) 2.68795 4.65566i 0.165746 0.287080i −0.771174 0.636624i \(-0.780330\pi\)
0.936920 + 0.349544i \(0.113664\pi\)
\(264\) 8.40224 + 14.5531i 0.517122 + 0.895681i
\(265\) 6.99102 0.429455
\(266\) −13.6264 23.6017i −0.835491 1.44711i
\(267\) −17.7785 30.7932i −1.08802 1.88451i
\(268\) 34.2212 2.09039
\(269\) 0.655192 + 1.13483i 0.0399478 + 0.0691916i 0.885308 0.465005i \(-0.153948\pi\)
−0.845360 + 0.534197i \(0.820614\pi\)
\(270\) −7.02271 + 12.1637i −0.427388 + 0.740258i
\(271\) 5.82266 10.0851i 0.353701 0.612629i −0.633194 0.773994i \(-0.718256\pi\)
0.986895 + 0.161365i \(0.0515896\pi\)
\(272\) 3.45214 0.209317
\(273\) 0 0
\(274\) −50.1838 −3.03171
\(275\) −0.534695 + 0.926118i −0.0322433 + 0.0558470i
\(276\) 22.8129 39.5130i 1.37317 2.37841i
\(277\) 10.1581 + 17.5943i 0.610338 + 1.05714i 0.991183 + 0.132498i \(0.0422999\pi\)
−0.380845 + 0.924639i \(0.624367\pi\)
\(278\) 51.9697 3.11693
\(279\) 3.65368 + 6.32835i 0.218740 + 0.378869i
\(280\) 5.29543 + 9.17196i 0.316463 + 0.548129i
\(281\) −11.8744 −0.708366 −0.354183 0.935176i \(-0.615241\pi\)
−0.354183 + 0.935176i \(0.615241\pi\)
\(282\) −33.3184 57.7091i −1.98408 3.43653i
\(283\) 11.3261 19.6173i 0.673264 1.16613i −0.303709 0.952765i \(-0.598225\pi\)
0.976973 0.213363i \(-0.0684418\pi\)
\(284\) −20.6408 + 35.7509i −1.22481 + 2.12143i
\(285\) 16.2036 0.959817
\(286\) 0 0
\(287\) 0.510500 0.0301339
\(288\) −5.99102 + 10.3767i −0.353024 + 0.611455i
\(289\) 8.29695 14.3707i 0.488056 0.845337i
\(290\) 11.7977 + 20.4341i 0.692782 + 1.19993i
\(291\) 11.9336 0.699562
\(292\) 7.85584 + 13.6067i 0.459728 + 0.796272i
\(293\) −9.30636 16.1191i −0.543683 0.941687i −0.998689 0.0511983i \(-0.983696\pi\)
0.455005 0.890489i \(-0.349637\pi\)
\(294\) 23.7745 1.38656
\(295\) 0.370518 + 0.641756i 0.0215724 + 0.0373645i
\(296\) −2.10529 + 3.64647i −0.122367 + 0.211946i
\(297\) 3.00941 5.21245i 0.174624 0.302457i
\(298\) 33.3593 1.93245
\(299\) 0 0
\(300\) −11.9506 −0.689970
\(301\) −0.607061 + 1.05146i −0.0349904 + 0.0606052i
\(302\) −22.8319 + 39.5459i −1.31383 + 2.27561i
\(303\) −21.5512 37.3278i −1.23808 2.14443i
\(304\) 31.0513 1.78091
\(305\) 2.09928 + 3.63606i 0.120204 + 0.208200i
\(306\) −3.96859 6.87381i −0.226869 0.392949i
\(307\) 3.14776 0.179652 0.0898262 0.995957i \(-0.471369\pi\)
0.0898262 + 0.995957i \(0.471369\pi\)
\(308\) −4.30664 7.45932i −0.245394 0.425034i
\(309\) −19.1192 + 33.1154i −1.08765 + 1.88387i
\(310\) −1.82684 + 3.16418i −0.103757 + 0.179713i
\(311\) −3.18059 −0.180355 −0.0901774 0.995926i \(-0.528743\pi\)
−0.0901774 + 0.995926i \(0.528743\pi\)
\(312\) 0 0
\(313\) 35.3533 1.99829 0.999144 0.0413596i \(-0.0131689\pi\)
0.999144 + 0.0413596i \(0.0131689\pi\)
\(314\) −3.02242 + 5.23499i −0.170565 + 0.295427i
\(315\) 4.75447 8.23499i 0.267884 0.463989i
\(316\) 19.6991 + 34.1198i 1.10816 + 1.91939i
\(317\) −13.6357 −0.765858 −0.382929 0.923778i \(-0.625085\pi\)
−0.382929 + 0.923778i \(0.625085\pi\)
\(318\) −24.6587 42.7101i −1.38279 2.39506i
\(319\) −5.05560 8.75656i −0.283059 0.490273i
\(320\) 4.84325 0.270746
\(321\) −10.4066 18.0248i −0.580842 1.00605i
\(322\) −9.07594 + 15.7200i −0.505782 + 0.876041i
\(323\) −1.82641 + 3.16344i −0.101624 + 0.176018i
\(324\) 3.96202 0.220112
\(325\) 0 0
\(326\) 39.8854 2.20905
\(327\) 14.2416 24.6671i 0.787560 1.36409i
\(328\) −0.744750 + 1.28994i −0.0411219 + 0.0712253i
\(329\) 8.99844 + 15.5858i 0.496100 + 0.859271i
\(330\) 7.54390 0.415278
\(331\) 14.3980 + 24.9380i 0.791383 + 1.37072i 0.925110 + 0.379698i \(0.123972\pi\)
−0.133727 + 0.991018i \(0.542695\pi\)
\(332\) −10.8179 18.7371i −0.593707 1.02833i
\(333\) 3.78044 0.207167
\(334\) 17.9591 + 31.1061i 0.982679 + 1.70205i
\(335\) 4.04739 7.01029i 0.221133 0.383013i
\(336\) 14.5876 25.2665i 0.795819 1.37840i
\(337\) 11.7493 0.640026 0.320013 0.947413i \(-0.396313\pi\)
0.320013 + 0.947413i \(0.396313\pi\)
\(338\) 0 0
\(339\) 18.9061 1.02684
\(340\) 1.34703 2.33313i 0.0730532 0.126532i
\(341\) 0.782847 1.35593i 0.0423936 0.0734278i
\(342\) −35.6967 61.8285i −1.93026 3.34330i
\(343\) −19.7574 −1.06680
\(344\) −1.77124 3.06787i −0.0954987 0.165409i
\(345\) −5.39623 9.34654i −0.290523 0.503201i
\(346\) −60.7630 −3.26664
\(347\) −0.949887 1.64525i −0.0509926 0.0883218i 0.839402 0.543510i \(-0.182905\pi\)
−0.890395 + 0.455189i \(0.849572\pi\)
\(348\) 56.4973 97.8562i 3.02857 5.24564i
\(349\) 5.13454 8.89329i 0.274846 0.476047i −0.695250 0.718768i \(-0.744707\pi\)
0.970096 + 0.242721i \(0.0780398\pi\)
\(350\) 4.75447 0.254137
\(351\) 0 0
\(352\) 2.56730 0.136838
\(353\) −0.400294 + 0.693330i −0.0213055 + 0.0369022i −0.876482 0.481435i \(-0.840116\pi\)
0.855176 + 0.518338i \(0.173449\pi\)
\(354\) 2.61378 4.52720i 0.138921 0.240618i
\(355\) 4.88244 + 8.45663i 0.259133 + 0.448831i
\(356\) −53.1756 −2.81830
