Properties

Label 105.4.b.a.41.10
Level $105$
Weight $4$
Character 105.41
Analytic conductor $6.195$
Analytic rank $0$
Dimension $16$
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] = [105,4,Mod(41,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.41");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 96 x^{14} + 3618 x^{12} + 68560 x^{10} + 697017 x^{8} + 3791184 x^{6} + 10461796 x^{4} + 13209792 x^{2} + 5760000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 41.10
Root \(1.39379i\) of defining polynomial
Character \(\chi\) \(=\) 105.41
Dual form 105.4.b.a.41.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.39379i q^{2} +(-5.17944 - 0.416449i) q^{3} +6.05735 q^{4} -5.00000 q^{5} +(0.580442 - 7.21904i) q^{6} +(-10.8253 - 15.0271i) q^{7} +19.5930i q^{8} +(26.6531 + 4.31394i) q^{9} +O(q^{10})\) \(q+1.39379i q^{2} +(-5.17944 - 0.416449i) q^{3} +6.05735 q^{4} -5.00000 q^{5} +(0.580442 - 7.21904i) q^{6} +(-10.8253 - 15.0271i) q^{7} +19.5930i q^{8} +(26.6531 + 4.31394i) q^{9} -6.96894i q^{10} -67.7901i q^{11} +(-31.3737 - 2.52258i) q^{12} -2.57864i q^{13} +(20.9446 - 15.0882i) q^{14} +(25.8972 + 2.08225i) q^{15} +21.1504 q^{16} +62.5926 q^{17} +(-6.01273 + 37.1488i) q^{18} -134.611i q^{19} -30.2868 q^{20} +(49.8109 + 82.3400i) q^{21} +94.4850 q^{22} -58.4546i q^{23} +(8.15948 - 101.481i) q^{24} +25.0000 q^{25} +3.59408 q^{26} +(-136.252 - 33.4435i) q^{27} +(-65.5726 - 91.0244i) q^{28} -91.3578i q^{29} +(-2.90221 + 36.0952i) q^{30} +182.870i q^{31} +186.223i q^{32} +(-28.2311 + 351.114i) q^{33} +87.2408i q^{34} +(54.1264 + 75.1354i) q^{35} +(161.447 + 26.1311i) q^{36} -340.482 q^{37} +187.620 q^{38} +(-1.07387 + 13.3559i) q^{39} -97.9649i q^{40} -67.1808 q^{41} +(-114.765 + 69.4258i) q^{42} -88.7823 q^{43} -410.628i q^{44} +(-133.266 - 21.5697i) q^{45} +81.4734 q^{46} -157.841 q^{47} +(-109.547 - 8.80805i) q^{48} +(-108.626 + 325.345i) q^{49} +34.8447i q^{50} +(-324.194 - 26.0666i) q^{51} -15.6198i q^{52} -458.943i q^{53} +(46.6131 - 189.906i) q^{54} +338.950i q^{55} +(294.425 - 212.100i) q^{56} +(-56.0588 + 697.211i) q^{57} +127.333 q^{58} +589.112 q^{59} +(156.868 + 12.6129i) q^{60} +431.560i q^{61} -254.883 q^{62} +(-223.702 - 447.219i) q^{63} -90.3525 q^{64} +12.8932i q^{65} +(-489.379 - 39.3482i) q^{66} +809.483 q^{67} +379.145 q^{68} +(-24.3434 + 302.762i) q^{69} +(-104.723 + 75.4408i) q^{70} +80.5430i q^{71} +(-84.5230 + 522.214i) q^{72} -406.079i q^{73} -474.560i q^{74} +(-129.486 - 10.4112i) q^{75} -815.389i q^{76} +(-1018.69 + 733.847i) q^{77} +(-18.6153 - 1.49675i) q^{78} -657.971 q^{79} -105.752 q^{80} +(691.780 + 229.960i) q^{81} -93.6358i q^{82} +649.146 q^{83} +(301.722 + 498.763i) q^{84} -312.963 q^{85} -123.744i q^{86} +(-38.0459 + 473.182i) q^{87} +1328.21 q^{88} +600.574 q^{89} +(30.0636 - 185.744i) q^{90} +(-38.7495 + 27.9145i) q^{91} -354.080i q^{92} +(76.1562 - 947.166i) q^{93} -219.996i q^{94} +673.057i q^{95} +(77.5524 - 964.530i) q^{96} -813.824i q^{97} +(-453.462 - 151.402i) q^{98} +(292.443 - 1806.82i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 2 q^{3} - 64 q^{4} - 80 q^{5} - 28 q^{6} - 4 q^{7} - 22 q^{9} - 66 q^{12} - 90 q^{14} + 10 q^{15} + 376 q^{16} - 72 q^{17} - 182 q^{18} + 320 q^{20} - 74 q^{21} - 276 q^{22} + 526 q^{24} + 400 q^{25} + 696 q^{26} - 128 q^{27} + 10 q^{28} + 140 q^{30} - 502 q^{33} + 20 q^{35} + 996 q^{36} - 812 q^{37} - 1200 q^{38} - 594 q^{39} - 936 q^{41} - 1834 q^{42} - 548 q^{43} + 110 q^{45} + 1224 q^{46} + 912 q^{47} + 1850 q^{48} + 328 q^{49} + 750 q^{51} - 2950 q^{54} + 1254 q^{56} + 432 q^{57} + 576 q^{58} - 552 q^{59} + 330 q^{60} - 1860 q^{62} - 898 q^{63} - 4000 q^{64} + 1378 q^{66} + 1004 q^{67} + 3828 q^{68} + 1988 q^{69} + 450 q^{70} + 1988 q^{72} - 50 q^{75} + 1152 q^{77} + 1446 q^{78} + 1292 q^{79} - 1880 q^{80} - 2950 q^{81} - 1752 q^{83} + 1068 q^{84} + 360 q^{85} + 1910 q^{87} - 912 q^{88} + 6096 q^{89} + 910 q^{90} - 552 q^{91} - 1080 q^{93} - 9546 q^{96} - 4824 q^{98} + 2530 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39379i 0.492779i 0.969171 + 0.246389i \(0.0792442\pi\)
−0.969171 + 0.246389i \(0.920756\pi\)
\(3\) −5.17944 0.416449i −0.996783 0.0801457i
\(4\) 6.05735 0.757169
\(5\) −5.00000 −0.447214
\(6\) 0.580442 7.21904i 0.0394941 0.491193i
\(7\) −10.8253 15.0271i −0.584510 0.811386i
\(8\) 19.5930i 0.865895i
\(9\) 26.6531 + 4.31394i 0.987153 + 0.159776i
\(10\) 6.96894i 0.220377i
\(11\) 67.7901i 1.85813i −0.369912 0.929067i \(-0.620612\pi\)
0.369912 0.929067i \(-0.379388\pi\)
\(12\) −31.3737 2.52258i −0.754733 0.0606838i
\(13\) 2.57864i 0.0550144i −0.999622 0.0275072i \(-0.991243\pi\)
0.999622 0.0275072i \(-0.00875692\pi\)
\(14\) 20.9446 15.0882i 0.399834 0.288034i
\(15\) 25.8972 + 2.08225i 0.445775 + 0.0358422i
\(16\) 21.1504 0.330474
\(17\) 62.5926 0.892996 0.446498 0.894785i \(-0.352671\pi\)
0.446498 + 0.894785i \(0.352671\pi\)
\(18\) −6.01273 + 37.1488i −0.0787341 + 0.486448i
\(19\) 134.611i 1.62537i −0.582705 0.812684i \(-0.698006\pi\)
0.582705 0.812684i \(-0.301994\pi\)
\(20\) −30.2868 −0.338616
\(21\) 49.8109 + 82.3400i 0.517601 + 0.855622i
\(22\) 94.4850 0.915649
\(23\) 58.4546i 0.529940i −0.964257 0.264970i \(-0.914638\pi\)
0.964257 0.264970i \(-0.0853621\pi\)
\(24\) 8.15948 101.481i 0.0693978 0.863110i
\(25\) 25.0000 0.200000
\(26\) 3.59408 0.0271099
\(27\) −136.252 33.4435i −0.971172 0.238378i
\(28\) −65.5726 91.0244i −0.442573 0.614357i
\(29\) 91.3578i 0.584990i −0.956267 0.292495i \(-0.905514\pi\)
0.956267 0.292495i \(-0.0944855\pi\)
\(30\) −2.90221 + 36.0952i −0.0176623 + 0.219668i
\(31\) 182.870i 1.05950i 0.848154 + 0.529750i \(0.177714\pi\)
−0.848154 + 0.529750i \(0.822286\pi\)
\(32\) 186.223i 1.02875i
\(33\) −28.2311 + 351.114i −0.148921 + 1.85216i
\(34\) 87.2408i 0.440049i
\(35\) 54.1264 + 75.1354i 0.261401 + 0.362863i
\(36\) 161.447 + 26.1311i 0.747442 + 0.120977i
\(37\) −340.482 −1.51284 −0.756418 0.654089i \(-0.773052\pi\)
−0.756418 + 0.654089i \(0.773052\pi\)
\(38\) 187.620 0.800946
\(39\) −1.07387 + 13.3559i −0.00440916 + 0.0548374i
\(40\) 97.9649i 0.387240i
\(41\) −67.1808 −0.255899 −0.127950 0.991781i \(-0.540840\pi\)
−0.127950 + 0.991781i \(0.540840\pi\)
\(42\) −114.765 + 69.4258i −0.421632 + 0.255063i
\(43\) −88.7823 −0.314864 −0.157432 0.987530i \(-0.550322\pi\)
−0.157432 + 0.987530i \(0.550322\pi\)
\(44\) 410.628i 1.40692i
\(45\) −133.266 21.5697i −0.441468 0.0714539i
\(46\) 81.4734 0.261143
\(47\) −157.841 −0.489860 −0.244930 0.969541i \(-0.578765\pi\)
−0.244930 + 0.969541i \(0.578765\pi\)
\(48\) −109.547 8.80805i −0.329411 0.0264861i
