Properties

Label 507.2.e.l.484.2
Level $507$
Weight $2$
Character 507.484
Analytic conductor $4.048$
Analytic rank $0$
Dimension $6$
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] = [507,2,Mod(22,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 484.2
Root \(0.222521 + 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 507.484
Dual form 507.2.e.l.22.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.17845 + 2.04113i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.77748 + 3.07868i) q^{4} -3.69202 q^{5} +(-1.17845 + 2.04113i) q^{6} +(-0.400969 + 0.694498i) q^{7} -3.66487 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.17845 + 2.04113i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.77748 + 3.07868i) q^{4} -3.69202 q^{5} +(-1.17845 + 2.04113i) q^{6} +(-0.400969 + 0.694498i) q^{7} -3.66487 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.35086 - 7.53590i) q^{10} +(-1.42543 - 2.46891i) q^{11} -3.55496 q^{12} -1.89008 q^{14} +(-1.84601 - 3.19738i) q^{15} +(-0.763906 - 1.32312i) q^{16} +(-1.46950 + 2.54525i) q^{17} -2.35690 q^{18} +(-1.22252 + 2.11747i) q^{19} +(6.56249 - 11.3666i) q^{20} -0.801938 q^{21} +(3.35958 - 5.81897i) q^{22} +(3.89493 + 6.74621i) q^{23} +(-1.83244 - 3.17387i) q^{24} +8.63102 q^{25} -1.00000 q^{27} +(-1.42543 - 2.46891i) q^{28} +(-1.92543 - 3.33494i) q^{29} +(4.35086 - 7.53590i) q^{30} -2.34481 q^{31} +(-1.86443 + 3.22929i) q^{32} +(1.42543 - 2.46891i) q^{33} -6.92692 q^{34} +(1.48039 - 2.56410i) q^{35} +(-1.77748 - 3.07868i) q^{36} +(3.72252 + 6.44760i) q^{37} -5.76271 q^{38} +13.5308 q^{40} +(-0.425428 - 0.736862i) q^{41} +(-0.945042 - 1.63686i) q^{42} +(0.807979 - 1.39946i) q^{43} +10.1347 q^{44} +(1.84601 - 3.19738i) q^{45} +(-9.17994 + 15.9001i) q^{46} -2.44504 q^{47} +(0.763906 - 1.32312i) q^{48} +(3.17845 + 5.50523i) q^{49} +(10.1712 + 17.6171i) q^{50} -2.93900 q^{51} -9.96077 q^{53} +(-1.17845 - 2.04113i) q^{54} +(5.26271 + 9.11528i) q^{55} +(1.46950 - 2.54525i) q^{56} -2.44504 q^{57} +(4.53803 - 7.86010i) q^{58} +(-2.69202 + 4.66272i) q^{59} +13.1250 q^{60} +(6.62833 - 11.4806i) q^{61} +(-2.76324 - 4.78607i) q^{62} +(-0.400969 - 0.694498i) q^{63} -11.8442 q^{64} +6.71917 q^{66} +(7.19687 + 12.4653i) q^{67} +(-5.22401 - 9.04826i) q^{68} +(-3.89493 + 6.74621i) q^{69} +6.97823 q^{70} +(4.06249 - 7.03644i) q^{71} +(1.83244 - 3.17387i) q^{72} +11.8877 q^{73} +(-8.77359 + 15.1963i) q^{74} +(4.31551 + 7.47468i) q^{75} +(-4.34601 - 7.52751i) q^{76} +2.28621 q^{77} +5.40581 q^{79} +(2.82036 + 4.88500i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00269 - 1.73671i) q^{82} -7.04892 q^{83} +(1.42543 - 2.46891i) q^{84} +(5.42543 - 9.39712i) q^{85} +3.80864 q^{86} +(1.92543 - 3.33494i) q^{87} +(5.22401 + 9.04826i) q^{88} +(0.565843 + 0.980069i) q^{89} +8.70171 q^{90} -27.6926 q^{92} +(-1.17241 - 2.03067i) q^{93} +(-2.88135 - 4.99065i) q^{94} +(4.51357 - 7.81774i) q^{95} -3.72886 q^{96} +(-2.97219 + 5.14798i) q^{97} +(-7.49127 + 12.9753i) q^{98} +2.85086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} + 3 q^{3} - 11 q^{4} - 12 q^{5} - 3 q^{6} + 2 q^{7} - 24 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} + 3 q^{3} - 11 q^{4} - 12 q^{5} - 3 q^{6} + 2 q^{7} - 24 q^{8} - 3 q^{9} + q^{10} + 5 q^{11} - 22 q^{12} - 10 q^{14} - 6 q^{15} - 11 q^{16} + q^{17} - 6 q^{18} - 7 q^{19} + 15 q^{20} + 4 q^{21} + 9 q^{22} - 12 q^{24} + 22 q^{25} - 6 q^{27} + 5 q^{28} + 2 q^{29} - q^{30} + 32 q^{31} + 22 q^{32} - 5 q^{33} + 16 q^{34} - 4 q^{35} - 11 q^{36} + 22 q^{37} + 6 q^{40} + 11 q^{41} - 5 q^{42} + 15 q^{43} - 32 q^{44} + 6 q^{45} - 7 q^{46} - 14 q^{47} + 11 q^{48} + 15 q^{49} - 3 q^{50} + 2 q^{51} - 34 q^{53} - 3 q^{54} - 3 q^{55} - q^{56} - 14 q^{57} + 12 q^{58} - 6 q^{59} + 30 q^{60} + 13 q^{61} + 2 q^{62} + 2 q^{63} + 18 q^{66} + 11 q^{67} + 13 q^{68} + 48 q^{70} + 12 q^{72} - 12 q^{73} - 15 q^{74} + 11 q^{75} - 21 q^{76} + 30 q^{77} + 6 q^{79} - 20 q^{80} - 3 q^{81} + 3 q^{82} - 24 q^{83} - 5 q^{84} + 19 q^{85} + 58 q^{86} - 2 q^{87} - 13 q^{88} + q^{89} - 2 q^{90} + 14 q^{92} + 16 q^{93} + 21 q^{95} + 44 q^{96} - 5 q^{97} - 29 q^{98} - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.17845 + 2.04113i 0.833289 + 1.44330i 0.895416 + 0.445230i \(0.146878\pi\)
−0.0621278 + 0.998068i \(0.519789\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −1.77748 + 3.07868i −0.888740 + 1.53934i
\(5\) −3.69202 −1.65112 −0.825561 0.564313i \(-0.809141\pi\)
−0.825561 + 0.564313i \(0.809141\pi\)
\(6\) −1.17845 + 2.04113i −0.481099 + 0.833289i
\(7\) −0.400969 + 0.694498i −0.151552 + 0.262496i −0.931798 0.362977i \(-0.881760\pi\)
0.780246 + 0.625473i \(0.215094\pi\)
\(8\) −3.66487 −1.29573
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −4.35086 7.53590i −1.37586 2.38306i
\(11\) −1.42543 2.46891i −0.429783 0.744405i 0.567071 0.823669i \(-0.308076\pi\)
−0.996854 + 0.0792636i \(0.974743\pi\)
\(12\) −3.55496 −1.02623
\(13\) 0 0
\(14\) −1.89008 −0.505146
\(15\) −1.84601 3.19738i −0.476638 0.825561i
\(16\) −0.763906 1.32312i −0.190976 0.330781i
\(17\) −1.46950 + 2.54525i −0.356406 + 0.617314i −0.987358 0.158509i \(-0.949331\pi\)
0.630951 + 0.775822i \(0.282665\pi\)
\(18\) −2.35690 −0.555526
\(19\) −1.22252 + 2.11747i −0.280466 + 0.485781i −0.971499 0.237042i \(-0.923822\pi\)
0.691034 + 0.722822i \(0.257156\pi\)
\(20\) 6.56249 11.3666i 1.46742 2.54164i
\(21\) −0.801938 −0.174997
\(22\) 3.35958 5.81897i 0.716266 1.24061i
\(23\) 3.89493 + 6.74621i 0.812149 + 1.40668i 0.911357 + 0.411616i \(0.135036\pi\)
−0.0992087 + 0.995067i \(0.531631\pi\)
\(24\) −1.83244 3.17387i −0.374045 0.647864i
\(25\) 8.63102 1.72620
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.42543 2.46891i −0.269380 0.466581i
\(29\) −1.92543 3.33494i −0.357543 0.619282i 0.630007 0.776590i \(-0.283052\pi\)
−0.987550 + 0.157307i \(0.949719\pi\)
\(30\) 4.35086 7.53590i 0.794354 1.37586i
\(31\) −2.34481 −0.421141 −0.210571 0.977579i \(-0.567532\pi\)
−0.210571 + 0.977579i \(0.567532\pi\)
\(32\) −1.86443 + 3.22929i −0.329588 + 0.570862i
\(33\) 1.42543 2.46891i 0.248135 0.429783i
\(34\) −6.92692 −1.18796
\(35\) 1.48039 2.56410i 0.250231 0.433413i
\(36\) −1.77748 3.07868i −0.296247 0.513114i
\(37\) 3.72252 + 6.44760i 0.611979 + 1.05998i 0.990907 + 0.134552i \(0.0429595\pi\)
−0.378928 + 0.925426i \(0.623707\pi\)
\(38\) −5.76271 −0.934835
\(39\) 0 0
\(40\) 13.5308 2.13941
\(41\) −0.425428 0.736862i −0.0664406 0.115079i 0.830892 0.556434i \(-0.187831\pi\)
−0.897332 + 0.441356i \(0.854498\pi\)
\(42\) −0.945042 1.63686i −0.145823 0.252573i
\(43\) 0.807979 1.39946i 0.123216 0.213416i −0.797818 0.602898i \(-0.794013\pi\)
0.921034 + 0.389482i \(0.127346\pi\)
\(44\) 10.1347 1.52786
\(45\) 1.84601 3.19738i 0.275187 0.476638i
\(46\) −9.17994 + 15.9001i −1.35351 + 2.34435i
\(47\) −2.44504 −0.356646 −0.178323 0.983972i \(-0.557067\pi\)
−0.178323 + 0.983972i \(0.557067\pi\)
\(48\) 0.763906 1.32312i 0.110260 0.190976i
\(49\) 3.17845 + 5.50523i 0.454064 + 0.786462i
\(50\) 10.1712 + 17.6171i 1.43843 + 2.49143i