\(357\) 1.71606 + 2.97231i 0.0908237 + 0.157311i
\(358\) −4.72685 8.18714i −0.249822 0.432704i
\(359\) 8.13272 0.429228 0.214614 0.976699i \(-0.431151\pi\)
0.214614 + 0.976699i \(0.431151\pi\)
\(360\) 13.8723 + 24.0274i 0.731132 + 1.26636i
\(361\) −6.92820 + 12.0000i −0.364642 + 0.631579i
\(362\) 10.5909 18.3439i 0.556643 0.964135i
\(363\) 27.8625 1.46240
\(364\) 0 0
\(365\) 3.71649 0.194530
\(366\) 14.8092 25.6502i 0.774087 1.34076i
\(367\) 10.2632 17.7765i 0.535737 0.927924i −0.463390 0.886154i \(-0.653367\pi\)
0.999127 0.0417696i \(-0.0132996\pi\)
\(368\) −10.3409 17.9110i −0.539057 0.933675i
\(369\) 1.33734 0.0696191
\(370\) 0.945110 + 1.63698i 0.0491339 + 0.0851025i
\(371\) 6.65968 + 11.5349i 0.345754 + 0.598863i
\(372\) 17.4969 0.907173
\(373\) 8.90292 + 15.4203i 0.460976 + 0.798433i 0.999010 0.0444897i \(-0.0141662\pi\)
−0.538034 + 0.842923i \(0.680833\pi\)
\(374\) −0.850322 + 1.47280i −0.0439691 + 0.0761568i
\(375\) −1.41342 + 2.44811i −0.0729887 + 0.126420i
\(376\) −52.5100 −2.70800
\(377\) 0 0
\(378\) −26.7595 −1.37636
\(379\) −1.02277 + 1.77150i −0.0525363 + 0.0909956i −0.891098 0.453812i \(-0.850064\pi\)
0.838561 + 0.544807i \(0.183397\pi\)
\(380\) 12.1163 20.9860i 0.621553 1.07656i
\(381\) 2.10529 + 3.64647i 0.107857 + 0.186814i
\(382\) −13.5833 −0.694982
\(383\) 3.95261 + 6.84611i 0.201969 + 0.349820i 0.949163 0.314786i \(-0.101933\pi\)
−0.747194 + 0.664606i \(0.768599\pi\)
\(384\) −23.8696 41.3433i −1.21809 2.10979i
\(385\) −2.03741 −0.103836
\(386\) −15.1697 26.2747i −0.772117 1.33735i
\(387\) −1.59030 + 2.75447i −0.0808393 + 0.140018i
\(388\) 8.92343 15.4558i 0.453018 0.784651i
\(389\) −9.21171 −0.467052 −0.233526 0.972351i \(-0.575026\pi\)
−0.233526 + 0.972351i \(0.575026\pi\)
\(390\) 0 0
\(391\) 2.43298 0.123041
\(392\) 9.36719 16.2244i 0.473114 0.819458i
\(393\) 5.83285 10.1028i 0.294228 0.509618i
\(394\) 5.46304 + 9.46226i 0.275224 + 0.476702i
\(395\) 9.31937 0.468908
\(396\) −11.2820 19.5409i −0.566940 0.981968i
\(397\) 3.17719 + 5.50305i 0.159458 + 0.276190i 0.934674 0.355507i \(-0.115692\pi\)
−0.775215 + 0.631697i \(0.782359\pi\)
\(398\) 51.9996 2.60651
\(399\) 15.4356 + 26.7353i 0.772748 + 1.33844i
\(400\) −2.70857 + 4.69138i −0.135428 + 0.234569i
\(401\) −2.08460 + 3.61063i −0.104100 + 0.180306i −0.913370 0.407130i \(-0.866530\pi\)
0.809270 + 0.587437i \(0.199863\pi\)
\(402\) −57.1038 −2.84808
\(403\) 0 0
\(404\) −64.4600 −3.20701
\(405\) 0.468594 0.811629i 0.0232846 0.0403301i
\(406\) −22.4770 + 38.9314i −1.11552 + 1.93213i
\(407\) −0.405004 0.701487i −0.0200753 0.0347714i
\(408\) −10.0140 −0.495767
\(409\) −5.08403 8.80580i −0.251389 0.435419i 0.712519 0.701652i \(-0.247554\pi\)
−0.963909 + 0.266234i \(0.914221\pi\)
\(410\) 0.334335 + 0.579085i 0.0165116 + 0.0285989i
\(411\) 56.8467 2.80404
\(412\) 28.5929 + 49.5244i 1.40867 + 2.43989i
\(413\) −0.705915 + 1.22268i −0.0347358 + 0.0601642i
\(414\) −23.7759 + 41.1811i −1.16852 + 2.02394i
\(415\) −5.11778 −0.251222
\(416\) 0 0
\(417\) −58.8697 −2.88286
\(418\) −7.64847 + 13.2475i −0.374099 + 0.647959i
\(419\) −14.2954 + 24.7604i −0.698378 + 1.20963i 0.270651 + 0.962677i \(0.412761\pi\)
−0.969029 + 0.246948i \(0.920572\pi\)
\(420\) −11.3842 19.7181i −0.555494 0.962144i
\(421\) 2.01797 0.0983498 0.0491749 0.998790i \(-0.484341\pi\)
0.0491749 + 0.998790i \(0.484341\pi\)
\(422\) 13.2932 + 23.0244i 0.647101 + 1.12081i
\(423\) 23.5729 + 40.8295i 1.14615 + 1.98520i
\(424\) −38.8623 −1.88732
\(425\) −0.318632 0.551886i −0.0154559 0.0267704i
\(426\) 34.4427 59.6564i 1.66875 2.89036i
\(427\) −3.99957 + 6.92747i −0.193553 + 0.335244i
\(428\) −31.1264 −1.50455
\(429\) 0 0
\(430\) −1.59030 −0.0766908
\(431\) 10.3061 17.8508i 0.496430 0.859842i −0.503562 0.863959i \(-0.667977\pi\)
0.999992 + 0.00411765i \(0.00131069\pi\)
\(432\) 15.2446 26.4044i 0.733455 1.27038i
\(433\) −14.7178 25.4920i −0.707292 1.22507i −0.965858 0.259072i \(-0.916583\pi\)
0.258566 0.965994i \(-0.416750\pi\)
\(434\) −6.96103 −0.334140
\(435\) −13.3640 23.1472i −0.640757 1.10982i
\(436\) −21.2984 36.8899i −1.02001 1.76670i
\(437\) 21.8841 1.04686
\(438\) −13.1088 22.7051i −0.626362 1.08489i
\(439\) −8.47602 + 14.6809i −0.404538 + 0.700681i −0.994268 0.106920i \(-0.965901\pi\)
0.589729 + 0.807601i \(0.299235\pi\)
\(440\) 2.97231 5.14819i 0.141699 0.245430i
\(441\) −16.8205 −0.800978
\(442\) 0 0
\(443\) −24.1399 −1.14692 −0.573461 0.819233i \(-0.694400\pi\)
−0.573461 + 0.819233i \(0.694400\pi\)
\(444\) 4.52599 7.83925i 0.214794 0.372034i
\(445\) −6.28917 + 10.8932i −0.298135 + 0.516385i
\(446\) −26.6262 46.1180i −1.26079 2.18375i
\(447\) −37.7885 −1.78733
\(448\) 4.61371 + 7.99118i 0.217977 + 0.377548i
\(449\) 10.4315 + 18.0679i 0.492293 + 0.852676i 0.999961 0.00887706i \(-0.00282569\pi\)
−0.507668 + 0.861553i \(0.669492\pi\)
\(450\) 12.4551 0.587140