\(49\) −108.626 + 325.345i −0.316695 + 0.948527i
\(50\) 34.8447i 0.0985557i
\(51\) −324.194 26.0666i −0.890123 0.0715697i
\(52\) 15.6198i 0.0416552i
\(53\) 458.943i 1.18945i −0.803931 0.594723i \(-0.797262\pi\)
0.803931 0.594723i \(-0.202738\pi\)
\(54\) 46.6131 189.906i 0.117467 0.478573i
\(55\) 338.950i 0.830983i
\(56\) 294.425 212.100i 0.702576 0.506125i
\(57\) −56.0588 + 697.211i −0.130266 + 1.62014i
\(58\) 127.333 0.288271
\(59\) 589.112 1.29993 0.649965 0.759964i \(-0.274784\pi\)
0.649965 + 0.759964i \(0.274784\pi\)
\(60\) 156.868 + 12.6129i 0.337527 + 0.0271386i
\(61\) 431.560i 0.905829i 0.891554 + 0.452915i \(0.149616\pi\)
−0.891554 + 0.452915i \(0.850384\pi\)
\(62\) −254.883 −0.522099
\(63\) −223.702 447.219i −0.447362 0.894353i
\(64\) −90.3525 −0.176470
\(65\) 12.8932i 0.0246032i
\(66\) −489.379 39.3482i −0.912703 0.0733853i
\(67\) 809.483 1.47603 0.738016 0.674783i \(-0.235763\pi\)
0.738016 + 0.674783i \(0.235763\pi\)
\(68\) 379.145 0.676149
\(69\) −24.3434 + 302.762i −0.0424724 + 0.528236i
\(70\) −104.723 + 75.4408i −0.178811 + 0.128813i
\(71\) 80.5430i 0.134629i 0.997732 + 0.0673147i \(0.0214432\pi\)
−0.997732 + 0.0673147i \(0.978557\pi\)
\(72\) −84.5230 + 522.214i −0.138349 + 0.854772i
\(73\) 406.079i 0.651068i −0.945530 0.325534i \(-0.894456\pi\)
0.945530 0.325534i \(-0.105544\pi\)
\(74\) 474.560i 0.745493i
\(75\) −129.486 10.4112i −0.199357 0.0160291i
\(76\) 815.389i 1.23068i
\(77\) −1018.69 + 733.847i −1.50766 + 1.08610i
\(78\) −18.6153 1.49675i −0.0270227 0.00217274i
\(79\) −657.971 −0.937058 −0.468529 0.883448i \(-0.655216\pi\)
−0.468529 + 0.883448i \(0.655216\pi\)
\(80\) −105.752 −0.147793
\(81\) 691.780 + 229.960i 0.948943 + 0.315446i
\(82\) 93.6358i 0.126102i
\(83\) 649.146 0.858471 0.429235 0.903193i \(-0.358783\pi\)
0.429235 + 0.903193i \(0.358783\pi\)
\(84\) 301.722 + 498.763i 0.391912 + 0.647851i
\(85\) −312.963 −0.399360
\(86\) 123.744i 0.155158i
\(87\) −38.0459 + 473.182i −0.0468844 + 0.583108i
\(88\) 1328.21 1.60895
\(89\) 600.574 0.715289 0.357644 0.933858i \(-0.383580\pi\)
0.357644 + 0.933858i \(0.383580\pi\)
\(90\) 30.0636 185.744i 0.0352109 0.217546i
\(91\) −38.7495 + 27.9145i −0.0446379 + 0.0321565i
\(92\) 354.080i 0.401255i
\(93\) 76.1562 947.166i 0.0849144 1.05609i
\(94\) 219.996i 0.241392i
\(95\) 673.057i 0.726886i
\(96\) 77.5524 964.530i 0.0824496 1.02544i
\(97\) 813.824i 0.851869i −0.904754 0.425934i \(-0.859945\pi\)
0.904754 0.425934i \(-0.140055\pi\)
\(98\) −453.462 151.402i −0.467414 0.156061i
\(99\) 292.443 1806.82i 0.296885 1.83426i
\(100\) 151.434 0.151434
\(101\) −293.929 −0.289575 −0.144787 0.989463i \(-0.546250\pi\)
−0.144787 + 0.989463i \(0.546250\pi\)
\(102\) 36.3314 451.858i 0.0352680 0.438634i
\(103\) 658.984i 0.630405i −0.949025 0.315202i \(-0.897928\pi\)
0.949025 0.315202i \(-0.102072\pi\)
\(104\) 50.5233 0.0476367
\(105\) −249.054 411.700i −0.231478 0.382646i
\(106\) 639.669 0.586133
\(107\) 514.453i 0.464804i 0.972620 + 0.232402i \(0.0746585\pi\)
−0.972620 + 0.232402i \(0.925341\pi\)
\(108\) −825.325 202.579i −0.735342 0.180492i
\(109\) 1628.10 1.43068 0.715340 0.698777i \(-0.246272\pi\)
0.715340 + 0.698777i \(0.246272\pi\)
\(110\) −472.425 −0.409491
\(111\) 1763.51 + 141.794i 1.50797 + 0.121247i
\(112\) −228.959 317.828i −0.193166 0.268142i
\(113\) 771.780i 0.642504i 0.946994 + 0.321252i \(0.104104\pi\)
−0.946994 + 0.321252i \(0.895896\pi\)
\(114\) −971.765 78.1341i −0.798370 0.0641924i
\(115\) 292.273i 0.236997i
\(116\) 553.386i 0.442937i
\(117\) 11.1241 68.7289i 0.00878996 0.0543076i
\(118\) 821.098i 0.640578i
\(119\) −677.582 940.584i −0.521965 0.724564i
\(120\) −40.7974 + 507.403i −0.0310356 + 0.385995i
\(121\) −3264.49 −2.45266
\(122\) −601.503 −0.446373
\(123\) 347.959 + 27.9774i 0.255076 + 0.0205092i
\(124\) 1107.71i 0.802221i
\(125\) −125.000 −0.0894427
\(126\) 623.328 311.793i 0.440718 0.220450i
\(127\) 1500.54 1.04844 0.524218 0.851584i \(-0.324358\pi\)
0.524218 + 0.851584i \(0.324358\pi\)
\(128\) 1363.85i 0.941786i
\(129\) 459.842 + 36.9733i 0.313852 + 0.0252350i
\(130\) −17.9704 −0.0121239
\(131\) −1840.55 −1.22756 −0.613778 0.789479i \(-0.710351\pi\)
−0.613778 + 0.789479i \(0.710351\pi\)
\(132\) −171.006 + 2126.82i −0.112759 + 1.40240i
\(133\) −2022.82 + 1457.21i −1.31880 + 0.950044i
\(134\) 1128.25i 0.727357i
\(135\) 681.259 + 167.217i 0.434322 + 0.106606i
\(136\) 1226.37i 0.773241i
\(137\) 1789.29i 1.11583i 0.829897 + 0.557916i \(0.188399\pi\)
−0.829897 + 0.557916i \(0.811601\pi\)
\(138\) −421.986 33.9295i −0.260303 0.0209295i
\(139\) 2246.13i 1.37061i −0.728258 0.685303i \(-0.759670\pi\)
0.728258 0.685303i \(-0.240330\pi\)
\(140\) 327.863 + 455.122i 0.197925 + 0.274749i
\(141\) 817.525 + 65.7325i 0.488284 + 0.0392601i
\(142\) −112.260 −0.0663425
\(143\) −174.806 −0.102224
\(144\) 563.723 + 91.2415i 0.326229 + 0.0528018i
\(145\) 456.789i 0.261616i
\(146\) 565.989 0.320833
\(147\) 698.113 1639.87i 0.391697 0.920094i
\(148\) −2062.42 −1.14547
\(149\) 293.931i 0.161609i 0.996730 + 0.0808046i \(0.0257490\pi\)
−0.996730 + 0.0808046i \(0.974251\pi\)
\(150\) 14.5111 180.476i 0.00789882 0.0982387i
\(151\) −951.272 −0.512672 −0.256336 0.966588i \(-0.582515\pi\)
−0.256336 + 0.966588i \(0.582515\pi\)
\(152\) 2637.44 1.40740
\(153\) 1668.29 + 270.021i 0.881524 + 0.142679i
\(154\) −1022.83 1419.83i −0.535206 0.742945i
\(155\) 914.352i 0.473823i
\(156\) −6.50483 + 80.9015i −0.00333848 + 0.0415212i
\(157\) 1703.52i 0.865960i 0.901404 + 0.432980i \(0.142538\pi\)
−0.901404 + 0.432980i \(0.857462\pi\)
\(158\) 917.073i 0.461762i
\(159\) −191.126 + 2377.06i −0.0953289 + 1.18562i
\(160\) 931.115i 0.460069i
\(161\) −878.402 + 632.788i −0.429986 + 0.309756i
\(162\) −320.516 + 964.195i −0.155445 + 0.467619i
\(163\) 1738.35 0.835325 0.417663 0.908602i \(-0.362849\pi\)
0.417663 + 0.908602i \(0.362849\pi\)
\(164\) −406.938 −0.193759
\(165\) 141.156 1755.57i 0.0665997 0.828310i
\(166\) 904.773i 0.423036i
\(167\) −1674.27 −0.775802 −0.387901 0.921701i \(-0.626800\pi\)
−0.387901 + 0.921701i \(0.626800\pi\)
\(168\) −1613.29 + 975.943i −0.740879 + 0.448188i
\(169\) 2190.35 0.996973
\(170\) 436.204i 0.196796i
\(171\) 580.706 3587.82i 0.259694 1.60449i
\(172\) −537.786 −0.238406
\(173\) 1741.35 0.765275 0.382638 0.923899i \(-0.375016\pi\)
0.382638 + 0.923899i \(0.375016\pi\)
\(174\) −659.516 53.0279i −0.287343 0.0231036i
\(175\) −270.632 375.677i −0.116902 0.162277i
\(176\) 1433.78i 0.614066i
\(177\) −3051.27 245.335i −1.29575 0.104184i
\(178\) 837.073i 0.352479i
\(179\) 1666.76i 0.695976i 0.937499 + 0.347988i \(0.113135\pi\)
