Properties

Label 63.3.n.b.2.4
Level $63$
Weight $3$
Character 63.2
Analytic conductor $1.717$
Analytic rank $0$
Dimension $22$
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] = [63,3,Mod(2,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.2");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 63.n (of order \(6\), degree \(2\), 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: \(1.71662566547\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2.4
Character \(\chi\) \(=\) 63.2
Dual form 63.3.n.b.32.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.26920 + 0.732774i) q^{2} +(1.95453 + 2.27592i) q^{3} +(-0.926086 + 1.60403i) q^{4} -1.15270i q^{5} +(-4.14843 - 1.45637i) q^{6} +(-2.90907 + 6.36689i) q^{7} -8.57663i q^{8} +(-1.35961 + 8.89671i) q^{9} +O(q^{10})\) \(q+(-1.26920 + 0.732774i) q^{2} +(1.95453 + 2.27592i) q^{3} +(-0.926086 + 1.60403i) q^{4} -1.15270i q^{5} +(-4.14843 - 1.45637i) q^{6} +(-2.90907 + 6.36689i) q^{7} -8.57663i q^{8} +(-1.35961 + 8.89671i) q^{9} +(0.844669 + 1.46301i) q^{10} +0.241349i q^{11} +(-5.46070 + 1.02743i) q^{12} +(7.70332 + 13.3426i) q^{13} +(-0.973295 - 10.2126i) q^{14} +(2.62345 - 2.25299i) q^{15} +(2.58039 + 4.46937i) q^{16} +(10.9102 - 6.29901i) q^{17} +(-4.79366 - 12.2880i) q^{18} +(13.7090 - 23.7446i) q^{19} +(1.84896 + 1.06750i) q^{20} +(-20.1764 + 5.82348i) q^{21} +(-0.176854 - 0.306320i) q^{22} -20.3881i q^{23} +(19.5197 - 16.7633i) q^{24} +23.6713 q^{25} +(-19.5541 - 11.2896i) q^{26} +(-22.9056 + 14.2945i) q^{27} +(-7.51862 - 10.5625i) q^{28} +(16.9161 + 9.76653i) q^{29} +(-1.67876 + 4.78190i) q^{30} +(1.36337 - 2.36142i) q^{31} +(23.1603 + 13.3716i) q^{32} +(-0.549290 + 0.471724i) q^{33} +(-9.23150 + 15.9894i) q^{34} +(7.33912 + 3.35329i) q^{35} +(-13.0114 - 10.4200i) q^{36} +(-11.4455 + 19.8242i) q^{37} +40.1823i q^{38} +(-15.3102 + 43.6106i) q^{39} -9.88629 q^{40} +(-61.9933 + 35.7918i) q^{41} +(21.3406 - 22.1759i) q^{42} +(14.8972 - 25.8028i) q^{43} +(-0.387130 - 0.223510i) q^{44} +(10.2552 + 1.56722i) q^{45} +(14.9398 + 25.8766i) q^{46} +(-25.9734 + 14.9958i) q^{47} +(-5.12846 + 14.6083i) q^{48} +(-32.0746 - 37.0435i) q^{49} +(-30.0436 + 17.3457i) q^{50} +(35.6604 + 12.5191i) q^{51} -28.5358 q^{52} +(90.5906 - 52.3025i) q^{53} +(18.5971 - 34.9273i) q^{54} +0.278203 q^{55} +(54.6065 + 24.9500i) q^{56} +(80.8355 - 15.2091i) q^{57} -28.6266 q^{58} +(-75.0951 - 43.3562i) q^{59} +(1.18432 + 6.29455i) q^{60} +(-8.94224 - 15.4884i) q^{61} +3.99616i q^{62} +(-52.6892 - 34.5377i) q^{63} -59.8365 q^{64} +(15.3800 - 8.87963i) q^{65} +(0.351493 - 1.00122i) q^{66} +(9.02196 - 15.6265i) q^{67} +23.3337i q^{68} +(46.4016 - 39.8491i) q^{69} +(-11.7720 + 1.12192i) q^{70} +74.2118i q^{71} +(76.3038 + 11.6609i) q^{72} +(13.0598 + 22.6203i) q^{73} -33.5479i q^{74} +(46.2663 + 53.8739i) q^{75} +(25.3914 + 43.9791i) q^{76} +(-1.53664 - 0.702101i) q^{77} +(-12.5250 - 66.5695i) q^{78} +(-11.2561 - 19.4962i) q^{79} +(5.15184 - 2.97442i) q^{80} +(-77.3029 - 24.1921i) q^{81} +(52.4546 - 90.8541i) q^{82} +(-77.0996 - 44.5135i) q^{83} +(9.34404 - 37.7565i) q^{84} +(-7.26088 - 12.5762i) q^{85} +43.6652i q^{86} +(10.8353 + 57.5887i) q^{87} +2.06996 q^{88} +(-49.7459 - 28.7208i) q^{89} +(-14.1644 + 5.52565i) q^{90} +(-107.360 + 10.2318i) q^{91} +(32.7030 + 18.8811i) q^{92} +(8.03915 - 1.51256i) q^{93} +(21.9770 - 38.0653i) q^{94} +(-27.3705 - 15.8023i) q^{95} +(14.8348 + 78.8461i) q^{96} +(73.9883 - 128.152i) q^{97} +(67.8536 + 23.5122i) q^{98} +(-2.14721 - 0.328140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26920 + 0.732774i −0.634601 + 0.366387i −0.782532 0.622611i \(-0.786072\pi\)
0.147931 + 0.988998i \(0.452739\pi\)
\(3\) 1.95453 + 2.27592i 0.651511 + 0.758640i
\(4\) −0.926086 + 1.60403i −0.231521 + 0.401007i
\(5\) 1.15270i 0.230540i −0.993334 0.115270i \(-0.963227\pi\)
0.993334 0.115270i \(-0.0367734\pi\)
\(6\) −4.14843 1.45637i −0.691405 0.242728i
\(7\) −2.90907 + 6.36689i −0.415582 + 0.909556i
\(8\) 8.57663i 1.07208i
\(9\) −1.35961 + 8.89671i −0.151068 + 0.988523i
\(10\) 0.844669 + 1.46301i 0.0844669 + 0.146301i
\(11\) 0.241349i 0.0219408i 0.999940 + 0.0109704i \(0.00349206\pi\)
−0.999940 + 0.0109704i \(0.996508\pi\)
\(12\) −5.46070 + 1.02743i −0.455058 + 0.0856189i
\(13\) 7.70332 + 13.3426i 0.592563 + 1.02635i 0.993886 + 0.110413i \(0.0352174\pi\)
−0.401322 + 0.915937i \(0.631449\pi\)
\(14\) −0.973295 10.2126i −0.0695210 0.729468i
\(15\) 2.62345 2.25299i 0.174897 0.150199i
\(16\) 2.58039 + 4.46937i 0.161274 + 0.279335i
\(17\) 10.9102 6.29901i 0.641777 0.370530i −0.143522 0.989647i \(-0.545843\pi\)
0.785299 + 0.619117i \(0.212509\pi\)
\(18\) −4.79366 12.2880i −0.266314 0.682667i
\(19\) 13.7090 23.7446i 0.721525 1.24972i −0.238864 0.971053i \(-0.576775\pi\)
0.960389 0.278664i \(-0.0898917\pi\)
\(20\) 1.84896 + 1.06750i 0.0924482 + 0.0533750i
\(21\) −20.1764 + 5.82348i −0.960781 + 0.277309i
\(22\) −0.176854 0.306320i −0.00803882 0.0139236i
\(23\) 20.3881i 0.886438i −0.896413 0.443219i \(-0.853836\pi\)
0.896413 0.443219i \(-0.146164\pi\)
\(24\) 19.5197 16.7633i 0.813322 0.698471i
\(25\) 23.6713 0.946851
\(26\) −19.5541 11.2896i −0.752082 0.434215i
\(27\) −22.9056 + 14.2945i −0.848355 + 0.529427i
\(28\) −7.51862 10.5625i −0.268522 0.377233i
\(29\) 16.9161 + 9.76653i 0.583315 + 0.336777i 0.762450 0.647048i \(-0.223997\pi\)
−0.179135 + 0.983825i \(0.557330\pi\)
\(30\) −1.67876 + 4.78190i −0.0559586 + 0.159397i
\(31\) 1.36337 2.36142i 0.0439796 0.0761749i −0.843198 0.537604i \(-0.819330\pi\)
0.887177 + 0.461429i \(0.152663\pi\)
\(32\) 23.1603 + 13.3716i 0.723758 + 0.417862i
\(33\) −0.549290 + 0.471724i −0.0166452 + 0.0142947i
\(34\) −9.23150 + 15.9894i −0.271515 + 0.470277i
\(35\) 7.33912 + 3.35329i 0.209689 + 0.0958082i
\(36\) −13.0114 10.4200i −0.361429 0.289444i
\(37\) −11.4455 + 19.8242i −0.309338 + 0.535789i −0.978218 0.207582i \(-0.933441\pi\)
0.668880 + 0.743371i \(0.266774\pi\)
\(38\) 40.1823i 1.05743i
\(39\) −15.3102 + 43.6106i −0.392568 + 1.11822i
\(40\) −9.88629 −0.247157
\(41\) −61.9933 + 35.7918i −1.51203 + 0.872972i −0.512130 + 0.858908i \(0.671144\pi\)
−0.999901 + 0.0140641i \(0.995523\pi\)
\(42\) 21.3406 22.1759i 0.508110 0.527998i
\(43\) 14.8972 25.8028i 0.346447 0.600064i −0.639168 0.769067i \(-0.720721\pi\)
0.985616 + 0.169003i \(0.0540546\pi\)
\(44\) −0.387130 0.223510i −0.00879841 0.00507977i
\(45\) 10.2552 + 1.56722i 0.227894 + 0.0348272i
\(46\) 14.9398 + 25.8766i 0.324779 + 0.562534i
\(47\) −25.9734 + 14.9958i −0.552626 + 0.319059i −0.750180 0.661233i \(-0.770033\pi\)
0.197555 + 0.980292i \(0.436700\pi\)
\(48\) −5.12846 + 14.6083i −0.106843 + 0.304339i
\(49\) −32.0746 37.0435i −0.654584 0.755989i
\(50\) −30.0436 + 17.3457i −0.600872 + 0.346914i
\(51\) 35.6604 + 12.5191i 0.699223 + 0.245473i
\(52\) −28.5358 −0.548764
\(53\) 90.5906 52.3025i 1.70926 0.986840i 0.773778 0.633457i \(-0.218365\pi\)
0.935479 0.353383i \(-0.114969\pi\)
\(54\) 18.5971 34.9273i 0.344392 0.646801i
\(55\) 0.278203 0.00505824
\(56\) 54.6065 + 24.9500i 0.975116 + 0.445536i
\(57\) 80.8355 15.2091i 1.41817 0.266827i
\(58\) −28.6266 −0.493563
\(59\) −75.0951 43.3562i −1.27280 0.734850i −0.297284 0.954789i \(-0.596081\pi\)
−0.975514 + 0.219939i \(0.929414\pi\)
\(60\) 1.18432 + 6.29455i 0.0197386 + 0.104909i
\(61\) −8.94224 15.4884i −0.146594 0.253908i 0.783372 0.621553i \(-0.213498\pi\)
−0.929967 + 0.367644i \(0.880164\pi\)
\(62\) 3.99616i 0.0644542i
\(63\) −52.6892 34.5377i −0.836336 0.548217i
\(64\) −59.8365 −0.934945
\(65\) 15.3800 8.87963i 0.236615 0.136610i
\(66\) 0.351493 1.00122i 0.00532565 0.0151700i
\(67\) 9.02196 15.6265i 0.134656 0.233231i −0.790810 0.612062i \(-0.790340\pi\)