\(451\) −0.143271 0.248153i −0.00674637 0.0116851i
\(452\) 14.1371 24.4861i 0.664952 1.15173i
\(453\) 25.8633 44.7965i 1.21516 2.10472i
\(454\) 39.1437 1.83710
\(455\) 0 0
\(456\) −90.0739 −4.21810
\(457\) 15.2830 26.4708i 0.714906 1.23825i −0.248089 0.968737i \(-0.579803\pi\)
0.962996 0.269517i \(-0.0868640\pi\)
\(458\) 9.50894 16.4700i 0.444324 0.769591i
\(459\) 1.79335 + 3.10617i 0.0837063 + 0.144984i
\(460\) −16.1402 −0.752541
\(461\) −2.33911 4.05146i −0.108943 0.188695i 0.806399 0.591372i \(-0.201413\pi\)
−0.915342 + 0.402676i \(0.868080\pi\)
\(462\) 7.18636 + 12.4471i 0.334340 + 0.579094i
\(463\) −14.0011 −0.650688 −0.325344 0.945596i \(-0.605480\pi\)
−0.325344 + 0.945596i \(0.605480\pi\)
\(464\) −25.6098 44.3575i −1.18891 2.05925i
\(465\) 2.06939 3.58429i 0.0959656 0.166217i
\(466\) 23.7759 41.1811i 1.10140 1.90768i
\(467\) −6.98506 −0.323230 −0.161615 0.986854i \(-0.551670\pi\)
−0.161615 + 0.986854i \(0.551670\pi\)
\(468\) 0 0
\(469\) 15.4223 0.712135
\(470\) −11.7864 + 20.4147i −0.543668 + 0.941661i
\(471\) 3.42371 5.93004i 0.157756 0.273242i
\(472\) −2.05967 3.56745i −0.0948039 0.164205i
\(473\) 0.681482 0.0313346
\(474\) −32.8713 56.9347i −1.50983 2.61510i
\(475\) −2.86603 4.96410i −0.131502 0.227769i
\(476\) 5.13277 0.235260
\(477\) 17.4461 + 30.2176i 0.798804 + 1.38357i
\(478\) −15.9132 + 27.5625i −0.727853 + 1.26068i
\(479\) 8.14438 14.1065i 0.372126 0.644542i −0.617766 0.786362i \(-0.711962\pi\)
0.989892 + 0.141820i \(0.0452955\pi\)
\(480\) 6.78645 0.309758
\(481\) 0 0
\(482\) 64.7056 2.94726
\(483\) 10.2810 17.8071i 0.467800 0.810253i
\(484\) 20.8343 36.0860i 0.947012 1.64027i
\(485\) −2.11078 3.65597i −0.0958454 0.166009i
\(486\) 35.5249 1.61144
\(487\) −10.0204 17.3559i −0.454069 0.786471i 0.544565 0.838719i \(-0.316695\pi\)
−0.998634 + 0.0522474i \(0.983362\pi\)
\(488\) −11.6697 20.2125i −0.528261 0.914975i
\(489\) −45.1810 −2.04316
\(490\) −4.20514 7.28351i −0.189969 0.329035i
\(491\) 7.89916 13.6818i 0.356484 0.617449i −0.630887 0.775875i \(-0.717309\pi\)
0.987371 + 0.158426i \(0.0506420\pi\)
\(492\) 1.60108 2.77315i 0.0721823 0.125023i
\(493\) 6.02540 0.271370
\(494\) 0 0
\(495\) −5.33734 −0.239896
\(496\) 3.96562 6.86865i 0.178061 0.308411i
\(497\) −9.30208 + 16.1117i −0.417255 + 0.722708i
\(498\) 18.0514 + 31.2660i 0.808903 + 1.40106i
\(499\) 1.24651 0.0558016 0.0279008 0.999611i \(-0.491118\pi\)
0.0279008 + 0.999611i \(0.491118\pi\)
\(500\) 2.11378 + 3.66117i 0.0945311 + 0.163733i
\(501\) −20.3436 35.2361i −0.908883 1.57423i
\(502\) 18.9955 0.847809
\(503\) 3.82672 + 6.62808i 0.170625 + 0.295532i 0.938639 0.344902i \(-0.112088\pi\)
−0.768013 + 0.640434i \(0.778755\pi\)
\(504\) −26.4296 + 45.7774i −1.17727 + 2.03909i
\(505\) −7.62379 + 13.2048i −0.339254 + 0.587605i
\(506\) 10.1886 0.452938
\(507\) 0 0
\(508\) 6.29695 0.279382
\(509\) −12.8621 + 22.2777i −0.570101 + 0.987444i 0.426454 + 0.904509i \(0.359763\pi\)
−0.996555 + 0.0829345i \(0.973571\pi\)
\(510\) −2.24775 + 3.89322i −0.0995322 + 0.172395i
\(511\) 3.54035 + 6.13207i 0.156616 + 0.271267i
\(512\) −47.2215 −2.08691
\(513\) 16.1308 + 27.9393i 0.712192 + 1.23355i
\(514\) −0.418974 0.725685i −0.0184802 0.0320086i
\(515\) 13.5269 0.596067
\(516\) 3.80785 + 6.59538i 0.167631 + 0.290346i
\(517\) 5.05080 8.74824i 0.222134 0.384747i
\(518\) −1.80064 + 3.11879i −0.0791154 + 0.137032i
\(519\) 68.8305 3.02132
\(520\) 0 0
\(521\) −30.1519 −1.32098 −0.660490 0.750835i \(-0.729651\pi\)
−0.660490 + 0.750835i \(0.729651\pi\)
\(522\) −58.8823 + 101.987i −2.57721 + 4.46386i
\(523\) −1.96876 + 3.41000i −0.0860880 + 0.149109i −0.905854 0.423589i \(-0.860770\pi\)
0.819766 + 0.572698i \(0.194103\pi\)
\(524\) −8.72307 15.1088i −0.381069 0.660031i
\(525\) −5.38573 −0.235052
\(526\) 6.70779 + 11.6182i 0.292473 + 0.506579i
\(527\) 0.466509 + 0.808017i 0.0203215 + 0.0351978i
\(528\) −16.3759 −0.712672
\(529\) 4.21200 + 7.29539i 0.183130 + 0.317191i
\(530\) −8.72307 + 15.1088i −0.378906 + 0.656284i
\(531\) −1.84926 + 3.20301i −0.0802510 + 0.138999i
\(532\) 46.1682 2.00165
\(533\) 0 0
\(534\) 88.7326 3.83983
\(535\) −3.68137 + 6.37632i −0.159159 + 0.275672i
\(536\) −22.4990 + 38.9694i −0.971809 + 1.68322i
\(537\) 5.35444 + 9.27415i 0.231061 + 0.400209i
\(538\) −3.27007 −0.140983
\(539\) 1.80201 + 3.12117i 0.0776180 + 0.134438i
\(540\) −11.8969 20.6061i −0.511963 0.886745i
\(541\) −15.8881 −0.683083 −0.341541 0.939867i \(-0.610949\pi\)
−0.341541 + 0.939867i \(0.610949\pi\)
\(542\) 14.5305 + 25.1675i 0.624138 + 1.08104i
\(543\) −11.9970 + 20.7795i −0.514842 + 0.891732i
\(544\) −0.764945 + 1.32492i −0.0327968 + 0.0568057i
\(545\) −10.0760 −0.431607
\(546\) 0 0
\(547\) −6.56107 −0.280531 −0.140266 0.990114i \(-0.544796\pi\)
−0.140266 + 0.990114i \(0.544796\pi\)
\(548\) 42.5074 73.6249i 1.81582 3.14510i
