Properties

Label 150.6.g.d.61.6
Level $150$
Weight $6$
Character 150.61
Analytic conductor $24.058$
Analytic rank $0$
Dimension $28$
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] = [150,6,Mod(31,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.31");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 150.g (of order \(5\), degree \(4\), 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: \(24.0575729719\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 61.6
Character \(\chi\) \(=\) 150.61
Dual form 150.6.g.d.91.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.23607 + 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(41.0391 - 37.9577i) q^{5} +(-11.1246 - 34.2380i) q^{6} -217.896 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +O(q^{10})\) \(q+(-3.23607 + 2.35114i) q^{2} +(-2.78115 + 8.55951i) q^{3} +(4.94427 - 15.2169i) q^{4} +(41.0391 - 37.9577i) q^{5} +(-11.1246 - 34.2380i) q^{6} -217.896 q^{7} +(19.7771 + 60.8676i) q^{8} +(-65.5304 - 47.6106i) q^{9} +(-43.5614 + 219.323i) q^{10} +(4.90062 - 3.56051i) q^{11} +(116.498 + 84.6411i) q^{12} +(49.9815 + 36.3137i) q^{13} +(705.125 - 512.303i) q^{14} +(210.763 + 456.841i) q^{15} +(-207.108 - 150.473i) q^{16} +(472.147 + 1453.12i) q^{17} +324.000 q^{18} +(-339.610 - 1045.21i) q^{19} +(-374.691 - 812.162i) q^{20} +(606.001 - 1865.08i) q^{21} +(-7.48748 + 23.0441i) q^{22} +(3027.50 - 2199.61i) q^{23} -576.000 q^{24} +(243.421 - 3115.50i) q^{25} -247.122 q^{26} +(589.773 - 428.495i) q^{27} +(-1077.34 + 3315.70i) q^{28} +(813.022 - 2502.22i) q^{29} +(-1756.14 - 982.834i) q^{30} +(2747.68 + 8456.49i) q^{31} +1024.00 q^{32} +(16.8468 + 51.8492i) q^{33} +(-4944.38 - 3592.30i) q^{34} +(-8942.25 + 8270.82i) q^{35} +(-1048.49 + 761.770i) q^{36} +(11585.8 + 8417.60i) q^{37} +(3556.44 + 2583.90i) q^{38} +(-449.833 + 326.823i) q^{39} +(3122.03 + 1747.26i) q^{40} +(4664.37 + 3388.86i) q^{41} +(2424.00 + 7460.32i) q^{42} +5419.24 q^{43} +(-29.9499 - 92.1763i) q^{44} +(-4496.50 + 533.487i) q^{45} +(-4625.61 + 14236.2i) q^{46} +(-5776.83 + 17779.3i) q^{47} +(1863.98 - 1354.26i) q^{48} +30671.5 q^{49} +(6537.27 + 10654.3i) q^{50} -13751.1 q^{51} +(799.704 - 581.019i) q^{52} +(-7948.72 + 24463.6i) q^{53} +(-901.094 + 2773.28i) q^{54} +(65.9683 - 332.136i) q^{55} +(-4309.34 - 13262.8i) q^{56} +9891.00 q^{57} +(3252.09 + 10008.9i) q^{58} +(-31049.1 - 22558.5i) q^{59} +(7993.78 - 948.421i) q^{60} +(40631.9 - 29520.8i) q^{61} +(-28774.1 - 20905.6i) q^{62} +(14278.8 + 10374.1i) q^{63} +(-3313.73 + 2407.57i) q^{64} +(3429.58 - 406.902i) q^{65} +(-176.422 - 128.178i) q^{66} +(15380.3 + 47335.6i) q^{67} +24446.4 q^{68} +(10407.6 + 32031.4i) q^{69} +(9491.85 - 47789.4i) q^{70} +(4893.83 - 15061.7i) q^{71} +(1601.94 - 4930.28i) q^{72} +(4522.11 - 3285.50i) q^{73} -57283.5 q^{74} +(25990.2 + 10748.3i) q^{75} -17584.0 q^{76} +(-1067.82 + 775.819i) q^{77} +(687.284 - 2115.24i) q^{78} +(-16570.3 + 50998.2i) q^{79} +(-14211.2 + 1686.08i) q^{80} +(2027.46 + 6239.88i) q^{81} -23061.9 q^{82} +(10806.8 + 33260.0i) q^{83} +(-25384.5 - 18442.9i) q^{84} +(74533.5 + 41713.1i) q^{85} +(-17537.0 + 12741.4i) q^{86} +(19156.7 + 13918.1i) q^{87} +(313.640 + 227.872i) q^{88} +(101616. - 73828.2i) q^{89} +(13296.7 - 12298.3i) q^{90} +(-10890.7 - 7912.59i) q^{91} +(-18502.5 - 56944.7i) q^{92} -80025.1 q^{93} +(-23107.3 - 71117.0i) q^{94} +(-53611.1 - 30003.7i) q^{95} +(-2847.90 + 8764.94i) q^{96} +(30213.3 - 92987.1i) q^{97} +(-99255.1 + 72113.0i) q^{98} -490.657 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 28 q^{2} + 63 q^{3} - 112 q^{4} + 11 q^{5} + 252 q^{6} - 62 q^{7} - 448 q^{8} - 567 q^{9} + 44 q^{10} - 135 q^{11} + 1008 q^{12} + 616 q^{13} - 48 q^{14} + 531 q^{15} - 1792 q^{16} - 3372 q^{17} + 9072 q^{18} + 488 q^{19} - 944 q^{20} - 387 q^{21} - 1920 q^{22} - 620 q^{23} - 16128 q^{24} + 6659 q^{25} - 1616 q^{26} + 5103 q^{27} + 688 q^{28} + 5682 q^{29} + 2844 q^{30} + 3339 q^{31} + 28672 q^{32} + 4320 q^{33} + 14032 q^{34} - 23984 q^{35} - 9072 q^{36} + 4506 q^{37} - 1528 q^{38} - 5544 q^{39} - 5056 q^{40} + 44962 q^{41} - 1548 q^{42} + 38028 q^{43} - 7680 q^{44} + 9396 q^{45} + 7480 q^{46} - 58300 q^{47} + 16128 q^{48} + 114402 q^{49} + 7476 q^{50} + 2448 q^{51} + 9856 q^{52} - 138 q^{53} + 20412 q^{54} + 96850 q^{55} + 2752 q^{56} + 1908 q^{57} + 22728 q^{58} + 40245 q^{59} - 16704 q^{60} + 79380 q^{61} - 54504 q^{62} - 972 q^{63} - 28672 q^{64} + 3532 q^{65} + 4860 q^{66} - 34352 q^{67} - 4352 q^{68} - 16830 q^{69} - 69476 q^{70} + 115860 q^{71} - 36288 q^{72} - 121214 q^{73} - 37856 q^{74} + 21969 q^{75} - 3392 q^{76} + 195005 q^{77} + 14904 q^{78} + 36224 q^{79} + 29696 q^{80} - 45927 q^{81} + 34608 q^{82} + 85051 q^{83} + 1728 q^{84} + 137496 q^{85} - 18568 q^{86} + 127062 q^{87} - 8640 q^{88} - 53826 q^{89} + 3564 q^{90} - 408104 q^{91} + 29920 q^{92} - 185166 q^{93} - 233200 q^{94} - 482004 q^{95} + 64512 q^{96} - 244169 q^{97} - 395952 q^{98} + 99630 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.23607 + 2.35114i −0.572061 + 0.415627i
\(3\) −2.78115 + 8.55951i −0.178411 + 0.549093i
\(4\) 4.94427 15.2169i 0.154508 0.475528i
\(5\) 41.0391 37.9577i 0.734130 0.679009i
\(6\) −11.1246 34.2380i −0.126156 0.388267i
\(7\) −217.896 −1.68075 −0.840376 0.542005i \(-0.817666\pi\)
−0.840376 + 0.542005i \(0.817666\pi\)
\(8\) 19.7771 + 60.8676i 0.109254 + 0.336249i
\(9\) −65.5304 47.6106i −0.269672 0.195928i
\(10\) −43.5614 + 219.323i −0.137753 + 0.693559i
\(11\) 4.90062 3.56051i 0.0122115 0.00887218i −0.581663 0.813430i \(-0.697598\pi\)
0.593874 + 0.804558i \(0.297598\pi\)
\(12\) 116.498 + 84.6411i 0.233543 + 0.169679i
\(13\) 49.9815 + 36.3137i 0.0820259 + 0.0595953i 0.628042 0.778179i \(-0.283856\pi\)
−0.546017 + 0.837774i \(0.683856\pi\)
\(14\) 705.125 512.303i 0.961493 0.698565i
\(15\) 210.763 + 456.841i 0.241862 + 0.524248i
\(16\) −207.108 150.473i −0.202254 0.146946i
\(17\) 472.147 + 1453.12i 0.396237 + 1.21949i 0.927994 + 0.372594i \(0.121532\pi\)
−0.531758 + 0.846896i \(0.678468\pi\)
\(18\) 324.000 0.235702
\(19\) −339.610 1045.21i −0.215822 0.664232i −0.999094 0.0425531i \(-0.986451\pi\)
0.783272 0.621679i \(-0.213549\pi\)
\(20\) −374.691 812.162i −0.209458 0.454012i
\(21\) 606.001 1865.08i 0.299865 0.922888i
\(22\) −7.48748 + 23.0441i −0.00329821 + 0.0101509i
\(23\) 3027.50 2199.61i 1.19334 0.867014i 0.199729 0.979851i \(-0.435994\pi\)
0.993613 + 0.112837i \(0.0359939\pi\)
\(24\) −576.000 −0.204124
\(25\) 243.421 3115.50i 0.0778946 0.996962i
\(26\) −247.122 −0.0716932
\(27\) 589.773 428.495i 0.155695 0.113119i
\(28\) −1077.34 + 3315.70i −0.259690 + 0.799245i
\(29\) 813.022 2502.22i 0.179518 0.552498i −0.820293 0.571943i \(-0.806190\pi\)
0.999811 + 0.0194447i \(0.00618982\pi\)
\(30\) −1756.14 982.834i −0.356251 0.199378i
\(31\) 2747.68 + 8456.49i 0.513526 + 1.58047i 0.785949 + 0.618292i \(0.212175\pi\)
−0.272423 + 0.962178i \(0.587825\pi\)
\(32\) 1024.00 0.176777
\(33\) 16.8468 + 51.8492i 0.00269298 + 0.00828814i
\(34\) −4944.38 3592.30i −0.733525 0.532937i
\(35\) −8942.25 + 8270.82i −1.23389 + 1.14124i
\(36\) −1048.49 + 761.770i −0.134836 + 0.0979642i
\(37\) 11585.8 + 8417.60i 1.39131 + 1.01084i 0.995721 + 0.0924149i \(0.0294586\pi\)
0.395586 + 0.918429i \(0.370541\pi\)
\(38\) 3556.44 + 2583.90i 0.399536 + 0.290280i
\(39\) −449.833 + 326.823i −0.0473576 + 0.0344073i
\(40\) 3122.03 + 1747.26i 0.308523 + 0.172666i
\(41\) 4664.37 + 3388.86i 0.433344 + 0.314843i 0.782985 0.622041i \(-0.213696\pi\)
−0.349641 + 0.936884i \(0.613696\pi\)
\(42\) 2424.00 + 7460.32i 0.212036 + 0.652581i
\(43\) 5419.24 0.446959 0.223479 0.974709i \(-0.428258\pi\)
0.223479 + 0.974709i \(0.428258\pi\)
\(44\) −29.9499 92.1763i −0.00233219 0.00717774i
\(45\) −4496.50 + 533.487i −0.331012 + 0.0392728i
\(46\) −4625.61 + 14236.2i −0.322311 + 0.991970i
\(47\) −5776.83 + 17779.3i −0.381456 + 1.17400i 0.557562 + 0.830135i \(0.311737\pi\)
−0.939018 + 0.343867i \(0.888263\pi\)
\(48\) 1863.98 1354.26i 0.116772 0.0848395i
