Properties

Label 9.5.d.a.5.3
Level $9$
Weight $5$
Character 9.5
Analytic conductor $0.930$
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] = [9,5,Mod(2,9)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("9.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 9.d (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: \(0.930329667755\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.39400128.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.3
Root \(-1.28901 - 2.23263i\) of defining polynomial
Character \(\chi\) \(=\) 9.5
Dual form 9.5.d.a.2.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.86703 - 2.23263i) q^{2} +(-8.70335 + 2.29167i) q^{3} +(1.96929 - 3.41090i) q^{4} +(13.8760 + 8.01130i) q^{5} +(-28.5397 + 28.2933i) q^{6} +(-36.2418 - 62.7727i) q^{7} +53.8574i q^{8} +(70.4965 - 39.8904i) q^{9} +O(q^{10})\) \(q+(3.86703 - 2.23263i) q^{2} +(-8.70335 + 2.29167i) q^{3} +(1.96929 - 3.41090i) q^{4} +(13.8760 + 8.01130i) q^{5} +(-28.5397 + 28.2933i) q^{6} +(-36.2418 - 62.7727i) q^{7} +53.8574i q^{8} +(70.4965 - 39.8904i) q^{9} +71.5451 q^{10} +(83.2749 - 48.0788i) q^{11} +(-9.32272 + 34.1992i) q^{12} +(-76.9530 + 133.286i) q^{13} +(-280.297 - 161.829i) q^{14} +(-139.127 - 37.9260i) q^{15} +(151.752 + 262.843i) q^{16} +72.7905i q^{17} +(183.552 - 311.650i) q^{18} -190.660 q^{19} +(54.6515 - 31.5531i) q^{20} +(459.280 + 463.279i) q^{21} +(214.684 - 371.844i) q^{22} +(-12.5186 - 7.22762i) q^{23} +(-123.423 - 468.740i) q^{24} +(-184.138 - 318.937i) q^{25} +687.231i q^{26} +(-522.140 + 508.734i) q^{27} -285.482 q^{28} +(620.301 - 358.131i) q^{29} +(-622.682 + 163.958i) q^{30} +(151.284 - 262.031i) q^{31} +(427.392 + 246.755i) q^{32} +(-614.590 + 609.285i) q^{33} +(162.514 + 281.483i) q^{34} -1161.38i q^{35} +(2.76561 - 319.012i) q^{36} +826.277 q^{37} +(-737.289 + 425.674i) q^{38} +(364.300 - 1336.39i) q^{39} +(-431.468 + 747.325i) q^{40} +(481.613 + 278.059i) q^{41} +(2810.38 + 766.110i) q^{42} +(-446.340 - 773.084i) q^{43} -378.723i q^{44} +(1297.78 + 11.2508i) q^{45} -64.5464 q^{46} +(-3425.50 + 1977.72i) q^{47} +(-1923.10 - 1939.85i) q^{48} +(-1426.44 + 2470.67i) q^{49} +(-1424.14 - 822.225i) q^{50} +(-166.812 - 633.521i) q^{51} +(303.085 + 524.958i) q^{52} -1966.96i q^{53} +(-883.316 + 3133.04i) q^{54} +1540.69 q^{55} +(3380.78 - 1951.89i) q^{56} +(1659.38 - 436.930i) q^{57} +(1599.15 - 2769.81i) q^{58} +(4689.48 + 2707.47i) q^{59} +(-403.342 + 399.861i) q^{60} +(856.210 + 1483.00i) q^{61} -1351.04i q^{62} +(-5058.95 - 2979.56i) q^{63} -2652.43 q^{64} +(-2135.60 + 1232.99i) q^{65} +(-1016.33 + 3728.28i) q^{66} +(2317.24 - 4013.58i) q^{67} +(248.281 + 143.345i) q^{68} +(125.517 + 34.2160i) q^{69} +(-2592.93 - 4491.08i) q^{70} +6697.12i q^{71} +(2148.39 + 3796.76i) q^{72} -4823.86 q^{73} +(3195.24 - 1844.77i) q^{74} +(2333.51 + 2353.83i) q^{75} +(-375.464 + 650.324i) q^{76} +(-6036.07 - 3484.93i) q^{77} +(-1574.90 - 5981.21i) q^{78} +(2864.40 + 4961.28i) q^{79} +4862.94i q^{80} +(3378.52 - 5624.26i) q^{81} +2483.22 q^{82} +(2452.78 - 1416.12i) q^{83} +(2484.65 - 654.230i) q^{84} +(-583.147 + 1010.04i) q^{85} +(-3452.02 - 1993.03i) q^{86} +(-4577.98 + 4538.46i) q^{87} +(2589.40 + 4484.97i) q^{88} -14277.7i q^{89} +(5043.68 - 2853.96i) q^{90} +11155.7 q^{91} +(-49.3054 + 28.4665i) q^{92} +(-716.187 + 2627.24i) q^{93} +(-8831.02 + 15295.8i) q^{94} +(-2645.60 - 1527.44i) q^{95} +(-4285.22 - 1168.15i) q^{96} +(-3582.65 - 6205.34i) q^{97} +12738.9i q^{98} +(3952.71 - 6711.25i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{2} - 3 q^{3} + 15 q^{4} - 12 q^{5} - 99 q^{6} + 12 q^{7} + 99 q^{9} - 36 q^{10} + 483 q^{11} + 330 q^{12} - 6 q^{13} - 1146 q^{14} - 1026 q^{15} + 15 q^{16} + 1404 q^{18} - 258 q^{19} + 1614 q^{20} + 480 q^{21} - 369 q^{22} - 282 q^{23} - 1449 q^{24} - 273 q^{25} + 54 q^{27} + 1308 q^{28} - 1056 q^{29} - 1278 q^{30} + 1290 q^{31} - 1161 q^{32} + 279 q^{33} + 513 q^{34} - 2385 q^{36} + 12 q^{37} - 789 q^{38} + 1974 q^{39} - 1314 q^{40} + 7629 q^{41} + 9612 q^{42} - 285 q^{43} - 4212 q^{45} - 5760 q^{46} - 9642 q^{47} - 6771 q^{48} - 1863 q^{49} + 3027 q^{50} + 2457 q^{51} - 240 q^{52} - 405 q^{54} + 2016 q^{55} - 462 q^{56} + 5367 q^{57} + 6462 q^{58} + 6225 q^{59} + 7470 q^{60} + 3630 q^{61} - 7578 q^{63} + 15450 q^{64} - 7158 q^{65} - 13734 q^{66} - 5055 q^{67} - 10503 q^{68} - 13878 q^{69} - 9684 q^{70} + 8451 q^{72} - 14622 q^{73} + 26454 q^{74} + 21021 q^{75} - 4047 q^{76} + 2580 q^{77} - 12060 q^{78} + 4764 q^{79} + 18387 q^{81} - 9702 q^{82} - 1866 q^{83} - 6486 q^{84} + 12366 q^{85} - 37731 q^{86} - 21564 q^{87} + 14787 q^{88} + 20790 q^{90} + 34836 q^{91} + 33636 q^{92} + 19254 q^{93} - 12708 q^{94} - 13362 q^{95} - 3672 q^{96} - 28959 q^{97} - 9126 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/9\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.86703 2.23263i 0.966758 0.558158i 0.0685115 0.997650i \(-0.478175\pi\)
0.898246 + 0.439492i \(0.144842\pi\)
\(3\) −8.70335 + 2.29167i −0.967039 + 0.254630i
\(4\) 1.96929 3.41090i 0.123080 0.213181i
\(5\) 13.8760 + 8.01130i 0.555039 + 0.320452i 0.751152 0.660129i \(-0.229499\pi\)
−0.196113 + 0.980581i \(0.562832\pi\)
\(6\) −28.5397 + 28.2933i −0.792768 + 0.785925i
\(7\) −36.2418 62.7727i −0.739630 1.28108i −0.952662 0.304031i \(-0.901667\pi\)
0.213033 0.977045i \(-0.431666\pi\)
\(8\) 53.8574i 0.841523i
\(9\) 70.4965 39.8904i 0.870327 0.492474i
\(10\) 71.5451 0.715451
\(11\) 83.2749 48.0788i 0.688222 0.397345i −0.114723 0.993397i \(-0.536598\pi\)
0.802946 + 0.596052i \(0.203265\pi\)
\(12\) −9.32272 + 34.1992i −0.0647411 + 0.237495i
\(13\) −76.9530 + 133.286i −0.455343 + 0.788677i −0.998708 0.0508193i \(-0.983817\pi\)
0.543365 + 0.839497i \(0.317150\pi\)
\(14\) −280.297 161.829i −1.43009 0.825660i
\(15\) −139.127 37.9260i −0.618341 0.168560i
\(16\) 151.752 + 262.843i 0.592783 + 1.02673i
\(17\) 72.7905i 0.251870i 0.992038 + 0.125935i \(0.0401931\pi\)
−0.992038 + 0.125935i \(0.959807\pi\)
\(18\) 183.552 311.650i 0.566518 0.961883i
\(19\) −190.660 −0.528145 −0.264072 0.964503i \(-0.585066\pi\)
−0.264072 + 0.964503i \(0.585066\pi\)
\(20\) 54.6515 31.5531i 0.136629 0.0788827i
\(21\) 459.280 + 463.279i 1.04145 + 1.05052i
\(22\) 214.684 371.844i 0.443563 0.768273i
\(23\) −12.5186 7.22762i −0.0236647 0.0136628i 0.488121 0.872776i \(-0.337682\pi\)
−0.511786 + 0.859113i \(0.671016\pi\)
\(24\) −123.423 468.740i −0.214277 0.813785i
\(25\) −184.138 318.937i −0.294621 0.510298i
\(26\) 687.231i 1.01661i
\(27\) −522.140 + 508.734i −0.716242 + 0.697852i
\(28\) −285.482 −0.364135
\(29\) 620.301 358.131i 0.737575 0.425839i −0.0836117 0.996498i \(-0.526646\pi\)
0.821187 + 0.570659i \(0.193312\pi\)
\(30\) −622.682 + 163.958i −0.691869 + 0.182175i
\(31\) 151.284 262.031i 0.157423 0.272665i −0.776515 0.630098i \(-0.783015\pi\)
0.933939 + 0.357433i \(0.116348\pi\)
\(32\) 427.392 + 246.755i 0.417375 + 0.240971i
\(33\) −614.590 + 609.285i −0.564362 + 0.559490i
\(34\) 162.514 + 281.483i 0.140583 + 0.243498i
\(35\) 1161.38i 0.948063i
\(36\) 2.76561 319.012i 0.00213396 0.246151i
\(37\) 826.277 0.603562 0.301781 0.953377i \(-0.402419\pi\)
0.301781 + 0.953377i \(0.402419\pi\)
\(38\) −737.289 + 425.674i −0.510588 + 0.294788i
\(39\) 364.300 1336.39i 0.239514 0.878625i
\(40\) −431.468 + 747.325i −0.269668 + 0.467078i
\(41\) 481.613 + 278.059i 0.286504 + 0.165413i 0.636364 0.771389i \(-0.280438\pi\)
−0.349860 + 0.936802i \(0.613771\pi\)
\(42\) 2810.38 + 766.110i 1.59319 + 0.434303i
\(43\) −446.340 773.084i −0.241395 0.418109i 0.719717 0.694268i \(-0.244272\pi\)
−0.961112 + 0.276159i \(0.910938\pi\)
\(44\) 378.723i 0.195622i
\(45\) 1297.78 + 11.2508i 0.640880 + 0.00555597i
