Properties

Label 150.6.g.c.31.1
Level $150$
Weight $6$
Character 150.31
Analytic conductor $24.058$
Analytic rank $0$
Dimension $24$
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: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 31.1
Character \(\chi\) \(=\) 150.31
Dual form 150.6.g.c.121.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-49.3905 + 26.1836i) q^{5} +(29.1246 + 21.1603i) q^{6} -91.4091 q^{7} +(51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\) \(q+(-1.23607 - 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-49.3905 + 26.1836i) q^{5} +(29.1246 + 21.1603i) q^{6} -91.4091 q^{7} +(51.7771 + 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(160.658 + 155.528i) q^{10} +(173.813 + 534.942i) q^{11} +(44.4984 - 136.952i) q^{12} +(-219.833 + 676.576i) q^{13} +(112.988 + 347.741i) q^{14} +(221.106 - 451.926i) q^{15} +(79.1084 - 243.470i) q^{16} +(-1793.05 - 1302.73i) q^{17} -324.000 q^{18} +(563.030 + 409.066i) q^{19} +(393.078 - 803.424i) q^{20} +(665.564 - 483.560i) q^{21} +(1820.20 - 1322.45i) q^{22} +(550.562 + 1694.46i) q^{23} -576.000 q^{24} +(1753.83 - 2586.44i) q^{25} +2845.58 q^{26} +(225.273 + 693.320i) q^{27} +(1183.22 - 859.663i) q^{28} +(4759.74 - 3458.15i) q^{29} +(-1992.53 - 282.527i) q^{30} +(-6919.50 - 5027.31i) q^{31} -1024.00 q^{32} +(-4095.44 - 2975.51i) q^{33} +(-2739.54 + 8431.45i) q^{34} +(4514.74 - 2393.42i) q^{35} +(400.486 + 1232.57i) q^{36} +(2039.96 - 6278.35i) q^{37} +(860.234 - 2647.53i) q^{38} +(-1978.50 - 6089.18i) q^{39} +(-3542.28 - 502.270i) q^{40} +(1074.34 - 3306.48i) q^{41} +(-2662.25 - 1934.24i) q^{42} -2484.63 q^{43} +(-7280.78 - 5289.80i) q^{44} +(780.810 + 4460.21i) q^{45} +(5765.57 - 4188.93i) q^{46} +(7804.71 - 5670.45i) q^{47} +(711.975 + 2191.23i) q^{48} -8451.38 q^{49} +(-12007.3 - 3474.96i) q^{50} +19947.0 q^{51} +(-3517.33 - 10825.2i) q^{52} +(-6804.92 + 4944.06i) q^{53} +(2359.09 - 1713.98i) q^{54} +(-22591.4 - 21870.0i) q^{55} +(-4732.90 - 3438.65i) q^{56} -6263.50 q^{57} +(-19039.0 - 13832.6i) q^{58} +(6729.21 - 20710.4i) q^{59} +(1388.11 + 7929.26i) q^{60} +(12388.1 + 38126.5i) q^{61} +(-10572.1 + 32537.4i) q^{62} +(-2288.00 + 7041.75i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-6857.58 - 39172.4i) q^{65} +(-6257.27 + 19257.9i) q^{66} +(-23736.7 - 17245.7i) q^{67} +35461.4 q^{68} +(-12972.5 - 9425.09i) q^{69} +(-14685.6 - 14216.6i) q^{70} +(56961.1 - 41384.7i) q^{71} +(4193.94 - 3047.08i) q^{72} +(-10088.1 - 31048.1i) q^{73} -26405.8 q^{74} +(912.531 + 28110.2i) q^{75} -11135.1 q^{76} +(-15888.1 - 48898.6i) q^{77} +(-20719.1 + 15053.3i) q^{78} +(-32817.0 + 23843.0i) q^{79} +(2467.75 + 14096.5i) q^{80} +(-5307.96 - 3856.46i) q^{81} -13906.5 q^{82} +(70220.7 + 51018.3i) q^{83} +(-4067.56 + 12518.7i) q^{84} +(122670. + 17393.7i) q^{85} +(3071.17 + 9452.09i) q^{86} +(-16362.5 + 50358.7i) q^{87} +(-11124.0 + 34236.3i) q^{88} +(30083.1 + 92586.2i) q^{89} +(16002.5 - 8483.50i) q^{90} +(20094.7 - 61845.2i) q^{91} +(-23062.3 - 16755.7i) q^{92} +76976.8 q^{93} +(-31218.8 - 22681.8i) q^{94} +(-38519.2 - 5461.75i) q^{95} +(7455.90 - 5417.03i) q^{96} +(-47487.7 + 34501.9i) q^{97} +(10446.5 + 32151.0i) q^{98} +45560.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} - 54 q^{3} - 96 q^{4} + 80 q^{5} + 216 q^{6} - 454 q^{7} + 384 q^{8} - 486 q^{9} + 120 q^{10} + 125 q^{11} - 864 q^{12} - 578 q^{13} - 344 q^{14} + 855 q^{15} - 1536 q^{16} - 2664 q^{17} - 7776 q^{18} + 1424 q^{19} + 1520 q^{20} + 1269 q^{21} + 1280 q^{22} - 4810 q^{23} - 13824 q^{24} - 10880 q^{25} + 6392 q^{26} - 4374 q^{27} + 2256 q^{28} - 1554 q^{29} + 4320 q^{30} - 24513 q^{31} - 24576 q^{32} - 2880 q^{33} - 4004 q^{34} + 15310 q^{35} - 7776 q^{36} - 28123 q^{37} + 8384 q^{38} - 5202 q^{39} + 7680 q^{40} - 17914 q^{41} - 5076 q^{42} + 1256 q^{43} - 5120 q^{44} - 2025 q^{45} - 13040 q^{46} + 930 q^{47} - 13824 q^{48} + 24606 q^{49} - 7880 q^{50} + 29934 q^{51} - 9248 q^{52} - 49701 q^{53} + 17496 q^{54} - 99060 q^{55} - 9024 q^{56} + 12096 q^{57} + 6216 q^{58} - 14465 q^{59} - 3600 q^{60} - 52750 q^{61} - 72528 q^{62} + 6966 q^{63} - 24576 q^{64} - 34885 q^{65} - 4500 q^{66} + 199846 q^{67} + 53216 q^{68} + 29340 q^{69} + 116820 q^{70} - 42880 q^{71} + 31104 q^{72} + 35852 q^{73} + 21832 q^{74} - 28620 q^{75} + 21504 q^{76} - 114745 q^{77} - 49572 q^{78} - 236128 q^{79} - 6400 q^{80} - 39366 q^{81} + 46216 q^{82} - 97273 q^{83} + 12384 q^{84} + 372975 q^{85} - 232304 q^{86} + 21609 q^{87} - 8000 q^{88} + 278147 q^{89} - 25920 q^{90} - 103052 q^{91} + 52160 q^{92} + 114858 q^{93} - 3720 q^{94} + 79590 q^{95} + 55296 q^{96} - 249803 q^{97} - 28164 q^{98} + 31590 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23607 3.80423i −0.218508 0.672499i
\(3\) −7.28115 + 5.29007i −0.467086 + 0.339358i
\(4\) −12.9443 + 9.40456i −0.404508 + 0.293893i
\(5\) −49.3905 + 26.1836i −0.883523 + 0.468387i
\(6\) 29.1246 + 21.1603i 0.330280 + 0.239962i
\(7\) −91.4091 −0.705090 −0.352545 0.935795i \(-0.614684\pi\)
−0.352545 + 0.935795i \(0.614684\pi\)
\(8\) 51.7771 + 37.6183i 0.286031 + 0.207813i
\(9\) 25.0304 77.0356i 0.103006 0.317019i
\(10\) 160.658 + 155.528i 0.508047 + 0.491822i
\(11\) 173.813 + 534.942i 0.433113 + 1.33298i 0.895008 + 0.446050i \(0.147170\pi\)
−0.461895 + 0.886934i \(0.652830\pi\)
\(12\) 44.4984 136.952i 0.0892055 0.274546i
\(13\) −219.833 + 676.576i −0.360773 + 1.11035i 0.591813 + 0.806076i \(0.298413\pi\)
−0.952586 + 0.304270i \(0.901587\pi\)
\(14\) 112.988 + 347.741i 0.154068 + 0.474172i
\(15\) 221.106 451.926i 0.253731 0.518608i
\(16\) 79.1084 243.470i 0.0772542 0.237764i
