Properties

Label 27.6.e.a.4.11
Level $27$
Weight $6$
Character 27.4
Analytic conductor $4.330$
Analytic rank $0$
Dimension $84$
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] = [27,6,Mod(4,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 27.e (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.33036313495\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(14\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 4.11
Character \(\chi\) \(=\) 27.4
Dual form 27.6.e.a.7.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.36004 + 1.95090i) q^{2} +(9.76327 + 12.1523i) q^{3} +(0.410645 + 0.344572i) q^{4} +(-14.4659 + 82.0402i) q^{5} +(28.6236 + 84.1840i) q^{6} +(131.197 - 110.088i) q^{7} +(-89.7358 - 155.427i) q^{8} +(-52.3572 + 237.292i) q^{9} +O(q^{10})\) \(q+(5.36004 + 1.95090i) q^{2} +(9.76327 + 12.1523i) q^{3} +(0.410645 + 0.344572i) q^{4} +(-14.4659 + 82.0402i) q^{5} +(28.6236 + 84.1840i) q^{6} +(131.197 - 110.088i) q^{7} +(-89.7358 - 155.427i) q^{8} +(-52.3572 + 237.292i) q^{9} +(-237.590 + 411.517i) q^{10} +(-10.5058 - 59.5813i) q^{11} +(-0.178108 + 8.35443i) q^{12} +(790.371 - 287.672i) q^{13} +(917.994 - 334.122i) q^{14} +(-1138.21 + 625.186i) q^{15} +(-180.745 - 1025.05i) q^{16} +(-173.221 + 300.027i) q^{17} +(-743.570 + 1169.75i) q^{18} +(-1016.68 - 1760.95i) q^{19} +(-34.2091 + 28.7048i) q^{20} +(2618.74 + 519.536i) q^{21} +(59.9254 - 339.854i) q^{22} +(-1790.96 - 1502.79i) q^{23} +(1012.68 - 2607.97i) q^{24} +(-3584.79 - 1304.76i) q^{25} +4797.64 q^{26} +(-3394.83 + 1680.49i) q^{27} +91.8086 q^{28} +(7235.39 + 2633.47i) q^{29} +(-7320.54 + 1130.49i) q^{30} +(-2053.60 - 1723.18i) q^{31} +(33.6971 - 191.106i) q^{32} +(621.479 - 709.377i) q^{33} +(-1513.79 + 1270.22i) q^{34} +(7133.73 + 12356.0i) q^{35} +(-103.264 + 79.4021i) q^{36} +(-5490.42 + 9509.69i) q^{37} +(-2014.04 - 11422.2i) q^{38} +(11212.5 + 6796.22i) q^{39} +(14049.4 - 5113.55i) q^{40} +(-8626.75 + 3139.88i) q^{41} +(13023.0 + 7893.61i) q^{42} +(1320.52 + 7489.05i) q^{43} +(16.2159 - 28.0867i) q^{44} +(-18710.1 - 7728.04i) q^{45} +(-6667.81 - 11549.0i) q^{46} +(-5301.15 + 4448.19i) q^{47} +(10692.1 - 12204.3i) q^{48} +(2174.96 - 12334.8i) q^{49} +(-16669.2 - 13987.1i) q^{50} +(-5337.23 + 824.214i) q^{51} +(423.685 + 154.209i) q^{52} -1428.94 q^{53} +(-21474.9 + 2384.54i) q^{54} +5040.03 q^{55} +(-28883.7 - 10512.8i) q^{56} +(11473.4 - 29547.6i) q^{57} +(33644.4 + 28231.0i) q^{58} +(6586.05 - 37351.3i) q^{59} +(-682.822 - 135.466i) q^{60} +(5320.79 - 4464.67i) q^{61} +(-7645.65 - 13242.7i) q^{62} +(19253.9 + 36896.0i) q^{63} +(-16100.4 + 27886.7i) q^{64} +(12167.2 + 69003.6i) q^{65} +(4715.08 - 2589.85i) q^{66} +(15558.7 - 5662.90i) q^{67} +(-174.513 + 63.5176i) q^{68} +(776.789 - 36436.4i) q^{69} +(14131.9 + 80145.7i) q^{70} +(2175.24 - 3767.63i) q^{71} +(41580.0 - 13155.9i) q^{72} +(-24178.2 - 41877.8i) q^{73} +(-47981.3 + 40261.1i) q^{74} +(-19143.4 - 56302.1i) q^{75} +(189.277 - 1073.44i) q^{76} +(-7937.50 - 6660.35i) q^{77} +(46840.7 + 58302.4i) q^{78} +(-21195.8 - 7714.64i) q^{79} +86710.2 q^{80} +(-53566.5 - 24847.9i) q^{81} -52365.3 q^{82} +(-34164.4 - 12434.8i) q^{83} +(896.352 + 1115.69i) q^{84} +(-22108.5 - 18551.2i) q^{85} +(-7532.31 + 42717.9i) q^{86} +(38638.4 + 113638. i) q^{87} +(-8317.79 + 6979.45i) q^{88} +(22962.3 + 39771.9i) q^{89} +(-85210.5 - 77924.1i) q^{90} +(72025.6 - 124752. i) q^{91} +(-217.627 - 1234.23i) q^{92} +(890.706 - 41779.8i) q^{93} +(-37092.3 + 13500.5i) q^{94} +(159176. - 57935.2i) q^{95} +(2651.37 - 1456.32i) q^{96} +(27918.1 + 158332. i) q^{97} +(35721.7 - 61871.9i) q^{98} +(14688.2 + 626.563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 93 q^{5} - 126 q^{6} - 6 q^{7} + 573 q^{8} + 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 93 q^{5} - 126 q^{6} - 6 q^{7} + 573 q^{8} + 324 q^{9} - 3 q^{10} + 111 q^{11} - 2769 q^{12} - 6 q^{13} - 1641 q^{14} + 1989 q^{15} + 90 q^{16} + 3465 q^{17} - 99 q^{18} - 3 q^{19} + 9987 q^{20} + 5424 q^{21} - 2850 q^{22} - 7716 q^{23} - 18486 q^{24} + 4953 q^{25} - 7806 q^{26} - 8109 q^{27} - 12 q^{28} - 20418 q^{29} - 6453 q^{30} - 6657 q^{31} + 51192 q^{32} + 50634 q^{33} - 11394 q^{34} + 35868 q^{35} - 3600 q^{36} - 3 q^{37} - 44076 q^{38} - 13971 q^{39} + 12441 q^{40} - 79077 q^{41} - 64422 q^{42} - 9465 q^{43} + 110757 q^{44} + 92493 q^{45} - 3 q^{46} + 103557 q^{47} + 134049 q^{48} + 5484 q^{49} - 105513 q^{50} - 124866 q^{51} + 68625 q^{52} - 206406 q^{53} - 350946 q^{54} - 12 q^{55} - 147237 q^{56} + 67767 q^{57} - 9753 q^{58} + 116484 q^{59} + 241290 q^{60} - 70116 q^{61} + 246066 q^{62} + 135981 q^{63} - 86019 q^{64} - 19815 q^{65} - 32931 q^{66} + 48117 q^{67} - 48105 q^{68} + 25263 q^{69} + 270111 q^{70} + 279531 q^{71} + 441684 q^{72} - 27012 q^{73} + 233691 q^{74} + 18399 q^{75} - 125670 q^{76} - 345135 q^{77} - 520974 q^{78} - 216186 q^{79} - 924114 q^{80} - 428616 q^{81} - 12 q^{82} - 370401 q^{83} - 522390 q^{84} - 43731 q^{85} + 116682 q^{86} + 304173 q^{87} + 371418 q^{88} + 154827 q^{89} + 327366 q^{90} - 91002 q^{91} + 1279059 q^{92} + 890079 q^{93} + 11667 q^{94} + 1087671 q^{95} + 1165698 q^{96} - 420621 q^{97} + 463410 q^{98} - 28323 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.36004 + 1.95090i 0.947531 + 0.344873i 0.769135 0.639086i \(-0.220687\pi\)
0.178395 + 0.983959i \(0.442909\pi\)
\(3\) 9.76327 + 12.1523i 0.626314 + 0.779571i
\(4\) 0.410645 + 0.344572i 0.0128326 + 0.0107679i
\(5\) −14.4659 + 82.0402i −0.258774 + 1.46758i 0.527423 + 0.849603i \(0.323158\pi\)
−0.786197 + 0.617976i \(0.787953\pi\)
\(6\) 28.6236 + 84.1840i 0.324599 + 0.954666i
\(7\) 131.197 110.088i 1.01200 0.849168i 0.0233981 0.999726i \(-0.492551\pi\)
0.988601 + 0.150558i \(0.0481070\pi\)
\(8\) −89.7358 155.427i −0.495725 0.858621i
\(9\) −52.3572 + 237.292i −0.215462 + 0.976512i
\(10\) −237.590 + 411.517i −0.751324 + 1.30133i
\(11\) −10.5058 59.5813i −0.0261786 0.148466i 0.968917 0.247387i \(-0.0795720\pi\)
−0.995095 + 0.0989210i \(0.968461\pi\)
\(12\) −0.178108 + 8.35443i −0.000357052 + 0.0167480i
\(13\) 790.371 287.672i 1.29710 0.472105i 0.401047 0.916057i \(-0.368646\pi\)
0.896050 + 0.443952i \(0.146424\pi\)
\(14\) 917.994 334.122i 1.25176 0.455602i
\(15\) −1138.21 + 625.186i −1.30616 + 0.717433i
\(16\) −180.745 1025.05i −0.176508 1.00103i
\(17\) −173.221 + 300.027i −0.145371 + 0.251790i −0.929511 0.368794i \(-0.879771\pi\)
0.784140 + 0.620584i \(0.213104\pi\)
\(18\) −743.570 + 1169.75i −0.540929 + 0.850969i
\(19\) −1016.68 1760.95i −0.646103 1.11908i −0.984046 0.177916i \(-0.943064\pi\)
0.337943 0.941167i \(-0.390269\pi\)
\(20\) −34.2091 + 28.7048i −0.0191235 + 0.0160465i
\(21\) 2618.74 + 519.536i 1.29582 + 0.257079i
\(22\) 59.9254 339.854i 0.0263970 0.149705i
\(23\) −1790.96 1502.79i −0.705936 0.592351i 0.217520 0.976056i \(-0.430203\pi\)
−0.923456 + 0.383705i \(0.874648\pi\)
\(24\) 1012.68 2607.97i 0.358876 0.924219i
\(25\) −3584.79 1304.76i −1.14713 0.417522i
\(26\) 4797.64 1.39186
\(27\) −3394.83 + 1680.49i −0.896207 + 0.443636i
\(28\) 91.8086 0.0221304
\(29\) 7235.39 + 2633.47i 1.59760 + 0.581478i 0.978934 0.204179i \(-0.0654525\pi\)
0.618663 + 0.785657i \(0.287675\pi\)
\(30\) −7320.54 + 1130.49i −1.48505 + 0.229332i
\(31\) −2053.60 1723.18i −0.383806 0.322052i 0.430388 0.902644i \(-0.358377\pi\)
−0.814194 + 0.580592i \(0.802821\pi\)
\(32\) 33.6971 191.106i 0.00581724 0.0329912i
\(33\) 621.479 709.377i 0.0993440 0.113395i
\(34\) −1513.79 + 1270.22i −0.224579 + 0.188444i
\(35\) 7133.73 + 12356.0i 0.984343 + 1.70493i
\(36\) −103.264 + 79.4021i −0.0132799 + 0.0102112i
\(37\) −5490.42 + 9509.69i −0.659328 + 1.14199i 0.321462 + 0.946923i \(0.395826\pi\)
−0.980790 + 0.195067i \(0.937507\pi\)
\(38\) −2014.04 11422.2i −0.226261 1.28319i
\(39\) 11212.5 + 6796.22i 1.18043 + 0.715494i
\(40\) 14049.4 5113.55i 1.38837 0.505327i
\(41\) −8626.75 + 3139.88i −0.801471 + 0.291712i −0.710096 0.704105i \(-0.751348\pi\)
−0.0913750 + 0.995817i \(0.529126\pi\)
\(42\) 13023.0 + 7893.61i 1.13917 + 0.690483i
\(43\) 1320.52 + 7489.05i 0.108912 + 0.617669i 0.989586 + 0.143946i \(0.0459791\pi\)
−0.880674 + 0.473723i \(0.842910\pi\)
\(44\) 16.2159 28.0867i 0.00126273 0.00218710i
\(45\) −18710.1 7728.04i −1.37735 0.568903i
\(46\) −6667.81 11549.0i −0.464610 0.804729i