\(46\) −64.5464 −0.0305040
\(47\) −3425.50 + 1977.72i −1.55070 + 0.895299i −0.552619 + 0.833434i \(0.686372\pi\)
−0.998085 + 0.0618654i \(0.980295\pi\)
\(48\) −1923.10 1939.85i −0.834680 0.841947i
\(49\) −1426.44 + 2470.67i −0.594104 + 1.02902i
\(50\) −1424.14 822.225i −0.569654 0.328890i
\(51\) −166.812 633.521i −0.0641337 0.243568i
\(52\) 303.085 + 524.958i 0.112088 + 0.194141i
\(53\) 1966.96i 0.700234i −0.936706 0.350117i \(-0.886142\pi\)
0.936706 0.350117i \(-0.113858\pi\)
\(54\) −883.316 + 3133.04i −0.302920 + 1.07443i
\(55\) 1540.69 0.509320
\(56\) 3380.78 1951.89i 1.07805 0.622415i
\(57\) 1659.38 436.930i 0.510736 0.134481i
\(58\) 1599.15 2769.81i 0.475371 0.823367i
\(59\) 4689.48 + 2707.47i 1.34716 + 0.777785i 0.987847 0.155431i \(-0.0496765\pi\)
0.359316 + 0.933216i \(0.383010\pi\)
\(60\) −403.342 + 399.861i −0.112039 + 0.111072i
\(61\) 856.210 + 1483.00i 0.230102 + 0.398549i 0.957838 0.287309i \(-0.0927606\pi\)
−0.727736 + 0.685858i \(0.759427\pi\)
\(62\) 1351.04i 0.351468i
\(63\) −5058.95 2979.56i −1.27462 0.750707i
\(64\) −2652.43 −0.647565
\(65\) −2135.60 + 1232.99i −0.505467 + 0.291831i
\(66\) −1016.33 + 3728.28i −0.233317 + 0.855894i
\(67\) 2317.24 4013.58i 0.516205 0.894093i −0.483618 0.875279i \(-0.660678\pi\)
0.999823 0.0188141i \(-0.00598907\pi\)
\(68\) 248.281 + 143.345i 0.0536941 + 0.0310003i
\(69\) 125.517 + 34.2160i 0.0263636 + 0.00718672i
\(70\) −2592.93 4491.08i −0.529169 0.916547i
\(71\) 6697.12i 1.32853i 0.747497 + 0.664265i \(0.231256\pi\)
−0.747497 + 0.664265i \(0.768744\pi\)
\(72\) 2148.39 + 3796.76i 0.414428 + 0.732400i
\(73\) −4823.86 −0.905208 −0.452604 0.891712i \(-0.649505\pi\)
−0.452604 + 0.891712i \(0.649505\pi\)
\(74\) 3195.24 1844.77i 0.583499 0.336883i
\(75\) 2333.51 + 2353.83i 0.414847 + 0.418459i
\(76\) −375.464 + 650.324i −0.0650042 + 0.112591i
\(77\) −6036.07 3484.93i −1.01806 0.587777i
\(78\) −1574.90 5981.21i −0.258860 0.983104i
\(79\) 2864.40 + 4961.28i 0.458964 + 0.794950i 0.998907 0.0467524i \(-0.0148872\pi\)
−0.539942 + 0.841702i \(0.681554\pi\)
\(80\) 4862.94i 0.759834i
\(81\) 3378.52 5624.26i 0.514939 0.857227i
\(82\) 2483.22 0.369307
\(83\) 2452.78 1416.12i 0.356044 0.205562i −0.311300 0.950312i \(-0.600765\pi\)
0.667344 + 0.744750i \(0.267431\pi\)
\(84\) 2484.65 654.230i 0.352133 0.0927197i
\(85\) −583.147 + 1010.04i −0.0807124 + 0.139798i
\(86\) −3452.02 1993.03i −0.466742 0.269474i
\(87\) −4577.98 + 4538.46i −0.604832 + 0.599612i
\(88\) 2589.40 + 4484.97i 0.334375 + 0.579155i
\(89\) 14277.7i 1.80251i −0.433290 0.901255i \(-0.642647\pi\)
0.433290 0.901255i \(-0.357353\pi\)
\(90\) 5043.68 2853.96i 0.622677 0.352341i
\(91\) 11155.7 1.34714
\(92\) −49.3054 + 28.4665i −0.00582531 + 0.00336324i
\(93\) −716.187 + 2627.24i −0.0828058 + 0.303763i
\(94\) −8831.02 + 15295.8i −0.999437 + 1.73107i
\(95\) −2645.60 1527.44i −0.293141 0.169245i
\(96\) −4285.22 1168.15i −0.464976 0.126753i
\(97\) −3582.65 6205.34i −0.380769 0.659511i 0.610403 0.792091i \(-0.291007\pi\)
−0.991172 + 0.132580i \(0.957674\pi\)
\(98\) 12738.9i 1.32641i
\(99\) 3952.71 6711.25i 0.403297 0.684752i
\(100\) −1450.48 −0.145048
\(101\) −1696.72 + 979.600i −0.166328 + 0.0960298i −0.580853 0.814008i \(-0.697281\pi\)
0.414525 + 0.910038i \(0.363948\pi\)
\(102\) −2059.49 2077.42i −0.197951 0.199675i
\(103\) 2577.74 4464.77i 0.242976 0.420848i −0.718584 0.695440i \(-0.755210\pi\)
0.961561 + 0.274592i \(0.0885429\pi\)
\(104\) −7178.47 4144.49i −0.663690 0.383182i
\(105\) 2661.49 + 10107.9i 0.241405 + 0.916814i
\(106\) −4391.49 7606.29i −0.390841 0.676957i
\(107\) 9117.08i 0.796321i 0.917316 + 0.398161i \(0.130351\pi\)
−0.917316 + 0.398161i \(0.869649\pi\)
\(108\) 707.000 + 2782.81i 0.0606139 + 0.238581i
\(109\) −16161.1 −1.36024 −0.680122 0.733099i \(-0.738073\pi\)
−0.680122 + 0.733099i \(0.738073\pi\)
\(110\) 5957.91 3439.80i 0.492389 0.284281i
\(111\) −7191.38 + 1893.55i −0.583668 + 0.153685i
\(112\) 10999.6 19051.8i 0.876879 1.51880i
\(113\) 18272.5 + 10549.6i 1.43100 + 0.826189i 0.997197 0.0748185i \(-0.0238377\pi\)
0.433804 + 0.901007i \(0.357171\pi\)
\(114\) 5441.38 5394.41i 0.418696 0.415082i
\(115\) −115.805 200.581i −0.00875654 0.0151668i
\(116\) 2821.05i 0.209650i
\(117\) −108.071 + 12465.9i −0.00789470 + 0.910652i
\(118\) 24179.1 1.73651
\(119\) 4569.26 2638.06i 0.322665 0.186291i
\(120\) 2042.60 7493.01i 0.141847 0.520348i
\(121\) −2697.36 + 4671.97i −0.184233 + 0.319102i
\(122\) 6621.98 + 3823.20i 0.444906 + 0.256867i
\(123\) −4828.87 1316.35i −0.319180 0.0870084i
\(124\) −595.842 1032.03i −0.0387514 0.0671195i
\(125\) 15914.9i 1.01855i
\(126\) −26215.4 227.269i −1.65126 0.0143152i
\(127\) −20660.9 −1.28098 −0.640489 0.767968i \(-0.721268\pi\)
−0.640489 + 0.767968i \(0.721268\pi\)
\(128\) −17095.3 + 9869.97i −1.04341 + 0.602415i
\(129\) 5656.31 + 5705.55i 0.339902 + 0.342861i
\(130\) −5505.61 + 9536.00i −0.325776 + 0.564260i
\(131\) 2772.53 + 1600.72i 0.161560 + 0.0932768i 0.578600 0.815611i \(-0.303599\pi\)
−0.417040 + 0.908888i \(0.636933\pi\)
\(132\) 867.908 + 3296.16i 0.0498111 + 0.189174i
\(133\) 6909.88 + 11968.3i 0.390631 + 0.676594i
\(134\) 20694.2i 1.15250i
\(135\) −11320.8 + 2876.17i −0.621170 + 0.157814i
\(136\) −3920.31 −0.211955
\(137\) −3353.18 + 1935.96i −0.178655 + 0.103147i −0.586661 0.809833i \(-0.699558\pi\)
0.408005 + 0.912980i \(0.366224\pi\)
\(138\) 561.770 147.919i 0.0294985 0.00776722i
\(139\) 5839.62 10114.5i 0.302242 0.523499i −0.674401 0.738365i \(-0.735598\pi\)
0.976644 + 0.214866i \(0.0689315\pi\)
\(140\) −3961.35 2287.08i −0.202109 0.116688i
\(141\) 25281.1 25062.9i 1.27162 1.26064i
\(142\) 14952.2 + 25898.0i 0.741530 + 1.28437i
\(143\) 14799.2i 0.723714i
\(144\) 21182.9 + 12476.0i 1.02155 + 0.601661i
\(145\) 11476.4 0.545844
\(146\) −18654.0 + 10769.9i −0.875117 + 0.505249i
\(147\) 6752.87 24772.1i 0.312503 1.14638i
\(148\) 1627.18 2818.35i 0.0742867 0.128668i
\(149\) −13069.8 7545.88i −0.588705 0.339889i 0.175880 0.984412i \(-0.443723\pi\)
−0.764585 + 0.644522i \(0.777056\pi\)
\(150\) 14279.0 + 3892.46i 0.634623 + 0.172998i
\(151\) −15127.7 26201.9i −0.663465 1.14915i −0.979699 0.200474i \(-0.935752\pi\)
0.316234 0.948681i \(-0.397581\pi\)
\(152\) 10268.5i 0.444446i
\(153\) 2903.64 + 5131.48i 0.124040 + 0.219210i
\(154\) −31122.2 −1.31229
\(155\) 4198.42 2423.96i 0.174752 0.100893i
\(156\) −3840.88 3874.32i −0.157827 0.159201i
\(157\) −10311.4 + 17859.8i −0.418328 + 0.724565i −0.995771 0.0918653i \(-0.970717\pi\)
0.577443 + 0.816431i \(0.304050\pi\)
\(158\) 22153.4 + 12790.3i 0.887415 + 0.512349i
\(159\) 4507.61 + 17119.1i 0.178300 + 0.677153i
\(160\) 3953.65 + 6847.93i 0.154440 + 0.267497i
\(161\) 1047.77i 0.0404216i
\(162\) 507.923 29292.2i 0.0193539 1.11615i
\(163\) 39790.7 1.49764 0.748818 0.662776i \(-0.230622\pi\)
0.748818 + 0.662776i \(0.230622\pi\)
\(164\) 1896.87 1095.16i 0.0705260 0.0407182i
\(165\) −13409.2 + 3530.76i −0.492533 + 0.129688i
\(166\) 6323.33 10952.3i 0.229472 0.397457i
\(167\) −23773.0 13725.3i −0.852414 0.492141i 0.00905084 0.999959i \(-0.497119\pi\)
−0.861465 + 0.507818i \(0.830452\pi\)
\(168\) −24951.0 + 24735.6i −0.884035 + 0.876404i
\(169\) 2436.98 + 4220.97i 0.0853253 + 0.147788i
\(170\) 5207.81i 0.180201i
\(171\) −13440.9 + 7605.51i −0.459659 + 0.260097i
\(172\) −3515.89 −0.118844
\(173\) 8729.26 5039.84i 0.291666 0.168393i −0.347027 0.937855i \(-0.612809\pi\)
0.638693 + 0.769462i \(0.279475\pi\)
\(174\) −7570.47 + 27771.3i −0.250048 + 0.917271i
\(175\) −13347.0 + 23117.7i −0.435821 + 0.754864i
\(176\) 25274.3 + 14592.1i 0.815933 + 0.471079i
\(177\) −47018.8 12817.3i −1.50081 0.409120i
\(178\) −31876.8 55212.2i −1.00608 1.74259i