\(17\) −1793.05 1302.73i −1.50477 1.09328i −0.968431 0.249282i \(-0.919805\pi\)
−0.536343 0.844000i \(-0.680195\pi\)
\(18\) −324.000 −0.235702
\(19\) 563.030 + 409.066i 0.357806 + 0.259961i 0.752137 0.659007i \(-0.229023\pi\)
−0.394330 + 0.918969i \(0.629023\pi\)
\(20\) 393.078 803.424i 0.219737 0.449128i
\(21\) 665.564 483.560i 0.329338 0.239278i
\(22\) 1820.20 1322.45i 0.801791 0.582535i
\(23\) 550.562 + 1694.46i 0.217014 + 0.667899i 0.999005 + 0.0446094i \(0.0142043\pi\)
−0.781991 + 0.623290i \(0.785796\pi\)
\(24\) −576.000 −0.204124
\(25\) 1753.83 2586.44i 0.561227 0.827662i
\(26\) 2845.58 0.825538
\(27\) 225.273 + 693.320i 0.0594703 + 0.183031i
\(28\) 1183.22 859.663i 0.285215 0.207221i
\(29\) 4759.74 3458.15i 1.05097 0.763571i 0.0785694 0.996909i \(-0.474965\pi\)
0.972396 + 0.233338i \(0.0749648\pi\)
\(30\) −1992.53 282.527i −0.404205 0.0573135i
\(31\) −6919.50 5027.31i −1.29321 0.939575i −0.293349 0.956005i \(-0.594770\pi\)
−0.999865 + 0.0164300i \(0.994770\pi\)
\(32\) −1024.00 −0.176777
\(33\) −4095.44 2975.51i −0.654660 0.475638i
\(34\) −2739.54 + 8431.45i −0.406426 + 1.25085i
\(35\) 4514.74 2393.42i 0.622963 0.330255i
\(36\) 400.486 + 1232.57i 0.0515028 + 0.158509i
\(37\) 2039.96 6278.35i 0.244972 0.753947i −0.750669 0.660679i \(-0.770269\pi\)
0.995641 0.0932684i \(-0.0297315\pi\)
\(38\) 860.234 2647.53i 0.0966402 0.297428i
\(39\) −1978.50 6089.18i −0.208293 0.641058i
\(40\) −3542.28 502.270i −0.350052 0.0496349i
\(41\) 1074.34 3306.48i 0.0998118 0.307189i −0.888666 0.458555i \(-0.848367\pi\)
0.988478 + 0.151366i \(0.0483672\pi\)
\(42\) −2662.25 1934.24i −0.232877 0.169195i
\(43\) −2484.63 −0.204923 −0.102461 0.994737i \(-0.532672\pi\)
−0.102461 + 0.994737i \(0.532672\pi\)
\(44\) −7280.78 5289.80i −0.566952 0.411915i
\(45\) 780.810 + 4460.21i 0.0574797 + 0.328340i
\(46\) 5765.57 4188.93i 0.401742 0.291883i
\(47\) 7804.71 5670.45i 0.515362 0.374432i −0.299492 0.954099i \(-0.596817\pi\)
0.814854 + 0.579667i \(0.196817\pi\)
\(48\) 711.975 + 2191.23i 0.0446028 + 0.137273i
\(49\) −8451.38 −0.502849
\(50\) −12007.3 3474.96i −0.679234 0.196573i
\(51\) 19947.0 1.07387
\(52\) −3517.33 10825.2i −0.180387 0.555173i
\(53\) −6804.92 + 4944.06i −0.332761 + 0.241765i −0.741601 0.670841i \(-0.765933\pi\)
0.408840 + 0.912606i \(0.365933\pi\)
\(54\) 2359.09 1713.98i 0.110093 0.0799874i
\(55\) −22591.4 21870.0i −1.00702 0.974858i
\(56\) −4732.90 3438.65i −0.201677 0.146527i
\(57\) −6263.50 −0.255346
\(58\) −19039.0 13832.6i −0.743145 0.539926i
\(59\) 6729.21 20710.4i 0.251671 0.774565i −0.742796 0.669518i \(-0.766501\pi\)
0.994467 0.105047i \(-0.0334993\pi\)
\(60\) 1388.11 + 7929.26i 0.0497789 + 0.284351i
\(61\) 12388.1 + 38126.5i 0.426264 + 1.31191i 0.901779 + 0.432198i \(0.142262\pi\)
−0.475514 + 0.879708i \(0.657738\pi\)
\(62\) −10572.1 + 32537.4i −0.349285 + 1.07499i
\(63\) −2288.00 + 7041.75i −0.0726282 + 0.223527i
\(64\) 1265.73 + 3895.53i 0.0386271 + 0.118882i
\(65\) −6857.58 39172.4i −0.201320 1.15000i
\(66\) −6257.27 + 19257.9i −0.176818 + 0.544188i
\(67\) −23736.7 17245.7i −0.646002 0.469348i 0.215905 0.976414i \(-0.430730\pi\)
−0.861907 + 0.507066i \(0.830730\pi\)
\(68\) 35461.4 0.930001
\(69\) −12972.5 9425.09i −0.328021 0.238321i
\(70\) −14685.6 14216.6i −0.358218 0.346778i
\(71\) 56961.1 41384.7i 1.34101 0.974302i 0.341606 0.939843i \(-0.389029\pi\)
0.999406 0.0344586i \(-0.0109707\pi\)
\(72\) 4193.94 3047.08i 0.0953436 0.0692712i
\(73\) −10088.1 31048.1i −0.221566 0.681910i −0.998622 0.0524788i \(-0.983288\pi\)
0.777056 0.629432i \(-0.216712\pi\)
\(74\) −26405.8 −0.560557
\(75\) 912.531 + 28110.2i 0.0187325 + 0.577046i
\(76\) −11135.1 −0.221136
\(77\) −15888.1 48898.6i −0.305383 0.939873i
\(78\) −20719.1 + 15053.3i −0.385597 + 0.280153i
\(79\) −32817.0 + 23843.0i −0.591605 + 0.429826i −0.842889 0.538087i \(-0.819147\pi\)
0.251284 + 0.967913i \(0.419147\pi\)
\(80\) 2467.75 + 14096.5i 0.0431098 + 0.246255i
\(81\) −5307.96 3856.46i −0.0898908 0.0653095i
\(82\) −13906.5 −0.228394
\(83\) 70220.7 + 51018.3i 1.11884 + 0.812888i 0.984034 0.177983i \(-0.0569573\pi\)
0.134811 + 0.990871i \(0.456957\pi\)
\(84\) −4067.56 + 12518.7i −0.0628979 + 0.193580i
\(85\) 122670. + 17393.7i 1.84158 + 0.261123i
\(86\) 3071.17 + 9452.09i 0.0447773 + 0.137810i
\(87\) −16362.5 + 50358.7i −0.231767 + 0.713307i
\(88\) −11124.0 + 34236.3i −0.153128 + 0.471281i
\(89\) 30083.1 + 92586.2i 0.402575 + 1.23900i 0.922903 + 0.385033i \(0.125810\pi\)
−0.520327 + 0.853967i \(0.674190\pi\)
\(90\) 16002.5 8483.50i 0.208248 0.110400i
\(91\) 20094.7 61845.2i 0.254377 0.782893i
\(92\) −23062.3 16755.7i −0.284075 0.206392i
\(93\) 76976.8 0.922895
\(94\) −31218.8 22681.8i −0.364416 0.264764i
\(95\) −38519.2 5461.75i −0.437893 0.0620901i
\(96\) 7455.90 5417.03i 0.0825700 0.0599906i
\(97\) −47487.7 + 34501.9i −0.512451 + 0.372317i −0.813752 0.581212i \(-0.802579\pi\)
0.301302 + 0.953529i \(0.402579\pi\)
\(98\) 10446.5 + 32151.0i 0.109876 + 0.338165i
\(99\) 45560.2 0.467194
\(100\) 1622.28 + 49973.7i 0.0162228 + 0.499737i
\(101\) 168732. 1.64586 0.822930 0.568143i \(-0.192338\pi\)
0.822930 + 0.568143i \(0.192338\pi\)
\(102\) −24655.9 75883.0i −0.234650 0.722178i
\(103\) −48264.3 + 35066.0i −0.448263 + 0.325682i −0.788909 0.614509i \(-0.789354\pi\)
0.340647 + 0.940191i \(0.389354\pi\)
\(104\) −36833.9 + 26761.4i −0.333937 + 0.242619i
\(105\) −20211.1 + 41310.1i −0.178903 + 0.365665i
\(106\) 27219.7 + 19776.2i 0.235298 + 0.170954i
\(107\) 41884.2 0.353664 0.176832 0.984241i \(-0.443415\pi\)
0.176832 + 0.984241i \(0.443415\pi\)
\(108\) −9436.37 6855.93i −0.0778477 0.0565597i
