Properties

Label 63.4.i.a.5.22
Level $63$
Weight $4$
Character 63.5
Analytic conductor $3.717$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,4,Mod(5,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.i (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: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.22
Character \(\chi\) \(=\) 63.5
Dual form 63.4.i.a.38.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.23841i q^{2} +(-2.33478 - 4.64207i) q^{3} -19.4409 q^{4} +(-6.10572 - 10.5754i) q^{5} +(24.3171 - 12.2305i) q^{6} +(18.4237 - 1.88889i) q^{7} -59.9322i q^{8} +(-16.0976 + 21.6764i) q^{9} +O(q^{10})\) \(q+5.23841i q^{2} +(-2.33478 - 4.64207i) q^{3} -19.4409 q^{4} +(-6.10572 - 10.5754i) q^{5} +(24.3171 - 12.2305i) q^{6} +(18.4237 - 1.88889i) q^{7} -59.9322i q^{8} +(-16.0976 + 21.6764i) q^{9} +(55.3983 - 31.9842i) q^{10} +(-55.0881 - 31.8051i) q^{11} +(45.3902 + 90.2461i) q^{12} +(-13.7938 - 7.96386i) q^{13} +(9.89475 + 96.5108i) q^{14} +(-34.8363 + 53.0344i) q^{15} +158.422 q^{16} +(-17.9283 - 31.0528i) q^{17} +(-113.550 - 84.3259i) q^{18} +(-13.8136 - 7.97531i) q^{19} +(118.701 + 205.596i) q^{20} +(-51.7836 - 81.1139i) q^{21} +(166.608 - 288.574i) q^{22} +(39.5226 - 22.8184i) q^{23} +(-278.209 + 139.928i) q^{24} +(-12.0596 + 20.8878i) q^{25} +(41.7179 - 72.2576i) q^{26} +(138.208 + 24.1166i) q^{27} +(-358.173 + 36.7217i) q^{28} +(-206.656 + 119.313i) q^{29} +(-277.816 - 182.487i) q^{30} +135.296i q^{31} +350.421i q^{32} +(-19.0231 + 329.981i) q^{33} +(162.667 - 93.9160i) q^{34} +(-132.466 - 183.305i) q^{35} +(312.952 - 421.409i) q^{36} +(18.0766 - 31.3095i) q^{37} +(41.7779 - 72.3615i) q^{38} +(-4.76329 + 82.6257i) q^{39} +(-633.807 + 365.929i) q^{40} +(84.5046 - 146.366i) q^{41} +(424.908 - 271.263i) q^{42} +(-37.8895 - 65.6266i) q^{43} +(1070.96 + 618.321i) q^{44} +(327.525 + 37.8889i) q^{45} +(119.532 + 207.036i) q^{46} +6.93563 q^{47} +(-369.880 - 735.405i) q^{48} +(335.864 - 69.6005i) q^{49} +(-109.419 - 63.1731i) q^{50} +(-102.291 + 155.726i) q^{51} +(268.164 + 154.825i) q^{52} +(33.2929 - 19.2216i) q^{53} +(-126.333 + 723.989i) q^{54} +776.773i q^{55} +(-113.205 - 1104.17i) q^{56} +(-4.77014 + 82.7444i) q^{57} +(-625.011 - 1082.55i) q^{58} -124.484 q^{59} +(677.250 - 1031.04i) q^{60} -514.833i q^{61} -708.735 q^{62} +(-255.633 + 429.766i) q^{63} -568.272 q^{64} +194.500i q^{65} +(-1728.57 - 99.6507i) q^{66} +335.932 q^{67} +(348.543 + 603.695i) q^{68} +(-198.201 - 130.191i) q^{69} +(960.227 - 693.909i) q^{70} +716.432i q^{71} +(1299.11 + 964.765i) q^{72} +(725.427 - 418.826i) q^{73} +(164.012 + 94.6923i) q^{74} +(125.119 + 7.21301i) q^{75} +(268.550 + 155.047i) q^{76} +(-1075.00 - 481.913i) q^{77} +(-432.827 - 24.9521i) q^{78} -409.854 q^{79} +(-967.279 - 1675.38i) q^{80} +(-210.734 - 697.877i) q^{81} +(766.726 + 442.670i) q^{82} +(-135.674 - 234.994i) q^{83} +(1006.72 + 1576.93i) q^{84} +(-218.931 + 379.199i) q^{85} +(343.779 - 198.481i) q^{86} +(1036.36 + 680.744i) q^{87} +(-1906.15 + 3301.55i) q^{88} +(717.489 - 1242.73i) q^{89} +(-198.477 + 1715.71i) q^{90} +(-269.176 - 120.669i) q^{91} +(-768.356 + 443.611i) q^{92} +(628.053 - 315.886i) q^{93} +36.3317i q^{94} +194.780i q^{95} +(1626.68 - 818.155i) q^{96} +(-433.147 + 250.077i) q^{97} +(364.596 + 1759.39i) q^{98} +(1576.21 - 682.126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 3 q^{3} - 162 q^{4} - 3 q^{5} + 24 q^{6} + 5 q^{7} - 45 q^{9} - 6 q^{10} + 9 q^{11} + 186 q^{12} - 36 q^{13} + 54 q^{14} - 141 q^{15} + 526 q^{16} - 72 q^{17} - 54 q^{18} - 6 q^{19} + 24 q^{20} - 81 q^{21} + 14 q^{22} - 285 q^{23} - 114 q^{24} - 349 q^{25} - 96 q^{26} + 432 q^{27} - 156 q^{28} - 132 q^{29} - 447 q^{30} - 3 q^{33} + 24 q^{34} + 765 q^{35} + 1122 q^{36} + 82 q^{37} - 873 q^{38} + 306 q^{39} + 420 q^{40} + 618 q^{41} - 282 q^{42} + 82 q^{43} + 603 q^{44} + 291 q^{45} + 266 q^{46} - 402 q^{47} - 1569 q^{48} - 79 q^{49} - 1845 q^{50} + 453 q^{51} + 189 q^{52} + 564 q^{53} - 2385 q^{54} + 66 q^{56} + 1170 q^{57} + 269 q^{58} + 1494 q^{59} + 2265 q^{60} - 2904 q^{62} - 636 q^{63} - 1144 q^{64} - 372 q^{66} - 590 q^{67} + 3504 q^{68} - 1005 q^{69} - 105 q^{70} + 1830 q^{72} - 6 q^{73} + 1515 q^{74} - 33 q^{75} - 144 q^{76} - 4443 q^{77} - 5985 q^{78} + 1102 q^{79} - 4239 q^{80} - 4017 q^{81} + 18 q^{82} + 1830 q^{83} + 3165 q^{84} - 237 q^{85} + 1209 q^{86} + 2013 q^{87} - 623 q^{88} + 4266 q^{89} + 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 729 q^{93} + 3975 q^{96} - 792 q^{97} + 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.23841i 1.85206i 0.377454 + 0.926028i \(0.376800\pi\)
−0.377454 + 0.926028i \(0.623200\pi\)
\(3\) −2.33478 4.64207i −0.449328 0.893367i
\(4\) −19.4409 −2.43011
\(5\) −6.10572 10.5754i −0.546112 0.945894i −0.998536 0.0540908i \(-0.982774\pi\)
0.452424 0.891803i \(-0.350559\pi\)
\(6\) 24.3171 12.2305i 1.65457 0.832182i
\(7\) 18.4237 1.88889i 0.994785 0.101990i
\(8\) 59.9322i 2.64865i
\(9\) −16.0976 + 21.6764i −0.596208 + 0.802830i
\(10\) 55.3983 31.9842i 1.75185 1.01143i
\(11\) −55.0881 31.8051i −1.50997 0.871783i −0.999932 0.0116323i \(-0.996297\pi\)
−0.510040 0.860151i \(-0.670369\pi\)
\(12\) 45.3902 + 90.2461i 1.09192 + 2.17098i
\(13\) −13.7938 7.96386i −0.294286 0.169906i 0.345587 0.938387i \(-0.387680\pi\)
−0.639873 + 0.768481i \(0.721013\pi\)
\(14\) 9.89475 + 96.5108i 0.188892 + 1.84240i
\(15\) −34.8363 + 53.0344i −0.599646 + 0.912895i
\(16\) 158.422 2.47534
\(17\) −17.9283 31.0528i −0.255780 0.443024i 0.709327 0.704880i \(-0.248999\pi\)
−0.965107 + 0.261855i \(0.915666\pi\)
\(18\) −113.550 84.3259i −1.48689 1.10421i
\(19\) −13.8136 7.97531i −0.166793 0.0962979i 0.414280 0.910150i \(-0.364033\pi\)
−0.581073 + 0.813852i \(0.697367\pi\)
\(20\) 118.701 + 205.596i 1.32711 + 2.29863i
\(21\) −51.7836 81.1139i −0.538100 0.842881i
\(22\) 166.608 288.574i 1.61459 2.79655i
\(23\) 39.5226 22.8184i 0.358306 0.206868i −0.310031 0.950726i \(-0.600340\pi\)
0.668337 + 0.743858i \(0.267006\pi\)
\(24\) −278.209 + 139.928i −2.36622 + 1.19011i
\(25\) −12.0596 + 20.8878i −0.0964767 + 0.167103i
\(26\) 41.7179 72.2576i 0.314675 0.545034i
\(27\) 138.208 + 24.1166i 0.985115 + 0.171898i
\(28\) −358.173 + 36.7217i −2.41744 + 0.247848i
\(29\) −206.656 + 119.313i −1.32328 + 0.763996i −0.984251 0.176779i \(-0.943432\pi\)
−0.339030 + 0.940776i \(0.610099\pi\)
\(30\) −277.816 182.487i −1.69073 1.11058i
\(31\) 135.296i 0.783867i 0.919994 + 0.391933i \(0.128194\pi\)
−0.919994 + 0.391933i \(0.871806\pi\)
\(32\) 350.421i 1.93582i
\(33\) −19.0231 + 329.981i −0.100348 + 1.74068i
\(34\) 162.667 93.9160i 0.820506 0.473719i
\(35\) −132.466 183.305i −0.639736 0.885263i
\(36\) 312.952 421.409i 1.44885 1.95097i
\(37\) 18.0766 31.3095i 0.0803180 0.139115i −0.823069 0.567942i \(-0.807740\pi\)
0.903387 + 0.428827i \(0.141073\pi\)
\(38\) 41.7779 72.3615i 0.178349 0.308910i
\(39\) −4.76329 + 82.6257i −0.0195574 + 0.339249i
\(40\) −633.807 + 365.929i −2.50534 + 1.44646i
\(41\) 84.5046 146.366i 0.321888 0.557526i −0.658990 0.752152i \(-0.729016\pi\)
0.980878 + 0.194626i \(0.0623493\pi\)
\(42\) 424.908 271.263i 1.56106 0.996592i
\(43\) −37.8895 65.6266i −0.134374 0.232743i 0.790984 0.611837i \(-0.209569\pi\)
−0.925358 + 0.379094i \(0.876236\pi\)
\(44\) 1070.96 + 618.321i 3.66941 + 2.11853i
\(45\) 327.525 + 37.8889i 1.08499 + 0.125514i
\(46\) 119.532 + 207.036i 0.383131 + 0.663603i
\(47\) 6.93563 0.0215248 0.0107624 0.999942i \(-0.496574\pi\)
0.0107624 + 0.999942i \(0.496574\pi\)
\(48\) −369.880 735.405i −1.11224 2.21139i
\(49\) 335.864 69.6005i 0.979196 0.202917i
\(50\) −109.419 63.1731i −0.309484 0.178680i