\(179\) 1215.45i 0.0379343i 0.999820 + 0.0189672i \(0.00603779\pi\)
−0.999820 + 0.0189672i \(0.993962\pi\)
\(180\) 2594.08 4404.45i 0.0800642 0.135940i
\(181\) 28359.9 0.865661 0.432831 0.901475i \(-0.357515\pi\)
0.432831 + 0.901475i \(0.357515\pi\)
\(182\) 43139.3 24906.5i 1.30236 0.751917i
\(183\) −10850.4 10944.9i −0.324000 0.326821i
\(184\) 389.261 674.220i 0.0114976 0.0199143i
\(185\) 11465.4 + 6619.55i 0.335001 + 0.193413i
\(186\) 3096.15 + 11758.6i 0.0894943 + 0.339883i
\(187\) 3499.68 + 6061.62i 0.100079 + 0.173343i
\(188\) 15578.8i 0.440775i
\(189\) 50858.0 + 14338.7i 1.42376 + 0.401408i
\(190\) −13640.8 −0.377862
\(191\) −8445.34 + 4875.92i −0.231500 + 0.133656i −0.611264 0.791427i \(-0.709339\pi\)
0.379764 + 0.925083i \(0.376005\pi\)
\(192\) 23085.0 6078.48i 0.626221 0.164889i
\(193\) 26701.4 46248.2i 0.716836 1.24160i −0.245411 0.969419i \(-0.578923\pi\)
0.962247 0.272177i \(-0.0877436\pi\)
\(194\) −27708.5 15997.5i −0.736223 0.425058i
\(195\) 15761.2 15625.2i 0.414497 0.410919i
\(196\) 5618.15 + 9730.92i 0.146245 + 0.253304i
\(197\) 68537.7i 1.76603i 0.469349 + 0.883013i \(0.344489\pi\)
−0.469349 + 0.883013i \(0.655511\pi\)
\(198\) 301.497 34777.6i 0.00769046 0.887092i
\(199\) −8237.42 −0.208010 −0.104005 0.994577i \(-0.533166\pi\)
−0.104005 + 0.994577i \(0.533166\pi\)
\(200\) 17177.1 9917.21i 0.429428 0.247930i
\(201\) −10970.0 + 40242.0i −0.271527 + 0.996064i
\(202\) −4374.17 + 7576.28i −0.107200 + 0.185675i
\(203\) −44961.7 25958.7i −1.09107 0.629927i
\(204\) −2489.38 678.606i −0.0598178 0.0163064i
\(205\) 4455.24 + 7716.70i 0.106014 + 0.183622i
\(206\) 23020.6i 0.542477i
\(207\) −1170.83 10.1503i −0.0273246 0.000236884i
\(208\) −46711.2 −1.07968
\(209\) −15877.2 + 9166.71i −0.363481 + 0.209856i
\(210\) 32859.2 + 33145.3i 0.745107 + 0.751595i
\(211\) −20393.7 + 35322.9i −0.458069 + 0.793399i −0.998859 0.0477587i \(-0.984792\pi\)
0.540790 + 0.841158i \(0.318125\pi\)
\(212\) −6709.10 3873.50i −0.149277 0.0861851i
\(213\) −15347.6 58287.4i −0.338284 1.28474i
\(214\) 20355.1 + 35256.0i 0.444473 + 0.769850i
\(215\) 14303.1i 0.309423i
\(216\) −27399.1 28121.1i −0.587259 0.602734i
\(217\) −21931.2 −0.465740
\(218\) −62495.4 + 36081.7i −1.31503 + 0.759231i
\(219\) 41983.7 11054.7i 0.875371 0.230493i
\(220\) 3034.07 5255.16i 0.0626873 0.108578i
\(221\) −9701.99 5601.45i −0.198644 0.114687i
\(222\) −23581.7 + 23378.1i −0.478485 + 0.474355i
\(223\) 29959.8 + 51891.9i 0.602461 + 1.04349i 0.992447 + 0.122672i \(0.0391464\pi\)
−0.389986 + 0.920821i \(0.627520\pi\)
\(224\) 35771.4i 0.712918i
\(225\) −25703.6 15138.6i −0.507725 0.299034i
\(226\) 94213.5 1.84458
\(227\) 85572.3 49405.2i 1.66066 0.958785i 0.688265 0.725459i \(-0.258373\pi\)
0.972399 0.233325i \(-0.0749607\pi\)
\(228\) 1777.47 6520.43i 0.0341927 0.125432i
\(229\) 2658.97 4605.47i 0.0507040 0.0878220i −0.839559 0.543268i \(-0.817187\pi\)
0.890263 + 0.455446i \(0.150520\pi\)
\(230\) −895.645 517.101i −0.0169309 0.00977506i
\(231\) 60520.3 + 16497.9i 1.13417 + 0.309175i
\(232\) 19288.0 + 33407.8i 0.358353 + 0.620686i
\(233\) 18467.8i 0.340176i −0.985429 0.170088i \(-0.945595\pi\)
0.985429 0.170088i \(-0.0544052\pi\)
\(234\) 27413.9 + 48447.4i 0.500655 + 0.884786i
\(235\) −63376.3 −1.14760
\(236\) 18469.8 10663.6i 0.331619 0.191460i
\(237\) −36299.5 36615.5i −0.646254 0.651881i
\(238\) 11779.6 20402.9i 0.207959 0.360196i
\(239\) 22383.5 + 12923.1i 0.391861 + 0.226241i 0.682966 0.730450i \(-0.260690\pi\)
−0.291105 + 0.956691i \(0.594023\pi\)
\(240\) −11144.2 42323.8i −0.193476 0.734789i
\(241\) −41536.2 71942.7i −0.715142 1.23866i −0.962905 0.269841i \(-0.913029\pi\)
0.247763 0.968821i \(-0.420305\pi\)
\(242\) 24088.9i 0.411325i
\(243\) −16515.5 + 56692.4i −0.279691 + 0.960090i
\(244\) 6744.49 0.113284
\(245\) −39586.6 + 22855.3i −0.659502 + 0.380764i
\(246\) −21612.3 + 5690.71i −0.357134 + 0.0940365i
\(247\) 14671.9 25412.4i 0.240487 0.416536i
\(248\) 14112.3 + 8147.76i 0.229454 + 0.132475i
\(249\) −18102.2 + 17945.9i −0.291966 + 0.289446i
\(250\) −35532.0 61543.3i −0.568513 0.984693i
\(251\) 49051.6i 0.778585i 0.921114 + 0.389292i \(0.127280\pi\)
−0.921114 + 0.389292i \(0.872720\pi\)
\(252\) −20125.5 + 11388.0i −0.316917 + 0.179327i
\(253\) −1389.98 −0.0217154
\(254\) −79896.3 + 46128.1i −1.23839 + 0.714988i
\(255\) 2760.65 10127.1i 0.0424553 0.155742i
\(256\) −22852.6 + 39581.8i −0.348703 + 0.603971i
\(257\) 84096.0 + 48552.9i 1.27324 + 0.735104i 0.975596 0.219574i \(-0.0704668\pi\)
0.297641 + 0.954678i \(0.403800\pi\)
\(258\) 34611.5 + 9435.11i 0.519973 + 0.141745i
\(259\) −29945.8 51867.7i −0.446413 0.773209i
\(260\) 9712.41i 0.143675i
\(261\) 29443.1 49991.0i 0.432217 0.733856i
\(262\) 14295.3 0.208253
\(263\) 35921.0 20739.0i 0.519323 0.299831i −0.217335 0.976097i \(-0.569736\pi\)
0.736658 + 0.676266i \(0.236403\pi\)
\(264\) −32814.5 33100.2i −0.470824 0.474923i
\(265\) 15757.9 27293.5i 0.224391 0.388657i
\(266\) 53441.4 + 30854.4i 0.755292 + 0.436068i
\(267\) 32719.7 + 124264.i 0.458973 + 1.74310i
\(268\) −9126.63 15807.8i −0.127069 0.220091i
\(269\) 115737.i 1.59944i −0.600370 0.799722i \(-0.704980\pi\)
0.600370 0.799722i \(-0.295020\pi\)
\(270\) −37356.6 + 36397.5i −0.512436 + 0.499279i
\(271\) −5077.71 −0.0691400 −0.0345700 0.999402i \(-0.511006\pi\)
−0.0345700 + 0.999402i \(0.511006\pi\)
\(272\) −19132.5 + 11046.1i −0.258603 + 0.149304i
\(273\) −97091.7 + 25565.1i −1.30274 + 0.343022i
\(274\) −8644.57 + 14972.8i −0.115144 + 0.199436i
\(275\) −30668.2 17706.3i −0.405529 0.234133i
\(276\) 363.886 360.745i 0.00477692 0.00473568i
\(277\) 21192.9 + 36707.2i 0.276205 + 0.478401i 0.970438 0.241349i \(-0.0775899\pi\)
−0.694234 + 0.719750i \(0.744257\pi\)
\(278\) 52150.9i 0.674795i
\(279\) 212.459 24507.1i 0.00272939 0.314835i
\(280\) 62548.8 0.797817
\(281\) −35902.5 + 20728.3i −0.454687 + 0.262513i −0.709807 0.704396i \(-0.751218\pi\)
0.255121 + 0.966909i \(0.417885\pi\)
\(282\) 41806.6 153362.i 0.525711 1.92850i
\(283\) −19194.0 + 33245.0i −0.239658 + 0.415100i −0.960616 0.277879i \(-0.910369\pi\)
0.720958 + 0.692979i \(0.243702\pi\)
\(284\) 22843.2 + 13188.5i 0.283218 + 0.163516i
\(285\) 26525.9 + 7230.98i 0.326574 + 0.0890241i
\(286\) 33041.2 + 57229.1i 0.403946 + 0.699656i
\(287\) 40309.6i 0.489378i
\(288\) 39972.8 + 346.535i 0.481925 + 0.00417794i
\(289\) 78222.5 0.936561
\(290\) 44379.5 25622.5i 0.527699 0.304667i
\(291\) 45401.7 + 45797.0i 0.536149 + 0.540818i
\(292\) −9499.55 + 16453.7i −0.111413 + 0.192974i
\(293\) −11239.5 6489.12i −0.130922 0.0755876i 0.433109 0.901342i \(-0.357417\pi\)
−0.564030 + 0.825754i \(0.690750\pi\)
\(294\) −29193.3 110871.i −0.337745 1.28269i
\(295\) 43380.7 + 75137.6i 0.498486 + 0.863402i
\(296\) 44501.2i 0.507911i
\(297\) −19021.8 + 67468.7i −0.215645 + 0.764873i
\(298\) −67388.7 −0.758847
\(299\) 1926.69 1112.37i 0.0215511 0.0124425i
\(300\) 12624.0 3324.02i 0.140267 0.0369336i
\(301\) −32352.4 + 56036.0i −0.357086 + 0.618492i
\(302\) −116998. 67549.0i −1.28282 0.740636i
\(303\) 12522.2 12414.1i 0.136394 0.135217i
\(304\) −28933.2 50113.7i −0.313075 0.542262i
\(305\) 27437.4i 0.294947i
\(306\) 22685.2 + 13360.8i 0.242270 + 0.142689i
\(307\) −126105. −1.33799 −0.668997 0.743265i \(-0.733276\pi\)
−0.668997 + 0.743265i \(0.733276\pi\)
\(308\) −23773.5 + 13725.6i −0.250606 + 0.144688i
\(309\) −12203.2 + 44765.8i −0.127807 + 0.468845i
\(310\) 10823.6 18747.1i 0.112629 0.195079i
\(311\) −86432.4 49901.7i −0.893626 0.515935i −0.0184989 0.999829i \(-0.505889\pi\)
−0.875127 + 0.483894i \(0.839222\pi\)
\(312\) 71974.5 + 19620.3i 0.739383 + 0.201556i
\(313\) 1112.68 + 1927.21i 0.0113574 + 0.0196716i 0.871648 0.490132i \(-0.163051\pi\)