\(109\) 49742.8 153093.i 0.401018 1.23421i −0.523157 0.852236i \(-0.675246\pi\)
0.924175 0.381970i \(-0.124754\pi\)
\(110\) −55273.7 + 112976.i −0.435549 + 0.890232i
\(111\) 18359.6 + 56505.1i 0.141435 + 0.435292i
\(112\) −7231.22 + 22255.4i −0.0544712 + 0.167645i
\(113\) 4717.30 14518.4i 0.0347534 0.106960i −0.932175 0.362008i \(-0.882091\pi\)
0.966928 + 0.255048i \(0.0820913\pi\)
\(114\) 7742.11 + 23827.8i 0.0557952 + 0.171720i
\(115\) −71559.6 69274.3i −0.504572 0.488458i
\(116\) −29088.9 + 89526.6i −0.200716 + 0.617742i
\(117\) 46617.9 + 33869.9i 0.314839 + 0.228744i
\(118\) −87104.7 −0.575886
\(119\) 163902. + 119081.i 1.06100 + 0.770862i
\(120\) 28448.9 15081.8i 0.180348 0.0956091i
\(121\) −125659. + 91296.5i −0.780243 + 0.566880i
\(122\) 129729. 94254.0i 0.789113 0.573324i
\(123\) 9669.06 + 29758.3i 0.0576264 + 0.177356i
\(124\) 136848. 0.799250
\(125\) −18900.1 + 173667.i −0.108191 + 0.994130i
\(126\) 29616.5 0.166191
\(127\) −92835.1 285717.i −0.510744 1.57191i −0.790895 0.611952i \(-0.790385\pi\)
0.280152 0.959956i \(-0.409615\pi\)
\(128\) 13254.9 9630.27i 0.0715077 0.0519534i
\(129\) 18091.0 13143.9i 0.0957166 0.0695422i
\(130\) −140544. + 74507.6i −0.729382 + 0.386671i
\(131\) 207275. + 150594.i 1.05528 + 0.766706i 0.973209 0.229921i \(-0.0738466\pi\)
0.0820708 + 0.996626i \(0.473847\pi\)
\(132\) 80995.9 0.404602
\(133\) −51466.1 37392.3i −0.252285 0.183296i
\(134\) −36266.5 + 111617.i −0.174479 + 0.536992i
\(135\) −29280.0 28344.9i −0.138273 0.133857i
\(136\) −43832.7 134903.i −0.203213 0.625425i
\(137\) 13413.0 41281.0i 0.0610556 0.187910i −0.915876 0.401460i \(-0.868503\pi\)
0.976932 + 0.213551i \(0.0685028\pi\)
\(138\) −19820.2 + 61000.5i −0.0885954 + 0.272669i
\(139\) −5458.58 16799.8i −0.0239631 0.0737508i 0.938360 0.345660i \(-0.112345\pi\)
−0.962323 + 0.271909i \(0.912345\pi\)
\(140\) −35930.9 + 73440.2i −0.154934 + 0.316675i
\(141\) −26830.2 + 82574.9i −0.113652 + 0.349784i
\(142\) −227844. 165539.i −0.948238 0.688936i
\(143\) −400139. −1.63633
\(144\) −16775.8 12188.3i −0.0674181 0.0489821i
\(145\) −144539. + 295427.i −0.570905 + 1.16689i
\(146\) −105644. + 76755.0i −0.410170 + 0.298006i
\(147\) 61535.8 44708.4i 0.234874 0.170646i
\(148\) 32639.3 + 100454.i 0.122486 + 0.376974i
\(149\) −437239. −1.61344 −0.806721 0.590933i \(-0.798760\pi\)
−0.806721 + 0.590933i \(0.798760\pi\)
\(150\) 105810. 38217.6i 0.383970 0.138687i
\(151\) 403747. 1.44101 0.720504 0.693451i \(-0.243910\pi\)
0.720504 + 0.693451i \(0.243910\pi\)
\(152\) 13763.7 + 42360.4i 0.0483201 + 0.148714i
\(153\) −145237. + 105521.i −0.501591 + 0.364427i
\(154\) −166382. + 120884.i −0.565335 + 0.410740i
\(155\) 473391. + 67123.5i 1.58267 + 0.224411i
\(156\) 82876.3 + 60213.2i 0.272658 + 0.198098i
\(157\) −87421.1 −0.283053 −0.141526 0.989934i \(-0.545201\pi\)
−0.141526 + 0.989934i \(0.545201\pi\)
\(158\) 131268. + 95371.9i 0.418328 + 0.303933i
\(159\) 23393.2 71996.9i 0.0733833 0.225851i
\(160\) 50575.8 26812.1i 0.156186 0.0827999i
\(161\) −50326.4 154889.i −0.153014 0.470929i
\(162\) −8109.84 + 24959.5i −0.0242787 + 0.0747221i
\(163\) −53481.4 + 164599.i −0.157664 + 0.485241i −0.998421 0.0561721i \(-0.982110\pi\)
0.840757 + 0.541413i \(0.182110\pi\)
\(164\) 17189.4 + 52903.6i 0.0499059 + 0.153595i
\(165\) 280185. + 39728.3i 0.801190 + 0.113603i
\(166\) 107288. 330197.i 0.302190 0.930044i
\(167\) −294619. 214053.i −0.817465 0.593923i 0.0985202 0.995135i \(-0.468589\pi\)
−0.915985 + 0.401212i \(0.868589\pi\)
\(168\) 52651.6 0.143926
\(169\) −109046. 79226.8i −0.293694 0.213381i
\(170\) −85458.7 488164.i −0.226795 1.29552i
\(171\) 45605.5 33134.3i 0.119269 0.0866538i
\(172\) 32161.7 23366.9i 0.0828930 0.0602253i
\(173\) −219167. 674527.i −0.556750 1.71350i −0.691278 0.722589i \(-0.742952\pi\)
0.134528 0.990910i \(-0.457048\pi\)
\(174\) 211801. 0.530341
\(175\) −160316. + 236424.i −0.395715 + 0.583576i
\(176\) 143993. 0.350396
\(177\) 60562.9 + 186393.i 0.145303 + 0.447195i
\(178\) 315034. 228886.i 0.745259 0.541463i
\(179\) 68215.2 49561.3i 0.159129 0.115614i −0.505371 0.862902i \(-0.668644\pi\)
0.664500 + 0.747288i \(0.268644\pi\)
\(180\) −52053.3 50391.0i −0.119748 0.115923i
\(181\) −303317. 220372.i −0.688176 0.499989i 0.187884 0.982191i \(-0.439837\pi\)
−0.876060 + 0.482202i \(0.839837\pi\)
\(182\) −260112. −0.582078
\(183\) −291891. 212071.i −0.644308 0.468117i
\(184\) −35236.0 + 108445.i −0.0767259 + 0.236138i
\(185\) 63635.5 + 363504.i 0.136701 + 0.780872i
\(186\) −95148.5 292837.i −0.201660 0.620645i
\(187\) 385229. 1.18561e6i 0.805591 2.47935i
\(188\) −47698.1 + 146800.i −0.0984253 + 0.302922i
\(189\) −20592.0 63375.8i −0.0419319 0.129053i
\(190\) 26834.6 + 153287.i 0.0539276 + 0.308049i
\(191\) 177625. 546675.i 0.352308 1.08429i −0.605247 0.796038i \(-0.706926\pi\)
0.957554 0.288253i \(-0.0930744\pi\)
\(192\) −29823.6 21668.1i −0.0583858 0.0424197i
\(193\) −721580. −1.39441 −0.697206 0.716871i \(-0.745574\pi\)
−0.697206 + 0.716871i \(0.745574\pi\)
\(194\) 189951. + 138007.i 0.362357 + 0.263268i
\(195\) 257156. + 248943.i 0.484295 + 0.468829i
\(196\) 109397. 79481.5i 0.203407 0.147784i
\(197\) −260806. + 189487.i −0.478798 + 0.347867i −0.800860 0.598851i \(-0.795624\pi\)
0.322062 + 0.946719i \(0.395624\pi\)
\(198\) −56315.5 173321.i −0.102086 0.314187i
\(199\) 531953. 0.952228 0.476114 0.879384i \(-0.342045\pi\)
0.476114 + 0.879384i \(0.342045\pi\)
\(200\) 188106. 67942.4i 0.332527 0.120106i
\(201\) 264062. 0.461016
\(202\) −208564. 641893.i −0.359634 1.10684i
\(203\) −435084. + 316107.i −0.741025 + 0.538386i
\(204\) −258200. + 187593.i −0.434391 + 0.315603i