\(51\) −102.291 + 155.726i −0.280854 + 0.427569i
\(52\) 268.164 + 154.825i 0.715148 + 0.412891i
\(53\) 33.2929 19.2216i 0.0862854 0.0498169i −0.456236 0.889859i \(-0.650803\pi\)
0.542522 + 0.840042i \(0.317470\pi\)
\(54\) −126.333 + 723.989i −0.318365 + 1.82449i
\(55\) 776.773i 1.90436i
\(56\) −113.205 1104.17i −0.270137 2.63484i
\(57\) −4.77014 + 82.7444i −0.0110846 + 0.192277i
\(58\) −625.011 1082.55i −1.41496 2.45079i
\(59\) −124.484 −0.274686 −0.137343 0.990524i \(-0.543856\pi\)
−0.137343 + 0.990524i \(0.543856\pi\)
\(60\) 677.250 1031.04i 1.45721 2.21844i
\(61\) 514.833i 1.08062i −0.841467 0.540308i \(-0.818308\pi\)
0.841467 0.540308i \(-0.181692\pi\)
\(62\) −708.735 −1.45177
\(63\) −255.633 + 429.766i −0.511218 + 0.859451i
\(64\) −568.272 −1.10991
\(65\) 194.500i 0.371151i
\(66\) −1728.57 99.6507i −3.22383 0.185851i
\(67\) 335.932 0.612547 0.306273 0.951944i \(-0.400918\pi\)
0.306273 + 0.951944i \(0.400918\pi\)
\(68\) 348.543 + 603.695i 0.621575 + 1.07660i
\(69\) −198.201 130.191i −0.345806 0.227147i
\(70\) 960.227 693.909i 1.63956 1.18483i
\(71\) 716.432i 1.19753i 0.800924 + 0.598767i \(0.204342\pi\)
−0.800924 + 0.598767i \(0.795658\pi\)
\(72\) 1299.11 + 964.765i 2.12642 + 1.57915i
\(73\) 725.427 418.826i 1.16308 0.671504i 0.211040 0.977478i \(-0.432315\pi\)
0.952040 + 0.305973i \(0.0989818\pi\)
\(74\) 164.012 + 94.6923i 0.257649 + 0.148754i
\(75\) 125.119 + 7.21301i 0.192634 + 0.0111051i
\(76\) 268.550 + 155.047i 0.405326 + 0.234015i
\(77\) −1075.00 481.913i −1.59101 0.713235i
\(78\) −432.827 24.9521i −0.628308 0.0362213i
\(79\) −409.854 −0.583699 −0.291849 0.956464i \(-0.594271\pi\)
−0.291849 + 0.956464i \(0.594271\pi\)
\(80\) −967.279 1675.38i −1.35181 2.34141i
\(81\) −210.734 697.877i −0.289072 0.957307i
\(82\) 766.726 + 442.670i 1.03257 + 0.596155i
\(83\) −135.674 234.994i −0.179423 0.310770i 0.762260 0.647271i \(-0.224090\pi\)
−0.941683 + 0.336501i \(0.890757\pi\)
\(84\) 1006.72 + 1576.93i 1.30764 + 2.04830i
\(85\) −218.931 + 379.199i −0.279369 + 0.483882i
\(86\) 343.779 198.481i 0.431054 0.248869i
\(87\) 1036.36 + 680.744i 1.27712 + 0.838889i
\(88\) −1906.15 + 3301.55i −2.30905 + 3.99939i
\(89\) 717.489 1242.73i 0.854535 1.48010i −0.0225404 0.999746i \(-0.507175\pi\)
0.877076 0.480352i \(-0.159491\pi\)
\(90\) −198.477 + 1715.71i −0.232459 + 2.00946i
\(91\) −269.176 120.669i −0.310080 0.139006i
\(92\) −768.356 + 443.611i −0.870725 + 0.502713i
\(93\) 628.053 315.886i 0.700280 0.352214i
\(94\) 36.3317i 0.0398652i
\(95\) 194.780i 0.210358i
\(96\) 1626.68 818.155i 1.72940 0.869818i
\(97\) −433.147 + 250.077i −0.453396 + 0.261768i −0.709263 0.704944i \(-0.750972\pi\)
0.255868 + 0.966712i \(0.417639\pi\)
\(98\) 364.596 + 1759.39i 0.375813 + 1.81353i
\(99\) 1576.21 682.126i 1.60015 0.692487i
\(100\) 234.450 406.078i 0.234450 0.406078i
\(101\) 918.553 1590.98i 0.904945 1.56741i 0.0839535 0.996470i \(-0.473245\pi\)
0.820991 0.570941i \(-0.193421\pi\)
\(102\) −815.757 535.840i −0.791882 0.520157i
\(103\) −582.577 + 336.351i −0.557311 + 0.321764i −0.752066 0.659088i \(-0.770942\pi\)
0.194754 + 0.980852i \(0.437609\pi\)
\(104\) −477.291 + 826.693i −0.450022 + 0.779461i
\(105\) −541.637 + 1042.89i −0.503413 + 0.969293i
\(106\) 100.691 + 174.402i 0.0922637 + 0.159805i
\(107\) −837.754 483.678i −0.756904 0.436999i 0.0712787 0.997456i \(-0.477292\pi\)
−0.828183 + 0.560457i \(0.810625\pi\)
\(108\) −2686.89 468.849i −2.39394 0.417732i
\(109\) −749.801 1298.69i −0.658880 1.14121i −0.980906 0.194483i \(-0.937697\pi\)
0.322026 0.946731i \(-0.395636\pi\)
\(110\) −4069.05 −3.52699
\(111\) −187.546 10.8118i −0.160370 0.00924517i
\(112\) 2918.71 299.241i 2.46243 0.252461i
\(113\) −1202.80 694.434i −1.00132 0.578114i −0.0926834 0.995696i \(-0.529544\pi\)
−0.908639 + 0.417582i \(0.862878\pi\)
\(114\) −433.449 24.9879i −0.356107 0.0205292i
\(115\) −482.628 278.646i −0.391351 0.225946i
\(116\) 4017.59 2319.56i 3.21572 1.85660i
\(117\) 394.675 170.801i 0.311861 0.134962i
\(118\) 652.100i 0.508734i
\(119\) −388.961 538.243i −0.299631 0.414627i
\(120\) 3178.47 + 2087.82i 2.41794 + 1.58825i
\(121\) 1357.63 + 2351.49i 1.02001 + 1.76671i
\(122\) 2696.90 2.00136
\(123\) −876.742 50.5433i −0.642709 0.0370515i
\(124\) 2630.28i 1.90489i
\(125\) −1231.90 −0.881476
\(126\) −2251.29 1339.11i −1.59175 0.946805i
\(127\) −404.036 −0.282302 −0.141151 0.989988i \(-0.545080\pi\)
−0.141151 + 0.989988i \(0.545080\pi\)
\(128\) 173.473i 0.119789i
\(129\) −216.180 + 329.110i −0.147547 + 0.224624i
\(130\) −1018.87 −0.687392
\(131\) 1367.10 + 2367.88i 0.911786 + 1.57926i 0.811540 + 0.584297i \(0.198630\pi\)
0.100246 + 0.994963i \(0.468037\pi\)
\(132\) 369.826 6415.13i 0.243858 4.23004i
\(133\) −269.562 120.842i −0.175745 0.0787845i
\(134\) 1759.75i 1.13447i
\(135\) −588.815 1608.85i −0.375386 1.02569i
\(136\) −1861.06 + 1074.48i −1.17342 + 0.677473i
\(137\) 743.037 + 428.993i 0.463372 + 0.267528i 0.713461 0.700695i \(-0.247127\pi\)
−0.250089 + 0.968223i \(0.580460\pi\)
\(138\) 681.993 1038.26i 0.420689 0.640453i
\(139\) −2002.26 1156.01i −1.22180 0.705404i −0.256496 0.966545i \(-0.582568\pi\)
−0.965301 + 0.261141i \(0.915901\pi\)
\(140\) 2575.25 + 3563.62i 1.55463 + 2.15129i
\(141\) −16.1932 32.1957i −0.00967171 0.0192295i
\(142\) −3752.96 −2.21790
\(143\) 506.583 + 877.428i 0.296242 + 0.513107i
\(144\) −2550.21 + 3434.02i −1.47582 + 1.98728i
\(145\) 2523.57 + 1456.98i 1.44532 + 0.834455i
\(146\) 2193.98 + 3800.08i 1.24366 + 2.15409i
\(147\) −1107.26 1396.60i −0.621260 0.783605i
\(148\) −351.425 + 608.685i −0.195182 + 0.338065i
\(149\) 1647.40 951.126i 0.905773 0.522948i 0.0267040 0.999643i \(-0.491499\pi\)
0.879069 + 0.476695i \(0.158166\pi\)
\(150\) −37.7847 + 655.426i −0.0205674 + 0.356768i
\(151\) 768.979 1331.91i 0.414428 0.717810i −0.580940 0.813946i \(-0.697315\pi\)
0.995368 + 0.0961358i \(0.0306483\pi\)
\(152\) −477.977 + 827.881i −0.255060 + 0.441776i
\(153\) 961.717 + 111.254i 0.508171 + 0.0587866i
\(154\) 2524.46 5631.30i 1.32095 2.94664i
\(155\) 1430.81 826.079i 0.741455 0.428079i
\(156\) 92.6027 1606.32i 0.0475266 0.824413i
\(157\) 2910.07i 1.47929i 0.672995 + 0.739647i \(0.265007\pi\)
−0.672995 + 0.739647i \(0.734993\pi\)
\(158\) 2146.98i 1.08104i
\(159\) −166.960 109.669i −0.0832752 0.0547003i
\(160\) 3705.84 2139.57i 1.83108 1.05717i
\(161\) 685.051 495.053i 0.335339 0.242333i
\(162\) 3655.76 1103.91i 1.77299 0.535378i
\(163\) −1133.65 + 1963.54i −0.544751 + 0.943536i 0.453872 + 0.891067i \(0.350042\pi\)
−0.998623 + 0.0524693i \(0.983291\pi\)
\(164\) −1642.85 + 2845.49i −0.782224 + 1.35485i
\(165\) 3605.83 1813.59i 1.70130 0.855685i
\(166\) 1230.99 710.715i 0.575564 0.332302i
\(167\) −671.601 + 1163.25i −0.311198 + 0.539011i −0.978622 0.205667i \(-0.934064\pi\)
0.667424 + 0.744678i \(0.267397\pi\)
\(168\) −4861.33 + 3103.50i −2.23250 + 1.42524i
\(169\) −971.654 1682.95i −0.442264 0.766024i
\(170\) −1986.40 1146.85i −0.896177 0.517408i
\(171\) 395.243 171.047i 0.176754 0.0764928i
\(172\) 736.607 + 1275.84i 0.326545 + 0.565593i
\(173\) 942.516 0.414209 0.207104 0.978319i \(-0.433596\pi\)
0.207104 + 0.978319i \(0.433596\pi\)
\(174\) −3566.01 + 5428.86i −1.55367 + 2.36529i
\(175\) −182.727 + 407.610i −0.0789308 + 0.176071i
\(176\) −8727.16 5038.63i −3.73770 2.15796i
\(177\) 290.643 + 577.865i 0.123424 + 0.245395i
\(178\) 6509.91 + 3758.50i 2.74123 + 1.58265i
\(179\) 62.9841 36.3639i 0.0262997 0.0151842i −0.486792 0.873518i \(-0.661833\pi\)
0.513092 + 0.858333i \(0.328500\pi\)
\(180\) −6367.38 736.594i −2.63665 0.305014i
\(181\) 1860.29i 0.763944i −0.924174 0.381972i \(-0.875245\pi\)
0.924174 0.381972i \(-0.124755\pi\)