−0.937499 + 0.347988i \(0.886865\pi\)
\(180\) −807.237 130.655i −0.334266 0.0541027i
\(181\) 4189.97i 1.72065i 0.509746 + 0.860325i \(0.329740\pi\)
−0.509746 + 0.860325i \(0.670260\pi\)
\(182\) −38.9070 54.0086i −0.0158460 0.0219966i
\(183\) 179.723 2235.24i 0.0725983 0.902915i
\(184\) 1145.30 0.458873
\(185\) 1702.41 0.676561
\(186\) 1320.15 + 106.146i 0.520420 + 0.0418440i
\(187\) 4243.15i 1.65931i
\(188\) −956.096 −0.370907
\(189\) 972.406 + 2409.50i 0.374244 + 0.927330i
\(190\) −938.099 −0.358194
\(191\) 3858.58i 1.46176i 0.682504 + 0.730882i \(0.260891\pi\)
−0.682504 + 0.730882i \(0.739109\pi\)
\(192\) 467.975 + 37.6272i 0.175902 + 0.0141433i
\(193\) 1129.53 0.421272 0.210636 0.977565i \(-0.432447\pi\)
0.210636 + 0.977565i \(0.432447\pi\)
\(194\) 1134.30 0.419783
\(195\) 5.36937 66.7796i 0.00197184 0.0245240i
\(196\) −657.989 + 1970.73i −0.239792 + 0.718196i
\(197\) 3793.36i 1.37191i −0.727646 0.685953i \(-0.759385\pi\)
0.727646 0.685953i \(-0.240615\pi\)
\(198\) 2518.32 + 407.603i 0.903886 + 0.146298i
\(199\) 2716.52i 0.967684i −0.875155 0.483842i \(-0.839241\pi\)
0.875155 0.483842i \(-0.160759\pi\)
\(200\) 489.824i 0.173179i
\(201\) −4192.67 337.109i −1.47128 0.118298i
\(202\) 409.675i 0.142696i
\(203\) −1372.84 + 988.974i −0.474653 + 0.341933i
\(204\) −1963.76 157.895i −0.673974 0.0541904i
\(205\) 335.904 0.114442
\(206\) 918.485 0.310650
\(207\) 252.170 1558.00i 0.0846716 0.523132i
\(208\) 54.5392i 0.0181808i
\(209\) −9125.32 −3.02015
\(210\) 573.823 347.129i 0.188560 0.114068i
\(211\) 2986.43 0.974379 0.487190 0.873296i \(-0.338022\pi\)
0.487190 + 0.873296i \(0.338022\pi\)
\(212\) 2779.98i 0.900611i
\(213\) 33.5421 417.167i 0.0107900 0.134196i
\(214\) −717.038 −0.229046
\(215\) 443.911 0.140812
\(216\) 655.257 2669.58i 0.206410 0.840934i
\(217\) 2748.01 1979.62i 0.859664 0.619289i
\(218\) 2269.23i 0.705009i
\(219\) −169.111 + 2103.26i −0.0521803 + 0.648974i
\(220\) 2053.14i 0.629195i
\(221\) 161.404i 0.0491276i
\(222\) −197.630 + 2457.95i −0.0597481 + 0.743095i
\(223\) 5668.92i 1.70233i −0.524900 0.851164i \(-0.675897\pi\)
0.524900 0.851164i \(-0.324103\pi\)
\(224\) 2798.39 2015.92i 0.834710 0.601313i
\(225\) 666.329 + 107.849i 0.197431 + 0.0319551i
\(226\) −1075.70 −0.316612
\(227\) 1778.27 0.519946 0.259973 0.965616i \(-0.416286\pi\)
0.259973 + 0.965616i \(0.416286\pi\)
\(228\) −339.568 + 4223.26i −0.0986335 + 1.22672i
\(229\) 1353.76i 0.390650i −0.980739 0.195325i \(-0.937424\pi\)
0.980739 0.195325i \(-0.0625762\pi\)
\(230\) −407.367 −0.116787
\(231\) 5581.83 3376.68i 1.58986 0.961772i
\(232\) 1789.97 0.506540
\(233\) 2216.62i 0.623242i −0.950206 0.311621i \(-0.899128\pi\)
0.950206 0.311621i \(-0.100872\pi\)
\(234\) 95.7936 + 15.5047i 0.0267616 + 0.00433151i
\(235\) 789.203 0.219072
\(236\) 3568.46 0.984267
\(237\) 3407.92 + 274.012i 0.934044 + 0.0751011i
\(238\) 1310.97 944.406i 0.357050 0.257213i
\(239\) 4546.46i 1.23048i 0.788338 + 0.615242i \(0.210942\pi\)
−0.788338 + 0.615242i \(0.789058\pi\)
\(240\) 547.735 + 44.0402i 0.147317 + 0.0118449i
\(241\) 35.5837i 0.00951099i 0.999989 + 0.00475549i \(0.00151373\pi\)
−0.999989 + 0.00475549i \(0.998486\pi\)
\(242\) 4550.01i 1.20862i
\(243\) −3487.26 1479.16i −0.920609 0.390485i
\(244\) 2614.11i 0.685866i
\(245\) 543.132 1626.72i 0.141630 0.424194i
\(246\) −38.9945 + 484.981i −0.0101065 + 0.125696i
\(247\) −347.115 −0.0894186
\(248\) −3582.98 −0.917416
\(249\) −3362.21 270.336i −0.855709 0.0688027i
\(250\) 174.224i 0.0440755i
\(251\) 555.734 0.139752 0.0698758 0.997556i \(-0.477740\pi\)
0.0698758 + 0.997556i \(0.477740\pi\)
\(252\) −1355.04 2708.96i −0.338728 0.677177i
\(253\) −3962.64 −0.984700
\(254\) 2091.43i 0.516647i
\(255\) 1620.97 + 130.333i 0.398075 + 0.0320070i
\(256\) −2623.74 −0.640562
\(257\) 5009.10 1.21580 0.607898 0.794016i \(-0.292013\pi\)
0.607898 + 0.794016i \(0.292013\pi\)
\(258\) −51.5330 + 640.923i −0.0124353 + 0.154659i
\(259\) 3685.82 + 5116.45i 0.884268 + 1.22749i
\(260\) 78.0988i 0.0186288i
\(261\) 394.112 2434.97i 0.0934672 0.577475i
\(262\) 2565.34i 0.604913i
\(263\) 334.413i 0.0784061i −0.999231 0.0392031i \(-0.987518\pi\)
0.999231 0.0392031i \(-0.0124819\pi\)
\(264\) −6879.38 553.132i −1.60377 0.128950i
\(265\) 2294.71i 0.531936i
\(266\) −2031.04 2819.38i −0.468162 0.649877i
\(267\) −3110.64 250.108i −0.712988 0.0573273i
\(268\) 4903.33 1.11761
\(269\) 5366.63 1.21639 0.608195 0.793787i \(-0.291894\pi\)
0.608195 + 0.793787i \(0.291894\pi\)
\(270\) −233.066 + 949.530i −0.0525331 + 0.214024i
\(271\) 2497.86i 0.559905i 0.960014 + 0.279953i \(0.0903188\pi\)
−0.960014 + 0.279953i \(0.909681\pi\)
\(272\) 1323.86 0.295112
\(273\) 212.326 128.444i 0.0470715 0.0284755i
\(274\) −2493.89 −0.549858
\(275\) 1694.75i 0.371627i
\(276\) −147.456 + 1833.94i −0.0321588 + 0.399964i
\(277\) −2734.48 −0.593136 −0.296568 0.955012i \(-0.595842\pi\)
−0.296568 + 0.955012i \(0.595842\pi\)
\(278\) 3130.63 0.675405
\(279\) −788.893 + 4874.07i −0.169282 + 1.04589i
\(280\) −1472.13 + 1060.50i −0.314201 + 0.226346i
\(281\) 561.914i 0.119292i 0.998220 + 0.0596459i \(0.0189972\pi\)
−0.998220 + 0.0596459i \(0.981003\pi\)
\(282\) −91.6173 + 1139.46i −0.0193466 + 0.240616i
\(283\) 312.314i 0.0656012i 0.999462 + 0.0328006i \(0.0104426\pi\)
−0.999462 + 0.0328006i \(0.989557\pi\)
\(284\) 487.877i 0.101937i
\(285\) 280.294 3486.06i 0.0582568 0.724548i
\(286\) 243.643i 0.0503738i
\(287\) 727.251 + 1009.53i 0.149576 + 0.207633i
\(288\) −803.355 + 4963.43i −0.164369 + 1.01553i
\(289\) −995.171 −0.202559
\(290\) −636.667 −0.128919
\(291\) −338.916 + 4215.15i −0.0682736 + 0.849128i
\(292\) 2459.77i 0.492969i
\(293\) 5189.02 1.03463 0.517313 0.855796i \(-0.326932\pi\)
0.517313 + 0.855796i \(0.326932\pi\)
\(294\) 2285.63 + 973.022i 0.453403 + 0.193020i
\(295\) −2945.56 −0.581346
\(296\) 6671.06i 1.30996i
\(297\) −2267.14 + 9236.51i −0.442938 + 1.80457i
\(298\) −409.678 −0.0796375
\(299\) −150.734 −0.0291543
\(300\) −784.342 63.0645i −0.150947 0.0121368i
\(301\) 961.093 + 1334.14i 0.184042 + 0.255477i
\(302\) 1325.87i 0.252634i
\(303\) 1522.39 + 122.406i 0.288643 + 0.0232082i
\(304\) 2847.08i 0.537142i
\(305\) 2157.80i 0.405099i
\(306\) −376.352 + 2325.24i −0.0703092 + 0.434396i
\(307\) 324.556i 0.0603367i 0.999545 + 0.0301684i \(0.00960434\pi\)
−0.999545 + 0.0301684i \(0.990396\pi\)
\(308\) −6170.55 + 4445.17i −1.14156 + 0.822360i
\(309\) −274.433 + 3413.17i −0.0505242 + 0.628377i
\(310\) 1274.41 0.233490
\(311\) −6882.09 −1.25481 −0.627407 0.778691i \(-0.715884\pi\)
−0.627407 + 0.778691i \(0.715884\pi\)
\(312\) −261.682 21.0404i −0.0474835 0.00381788i