\(549\) −10.4775 + 18.1476i −0.447170 + 0.774522i
\(550\) −1.33433 2.31114i −0.0568962 0.0985471i
\(551\) 54.1972 2.30888
\(552\) 29.9970 + 51.9564i 1.27676 + 2.21141i
\(553\) 8.87769 + 15.3766i 0.377518 + 0.653880i
\(554\) −50.6990 −2.15399
\(555\) −1.07059 1.85432i −0.0454441 0.0787116i
\(556\) −44.0200 + 76.2450i −1.86687 + 3.23351i
\(557\) −3.92503 + 6.79835i −0.166309 + 0.288055i −0.937119 0.349009i \(-0.886518\pi\)
0.770810 + 0.637065i \(0.219852\pi\)
\(558\) −18.2356 −0.771973
\(559\) 0 0
\(560\) −10.3208 −0.436133
\(561\) 0.963220 1.66835i 0.0406672 0.0704377i
\(562\) 14.8163 25.6626i 0.624988 1.08251i
\(563\) 7.77976 + 13.4749i 0.327878 + 0.567901i 0.982091 0.188410i \(-0.0603333\pi\)
−0.654213 + 0.756310i \(0.727000\pi\)
\(564\) 112.887 4.75341
\(565\) −3.34403 5.79203i −0.140684 0.243673i
\(566\) 28.2643 + 48.9552i 1.18804 + 2.05774i
\(567\) 1.78554 0.0749857
\(568\) −27.1409 47.0095i −1.13881 1.97247i
\(569\) −1.73957 + 3.01303i −0.0729267 + 0.126313i −0.900183 0.435512i \(-0.856567\pi\)
0.827256 + 0.561825i \(0.189901\pi\)
\(570\) −20.2181 + 35.0187i −0.846842 + 1.46677i
\(571\) −21.5118 −0.900240 −0.450120 0.892968i \(-0.648619\pi\)
−0.450120 + 0.892968i \(0.648619\pi\)
\(572\) 0 0
\(573\) 15.3868 0.642791
\(574\) −0.636978 + 1.10328i −0.0265870 + 0.0460500i
\(575\) −1.90893 + 3.30636i −0.0796078 + 0.137885i
\(576\) 12.0864 + 20.9342i 0.503599 + 0.872259i
\(577\) 9.97608 0.415310 0.207655 0.978202i \(-0.433417\pi\)
0.207655 + 0.978202i \(0.433417\pi\)
\(578\) 20.7051 + 35.8623i 0.861218 + 1.49167i
\(579\) 17.1838 + 29.7632i 0.714134 + 1.23692i
\(580\) −39.9721 −1.65975
\(581\) −4.87523 8.44414i −0.202259 0.350322i
\(582\) −14.8902 + 25.7907i −0.617221 + 1.06906i
\(583\) 3.73806 6.47451i 0.154815 0.268147i
\(584\) −20.6595 −0.854898
\(585\) 0 0
\(586\) 46.4482 1.91876
\(587\) 12.0286 20.8341i 0.496472 0.859915i −0.503519 0.863984i \(-0.667962\pi\)
0.999992 + 0.00406862i \(0.00129509\pi\)
\(588\) −20.1378 + 34.8797i −0.830469 + 1.43841i
\(589\) 4.19615 + 7.26795i 0.172899 + 0.299471i
\(590\) −1.84926 −0.0761328
\(591\) −6.18837 10.7186i −0.254556 0.440903i
\(592\) −2.05160 3.55348i −0.0843203 0.146047i
\(593\) 0.940219 0.0386102 0.0193051 0.999814i \(-0.493855\pi\)
0.0193051 + 0.999814i \(0.493855\pi\)
\(594\) 7.51001 + 13.0077i 0.308139 + 0.533713i
\(595\) 0.607061 1.05146i 0.0248871 0.0431057i
\(596\) −28.2565 + 48.9417i −1.15743 + 2.00473i
\(597\) −58.9037 −2.41077
\(598\) 0 0
\(599\) −11.4270 −0.466896 −0.233448 0.972369i \(-0.575001\pi\)
−0.233448 + 0.972369i \(0.575001\pi\)
\(600\) 7.85704 13.6088i 0.320762 0.555577i
\(601\) 18.0215 31.2142i 0.735114 1.27325i −0.219560 0.975599i \(-0.570462\pi\)
0.954674 0.297655i \(-0.0962045\pi\)
\(602\) −1.51493 2.62393i −0.0617437 0.106943i
\(603\) 40.4012 1.64526
\(604\) −38.6787 66.9935i −1.57381 2.72593i
\(605\) −4.92820 8.53590i −0.200360 0.347034i
\(606\) 107.562 4.36942
\(607\) −19.9454 34.5464i −0.809557 1.40219i −0.913171 0.407576i \(-0.866374\pi\)
0.103614 0.994618i \(-0.466959\pi\)
\(608\) −6.88052 + 11.9174i −0.279042 + 0.483315i
\(609\) 25.4613 44.1003i 1.03175 1.78704i
\(610\) −10.4775 −0.424223
\(611\) 0 0
\(612\) 13.4461 0.543528
\(613\) 0.172736 0.299187i 0.00697673 0.0120841i −0.862516 0.506030i \(-0.831113\pi\)
0.869493 + 0.493946i \(0.164446\pi\)
\(614\) −3.92763 + 6.80286i −0.158506 + 0.274541i
\(615\) −0.378725 0.655970i −0.0152716 0.0264513i
\(616\) 11.3258 0.456328
\(617\) −19.3425 33.5022i −0.778700 1.34875i −0.932691 0.360676i \(-0.882546\pi\)
0.153991 0.988072i \(-0.450787\pi\)
\(618\) −47.7121 82.6398i −1.91926 3.32426i
\(619\) 14.8971 0.598764 0.299382 0.954133i \(-0.403219\pi\)
0.299382 + 0.954133i \(0.403219\pi\)
\(620\) −3.09479 5.36033i −0.124290 0.215276i
\(621\) 10.7440 18.6091i 0.431141 0.746758i
\(622\) 3.96859 6.87381i 0.159126 0.275615i
\(623\) −23.9644 −0.960113
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −44.1123 + 76.4047i −1.76308 + 3.05374i
\(627\) 8.66397 15.0064i 0.346006 0.599299i
\(628\) −5.12019 8.86842i −0.204318 0.353889i
\(629\) 0.482694 0.0192463
\(630\) 11.8648 + 20.5505i 0.472706 + 0.818750i
\(631\) 19.4225 + 33.6408i 0.773198 + 1.33922i 0.935802 + 0.352526i \(0.114677\pi\)
−0.162604 + 0.986691i \(0.551989\pi\)
\(632\) −51.8053 −2.06071
\(633\) −15.0581 26.0814i −0.598506 1.03664i
\(634\) 17.0140 29.4691i 0.675713 1.17037i
\(635\) 0.744750 1.28994i 0.0295545 0.0511899i
\(636\) 83.5470 3.31285
\(637\) 0 0
\(638\) 25.2326 0.998967
\(639\) −24.3683 + 42.2072i −0.963996 + 1.66969i
\(640\) −8.44391 + 14.6253i −0.333775 + 0.578115i
\(641\) −18.5908 32.2003i −0.734293 1.27183i −0.955033 0.296501i \(-0.904180\pi\)
0.220739 0.975333i \(-0.429153\pi\)
\(642\) 51.9397 2.04990
\(643\) −4.55189 7.88410i −0.179509 0.310918i 0.762204 0.647337i \(-0.224118\pi\)