−0.860291 + 0.509804i \(0.829718\pi\)
\(314\) 92085.9i 0.933972i
\(315\) −46327.8 81873.1i −0.466896 0.825125i
\(316\) 22563.3 0.225958
\(317\) −145552. + 84034.3i −1.44843 + 0.836254i −0.998388 0.0567515i \(-0.981926\pi\)
−0.450046 + 0.893005i \(0.648592\pi\)
\(318\) 55651.8 + 56136.3i 0.550332 + 0.555124i
\(319\) 34437.0 59646.6i 0.338410 0.586144i
\(320\) −36805.0 21249.4i −0.359424 0.207514i
\(321\) −20893.3 79349.1i −0.202767 0.770073i
\(322\) 2339.28 + 4051.76i 0.0225617 + 0.0390779i
\(323\) 13878.3i 0.133024i
\(324\) −12530.6 22599.6i −0.119366 0.215283i
\(325\) 56679.9 0.536615
\(326\) 153872. 88837.9i 1.44785 0.835917i
\(327\) 140655. 37035.8i 1.31541 0.346359i
\(328\) −14975.6 + 25938.5i −0.139199 + 0.241100i
\(329\) 248293. + 143352.i 2.29389 + 1.32438i
\(330\) −43970.9 + 43591.4i −0.403773 + 0.400288i
\(331\) −3379.43 5853.34i −0.0308452 0.0534254i 0.850191 0.526475i \(-0.176487\pi\)
−0.881036 + 0.473049i \(0.843153\pi\)
\(332\) 11154.9i 0.101202i
\(333\) 58249.6 32960.5i 0.525297 0.297239i
\(334\) −122574. −1.09877
\(335\) 64308.1 37128.3i 0.573028 0.330838i
\(336\) −52072.7 + 191022.i −0.461245 + 1.69202i
\(337\) 111046. 192338.i 0.977787 1.69358i 0.307375 0.951589i \(-0.400550\pi\)
0.670413 0.741988i \(-0.266117\pi\)
\(338\) 18847.7 + 10881.7i 0.164978 + 0.0952500i
\(339\) −183208. 49942.5i −1.59421 0.434581i
\(340\) 2296.77 + 3978.11i 0.0198682 + 0.0344128i
\(341\) 29094.2i 0.250206i
\(342\) −34996.0 + 59419.3i −0.299203 + 0.508013i
\(343\) 32754.4 0.278408
\(344\) 41636.3 24038.7i 0.351848 0.203140i
\(345\) 1467.56 + 1480.34i 0.0123298 + 0.0124372i
\(346\) 22504.2 38978.4i 0.187980 0.325591i
\(347\) −140770. 81273.8i −1.16910 0.674981i −0.215633 0.976475i \(-0.569181\pi\)
−0.953468 + 0.301494i \(0.902515\pi\)
\(348\) 6464.91 + 24552.6i 0.0533831 + 0.202739i
\(349\) 36348.5 + 62957.4i 0.298425 + 0.516887i 0.975776 0.218773i \(-0.0702054\pi\)
−0.677351 + 0.735660i \(0.736872\pi\)
\(350\) 119196.i 0.973027i
\(351\) −27627.2 108743.i −0.224245 0.882646i
\(352\) 47454.7 0.382995
\(353\) 111396. 64314.6i 0.893966 0.516131i 0.0187281 0.999825i \(-0.494038\pi\)
0.875238 + 0.483693i \(0.160705\pi\)
\(354\) −210439. + 55410.5i −1.67927 + 0.442166i
\(355\) −53652.7 + 92929.2i −0.425730 + 0.737387i
\(356\) −48699.8 28116.8i −0.384261 0.221853i
\(357\) −33722.3 + 33431.2i −0.264594 + 0.262310i
\(358\) 2713.66 + 4700.19i 0.0211733 + 0.0366733i
\(359\) 95302.8i 0.739463i 0.929139 + 0.369732i \(0.120550\pi\)
−0.929139 + 0.369732i \(0.879450\pi\)
\(360\) −605.942 + 69895.2i −0.00467548 + 0.539315i
\(361\) −93969.7 −0.721063
\(362\) 109669. 63317.3i 0.836885 0.483176i
\(363\) 12769.5 46843.2i 0.0969081 0.355495i
\(364\) 21968.7 38050.9i 0.165807 0.287185i
\(365\) −66935.7 38645.4i −0.502426 0.290076i
\(366\) −66394.9 18099.3i −0.495647 0.135114i
\(367\) −52073.0 90193.1i −0.386616 0.669639i 0.605376 0.795940i \(-0.293023\pi\)
−0.991992 + 0.126301i \(0.959690\pi\)
\(368\) 4387.23i 0.0323963i
\(369\) 45043.9 + 390.499i 0.330814 + 0.00286792i
\(370\) 59116.1 0.431820
\(371\) −123471. + 71286.2i −0.897053 + 0.517914i
\(372\) 7550.89 + 7616.63i 0.0545648 + 0.0550399i
\(373\) −122915. + 212896.i −0.883463 + 1.53020i −0.0359975 + 0.999352i \(0.511461\pi\)
−0.847465 + 0.530851i \(0.821872\pi\)
\(374\) 27066.7 + 15627.0i 0.193505 + 0.111720i
\(375\) 36471.6 + 138513.i 0.259354 + 0.984979i
\(376\) −106515. 184489.i −0.753415 1.30495i
\(377\) 110237.i 0.775612i
\(378\) 228682. 58098.9i 1.60048 0.406616i
\(379\) 200830. 1.39814 0.699070 0.715053i \(-0.253597\pi\)
0.699070 + 0.715053i \(0.253597\pi\)
\(380\) −10419.9 + 6015.92i −0.0721598 + 0.0416615i
\(381\) 179819. 47347.9i 1.23875 0.326175i
\(382\) −21772.3 + 37710.7i −0.149203 + 0.258427i
\(383\) 117206. + 67668.8i 0.799008 + 0.461308i 0.843124 0.537719i \(-0.180714\pi\)
−0.0441160 + 0.999026i \(0.514047\pi\)
\(384\) 126168. 125078.i 0.855628 0.848243i
\(385\) −55837.6 96713.6i −0.376708 0.652478i
\(386\) 238458.i 1.60043i
\(387\) −62304.0 36695.0i −0.416001 0.245011i
\(388\) −28221.1 −0.187461
\(389\) −175090. + 101088.i −1.15708 + 0.668039i −0.950602 0.310413i \(-0.899533\pi\)
−0.206475 + 0.978452i \(0.566199\pi\)
\(390\) 26063.9 95612.1i 0.171360 0.628614i
\(391\) 526.102 911.236i 0.00344125 0.00596043i
\(392\) −133064. 76824.6i −0.865942 0.499952i
\(393\) −27798.7 7577.92i −0.179986 0.0490642i
\(394\) 153019. + 265037.i 0.985721 + 1.70732i
\(395\) 91790.2i 0.588304i
\(396\) −15107.4 26698.7i −0.0963385 0.170255i
\(397\) 102384. 0.649608 0.324804 0.945781i \(-0.394702\pi\)
0.324804 + 0.945781i \(0.394702\pi\)
\(398\) −31854.4 + 18391.1i −0.201096 + 0.116103i
\(399\) −87566.4 88328.8i −0.550037 0.554826i
\(400\) 55886.8 96798.8i 0.349292 0.604992i
\(401\) −78026.4 45048.6i −0.485236 0.280151i 0.237360 0.971422i \(-0.423718\pi\)
−0.722596 + 0.691271i \(0.757051\pi\)
\(402\) 47424.3 + 180109.i 0.293460 + 1.11451i
\(403\) 23283.5 + 40328.2i 0.143363 + 0.248313i
\(404\) 7716.45i 0.0472775i
\(405\) 91937.9 50975.9i 0.560512 0.310781i
\(406\) −231824. −1.40639
\(407\) 68808.1 39726.4i 0.415385 0.239823i
\(408\) 34119.8 8984.05i 0.204968 0.0539700i
\(409\) −74861.0 + 129663.i −0.447517 + 0.775122i −0.998224 0.0595770i \(-0.981025\pi\)
0.550707 + 0.834699i \(0.314358\pi\)
\(410\) 34457.1 + 19893.8i 0.204980 + 0.118345i
\(411\) 24747.3 24533.7i 0.146502 0.145238i
\(412\) −10152.6 17584.8i −0.0598113 0.103596i
\(413\) 392495.i 2.30109i
\(414\) −4550.30 + 2574.78i −0.0265485 + 0.0150224i
\(415\) 45379.7 0.263491
\(416\) −65778.1 + 37977.0i −0.380097 + 0.219449i
\(417\) −27645.1 + 101413.i −0.158981 + 0.583203i
\(418\) −40931.8 + 70895.9i −0.234265 + 0.405759i
\(419\) 109423. + 63175.3i 0.623276 + 0.359848i 0.778143 0.628087i \(-0.216162\pi\)
−0.154868 + 0.987935i \(0.549495\pi\)
\(420\) 39718.2 + 10827.2i 0.225160 + 0.0613787i
\(421\) 107645. + 186446.i 0.607335 + 1.05194i 0.991678 + 0.128745i \(0.0410949\pi\)
−0.384342 + 0.923191i \(0.625572\pi\)
\(422\) 182126.i 1.02270i
\(423\) −162594. + 276067.i −0.908709 + 1.54288i
\(424\) 105935. 0.589263
\(425\) 23215.6 13403.5i 0.128529 0.0742063i
\(426\) −189484. 191134.i −1.04413 1.05322i
\(427\) 62061.3 107493.i 0.340381 0.589557i
\(428\) 31097.5 + 17954.1i 0.169761 + 0.0980115i
\(429\) −33914.9 128803.i −0.184279 0.699859i
\(430\) −31933.5 55310.4i −0.172707 0.299137i
\(431\) 121972.i 0.656607i −0.944572 0.328304i \(-0.893523\pi\)
0.944572 0.328304i \(-0.106477\pi\)
\(432\) −212953. 60039.2i −1.14108 0.321712i
\(433\) −152419. −0.812951 −0.406475 0.913662i \(-0.633242\pi\)
−0.406475 + 0.913662i \(0.633242\pi\)
\(434\) −84808.7 + 48964.3i −0.450258 + 0.259956i
\(435\) −99882.9 + 26300.0i −0.527853 + 0.138988i
\(436\) −31825.8 + 55123.8i −0.167419 + 0.289979i
\(437\) 2386.80 + 1378.02i 0.0124984 + 0.00721593i
\(438\) 137671. 136483.i 0.717621 0.711426i
\(439\) −115564. 200162.i −0.599643 1.03861i −0.992874 0.119173i \(-0.961976\pi\)
0.393230 0.919440i \(-0.371358\pi\)
\(440\) 82977.9i 0.428605i
\(441\) −2003.26 + 231075.i −0.0103005 + 1.18816i
\(442\) −50023.9 −0.256055
\(443\) −17481.4 + 10092.9i −0.0890774 + 0.0514289i −0.543877 0.839165i \(-0.683044\pi\)
0.454800 + 0.890594i \(0.349711\pi\)
\(444\) −7703.15 + 28258.0i −0.0390753 + 0.143343i
\(445\) 114383. 198117.i 0.577618 1.00046i
\(446\) 231711. + 133778.i 1.16487 + 0.672537i
\(447\) 131044. + 35722.7i 0.655847 + 0.178784i
\(448\) 96128.9 + 166500.i 0.478958 + 0.829580i
\(449\) 92962.8i 0.461123i −0.973058 0.230561i \(-0.925944\pi\)
0.973058 0.230561i \(-0.0740562\pi\)
\(450\) −133195. 1154.71i −0.657755 0.00570227i
\(451\) 53475.0 0.262905