\(313\) 10414.6i 1.88072i 0.340181 + 0.940360i \(0.389512\pi\)
−0.340181 + 0.940360i \(0.610488\pi\)
\(314\) −2374.35 −0.426727
\(315\) 1118.51 + 2236.09i 0.200066 + 0.399967i
\(316\) −3985.57 −0.709511
\(317\) 2351.44i 0.416625i −0.978062 0.208312i \(-0.933203\pi\)
0.978062 0.208312i \(-0.0667971\pi\)
\(318\) −3313.12 266.390i −0.584248 0.0469760i
\(319\) −6193.15 −1.08699
\(320\) 451.763 0.0789197
\(321\) 214.243 2664.58i 0.0372520 0.463309i
\(322\) −881.972 1224.31i −0.152641 0.211888i
\(323\) 8425.68i 1.45145i
\(324\) 4190.35 + 1392.95i 0.718511 + 0.238846i
\(325\) 64.4661i 0.0110029i
\(326\) 2422.89i 0.411631i
\(327\) −8432.66 678.023i −1.42608 0.114663i
\(328\) 1316.27i 0.221582i
\(329\) 1708.67 + 2371.88i 0.286328 + 0.397465i
\(330\) 2446.90 + 196.741i 0.408173 + 0.0328189i
\(331\) 116.712 0.0193809 0.00969047 0.999953i \(-0.496915\pi\)
0.00969047 + 0.999953i \(0.496915\pi\)
\(332\) 3932.11 0.650008
\(333\) −9074.92 1468.82i −1.49340 0.241714i
\(334\) 2333.58i 0.382298i
\(335\) −4047.42 −0.660101
\(336\) 1053.52 + 1741.52i 0.171054 + 0.282761i
\(337\) −482.498 −0.0779921 −0.0389961 0.999239i \(-0.512416\pi\)
−0.0389961 + 0.999239i \(0.512416\pi\)
\(338\) 3052.89i 0.491287i
\(339\) 321.407 3997.39i 0.0514939 0.640437i
\(340\) −1895.73 −0.302383
\(341\) 12396.8 1.96869
\(342\) 5000.66 + 809.382i 0.790657 + 0.127972i
\(343\) 6064.90 1889.61i 0.954734 0.297462i
\(344\) 1739.51i 0.272640i
\(345\) 121.717 1513.81i 0.0189942 0.236234i
\(346\) 2427.08i 0.377111i
\(347\) 1524.90i 0.235911i 0.993019 + 0.117955i \(0.0376340\pi\)
−0.993019 + 0.117955i \(0.962366\pi\)
\(348\) −230.457 + 2866.23i −0.0354994 + 0.441512i
\(349\) 2797.89i 0.429133i −0.976709 0.214567i \(-0.931166\pi\)
0.976709 0.214567i \(-0.0688339\pi\)
\(350\) 523.614 377.204i 0.0799668 0.0576069i
\(351\) −86.2388 + 351.345i −0.0131142 + 0.0534285i
\(352\) 12624.1 1.91155
\(353\) −6871.80 −1.03612 −0.518058 0.855346i \(-0.673345\pi\)
−0.518058 + 0.855346i \(0.673345\pi\)
\(354\) 341.945 4252.82i 0.0513395 0.638517i
\(355\) 402.715i 0.0602081i
\(356\) 3637.89 0.541595
\(357\) 3117.79 + 5153.87i 0.462216 + 0.764067i
\(358\) −2323.11 −0.342962
\(359\) 9204.67i 1.35321i −0.736344 0.676607i \(-0.763450\pi\)
0.736344 0.676607i \(-0.236550\pi\)
\(360\) 422.615 2611.07i 0.0618716 0.382265i
\(361\) −11261.2 −1.64182
\(362\) −5839.93 −0.847900
\(363\) 16908.2 + 1359.50i 2.44477 + 0.196570i
\(364\) −234.719 + 169.088i −0.0337984 + 0.0243479i
\(365\) 2030.40i 0.291167i
\(366\) 3115.45 + 250.495i 0.444937 + 0.0357749i
\(367\) 3102.52i 0.441281i 0.975355 + 0.220641i \(0.0708148\pi\)
−0.975355 + 0.220641i \(0.929185\pi\)
\(368\) 1236.34i 0.175132i
\(369\) −1790.58 289.814i −0.252612 0.0408865i
\(370\) 2372.80i 0.333395i
\(371\) −6896.57 + 4968.18i −0.965100 + 0.695243i
\(372\) 461.305 5737.32i 0.0642945 0.799640i
\(373\) −6036.54 −0.837963 −0.418981 0.907995i \(-0.637613\pi\)
−0.418981 + 0.907995i \(0.637613\pi\)
\(374\) 5914.06 0.817670
\(375\) 647.430 + 52.0561i 0.0891550 + 0.00716845i
\(376\) 3092.57i 0.424167i
\(377\) −235.579 −0.0321829
\(378\) −3358.34 + 1355.33i −0.456969 + 0.184419i
\(379\) 8484.08 1.14986 0.574931 0.818202i \(-0.305029\pi\)
0.574931 + 0.818202i \(0.305029\pi\)
\(380\) 4076.95i 0.550376i
\(381\) −7771.95 624.898i −1.04506 0.0840276i
\(382\) −5378.04 −0.720326
\(383\) 6784.15 0.905101 0.452551 0.891739i \(-0.350514\pi\)
0.452551 + 0.891739i \(0.350514\pi\)
\(384\) 567.975 7063.98i 0.0754800 0.938756i
\(385\) 5093.43 3669.23i 0.674248 0.485718i
\(386\) 1574.33i 0.207594i
\(387\) −2366.33 383.002i −0.310819 0.0503077i
\(388\) 4929.62i 0.645009i
\(389\) 2023.40i 0.263729i 0.991268 + 0.131865i \(0.0420964\pi\)
−0.991268 + 0.131865i \(0.957904\pi\)
\(390\) 93.0766 + 7.48376i 0.0120849 + 0.000971680i
\(391\) 3658.82i 0.473234i
\(392\) −6374.48 2128.32i −0.821326 0.274225i
\(393\) 9533.03 + 766.497i 1.22361 + 0.0983833i
\(394\) 5287.14 0.676046
\(395\) 3289.86 0.419065
\(396\) 1771.43 10944.5i 0.224792 1.38885i
\(397\) 792.398i 0.100175i 0.998745 + 0.0500873i \(0.0159500\pi\)
−0.998745 + 0.0500873i \(0.984050\pi\)
\(398\) 3786.26 0.476854
\(399\) 11083.9 6705.11i 1.39070 0.841292i
\(400\) 528.759 0.0660949
\(401\) 13954.2i 1.73776i 0.495024 + 0.868880i \(0.335159\pi\)
−0.495024 + 0.868880i \(0.664841\pi\)
\(402\) 469.858 5843.69i 0.0582945 0.725017i
\(403\) 471.558 0.0582877
\(404\) −1780.43 −0.219257
\(405\) −3458.90 1149.80i −0.424380 0.141072i
\(406\) −1378.42 1913.45i −0.168497 0.233899i
\(407\) 23081.3i 2.81105i
\(408\) 510.723 6351.93i 0.0619719 0.770754i
\(409\) 2366.91i 0.286152i −0.989712 0.143076i \(-0.954301\pi\)
0.989712 0.143076i \(-0.0456993\pi\)
\(410\) 468.179i 0.0563944i
\(411\) 745.146 9267.49i 0.0894291 1.11224i
\(412\) 3991.70i 0.477323i
\(413\) −6377.31 8852.63i −0.759822 1.05474i
\(414\) 2171.52 + 351.472i 0.257788 + 0.0417244i
\(415\) −3245.73 −0.383920
\(416\) 480.203 0.0565958
\(417\) −935.399 + 11633.7i −0.109848 + 1.36620i
\(418\) 12718.8i 1.48827i
\(419\) −15398.7 −1.79541 −0.897703 0.440600i \(-0.854766\pi\)
−0.897703 + 0.440600i \(0.854766\pi\)
\(420\) −1508.61 2493.81i −0.175268 0.289728i
\(421\) 4342.52 0.502711 0.251356 0.967895i \(-0.419124\pi\)
0.251356 + 0.967895i \(0.419124\pi\)
\(422\) 4162.45i 0.480153i
\(423\) −4206.95 680.915i −0.483567 0.0782677i
\(424\) 8992.05 1.02994
\(425\) 1564.81 0.178599
\(426\) 581.443 + 46.7505i 0.0661291 + 0.00531707i
\(427\) 6485.08 4671.76i 0.734977 0.529467i
\(428\) 3116.22i 0.351935i
\(429\) 905.399 + 72.7980i 0.101895 + 0.00819282i
\(430\) 618.719i 0.0693890i
\(431\) 3165.86i 0.353814i −0.984228 0.176907i \(-0.943391\pi\)
0.984228 0.176907i \(-0.0566092\pi\)
\(432\) −2881.77 707.342i −0.320948 0.0787778i
\(433\) 11822.9i 1.31217i 0.754685 + 0.656087i \(0.227790\pi\)
−0.754685 + 0.656087i \(0.772210\pi\)
\(434\) 2759.18 + 3830.14i 0.305172 + 0.423624i
\(435\) 190.229 2365.91i 0.0209674 0.260774i
\(436\) 9862.00 1.08327
\(437\) −7868.66 −0.861348
\(438\) −2931.50 235.705i −0.319800 0.0257133i
\(439\) 11914.9i 1.29537i 0.761909 + 0.647684i \(0.224262\pi\)
−0.761909 + 0.647684i \(0.775738\pi\)
\(440\) −6641.05 −0.719544
\(441\) −4298.75 + 8202.85i −0.464178 + 0.885742i
\(442\) 224.963 0.0242090
\(443\) 8026.37i 0.860823i −0.902633 0.430411i \(-0.858368\pi\)
0.902633 0.430411i \(-0.141632\pi\)
\(444\) 10682.2 + 858.893i 1.14179 + 0.0918047i
\(445\) −3002.87 −0.319887
\(446\) 7901.28 0.838871
\(447\) 122.407 1522.40i 0.0129523 0.161089i
\(448\) 978.092 + 1357.74i 0.103148 + 0.143185i
\(449\) 15264.8i 1.60443i −0.597036 0.802214i \(-0.703655\pi\)