−0.941712 + 0.336419i \(0.890784\pi\)
\(644\) −15.3753 26.6307i −0.605870 1.04940i
\(645\) 1.80144 0.0709316
\(646\) −4.55783 7.89439i −0.179325 0.310601i
\(647\) 9.56118 16.5605i 0.375889 0.651059i −0.614571 0.788862i \(-0.710671\pi\)
0.990460 + 0.137803i \(0.0440041\pi\)
\(648\) −2.60486 + 4.51175i −0.102329 + 0.177238i
\(649\) 0.792455 0.0311066
\(650\) 0 0
\(651\) 7.88525 0.309047
\(652\) −33.7843 + 58.5161i −1.32309 + 2.29167i
\(653\) −17.3162 + 29.9926i −0.677636 + 1.17370i 0.298055 + 0.954549i \(0.403662\pi\)
−0.975691 + 0.219152i \(0.929671\pi\)
\(654\) 35.5399 + 61.5570i 1.38972 + 2.40707i
\(655\) −4.12676 −0.161246
\(656\) −0.725758 1.25705i −0.0283361 0.0490796i
\(657\) 9.27453 + 16.0640i 0.361834 + 0.626714i
\(658\) −44.9114 −1.75083
\(659\) 3.34926 + 5.80109i 0.130469 + 0.225978i 0.923857 0.382737i \(-0.125018\pi\)
−0.793389 + 0.608715i \(0.791685\pi\)
\(660\) −6.38994 + 11.0677i −0.248728 + 0.430809i
\(661\) −3.01379 + 5.22004i −0.117223 + 0.203036i −0.918666 0.395035i \(-0.870732\pi\)
0.801443 + 0.598071i \(0.204066\pi\)
\(662\) −71.8604 −2.79294
\(663\) 0 0
\(664\) 28.4492 1.10404
\(665\) 5.46039 9.45767i 0.211745 0.366753i
\(666\) −4.71706 + 8.17018i −0.182782 + 0.316588i
\(667\) −18.0491 31.2620i −0.698865 1.21047i
\(668\) −60.8479 −2.35428
\(669\) 30.1614 + 52.2411i 1.16611 + 2.01976i
\(670\) 10.1003 + 17.4942i 0.390209 + 0.675861i
\(671\) 4.48990 0.173330
\(672\) 6.46481 + 11.1974i 0.249386 + 0.431948i
\(673\) −11.6784 + 20.2276i −0.450169 + 0.779715i −0.998396 0.0566140i \(-0.981970\pi\)
0.548227 + 0.836329i \(0.315303\pi\)
\(674\) −14.6603 + 25.3923i −0.564692 + 0.978075i
\(675\) −5.62828 −0.216633
\(676\) 0 0
\(677\) −45.4042 −1.74503 −0.872513 0.488590i \(-0.837511\pi\)
−0.872513 + 0.488590i \(0.837511\pi\)
\(678\) −23.5901 + 40.8593i −0.905973 + 1.56919i
\(679\) 4.02148 6.96540i 0.154330 0.267308i
\(680\) 1.77124 + 3.06787i 0.0679239 + 0.117648i
\(681\) −44.3408 −1.69914
\(682\) 1.95360 + 3.38374i 0.0748073 + 0.129570i
\(683\) 12.7489 + 22.0817i 0.487823 + 0.844934i 0.999902 0.0140045i \(-0.00445791\pi\)
−0.512079 + 0.858938i \(0.671125\pi\)
\(684\) 120.945 4.62445
\(685\) −10.0548 17.4155i −0.384175 0.665411i
\(686\) 24.6523 42.6991i 0.941230 1.63026i
\(687\) −10.7715 + 18.6567i −0.410957 + 0.711798i
\(688\) 3.45214 0.131612
\(689\) 0 0
\(690\) 26.9327 1.02531
\(691\) 3.29815 5.71257i 0.125468 0.217316i −0.796448 0.604707i \(-0.793290\pi\)
0.921916 + 0.387391i \(0.126624\pi\)
\(692\) 51.4683 89.1457i 1.95653 3.38881i
\(693\) −5.08438 8.80641i −0.193140 0.334528i
\(694\) 4.74090 0.179962
\(695\) 10.4126 + 18.0352i 0.394974 + 0.684115i
\(696\) 74.2892 + 128.673i 2.81593 + 4.87733i
\(697\) 0.170754 0.00646778
\(698\) 12.8133 + 22.1933i 0.484990 + 0.840028i
\(699\) −26.9327 + 46.6487i −1.01869 + 1.76442i
\(700\) −4.02720 + 6.97531i −0.152214 + 0.263642i
\(701\) 29.2474 1.10466 0.552329 0.833626i \(-0.313739\pi\)
0.552329 + 0.833626i \(0.313739\pi\)
\(702\) 0 0
\(703\) 4.34174 0.163752
\(704\) 2.58966 4.48542i 0.0976015 0.169051i
\(705\) 13.3513 23.1252i 0.502841 0.870946i
\(706\) −0.998937 1.73021i −0.0375955 0.0651173i
\(707\) −29.0499 −1.09253
\(708\) 4.42792 + 7.66938i 0.166411 + 0.288233i
\(709\) −5.46673 9.46865i −0.205307 0.355603i 0.744923 0.667150i \(-0.232486\pi\)
−0.950231 + 0.311548i \(0.899153\pi\)
\(710\) −24.3683 −0.914527
\(711\) 23.2566 + 40.2815i 0.872189 + 1.51068i
\(712\) 34.9608 60.5538i 1.31021 2.26935i
\(713\) 2.79486 4.84084i 0.104668 0.181291i
\(714\) −8.56490 −0.320533
\(715\) 0 0
\(716\) 16.0152 0.598516
\(717\) 18.0260 31.2220i 0.673194 1.16601i
\(718\) −10.1476 + 17.5762i −0.378706 + 0.655938i
\(719\) −8.02989 13.9082i −0.299464 0.518688i 0.676549 0.736398i \(-0.263475\pi\)
−0.976014 + 0.217710i \(0.930141\pi\)
\(720\) −27.0370 −1.00761
\(721\) 12.8858 + 22.3189i 0.479893 + 0.831199i
\(722\) −17.2894 29.9461i −0.643444 1.11448i
\(723\) −73.2966 −2.72593
\(724\) 17.9416 + 31.0758i 0.666796 + 1.15492i
\(725\) −4.72756 + 8.18837i −0.175577 + 0.304108i
\(726\) −34.7655 + 60.2156i −1.29027 + 2.23481i
\(727\) 51.3754 1.90541 0.952704 0.303900i \(-0.0982889\pi\)
0.952704 + 0.303900i \(0.0982889\pi\)
\(728\) 0 0
\(729\) −43.0532 −1.59456
\(730\) −4.63726 + 8.03198i −0.171633 + 0.297277i
\(731\) −0.203052 + 0.351697i −0.00751016 + 0.0130080i
\(732\) 25.0877 + 43.4532i 0.927268 + 1.60608i
\(733\) −9.82358 −0.362842 −0.181421 0.983406i \(-0.558070\pi\)
−0.181421 + 0.983406i \(0.558070\pi\)
\(734\) 25.6120 + 44.3613i 0.945357 + 1.63741i
\(735\) 4.76346 + 8.25055i 0.175703 + 0.304326i
\(736\) 9.16560 0.337848
\(737\) −4.32824 7.49673i −0.159433 0.276146i
\(738\) −1.66867 + 2.89022i −0.0614246 + 0.106390i
\(739\) −24.5421 + 42.5082i −0.902797 + 1.56369i −0.0789487 + 0.996879i \(0.525156\pi\)