\(51\) −2.93900 −0.411542
\(52\) 0 0
\(53\) −9.96077 −1.36822 −0.684109 0.729380i \(-0.739809\pi\)
−0.684109 + 0.729380i \(0.739809\pi\)
\(54\) −1.17845 2.04113i −0.160366 0.277763i
\(55\) 5.26271 + 9.11528i 0.709624 + 1.22910i
\(56\) 1.46950 2.54525i 0.196370 0.340123i
\(57\) −2.44504 −0.323854
\(58\) 4.53803 7.86010i 0.595873 1.03208i
\(59\) −2.69202 + 4.66272i −0.350471 + 0.607034i −0.986332 0.164770i \(-0.947312\pi\)
0.635861 + 0.771804i \(0.280645\pi\)
\(60\) 13.1250 1.69443
\(61\) 6.62833 11.4806i 0.848671 1.46994i −0.0337232 0.999431i \(-0.510736\pi\)
0.882394 0.470510i \(-0.155930\pi\)
\(62\) −2.76324 4.78607i −0.350932 0.607832i
\(63\) −0.400969 0.694498i −0.0505173 0.0874986i
\(64\) −11.8442 −1.48052
\(65\) 0 0
\(66\) 6.71917 0.827072
\(67\) 7.19687 + 12.4653i 0.879237 + 1.52288i 0.852180 + 0.523249i \(0.175280\pi\)
0.0270575 + 0.999634i \(0.491386\pi\)
\(68\) −5.22401 9.04826i −0.633505 1.09726i
\(69\) −3.89493 + 6.74621i −0.468894 + 0.812149i
\(70\) 6.97823 0.834058
\(71\) 4.06249 7.03644i 0.482129 0.835072i −0.517661 0.855586i \(-0.673197\pi\)
0.999790 + 0.0205142i \(0.00653033\pi\)
\(72\) 1.83244 3.17387i 0.215955 0.374045i
\(73\) 11.8877 1.39135 0.695674 0.718357i \(-0.255106\pi\)
0.695674 + 0.718357i \(0.255106\pi\)
\(74\) −8.77359 + 15.1963i −1.01991 + 1.76654i
\(75\) 4.31551 + 7.47468i 0.498312 + 0.863102i
\(76\) −4.34601 7.52751i −0.498522 0.863465i
\(77\) 2.28621 0.260538
\(78\) 0 0
\(79\) 5.40581 0.608202 0.304101 0.952640i \(-0.401644\pi\)
0.304101 + 0.952640i \(0.401644\pi\)
\(80\) 2.82036 + 4.88500i 0.315325 + 0.546160i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00269 1.73671i 0.110728 0.191787i
\(83\) −7.04892 −0.773719 −0.386860 0.922139i \(-0.626440\pi\)
−0.386860 + 0.922139i \(0.626440\pi\)
\(84\) 1.42543 2.46891i 0.155527 0.269380i
\(85\) 5.42543 9.39712i 0.588470 1.01926i
\(86\) 3.80864 0.410696
\(87\) 1.92543 3.33494i 0.206427 0.357543i
\(88\) 5.22401 + 9.04826i 0.556882 + 0.964547i
\(89\) 0.565843 + 0.980069i 0.0599793 + 0.103887i 0.894456 0.447156i \(-0.147563\pi\)
−0.834477 + 0.551043i \(0.814230\pi\)
\(90\) 8.70171 0.917241
\(91\) 0 0
\(92\) −27.6926 −2.88715
\(93\) −1.17241 2.03067i −0.121573 0.210571i
\(94\) −2.88135 4.99065i −0.297189 0.514746i
\(95\) 4.51357 7.81774i 0.463083 0.802083i
\(96\) −3.72886 −0.380575
\(97\) −2.97219 + 5.14798i −0.301780 + 0.522698i −0.976539 0.215340i \(-0.930914\pi\)
0.674759 + 0.738038i \(0.264247\pi\)
\(98\) −7.49127 + 12.9753i −0.756733 + 1.31070i
\(99\) 2.85086 0.286522
\(100\) −15.3415 + 26.5722i −1.53415 + 2.65722i
\(101\) −2.31282 4.00593i −0.230134 0.398605i 0.727713 0.685882i \(-0.240583\pi\)
−0.957848 + 0.287277i \(0.907250\pi\)
\(102\) −3.46346 5.99889i −0.342934 0.593978i
\(103\) 1.20775 0.119003 0.0595016 0.998228i \(-0.481049\pi\)
0.0595016 + 0.998228i \(0.481049\pi\)
\(104\) 0 0
\(105\) 2.96077 0.288942
\(106\) −11.7383 20.3312i −1.14012 1.97475i
\(107\) 4.76055 + 8.24552i 0.460220 + 0.797124i 0.998972 0.0453402i \(-0.0144372\pi\)
−0.538752 + 0.842465i \(0.681104\pi\)
\(108\) 1.77748 3.07868i 0.171038 0.296247i
\(109\) 1.78448 0.170922 0.0854611 0.996342i \(-0.472764\pi\)
0.0854611 + 0.996342i \(0.472764\pi\)
\(110\) −12.4037 + 21.4838i −1.18264 + 2.04840i
\(111\) −3.72252 + 6.44760i −0.353326 + 0.611979i
\(112\) 1.22521 0.115771
\(113\) −2.47554 + 4.28776i −0.232879 + 0.403359i −0.958654 0.284573i \(-0.908148\pi\)
0.725775 + 0.687932i \(0.241481\pi\)
\(114\) −2.88135 4.99065i −0.269864 0.467417i
\(115\) −14.3802 24.9072i −1.34096 2.32261i
\(116\) 13.6896 1.27105
\(117\) 0 0
\(118\) −12.6896 −1.16817
\(119\) −1.17845 2.04113i −0.108028 0.187110i
\(120\) 6.76540 + 11.7180i 0.617593 + 1.06970i
\(121\) 1.43631 2.48777i 0.130574 0.226161i
\(122\) 31.2446 2.82875
\(123\) 0.425428 0.736862i 0.0383595 0.0664406i
\(124\) 4.16786 7.21894i 0.374285 0.648280i
\(125\) −13.4058 −1.19905
\(126\) 0.945042 1.63686i 0.0841910 0.145823i
\(127\) −2.83513 4.91058i −0.251577 0.435744i 0.712383 0.701791i \(-0.247616\pi\)
−0.963960 + 0.266047i \(0.914282\pi\)
\(128\) −10.2289 17.7169i −0.904112 1.56597i
\(129\) 1.61596 0.142277
\(130\) 0 0
\(131\) 18.2228 1.59213 0.796067 0.605208i \(-0.206910\pi\)
0.796067 + 0.605208i \(0.206910\pi\)
\(132\) 5.06734 + 8.77688i 0.441055 + 0.763930i
\(133\) −0.980386 1.69808i −0.0850102 0.147242i
\(134\) −16.9623 + 29.3795i −1.46532 + 2.53800i
\(135\) 3.69202 0.317759
\(136\) 5.38553 9.32802i 0.461806 0.799871i
\(137\) 4.72521 8.18430i 0.403702 0.699232i −0.590468 0.807061i \(-0.701057\pi\)
0.994169 + 0.107829i \(0.0343900\pi\)
\(138\) −18.3599 −1.56290
\(139\) −2.00753 + 3.47715i −0.170277 + 0.294928i −0.938517 0.345234i \(-0.887799\pi\)
0.768240 + 0.640162i \(0.221133\pi\)
\(140\) 5.26271 + 9.11528i 0.444780 + 0.770382i
\(141\) −1.22252 2.11747i −0.102955 0.178323i
\(142\) 19.1497 1.60701
\(143\) 0 0
\(144\) 1.52781 0.127318
\(145\) 7.10872 + 12.3127i 0.590347 + 1.02251i
\(146\) 14.0090 + 24.2643i 1.15940 + 2.00813i
\(147\) −3.17845 + 5.50523i −0.262154 + 0.454064i
\(148\) −26.4668 −2.17556
\(149\) 9.70291 16.8059i 0.794893 1.37680i −0.128014 0.991772i \(-0.540860\pi\)
0.922907 0.385023i \(-0.125806\pi\)
\(150\) −10.1712 + 17.6171i −0.830476 + 1.43843i
\(151\) 12.3623 1.00603 0.503014 0.864278i \(-0.332225\pi\)
0.503014 + 0.864278i \(0.332225\pi\)
\(152\) 4.48039 7.76026i 0.363407 0.629440i
\(153\) −1.46950 2.54525i −0.118802 0.205771i
\(154\) 2.69418 + 4.66645i 0.217103 + 0.376033i
\(155\) 8.65710 0.695355
\(156\) 0 0
\(157\) −18.6775 −1.49063 −0.745315 0.666712i \(-0.767701\pi\)
−0.745315 + 0.666712i \(0.767701\pi\)
\(158\) 6.37047 + 11.0340i 0.506807 + 0.877816i
\(159\) −4.98039 8.62628i −0.394970 0.684109i
\(160\) 6.88351 11.9226i 0.544189 0.942563i
\(161\) −6.24698 −0.492331
\(162\) 1.17845 2.04113i 0.0925876 0.160366i
\(163\) 6.16972 10.6863i 0.483250 0.837013i −0.516565 0.856248i \(-0.672790\pi\)
0.999815 + 0.0192348i \(0.00612301\pi\)
\(164\) 3.02475 0.236194
\(165\) −5.26271 + 9.11528i −0.409701 + 0.709624i
\(166\) −8.30678 14.3878i −0.644731 1.11671i
\(167\) 5.74698 + 9.95406i 0.444715 + 0.770268i 0.998032 0.0627020i \(-0.0199718\pi\)
−0.553318 + 0.832970i \(0.686638\pi\)
\(168\) 2.93900 0.226749
\(169\) 0 0
\(170\) 25.5743 1.96146
\(171\) −1.22252 2.11747i −0.0934885 0.161927i
\(172\) 2.87233 + 4.97502i 0.219013 + 0.379342i
\(173\) −6.05711 + 10.4912i −0.460514 + 0.797633i −0.998987 0.0450096i \(-0.985668\pi\)
0.538473 + 0.842643i \(0.319002\pi\)
\(174\) 9.07606 0.688055
\(175\) −3.46077 + 5.99423i −0.261610 + 0.453121i
\(176\) −2.17778 + 3.77203i −0.164157 + 0.284328i
\(177\) −5.38404 −0.404689
\(178\) −1.33363 + 2.30992i −0.0999601 + 0.173136i
\(179\) 0.269282 + 0.466411i 0.0201271 + 0.0348612i 0.875914 0.482468i \(-0.160260\pi\)
−0.855786 + 0.517329i \(0.826926\pi\)
\(180\) 6.56249 + 11.3666i 0.489139 + 0.847214i
\(181\) −23.2838 −1.73067 −0.865336 0.501192i \(-0.832895\pi\)
−0.865336 + 0.501192i \(0.832895\pi\)
\(182\) 0 0
\(183\) 13.2567 0.979961