\(47\) −5301.15 + 4448.19i −0.350046 + 0.293724i −0.800809 0.598920i \(-0.795597\pi\)
0.450762 + 0.892644i \(0.351152\pi\)
\(48\) 10692.1 12204.3i 0.669823 0.764559i
\(49\) 2174.96 12334.8i 0.129408 0.733908i
\(50\) −16669.2 13987.1i −0.942951 0.791230i
\(51\) −5337.23 + 824.214i −0.287336 + 0.0443726i
\(52\) 423.685 + 154.209i 0.0217288 + 0.00790862i
\(53\) −1428.94 −0.0698753 −0.0349377 0.999389i \(-0.511123\pi\)
−0.0349377 + 0.999389i \(0.511123\pi\)
\(54\) −21474.9 + 2384.54i −1.00218 + 0.111281i
\(55\) 5040.03 0.224660
\(56\) −28883.7 10512.8i −1.23079 0.447970i
\(57\) 11473.4 29547.6i 0.467741 1.20458i
\(58\) 33644.4 + 28231.0i 1.31324 + 1.10194i
\(59\) 6586.05 37351.3i 0.246317 1.39693i −0.571096 0.820883i \(-0.693482\pi\)
0.817414 0.576051i \(-0.195407\pi\)
\(60\) −682.822 135.466i −0.0244867 0.00485795i
\(61\) 5320.79 4464.67i 0.183084 0.153626i −0.546639 0.837368i \(-0.684093\pi\)
0.729724 + 0.683742i \(0.239649\pi\)
\(62\) −7645.65 13242.7i −0.252601 0.437518i
\(63\) 19253.9 + 36896.0i 0.611176 + 1.17119i
\(64\) −16100.4 + 27886.7i −0.491346 + 0.851036i
\(65\) 12167.2 + 69003.6i 0.357197 + 2.02576i
\(66\) 4715.08 2589.85i 0.133238 0.0731838i
\(67\) 15558.7 5662.90i 0.423434 0.154118i −0.121509 0.992590i \(-0.538773\pi\)
0.544943 + 0.838473i \(0.316551\pi\)
\(68\) −174.513 + 63.5176i −0.00457674 + 0.00166580i
\(69\) 776.789 36436.4i 0.0196418 0.921325i
\(70\) 14131.9 + 80145.7i 0.344710 + 1.95495i
\(71\) 2175.24 3767.63i 0.0512108 0.0886996i −0.839284 0.543694i \(-0.817025\pi\)
0.890494 + 0.454994i \(0.150359\pi\)
\(72\) 41580.0 13155.9i 0.945263 0.299082i
\(73\) −24178.2 41877.8i −0.531026 0.919765i −0.999344 0.0362047i \(-0.988473\pi\)
0.468318 0.883560i \(-0.344860\pi\)
\(74\) −47981.3 + 40261.1i −1.01858 + 0.854686i
\(75\) −19143.4 56302.1i −0.392977 1.15577i
\(76\) 189.277 1073.44i 0.00375893 0.0213179i
\(77\) −7937.50 6660.35i −0.152566 0.128018i
\(78\) 46840.7 + 58302.4i 0.871739 + 1.08505i
\(79\) −21195.8 7714.64i −0.382105 0.139075i 0.143824 0.989603i \(-0.454060\pi\)
−0.525929 + 0.850529i \(0.676282\pi\)
\(80\) 86710.2 1.51476
\(81\) −53566.5 24847.9i −0.907153 0.420802i
\(82\) −52365.3 −0.860022
\(83\) −34164.4 12434.8i −0.544350 0.198127i 0.0551843 0.998476i \(-0.482425\pi\)
−0.599535 + 0.800349i \(0.704648\pi\)
\(84\) 896.352 + 1115.69i 0.0138606 + 0.0172522i
\(85\) −22108.5 18551.2i −0.331904 0.278500i
\(86\) −7532.31 + 42717.9i −0.109820 + 0.622821i
\(87\) 38638.4 + 113638.i 0.547294 + 1.60963i
\(88\) −8317.79 + 6979.45i −0.114499 + 0.0960759i
\(89\) 22962.3 + 39771.9i 0.307284 + 0.532232i 0.977767 0.209693i \(-0.0672464\pi\)
−0.670483 + 0.741925i \(0.733913\pi\)
\(90\) −85210.5 77924.1i −1.10889 1.01406i
\(91\) 72025.6 124752.i 0.911766 1.57922i
\(92\) −217.627 1234.23i −0.00268067 0.0152029i
\(93\) 890.706 41779.8i 0.0106789 0.500909i
\(94\) −37092.3 + 13500.5i −0.432977 + 0.157591i
\(95\) 159176. 57935.2i 1.80954 0.658617i
\(96\) 2651.37 1456.32i 0.0293624 0.0161279i
\(97\) 27918.1 + 158332.i 0.301271 + 1.70859i 0.640559 + 0.767909i \(0.278703\pi\)
−0.339288 + 0.940683i \(0.610186\pi\)
\(98\) 35721.7 61871.9i 0.375723 0.650771i
\(99\) 14688.2 + 626.563i 0.150620 + 0.00642505i
\(100\) −1022.49 1771.01i −0.0102249 0.0177101i
\(101\) 33331.9 27968.8i 0.325129 0.272816i −0.465582 0.885005i \(-0.654155\pi\)
0.790712 + 0.612189i \(0.209711\pi\)
\(102\) −30215.7 5994.55i −0.287563 0.0570501i
\(103\) 24292.0 137767.i 0.225617 1.27954i −0.635886 0.771783i \(-0.719365\pi\)
0.861503 0.507753i \(-0.169524\pi\)
\(104\) −115636. 97030.5i −1.04836 0.879681i
\(105\) −80505.1 + 207326.i −0.712607 + 1.83519i
\(106\) −7659.17 2787.71i −0.0662090 0.0240981i
\(107\) −56007.5 −0.472919 −0.236459 0.971641i \(-0.575987\pi\)
−0.236459 + 0.971641i \(0.575987\pi\)
\(108\) −1973.12 479.678i −0.0162777 0.00395722i
\(109\) −151535. −1.22165 −0.610826 0.791765i \(-0.709162\pi\)
−0.610826 + 0.791765i \(0.709162\pi\)
\(110\) 27014.8 + 9832.58i 0.212873 + 0.0774793i
\(111\) −169169. + 26124.4i −1.30321 + 0.201251i
\(112\) −136559. 114587.i −1.02867 0.863155i
\(113\) −9672.57 + 54855.9i −0.0712600 + 0.404135i 0.928224 + 0.372021i \(0.121335\pi\)
−0.999484 + 0.0321142i \(0.989776\pi\)
\(114\) 119142. 135993.i 0.858626 0.980065i
\(115\) 149197. 125191.i 1.05200 0.882732i
\(116\) 2063.76 + 3574.53i 0.0142401 + 0.0246646i
\(117\) 26880.7 + 202611.i 0.181542 + 1.36835i
\(118\) 108170. 187356.i 0.715158 1.23869i
\(119\) 10303.2 + 58432.3i 0.0666967 + 0.378256i
\(120\) 199309. + 120807.i 1.26350 + 0.765843i
\(121\) 147899. 53830.8i 0.918336 0.334247i
\(122\) 37229.8 13550.5i 0.226460 0.0824245i
\(123\) −122382. 74179.5i −0.729382 0.442100i
\(124\) −249.543 1415.23i −0.00145744 0.00826555i
\(125\) 28734.3 49769.2i 0.164485 0.284896i
\(126\) 31221.2 + 235327.i 0.175195 + 1.32052i
\(127\) 82065.4 + 142141.i 0.451493 + 0.782008i 0.998479 0.0551334i \(-0.0175584\pi\)
−0.546986 + 0.837141i \(0.684225\pi\)
\(128\) −145460. + 122055.i −0.784727 + 0.658464i
\(129\) −78116.7 + 89165.0i −0.413304 + 0.471759i
\(130\) −69402.2 + 393599.i −0.360176 + 2.04266i
\(131\) 57894.8 + 48579.5i 0.294755 + 0.247329i 0.778157 0.628070i \(-0.216155\pi\)
−0.483402 + 0.875398i \(0.660599\pi\)
\(132\) 499.639 77.1579i 0.00249586 0.000385430i
\(133\) −327245. 119107.i −1.60414 0.583861i
\(134\) 94443.0 0.454368
\(135\) −88758.4 302822.i −0.419156 1.43006i
\(136\) 62176.4 0.288256
\(137\) 152174. + 55386.7i 0.692689 + 0.252118i 0.664286 0.747478i \(-0.268736\pi\)
0.0284028 + 0.999597i \(0.490958\pi\)
\(138\) 75247.2 193785.i 0.336351 0.866209i
\(139\) 288496. + 242077.i 1.26649 + 1.06271i 0.994959 + 0.100286i \(0.0319756\pi\)
0.271535 + 0.962429i \(0.412469\pi\)
\(140\) −1328.09 + 7532.00i −0.00572676 + 0.0324781i
\(141\) −105812. 20992.3i −0.448217 0.0889226i
\(142\) 19009.6 15951.0i 0.0791139 0.0663844i
\(143\) −25443.3 44069.1i −0.104048 0.180216i
\(144\) 252701. + 10779.6i 1.01555 + 0.0433207i
\(145\) −320717. + 555497.i −1.26678 + 2.19413i
\(146\) −47896.7 271636.i −0.185962 1.05464i
\(147\) 171131. 93997.1i 0.653183 0.358774i
\(148\) −5531.39 + 2013.26i −0.0207577 + 0.00755519i
\(149\) −49809.4 + 18129.1i −0.183800 + 0.0668977i −0.432281 0.901739i \(-0.642291\pi\)
0.248481 + 0.968637i \(0.420069\pi\)
\(150\) 7229.90 339129.i 0.0262364 1.23066i
\(151\) −38705.3 219509.i −0.138143 0.783447i −0.972619 0.232404i \(-0.925341\pi\)
0.834477 0.551043i \(-0.185770\pi\)
\(152\) −182466. + 316040.i −0.640578 + 1.10951i
\(153\) −62124.9 56812.6i −0.214554 0.196208i
\(154\) −29551.7 51185.0i −0.100411 0.173917i
\(155\) 171077. 143551.i 0.571955 0.479927i
\(156\) 2262.56 + 6654.34i 0.00744370 + 0.0218924i
\(157\) 72672.4 412145.i 0.235299 1.33445i −0.606684 0.794943i \(-0.707501\pi\)
0.841983 0.539504i \(-0.181388\pi\)
\(158\) −98560.0 82701.6i −0.314093 0.263555i
\(159\) −13951.1 17364.9i −0.0437639 0.0544728i
\(160\) 15190.9 + 5529.02i 0.0469119 + 0.0170745i
\(161\) −400408. −1.21741
\(162\) −238643. 237689.i −0.714432 0.711575i
\(163\) 239195. 0.705154 0.352577 0.935783i \(-0.385306\pi\)
0.352577 + 0.935783i \(0.385306\pi\)
\(164\) −4624.44 1683.16i −0.0134261 0.00488670i
\(165\) 49207.2 + 61248.0i 0.140708 + 0.175139i
\(166\) −158864. 133302.i −0.447460 0.375463i
\(167\) −120668. + 684341.i −0.334811 + 1.89881i 0.0942756 + 0.995546i \(0.469947\pi\)
−0.429087 + 0.903263i \(0.641165\pi\)
\(168\) −154244. 453643.i −0.421635 1.24005i
\(169\) 257505. 216072.i 0.693535 0.581945i
\(170\) −82311.0 142567.i −0.218442 0.378352i
\(171\) 471090. 149053.i 1.23201 0.389808i
\(172\) −2038.25 + 3530.36i −0.00525335 + 0.00909908i
\(173\) −89777.4 509153.i −0.228061 1.29340i −0.856745 0.515739i \(-0.827517\pi\)
0.628684 0.777661i \(-0.283594\pi\)
\(174\) −14592.5 + 684484.i −0.0365391 + 1.71392i
\(175\) −613952. + 223460.i −1.51544 + 0.551576i
\(176\) −59175.1 + 21538.0i −0.143998 + 0.0524111i
\(177\) 518206. 284635.i 1.24328 0.682898i
\(178\) 45488.1 + 257976.i 0.107609 + 0.610280i
\(179\) −169167. + 293005.i −0.394623 + 0.683507i −0.993053 0.117668i \(-0.962458\pi\)
0.598430 + 0.801175i \(0.295791\pi\)
\(180\) −5020.35 9620.46i −0.0115492 0.0221317i
\(181\) 349422. + 605217.i 0.792783 + 1.37314i 0.924237 + 0.381818i \(0.124702\pi\)
−0.131454 + 0.991322i \(0.541965\pi\)
\(182\) 629438. 528161.i 1.40856 1.18192i