\(205\) 33513.5 + 191439.i 0.0556974 + 0.318159i
\(206\) 193057. + 140264.i 0.316970 + 0.230292i
\(207\) 144314. 0.234090
\(208\) 147336. + 107046.i 0.236129 + 0.171558i
\(209\) −120964. + 372290.i −0.191554 + 0.589543i
\(210\) 182135. + 25825.5i 0.285001 + 0.0404111i
\(211\) −230134. 708281.i −0.355857 1.09521i −0.955511 0.294956i \(-0.904695\pi\)
0.599654 0.800259i \(-0.295305\pi\)
\(212\) 41587.9 127995.i 0.0635518 0.195592i
\(213\) −195815. + 602656.i −0.295731 + 0.910166i
\(214\) −51771.7 159337.i −0.0772784 0.237839i
\(215\) 122717. 65056.6i 0.181054 0.0959832i
\(216\) −14417.5 + 44372.5i −0.0210259 + 0.0647112i
\(217\) 632505. + 459542.i 0.911832 + 0.662485i
\(218\) −643884. −0.917627
\(219\) 237700. + 172699.i 0.334902 + 0.243321i
\(220\) 498107. + 70628.1i 0.693851 + 0.0983832i
\(221\) 1.27557e6 926755.i 1.75680 1.27639i
\(222\) 192264. 139688.i 0.261828 0.190229i
\(223\) −315414. 970743.i −0.424735 1.30720i −0.903248 0.429120i \(-0.858824\pi\)
0.478512 0.878081i \(-0.341176\pi\)
\(224\) 93602.9 0.124643
\(225\) −155349. 199847.i −0.204575 0.263173i
\(226\) −61062.0 −0.0795243
\(227\) 166163. + 511398.i 0.214028 + 0.658710i 0.999221 + 0.0394592i \(0.0125635\pi\)
−0.785193 + 0.619251i \(0.787436\pi\)
\(228\) 81076.4 58905.4i 0.103290 0.0750444i
\(229\) −1.17955e6 + 856994.i −1.48637 + 1.07991i −0.510940 + 0.859616i \(0.670703\pi\)
−0.975433 + 0.220297i \(0.929297\pi\)
\(230\) −175082. + 357857.i −0.218234 + 0.446056i
\(231\) 374360. + 271989.i 0.461594 + 0.335367i
\(232\) 376535. 0.459289
\(233\) 607318. + 441242.i 0.732869 + 0.532461i 0.890470 0.455042i \(-0.150376\pi\)
−0.157601 + 0.987503i \(0.550376\pi\)
\(234\) 71225.9 219211.i 0.0850351 0.261711i
\(235\) −237005. + 484422.i −0.279955 + 0.572208i
\(236\) 107667. + 331366.i 0.125836 + 0.387282i
\(237\) 112815. 347209.i 0.130466 0.401532i
\(238\) 250419. 770711.i 0.286566 0.881961i
\(239\) −239223. 736253.i −0.270900 0.833743i −0.990275 0.139122i \(-0.955572\pi\)
0.719376 0.694621i \(-0.244428\pi\)
\(240\) −92539.3 89583.9i −0.103705 0.100393i
\(241\) −337257. + 1.03797e6i −0.374041 + 1.15118i 0.570083 + 0.821587i \(0.306911\pi\)
−0.944123 + 0.329592i \(0.893089\pi\)
\(242\) 502636. + 365186.i 0.551715 + 0.400844i
\(243\) 59049.0 0.0641500
\(244\) −518918. 377016.i −0.557987 0.405401i
\(245\) 417417. 221288.i 0.444279 0.235528i
\(246\) 101256. 73566.6i 0.106680 0.0775073i
\(247\) −400537. + 291007.i −0.417734 + 0.303502i
\(248\) −169153. 520599.i −0.174643 0.537495i
\(249\) −781178. −0.798457
\(250\) 684032. 142764.i 0.692192 0.144467i
\(251\) −1.70703e6 −1.71024 −0.855119 0.518432i \(-0.826516\pi\)
−0.855119 + 0.518432i \(0.826516\pi\)
\(252\) −36608.1 112668.i −0.0363141 0.111763i
\(253\) −810741. + 589038.i −0.796308 + 0.578551i
\(254\) −972182. + 706332.i −0.945504 + 0.686949i
\(255\) −985193. + 522286.i −0.948792 + 0.502989i
\(256\) −53019.7 38521.1i −0.0505636 0.0367366i
\(257\) 418279. 0.395033 0.197516 0.980300i \(-0.436712\pi\)
0.197516 + 0.980300i \(0.436712\pi\)
\(258\) −72363.8 52575.4i −0.0676819 0.0491738i
\(259\) −186471. + 573898.i −0.172727 + 0.531600i
\(260\) 457166. + 442566.i 0.419412 + 0.406017i
\(261\) −147263. 453228.i −0.133811 0.411828i
\(262\) 316687. 974664.i 0.285021 0.877206i
\(263\) 583643. 1.79627e6i 0.520305 1.60133i −0.253112 0.967437i \(-0.581454\pi\)
0.773417 0.633897i \(-0.218546\pi\)
\(264\) −100116. 308127.i −0.0884088 0.272094i
\(265\) 206644. 422367.i 0.180763 0.369467i
\(266\) −78633.2 + 242008.i −0.0681400 + 0.209713i
\(267\) −708827. 514993.i −0.608502 0.442102i
\(268\) 469443. 0.399251
\(269\) 174187. + 126554.i 0.146769 + 0.106634i 0.658747 0.752365i \(-0.271087\pi\)
−0.511978 + 0.858999i \(0.671087\pi\)
\(270\) −71638.4 + 146424.i −0.0598049 + 0.122237i
\(271\) 581101. 422195.i 0.480650 0.349212i −0.320928 0.947104i \(-0.603995\pi\)
0.801577 + 0.597891i \(0.203995\pi\)
\(272\) −459022. + 333499.i −0.376193 + 0.273321i
\(273\) 180853. + 556607.i 0.146865 + 0.452004i
\(274\) −173622. −0.139710
\(275\) 1.68844e6 + 488641.i 1.34633 + 0.389635i
\(276\) 256559. 0.202728
\(277\) 174210. + 536162.i 0.136418 + 0.419852i 0.995808 0.0914689i \(-0.0291562\pi\)
−0.859390 + 0.511321i \(0.829156\pi\)
\(278\) −57163.0 + 41531.3i −0.0443611 + 0.0322303i
\(279\) −560480. + 407212.i −0.431071 + 0.313192i
\(280\) 323796. + 45912.0i 0.246818 + 0.0349971i
\(281\) 476853. + 346454.i 0.360262 + 0.261746i 0.753161 0.657836i \(-0.228528\pi\)
−0.392899 + 0.919581i \(0.628528\pi\)
\(282\) 347298. 0.260063
\(283\) −1.14093e6 828931.i −0.846820 0.615251i 0.0774470 0.996996i \(-0.475323\pi\)
−0.924268 + 0.381745i \(0.875323\pi\)
\(284\) −348115. + 1.07139e6i −0.256110 + 0.788227i
\(285\) 309357. 164001.i 0.225604 0.119601i
\(286\) 494599. + 1.52222e6i 0.357551 + 1.10043i
\(287\) −98204.4 + 302242.i −0.0703763 + 0.216596i
\(288\) −25631.1 + 78884.4i −0.0182090 + 0.0560415i
\(289\) 1.07918e6 + 3.32137e6i 0.760062 + 2.33923i
\(290\) 1.30253e6 + 184690.i 0.909480 + 0.128958i
\(291\) 163248. 502427.i 0.113010 0.347809i
\(292\) 422577. + 307020.i 0.290034 + 0.210722i
\(293\) −2.26207e6 −1.53935 −0.769673 0.638439i \(-0.779581\pi\)
−0.769673 + 0.638439i \(0.779581\pi\)
\(294\) −246143. 178833.i −0.166081 0.120665i
\(295\) 209914. + 1.19909e6i 0.140439 + 0.802226i
\(296\) 341804. 248335.i 0.226750 0.164744i
\(297\) −331731. + 241016.i −0.218220 + 0.158546i
\(298\) 540457. + 1.66336e6i 0.352550 + 1.08504i
\(299\) −1.26746e6 −0.819892
\(300\) −276176. 355284.i −0.177167 0.227915i
\(301\) 227118. 0.144489
\(302\) −499058. 1.53594e6i −0.314872 0.969076i