\(184\) −14.2744 24.7240i −1.05232 1.82268i
\(185\) −13.7436 23.8047i −1.01045 1.75015i
\(186\) 2.76324 4.78607i 0.202611 0.350932i
\(187\) 8.37867 0.612709
\(188\) 4.34601 7.52751i 0.316965 0.549000i
\(189\) 0.400969 0.694498i 0.0291662 0.0505173i
\(190\) 21.2760 1.54353
\(191\) −8.38285 + 14.5195i −0.606561 + 1.05060i 0.385241 + 0.922816i \(0.374118\pi\)
−0.991803 + 0.127779i \(0.959215\pi\)
\(192\) −5.92208 10.2573i −0.427389 0.740259i
\(193\) 12.8720 + 22.2949i 0.926544 + 1.60482i 0.789059 + 0.614318i \(0.210569\pi\)
0.137485 + 0.990504i \(0.456098\pi\)
\(194\) −14.0103 −1.00588
\(195\) 0 0
\(196\) −22.5985 −1.61418
\(197\) 10.7104 + 18.5510i 0.763087 + 1.32171i 0.941252 + 0.337705i \(0.109651\pi\)
−0.178165 + 0.984001i \(0.557016\pi\)
\(198\) 3.35958 + 5.81897i 0.238755 + 0.413536i
\(199\) −1.76391 + 3.05517i −0.125040 + 0.216576i −0.921749 0.387788i \(-0.873239\pi\)
0.796709 + 0.604364i \(0.206573\pi\)
\(200\) −31.6316 −2.23669
\(201\) −7.19687 + 12.4653i −0.507628 + 0.879237i
\(202\) 5.45108 9.44155i 0.383537 0.664305i
\(203\) 3.08815 0.216745
\(204\) 5.22401 9.04826i 0.365754 0.633505i
\(205\) 1.57069 + 2.72051i 0.109702 + 0.190009i
\(206\) 1.42327 + 2.46518i 0.0991640 + 0.171757i
\(207\) −7.78986 −0.541432
\(208\) 0 0
\(209\) 6.97046 0.482157
\(210\) 3.48911 + 6.04332i 0.240772 + 0.417029i
\(211\) −0.607760 1.05267i −0.0418399 0.0724689i 0.844347 0.535797i \(-0.179989\pi\)
−0.886187 + 0.463328i \(0.846655\pi\)
\(212\) 17.7051 30.6661i 1.21599 2.10615i
\(213\) 8.12498 0.556715
\(214\) −11.2201 + 19.4338i −0.766992 + 1.32847i
\(215\) −2.98307 + 5.16684i −0.203444 + 0.352375i
\(216\) 3.66487 0.249363
\(217\) 0.940198 1.62847i 0.0638248 0.110548i
\(218\) 2.10292 + 3.64236i 0.142427 + 0.246692i
\(219\) 5.94385 + 10.2950i 0.401648 + 0.695674i
\(220\) −37.4174 −2.52268
\(221\) 0 0
\(222\) −17.5472 −1.17769
\(223\) −8.69418 15.0588i −0.582205 1.00841i −0.995218 0.0976835i \(-0.968857\pi\)
0.413012 0.910725i \(-0.364477\pi\)
\(224\) −1.49516 2.58969i −0.0998993 0.173031i
\(225\) −4.31551 + 7.47468i −0.287701 + 0.498312i
\(226\) −11.6692 −0.776223
\(227\) 8.70775 15.0823i 0.577954 1.00105i −0.417760 0.908557i \(-0.637185\pi\)
0.995714 0.0924878i \(-0.0294819\pi\)
\(228\) 4.34601 7.52751i 0.287822 0.498522i
\(229\) −18.7603 −1.23972 −0.619858 0.784714i \(-0.712810\pi\)
−0.619858 + 0.784714i \(0.712810\pi\)
\(230\) 33.8925 58.7036i 2.23481 3.87080i
\(231\) 1.14310 + 1.97991i 0.0752107 + 0.130269i
\(232\) 7.05645 + 12.2221i 0.463279 + 0.802422i
\(233\) 3.95108 0.258844 0.129422 0.991590i \(-0.458688\pi\)
0.129422 + 0.991590i \(0.458688\pi\)
\(234\) 0 0
\(235\) 9.02715 0.588866
\(236\) −9.57002 16.5758i −0.622955 1.07899i
\(237\) 2.70291 + 4.68157i 0.175573 + 0.304101i
\(238\) 2.77748 4.81073i 0.180037 0.311834i
\(239\) −0.818331 −0.0529334 −0.0264667 0.999650i \(-0.508426\pi\)
−0.0264667 + 0.999650i \(0.508426\pi\)
\(240\) −2.82036 + 4.88500i −0.182053 + 0.315325i
\(241\) 3.01626 5.22432i 0.194295 0.336528i −0.752375 0.658736i \(-0.771092\pi\)
0.946669 + 0.322208i \(0.104425\pi\)
\(242\) 6.77048 0.435223
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 23.5635 + 40.8131i 1.50850 + 2.61279i
\(245\) −11.7349 20.3254i −0.749715 1.29854i
\(246\) 2.00538 0.127858
\(247\) 0 0
\(248\) 8.59345 0.545685
\(249\) −3.52446 6.10454i −0.223353 0.386860i
\(250\) −15.7981 27.3630i −0.999157 1.73059i
\(251\) 13.4400 23.2787i 0.848323 1.46934i −0.0343812 0.999409i \(-0.510946\pi\)
0.882704 0.469929i \(-0.155721\pi\)
\(252\) 2.85086 0.179587
\(253\) 11.1039 19.2325i 0.698095 1.20914i
\(254\) 6.68210 11.5737i 0.419272 0.726200i
\(255\) 10.8509 0.679507
\(256\) 12.2642 21.2422i 0.766513 1.32764i
\(257\) 4.52661 + 7.84033i 0.282362 + 0.489066i 0.971966 0.235121i \(-0.0755486\pi\)
−0.689604 + 0.724187i \(0.742215\pi\)
\(258\) 1.90432 + 3.29838i 0.118558 + 0.205348i
\(259\) −5.97046 −0.370986
\(260\) 0 0
\(261\) 3.85086 0.238362
\(262\) 21.4746 + 37.1952i 1.32671 + 2.29793i
\(263\) −11.5755 20.0494i −0.713778 1.23630i −0.963429 0.267964i \(-0.913649\pi\)
0.249651 0.968336i \(-0.419684\pi\)
\(264\) −5.22401 + 9.04826i −0.321516 + 0.556882i
\(265\) 36.7754 2.25909
\(266\) 2.31067 4.00219i 0.141676 0.245390i
\(267\) −0.565843 + 0.980069i −0.0346290 + 0.0599793i
\(268\) −51.1691 −3.12565
\(269\) 1.21044 2.09654i 0.0738018 0.127828i −0.826763 0.562551i \(-0.809820\pi\)
0.900565 + 0.434722i \(0.143153\pi\)
\(270\) 4.35086 + 7.53590i 0.264785 + 0.458620i
\(271\) −10.7225 18.5720i −0.651347 1.12817i −0.982796 0.184693i \(-0.940871\pi\)
0.331450 0.943473i \(-0.392462\pi\)
\(272\) 4.49024 0.272261
\(273\) 0 0
\(274\) 22.2737 1.34560
\(275\) −12.3029 21.3092i −0.741893 1.28500i
\(276\) −13.8463 23.9825i −0.833450 1.44358i
\(277\) 7.40366 12.8235i 0.444843 0.770490i −0.553199 0.833049i \(-0.686593\pi\)
0.998041 + 0.0625593i \(0.0199263\pi\)
\(278\) −9.46309 −0.567558
\(279\) 1.17241 2.03067i 0.0701902 0.121573i
\(280\) −5.42543 + 9.39712i −0.324231 + 0.561585i
\(281\) −14.5036 −0.865215 −0.432608 0.901582i \(-0.642406\pi\)
−0.432608 + 0.901582i \(0.642406\pi\)
\(282\) 2.88135 4.99065i 0.171582 0.297189i
\(283\) −12.8361 22.2328i −0.763026 1.32160i −0.941284 0.337616i \(-0.890379\pi\)
0.178258 0.983984i \(-0.442954\pi\)
\(284\) 14.4420 + 25.0143i 0.856974 + 1.48432i
\(285\) 9.02715 0.534722
\(286\) 0 0
\(287\) 0.682333 0.0402768
\(288\) −1.86443 3.22929i −0.109863 0.190287i
\(289\) 4.18114 + 7.24194i 0.245949 + 0.425997i
\(290\) −16.7545 + 29.0197i −0.983859 + 1.70409i
\(291\) −5.94438 −0.348466
\(292\) −21.1301 + 36.5984i −1.23655 + 2.14176i
\(293\) −13.2615 + 22.9696i −0.774746 + 1.34190i 0.160191 + 0.987086i \(0.448789\pi\)
−0.934937 + 0.354813i \(0.884544\pi\)
\(294\) −14.9825 −0.873800
\(295\) 9.93900 17.2149i 0.578671 1.00229i
\(296\) −13.6426 23.6296i −0.792958 1.37344i
\(297\) 1.42543 + 2.46891i 0.0827117 + 0.143261i
\(298\) 45.7375 2.64950
\(299\) 0 0
\(300\) −30.6829 −1.77148
\(301\) 0.647948 + 1.12228i 0.0373471 + 0.0646871i
\(302\) 14.5683 + 25.2330i 0.838311 + 1.45200i
\(303\) 2.31282 4.00593i 0.132868 0.230134i
\(304\) 3.73556 0.214249
\(305\) −24.4720 + 42.3867i −1.40126 + 2.42705i
\(306\) 3.46346 5.99889i 0.197993 0.342934i
\(307\) 8.24698 0.470680 0.235340 0.971913i \(-0.424380\pi\)
0.235340 + 0.971913i \(0.424380\pi\)
\(308\) −4.06369 + 7.03851i −0.231550 + 0.401056i
\(309\) 0.603875 + 1.04594i 0.0343533 + 0.0595016i
\(310\) 10.2019 + 17.6703i 0.579432 + 1.00361i
\(311\) −14.4179 −0.817564 −0.408782 0.912632i \(-0.634046\pi\)
−0.408782 + 0.912632i \(0.634046\pi\)
\(312\) 0 0
\(313\) 14.2338 0.804544 0.402272 0.915520i \(-0.368221\pi\)
0.402272 + 0.915520i \(0.368221\pi\)
\(314\) −22.0105 38.1233i −1.24213 2.15142i
\(315\) 1.48039 + 2.56410i 0.0834103 + 0.144471i
\(316\) −9.60872 + 16.6428i −0.540533 + 0.936230i
\(317\) 6.84415 0.384406 0.192203 0.981355i \(-0.438437\pi\)
0.192203 + 0.981355i \(0.438437\pi\)
\(318\) 11.7383 20.3312i 0.658248 1.14012i
\(319\) −5.48911 + 9.50743i −0.307331 + 0.532314i