0.597036 0.802214i \(-0.296345\pi\)
\(450\) −150.318 + 928.721i −0.0157468 + 0.0972896i
\(451\) 4554.19i 0.475495i
\(452\) 4674.95i 0.486484i
\(453\) 4927.06 + 396.157i 0.511023 + 0.0410884i
\(454\) 2478.53i 0.256218i
\(455\) 193.747 139.573i 0.0199627 0.0143808i
\(456\) −13660.4 1098.36i −1.40287 0.112797i
\(457\) −1121.90 −0.114836 −0.0574180 0.998350i \(-0.518287\pi\)
−0.0574180 + 0.998350i \(0.518287\pi\)
\(458\) 1886.85 0.192504
\(459\) −8528.35 2093.31i −0.867253 0.212870i
\(460\) 1770.40i 0.179446i
\(461\) −7671.75 −0.775074 −0.387537 0.921854i \(-0.626674\pi\)
−0.387537 + 0.921854i \(0.626674\pi\)
\(462\) 4706.38 + 7779.90i 0.473941 + 0.783449i
\(463\) 3491.25 0.350436 0.175218 0.984530i \(-0.443937\pi\)
0.175218 + 0.984530i \(0.443937\pi\)
\(464\) 1932.25i 0.193324i
\(465\) −380.781 + 4735.83i −0.0379749 + 0.472299i
\(466\) 3089.50 0.307121
\(467\) −4518.50 −0.447733 −0.223866 0.974620i \(-0.571868\pi\)
−0.223866 + 0.974620i \(0.571868\pi\)
\(468\) 67.3827 416.315i 0.00665549 0.0411201i
\(469\) −8762.89 12164.2i −0.862756 1.19763i
\(470\) 1099.98i 0.107954i
\(471\) 709.430 8823.28i 0.0694030 0.863174i
\(472\) 11542.5i 1.12560i
\(473\) 6018.56i 0.585060i
\(474\) −381.914 + 4749.92i −0.0370082 + 0.460277i
\(475\) 3365.29i 0.325073i
\(476\) −4104.36 5697.45i −0.395216 0.548618i
\(477\) 1979.85 12232.3i 0.190044 1.17416i
\(478\) −6336.80 −0.606357
\(479\) 18591.3 1.77340 0.886698 0.462348i \(-0.152993\pi\)
0.886698 + 0.462348i \(0.152993\pi\)
\(480\) −387.762 + 4822.65i −0.0368726 + 0.458589i
\(481\) 877.982i 0.0832277i
\(482\) −49.5962 −0.00468681
\(483\) 4813.15 2911.67i 0.453429 0.274298i
\(484\) −19774.2 −1.85708
\(485\) 4069.12i 0.380967i
\(486\) 2061.63 4860.51i 0.192423 0.453657i
\(487\) 62.4942 0.00581495 0.00290748 0.999996i \(-0.499075\pi\)
0.00290748 + 0.999996i \(0.499075\pi\)
\(488\) −8455.54 −0.784353
\(489\) −9003.67 723.934i −0.832638 0.0669477i
\(490\) 2267.31 + 757.011i 0.209034 + 0.0697924i
\(491\) 11712.0i 1.07649i −0.842789 0.538244i \(-0.819088\pi\)
0.842789 0.538244i \(-0.180912\pi\)
\(492\) 2107.71 + 169.469i 0.193136 + 0.0155290i
\(493\) 5718.32i 0.522394i
\(494\) 483.805i 0.0440636i
\(495\) −1462.21 + 9034.09i −0.132771 + 0.820307i
\(496\) 3867.78i 0.350138i
\(497\) 1210.33 871.901i 0.109236 0.0786923i
\(498\) 376.792 4686.21i 0.0339045 0.421675i
\(499\) −10826.2 −0.971237 −0.485618 0.874171i \(-0.661405\pi\)
−0.485618 + 0.874171i \(0.661405\pi\)
\(500\) −757.169 −0.0677233
\(501\) 8671.77 + 697.248i 0.773306 + 0.0621771i
\(502\) 774.576i 0.0688666i
\(503\) 11386.8 1.00937 0.504684 0.863304i \(-0.331609\pi\)
0.504684 + 0.863304i \(0.331609\pi\)
\(504\) 8762.34 4382.99i 0.774416 0.387368i
\(505\) 1469.65 0.129502
\(506\) 5523.08i 0.485239i
\(507\) −11344.8 912.170i −0.993766 0.0799031i
\(508\) 9089.29 0.793843
\(509\) 755.673 0.0658047 0.0329024 0.999459i \(-0.489525\pi\)
0.0329024 + 0.999459i \(0.489525\pi\)
\(510\) −181.657 + 2259.29i −0.0157723 + 0.196163i
\(511\) −6102.19 + 4395.92i −0.528268 + 0.380556i
\(512\) 7253.87i 0.626131i
\(513\) −4501.87 + 18341.0i −0.387452 + 1.57851i
\(514\) 6981.63i 0.599118i
\(515\) 3294.92i 0.281925i
\(516\) 2785.43 + 223.960i 0.237639 + 0.0191072i
\(517\) 10700.0i 0.910225i
\(518\) −7131.26 + 5137.25i −0.604883 + 0.435749i
\(519\) −9019.23 725.185i −0.762813 0.0613335i
\(520\) −252.616 −0.0213038
\(521\) 14676.3 1.23413 0.617064 0.786913i \(-0.288322\pi\)
0.617064 + 0.786913i \(0.288322\pi\)
\(522\) 3393.84 + 549.309i 0.284567 + 0.0460587i
\(523\) 10547.2i 0.881832i −0.897548 0.440916i \(-0.854654\pi\)
0.897548 0.440916i \(-0.145346\pi\)
\(524\) −11148.9 −0.929468
\(525\) 1245.27 + 2058.50i 0.103520 + 0.171124i
\(526\) 466.101 0.0386369
\(527\) 11446.3i 0.946129i
\(528\) −597.098 + 7426.20i −0.0492147 + 0.612090i
\(529\) 8750.06 0.719163
\(530\) −3198.34 −0.262127
\(531\) 15701.7 + 2541.40i 1.28323 + 0.207697i
\(532\) −12252.9 + 8826.82i −0.998555 + 0.719344i
\(533\) 173.235i 0.0140781i
\(534\) 348.598 4335.57i 0.0282497 0.351345i
\(535\) 2572.26i 0.207867i
\(536\) 15860.2i 1.27809i
\(537\) 694.121 8632.89i 0.0557794 0.693737i
\(538\) 7479.95i 0.599411i
\(539\) 22055.2 + 7363.79i 1.76249 + 0.588462i
\(540\) 4126.62 + 1012.89i 0.328855 + 0.0807186i
\(541\) 7767.39 0.617276 0.308638 0.951180i \(-0.400127\pi\)
0.308638 + 0.951180i \(0.400127\pi\)
\(542\) −3481.49 −0.275909
\(543\) 1744.91 21701.7i 0.137903 1.71512i
\(544\) 11656.2i 0.918666i
\(545\) −8140.52 −0.639820
\(546\) 179.024 + 295.937i 0.0140321 + 0.0231958i
\(547\) −10163.9 −0.794473 −0.397237 0.917716i \(-0.630031\pi\)
−0.397237 + 0.917716i \(0.630031\pi\)
\(548\) 10838.3i 0.844874i
\(549\) −1861.72 + 11502.4i −0.144729 + 0.894192i
\(550\) 2362.13 0.183130
\(551\) −12297.8 −0.950824
\(552\) −5932.01 476.959i −0.457397 0.0367767i
\(553\) 7122.73 + 9887.39i 0.547720 + 0.760316i
\(554\) 3811.28i 0.292285i
\(555\) −8817.53 708.968i −0.674384 0.0542234i
\(556\) 13605.6i 1.03778i
\(557\) 16917.4i 1.28692i −0.765480 0.643460i \(-0.777498\pi\)
0.765480 0.643460i \(-0.222502\pi\)
\(558\) −6793.43 1099.55i −0.515392 0.0834188i
\(559\) 228.938i 0.0173221i
\(560\) 1144.79 + 1589.14i 0.0863863 + 0.119917i
\(561\) −1767.06 + 21977.1i −0.132986 + 1.65397i
\(562\) −783.190 −0.0587845
\(563\) −13413.1 −1.00408 −0.502038 0.864846i \(-0.667416\pi\)
−0.502038 + 0.864846i \(0.667416\pi\)
\(564\) 4952.04 + 398.165i 0.369713 + 0.0297266i
\(565\) 3858.90i 0.287337i
\(566\) −435.300 −0.0323269
\(567\) −4033.08 12884.8i −0.298719 0.954341i
\(568\) −1578.08 −0.116575
\(569\) 8625.40i 0.635493i 0.948176 + 0.317747i \(0.102926\pi\)
−0.948176 + 0.317747i \(0.897074\pi\)
\(570\) 4858.83 + 390.671i 0.357042 + 0.0287077i
\(571\) 17682.5 1.29596 0.647978 0.761659i \(-0.275615\pi\)
0.647978 + 0.761659i \(0.275615\pi\)
\(572\) −1058.86 −0.0774009
\(573\) 1606.90 19985.3i 0.117154 1.45706i
\(574\) −1407.07 + 1013.63i −0.102317 + 0.0737078i
\(575\) 1461.37i 0.105988i
\(576\) −2408.18 389.776i −0.174203 0.0281956i
\(577\) 22409.4i 1.61684i −0.588606 0.808420i \(-0.700323\pi\)
0.588606 0.808420i \(-0.299677\pi\)
\(578\) 1387.06i 0.0998166i
\(579\) −5850.33 470.392i −0.419916 0.0337631i
\(580\) 2766.93i 0.198087i
\(581\) −7027.19 9754.78i −0.501785 0.696551i
\(582\) −5875.02 472.377i −0.418432 0.0336438i
\(583\) −31111.7 −2.21015
\(584\) 7956.30 0.563757
\(585\) −55.6206 + 343.645i −0.00393099 + 0.0242871i
\(586\) 7232.39i 0.509842i
\(587\) 273.325 0.0192186 0.00960930 0.999954i \(-0.496941\pi\)
0.00960930 + 0.999954i \(0.496941\pi\)
\(588\) 4228.72 9933.25i 0.296581 0.696667i
\(589\) 24616.5 1.72208