−0.823848 + 0.566811i \(0.808177\pi\)
\(740\) −3.20216 −0.117714
\(741\) 0 0
\(742\) −33.2386 −1.22023
\(743\) −20.4188 + 35.3663i −0.749091 + 1.29746i 0.199167 + 0.979966i \(0.436176\pi\)
−0.948259 + 0.317499i \(0.897157\pi\)
\(744\) −11.5035 + 19.9247i −0.421739 + 0.730473i
\(745\) 6.68388 + 11.5768i 0.244878 + 0.424142i
\(746\) −44.4346 −1.62687
\(747\) −12.7715 22.1208i −0.467283 0.809358i
\(748\) −1.44050 2.49503i −0.0526700 0.0912272i
\(749\) −14.0276 −0.512557
\(750\) −3.52720 6.10929i −0.128795 0.223080i
\(751\) 1.36340 2.36148i 0.0497512 0.0861716i −0.840077 0.542467i \(-0.817490\pi\)
0.889829 + 0.456295i \(0.150824\pi\)
\(752\) 25.5855 44.3154i 0.933006 1.61601i
\(753\) −21.5175 −0.784142
\(754\) 0 0
\(755\) −18.2984 −0.665946
\(756\) 22.6662 39.2590i 0.824362 1.42784i
\(757\) −7.40301 + 12.8224i −0.269067 + 0.466038i −0.968621 0.248542i \(-0.920049\pi\)
0.699554 + 0.714580i \(0.253382\pi\)
\(758\) −2.55234 4.42078i −0.0927051 0.160570i
\(759\) −11.5413 −0.418924
\(760\) 15.9319 + 27.5949i 0.577911 + 1.00097i
\(761\) 5.68445 + 9.84575i 0.206061 + 0.356908i 0.950470 0.310815i \(-0.100602\pi\)
−0.744409 + 0.667724i \(0.767269\pi\)
\(762\) −10.5075 −0.380647
\(763\) −9.59843 16.6250i −0.347486 0.601864i
\(764\) 11.5055 19.9281i 0.416255 0.720975i
\(765\) 1.59030 2.75447i 0.0574972 0.0995882i
\(766\) −19.7275 −0.712784
\(767\) 0 0
\(768\) 91.7512 3.31078
\(769\) 10.5281 18.2352i 0.379654 0.657579i −0.611358 0.791354i \(-0.709377\pi\)
0.991012 + 0.133775i \(0.0427098\pi\)
\(770\) 2.54219 4.40320i 0.0916142 0.158680i
\(771\) 0.474602 + 0.822034i 0.0170924 + 0.0296048i
\(772\) 51.3970 1.84982
\(773\) −7.04144 12.1961i −0.253263 0.438664i 0.711159 0.703031i \(-0.248170\pi\)
−0.964422 + 0.264367i \(0.914837\pi\)
\(774\) −3.96859 6.87381i −0.142648 0.247074i
\(775\) −1.46410 −0.0525921
\(776\) 11.7336 + 20.3231i 0.421210 + 0.729558i
\(777\) 2.03971 3.53288i 0.0731741 0.126741i
\(778\) 11.4940 19.9081i 0.412078 0.713740i
\(779\) 1.53590 0.0550293
\(780\) 0 0
\(781\) 10.4425 0.373660
\(782\) −3.03576 + 5.25809i −0.108558 + 0.188029i
\(783\) 26.6080 46.0864i 0.950893 1.64699i
\(784\) 9.12832 + 15.8107i 0.326011 + 0.564668i
\(785\) −2.42229 −0.0864552
\(786\) 14.5559 + 25.2116i 0.519192 + 0.899267i
\(787\) −16.5121 28.5998i −0.588593 1.01947i −0.994417 0.105522i \(-0.966349\pi\)
0.405823 0.913951i \(-0.366985\pi\)
\(788\) −18.5095 −0.659374
\(789\) −7.59839 13.1608i −0.270510 0.468537i
\(790\) −11.6283 + 20.1408i −0.413716 + 0.716576i
\(791\) 6.37109 11.0350i 0.226530 0.392361i
\(792\) 29.6697 1.05427
\(793\) 0 0
\(794\) −15.8574 −0.562758
\(795\) 9.88124 17.1148i 0.350451 0.606999i
\(796\) −44.0454 + 76.2890i −1.56115 + 2.70399i
\(797\) 8.47079 + 14.6718i 0.300051 + 0.519703i 0.976147 0.217110i \(-0.0696630\pi\)
−0.676096 + 0.736813i \(0.736330\pi\)
\(798\) −77.0395 −2.72717
\(799\) 3.00984 + 5.21319i 0.106480 + 0.184429i
\(800\) −1.20036 2.07908i −0.0424391 0.0735067i
\(801\) −62.7787 −2.21817
\(802\) −5.20213 9.01036i −0.183694 0.318167i
\(803\) 1.98719 3.44191i 0.0701263 0.121462i
\(804\) 48.3689 83.7774i 1.70584 2.95460i
\(805\) −7.27382 −0.256369
\(806\) 0 0
\(807\) 3.70425 0.130396
\(808\) 42.3798 73.4039i 1.49092 2.58234i
\(809\) 25.8818 44.8285i 0.909954 1.57609i 0.0958292 0.995398i \(-0.469450\pi\)
0.814125 0.580689i \(-0.197217\pi\)
\(810\) 1.16938 + 2.02543i 0.0410878 + 0.0711662i
\(811\) 22.6699 0.796047 0.398023 0.917375i \(-0.369696\pi\)
0.398023 + 0.917375i \(0.369696\pi\)
\(812\) −38.0776 65.9524i −1.33626 2.31448i
\(813\) −16.4597 28.5091i −0.577267 0.999856i
\(814\) 2.02138 0.0708494
\(815\) 7.99144 + 13.8416i 0.279928 + 0.484849i
\(816\) 4.87932 8.45123i 0.170810 0.295852i
\(817\) −1.82641 + 3.16344i −0.0638981 + 0.110675i
\(818\) 25.3745 0.887198
\(819\) 0 0
\(820\) −1.13277 −0.0395581
\(821\) −14.3315 + 24.8230i −0.500174 + 0.866328i 0.499826 + 0.866126i \(0.333397\pi\)
−1.00000 0.000201482i \(0.999936\pi\)
\(822\) −70.9307 + 122.856i −2.47399 + 4.28508i
\(823\) 12.9164 + 22.3718i 0.450236 + 0.779831i 0.998400 0.0565391i \(-0.0180066\pi\)
−0.548165 + 0.836371i \(0.684673\pi\)
\(824\) −75.1946 −2.61953
\(825\) 1.51150 + 2.61799i 0.0526235 + 0.0911466i
\(826\) −1.76162 3.05121i −0.0612945 0.106165i
\(827\) −16.0820 −0.559227 −0.279613 0.960113i \(-0.590206\pi\)
−0.279613 + 0.960113i \(0.590206\pi\)
\(828\) −40.2780 69.7635i −1.39976 2.42445i
\(829\) 11.2909 19.5564i 0.392149 0.679222i −0.600584 0.799562i \(-0.705065\pi\)
0.992733 + 0.120340i \(0.0383984\pi\)
\(830\) 6.38573 11.0604i 0.221652 0.383912i
\(831\) 57.4304 1.99224
\(832\) 0 0
\(833\) −2.14768 −0.0744128
\(834\) 73.4549 127.228i 2.54354 4.40553i
\(835\) −7.19658 + 12.4648i −0.249048 + 0.431364i
\(836\) −12.9570 22.4422i −0.448128 0.776181i
\(837\) 8.24037 0.284829
\(838\) −35.6744 61.7898i −1.23235 2.13449i