0.925466 + 0.378831i \(0.123674\pi\)
\(68\) 23.3337i 0.343143i
\(69\) 46.4016 39.8491i 0.672487 0.577524i
\(70\) −11.7720 + 1.12192i −0.168172 + 0.0160274i
\(71\) 74.2118i 1.04524i 0.852567 + 0.522618i \(0.175045\pi\)
−0.852567 + 0.522618i \(0.824955\pi\)
\(72\) 76.3038 + 11.6609i 1.05978 + 0.161957i
\(73\) 13.0598 + 22.6203i 0.178902 + 0.309867i 0.941505 0.337000i \(-0.109412\pi\)
−0.762603 + 0.646867i \(0.776079\pi\)
\(74\) 33.5479i 0.453349i
\(75\) 46.2663 + 53.8739i 0.616884 + 0.718319i
\(76\) 25.3914 + 43.9791i 0.334097 + 0.578673i
\(77\) −1.53664 0.702101i −0.0199564 0.00911819i
\(78\) −12.5250 66.5695i −0.160577 0.853455i
\(79\) −11.2561 19.4962i −0.142483 0.246788i 0.785948 0.618292i \(-0.212175\pi\)
−0.928431 + 0.371505i \(0.878842\pi\)
\(80\) 5.15184 2.97442i 0.0643980 0.0371802i
\(81\) −77.3029 24.1921i −0.954357 0.298668i
\(82\) 52.4546 90.8541i 0.639691 1.10798i
\(83\) −77.0996 44.5135i −0.928911 0.536307i −0.0424438 0.999099i \(-0.513514\pi\)
−0.886467 + 0.462792i \(0.846848\pi\)
\(84\) 9.34404 37.7565i 0.111239 0.449483i
\(85\) −7.26088 12.5762i −0.0854221 0.147955i
\(86\) 43.6652i 0.507735i
\(87\) 10.8353 + 57.5887i 0.124543 + 0.661939i
\(88\) 2.06996 0.0235223
\(89\) −49.7459 28.7208i −0.558942 0.322706i 0.193779 0.981045i \(-0.437926\pi\)
−0.752721 + 0.658340i \(0.771259\pi\)
\(90\) −14.1644 + 5.52565i −0.157382 + 0.0613961i
\(91\) −107.360 + 10.2318i −1.17978 + 0.112438i
\(92\) 32.7030 + 18.8811i 0.355468 + 0.205229i
\(93\) 8.03915 1.51256i 0.0864425 0.0162641i
\(94\) 21.9770 38.0653i 0.233798 0.404950i
\(95\) −27.3705 15.8023i −0.288110 0.166340i
\(96\) 14.8348 + 78.8461i 0.154530 + 0.821313i
\(97\) 73.9883 128.152i 0.762766 1.32115i −0.178653 0.983912i \(-0.557174\pi\)
0.941419 0.337238i \(-0.109493\pi\)
\(98\) 67.8536 + 23.5122i 0.692384 + 0.239920i
\(99\) −2.14721 0.328140i −0.0216890 0.00331455i
\(100\) −21.9216 + 37.9694i −0.219216 + 0.379694i
\(101\) 84.1369i 0.833039i 0.909127 + 0.416519i \(0.136750\pi\)
−0.909127 + 0.416519i \(0.863250\pi\)
\(102\) −54.4339 + 10.2417i −0.533666 + 0.100409i
\(103\) 58.9675 0.572500 0.286250 0.958155i \(-0.407591\pi\)
0.286250 + 0.958155i \(0.407591\pi\)
\(104\) 114.434 66.0686i 1.10033 0.635275i
\(105\) 6.71274 + 23.2574i 0.0639308 + 0.221499i
\(106\) −76.6518 + 132.765i −0.723130 + 1.25250i
\(107\) −76.9320 44.4167i −0.718990 0.415109i 0.0953906 0.995440i \(-0.469590\pi\)
−0.814381 + 0.580331i \(0.802923\pi\)
\(108\) −1.71629 49.9792i −0.0158916 0.462770i
\(109\) 94.4610 + 163.611i 0.866615 + 1.50102i 0.865435 + 0.501021i \(0.167042\pi\)
0.00117990 + 0.999999i \(0.499624\pi\)
\(110\) −0.353096 + 0.203860i −0.00320996 + 0.00185327i
\(111\) −67.4889 + 12.6980i −0.608008 + 0.114396i
\(112\) −35.9625 + 3.42736i −0.321094 + 0.0306014i
\(113\) 101.115 58.3790i 0.894827 0.516629i 0.0193087 0.999814i \(-0.493853\pi\)
0.875518 + 0.483185i \(0.160520\pi\)
\(114\) −91.4516 + 78.5376i −0.802207 + 0.688926i
\(115\) −23.5014 −0.204360
\(116\) −31.3316 + 18.0893i −0.270100 + 0.155942i
\(117\) −129.178 + 50.3936i −1.10409 + 0.430714i
\(118\) 127.081 1.07696
\(119\) 8.36656 + 87.7884i 0.0703072 + 0.737718i
\(120\) −19.3231 22.5004i −0.161026 0.187503i
\(121\) 120.942 0.999519
\(122\) 22.6990 + 13.1053i 0.186057 + 0.107420i
\(123\) −202.627 71.1354i −1.64738 0.578336i
\(124\) 2.52519 + 4.37376i 0.0203644 + 0.0352722i
\(125\) 56.1034i 0.448827i
\(126\) 92.1815 + 5.22598i 0.731599 + 0.0414760i
\(127\) −33.5427 −0.264116 −0.132058 0.991242i \(-0.542159\pi\)
−0.132058 + 0.991242i \(0.542159\pi\)
\(128\) −16.6965 + 9.63973i −0.130441 + 0.0753104i
\(129\) 87.8421 16.5274i 0.680947 0.128120i
\(130\) −13.0135 + 22.5401i −0.100104 + 0.173385i
\(131\) 71.4985i 0.545790i 0.962044 + 0.272895i \(0.0879812\pi\)
−0.962044 + 0.272895i \(0.912019\pi\)
\(132\) −0.247968 1.31793i −0.00187855 0.00998434i
\(133\) 111.299 + 156.358i 0.836836 + 1.17563i
\(134\) 26.4442i 0.197345i
\(135\) 16.4773 + 26.4033i 0.122054 + 0.195580i
\(136\) −54.0243 93.5729i −0.397238 0.688036i
\(137\) 216.764i 1.58222i −0.611677 0.791108i \(-0.709505\pi\)
0.611677 0.791108i \(-0.290495\pi\)
\(138\) −29.6926 + 84.5785i −0.215164 + 0.612887i
\(139\) 53.7032 + 93.0167i 0.386354 + 0.669185i 0.991956 0.126583i \(-0.0404009\pi\)
−0.605602 + 0.795768i \(0.707068\pi\)
\(140\) −12.1754 + 8.66672i −0.0869673 + 0.0619051i
\(141\) −84.8950 29.8037i −0.602092 0.211374i
\(142\) −54.3804 94.1897i −0.382961 0.663307i
\(143\) −3.22021 + 1.85919i −0.0225189 + 0.0130013i
\(144\) −43.2710 + 16.8804i −0.300493 + 0.117225i
\(145\) 11.2579 19.4992i 0.0776406 0.134477i
\(146\) −33.1511 19.1398i −0.227062 0.131094i
\(147\) 21.6171 145.402i 0.147055 0.989128i
\(148\) −21.1990 36.7178i −0.143237 0.248093i
\(149\) 157.089i 1.05429i −0.849777 0.527143i \(-0.823263\pi\)
0.849777 0.527143i \(-0.176737\pi\)
\(150\) −98.1986 34.4741i −0.654657 0.229827i
\(151\) −120.482 −0.797897 −0.398948 0.916973i \(-0.630625\pi\)
−0.398948 + 0.916973i \(0.630625\pi\)
\(152\) −203.649 117.577i −1.33980 0.773532i
\(153\) 41.2069 + 105.629i 0.269326 + 0.690387i
\(154\) 2.46479 0.234904i 0.0160051 0.00152535i
\(155\) −2.72201 1.57156i −0.0175614 0.0101391i
\(156\) −55.7740 64.9450i −0.357526 0.416314i
\(157\) −3.87777 + 6.71650i −0.0246992 + 0.0427802i −0.878111 0.478457i \(-0.841196\pi\)
0.853412 + 0.521238i \(0.174529\pi\)
\(158\) 28.5726 + 16.4964i 0.180839 + 0.104408i
\(159\) 296.098 + 103.950i 1.86225 + 0.653773i
\(160\) 15.4134 26.6969i 0.0963340 0.166855i
\(161\) 129.809 + 59.3104i 0.806265 + 0.368387i
\(162\) 115.840 25.9409i 0.715064 0.160129i
\(163\) 129.964 225.104i 0.797323 1.38100i −0.124031 0.992278i \(-0.539582\pi\)
0.921354 0.388725i \(-0.127084\pi\)
\(164\) 132.585i 0.808447i
\(165\) 0.543757 + 0.633168i 0.00329550 + 0.00383738i
\(166\) 130.473 0.785983
\(167\) 97.3809 56.2229i 0.583119 0.336664i −0.179253 0.983803i \(-0.557368\pi\)
0.762372 + 0.647139i \(0.224035\pi\)
\(168\) 49.9459 + 173.046i 0.297297 + 1.03003i
\(169\) −34.1824 + 59.2057i −0.202263 + 0.350330i
\(170\) 18.4310 + 10.6412i 0.108418 + 0.0625951i
\(171\) 192.610 + 154.248i 1.12638 + 0.902036i
\(172\) 27.5922 + 47.7911i 0.160420 + 0.277855i
\(173\) 12.1128 6.99333i 0.0700162 0.0404239i −0.464583 0.885529i \(-0.653796\pi\)
0.534599 + 0.845106i \(0.320463\pi\)
\(174\) −55.9517 65.1519i −0.321561 0.374436i
\(175\) −68.8614 + 150.712i −0.393494 + 0.861214i
\(176\) −1.07868 + 0.622774i −0.00612884 + 0.00353849i
\(177\) −48.1006 255.651i −0.271755 1.44436i
\(178\) 84.1834 0.472940
\(179\) −44.1214 + 25.4735i −0.246488 + 0.142310i −0.618155 0.786056i \(-0.712120\pi\)
0.371667 + 0.928366i \(0.378786\pi\)
\(180\) −12.0111 + 14.9983i −0.0667284 + 0.0833239i
\(181\) −239.784 −1.32477 −0.662387 0.749161i \(-0.730457\pi\)
−0.662387 + 0.749161i \(0.730457\pi\)
\(182\) 128.764 91.6569i 0.707494 0.503609i
\(183\) 17.7725 50.6244i 0.0971174 0.276636i
\(184\) −174.861 −0.950332
\(185\) 22.8514 + 13.1932i 0.123521 + 0.0713148i
\(186\) −9.09493 + 7.81062i −0.0488975 + 0.0419926i
\(187\) 1.52026 + 2.63317i 0.00812973 + 0.0140811i
\(188\) 55.5494i 0.295476i
\(189\) −24.3778 187.421i −0.128983 0.991647i
\(190\) 46.3182 0.243780
\(191\) −159.211 + 91.9205i −0.833566 + 0.481259i −0.855072 0.518509i \(-0.826487\pi\)
0.0215064 + 0.999769i \(0.493154\pi\)
\(192\) −116.952 136.183i −0.609127 0.709286i
\(193\) −76.3985 + 132.326i −0.395847 + 0.685628i −0.993209 0.116344i \(-0.962882\pi\)
0.597362 + 0.801972i \(0.296216\pi\)
\(194\) 216.867i 1.11787i
\(195\) 50.2700 + 17.6480i 0.257795 + 0.0905028i
\(196\) 89.1226 17.1431i 0.454707 0.0874650i