\(320\) 43.7289 2.44452
\(321\) −4.76055 + 8.24552i −0.265708 + 0.460220i
\(322\) −7.36174 12.7509i −0.410254 0.710580i
\(323\) −3.59299 6.22324i −0.199919 0.346270i
\(324\) 3.55496 0.197498
\(325\) 0 0
\(326\) 29.0828 1.61075
\(327\) 0.892240 + 1.54540i 0.0493410 + 0.0854611i
\(328\) 1.55914 + 2.70051i 0.0860890 + 0.149111i
\(329\) 0.980386 1.69808i 0.0540504 0.0936181i
\(330\) −24.8073 −1.36560
\(331\) 4.72132 8.17757i 0.259507 0.449480i −0.706603 0.707611i \(-0.749773\pi\)
0.966110 + 0.258130i \(0.0831065\pi\)
\(332\) 12.5293 21.7014i 0.687635 1.19102i
\(333\) −7.44504 −0.407986
\(334\) −13.5450 + 23.4607i −0.741151 + 1.28371i
\(335\) −26.5710 46.0223i −1.45173 2.51447i
\(336\) 0.612605 + 1.06106i 0.0334203 + 0.0578857i
\(337\) 2.64310 0.143979 0.0719895 0.997405i \(-0.477065\pi\)
0.0719895 + 0.997405i \(0.477065\pi\)
\(338\) 0 0
\(339\) −4.95108 −0.268906
\(340\) 19.2872 + 33.4064i 1.04599 + 1.81171i
\(341\) 3.34236 + 5.78914i 0.180999 + 0.313500i
\(342\) 2.88135 4.99065i 0.155806 0.269864i
\(343\) −10.7114 −0.578361
\(344\) −2.96114 + 5.12884i −0.159654 + 0.276529i
\(345\) 14.3802 24.9072i 0.774202 1.34096i
\(346\) −28.5520 −1.53496
\(347\) 5.07942 8.79781i 0.272677 0.472291i −0.696869 0.717198i \(-0.745424\pi\)
0.969547 + 0.244907i \(0.0787575\pi\)
\(348\) 6.84481 + 11.8556i 0.366921 + 0.635525i
\(349\) 5.21983 + 9.04102i 0.279411 + 0.483954i 0.971239 0.238109i \(-0.0765274\pi\)
−0.691827 + 0.722063i \(0.743194\pi\)
\(350\) −16.3134 −0.871986
\(351\) 0 0
\(352\) 10.6304 0.566604
\(353\) 9.14556 + 15.8406i 0.486769 + 0.843108i 0.999884 0.0152113i \(-0.00484208\pi\)
−0.513115 + 0.858320i \(0.671509\pi\)
\(354\) −6.34481 10.9895i −0.337223 0.584087i
\(355\) −14.9988 + 25.9787i −0.796054 + 1.37881i
\(356\) −4.02310 −0.213224
\(357\) 1.17845 2.04113i 0.0623701 0.108028i
\(358\) −0.634670 + 1.09928i −0.0335434 + 0.0580988i
\(359\) 15.2731 0.806081 0.403041 0.915182i \(-0.367953\pi\)
0.403041 + 0.915182i \(0.367953\pi\)
\(360\) −6.76540 + 11.7180i −0.356568 + 0.617593i
\(361\) 6.51089 + 11.2772i 0.342678 + 0.593536i
\(362\) −27.4388 47.5253i −1.44215 2.49788i
\(363\) 2.87263 0.150774
\(364\) 0 0
\(365\) −43.8896 −2.29729
\(366\) 15.6223 + 27.0586i 0.816590 + 1.41438i
\(367\) 11.1359 + 19.2879i 0.581288 + 1.00682i 0.995327 + 0.0965606i \(0.0307842\pi\)
−0.414040 + 0.910259i \(0.635882\pi\)
\(368\) 5.95071 10.3069i 0.310202 0.537286i
\(369\) 0.850855 0.0442937
\(370\) 32.3923 56.1051i 1.68400 2.91677i
\(371\) 3.99396 6.91774i 0.207356 0.359151i
\(372\) 8.33572 0.432187
\(373\) −2.06315 + 3.57349i −0.106826 + 0.185028i −0.914483 0.404625i \(-0.867402\pi\)
0.807657 + 0.589653i \(0.200735\pi\)
\(374\) 9.87382 + 17.1020i 0.510563 + 0.884321i
\(375\) −6.70291 11.6098i −0.346137 0.599526i
\(376\) 8.96077 0.462116
\(377\) 0 0
\(378\) 1.89008 0.0972154
\(379\) −5.35354 9.27261i −0.274993 0.476302i 0.695140 0.718874i \(-0.255342\pi\)
−0.970133 + 0.242572i \(0.922009\pi\)
\(380\) 16.0456 + 27.7917i 0.823120 + 1.42569i
\(381\) 2.83513 4.91058i 0.145248 0.251577i
\(382\) −39.5150 −2.02176
\(383\) 3.26324 5.65210i 0.166744 0.288809i −0.770529 0.637405i \(-0.780008\pi\)
0.937273 + 0.348596i \(0.113341\pi\)
\(384\) 10.2289 17.7169i 0.521989 0.904112i
\(385\) −8.44073 −0.430179
\(386\) −30.3379 + 52.5467i −1.54416 + 2.67456i
\(387\) 0.807979 + 1.39946i 0.0410719 + 0.0711385i
\(388\) −10.5660 18.3009i −0.536408 0.929085i
\(389\) −11.7922 −0.597891 −0.298945 0.954270i \(-0.596635\pi\)
−0.298945 + 0.954270i \(0.596635\pi\)
\(390\) 0 0
\(391\) −22.8944 −1.15782
\(392\) −11.6486 20.1760i −0.588344 1.01904i
\(393\) 9.11141 + 15.7814i 0.459610 + 0.796067i
\(394\) −25.2434 + 43.7228i −1.27174 + 2.20272i
\(395\) −19.9584 −1.00422
\(396\) −5.06734 + 8.77688i −0.254643 + 0.441055i
\(397\) −6.27144 + 10.8624i −0.314754 + 0.545171i −0.979385 0.202001i \(-0.935256\pi\)
0.664631 + 0.747172i \(0.268589\pi\)
\(398\) −8.31468 −0.416777
\(399\) 0.980386 1.69808i 0.0490807 0.0850102i
\(400\) −6.59329 11.4199i −0.329664 0.570995i
\(401\) 8.93512 + 15.4761i 0.446198 + 0.772838i 0.998135 0.0610479i \(-0.0194442\pi\)
−0.551936 + 0.833886i \(0.686111\pi\)
\(402\) −33.9245 −1.69200
\(403\) 0 0
\(404\) 16.4440 0.818118
\(405\) 1.84601 + 3.19738i 0.0917290 + 0.158879i
\(406\) 3.63922 + 6.30331i 0.180611 + 0.312828i
\(407\) 10.6124 18.3812i 0.526036 0.911120i
\(408\) 10.7711 0.533247
\(409\) −13.9559 + 24.1724i −0.690076 + 1.19525i 0.281736 + 0.959492i \(0.409090\pi\)
−0.971812 + 0.235755i \(0.924244\pi\)
\(410\) −3.70195 + 6.41196i −0.182826 + 0.316664i
\(411\) 9.45042 0.466155
\(412\) −2.14675 + 3.71828i −0.105763 + 0.183187i
\(413\) −2.15883 3.73921i −0.106229 0.183994i
\(414\) −9.17994 15.9001i −0.451169 0.781448i
\(415\) 26.0248 1.27750
\(416\) 0 0
\(417\) −4.01507 −0.196619
\(418\) 8.21432 + 14.2276i 0.401776 + 0.695896i
\(419\) 8.20171 + 14.2058i 0.400680 + 0.693998i 0.993808 0.111110i \(-0.0354407\pi\)
−0.593128 + 0.805108i \(0.702107\pi\)
\(420\) −5.26271 + 9.11528i −0.256794 + 0.444780i
\(421\) 3.03684 0.148006 0.0740032 0.997258i \(-0.476423\pi\)
0.0740032 + 0.997258i \(0.476423\pi\)
\(422\) 1.43243 2.48104i 0.0697295 0.120775i
\(423\) 1.22252 2.11747i 0.0594410 0.102955i
\(424\) 36.5050 1.77284
\(425\) −12.6833 + 21.9681i −0.615230 + 1.06561i
\(426\) 9.57487 + 16.5842i 0.463904 + 0.803505i
\(427\) 5.31551 + 9.20674i 0.257236 + 0.445545i
\(428\) −33.8471 −1.63606
\(429\) 0 0
\(430\) −14.0616 −0.678110
\(431\) −1.66905 2.89089i −0.0803955 0.139249i 0.823024 0.568006i \(-0.192285\pi\)
−0.903420 + 0.428757i \(0.858952\pi\)
\(432\) 0.763906 + 1.32312i 0.0367534 + 0.0636588i
\(433\) −5.95138 + 10.3081i −0.286005 + 0.495375i −0.972852 0.231426i \(-0.925661\pi\)
0.686847 + 0.726802i \(0.258994\pi\)
\(434\) 4.43190 0.212738
\(435\) −7.10872 + 12.3127i −0.340837 + 0.590347i
\(436\) −3.17187 + 5.49385i −0.151905 + 0.263108i
\(437\) −19.0465 −0.911119
\(438\) −14.0090 + 24.2643i −0.669377 + 1.15940i
\(439\) −1.85905 3.21997i −0.0887277 0.153681i 0.818246 0.574868i \(-0.194947\pi\)
−0.906974 + 0.421188i \(0.861613\pi\)
\(440\) −19.2872 33.4064i −0.919480 1.59259i
\(441\) −6.35690 −0.302709
\(442\) 0 0
\(443\) 1.45712 0.0692300 0.0346150 0.999401i \(-0.488979\pi\)
0.0346150 + 0.999401i \(0.488979\pi\)
\(444\) −13.2334 22.9209i −0.628030 1.08778i
\(445\) −2.08911 3.61844i −0.0990331 0.171530i
\(446\) 20.4913 35.4919i 0.970290 1.68059i
\(447\) 19.4058 0.917863
\(448\) 4.74914 8.22574i 0.224376 0.388630i
\(449\) −6.06369 + 10.5026i −0.286163 + 0.495649i −0.972891 0.231266i \(-0.925713\pi\)
0.686727 + 0.726915i \(0.259047\pi\)
\(450\) −20.3424 −0.958951
\(451\) −1.21283 + 2.10069i −0.0571100 + 0.0989175i
\(452\) −8.80045 15.2428i −0.413938 0.716962i
\(453\) 6.18114 + 10.7060i 0.290415 + 0.503014i
\(454\) 41.0465 1.92641
\(455\) 0 0
\(456\) 8.96077 0.419627
\(457\) −1.72401 2.98608i −0.0806459 0.139683i 0.822882 0.568213i \(-0.192365\pi\)
−0.903528 + 0.428530i \(0.859032\pi\)
\(458\) −22.1081 38.2923i −1.03304 1.78928i