\(452\) 71967.4 41550.4i 0.352256 0.203375i
\(453\) 191707. + 193376.i 0.934205 + 0.942339i
\(454\) 220607. 382103.i 1.07031 1.85383i
\(455\) 154796. + 89371.5i 0.747716 + 0.431694i
\(456\) 23531.9 + 89370.1i 0.113169 + 0.429796i
\(457\) −110443. 191293.i −0.528819 0.915941i −0.999435 0.0336033i \(-0.989302\pi\)
0.470616 0.882338i \(-0.344032\pi\)
\(458\) 23746.0i 0.113203i
\(459\) −37031.0 38006.9i −0.175768 0.180400i
\(460\) −912.215 −0.00431103
\(461\) 91967.2 53097.3i 0.432744 0.249845i −0.267771 0.963483i \(-0.586287\pi\)
0.700515 + 0.713638i \(0.252954\pi\)
\(462\) 270868. 71321.8i 1.26903 0.334148i
\(463\) 34090.0 59045.5i 0.159025 0.275439i −0.775493 0.631357i \(-0.782498\pi\)
0.934517 + 0.355918i \(0.115832\pi\)
\(464\) 188264. + 108694.i 0.874444 + 0.504860i
\(465\) −30985.4 + 30718.0i −0.143302 + 0.142065i
\(466\) −41231.8 71415.6i −0.189872 0.328868i
\(467\) 224350.i 1.02871i 0.857578 + 0.514353i \(0.171968\pi\)
−0.857578 + 0.514353i \(0.828032\pi\)
\(468\) 42307.2 + 24917.6i 0.193162 + 0.113766i
\(469\) −335925. −1.52720
\(470\) −245078. + 141496.i −1.10945 + 0.640543i
\(471\) 48814.7 179070.i 0.220043 0.807202i
\(472\) −145817. + 252563.i −0.654524 + 1.13367i
\(473\) −74337.9 42919.0i −0.332267 0.191835i
\(474\) −222120. 60550.0i −0.988624 0.269499i
\(475\) 35107.8 + 60808.5i 0.155603 + 0.269511i
\(476\) 20780.4i 0.0917149i
\(477\) −78462.7 138664.i −0.344847 0.609433i
\(478\) 115410. 0.505113
\(479\) −94542.7 + 54584.3i −0.412057 + 0.237901i −0.691673 0.722211i \(-0.743126\pi\)
0.279616 + 0.960112i \(0.409793\pi\)
\(480\) −50103.2 50539.4i −0.217462 0.219355i
\(481\) −63584.5 + 110132.i −0.274828 + 0.476016i
\(482\) −321243. 185470.i −1.38274 0.798324i
\(483\) −2401.14 9119.10i −0.0102926 0.0390893i
\(484\) 10623.8 + 18400.9i 0.0453510 + 0.0785503i
\(485\) 114807.i 0.488073i
\(486\) 62707.3 + 256104.i 0.265489 + 1.08429i
\(487\) 106309. 0.448240 0.224120 0.974562i \(-0.428049\pi\)
0.224120 + 0.974562i \(0.428049\pi\)
\(488\) −79870.6 + 46113.3i −0.335388 + 0.193636i
\(489\) −346312. + 91187.0i −1.44827 + 0.381343i
\(490\) −102055. + 176765.i −0.425052 + 0.736212i
\(491\) −64472.7 37223.3i −0.267432 0.154402i 0.360288 0.932841i \(-0.382678\pi\)
−0.627720 + 0.778439i \(0.716012\pi\)
\(492\) −13999.4 + 13878.5i −0.0578333 + 0.0573341i
\(493\) 26068.5 + 45152.0i 0.107256 + 0.185773i
\(494\) 131028.i 0.536919i
\(495\) 108614. 61458.9i 0.443275 0.250827i
\(496\) 91830.8 0.373271
\(497\) 420397. 242716.i 1.70195 0.982621i
\(498\) −29935.0 + 109813.i −0.120704 + 0.442787i
\(499\) 55603.4 96308.0i 0.223306 0.386777i −0.732504 0.680763i \(-0.761648\pi\)
0.955810 + 0.293985i \(0.0949817\pi\)
\(500\) −54284.1 31340.9i −0.217136 0.125364i
\(501\) 238358. + 64976.6i 0.949631 + 0.258870i
\(502\) 109514. + 189684.i 0.434573 + 0.752703i
\(503\) 115897.i 0.458077i 0.973417 + 0.229038i \(0.0735581\pi\)
−0.973417 + 0.229038i \(0.926442\pi\)
\(504\) 160471. 272462.i 0.631737 1.07262i
\(505\) −31391.5 −0.123092
\(506\) −5375.10 + 3103.31i −0.0209935 + 0.0121206i
\(507\) −30882.9 31151.8i −0.120144 0.121190i
\(508\) −40687.2 + 70472.3i −0.157663 + 0.273081i
\(509\) −170299. 98322.1i −0.657319 0.379503i 0.133936 0.990990i \(-0.457238\pi\)
−0.791255 + 0.611487i \(0.790572\pi\)
\(510\) −11934.6 45325.4i −0.0458845 0.174261i
\(511\) 174825. + 302807.i 0.669519 + 1.15964i
\(512\) 111753.i 0.426305i
\(513\) 99551.4 96995.4i 0.378279 0.368567i
\(514\) 433603. 1.64122
\(515\) 71537.3 41302.1i 0.269723 0.155725i
\(516\) 30600.0 8057.24i 0.114927 0.0302613i
\(517\) −190172. + 329388.i −0.711486 + 1.23233i
\(518\) −231603. 133716.i −0.863146 0.498337i
\(519\) −64424.2 + 63868.1i −0.239174 + 0.237110i
\(520\) −66405.5 115018.i −0.245583 0.425362i
\(521\) 299306.i 1.10266i 0.834289 + 0.551328i \(0.185879\pi\)
−0.834289 + 0.551328i \(0.814121\pi\)
\(522\) 2245.80 259052.i 0.00824195 0.950707i
\(523\) −162892. −0.595520 −0.297760 0.954641i \(-0.596240\pi\)
−0.297760 + 0.954641i \(0.596240\pi\)
\(524\) 10919.8 6304.56i 0.0397698 0.0229611i
\(525\) 63185.6 231788.i 0.229245 0.840955i
\(526\) 92605.2 160397.i 0.334706 0.579728i
\(527\) 19073.4 + 11012.0i 0.0686763 + 0.0396503i
\(528\) −253412. 69080.1i −0.908989 0.247791i
\(529\) −139816. 242168.i −0.499627 0.865379i
\(530\) 140726.i 0.500983i
\(531\) 438594. + 3802.29i 1.55551 + 0.0134852i
\(532\) 54430.1 0.192316
\(533\) −74123.1 + 42795.0i −0.260915 + 0.150639i
\(534\) 403963. + 407480.i 1.41664 + 1.42897i
\(535\) −73039.7 + 126508.i −0.255183 + 0.441989i
\(536\) 216161. + 124801.i 0.752400 + 0.434398i
\(537\) −2785.41 10578.5i −0.00965920 0.0366839i
\(538\) −258399. 447560.i −0.892742 1.54628i
\(539\) 274327.i 0.944257i
\(540\) −12483.6 + 44278.2i −0.0428108 + 0.151846i
\(541\) −62918.7 −0.214974 −0.107487 0.994207i \(-0.534280\pi\)
−0.107487 + 0.994207i \(0.534280\pi\)
\(542\) −19635.7 + 11336.7i −0.0668416 + 0.0385910i
\(543\) −246826. + 64991.5i −0.837128 + 0.220423i
\(544\) −17961.4 + 31110.1i −0.0606936 + 0.105124i
\(545\) −224251. 129471.i −0.754989 0.435893i
\(546\) −318379. + 315631.i −1.06797 + 1.05875i
\(547\) 7403.57 + 12823.4i 0.0247438 + 0.0428575i 0.878132 0.478418i \(-0.158790\pi\)
−0.853388 + 0.521276i \(0.825456\pi\)
\(548\) 15249.8i 0.0507813i
\(549\) 119517. + 70391.8i 0.396539 + 0.233549i
\(550\) −158126. −0.522732
\(551\) −118267. + 68281.3i −0.389547 + 0.224905i
\(552\) −1842.79 + 6760.03i −0.00604779 + 0.0221856i
\(553\) 207622. 359612.i 0.678927 1.17594i
\(554\) 163907. + 94631.9i 0.534046 + 0.308332i
\(555\) −114957. 31337.4i −0.373207 0.101736i
\(556\) −22999.8 39836.8i −0.0744002 0.128865i
\(557\) 254392.i 0.819962i 0.912094 + 0.409981i \(0.134465\pi\)
−0.912094 + 0.409981i \(0.865535\pi\)
\(558\) −53893.7 95243.9i −0.173089 0.305893i
\(559\) 137389. 0.439671
\(560\) 305260. 176242.i 0.973405 0.561996i
\(561\) −44350.2 44736.3i −0.140919 0.142146i
\(562\) −92557.4 + 160314.i −0.293048 + 0.507574i
\(563\) 80806.7 + 46653.8i 0.254936 + 0.147187i 0.622022 0.783000i \(-0.286311\pi\)
−0.367087 + 0.930187i \(0.619645\pi\)
\(564\) −35701.3 135587.i −0.112234 0.426246i
\(565\) 169032. + 292772.i 0.529508 + 0.917134i
\(566\) 171412.i 0.535068i
\(567\) −475494. 8245.01i −1.47904 0.0256463i
\(568\) −360690. −1.11799
\(569\) −136853. + 79012.1i −0.422698 + 0.244045i −0.696231 0.717818i \(-0.745141\pi\)
0.273533 + 0.961863i \(0.411808\pi\)
\(570\) 118721. 31260.2i 0.365407 0.0962149i
\(571\) 219188. 379644.i 0.672270 1.16441i −0.304988 0.952356i \(-0.598653\pi\)
0.977259 0.212050i \(-0.0680141\pi\)
\(572\) 50478.7 + 29143.9i 0.154282 + 0.0890749i
\(573\) 62328.8 61790.8i 0.189836 0.188198i
\(574\) −89996.4 155878.i −0.273150 0.473110i
\(575\) 5323.52i 0.0161014i
\(576\) −186987. + 105806.i −0.563594 + 0.318909i
\(577\) 214770. 0.645094 0.322547 0.946554i \(-0.395461\pi\)
0.322547 + 0.946554i \(0.395461\pi\)
\(578\) 302489. 174642.i 0.905428 0.522749i
\(579\) −126406. + 463705.i −0.377061 + 1.38320i
\(580\) 22600.3 39144.8i 0.0671827 0.116364i
\(581\) −177787. 102645.i −0.526681 0.304079i
\(582\) 277817. + 75733.1i 0.820188 + 0.223584i
\(583\) −94568.9 163798.i −0.278235 0.481917i
\(584\) 259801.i 0.761753i
\(585\) −101368. + 172111.i −0.296202 + 0.502918i
\(586\) −57951.3 −0.168759
\(587\) 568470. 328206.i 1.64980 0.952512i 0.672649 0.739962i \(-0.265157\pi\)
0.977150 0.212550i \(-0.0681767\pi\)
\(588\) −71196.7 71816.6i −0.205923 0.207716i
\(589\) −28843.8 + 49959.0i −0.0831423 + 0.144007i
\(590\) 335509. + 193706.i 0.963830 + 0.556467i
\(591\) −157066. 596507.i −0.449683 1.70781i
\(592\) 125390. + 217181.i 0.357781 + 0.619696i
\(593\) 118369.i 0.336612i −0.985735 0.168306i \(-0.946170\pi\)