\(839\) 8.92198 + 15.4533i 0.308021 + 0.533508i 0.977929 0.208936i \(-0.0670000\pi\)
−0.669908 + 0.742444i \(0.733667\pi\)
\(840\) 29.9387 1.03298
\(841\) −30.1996 52.3073i −1.04137 1.80370i
\(842\) −2.51793 + 4.36118i −0.0867736 + 0.150296i
\(843\) −16.7835 + 29.0698i −0.578053 + 1.00122i
\(844\) −45.0390 −1.55031
\(845\) 0 0
\(846\) −117.653 −4.04498
\(847\) 9.38927 16.2627i 0.322619 0.558793i
\(848\) 18.9356 32.7975i 0.650252 1.12627i
\(849\) −32.0169 55.4550i −1.09882 1.90321i
\(850\) 1.59030 0.0545467
\(851\) −1.44591 2.50440i −0.0495653 0.0858497i
\(852\) 58.3482 + 101.062i 1.99898 + 3.46233i
\(853\) 19.7936 0.677720 0.338860 0.940837i \(-0.389959\pi\)
0.338860 + 0.940837i \(0.389959\pi\)
\(854\) −9.98097 17.2875i −0.341542 0.591568i
\(855\) 14.3044 24.7759i 0.489199 0.847318i
\(856\) 20.4643 35.4452i 0.699456 1.21149i
\(857\) −11.7302 −0.400696 −0.200348 0.979725i \(-0.564207\pi\)
−0.200348 + 0.979725i \(0.564207\pi\)
\(858\) 0 0
\(859\) 5.37452 0.183376 0.0916882 0.995788i \(-0.470774\pi\)
0.0916882 + 0.995788i \(0.470774\pi\)
\(860\) 1.34703 2.33313i 0.0459335 0.0795591i
\(861\) 0.721551 1.24976i 0.0245904 0.0425918i
\(862\) 25.7191 + 44.5467i 0.875995 + 1.51727i
\(863\) −25.3234 −0.862017 −0.431008 0.902348i \(-0.641842\pi\)
−0.431008 + 0.902348i \(0.641842\pi\)
\(864\) 6.75596 + 11.7017i 0.229842 + 0.398099i
\(865\) −12.1745 21.0868i −0.413944 0.716973i
\(866\) 73.4567 2.49616
\(867\) −23.4541 40.6237i −0.796544 1.37965i
\(868\) 5.89623 10.2126i 0.200131 0.346637i
\(869\) 4.98302 8.63084i 0.169037 0.292781i
\(870\) 66.7001 2.26135
\(871\) 0 0
\(872\) 56.0112 1.89678
\(873\) 10.5349 18.2470i 0.356553 0.617567i
\(874\) −27.3060 + 47.2954i −0.923640 + 1.59979i
\(875\) 0.952606 + 1.64996i 0.0322040 + 0.0557789i
\(876\) 44.4144 1.50062
\(877\) −10.3458 17.9194i −0.349352 0.605095i 0.636783 0.771043i \(-0.280265\pi\)
−0.986134 + 0.165949i \(0.946931\pi\)
\(878\) −21.1520 36.6363i −0.713845 1.23642i
\(879\) −52.6151 −1.77466
\(880\) 2.89651 + 5.01691i 0.0976414 + 0.169120i
\(881\) −24.1997 + 41.9150i −0.815307 + 1.41215i 0.0937999 + 0.995591i \(0.470099\pi\)
−0.909107 + 0.416562i \(0.863235\pi\)
\(882\) 20.9879 36.3521i 0.706699 1.22404i
\(883\) 45.8550 1.54314 0.771572 0.636142i \(-0.219471\pi\)
0.771572 + 0.636142i \(0.219471\pi\)
\(884\) 0 0
\(885\) 2.09479 0.0704155
\(886\) 30.1207 52.1705i 1.01192 1.75270i
\(887\) 0.541169 0.937332i 0.0181707 0.0314725i −0.856797 0.515654i \(-0.827549\pi\)
0.874968 + 0.484181i \(0.160882\pi\)
\(888\) 5.95131 + 10.3080i 0.199713 + 0.345913i
\(889\) 2.83781 0.0951772
\(890\) −15.6947 27.1840i −0.526086 0.911208i
\(891\) −0.501109 0.867947i −0.0167878 0.0290773i
\(892\) 90.2133 3.02056
\(893\) 27.0729 + 46.8916i 0.905959 + 1.56917i
\(894\) 47.1507 81.6675i 1.57696 2.73137i
\(895\) 1.89414 3.28075i 0.0633142 0.109663i
\(896\) −32.1749 −1.07489
\(897\) 0 0
\(898\) −52.0637 −1.73739
\(899\) 6.92163 11.9886i 0.230849 0.399842i
\(900\) −10.5499 + 18.2730i −0.351663 + 0.609099i
\(901\) 2.22756 + 3.85824i 0.0742107 + 0.128537i
\(902\) 0.715068 0.0238092
\(903\) 1.71606 + 2.97231i 0.0571070 + 0.0989122i
\(904\) 18.5891 + 32.1973i 0.618264 + 1.07086i
\(905\) 8.48794 0.282149
\(906\) 64.5420 + 111.790i 2.14426 + 3.71397i
\(907\) 22.7653 39.4307i 0.755910 1.30928i −0.189010 0.981975i \(-0.560528\pi\)
0.944920 0.327300i \(-0.106139\pi\)
\(908\) −33.1560 + 57.4279i −1.10032 + 1.90581i
\(909\) −76.1009 −2.52411
\(910\) 0 0
\(911\) 39.7417 1.31670 0.658350 0.752712i \(-0.271255\pi\)
0.658350 + 0.752712i \(0.271255\pi\)
\(912\) 43.8885 76.0171i 1.45329 2.51718i
\(913\) −2.73645 + 4.73967i −0.0905632 + 0.156860i
\(914\) 38.1387 + 66.0582i 1.26152 + 2.18501i
\(915\) 11.8687 0.392365
\(916\) 16.1088 + 27.9012i 0.532250 + 0.921883i
\(917\) −3.93118 6.80900i −0.129819 0.224853i
\(918\) −8.95062 −0.295415
\(919\) −23.4969 40.6978i −0.775091 1.34250i −0.934743 0.355323i \(-0.884371\pi\)
0.159653 0.987173i \(-0.448963\pi\)
\(920\) 10.6115 18.3797i 0.349851 0.605960i
\(921\) 4.44911 7.70608i 0.146603 0.253924i
\(922\) 11.6745 0.384481
\(923\) 0 0
\(924\) −24.3484 −0.801002
\(925\) −0.378725 + 0.655970i −0.0124524 + 0.0215682i
\(926\) 17.4700 30.2589i 0.574099 0.994369i
\(927\) 33.7565 + 58.4680i 1.10871 + 1.92034i
\(928\) 22.6991 0.745134
\(929\) 7.61066 + 13.1821i 0.249698 + 0.432489i 0.963442 0.267917i \(-0.0863354\pi\)
−0.713744 + 0.700406i \(0.753002\pi\)
\(930\) 5.16418 + 8.94462i 0.169340 + 0.293306i
\(931\) −19.3180 −0.633121
\(932\) 40.2780 + 69.7635i 1.31935 + 2.28518i
\(933\) −4.49551 + 7.78645i −0.147176 + 0.254917i
\(934\) 8.71564 15.0959i 0.285184 0.493954i
\(935\) −0.681482 −0.0222869
\(936\) 0 0
\(937\) 6.07285 0.198392 0.0991958 0.995068i \(-0.468373\pi\)
0.0991958 + 0.995068i \(0.468373\pi\)