\(590\) 4105.49i 0.286475i
\(591\) −1579.74 + 19647.5i −0.109952 + 1.36749i
\(592\) −7201.32 −0.499954
\(593\) 21856.6 1.51356 0.756780 0.653669i \(-0.226771\pi\)
0.756780 + 0.653669i \(0.226771\pi\)
\(594\) −12873.7 3159.91i −0.889253 0.218270i
\(595\) 3387.91 + 4702.92i 0.233430 + 0.324035i
\(596\) 1780.44i 0.122365i
\(597\) −1131.29 + 14070.1i −0.0775557 + 0.964571i
\(598\) 210.091i 0.0143666i
\(599\) 11295.6i 0.770493i −0.922814 0.385246i \(-0.874116\pi\)
0.922814 0.385246i \(-0.125884\pi\)
\(600\) 203.987 2537.02i 0.0138796 0.172622i
\(601\) 4883.39i 0.331443i −0.986173 0.165722i \(-0.947005\pi\)
0.986173 0.165722i \(-0.0529953\pi\)
\(602\) −1859.51 + 1339.56i −0.125893 + 0.0906917i
\(603\) 21575.3 + 3492.07i 1.45707 + 0.235834i
\(604\) −5762.19 −0.388179
\(605\) 16322.5 1.09686
\(606\) −170.609 + 2121.89i −0.0114365 + 0.142237i
\(607\) 11389.4i 0.761583i 0.924661 + 0.380792i \(0.124348\pi\)
−0.924661 + 0.380792i \(0.875652\pi\)
\(608\) 25067.7 1.67209
\(609\) 7522.40 4550.61i 0.500531 0.302792i
\(610\) 3007.52 0.199624
\(611\) 407.014i 0.0269493i
\(612\) 10105.4 + 1635.61i 0.667463 + 0.108032i
\(613\) −683.834 −0.0450567 −0.0225284 0.999746i \(-0.507172\pi\)
−0.0225284 + 0.999746i \(0.507172\pi\)
\(614\) −452.362 −0.0297326
\(615\) −1739.79 139.887i −0.114074 0.00917200i
\(616\) −14378.2 19959.1i −0.940448 1.30548i
\(617\) 7945.11i 0.518409i −0.965822 0.259204i \(-0.916540\pi\)
0.965822 0.259204i \(-0.0834603\pi\)
\(618\) −4757.24 382.502i −0.309651 0.0248972i
\(619\) 18920.0i 1.22853i −0.789100 0.614264i \(-0.789453\pi\)
0.789100 0.614264i \(-0.210547\pi\)
\(620\) 5538.56i 0.358764i
\(621\) −1954.93 + 7964.54i −0.126326 + 0.514664i
\(622\) 9592.17i 0.618346i
\(623\) −6501.38 9024.87i −0.418094 0.580376i
\(624\) −22.7128 + 282.483i −0.00145712 + 0.0181224i
\(625\) 625.000 0.0400000
\(626\) −14515.7 −0.926779
\(627\) 47264.0 + 3800.23i 3.01044 + 0.242052i
\(628\) 10318.8i 0.655678i
\(629\) −21311.7 −1.35096
\(630\) −3116.64 + 1558.97i −0.197095 + 0.0985884i
\(631\) −1816.54 −0.114604 −0.0573022 0.998357i \(-0.518250\pi\)
−0.0573022 + 0.998357i \(0.518250\pi\)
\(632\) 12891.6i 0.811394i
\(633\) −15468.0 1243.69i −0.971245 0.0780923i
\(634\) 3277.41 0.205304
\(635\) −7502.69 −0.468875
\(636\) −1157.72 + 14398.7i −0.0721801 + 0.897714i
\(637\) 838.948 + 280.109i 0.0521826 + 0.0174228i
\(638\) 8631.94i 0.535646i
\(639\) −347.458 + 2146.72i −0.0215105 + 0.132900i
\(640\) 6819.26i 0.421179i
\(641\) 15359.9i 0.946457i −0.880940 0.473229i \(-0.843088\pi\)
0.880940 0.473229i \(-0.156912\pi\)
\(642\) 3713.86 + 298.610i 0.228309 + 0.0183570i
\(643\) 11392.9i 0.698745i −0.936984 0.349373i \(-0.886395\pi\)
0.936984 0.349373i \(-0.113605\pi\)
\(644\) −5320.79 + 3833.02i −0.325572 + 0.234537i
\(645\) −2299.21 184.866i −0.140359 0.0112854i
\(646\) 11743.6 0.715242
\(647\) −4600.01 −0.279513 −0.139757 0.990186i \(-0.544632\pi\)
−0.139757 + 0.990186i \(0.544632\pi\)
\(648\) −4505.61 + 13554.0i −0.273143 + 0.821686i
\(649\) 39935.9i 2.41544i
\(650\) 89.8521 0.00542198
\(651\) −15057.6 + 9108.94i −0.906532 + 0.548398i
\(652\) 10529.8 0.632483
\(653\) 19253.3i 1.15381i −0.816810 0.576907i \(-0.804259\pi\)
0.816810 0.576907i \(-0.195741\pi\)
\(654\) 945.020 11753.4i 0.0565034 0.702741i
\(655\) 9202.76 0.548980
\(656\) −1420.90 −0.0845682
\(657\) 1751.80 10823.3i 0.104025 0.642704i
\(658\) −3305.90 + 2381.52i −0.195862 + 0.141096i
\(659\) 1117.61i 0.0660635i 0.999454 + 0.0330317i \(0.0105162\pi\)
−0.999454 + 0.0330317i \(0.989484\pi\)
\(660\) 855.029 10634.1i 0.0504272 0.627171i
\(661\) 15114.5i 0.889390i −0.895682 0.444695i \(-0.853312\pi\)
0.895682 0.444695i \(-0.146688\pi\)
\(662\) 162.672i 0.00955051i
\(663\) −67.2165 + 835.981i −0.00393736 + 0.0489696i
\(664\) 12718.7i 0.743346i
\(665\) 10114.1 7286.04i 0.589786 0.424873i
\(666\) 2047.23 12648.5i 0.119112 0.735916i
\(667\) −5340.28 −0.310010
\(668\) −10141.6 −0.587413
\(669\) −2360.82 + 29361.8i −0.136434 + 1.69685i
\(670\) 5641.24i 0.325284i
\(671\) 29255.5 1.68315
\(672\) −15333.6 + 9275.93i −0.880218 + 0.532480i
\(673\) 20340.5 1.16503 0.582516 0.812819i \(-0.302068\pi\)
0.582516 + 0.812819i \(0.302068\pi\)
\(674\) 672.500i 0.0384329i
\(675\) −3406.29 836.087i −0.194234 0.0476756i
\(676\) 13267.7 0.754878
\(677\) 28057.2 1.59280 0.796399 0.604772i \(-0.206736\pi\)
0.796399 + 0.604772i \(0.206736\pi\)
\(678\) 5571.51 + 447.974i 0.315594 + 0.0253751i
\(679\) −12229.4 + 8809.87i −0.691194 + 0.497926i
\(680\) 6131.87i 0.345804i
\(681\) −9210.42 740.557i −0.518273 0.0416714i
\(682\) 17278.5i 0.970130i
\(683\) 19325.6i 1.08268i 0.840802 + 0.541342i \(0.182084\pi\)
−0.840802 + 0.541342i \(0.817916\pi\)
\(684\) 3517.54 21732.7i 0.196632 1.21487i
\(685\) 8946.43i 0.499015i
\(686\) 2633.72 + 8453.18i 0.146583 + 0.470472i
\(687\) −563.772 + 7011.71i −0.0313089 + 0.389393i
\(688\) −1877.78 −0.104055
\(689\) −1183.45 −0.0654366
\(690\) 2109.93 + 169.648i 0.116411 + 0.00935996i
\(691\) 13253.9i 0.729669i −0.931072 0.364835i \(-0.881126\pi\)
0.931072 0.364835i \(-0.118874\pi\)
\(692\) 10548.0 0.579443
\(693\) −30317.0 + 15164.8i −1.66183 + 0.831258i
\(694\) −2125.39 −0.116252
\(695\) 11230.7i 0.612954i
\(696\) −9271.04 745.432i −0.504911 0.0405970i
\(697\) −4205.02 −0.228517
\(698\) 3899.66 0.211468
\(699\) −923.109 + 11480.8i −0.0499502 + 0.621238i
\(700\) −1639.31 2275.61i −0.0885147 0.122871i
\(701\) 3313.99i 0.178556i 0.996007 + 0.0892779i \(0.0284559\pi\)
−0.996007 + 0.0892779i \(0.971544\pi\)
\(702\) −489.700 120.199i −0.0263284 0.00646240i
\(703\) 45832.8i 2.45891i
\(704\) 6125.00i 0.327905i
\(705\) −4087.62 328.663i −0.218367 0.0175577i
\(706\) 9577.83i 0.510576i
\(707\) 3181.87 + 4416.90i 0.169259 + 0.234957i
\(708\) −18482.6 1486.08i −0.981100 0.0788847i
\(709\) 1427.42 0.0756104 0.0378052 0.999285i \(-0.487963\pi\)
0.0378052 + 0.999285i \(0.487963\pi\)
\(710\) 561.299 0.0296693
\(711\) −17537.0 2838.45i −0.925020 0.149719i
\(712\) 11767.0i 0.619365i
\(713\) 10689.6 0.561472
\(714\) −7183.41 + 4345.54i −0.376516 + 0.227770i
\(715\) 874.032 0.0457160
\(716\) 10096.2i 0.526971i
\(717\) 1893.37 23548.1i 0.0986180 1.22653i
\(718\) 12829.4 0.666835
\(719\) −25522.1 −1.32380 −0.661902 0.749591i \(-0.730250\pi\)
−0.661902 + 0.749591i \(0.730250\pi\)
\(720\) −2818.62 456.207i −0.145894 0.0236137i
\(721\) −9902.61 + 7133.69i −0.511502 + 0.368478i
\(722\) 15695.8i 0.809054i
\(723\) 14.8188 184.304i 0.000762265 0.00948039i
\(724\) 25380.1i 1.30282i
\(725\) 2283.94i 0.116998i
\(726\) −1894.85 + 23566.5i −0.0968656 + 1.20473i