\(303\) −1.22856e6 + 892601.i −0.768759 + 0.558536i
\(304\) 144136. 104721.i 0.0894516 0.0649904i
\(305\) −1.61014e6 1.55872e6i −0.991094 0.959443i
\(306\) 580950. + 422085.i 0.354679 + 0.257689i
\(307\) 160273. 0.0970541 0.0485270 0.998822i \(-0.484547\pi\)
0.0485270 + 0.998822i \(0.484547\pi\)
\(308\) 665530. + 483536.i 0.399752 + 0.290437i
\(309\) 165918. 510642.i 0.0988545 0.304243i
\(310\) −329790. 1.88385e6i −0.194910 1.11338i
\(311\) 525400. + 1.61701e6i 0.308027 + 0.948010i 0.978530 + 0.206103i \(0.0660783\pi\)
−0.670503 + 0.741907i \(0.733922\pi\)
\(312\) 126624. 389708.i 0.0736425 0.226648i
\(313\) −231703. + 713108.i −0.133681 + 0.411429i −0.995383 0.0959873i \(-0.969399\pi\)
0.861701 + 0.507416i \(0.169399\pi\)
\(314\) 108058. + 332570.i 0.0618493 + 0.190353i
\(315\) −71373.2 407704.i −0.0405283 0.231509i
\(316\) 200560. 617260.i 0.112986 0.347737i
\(317\) −520381. 378079.i −0.290853 0.211317i 0.432784 0.901497i \(-0.357531\pi\)
−0.723637 + 0.690180i \(0.757531\pi\)
\(318\) −302808. −0.167919
\(319\) 2.67722e6 + 1.94511e6i 1.47301 + 1.07021i
\(320\) −164514. 159260.i −0.0898108 0.0869426i
\(321\) −304965. + 221570.i −0.165192 + 0.120019i
\(322\) −527025. + 382906.i −0.283264 + 0.205803i
\(323\) −476642. 1.46695e6i −0.254206 0.782366i
\(324\) 104976. 0.0555556
\(325\) 1.36438e6 + 1.75519e6i 0.716516 + 0.921754i
\(326\) 692277. 0.360775
\(327\) 447685. + 1.37783e6i 0.231528 + 0.712569i
\(328\) 180010. 130785.i 0.0923873 0.0671233i
\(329\) −713422. + 518331.i −0.363376 + 0.264008i
\(330\) −195193. 1.11500e6i −0.0986685 0.563622i
\(331\) 470767. + 342032.i 0.236176 + 0.171592i 0.699578 0.714556i \(-0.253371\pi\)
−0.463402 + 0.886148i \(0.653371\pi\)
\(332\) −1.38876e6 −0.691484
\(333\) −432595. 314299.i −0.213782 0.155322i
\(334\) −450137. + 1.38538e6i −0.220790 + 0.679521i
\(335\) 1.62392e6 + 230261.i 0.790595 + 0.112101i
\(336\) −65081.0 200299.i −0.0314489 0.0967899i
\(337\) 726099. 2.23470e6i 0.348274 1.07188i −0.611534 0.791218i \(-0.709447\pi\)
0.959808 0.280659i \(-0.0905528\pi\)
\(338\) −166608. + 512767.i −0.0793239 + 0.244134i
\(339\) 42455.7 + 130665.i 0.0200649 + 0.0617534i
\(340\) −1.75145e6 + 928509.i −0.821678 + 0.435601i
\(341\) 1.48662e6 4.57534e6i 0.692331 2.13078i
\(342\) −182422. 132537.i −0.0843357 0.0612735i
\(343\) 2.30885e6 1.05964
\(344\) −128647. 93467.4i −0.0586142 0.0425857i
\(345\) 887502. + 125842.i 0.401441 + 0.0569215i
\(346\) −2.29515e6 + 1.66752e6i −1.03067 + 0.748827i
\(347\) 2.53090e6 1.83880e6i 1.12837 0.819807i 0.142911 0.989736i \(-0.454354\pi\)
0.985456 + 0.169929i \(0.0543537\pi\)
\(348\) −261801. 805739.i −0.115884 0.356653i
\(349\) 1.92061e6 0.844066 0.422033 0.906581i \(-0.361317\pi\)
0.422033 + 0.906581i \(0.361317\pi\)
\(350\) 1.09757e6 + 317643.i 0.478921 + 0.138602i
\(351\) −518606. −0.224683
\(352\) −177985. 547781.i −0.0765642 0.235641i
\(353\) 1.52065e6 1.10482e6i 0.649522 0.471905i −0.213586 0.976924i \(-0.568514\pi\)
0.863108 + 0.505019i \(0.168514\pi\)
\(354\) 634223. 460790.i 0.268988 0.195431i
\(355\) −1.72973e6 + 3.53546e6i −0.728464 + 1.48893i
\(356\) −1.26014e6 915543.i −0.526978 0.382872i
\(357\) −1.82334e6 −0.757177
\(358\) −272861. 198245.i −0.112521 0.0817513i
\(359\) 584141. 1.79780e6i 0.239211 0.736216i −0.757324 0.653040i \(-0.773493\pi\)
0.996535 0.0831765i \(-0.0265065\pi\)
\(360\) −127357. + 260309.i −0.0517925 + 0.105860i
\(361\) −615488. 1.89428e6i −0.248572 0.765025i
\(362\) −463427. + 1.42628e6i −0.185870 + 0.572049i
\(363\) 431977. 1.32949e6i 0.172066 0.529563i
\(364\) 321516. + 989523.i 0.127189 + 0.391447i
\(365\) 1.31121e6 + 1.26933e6i 0.515157 + 0.498705i
\(366\) −445970. + 1.37256e6i −0.174022 + 0.535583i
\(367\) −387024. 281190.i −0.149994 0.108977i 0.510257 0.860022i \(-0.329550\pi\)
−0.660251 + 0.751045i \(0.729550\pi\)
\(368\) 456104. 0.175568
\(369\) −227825. 165525.i −0.0871036 0.0632845i
\(370\) 1.30419e6 691399.i 0.495265 0.262558i
\(371\) 622031. 451932.i 0.234627 0.170466i
\(372\) −996408. + 723933.i −0.373319 + 0.271232i
\(373\) 379684. + 1.16855e6i 0.141303 + 0.434885i 0.996517 0.0833896i \(-0.0265746\pi\)
−0.855214 + 0.518274i \(0.826575\pi\)
\(374\) −4.98651e6 −1.84339
\(375\) −781098. 1.36448e6i −0.286832 0.501060i
\(376\) 617418. 0.225221
\(377\) 1.29336e6 + 3.98054e6i 0.468668 + 1.44241i
\(378\) −215643. + 156674.i −0.0776256 + 0.0563983i
\(379\) −229912. + 167041.i −0.0822172 + 0.0597343i −0.628135 0.778105i \(-0.716181\pi\)
0.545917 + 0.837839i \(0.316181\pi\)
\(380\) 549968. 291558.i 0.195379 0.103577i
\(381\) 2.18741e6 + 1.58925e6i 0.772001 + 0.560891i
\(382\) −2.29923e6 −0.806166
\(383\) −2.43476e6 1.76896e6i −0.848125 0.616199i 0.0765033 0.997069i \(-0.475624\pi\)
−0.924628 + 0.380870i \(0.875624\pi\)
\(384\) −45566.4 + 140239.i −0.0157695 + 0.0485334i
\(385\) 2.06506e6 + 1.99911e6i 0.710038 + 0.687362i
\(386\) 891921. + 2.74505e6i 0.304690 + 0.937740i
\(387\) −62191.2 + 191405.i −0.0211082 + 0.0649644i
\(388\) 290219. 893203.i 0.0978694 0.301211i
\(389\) 784873. + 2.41559e6i 0.262981 + 0.809374i 0.992152 + 0.125041i \(0.0399063\pi\)
−0.729170 + 0.684333i \(0.760094\pi\)
\(390\) 629175. 1.28599e6i 0.209464 0.428130i
\(391\) 1.22023e6 3.75549e6i 0.403646 1.24229i
\(392\) −437588. 317926.i −0.143830 0.104499i
\(393\) −2.30585e6 −0.753095
\(394\) 1.04322e6 + 757947.i 0.338561 + 0.245979i
\(395\) 996552. 2.03688e6i 0.321372 0.656861i
\(396\) −589743. + 428474.i −0.188984 + 0.137305i
\(397\) 1.15972e6 842584.i 0.369297 0.268310i −0.387622 0.921818i \(-0.626704\pi\)
0.756919 + 0.653508i \(0.226704\pi\)