\(183\) 106204. + 21070.1i 0.234431 + 0.0465091i
\(184\) −72861.3 + 413217.i −0.158654 + 0.899774i
\(185\) −700753. 588002.i −1.50534 1.26313i
\(186\) 86282.3 222204.i 0.182869 0.470944i
\(187\) 19695.8 + 7168.69i 0.0411880 + 0.0149912i
\(188\) −3709.61 −0.00765479
\(189\) −260392. + 594205.i −0.530240 + 1.20999i
\(190\) 966213. 1.94173
\(191\) 117622. + 42810.9i 0.233295 + 0.0849123i 0.456022 0.889968i \(-0.349274\pi\)
−0.222728 + 0.974881i \(0.571496\pi\)
\(192\) −496081. + 76608.5i −0.971180 + 0.149977i
\(193\) 57597.5 + 48330.0i 0.111304 + 0.0933950i 0.696741 0.717323i \(-0.254633\pi\)
−0.585437 + 0.810718i \(0.699077\pi\)
\(194\) −159246. + 903130.i −0.303784 + 1.72284i
\(195\) −719762. + 821560.i −1.35551 + 1.54722i
\(196\) 5143.35 4315.79i 0.00956326 0.00802453i
\(197\) 75692.7 + 131104.i 0.138959 + 0.240685i 0.927103 0.374807i \(-0.122291\pi\)
−0.788144 + 0.615491i \(0.788958\pi\)
\(198\) 77507.2 + 32013.6i 0.140501 + 0.0580326i
\(199\) 120924. 209447.i 0.216461 0.374922i −0.737262 0.675607i \(-0.763882\pi\)
0.953724 + 0.300684i \(0.0972151\pi\)
\(200\) 118889. + 674256.i 0.210169 + 1.19193i
\(201\) 220721. + 133786.i 0.385348 + 0.233571i
\(202\) 233224. 84886.7i 0.402157 0.146373i
\(203\) 1.23918e6 451024.i 2.11054 0.768173i
\(204\) −2475.70 1500.60i −0.00416508 0.00252458i
\(205\) −132803. 753161.i −0.220710 1.25171i
\(206\) 398976. 691046.i 0.655056 1.13459i
\(207\) 450370. 346299.i 0.730540 0.561726i
\(208\) −437734. 758178.i −0.701539 1.21510i
\(209\) −94238.4 + 79075.4i −0.149232 + 0.125221i
\(210\) −835982. + 954219.i −1.30812 + 1.49314i
\(211\) 18660.3 105828.i 0.0288544 0.163642i −0.966976 0.254869i \(-0.917968\pi\)
0.995830 + 0.0912270i \(0.0290789\pi\)
\(212\) −586.786 492.372i −0.000896685 0.000752408i
\(213\) 67022.8 10350.2i 0.101222 0.0156314i
\(214\) −300203. 109265.i −0.448105 0.163097i
\(215\) −633506. −0.934662
\(216\) 565831. + 376848.i 0.825187 + 0.549581i
\(217\) −459128. −0.661888
\(218\) −812235. 295629.i −1.15755 0.421315i
\(219\) 272854. 702685.i 0.384433 0.990034i
\(220\) 2069.66 + 1736.65i 0.00288299 + 0.00241911i
\(221\) −50599.4 + 286964.i −0.0696891 + 0.395227i
\(222\) −957720. 190004.i −1.30424 0.258750i
\(223\) −374072. + 313883.i −0.503724 + 0.422674i −0.858914 0.512119i \(-0.828860\pi\)
0.355190 + 0.934794i \(0.384416\pi\)
\(224\) −16617.4 28782.2i −0.0221280 0.0383269i
\(225\) 497298. 782330.i 0.654878 1.03023i
\(226\) −158863. + 275160.i −0.206896 + 0.358355i
\(227\) 32422.3 + 183876.i 0.0417618 + 0.236843i 0.998543 0.0539667i \(-0.0171865\pi\)
−0.956781 + 0.290810i \(0.906075\pi\)
\(228\) 14892.8 8180.16i 0.0189731 0.0104214i
\(229\) −624170. + 227179.i −0.786528 + 0.286273i −0.703892 0.710307i \(-0.748556\pi\)
−0.0826360 + 0.996580i \(0.526334\pi\)
\(230\) 1.04394e6 379962.i 1.30123 0.473610i
\(231\) 3442.72 161486.i 0.00424494 0.199115i
\(232\) −239962. 1.36089e6i −0.292700 1.65998i
\(233\) 81499.7 141162.i 0.0983482 0.170344i −0.812653 0.582748i \(-0.801977\pi\)
0.911001 + 0.412404i \(0.135311\pi\)
\(234\) −251191. + 1.13844e6i −0.299892 + 1.35916i
\(235\) −288244. 499254.i −0.340480 0.589728i
\(236\) 15574.7 13068.8i 0.0182029 0.0152741i
\(237\) −113190. 332898.i −0.130899 0.384982i
\(238\) −58769.8 + 333300.i −0.0672530 + 0.381411i
\(239\) 1.06412e6 + 892905.i 1.20503 + 1.01114i 0.999472 + 0.0324922i \(0.0103444\pi\)
0.205555 + 0.978646i \(0.434100\pi\)
\(240\) 846575. + 1.05373e6i 0.948718 + 1.18087i
\(241\) 1.39867e6 + 509074.i 1.55122 + 0.564597i 0.968703 0.248224i \(-0.0798469\pi\)
0.582514 + 0.812821i \(0.302069\pi\)
\(242\) 897763. 0.985424
\(243\) −221024. 893553.i −0.240117 0.970744i
\(244\) 3723.35 0.00400368
\(245\) 980485. + 356867.i 1.04358 + 0.379832i
\(246\) −511257. 636360.i −0.538644 0.670448i
\(247\) −1.31013e6 1.09933e6i −1.36638 1.14653i
\(248\) −83546.4 + 473815.i −0.0862579 + 0.489193i
\(249\) −182444. 536581.i −0.186480 0.548449i
\(250\) 251112. 210708.i 0.254107 0.213221i
\(251\) −925163. 1.60243e6i −0.926902 1.60544i −0.788473 0.615069i \(-0.789128\pi\)
−0.138429 0.990372i \(-0.544205\pi\)
\(252\) −4806.84 + 21785.5i −0.00476824 + 0.0216106i
\(253\) −70722.8 + 122495.i −0.0694637 + 0.120315i
\(254\) 162571. + 921985.i 0.158110 + 0.896684i
\(255\) 9589.09 449790.i 0.00923478 0.433171i
\(256\) −49504.9 + 18018.3i −0.0472115 + 0.0171836i
\(257\) 379835. 138249.i 0.358726 0.130566i −0.156369 0.987699i \(-0.549979\pi\)
0.515095 + 0.857133i \(0.327757\pi\)
\(258\) −592661. + 325531.i −0.554315 + 0.304469i
\(259\) 326571. + 1.85208e6i 0.302502 + 1.71557i
\(260\) −18780.3 + 32528.4i −0.0172294 + 0.0298421i
\(261\) −1.00373e6 + 1.57902e6i −0.912041 + 1.43479i
\(262\) 215545. + 373335.i 0.193992 + 0.336005i
\(263\) −229128. + 192261.i −0.204263 + 0.171397i −0.739181 0.673507i \(-0.764787\pi\)
0.534918 + 0.844904i \(0.320343\pi\)
\(264\) −166025. 32938.0i −0.146610 0.0290863i
\(265\) 20670.9 117230.i 0.0180819 0.102548i
\(266\) −1.52168e6 1.27684e6i −1.31862 1.10645i
\(267\) −259133. + 667348.i −0.222456 + 0.572894i
\(268\) 8340.37 + 3035.65i 0.00709330 + 0.00258175i
\(269\) −658980. −0.555254 −0.277627 0.960689i \(-0.589548\pi\)
−0.277627 + 0.960689i \(0.589548\pi\)
\(270\) 115025. 1.79630e6i 0.0960250 1.49958i
\(271\) −820179. −0.678399 −0.339199 0.940714i \(-0.610156\pi\)
−0.339199 + 0.940714i \(0.610156\pi\)
\(272\) 338853. + 123332.i 0.277708 + 0.101078i
\(273\) 2.21923e6 342710.i 1.80217 0.278304i
\(274\) 707604. + 593750.i 0.569395 + 0.477779i
\(275\) −40078.0 + 227294.i −0.0319576 + 0.181241i
\(276\) 12873.9 14694.8i 0.0101728 0.0116115i
\(277\) −1.71884e6 + 1.44228e6i −1.34597 + 1.12940i −0.365923 + 0.930645i \(0.619247\pi\)
−0.980048 + 0.198759i \(0.936309\pi\)
\(278\) 1.07408e6 + 1.86037e6i 0.833540 + 1.44373i
\(279\) 516418. 397084.i 0.397183 0.305402i
\(280\) 1.28030e6 2.21755e6i 0.975926 1.69035i
\(281\) −395906. 2.24529e6i −0.299106 1.69632i −0.650026 0.759912i \(-0.725242\pi\)
0.350920 0.936406i \(-0.385869\pi\)
\(282\) −526205. 318948.i −0.394032 0.238835i
\(283\) 1.38550e6 504280.i 1.02835 0.374287i 0.227895 0.973686i \(-0.426816\pi\)
0.800451 + 0.599398i \(0.204593\pi\)
\(284\) 2191.47 797.629i 0.00161228 0.000586820i
\(285\) 2.25812e6 + 1.36871e6i 1.64678 + 0.998161i
\(286\) −50403.0 285850.i −0.0364369 0.206644i
\(287\) −786145. + 1.36164e6i −0.563376 + 0.975795i
\(288\) 43583.6 + 18001.8i 0.0309629 + 0.0127889i
\(289\) 649918. + 1.12569e6i 0.457735 + 0.792819i
\(290\) −2.80277e6 + 2.35181e6i −1.95701 + 1.64213i
\(291\) −1.65152e6 + 1.88510e6i −1.14328 + 1.30498i
\(292\) 4501.28 25528.0i 0.00308943 0.0175210i
\(293\) −1.65170e6 1.38594e6i −1.12399 0.943138i −0.125189 0.992133i \(-0.539954\pi\)
−0.998799 + 0.0489951i \(0.984398\pi\)
\(294\) 1.10065e6 169970.i 0.742642 0.114684i
\(295\) 2.96904e6 + 1.08064e6i 1.98637 + 0.722980i
\(296\) 1.97075e6 1.30738
\(297\) 135791. + 184613.i 0.0893264 + 0.121443i
\(298\) −302348. −0.197227
\(299\) −1.84783e6 672555.i −1.19532 0.435061i
\(300\) 11539.0 29716.5i 0.00740225 0.0190631i
\(301\) 997702. + 837171.i 0.634724 + 0.532596i
\(302\) 220777. 1.25209e6i 0.139295 0.789982i
\(303\) 665313. + 131993.i 0.416312 + 0.0825930i
\(304\) −1.62130e6 + 1.36044e6i −1.00619 + 0.844295i
\(305\) 289312. + 501104.i 0.178081 + 0.308445i
\(306\) −222157. 425717.i −0.135630 0.259907i
\(307\) 510371. 883988.i 0.309058 0.535304i −0.669099 0.743174i \(-0.733320\pi\)
0.978157 + 0.207870i \(0.0666530\pi\)
\(308\) −964.522 5470.08i −0.000579342 0.00328561i
\(309\) 1.91136e6 1.04985e6i 1.13880 0.625507i
\(310\) 1.19703e6 435684.i 0.707459 0.257494i
\(311\) −1.97227e6 + 717847.i −1.15629 + 0.420854i −0.847769 0.530365i \(-0.822055\pi\)
−0.308517 + 0.951219i \(0.599833\pi\)
\(312\) 50154.8 2.35259e6i 0.0291693 1.36823i
\(313\) −66359.5 376343.i −0.0382862 0.217132i 0.959662 0.281156i \(-0.0907177\pi\)
−0.997948 + 0.0640239i \(0.979607\pi\)
\(314\) 1.19358e6 2.06734e6i 0.683168 1.18328i
\(315\) −3.30548e6 + 1.04586e6i −1.87697 + 0.593875i
\(316\) −6045.70 10471.5i −0.00340587 0.00589915i
\(317\) 1.01522e6 851871.i 0.567430 0.476130i −0.313362 0.949634i \(-0.601455\pi\)
0.880792 + 0.473504i \(0.157011\pi\)
\(318\) −40901.4 120294.i −0.0226814 0.0667076i
\(319\) 80891.8 458760.i 0.0445070 0.252412i
\(320\) −2.05493e6 1.72429e6i −1.12182 0.941315i