\(459\) 1.46950 2.54525i 0.0685904 0.118802i
\(460\) 102.242 4.76704
\(461\) −3.37800 + 5.85087i −0.157329 + 0.272502i −0.933905 0.357522i \(-0.883622\pi\)
0.776575 + 0.630024i \(0.216955\pi\)
\(462\) −2.69418 + 4.66645i −0.125344 + 0.217103i
\(463\) 7.45175 0.346312 0.173156 0.984894i \(-0.444604\pi\)
0.173156 + 0.984894i \(0.444604\pi\)
\(464\) −2.94169 + 5.09516i −0.136565 + 0.236537i
\(465\) 4.32855 + 7.49727i 0.200732 + 0.347678i
\(466\) 4.65615 + 8.06468i 0.215692 + 0.373589i
\(467\) 32.6098 1.50900 0.754502 0.656298i \(-0.227879\pi\)
0.754502 + 0.656298i \(0.227879\pi\)
\(468\) 0 0
\(469\) −11.5429 −0.533001
\(470\) 10.6380 + 18.4256i 0.490695 + 0.849909i
\(471\) −9.33877 16.1752i −0.430308 0.745315i
\(472\) 9.86592 17.0883i 0.454116 0.786552i
\(473\) −4.60686 −0.211824
\(474\) −6.37047 + 11.0340i −0.292605 + 0.506807i
\(475\) −10.5516 + 18.2759i −0.484141 + 0.838557i
\(476\) 8.37867 0.384036
\(477\) 4.98039 8.62628i 0.228036 0.394970i
\(478\) −0.964361 1.67032i −0.0441088 0.0763987i
\(479\) 1.41454 + 2.45006i 0.0646321 + 0.111946i 0.896531 0.442982i \(-0.146079\pi\)
−0.831899 + 0.554928i \(0.812746\pi\)
\(480\) 13.7670 0.628376
\(481\) 0 0
\(482\) 14.2180 0.647614
\(483\) −3.12349 5.41004i −0.142124 0.246165i
\(484\) 5.10603 + 8.84391i 0.232092 + 0.401996i
\(485\) 10.9734 19.0065i 0.498276 0.863039i
\(486\) 2.35690 0.106911
\(487\) −20.6468 + 35.7612i −0.935594 + 1.62050i −0.162022 + 0.986787i \(0.551801\pi\)
−0.773572 + 0.633709i \(0.781532\pi\)
\(488\) −24.2920 + 42.0750i −1.09965 + 1.90465i
\(489\) 12.3394 0.558009
\(490\) 27.6579 47.9049i 1.24946 2.16412i
\(491\) 17.3349 + 30.0249i 0.782313 + 1.35501i 0.930591 + 0.366060i \(0.119293\pi\)
−0.148279 + 0.988946i \(0.547373\pi\)
\(492\) 1.51238 + 2.61951i 0.0681832 + 0.118097i
\(493\) 11.3177 0.509722
\(494\) 0 0
\(495\) −10.5254 −0.473082
\(496\) 1.79122 + 3.10248i 0.0804280 + 0.139305i
\(497\) 3.25786 + 5.64279i 0.146135 + 0.253114i
\(498\) 8.30678 14.3878i 0.372236 0.644731i
\(499\) −17.9409 −0.803146 −0.401573 0.915827i \(-0.631536\pi\)
−0.401573 + 0.915827i \(0.631536\pi\)
\(500\) 23.8286 41.2723i 1.06565 1.84575i
\(501\) −5.74698 + 9.95406i −0.256756 + 0.444715i
\(502\) 63.3532 2.82759
\(503\) 13.0906 22.6736i 0.583681 1.01096i −0.411358 0.911474i \(-0.634945\pi\)
0.995038 0.0994909i \(-0.0317214\pi\)
\(504\) 1.46950 + 2.54525i 0.0654568 + 0.113374i
\(505\) 8.53899 + 14.7900i 0.379980 + 0.658145i
\(506\) 52.3414 2.32686
\(507\) 0 0
\(508\) 20.1575 0.894345
\(509\) −2.75302 4.76837i −0.122025 0.211354i 0.798541 0.601941i \(-0.205606\pi\)
−0.920566 + 0.390586i \(0.872272\pi\)
\(510\) 12.7872 + 22.1480i 0.566225 + 0.980731i
\(511\) −4.76659 + 8.25598i −0.210862 + 0.365223i
\(512\) 16.8955 0.746681
\(513\) 1.22252 2.11747i 0.0539756 0.0934885i
\(514\) −10.6688 + 18.4788i −0.470579 + 0.815066i
\(515\) −4.45904 −0.196489
\(516\) −2.87233 + 4.97502i −0.126447 + 0.219013i
\(517\) 3.48523 + 6.03660i 0.153280 + 0.265489i
\(518\) −7.03588 12.1865i −0.309139 0.535444i
\(519\) −12.1142 −0.531756
\(520\) 0 0
\(521\) −26.7211 −1.17067 −0.585336 0.810791i \(-0.699037\pi\)
−0.585336 + 0.810791i \(0.699037\pi\)
\(522\) 4.53803 + 7.86010i 0.198624 + 0.344027i
\(523\) −18.2615 31.6299i −0.798520 1.38308i −0.920580 0.390555i \(-0.872283\pi\)
0.122060 0.992523i \(-0.461050\pi\)
\(524\) −32.3907 + 56.1023i −1.41499 + 2.45084i
\(525\) −6.92154 −0.302081
\(526\) 27.2823 47.2544i 1.18957 2.06039i
\(527\) 3.44571 5.96814i 0.150097 0.259976i
\(528\) −4.35557 −0.189552
\(529\) −18.8409 + 32.6334i −0.819171 + 1.41885i
\(530\) 43.3379 + 75.0634i 1.88248 + 3.26055i
\(531\) −2.69202 4.66272i −0.116824 0.202345i
\(532\) 6.97046 0.302208
\(533\) 0 0
\(534\) −2.66727 −0.115424
\(535\) −17.5761 30.4426i −0.759880 1.31615i
\(536\) −26.3756 45.6839i −1.13925 1.97324i
\(537\) −0.269282 + 0.466411i −0.0116204 + 0.0201271i
\(538\) 5.70576 0.245993
\(539\) 9.06129 15.6946i 0.390298 0.676015i
\(540\) −6.56249 + 11.3666i −0.282405 + 0.489139i
\(541\) −18.4655 −0.793893 −0.396947 0.917842i \(-0.629930\pi\)
−0.396947 + 0.917842i \(0.629930\pi\)
\(542\) 25.2719 43.7722i 1.08552 1.88018i
\(543\) −11.6419 20.1644i −0.499602 0.865336i
\(544\) −5.47956 9.49087i −0.234934 0.406918i
\(545\) −6.58834 −0.282213
\(546\) 0 0
\(547\) 39.8471 1.70374 0.851870 0.523753i \(-0.175468\pi\)
0.851870 + 0.523753i \(0.175468\pi\)
\(548\) 16.7979 + 29.0949i 0.717572 + 1.24287i
\(549\) 6.62833 + 11.4806i 0.282890 + 0.489981i
\(550\) 28.9966 50.2237i 1.23642 2.14154i
\(551\) 9.41550 0.401114
\(552\) 14.2744 24.7240i 0.607560 1.05232i
\(553\) −2.16756 + 3.75433i −0.0921741 + 0.159650i
\(554\) 34.8993 1.48273
\(555\) 13.7436 23.8047i 0.583384 1.01045i
\(556\) −7.13669 12.3611i −0.302663 0.524228i
\(557\) 4.60238 + 7.97156i 0.195009 + 0.337766i 0.946904 0.321518i \(-0.104193\pi\)
−0.751894 + 0.659284i \(0.770860\pi\)
\(558\) 5.52648 0.233955
\(559\) 0 0
\(560\) −4.52350 −0.191153
\(561\) 4.18933 + 7.25614i 0.176874 + 0.306354i
\(562\) −17.0918 29.6039i −0.720974 1.24876i
\(563\) 0.487623 0.844588i 0.0205509 0.0355951i −0.855567 0.517692i \(-0.826791\pi\)
0.876118 + 0.482097i \(0.160125\pi\)
\(564\) 8.69202 0.366000
\(565\) 9.13975 15.8305i 0.384512 0.665995i
\(566\) 30.2533 52.4003i 1.27164 2.20255i
\(567\) 0.801938 0.0336782
\(568\) −14.8885 + 25.7877i −0.624708 + 1.08203i
\(569\) 8.44720 + 14.6310i 0.354125 + 0.613362i 0.986968 0.160918i \(-0.0514454\pi\)
−0.632843 + 0.774280i \(0.718112\pi\)
\(570\) 10.6380 + 18.4256i 0.445578 + 0.771763i
\(571\) −44.3226 −1.85484 −0.927421 0.374019i \(-0.877979\pi\)
−0.927421 + 0.374019i \(0.877979\pi\)
\(572\) 0 0
\(573\) −16.7657 −0.700397
\(574\) 0.804094 + 1.39273i 0.0335622 + 0.0581315i
\(575\) 33.6172 + 58.2267i 1.40193 + 2.42822i
\(576\) 5.92208 10.2573i 0.246753 0.427389i
\(577\) −3.56704 −0.148498 −0.0742489 0.997240i \(-0.523656\pi\)
−0.0742489 + 0.997240i \(0.523656\pi\)
\(578\) −9.85450 + 17.0685i −0.409893 + 0.709956i
\(579\) −12.8720 + 22.2949i −0.534940 + 0.926544i
\(580\) −50.5424 −2.09866
\(581\) 2.82640 4.89546i 0.117259 0.203098i
\(582\) −7.00514 12.1333i −0.290372 0.502940i
\(583\) 14.1984 + 24.5923i 0.588036 + 1.01851i
\(584\) −43.5669 −1.80281
\(585\) 0 0
\(586\) −62.5120 −2.58235
\(587\) −8.05861 13.9579i −0.332614 0.576105i 0.650409 0.759584i \(-0.274597\pi\)
−0.983024 + 0.183479i \(0.941264\pi\)
\(588\) −11.2992 19.5709i −0.465973 0.807089i
\(589\) 2.86658 4.96507i 0.118116 0.204582i
\(590\) 46.8504 1.92880
\(591\) −10.7104 + 18.5510i −0.440569 + 0.763087i
\(592\) 5.68731 9.85071i 0.233747 0.404862i
\(593\) 42.8611 1.76010 0.880048 0.474885i \(-0.157510\pi\)
0.880048 + 0.474885i \(0.157510\pi\)
\(594\) −3.35958 + 5.81897i −0.137845 + 0.238755i
\(595\) 4.35086 + 7.53590i 0.178368 + 0.308942i
\(596\) 34.4934 + 59.7444i 1.41291 + 2.44722i
\(597\) −3.52781 −0.144384
\(598\) 0 0
\(599\) 40.9420 1.67284 0.836422 0.548086i \(-0.184643\pi\)
0.836422 + 0.548086i \(0.184643\pi\)
\(600\) −15.8158 27.3938i −0.645678 1.11835i