\(398\) −657531. 2.02367e6i −0.208069 0.640372i
\(399\) 572540. 0.180042
\(400\) −490980. 631616.i −0.153431 0.197380i
\(401\) −4.67485e6 −1.45180 −0.725901 0.687800i \(-0.758577\pi\)
−0.725901 + 0.687800i \(0.758577\pi\)
\(402\) −326399. 1.00455e6i −0.100736 0.310032i
\(403\) 4.92249e6 3.57640e6i 1.50981 1.09694i
\(404\) −2.18411e6 + 1.58685e6i −0.665764 + 0.483706i
\(405\) 363139. + 51490.5i 0.110011 + 0.0155987i
\(406\) 1.74033e6 + 1.26443e6i 0.523983 + 0.380696i
\(407\) 3.71312e6 1.11110
\(408\) 1.03280e6 + 750373.i 0.307161 + 0.223165i
\(409\) 1.51728e6 4.66970e6i 0.448494 1.38032i −0.430113 0.902775i \(-0.641526\pi\)
0.878606 0.477547i \(-0.158474\pi\)
\(410\) 686851. 364124.i 0.201791 0.106977i
\(411\) 120717. + 371529.i 0.0352504 + 0.108490i
\(412\) 294965. 907808.i 0.0856105 0.263482i
\(413\) −615111. + 1.89312e6i −0.177451 + 0.546138i
\(414\) −178382. 549004.i −0.0511506 0.157425i
\(415\) −4.80408e6 681184.i −1.36927 0.194153i
\(416\) 225109. 692814.i 0.0637763 0.196283i
\(417\) 128617. + 93445.5i 0.0362207 + 0.0263159i
\(418\) 1.56579e6 0.438323
\(419\) −4.89035e6 3.55305e6i −1.36083 0.988704i −0.998391 0.0566982i \(-0.981943\pi\)
−0.362443 0.932006i \(-0.618057\pi\)
\(420\) −126886. 724806.i −0.0350986 0.200493i
\(421\) −3.42244e6 + 2.48655e6i −0.941090 + 0.683742i −0.948683 0.316229i \(-0.897583\pi\)
0.00759274 + 0.999971i \(0.497583\pi\)
\(422\) −2.41000e6 + 1.75097e6i −0.658773 + 0.478626i
\(423\) −241472. 743174.i −0.0656169 0.201948i
\(424\) −538326. −0.145422
\(425\) −6.51416e6 + 2.35286e6i −1.74939 + 0.631865i
\(426\) 2.53468e6 0.676705
\(427\) −1.13238e6 3.48511e6i −0.300554 0.925011i
\(428\) −542161. + 393903.i −0.143060 + 0.103939i
\(429\) 2.91347e6 2.11676e6i 0.764307 0.555301i
\(430\) −399177. 386429.i −0.104110 0.100786i
\(431\) −4.45804e6 3.23896e6i −1.15598 0.839870i −0.166718 0.986005i \(-0.553317\pi\)
−0.989265 + 0.146134i \(0.953317\pi\)
\(432\) 186624. 0.0481125
\(433\) 3.54800e6 + 2.57777e6i 0.909419 + 0.660732i 0.940868 0.338774i \(-0.110012\pi\)
−0.0314486 + 0.999505i \(0.510012\pi\)
\(434\) 966382. 2.97422e6i 0.246277 0.757964i
\(435\) −510421. 2.91567e6i −0.129332 0.738780i
\(436\) 795884. + 2.44948e6i 0.200509 + 0.617103i
\(437\) −383161. + 1.17925e6i −0.0959792 + 0.295394i
\(438\) 363173. 1.11773e6i 0.0904540 0.278389i
\(439\) −2.01860e6 6.21260e6i −0.499906 1.53855i −0.809170 0.587575i \(-0.800083\pi\)
0.309264 0.950976i \(-0.399917\pi\)
\(440\) −347009. 1.98221e6i −0.0854494 0.488111i
\(441\) −211541. + 651057.i −0.0517963 + 0.159413i
\(442\) −5.10228e6 3.70702e6i −1.24225 0.902546i
\(443\) 3.73511e6 0.904262 0.452131 0.891952i \(-0.350664\pi\)
0.452131 + 0.891952i \(0.350664\pi\)
\(444\) −769058. 558753.i −0.185141 0.134513i
\(445\) −3.91006e6 3.78519e6i −0.936016 0.906124i
\(446\) −3.30305e6 + 2.39981e6i −0.786282 + 0.571268i
\(447\) 3.18360e6 2.31302e6i 0.753616 0.547534i
\(448\) −115700. 356087.i −0.0272356 0.0838225i
\(449\) 6.57835e6 1.53993 0.769965 0.638086i \(-0.220274\pi\)
0.769965 + 0.638086i \(0.220274\pi\)
\(450\) −568242. + 838008.i −0.132282 + 0.195082i
\(451\) 1.95551e6 0.452708
\(452\) 75476.8 + 232294.i 0.0173767 + 0.0534800i
\(453\) −2.93974e6 + 2.13585e6i −0.673075 + 0.489018i
\(454\) 1.74008e6 1.26424e6i 0.396215 0.287867i
\(455\) 626845. + 3.58072e6i 0.141949 + 0.810852i
\(456\) −324306. 235622.i −0.0730369 0.0530644i
\(457\) −1.78358e6 −0.399487 −0.199744 0.979848i \(-0.564011\pi\)
−0.199744 + 0.979848i \(0.564011\pi\)
\(458\) 4.71820e6 + 3.42797e6i 1.05102 + 0.763614i
\(459\) 499282. 1.53663e6i 0.110615 0.340438i
\(460\) 1.57778e6 + 223718.i 0.347658 + 0.0492955i
\(461\) −1.09151e6 3.35932e6i −0.239208 0.736205i −0.996535 0.0831702i \(-0.973495\pi\)
0.757328 0.653035i \(-0.226505\pi\)
\(462\) 571972. 1.76035e6i 0.124672 0.383702i
\(463\) −1.24520e6 + 3.83234e6i −0.269952 + 0.830828i 0.720559 + 0.693394i \(0.243885\pi\)
−0.990511 + 0.137434i \(0.956115\pi\)
\(464\) −465423. 1.43243e6i −0.100358 0.308871i
\(465\) −3.80192e6 + 2.01553e6i −0.815399 + 0.432272i
\(466\) 927900. 2.85578e6i 0.197941 0.609200i
\(467\) 925773. + 672614.i 0.196432 + 0.142716i 0.681654 0.731675i \(-0.261261\pi\)
−0.485222 + 0.874391i \(0.661261\pi\)
\(468\) −921967. −0.194581
\(469\) 2.16975e6 + 1.57642e6i 0.455489 + 0.330932i
\(470\) 2.13581e6 + 302842.i 0.445982 + 0.0632371i
\(471\) 636527. 462464.i 0.132210 0.0960562i
\(472\) 1.12751e6 819182.i 0.232951 0.169249i
\(473\) −431861. 1.32913e6i −0.0887547 0.273159i
\(474\) −1.46031e6 −0.298537
\(475\) 2.04549e6 738814.i 0.415971 0.150245i
\(476\) −3.24149e6 −0.655734
\(477\) 210539. + 647972.i 0.0423679 + 0.130395i
\(478\) −2.50518e6 + 1.82012e6i −0.501497 + 0.364359i
\(479\) −172686. + 125464.i −0.0343890 + 0.0249850i −0.604847 0.796342i \(-0.706766\pi\)
0.570458 + 0.821327i \(0.306766\pi\)
\(480\) −226413. + 462772.i −0.0448537 + 0.0916778i
\(481\) 3.79933e6 + 2.76037e6i 0.748763 + 0.544008i
\(482\) 4.36555e6 0.855897
\(483\) 1.18581e6 + 861539.i 0.231284 + 0.168038i
\(484\) 767959. 2.36353e6i 0.149013 0.458615i
\(485\) 1.44206e6 2.94746e6i 0.278374 0.568976i
\(486\) −72988.6 224636.i −0.0140173 0.0431408i
\(487\) −746522. + 2.29756e6i −0.142633 + 0.438980i −0.996699 0.0811852i \(-0.974129\pi\)
0.854066 + 0.520165i \(0.174129\pi\)
\(488\) −792836. + 2.44010e6i −0.150707 + 0.463829i
\(489\) −481332. 1.48139e6i −0.0910276 0.280154i
\(490\) −1.35779e6 1.31442e6i −0.255471 0.247312i
\(491\) 2.68389e6 8.26015e6i 0.502412 1.54627i −0.302665 0.953097i \(-0.597876\pi\)
0.805078 0.593169i \(-0.202124\pi\)
\(492\) −405023. 294266.i −0.0754339 0.0548059i
\(493\) −1.30395e7 −2.41626