\(321\) −546816. 680620.i −0.296196 0.368674i
\(322\) −2.14620e6 781154.i −1.15354 0.419853i
\(323\) 704443. 0.375698
\(324\) −13434.9 28661.2i −0.00711003 0.0151681i
\(325\) −3.20865e6 −1.68506
\(326\) 1.28210e6 + 466645.i 0.668155 + 0.243188i
\(327\) −1.47948e6 1.84150e6i −0.765137 0.952364i
\(328\) 1.26215e6 + 1.05907e6i 0.647778 + 0.543551i
\(329\) −205806. + 1.16718e6i −0.104826 + 0.594496i
\(330\) 144264. + 424290.i 0.0729245 + 0.214476i
\(331\) 1.67508e6 1.40556e6i 0.840363 0.705148i −0.117283 0.993099i \(-0.537418\pi\)
0.957645 + 0.287951i \(0.0929739\pi\)
\(332\) −9744.74 16878.4i −0.00485205 0.00840399i
\(333\) −1.96912e6 1.80074e6i −0.973107 0.889897i
\(334\) −1.98186e6 + 3.43269e6i −0.972092 + 1.68371i
\(335\) 239515. + 1.35836e6i 0.116606 + 0.661305i
\(336\) 59229.5 2.77825e6i 0.0286214 1.34253i
\(337\) 352011. 128122.i 0.168843 0.0614537i −0.256216 0.966620i \(-0.582476\pi\)
0.425058 + 0.905166i \(0.360254\pi\)
\(338\) 1.80177e6 655791.i 0.857843 0.312229i
\(339\) −761061. + 418028.i −0.359683 + 0.197563i
\(340\) −2686.50 15235.9i −0.00126035 0.00714779i
\(341\) −81094.3 + 140459.i −0.0377663 + 0.0654132i
\(342\) 2.81585e6 + 120117.i 1.30180 + 0.0555315i
\(343\) 366675. + 635099.i 0.168285 + 0.291478i
\(344\) 1.04550e6 877281.i 0.476353 0.399708i
\(345\) 2.97801e6 + 590813.i 1.34703 + 0.267240i
\(346\) 512094. 2.90423e6i 0.229964 1.30419i
\(347\) 359203. + 301407.i 0.160146 + 0.134378i 0.719339 0.694659i \(-0.244445\pi\)
−0.559193 + 0.829037i \(0.688889\pi\)
\(348\) −23289.8 + 59978.5i −0.0103090 + 0.0265490i
\(349\) −655226. 238483.i −0.287957 0.104808i 0.194003 0.981001i \(-0.437853\pi\)
−0.481960 + 0.876193i \(0.660075\pi\)
\(350\) −3.72676e6 −1.62615
\(351\) −2.19975e6 + 2.30481e6i −0.953026 + 0.998543i
\(352\) −11740.3 −0.00505037
\(353\) −746614. 271745.i −0.318903 0.116071i 0.177609 0.984101i \(-0.443164\pi\)
−0.496512 + 0.868030i \(0.665386\pi\)
\(354\) 3.33290e6 514691.i 1.41356 0.218292i
\(355\) 277630. + 232959.i 0.116922 + 0.0981090i
\(356\) −4274.92 + 24244.3i −0.00178773 + 0.0101387i
\(357\) −609494. + 695698.i −0.253104 + 0.288902i
\(358\) −1.47836e6 + 1.24049e6i −0.609641 + 0.511549i
\(359\) 1.61932e6 + 2.80475e6i 0.663129 + 1.14857i 0.979789 + 0.200033i \(0.0641051\pi\)
−0.316661 + 0.948539i \(0.602562\pi\)
\(360\) 477822. + 3.60154e6i 0.194317 + 1.46464i
\(361\) −829239. + 1.43628e6i −0.334897 + 0.580059i
\(362\) 692203. + 3.92568e6i 0.277627 + 1.57450i
\(363\) 2.09814e6 + 1.27175e6i 0.835736 + 0.506564i
\(364\) 72562.9 26410.7i 0.0287052 0.0104479i
\(365\) 3.78542e6 1.37778e6i 1.48724 0.541312i
\(366\) 528154. + 320130.i 0.206091 + 0.124918i
\(367\) −148483. 842086.i −0.0575453 0.326356i 0.942422 0.334426i \(-0.108542\pi\)
−0.999967 + 0.00806992i \(0.997431\pi\)
\(368\) −1.21673e6 + 2.10745e6i −0.468356 + 0.811217i
\(369\) −293398. 2.21146e6i −0.112174 0.845499i
\(370\) −2.60894e6 4.51881e6i −0.990739 1.71601i
\(371\) −187473. + 157309.i −0.0707138 + 0.0593359i
\(372\) 14761.9 16849.8i 0.00553077 0.00631301i
\(373\) 130100. 737836.i 0.0484180 0.274592i −0.950981 0.309248i \(-0.899923\pi\)
0.999399 + 0.0346563i \(0.0110337\pi\)
\(374\) 91585.1 + 76849.0i 0.0338568 + 0.0284092i
\(375\) 885352. 136723.i 0.325115 0.0502067i
\(376\) 1.16707e6 + 424779.i 0.425724 + 0.154951i
\(377\) 6.47622e6 2.34676
\(378\) −2.55494e6 + 2.67697e6i −0.919711 + 0.963637i
\(379\) −374614. −0.133963 −0.0669816 0.997754i \(-0.521337\pi\)
−0.0669816 + 0.997754i \(0.521337\pi\)
\(380\) 85327.4 + 31056.6i 0.0303130 + 0.0110330i
\(381\) −926120. + 2.38505e6i −0.326855 + 0.841753i
\(382\) 546939. + 458936.i 0.191770 + 0.160914i
\(383\) −573.937 + 3254.96i −0.000199925 + 0.00113383i −0.984908 0.173081i \(-0.944628\pi\)
0.984708 + 0.174215i \(0.0557388\pi\)
\(384\) −2.90342e6 576015.i −1.00481 0.199345i
\(385\) 661239. 554846.i 0.227356 0.190775i
\(386\) 214438. + 371418.i 0.0732544 + 0.126880i
\(387\) −1.84624e6 78755.7i −0.626628 0.0267303i
\(388\) −43092.2 + 74637.8i −0.0145318 + 0.0251698i
\(389\) −649609. 3.68412e6i −0.217660 1.23441i −0.876231 0.481891i \(-0.839950\pi\)
0.658571 0.752519i \(-0.271161\pi\)
\(390\) −5.46073e6 + 2.99942e6i −1.81798 + 0.998563i
\(391\) 761109. 277021.i 0.251771 0.0916370i
\(392\) −2.11233e6 + 768825.i −0.694299 + 0.252704i
\(393\) −25110.6 + 1.17785e6i −0.00820117 + 0.384688i
\(394\) 149947. + 850389.i 0.0486627 + 0.275980i
\(395\) 939527. 1.62731e6i 0.302982 0.524780i
\(396\) 5815.75 + 5318.45i 0.00186367 + 0.00170430i
\(397\) −692020. 1.19861e6i −0.220365 0.381683i 0.734554 0.678550i \(-0.237392\pi\)
−0.954919 + 0.296867i \(0.904058\pi\)
\(398\) 1.05677e6 886734.i 0.334404 0.280599i
\(399\) −1.74755e6 5.13966e6i −0.549537 1.61622i
\(400\) −689514. + 3.91043e6i −0.215473 + 1.22201i
\(401\) 1.47773e6 + 1.23996e6i 0.458916 + 0.385076i 0.842732 0.538333i \(-0.180946\pi\)
−0.383816 + 0.923410i \(0.625390\pi\)
\(402\) 922072. + 1.14770e6i 0.284577 + 0.354212i
\(403\) −2.11882e6 771186.i −0.649876 0.236536i
\(404\) 23324.8 0.00710992
\(405\) 2.81341e6 4.03515e6i 0.852307 1.22243i
\(406\) 7.52194e6 2.26472
\(407\) 624281. + 227220.i 0.186807 + 0.0679923i
\(408\) 607045. + 755587.i 0.180539 + 0.224716i
\(409\) −4.46374e6 3.74552e6i −1.31944 1.10714i −0.986423 0.164223i \(-0.947488\pi\)
−0.333019 0.942920i \(-0.608067\pi\)
\(410\) 757512. 4.29606e6i 0.222551 1.26215i
\(411\) 812637. + 2.39002e6i 0.237297 + 0.697905i
\(412\) 57446.0 48202.9i 0.0166731 0.0139904i
\(413\) −3.24785e6 5.62544e6i −0.936959 1.62286i
\(414\) 3.08960e6 977549.i 0.885933 0.280310i
\(415\) 1.51437e6 2.62297e6i 0.431631 0.747607i
\(416\) −28342.4 160738.i −0.00802979 0.0455392i
\(417\) −125129. + 5.86936e6i −0.0352385 + 1.65291i
\(418\) −659390. + 239998.i −0.184587 + 0.0671842i
\(419\) −4.71805e6 + 1.71723e6i −1.31289 + 0.477852i −0.901172 0.433461i \(-0.857292\pi\)
−0.411714 + 0.911313i \(0.635070\pi\)
\(420\) −104498. + 57397.5i −0.0289057 + 0.0158770i
\(421\) −186623. 1.05839e6i −0.0513168 0.291032i 0.948339 0.317258i \(-0.102762\pi\)
−0.999656 + 0.0262260i \(0.991651\pi\)
\(422\) 306479. 530837.i 0.0837760 0.145104i
\(423\) −777969. 1.49082e6i −0.211403 0.405110i
\(424\) 128227. + 222095.i 0.0346389 + 0.0599964i
\(425\) 1.01242e6 849523.i 0.271888 0.228141i
\(426\) 379437. + 75277.2i 0.101301 + 0.0200974i
\(427\) 206568. 1.17151e6i 0.0548269 0.310939i
\(428\) −22999.2 19298.6i −0.00606880 0.00509233i
\(429\) 287131. 739453.i 0.0753247 0.193985i
\(430\) −3.39562e6 1.23590e6i −0.885621 0.322340i
\(431\) −2.16988e6 −0.562654 −0.281327 0.959612i \(-0.590775\pi\)
−0.281327 + 0.959612i \(0.590775\pi\)
\(432\) 2.33619e6 + 3.17614e6i 0.602280 + 0.818824i
\(433\) 2.36558e6 0.606343 0.303171 0.952936i \(-0.401955\pi\)
0.303171 + 0.952936i \(0.401955\pi\)
\(434\) −2.46094e6 895711.i −0.627159 0.228267i
\(435\) −9.88182e6 + 1.52602e6i −2.50388 + 0.386668i
\(436\) −62227.1 52214.8i −0.0156770 0.0131546i
\(437\) −825499. + 4.68164e6i −0.206782 + 1.17272i
\(438\) 2.83337e6 3.23411e6i 0.705698 0.805507i
\(439\) 5.90020e6 4.95085e6i 1.46118 1.22608i 0.537310 0.843385i \(-0.319440\pi\)
0.923875 0.382695i \(-0.125004\pi\)
\(440\) −452271. 783357.i −0.111370 0.192898i
\(441\) 2.81308e6 + 1.16192e6i 0.688787 + 0.284497i
\(442\) −831051. + 1.43942e6i −0.202336 + 0.350455i
\(443\) 349582. + 1.98258e6i 0.0846331 + 0.479978i 0.997435 + 0.0715760i \(0.0228028\pi\)
−0.912802 + 0.408402i \(0.866086\pi\)
\(444\) −78470.2 47563.1i −0.0188907 0.0114502i
\(445\) −3.59506e6 + 1.30850e6i −0.860610 + 0.313236i
\(446\) −2.61739e6 + 952653.i −0.623063 + 0.226776i
\(447\) −706613. 428299.i −0.167268 0.101386i
\(448\) 957654. + 5.43113e6i 0.225431 + 1.27848i
\(449\) −553618. + 958895.i −0.129597 + 0.224468i −0.923520 0.383549i \(-0.874702\pi\)
0.793924 + 0.608018i \(0.208035\pi\)
\(450\) 4.19178e6 3.22314e6i 0.975815 0.750323i
\(451\) 277709. + 481006.i 0.0642907 + 0.111355i
\(452\) −22873.8 + 19193.4i −0.00526613 + 0.00441881i
\(453\) 2.28965e6 2.61348e6i 0.524232 0.598376i
\(454\) −184938. + 1.04884e6i −0.0421101 + 0.238818i
\(455\) 9.19276e6 + 7.71364e6i 2.08170 + 1.74675i
\(456\) −5.62207e6 + 868202.i −1.26615 + 0.195528i
\(457\) 3.56091e6 + 1.29607e6i 0.797574 + 0.290293i 0.708481 0.705730i \(-0.249381\pi\)
0.0890930 + 0.996023i \(0.471603\pi\)