\(601\) −0.593523 1.02801i −0.0242103 0.0419335i 0.853666 0.520820i \(-0.174374\pi\)
−0.877877 + 0.478887i \(0.841040\pi\)
\(602\) −1.52715 + 2.64510i −0.0622419 + 0.107806i
\(603\) −14.3937 −0.586158
\(604\) −21.9737 + 38.0595i −0.894096 + 1.54862i
\(605\) −5.30290 + 9.18489i −0.215593 + 0.373419i
\(606\) 10.9022 0.442870
\(607\) −9.99612 + 17.3138i −0.405730 + 0.702745i −0.994406 0.105624i \(-0.966316\pi\)
0.588676 + 0.808369i \(0.299649\pi\)
\(608\) −4.55861 7.89574i −0.184876 0.320214i
\(609\) 1.54407 + 2.67441i 0.0625690 + 0.108373i
\(610\) −115.356 −4.67062
\(611\) 0 0
\(612\) 10.4480 0.422336
\(613\) −16.6809 28.8922i −0.673735 1.16694i −0.976837 0.213985i \(-0.931356\pi\)
0.303102 0.952958i \(-0.401978\pi\)
\(614\) 9.71864 + 16.8332i 0.392212 + 0.679332i
\(615\) −1.57069 + 2.72051i −0.0633362 + 0.109702i
\(616\) −8.37867 −0.337586
\(617\) 5.81163 10.0660i 0.233967 0.405243i −0.725005 0.688744i \(-0.758162\pi\)
0.958972 + 0.283501i \(0.0914958\pi\)
\(618\) −1.42327 + 2.46518i −0.0572524 + 0.0991640i
\(619\) 16.5381 0.664722 0.332361 0.943152i \(-0.392155\pi\)
0.332361 + 0.943152i \(0.392155\pi\)
\(620\) −15.3878 + 26.6525i −0.617990 + 1.07039i
\(621\) −3.89493 6.74621i −0.156298 0.270716i
\(622\) −16.9907 29.4288i −0.681267 1.17999i
\(623\) −0.907542 −0.0363599
\(624\) 0 0
\(625\) 6.33944 0.253577
\(626\) 16.7738 + 29.0531i 0.670417 + 1.16120i
\(627\) 3.48523 + 6.03660i 0.139187 + 0.241078i
\(628\) 33.1989 57.5023i 1.32478 2.29459i
\(629\) −21.8810 −0.872452
\(630\) −3.48911 + 6.04332i −0.139010 + 0.240772i
\(631\) −18.2208 + 31.5593i −0.725358 + 1.25636i 0.233468 + 0.972364i \(0.424993\pi\)
−0.958826 + 0.283993i \(0.908341\pi\)
\(632\) −19.8116 −0.788064
\(633\) 0.607760 1.05267i 0.0241563 0.0418399i
\(634\) 8.06547 + 13.9698i 0.320321 + 0.554812i
\(635\) 10.4673 + 18.1300i 0.415384 + 0.719466i
\(636\) 35.4101 1.40410
\(637\) 0 0
\(638\) −25.8745 −1.02438
\(639\) 4.06249 + 7.03644i 0.160710 + 0.278357i
\(640\) 37.7652 + 65.4112i 1.49280 + 2.58560i
\(641\) −13.6033 + 23.5617i −0.537300 + 0.930630i 0.461748 + 0.887011i \(0.347222\pi\)
−0.999048 + 0.0436195i \(0.986111\pi\)
\(642\) −22.4403 −0.885646
\(643\) −2.53481 + 4.39042i −0.0999632 + 0.173141i −0.911669 0.410925i \(-0.865206\pi\)
0.811706 + 0.584066i \(0.198539\pi\)
\(644\) 11.1039 19.2325i 0.437554 0.757866i
\(645\) −5.96615 −0.234917
\(646\) 8.46830 14.6675i 0.333181 0.577086i
\(647\) −9.66033 16.7322i −0.379787 0.657810i 0.611244 0.791442i \(-0.290669\pi\)
−0.991031 + 0.133632i \(0.957336\pi\)
\(648\) 1.83244 + 3.17387i 0.0719849 + 0.124682i
\(649\) 15.3491 0.602506
\(650\) 0 0
\(651\) 1.88040 0.0736985
\(652\) 21.9331 + 37.9892i 0.858966 + 1.48777i
\(653\) −17.6177 30.5148i −0.689436 1.19414i −0.972021 0.234895i \(-0.924525\pi\)
0.282585 0.959242i \(-0.408808\pi\)
\(654\) −2.10292 + 3.64236i −0.0822305 + 0.142427i
\(655\) −67.2790 −2.62881
\(656\) −0.649973 + 1.12579i −0.0253772 + 0.0439546i
\(657\) −5.94385 + 10.2950i −0.231891 + 0.401648i
\(658\) 4.62133 0.180158
\(659\) 2.18084 3.77733i 0.0849535 0.147144i −0.820418 0.571764i \(-0.806259\pi\)
0.905371 + 0.424621i \(0.139592\pi\)
\(660\) −18.7087 32.4044i −0.728236 1.26134i
\(661\) −7.73543 13.3982i −0.300873 0.521128i 0.675461 0.737396i \(-0.263945\pi\)
−0.976334 + 0.216268i \(0.930611\pi\)
\(662\) 22.2553 0.864978
\(663\) 0 0
\(664\) 25.8334 1.00253
\(665\) 3.61960 + 6.26934i 0.140362 + 0.243115i
\(666\) −8.77359 15.1963i −0.339970 0.588845i
\(667\) 14.9988 25.9787i 0.580756 1.00590i
\(668\) −40.8605 −1.58094
\(669\) 8.69418 15.0588i 0.336136 0.582205i
\(670\) 62.6250 108.470i 2.41942 4.19055i
\(671\) −37.7928 −1.45898
\(672\) 1.49516 2.58969i 0.0576769 0.0998993i
\(673\) 5.87047 + 10.1680i 0.226290 + 0.391946i 0.956706 0.291057i \(-0.0940070\pi\)
−0.730416 + 0.683003i \(0.760674\pi\)
\(674\) 3.11476 + 5.39492i 0.119976 + 0.207805i
\(675\) −8.63102 −0.332208
\(676\) 0 0
\(677\) 3.44504 0.132404 0.0662019 0.997806i \(-0.478912\pi\)
0.0662019 + 0.997806i \(0.478912\pi\)
\(678\) −5.83459 10.1058i −0.224076 0.388111i
\(679\) −2.38351 4.12836i −0.0914707 0.158432i
\(680\) −19.8835 + 34.4393i −0.762498 + 1.32068i
\(681\) 17.4155 0.667363
\(682\) −7.87760 + 13.6444i −0.301649 + 0.522471i
\(683\) 10.2029 17.6720i 0.390403 0.676198i −0.602099 0.798421i \(-0.705669\pi\)
0.992503 + 0.122223i \(0.0390022\pi\)
\(684\) 8.69202 0.332348
\(685\) −17.4456 + 30.2166i −0.666561 + 1.15452i
\(686\) −12.6228 21.8634i −0.481942 0.834748i
\(687\) −9.38016 16.2469i −0.357875 0.619858i
\(688\) −2.46888 −0.0941251
\(689\) 0 0
\(690\) 67.7851 2.58053
\(691\) 13.9019 + 24.0788i 0.528854 + 0.916002i 0.999434 + 0.0336449i \(0.0107115\pi\)
−0.470580 + 0.882358i \(0.655955\pi\)
\(692\) −21.5328 37.2959i −0.818554 1.41778i
\(693\) −1.14310 + 1.97991i −0.0434229 + 0.0752107i
\(694\) 23.9433 0.908876
\(695\) 7.41185 12.8377i 0.281148 0.486962i
\(696\) −7.05645 + 12.2221i −0.267474 + 0.463279i
\(697\) 2.50066 0.0947194
\(698\) −12.3026 + 21.3087i −0.465660 + 0.806547i
\(699\) 1.97554 + 3.42174i 0.0747218 + 0.129422i
\(700\) −12.3029 21.3092i −0.465006 0.805414i
\(701\) 11.9715 0.452158 0.226079 0.974109i \(-0.427409\pi\)
0.226079 + 0.974109i \(0.427409\pi\)
\(702\) 0 0
\(703\) −18.2034 −0.686556
\(704\) 16.8830 + 29.2422i 0.636301 + 1.10211i
\(705\) 4.51357 + 7.81774i 0.169991 + 0.294433i
\(706\) −21.5551 + 37.3346i −0.811238 + 1.40510i
\(707\) 3.70948 0.139509
\(708\) 9.57002 16.5758i 0.359664 0.622955i
\(709\) 16.1332 27.9435i 0.605894 1.04944i −0.386015 0.922492i \(-0.626149\pi\)
0.991909 0.126947i \(-0.0405179\pi\)
\(710\) −70.7012 −2.65337
\(711\) −2.70291 + 4.68157i −0.101367 + 0.175573i
\(712\) −2.07374 3.59183i −0.0777169 0.134610i
\(713\) −9.13288 15.8186i −0.342029 0.592412i
\(714\) 5.55496 0.207889
\(715\) 0 0
\(716\) −1.91457 −0.0715510
\(717\) −0.409166 0.708696i −0.0152806 0.0264667i
\(718\) 17.9985 + 31.1743i 0.671698 + 1.16342i
\(719\) −6.05429 + 10.4863i −0.225787 + 0.391075i −0.956555 0.291551i \(-0.905829\pi\)
0.730768 + 0.682626i \(0.239162\pi\)
\(720\) −5.64071 −0.210217
\(721\) −0.484271 + 0.838781i −0.0180352 + 0.0312378i
\(722\) −15.3455 + 26.5791i −0.571100 + 0.989173i
\(723\) 6.03252 0.224352
\(724\) 41.3865 71.6835i 1.53812 2.66410i
\(725\) −16.6184 28.7839i −0.617192 1.06901i
\(726\) 3.38524 + 5.86341i 0.125638 + 0.217611i
\(727\) −16.6200 −0.616402 −0.308201 0.951321i \(-0.599727\pi\)
−0.308201 + 0.951321i \(0.599727\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −51.7216 89.5845i −1.91430 3.31567i
\(731\) 2.37465 + 4.11301i 0.0878296 + 0.152125i
\(732\) −23.5635 + 40.8131i −0.870930 + 1.50850i
\(733\) −17.7912 −0.657132 −0.328566 0.944481i \(-0.606565\pi\)
−0.328566 + 0.944481i \(0.606565\pi\)
\(734\) −26.2461 + 45.4595i −0.968760 + 1.67794i
\(735\) 11.7349 20.3254i 0.432848 0.749715i
\(736\) −29.0473 −1.07070
\(737\) 20.5172 35.5369i 0.755762 1.30902i
\(738\) 1.00269 + 1.73671i 0.0369095 + 0.0639291i
\(739\) −13.6809 23.6960i −0.503260 0.871672i −0.999993 0.00376844i \(-0.998800\pi\)