\(49\) 30671.5 1.82492
\(50\) 6537.27 + 10654.3i 0.369804 + 0.602698i
\(51\) −13751.1 −0.740306
\(52\) 799.704 581.019i 0.0410129 0.0297976i
\(53\) −7948.72 + 24463.6i −0.388694 + 1.19628i 0.545071 + 0.838390i \(0.316503\pi\)
−0.933765 + 0.357887i \(0.883497\pi\)
\(54\) −901.094 + 2773.28i −0.0420519 + 0.129422i
\(55\) 65.9683 332.136i 0.00294055 0.0148050i
\(56\) −4309.34 13262.8i −0.183629 0.565151i
\(57\) 9891.00 0.403230
\(58\) 3252.09 + 10008.9i 0.126938 + 0.390675i
\(59\) −31049.1 22558.5i −1.16123 0.843686i −0.171300 0.985219i \(-0.554797\pi\)
−0.989933 + 0.141533i \(0.954797\pi\)
\(60\) 7993.78 948.421i 0.286665 0.0340113i
\(61\) 40631.9 29520.8i 1.39811 1.01579i 0.403193 0.915115i \(-0.367900\pi\)
0.994920 0.100673i \(-0.0320995\pi\)
\(62\) −28774.1 20905.6i −0.950654 0.690690i
\(63\) 14278.8 + 10374.1i 0.453252 + 0.329307i
\(64\) −3313.73 + 2407.57i −0.101127 + 0.0734732i
\(65\) 3429.58 406.902i 0.100683 0.0119456i
\(66\) −176.422 128.178i −0.00498532 0.00362205i
\(67\) 15380.3 + 47335.6i 0.418578 + 1.28825i 0.909011 + 0.416772i \(0.136839\pi\)
−0.490433 + 0.871479i \(0.663161\pi\)
\(68\) 24446.4 0.641124
\(69\) 10407.6 + 32031.4i 0.263166 + 0.809940i
\(70\) 9491.85 47789.4i 0.231529 1.16570i
\(71\) 4893.83 15061.7i 0.115213 0.354590i −0.876778 0.480895i \(-0.840312\pi\)
0.991991 + 0.126305i \(0.0403117\pi\)
\(72\) 1601.94 4930.28i 0.0364180 0.112083i
\(73\) 4522.11 3285.50i 0.0993194 0.0721597i −0.537017 0.843571i \(-0.680449\pi\)
0.636337 + 0.771412i \(0.280449\pi\)
\(74\) −57283.5 −1.21605
\(75\) 25990.2 + 10748.3i 0.533527 + 0.220640i
\(76\) −17584.0 −0.349207
\(77\) −1067.82 + 775.819i −0.0205245 + 0.0149119i
\(78\) 687.284 2115.24i 0.0127909 0.0393662i
\(79\) −16570.3 + 50998.2i −0.298719 + 0.919364i 0.683227 + 0.730206i \(0.260576\pi\)
−0.981947 + 0.189158i \(0.939424\pi\)
\(80\) −14211.2 + 1686.08i −0.248259 + 0.0294546i
\(81\) 2027.46 + 6239.88i 0.0343352 + 0.105673i
\(82\) −23061.9 −0.378757
\(83\) 10806.8 + 33260.0i 0.172188 + 0.529940i 0.999494 0.0318117i \(-0.0101277\pi\)
−0.827306 + 0.561752i \(0.810128\pi\)
\(84\) −25384.5 18442.9i −0.392528 0.285188i
\(85\) 74533.5 + 41713.1i 1.11893 + 0.626217i
\(86\) −17537.0 + 12741.4i −0.255688 + 0.185768i
\(87\) 19156.7 + 13918.1i 0.271345 + 0.197144i
\(88\) 313.640 + 227.872i 0.00431742 + 0.00313679i
\(89\) 101616. 73828.2i 1.35983 0.987978i 0.361379 0.932419i \(-0.382306\pi\)
0.998455 0.0555586i \(-0.0176940\pi\)
\(90\) 13296.7 12298.3i 0.173036 0.160044i
\(91\) −10890.7 7912.59i −0.137865 0.100165i
\(92\) −18502.5 56944.7i −0.227908 0.701429i
\(93\) −80025.1 −0.959443
\(94\) −23107.3 71117.0i −0.269730 0.830145i
\(95\) −53611.1 30003.7i −0.609461 0.341088i
\(96\) −2847.90 + 8764.94i −0.0315389 + 0.0970668i
\(97\) 30213.3 92987.1i 0.326039 1.00344i −0.644931 0.764241i \(-0.723114\pi\)
0.970969 0.239203i \(-0.0768863\pi\)
\(98\) −99255.1 + 72113.0i −1.04397 + 0.758488i
\(99\) −490.657 −0.00503142
\(100\) −46204.8 19108.0i −0.462048 0.191080i
\(101\) 769.198 0.00750300 0.00375150 0.999993i \(-0.498806\pi\)
0.00375150 + 0.999993i \(0.498806\pi\)
\(102\) 44499.4 32330.7i 0.423501 0.307691i
\(103\) 19851.7 61097.4i 0.184376 0.567452i −0.815561 0.578672i \(-0.803571\pi\)
0.999937 + 0.0112192i \(0.00357126\pi\)
\(104\) −1221.84 + 3760.43i −0.0110772 + 0.0340922i
\(105\) −45924.4 99543.7i −0.406509 0.881131i
\(106\) −31794.9 97854.6i −0.274848 0.845895i
\(107\) −133642. −1.12845 −0.564227 0.825620i \(-0.690826\pi\)
−0.564227 + 0.825620i \(0.690826\pi\)
\(108\) −3604.37 11093.1i −0.0297352 0.0915155i
\(109\) −67561.7 49086.5i −0.544671 0.395727i 0.281146 0.959665i \(-0.409286\pi\)
−0.825817 + 0.563938i \(0.809286\pi\)
\(110\) 567.422 + 1229.92i 0.00447120 + 0.00969157i
\(111\) −104272. + 75758.4i −0.803271 + 0.583611i
\(112\) 45128.0 + 32787.4i 0.339939 + 0.246980i
\(113\) 125365. + 91083.0i 0.923592 + 0.671029i 0.944416 0.328754i \(-0.106629\pi\)
−0.0208233 + 0.999783i \(0.506629\pi\)
\(114\) −32007.9 + 23255.1i −0.230672 + 0.167593i
\(115\) 40753.9 205187.i 0.287359 1.44679i
\(116\) −34056.3 24743.3i −0.234992 0.170731i
\(117\) −1546.39 4759.30i −0.0104437 0.0321424i
\(118\) 153515. 1.01496
\(119\) −102879. 316628.i −0.665975 2.04966i
\(120\) −23638.5 + 21863.7i −0.149854 + 0.138602i
\(121\) −49756.2 + 153134.i −0.308947 + 0.950840i
\(122\) −62079.9 + 191062.i −0.377617 + 1.16219i
\(123\) −41979.3 + 30499.7i −0.250191 + 0.181775i
\(124\) 142267. 0.830902
\(125\) −108268. 137097.i −0.619761 0.784791i
\(126\) −70598.2 −0.396157
\(127\) 262584. 190779.i 1.44464 1.04959i 0.457593 0.889162i \(-0.348712\pi\)
0.987047 0.160430i \(-0.0512881\pi\)
\(128\) 5062.93 15582.1i 0.0273135 0.0840623i
\(129\) −15071.7 + 46386.1i −0.0797424 + 0.245422i
\(130\) −10141.7 + 9380.19i −0.0526322 + 0.0486803i
\(131\) 36915.9 + 113616.i 0.187947 + 0.578442i 0.999987 0.00516059i \(-0.00164268\pi\)
−0.812040 + 0.583602i \(0.801643\pi\)
\(132\) 872.279 0.00435733
\(133\) 73999.4 + 227747.i 0.362743 + 1.11641i
\(134\) −161064. 117020.i −0.774884 0.562986i
\(135\) 7939.07 39971.5i 0.0374917 0.188763i
\(136\) −79110.1 + 57476.9i −0.366762 + 0.266468i
\(137\) 140582. + 102139.i 0.639924 + 0.464932i 0.859824 0.510590i \(-0.170573\pi\)
−0.219900 + 0.975522i \(0.570573\pi\)
\(138\) −108990. 79186.0i −0.487180 0.353957i
\(139\) 105648. 76758.0i 0.463794 0.336966i −0.331224 0.943552i \(-0.607461\pi\)
0.795018 + 0.606586i \(0.207461\pi\)
\(140\) 81643.4 + 176967.i 0.352047 + 0.763082i
\(141\) −136115. 98893.7i −0.576580 0.418910i
\(142\) 19575.3 + 60246.6i 0.0814682 + 0.250733i
\(143\) 374.235 0.00153040
\(144\) 6407.78 + 19721.1i 0.0257514 + 0.0792547i
\(145\) −61613.0 133550.i −0.243362 0.527500i
\(146\) −6909.17 + 21264.2i −0.0268252 + 0.0825596i
\(147\) −85302.1 + 262533.i −0.325587 + 1.00205i
\(148\) 185373. 134682.i 0.695653 0.505422i
\(149\) 244176. 0.901026 0.450513 0.892770i \(-0.351241\pi\)
0.450513 + 0.892770i \(0.351241\pi\)
\(150\) −109377. + 26324.5i −0.396914 + 0.0955284i
\(151\) −173628. −0.619695 −0.309847 0.950786i \(-0.600278\pi\)
−0.309847 + 0.950786i \(0.600278\pi\)
\(152\) 56903.0 41342.4i 0.199768 0.145140i
\(153\) 38243.9 117703.i 0.132079 0.406497i
\(154\) 1631.49 5021.21i 0.00554348 0.0170611i
\(155\) 433752. + 242751.i 1.45015 + 0.811582i
\(156\) 2749.14 + 8460.97i 0.00904451 + 0.0278361i
\(157\) 265895. 0.860917 0.430459 0.902610i \(-0.358352\pi\)
0.430459 + 0.902610i \(0.358352\pi\)
\(158\) −66281.3 203993.i −0.211226 0.650088i
\(159\) −187290. 136074.i −0.587519 0.426858i
\(160\) 42024.1 38868.7i 0.129777 0.120033i
\(161\) −659680. + 479285.i −2.00571 + 1.45723i
\(162\) −21231.8 15425.8i −0.0635624 0.0461808i
\(163\) 226738. + 164735.i 0.668429 + 0.485642i 0.869499 0.493935i \(-0.164442\pi\)
−0.201070 + 0.979577i \(0.564442\pi\)
\(164\) 74629.9 54221.8i 0.216672 0.157421i
\(165\) 2659.46 + 1488.38i 0.00760472 + 0.00425602i
\(166\) −113170. 82223.2i −0.318759 0.231592i
\(167\) −121716. 374603.i −0.337720 1.03939i −0.965367 0.260897i \(-0.915982\pi\)
0.627647 0.778498i \(-0.284018\pi\)
\(168\) 125508. 0.343082
\(169\) −113556. 349491.i −0.305840 0.941280i
\(170\) −339269. + 40252.5i −0.900372 + 0.106824i
\(171\) −27508.4 + 84662.1i −0.0719407 + 0.221411i
\(172\) 26794.2 82464.1i 0.0690589 0.212542i
\(173\) −85938.8 + 62438.2i −0.218310 + 0.158612i −0.691566 0.722314i \(-0.743079\pi\)
0.473255 + 0.880925i \(0.343079\pi\)
\(174\) −94715.7 −0.237164
\(175\) −53040.3 + 678855.i −0.130921 + 1.67564i
\(176\) −1550.72 −0.00377356
\(177\) 279442. 203027.i 0.670439 0.487102i
\(178\) −155255. + 477826.i −0.367279 + 1.13037i
\(179\) −51064.2 + 157159.i −0.119120 + 0.366613i −0.992784 0.119916i \(-0.961737\pi\)
0.873664 + 0.486529i \(0.161737\pi\)
\(180\) −14113.9 + 71060.5i −0.0324688 + 0.163473i
\(181\) 244490. + 752464.i 0.554709 + 1.70722i 0.696710 + 0.717353i \(0.254647\pi\)
−0.142001 + 0.989867i \(0.545353\pi\)
\(182\) 53846.8 0.120498
\(183\) 139680. + 429890.i 0.308323 + 0.948921i
\(184\) 193760. + 140775.i 0.421910 + 0.306536i