\(458\) −3.78878e6 −0.843987
\(459\) 83862.3 1.30964e6i 0.0185795 0.290148i
\(460\) 104404. 0.0230051
\(461\) 1.32800e6 + 483353.i 0.291036 + 0.105928i 0.483412 0.875393i \(-0.339397\pi\)
−0.192377 + 0.981321i \(0.561619\pi\)
\(462\) 333495. 858854.i 0.0726916 0.187204i
\(463\) −2.97520e6 2.49649e6i −0.645006 0.541224i 0.260545 0.965462i \(-0.416098\pi\)
−0.905551 + 0.424238i \(0.860542\pi\)
\(464\) 1.39169e6 7.89265e6i 0.300087 1.70188i
\(465\) 3.41474e6 + 677456.i 0.732361 + 0.145294i
\(466\) 712234. 597635.i 0.151935 0.127489i
\(467\) 1.92081e6 + 3.32694e6i 0.407560 + 0.705915i 0.994616 0.103632i \(-0.0330464\pi\)
−0.587056 + 0.809546i \(0.699713\pi\)
\(468\) −58775.6 + 92463.4i −0.0124046 + 0.0195144i
\(469\) 1.41784e6 2.45578e6i 0.297644 0.515534i
\(470\) −571010. 3.23836e6i −0.119234 0.676208i
\(471\) 5.71804e6 3.14075e6i 1.18767 0.652351i
\(472\) −6.39640e6 + 2.32810e6i −1.32154 + 0.481002i
\(473\) 432334. 157357.i 0.0888519 0.0323395i
\(474\) 42748.3 2.00517e6i 0.00873922 0.409926i
\(475\) 1.34699e6 + 7.63914e6i 0.273923 + 1.55350i
\(476\) −15903.2 + 27545.1i −0.00321711 + 0.00557220i
\(477\) 74815.2 339076.i 0.0150554 0.0682341i
\(478\) 3.96178e6 + 6.86200e6i 0.793086 + 1.37367i
\(479\) −1.55050e6 + 1.30102e6i −0.308768 + 0.259087i −0.783983 0.620783i \(-0.786815\pi\)
0.475214 + 0.879870i \(0.342370\pi\)
\(480\) 81122.1 + 238585.i 0.0160708 + 0.0472651i
\(481\) −1.60380e6 + 9.09563e6i −0.316074 + 1.79254i
\(482\) 6.50378e6 + 5.45732e6i 1.27511 + 1.06995i
\(483\) −3.90929e6 4.86588e6i −0.762482 0.949059i
\(484\) 79282.5 + 28856.5i 0.0153838 + 0.00559925i
\(485\) −1.33934e7 −2.58545
\(486\) 558531. 5.22068e6i 0.107265 1.00262i
\(487\) −4.43291e6 −0.846967 −0.423484 0.905904i \(-0.639193\pi\)
−0.423484 + 0.905904i \(0.639193\pi\)
\(488\) −1.17139e6 426353.i −0.222666 0.0810438i
\(489\) 2.33533e6 + 2.90678e6i 0.441648 + 0.549717i
\(490\) 4.55923e6 + 3.82565e6i 0.857830 + 0.719805i
\(491\) −251122. + 1.42419e6i −0.0470090 + 0.266602i −0.999249 0.0387493i \(-0.987663\pi\)
0.952240 + 0.305351i \(0.0987737\pi\)
\(492\) −24695.4 72630.8i −0.00459943 0.0135272i
\(493\) −2.04343e6 + 1.71464e6i −0.378654 + 0.317729i
\(494\) −4.87768e6 8.44839e6i −0.899282 1.55760i
\(495\) −263882. + 1.19596e6i −0.0484057 + 0.219384i
\(496\) −1.39517e6 + 2.41651e6i −0.254638 + 0.441046i
\(497\) −129383. 733770.i −0.0234957 0.133251i
\(498\) 68903.7 3.23203e6i 0.0124500 0.583985i
\(499\) 4.11362e6 1.49723e6i 0.739558 0.269177i 0.0553531 0.998467i \(-0.482372\pi\)
0.684205 + 0.729290i \(0.260149\pi\)
\(500\) 28948.7 10536.4i 0.00517849 0.00188482i
\(501\) −9.49443e6 + 5.21501e6i −1.68995 + 0.928242i
\(502\) −1.83274e6 1.03940e7i −0.324595 1.84087i
\(503\) −66422.0 + 115046.i −0.0117056 + 0.0202746i −0.871819 0.489828i \(-0.837059\pi\)
0.860113 + 0.510103i \(0.170393\pi\)
\(504\) 4.00688e6 6.30346e6i 0.702635 1.10536i
\(505\) 1.81239e6 + 3.13915e6i 0.316244 + 0.547751i
\(506\) −618053. + 518608.i −0.107312 + 0.0900457i
\(507\) 5.13986e6 + 1.01971e6i 0.888038 + 0.176180i
\(508\) −15278.2 + 86647.0i −0.00262672 + 0.0148968i
\(509\) −3.15217e6 2.64498e6i −0.539280 0.452510i 0.332011 0.943275i \(-0.392273\pi\)
−0.871292 + 0.490765i \(0.836717\pi\)
\(510\) 928891. 2.39219e6i 0.158139 0.407258i
\(511\) −7.78234e6 2.83254e6i −1.31843 0.479870i
\(512\) 5.77581e6 0.973728
\(513\) 6.41072e6 + 4.26959e6i 1.07551 + 0.716296i
\(514\) 2.30564e6 0.384932
\(515\) 1.09510e7 + 3.98585e6i 1.81944 + 0.662220i
\(516\) −62802.0 + 9698.35i −0.0103836 + 0.00160352i
\(517\) 320722. + 269117.i 0.0527718 + 0.0442808i
\(518\) −1.86277e6 + 1.05643e7i −0.305025 + 1.72988i
\(519\) 5.31086e6 6.06200e6i 0.865459 0.987865i
\(520\) 9.63319e6 8.08320e6i 1.56229 1.31092i
\(521\) 629944. + 1.09110e6i 0.101674 + 0.176104i 0.912374 0.409357i \(-0.134247\pi\)
−0.810701 + 0.585461i \(0.800914\pi\)
\(522\) −8.46053e6 + 6.50547e6i −1.35901 + 1.04497i
\(523\) 970649. 1.68121e6i 0.155170 0.268762i −0.777951 0.628325i \(-0.783741\pi\)
0.933121 + 0.359563i \(0.117074\pi\)
\(524\) 7035.06 + 39897.8i 0.00111928 + 0.00634777i
\(525\) −8.70974e6 5.27924e6i −1.37914 0.835935i
\(526\) −1.60322e6 + 583524.i −0.252655 + 0.0919590i
\(527\) 872726. 317646.i 0.136884 0.0498216i
\(528\) −839479. 508833.i −0.131046 0.0794311i
\(529\) −168515. 955698.i −0.0261818 0.148485i
\(530\) 339501. 588033.i 0.0524990 0.0909310i
\(531\) 8.51836e6 + 3.51843e6i 1.31105 + 0.541517i
\(532\) −93340.3 161670.i −0.0142985 0.0247657i
\(533\) −5.91508e6 + 4.96334e6i −0.901868 + 0.756757i
\(534\) −2.69089e6 + 3.07147e6i −0.408360 + 0.466116i
\(535\) 810199. 4.59486e6i 0.122379 0.694046i
\(536\) −2.27634e6 1.91008e6i −0.342235 0.287170i
\(537\) −5.21231e6 + 804924.i −0.780000 + 0.120453i
\(538\) −3.53216e6 1.28560e6i −0.526120 0.191492i
\(539\) −757772. −0.112348
\(540\) 67895.8 154936.i 0.0100198 0.0228648i
\(541\) 128241. 0.0188379 0.00941897 0.999956i \(-0.497002\pi\)
0.00941897 + 0.999956i \(0.497002\pi\)
\(542\) −4.39619e6 1.60008e6i −0.642804 0.233961i
\(543\) −3.94328e6 + 1.01552e7i −0.573929 + 1.47805i
\(544\) 51499.8 + 43213.5i 0.00746120 + 0.00626069i
\(545\) 2.19209e6 1.24320e7i 0.316131 1.79287i
\(546\) 1.25638e7 + 2.49255e6i 1.80359 + 0.357817i
\(547\) 2.17955e6 1.82886e6i 0.311457 0.261343i −0.473637 0.880720i \(-0.657059\pi\)
0.785094 + 0.619377i \(0.212615\pi\)
\(548\) 43404.6 + 75179.0i 0.00617426 + 0.0106941i
\(549\) 780851. + 1.49634e6i 0.110570 + 0.211885i
\(550\) −658246. + 1.14012e6i −0.0927858 + 0.160710i
\(551\) −2.71870e6 1.54185e7i −0.381490 2.16354i
\(552\) −5.73290e6 + 3.14891e6i −0.800805 + 0.439859i
\(553\) −3.63012e6 + 1.32126e6i −0.504787 + 0.183728i
\(554\) −1.20268e7 + 4.37739e6i −1.66485 + 0.605956i
\(555\) 303937. 1.42566e7i 0.0418842 1.96464i
\(556\) 35056.5 + 198815.i 0.00480930 + 0.0272749i
\(557\) 537968. 931788.i 0.0734715 0.127256i −0.826949 0.562277i \(-0.809926\pi\)
0.900421 + 0.435021i \(0.143259\pi\)
\(558\) 3.54269e6 1.12091e6i 0.481668 0.152400i
\(559\) 3.19809e6 + 5.53926e6i 0.432874 + 0.749760i
\(560\) 1.13762e7 9.54573e6i 1.53294 1.28629i
\(561\) 105179. + 309340.i 0.0141099 + 0.0414981i
\(562\) 2.25826e6 1.28072e7i 0.301601 1.71047i
\(563\) −3.37213e6 2.82955e6i −0.448367 0.376224i 0.390463 0.920619i \(-0.372315\pi\)
−0.838829 + 0.544395i \(0.816759\pi\)
\(564\) −36217.9 45080.3i −0.00479430 0.00596745i
\(565\) −4.36046e6 1.58708e6i −0.574661 0.209159i
\(566\) 8.41012e6 1.10347
\(567\) −9.76323e6 + 2.63702e6i −1.27537 + 0.344474i
\(568\) −780787. −0.101546
\(569\) −2.37185e6 863283.i −0.307119 0.111782i 0.183863 0.982952i \(-0.441140\pi\)
−0.490982 + 0.871170i \(0.663362\pi\)
\(570\) 9.43340e6 + 1.17417e7i 1.21613 + 1.51372i
\(571\) 6.63834e6 + 5.57023e6i 0.852058 + 0.714961i 0.960242 0.279169i \(-0.0900591\pi\)
−0.108184 + 0.994131i \(0.534504\pi\)
\(572\) 4736.81 26863.8i 0.000605335 0.00343303i
\(573\) 628123. + 1.84735e6i 0.0799205 + 0.235051i
\(574\) −6.87020e6 + 5.76478e6i −0.870341 + 0.730303i
\(575\) 4.45942e6 + 7.72394e6i 0.562482 + 0.974248i
\(576\) −5.77434e6 5.28058e6i −0.725181 0.663171i
\(577\) 4.96402e6 8.59793e6i 0.620717 1.07511i −0.368636 0.929574i \(-0.620175\pi\)
0.989352 0.145539i \(-0.0464917\pi\)
\(578\) 1.28748e6 + 7.30167e6i 0.160296 + 0.909081i
\(579\) −24981.7 + 1.17180e6i −0.00309688 + 0.145264i
\(580\) −323109. + 117602.i −0.0398822 + 0.0145159i
\(581\) −5.85120e6 + 2.12966e6i −0.719125 + 0.261740i
\(582\) −1.25299e7 + 6.88229e6i −1.53334 + 0.842220i
\(583\) 15012.1 + 85137.9i 0.00182924 + 0.0103741i
\(584\) −4.33929e6 + 7.51587e6i −0.526486 + 0.911900i
\(585\) −1.70111e7 725649.i −2.05514 0.0876672i
\(586\) −6.14935e6 1.06510e7i −0.739750 1.28129i
\(587\) 8.61774e6 7.23114e6i 1.03228 0.866187i 0.0411608 0.999153i \(-0.486894\pi\)
0.991121 + 0.132966i \(0.0424500\pi\)
\(588\) 102663. + 20367.4i 0.0122453 + 0.00242937i
\(589\) −946559. + 5.36821e6i −0.112424 + 0.637589i
\(590\) 1.38059e7 + 1.15846e7i 1.63281 + 1.37009i
\(591\) −854203. + 2.19984e6i −0.100599 + 0.259073i
\(592\) 1.07403e7 + 3.90915e6i 1.25954 + 0.458436i
\(593\) 9.00454e6 1.05154 0.525769 0.850628i \(-0.323778\pi\)
0.525769 + 0.850628i \(0.323778\pi\)
\(594\) 367684. + 1.25445e6i 0.0427572 + 0.145877i
\(595\) −4.94284e6 −0.572380
\(596\) −26700.7 9718.27i −0.00307899 0.00112066i