0.496733 0.867903i \(-0.334533\pi\)
\(740\) 97.7160 3.59211
\(741\) 0 0
\(742\) 18.8267 0.691150
\(743\) 4.19298 + 7.26246i 0.153826 + 0.266434i 0.932631 0.360832i \(-0.117507\pi\)
−0.778805 + 0.627266i \(0.784174\pi\)
\(744\) 4.29672 + 7.44215i 0.157526 + 0.272842i
\(745\) −35.8233 + 62.0478i −1.31247 + 2.27326i
\(746\) −9.72528 −0.356068
\(747\) 3.52446 6.10454i 0.128953 0.223353i
\(748\) −14.8929 + 25.7953i −0.544538 + 0.943168i
\(749\) −7.63533 −0.278989
\(750\) 15.7981 27.3630i 0.576863 0.999157i
\(751\) 19.3889 + 33.5825i 0.707511 + 1.22544i 0.965778 + 0.259371i \(0.0835151\pi\)
−0.258267 + 0.966073i \(0.583152\pi\)
\(752\) 1.86778 + 3.23509i 0.0681110 + 0.117972i
\(753\) 26.8799 0.979559
\(754\) 0 0
\(755\) −45.6418 −1.66107
\(756\) 1.42543 + 2.46891i 0.0518423 + 0.0897935i
\(757\) −6.48643 11.2348i −0.235753 0.408336i 0.723738 0.690075i \(-0.242422\pi\)
−0.959491 + 0.281738i \(0.909089\pi\)
\(758\) 12.6177 21.8546i 0.458297 0.793794i
\(759\) 22.2078 0.806090
\(760\) −16.5417 + 28.6510i −0.600030 + 1.03928i
\(761\) −2.57792 + 4.46510i −0.0934497 + 0.161860i −0.908961 0.416882i \(-0.863123\pi\)
0.815511 + 0.578742i \(0.196456\pi\)
\(762\) 13.3642 0.484134
\(763\) −0.715521 + 1.23932i −0.0259036 + 0.0448663i
\(764\) −29.8007 51.6163i −1.07815 1.86741i
\(765\) 5.42543 + 9.39712i 0.196157 + 0.339753i
\(766\) 15.3822 0.555783
\(767\) 0 0
\(768\) 24.5284 0.885092
\(769\) −17.7506 30.7450i −0.640104 1.10869i −0.985409 0.170202i \(-0.945558\pi\)
0.345305 0.938490i \(-0.387775\pi\)
\(770\) −9.94696 17.2286i −0.358464 0.620877i
\(771\) −4.52661 + 7.84033i −0.163022 + 0.282362i
\(772\) −91.5186 −3.29383
\(773\) −3.07792 + 5.33112i −0.110705 + 0.191747i −0.916055 0.401053i \(-0.868644\pi\)
0.805350 + 0.592800i \(0.201978\pi\)
\(774\) −1.90432 + 3.29838i −0.0684494 + 0.118558i
\(775\) −20.2381 −0.726976
\(776\) 10.8927 18.8667i 0.391025 0.677275i
\(777\) −2.98523 5.17057i −0.107095 0.185493i
\(778\) −13.8966 24.0695i −0.498216 0.862935i
\(779\) 2.08038 0.0745372
\(780\) 0 0
\(781\) −23.1631 −0.828843
\(782\) −26.9799 46.7305i −0.964798 1.67108i
\(783\) 1.92543 + 3.33494i 0.0688092 + 0.119181i
\(784\) 4.85607 8.41096i 0.173431 0.300391i
\(785\) 68.9579 2.46121
\(786\) −21.4746 + 37.1952i −0.765975 + 1.32671i
\(787\) 7.10537 12.3069i 0.253279 0.438692i −0.711148 0.703043i \(-0.751824\pi\)
0.964427 + 0.264351i \(0.0851576\pi\)
\(788\) −76.1503 −2.71274
\(789\) 11.5755 20.0494i 0.412100 0.713778i
\(790\) −23.5199 40.7377i −0.836801 1.44938i
\(791\) −1.98523 3.43852i −0.0705867 0.122260i
\(792\) −10.4480 −0.371254
\(793\) 0 0
\(794\) −29.5623 −1.04913
\(795\) 18.3877 + 31.8484i 0.652144 + 1.12955i
\(796\) −6.27061 10.8610i −0.222256 0.384958i
\(797\) −5.95108 + 10.3076i −0.210798 + 0.365113i −0.951965 0.306208i \(-0.900940\pi\)
0.741166 + 0.671321i \(0.234273\pi\)
\(798\) 4.62133 0.163593
\(799\) 3.59299 6.22324i 0.127111 0.220162i
\(800\) −16.0919 + 27.8720i −0.568935 + 0.985425i
\(801\) −1.13169 −0.0399862
\(802\) −21.0591 + 36.4755i −0.743624 + 1.28799i
\(803\) −16.9450 29.3497i −0.597978 1.03573i
\(804\) −25.5846 44.3138i −0.902298 1.56283i
\(805\) 23.0640 0.812899
\(806\) 0 0
\(807\) 2.42088 0.0852190
\(808\) 8.47621 + 14.6812i 0.298192 + 0.516483i
\(809\) −0.807979 1.39946i −0.0284070 0.0492024i 0.851472 0.524399i \(-0.175710\pi\)
−0.879879 + 0.475197i \(0.842377\pi\)
\(810\) −4.35086 + 7.53590i −0.152873 + 0.264785i
\(811\) 51.9657 1.82476 0.912381 0.409342i \(-0.134242\pi\)
0.912381 + 0.409342i \(0.134242\pi\)
\(812\) −5.48911 + 9.50743i −0.192630 + 0.333645i
\(813\) 10.7225 18.5720i 0.376055 0.651347i
\(814\) 50.0245 1.75336
\(815\) −22.7787 + 39.4539i −0.797904 + 1.38201i
\(816\) 2.24512 + 3.88866i 0.0785949 + 0.136130i
\(817\) 1.97554 + 3.42174i 0.0691154 + 0.119711i
\(818\) −65.7853 −2.30013
\(819\) 0 0
\(820\) −11.1675 −0.389985
\(821\) 27.4163 + 47.4865i 0.956837 + 1.65729i 0.730108 + 0.683331i \(0.239470\pi\)
0.226728 + 0.973958i \(0.427197\pi\)
\(822\) 11.1368 + 19.2895i 0.388441 + 0.672800i
\(823\) 23.4257 40.5745i 0.816569 1.41434i −0.0916262 0.995793i \(-0.529206\pi\)
0.908196 0.418546i \(-0.137460\pi\)
\(824\) −4.42626 −0.154196
\(825\) 12.3029 21.3092i 0.428332 0.741893i
\(826\) 5.08815 8.81293i 0.177039 0.306641i
\(827\) −21.2021 −0.737270 −0.368635 0.929574i \(-0.620175\pi\)
−0.368635 + 0.929574i \(0.620175\pi\)
\(828\) 13.8463 23.9825i 0.481192 0.833450i
\(829\) −9.14861 15.8459i −0.317744 0.550350i 0.662273 0.749263i \(-0.269592\pi\)
−0.980017 + 0.198913i \(0.936259\pi\)
\(830\) 30.6688 + 53.1200i 1.06453 + 1.84382i
\(831\) 14.8073 0.513660
\(832\) 0 0
\(833\) −18.6829 −0.647325
\(834\) −4.73155 8.19528i −0.163840 0.283779i
\(835\) −21.2180 36.7506i −0.734278 1.27181i
\(836\) −12.3898 + 21.4598i −0.428512 + 0.742204i
\(837\) 2.34481 0.0810486
\(838\) −19.3306 + 33.4815i −0.667764 + 1.15660i
\(839\) 10.5707 18.3090i 0.364941 0.632096i −0.623826 0.781563i \(-0.714423\pi\)
0.988767 + 0.149468i \(0.0477559\pi\)
\(840\) −10.8509 −0.374390
\(841\) 7.08546 12.2724i 0.244326 0.423185i
\(842\) 3.57875 + 6.19858i 0.123332 + 0.213617i
\(843\) −7.25182 12.5605i −0.249766 0.432608i
\(844\) 4.32113 0.148739
\(845\) 0 0
\(846\) 5.76271 0.198126
\(847\) 1.15183 + 1.99503i 0.0395775 + 0.0685502i
\(848\) 7.60909 + 13.1793i 0.261297 + 0.452580i
\(849\) 12.8361 22.2328i 0.440533 0.763026i
\(850\) −59.7864 −2.05066
\(851\) −28.9979 + 50.2258i −0.994035 + 1.72172i
\(852\) −14.4420 + 25.0143i −0.494774 + 0.856974i
\(853\) 7.13036 0.244139 0.122069 0.992522i \(-0.461047\pi\)
0.122069 + 0.992522i \(0.461047\pi\)
\(854\) −12.5281 + 21.6993i −0.428703 + 0.742535i
\(855\) 4.51357 + 7.81774i 0.154361 + 0.267361i
\(856\) −17.4468 30.2188i −0.596320 1.03286i
\(857\) −44.7741 −1.52945 −0.764726 0.644355i \(-0.777126\pi\)
−0.764726 + 0.644355i \(0.777126\pi\)
\(858\) 0 0
\(859\) 57.3782 1.95772 0.978859 0.204535i \(-0.0655681\pi\)
0.978859 + 0.204535i \(0.0655681\pi\)
\(860\) −10.6047 18.3679i −0.361617 0.626340i
\(861\) 0.341166 + 0.590918i 0.0116269 + 0.0201384i
\(862\) 3.93379 6.81352i 0.133985 0.232069i
\(863\) 6.67563 0.227241 0.113621 0.993524i \(-0.463755\pi\)
0.113621 + 0.993524i \(0.463755\pi\)
\(864\) 1.86443 3.22929i 0.0634291 0.109863i
\(865\) 22.3630 38.7338i 0.760365 1.31699i
\(866\) −28.0536 −0.953299
\(867\) −4.18114 + 7.24194i −0.141999 + 0.245949i
\(868\) 3.34236 + 5.78914i 0.113447 + 0.196496i
\(869\) −7.70560 13.3465i −0.261394 0.452748i
\(870\) −33.5090 −1.13606
\(871\) 0 0
\(872\) −6.53989 −0.221469
\(873\) −2.97219 5.14798i −0.100593 0.174233i
\(874\) −22.4453 38.8765i −0.759225 1.31502i
\(875\) 5.37531 9.31032i 0.181719 0.314746i
\(876\) −42.2602 −1.42784
\(877\) 12.6491 21.9090i 0.427131 0.739813i −0.569486 0.822001i \(-0.692858\pi\)
0.996617 + 0.0821883i \(0.0261909\pi\)
\(878\) 4.38159 7.58914i 0.147872 0.256121i
\(879\) −26.5230 −0.894599
\(880\) 8.04043 13.9264i 0.271043 0.469460i
\(881\) 17.6893 + 30.6388i 0.595969 + 1.03225i 0.993409 + 0.114620i \(0.0365651\pi\)