\(197\) 386.007i 1.95943i 0.200402 + 0.979714i \(0.435775\pi\)
−0.200402 + 0.979714i \(0.564225\pi\)
\(198\) 2.96570 1.15694i 0.0149783 0.00584315i
\(199\) −22.8387 39.5577i −0.114767 0.198782i 0.802920 0.596087i \(-0.203279\pi\)
−0.917687 + 0.397305i \(0.869946\pi\)
\(200\) 203.020i 1.01510i
\(201\) 53.1983 10.0092i 0.264668 0.0497972i
\(202\) −61.6533 106.787i −0.305214 0.528647i
\(203\) −111.393 + 79.2916i −0.548732 + 0.390599i
\(204\) −53.1056 + 45.6065i −0.260322 + 0.223561i
\(205\) 41.2573 + 71.4597i 0.201255 + 0.348584i
\(206\) −74.8417 + 43.2099i −0.363309 + 0.209757i
\(207\) 181.387 + 27.7199i 0.876265 + 0.133912i
\(208\) −39.7552 + 68.8579i −0.191131 + 0.331048i
\(209\) 5.73074 + 3.30864i 0.0274198 + 0.0158308i
\(210\) −25.5622 24.5993i −0.121725 0.117140i
\(211\) −169.338 293.302i −0.802550 1.39006i −0.917933 0.396736i \(-0.870143\pi\)
0.115383 0.993321i \(-0.463190\pi\)
\(212\) 193.746i 0.913898i
\(213\) −168.900 + 145.049i −0.792957 + 0.680982i
\(214\) 130.190 0.608362
\(215\) −29.7429 17.1721i −0.138339 0.0798700i
\(216\) 122.599 + 196.453i 0.567588 + 0.909504i
\(217\) 11.0688 + 15.5500i 0.0510082 + 0.0716588i
\(218\) −239.780 138.437i −1.09991 0.635032i
\(219\) −25.9561 + 73.9351i −0.118521 + 0.337603i
\(220\) −0.257640 + 0.446245i −0.00117109 + 0.00202839i
\(221\) 168.090 + 97.0467i 0.760587 + 0.439125i
\(222\) 76.3522 65.5703i 0.343929 0.295362i
\(223\) 43.8681 75.9817i 0.196718 0.340725i −0.750745 0.660593i \(-0.770305\pi\)
0.947462 + 0.319868i \(0.103638\pi\)
\(224\) −152.510 + 108.560i −0.680849 + 0.484643i
\(225\) −32.1837 + 210.597i −0.143039 + 0.935985i
\(226\) −85.5572 + 148.189i −0.378572 + 0.655706i
\(227\) 352.696i 1.55373i 0.629668 + 0.776864i \(0.283191\pi\)
−0.629668 + 0.776864i \(0.716809\pi\)
\(228\) −50.4647 + 143.747i −0.221336 + 0.630470i
\(229\) −380.791 −1.66284 −0.831421 0.555644i \(-0.812472\pi\)
−0.831421 + 0.555644i \(0.812472\pi\)
\(230\) 29.8280 17.2212i 0.129687 0.0748747i
\(231\) −1.40549 4.86955i −0.00608438 0.0210803i
\(232\) 83.7640 145.083i 0.361052 0.625360i
\(233\) 271.555 + 156.782i 1.16547 + 0.672885i 0.952609 0.304197i \(-0.0983882\pi\)
0.212862 + 0.977082i \(0.431722\pi\)
\(234\) 127.026 158.618i 0.542847 0.677855i
\(235\) 17.2856 + 29.9396i 0.0735558 + 0.127402i
\(236\) 139.089 80.3030i 0.589360 0.340267i
\(237\) 22.3713 63.7241i 0.0943937 0.268878i
\(238\) −74.9479 105.290i −0.314907 0.442396i
\(239\) 199.851 115.384i 0.836195 0.482777i −0.0197741 0.999804i \(-0.506295\pi\)
0.855969 + 0.517027i \(0.172961\pi\)
\(240\) 16.8390 + 5.91158i 0.0701624 + 0.0246316i
\(241\) −180.856 −0.750442 −0.375221 0.926935i \(-0.622433\pi\)
−0.375221 + 0.926935i \(0.622433\pi\)
\(242\) −153.499 + 88.6229i −0.634295 + 0.366210i
\(243\) −96.0317 223.219i −0.395192 0.918598i
\(244\) 33.1251 0.135759
\(245\) −42.7000 + 36.9724i −0.174286 + 0.150908i
\(246\) 309.301 58.1947i 1.25732 0.236564i
\(247\) 422.419 1.71020
\(248\) −20.2531 11.6931i −0.0816655 0.0471496i
\(249\) −49.3846 262.475i −0.198332 1.05412i
\(250\) 41.1111 + 71.2065i 0.164444 + 0.284826i
\(251\) 161.864i 0.644878i 0.946590 + 0.322439i \(0.104503\pi\)
−0.946590 + 0.322439i \(0.895497\pi\)
\(252\) 104.194 52.5301i 0.413468 0.208453i
\(253\) 4.92064 0.0194492
\(254\) 42.5725 24.5792i 0.167608 0.0967687i
\(255\) 14.4308 41.1058i 0.0565914 0.161199i
\(256\) 133.800 231.749i 0.522658 0.905270i
\(257\) 75.6745i 0.294453i −0.989103 0.147227i \(-0.952965\pi\)
0.989103 0.147227i \(-0.0470347\pi\)
\(258\) −99.3784 + 85.3450i −0.385188 + 0.330795i
\(259\) −92.9227 130.542i −0.358775 0.504024i
\(260\) 32.8932i 0.126512i
\(261\) −109.889 + 137.219i −0.421032 + 0.525744i
\(262\) −52.3922 90.7460i −0.199970 0.346359i
\(263\) 11.6465i 0.0442833i 0.999755 + 0.0221417i \(0.00704849\pi\)
−0.999755 + 0.0221417i \(0.992952\pi\)
\(264\) 4.04580 + 4.71106i 0.0153250 + 0.0178449i
\(265\) −60.2892 104.424i −0.227506 0.394052i
\(266\) −255.836 116.893i −0.961791 0.439448i
\(267\) −31.8637 169.353i −0.119340 0.634282i
\(268\) 16.7102 + 28.9429i 0.0623516 + 0.107996i
\(269\) 265.976 153.562i 0.988760 0.570861i 0.0838565 0.996478i \(-0.473276\pi\)
0.904903 + 0.425617i \(0.139943\pi\)
\(270\) −40.2607 21.4369i −0.149114 0.0793961i
\(271\) 169.039 292.784i 0.623759 1.08038i −0.365020 0.931000i \(-0.618938\pi\)
0.988779 0.149383i \(-0.0477287\pi\)
\(272\) 56.3052 + 32.5078i 0.207004 + 0.119514i
\(273\) −233.125 224.344i −0.853939 0.821774i
\(274\) 158.839 + 275.117i 0.579703 + 1.00408i
\(275\) 5.71304i 0.0207747i
\(276\) 20.9473 + 111.333i 0.0758959 + 0.403381i
\(277\) −132.022 −0.476614 −0.238307 0.971190i \(-0.576592\pi\)
−0.238307 + 0.971190i \(0.576592\pi\)
\(278\) −136.320 78.7046i −0.490361 0.283110i
\(279\) 19.1552 + 15.3401i 0.0686568 + 0.0549824i
\(280\) 28.7599 62.9450i 0.102714 0.224803i
\(281\) −64.2832 37.1139i −0.228766 0.132078i 0.381237 0.924477i \(-0.375498\pi\)
−0.610003 + 0.792399i \(0.708832\pi\)
\(282\) 129.588 24.3819i 0.459533 0.0864607i
\(283\) 5.65152 9.78873i 0.0199701 0.0345891i −0.855868 0.517195i \(-0.826976\pi\)
0.875838 + 0.482606i \(0.160310\pi\)
\(284\) −119.038 68.7264i −0.419147 0.241994i
\(285\) −17.5316 93.1791i −0.0615144 0.326944i
\(286\) 2.72473 4.71937i 0.00952702 0.0165013i
\(287\) −47.5399 498.826i −0.165644 1.73807i
\(288\) −150.452 + 187.870i −0.522403 + 0.652326i
\(289\) −65.1449 + 112.834i −0.225415 + 0.390430i
\(290\) 32.9979i 0.113786i
\(291\) 436.275 82.0849i 1.49923 0.282079i
\(292\) −48.3781 −0.165678
\(293\) −144.131 + 83.2139i −0.491913 + 0.284006i −0.725368 0.688361i \(-0.758330\pi\)
0.233454 + 0.972368i \(0.424997\pi\)
\(294\) 79.1102 + 200.385i 0.269082 + 0.681580i
\(295\) −49.9767 + 86.5621i −0.169412 + 0.293431i
\(296\) 170.025 + 98.1639i 0.574408 + 0.331635i
\(297\) −3.44997 5.52824i −0.0116161 0.0186136i
\(298\) 115.110 + 199.377i 0.386276 + 0.669050i
\(299\) 272.029 157.056i 0.909796 0.525271i
\(300\) −129.262 + 24.3205i −0.430872 + 0.0810684i
\(301\) 120.946 + 169.911i 0.401815 + 0.564489i
\(302\) 152.916 88.2864i 0.506346 0.292339i
\(303\) −191.489 + 164.448i −0.631976 + 0.542734i
\(304\) 141.498 0.465454
\(305\) −17.8535 + 10.3077i −0.0585361 + 0.0337958i
\(306\) −129.702 103.869i −0.423863 0.339443i
\(307\) −382.982 −1.24750 −0.623749 0.781625i \(-0.714391\pi\)
−0.623749 + 0.781625i \(0.714391\pi\)
\(308\) 2.54925 1.81461i 0.00827679 0.00589159i
\(309\) 115.254 + 134.205i 0.372990 + 0.434321i
\(310\) 4.60638 0.0148593
\(311\) −135.109 78.0053i −0.434435 0.250821i 0.266799 0.963752i \(-0.414034\pi\)
−0.701234 + 0.712931i \(0.747367\pi\)
\(312\) 374.032 + 131.310i 1.19882 + 0.420864i
\(313\) −58.2651 100.918i −0.186150 0.322422i 0.757813 0.652472i \(-0.226268\pi\)
−0.943964 + 0.330050i \(0.892935\pi\)
\(314\) 11.3661i 0.0361978i
\(315\) −39.8116 + 60.7349i −0.126386 + 0.192809i
\(316\) 41.6966 0.131951
\(317\) −162.694 + 93.9313i −0.513229 + 0.296313i −0.734160 0.678976i \(-0.762424\pi\)
0.220931 + 0.975290i \(0.429091\pi\)
\(318\) −451.980 + 85.0398i −1.42132 + 0.267421i
\(319\) −2.35714 + 4.08269i −0.00738916 + 0.0127984i
\(320\) 68.9736i 0.215542i
\(321\) −49.2772 261.905i −0.153512 0.815903i
\(322\) −208.214 + 19.8436i −0.646629 + 0.0616261i
\(323\) 345.412i 1.06939i
\(324\) 110.394 101.592i 0.340722 0.313556i
\(325\) 182.348 + 315.835i 0.561069 + 0.971801i
\(326\) 380.936i 1.16851i
\(327\) −187.739 + 534.769i −0.574125 + 1.63538i
\(328\) 306.974 + 531.694i 0.935895 + 1.62102i
\(329\) −19.9179 208.994i −0.0605406 0.635239i
\(330\) −1.15411 0.405166i −0.00349729 0.00122778i
\(331\) 31.7161 + 54.9338i 0.0958189 + 0.165963i 0.909950 0.414718i \(-0.136120\pi\)
−0.814131 + 0.580681i \(0.802786\pi\)