\(597\) 3.72588e6 575378.i 0.427851 0.0660720i
\(598\) −8.59236e6 7.20985e6i −0.982561 0.824467i
\(599\) 2.83453e6 1.60754e7i 0.322786 1.83061i −0.202011 0.979383i \(-0.564748\pi\)
0.524797 0.851227i \(-0.324141\pi\)
\(600\) −7.03301e6 + 8.02772e6i −0.797560 + 0.910362i
\(601\) −4.97312e6 + 4.17294e6i −0.561620 + 0.471255i −0.878853 0.477092i \(-0.841691\pi\)
0.317233 + 0.948348i \(0.397246\pi\)
\(602\) 3.71449e6 + 6.43369e6i 0.417742 + 0.723550i
\(603\) 529155. + 3.98845e6i 0.0592638 + 0.446695i
\(604\) 59742.4 103477.i 0.00666332 0.0115412i
\(605\) 2.27680e6 + 1.29124e7i 0.252892 + 1.43422i
\(606\) 3.30860e6 + 2.00544e6i 0.365985 + 0.221834i
\(607\) 1.25383e7 4.56357e6i 1.38123 0.502728i 0.458682 0.888601i \(-0.348322\pi\)
0.922552 + 0.385873i \(0.126100\pi\)
\(608\) −370786. + 134955.i −0.0406784 + 0.0148057i
\(609\) 1.75794e7 + 1.06554e7i 1.92071 + 1.16420i
\(610\) 573125. + 3.25036e6i 0.0623627 + 0.353677i
\(611\) −2.91026e6 + 5.04071e6i −0.315376 + 0.546247i
\(612\) −5935.23 44736.3i −0.000640559 0.00482815i
\(613\) 9.01424e6 + 1.56131e7i 0.968897 + 1.67818i 0.698758 + 0.715358i \(0.253736\pi\)
0.270139 + 0.962821i \(0.412930\pi\)
\(614\) 4.46018e6 3.74253e6i 0.477454 0.400631i
\(615\) 7.85606e6 8.96718e6i 0.837562 0.956022i
\(616\) −322920. + 1.83137e6i −0.0342881 + 0.194458i
\(617\) 1.96709e6 + 1.65058e6i 0.208023 + 0.174552i 0.740846 0.671675i \(-0.234425\pi\)
−0.532824 + 0.846226i \(0.678869\pi\)
\(618\) 1.22931e7 1.89839e6i 1.29476 0.199947i
\(619\) −8.86766e6 3.22756e6i −0.930213 0.338570i −0.167919 0.985801i \(-0.553705\pi\)
−0.762294 + 0.647231i \(0.775927\pi\)
\(620\) 119715. 0.0125075
\(621\) 8.60541e6 + 2.09203e6i 0.895453 + 0.217691i
\(622\) −1.19719e7 −1.24076
\(623\) 7.39099e6 + 2.69010e6i 0.762926 + 0.277682i
\(624\) 4.93989e6 1.27218e7i 0.507874 1.30793i
\(625\) −5.46492e6 4.58561e6i −0.559608 0.469567i
\(626\) 378517. 2.14668e6i 0.0386056 0.218943i
\(627\) −1.88102e6 373179.i −0.191084 0.0379096i
\(628\) 171856. 144204.i 0.0173887 0.0145908i
\(629\) −1.90211e6 3.29455e6i −0.191694 0.332024i
\(630\) −1.97579e7 842821.i −1.98330 0.0846027i
\(631\) −3.82533e6 + 6.62566e6i −0.382468 + 0.662454i −0.991414 0.130757i \(-0.958259\pi\)
0.608946 + 0.793211i \(0.291592\pi\)
\(632\) 702959. + 3.98668e6i 0.0700063 + 0.397026i
\(633\) 1.46824e6 806460.i 0.145642 0.0799969i
\(634\) 7.10354e6 2.58548e6i 0.701861 0.255457i
\(635\) −1.28485e7 + 4.67645e6i −1.26449 + 0.460238i
\(636\) 254.506 11938.0i 2.49491e−5 0.00117027i
\(637\) −1.82935e6 1.03747e7i −0.178627 1.01304i
\(638\) 1.32858e6 2.30116e6i 0.129222 0.223818i
\(639\) 780140. + 713430.i 0.0755823 + 0.0691193i
\(640\) −7.90924e6 1.36992e7i −0.763282 1.32204i
\(641\) −1.32103e7 + 1.10848e7i −1.26990 + 1.06557i −0.275343 + 0.961346i \(0.588792\pi\)
−0.994554 + 0.104224i \(0.966764\pi\)
\(642\) −1.60314e6 4.71494e6i −0.153509 0.451480i
\(643\) 887197. 5.03154e6i 0.0846238 0.479925i −0.912813 0.408377i \(-0.866095\pi\)
0.997437 0.0715483i \(-0.0227940\pi\)
\(644\) −164425. 137969.i −0.0156226 0.0131089i
\(645\) −6.18509e6 7.69856e6i −0.585392 0.728635i
\(646\) 3.77584e6 + 1.37429e6i 0.355986 + 0.129568i
\(647\) −7.51130e6 −0.705431 −0.352715 0.935731i \(-0.614742\pi\)
−0.352715 + 0.935731i \(0.614742\pi\)
\(648\) 944790. + 1.05554e7i 0.0883889 + 0.987502i
\(649\) −2.29463e6 −0.213846
\(650\) −1.71985e7 6.25975e6i −1.59664 0.581130i
\(651\) −4.48259e6 5.57946e6i −0.414549 0.515988i
\(652\) 98224.3 + 82420.0i 0.00904899 + 0.00759300i
\(653\) 2.18834e6 1.24107e7i 0.200832 1.13897i −0.703034 0.711156i \(-0.748172\pi\)
0.903866 0.427816i \(-0.140717\pi\)
\(654\) −4.33749e6 1.27568e7i −0.396547 1.16627i
\(655\) −4.82297e6 + 4.04695e6i −0.439249 + 0.368574i
\(656\) 4.77778e6 + 8.27537e6i 0.433478 + 0.750806i
\(657\) 1.12032e7 3.54469e6i 1.01258 0.320380i
\(658\) −3.38018e6 + 5.85464e6i −0.304351 + 0.527152i
\(659\) 92980.5 + 527319.i 0.00834024 + 0.0472998i 0.988694 0.149948i \(-0.0479107\pi\)
−0.980354 + 0.197248i \(0.936800\pi\)
\(660\) −897.672 + 42106.6i −8.02154e−5 + 0.00376262i
\(661\) −3.21197e6 + 1.16906e6i −0.285935 + 0.104072i −0.481006 0.876717i \(-0.659729\pi\)
0.195071 + 0.980789i \(0.437506\pi\)
\(662\) 1.17206e7 4.26596e6i 1.03946 0.378331i
\(663\) −3.98129e6 + 2.18680e6i −0.351754 + 0.193208i
\(664\) 1.13306e6 + 6.42591e6i 0.0997318 + 0.565607i
\(665\) 1.45055e7 2.51242e7i 1.27197 2.20312i
\(666\) −7.04150e6 1.34936e7i −0.615148 1.17880i
\(667\) −9.00072e6 1.55897e7i −0.783362 1.35682i
\(668\) −285356. + 239442.i −0.0247426 + 0.0207615i
\(669\) −7.46657e6 1.48131e6i −0.644994 0.127962i
\(670\) −1.36620e6 + 7.74812e6i −0.117579 + 0.666821i
\(671\) −321910. 270114.i −0.0276012 0.0231601i
\(672\) 187530. 482948.i 0.0160194 0.0412551i
\(673\) 1.94973e7 + 7.09644e6i 1.65935 + 0.603952i 0.990260 0.139233i \(-0.0444637\pi\)
0.669086 + 0.743185i \(0.266686\pi\)
\(674\) 2.13675e6 0.181177
\(675\) 1.43624e7 1.59478e6i 1.21330 0.134723i
\(676\) 180195. 0.0151662
\(677\) −4.70694e6 1.71318e6i −0.394700 0.143659i 0.137043 0.990565i \(-0.456240\pi\)
−0.531742 + 0.846906i \(0.678462\pi\)
\(678\) −4.89485e6 + 755899.i −0.408945 + 0.0631524i
\(679\) 2.10932e7 + 1.76993e7i 1.75577 + 1.47326i
\(680\) −899438. + 5.10096e6i −0.0745931 + 0.423039i
\(681\) −1.91797e6 + 2.18924e6i −0.158480 + 0.180894i
\(682\) −708691. + 594662.i −0.0583440 + 0.0489564i
\(683\) −7.69704e6 1.33317e7i −0.631353 1.09353i −0.987275 0.159019i \(-0.949167\pi\)
0.355923 0.934515i \(-0.384167\pi\)
\(684\) 244810. + 101116.i 0.0200073 + 0.00826384i
\(685\) −6.74526e6 + 1.16831e7i −0.549253 + 0.951334i
\(686\) 726380. + 4.11950e6i 0.0589323 + 0.334222i
\(687\) −8.85469e6 5.36709e6i −0.715783 0.433858i
\(688\) 7.43800e6 2.70721e6i 0.599081 0.218048i
\(689\) −1.12939e6 + 411065.i −0.0906351 + 0.0329885i
\(690\) 1.48097e7 + 8.97657e6i 1.18419 + 0.717774i
\(691\) −65140.1 369428.i −0.00518983 0.0294330i 0.982103 0.188345i \(-0.0603124\pi\)
−0.987293 + 0.158912i \(0.949201\pi\)
\(692\) 138573. 240016.i 0.0110005 0.0190535i
\(693\) 1.99604e6 1.53479e6i 0.157883 0.121399i
\(694\) 1.33733e6 + 2.31632e6i 0.105400 + 0.182558i
\(695\) −2.40334e7 + 2.01664e7i −1.88735 + 1.58368i
\(696\) 1.41952e7 1.62028e7i 1.11075 1.26785i
\(697\) 552283. 3.13215e6i 0.0430606 0.244209i
\(698\) −3.04679e6 2.55656e6i −0.236703 0.198617i
\(699\) 2.51114e6 387789.i 0.194392 0.0300195i
\(700\) −329114. 119788.i −0.0253864 0.00923991i
\(701\) 1.41346e7 1.08639 0.543197 0.839605i \(-0.317214\pi\)
0.543197 + 0.839605i \(0.317214\pi\)
\(702\) −1.62872e7 + 8.06239e6i −1.24739 + 0.617477i
\(703\) 2.23281e7 1.70397
\(704\) 1.83068e6 + 666311.i 0.139213 + 0.0506694i
\(705\) 3.25288e6 8.37719e6i 0.246488 0.634783i
\(706\) −3.47173e6 2.91313e6i −0.262141 0.219962i
\(707\) 1.29404e6 7.33886e6i 0.0973641 0.552179i
\(708\) 310876. + 61675.2i 0.0233079 + 0.00462410i
\(709\) −1.33424e7 + 1.11956e7i −0.996826 + 0.836436i −0.986542 0.163511i \(-0.947718\pi\)
−0.0102846 + 0.999947i \(0.503274\pi\)
\(710\) 1.03363e6 + 1.79030e6i 0.0769518 + 0.133284i
\(711\) 2.94038e6 4.62569e6i 0.218137 0.343165i
\(712\) 4.12108e6 7.13792e6i 0.304657 0.527681i
\(713\) 1.08834e6 + 6.17226e6i 0.0801751 + 0.454696i
\(714\) −4.62415e6 + 2.53991e6i −0.339458 + 0.186454i
\(715\) 3.98350e6 1.44987e6i 0.291407 0.106063i
\(716\) −170429. + 62031.0i −0.0124240 + 0.00452196i
\(717\) −461540. + 2.16492e7i −0.0335283 + 1.57269i
\(718\) 3.20787e6 + 1.81927e7i 0.232223 + 1.31700i
\(719\) −9.46989e6 + 1.64023e7i −0.683160 + 1.18327i 0.290851 + 0.956768i \(0.406062\pi\)
−0.974011 + 0.226500i \(0.927272\pi\)
\(720\) −4.53990e6 + 2.05757e7i −0.326374 + 1.47919i
\(721\) −1.19794e7 2.07489e7i −0.858217 1.48648i
\(722\) −7.24679e6 + 6.08078e6i −0.517372 + 0.434127i
\(723\) 7.46916e6 + 2.19673e7i 0.531405 + 1.56290i
\(724\) −65052.4 + 368930.i −0.00461229 + 0.0261576i
\(725\) −2.25013e7 1.88808e7i −1.58987 1.33406i
\(726\) 8.76510e6 + 1.09099e7i 0.617185 + 0.768208i
\(727\) 6.37724e6 + 2.32113e6i 0.447504 + 0.162878i 0.555935 0.831226i \(-0.312360\pi\)
−0.108431 + 0.994104i \(0.534583\pi\)
\(728\) −2.58531e7 −1.80794
\(729\) 8.70082e6 1.14099e7i 0.606375 0.795179i
\(730\) 2.29779e7 1.59589
\(731\) −2.47566e6 901068.i −0.171356 0.0623683i
\(732\) 36352.1 + 45247.3i 0.00250756 + 0.00312115i