−0.397441 + 0.917628i \(0.630102\pi\)
\(882\) −7.49127 12.9753i −0.252244 0.436900i
\(883\) −11.5851 −0.389869 −0.194935 0.980816i \(-0.562449\pi\)
−0.194935 + 0.980816i \(0.562449\pi\)
\(884\) 0 0
\(885\) 19.8780 0.668192
\(886\) 1.71714 + 2.97418i 0.0576886 + 0.0999196i
\(887\) 13.6446 + 23.6331i 0.458141 + 0.793523i 0.998863 0.0476784i \(-0.0151822\pi\)
−0.540722 + 0.841201i \(0.681849\pi\)
\(888\) 13.6426 23.6296i 0.457815 0.792958i
\(889\) 4.54719 0.152508
\(890\) 4.92380 8.52828i 0.165046 0.285869i
\(891\) −1.42543 + 2.46891i −0.0477536 + 0.0827117i
\(892\) 61.8149 2.06972
\(893\) 2.98911 5.17730i 0.100027 0.173252i
\(894\) 22.8687 + 39.6098i 0.764845 + 1.32475i
\(895\) −0.994196 1.72200i −0.0332323 0.0575601i
\(896\) 16.4058 0.548080
\(897\) 0 0
\(898\) −28.5830 −0.953826
\(899\) 4.51477 + 7.81981i 0.150576 + 0.260805i
\(900\) −15.3415 26.5722i −0.511382 0.885740i
\(901\) 14.6374 25.3526i 0.487641 0.844619i
\(902\) −5.71704 −0.190357
\(903\) −0.647948 + 1.12228i −0.0215624 + 0.0373471i
\(904\) 9.07255 15.7141i 0.301748 0.522644i
\(905\) 85.9643 2.85755
\(906\) −14.5683 + 25.2330i −0.483999 + 0.838311i
\(907\) 15.2110 + 26.3462i 0.505072 + 0.874810i 0.999983 + 0.00586661i \(0.00186741\pi\)
−0.494911 + 0.868944i \(0.664799\pi\)
\(908\) 30.9557 + 53.6168i 1.02730 + 1.77934i
\(909\) 4.62565 0.153423
\(910\) 0 0
\(911\) 53.5719 1.77492 0.887459 0.460887i \(-0.152469\pi\)
0.887459 + 0.460887i \(0.152469\pi\)
\(912\) 1.86778 + 3.23509i 0.0618484 + 0.107125i
\(913\) 10.0477 + 17.4032i 0.332531 + 0.575961i
\(914\) 4.06332 7.03787i 0.134403 0.232792i
\(915\) −48.9439 −1.61804
\(916\) 33.3461 57.7571i 1.10179 1.90835i
\(917\) −7.30678 + 12.6557i −0.241291 + 0.417929i
\(918\) 6.92692 0.228622
\(919\) 18.0836 31.3217i 0.596523 1.03321i −0.396807 0.917902i \(-0.629882\pi\)
0.993330 0.115306i \(-0.0367848\pi\)
\(920\) 52.7015 + 91.2816i 1.73752 + 3.00947i
\(921\) 4.12349 + 7.14209i 0.135874 + 0.235340i
\(922\) −15.9232 −0.524403
\(923\) 0 0
\(924\) −8.12737 −0.267371
\(925\) 32.1292 + 55.6493i 1.05640 + 1.82974i
\(926\) 8.78150 + 15.2100i 0.288578 + 0.499831i
\(927\) −0.603875 + 1.04594i −0.0198339 + 0.0343533i
\(928\) 14.3593 0.471367
\(929\) −6.67390 + 11.5595i −0.218964 + 0.379256i −0.954491 0.298239i \(-0.903601\pi\)
0.735528 + 0.677494i \(0.236934\pi\)
\(930\) −10.2019 + 17.6703i −0.334535 + 0.579432i
\(931\) −15.5429 −0.509397
\(932\) −7.02297 + 12.1641i −0.230045 + 0.398449i
\(933\) −7.20895 12.4863i −0.236010 0.408782i
\(934\) 38.4290 + 66.5610i 1.25744 + 2.17794i
\(935\) −30.9342 −1.01166
\(936\) 0 0
\(937\) 38.6872 1.26386 0.631928 0.775027i \(-0.282264\pi\)
0.631928 + 0.775027i \(0.282264\pi\)
\(938\) −13.6027 23.5605i −0.444143 0.769279i
\(939\) 7.11692 + 12.3269i 0.232252 + 0.402272i
\(940\) −16.0456 + 27.7917i −0.523349 + 0.906466i
\(941\) −35.7275 −1.16468 −0.582342 0.812944i \(-0.697864\pi\)
−0.582342 + 0.812944i \(0.697864\pi\)
\(942\) 22.0105 38.1233i 0.717141 1.24213i
\(943\) 3.31402 5.74005i 0.107919 0.186922i
\(944\) 8.22580 0.267727
\(945\) −1.48039 + 2.56410i −0.0481569 + 0.0834103i
\(946\) −5.42894 9.40321i −0.176510 0.305725i
\(947\) −8.92178 15.4530i −0.289919 0.502154i 0.683871 0.729603i \(-0.260295\pi\)
−0.973790 + 0.227448i \(0.926962\pi\)
\(948\) −19.2174 −0.624153
\(949\) 0 0
\(950\) −49.7381 −1.61372
\(951\) 3.42208 + 5.92721i 0.110968 + 0.192203i
\(952\) 4.31886 + 7.48049i 0.139975 + 0.242444i
\(953\) −10.0846 + 17.4670i −0.326671 + 0.565810i −0.981849 0.189664i \(-0.939260\pi\)
0.655178 + 0.755474i \(0.272594\pi\)
\(954\) 23.4765 0.760080
\(955\) 30.9496 53.6064i 1.00151 1.73466i
\(956\) 1.45457 2.51938i 0.0470440 0.0814827i
\(957\) −10.9782 −0.354876
\(958\) −3.33393 + 5.77453i −0.107714 + 0.186567i
\(959\) 3.78932 + 6.56330i 0.122364 + 0.211940i
\(960\) 21.8644 + 37.8703i 0.705671 + 1.22226i
\(961\) −25.5018 −0.822640
\(962\) 0 0
\(963\) −9.52111 −0.306813
\(964\) 10.7227 + 18.5722i 0.345354 + 0.598171i
\(965\) −47.5236 82.3132i −1.52984 2.64976i
\(966\) 7.36174 12.7509i 0.236860 0.410254i
\(967\) 32.7894 1.05444 0.527218 0.849730i \(-0.323235\pi\)
0.527218 + 0.849730i \(0.323235\pi\)
\(968\) −5.26391 + 9.11735i −0.169188 + 0.293043i
\(969\) 3.59299 6.22324i 0.115423 0.199919i
\(970\) 51.7263 1.66083
\(971\) 13.4922 23.3692i 0.432986 0.749954i −0.564143 0.825677i \(-0.690793\pi\)
0.997129 + 0.0757231i \(0.0241265\pi\)
\(972\) 1.77748 + 3.07868i 0.0570127 + 0.0987488i
\(973\) −1.60992 2.78846i −0.0516115 0.0893938i
\(974\) −97.3245 −3.11848
\(975\) 0 0
\(976\) −20.2537 −0.648305
\(977\) −8.47853 14.6852i −0.271252 0.469822i 0.697931 0.716165i \(-0.254104\pi\)
−0.969183 + 0.246343i \(0.920771\pi\)
\(978\) 14.5414 + 25.1864i 0.464982 + 0.805373i
\(979\) 1.61314 2.79404i 0.0515561 0.0892978i
\(980\) 83.4341 2.66521
\(981\) −0.892240 + 1.54540i −0.0284870 + 0.0493410i
\(982\) −40.8565 + 70.7656i −1.30378 + 2.25822i
\(983\) 32.6631 1.04179 0.520895 0.853621i \(-0.325598\pi\)
0.520895 + 0.853621i \(0.325598\pi\)
\(984\) −1.55914 + 2.70051i −0.0497035 + 0.0860890i
\(985\) −39.5432 68.4908i −1.25995 2.18230i
\(986\) 13.3373 + 23.1008i 0.424746 + 0.735681i
\(987\) 1.96077 0.0624120
\(988\) 0 0
\(989\) 12.5881 0.400277
\(990\) −12.4037 21.4838i −0.394214 0.682799i
\(991\) −3.82155 6.61912i −0.121396 0.210263i 0.798923 0.601434i \(-0.205404\pi\)
−0.920318 + 0.391170i \(0.872070\pi\)
\(992\) 4.37174 7.57207i 0.138803 0.240414i
\(993\) 9.44265 0.299653
\(994\) −7.67845 + 13.2995i −0.243546 + 0.421833i
\(995\) 6.51238 11.2798i 0.206456 0.357593i
\(996\) 25.0586 0.794012
\(997\) −18.0628 + 31.2857i −0.572054 + 0.990827i 0.424301 + 0.905521i \(0.360520\pi\)
−0.996355 + 0.0853055i \(0.972813\pi\)
\(998\) −21.1424 36.6198i −0.669252 1.15918i
\(999\) −3.72252 6.44760i −0.117775 0.203993i
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 507.2.e.l.484.2 6
13.2 odd 12 507.2.b.f.337.5 6
13.3 even 3 507.2.a.i.1.2 3
13.4 even 6 507.2.e.i.22.2 6
13.5 odd 4 507.2.j.i.361.5 12
13.6 odd 12 507.2.j.i.316.2 12
13.7 odd 12 507.2.j.i.316.5 12
13.8 odd 4 507.2.j.i.361.2 12
13.9 even 3 inner 507.2.e.l.22.2 6
13.10 even 6 507.2.a.l.1.2 yes 3
13.11 odd 12 507.2.b.f.337.2 6
13.12 even 2 507.2.e.i.484.2 6
39.2 even 12 1521.2.b.k.1351.2 6
39.11 even 12 1521.2.b.k.1351.5 6
39.23 odd 6 1521.2.a.n.1.2 3
39.29 odd 6 1521.2.a.s.1.2 3
52.3 odd 6 8112.2.a.cg.1.1 3
52.23 odd 6 8112.2.a.cp.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
507.2.a.i.1.2 3 13.3 even 3
507.2.a.l.1.2 yes 3 13.10 even 6
507.2.b.f.337.2 6 13.11 odd 12
507.2.b.f.337.5 6 13.2 odd 12
507.2.e.i.22.2 6 13.4 even 6
507.2.e.i.484.2 6 13.12 even 2
507.2.e.l.22.2 6 13.9 even 3 inner
507.2.e.l.484.2 6 1.1 even 1 trivial
507.2.j.i.316.2 12 13.6 odd 12
507.2.j.i.316.5 12 13.7 odd 12
507.2.j.i.361.2 12 13.8 odd 4
507.2.j.i.361.5 12 13.5 odd 4
1521.2.a.n.1.2 3 39.23 odd 6
1521.2.a.s.1.2 3 39.29 odd 6
1521.2.b.k.1351.2 6 39.2 even 12
1521.2.b.k.1351.5 6 39.11 even 12
8112.2.a.cg.1.1 3 52.3 odd 6
8112.2.a.cp.1.3 3 52.23 odd 6