\(182\) 632.112 1410.05i 0.257446 0.574286i
\(183\) −2389.89 + 1202.02i −0.965386 + 0.485551i
\(184\) −1367.56 2368.68i −0.547922 0.949028i
\(185\) −441.481 −0.175451
\(186\) 1654.74 + 3290.00i 0.652319 + 1.29696i
\(187\) 2280.86i 0.891939i
\(188\) −134.835 −0.0523077
\(189\) 2591.85 + 183.258i 0.997510 + 0.0705295i
\(190\) −1020.34 −0.389595
\(191\) 4.08168i 0.00154628i −1.00000 0.000773141i \(-0.999754\pi\)
1.00000 0.000773141i \(-0.000246098\pi\)
\(192\) 1326.79 + 2637.96i 0.498712 + 0.991553i
\(193\) −4402.88 −1.64211 −0.821053 0.570853i \(-0.806613\pi\)
−0.821053 + 0.570853i \(0.806613\pi\)
\(194\) −1310.01 2269.00i −0.484809 0.839714i
\(195\) 902.884 454.115i 0.331574 0.166769i
\(196\) −6529.51 + 1353.10i −2.37956 + 0.493111i
\(197\) 389.909i 0.141014i −0.997511 0.0705072i \(-0.977538\pi\)
0.997511 0.0705072i \(-0.0224618\pi\)
\(198\) 3573.25 + 8256.82i 1.28253 + 2.96357i
\(199\) 912.641 526.914i 0.325103 0.187698i −0.328562 0.944482i \(-0.606564\pi\)
0.653665 + 0.756784i \(0.273231\pi\)
\(200\) 1251.85 + 722.758i 0.442597 + 0.255533i
\(201\) −784.327 1559.42i −0.275235 0.547229i
\(202\) 8334.20 + 4811.75i 2.90293 + 1.67601i
\(203\) −3582.00 + 2588.54i −1.23846 + 0.894974i
\(204\) 1988.62 3027.46i 0.682507 1.03904i
\(205\) −2063.85 −0.703147
\(206\) −1761.95 3051.78i −0.595925 1.03217i
\(207\) −141.599 + 1224.03i −0.0475450 + 0.410995i
\(208\) −2185.24 1261.65i −0.728457 0.420575i
\(209\) 507.312 + 878.689i 0.167902 + 0.290814i
\(210\) −5463.09 2837.32i −1.79519 0.932349i
\(211\) −561.416 + 972.401i −0.183173 + 0.317265i −0.942959 0.332908i \(-0.891970\pi\)
0.759786 + 0.650173i \(0.225303\pi\)
\(212\) −647.243 + 373.686i −0.209683 + 0.121061i
\(213\) 3325.73 1672.71i 1.06984 0.538086i
\(214\) 2533.70 4388.50i 0.809347 1.40183i
\(215\) −462.686 + 801.395i −0.146767 + 0.254208i
\(216\) 1445.36 8283.09i 0.455298 2.60923i
\(217\) 255.558 + 2492.65i 0.0799467 + 0.779779i
\(218\) 6803.09 3927.77i 2.11359 1.22028i
\(219\) −3637.93 2389.62i −1.12250 0.737331i
\(220\) 15101.2i 4.62782i
\(221\) 571.115i 0.173834i
\(222\) 56.6368 982.441i 0.0171226 0.297014i
\(223\) 3850.81 2223.27i 1.15637 0.667628i 0.205935 0.978566i \(-0.433976\pi\)
0.950430 + 0.310937i \(0.100643\pi\)
\(224\) 661.904 + 6456.04i 0.197435 + 1.92572i
\(225\) −258.642 597.653i −0.0766348 0.177082i
\(226\) 3637.73 6300.73i 1.07070 1.85451i
\(227\) −23.6177 + 40.9071i −0.00690556 + 0.0119608i −0.869458 0.494008i \(-0.835531\pi\)
0.862552 + 0.505968i \(0.168865\pi\)
\(228\) 92.7358 1608.63i 0.0269368 0.467254i
\(229\) −2860.63 + 1651.59i −0.825485 + 0.476594i −0.852304 0.523046i \(-0.824795\pi\)
0.0268193 + 0.999640i \(0.491462\pi\)
\(230\) 1459.66 2528.20i 0.418465 0.724803i
\(231\) 272.821 + 6115.40i 0.0777069 + 1.74183i
\(232\) 7150.70 + 12385.4i 2.02356 + 3.50491i
\(233\) 4018.91 + 2320.32i 1.12999 + 0.652400i 0.943932 0.330139i \(-0.107096\pi\)
0.186057 + 0.982539i \(0.440429\pi\)
\(234\) 894.726 + 2067.47i 0.249958 + 0.577584i
\(235\) −42.3470 73.3472i −0.0117550 0.0203602i
\(236\) 2420.09 0.667519
\(237\) 956.919 + 1902.57i 0.262273 + 0.521457i
\(238\) 2819.53 2037.54i 0.767913 0.554933i
\(239\) 3801.25 + 2194.65i 1.02880 + 0.593976i 0.916640 0.399715i \(-0.130891\pi\)
0.112157 + 0.993691i \(0.464224\pi\)
\(240\) −5518.83 + 8401.81i −1.48433 + 2.25973i
\(241\) −962.435 555.662i −0.257244 0.148520i 0.365833 0.930681i \(-0.380784\pi\)
−0.623077 + 0.782161i \(0.714118\pi\)
\(242\) −12318.1 + 7111.84i −3.27205 + 1.88912i
\(243\) −2747.58 + 2607.63i −0.725338 + 0.688393i
\(244\) 10008.8i 2.62602i
\(245\) −2786.75 3126.94i −0.726688 0.815400i
\(246\) 264.767 4592.73i 0.0686216 1.19033i
\(247\) 127.028 + 220.020i 0.0327232 + 0.0566782i
\(248\) 8108.58 2.07619
\(249\) −774.090 + 1178.47i −0.197012 + 0.299929i
\(250\) 6453.19i 1.63254i
\(251\) 1262.49 0.317480 0.158740 0.987320i \(-0.449257\pi\)
0.158740 + 0.987320i \(0.449257\pi\)
\(252\) 4969.74 8355.04i 1.24232 2.08856i
\(253\) −2902.97 −0.721376
\(254\) 2116.50i 0.522839i
\(255\) 2271.43 + 130.946i 0.557812 + 0.0321574i
\(256\) −3637.45 −0.888049
\(257\) −2670.98 4626.27i −0.648291 1.12287i −0.983531 0.180741i \(-0.942151\pi\)
0.335239 0.942133i \(-0.391183\pi\)
\(258\) −1724.01 1132.44i −0.416016 0.273265i
\(259\) 273.897 610.981i 0.0657108 0.146581i
\(260\) 3781.26i 0.901939i
\(261\) 740.395 6400.23i 0.175591 1.51787i
\(262\) −12403.9 + 7161.42i −2.92488 + 1.68868i
\(263\) −900.046 519.642i −0.211024 0.121835i 0.390763 0.920491i \(-0.372211\pi\)
−0.601787 + 0.798657i \(0.705544\pi\)
\(264\) 19776.5 + 1140.09i 4.61045 + 0.265788i
\(265\) −406.554 234.724i −0.0942430 0.0544112i
\(266\) 633.020 1412.08i 0.145913 0.325489i
\(267\) −7444.00 429.140i −1.70624 0.0983630i
\(268\) −6530.83 −1.48856
\(269\) 2118.62 + 3669.55i 0.480202 + 0.831735i 0.999742 0.0227115i \(-0.00722993\pi\)
−0.519540 + 0.854446i \(0.673897\pi\)
\(270\) 8427.83 3084.45i 1.89964 0.695236i
\(271\) 5981.42 + 3453.38i 1.34076 + 0.774087i 0.986919 0.161219i \(-0.0515425\pi\)
0.353840 + 0.935306i \(0.384876\pi\)
\(272\) −2840.24 4919.44i −0.633143 1.09664i
\(273\) 68.3131 + 1531.27i 0.0151447 + 0.339474i
\(274\) −2247.24 + 3892.33i −0.495477 + 0.858191i
\(275\) 1328.68 767.114i 0.291354 0.168214i
\(276\) 3853.21 + 2531.03i 0.840349 + 0.551993i
\(277\) 1226.23 2123.90i 0.265983 0.460696i −0.701838 0.712337i \(-0.747637\pi\)
0.967821 + 0.251641i \(0.0809702\pi\)
\(278\) 6055.63 10488.7i 1.30645 2.26284i
\(279\) −2932.73 2177.94i −0.629312 0.467347i
\(280\) −10985.9 + 7938.95i −2.34475 + 1.69444i
\(281\) −7204.13 + 4159.31i −1.52940 + 0.883002i −0.530017 + 0.847987i \(0.677815\pi\)
−0.999387 + 0.0350152i \(0.988852\pi\)
\(282\) 168.654 84.8264i 0.0356142 0.0179125i
\(283\) 6851.81i 1.43922i −0.694381 0.719608i \(-0.744322\pi\)
0.694381 0.719608i \(-0.255678\pi\)
\(284\) 13928.1i 2.91014i
\(285\) 904.182 454.768i 0.187927 0.0945198i
\(286\) −4596.33 + 2653.69i −0.950302 + 0.548657i
\(287\) 1280.42 2856.23i 0.263347 0.587448i
\(288\) −7595.86 5640.94i −1.55413 1.15415i
\(289\) 1813.65 3141.33i 0.369153 0.639392i
\(290\) −7632.28 + 13219.5i −1.54546 + 2.67681i
\(291\) 2172.18 + 1426.82i 0.437578 + 0.287429i
\(292\) −14103.0 + 8142.35i −2.82642 + 1.63183i
\(293\) 388.740 673.317i 0.0775100 0.134251i −0.824665 0.565621i \(-0.808636\pi\)
0.902175 + 0.431370i \(0.141970\pi\)
\(294\) 7315.98 5800.27i 1.45128 1.15061i
\(295\) 760.066 + 1316.47i 0.150009 + 0.259824i
\(296\) −1876.45 1083.37i −0.368467 0.212735i
\(297\) −6846.58 5724.26i −1.33764 1.11837i
\(298\) 4982.38 + 8629.74i 0.968529 + 1.67754i
\(299\) −726.890 −0.140592
\(300\) −2432.43 140.227i −0.468122 0.0269868i
\(301\) −822.026 1137.51i −0.157411 0.217825i
\(302\) 6977.09 + 4028.23i 1.32943 + 0.767544i
\(303\) −9530.06 549.399i −1.80689 0.104165i
\(304\) −2188.38 1263.46i −0.412869 0.238370i
\(305\) −5444.57 + 3143.42i −1.02215 + 0.590137i
\(306\) −582.793 + 5037.87i −0.108876 + 0.941162i
\(307\) 5502.32i 1.02291i −0.859309 0.511456i \(-0.829106\pi\)
0.859309 0.511456i \(-0.170894\pi\)
\(308\) 20899.0 + 9368.82i 3.86634 + 1.73324i
\(309\) 2921.56 + 1919.06i 0.537869 + 0.353306i
\(310\) 4327.34 + 7495.17i 0.792827 + 1.37322i
\(311\) −2147.49 −0.391554 −0.195777 0.980648i \(-0.562723\pi\)
−0.195777 + 0.980648i \(0.562723\pi\)
\(312\) 4951.94 + 285.474i 0.898552 + 0.0518007i
\(313\) 1969.86i 0.355729i 0.984055 + 0.177864i \(0.0569188\pi\)
−0.984055 + 0.177864i \(0.943081\pi\)
\(314\) −15244.1 −2.73974
\(315\) 6105.78 + 79.3964i 1.09213 + 0.0142015i
\(316\) 7967.94 1.41846
\(317\) 1451.03i 0.257091i −0.991704 0.128545i \(-0.958969\pi\)