\(185\) 794986. 94321.0i 1.70777 0.202618i
\(186\) 258967. 188150.i 0.548860 0.398770i
\(187\) 7487.65 + 5440.09i 0.0156582 + 0.0113763i
\(188\) 241983. + 175811.i 0.499333 + 0.362787i
\(189\) −128509. + 93367.3i −0.261685 + 0.190125i
\(190\) 244032. 28953.2i 0.490414 0.0581851i
\(191\) −520965. 378503.i −1.03330 0.750734i −0.0643304 0.997929i \(-0.520491\pi\)
−0.968966 + 0.247195i \(0.920491\pi\)
\(192\) −11391.6 35059.7i −0.0223014 0.0686366i
\(193\) −533043. −1.03007 −0.515037 0.857168i \(-0.672222\pi\)
−0.515037 + 0.857168i \(0.672222\pi\)
\(194\) 120853. + 371948.i 0.230544 + 0.709542i
\(195\) −6055.31 + 30487.2i −0.0114038 + 0.0574157i
\(196\) 151648. 466725.i 0.281966 0.867803i
\(197\) 59303.6 182518.i 0.108872 0.335073i −0.881748 0.471721i \(-0.843633\pi\)
0.990620 + 0.136648i \(0.0436330\pi\)
\(198\) 1587.80 1153.60i 0.00287828 0.00209119i
\(199\) 53695.0 0.0961173 0.0480586 0.998845i \(-0.484697\pi\)
0.0480586 + 0.998845i \(0.484697\pi\)
\(200\) 194448. 46799.2i 0.343738 0.0827300i
\(201\) −447944. −0.782048
\(202\) −2489.18 + 1808.49i −0.00429218 + 0.00311845i
\(203\) −177154. + 545223.i −0.301724 + 0.928612i
\(204\) −67989.1 + 209249.i −0.114384 + 0.352037i
\(205\) 320055. 37972.9i 0.531912 0.0631087i
\(206\) 79407.0 + 244390.i 0.130374 + 0.401250i
\(207\) −303118. −0.491684
\(208\) −4887.35 15041.7i −0.00783277 0.0241068i
\(209\) −5385.78 3913.00i −0.00852870 0.00619646i
\(210\) 382656. + 214155.i 0.598770 + 0.335105i
\(211\) 489154. 355391.i 0.756378 0.549541i −0.141419 0.989950i \(-0.545166\pi\)
0.897797 + 0.440409i \(0.145166\pi\)
\(212\) 332960. + 241910.i 0.508807 + 0.369670i
\(213\) 115310. + 83777.6i 0.174148 + 0.126526i
\(214\) 432475. 314211.i 0.645545 0.469016i
\(215\) 222401. 205702.i 0.328126 0.303489i
\(216\) 37745.5 + 27423.7i 0.0550466 + 0.0399937i
\(217\) −598708. 1.84263e6i −0.863109 2.65638i
\(218\) 334044. 0.476060
\(219\) 15545.6 + 47844.5i 0.0219027 + 0.0674096i
\(220\) −4727.92 2646.01i −0.00658588 0.00368582i
\(221\) −29169.5 + 89774.4i −0.0401742 + 0.123644i
\(222\) 159314. 490319.i 0.216956 0.667722i
\(223\) −595860. + 432918.i −0.802384 + 0.582966i −0.911613 0.411051i \(-0.865162\pi\)
0.109229 + 0.994017i \(0.465162\pi\)
\(224\) −223125. −0.297118
\(225\) −164283. + 192571.i −0.216339 + 0.253591i
\(226\) −619839. −0.807249
\(227\) −298530. + 216895.i −0.384524 + 0.279373i −0.763208 0.646153i \(-0.776377\pi\)
0.378684 + 0.925526i \(0.376377\pi\)
\(228\) 48903.8 150510.i 0.0623025 0.191747i
\(229\) 85315.8 262575.i 0.107508 0.330875i −0.882803 0.469743i \(-0.844346\pi\)
0.990311 + 0.138868i \(0.0443464\pi\)
\(230\) 350542. + 759818.i 0.436938 + 0.947087i
\(231\) −3670.85 11297.7i −0.00452623 0.0139303i
\(232\) 168384. 0.205390
\(233\) −195578. 601928.i −0.236010 0.726364i −0.996986 0.0775840i \(-0.975279\pi\)
0.760976 0.648780i \(-0.224721\pi\)
\(234\) 16194.0 + 11765.6i 0.0193337 + 0.0140467i
\(235\) 437784. + 948921.i 0.517119 + 1.12088i
\(236\) −496786. + 360936.i −0.580617 + 0.421843i
\(237\) −390435. 283668.i −0.451521 0.328049i
\(238\) 1.07736e6 + 782747.i 1.23287 + 0.895734i
\(239\) −283936. + 206292.i −0.321533 + 0.233607i −0.736829 0.676079i \(-0.763678\pi\)
0.415296 + 0.909686i \(0.363678\pi\)
\(240\) 25091.4 126330.i 0.0281188 0.141572i
\(241\) 632191. + 459314.i 0.701142 + 0.509409i 0.880304 0.474410i \(-0.157339\pi\)
−0.179162 + 0.983820i \(0.557339\pi\)
\(242\) −199025. 612535.i −0.218458 0.672345i
\(243\) −59049.0 −0.0641500
\(244\) −248320. 764250.i −0.267016 0.821790i
\(245\) 1.25873e6 1.16422e6i 1.33973 1.23914i
\(246\) 64138.7 197398.i 0.0675744 0.207973i
\(247\) 20981.3 64573.7i 0.0218821 0.0673462i
\(248\) −460385. + 334490.i −0.475327 + 0.345345i
\(249\) −314744. −0.321706
\(250\) 672697. + 189104.i 0.680721 + 0.191359i
\(251\) 305776. 0.306351 0.153175 0.988199i \(-0.451050\pi\)
0.153175 + 0.988199i \(0.451050\pi\)
\(252\) 228461. 165986.i 0.226626 0.164653i
\(253\) 7004.91 21558.9i 0.00688020 0.0211751i
\(254\) −401193. + 1.23475e6i −0.390184 + 1.20086i
\(255\) −564333. + 521960.i −0.543481 + 0.502674i
\(256\) 20251.7 + 62328.4i 0.0193136 + 0.0594410i
\(257\) 1.71377e6 1.61853 0.809264 0.587445i \(-0.199866\pi\)
0.809264 + 0.587445i \(0.199866\pi\)
\(258\) −60287.0 185544.i −0.0563864 0.173539i
\(259\) −2.52450e6 1.83416e6i −2.33844 1.69898i
\(260\) 10765.0 54199.4i 0.00987598 0.0497235i
\(261\) −172410. + 125263.i −0.156661 + 0.113821i
\(262\) −386589. 280873.i −0.347933 0.252788i
\(263\) −264914. 192472.i −0.236165 0.171584i 0.463408 0.886145i \(-0.346627\pi\)
−0.699573 + 0.714561i \(0.746627\pi\)
\(264\) −2822.76 + 2050.85i −0.00249266 + 0.00181103i
\(265\) 602376. + 1.30568e6i 0.526930 + 1.14215i
\(266\) −774932. 563021.i −0.671521 0.487889i
\(267\) 349324. + 1.07511e6i 0.299882 + 0.922941i
\(268\) 796345. 0.677274
\(269\) −247804. 762662.i −0.208799 0.642616i −0.999536 0.0304605i \(-0.990303\pi\)
0.790737 0.612156i \(-0.209697\pi\)
\(270\) 68287.4 + 148017.i 0.0570074 + 0.123566i
\(271\) 27129.8 83496.9i 0.0224400 0.0690633i −0.939209 0.343345i \(-0.888440\pi\)
0.961649 + 0.274282i \(0.0884400\pi\)
\(272\) 120870. 371998.i 0.0990591 0.304873i
\(273\) 98016.7 71213.3i 0.0795964 0.0578302i
\(274\) −695076. −0.559314
\(275\) −9899.87 16134.6i −0.00789401 0.0128655i
\(276\) 538877. 0.425811
\(277\) −403606. + 293237.i −0.316052 + 0.229625i −0.734489 0.678621i \(-0.762578\pi\)
0.418437 + 0.908246i \(0.362578\pi\)
\(278\) −161416. + 496788.i −0.125267 + 0.385531i
\(279\) 222562. 684976.i 0.171175 0.526823i
\(280\) −680277. 380720.i −0.518550 0.290209i
\(281\) −375608. 1.15600e6i −0.283772 0.873360i −0.986764 0.162163i \(-0.948153\pi\)
0.702992 0.711198i \(-0.251847\pi\)
\(282\) 672992. 0.503949
\(283\) 552484. + 1.70037e6i 0.410066 + 1.26205i 0.916590 + 0.399828i \(0.130930\pi\)
−0.506524 + 0.862226i \(0.669070\pi\)
\(284\) −204995. 148938.i −0.150816 0.109574i
\(285\) 405918. 375440.i 0.296023 0.273797i
\(286\) −1211.05 + 879.880i −0.000875482 + 0.000636075i
\(287\) −1.01634e6 738418.i −0.728344 0.529173i
\(288\) −67103.1 48753.3i −0.0476718 0.0346356i
\(289\) −739940. + 537598.i −0.521137 + 0.378628i
\(290\) 513378. + 287314.i 0.358461 + 0.200615i
\(291\) 711896. + 517223.i 0.492815 + 0.358051i
\(292\) −27636.7 85056.9i −0.0189683 0.0583785i
\(293\) −2.29699e6 −1.56311 −0.781554 0.623837i \(-0.785573\pi\)
−0.781554 + 0.623837i \(0.785573\pi\)
\(294\) −341209. 1.05013e6i −0.230225 0.708558i
\(295\) −2.13050e6 + 252773.i −1.42537 + 0.169112i
\(296\) −283225. + 871678.i −0.187890 + 0.578265i
\(297\) 1364.59 4199.78i 0.000897660 0.00276271i
\(298\) −790171. + 574092.i −0.515442 + 0.374491i
\(299\) 231195. 0.149555
\(300\) 292058. 342348.i 0.187355 0.219616i
\(301\) −1.18083e6 −0.751227
\(302\) 561872. 408224.i 0.354503 0.257562i
\(303\) −2139.26 + 6583.96i −0.00133862 + 0.00411984i
\(304\) −86940.0 + 267574.i −0.0539555 + 0.166058i
\(305\) 546954. 2.75380e6i 0.336668 1.69505i
\(306\) 152975. + 470810.i 0.0933938 + 0.287437i
\(307\) −467443. −0.283063 −0.141531 0.989934i \(-0.545203\pi\)
−0.141531 + 0.989934i \(0.545203\pi\)
\(308\) 6525.95 + 20084.8i 0.00391983 + 0.0120640i
\(309\) 467753. + 339842.i 0.278689 + 0.202480i
\(310\) −1.97439e6 + 234252.i −1.16689 + 0.138445i
\(311\) −1.59708e6 + 1.16035e6i −0.936322 + 0.680278i −0.947533 0.319659i \(-0.896432\pi\)
0.0112102 + 0.999937i \(0.496432\pi\)
\(312\) −28789.3 20916.7i −0.0167435 0.0121648i
\(313\) −477870. 347193.i −0.275708 0.200314i 0.441335 0.897342i \(-0.354505\pi\)
−0.717043 + 0.697029i \(0.754505\pi\)
\(314\) −860455. + 625157.i −0.492497 + 0.357820i
\(315\) 979768. 116244.i 0.556348 0.0660079i
\(316\) 694107. + 504298.i 0.391029 + 0.284099i
\(317\) 437847. + 1.34755e6i 0.244722 + 0.753178i 0.995682 + 0.0928300i \(0.0295913\pi\)
−0.750960 + 0.660348i \(0.770409\pi\)
\(318\) 926014. 0.513511
\(319\) −4924.87 15157.2i −0.00270968 0.00833955i
\(320\) −44606.9 + 224586.i −0.0243516 + 0.122605i