0.985735 0.168306i \(-0.0538296\pi\)
\(594\) 77074.6 + 303372.i 0.218443 + 0.859811i
\(595\) 84537.3 0.238789
\(596\) −51476.5 + 29720.0i −0.144916 + 0.0836673i
\(597\) 71693.1 18877.4i 0.201154 0.0529656i
\(598\) 4967.04 8603.17i 0.0138898 0.0240578i
\(599\) −306693. 177069.i −0.854772 0.493503i 0.00748620 0.999972i \(-0.497617\pi\)
−0.862258 + 0.506469i \(0.830950\pi\)
\(600\) −126771. + 125677.i −0.352143 + 0.349103i
\(601\) 297820. + 515839.i 0.824526 + 1.42812i 0.902281 + 0.431148i \(0.141891\pi\)
−0.0777554 + 0.996972i \(0.524775\pi\)
\(602\) 288924.i 0.797242i
\(603\) 3254.27 375379.i 0.00894992 1.03237i
\(604\) −119163. −0.326638
\(605\) −74857.1 + 43218.8i −0.204514 + 0.118076i
\(606\) 20707.6 75963.2i 0.0563877 0.206851i
\(607\) −4860.81 + 8419.17i −0.0131926 + 0.0228503i −0.872546 0.488531i \(-0.837533\pi\)
0.859354 + 0.511382i \(0.170866\pi\)
\(608\) −81486.6 47046.3i −0.220434 0.127268i
\(609\) 450806. + 122890.i 1.21550 + 0.331346i
\(610\) 61257.7 + 106101.i 0.164627 + 0.285142i
\(611\) 608765.i 1.63067i
\(612\) 23221.1 + 201.310i 0.0619982 + 0.000537480i
\(613\) 194450. 0.517473 0.258736 0.965948i \(-0.416694\pi\)
0.258736 + 0.965948i \(0.416694\pi\)
\(614\) −487650. + 281545.i −1.29352 + 0.746811i
\(615\) −56459.6 56951.2i −0.149275 0.150575i
\(616\) 187689. 325087.i 0.494627 0.856720i
\(617\) 422308. + 243819.i 1.10932 + 0.640469i 0.938654 0.344860i \(-0.112073\pi\)
0.170670 + 0.985328i \(0.445407\pi\)
\(618\) 52755.5 + 200356.i 0.138131 + 0.524596i
\(619\) −8628.23 14944.5i −0.0225185 0.0390033i 0.854547 0.519375i \(-0.173835\pi\)
−0.877065 + 0.480372i \(0.840502\pi\)
\(620\) 19093.9i 0.0496719i
\(621\) 10213.4 2594.81i 0.0264842 0.00672857i
\(622\) −445649. −1.15189
\(623\) −896249. + 517449.i −2.30915 + 1.33319i
\(624\) 406544. 107047.i 1.04409 0.274918i
\(625\) 12412.5 21499.1i 0.0317760 0.0550376i
\(626\) 8605.50 + 4968.39i 0.0219598 + 0.0126785i
\(627\) 117178. 116166.i 0.298065 0.295492i
\(628\) 40612.1 + 70342.1i 0.102976 + 0.178360i
\(629\) 60145.1i 0.152019i
\(630\) −361943. 213173.i −0.911926 0.537095i
\(631\) −429836. −1.07955 −0.539777 0.841808i \(-0.681491\pi\)
−0.539777 + 0.841808i \(0.681491\pi\)
\(632\) −267202. + 154269.i −0.668968 + 0.386229i
\(633\) 96545.0 354163.i 0.240948 0.883886i
\(634\) −375235. + 649927.i −0.933523 + 1.61691i
\(635\) −286690. 165521.i −0.710993 0.410492i
\(636\) 67268.4 + 18337.4i 0.166302 + 0.0453339i
\(637\) −219538. 380251.i −0.541042 0.937113i
\(638\) 307540.i 0.755546i
\(639\) 267151. + 472124.i 0.654266 + 1.15626i
\(640\) −316285. −0.772181
\(641\) −27979.5 + 16154.0i −0.0680964 + 0.0393155i −0.533662 0.845698i \(-0.679184\pi\)
0.465565 + 0.885014i \(0.345851\pi\)
\(642\) −257952. 260198.i −0.625849 0.631298i
\(643\) −138524. + 239931.i −0.335045 + 0.580315i −0.983494 0.180943i \(-0.942085\pi\)
0.648448 + 0.761259i \(0.275418\pi\)
\(644\) 3573.84 + 2063.36i 0.00861714 + 0.00497511i
\(645\) 32777.9 + 124485.i 0.0787882 + 0.299224i
\(646\) −30985.0 53667.7i −0.0742484 0.128602i
\(647\) 125452.i 0.299689i −0.988710 0.149844i \(-0.952123\pi\)
0.988710 0.149844i \(-0.0478773\pi\)
\(648\) 302908. + 181958.i 0.721376 + 0.433333i
\(649\) 520687. 1.23620
\(650\) 219183. 126545.i 0.518776 0.299516i
\(651\) 190875. 50259.1i 0.450388 0.118591i
\(652\) 78359.2 135722.i 0.184330 0.319268i
\(653\) 245936. + 141991.i 0.576760 + 0.332992i 0.759845 0.650105i \(-0.225275\pi\)
−0.183085 + 0.983097i \(0.558608\pi\)
\(654\) 461231. 457250.i 1.07836 1.06905i
\(655\) 25647.8 + 44423.2i 0.0597815 + 0.103545i
\(656\) 168785.i 0.392216i
\(657\) −340065. + 192425.i −0.787828 + 0.445791i
\(658\) 1.28021e6 2.95685
\(659\) 311139. 179636.i 0.716446 0.413640i −0.0969973 0.995285i \(-0.530924\pi\)
0.813443 + 0.581644i \(0.197590\pi\)
\(660\) −14363.5 + 52690.5i −0.0329740 + 0.120961i
\(661\) −98902.1 + 171303.i −0.226362 + 0.392070i −0.956727 0.290987i \(-0.906016\pi\)
0.730366 + 0.683057i \(0.239350\pi\)
\(662\) −26136.7 15090.0i −0.0596396 0.0344330i
\(663\) 97276.5 + 26517.6i 0.221300 + 0.0603264i
\(664\) 76268.4 + 132101.i 0.172985 + 0.299619i
\(665\) 221429.i 0.500715i
\(666\) 151665. 257509.i 0.341929 0.580556i
\(667\) −10353.7 −0.0232726
\(668\) −93631.5 + 54058.2i −0.209831 + 0.121146i
\(669\) −379669. 382975.i −0.848307 0.855693i
\(670\) 165788. 287152.i 0.369320 0.639680i
\(671\) 142602. + 82331.1i 0.316723 + 0.182860i
\(672\) 81976.2 + 311331.i 0.181530 + 0.689420i
\(673\) −119036. 206176.i −0.262814 0.455207i 0.704175 0.710027i \(-0.251317\pi\)
−0.966989 + 0.254820i \(0.917984\pi\)
\(674\) 991702.i 2.18304i
\(675\) 258400. + 72852.2i 0.567133 + 0.159895i
\(676\) 19196.4 0.0420075
\(677\) 216636. 125075.i 0.472666 0.272894i −0.244689 0.969602i \(-0.578686\pi\)
0.717355 + 0.696708i \(0.245353\pi\)
\(678\) −819973. + 215906.i −1.78378 + 0.469684i
\(679\) −259684. + 449786.i −0.563256 + 0.975588i
\(680\) −54398.2 31406.8i −0.117643 0.0679213i
\(681\) −631545. + 626094.i −1.36179 + 1.35004i
\(682\) −64956.6 112508.i −0.139654 0.241888i
\(683\) 267358.i 0.573129i 0.958061 + 0.286564i \(0.0925132\pi\)
−0.958061 + 0.286564i \(0.907487\pi\)
\(684\) −527.292 + 60823.0i −0.00112704 + 0.130004i
\(685\) −62038.2 −0.132214
\(686\) 126662. 73128.5i 0.269153 0.155396i
\(687\) −12587.7 + 46176.5i −0.0266707 + 0.0978380i
\(688\) 135466. 234635.i 0.286190 0.495696i
\(689\) 262169. + 151363.i 0.552259 + 0.318847i
\(690\) 8980.13 + 2447.99i 0.0188619 + 0.00514175i
\(691\) −168343. 291579.i −0.352565 0.610660i 0.634133 0.773224i \(-0.281357\pi\)
−0.986698 + 0.162564i \(0.948024\pi\)
\(692\) 39699.5i 0.0829036i
\(693\) −564537. 4894.13i −1.17551 0.0101908i
\(694\) −725817. −1.50698
\(695\) 162061. 93565.9i 0.335513 0.193708i
\(696\) −244430. 246558.i −0.504587 0.508980i
\(697\) −20240.1 + 35056.9i −0.0416627 + 0.0721618i
\(698\) 281121. + 162305.i 0.577009 + 0.333137i
\(699\) 42322.1 + 160732.i 0.0866189 + 0.328963i
\(700\) 52568.2 + 91050.7i 0.107282 + 0.185818i
\(701\) 635795.i 1.29384i 0.762557 + 0.646921i \(0.223944\pi\)
−0.762557 + 0.646921i \(0.776056\pi\)
\(702\) −349618. 358831.i −0.709446 0.728141i
\(703\) −157538. −0.318768
\(704\) −220881. + 127525.i −0.445669 + 0.257307i
\(705\) 551586. 145237.i 1.10978 0.292214i
\(706\) 287182. 497413.i 0.576165 0.997948i
\(707\) 122984. + 71005.0i 0.246043 + 0.142053i
\(708\) −136312. + 135135.i −0.271937 + 0.269589i
\(709\) −215513. 373280.i −0.428728 0.742578i 0.568033 0.823006i \(-0.307705\pi\)
−0.996760 + 0.0804279i \(0.974371\pi\)
\(710\) 479147.i 0.950499i
\(711\) 399837. + 235491.i 0.790941 + 0.465839i
\(712\) 768959. 1.51685
\(713\) −3787.73 + 2186.84i −0.00745074 + 0.00430169i
\(714\) −55765.6 + 204569.i −0.109388 + 0.401276i
\(715\) −118561. + 205354.i −0.231916 + 0.401690i
\(716\) 4145.79 + 2393.57i 0.00808689 + 0.00466897i
\(717\) −224427. 61178.9i −0.436553 0.119004i
\(718\) 212776. + 368539.i 0.412737 + 0.714882i
\(719\) 798370.i 1.54435i −0.635409 0.772176i \(-0.719168\pi\)
0.635409 0.772176i \(-0.280832\pi\)
\(720\) 193984. + 342820.i 0.374198 + 0.661304i
\(721\) −373688. −0.718850
\(722\) −363384. + 209800.i −0.697093 + 0.402467i
\(723\) 526372. + 530956.i 1.00697 + 1.01574i
\(724\) 55848.8 96732.9i 0.106546 0.184543i
\(725\) −228442. 131891.i −0.434610 0.250922i
\(726\) −55203.7 209654.i −0.104736 0.397768i
\(727\) −158557. 274628.i −0.299996 0.519609i 0.676139 0.736775i \(-0.263652\pi\)
−0.976135 + 0.217166i \(0.930319\pi\)
\(728\) 600816.i 1.13365i
\(729\) 13819.7 531261.i 0.0260043 0.999662i
\(730\) −345123. −0.647632
\(731\) 56273.2 32489.3i 0.105309 0.0608004i
\(732\) −58699.6 + 15456.1i −0.109550 + 0.0288455i