0.991704 0.128545i \(-0.0410308\pi\)
\(318\) 574.493 874.603i 0.101308 0.154230i
\(319\) 15179.1 2.66416
\(320\) 3469.71 + 6009.71i 0.606133 + 1.04985i
\(321\) −289.294 + 5018.19i −0.0503016 + 0.872549i
\(322\) 2593.29 + 3588.58i 0.448815 + 0.621067i
\(323\) 571.936i 0.0985244i
\(324\) 4096.85 + 13567.4i 0.702478 + 2.32637i
\(325\) 332.695 192.082i 0.0567835 0.0327839i
\(326\) −10285.8 5938.53i −1.74748 1.00891i
\(327\) −4278.01 + 6512.79i −0.723469 + 1.10140i
\(328\) −8772.05 5064.54i −1.47669 0.852569i
\(329\) 127.780 13.1006i 0.0214126 0.00219532i
\(330\) 9500.34 + 18888.8i 1.58478 + 3.15090i
\(331\) −1188.85 −0.197417 −0.0987086 0.995116i \(-0.531471\pi\)
−0.0987086 + 0.995116i \(0.531471\pi\)
\(332\) 2637.62 + 4568.50i 0.436019 + 0.755207i
\(333\) 387.688 + 895.843i 0.0637994 + 0.147423i
\(334\) −6093.56 3518.12i −0.998279 0.576356i
\(335\) −2051.11 3552.62i −0.334519 0.579404i
\(336\) −8203.65 12850.2i −1.33198 2.08642i
\(337\) 3178.71 5505.69i 0.513814 0.889952i −0.486058 0.873927i \(-0.661565\pi\)
0.999872 0.0160253i \(-0.00510122\pi\)
\(338\) 8816.00 5089.92i 1.41872 0.819098i
\(339\) −415.351 + 7204.81i −0.0665450 + 1.15431i
\(340\) 4256.22 7371.98i 0.678899 1.17589i
\(341\) 4303.11 7453.20i 0.683361 1.18362i
\(342\) 896.012 + 2070.44i 0.141669 + 0.327359i
\(343\) 6056.39 1916.71i 0.953394 0.301727i
\(344\) −3933.15 + 2270.80i −0.616456 + 0.355911i
\(345\) −166.662 + 2890.97i −0.0260080 + 0.451144i
\(346\) 4937.28i 0.767138i
\(347\) 11126.9i 1.72140i 0.509115 + 0.860698i \(0.329973\pi\)
−0.509115 + 0.860698i \(0.670027\pi\)
\(348\) −20147.7 13234.3i −3.10354 2.03860i
\(349\) 2318.23 1338.43i 0.355564 0.205285i −0.311569 0.950224i \(-0.600855\pi\)
0.667133 + 0.744938i \(0.267521\pi\)
\(350\) −2135.23 957.201i −0.326093 0.146184i
\(351\) −1714.35 1433.33i −0.260699 0.217964i
\(352\) 11145.2 19304.0i 1.68761 2.92303i
\(353\) 3764.40 6520.13i 0.567589 0.983092i −0.429215 0.903202i \(-0.641210\pi\)
0.996804 0.0798900i \(-0.0254569\pi\)
\(354\) −3027.09 + 1522.51i −0.454486 + 0.228589i
\(355\) 7576.57 4374.33i 1.13274 0.653987i
\(356\) −13948.6 + 24159.7i −2.07662 + 3.59681i
\(357\) −1590.42 + 3062.26i −0.235781 + 0.453984i
\(358\) 190.489 + 329.936i 0.0281219 + 0.0487086i
\(359\) 9009.61 + 5201.70i 1.32454 + 0.764722i 0.984449 0.175671i \(-0.0562094\pi\)
0.340089 + 0.940393i \(0.389543\pi\)
\(360\) 2270.76 19629.3i 0.332444 2.87376i
\(361\) −3302.29 5719.73i −0.481453 0.833902i
\(362\) 9744.93 1.41487
\(363\) 7746.01 11792.4i 1.12000 1.70508i
\(364\) 5233.02 + 2345.91i 0.753530 + 0.337800i
\(365\) −8858.51 5114.46i −1.27034 0.733433i
\(366\) −6296.67 12519.2i −0.899269 1.78795i
\(367\) −10537.2 6083.67i −1.49874 0.865299i −0.498743 0.866750i \(-0.666205\pi\)
−0.999999 + 0.00145066i \(0.999538\pi\)
\(368\) 6261.25 3614.93i 0.886930 0.512069i
\(369\) 1812.37 + 4187.90i 0.255687 + 0.590823i
\(370\) 2312.66i 0.324944i
\(371\) 577.070 417.020i 0.0807546 0.0583574i
\(372\) −12209.9 + 6141.11i −1.70176 + 0.855919i
\(373\) 1108.39 + 1919.79i 0.153862 + 0.266496i 0.932644 0.360798i \(-0.117496\pi\)
−0.778782 + 0.627294i \(0.784162\pi\)
\(374\) −11948.0 −1.65192
\(375\) 2876.21 + 5718.56i 0.396072 + 0.787481i
\(376\) 415.667i 0.0570117i
\(377\) 3800.77 0.519230
\(378\) −959.981 + 13577.2i −0.130625 + 1.84744i
\(379\) −2955.89 −0.400617 −0.200308 0.979733i \(-0.564194\pi\)
−0.200308 + 0.979733i \(0.564194\pi\)
\(380\) 3786.70i 0.511194i
\(381\) 943.334 + 1875.56i 0.126846 + 0.252199i
\(382\) 21.3815 0.00286380
\(383\) −3724.64 6451.27i −0.496920 0.860691i 0.503074 0.864244i \(-0.332202\pi\)
−0.999994 + 0.00355274i \(0.998869\pi\)
\(384\) −805.276 + 405.022i −0.107016 + 0.0538247i
\(385\) 1467.24 + 14311.0i 0.194227 + 1.89443i
\(386\) 23064.1i 3.04127i
\(387\) 2032.48 + 235.123i 0.266968 + 0.0308836i
\(388\) 8420.76 4861.73i 1.10180 0.636126i
\(389\) 5221.02 + 3014.36i 0.680505 + 0.392890i 0.800045 0.599940i \(-0.204809\pi\)
−0.119540 + 0.992829i \(0.538142\pi\)
\(390\) 2378.84 + 4729.67i 0.308865 + 0.614093i
\(391\) −1417.15 818.193i −0.183295 0.105826i
\(392\) −4171.31 20129.1i −0.537456 2.59355i
\(393\) 7800.01 11874.7i 1.00117 1.52417i
\(394\) 2042.50 0.261167
\(395\) 2502.46 + 4334.38i 0.318765 + 0.552117i
\(396\) −30642.9 + 13261.2i −3.88855 + 1.68282i
\(397\) 12778.7 + 7377.79i 1.61548 + 0.932696i 0.988070 + 0.154005i \(0.0492172\pi\)
0.627407 + 0.778691i \(0.284116\pi\)
\(398\) 2760.19 + 4780.79i 0.347628 + 0.602109i
\(399\) 68.4112 + 1533.47i 0.00858357 + 0.192405i
\(400\) −1910.50 + 3309.09i −0.238813 + 0.413636i
\(401\) −3293.14 + 1901.29i −0.410103 + 0.236773i −0.690834 0.723013i \(-0.742756\pi\)
0.280731 + 0.959787i \(0.409423\pi\)
\(402\) 8168.88 4108.62i 1.01350 0.509750i
\(403\) 1077.48 1866.25i 0.133184 0.230681i
\(404\) −17857.5 + 30930.1i −2.19912 + 3.80899i
\(405\) −6093.66 + 6489.64i −0.747645 + 0.796229i
\(406\) −13559.8 18764.0i −1.65754 2.29370i
\(407\) −1991.61 + 1149.85i −0.242556 + 0.140040i
\(408\) 9333.00 + 6130.50i 1.13248 + 0.743884i
\(409\) 4356.56i 0.526694i 0.964701 + 0.263347i \(0.0848264\pi\)
−0.964701 + 0.263347i \(0.915174\pi\)
\(410\) 10811.3i 1.30227i
\(411\) 256.586 4450.83i 0.0307943 0.534169i
\(412\) 11325.8 6538.98i 1.35433 0.781923i
\(413\) −2293.46 + 235.137i −0.273254 + 0.0280153i
\(414\) −6411.97 741.753i −0.761187 0.0880560i
\(415\) −1656.77 + 2869.61i −0.195970 + 0.339431i
\(416\) 2790.70 4833.64i 0.328907 0.569684i
\(417\) −691.423 + 11993.7i −0.0811970 + 1.40847i
\(418\) −4602.93 + 2657.50i −0.538605 + 0.310964i
\(419\) 4875.07 8443.88i 0.568408 0.984512i −0.428316 0.903629i \(-0.640893\pi\)
0.996724 0.0808824i \(-0.0257738\pi\)
\(420\) 10529.9 20274.8i 1.22335 2.35549i
\(421\) 4245.69 + 7353.75i 0.491502 + 0.851306i 0.999952 0.00978535i \(-0.00311482\pi\)
−0.508450 + 0.861091i \(0.669781\pi\)
\(422\) −5093.83 2940.93i −0.587592 0.339246i
\(423\) −111.647 + 150.340i −0.0128333 + 0.0172808i
\(424\) −1151.99 1995.31i −0.131948 0.228540i
\(425\) 864.834 0.0987074
\(426\) 8762.34 + 17421.5i 0.996565 + 1.98140i
\(427\) −972.460 9485.11i −0.110212 1.07498i
\(428\) 16286.7 + 9403.14i 1.83936 + 1.06196i
\(429\) 2890.32 4400.20i 0.325282 0.495206i
\(430\) −4198.04 2423.74i −0.470808 0.271821i
\(431\) −3582.61 + 2068.42i −0.400390 + 0.231166i −0.686652 0.726986i \(-0.740921\pi\)
0.286262 + 0.958151i \(0.407587\pi\)
\(432\) 21895.1 + 3820.60i 2.43849 + 0.425506i
\(433\) 1005.45i 0.111591i 0.998442 + 0.0557953i \(0.0177694\pi\)
−0.998442 + 0.0557953i \(0.982231\pi\)
\(434\) −13057.5 + 1338.72i −1.44419 + 0.148066i
\(435\) 871.442 15116.3i 0.0960516 1.66614i
\(436\) 14576.8 + 25247.8i 1.60115 + 2.77328i
\(437\) −727.935 −0.0796839
\(438\) 12517.8 19057.0i 1.36558 2.07894i
\(439\) 8230.57i 0.894814i −0.894330 0.447407i \(-0.852348\pi\)
0.894330 0.447407i \(-0.147652\pi\)
\(440\) 46553.7 5.04400
\(441\) −3897.92 + 8400.73i −0.420897 + 0.907109i
\(442\) −2991.74 −0.321951
\(443\) 1353.60i 0.145173i 0.997362 + 0.0725863i \(0.0231253\pi\)
−0.997362 + 0.0725863i \(0.976875\pi\)
\(444\) 3646.06 + 210.192i 0.389717 + 0.0224668i
\(445\) −17523.1 −1.86669
\(446\) 11646.4 + 20172.1i 1.23649 + 2.14166i
\(447\) −8261.50 5426.67i −0.874174 0.574212i
\(448\) −10469.7 + 1073.40i −1.10412 + 0.113200i
\(449\) 11342.5i 1.19217i 0.802922 + 0.596084i \(0.203278\pi\)
−0.802922 + 0.596084i \(0.796722\pi\)
\(450\) 3130.75 1354.87i 0.327967 0.141932i
\(451\) −9310.40 + 5375.36i −0.972084 + 0.561233i
\(452\) 23383.4 + 13500.4i 2.43333 + 1.40488i
\(453\) −7978.22 459.937i −0.827482 0.0477036i
\(454\) −214.288 123.719i −0.0221520 0.0127895i
\(455\) 367.389 + 3583.41i 0.0378538 + 0.369215i