\(727\) 28266.9i 1.44204i 0.692916 + 0.721018i \(0.256326\pi\)
−0.692916 + 0.721018i \(0.743674\pi\)
\(728\) −546.929 759.218i −0.0278442 0.0386518i
\(729\) 17446.1 + 9113.46i 0.886352 + 0.463012i
\(730\) −2829.94 −0.143481
\(731\) −5557.11 −0.281173
\(732\) 1088.64 13539.6i 0.0549692 0.683659i
\(733\) 24004.4i 1.20958i 0.796385 + 0.604790i \(0.206743\pi\)
−0.796385 + 0.604790i \(0.793257\pi\)
\(734\) −4324.26 −0.217454
\(735\) −3490.57 + 8199.33i −0.175172 + 0.411479i
\(736\) 10885.6 0.545174
\(737\) 54874.9i 2.74266i
\(738\) 403.939 2495.69i 0.0201480 0.124482i
\(739\) 12241.0 0.609324 0.304662 0.952460i \(-0.401456\pi\)
0.304662 + 0.952460i \(0.401456\pi\)
\(740\) 10312.1 0.512271
\(741\) 1797.86 + 144.556i 0.0891309 + 0.00716651i
\(742\) −6924.60 9612.36i −0.342601 0.475580i
\(743\) 33949.2i 1.67628i 0.545455 + 0.838140i \(0.316357\pi\)
−0.545455 + 0.838140i \(0.683643\pi\)
\(744\) 18557.8 + 1492.13i 0.914465 + 0.0735270i
\(745\) 1469.65i 0.0722738i
\(746\) 8413.66i 0.412930i
\(747\) 17301.8 + 2800.38i 0.847442 + 0.137163i
\(748\) 25702.3i 1.25638i
\(749\) 7730.73 5569.10i 0.377136 0.271683i
\(750\) −72.5553 + 902.380i −0.00353246 + 0.0439337i
\(751\) −14152.1 −0.687640 −0.343820 0.939036i \(-0.611721\pi\)
−0.343820 + 0.939036i \(0.611721\pi\)
\(752\) −3338.38 −0.161886
\(753\) −2878.39 231.435i −0.139302 0.0112005i
\(754\) 328.348i 0.0158590i
\(755\) 4756.36 0.229274
\(756\) 5890.21 + 14595.2i 0.283366 + 0.702146i
\(757\) −17424.1 −0.836579 −0.418290 0.908314i \(-0.637370\pi\)
−0.418290 + 0.908314i \(0.637370\pi\)
\(758\) 11825.0i 0.566628i
\(759\) 20524.3 + 1650.24i 0.981533 + 0.0789195i
\(760\) −13187.2 −0.629408
\(761\) −10979.4 −0.522999 −0.261500 0.965204i \(-0.584217\pi\)
−0.261500 + 0.965204i \(0.584217\pi\)
\(762\) 870.976 10832.4i 0.0414070 0.514985i
\(763\) −17624.7 24465.7i −0.836247 1.16083i
\(764\) 23372.8i 1.10680i
\(765\) −8341.44 1350.10i −0.394229 0.0638080i
\(766\) 9455.67i 0.446015i
\(767\) 1519.11i 0.0715148i
\(768\) 13589.5 + 1092.65i 0.638501 + 0.0513382i
\(769\) 20853.1i 0.977868i 0.872321 + 0.488934i \(0.162614\pi\)
−0.872321 + 0.488934i \(0.837386\pi\)
\(770\) 5114.14 + 7099.17i 0.239352 + 0.332255i
\(771\) −25944.3 2086.04i −1.21188 0.0974407i
\(772\) 6841.97 0.318974
\(773\) −7220.83 −0.335983 −0.167992 0.985788i \(-0.553728\pi\)
−0.167992 + 0.985788i \(0.553728\pi\)
\(774\) 533.823 3298.16i 0.0247906 0.153165i
\(775\) 4571.76i 0.211900i
\(776\) 15945.2 0.737629
\(777\) −16959.7 28035.3i −0.783046 1.29442i
\(778\) −2820.20 −0.129960
\(779\) 9043.30i 0.415930i
\(780\) 32.5242 404.508i 0.00149302 0.0185688i
\(781\) 5460.01 0.250160
\(782\) 5099.63 0.233200
\(783\) −3055.32 + 12447.7i −0.139449 + 0.568126i
\(784\) −2297.49 + 6881.16i −0.104660 + 0.313464i
\(785\) 8517.60i 0.387269i
\(786\) −1068.33 + 13287.0i −0.0484812 + 0.602967i
\(787\) 6781.22i 0.307147i −0.988137 0.153573i \(-0.950922\pi\)
0.988137 0.153573i \(-0.0490781\pi\)
\(788\) 22977.7i 1.03877i
\(789\) −139.266 + 1732.07i −0.00628391 + 0.0781539i
\(790\) 4585.37i 0.206506i
\(791\) 11597.6 8354.74i 0.521319 0.375550i
\(792\) 35400.9 + 5729.82i 1.58828 + 0.257071i
\(793\) 1112.84 0.0498336
\(794\) −1104.44 −0.0493639
\(795\) 955.631 11885.3i 0.0426324 0.530225i
\(796\) 16454.9i 0.732701i
\(797\) 13204.8 0.586873 0.293436 0.955979i \(-0.405201\pi\)
0.293436 + 0.955979i \(0.405201\pi\)
\(798\) 9345.51 + 15448.6i 0.414571 + 0.685307i
\(799\) −9879.64 −0.437443
\(800\) 4655.57i 0.205749i
\(801\) 16007.2 + 2590.84i 0.706100 + 0.114286i
\(802\) −19449.3 −0.856331
\(803\) −27528.1 −1.20977
\(804\) −25396.5 2041.99i −1.11401 0.0895713i
\(805\) 4392.01 3163.94i 0.192296 0.138527i
\(806\) 657.252i 0.0287230i
\(807\) −27796.1 2234.93i −1.21248 0.0974885i
\(808\) 5758.95i 0.250741i
\(809\) 14180.1i 0.616248i −0.951346 0.308124i \(-0.900299\pi\)
0.951346 0.308124i \(-0.0997012\pi\)
\(810\) 1602.58 4820.97i 0.0695172 0.209126i
\(811\) 4883.94i 0.211465i −0.994395 0.105733i \(-0.966281\pi\)
0.994395 0.105733i \(-0.0337188\pi\)
\(812\) −8315.78 + 5990.57i −0.359393 + 0.258901i
\(813\) 1040.23 12937.5i 0.0448740 0.558104i
\(814\) −32170.5 −1.38523
\(815\) −8691.75 −0.373569
\(816\) −6856.82 551.318i −0.294163 0.0236520i
\(817\) 11951.1i 0.511770i
\(818\) 3298.97 0.141009
\(819\) −1153.22 + 576.847i −0.0492023 + 0.0246113i
\(820\) 2034.69 0.0866517
\(821\) 5023.86i 0.213561i −0.994283 0.106781i \(-0.965946\pi\)
0.994283 0.106781i \(-0.0340543\pi\)
\(822\) 12916.9 + 1038.58i 0.548089 + 0.0440688i
\(823\) 8525.75 0.361104 0.180552 0.983565i \(-0.442212\pi\)
0.180552 + 0.983565i \(0.442212\pi\)
\(824\) 12911.5 0.545864
\(825\) −705.778 + 8777.86i −0.0297843 + 0.370431i
\(826\) 12338.7 8888.62i 0.519756 0.374424i
\(827\) 12413.7i 0.521965i −0.965344 0.260983i \(-0.915953\pi\)
0.965344 0.260983i \(-0.0840465\pi\)
\(828\) 1527.48 9437.35i 0.0641107 0.396100i
\(829\) 33996.1i 1.42429i 0.702034 + 0.712144i \(0.252275\pi\)
−0.702034 + 0.712144i \(0.747725\pi\)
\(830\) 4523.86i 0.189187i
\(831\) 14163.1 + 1138.77i 0.591228 + 0.0475373i
\(832\) 232.987i 0.00970838i
\(833\) −6799.21 + 20364.2i −0.282807 + 0.847031i
\(834\) −16214.9 1303.75i −0.673233 0.0541308i
\(835\) 8371.35 0.346949
\(836\) −55275.3 −2.28676
\(837\) 6115.82 24916.4i 0.252561 1.02896i
\(838\) 21462.5i 0.884738i
\(839\) −31623.9 −1.30129 −0.650643 0.759384i \(-0.725500\pi\)
−0.650643 + 0.759384i \(0.725500\pi\)
\(840\) 8066.43 4879.72i 0.331331 0.200436i
\(841\) 16042.8 0.657786
\(842\) 6052.55i 0.247725i
\(843\) 234.009 2910.40i 0.00956072 0.118908i
\(844\) 18089.8 0.737770
\(845\) −10951.8 −0.445860
\(846\) 949.052 5863.59i 0.0385686 0.238291i
\(847\) 35339.1 + 49055.8i 1.43361 + 1.99006i
\(848\) 9706.80i 0.393081i
\(849\) 130.063 1617.61i 0.00525765 0.0653902i
\(850\) 2181.02i 0.0880098i
\(851\) 19902.8i 0.801713i
\(852\) 203.176 2526.93i 0.00816983 0.101609i
\(853\) 8122.18i 0.326024i −0.986624 0.163012i \(-0.947879\pi\)
0.986624 0.163012i \(-0.0521209\pi\)
\(854\) 6511.44 + 9038.84i 0.260910 + 0.362181i
\(855\) −2903.53 + 17939.1i −0.116139 + 0.717548i
\(856\) −10079.7 −0.402472
\(857\) 32466.5 1.29409 0.647045 0.762451i \(-0.276004\pi\)
0.647045 + 0.762451i \(0.276004\pi\)
\(858\) −101.465 + 1261.93i −0.00403725 + 0.0502118i
\(859\) 36463.5i 1.44833i 0.689625 + 0.724166i \(0.257775\pi\)
−0.689625 + 0.724166i \(0.742225\pi\)
\(860\) 2688.93 0.106618
\(861\) −3346.33 5531.66i −0.132454 0.218953i
\(862\) 4412.53 0.174352
\(863\) 27677.6i 1.09172i 0.837876 + 0.545860i \(0.183797\pi\)
−0.837876 + 0.545860i \(0.816203\pi\)
\(864\) 6227.94 25373.2i 0.245230 0.999090i