\(321\) 371679. 1.14391e6i 0.201329 0.619626i
\(322\) 1.00790e6 3.10200e6i 0.541724 1.66726i
\(323\) 1.35847e6 986985.i 0.724508 0.526386i
\(324\) 104976. 0.0555556
\(325\) 125302. 146878.i 0.0658036 0.0771345i
\(326\) −1.12105e6 −0.584228
\(327\) 608055. 441778.i 0.314466 0.228473i
\(328\) −114024. + 350931.i −0.0585211 + 0.180110i
\(329\) 1.25875e6 3.87402e6i 0.641133 1.97321i
\(330\) −12105.6 + 1436.26i −0.00611928 + 0.000726021i
\(331\) 291944. + 898512.i 0.146464 + 0.450769i 0.997196 0.0748298i \(-0.0238413\pi\)
−0.850733 + 0.525599i \(0.823841\pi\)
\(332\) 559546. 0.278606
\(333\) −358457. 1.10322e6i −0.177144 0.545193i
\(334\) 1.27463e6 + 926070.i 0.625197 + 0.454232i
\(335\) 2.42794e6 + 1.35881e6i 1.18202 + 0.661526i
\(336\) −406152. + 295087.i −0.196264 + 0.142594i
\(337\) 204470. + 148556.i 0.0980740 + 0.0712550i 0.635742 0.771902i \(-0.280694\pi\)
−0.537667 + 0.843157i \(0.680694\pi\)
\(338\) 1.18918e6 + 863988.i 0.566181 + 0.411354i
\(339\) −1.12829e6 + 819747.i −0.533236 + 0.387419i
\(340\) 1.00326e6 927929.i 0.470669 0.435329i
\(341\) 43574.7 + 31658.9i 0.0202931 + 0.0147438i
\(342\) −110033. 338648.i −0.0508698 0.156561i
\(343\) −3.02101e6 −1.38649
\(344\) 107177. + 329856.i 0.0488320 + 0.150290i
\(345\) 1.64296e6 + 919490.i 0.743154 + 0.415910i
\(346\) 131303. 404109.i 0.0589636 0.181471i
\(347\) −256445. + 789256.i −0.114333 + 0.351880i −0.991807 0.127743i \(-0.959227\pi\)
0.877475 + 0.479623i \(0.159227\pi\)
\(348\) 306507. 222690.i 0.135672 0.0985718i
\(349\) −434928. −0.191141 −0.0955705 0.995423i \(-0.530468\pi\)
−0.0955705 + 0.995423i \(0.530468\pi\)
\(350\) −1.42444e6 2.32153e6i −0.621548 1.01299i
\(351\) 45038.0 0.0195124
\(352\) 5018.23 3645.96i 0.00215871 0.00156839i
\(353\) −200524. + 617148.i −0.0856503 + 0.263604i −0.984704 0.174233i \(-0.944255\pi\)
0.899054 + 0.437837i \(0.144255\pi\)
\(354\) −426950. + 1.31402e6i −0.181079 + 0.557305i
\(355\) −370868. 803876.i −0.156188 0.338546i
\(356\) −621020. 1.91130e6i −0.259705 0.799291i
\(357\) 2.99630e6 1.24427
\(358\) −204257. 628638.i −0.0842304 0.259235i
\(359\) 674193. + 489830.i 0.276089 + 0.200590i 0.717210 0.696858i \(-0.245419\pi\)
−0.441121 + 0.897448i \(0.645419\pi\)
\(360\) −121400. 263140.i −0.0493698 0.107012i
\(361\) 1.02608e6 745487.i 0.414392 0.301073i
\(362\) −2.56034e6 1.86019e6i −1.02689 0.746082i
\(363\) −1.17237e6 851777.i −0.466980 0.339281i
\(364\) −174252. + 126601.i −0.0689325 + 0.0500824i
\(365\) 60873.1 306483.i 0.0239163 0.120413i
\(366\) −1.46275e6 1.06275e6i −0.570777 0.414694i
\(367\) −35263.8 108531.i −0.0136667 0.0420618i 0.943991 0.329972i \(-0.107039\pi\)
−0.957657 + 0.287911i \(0.907039\pi\)
\(368\) −958003. −0.368763
\(369\) −144312. 444147.i −0.0551742 0.169809i
\(370\) −2.35087e6 + 2.17435e6i −0.892737 + 0.825706i
\(371\) 1.73199e6 5.33052e6i 0.653297 2.01064i
\(372\) −395666. + 1.21773e6i −0.148242 + 0.456242i
\(373\) −784356. + 569868.i −0.291905 + 0.212081i −0.724093 0.689702i \(-0.757741\pi\)
0.432189 + 0.901783i \(0.357741\pi\)
\(374\) −37021.0 −0.0136857
\(375\) 1.47459e6 545430.i 0.541495 0.200291i
\(376\) −1.19643e6 −0.436433
\(377\) 131501. 95541.0i 0.0476514 0.0346208i
\(378\) 196344. 604286.i 0.0706788 0.217527i
\(379\) 890187. 2.73971e6i 0.318334 0.979732i −0.656026 0.754738i \(-0.727764\pi\)
0.974360 0.224993i \(-0.0722361\pi\)
\(380\) −721632. + 667449.i −0.256364 + 0.237115i
\(381\) 902685. + 2.77818e6i 0.318584 + 0.980500i
\(382\) 2.57579e6 0.903134
\(383\) 782034. + 2.40685e6i 0.272414 + 0.838403i 0.989892 + 0.141822i \(0.0452961\pi\)
−0.717479 + 0.696581i \(0.754704\pi\)
\(384\) 119294. + 86672.5i 0.0412850 + 0.0299953i
\(385\) −14374.2 + 72371.1i −0.00494233 + 0.0248836i
\(386\) 1.72496e6 1.25326e6i 0.589266 0.428127i
\(387\) −355125. 258013.i −0.120532 0.0875719i
\(388\) −1.26559e6 919507.i −0.426790 0.310081i
\(389\) −3.19616e6 + 2.32214e6i −1.07091 + 0.778063i −0.976076 0.217429i \(-0.930233\pi\)
−0.0948364 + 0.995493i \(0.530233\pi\)
\(390\) −52084.3 112896.i −0.0173398 0.0375850i
\(391\) 4.62572e6 + 3.36078e6i 1.53016 + 1.11173i
\(392\) 606593. + 1.86690e6i 0.199380 + 0.613629i
\(393\) −1.07516e6 −0.351150
\(394\) 237214. + 730070.i 0.0769840 + 0.236932i
\(395\) 1.25575e6 + 2.72189e6i 0.404957 + 0.877766i
\(396\) −2425.94 + 7466.28i −0.000777396 + 0.00239258i
\(397\) 500257. 1.53963e6i 0.159300 0.490276i −0.839271 0.543714i \(-0.817018\pi\)
0.998571 + 0.0534375i \(0.0170178\pi\)
\(398\) −173761. + 126245.i −0.0549850 + 0.0399489i
\(399\) −2.15520e6 −0.677729
\(400\) −519214. + 608619.i −0.162254 + 0.190193i
\(401\) 1.59464e6 0.495223 0.247612 0.968859i \(-0.420354\pi\)
0.247612 + 0.968859i \(0.420354\pi\)
\(402\) 1.44958e6 1.05318e6i 0.447380 0.325040i
\(403\) −169753. + 522446.i −0.0520661 + 0.160243i
\(404\) 3803.12 11704.8i 0.00115928 0.00356789i
\(405\) 320057. + 179122.i 0.0969594 + 0.0542638i
\(406\) −708615. 2.18089e6i −0.213351 0.656628i
\(407\) 86748.7 0.0259583
\(408\) −271956. 836996.i −0.0808814 0.248927i
\(409\) 4.06504e6 + 2.95343e6i 1.20159 + 0.873008i 0.994440 0.105301i \(-0.0335807\pi\)
0.207151 + 0.978309i \(0.433581\pi\)
\(410\) −946440. + 875377.i −0.278057 + 0.257179i
\(411\) −1.26524e6 + 919250.i −0.369460 + 0.268429i
\(412\) −831561. 604164.i −0.241352 0.175352i
\(413\) 6.76547e6 + 4.91540e6i 1.95174 + 1.41803i
\(414\) 980911. 712674.i 0.281273 0.204357i
\(415\) 1.70598e6 + 954758.i 0.486242 + 0.272128i
\(416\) 51181.0 + 37185.2i 0.0145003 + 0.0105351i
\(417\) 363186. + 1.11777e6i 0.102280 + 0.314785i
\(418\) 26628.7 0.00745435
\(419\) 773689. + 2.38117e6i 0.215294 + 0.662606i 0.999133 + 0.0416415i \(0.0132587\pi\)
−0.783839 + 0.620964i \(0.786741\pi\)
\(420\) −1.74181e6 + 206657.i −0.481812 + 0.0571645i
\(421\) −1.83302e6 + 5.64146e6i −0.504037 + 1.55127i 0.298348 + 0.954457i \(0.403565\pi\)
−0.802384 + 0.596808i \(0.796435\pi\)
\(422\) −747360. + 2.30014e6i −0.204291 + 0.628743i
\(423\) 1.22504e6 890043.i 0.332889 0.241858i
\(424\) −1.64625e6 −0.444713
\(425\) 4.64213e6 1.11726e6i 1.24665 0.300041i
\(426\) −570124. −0.152211
\(427\) −8.85350e6 + 6.43245e6i −2.34988 + 1.70729i
\(428\) −660763. + 2.03362e6i −0.174356 + 0.536612i
\(429\) −1040.81 + 3203.27i −0.000273040 + 0.000840331i
\(430\) −236070. + 1.18856e6i −0.0615701 + 0.309992i
\(431\) 1.64998e6 + 5.07813e6i 0.427845 + 1.31677i 0.900243 + 0.435387i \(0.143388\pi\)
−0.472398 + 0.881385i \(0.656612\pi\)
\(432\) −186624. −0.0481125
\(433\) −455405. 1.40159e6i −0.116729 0.359254i 0.875575 0.483082i \(-0.160483\pi\)
−0.992304 + 0.123828i \(0.960483\pi\)
\(434\) 6.26975e6 + 4.55524e6i 1.59781 + 1.16088i
\(435\) 1.31447e6 155956.i 0.333065 0.0395164i
\(436\) −1.08099e6 + 785383.i −0.272336 + 0.197863i
\(437\) −3.32722e6 2.41737e6i −0.833448 0.605535i
\(438\) −162796. 118278.i −0.0405470 0.0294591i
\(439\) −4.08915e6 + 2.97094e6i −1.01268 + 0.735755i −0.964769 0.263097i \(-0.915256\pi\)
−0.0479104 + 0.998852i \(0.515256\pi\)
\(440\) 21521.0 2553.36i 0.00529945 0.000628753i
\(441\) −2.00991e6 1.46029e6i −0.492132 0.357555i
\(442\) −116678. 359097.i −0.0284075 0.0874292i
\(443\) −1.66444e6 −0.402958 −0.201479 0.979493i \(-0.564575\pi\)
−0.201479 + 0.979493i \(0.564575\pi\)
\(444\) 637257. + 1.96127e6i 0.153411 + 0.472151i
\(445\) 1.36787e6 6.88695e6i 0.327450 1.64864i
\(446\) 910393. 2.80190e6i 0.216717 0.666985i
\(447\) −679091. + 2.09003e6i −0.160753 + 0.494747i
\(448\) 722048. 524599.i 0.169970 0.123490i
\(449\) 8.23404e6 1.92751 0.963756 0.266785i \(-0.0859614\pi\)
0.963756 + 0.266785i \(0.0859614\pi\)
\(450\) 78868.3 1.00942e6i 0.0183599 0.234986i
\(451\) 34924.3 0.00808513
\(452\) 2.00584e6 1.45733e6i 0.461796 0.335515i
\(453\) 482886. 1.48617e6i 0.110560 0.340270i
\(454\) 456114. 1.40377e6i 0.103856 0.319637i
\(455\) −747291. + 88662.2i −0.169224 + 0.0200775i
\(456\) 195615. + 602041.i 0.0440545 + 0.135586i
\(457\) −1.28335e6 −0.287445 −0.143722 0.989618i \(-0.545907\pi\)
−0.143722 + 0.989618i \(0.545907\pi\)
\(458\) 341263. + 1.05030e6i 0.0760196 + 0.233964i