\(456\) 4959.05 + 285.885i 0.509274 + 0.0293592i
\(457\) −7267.52 −0.743895 −0.371948 0.928254i \(-0.621310\pi\)
−0.371948 + 0.928254i \(0.621310\pi\)
\(458\) −8651.69 14985.2i −0.882679 1.52884i
\(459\) −1728.95 4724.11i −0.175818 0.480398i
\(460\) 9382.73 + 5417.12i 0.951027 + 0.549075i
\(461\) −6216.19 10766.8i −0.628019 1.08776i −0.987949 0.154782i \(-0.950533\pi\)
0.359930 0.932979i \(-0.382801\pi\)
\(462\) −32034.9 + 1429.15i −3.22597 + 0.143918i
\(463\) 1444.49 2501.94i 0.144992 0.251134i −0.784378 0.620283i \(-0.787018\pi\)
0.929370 + 0.369150i \(0.120351\pi\)
\(464\) −32738.9 + 18901.8i −3.27557 + 1.89115i
\(465\) −7175.34 4713.21i −0.715588 0.470043i
\(466\) −12154.8 + 21052.7i −1.20828 + 2.09280i
\(467\) −1313.23 + 2274.59i −0.130127 + 0.225386i −0.923725 0.383055i \(-0.874872\pi\)
0.793598 + 0.608442i \(0.208205\pi\)
\(468\) −7672.85 + 3320.53i −0.757858 + 0.327973i
\(469\) 6189.11 634.537i 0.609353 0.0624738i
\(470\) 384.222 221.831i 0.0377082 0.0217708i
\(471\) 13508.8 6794.38i 1.32155 0.664689i
\(472\) 7460.62i 0.727548i
\(473\) 4820.33i 0.468581i
\(474\) −9966.45 + 5012.73i −0.965768 + 0.485744i
\(475\) 333.174 192.358i 0.0321833 0.0185810i
\(476\) 7561.77 + 10463.9i 0.728136 + 1.00759i
\(477\) −119.279 + 1031.09i −0.0114495 + 0.0989737i
\(478\) −11496.5 + 19912.5i −1.10008 + 1.90539i
\(479\) 380.831 659.619i 0.0363270 0.0629202i −0.847290 0.531130i \(-0.821768\pi\)
0.883617 + 0.468210i \(0.155101\pi\)
\(480\) −18584.4 12207.4i −1.76720 1.16081i
\(481\) −498.689 + 287.918i −0.0472729 + 0.0272930i
\(482\) 2910.78 5041.62i 0.275068 0.476431i
\(483\) −3897.51 2024.22i −0.367170 0.190694i
\(484\) −26393.7 45715.2i −2.47874 4.29331i
\(485\) 5289.34 + 3053.80i 0.495210 + 0.285909i
\(486\) −13659.8 14392.9i −1.27494 1.34337i
\(487\) −8677.57 15030.0i −0.807430 1.39851i −0.914639 0.404273i \(-0.867525\pi\)
0.107209 0.994237i \(-0.465809\pi\)
\(488\) −30855.0 −2.86218
\(489\) 11761.7 + 678.052i 1.08770 + 0.0627046i
\(490\) 16380.2 14598.1i 1.51017 1.34587i
\(491\) 17290.8 + 9982.86i 1.58925 + 0.917557i 0.993430 + 0.114442i \(0.0365081\pi\)
0.595825 + 0.803114i \(0.296825\pi\)
\(492\) 17044.7 + 982.609i 1.56186 + 0.0900395i
\(493\) 7410.02 + 4278.18i 0.676938 + 0.390830i
\(494\) −1152.55 + 665.427i −0.104971 + 0.0606052i
\(495\) −16837.7 12504.2i −1.52888 1.13540i
\(496\) 21433.8i 1.94034i
\(497\) 1353.26 + 13199.3i 0.122137 + 1.19129i
\(498\) −6173.29 4055.00i −0.555485 0.364877i
\(499\) 770.803 + 1335.07i 0.0691500 + 0.119771i 0.898527 0.438917i \(-0.144638\pi\)
−0.829377 + 0.558689i \(0.811305\pi\)
\(500\) 23949.3 2.14209
\(501\) 6967.92 + 401.694i 0.621364 + 0.0358211i
\(502\) 6613.43i 0.587992i
\(503\) 578.894 0.0513153 0.0256577 0.999671i \(-0.491832\pi\)
0.0256577 + 0.999671i \(0.491832\pi\)
\(504\) 25756.8 + 15320.6i 2.27639 + 1.35404i
\(505\) −22433.7 −1.97681
\(506\) 15206.9i 1.33603i
\(507\) −5543.79 + 8439.81i −0.485618 + 0.739300i
\(508\) 7854.82 0.686026
\(509\) −4581.00 7934.52i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113021i \(0.963947\pi\)
\(510\) −685.946 + 11898.7i −0.0595573 + 1.03310i
\(511\) 12573.9 9086.56i 1.08853 0.786626i
\(512\) 20442.2i 1.76451i
\(513\) −1716.81 1435.39i −0.147757 0.123536i
\(514\) 24234.3 13991.7i 2.07963 1.20067i
\(515\) 7114.11 + 4107.33i 0.608709 + 0.351438i
\(516\) 4202.73 6398.19i 0.358556 0.545862i
\(517\) −382.071 220.589i −0.0325019 0.0187650i
\(518\) 3200.57 + 1434.78i 0.271477 + 0.121700i
\(519\) −2200.57 4375.22i −0.186116 0.370040i
\(520\) 11656.8 0.983049
\(521\) −6093.28 10553.9i −0.512382 0.887473i −0.999897 0.0143576i \(-0.995430\pi\)
0.487514 0.873115i \(-0.337904\pi\)
\(522\) 33527.0 + 3878.49i 2.81118 + 0.325205i
\(523\) −8988.68 5189.62i −0.751525 0.433893i 0.0747195 0.997205i \(-0.476194\pi\)
−0.826245 + 0.563311i \(0.809527\pi\)
\(524\) −26577.6 46033.8i −2.21574 3.83778i
\(525\) 2318.78 103.446i 0.192762 0.00859951i
\(526\) 2722.10 4714.81i 0.225644 0.390828i
\(527\) 4201.32 2425.63i 0.347272 0.200498i
\(528\) −3013.67 + 52276.2i −0.248396 + 4.30877i
\(529\) −5042.14 + 8733.24i −0.414411 + 0.717781i
\(530\) 1229.58 2129.69i 0.100773 0.174543i
\(531\) 2003.90 2698.37i 0.163770 0.220526i
\(532\) 5240.54 + 2349.28i 0.427079 + 0.191455i
\(533\) −2331.28 + 1345.97i −0.189454 + 0.109381i
\(534\) 2248.01 38994.7i 0.182174 3.16005i
\(535\) 11812.8i 0.954602i
\(536\) 20133.1i 1.62242i
\(537\) −315.857 207.475i −0.0253822 0.0166726i
\(538\) −19222.6 + 11098.2i −1.54042 + 0.889362i
\(539\) −20715.8 6848.05i −1.65546 0.547248i
\(540\) 11447.1 + 31277.6i 0.912230 + 2.49254i
\(541\) 2598.10 4500.05i 0.206472 0.357619i −0.744129 0.668036i \(-0.767135\pi\)
0.950601 + 0.310417i \(0.100469\pi\)
\(542\) −18090.2 + 31333.1i −1.43365 + 2.48316i
\(543\) −8635.57 + 4343.36i −0.682482 + 0.343262i
\(544\) 10881.5 6282.46i 0.857615 0.495144i
\(545\) −9156.15 + 15858.9i −0.719645 + 1.24646i
\(546\) −8021.40 + 357.852i −0.628726 + 0.0280488i
\(547\) 10154.0 + 17587.3i 0.793703 + 1.37473i 0.923660 + 0.383214i \(0.125183\pi\)
−0.129957 + 0.991520i \(0.541484\pi\)
\(548\) −14445.3 8340.01i −1.12605 0.650123i
\(549\) 11159.7 + 8287.58i 0.867551 + 0.644272i
\(550\) 4018.46 + 6960.17i 0.311541 + 0.539605i
\(551\) 3806.24 0.294285
\(552\) −7802.62 + 11878.6i −0.601633 + 0.915920i
\(553\) −7551.03 + 774.168i −0.580655 + 0.0595316i
\(554\) 11125.8 + 6423.51i 0.853235 + 0.492615i
\(555\) 1030.76 + 2049.39i 0.0788349 + 0.156742i
\(556\) 38925.8 + 22473.8i 2.96910 + 1.71421i
\(557\) 8891.43 5133.47i 0.676377 0.390507i −0.122111 0.992516i \(-0.538967\pi\)
0.798489 + 0.602010i \(0.205633\pi\)
\(558\) 11408.9 15362.8i 0.865554 1.16552i
\(559\) 1206.99i 0.0913241i
\(560\) −20985.4 29039.5i −1.58357 2.19133i
\(561\) 10587.9 5325.29i 0.796829 0.400774i
\(562\) −21788.2 37738.2i −1.63537 2.83254i
\(563\) 8350.36 0.625090 0.312545 0.949903i \(-0.398818\pi\)
0.312545 + 0.949903i \(0.398818\pi\)
\(564\) 314.810 + 625.913i 0.0235034 + 0.0467300i
\(565\) 16960.1i 1.26286i
\(566\) 35892.6 2.66551
\(567\) −5200.70 12459.4i −0.385201 0.922833i
\(568\) 42937.3 3.17185
\(569\) 3165.00i 0.233188i 0.993180 + 0.116594i \(0.0371975\pi\)
−0.993180 + 0.116594i \(0.962802\pi\)
\(570\) 2382.26 + 4736.47i 0.175056 + 0.348051i
\(571\) −2957.30 −0.216741 −0.108371 0.994111i \(-0.534563\pi\)
−0.108371 + 0.994111i \(0.534563\pi\)
\(572\) −9848.45 17058.0i −0.719902 1.24691i
\(573\) −18.9474 + 9.52982i −0.00138140 + 0.000694788i
\(574\) 14962.1 + 6707.35i 1.08799 + 0.487734i
\(575\) 1100.72i 0.0798319i
\(576\) 9147.82 12318.1i 0.661735 0.891066i
\(577\) −21694.0 + 12525.0i −1.56522 + 0.903681i −0.568507 + 0.822678i \(0.692479\pi\)
−0.996714 + 0.0810022i \(0.974188\pi\)
\(578\) 16455.6 + 9500.63i 1.18419 + 0.683692i
\(579\) 10279.8 + 20438.5i 0.737844 + 1.46700i
\(580\) −49060.5 28325.1i −3.51229 2.02782i
\(581\) −2943.49 4073.18i −0.210183 0.290850i
\(582\) −7474.27 + 11378.8i −0.532334 + 0.810420i
\(583\) −2445.39 −0.173718
\(584\) −25101.1 43476.4i −1.77858 3.08059i
\(585\) −4216.07 3130.99i −0.297971 0.221283i
\(586\) 3527.11 + 2036.38i 0.248641 + 0.143553i
\(587\) 6544.89 + 11336.1i 0.460198 + 0.797087i 0.998970 0.0453646i \(-0.0144450\pi\)
−0.538772 + 0.842452i \(0.681112\pi\)
\(588\) 21526.1 + 27151.2i 1.50973 + 1.90425i
\(589\) 1079.03 1868.93i 0.0754847 0.130743i
\(590\) −6896.22 + 3981.54i −0.481209 + 0.277826i
\(591\) −1809.98 + 910.350i −0.125978 + 0.0633618i
\(592\) 2863.72 4960.11i 0.198814 0.344357i
\(593\) 3549.51 6147.93i 0.245803 0.425743i −0.716554 0.697531i \(-0.754282\pi\)
0.962357 + 0.271789i \(0.0876151\pi\)
\(594\) 29986.0 35865.2i 2.07128 2.47738i