\(332\) 142.802 82.4466i 0.430125 0.248333i
\(333\) −160.809 128.781i −0.482909 0.386728i
\(334\) −82.3973 + 142.716i −0.246698 + 0.427294i
\(335\) −18.0127 10.3996i −0.0537692 0.0310437i
\(336\) −78.0902 75.1488i −0.232411 0.223657i
\(337\) 88.4049 + 153.122i 0.262329 + 0.454367i 0.966860 0.255306i \(-0.0821761\pi\)
−0.704531 + 0.709673i \(0.748843\pi\)
\(338\) 100.192i 0.296426i
\(339\) 330.499 + 116.027i 0.974924 + 0.342262i
\(340\) 26.8968 0.0791082
\(341\) 0.569926 + 0.329047i 0.00167134 + 0.000964948i
\(342\) −357.490 54.6323i −1.04529 0.159743i
\(343\) 329.159 96.4535i 0.959648 0.281206i
\(344\) −221.301 127.768i −0.643316 0.371419i
\(345\) −45.9342 53.4872i −0.133142 0.155035i
\(346\) −10.2491 + 17.7519i −0.0296216 + 0.0513060i
\(347\) 210.706 + 121.651i 0.607223 + 0.350580i 0.771878 0.635771i \(-0.219318\pi\)
−0.164655 + 0.986351i \(0.552651\pi\)
\(348\) −102.408 35.9520i −0.294277 0.103310i
\(349\) −209.668 + 363.156i −0.600768 + 1.04056i 0.391937 + 0.919992i \(0.371805\pi\)
−0.992705 + 0.120568i \(0.961528\pi\)
\(350\) −23.0391 241.744i −0.0658261 0.690698i
\(351\) −367.175 195.504i −1.04608 0.556990i
\(352\) −3.22722 + 5.58970i −0.00916823 + 0.0158798i
\(353\) 347.861i 0.985443i −0.870187 0.492722i \(-0.836002\pi\)
0.870187 0.492722i \(-0.163998\pi\)
\(354\) 248.384 + 289.226i 0.701649 + 0.817023i
\(355\) 85.5440 0.240969
\(356\) 92.1379 53.1958i 0.258814 0.149426i
\(357\) −183.447 + 190.627i −0.513856 + 0.533969i
\(358\) 37.3326 64.6620i 0.104281 0.180620i
\(359\) −392.233 226.456i −1.09257 0.630796i −0.158311 0.987389i \(-0.550605\pi\)
−0.934260 + 0.356593i \(0.883938\pi\)
\(360\) 13.4415 87.9555i 0.0373375 0.244321i
\(361\) −195.372 338.394i −0.541196 0.937379i
\(362\) 304.334 175.708i 0.840703 0.485380i
\(363\) 236.384 + 275.254i 0.651197 + 0.758274i
\(364\) 83.0125 181.684i 0.228056 0.499132i
\(365\) 26.0744 15.0541i 0.0714368 0.0412440i
\(366\) 14.5394 + 77.2758i 0.0397251 + 0.211136i
\(367\) −3.19960 −0.00871826 −0.00435913 0.999990i \(-0.501388\pi\)
−0.00435913 + 0.999990i \(0.501388\pi\)
\(368\) 91.1218 52.6092i 0.247613 0.142960i
\(369\) −234.143 600.199i −0.634534 1.62656i
\(370\) −38.6706 −0.104515
\(371\) 69.4700 + 728.932i 0.187251 + 1.96478i
\(372\) −5.01875 + 14.2958i −0.0134913 + 0.0384295i
\(373\) −149.443 −0.400652 −0.200326 0.979729i \(-0.564200\pi\)
−0.200326 + 0.979729i \(0.564200\pi\)
\(374\) −3.85903 2.22801i −0.0103183 0.00595725i
\(375\) 127.687 109.656i 0.340498 0.292416i
\(376\) 128.613 + 222.764i 0.342056 + 0.592459i
\(377\) 300.939i 0.798247i
\(378\) 168.278 + 220.012i 0.445179 + 0.582042i
\(379\) 431.217 1.13778 0.568888 0.822415i \(-0.307374\pi\)
0.568888 + 0.822415i \(0.307374\pi\)
\(380\) 50.6948 29.2686i 0.133407 0.0770227i
\(381\) −65.5604 76.3406i −0.172074 0.200369i
\(382\) 134.714 233.331i 0.352654 0.610815i
\(383\) 179.770i 0.469373i 0.972071 + 0.234687i \(0.0754064\pi\)
−0.972071 + 0.234687i \(0.924594\pi\)
\(384\) −54.5731 19.1587i −0.142117 0.0498925i
\(385\) −0.809312 + 1.77129i −0.00210211 + 0.00460075i
\(386\) 223.931i 0.580133i
\(387\) 209.305 + 167.618i 0.540841 + 0.433122i
\(388\) 137.039 + 237.359i 0.353193 + 0.611749i
\(389\) 337.148i 0.866703i 0.901225 + 0.433352i \(0.142669\pi\)
−0.901225 + 0.433352i \(0.857331\pi\)
\(390\) −76.7347 + 14.4376i −0.196756 + 0.0370194i
\(391\) −128.425 222.438i −0.328452 0.568896i
\(392\) −317.708 + 275.092i −0.810480 + 0.701766i
\(393\) −162.725 + 139.746i −0.414058 + 0.355588i
\(394\) −282.856 489.921i −0.717908 1.24345i
\(395\) −22.4733 + 12.9750i −0.0568945 + 0.0328480i
\(396\) 2.51485 3.14030i 0.00635062 0.00793005i
\(397\) −266.853 + 462.203i −0.672174 + 1.16424i 0.305113 + 0.952316i \(0.401306\pi\)
−0.977286 + 0.211923i \(0.932027\pi\)
\(398\) 57.9737 + 33.4711i 0.145663 + 0.0840983i
\(399\) −138.321 + 558.915i −0.346670 + 1.40079i
\(400\) 61.0811 + 105.796i 0.152703 + 0.264489i
\(401\) 606.232i 1.51180i −0.654687 0.755900i \(-0.727199\pi\)
0.654687 0.755900i \(-0.272801\pi\)
\(402\) −60.1849 + 51.6861i −0.149714 + 0.128572i
\(403\) 42.0099 0.104243
\(404\) −134.958 77.9180i −0.334054 0.192866i
\(405\) −27.8863 + 89.1071i −0.0688550 + 0.220018i
\(406\) 83.2769 182.263i 0.205115 0.448923i
\(407\) −4.78455 2.76236i −0.0117556 0.00678712i
\(408\) 107.372 305.846i 0.263167 0.749623i
\(409\) 196.056 339.580i 0.479355 0.830268i −0.520364 0.853944i \(-0.674204\pi\)
0.999720 + 0.0236765i \(0.00753715\pi\)
\(410\) −104.728 60.4645i −0.255433 0.147474i
\(411\) 493.336 423.671i 1.20033 1.03083i
\(412\) −54.6090 + 94.5855i −0.132546 + 0.229577i
\(413\) 494.501 351.996i 1.19734 0.852291i
\(414\) −250.529 + 97.7334i −0.605142 + 0.236071i
\(415\) −51.3107 + 88.8728i −0.123640 + 0.214151i
\(416\) 412.023i 0.990439i
\(417\) −106.734 + 304.028i −0.255956 + 0.729085i
\(418\) −9.69795 −0.0232008
\(419\) −577.328 + 333.321i −1.37787 + 0.795515i −0.991903 0.126997i \(-0.959466\pi\)
−0.385969 + 0.922512i \(0.626133\pi\)
\(420\) −43.5220 10.7709i −0.103624 0.0256450i
\(421\) 235.637 408.136i 0.559708 0.969443i −0.437812 0.899067i \(-0.644246\pi\)
0.997520 0.0703769i \(-0.0224202\pi\)
\(422\) 429.848 + 248.173i 1.01860 + 0.588087i
\(423\) −98.0992 251.466i −0.231913 0.594483i
\(424\) −448.579 776.962i −1.05797 1.83246i
\(425\) 258.259 149.106i 0.607667 0.350837i
\(426\) 108.080 307.862i 0.253708 0.722681i
\(427\) 124.627 11.8774i 0.291866 0.0278159i
\(428\) 142.491 82.2673i 0.332923 0.192213i
\(429\) −10.5254 3.69509i −0.0245346 0.00861326i
\(430\) 50.3329 0.117053
\(431\) −204.379 + 117.998i −0.474197 + 0.273778i −0.717995 0.696048i \(-0.754940\pi\)
0.243798 + 0.969826i \(0.421607\pi\)
\(432\) −122.993 65.4880i −0.284706 0.151593i
\(433\) 388.304 0.896776 0.448388 0.893839i \(-0.351998\pi\)
0.448388 + 0.893839i \(0.351998\pi\)
\(434\) −25.4431 11.6251i −0.0586247 0.0267860i
\(435\) 66.3826 12.4898i 0.152604 0.0287123i
\(436\) −349.916 −0.802559
\(437\) −484.107 279.500i −1.10780 0.639587i
\(438\) −21.2343 112.858i −0.0484800 0.257668i
\(439\) 175.658 + 304.248i 0.400132 + 0.693049i 0.993741 0.111704i \(-0.0356309\pi\)
−0.593610 + 0.804753i \(0.702298\pi\)
\(440\) 2.38605i 0.00542283i
\(441\) 373.174 234.994i 0.846200 0.532866i
\(442\) −284.453 −0.643559
\(443\) 46.0205 26.5700i 0.103884 0.0599773i −0.447158 0.894455i \(-0.647564\pi\)
0.551042 + 0.834478i \(0.314230\pi\)
\(444\) 42.1325 120.013i 0.0948931 0.270300i
\(445\) −33.1065 + 57.3421i −0.0743966 + 0.128859i
\(446\) 128.581i 0.288299i
\(447\) 357.521 307.035i 0.799823 0.686878i
\(448\) 174.069 380.972i 0.388546 0.850385i
\(449\) 526.389i 1.17236i 0.810181 + 0.586179i \(0.199369\pi\)
−0.810181 + 0.586179i \(0.800631\pi\)
\(450\) −113.472 290.873i −0.252160 0.646384i
\(451\) −8.63832 14.9620i −0.0191537 0.0331752i
\(452\) 216.256i 0.478442i
\(453\) −235.487 274.208i −0.519838 0.605316i
\(454\) −258.447 447.643i −0.569266 0.985997i
\(455\) 11.7942 + 123.754i 0.0259214 + 0.271987i
\(456\) −130.443 693.296i −0.286060 1.52039i
\(457\) 369.881 + 640.652i 0.809367 + 1.40186i 0.913303 + 0.407280i \(0.133523\pi\)
−0.103936 + 0.994584i \(0.533144\pi\)
\(458\) 483.300 279.033i 1.05524 0.609243i
\(459\) −159.863 + 300.239i −0.348286 + 0.654116i
\(460\) 21.7643 37.6968i 0.0473136 0.0819496i
\(461\) 284.624 + 164.328i 0.617406 + 0.356460i 0.775858 0.630907i \(-0.217317\pi\)
−0.158452 + 0.987367i \(0.550650\pi\)
\(462\) 5.35213 + 5.15053i 0.0115847 + 0.0111483i
\(463\) 3.64605 + 6.31515i 0.00787484 + 0.0136396i 0.869936 0.493165i \(-0.164160\pi\)
−0.862061 + 0.506804i \(0.830827\pi\)
\(464\) 100.806i 0.217254i
\(465\) −1.74353 9.26674i −0.00374953 0.0199285i
\(466\) −459.543 −0.986145