\(459\) 901114. + 654697.i 0.199640 + 0.145047i
\(460\) −2.92082e6 1.63465e6i −0.643591 0.360189i
\(461\) 2.82604e6 2.05324e6i 0.619335 0.449973i −0.233354 0.972392i \(-0.574970\pi\)
0.852689 + 0.522419i \(0.174970\pi\)
\(462\) 38441.6 + 27929.5i 0.00837909 + 0.00608777i
\(463\) −141911. 103105.i −0.0307655 0.0223525i 0.572296 0.820047i \(-0.306053\pi\)
−0.603062 + 0.797695i \(0.706053\pi\)
\(464\) −544901. + 395893.i −0.117496 + 0.0853657i
\(465\) −3.28416e6 + 3.03757e6i −0.704356 + 0.651470i
\(466\) 2.04812e6 + 1.48805e6i 0.436909 + 0.317433i
\(467\) 2.24608e6 + 6.91271e6i 0.476576 + 1.46675i 0.843820 + 0.536626i \(0.180301\pi\)
−0.367244 + 0.930125i \(0.619699\pi\)
\(468\) −80067.5 −0.0168983
\(469\) −3.35129e6 1.03142e7i −0.703526 2.16523i
\(470\) −3.64775e6 2.04148e6i −0.761693 0.426285i
\(471\) −739495. + 2.27593e6i −0.153597 + 0.472723i
\(472\) 759022. 2.33603e6i 0.156819 0.482640i
\(473\) 26557.6 19295.3i 0.00545804 0.00396550i
\(474\) 1.93042e6 0.394644
\(475\) −3.33903e6 + 803629.i −0.679025 + 0.163426i
\(476\) −5.32676e6 −1.07757
\(477\) 1.68561e6 1.22467e6i 0.339205 0.246446i
\(478\) 433816. 1.33515e6i 0.0868431 0.267276i
\(479\) 1.50845e6 4.64252e6i 0.300394 0.924518i −0.680962 0.732319i \(-0.738438\pi\)
0.981356 0.192199i \(-0.0615619\pi\)
\(480\) 215822. + 467805.i 0.0427555 + 0.0926749i
\(481\) 273403. + 841448.i 0.0538816 + 0.165831i
\(482\) −3.12572e6 −0.612820
\(483\) −2.26778e6 6.97950e6i −0.442316 1.36131i
\(484\) 2.08421e6 + 1.51427e6i 0.404416 + 0.293826i
\(485\) −2.28965e6 4.96294e6i −0.441992 0.958042i
\(486\) 191087. 138833.i 0.0366978 0.0266625i
\(487\) 6.57300e6 + 4.77556e6i 1.25586 + 0.912435i 0.998547 0.0538930i \(-0.0171630\pi\)
0.257313 + 0.966328i \(0.417163\pi\)
\(488\) 2.60044e6 + 1.88933e6i 0.494307 + 0.359135i
\(489\) −2.04064e6 + 1.48261e6i −0.385918 + 0.280386i
\(490\) −1.33609e6 + 6.72695e6i −0.251389 + 1.26569i
\(491\) −6.24817e6 4.53956e6i −1.16963 0.849787i −0.178667 0.983910i \(-0.557178\pi\)
−0.990965 + 0.134123i \(0.957178\pi\)
\(492\) 256555. + 789594.i 0.0477823 + 0.147059i
\(493\) 4.01989e6 0.744898
\(494\) 83925.0 + 258295.i 0.0154730 + 0.0476209i
\(495\) −20136.1 + 18624.2i −0.00369371 + 0.00341637i
\(496\) 703406. 2.16486e6i 0.128381 0.395117i
\(497\) −1.06634e6 + 3.28187e6i −0.193645 + 0.595978i
\(498\) 1.01853e6 740008.i 0.184036 0.133710i
\(499\) 7.25633e6 1.30456 0.652282 0.757976i \(-0.273812\pi\)
0.652282 + 0.757976i \(0.273812\pi\)
\(500\) −2.62150e6 + 969653.i −0.468949 + 0.173457i
\(501\) 3.54493e6 0.630977
\(502\) −989511. + 718922.i −0.175251 + 0.127328i
\(503\) 1.32247e6 4.07016e6i 0.233060 0.717284i −0.764313 0.644845i \(-0.776922\pi\)
0.997373 0.0724386i \(-0.0230781\pi\)
\(504\) −349057. + 1.07429e6i −0.0612096 + 0.188384i
\(505\) 31567.2 29197.0i 0.00550818 0.00509460i
\(506\) 28019.6 + 86235.6i 0.00486504 + 0.0149730i
\(507\) 3.30729e6 0.571415
\(508\) −1.60477e6 4.93898e6i −0.275902 0.849138i
\(509\) −1.94035e6 1.40975e6i −0.331960 0.241183i 0.409302 0.912399i \(-0.365772\pi\)
−0.741262 + 0.671216i \(0.765772\pi\)
\(510\) 599017. 3.01592e6i 0.101980 0.513446i
\(511\) −985348. + 715897.i −0.166931 + 0.121283i
\(512\) −212079. 154084.i −0.0357538 0.0259767i
\(513\) −648161. 470916.i −0.108740 0.0790042i
\(514\) −5.54588e6 + 4.02932e6i −0.925897 + 0.672704i
\(515\) −1.50442e6 3.26091e6i −0.249949 0.541777i
\(516\) 631333. + 458691.i 0.104384 + 0.0758395i
\(517\) 34993.1 + 107698.i 0.00575780 + 0.0177207i
\(518\) 1.24818e7 2.04387
\(519\) −295431. 909244.i −0.0481436 0.148171i
\(520\) 92594.3 + 200703.i 0.0150167 + 0.0325496i
\(521\) 396797. 1.22122e6i 0.0640434 0.197105i −0.913915 0.405906i \(-0.866956\pi\)
0.977958 + 0.208801i \(0.0669560\pi\)
\(522\) 263419. 810720.i 0.0423127 0.130225i
\(523\) 7.28482e6 5.29273e6i 1.16457 0.846108i 0.174219 0.984707i \(-0.444260\pi\)
0.990349 + 0.138599i \(0.0442600\pi\)
\(524\) 1.91140e6 0.304105
\(525\) −5.66315e6 2.34200e6i −0.896726 0.370841i
\(526\) 1.30981e6 0.206416
\(527\) −1.09910e7 + 7.98541e6i −1.72389 + 1.25248i
\(528\) 4312.79 13273.4i 0.000673245 0.00207204i
\(529\) 2.33855e6 7.19733e6i 0.363336 1.11823i
\(530\) −5.01917e6 2.80901e6i −0.776144 0.434373i
\(531\) 960637. + 2.95654e6i 0.147851 + 0.455037i
\(532\) 3.83147e6 0.586931
\(533\) 110070. + 338761.i 0.0167823 + 0.0516505i
\(534\) −3.65817e6 2.65781e6i −0.555150 0.403340i
\(535\) −5.48456e6 + 5.07275e6i −0.828432 + 0.766230i
\(536\) −2.57703e6 + 1.87232e6i −0.387442 + 0.281493i
\(537\) −1.20319e6 874169.i −0.180052 0.130816i
\(538\) 2.59504e6 + 1.88540e6i 0.386534 + 0.280833i
\(539\) 150309. 109206.i 0.0222851 0.0161910i
\(540\) −568990. 318438.i −0.0839693 0.0469938i
\(541\) 5.67831e6 + 4.12553e6i 0.834115 + 0.606020i 0.920720 0.390223i \(-0.127602\pi\)
−0.0866058 + 0.996243i \(0.527602\pi\)
\(542\) 108519. + 333988.i 0.0158675 + 0.0488351i
\(543\) −7.12069e6 −1.03639
\(544\) 483478. + 1.48799e6i 0.0700454 + 0.215578i
\(545\) −4.63589e6 + 550024.i −0.668562 + 0.0793214i
\(546\) −149756. + 460902.i −0.0214983 + 0.0661648i
\(547\) 1.53867e6 4.73554e6i 0.219876 0.676707i −0.778896 0.627153i \(-0.784220\pi\)
0.998771 0.0495541i \(-0.0157800\pi\)
\(548\) 2.24931e6 1.63422e6i 0.319962 0.232466i
\(549\) −4.06812e6 −0.576054
\(550\) 69971.4 + 28936.7i 0.00986310 + 0.00407889i
\(551\) −2.89146e6 −0.405731
\(552\) −1.74384e6 + 1.26698e6i −0.243590 + 0.176978i
\(553\) 3.61060e6 1.11123e7i 0.502073 1.54522i
\(554\) 616655. 1.89787e6i 0.0853626 0.262719i
\(555\) −1.40364e6 + 7.06701e6i −0.193429 + 0.973875i
\(556\) −645665. 1.98715e6i −0.0885768 0.272611i
\(557\) −1.21560e7 −1.66017 −0.830087 0.557633i \(-0.811710\pi\)
−0.830087 + 0.557633i \(0.811710\pi\)
\(558\) 890249. + 2.73990e6i 0.121039 + 0.372520i
\(559\) 270862. + 196793.i 0.0366622 + 0.0266366i
\(560\) 3.09655e6 367390.i 0.417261 0.0495059i
\(561\) −67388.8 + 48960.8i −0.00904025 + 0.00656813i
\(562\) 3.93342e6 + 2.85780e6i 0.525327 + 0.381672i
\(563\) −1.15294e7 8.37661e6i −1.53298 1.11377i −0.954554 0.298038i \(-0.903668\pi\)
−0.578425 0.815736i \(-0.696332\pi\)
\(564\) −2.17785e6 + 1.58230e6i −0.288290 + 0.209455i
\(565\) 8.60218e6 1.02060e6i 1.13367 0.134504i
\(566\) −5.78569e6 4.20355e6i −0.759127 0.551538i
\(567\) −441775. 1.35964e6i −0.0577090 0.177610i
\(568\) 1.01355e6 0.131818
\(569\) 1.29238e6 + 3.97753e6i 0.167344 + 0.515031i 0.999201 0.0399582i \(-0.0127225\pi\)
−0.831858 + 0.554989i \(0.812722\pi\)
\(570\) −430866. + 2.16932e6i −0.0555463 + 0.279664i
\(571\) 3.74244e6 1.15180e7i 0.480358 1.47839i −0.358236 0.933631i \(-0.616622\pi\)
0.838594 0.544758i \(-0.183378\pi\)
\(572\) 1850.32 5694.70i 0.000236460 0.000727748i
\(573\) 4.68868e6 3.40653e6i 0.596574 0.433436i
\(574\) 5.02509e6 0.636596
\(575\) −6.11594e6 9.96763e6i −0.771425 1.25725i
\(576\) 331776. 0.0416667
\(577\) −1.10770e7 + 8.04790e6i −1.38510 + 1.00634i −0.388721 + 0.921356i \(0.627083\pi\)
−0.996383 + 0.0849808i \(0.972917\pi\)
\(578\) 1.13053e6 3.47941e6i 0.140754 0.433197i
\(579\) 1.48247e6 4.56258e6i 0.183777 0.565607i
\(580\) −2.33684e6 + 277254.i −0.288443 + 0.0342222i
\(581\) −2.35476e6 7.24720e6i −0.289405 0.890697i
\(582\) −3.51981e6 −0.430736
\(583\) 48149.3 + 148188.i 0.00586704 + 0.0180569i
\(584\) 289415. + 210272.i 0.0351147 + 0.0255123i
\(585\) −244115. 136620.i −0.0294920 0.0165053i
\(586\) 7.43320e6 5.40054e6i 0.894194 0.649670i
\(587\) −7.38451e6 5.36516e6i −0.884558 0.642669i 0.0498953 0.998754i \(-0.484111\pi\)
−0.934453 + 0.356085i \(0.884111\pi\)
\(588\) 3.57318e6 + 2.59607e6i 0.426198 + 0.309651i
\(589\) 7.90568e6 5.74381e6i 0.938968 0.682200i
\(590\) 6.30014e6 5.82710e6i 0.745110 0.689163i
\(591\) 1.39733e6 + 1.01522e6i 0.164562 + 0.119561i
\(592\) −1.13290e6 3.48671e6i −0.132858 0.408895i
\(593\) −1.08242e7 −1.26404 −0.632019 0.774953i \(-0.717773\pi\)
−0.632019 + 0.774953i \(0.717773\pi\)
\(594\) 5458.37 + 16799.1i 0.000634742 + 0.00195353i
\(595\) −1.62405e7 9.08910e6i −1.88065 1.05251i
\(596\) 1.20727e6 3.71560e6i 0.139216 0.428464i