\(595\) −3317.25 + 7399.79i −0.228561 + 0.509852i
\(596\) −32026.9 + 18490.8i −2.20113 + 1.27082i
\(597\) −4576.79 3006.32i −0.313761 0.206098i
\(598\) 3807.75i 0.260385i
\(599\) 16385.4i 1.11768i 0.829276 + 0.558840i \(0.188753\pi\)
−0.829276 + 0.558840i \(0.811247\pi\)
\(600\) 432.291 7498.67i 0.0294137 0.510220i
\(601\) 1449.23 836.712i 0.0983615 0.0567890i −0.450012 0.893022i \(-0.648580\pi\)
0.548374 + 0.836233i \(0.315247\pi\)
\(602\) 5958.77 4306.11i 0.403424 0.291535i
\(603\) −5407.70 + 7281.80i −0.365205 + 0.491771i
\(604\) −14949.7 + 25893.6i −1.00711 + 1.74436i
\(605\) 16578.7 28715.1i 1.11408 1.92964i
\(606\) 2877.98 49922.3i 0.192920 3.34646i
\(607\) 8214.09 4742.41i 0.549258 0.317114i −0.199565 0.979885i \(-0.563953\pi\)
0.748823 + 0.662770i \(0.230619\pi\)
\(608\) 2794.71 4840.58i 0.186415 0.322881i
\(609\) 20379.4 + 10584.2i 1.35602 + 0.704262i
\(610\) −16466.5 28520.9i −1.09297 1.89308i
\(611\) −95.6688 55.2344i −0.00633444 0.00365719i
\(612\) −18696.7 2162.88i −1.23491 0.142858i
\(613\) 791.346 + 1370.65i 0.0521405 + 0.0903100i 0.890918 0.454165i \(-0.150062\pi\)
−0.838777 + 0.544475i \(0.816729\pi\)
\(614\) 28823.4 1.89449
\(615\) 4818.62 + 9580.51i 0.315944 + 0.628168i
\(616\) −28882.1 + 64427.2i −1.88911 + 4.21404i
\(617\) −19948.8 11517.5i −1.30164 0.751500i −0.320952 0.947095i \(-0.604003\pi\)
−0.980685 + 0.195595i \(0.937336\pi\)
\(618\) −10052.8 + 15304.3i −0.654342 + 0.996164i
\(619\) 978.859 + 565.145i 0.0635601 + 0.0366964i 0.531443 0.847094i \(-0.321650\pi\)
−0.467883 + 0.883790i \(0.654983\pi\)
\(620\) −27816.3 + 16059.7i −1.80182 + 1.04028i
\(621\) 6012.64 2200.53i 0.388533 0.142197i
\(622\) 11249.5i 0.725180i
\(623\) 10871.4 24250.9i 0.699124 1.55953i
\(624\) −754.609 + 13089.7i −0.0484111 + 0.839756i
\(625\) 9029.08 + 15638.8i 0.577861 + 1.00088i
\(626\) −10318.9 −0.658830
\(627\) 2894.48 4406.52i 0.184361 0.280669i
\(628\) 56574.5i 3.59485i
\(629\) −1296.33 −0.0821750
\(630\) −415.910 + 31984.5i −0.0263020 + 2.02269i
\(631\) 6214.42 0.392064 0.196032 0.980598i \(-0.437194\pi\)
0.196032 + 0.980598i \(0.437194\pi\)
\(632\) 24563.5i 1.54602i
\(633\) 5824.73 + 335.790i 0.365738 + 0.0210845i
\(634\) 7601.06 0.476146
\(635\) 2466.93 + 4272.84i 0.154169 + 0.267028i
\(636\) 3245.85 + 2132.07i 0.202368 + 0.132928i
\(637\) −5187.14 1714.72i −0.322640 0.106656i
\(638\) 79514.3i 4.93417i
\(639\) −15529.7 11532.9i −0.961416 0.713979i
\(640\) −1834.55 + 1059.18i −0.113308 + 0.0654184i
\(641\) −14285.1 8247.49i −0.880228 0.508200i −0.00949468 0.999955i \(-0.503022\pi\)
−0.870734 + 0.491755i \(0.836356\pi\)
\(642\) −26287.3 1515.44i −1.61601 0.0931615i
\(643\) 11470.6 + 6622.54i 0.703507 + 0.406170i 0.808652 0.588287i \(-0.200197\pi\)
−0.105145 + 0.994457i \(0.533531\pi\)
\(644\) −13318.0 + 9624.28i −0.814912 + 0.588897i
\(645\) 4800.40 + 276.739i 0.293047 + 0.0168939i
\(646\) −2996.04 −0.182473
\(647\) 5765.87 + 9986.78i 0.350355 + 0.606833i 0.986312 0.164892i \(-0.0527275\pi\)
−0.635956 + 0.771725i \(0.719394\pi\)
\(648\) −41825.3 + 12629.7i −2.53557 + 0.765652i
\(649\) 6857.61 + 3959.24i 0.414768 + 0.239467i
\(650\) 1006.20 + 1742.79i 0.0607177 + 0.105166i
\(651\) 10974.4 7006.10i 0.660706 0.421799i
\(652\) 22039.2 38173.0i 1.32381 2.29290i
\(653\) 11889.2 6864.22i 0.712495 0.411359i −0.0994890 0.995039i \(-0.531721\pi\)
0.811984 + 0.583679i \(0.198387\pi\)
\(654\) −34116.7 22409.9i −2.03986 1.33991i
\(655\) 16694.2 28915.3i 0.995874 1.72491i
\(656\) 13387.4 23187.6i 0.796782 1.38007i
\(657\) −2599.01 + 22466.7i −0.154333 + 1.33411i
\(658\) 68.6264 + 669.363i 0.00406586 + 0.0396573i
\(659\) −104.852 + 60.5365i −0.00619797 + 0.00357840i −0.503096 0.864231i \(-0.667806\pi\)
0.496898 + 0.867809i \(0.334472\pi\)
\(660\) −70100.7 + 35257.9i −4.13434 + 2.07941i
\(661\) 27841.9i 1.63831i −0.573571 0.819156i \(-0.694442\pi\)
0.573571 0.819156i \(-0.305558\pi\)
\(662\) 6227.68i 0.365628i
\(663\) 2651.16 1333.43i 0.155298 0.0781087i
\(664\) −14083.7 + 8131.23i −0.823123 + 0.475230i
\(665\) 367.917 + 3588.56i 0.0214544 + 0.209261i
\(666\) −4692.79 + 2030.87i −0.273036 + 0.118160i
\(667\) −5445.07 + 9431.14i −0.316093 + 0.547489i
\(668\) 13056.5 22614.6i 0.756247 1.30986i
\(669\) −19311.4 12684.9i −1.11602 0.733074i
\(670\) 18610.1 10744.5i 1.07309 0.619548i
\(671\) −16374.3 + 28361.2i −0.942062 + 1.63170i
\(672\) 28424.0 18146.0i 1.63166 1.04166i
\(673\) 10610.3 + 18377.6i 0.607724 + 1.05261i 0.991615 + 0.129230i \(0.0412507\pi\)
−0.383890 + 0.923379i \(0.625416\pi\)
\(674\) 28841.0 + 16651.4i 1.64824 + 0.951613i
\(675\) −2170.47 + 2596.02i −0.123765 + 0.148031i
\(676\) 18889.8 + 32718.2i 1.07475 + 1.86152i
\(677\) −10357.6 −0.587997 −0.293999 0.955806i \(-0.594986\pi\)
−0.293999 + 0.955806i \(0.594986\pi\)
\(678\) −37741.7 2175.78i −2.13785 0.123245i
\(679\) −7507.79 + 5425.51i −0.424333 + 0.306645i
\(680\) 22726.2 + 13121.0i 1.28163 + 0.739952i
\(681\) 245.036 + 14.1261i 0.0137882 + 0.000794878i
\(682\) 39042.9 + 22541.4i 2.19213 + 1.26562i
\(683\) 5821.72 3361.17i 0.326152 0.188304i −0.327979 0.944685i \(-0.606368\pi\)
0.654131 + 0.756381i \(0.273034\pi\)
\(684\) −7683.88 + 3325.30i −0.429533 + 0.185886i
\(685\) 10477.2i 0.584401i
\(686\) 10040.5 + 31725.8i 0.558816 + 1.76574i
\(687\) 14345.7 + 9423.17i 0.796687 + 0.523314i
\(688\) −6002.53 10396.7i −0.332623 0.576119i
\(689\) −612.314 −0.0338567
\(690\) −15144.1 873.042i −0.835544 0.0481683i
\(691\) 993.374i 0.0546884i 0.999626 + 0.0273442i \(0.00870502\pi\)
−0.999626 + 0.0273442i \(0.991295\pi\)
\(692\) −18323.4 −1.00657
\(693\) 27751.1 15544.6i 1.52118 0.852076i
\(694\) −58287.4 −3.18812
\(695\) 28233.0i 1.54092i
\(696\) 40798.4 62111.1i 2.22193 3.38264i
\(697\) −6060.11 −0.329330
\(698\) 7011.24 + 12143.8i 0.380200 + 0.658525i
\(699\) 1387.81 24073.5i 0.0750958 1.30264i
\(700\) 3552.39 7924.31i 0.191811 0.427872i
\(701\) 3345.02i 0.180228i 0.995931 + 0.0901138i \(0.0287231\pi\)
−0.995931 + 0.0901138i \(0.971277\pi\)
\(702\) 7508.35 8980.47i 0.403682 0.482829i
\(703\) −499.406 + 288.332i −0.0267930 + 0.0154689i
\(704\) 31305.0 + 18074.0i 1.67593 + 0.967597i
\(705\) −241.612 + 367.827i −0.0129073 + 0.0196499i
\(706\) 34155.1 + 19719.5i 1.82074 + 1.05121i
\(707\) 13917.9 31046.8i 0.740365 1.65153i
\(708\) −5650.37 11234.2i −0.299935 0.596339i
\(709\) −5556.67 −0.294337 −0.147169 0.989111i \(-0.547016\pi\)
−0.147169 + 0.989111i \(0.547016\pi\)
\(710\) 22914.5 + 39689.2i 1.21122 + 2.09790i
\(711\) 6597.68 8884.17i 0.348006 0.468611i
\(712\) −74479.3 43000.6i −3.92027 2.26337i
\(713\) 3087.24 + 5347.25i 0.162157 + 0.280864i
\(714\) −16041.4 8331.27i −0.840804 0.436681i
\(715\) 6186.11 10714.7i 0.323563 0.560427i
\(716\) −1224.47 + 706.947i −0.0639113 + 0.0368992i
\(717\) 1312.65 22769.7i 0.0683708 1.18598i
\(718\) −27248.6 + 47196.0i −1.41631 + 2.45312i
\(719\) 11984.2 20757.2i 0.621605 1.07665i −0.367582 0.929991i \(-0.619814\pi\)
0.989187 0.146660i \(-0.0468524\pi\)
\(720\) 51887.0 + 6002.42i 2.68572 + 0.310690i
\(721\) −10097.9 + 7297.25i −0.521588 + 0.376926i
\(722\) 29962.3 17298.7i 1.54443 0.891679i
\(723\) −332.349 + 5765.04i −0.0170957 + 0.296548i
\(724\) 36165.6i 1.85647i
\(725\) 5755.47i 0.294832i
\(726\) 61773.7 + 40576.8i 3.15790 + 2.07430i
\(727\) −28778.8 + 16615.4i −1.46815 + 0.847637i −0.999363 0.0356749i \(-0.988642\pi\)
−0.468786 + 0.883312i \(0.655309\pi\)
\(728\) −7231.94 + 16132.3i −0.368178 + 0.821294i
\(729\) 18519.8 + 6666.21i 0.940902 + 0.338678i
\(730\) 26791.6 46404.5i 1.35836 2.35275i
\(731\) −1358.59 + 2353.15i −0.0687407 + 0.119062i
\(732\) 46461.6 23368.4i 2.34600 1.17995i