\(865\) −8706.76 −0.342241
\(866\) −16478.6 −0.646612
\(867\) 5154.43 + 414.438i 0.201907 + 0.0162342i
\(868\) 16645.7 11991.3i 0.650911 0.468906i
\(869\) 44603.9i 1.74118i
\(870\) 3297.58 + 265.140i 0.128504 + 0.0103323i
\(871\) 2087.37i 0.0812030i
\(872\) 31899.4i 1.23882i
\(873\) 3510.79 21691.0i 0.136108 0.840925i
\(874\) 10967.2i 0.424454i
\(875\) 1353.16 + 1878.39i 0.0522802 + 0.0725726i
\(876\) −1024.37 + 12740.2i −0.0395093 + 0.491383i
\(877\) 21309.8 0.820504 0.410252 0.911972i \(-0.365441\pi\)
0.410252 + 0.911972i \(0.365441\pi\)
\(878\) −16606.8 −0.638330
\(879\) −26876.2 2160.96i −1.03130 0.0829208i
\(880\) 7168.92i 0.274618i
\(881\) −7499.34 −0.286787 −0.143393 0.989666i \(-0.545801\pi\)
−0.143393 + 0.989666i \(0.545801\pi\)
\(882\) −11433.0 5991.56i −0.436475 0.228737i
\(883\) −21250.7 −0.809902 −0.404951 0.914338i \(-0.632711\pi\)
−0.404951 + 0.914338i \(0.632711\pi\)
\(884\) 977.680i 0.0371979i
\(885\) 15256.3 + 1226.68i 0.579476 + 0.0465924i
\(886\) 11187.1 0.424195
\(887\) −24278.0 −0.919024 −0.459512 0.888171i \(-0.651976\pi\)
−0.459512 + 0.888171i \(0.651976\pi\)
\(888\) −2778.16 + 34552.3i −0.104987 + 1.30574i
\(889\) −16243.8 22548.7i −0.612821 0.850686i
\(890\) 4185.37i 0.157633i
\(891\) 15589.0 46895.8i 0.586141 1.76326i
\(892\) 34338.7i 1.28895i
\(893\) 21247.1i 0.796202i
\(894\) 2121.90 + 170.610i 0.0793813 + 0.00638260i
\(895\) 8333.81i 0.311250i
\(896\) 20494.7 14764.1i 0.764152 0.550484i
\(897\) 780.715 + 62.7729i 0.0290606 + 0.00233659i
\(898\) 21275.8 0.790628
\(899\) 16706.6 0.619797
\(900\) 4036.19 + 653.277i 0.149488 + 0.0241954i
\(901\) 28726.4i 1.06217i
\(902\) −6347.57 −0.234314
\(903\) −4422.32 7310.33i −0.162974 0.269405i
\(904\) −15121.5 −0.556342
\(905\) 20949.8i 0.769498i
\(906\) −552.158 + 6867.27i −0.0202475 + 0.251821i
\(907\) −38164.2 −1.39716 −0.698579 0.715533i \(-0.746184\pi\)
−0.698579 + 0.715533i \(0.746184\pi\)
\(908\) 10771.6 0.393687
\(909\) −7834.13 1267.99i −0.285855 0.0462670i
\(910\) 194.535 + 270.043i 0.00708656 + 0.00983718i
\(911\) 27030.1i 0.983038i −0.870867 0.491519i \(-0.836442\pi\)
0.870867 0.491519i \(-0.163558\pi\)
\(912\) −1185.66 + 14746.3i −0.0430496 + 0.535414i
\(913\) 44005.7i 1.59515i
\(914\) 1563.69i 0.0565888i
\(915\) −898.613 + 11176.2i −0.0324669 + 0.403796i
\(916\) 8200.19i 0.295788i
\(917\) 19924.5 + 27658.1i 0.717519 + 0.996022i
\(918\) 2917.64 11886.7i 0.104898 0.427364i
\(919\) 14738.9 0.529045 0.264523 0.964380i \(-0.414786\pi\)
0.264523 + 0.964380i \(0.414786\pi\)
\(920\) −5726.50 −0.205214
\(921\) 135.161 1681.02i 0.00483573 0.0601426i
\(922\) 10692.8i 0.381940i
\(923\) 207.692 0.00740656
\(924\) 33811.1 20453.8i 1.20379 0.728224i
\(925\) −8512.06 −0.302567
\(926\) 4866.06i 0.172688i
\(927\) 2842.82 17564.0i 0.100723 0.622306i
\(928\) 17012.9 0.601806
\(929\) −28651.5 −1.01187 −0.505933 0.862573i \(-0.668852\pi\)
−0.505933 + 0.862573i \(0.668852\pi\)
\(930\) −6600.75 530.729i −0.232739 0.0187132i
\(931\) 43795.1 + 14622.4i 1.54171 + 0.514746i
\(932\) 13426.8i 0.471900i
\(933\) 35645.3 + 2866.04i 1.25078 + 0.100568i
\(934\) 6297.83i 0.220633i
\(935\) 21215.8i 0.742064i
\(936\) 1346.60 + 217.955i 0.0470247 + 0.00761119i
\(937\) 40156.3i 1.40005i −0.714117 0.700026i \(-0.753172\pi\)
0.714117 0.700026i \(-0.246828\pi\)
\(938\) 16954.3 12213.6i 0.590167 0.425148i
\(939\) 4337.13 53941.5i 0.150732 1.87467i
\(940\) 4780.48 0.165874
\(941\) 16366.2 0.566973 0.283487 0.958976i \(-0.408509\pi\)
0.283487 + 0.958976i \(0.408509\pi\)
\(942\) 12297.8 + 988.795i 0.425354 + 0.0342003i
\(943\) 3927.03i 0.135611i
\(944\) 12459.9 0.429593
\(945\) −4862.03 12047.5i −0.167367 0.414715i
\(946\) −8388.59 −0.288305
\(947\) 33729.1i 1.15739i 0.815544 + 0.578695i \(0.196438\pi\)
−0.815544 + 0.578695i \(0.803562\pi\)
\(948\) 20643.0 + 1659.79i 0.707229 + 0.0568643i
\(949\) −1047.13 −0.0358181
\(950\) 4690.50 0.160189
\(951\) −979.255 + 12179.1i −0.0333907 + 0.415285i
\(952\) 18428.8 13275.9i 0.627397 0.451967i
\(953\) 4151.70i 0.141120i −0.997508 0.0705598i \(-0.977521\pi\)
0.997508 0.0705598i \(-0.0224785\pi\)
\(954\) 17049.2 + 2759.50i 0.578603 + 0.0936499i
\(955\) 19292.9i 0.653721i
\(956\) 27539.5i 0.931685i
\(957\) 32077.0 + 2579.13i 1.08349 + 0.0871176i
\(958\) 25912.3i 0.873892i
\(959\) 26887.7 19369.5i 0.905371 0.652215i
\(960\) −2339.88 188.136i −0.0786658 0.00632507i
\(961\) −3650.61 −0.122541
\(962\) −1223.72 −0.0410129
\(963\) −2219.32 + 13711.8i −0.0742644 + 0.458833i
\(964\) 215.543i 0.00720143i
\(965\) −5647.65 −0.188398
\(966\) 4058.26 + 6708.52i 0.135168 + 0.223440i
\(967\) −50915.8 −1.69322 −0.846609 0.532216i \(-0.821360\pi\)
−0.846609 + 0.532216i \(0.821360\pi\)
\(968\) 63961.1i 2.12375i
\(969\) −3508.87 + 43640.3i −0.116327 + 1.44678i
\(970\) −5671.49 −0.187733
\(971\) −22112.0 −0.730801 −0.365400 0.930850i \(-0.619068\pi\)
−0.365400 + 0.930850i \(0.619068\pi\)
\(972\) −21123.6 8959.77i −0.697057 0.295663i
\(973\) −33752.8 + 24315.0i −1.11209 + 0.801134i
\(974\) 87.1037i 0.00286548i
\(975\) −26.8468 + 333.898i −0.000881833 + 0.0109675i
\(976\) 9127.64i 0.299353i
\(977\) 14762.3i 0.483407i −0.970350 0.241704i \(-0.922294\pi\)
0.970350 0.241704i \(-0.0777061\pi\)
\(978\) 1009.01 12549.2i 0.0329904 0.410306i
\(979\) 40712.9i 1.32910i
\(980\) 3289.94 9853.65i 0.107238 0.321187i
\(981\) 43394.1 + 7023.55i 1.41230 + 0.228588i
\(982\) 16324.1 0.530471
\(983\) 21515.6 0.698110 0.349055 0.937102i \(-0.386503\pi\)
0.349055 + 0.937102i \(0.386503\pi\)
\(984\) −548.160 + 6817.54i −0.0177588 + 0.220869i
\(985\) 18966.8i 0.613535i
\(986\) 7970.13 0.257424
\(987\) −7862.17 12996.6i −0.253552 0.419135i
\(988\) −2102.60 −0.0677050
\(989\) 5189.73i 0.166859i
\(990\) −12591.6 2038.02i −0.404230 0.0654266i
\(991\) −25694.9 −0.823639 −0.411820 0.911265i \(-0.635107\pi\)
−0.411820 + 0.911265i \(0.635107\pi\)
\(992\) −34054.7 −1.08996
\(993\) −604.504 48.6047i −0.0193186 0.00155330i
\(994\) 1215.25 + 1686.94i 0.0387779 + 0.0538294i
\(995\) 13582.6i 0.432761i
\(996\) −20366.1 1637.52i −0.647917 0.0520953i
\(997\) 37820.6i 1.20140i 0.799476 + 0.600698i \(0.205110\pi\)
−0.799476 + 0.600698i \(0.794890\pi\)
\(998\) 15089.4i 0.478605i
\(999\) 46391.3 + 11386.9i 1.46922 + 0.360627i
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 105.4.b.a.41.10 yes 16
3.2 odd 2 105.4.b.b.41.7 yes 16
7.6 odd 2 105.4.b.b.41.10 yes 16
21.20 even 2 inner 105.4.b.a.41.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.b.a.41.7 16 21.20 even 2 inner
105.4.b.a.41.10 yes 16 1.1 even 1 trivial
105.4.b.b.41.7 yes 16 3.2 odd 2
105.4.b.b.41.10 yes 16 7.6 odd 2