\(597\) −149334. + 459603.i −0.0171484 + 0.0527773i
\(598\) −748163. + 543572.i −0.0855546 + 0.0621590i
\(599\) 1.28625e7 1.46473 0.732367 0.680910i \(-0.238415\pi\)
0.732367 + 0.680910i \(0.238415\pi\)
\(600\) −140210. + 1.79453e6i −0.0159002 + 0.203504i
\(601\) 5.46297e6 0.616940 0.308470 0.951234i \(-0.400183\pi\)
0.308470 + 0.951234i \(0.400183\pi\)
\(602\) 3.82124e6 2.77630e6i 0.429748 0.312230i
\(603\) 1.24580e6 3.83418e6i 0.139526 0.429417i
\(604\) −858465. + 2.64208e6i −0.0957481 + 0.294682i
\(605\) 3.77066e6 + 8.17311e6i 0.418821 + 0.907818i
\(606\) −8557.03 26335.8i −0.000946546 0.00291317i
\(607\) 1.04243e7 1.14835 0.574175 0.818732i \(-0.305323\pi\)
0.574175 + 0.818732i \(0.305323\pi\)
\(608\) −347760. 1.07030e6i −0.0381523 0.117421i
\(609\) −4.17415e6 3.03270e6i −0.456063 0.331349i
\(610\) 4.70459e6 + 1.01974e7i 0.511914 + 1.10960i
\(611\) −934365. + 678856.i −0.101254 + 0.0735655i
\(612\) −1.60198e6 1.16391e6i −0.172893 0.125614i
\(613\) −2.22489e6 1.61648e6i −0.239143 0.173747i 0.461759 0.887006i \(-0.347219\pi\)
−0.700901 + 0.713258i \(0.747219\pi\)
\(614\) 1.51268e6 1.09902e6i 0.161929 0.117648i
\(615\) −565093. + 2.84512e6i −0.0602465 + 0.303328i
\(616\) −68340.7 49652.4i −0.00725650 0.00527216i
\(617\) 5.33695e6 + 1.64255e7i 0.564392 + 1.73702i 0.669752 + 0.742585i \(0.266400\pi\)
−0.105360 + 0.994434i \(0.533600\pi\)
\(618\) −2.31270e6 −0.243583
\(619\) 5.00451e6 + 1.54023e7i 0.524970 + 1.61569i 0.764375 + 0.644772i \(0.223048\pi\)
−0.239405 + 0.970920i \(0.576952\pi\)
\(620\) 5.83851e6 5.40013e6i 0.609990 0.564190i
\(621\) 843018. 2.59454e6i 0.0877219 0.269980i
\(622\) 2.44012e6 7.50992e6i 0.252892 0.778322i
\(623\) −2.21416e7 + 1.60868e7i −2.28554 + 1.66054i
\(624\) 142342. 0.0146343
\(625\) −9.64712e6 1.51676e6i −0.987865 0.155316i
\(626\) 2.36272e6 0.240978
\(627\) 48472.0 35217.0i 0.00492404 0.00357753i
\(628\) 1.31466e6 4.04610e6i 0.133019 0.409390i
\(629\) −6.76155e6 + 2.08099e7i −0.681428 + 2.09722i
\(630\) −2.89729e6 + 2.67975e6i −0.290831 + 0.268994i
\(631\) 565577. + 1.74067e6i 0.0565481 + 0.174037i 0.975341 0.220702i \(-0.0708349\pi\)
−0.918793 + 0.394739i \(0.870835\pi\)
\(632\) −3.43185e6 −0.341772
\(633\) 1.68156e6 + 5.17531e6i 0.166803 + 0.513366i
\(634\) −4.58519e6 3.33133e6i −0.453037 0.329151i
\(635\) 3.53471e6 1.77965e7i 0.347872 1.75146i
\(636\) −2.99664e6 + 2.17719e6i −0.293760 + 0.213429i
\(637\) 1.53301e6 + 1.11379e6i 0.149691 + 0.108757i
\(638\) 51574.0 + 37470.7i 0.00501625 + 0.00364452i
\(639\) −1.03779e6 + 753998.i −0.100544 + 0.0730496i
\(640\) −383683. 831654.i −0.0370274 0.0802588i
\(641\) 3.77995e6 + 2.74630e6i 0.363364 + 0.263999i 0.754454 0.656353i \(-0.227902\pi\)
−0.391090 + 0.920352i \(0.627902\pi\)
\(642\) 1.48672e6 + 4.57564e6i 0.142361 + 0.438142i
\(643\) −1.20457e7 −1.14896 −0.574482 0.818517i \(-0.694796\pi\)
−0.574482 + 0.818517i \(0.694796\pi\)
\(644\) 4.03160e6 + 1.24080e7i 0.383057 + 1.17893i
\(645\) 1.14218e6 + 2.47573e6i 0.108102 + 0.234317i
\(646\) −2.07556e6 + 6.38790e6i −0.195683 + 0.602250i
\(647\) −1.91240e6 + 5.88575e6i −0.179604 + 0.552765i −0.999814 0.0192979i \(-0.993857\pi\)
0.820209 + 0.572063i \(0.193857\pi\)
\(648\) −339709. + 246813.i −0.0317812 + 0.0230904i
\(649\) −232480. −0.0216657
\(650\) −60154.6 + 769910.i −0.00558452 + 0.0714754i
\(651\) 1.74371e7 1.61258
\(652\) 3.62781e6 2.63576e6i 0.334214 0.242821i
\(653\) −1.02843e6 + 3.16518e6i −0.0943825 + 0.290479i −0.987092 0.160153i \(-0.948801\pi\)
0.892710 + 0.450632i \(0.148801\pi\)
\(654\) −929026. + 2.85925e6i −0.0849344 + 0.261401i
\(655\) 5.82759e6 + 3.26144e6i 0.530745 + 0.297034i
\(656\) −456097. 1.40372e6i −0.0413807 0.127357i
\(657\) −452760. −0.0409218
\(658\) 5.03498e6 + 1.54961e7i 0.453350 + 1.39527i
\(659\) 1.30594e7 + 9.48820e6i 1.17141 + 0.851080i 0.991177 0.132544i \(-0.0423147\pi\)
0.180233 + 0.983624i \(0.442315\pi\)
\(660\) 35797.6 33109.8i 0.00319885 0.00295867i
\(661\) 1.18285e7 8.59391e6i 1.05299 0.765045i 0.0802148 0.996778i \(-0.474439\pi\)
0.972780 + 0.231732i \(0.0744394\pi\)
\(662\) −3.05728e6 2.22124e6i −0.271138 0.196993i
\(663\) −687300. 499352.i −0.0607243 0.0441188i
\(664\) −1.81073e6 + 1.31557e6i −0.159380 + 0.115796i
\(665\) 1.16816e7 + 6.53768e6i 1.02435 + 0.573284i
\(666\) 3.75381e6 + 2.72730e6i 0.327934 + 0.238258i
\(667\) −3.04249e6 9.36382e6i −0.264798 0.814964i
\(668\) −6.30210e6 −0.546442
\(669\) −2.04839e6 6.30428e6i −0.176948 0.544591i
\(670\) −1.10517e7 + 1.31123e6i −0.951138 + 0.112848i
\(671\) 94012.3 289340.i 0.00806080 0.0248086i
\(672\) 620545. 1.90984e6i 0.0530091 0.163145i
\(673\) −3.88307e6 + 2.82121e6i −0.330474 + 0.240103i −0.740632 0.671911i \(-0.765474\pi\)
0.410158 + 0.912015i \(0.365474\pi\)
\(674\) −1.01095e6 −0.0857199
\(675\) −1.19142e6 1.94175e6i −0.100648 0.164034i
\(676\) −5.87962e6 −0.494860
\(677\) −3.18655e6 + 2.31517e6i −0.267208 + 0.194138i −0.713319 0.700840i \(-0.752809\pi\)
0.446111 + 0.894978i \(0.352809\pi\)
\(678\) 1.72387e6 5.30552e6i 0.144022 0.443255i
\(679\) −6.58335e6 + 2.02615e7i −0.547990 + 1.68654i
\(680\) −1.06492e6 + 5.36164e6i −0.0883170 + 0.444657i
\(681\) −1.02626e6 3.15849e6i −0.0847984 0.260983i
\(682\) −215445. −0.0177368
\(683\) −4.27177e6 1.31472e7i −0.350394 1.07840i −0.958632 0.284647i \(-0.908124\pi\)
0.608238 0.793754i \(-0.291876\pi\)
\(684\) 1.15229e6 + 837185.i 0.0941716 + 0.0684197i
\(685\) 9.64633e6 1.14449e6i 0.785481 0.0931933i
\(686\) 9.77621e6 7.10283e6i 0.793159 0.576264i
\(687\) 2.01024e6 + 1.46052e6i 0.162501 + 0.118064i
\(688\) −1.12237e6 815450.i −0.0903993 0.0656789i
\(689\) −1.28565e6 + 934082.i −0.103175 + 0.0749613i
\(690\) −7.47858e6 + 887295.i −0.597993 + 0.0709489i
\(691\) 1.74292e7 + 1.26631e7i 1.38862 + 1.00889i 0.996015 + 0.0891806i \(0.0284248\pi\)
0.392602 + 0.919709i \(0.371575\pi\)
\(692\) 525211. + 1.61643e6i 0.0416935 + 0.128320i
\(693\) 106912. 0.00845656
\(694\) −1.02578e6 3.15703e6i −0.0808454 0.248817i
\(695\) 1.42216e6 7.16025e6i 0.111682 0.562298i
\(696\) −468300. + 1.44128e6i −0.0366439 + 0.112778i
\(697\) −2.72215e6 + 8.37791e6i −0.212241 + 0.653211i
\(698\) 1.40746e6 1.02258e6i 0.109344 0.0794433i
\(699\) 5.69614e6 0.440948
\(700\) 1.00678e7 + 4.16355e6i 0.776588 + 0.321158i
\(701\) −1.65465e7 −1.27177 −0.635887 0.771782i \(-0.719366\pi\)
−0.635887 + 0.771782i \(0.719366\pi\)
\(702\) −145746. + 105891.i −0.0111623 + 0.00810989i
\(703\) 4.86351e6 1.49683e7i 0.371160 1.14231i
\(704\) −7667.18 + 23597.1i −0.000583047 + 0.00179444i
\(705\) −9.33984e6 + 1.10812e6i −0.707728 + 0.0839683i
\(706\) −802094. 2.46859e6i −0.0605639 0.186396i
\(707\) −167605. −0.0126107
\(708\) −1.70780e6 5.25607e6i −0.128042 0.394074i
\(709\) −2.05762e7 1.49495e7i −1.53727 1.11689i −0.952021 0.306031i \(-0.900999\pi\)
−0.585244 0.810857i \(-0.699001\pi\)
\(710\) 3.09018e6 + 1.72943e6i 0.230058 + 0.128753i
\(711\) 3.51392e6 2.55301e6i 0.260686 0.189399i
\(712\) 6.50341e6 + 4.72500e6i 0.480774 + 0.349303i
\(713\) 2.69196e7 + 1.95582e7i 1.98310 + 1.44081i
\(714\) −9.69623e6 + 7.04473e6i −0.711799 + 0.517152i
\(715\) 15358.3 14205.1i 0.00112351 0.00103915i
\(716\) 2.13900e6 + 1.55408e6i 0.155930 + 0.113290i
\(717\) −976085. 3.00408e6i −0.0709071 0.218230i
\(718\) −3.33340e6 −0.241310
\(719\) −7.09200e6 2.18269e7i −0.511619 1.57460i −0.789351 0.613942i \(-0.789583\pi\)
0.277732 0.960659i \(-0.410417\pi\)
\(720\) 1.01154e6 + 566112.i 0.0727195 + 0.0406979i
\(721\) −4.32561e6 + 1.33129e7i −0.309891 + 0.953746i
\(722\) −1.56770e6 + 4.82490e6i −0.111923 + 0.344465i
\(723\) −5.68972e6 + 4.13382e6i −0.404804 + 0.294108i
\(724\) 1.26590e7 0.897538
\(725\) −7.59778e6 3.14207e6i −0.536836 0.222009i
\(726\) 5.79652e6 0.408155
\(727\) 1.99614e7 1.45028e7i 1.40073 1.01769i 0.406141 0.913810i \(-0.366874\pi\)
0.994590 0.103880i \(-0.0331258\pi\)
\(728\) 266233. 819382.i 0.0186180 0.0573004i
\(729\) 164224. 505430.i 0.0114451 0.0352243i
\(730\) 523596. + 1.13492e6i 0.0363655 + 0.0788241i