\(733\) −19526.7 + 11273.7i −0.983950 + 0.568084i −0.903460 0.428672i \(-0.858982\pi\)
−0.0804895 + 0.996755i \(0.525648\pi\)
\(734\) 31868.7 55198.2i 1.60258 2.77576i
\(735\) −8009.05 + 20237.0i −0.401929 + 1.01558i
\(736\) 7996.04 + 13849.5i 0.400459 + 0.693616i
\(737\) −18505.9 10684.4i −0.924929 0.534008i
\(738\) −21938.0 + 9493.95i −1.09424 + 0.473546i
\(739\) 10873.2 + 18833.0i 0.541242 + 0.937458i 0.998833 + 0.0482957i \(0.0153790\pi\)
−0.457591 + 0.889163i \(0.651288\pi\)
\(740\) 8582.80 0.426365
\(741\) 724.763 1103.37i 0.0359310 0.0547009i
\(742\) 2184.52 + 3022.93i 0.108081 + 0.149562i
\(743\) −22091.4 12754.5i −1.09079 0.629766i −0.157000 0.987599i \(-0.550182\pi\)
−0.933786 + 0.357833i \(0.883516\pi\)
\(744\) −18931.7 37640.6i −0.932891 1.85480i
\(745\) −20117.1 11614.6i −0.989307 0.571176i
\(746\) −10056.7 + 5806.22i −0.493567 + 0.284961i
\(747\) 7277.85 + 841.920i 0.356469 + 0.0412373i
\(748\) 44341.9i 2.16751i
\(749\) −16348.1 7328.70i −0.797527 0.357523i
\(750\) −29956.2 + 15066.8i −1.45846 + 0.733548i
\(751\) −16281.1 28199.6i −0.791084 1.37020i −0.925296 0.379245i \(-0.876184\pi\)
0.134212 0.990953i \(-0.457150\pi\)
\(752\) 1098.76 0.0532812
\(753\) −2947.63 5860.56i −0.142653 0.283626i
\(754\) 19910.0i 0.961644i
\(755\) −18780.7 −0.905297
\(756\) −50387.9 3562.71i −2.42406 0.171395i
\(757\) −922.082 −0.0442717 −0.0221358 0.999755i \(-0.507047\pi\)
−0.0221358 + 0.999755i \(0.507047\pi\)
\(758\) 15484.1i 0.741965i
\(759\) 6777.80 + 13475.8i 0.324135 + 0.644454i
\(760\) 11673.6 0.557165
\(761\) −5138.37 8899.92i −0.244764 0.423944i 0.717301 0.696763i \(-0.245377\pi\)
−0.962065 + 0.272819i \(0.912044\pi\)
\(762\) −9824.95 + 4941.57i −0.467087 + 0.234927i
\(763\) −16267.2 22510.4i −0.771837 1.06806i
\(764\) 79.3516i 0.00375764i
\(765\) −4695.42 10849.8i −0.221913 0.512780i
\(766\) 33794.4 19511.2i 1.59405 0.920324i
\(767\) 1717.11 + 991.376i 0.0808362 + 0.0466708i
\(768\) 8492.64 + 16885.3i 0.399026 + 0.793353i
\(769\) 30344.0 + 17519.1i 1.42293 + 0.821528i 0.996548 0.0830156i \(-0.0264551\pi\)
0.426380 + 0.904544i \(0.359788\pi\)
\(770\) −74967.0 + 7685.98i −3.50860 + 0.359719i
\(771\) −15239.3 + 23200.2i −0.711842 + 1.08370i
\(772\) 85596.0 3.99050
\(773\) −4927.07 8533.94i −0.229256 0.397082i 0.728332 0.685224i \(-0.240296\pi\)
−0.957588 + 0.288142i \(0.906962\pi\)
\(774\) −1231.67 + 10647.0i −0.0571982 + 0.494441i
\(775\) −2826.04 1631.61i −0.130986 0.0756249i
\(776\) 14987.7 + 25959.4i 0.693333 + 1.20089i
\(777\) −3475.70 + 155.059i −0.160476 + 0.00715919i
\(778\) −15790.4 + 27349.9i −0.727654 + 1.26033i
\(779\) −2334.63 + 1347.90i −0.107377 + 0.0619943i
\(780\) −17552.9 + 8828.42i −0.805762 + 0.405267i
\(781\) 22786.2 39466.9i 1.04399 1.80824i
\(782\) 4286.03 7423.62i 0.195995 0.339473i
\(783\) −31439.0 + 11506.2i −1.43491 + 0.525155i
\(784\) 53208.2 11026.2i 2.42384 0.502288i
\(785\) 30775.2 17768.1i 1.39925 0.807860i
\(786\) 62204.3 + 40859.6i 2.82284 + 1.85422i
\(787\) 21139.5i 0.957485i 0.877955 + 0.478742i \(0.158907\pi\)
−0.877955 + 0.478742i \(0.841093\pi\)
\(788\) 7580.18i 0.342681i
\(789\) −310.805 + 5391.32i −0.0140240 + 0.243265i
\(790\) −22705.2 + 13108.9i −1.02255 + 0.590371i
\(791\) −23471.6 10522.1i −1.05506 0.472974i
\(792\) −40881.3 94465.6i −1.83416 4.23824i
\(793\) −4100.05 + 7101.50i −0.183603 + 0.318010i
\(794\) −38647.8 + 66940.0i −1.72741 + 2.99196i
\(795\) −140.391 + 2435.28i −0.00626311 + 0.108642i
\(796\) −17742.6 + 10243.7i −0.790037 + 0.456128i
\(797\) 10049.6 17406.5i 0.446645 0.773612i −0.551520 0.834161i \(-0.685952\pi\)
0.998165 + 0.0605498i \(0.0192854\pi\)
\(798\) −8032.93 + 358.366i −0.356344 + 0.0158973i
\(799\) −124.344 215.371i −0.00550562 0.00953601i
\(800\) −7319.53 4225.93i −0.323480 0.186761i
\(801\) 15388.0 + 35557.5i 0.678787 + 1.56849i
\(802\) −9959.74 17250.8i −0.438517 0.759534i
\(803\) −53283.2 −2.34162
\(804\) 15248.0 + 30316.5i 0.668852 + 1.32983i
\(805\) −9418.12 4222.05i −0.412354 0.184854i
\(806\) 9776.16 + 5644.27i 0.427234 + 0.246664i
\(807\) 12087.8 18402.4i 0.527276 0.802719i
\(808\) −95350.9 55050.9i −4.15153 2.39688i
\(809\) 25583.5 14770.7i 1.11183 0.641914i 0.172525 0.985005i \(-0.444807\pi\)
0.939302 + 0.343091i \(0.111474\pi\)
\(810\) −33995.4 31921.1i −1.47466 1.38468i
\(811\) 13234.7i 0.573036i −0.958075 0.286518i \(-0.907502\pi\)
0.958075 0.286518i \(-0.0924978\pi\)
\(812\) 69637.4 50323.5i 3.00960 2.17489i
\(813\) 2065.51 35829.0i 0.0891029 1.54561i
\(814\) −6023.41 10432.8i −0.259362 0.449227i
\(815\) 27687.0 1.18998
\(816\) −16205.1 + 24670.4i −0.695209 + 1.05838i
\(817\) 1208.72i 0.0517599i
\(818\) −22821.4 −0.975467
\(819\) 6948.75 3892.28i 0.296470 0.166065i
\(820\) 40123.0 1.70873
\(821\) 6483.12i 0.275594i 0.990461 + 0.137797i \(0.0440021\pi\)
−0.990461 + 0.137797i \(0.955998\pi\)
\(822\) 23315.3 + 1344.10i 0.989311 + 0.0570329i
\(823\) 15499.1 0.656459 0.328230 0.944598i \(-0.393548\pi\)
0.328230 + 0.944598i \(0.393548\pi\)
\(824\) 20158.3 + 34915.1i 0.852241 + 1.47612i
\(825\) −6663.17 4376.79i −0.281190 0.184703i
\(826\) −1231.74 12014.1i −0.0518859 0.506081i
\(827\) 7987.02i 0.335835i −0.985801 0.167918i \(-0.946296\pi\)
0.985801 0.167918i \(-0.0537043\pi\)
\(828\) 2752.81 23796.3i 0.115540 0.998766i
\(829\) 38491.6 22223.1i 1.61263 0.931051i 0.623870 0.781528i \(-0.285559\pi\)
0.988758 0.149524i \(-0.0477740\pi\)
\(830\) −15032.2 8678.85i −0.628645 0.362948i
\(831\) −12722.3 733.427i −0.531084 0.0306165i
\(832\) 7838.63 + 4525.64i 0.326629 + 0.188580i
\(833\) −8182.78 9181.71i −0.340356 0.381906i
\(834\) −62827.7 3621.96i −2.60857 0.150381i
\(835\) 16402.4 0.679796
\(836\) −9862.60 17082.5i −0.408021 0.706712i
\(837\) −3262.88 + 18698.9i −0.134745 + 0.772199i
\(838\) 44232.5 + 25537.6i 1.82337 + 1.05272i
\(839\) 8987.71 + 15567.2i 0.369833 + 0.640570i 0.989539 0.144264i \(-0.0460815\pi\)
−0.619706 + 0.784834i \(0.712748\pi\)
\(840\) 62502.7 + 32461.5i 2.56732 + 1.33337i
\(841\) 16276.8 28192.2i 0.667381 1.15594i
\(842\) −38521.9 + 22240.6i −1.57667 + 0.910289i
\(843\) 36127.9 + 23731.0i 1.47605 + 0.969561i
\(844\) 10914.4 18904.4i 0.445131 0.770989i
\(845\) −11865.3 + 20551.3i −0.483051 + 0.836669i
\(846\) −787.540 584.853i −0.0320049 0.0237679i
\(847\) 29454.3 + 40758.7i 1.19488 + 1.65347i
\(848\) 5274.31 3045.13i 0.213586 0.123314i
\(849\) −31806.6 + 15997.5i −1.28575 + 0.646680i
\(850\) 4530.36i 0.182812i
\(851\) 1649.91i 0.0664610i
\(852\) −64655.2 + 32519.0i −2.59982 + 1.30761i
\(853\) 21062.1 12160.2i 0.845431 0.488110i −0.0136759 0.999906i \(-0.504353\pi\)
0.859106 + 0.511797i \(0.171020\pi\)
\(854\) 49686.9 5094.14i 1.99093 0.204119i
\(855\) −4222.13 3135.49i −0.168882 0.125417i
\(856\) −28987.9 + 50208.4i −1.15746 + 2.00478i
\(857\) −11448.4 + 19829.2i −0.456324 + 0.790377i −0.998763 0.0497185i \(-0.984168\pi\)
0.542439 + 0.840095i \(0.317501\pi\)
\(858\) 23050.0 + 15140.7i 0.917150 + 0.602441i
\(859\) −7592.10 + 4383.30i −0.301559 + 0.174105i −0.643143 0.765746i \(-0.722370\pi\)
0.341584 + 0.939851i \(0.389037\pi\)
\(860\) 8995.03 15579.9i 0.356661 0.617754i
\(861\) −16248.3 + 724.871i −0.643136 + 0.0286917i
\(862\) −10835.2 18767.2i −0.428132 0.741546i
\(863\) −6585.65 3802.22i −0.259766 0.149976i 0.364462 0.931218i \(-0.381253\pi\)
−0.624228 + 0.781242i \(0.714586\pi\)
\(864\) −8450.96 + 48430.9i −0.332763 + 1.90700i
\(865\) −5754.73 9967.49i −0.226204 0.391798i
\(866\) −5266.95 −0.206672
\(867\) −18816.7 1084.77i −0.737082 0.0424921i
\(868\) −4968.29 48459.4i −0.194280 1.89495i
\(869\) 22578.1 + 13035.5i 0.881369 + 0.508859i
\(870\) 79185.5 + 4564.97i 3.08579 + 0.177893i