\(494\) 1.60215e6 + 1.16403e6i 0.295383 + 0.214608i
\(495\) −2.25024e6 + 1.19293e6i −0.412777 + 0.218828i
\(496\) −1.77139e6 + 1.28699e6i −0.323304 + 0.234894i
\(497\) −5.20676e6 + 3.78293e6i −0.945533 + 0.686970i
\(498\) 965589. + 2.97178e6i 0.174469 + 0.536961i
\(499\) 5.48868e6 0.986771 0.493386 0.869811i \(-0.335759\pi\)
0.493386 + 0.869811i \(0.335759\pi\)
\(500\) −1.38862e6 2.42575e6i −0.248404 0.433931i
\(501\) 3.27752e6 0.583379
\(502\) 2.11000e6 + 6.49392e6i 0.373701 + 1.15013i
\(503\) −638529. + 463918.i −0.112528 + 0.0817564i −0.642626 0.766180i \(-0.722155\pi\)
0.530098 + 0.847936i \(0.322155\pi\)
\(504\) −383365. + 278531.i −0.0672258 + 0.0488424i
\(505\) −8.33373e6 + 4.41801e6i −1.45416 + 0.770900i
\(506\) 3.24296e6 + 2.35615e6i 0.563075 + 0.409098i
\(507\) 1.21310e6 0.209593
\(508\) 3.88873e6 + 2.82533e6i 0.668572 + 0.485746i
\(509\) 671664. 2.06717e6i 0.114910 0.353656i −0.877018 0.480457i \(-0.840471\pi\)
0.991928 + 0.126801i \(0.0404709\pi\)
\(510\) 3.20466e6 + 3.10232e6i 0.545578 + 0.528154i
\(511\) 922146. + 2.83807e6i 0.156224 + 0.480808i
\(512\) −81007.0 + 249314.i −0.0136568 + 0.0420312i
\(513\) −156778. + 482512.i −0.0263021 + 0.0809496i
\(514\) −517021. 1.59123e6i −0.0863178 0.265659i
\(515\) 1.46564e6 2.99566e6i 0.243505 0.497708i
\(516\) −110562. + 340275.i −0.0182802 + 0.0562608i
\(517\) 4.38993e6 + 3.18947e6i 0.722322 + 0.524798i
\(518\) 2.41373e6 0.395243
\(519\) 5.16408e6 + 3.75192e6i 0.841540 + 0.611414i
\(520\) 1.11853e6 2.28620e6i 0.181401 0.370772i
\(521\) −7.81796e6 + 5.68008e6i −1.26182 + 0.916769i −0.998846 0.0480326i \(-0.984705\pi\)
−0.262979 + 0.964802i \(0.584705\pi\)
\(522\) −1.54216e6 + 1.12044e6i −0.247715 + 0.179975i
\(523\) 453933. + 1.39706e6i 0.0725667 + 0.223337i 0.980761 0.195211i \(-0.0625391\pi\)
−0.908195 + 0.418548i \(0.862539\pi\)
\(524\) −4.09929e6 −0.652199
\(525\) −83413.7 2.56953e6i −0.0132081 0.406869i
\(526\) −7.55483e6 −1.19059
\(527\) 5.85781e6 + 1.80285e7i 0.918774 + 2.82770i
\(528\) −1.04843e6 + 761731.i −0.163665 + 0.118910i
\(529\) 2.63905e6 1.91738e6i 0.410022 0.297899i
\(530\) −1.86221e6 264048.i −0.287964 0.0408312i
\(531\) −1.42700e6 1.03678e6i −0.219628 0.159569i
\(532\) 1.01785e6 0.155921
\(533\) 2.00091e6 + 1.45375e6i 0.305077 + 0.221651i
\(534\) −1.08299e6 + 3.33310e6i −0.164351 + 0.505819i
\(535\) −2.06868e6 + 1.09668e6i −0.312470 + 0.165652i
\(536\) −580264. 1.78587e6i −0.0872396 0.268496i
\(537\) −234503. + 721726.i −0.0350924 + 0.108003i
\(538\) 266133. 819074.i 0.0396409 0.122002i
\(539\) −1.46896e6 4.52100e6i −0.217790 0.670289i
\(540\) 645580. + 91538.7i 0.0952721 + 0.0135089i
\(541\) −881683. + 2.71354e6i −0.129515 + 0.398605i −0.994697 0.102853i \(-0.967203\pi\)
0.865182 + 0.501458i \(0.167203\pi\)
\(542\) −2.32440e6 1.68878e6i −0.339871 0.246930i
\(543\) 3.37428e6 0.491113
\(544\) 1.83609e6 + 1.33400e6i 0.266009 + 0.193267i
\(545\) 1.55170e6 + 8.86376e6i 0.223778 + 1.27828i
\(546\) 1.89391e6 1.37601e6i 0.271881 0.197533i
\(547\) 3.24829e6 2.36002e6i 0.464180 0.337247i −0.330989 0.943635i \(-0.607382\pi\)
0.795169 + 0.606388i \(0.207382\pi\)
\(548\) 214608. + 660497.i 0.0305278 + 0.0939548i
\(549\) 3.24718e6 0.459807
\(550\) −228121. 7.02719e6i −0.0321558 0.990547i
\(551\) 4.09449e6 0.574541
\(552\) −317124. 976007.i −0.0442977 0.136334i
\(553\) 2.99978e6 2.17946e6i 0.417134 0.303066i
\(554\) 1.82435e6 1.32547e6i 0.252542 0.183482i
\(555\) −2.38630e6 2.31009e6i −0.328846 0.318344i
\(556\) 228652. + 166125.i 0.0313681 + 0.0227902i
\(557\) −5.98510e6 −0.817397 −0.408699 0.912669i \(-0.634017\pi\)
−0.408699 + 0.912669i \(0.634017\pi\)
\(558\) 2.24192e6 + 1.62885e6i 0.304814 + 0.221460i
\(559\) 546203. 1.68104e6i 0.0739307 0.227535i
\(560\) −225574. 1.28854e6i −0.0303962 0.173632i
\(561\) 3.46706e6 + 1.06705e7i 0.465108 + 1.43146i
\(562\) 728566. 2.24230e6i 0.0973034 0.299469i
\(563\) −2.80534e6 + 8.63396e6i −0.373006 + 1.14799i 0.571809 + 0.820387i \(0.306242\pi\)
−0.944814 + 0.327606i \(0.893758\pi\)
\(564\) −429283. 1.32120e6i −0.0568259 0.174892i
\(565\) 147154. + 840584.i 0.0193933 + 0.110780i
\(566\) −1.74318e6 + 5.36496e6i −0.228718 + 0.703923i
\(567\) 485196. + 352515.i 0.0633810 + 0.0460490i
\(568\) 4.50610e6 0.586044
\(569\) 1.04219e6 + 757197.i 0.134948 + 0.0980457i 0.653212 0.757175i \(-0.273421\pi\)
−0.518263 + 0.855221i \(0.673421\pi\)
\(570\) −1.00628e6 974147.i −0.129728 0.125585i
\(571\) 593034. 430864.i 0.0761183 0.0553032i −0.549075 0.835773i \(-0.685020\pi\)
0.625194 + 0.780470i \(0.285020\pi\)
\(572\) 5.17951e6 3.76313e6i 0.661909 0.480905i
\(573\) 1.59863e6 + 4.92008e6i 0.203405 + 0.626016i
\(574\) 1.27118e6 0.161038
\(575\) 5.34821e6 + 1.54780e6i 0.674589 + 0.195229i
\(576\) 331776. 0.0416667
\(577\) 1.17647e6 + 3.62080e6i 0.147110 + 0.452757i 0.997276 0.0737568i \(-0.0234989\pi\)
−0.850167 + 0.526514i \(0.823499\pi\)
\(578\) 1.13013e7 8.21088e6i 1.40705 1.02228i
\(579\) 5.25393e6 3.81720e6i 0.651310 0.473205i
\(580\) −907416. 5.18341e6i −0.112005 0.639802i
\(581\) −6.41881e6 4.66354e6i −0.788886 0.573159i
\(582\) −2.11313e6 −0.258594
\(583\) −3.82757e6 2.78089e6i −0.466393 0.338854i
\(584\) 645640. 1.98708e6i 0.0783355 0.241092i
\(585\) −3.18932e6 452223.i −0.385308 0.0546340i
\(586\) 2.79607e6 + 8.60541e6i 0.336359 + 1.03521i
\(587\) −1.41100e6 + 4.34261e6i −0.169018 + 0.520183i −0.999310 0.0371455i \(-0.988174\pi\)
0.830292 + 0.557328i \(0.188174\pi\)
\(588\) −376073. + 1.15743e6i −0.0448569 + 0.138055i
\(589\) −1.83939e6 5.66106e6i −0.218467 0.672372i
\(590\) 4.30214e6 2.28072e6i 0.508809 0.269738i