\(731\) 2.55868e6 + 7.87480e6i 0.177101 + 0.545062i
\(732\) 7.23222e6 0.498877
\(733\) −8.15670e6 2.51037e7i −0.560731 1.72575i −0.680307 0.732927i \(-0.738153\pi\)
0.119576 0.992825i \(-0.461847\pi\)
\(734\) 369287. + 268303.i 0.0253002 + 0.0183817i
\(735\) 6.46443e6 + 1.40120e7i 0.441379 + 0.956713i
\(736\) 3.10016e6 2.25240e6i 0.210955 0.153268i
\(737\) 243911. + 177212.i 0.0165411 + 0.0120178i
\(738\) 1.51125e6 + 1.09799e6i 0.102140 + 0.0742092i
\(739\) −1.37980e7 + 1.00248e7i −0.929402 + 0.675250i −0.945846 0.324615i \(-0.894765\pi\)
0.0164445 + 0.999865i \(0.494765\pi\)
\(740\) 2.49535e6 1.25636e7i 0.167515 0.843400i
\(741\) 494367. + 359178.i 0.0330753 + 0.0240306i
\(742\) 6.92797e6 + 2.13221e7i 0.461951 + 1.42174i
\(743\) 1.55561e6 0.103378 0.0516889 0.998663i \(-0.483540\pi\)
0.0516889 + 0.998663i \(0.483540\pi\)
\(744\) −1.58266e6 4.87094e6i −0.104823 0.322612i
\(745\) 1.00208e7 9.26837e6i 0.661471 0.611805i
\(746\) 1.19839e6 3.68826e6i 0.0788407 0.242647i
\(747\) 875352. 2.69406e6i 0.0573960 0.176647i
\(748\) 119802. 87041.5i 0.00782909 0.00568817i
\(749\) 2.91200e7 1.89665
\(750\) −3.48951e6 + 5.23203e6i −0.226522 + 0.339639i
\(751\) 1.32017e7 0.854140 0.427070 0.904219i \(-0.359546\pi\)
0.427070 + 0.904219i \(0.359546\pi\)
\(752\) 3.87173e6 2.81298e6i 0.249666 0.181393i
\(753\) −850409. + 2.61729e6i −0.0546563 + 0.168215i
\(754\) −200916. + 618354.i −0.0128702 + 0.0396104i
\(755\) −7.12555e6 + 6.59053e6i −0.454937 + 0.420778i
\(756\) 785377. + 2.41714e6i 0.0499774 + 0.153815i
\(757\) −1.87072e7 −1.18651 −0.593253 0.805016i \(-0.702157\pi\)
−0.593253 + 0.805016i \(0.702157\pi\)
\(758\) 3.56075e6 + 1.09589e7i 0.225096 + 0.692775i
\(759\) 165052. + 119917.i 0.0103996 + 0.00755574i
\(760\) 765984. 3.85657e6i 0.0481045 0.242196i
\(761\) −1.56061e6 + 1.13385e6i −0.0976861 + 0.0709731i −0.635556 0.772055i \(-0.719229\pi\)
0.537870 + 0.843028i \(0.319229\pi\)
\(762\) −9.45304e6 6.86803e6i −0.589772 0.428494i
\(763\) 1.47214e7 + 1.06957e7i 0.915457 + 0.665118i
\(764\) −8.33543e6 + 6.05605e6i −0.516648 + 0.375367i
\(765\) −2.89823e6 6.28206e6i −0.179052 0.388104i
\(766\) −8.18957e6 5.95007e6i −0.504300 0.366395i
\(767\) −732699. 2.25502e6i −0.0449715 0.138408i
\(768\) −589824. −0.0360844
\(769\) 2.48713e6 + 7.65461e6i 0.151664 + 0.466775i 0.997808 0.0661807i \(-0.0210814\pi\)
−0.846143 + 0.532955i \(0.821081\pi\)
\(770\) −123639. 267994.i −0.00751498 0.0162891i
\(771\) −4.76626e6 + 1.46690e7i −0.288763 + 0.888722i
\(772\) −2.63551e6 + 8.11126e6i −0.159155 + 0.489830i
\(773\) −1.42379e7 + 1.03444e7i −0.857031 + 0.622669i −0.927076 0.374874i \(-0.877686\pi\)
0.0700446 + 0.997544i \(0.477686\pi\)
\(774\) 1.75583e6 0.105349
\(775\) 2.70151e7 6.50193e6i 1.61567 0.388855i
\(776\) 6.25744e6 0.373029
\(777\) 2.27205e7 1.65074e7i 1.35010 0.980905i
\(778\) 4.88329e6 1.50292e7i 0.289244 0.890200i
\(779\) 1.95801e6 6.02613e6i 0.115604 0.355791i
\(780\) 433982. + 242880.i 0.0255408 + 0.0142940i
\(781\) −29644.4 91235.9i −0.00173906 0.00535227i
\(782\) −2.28708e7 −1.33741
\(783\) −592693. 1.82412e6i −0.0345482 0.106328i
\(784\) −6.35232e6 4.61523e6i −0.369099 0.268166i
\(785\) 1.09121e7 1.00928e7i 0.632025 0.584570i
\(786\) 3.47930e6 2.52786e6i 0.200879 0.145947i
\(787\) 2.08449e7 + 1.51447e7i 1.19967 + 0.871614i 0.994253 0.107059i \(-0.0341435\pi\)
0.205422 + 0.978674i \(0.434143\pi\)
\(788\) −2.48414e6 1.80483e6i −0.142515 0.103543i
\(789\) 2.38423e6 1.73224e6i 0.136350 0.0990642i
\(790\) −1.04632e7 5.85580e6i −0.596483 0.333825i
\(791\) −2.73165e7 1.98466e7i −1.55233 1.12783i
\(792\) −9703.77 29865.1i −0.000549702 0.00169181i
\(793\) 3.10285e6 0.175218
\(794\) 2.00103e6 + 6.15853e6i 0.112642 + 0.346678i
\(795\) −1.28513e7 + 1.52474e6i −0.721156 + 0.0855615i
\(796\) 265483. 817072.i 0.0148509 0.0457065i
\(797\) 3.08104e6 9.48247e6i 0.171811 0.528781i −0.827662 0.561227i \(-0.810330\pi\)
0.999473 + 0.0324458i \(0.0103296\pi\)
\(798\) 6.97439e6 5.06719e6i 0.387703 0.281683i
\(799\) −2.85629e7 −1.58283
\(800\) 249263. 3.19028e6i 0.0137700 0.176240i
\(801\) −1.01739e7 −0.560283
\(802\) −5.16036e6 + 3.74922e6i −0.283298 + 0.205828i
\(803\) 10463.1 32202.0i 0.000572625 0.00176236i
\(804\) −2.21476e6 + 6.81632e6i −0.120833 + 0.371886i
\(805\) −8.88010e6 + 4.47094e7i −0.482979 + 2.43170i
\(806\) −679013. 2.08979e6i −0.0368163 0.113309i
\(807\) 7.21719e6 0.390108
\(808\) 15212.5 + 46819.3i 0.000819733 + 0.00252288i
\(809\) 1.64135e6 + 1.19251e6i 0.0881719 + 0.0640607i 0.630998 0.775785i \(-0.282646\pi\)
−0.542826 + 0.839845i \(0.682646\pi\)
\(810\) −1.45687e6 + 172850.i −0.0780202 + 0.00925670i
\(811\) −1.60365e7 + 1.16512e7i −0.856163 + 0.622039i −0.926838 0.375461i \(-0.877484\pi\)
0.0706756 + 0.997499i \(0.477484\pi\)
\(812\) 7.42072e6 + 5.39147e6i 0.394962 + 0.286957i
\(813\) 639240. + 464435.i 0.0339186 + 0.0246433i
\(814\) −280725. + 203958.i −0.0148498 + 0.0107890i
\(815\) 1.55581e7 1.84589e6i 0.820469 0.0973445i
\(816\) 2.84796e6 + 2.06917e6i 0.149730 + 0.108785i
\(817\) −1.84043e6 5.66425e6i −0.0964636 0.296884i
\(818\) −2.00987e7 −1.05023
\(819\) 336951. + 1.03703e6i 0.0175533 + 0.0540234i
\(820\) 1.00461e6 5.05799e6i 0.0521750 0.262690i
\(821\) −4.05024e6 + 1.24654e7i −0.209712 + 0.645427i 0.789775 + 0.613397i \(0.210197\pi\)
−0.999487 + 0.0320303i \(0.989803\pi\)
\(822\) 1.93311e6 5.94951e6i 0.0997879 0.307115i
\(823\) −6.66321e6 + 4.84111e6i −0.342913 + 0.249141i −0.745890 0.666069i \(-0.767976\pi\)
0.402977 + 0.915210i \(0.367976\pi\)
\(824\) 4.11146e6 0.210949
\(825\) 165637. 39865.2i 0.00847273 0.00203920i
\(826\) −3.34503e7 −1.70589
\(827\) −9.02043e6 + 6.55372e6i −0.458631 + 0.333215i −0.792994 0.609230i \(-0.791479\pi\)
0.334363 + 0.942444i \(0.391479\pi\)
\(828\) −1.49870e6 + 4.61252e6i −0.0759694 + 0.233810i
\(829\) 3.37244e6 1.03793e7i 0.170435 0.524544i −0.828961 0.559306i \(-0.811067\pi\)
0.999396 + 0.0347626i \(0.0110675\pi\)
\(830\) −7.76542e6 + 921328.i −0.391264 + 0.0464215i
\(831\) −1.38747e6 4.27020e6i −0.0696983 0.214509i
\(832\) −253053. −0.0126737
\(833\) 1.44814e7 + 4.45693e7i 0.723102 + 2.22548i
\(834\) −3.80334e6 2.76329e6i −0.189343 0.137566i
\(835\) −1.92142e7 1.07533e7i −0.953688 0.533736i
\(836\) −86172.4 + 62607.9i −0.00426435 + 0.00309823i
\(837\) 5.24408e6 + 3.81005e6i 0.258735 + 0.187982i
\(838\) −8.10217e6 5.88657e6i −0.398558 0.289569i
\(839\) 7.99781e6 5.81075e6i 0.392253 0.284988i −0.374125 0.927378i \(-0.622057\pi\)
0.766378 + 0.642390i \(0.222057\pi\)
\(840\) 5.15073e6 4.76399e6i 0.251867 0.232956i
\(841\) 1.09938e7 + 7.98743e6i 0.535989 + 0.389419i
\(842\) −7.33208e6 2.25658e7i −0.356408 1.09691i
\(843\) 1.09394e7 0.530184
\(844\) −2.98944e6 9.20055e6i −0.144455 0.444588i
\(845\) −1.79261e7 1.00324e7i −0.863664 0.483354i
\(846\) −1.87169e6 + 5.76048e6i −0.0899101 + 0.276715i
\(847\) 1.08416e7 3.33672e7i 0.519262 1.59813i
\(848\) 5.32737e6 3.87056e6i 0.254403 0.184835i
\(849\) −1.60909e7 −0.766145
\(850\) −1.23954e7 + 1.45298e7i −0.588455 + 0.689783i
\(851\) 5.35916e7 2.53672
\(852\) 1.84496e6 1.34044e6i 0.0870738 0.0632628i
\(853\) 3.66719e6 1.12865e7i 0.172568 0.531111i −0.826946 0.562282i \(-0.809924\pi\)
0.999514 + 0.0311711i \(0.00992369\pi\)
\(854\) 1.35269e7 4.16317e7i 0.634680 1.95335i
\(855\) 2.08466e6 + 4.51861e6i 0.0975259 + 0.211393i
\(856\) −2.64305e6 8.13448e6i −0.123288 0.379442i
\(857\) −6.11347e6 −0.284338 −0.142169 0.989842i \(-0.545408\pi\)
−0.142169 + 0.989842i \(0.545408\pi\)
\(858\) −4163.22 12813.1i −0.000193068 0.000594204i
\(859\) 3.20065e6 + 2.32541e6i 0.147998 + 0.107527i 0.659320 0.751862i \(-0.270844\pi\)
−0.511322 + 0.859389i \(0.670844\pi\)
\(860\) −2.03054e6 4.40130e6i −0.0936193 0.202925i
\(861\) 9.14710e6 6.64576e6i 0.420509 0.305518i
\(862\) −1.72789e7 1.25538e7i −0.792040 0.575451i
\(863\) 1.48744e7 + 1.08069e7i 0.679851 + 0.493941i 0.873308 0.487168i \(-0.161970\pi\)
−0.193457 + 0.981109i \(0.561970\pi\)
\(864\) 603928. 438779.i 0.0275233 0.0199969i
\(865\) −1.15684e6 + 5.82445e6i −0.0525695 + 0.264676i