\(871\) −4633.78 2675.32i −0.180264 0.104075i
\(872\) −77833.6 + 44937.2i −3.02268 + 1.74514i
\(873\) 1551.85 13414.7i 0.0601628 0.520068i
\(874\) 3813.22i 0.147579i
\(875\) −22696.1 + 2326.92i −0.876879 + 0.0899019i
\(876\) 70724.7 + 46456.4i 2.72781 + 1.79180i
\(877\) 18628.0 + 32264.7i 0.717244 + 1.24230i 0.962087 + 0.272741i \(0.0879302\pi\)
−0.244843 + 0.969563i \(0.578736\pi\)
\(878\) 43115.1 1.65725
\(879\) −4033.21 232.510i −0.154763 0.00892194i
\(880\) 123058.i 4.71395i
\(881\) −1271.30 −0.0486164 −0.0243082 0.999705i \(-0.507738\pi\)
−0.0243082 + 0.999705i \(0.507738\pi\)
\(882\) −44006.5 20418.9i −1.68002 0.779525i
\(883\) 29075.5 1.10812 0.554060 0.832477i \(-0.313078\pi\)
0.554060 + 0.832477i \(0.313078\pi\)
\(884\) 11103.0i 0.422437i
\(885\) 4336.57 6601.95i 0.164715 0.250760i
\(886\) −7090.70 −0.268868
\(887\) 14253.6 + 24688.0i 0.539560 + 0.934546i 0.998928 + 0.0462996i \(0.0147429\pi\)
−0.459367 + 0.888246i \(0.651924\pi\)
\(888\) −647.976 + 11240.0i −0.0244872 + 0.424764i
\(889\) −7443.82 + 763.177i −0.280830 + 0.0287921i
\(890\) 91793.3i 3.45721i
\(891\) −10587.2 + 45147.2i −0.398073 + 1.69752i
\(892\) −74863.3 + 43222.4i −2.81010 + 1.62241i
\(893\) −95.8063 55.3138i −0.00359018 0.00207279i
\(894\) 28427.1 43277.1i 1.06347 1.61902i
\(895\) −769.126 444.055i −0.0287252 0.0165845i
\(896\) −327.671 3196.02i −0.0122173 0.119165i
\(897\) 1697.13 + 3374.28i 0.0631722 + 0.125601i
\(898\) −59416.4 −2.20796
\(899\) −16142.6 27959.8i −0.598871 1.03728i
\(900\) 5028.25 + 11618.9i 0.186231 + 0.430330i
\(901\) −1193.77 689.224i −0.0441402 0.0254843i
\(902\) −28158.3 48771.7i −1.03943 1.80035i
\(903\) −3361.17 + 6471.75i −0.123868 + 0.238501i
\(904\) −41619.0 + 72086.1i −1.53122 + 2.65216i
\(905\) −19673.3 + 11358.4i −0.722610 + 0.417199i
\(906\) 2409.34 41793.2i 0.0883497 1.53254i
\(907\) −13155.3 + 22785.7i −0.481604 + 0.834163i −0.999777 0.0211130i \(-0.993279\pi\)
0.518173 + 0.855276i \(0.326612\pi\)
\(908\) 459.150 795.271i 0.0167813 0.0290661i
\(909\) 19700.2 + 45521.9i 0.718829 + 1.66102i
\(910\) −18771.4 + 1924.53i −0.683808 + 0.0701073i
\(911\) −12914.3 + 7456.08i −0.469671 + 0.271164i −0.716102 0.697996i \(-0.754075\pi\)
0.246431 + 0.969160i \(0.420742\pi\)
\(912\) −755.694 + 13108.5i −0.0274381 + 0.475950i
\(913\) 17260.5i 0.625673i
\(914\) 38070.2i 1.37774i
\(915\) 27303.8 + 17934.9i 0.986489 + 0.647987i
\(916\) 55613.3 32108.4i 2.00602 1.15818i
\(917\) 29659.7 + 41042.9i 1.06810 + 1.47803i
\(918\) 24746.8 9056.94i 0.889724 0.325625i
\(919\) 17879.8 30968.8i 0.641786 1.11161i −0.343248 0.939245i \(-0.611527\pi\)
0.985034 0.172361i \(-0.0551396\pi\)
\(920\) −16699.8 + 28925.0i −0.598453 + 1.03655i
\(921\) −25542.2 + 12846.7i −0.913836 + 0.459624i
\(922\) 56400.7 32562.9i 2.01460 1.16313i
\(923\) 5705.57 9882.33i 0.203468 0.352417i
\(924\) −5303.89 118889.i −0.188837 4.23285i
\(925\) 435.992 + 755.160i 0.0154976 + 0.0268427i
\(926\) 13106.2 + 7566.85i 0.465114 + 0.268534i
\(927\) 2087.22 18042.6i 0.0739518 0.639264i
\(928\) −41809.8 72416.7i −1.47896 2.56163i
\(929\) 34325.5 1.21225 0.606127 0.795368i \(-0.292722\pi\)
0.606127 + 0.795368i \(0.292722\pi\)
\(930\) 24689.7 37587.4i 0.870546 1.32531i
\(931\) −5194.59 1717.18i −0.182863 0.0604495i
\(932\) −78131.3 45109.1i −2.74600 1.58541i
\(933\) 5013.93 + 9968.82i 0.175936 + 0.349801i
\(934\) −11915.2 6879.26i −0.417428 0.241002i
\(935\) 24121.0 13926.3i 0.843680 0.487099i
\(936\) −10236.5 23653.7i −0.357468 0.826012i
\(937\) 14515.1i 0.506071i 0.967457 + 0.253036i \(0.0814289\pi\)
−0.967457 + 0.253036i \(0.918571\pi\)
\(938\) 3323.96 + 32421.1i 0.115705 + 1.12856i
\(939\) 9144.23 4599.19i 0.317796 0.159839i
\(940\) 823.265 + 1425.94i 0.0285659 + 0.0494776i
\(941\) −23852.5 −0.826323 −0.413162 0.910658i \(-0.635576\pi\)
−0.413162 + 0.910658i \(0.635576\pi\)
\(942\) 35591.7 + 70764.4i 1.23104 + 2.44759i
\(943\) 7713.04i 0.266353i
\(944\) −19721.0 −0.679942
\(945\) −13887.1 28528.8i −0.478039 0.982055i
\(946\) −25250.9 −0.867839
\(947\) 41604.5i 1.42763i −0.700335 0.713814i \(-0.746966\pi\)
0.700335 0.713814i \(-0.253034\pi\)
\(948\) −18603.4 36987.7i −0.637352 1.26720i
\(949\) −13341.9 −0.456370
\(950\) 1007.65 + 1745.30i 0.0344131 + 0.0596053i
\(951\) −6735.76 + 3387.82i −0.229676 + 0.115518i
\(952\) −32258.0 + 23311.3i −1.09820 + 0.793617i
\(953\) 21486.0i 0.730326i 0.930944 + 0.365163i \(0.118987\pi\)
−0.930944 + 0.365163i \(0.881013\pi\)
\(954\) −5401.28 624.834i −0.183305 0.0212052i
\(955\) −43.1654 + 24.9216i −0.00146262 + 0.000844443i
\(956\) −73899.8 42666.0i −2.50009 1.44343i
\(957\) −35439.8 70462.4i −1.19708 2.38007i
\(958\) 3455.36 + 1994.95i 0.116532 + 0.0672797i
\(959\) 14499.8 + 6500.11i 0.488241 + 0.218873i
\(960\) 19796.5 30138.0i 0.665551 1.01323i
\(961\) 11486.0 0.385553
\(962\) −1508.23 2612.34i −0.0505482 0.0875521i
\(963\) 23970.2 10373.5i 0.802108 0.347123i
\(964\) 18710.6 + 10802.6i 0.625133 + 0.360921i
\(965\) 26882.7 + 46562.3i 0.896773 + 1.55326i
\(966\) 10603.7 20416.8i 0.353175 0.680019i
\(967\) −8872.69 + 15367.9i −0.295064 + 0.511065i −0.975000 0.222206i \(-0.928674\pi\)
0.679936 + 0.733271i \(0.262007\pi\)
\(968\) 140930. 81366.0i 4.67940 2.70165i
\(969\) 2654.97 1335.34i 0.0880184 0.0442698i
\(970\) −15997.1 + 27707.7i −0.529520 + 0.917156i
\(971\) −17856.1 + 30927.8i −0.590145 + 1.02216i 0.404067 + 0.914729i \(0.367596\pi\)
−0.994212 + 0.107432i \(0.965737\pi\)
\(972\) 53415.4 50694.7i 1.76265 1.67287i
\(973\) −39072.6 17515.9i −1.28737 0.577115i
\(974\) 78733.2 45456.6i 2.59012 1.49541i
\(975\) −1668.43 1095.93i −0.0548025 0.0359977i
\(976\) 81560.7i 2.67489i
\(977\) 40832.8i 1.33711i −0.743662 0.668555i \(-0.766913\pi\)
0.743662 0.668555i \(-0.233087\pi\)
\(978\) −3551.91 + 61612.7i −0.116133 + 2.01447i
\(979\) −79050.2 + 45639.7i −2.58065 + 1.48994i
\(980\) 54176.9 + 60790.6i 1.76594 + 1.98152i
\(981\) 40221.0 + 4652.87i 1.30903 + 0.151432i
\(982\) −52294.3 + 90576.4i −1.69937 + 2.94339i
\(983\) −14795.7 + 25626.9i −0.480070 + 0.831506i −0.999739 0.0228618i \(-0.992722\pi\)
0.519668 + 0.854368i \(0.326056\pi\)
\(984\) −3029.17 + 52545.0i −0.0981367 + 1.70231i
\(985\) −4123.45 + 2380.67i −0.133385 + 0.0770097i
\(986\) −22410.8 + 38816.7i −0.723840 + 1.25373i
\(987\) −359.152 562.576i −0.0115825 0.0181428i
\(988\) −2469.55 4277.38i −0.0795211 0.137735i
\(989\) −2994.99 1729.16i −0.0962944 0.0555956i
\(990\) 65502.1 88202.5i 2.10282 2.83157i
\(991\) −21470.6 37188.1i −0.688230 1.19205i −0.972410 0.233278i \(-0.925055\pi\)
0.284181 0.958771i \(-0.408278\pi\)
\(992\) −47410.5 −1.51742
\(993\) 2775.70 + 5518.72i 0.0887052 + 0.176366i
\(994\) −69143.4 + 7088.92i −2.20633 + 0.226204i
\(995\) −11144.7 6434.37i −0.355085 0.205008i
\(996\) 15049.0 22910.5i 0.478761 0.728861i
\(997\) −37664.7 21745.7i −1.19644 0.690767i −0.236683 0.971587i \(-0.576060\pi\)
−0.959760 + 0.280820i \(0.909394\pi\)
\(998\) −6993.64 + 4037.78i −0.221823 + 0.128070i
\(999\) 3253.40 3891.27i 0.103036 0.123238i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 63.4.i.a.5.22 44
3.2 odd 2 189.4.i.a.152.1 44
7.3 odd 6 63.4.s.a.59.1 yes 44
9.2 odd 6 63.4.s.a.47.1 yes 44
9.7 even 3 189.4.s.a.89.22 44
21.17 even 6 189.4.s.a.17.22 44
63.38 even 6 inner 63.4.i.a.38.1 yes 44
63.52 odd 6 189.4.i.a.143.22 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.i.a.5.22 44 1.1 even 1 trivial
63.4.i.a.38.1 yes 44 63.38 even 6 inner
63.4.s.a.47.1 yes 44 9.2 odd 6
63.4.s.a.59.1 yes 44 7.3 odd 6
189.4.i.a.143.22 44 63.52 odd 6
189.4.i.a.152.1 44 3.2 odd 2
189.4.s.a.17.22 44 21.17 even 6
189.4.s.a.89.22 44 9.7 even 3