\(467\) 446.593 + 257.841i 0.956303 + 0.552122i 0.895033 0.445999i \(-0.147152\pi\)
0.0612697 + 0.998121i \(0.480485\pi\)
\(468\) 38.7975 253.874i 0.0829007 0.542466i
\(469\) 73.2467 + 102.900i 0.156176 + 0.219404i
\(470\) −43.8779 25.3329i −0.0933572 0.0538998i
\(471\) −22.8654 + 4.30211i −0.0485466 + 0.00913400i
\(472\) −371.850 + 644.063i −0.787817 + 1.36454i
\(473\) 6.22747 + 3.59543i 0.0131659 + 0.00760133i
\(474\) 18.3016 + 97.2718i 0.0386110 + 0.205215i
\(475\) 324.509 562.066i 0.683177 1.18330i
\(476\) −148.563 67.8794i −0.312107 0.142604i
\(477\) 342.152 + 877.070i 0.717301 + 1.83872i
\(478\) −169.100 + 292.890i −0.353767 + 0.612742i
\(479\) 289.661i 0.604720i −0.953194 0.302360i \(-0.902226\pi\)
0.953194 0.302360i \(-0.0977745\pi\)
\(480\) 90.8859 17.1001i 0.189346 0.0356253i
\(481\) −352.674 −0.733209
\(482\) 229.543 132.527i 0.476231 0.274952i
\(483\) 118.730 + 411.358i 0.245817 + 0.851673i
\(484\) −112.002 + 193.994i −0.231410 + 0.400814i
\(485\) −147.720 85.2864i −0.304578 0.175848i
\(486\) 285.453 + 212.941i 0.587352 + 0.438150i
\(487\) −252.275 436.953i −0.518018 0.897234i −0.999781 0.0209323i \(-0.993337\pi\)
0.481763 0.876302i \(-0.339997\pi\)
\(488\) −132.838 + 76.6943i −0.272210 + 0.157161i
\(489\) 766.335 144.185i 1.56715 0.294858i
\(490\) 27.1025 78.2149i 0.0553113 0.159622i
\(491\) −311.614 + 179.910i −0.634651 + 0.366416i −0.782551 0.622586i \(-0.786082\pi\)
0.147900 + 0.989002i \(0.452749\pi\)
\(492\) 301.753 259.142i 0.613320 0.526712i
\(493\) 246.078 0.499144
\(494\) −536.134 + 309.537i −1.08529 + 0.626594i
\(495\) −0.378248 + 2.47509i −0.000764137 + 0.00500019i
\(496\) 14.0721 0.0283711
\(497\) −472.498 215.887i −0.950701 0.434381i
\(498\) 255.014 + 296.946i 0.512076 + 0.596278i
\(499\) −647.042 −1.29668 −0.648338 0.761352i \(-0.724536\pi\)
−0.648338 + 0.761352i \(0.724536\pi\)
\(500\) 89.9914 + 51.9566i 0.179983 + 0.103913i
\(501\) 318.293 + 111.742i 0.635315 + 0.223037i
\(502\) −118.610 205.438i −0.236275 0.409240i
\(503\) 183.191i 0.364198i −0.983280 0.182099i \(-0.941711\pi\)
0.983280 0.182099i \(-0.0582891\pi\)
\(504\) −296.217 + 451.896i −0.587732 + 0.896619i
\(505\) 96.9847 0.192049
\(506\) −6.24528 + 3.60571i −0.0123425 + 0.00712592i
\(507\) −201.558 + 37.9230i −0.397550 + 0.0747988i
\(508\) 31.0635 53.8035i 0.0611485 0.105912i
\(509\) 867.180i 1.70369i 0.523792 + 0.851846i \(0.324517\pi\)
−0.523792 + 0.851846i \(0.675483\pi\)
\(510\) 11.8056 + 62.7460i 0.0231483 + 0.123031i
\(511\) −182.013 + 17.3465i −0.356189 + 0.0339462i
\(512\) 315.064i 0.615359i
\(513\) 25.4065 + 739.848i 0.0495254 + 1.44220i
\(514\) 55.4523 + 96.0462i 0.107884 + 0.186860i
\(515\) 67.9719i 0.131984i
\(516\) −54.8388 + 156.207i −0.106277 + 0.302727i
\(517\) −3.61921 6.26865i −0.00700040 0.0121251i
\(518\) 213.596 + 97.5931i 0.412347 + 0.188404i
\(519\) 39.5911 + 13.8991i 0.0762835 + 0.0267805i
\(520\) −76.1573 131.908i −0.146456 0.253670i
\(521\) −60.2047 + 34.7592i −0.115556 + 0.0667163i −0.556664 0.830738i \(-0.687919\pi\)
0.441108 + 0.897454i \(0.354586\pi\)
\(522\) 38.9211 254.683i 0.0745614 0.487898i
\(523\) −356.425 + 617.347i −0.681502 + 1.18040i 0.293021 + 0.956106i \(0.405339\pi\)
−0.974523 + 0.224290i \(0.927994\pi\)
\(524\) −114.686 66.2137i −0.218866 0.126362i
\(525\) −477.601 + 137.849i −0.909717 + 0.262570i
\(526\) −8.53426 14.7818i −0.0162248 0.0281022i
\(527\) 34.3515i 0.0651831i
\(528\) −3.52569 1.23775i −0.00667744 0.00234422i
\(529\) 113.326 0.214227
\(530\) 153.038 + 88.3566i 0.288751 + 0.166711i
\(531\) 487.827 609.152i 0.918695 1.14718i
\(532\) −353.876 + 33.7257i −0.665180 + 0.0633941i
\(533\) −955.109 551.432i −1.79195 1.03458i
\(534\) 164.539 + 191.594i 0.308126 + 0.358791i
\(535\) −51.1992 + 88.6796i −0.0956994 + 0.165756i
\(536\) −134.023 77.3781i −0.250042 0.144362i
\(537\) −144.212 50.6280i −0.268552 0.0942793i
\(538\) −225.052 + 389.801i −0.418312 + 0.724537i
\(539\) 8.94040 7.74117i 0.0165870 0.0143621i
\(540\) −57.6110 + 1.97837i −0.106687 + 0.00366366i
\(541\) 180.101 311.944i 0.332904 0.576607i −0.650176 0.759784i \(-0.725305\pi\)
0.983080 + 0.183177i \(0.0586381\pi\)
\(542\) 495.468i 0.914148i
\(543\) −468.666 545.729i −0.863105 1.00503i
\(544\) 336.911 0.619322
\(545\) 188.595 108.885i 0.346046 0.199790i
\(546\) 460.277 + 113.910i 0.842998 + 0.208626i
\(547\) −47.0212 + 81.4432i −0.0859620 + 0.148891i −0.905801 0.423704i \(-0.860730\pi\)
0.819839 + 0.572595i \(0.194063\pi\)
\(548\) 347.695 + 200.742i 0.634479 + 0.366317i
\(549\) 149.954 58.4983i 0.273140 0.106554i
\(550\) −4.18636 7.25099i −0.00761157 0.0131836i
\(551\) 463.805 267.778i 0.841752 0.485986i
\(552\) −341.772 397.970i −0.619151 0.720959i
\(553\) 156.875 14.9508i 0.283680 0.0270358i
\(554\) 167.562 96.7422i 0.302459 0.174625i
\(555\) 14.6370 + 77.7945i 0.0263729 + 0.140170i
\(556\) −198.935 −0.357797
\(557\) −516.609 + 298.264i −0.927484 + 0.535483i −0.886015 0.463657i \(-0.846537\pi\)
−0.0414691 + 0.999140i \(0.513204\pi\)
\(558\) −35.5527 5.43322i −0.0637145 0.00973696i
\(559\) 459.033 0.821168
\(560\) 3.95072 + 41.4540i 0.00705486 + 0.0740250i
\(561\) −3.02148 + 8.60660i −0.00538588 + 0.0153415i
\(562\) 108.784 0.193567
\(563\) −627.192 362.110i −1.11402 0.643179i −0.174151 0.984719i \(-0.555718\pi\)
−0.939867 + 0.341540i \(0.889051\pi\)
\(564\) 126.426 108.573i 0.224159 0.192505i
\(565\) −67.2936 116.556i −0.119104 0.206294i
\(566\) 16.5652i 0.0292671i
\(567\) 378.908 421.803i 0.668269 0.743920i
\(568\) 636.487 1.12058
\(569\) 284.852 164.459i 0.500619 0.289032i −0.228350 0.973579i \(-0.573333\pi\)
0.728969 + 0.684547i \(0.240000\pi\)
\(570\) 90.5303 + 105.416i 0.158825 + 0.184941i
\(571\) −3.75701 + 6.50734i −0.00657971 + 0.0113964i −0.869297 0.494291i \(-0.835428\pi\)
0.862717 + 0.505687i \(0.168761\pi\)
\(572\) 6.88707i 0.0120403i
\(573\) −520.387 182.690i −0.908179 0.318830i
\(574\) 425.864 + 598.274i 0.741923 + 1.04229i
\(575\) 482.612i 0.839325i
\(576\) 81.3543 532.348i 0.141240 0.924215i
\(577\) −367.284 636.154i −0.636540 1.10252i −0.986187 0.165638i \(-0.947032\pi\)
0.349647 0.936882i \(-0.386302\pi\)
\(578\) 190.946i 0.330356i
\(579\) −450.487 + 84.7588i −0.778043 + 0.146388i
\(580\) 20.8515 + 36.1159i 0.0359509 + 0.0622688i
\(581\) 507.701 361.392i 0.873839 0.622017i
\(582\) −493.571 + 423.873i −0.848061 + 0.728304i
\(583\) 12.6232 + 21.8639i 0.0216521 + 0.0375025i
\(584\) 194.006 112.009i 0.332202 0.191797i
\(585\) 58.0887 + 148.904i 0.0992970 + 0.254537i
\(586\) 121.954 211.230i 0.208112 0.360461i
\(587\) 125.855 + 72.6624i 0.214404 + 0.123786i 0.603356 0.797472i \(-0.293830\pi\)
−0.388953 + 0.921258i \(0.627163\pi\)
\(588\) 213.209 + 169.329i 0.362601 + 0.287974i
\(589\) −37.3807 64.7453i −0.0634647 0.109924i
\(590\) 146.486i 0.248282i
\(591\) −878.521 + 754.463i −1.48650 + 1.27659i
\(592\) −118.135 −0.199553
\(593\) −248.428 143.430i −0.418934 0.241872i 0.275687 0.961247i \(-0.411095\pi\)
−0.694621 + 0.719376i \(0.744428\pi\)
\(594\) 8.42965 + 4.48840i 0.0141913 + 0.00755623i
\(595\) 101.194 9.64414i 0.170074 0.0162086i
\(596\) 251.974 + 145.477i 0.422776 + 0.244090i
\(597\) 45.3913 129.296i 0.0760323 0.216576i
\(598\) −230.173 + 398.671i −0.384905 + 0.666674i
\(599\) 605.878 + 349.804i 1.01148 + 0.583980i 0.911626 0.411022i \(-0.134828\pi\)
0.0998576 + 0.995002i \(0.468161\pi\)
\(600\) 462.057 396.809i 0.770095 0.661348i
\(601\) 58.2075 100.818i 0.0968511 0.167751i −0.813529 0.581525i \(-0.802456\pi\)
0.910380 + 0.413774i \(0.135790\pi\)
\(602\) −278.012 127.025i −0.461813 0.211005i
\(603\) 126.758 + 101.512i 0.210212 + 0.168345i
\(604\) 111.577 193.257i 0.184730 0.319962i