\(733\) 488922. 846837.i 0.909979 1.57613i 0.0958883 0.995392i \(-0.469431\pi\)
0.814091 0.580738i \(-0.197236\pi\)
\(734\) −402736. 232520.i −0.747529 0.431586i
\(735\) 292159. 289637.i 0.540810 0.536142i
\(736\) −3566.90 6178.05i −0.00658469 0.0114050i
\(737\) 445641.i 0.820446i
\(738\) 175058. 99056.5i 0.321418 0.181874i
\(739\) −392565. −0.718825 −0.359412 0.933179i \(-0.617023\pi\)
−0.359412 + 0.933179i \(0.617023\pi\)
\(740\) 45157.3 26071.6i 0.0824640 0.0476106i
\(741\) −69457.6 + 254796.i −0.126498 + 0.464041i
\(742\) −318312. + 551332.i −0.578155 + 1.00139i
\(743\) 899450. + 519298.i 1.62929 + 0.940673i 0.984304 + 0.176482i \(0.0564719\pi\)
0.644990 + 0.764191i \(0.276861\pi\)
\(744\) −141497. 38572.0i −0.255623 0.0696829i
\(745\) −120905. 209413.i −0.217836 0.377304i
\(746\) 1.09770e6i 1.97245i
\(747\) 116423. 197674.i 0.208641 0.354248i
\(748\) 27567.5 0.0492713
\(749\) 572304. 330420.i 1.02015 0.588983i
\(750\) 450284. + 454205.i 0.800506 + 0.807476i
\(751\) −159783. + 276752.i −0.283302 + 0.490694i −0.972196 0.234168i \(-0.924763\pi\)
0.688894 + 0.724862i \(0.258097\pi\)
\(752\) −1.03966e6 600246.i −1.83846 1.06144i
\(753\) −112410. 426913.i −0.198251 0.752921i
\(754\) 246118. + 426290.i 0.432914 + 0.749829i
\(755\) 484769.i 0.850435i
\(756\) 149062. 145235.i 0.260809 0.254113i
\(757\) 500321. 0.873085 0.436543 0.899684i \(-0.356203\pi\)
0.436543 + 0.899684i \(0.356203\pi\)
\(758\) 776617. 448380.i 1.35166 0.780383i
\(759\) 12097.5 3185.37i 0.0209996 0.00552939i
\(760\) 82263.8 142485.i 0.142424 0.246685i
\(761\) −783645. 452437.i −1.35316 0.781249i −0.364471 0.931215i \(-0.618750\pi\)
−0.988691 + 0.149966i \(0.952083\pi\)
\(762\) 589655. 584565.i 1.01552 1.00675i
\(763\) 585707. + 1.01447e6i 1.00608 + 1.74258i
\(764\) 38408.3i 0.0658019i
\(765\) −818.955 + 94466.2i −0.00139938 + 0.161419i
\(766\) 604318. 1.02993
\(767\) −721738. + 416696.i −1.22684 + 0.708318i
\(768\) 108186. 396865.i 0.183420 0.672853i
\(769\) −71688.6 + 124168.i −0.121227 + 0.209970i −0.920252 0.391327i \(-0.872016\pi\)
0.799025 + 0.601298i \(0.205349\pi\)
\(770\) −431852. 249330.i −0.728372 0.420526i
\(771\) −843184. 229852.i −1.41845 0.386670i
\(772\) −105165. 182152.i −0.176457 0.305632i
\(773\) 710063.i 1.18833i 0.804342 + 0.594166i \(0.202518\pi\)
−0.804342 + 0.594166i \(0.797482\pi\)
\(774\) −322858. 2798.95i −0.538927 0.00467211i
\(775\) −111428. −0.185521
\(776\) 334204. 192953.i 0.554993 0.320426i
\(777\) 379492. + 382796.i 0.628580 + 0.634053i
\(778\) −451386. + 781823.i −0.745742 + 1.29166i
\(779\) −91824.5 53014.9i −0.151316 0.0873621i
\(780\) −22257.6 84530.5i −0.0365839 0.138939i
\(781\) 321990. + 557702.i 0.527885 + 0.914324i
\(782\) 4698.37i 0.00768305i
\(783\) −141691. + 502563.i −0.231109 + 0.819723i
\(784\) −865865. −1.40870
\(785\) −286161. + 165215.i −0.464377 + 0.268108i
\(786\) −124417. + 32760.1i −0.201388 + 0.0530274i
\(787\) 300855. 521097.i 0.485745 0.841335i −0.514121 0.857718i \(-0.671882\pi\)
0.999866 + 0.0163827i \(0.00521501\pi\)
\(788\) 233775. + 134970.i 0.376484 + 0.217363i
\(789\) −265106. + 262818.i −0.425859 + 0.422183i
\(790\) 204934. + 354956.i 0.328367 + 0.568748i
\(791\) 1.52935e6i 2.44429i
\(792\) 361451. + 212883.i 0.576234 + 0.339383i
\(793\) −263552. −0.419102
\(794\) 395923. 228586.i 0.628014 0.362584i
\(795\) −74598.8 + 273656.i −0.118031 + 0.432983i
\(796\) −16221.8 + 28097.0i −0.0256020 + 0.0443439i
\(797\) −372227. 214905.i −0.585991 0.338322i 0.177519 0.984117i \(-0.443193\pi\)
−0.763511 + 0.645795i \(0.776526\pi\)
\(798\) −535828. 146067.i −0.841432 0.229375i
\(799\) −143959. 249344.i −0.225499 0.390576i
\(800\) 181748.i 0.283981i
\(801\) −569542. 1.00653e6i −0.887688 1.56877i
\(802\) −402308. −0.625474
\(803\) −401706. + 231925.i −0.622984 + 0.359680i
\(804\) 115658. + 116665.i 0.178923 + 0.180480i
\(805\) −8393.99 + 14538.8i −0.0129532 + 0.0224356i
\(806\) 180076. + 103967.i 0.277195 + 0.160039i
\(807\) 265232. + 1.00730e6i 0.407266 + 1.54672i
\(808\) −52758.7 91380.8i −0.0808112 0.139969i
\(809\) 629639.i 0.962042i 0.876709 + 0.481021i \(0.159734\pi\)
−0.876709 + 0.481021i \(0.840266\pi\)
\(810\) 241716. 402389.i 0.368414 0.613304i
\(811\) 577760. 0.878428 0.439214 0.898383i \(-0.355257\pi\)
0.439214 + 0.898383i \(0.355257\pi\)
\(812\) −177085. + 102240.i −0.268577 + 0.155063i
\(813\) 44193.1 11636.4i 0.0668610 0.0176051i
\(814\) 177389. 307246.i 0.267718 0.463701i
\(815\) 552135. + 318775.i 0.831246 + 0.479920i
\(816\) 141202. 139984.i 0.212062 0.210231i
\(817\) 85099.3 + 147396.i 0.127492 + 0.220822i
\(818\) 668548.i 0.999140i
\(819\) 786436. 445004.i 1.17245 0.663431i
\(820\) 35094.5 0.0521929
\(821\) 38728.3 22359.8i 0.0574569 0.0331727i −0.470996 0.882135i \(-0.656106\pi\)
0.528453 + 0.848962i \(0.322772\pi\)
\(822\) 40923.9 150124.i 0.0605667 0.222181i
\(823\) 146289. 253380.i 0.215979 0.374087i −0.737596 0.675242i \(-0.764039\pi\)
0.953575 + 0.301155i \(0.0973723\pi\)
\(824\) 240461. + 138830.i 0.354153 + 0.204470i
\(825\) 307493. + 83822.6i 0.451780 + 0.123155i
\(826\) −876296. 1.51779e6i −1.28437 2.22460i
\(827\) 806491.i 1.17920i 0.807694 + 0.589601i \(0.200715\pi\)
−0.807694 + 0.589601i \(0.799285\pi\)
\(828\) −2340.32 + 3973.60i −0.00341362 + 0.00579593i
\(829\) 204904. 0.298154 0.149077 0.988826i \(-0.452370\pi\)
0.149077 + 0.988826i \(0.452370\pi\)
\(830\) 175485. 101316.i 0.254732 0.147069i
\(831\) −268570. 270908.i −0.388916 0.392302i
\(832\) 204112. 353533.i 0.294864 0.510720i
\(833\) −179842. 103832.i −0.259179 0.149637i
\(834\) 119513. + 453887.i 0.171823 + 0.652553i
\(835\) −219915. 380905.i −0.315415 0.546315i
\(836\) 72207.5i 0.103317i
\(837\) 54313.0 + 213780.i 0.0775269 + 0.305152i
\(838\) 564189. 0.803409
\(839\) 667796. 385552.i 0.948681 0.547721i 0.0560100 0.998430i \(-0.482162\pi\)
0.892671 + 0.450709i \(0.148829\pi\)
\(840\) −544384. + 143341.i −0.771520 + 0.203148i
\(841\) −97125.1 + 168226.i −0.137322 + 0.237848i
\(842\) 832531. + 480662.i 1.17429 + 0.677978i
\(843\) 264970. 262682.i 0.372856 0.369637i
\(844\) 80322.0 + 139122.i 0.112759 + 0.195304i
\(845\) 78093.4i 0.109371i
\(846\) −12402.0 + 1.43057e6i −0.0173281 + 1.99880i
\(847\) 391030. 0.545058
\(848\) 517001. 298491.i 0.718951 0.415087i
\(849\) 90865.5 333329.i 0.126062 0.462442i
\(850\) 59850.2 103664.i 0.0828376 0.143479i
\(851\) −10343.8 5972.02i −0.0142831 0.00824635i
\(852\) −229036. 62435.4i −0.315519 0.0860106i
\(853\) −541184. 937358.i −0.743784 1.28827i −0.950761 0.309925i \(-0.899696\pi\)
0.206977 0.978346i \(-0.433637\pi\)
\(854\) 554240.i 0.759945i
\(855\) −247435. 2145.09i −0.338477 0.00293436i
\(856\) −491023. −0.670122
\(857\) −461890. + 266672.i −0.628893 + 0.363092i −0.780323 0.625376i \(-0.784945\pi\)
0.151430 + 0.988468i \(0.451612\pi\)
\(858\) −418719. 422365.i −0.568785 0.573737i
\(859\) −565525. + 979517.i −0.766417 + 1.32747i 0.173077 + 0.984908i \(0.444629\pi\)
−0.939494 + 0.342565i \(0.888704\pi\)
\(860\) −48786.4 28166.8i −0.0659632 0.0380839i
\(861\) 92376.1 + 350828.i 0.124610 + 0.473247i
\(862\) −272319. 471670.i −0.366490 0.634780i
\(863\) 110025.i 0.147730i −0.997268 0.0738649i \(-0.976467\pi\)
0.997268 0.0738649i \(-0.0235334\pi\)
\(864\) −348691. + 88588.3i −0.467104 + 0.118672i
\(865\) 161503. 0.215848
\(866\) −589410. + 340296.i −0.785926 + 0.453755i
\(867\) −680798. + 179260.i −0.905691 + 0.238476i
\(868\) −43188.8 + 74805.3i −0.0573234 + 0.0992871i
\(869\) 477065. + 275433.i 0.631739 + 0.364735i
\(870\) −327532. + 324705.i −0.432728 + 0.428993i
\(871\) 356638. + 617715.i 0.470101 + 0.814238i
\(872\) 870394.i 1.14468i