\(866\) 4.76906e6 + 3.46493e6i 0.216092 + 0.157000i
\(867\) −2.54369e6 7.82867e6i −0.114925 0.353704i
\(868\) −3.09993e7 −1.39654
\(869\) 100375. + 308922.i 0.00450894 + 0.0138771i
\(870\) −3.88705e6 + 3.59520e6i −0.174109 + 0.161037i
\(871\) −950200. + 2.92441e6i −0.0424394 + 0.130615i
\(872\) 1.65160e6 5.08311e6i 0.0735553 0.226380i
\(873\) −6.40706e6 + 4.65500e6i −0.284527 + 0.206721i
\(874\) 1.64507e7 0.728460
\(875\) 2.35911e7 + 2.98729e7i 1.04166 + 1.31904i
\(876\) 804907. 0.0354393
\(877\) −6.52132e6 + 4.73802e6i −0.286310 + 0.208017i −0.721665 0.692242i \(-0.756623\pi\)
0.435355 + 0.900259i \(0.356623\pi\)
\(878\) 6.24767e6 1.92284e7i 0.273515 0.841794i
\(879\) 6.38827e6 1.96611e7i 0.278876 0.858292i
\(880\) −63640.2 + 58861.8i −0.00277029 + 0.00256228i
\(881\) −8.17913e6 2.51728e7i −0.355032 1.09268i −0.955991 0.293396i \(-0.905215\pi\)
0.600959 0.799280i \(-0.294785\pi\)
\(882\) 9.93757e6 0.430139
\(883\) −7.49720e6 2.30740e7i −0.323591 0.995912i −0.972072 0.234681i \(-0.924595\pi\)
0.648481 0.761231i \(-0.275405\pi\)
\(884\) 1.22187e6 + 887738.i 0.0525888 + 0.0382080i
\(885\) 3.76164e6 1.89390e7i 0.161443 0.812830i
\(886\) 5.38625e6 3.91334e6i 0.230517 0.167480i
\(887\) −2.80981e7 2.04145e7i −1.19913 0.871222i −0.204935 0.978776i \(-0.565698\pi\)
−0.994199 + 0.107553i \(0.965698\pi\)
\(888\) −6.67344e6 4.84854e6i −0.283999 0.206338i
\(889\) −5.72160e7 + 4.15698e7i −2.42808 + 1.76410i
\(890\) 1.17657e7 + 2.55027e7i 0.497899 + 1.07922i
\(891\) 32153.0 + 23360.5i 0.00135683 + 0.000985797i
\(892\) 3.64157e6 + 1.12076e7i 0.153242 + 0.471629i
\(893\) 2.05449e7 0.862137
\(894\) −2.71636e6 8.36011e6i −0.113670 0.349839i
\(895\) 3.86979e6 + 8.38797e6i 0.161484 + 0.350025i
\(896\) −1.10319e6 + 3.39527e6i −0.0459072 + 0.141288i
\(897\) −642989. + 1.97892e6i −0.0266822 + 0.0821195i
\(898\) −2.66459e7 + 1.93594e7i −1.10266 + 0.801126i
\(899\) 2.33940e7 0.965394
\(900\) 2.11807e6 + 3.45199e6i 0.0871635 + 0.142057i
\(901\) −3.93015e7 −1.61286
\(902\) −113018. + 82112.0i −0.00462519 + 0.00336040i
\(903\) 3.28407e6 1.01073e7i 0.134027 0.412493i
\(904\) −3.06465e6 + 9.43203e6i −0.124727 + 0.383870i
\(905\) 3.85955e7 + 2.16002e7i 1.56645 + 0.876669i
\(906\) 1.93155e6 + 5.94469e6i 0.0781780 + 0.240607i
\(907\) 2.85388e7 1.15191 0.575953 0.817483i \(-0.304631\pi\)
0.575953 + 0.817483i \(0.304631\pi\)
\(908\) 1.82445e6 + 5.61509e6i 0.0734376 + 0.226018i
\(909\) −50405.8 36622.0i −0.00202335 0.00147005i
\(910\) 2.20983e6 2.04390e6i 0.0884616 0.0818195i
\(911\) −1.12976e7 + 8.20818e6i −0.451014 + 0.327681i −0.789996 0.613112i \(-0.789917\pi\)
0.338982 + 0.940793i \(0.389917\pi\)
\(912\) −2.04851e6 1.48833e6i −0.0815550 0.0592532i
\(913\) 171382. + 124517.i 0.00680439 + 0.00494368i
\(914\) 4.15301e6 3.01734e6i 0.164436 0.119470i
\(915\) 2.20500e7 + 1.23404e7i 0.870675 + 0.487278i
\(916\) −3.57375e6 2.59648e6i −0.140730 0.102246i
\(917\) −8.04382e6 2.47563e7i −0.315892 0.972217i
\(918\) −4.45535e6 −0.174492
\(919\) 1.24281e6 + 3.82498e6i 0.0485419 + 0.149397i 0.972389 0.233364i \(-0.0749734\pi\)
−0.923848 + 0.382761i \(0.874973\pi\)
\(920\) 1.32953e7 1.57741e6i 0.517877 0.0614435i
\(921\) 1.30003e6 4.00108e6i 0.0505015 0.155428i
\(922\) −4.31780e6 + 1.32888e7i −0.167277 + 0.514824i
\(923\) 791545. 575091.i 0.0305824 0.0222194i
\(924\) −190066. −0.00732359
\(925\) 2.90453e7 3.40467e7i 1.11615 1.30834i
\(926\) 701648. 0.0268901
\(927\) −4.20978e6 + 3.05858e6i −0.160901 + 0.116902i
\(928\) 832534. 2.56228e6i 0.0317345 0.0976688i
\(929\) 7.66441e6 2.35886e7i 0.291367 0.896734i −0.693051 0.720888i \(-0.743734\pi\)
0.984418 0.175846i \(-0.0562660\pi\)
\(930\) 3.48601e6 1.75513e7i 0.132166 0.665430i
\(931\) −1.04163e7 3.20582e7i −0.393859 1.21217i
\(932\) −1.01265e7 −0.381872
\(933\) −5.49027e6 1.68973e7i −0.206485 0.635497i
\(934\) −2.35212e7 1.70892e7i −0.882252 0.640994i
\(935\) 513780. 60957.4i 0.0192198 0.00228033i
\(936\) 259104. 188250.i 0.00966684 0.00702337i
\(937\) −2.01357e7 1.46295e7i −0.749235 0.544351i 0.146354 0.989232i \(-0.453246\pi\)
−0.895590 + 0.444881i \(0.853246\pi\)
\(938\) 3.50952e7 + 2.54981e7i 1.30239 + 0.946240i
\(939\) 4.30083e6 3.12474e6i 0.159180 0.115651i
\(940\) 1.66042e7 1.97000e6i 0.612911 0.0727187i
\(941\) −3.39946e7 2.46985e7i −1.25152 0.909279i −0.253207 0.967412i \(-0.581485\pi\)
−0.998309 + 0.0581328i \(0.981485\pi\)
\(942\) −2.95798e6 9.10373e6i −0.108610 0.334266i
\(943\) 2.15756e7 0.790101
\(944\) 3.03609e6 + 9.34412e6i 0.110888 + 0.341278i
\(945\) −1.72989e6 + 8.70962e6i −0.0630142 + 0.317263i
\(946\) −40576.5 + 124882.i −0.00147417 + 0.00453702i
\(947\) 1.61911e6 4.98311e6i 0.0586680 0.180562i −0.917428 0.397902i \(-0.869738\pi\)
0.976096 + 0.217341i \(0.0697383\pi\)
\(948\) −6.24696e6 + 4.53868e6i −0.225761 + 0.164025i
\(949\) 345330. 0.0124471
\(950\) 8.91587e6 1.04511e7i 0.320520 0.375711i
\(951\) −1.27521e7 −0.457226
\(952\) 1.72377e7 1.25240e7i 0.616436 0.447867i
\(953\) −1.31954e7 + 4.06113e7i −0.470642 + 1.44849i 0.381105 + 0.924532i \(0.375544\pi\)
−0.851746 + 0.523954i \(0.824456\pi\)
\(954\) −2.57539e6 + 7.92622e6i −0.0916160 + 0.281965i
\(955\) −3.57470e7 + 4.24120e6i −1.26833 + 0.150481i
\(956\) 1.73526e6 + 5.34059e6i 0.0614073 + 0.188992i
\(957\) 143435. 0.00506262
\(958\) 6.03379e6 + 1.85701e7i 0.212411 + 0.653733i
\(959\) −3.06322e7 2.22556e7i −1.07555 0.781435i
\(960\) −1.79829e6 1.00642e6i −0.0629770 0.0352454i
\(961\) −4.08010e7 + 2.96437e7i −1.42516 + 1.03544i
\(962\) −2.86311e6 2.08017e6i −0.0997473 0.0724706i
\(963\) 8.75762e6 + 6.36278e6i 0.304313 + 0.221096i
\(964\) 1.01151e7 7.34902e6i 0.350571 0.254705i
\(965\) −2.18756e7 + 2.02331e7i −0.756209 + 0.699430i
\(966\) 2.37485e7 + 1.72543e7i 0.818828 + 0.594914i
\(967\) −3.00282e6 9.24174e6i −0.103267 0.317825i 0.886052 0.463585i \(-0.153437\pi\)
−0.989320 + 0.145760i \(0.953437\pi\)
\(968\) −1.03049e7 −0.353473
\(969\) 4.67000e6 + 1.43728e7i 0.159774 + 0.491735i
\(970\) 1.90780e7 + 1.06771e7i 0.651035 + 0.364355i
\(971\) 1.35947e7 4.18403e7i 0.462725 1.42412i −0.399096 0.916909i \(-0.630676\pi\)
0.861821 0.507212i \(-0.169324\pi\)
\(972\) −291954. + 898543.i −0.00991172 + 0.0305052i
\(973\) −2.30203e7 + 1.67252e7i −0.779523 + 0.566356i
\(974\) −3.24987e7 −1.09766
\(975\) 908720. + 1.48101e6i 0.0306139 + 0.0498939i
\(976\) −1.28573e7 −0.432040
\(977\) −4.58907e7 + 3.33415e7i −1.53811 + 1.11750i −0.586607 + 0.809872i \(0.699537\pi\)
−0.951505 + 0.307632i \(0.900463\pi\)
\(978\) 3.11782e6 9.59567e6i 0.104233 0.320796i
\(979\) 235114. 723607.i 0.00784011 0.0241294i
\(980\) −1.14923e7 2.49102e7i −0.382246 0.828538i
\(981\) 2.09031e6 + 6.43331e6i 0.0693486 + 0.213433i
\(982\) 3.08926e7 1.02230
\(983\) 5.73941e6 + 1.76641e7i 0.189445 + 0.583052i 0.999997 0.00261530i \(-0.000832476\pi\)
−0.810551 + 0.585667i \(0.800832\pi\)
\(984\) −2.68667e6 1.95198e6i −0.0884560 0.0642671i
\(985\) −4.49419e6 9.74139e6i −0.147591 0.319912i
\(986\) −1.30086e7 + 9.45133e6i −0.426127 + 0.309600i
\(987\) 2.96590e7 + 2.15485e7i 0.969088 + 0.704083i
\(988\) −878874. 638539.i −0.0286440 0.0208111i
\(989\) 1.64068e7 1.19202e7i 0.533375 0.387520i
\(990\) 21373.7 107612.i 0.000693094 0.00348958i
\(991\) −2.17073e7 1.57713e7i −0.702138 0.510133i 0.178490 0.983942i \(-0.442879\pi\)
−0.880628 + 0.473808i \(0.842879\pi\)
\(992\) 2.81363e6 + 8.65945e6i 0.0907794 + 0.279390i
\(993\) −8.50277e6 −0.273645
\(994\) −4.26538e6 1.31275e7i −0.136928 0.421420i
\(995\) 2.20360e6 2.03814e6i 0.0705626 0.0652645i
\(996\) −1.55618e6 + 4.78943e6i −0.0497064 + 0.152980i
\(997\) 7.67348e6 2.36166e7i 0.244486 0.752452i −0.751234 0.660036i \(-0.770541\pi\)
0.995720 0.0924159i \(-0.0294589\pi\)
\(998\) −2.34820e7 + 1.70606e7i −0.746291 + 0.542212i
\(999\) 1.04399e7 0.330966
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 150.6.g.d.61.6 28
25.16 even 5 inner 150.6.g.d.91.6 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.6.g.d.61.6 28 1.1 even 1 trivial
150.6.g.d.91.6 yes 28 25.16 even 5 inner