\(605\) 139.410i 0.230429i
\(606\) 122.534 349.036i 0.202202 0.575967i
\(607\) 642.310 1.05817 0.529086 0.848568i \(-0.322535\pi\)
0.529086 + 0.848568i \(0.322535\pi\)
\(608\) 635.007 366.621i 1.04442 0.602996i
\(609\) −398.182 98.5426i −0.653829 0.161811i
\(610\) 15.1065 26.1652i 0.0247647 0.0428937i
\(611\) −400.163 231.034i −0.654932 0.378125i
\(612\) −207.593 31.7248i −0.339205 0.0518378i
\(613\) 257.842 + 446.595i 0.420623 + 0.728540i 0.996000 0.0893481i \(-0.0284783\pi\)
−0.575378 + 0.817888i \(0.695145\pi\)
\(614\) 486.081 280.639i 0.791663 0.457067i
\(615\) −81.9978 + 233.569i −0.133330 + 0.379786i
\(616\) −6.02166 + 13.1792i −0.00977542 + 0.0213948i
\(617\) 352.937 203.768i 0.572021 0.330257i −0.185935 0.982562i \(-0.559531\pi\)
0.757956 + 0.652305i \(0.226198\pi\)
\(618\) −244.623 85.8785i −0.395829 0.138962i
\(619\) −42.3520 −0.0684201 −0.0342100 0.999415i \(-0.510892\pi\)
−0.0342100 + 0.999415i \(0.510892\pi\)
\(620\) 5.04163 2.91079i 0.00813167 0.00469482i
\(621\) 291.438 + 467.001i 0.469305 + 0.752015i
\(622\) 228.641 0.367590
\(623\) 327.576 233.176i 0.525805 0.374279i
\(624\) −234.418 + 44.1055i −0.375670 + 0.0706820i
\(625\) 527.112 0.843378
\(626\) 147.900 + 85.3902i 0.236262 + 0.136406i
\(627\) 3.67071 + 19.5095i 0.00585440 + 0.0311157i
\(628\) −7.18230 12.4401i −0.0114368 0.0198091i
\(629\) 288.382i 0.458476i
\(630\) 6.02399 106.258i 0.00956190 0.168663i
\(631\) −534.410 −0.846926 −0.423463 0.905914i \(-0.639186\pi\)
−0.423463 + 0.905914i \(0.639186\pi\)
\(632\) −167.212 + 96.5399i −0.264576 + 0.152753i
\(633\) 336.555 958.668i 0.531683 1.51448i
\(634\) 137.661 238.435i 0.217130 0.376081i
\(635\) 38.6648i 0.0608894i
\(636\) −440.951 + 378.684i −0.693319 + 0.595414i
\(637\) 247.173 713.315i 0.388027 1.11980i
\(638\) 6.90900i 0.0108292i
\(639\) −660.241 100.899i −1.03324 0.157902i
\(640\) 11.1117 + 19.2461i 0.0173621 + 0.0300720i
\(641\) 350.735i 0.547169i −0.961848 0.273584i \(-0.911791\pi\)
0.961848 0.273584i \(-0.0882093\pi\)
\(642\) 254.460 + 296.301i 0.396355 + 0.461528i
\(643\) −329.068 569.963i −0.511770 0.886412i −0.999907 0.0136450i \(-0.995657\pi\)
0.488137 0.872767i \(-0.337677\pi\)
\(644\) −215.349 + 153.290i −0.334393 + 0.238028i
\(645\) −19.0512 101.256i −0.0295367 0.156986i
\(646\) 253.109 + 438.397i 0.391809 + 0.678634i
\(647\) −482.718 + 278.697i −0.746087 + 0.430753i −0.824278 0.566185i \(-0.808419\pi\)
0.0781915 + 0.996938i \(0.475085\pi\)
\(648\) −207.487 + 662.999i −0.320196 + 1.02315i
\(649\) 10.4640 18.1241i 0.0161232 0.0279262i
\(650\) −462.871 267.239i −0.712110 0.411137i
\(651\) −13.7561 + 55.5845i −0.0211308 + 0.0853833i
\(652\) 240.715 + 416.930i 0.369194 + 0.639464i
\(653\) 182.445i 0.279395i −0.990194 0.139697i \(-0.955387\pi\)
0.990194 0.139697i \(-0.0446130\pi\)
\(654\) −153.586 816.300i −0.234841 1.24816i
\(655\) 82.4164 0.125827
\(656\) −319.934 184.714i −0.487704 0.281576i
\(657\) −219.002 + 85.4347i −0.333337 + 0.130038i
\(658\) 178.425 + 250.660i 0.271162 + 0.380942i
\(659\) −10.7149 6.18625i −0.0162593 0.00938733i 0.491848 0.870681i \(-0.336321\pi\)
−0.508108 + 0.861294i \(0.669655\pi\)
\(660\) −1.51918 + 0.285833i −0.00230179 + 0.000433081i
\(661\) 265.629 460.083i 0.401860 0.696041i −0.592091 0.805871i \(-0.701697\pi\)
0.993950 + 0.109830i \(0.0350307\pi\)
\(662\) −80.5081 46.4814i −0.121613 0.0702136i
\(663\) 107.666 + 572.240i 0.162393 + 0.863106i
\(664\) −381.776 + 661.255i −0.574963 + 0.995866i
\(665\) 180.234 128.295i 0.271029 0.192924i
\(666\) 298.466 + 45.6120i 0.448146 + 0.0684865i
\(667\) 199.121 344.887i 0.298532 0.517072i
\(668\) 208.269i 0.311780i
\(669\) 258.670 48.6685i 0.386651 0.0727482i
\(670\) 30.4823 0.0454959
\(671\) 3.73811 2.15820i 0.00557096 0.00321639i
\(672\) −545.160 134.917i −0.811250 0.200769i
\(673\) −29.8818 + 51.7568i −0.0444009 + 0.0769046i −0.887372 0.461055i \(-0.847471\pi\)
0.842971 + 0.537959i \(0.180805\pi\)
\(674\) −224.407 129.561i −0.332948 0.192228i
\(675\) −542.205 + 338.370i −0.803266 + 0.501289i
\(676\) −63.3117 109.659i −0.0936564 0.162218i
\(677\) −797.131 + 460.224i −1.17745 + 0.679799i −0.955422 0.295243i \(-0.904599\pi\)
−0.222023 + 0.975041i \(0.571266\pi\)
\(678\) −504.491 + 94.9197i −0.744088 + 0.140000i
\(679\) 600.690 + 843.878i 0.884668 + 1.24282i
\(680\) −107.862 + 62.2739i −0.158620 + 0.0915793i
\(681\) −802.708 + 689.356i −1.17872 + 1.01227i
\(682\) −0.964468 −0.00141418
\(683\) 487.711 281.580i 0.714071 0.412269i −0.0984954 0.995138i \(-0.531403\pi\)
0.812567 + 0.582868i \(0.198070\pi\)
\(684\) −425.792 + 166.105i −0.622503 + 0.242844i
\(685\) −249.864 −0.364764
\(686\) −347.091 + 363.618i −0.505963 + 0.530055i
\(687\) −744.267 866.648i −1.08336 1.26150i
\(688\) 153.763 0.223492
\(689\) 1395.70 + 805.807i 2.02569 + 1.16953i
\(690\) 97.4937 + 34.2267i 0.141295 + 0.0496038i
\(691\) −210.654 364.864i −0.304854 0.528023i 0.672375 0.740211i \(-0.265274\pi\)
−0.977229 + 0.212188i \(0.931941\pi\)
\(692\) 25.9057i 0.0374360i
\(693\) 8.33562 12.7165i 0.0120283 0.0183499i
\(694\) −356.572 −0.513792
\(695\) 107.220 61.9038i 0.154274 0.0890702i
\(696\) 493.917 92.9302i 0.709651 0.133520i
\(697\) −450.907 + 780.993i −0.646925 + 1.12051i
\(698\) 614.557i 0.880454i
\(699\) 173.939 + 924.472i 0.248840 + 1.32256i
\(700\) −177.975 250.028i −0.254250 0.357183i
\(701\) 523.850i 0.747289i 0.927572 + 0.373645i \(0.121892\pi\)
−0.927572 + 0.373645i \(0.878108\pi\)
\(702\) 609.279 20.9228i 0.867918 0.0298045i
\(703\) 313.812 + 543.539i 0.446390 + 0.773170i
\(704\) 14.4415i 0.0205134i
\(705\) −34.3547 + 97.8585i −0.0487301 + 0.138806i
\(706\) 254.904 + 441.506i 0.361053 + 0.625363i
\(707\) −535.691 244.760i −0.757695 0.346196i
\(708\) 454.617 + 159.600i 0.642114 + 0.225424i
\(709\) −33.9678 58.8340i −0.0479095 0.0829817i 0.841076 0.540917i \(-0.181923\pi\)
−0.888986 + 0.457935i \(0.848589\pi\)
\(710\) −108.573 + 62.6844i −0.152919 + 0.0882878i
\(711\) 188.756 73.6354i 0.265480 0.103566i
\(712\) −246.328 + 426.652i −0.345966 + 0.599230i
\(713\) −48.1449 27.7964i −0.0675243 0.0389852i
\(714\) 93.1443 376.369i 0.130454 0.527127i
\(715\) 2.14309 + 3.71194i 0.00299733 + 0.00519152i
\(716\) 94.3626i 0.131791i
\(717\) 653.218 + 229.322i 0.911044 + 0.319836i
\(718\) 663.764 0.924462
\(719\) −766.286 442.415i −1.06577 0.615321i −0.138745 0.990328i \(-0.544307\pi\)
−0.927022 + 0.375008i \(0.877640\pi\)
\(720\) 19.4580 + 49.8785i 0.0270250 + 0.0692757i
\(721\) −171.541 + 375.440i −0.237921 + 0.520721i
\(722\) 495.932 + 286.327i 0.686887 + 0.396574i
\(723\) −353.490 411.615i −0.488921 0.569315i
\(724\) 222.061 384.620i 0.306714 0.531244i
\(725\) 400.426 + 231.186i 0.552312 + 0.318878i
\(726\) −501.718 176.136i −0.691072 0.242611i
\(727\) −228.413 + 395.623i −0.314186 + 0.544186i −0.979264 0.202588i \(-0.935065\pi\)
0.665078 + 0.746774i \(0.268398\pi\)
\(728\) 87.7545 + 920.788i 0.120542 + 1.26482i
\(729\) 320.332 654.850i 0.439413 0.898285i
\(730\) −22.0625 + 38.2133i −0.0302225 + 0.0523470i
\(731\) 375.351i 0.513477i
\(732\) 64.7441 + 75.3901i 0.0884482 + 0.102992i
\(733\) −105.338 −0.143709 −0.0718543 0.997415i \(-0.522892\pi\)
−0.0718543 + 0.997415i \(0.522892\pi\)
\(734\) 4.06094 2.34458i 0.00553261 0.00319426i
\(735\) −167.605 24.9180i −0.228034 0.0339021i
\(736\) 272.621 472.193i 0.370409 0.641567i
\(737\) 3.77144 + 2.17744i 0.00511728 + 0.00295446i
\(738\) 736.985 + 590.200i 0.998624 + 0.799729i
\(739\) 169.442 + 293.482i 0.229285 + 0.397133i 0.957596 0.288113i \(-0.0930279\pi\)
−0.728311 + 0.685246i \(0.759695\pi\)
\(740\) −42.3246 + 24.4361i −0.0571955 + 0.0330218i
\(741\) 825.631 + 961.390i 1.11421 + 1.29742i