\(938\) −19.2432 + 33.3302i −0.628313 + 1.08827i
\(939\) 49.9691 86.5490i 1.63068 2.82442i
\(940\) −19.9670 34.5839i −0.651253 1.12800i
\(941\) −0.0496576 −0.00161879 −0.000809396 1.00000i \(-0.500258\pi\)
−0.000809396 1.00000i \(0.500258\pi\)
\(942\) 8.54390 + 14.7985i 0.278375 + 0.482160i
\(943\) −0.511495 0.885936i −0.0166566 0.0288500i
\(944\) 4.01429 0.130654
\(945\) −5.36153 9.28645i −0.174411 0.302088i
\(946\) −0.850322 + 1.47280i −0.0276464 + 0.0478849i
\(947\) 9.32907 16.1584i 0.303154 0.525078i −0.673695 0.739010i \(-0.735294\pi\)
0.976849 + 0.213932i \(0.0686270\pi\)
\(948\) 111.372 3.61720
\(949\) 0 0
\(950\) 14.3044 0.464095
\(951\) −19.2730 + 33.3818i −0.624969 + 1.08248i
\(952\) −3.37458 + 5.84495i −0.109371 + 0.189436i
\(953\) 0.764764 + 1.32461i 0.0247731 + 0.0429083i 0.878146 0.478392i \(-0.158780\pi\)
−0.853373 + 0.521301i \(0.825447\pi\)
\(954\) −87.0739 −2.81912
\(955\) −2.72155 4.71386i −0.0880673 0.152537i
\(956\) −26.9581 46.6927i −0.871886 1.51015i
\(957\) −28.5827 −0.923948
\(958\) 20.3244 + 35.2028i 0.656650 + 1.13735i
\(959\) 19.1566 33.1802i 0.618598 1.07144i
\(960\) 6.84555 11.8568i 0.220939 0.382678i
\(961\) −28.8564 −0.930852
\(962\) 0 0
\(963\) −36.7475 −1.18417
\(964\) −54.8078 + 94.9299i −1.76524 + 3.05749i
\(965\) 6.07880 10.5288i 0.195683 0.338934i
\(966\) 25.6562 + 44.4379i 0.825475 + 1.42976i
\(967\) 32.1716 1.03457 0.517285 0.855813i \(-0.326943\pi\)
0.517285 + 0.855813i \(0.326943\pi\)
\(968\) 27.3953 + 47.4501i 0.880519 + 1.52510i
\(969\) 5.16297 + 8.94253i 0.165859 + 0.287276i
\(970\) 10.5349 0.338256
\(971\) 8.62705 + 14.9425i 0.276855 + 0.479527i 0.970601 0.240692i \(-0.0773745\pi\)
−0.693746 + 0.720219i \(0.744041\pi\)
\(972\) −30.0908 + 52.1188i −0.965164 + 1.67171i
\(973\) −19.8383 + 34.3609i −0.635986 + 1.10156i
\(974\) 50.0122 1.60249
\(975\) 0 0
\(976\) 22.7442 0.728023
\(977\) −7.86142 + 13.6164i −0.251509 + 0.435626i −0.963942 0.266114i \(-0.914260\pi\)
0.712432 + 0.701741i \(0.247593\pi\)
\(978\) 56.3748 97.6440i 1.80267 3.12231i
\(979\) 6.72557 + 11.6490i 0.214950 + 0.372304i
\(980\) 14.2476 0.455122
\(981\) −25.1447 43.5518i −0.802807 1.39050i
\(982\) 19.7124 + 34.1429i 0.629049 + 1.08954i
\(983\) 38.5356 1.22910 0.614548 0.788880i \(-0.289338\pi\)
0.614548 + 0.788880i \(0.289338\pi\)
\(984\) 2.10529 + 3.64647i 0.0671141 + 0.116245i
\(985\) −2.18915 + 3.79172i −0.0697521 + 0.120814i
\(986\) −7.51821 + 13.0219i −0.239429 + 0.414703i
\(987\) 50.8743 1.61935
\(988\) 0 0
\(989\) 2.43298 0.0773642
\(990\) 6.65968 11.5349i 0.211659 0.366604i
\(991\) −4.29571 + 7.44040i −0.136458 + 0.236352i −0.926153 0.377147i \(-0.876905\pi\)
0.789696 + 0.613499i \(0.210238\pi\)
\(992\) 1.75745 + 3.04399i 0.0557991 + 0.0966468i
\(993\) 81.4014 2.58320
\(994\) −23.2134 40.2068i −0.736285 1.27528i
\(995\) 10.4186 + 18.0456i 0.330293 + 0.572085i
\(996\) −61.1606 −1.93795
\(997\) 10.2687 + 17.7859i 0.325213 + 0.563285i 0.981555 0.191178i \(-0.0612308\pi\)
−0.656343 + 0.754463i \(0.727897\pi\)
\(998\) −1.55534 + 2.69393i −0.0492335 + 0.0852750i
\(999\) 2.13157 3.69198i 0.0674398 0.116809i
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 845.2.e.m.191.1 8
13.2 odd 12 65.2.m.a.36.1 8
13.3 even 3 inner 845.2.e.m.146.1 8
13.4 even 6 845.2.a.l.1.1 4
13.5 odd 4 845.2.m.g.316.4 8
13.6 odd 12 845.2.c.g.506.1 8
13.7 odd 12 845.2.c.g.506.8 8
13.8 odd 4 65.2.m.a.56.1 yes 8
13.9 even 3 845.2.a.m.1.4 4
13.10 even 6 845.2.e.n.146.4 8
13.11 odd 12 845.2.m.g.361.4 8
13.12 even 2 845.2.e.n.191.4 8
39.2 even 12 585.2.bu.c.361.4 8
39.8 even 4 585.2.bu.c.316.4 8
39.17 odd 6 7605.2.a.cj.1.4 4
39.35 odd 6 7605.2.a.cf.1.1 4
52.15 even 12 1040.2.da.b.881.1 8
52.47 even 4 1040.2.da.b.641.1 8
65.2 even 12 325.2.m.b.49.1 8
65.4 even 6 4225.2.a.bl.1.4 4
65.8 even 4 325.2.m.b.199.1 8
65.9 even 6 4225.2.a.bi.1.1 4
65.28 even 12 325.2.m.c.49.4 8
65.34 odd 4 325.2.n.d.251.4 8
65.47 even 4 325.2.m.c.199.4 8
65.54 odd 12 325.2.n.d.101.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.m.a.36.1 8 13.2 odd 12
65.2.m.a.56.1 yes 8 13.8 odd 4
325.2.m.b.49.1 8 65.2 even 12
325.2.m.b.199.1 8 65.8 even 4
325.2.m.c.49.4 8 65.28 even 12
325.2.m.c.199.4 8 65.47 even 4
325.2.n.d.101.4 8 65.54 odd 12
325.2.n.d.251.4 8 65.34 odd 4
585.2.bu.c.316.4 8 39.8 even 4
585.2.bu.c.361.4 8 39.2 even 12
845.2.a.l.1.1 4 13.4 even 6
845.2.a.m.1.4 4 13.9 even 3
845.2.c.g.506.1 8 13.6 odd 12
845.2.c.g.506.8 8 13.7 odd 12
845.2.e.m.146.1 8 13.3 even 3 inner
845.2.e.m.191.1 8 1.1 even 1 trivial
845.2.e.n.146.4 8 13.10 even 6
845.2.e.n.191.4 8 13.12 even 2
845.2.m.g.316.4 8 13.5 odd 4
845.2.m.g.361.4 8 13.11 odd 12
1040.2.da.b.641.1 8 52.47 even 4
1040.2.da.b.881.1 8 52.15 even 12
4225.2.a.bi.1.1 4 65.9 even 6
4225.2.a.bl.1.4 4 65.4 even 6
7605.2.a.cf.1.1 4 39.35 odd 6
7605.2.a.cj.1.4 4 39.17 odd 6