\(733\) 1.06213e6 + 891233.i 0.0730160 + 0.0612677i 0.678565 0.734540i \(-0.262602\pi\)
−0.605549 + 0.795808i \(0.707047\pi\)
\(734\) 846950. 4.80329e6i 0.0580253 0.329078i
\(735\) 5.23598e6 + 1.53994e7i 0.357503 + 1.05144i
\(736\) −347541. + 291622.i −0.0236490 + 0.0198438i
\(737\) −500859. 867513.i −0.0339662 0.0588312i
\(738\) 2.74170e6 1.24259e7i 0.185302 0.839822i
\(739\) 3.67789e6 6.37029e6i 0.247735 0.429090i −0.715162 0.698959i \(-0.753647\pi\)
0.962897 + 0.269869i \(0.0869804\pi\)
\(740\) −85151.7 482919.i −0.00571629 0.0324187i
\(741\) 568241. 2.66542e7i 0.0380178 1.78328i
\(742\) −1.31176e6 + 477440.i −0.0874668 + 0.0318353i
\(743\) 6.39066e6 2.32601e6i 0.424691 0.154575i −0.120828 0.992674i \(-0.538555\pi\)
0.545519 + 0.838098i \(0.316333\pi\)
\(744\) −6.57364e6 + 3.61071e6i −0.435385 + 0.239144i
\(745\) −766780. 4.34862e6i −0.0506151 0.287052i
\(746\) 2.13679e6 3.70102e6i 0.140577 0.243486i
\(747\) 4.73944e6 7.45590e6i 0.310760 0.488876i
\(748\) 5617.86 + 9730.41i 0.000367127 + 0.000635883i
\(749\) −7.34804e6 + 6.16574e6i −0.478594 + 0.401588i
\(750\) 5.01225e6 + 994390.i 0.325372 + 0.0645511i
\(751\) −2.44936e6 + 1.38910e7i −0.158472 + 0.898740i 0.797070 + 0.603886i \(0.206382\pi\)
−0.955542 + 0.294854i \(0.904729\pi\)
\(752\) 5.51779e6 + 4.62997e6i 0.355812 + 0.298562i
\(753\) 1.04406e7 2.68878e7i 0.671024 1.72810i
\(754\) 3.47128e7 + 1.26344e7i 2.22362 + 0.809333i
\(755\) 1.85685e7 1.18552
\(756\) −311675. + 154283.i −0.0198334 + 0.00981782i
\(757\) −1.29168e7 −0.819247 −0.409623 0.912255i \(-0.634340\pi\)
−0.409623 + 0.912255i \(0.634340\pi\)
\(758\) −2.00795e6 730833.i −0.126934 0.0462003i
\(759\) −2.17909e6 + 336511.i −0.137300 + 0.0212029i
\(760\) −2.32884e7 1.95413e7i −1.46253 1.22721i
\(761\) −4.44499e6 + 2.52088e7i −0.278233 + 1.57794i 0.450268 + 0.892894i \(0.351329\pi\)
−0.728501 + 0.685045i \(0.759783\pi\)
\(762\) −9.61702e6 + 1.09772e7i −0.600003 + 0.684864i
\(763\) −1.98810e7 + 1.66822e7i −1.23631 + 1.03739i
\(764\) 33549.4 + 58109.2i 0.00207946 + 0.00360173i
\(765\) 5.55961e6 4.27489e6i 0.343471 0.264102i
\(766\) −9426.41 + 16327.0i −0.000580463 + 0.00100539i
\(767\) −5.53949e6 3.14160e7i −0.340002 1.92825i
\(768\) −702293. 425681.i −0.0429651 0.0260424i
\(769\) −2.14573e7 + 7.80983e6i −1.30846 + 0.476240i −0.899742 0.436422i \(-0.856246\pi\)
−0.408716 + 0.912662i \(0.634023\pi\)
\(770\) 4.62672e6 1.68399e6i 0.281220 0.102356i
\(771\) 5.38848e6 + 3.26612e6i 0.326460 + 0.197877i
\(772\) 6998.93 + 39692.9i 0.000422658 + 0.00239701i
\(773\) −3.40235e6 + 5.89305e6i −0.204800 + 0.354725i −0.950069 0.312040i \(-0.898988\pi\)
0.745269 + 0.666764i \(0.232321\pi\)
\(774\) −9.74226e6 4.02395e6i −0.584530 0.241435i
\(775\) 5.11340e6 + 8.85667e6i 0.305813 + 0.529683i
\(776\) 2.21037e7 1.85472e7i 1.31768 1.10567i
\(777\) −1.93186e7 + 2.20509e7i −1.14795 + 1.31031i
\(778\) 3.70540e6 2.10143e7i 0.219475 1.24471i
\(779\) 1.42998e7 + 1.19990e7i 0.844282 + 0.708436i
\(780\) −578653. + 89359.9i −0.0340551 + 0.00525903i
\(781\) −247332. 90021.7i −0.0145095 0.00528104i
\(782\) 4.62002e6 0.270163
\(783\) −2.89884e7 + 3.21883e6i −1.68974 + 0.187626i
\(784\) −1.30369e7 −0.757504
\(785\) 3.27612e7 + 1.19241e7i 1.89752 + 0.690640i
\(786\) −2.43246e6 + 6.26434e6i −0.140439 + 0.361675i
\(787\) −441041. 370078.i −0.0253830 0.0212989i 0.630008 0.776589i \(-0.283052\pi\)
−0.655391 + 0.755290i \(0.727496\pi\)
\(788\) −14091.8 + 79918.5i −0.000808445 + 0.00458492i
\(789\) −4.57346e6 907337.i −0.261549 0.0518891i
\(790\) 8.21061e6 6.88952e6i 0.468067 0.392755i
\(791\) 4.76994e6 + 8.26178e6i 0.271064 + 0.469496i
\(792\) −1.22068e6 2.33917e6i −0.0691492 0.132510i
\(793\) 2.92104e6 5.05939e6i 0.164951 0.285703i
\(794\) −1.37089e6 7.77469e6i −0.0771703 0.437655i
\(795\) 1.62643e6 893352.i 0.0912680 0.0501308i
\(796\) 121826. 44341.2i 0.00681489 0.00248042i
\(797\) 1.96495e7 7.15185e6i 1.09574 0.398816i 0.269994 0.962862i \(-0.412978\pi\)
0.825743 + 0.564046i \(0.190756\pi\)
\(798\) 659996. 3.09581e7i 0.0366889 1.72094i
\(799\) −416309. 2.36101e6i −0.0230701 0.130837i
\(800\) −370143. + 641106.i −0.0204477 + 0.0354164i
\(801\) −1.06398e7 + 3.36644e6i −0.585939 + 0.185391i
\(802\) 5.50165e6 + 9.52914e6i 0.302035 + 0.523140i
\(803\) −2.24112e6 + 1.88052e6i −0.122653 + 0.102918i
\(804\) 44539.2 + 130993.i 0.00242998 + 0.00714672i
\(805\) 5.79225e6 3.28495e7i 0.315034 1.78665i
\(806\) −9.85244e6 8.26718e6i −0.534203 0.448250i
\(807\) −6.43380e6 8.00813e6i −0.347763 0.432860i
\(808\) −7.33816e6 2.67087e6i −0.395420 0.143921i
\(809\) 1.20869e7 0.649297 0.324649 0.945835i \(-0.394754\pi\)
0.324649 + 0.945835i \(0.394754\pi\)
\(810\) 2.29522e7 1.61399e7i 1.22917 0.864348i
\(811\) −2.09741e7 −1.11977 −0.559887 0.828569i \(-0.689155\pi\)
−0.559887 + 0.828569i \(0.689155\pi\)
\(812\) 664272. + 241775.i 0.0353554 + 0.0128683i
\(813\) −8.00762e6 9.96706e6i −0.424891 0.528860i
\(814\) 2.90289e6 + 2.43581e6i 0.153557 + 0.128850i
\(815\) −3.46017e6 + 1.96236e7i −0.182475 + 1.03487i
\(816\) 1.80954e6 + 5.32197e6i 0.0951354 + 0.279800i
\(817\) 1.18453e7 9.93936e6i 0.620855 0.520959i
\(818\) −1.66187e7 2.87844e7i −0.868388 1.50409i
\(819\) 2.58316e7 + 2.36228e7i 1.34568 + 1.23061i
\(820\) 204983. 355042.i 0.0106459 0.0184393i
\(821\) 5.98741e6 + 3.39563e7i 0.310014 + 1.75818i 0.598911 + 0.800815i \(0.295600\pi\)
−0.288897 + 0.957360i \(0.593289\pi\)
\(822\) −306908. + 1.43960e7i −0.0158427 + 0.743124i
\(823\) −1.72434e7 + 6.27608e6i −0.887408 + 0.322990i −0.745195 0.666846i \(-0.767644\pi\)
−0.142212 + 0.989836i \(0.545422\pi\)
\(824\) −2.35926e7 + 8.58699e6i −1.21048 + 0.440578i
\(825\) −3.15343e6 + 1.73209e6i −0.161305 + 0.0886003i
\(826\) −6.43396e6 3.64888e7i −0.328117 1.86084i
\(827\) 5.56468e6 9.63830e6i 0.282928 0.490046i −0.689177 0.724593i \(-0.742028\pi\)
0.972105 + 0.234548i \(0.0753609\pi\)
\(828\) 304267. + 12979.3i 0.0154234 + 0.000657921i
\(829\) 9.97762e6 + 1.72817e7i 0.504244 + 0.873376i 0.999988 + 0.00490734i \(0.00156206\pi\)
−0.495744 + 0.868469i \(0.665105\pi\)
\(830\) 1.32342e7 1.11049e7i 0.666813 0.559523i
\(831\) −3.43085e7 6.80652e6i −1.72345 0.341919i
\(832\) −4.70308e6 + 2.66725e7i −0.235545 + 1.33584i
\(833\) 3.32402e6 + 2.78919e6i 0.165978 + 0.139272i
\(834\) −1.21212e7 + 3.12159e7i −0.603435 + 1.55403i
\(835\) −5.43979e7 1.97992e7i −2.70001 0.982724i
\(836\) −65945.6 −0.00326340
\(837\) 9.86740e6 + 2.39883e6i 0.486843 + 0.118355i
\(838\) −2.86391e7 −1.40880
\(839\) −2.42276e7 8.81812e6i −1.18824 0.432485i −0.329136 0.944282i \(-0.606758\pi\)
−0.859106 + 0.511797i \(0.828980\pi\)
\(840\) 3.94482e7 6.09189e6i 1.92899 0.297888i
\(841\) 2.97033e7 + 2.49240e7i 1.44815 + 1.21515i
\(842\) 1.06450e6 6.03710e6i 0.0517448 0.293460i
\(843\) 2.34201e7 2.67326e7i 1.13506 1.29560i
\(844\) 44128.0 37027.8i 0.00213235 0.00178925i
\(845\) 1.40016e7 + 2.42514e7i 0.674582 + 1.16841i
\(846\) −1.26152e6 9.50858e6i −0.0605993 0.456762i
\(847\) 1.34778e7 2.33443e7i 0.645523 1.11808i
\(848\) 258273. + 1.46474e6i 0.0123336 + 0.0699472i
\(849\) 1.96551e7 + 1.19136e7i 0.935851 + 0.567247i
\(850\) 7.08396e6 2.57835e6i 0.336301 0.122404i
\(851\) 2.41242e7 8.78049e6i 1.14190 0.415618i
\(852\) 31088.9 + 18843.9i 0.00146726 + 0.000889349i
\(853\) −6.71342e6 3.80737e7i −0.315916 1.79165i −0.567038 0.823692i \(-0.691911\pi\)
0.251122 0.967956i \(-0.419201\pi\)
\(854\) 3.39270e6 5.87633e6i 0.159185 0.275716i
\(855\) 5.41360e6 + 4.08045e7i 0.253262 + 1.90894i
\(856\) 5.02588e6 + 8.70507e6i 0.234438 + 0.406058i
\(857\) 8.34357e6 7.00109e6i 0.388061 0.325622i −0.427796 0.903875i \(-0.640710\pi\)
0.815857 + 0.578253i \(0.196266\pi\)
\(858\) 2.98163e6 3.40334e6i 0.138273 0.157829i
\(859\) −2.72863e6 + 1.54748e7i −0.126171 + 0.715554i 0.854434 + 0.519560i \(0.173904\pi\)
−0.980605 + 0.195993i \(0.937207\pi\)
\(860\) −260146. 218288.i −0.0119942 0.0100643i
\(861\) −2.42225e7 + 3.74061e6i −1.11355 + 0.171963i
\(862\) −1.16306e7 4.23320e6i −0.533132 0.194044i
\(863\) −3.19816e7 −1.46175 −0.730875 0.682512i \(-0.760888\pi\)
−0.730875 + 0.682512i \(0.760888\pi\)
\(864\) 206755. + 705398.i 0.00942263 + 0.0321477i
\(865\) 4.30697e7 1.95718
\(866\) 1.26796e7 + 4.61500e6i 0.574528 + 0.209111i
\(867\) −7.33441e6 + 1.88884e7i −0.331373 + 0.853390i
\(868\) −188538. 158202.i −0.00849377 0.00712712i