\(742\) −622.314 874.256i −0.838698 1.17824i
\(743\) 200.529 115.776i 0.269891 0.155822i −0.358947 0.933358i \(-0.616864\pi\)
0.628838 + 0.777536i \(0.283531\pi\)
\(744\) −12.9727 68.9488i −0.0174364 0.0926732i
\(745\) −181.076 −0.243055
\(746\) 189.673 109.508i 0.254254 0.146793i
\(747\) 500.849 625.412i 0.670480 0.837231i
\(748\) −5.63156 −0.00752883
\(749\) 506.597 360.606i 0.676364 0.481450i
\(750\) −81.7073 + 232.741i −0.108943 + 0.310321i
\(751\) −122.582 −0.163225 −0.0816127 0.996664i \(-0.526007\pi\)
−0.0816127 + 0.996664i \(0.526007\pi\)
\(752\) −134.043 77.3898i −0.178249 0.102912i
\(753\) −368.390 + 316.369i −0.489230 + 0.420145i
\(754\) −220.520 381.952i −0.292467 0.506568i
\(755\) 138.880i 0.183947i
\(756\) 323.205 + 134.465i 0.427519 + 0.177864i
\(757\) 162.273 0.214363 0.107181 0.994239i \(-0.465817\pi\)
0.107181 + 0.994239i \(0.465817\pi\)
\(758\) −547.301 + 315.984i −0.722033 + 0.416866i
\(759\) 9.61755 + 11.1990i 0.0126713 + 0.0147549i
\(760\) −135.531 + 234.746i −0.178330 + 0.308877i
\(761\) 347.668i 0.456857i −0.973561 0.228429i \(-0.926641\pi\)
0.973561 0.228429i \(-0.0733588\pi\)
\(762\) 139.150 + 48.8506i 0.182611 + 0.0641084i
\(763\) −1316.49 + 125.466i −1.72541 + 0.164438i
\(764\) 340.505i 0.445687i
\(765\) 121.759 47.4992i 0.159162 0.0620904i
\(766\) −131.731 228.164i −0.171972 0.297865i
\(767\) 1335.95i 1.74178i
\(768\) 788.960 148.442i 1.02729 0.193284i
\(769\) 21.9448 + 38.0094i 0.0285367 + 0.0494271i 0.879941 0.475083i \(-0.157582\pi\)
−0.851404 + 0.524510i \(0.824249\pi\)
\(770\) −0.270774 2.84116i −0.000351654 0.00368982i
\(771\) 172.229 147.908i 0.223384 0.191839i
\(772\) −141.503 245.091i −0.183294 0.317475i
\(773\) 31.3486 18.0991i 0.0405545 0.0234141i −0.479586 0.877495i \(-0.659213\pi\)
0.520140 + 0.854081i \(0.325880\pi\)
\(774\) −388.477 59.3677i −0.501908 0.0767024i
\(775\) 32.2727 55.8979i 0.0416421 0.0721263i
\(776\) −1099.11 634.571i −1.41638 0.817746i
\(777\) 115.483 466.634i 0.148627 0.600558i
\(778\) −247.053 427.908i −0.317549 0.550010i
\(779\) 1962.68i 2.51948i
\(780\) −74.8622 + 64.2908i −0.0959772 + 0.0824241i
\(781\) −17.9109 −0.0229333
\(782\) 325.994 + 188.213i 0.416872 + 0.240681i
\(783\) −527.082 + 18.1001i −0.673157 + 0.0231164i
\(784\) 82.7958 238.940i 0.105607 0.304770i
\(785\) 7.74211 + 4.46991i 0.00986256 + 0.00569415i
\(786\) 104.128 296.606i 0.132479 0.377362i
\(787\) 334.824 579.932i 0.425443 0.736890i −0.571018 0.820937i \(-0.693451\pi\)
0.996462 + 0.0840478i \(0.0267848\pi\)
\(788\) −619.166 357.476i −0.785744 0.453649i
\(789\) −26.5065 + 22.7635i −0.0335951 + 0.0288511i
\(790\) 19.0154 32.9357i 0.0240702 0.0416908i
\(791\) 77.5410 + 813.620i 0.0980291 + 1.02860i
\(792\) −2.81434 + 18.4158i −0.00355346 + 0.0232523i
\(793\) 137.770 238.625i 0.173733 0.300914i
\(794\) 782.171i 0.985102i
\(795\) 119.823 341.313i 0.150721 0.429325i
\(796\) 84.6022 0.106284
\(797\) 12.4445 7.18485i 0.0156142 0.00901487i −0.492173 0.870498i \(-0.663797\pi\)
0.507787 + 0.861483i \(0.330464\pi\)
\(798\) −234.001 810.734i −0.293234 1.01596i
\(799\) −188.917 + 327.214i −0.236442 + 0.409529i
\(800\) 548.233 + 316.523i 0.685291 + 0.395653i
\(801\) 323.156 403.525i 0.403440 0.503777i
\(802\) 444.231 + 769.431i 0.553904 + 0.959390i
\(803\) −5.45938 + 3.15197i −0.00679873 + 0.00392525i
\(804\) −33.2111 + 94.6010i −0.0413074 + 0.117663i
\(805\) 68.3671 149.631i 0.0849281 0.185877i
\(806\) −53.3190 + 30.7837i −0.0661526 + 0.0381932i
\(807\) 869.353 + 305.200i 1.07727 + 0.378190i
\(808\) 721.611 0.893084
\(809\) −134.305 + 77.5408i −0.166013 + 0.0958478i −0.580705 0.814114i \(-0.697223\pi\)
0.414691 + 0.909962i \(0.363890\pi\)
\(810\) −29.9021 133.529i −0.0369161 0.164851i
\(811\) −758.588 −0.935374 −0.467687 0.883894i \(-0.654913\pi\)
−0.467687 + 0.883894i \(0.654913\pi\)
\(812\) −24.0268 252.108i −0.0295897 0.310477i
\(813\) 996.743 187.537i 1.22601 0.230672i
\(814\) 8.09674 0.00994685
\(815\) −259.477 149.809i −0.318377 0.183815i
\(816\) 36.0651 + 191.684i 0.0441975 + 0.234906i
\(817\) −408.451 707.459i −0.499941 0.865922i
\(818\) 574.660i 0.702518i
\(819\) 54.9384 969.063i 0.0670799 1.18323i
\(820\) −152.831 −0.186379
\(821\) 195.171 112.682i 0.237724 0.137250i −0.376406 0.926455i \(-0.622840\pi\)
0.614130 + 0.789205i \(0.289507\pi\)
\(822\) −315.688 + 899.228i −0.384048 + 1.09395i
\(823\) −299.847 + 519.350i −0.364334 + 0.631045i −0.988669 0.150112i \(-0.952037\pi\)
0.624335 + 0.781157i \(0.285370\pi\)
\(824\) 505.743i 0.613766i
\(825\) −13.0024 + 11.1663i −0.0157605 + 0.0135349i
\(826\) −369.688 + 809.111i −0.447564 + 0.979553i
\(827\) 634.083i 0.766727i 0.923598 + 0.383363i \(0.125234\pi\)
−0.923598 + 0.383363i \(0.874766\pi\)
\(828\) −212.443 + 265.278i −0.256574 + 0.320385i
\(829\) −376.723 652.503i −0.454431 0.787097i 0.544225 0.838940i \(-0.316824\pi\)
−0.998655 + 0.0518425i \(0.983491\pi\)
\(830\) 150.397i 0.181201i
\(831\) −258.041 300.471i −0.310519 0.361578i
\(832\) −460.940 798.371i −0.554014 0.959581i
\(833\) −583.278 202.114i −0.700214 0.242633i
\(834\) −87.3173 464.085i −0.104697 0.556457i
\(835\) −64.8082 112.251i −0.0776146 0.134432i
\(836\) −10.6143 + 6.12817i −0.0126965 + 0.00733035i
\(837\) 2.52670 + 73.5785i 0.00301876 + 0.0879074i
\(838\) 488.497 846.102i 0.582932 1.00967i
\(839\) 953.473 + 550.488i 1.13644 + 0.656124i 0.945547 0.325487i \(-0.105528\pi\)
0.190893 + 0.981611i \(0.438862\pi\)
\(840\) 199.470 57.5727i 0.237464 0.0685389i
\(841\) −229.730 397.904i −0.273163 0.473132i
\(842\) 690.675i 0.820279i
\(843\) −41.1753 218.844i −0.0488438 0.259601i
\(844\) 627.286 0.743230
\(845\) 68.2465 + 39.4021i 0.0807651 + 0.0466297i
\(846\) 308.776 + 247.277i 0.364983 + 0.292289i
\(847\) −351.828 + 770.023i −0.415381 + 0.909118i
\(848\) 467.518 + 269.922i 0.551318 + 0.318304i
\(849\) 33.3244 6.26997i 0.0392514 0.00738512i
\(850\) −218.521 + 378.490i −0.257084 + 0.445283i
\(851\) 404.177 + 233.352i 0.474944 + 0.274209i
\(852\) −76.2472 405.248i −0.0894920 0.475643i
\(853\) 161.623 279.939i 0.189476 0.328181i −0.755600 0.655033i \(-0.772655\pi\)
0.945076 + 0.326852i \(0.105988\pi\)
\(854\) −149.473 + 106.398i −0.175027 + 0.124588i
\(855\) 177.802 222.022i 0.207956 0.259675i
\(856\) −380.946 + 659.817i −0.445030 + 0.770815i
\(857\) 1303.35i 1.52083i 0.649439 + 0.760414i \(0.275004\pi\)
−0.649439 + 0.760414i \(0.724996\pi\)
\(858\) 16.0665 3.02290i 0.0187255 0.00352319i
\(859\) −175.654 −0.204486 −0.102243 0.994759i \(-0.532602\pi\)
−0.102243 + 0.994759i \(0.532602\pi\)
\(860\) 55.0889 31.8056i 0.0640568 0.0369832i
\(861\) 1042.37 1083.17i 1.21065 1.25803i
\(862\) 172.932 299.527i 0.200617 0.347479i
\(863\) −289.608 167.205i −0.335582 0.193749i 0.322734 0.946490i \(-0.395398\pi\)
−0.658317 + 0.752741i \(0.728731\pi\)
\(864\) −721.640 + 24.7813i −0.835232 + 0.0286820i
\(865\) −8.06122 13.9624i −0.00931933 0.0161416i
\(866\) −492.836 + 284.539i −0.569094 + 0.328567i
\(867\) −384.129 + 72.2736i −0.443056 + 0.0833606i
\(868\) −35.1932 + 3.35404i −0.0405452 + 0.00386410i
\(869\) 4.70539 2.71666i 0.00541472 0.00312619i
\(870\) −75.1006 + 64.4955i −0.0863226 + 0.0741328i
\(871\) 277.996 0.319169
\(872\) 1403.23 810.157i 1.60921 0.929080i
\(873\) 1039.53 + 832.489i 1.19076 + 0.953596i
\(874\) 819.240 0.937345
\(875\) 357.204 + 163.209i 0.408234 + 0.186524i
\(876\) −94.5564 110.105i −0.107941 0.125690i
\(877\) 791.230 0.902200 0.451100 0.892473i \(-0.351032\pi\)
0.451100 + 0.892473i \(0.351032\pi\)
\(878\) −445.891 257.435i −0.507848 0.293206i
\(879\) −471.096 165.385i −0.535945 0.188152i
\(880\) 0.717872 + 1.24339i 0.000815764 + 0.00141294i