\(873\) −500098. 294541.i −0.656185 0.386472i
\(874\) 12306.4 0.0161105
\(875\) −999020. + 576784.i −1.30484 + 0.753351i
\(876\) 44971.5 164972.i 0.0586042 0.214982i
\(877\) 204377. 353991.i 0.265725 0.460249i −0.702028 0.712149i \(-0.747722\pi\)
0.967753 + 0.251900i \(0.0810554\pi\)
\(878\) −893778. 516023.i −1.15942 0.669391i
\(879\) 112692. + 30719.9i 0.145853 + 0.0397596i
\(880\) 233804. + 404960.i 0.301916 + 0.522935i
\(881\) 235809.i 0.303815i 0.988395 + 0.151907i \(0.0485416\pi\)
−0.988395 + 0.151907i \(0.951458\pi\)
\(882\) 508159. + 898047.i 0.653224 + 1.15442i
\(883\) −273719. −0.351061 −0.175531 0.984474i \(-0.556164\pi\)
−0.175531 + 0.984474i \(0.556164\pi\)
\(884\) −38212.0 + 22061.7i −0.0488985 + 0.0282315i
\(885\) −549748. 554534.i −0.701903 0.708014i
\(886\) −45067.3 + 78058.8i −0.0574109 + 0.0994385i
\(887\) 322071. + 185948.i 0.409359 + 0.236344i 0.690514 0.723319i \(-0.257384\pi\)
−0.281155 + 0.959662i \(0.590718\pi\)
\(888\) −101982. 387309.i −0.129329 0.491170i
\(889\) 748789. + 1.29694e6i 0.947449 + 1.64103i
\(890\) 1.02150e6i 1.28961i
\(891\) 10937.9 630795.i 0.0137778 0.794571i
\(892\) 235997. 0.296604
\(893\) 653108. 377072.i 0.818996 0.472848i
\(894\) 586507. 154432.i 0.733835 0.193225i
\(895\) −9737.36 + 16865.6i −0.0121561 + 0.0210550i
\(896\) 1.23913e6 + 715412.i 1.54348 + 0.891128i
\(897\) −14219.4 + 14096.7i −0.0176725 + 0.0175199i
\(898\) −207552. 359490.i −0.257379 0.445794i
\(899\) 216718.i 0.268148i
\(900\) −102254. + 57860.3i −0.126239 + 0.0714324i
\(901\) 143176. 0.176368
\(902\) 206790. 119390.i 0.254165 0.146742i
\(903\) 153158. 561842.i 0.187830 0.689030i
\(904\) −568175. + 984108.i −0.695257 + 1.20422i
\(905\) 393522. + 227200.i 0.480476 + 0.277403i
\(906\) 1.17308e6 + 319781.i 1.42912 + 0.389580i
\(907\) 71965.4 + 124648.i 0.0874801 + 0.151520i 0.906445 0.422323i \(-0.138785\pi\)
−0.818965 + 0.573843i \(0.805452\pi\)
\(908\) 389172.i 0.472030i
\(909\) −80536.0 + 136741.i −0.0974680 + 0.165490i
\(910\) 798134. 0.963814
\(911\) −772201. + 445830.i −0.930451 + 0.537196i −0.886954 0.461857i \(-0.847183\pi\)
−0.0434969 + 0.999054i \(0.513850\pi\)
\(912\) 366659. + 369852.i 0.440832 + 0.444670i
\(913\) 136170. 235854.i 0.163358 0.282944i
\(914\) −854175. 493158.i −1.02248 0.590329i
\(915\) −62877.5 238798.i −0.0751023 0.285225i
\(916\) −10472.5 18139.0i −0.0124813 0.0216183i
\(917\) 232053.i 0.275961i
\(918\) −228055. 64297.0i −0.270617 0.0762967i
\(919\) −582156. −0.689300 −0.344650 0.938731i \(-0.612002\pi\)
−0.344650 + 0.938731i \(0.612002\pi\)
\(920\) 10802.8 6236.98i 0.0127632 0.00736883i
\(921\) 1.09753e6 288990.i 1.29389 0.340693i
\(922\) 237093. 410658.i 0.278906 0.483079i
\(923\) −892636. 515364.i −1.04778 0.604937i
\(924\) 175454. 173940.i 0.205504 0.203730i
\(925\) −152149. 263530.i −0.177822 0.307997i
\(926\) 304441.i 0.355043i
\(927\) 3620.10 417578.i 0.00421271 0.485935i
\(928\) 353482. 0.410460
\(929\) −668027. + 385685.i −0.774038 + 0.446891i −0.834313 0.551291i \(-0.814136\pi\)
0.0602751 + 0.998182i \(0.480802\pi\)
\(930\) −51239.7 + 187966.i −0.0592435 + 0.217327i
\(931\) 271966. 471059.i 0.313773 0.543470i
\(932\) −62991.9 36368.4i −0.0725192 0.0418690i
\(933\) 866609. + 236238.i 0.995543 + 0.271385i
\(934\) 500890. + 867567.i 0.574181 + 0.994510i
\(935\) 112148.i 0.128283i
\(936\) −671382. 5820.41i −0.766334 0.00664357i
\(937\) −1.46097e6 −1.66403 −0.832015 0.554753i \(-0.812813\pi\)
−0.832015 + 0.554753i \(0.812813\pi\)
\(938\) −1.29903e6 + 749996.i −1.47643 + 0.852420i
\(939\) −14100.5 14223.3i −0.0159921 0.0161313i
\(940\) −124806. + 216170.i −0.141247 + 0.244647i
\(941\) 146658. + 84673.2i 0.165626 + 0.0956240i 0.580522 0.814245i \(-0.302849\pi\)
−0.414896 + 0.909869i \(0.636182\pi\)
\(942\) −211030. 801456.i −0.237817 0.903187i
\(943\) −4019.42 6961.83i −0.00452001 0.00782889i
\(944\) 1.64346e6i 1.84423i
\(945\) 590833. + 606402.i 0.661608 + 0.679042i
\(946\) −383289. −0.428296
\(947\) 514322. 296944.i 0.573503 0.331112i −0.185044 0.982730i \(-0.559243\pi\)
0.758547 + 0.651618i \(0.225910\pi\)
\(948\) −196376. + 51707.5i −0.218510 + 0.0575356i
\(949\) 371210. 642955.i 0.412180 0.713917i
\(950\) 271526. + 156766.i 0.300860 + 0.173702i
\(951\) 1.07421e6 1.06494e6i 1.18776 1.17750i
\(952\) 142079. + 246089.i 0.156768 + 0.271530i
\(953\) 1.25477e6i 1.38159i −0.723050 0.690796i \(-0.757260\pi\)
0.723050 0.690796i \(-0.242740\pi\)
\(954\) −613002. 361038.i −0.673543 0.396695i
\(955\) −156250. −0.171322
\(956\) 88159.0 50898.6i 0.0964608 0.0556917i
\(957\) −163027. + 598043.i −0.178006 + 0.652993i
\(958\) −243733. + 422158.i −0.265573 + 0.459985i
\(959\) 243051. + 140326.i 0.264278 + 0.152581i
\(960\) 369024. + 100596.i 0.400416 + 0.109154i
\(961\) 415987. + 720510.i 0.450436 + 0.780178i
\(962\) 567843.i 0.613590i
\(963\) 363684. + 642722.i 0.392167 + 0.693060i
\(964\) −327186. −0.352080
\(965\) 741017. 427826.i 0.795744 0.459423i
\(966\) −29644.9 29903.0i −0.0317684 0.0320450i
\(967\) 528928. 916130.i 0.565645 0.979725i −0.431345 0.902187i \(-0.641961\pi\)
0.996989 0.0775381i \(-0.0247059\pi\)
\(968\) −251620. 145273.i −0.268531 0.155037i
\(969\) 31804.4 + 120787.i 0.0338719 + 0.128639i
\(970\) −256321. 443962.i −0.272422 0.471848i
\(971\) 775745.i 0.822774i 0.911461 + 0.411387i \(0.134956\pi\)
−0.911461 + 0.411387i \(0.865044\pi\)
\(972\) 160848. + 167976.i 0.170249 + 0.177793i
\(973\) −846555. −0.894189
\(974\) 411099. 237348.i 0.433339 0.250189i
\(975\) −493305. + 129892.i −0.518927 + 0.136638i
\(976\) −259864. + 450098.i −0.272801 + 0.472506i
\(977\) −429995. 248258.i −0.450479 0.260084i 0.257554 0.966264i \(-0.417084\pi\)
−0.708032 + 0.706180i \(0.750417\pi\)
\(978\) −1.13561e6 + 1.12581e6i −1.18728 + 1.17703i
\(979\) −686453. 1.18897e6i −0.716218 1.24053i
\(980\) 180035.i 0.187458i
\(981\) −1.13930e6 + 644671.i −1.18386 + 0.669885i
\(982\) −332424. −0.344722
\(983\) 260643. 150482.i 0.269736 0.155732i −0.359032 0.933325i \(-0.616893\pi\)
0.628768 + 0.777593i \(0.283560\pi\)
\(984\) 70895.3 260070.i 0.0732196 0.268597i
\(985\) −549076. + 951028.i −0.565927 + 0.980214i
\(986\) 201616. + 116403.i 0.207382 + 0.119732i
\(987\) −2.48950e6 678638.i −2.55551 0.696633i
\(988\) −57786.2 100089.i −0.0591985 0.102535i
\(989\) 12903.9i 0.0131925i
\(990\) 282797. 480157.i 0.288539 0.489907i
\(991\) 1.70094e6 1.73197 0.865987 0.500067i \(-0.166691\pi\)
0.865987 + 0.500067i \(0.166691\pi\)
\(992\) 129315. 74660.0i 0.131409 0.0758691i
\(993\) 42826.3 + 43199.1i 0.0434322 + 0.0438103i
\(994\) 1.08379e6 1.87718e6i 1.09691 1.89991i
\(995\) −114302. 65992.4i −0.115454 0.0666573i
\(996\) 25563.4 + 97085.3i 0.0257692 + 0.0978667i
\(997\) 312919. + 541991.i 0.314805 + 0.545258i 0.979396 0.201949i \(-0.0647276\pi\)
−0.664591 + 0.747207i \(0.731394\pi\)
\(998\) 496568.i 0.498560i
\(999\) −431432. + 420355.i −0.432297 + 0.421197i
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 9.5.d.a.5.3 yes 6
3.2 odd 2 27.5.d.a.17.1 6
4.3 odd 2 144.5.q.a.113.3 6
9.2 odd 6 inner 9.5.d.a.2.3 6
9.4 even 3 81.5.b.a.80.5 6
9.5 odd 6 81.5.b.a.80.2 6
9.7 even 3 27.5.d.a.8.1 6
12.11 even 2 432.5.q.a.17.1 6
36.7 odd 6 432.5.q.a.305.1 6
36.11 even 6 144.5.q.a.65.3 6
36.23 even 6 1296.5.e.c.161.5 6
36.31 odd 6 1296.5.e.c.161.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.5.d.a.2.3 6 9.2 odd 6 inner
9.5.d.a.5.3 yes 6 1.1 even 1 trivial
27.5.d.a.8.1 6 9.7 even 3
27.5.d.a.17.1 6 3.2 odd 2
81.5.b.a.80.2 6 9.5 odd 6
81.5.b.a.80.5 6 9.4 even 3
144.5.q.a.65.3 6 36.11 even 6
144.5.q.a.113.3 6 4.3 odd 2
432.5.q.a.17.1 6 12.11 even 2
432.5.q.a.305.1 6 36.7 odd 6
1296.5.e.c.161.2 6 36.31 odd 6
1296.5.e.c.161.5 6 36.23 even 6