\(869\) −236970. + 1.34392e6i −0.0106449 + 0.0603705i
\(870\) −5.59441e7 1.10988e7i −2.50586 0.497141i
\(871\) 1.06681e7 8.95159e6i 0.476476 0.399811i
\(872\) 1.35981e7 + 2.35526e7i 0.605603 + 1.04893i
\(873\) −3.90326e7 1.66503e6i −1.73337 0.0739413i
\(874\) −1.35581e7 + 2.34833e7i −0.600372 + 1.03987i
\(875\) −1.70912e6 9.69289e6i −0.0754661 0.427989i
\(876\) 354171. 194536.i 0.0155938 0.00856524i
\(877\) 2.53799e7 9.23754e6i 1.11427 0.405562i 0.281714 0.959499i \(-0.409097\pi\)
0.832559 + 0.553936i \(0.186875\pi\)
\(878\) 4.12839e7 1.50261e7i 1.80736 0.657825i
\(879\) 716389. 3.36032e7i 0.0312735 1.46693i
\(880\) −910959. 5.16630e6i −0.0396544 0.224892i
\(881\) −8.03935e6 + 1.39246e7i −0.348965 + 0.604424i −0.986066 0.166356i \(-0.946800\pi\)
0.637101 + 0.770780i \(0.280133\pi\)
\(882\) 1.28114e7 + 1.17159e7i 0.554532 + 0.507114i
\(883\) −9.99319e6 1.73087e7i −0.431323 0.747073i 0.565665 0.824635i \(-0.308620\pi\)
−0.996988 + 0.0775623i \(0.975286\pi\)
\(884\) −119658. + 100405.i −0.00515004 + 0.00432140i
\(885\) 1.58552e7 + 4.66312e7i 0.680478 + 2.00133i
\(886\) −1.99403e6 + 1.13087e7i −0.0853391 + 0.483982i
\(887\) −1.77087e7 1.48594e7i −0.755750 0.634150i 0.181267 0.983434i \(-0.441980\pi\)
−0.937017 + 0.349284i \(0.886425\pi\)
\(888\) 1.92410e7 + 2.39492e7i 0.818831 + 1.01920i
\(889\) 2.64148e7 + 9.61420e6i 1.12097 + 0.407999i
\(890\) −2.18224e7 −0.923481
\(891\) −917713. + 3.45260e6i −0.0387269 + 0.145698i
\(892\) −261766. −0.0110154
\(893\) 1.32226e7 + 4.81264e6i 0.554867 + 0.201955i
\(894\) −2.95191e6 3.67423e6i −0.123526 0.153753i
\(895\) −2.15911e7 1.81171e7i −0.900983 0.756014i
\(896\) −5.64717e6 + 3.20267e7i −0.234996 + 1.33273i
\(897\) −9.86776e6 2.90217e7i −0.409485 1.20432i
\(898\) −4.83812e6 + 4.05967e6i −0.200210 + 0.167996i
\(899\) −1.03207e7 1.78759e7i −0.425902 0.737683i
\(900\) 473782. 149905.i 0.0194972 0.00616892i
\(901\) 247522. 428720.i 0.0101578 0.0175939i
\(902\) 550139. + 3.11999e6i 0.0225142 + 0.127684i
\(903\) −432732. + 2.02979e7i −0.0176604 + 0.828385i
\(904\) 9.39405e6 3.41916e6i 0.382324 0.139155i
\(905\) −5.47068e7 + 1.99117e7i −2.22034 + 0.808139i
\(906\) 1.73713e7 9.54152e6i 0.703090 0.386186i
\(907\) 5.55703e6 + 3.15155e7i 0.224297 + 1.27205i 0.864024 + 0.503451i \(0.167937\pi\)
−0.639726 + 0.768603i \(0.720952\pi\)
\(908\) −50044.4 + 86679.5i −0.00201438 + 0.00348901i
\(909\) 4.89161e6 + 9.37377e6i 0.196355 + 0.376274i
\(910\) 3.42251e7 + 5.92795e7i 1.37006 + 2.37302i
\(911\) 3.41771e7 2.86780e7i 1.36439 1.14486i 0.389794 0.920902i \(-0.372546\pi\)
0.974599 0.223959i \(-0.0718981\pi\)
\(912\) −3.23617e7 6.42029e6i −1.28838 0.255604i
\(913\) −381959. + 2.16619e6i −0.0151649 + 0.0860044i
\(914\) 1.65582e7 + 1.38939e7i 0.655611 + 0.550123i
\(915\) −3.26493e6 + 8.40822e6i −0.128920 + 0.332010i
\(916\) −334592. 121781.i −0.0131758 0.00479559i
\(917\) 1.29437e7 0.508316
\(918\) 3.00447e6 6.85610e6i 0.117669 0.268516i
\(919\) −1.15175e7 −0.449851 −0.224926 0.974376i \(-0.572214\pi\)
−0.224926 + 0.974376i \(0.572214\pi\)
\(920\) −3.28464e7 1.19551e7i −1.27943 0.465676i
\(921\) 1.57254e7 2.42843e6i 0.610875 0.0943358i
\(922\) 6.17517e6 + 5.18159e6i 0.239233 + 0.200741i
\(923\) 635408. 3.60358e6i 0.0245498 0.139229i
\(924\) 57057.2 65127.0i 0.00219852 0.00250946i
\(925\) 3.20898e7 2.69266e7i 1.23314 1.03473i
\(926\) −1.10768e7 1.91856e7i −0.424509 0.735271i
\(927\) 3.14192e7 + 1.29774e7i 1.20087 + 0.496008i
\(928\) 747082. 1.29398e6i 0.0284773 0.0493240i
\(929\) −7.19492e6 4.08044e7i −0.273519 1.55120i −0.743628 0.668593i \(-0.766897\pi\)
0.470110 0.882608i \(-0.344214\pi\)
\(930\) 1.69815e7 + 1.02930e7i 0.643826 + 0.390242i
\(931\) −2.39321e7 + 8.71059e6i −0.904914 + 0.329362i
\(932\) 82107.8 29884.8i 0.00309631 0.00112696i
\(933\) −2.79793e7 1.69591e7i −1.05228 0.637820i
\(934\) 3.80510e6 + 2.15798e7i 0.142725 + 0.809432i
\(935\) −873039. + 1.51215e6i −0.0326591 + 0.0565672i
\(936\) 2.90790e7 2.23594e7i 1.08490 0.834202i
\(937\) 2.49438e6 + 4.32039e6i 0.0928140 + 0.160759i 0.908694 0.417462i \(-0.137080\pi\)
−0.815880 + 0.578221i \(0.803747\pi\)
\(938\) 1.23907e7 1.03970e7i 0.459820 0.385835i
\(939\) 3.92556e6 4.48076e6i 0.145290 0.165840i
\(940\) 53662.8 304337.i 0.00198086 0.0112340i
\(941\) −2.90495e7 2.43755e7i −1.06946 0.897385i −0.0744580 0.997224i \(-0.523723\pi\)
−0.995004 + 0.0998393i \(0.968167\pi\)
\(942\) 3.67762e7 5.67925e6i 1.35033 0.208528i
\(943\) 2.01687e7 + 7.34081e6i 0.738583 + 0.268822i
\(944\) −3.94775e7 −1.44185
\(945\) −4.49819e7 2.99583e7i −1.63854 1.09128i
\(946\) 2.62432e6 0.0953429
\(947\) 3.11399e7 + 1.13340e7i 1.12834 + 0.410684i 0.837691 0.546145i \(-0.183905\pi\)
0.290653 + 0.956828i \(0.406127\pi\)
\(948\) 68226.6 175705.i 0.00246566 0.00634984i
\(949\) −3.11568e7 2.61436e7i −1.12302 0.942325i
\(950\) −7.68326e6 + 4.35740e7i −0.276208 + 1.56646i
\(951\) 2.02641e7 + 4.02022e6i 0.726566 + 0.144145i
\(952\) 8.15739e6 6.84486e6i 0.291715 0.244778i
\(953\) −5.18454e6 8.97989e6i −0.184918 0.320287i 0.758631 0.651520i \(-0.225868\pi\)
−0.943549 + 0.331234i \(0.892535\pi\)
\(954\) 1.06252e6 1.67151e6i 0.0377976 0.0594617i
\(955\) −5.21371e6 + 9.03042e6i −0.184986 + 0.320405i
\(956\) 129306. + 733333.i 0.00457589 + 0.0259511i
\(957\) 6.36477e6 3.49598e6i 0.224648 0.123393i
\(958\) −1.08489e7 + 3.94868e6i −0.381920 + 0.139007i
\(959\) 2.60622e7 9.48586e6i 0.915091 0.333066i
\(960\) 891280. 4.18068e7i 0.0312130 1.46409i
\(961\) −3.72346e6 2.11168e7i −0.130058 0.737597i
\(962\) −2.63411e7 + 4.56241e7i −0.917690 + 1.58949i
\(963\) 2.93239e6 1.32902e7i 0.101896 0.461811i
\(964\) 398944. + 690990.i 0.0138267 + 0.0239486i
\(965\) −4.79820e6 + 4.02617e6i −0.165867 + 0.139179i
\(966\) −1.14611e7 3.37079e7i −0.395170 1.16222i
\(967\) −1.33382e6 + 7.56448e6i −0.0458703 + 0.260143i −0.999115 0.0420551i \(-0.986609\pi\)
0.953245 + 0.302199i \(0.0977206\pi\)
\(968\) −2.16386e7 1.81569e7i −0.742233 0.622807i
\(969\) 6.87766e6 + 8.56060e6i 0.235305 + 0.292884i
\(970\) −7.17893e7 2.61292e7i −2.44980 0.891654i
\(971\) 3.63281e6 0.123650 0.0618250 0.998087i \(-0.480308\pi\)
0.0618250 + 0.998087i \(0.480308\pi\)
\(972\) 217131. 443091.i 0.00737150 0.0150428i
\(973\) 6.44996e7 2.18411
\(974\) −2.37606e7 8.64815e6i −0.802528 0.292096i
\(975\) −3.13270e7 3.89926e7i −1.05537 1.31362i
\(976\) −5.53823e6 4.64713e6i −0.186100 0.156156i
\(977\) −6.47418e6 + 3.67169e7i −0.216994 + 1.23064i 0.660418 + 0.750898i \(0.270379\pi\)
−0.877412 + 0.479737i \(0.840732\pi\)
\(978\) 6.84664e6 + 2.01364e7i 0.228892 + 0.673186i
\(979\) 2.12842e6 1.78596e6i 0.0709743 0.0595545i
\(980\) 279665. + 484393.i 0.00930191 + 0.0161114i
\(981\) 7.93396e6 3.59582e7i 0.263219 1.19296i
\(982\) −4.12446e6 + 7.14378e6i −0.136486 + 0.236401i
\(983\) −435244. 2.46839e6i −0.0143664 0.0814761i 0.976782 0.214238i \(-0.0687267\pi\)
−0.991148 + 0.132761i \(0.957616\pi\)
\(984\) −547431. + 2.56780e7i −0.0180236 + 0.845423i
\(985\) −1.18507e7 + 4.31331e6i −0.389183 + 0.141651i
\(986\) −1.42980e7 + 5.20404e6i −0.468363 + 0.170470i
\(987\) −1.61933e7 + 8.89450e6i −0.529106 + 0.290622i
\(988\) −159200. 902869.i −0.00518861 0.0294261i
\(989\) 8.88948e6 1.53970e7i 0.288992 0.500549i
\(990\) −3.74762e6 + 5.89560e6i −0.121525 + 0.191179i
\(991\) −1.27803e7 2.21361e7i −0.413386 0.716006i 0.581871 0.813281i \(-0.302321\pi\)
−0.995258 + 0.0972748i \(0.968987\pi\)
\(992\) −398509. + 334389.i −0.0128576 + 0.0107888i
\(993\) 3.34351e7 + 6.63326e6i 1.07604 + 0.213478i
\(994\) 738008. 4.18545e6i 0.0236916 0.134362i
\(995\) 1.54338e7 + 1.29505e7i 0.494214 + 0.414694i
\(996\) 109971. 283209.i 0.00351260 0.00904605i
\(997\) −8.58197e6 3.12358e6i −0.273432 0.0995211i 0.201665 0.979455i \(-0.435365\pi\)
−0.475097 + 0.879933i \(0.657587\pi\)
\(998\) 2.49701e7 0.793586
\(999\) 2.65811e6 4.15104e7i 0.0842672 1.31596i
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 27.6.e.a.4.11 84
3.2 odd 2 81.6.e.a.64.4 84
27.7 even 9 inner 27.6.e.a.7.11 yes 84
27.13 even 9 729.6.a.c.1.12 42
27.14 odd 18 729.6.a.e.1.31 42
27.20 odd 18 81.6.e.a.19.4 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.6.e.a.4.11 84 1.1 even 1 trivial
27.6.e.a.7.11 yes 84 27.7 even 9 inner
81.6.e.a.19.4 84 27.20 odd 18
81.6.e.a.64.4 84 3.2 odd 2
729.6.a.c.1.12 42 27.13 even 9
729.6.a.e.1.31 42 27.14 odd 18