\(881\) 307.622i 0.349174i −0.984642 0.174587i \(-0.944141\pi\)
0.984642 0.174587i \(-0.0558591\pi\)
\(882\) −301.436 + 571.707i −0.341764 + 0.648193i
\(883\) −1744.35 −1.97548 −0.987742 0.156094i \(-0.950110\pi\)
−0.987742 + 0.156094i \(0.950110\pi\)
\(884\) −311.331 + 179.747i −0.352184 + 0.203334i
\(885\) −294.689 + 55.4456i −0.332982 + 0.0626504i
\(886\) −38.9395 + 67.4452i −0.0439498 + 0.0761233i
\(887\) 176.500i 0.198986i −0.995038 0.0994928i \(-0.968278\pi\)
0.995038 0.0994928i \(-0.0317220\pi\)
\(888\) 108.906 + 578.827i 0.122642 + 0.651832i
\(889\) 97.5782 213.563i 0.109762 0.240228i
\(890\) 97.0382i 0.109032i
\(891\) 5.83874 18.6570i 0.00655302 0.0209394i
\(892\) 81.2511 + 140.731i 0.0910887 + 0.157770i
\(893\) 822.306i 0.920835i
\(894\) −228.779 + 651.671i −0.255905 + 0.728938i
\(895\) 29.3634 + 50.8588i 0.0328082 + 0.0568255i
\(896\) −12.8038 134.348i −0.0142900 0.149941i
\(897\) 889.136 + 312.145i 0.991233 + 0.347988i
\(898\) −385.724 668.094i −0.429537 0.743980i
\(899\) 46.1258 26.6307i 0.0513079 0.0296226i
\(900\) −307.998 246.654i −0.342220 0.274060i
\(901\) 658.908 1141.26i 0.731308 1.26666i
\(902\) 21.9275 + 12.6599i 0.0243099 + 0.0140353i
\(903\) −150.310 + 607.361i −0.166457 + 0.672603i
\(904\) −500.696 867.230i −0.553867 0.959325i
\(905\) 276.400i 0.305414i
\(906\) 499.813 + 175.467i 0.551670 + 0.193672i
\(907\) 1694.96 1.86876 0.934379 0.356280i \(-0.115955\pi\)
0.934379 + 0.356280i \(0.115955\pi\)
\(908\) −565.735 326.627i −0.623056 0.359721i
\(909\) −748.542 114.393i −0.823478 0.125845i
\(910\) −105.653 148.426i −0.116102 0.163106i
\(911\) 893.443 + 515.830i 0.980728 + 0.566224i 0.902490 0.430711i \(-0.141737\pi\)
0.0782381 + 0.996935i \(0.475071\pi\)
\(912\) 276.562 + 322.038i 0.303248 + 0.353112i
\(913\) 10.7433 18.6079i 0.0117670 0.0203810i
\(914\) −938.906 542.078i −1.02725 0.593083i
\(915\) −58.3548 20.4864i −0.0637758 0.0223895i
\(916\) 352.645 610.798i 0.384983 0.666811i
\(917\) −455.223 207.994i −0.496427 0.226820i
\(918\) −17.1085 498.207i −0.0186368 0.542710i
\(919\) 362.145 627.254i 0.394064 0.682539i −0.598917 0.800811i \(-0.704402\pi\)
0.992981 + 0.118272i \(0.0377354\pi\)
\(920\) 201.563i 0.219090i
\(921\) −748.550 871.635i −0.812758 0.946401i
\(922\) −481.661 −0.522409
\(923\) −990.174 + 571.677i −1.07278 + 0.619369i
\(924\) 9.11250 + 2.25517i 0.00986201 + 0.00244066i
\(925\) −270.930 + 469.264i −0.292897 + 0.507312i
\(926\) −9.25515 5.34346i −0.00999476 0.00577048i
\(927\) −80.1729 + 524.617i −0.0864864 + 0.565930i
\(928\) 261.188 + 452.391i 0.281453 + 0.487490i
\(929\) −1267.59 + 731.841i −1.36446 + 0.787773i −0.990214 0.139556i \(-0.955433\pi\)
−0.374248 + 0.927328i \(0.622099\pi\)
\(930\) 9.00331 + 10.4837i 0.00968098 + 0.0112728i
\(931\) −1319.29 + 253.772i −1.41707 + 0.272580i
\(932\) −502.966 + 290.387i −0.539663 + 0.311575i
\(933\) −86.5414 459.961i −0.0927561 0.492992i
\(934\) −755.756 −0.809161
\(935\) 3.03525 1.75240i 0.00324626 0.00187423i
\(936\) 432.207 + 1107.92i 0.461760 + 1.18367i
\(937\) 282.325 0.301308 0.150654 0.988587i \(-0.451862\pi\)
0.150654 + 0.988587i \(0.451862\pi\)
\(938\) −168.368 76.9281i −0.179496 0.0820129i
\(939\) 115.800 329.854i 0.123323 0.351282i
\(940\) −64.0319 −0.0681190
\(941\) 255.008 + 147.229i 0.270997 + 0.156460i 0.629341 0.777129i \(-0.283325\pi\)
−0.358344 + 0.933590i \(0.616658\pi\)
\(942\) 25.8683 22.2154i 0.0274611 0.0235833i
\(943\) 729.727 + 1263.92i 0.773836 + 1.34032i
\(944\) 447.503i 0.474050i
\(945\) −216.041 + 28.1003i −0.228614 + 0.0297358i
\(946\) −10.5385 −0.0111401
\(947\) 763.933 441.057i 0.806687 0.465741i −0.0391168 0.999235i \(-0.512454\pi\)
0.845804 + 0.533493i \(0.179121\pi\)
\(948\) 81.4974 + 94.8981i 0.0859677 + 0.100103i
\(949\) −201.208 + 348.503i −0.212021 + 0.367231i
\(950\) 951.166i 1.00123i
\(951\) −531.770 186.686i −0.559169 0.196305i
\(952\) 752.929 71.7569i 0.790892 0.0753749i
\(953\) 347.203i 0.364326i −0.983268 0.182163i \(-0.941690\pi\)
0.983268 0.182163i \(-0.0583099\pi\)
\(954\) −1076.95 862.457i −1.12888 0.904043i
\(955\) 105.957 + 183.523i 0.110950 + 0.192170i
\(956\) 427.421i 0.447093i
\(957\) −13.8990 + 2.61508i −0.0145235 + 0.00273258i
\(958\) 212.256 + 367.638i 0.221561 + 0.383756i
\(959\) 1380.11 + 630.581i 1.43911 + 0.657540i
\(960\) −156.978 + 134.811i −0.163519 + 0.140428i
\(961\) 476.782 + 825.811i 0.496132 + 0.859325i
\(962\) 447.614 258.430i 0.465295 0.268638i
\(963\) 499.760 624.052i 0.518962 0.648029i
\(964\) 167.489 290.099i 0.173743 0.300932i
\(965\) 152.532 + 88.0647i 0.158065 + 0.0912587i
\(966\) −452.124 435.094i −0.468037 0.450408i
\(967\) 774.207 + 1340.97i 0.800627 + 1.38673i 0.919204 + 0.393782i \(0.128834\pi\)
−0.118577 + 0.992945i \(0.537833\pi\)
\(968\) 1037.27i 1.07156i
\(969\) 786.129 675.119i 0.811279 0.696717i
\(970\) 249.983 0.257714
\(971\) 859.844 + 496.431i 0.885525 + 0.511258i 0.872476 0.488657i \(-0.162513\pi\)
0.0130486 + 0.999915i \(0.495846\pi\)
\(972\) 446.984 + 52.6828i 0.459860 + 0.0542004i
\(973\) −748.454 + 71.3304i −0.769223 + 0.0733098i
\(974\) 640.375 + 369.721i 0.657470 + 0.379590i
\(975\) −362.411 + 1032.32i −0.371704 + 1.05879i
\(976\) 46.1489 79.9323i 0.0472837 0.0818978i
\(977\) −206.132 119.011i −0.210985 0.121812i 0.390784 0.920482i \(-0.372204\pi\)
−0.601769 + 0.798670i \(0.705537\pi\)
\(978\) −866.978 + 744.551i −0.886481 + 0.761299i
\(979\) 6.93173 12.0061i 0.00708042 0.0122636i
\(980\) −19.7609 102.732i −0.0201642 0.104828i
\(981\) −1584.03 + 617.945i −1.61471 + 0.629913i
\(982\) 263.667 456.685i 0.268500 0.465056i
\(983\) 632.857i 0.643801i 0.946773 + 0.321901i \(0.104322\pi\)
−0.946773 + 0.321901i \(0.895678\pi\)
\(984\) −610.102 + 1737.86i −0.620023 + 1.76612i
\(985\) 444.951 0.451727
\(986\) −312.323 + 180.320i −0.316757 + 0.182880i
\(987\) 436.722 453.816i 0.442475 0.459793i
\(988\) −391.196 + 677.571i −0.395947 + 0.685801i
\(989\) −526.069 303.726i −0.531920 0.307104i
\(990\) −1.33361 3.41856i −0.00134708 0.00345309i
\(991\) 589.789 + 1021.54i 0.595145 + 1.03082i 0.993526 + 0.113602i \(0.0362389\pi\)
−0.398381 + 0.917220i \(0.630428\pi\)
\(992\) 63.1519 36.4608i 0.0636612 0.0367548i
\(993\) −63.0349 + 179.553i −0.0634792 + 0.180819i
\(994\) 757.892 72.2299i 0.762467 0.0726659i
\(995\) −45.5982 + 26.3261i −0.0458274 + 0.0264584i
\(996\) 466.752 + 163.860i 0.468626 + 0.164519i
\(997\) −1492.30 −1.49679 −0.748394 0.663254i \(-0.769175\pi\)
−0.748394 + 0.663254i \(0.769175\pi\)
\(998\) 821.226 474.135i 0.822872 0.475085i
\(999\) −21.2117 617.693i −0.0212329 0.618311i
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 63.3.n.b.2.4 yes 22
3.2 odd 2 189.3.n.b.170.8 22
7.2 even 3 441.3.r.g.344.8 22
7.3 odd 6 441.3.j.f.263.4 22
7.4 even 3 63.3.j.b.11.4 22
7.5 odd 6 441.3.r.f.344.8 22
7.6 odd 2 441.3.n.f.128.4 22
9.4 even 3 189.3.j.b.44.4 22
9.5 odd 6 63.3.j.b.23.8 yes 22
21.11 odd 6 189.3.j.b.116.8 22
63.4 even 3 189.3.n.b.179.8 22
63.5 even 6 441.3.r.f.50.8 22
63.23 odd 6 441.3.r.g.50.8 22
63.32 odd 6 inner 63.3.n.b.32.4 yes 22
63.41 even 6 441.3.j.f.275.8 22
63.59 even 6 441.3.n.f.410.4 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.3.j.b.11.4 22 7.4 even 3
63.3.j.b.23.8 yes 22 9.5 odd 6
63.3.n.b.2.4 yes 22 1.1 even 1 trivial
63.3.n.b.32.4 yes 22 63.32 odd 6 inner
189.3.j.b.44.4 22 9.4 even 3
189.3.j.b.116.8 22 21.11 odd 6
189.3.n.b.170.8 22 3.2 odd 2
189.3.n.b.179.8 22 63.4 even 3
441.3.j.f.263.4 22 7.3 odd 6
441.3.j.f.275.8 22 63.41 even 6
441.3.n.f.128.4 22 7.6 odd 2
441.3.n.f.410.4 22 63.59 even 6
441.3.r.f.50.8 22 63.5 even 6
441.3.r.f.344.8 22 7.5 odd 6
441.3.r.g.50.8 22 63.23 odd 6
441.3.r.g.344.8 22 7.2 even 3