\(591\) 896572. 2.75936e6i 0.105588 0.324968i
\(592\) −1.36721e6 993339.i −0.160336 0.116491i
\(593\) 1.12241e7 1.31073 0.655366 0.755312i \(-0.272514\pi\)
0.655366 + 0.755312i \(0.272514\pi\)
\(594\) 1.32692e6 + 964066.i 0.154305 + 0.112109i
\(595\) −1.12132e7 1.58995e6i −1.29848 0.184115i
\(596\) 5.65974e6 4.11204e6i 0.652651 0.474178i
\(597\) −3.87323e6 + 2.81407e6i −0.444772 + 0.323146i
\(598\) 1.56667e6 + 4.82171e6i 0.179153 + 0.551376i
\(599\) 1.28940e6 0.146832 0.0734159 0.997301i \(-0.476610\pi\)
0.0734159 + 0.997301i \(0.476610\pi\)
\(600\) −1.01021e6 + 1.48979e6i −0.114560 + 0.168946i
\(601\) −1.35813e7 −1.53376 −0.766879 0.641792i \(-0.778191\pi\)
−0.766879 + 0.641792i \(0.778191\pi\)
\(602\) −280733. 864007.i −0.0315720 0.0971686i
\(603\) −1.92268e6 + 1.39691e6i −0.215334 + 0.156449i
\(604\) −5.22620e6 + 3.79706e6i −0.582900 + 0.423502i
\(605\) 3.81587e6 7.79938e6i 0.423844 0.866307i
\(606\) 4.91424e6 + 3.57041e6i 0.543594 + 0.394944i
\(607\) −7.38309e6 −0.813330 −0.406665 0.913577i \(-0.633308\pi\)
−0.406665 + 0.913577i \(0.633308\pi\)
\(608\) −576543. 418883.i −0.0632518 0.0459551i
\(609\) 1.49568e6 4.60324e6i 0.163417 0.502945i
\(610\) −3.93949e6 + 8.05204e6i −0.428662 + 0.876156i
\(611\) 2.12076e6 + 6.52703e6i 0.229821 + 0.707315i
\(612\) 887612. 2.73179e6i 0.0957954 0.294828i
\(613\) −506293. + 1.55821e6i −0.0544191 + 0.167485i −0.974572 0.224074i \(-0.928064\pi\)
0.920153 + 0.391559i \(0.128064\pi\)
\(614\) −198108. 609714.i −0.0212071 0.0652687i
\(615\) −1.25674e6 1.21660e6i −0.133985 0.129706i
\(616\) 1.01684e6 3.12951e6i 0.107969 0.332295i
\(617\) 1.00628e7 + 7.31106e6i 1.06416 + 0.773157i 0.974853 0.222847i \(-0.0715351\pi\)
0.0893059 + 0.996004i \(0.471535\pi\)
\(618\) −2.14768e6 −0.226203
\(619\) −7.15552e6 5.19879e6i −0.750610 0.545350i 0.145406 0.989372i \(-0.453551\pi\)
−0.896016 + 0.444022i \(0.853551\pi\)
\(620\) −6.75896e6 + 3.58317e6i −0.706156 + 0.374359i
\(621\) −1.05077e6 + 763432.i −0.109340 + 0.0794404i
\(622\) 5.50206e6 3.99748e6i 0.570229 0.414296i
\(623\) −2.74987e6 8.46322e6i −0.283852 0.873606i
\(624\) −1.63905e6 −0.168512
\(625\) −3.61376e6 9.07239e6i −0.370049 0.929012i
\(626\) 2.99922e6 0.305896
\(627\) −1.08868e6 3.35061e6i −0.110594 0.340373i
\(628\) 1.13160e6 822158.i 0.114497 0.0831871i
\(629\) −1.18368e7 + 8.59990e6i −1.19291 + 0.866696i
\(630\) −1.46277e6 + 775469.i −0.146834 + 0.0778418i
\(631\) −5.33749e6 3.87792e6i −0.533659 0.387726i 0.288066 0.957611i \(-0.406988\pi\)
−0.821725 + 0.569885i \(0.806988\pi\)
\(632\) −2.59610e6 −0.258541
\(633\) 5.42250e6 + 3.93967e6i 0.537886 + 0.390797i
\(634\) −795072. + 2.44698e6i −0.0785567 + 0.241773i
\(635\) 1.20663e7 + 1.16809e7i 1.18752 + 1.14959i
\(636\) 374291. + 1.15195e6i 0.0366916 + 0.112925i
\(637\) 1.85789e6 5.71800e6i 0.181414 0.558336i
\(638\) 4.09042e6 1.25890e7i 0.397848 1.22445i
\(639\) −1.76233e6 5.42391e6i −0.170740 0.525485i
\(640\) −402512. + 822706.i −0.0388444 + 0.0793953i
\(641\) 3.55765e6 1.09493e7i 0.341993 1.05255i −0.621180 0.783668i \(-0.713347\pi\)
0.963174 0.268880i \(-0.0866534\pi\)
\(642\) 1.21986e6 + 886281.i 0.116808 + 0.0848661i
\(643\) 48772.9 0.00465212 0.00232606 0.999997i \(-0.499260\pi\)
0.00232606 + 0.999997i \(0.499260\pi\)
\(644\) 2.10810e6 + 1.53162e6i 0.200298 + 0.145525i
\(645\) −549367. + 1.12287e6i −0.0519952 + 0.106275i
\(646\) −4.99146e6 + 3.62651e6i −0.470594 + 0.341907i
\(647\) −1.43172e7 + 1.04021e7i −1.34461 + 0.976919i −0.345354 + 0.938473i \(0.612241\pi\)
−0.999261 + 0.0384467i \(0.987759\pi\)
\(648\) −129757. 399352.i −0.0121393 0.0373610i
\(649\) 1.22485e7 1.14148
\(650\) 4.99067e6 7.35993e6i 0.463314 0.683266i
\(651\) −7.03638e6 −0.650724
\(652\) −855702. 2.63358e6i −0.0788322 0.242620i
\(653\) 6.84862e6 4.97581e6i 0.628521 0.456647i −0.227366 0.973809i \(-0.573012\pi\)
0.855888 + 0.517162i \(0.173012\pi\)
\(654\) 4.68822e6 3.40619e6i 0.428611 0.311404i
\(655\) −1.41805e7 2.01069e6i −1.29148 0.183123i
\(656\) −720040. 523140.i −0.0653277 0.0474633i
\(657\) −2.64431e6 −0.239001
\(658\) 2.85369e6 + 2.07332e6i 0.256946 + 0.186682i
\(659\) −2.22370e6 + 6.84386e6i −0.199464 + 0.613886i 0.800432 + 0.599424i \(0.204604\pi\)
−0.999895 + 0.0144619i \(0.995396\pi\)
\(660\) −4.00042e6 + 2.12077e6i −0.357475 + 0.189510i
\(661\) −3.46478e6 1.06635e7i −0.308441 0.949285i −0.978371 0.206860i \(-0.933676\pi\)
0.669929 0.742425i \(-0.266324\pi\)
\(662\) 719267. 2.21368e6i 0.0637889 0.196322i
\(663\) −4.38502e6 + 1.34957e7i −0.387425 + 1.19237i
\(664\) 1.71660e6 + 5.28316e6i 0.151095 + 0.465022i
\(665\) 3.52100e6 + 499253.i 0.308754 + 0.0437791i
\(666\) −660946. + 2.03418e6i −0.0577405 + 0.177707i
\(667\) 8.48023e6 + 6.16125e6i 0.738062 + 0.536234i
\(668\) 5.82670e6 0.505221
\(669\) 7.43187e6 + 5.39957e6i 0.641997 + 0.466438i
\(670\) −1.13132e6 6.46239e6i −0.0973637 0.556169i
\(671\) −1.82423e7 + 1.32538e7i −1.56413 + 1.13641i
\(672\) −681537. + 495166.i −0.0582192 + 0.0422987i
\(673\) −642564. 1.97761e6i −0.0546863 0.168307i 0.919983 0.391959i \(-0.128202\pi\)
−0.974669 + 0.223651i \(0.928202\pi\)
\(674\) −9.39882e6 −0.796936
\(675\) 2.18833e6 + 633311.i 0.184864 + 0.0535005i
\(676\) 2.15662e6 0.181513
\(677\) 5.33624e6 + 1.64233e7i 0.447470 + 1.37717i 0.879752 + 0.475432i \(0.157708\pi\)
−0.432282 + 0.901738i \(0.642292\pi\)
\(678\) 444602. 323022.i 0.0371447 0.0269872i
\(679\) 4.34081e6 3.15378e6i 0.361324 0.262517i
\(680\) 5.69717e6 + 5.51523e6i 0.472484 + 0.457395i
\(681\) −3.91519e6 2.84455e6i −0.323508 0.235042i
\(682\) −1.92432e7 −1.58422
\(683\) −6.37421e6 4.63114e6i −0.522847 0.379871i 0.294828 0.955550i \(-0.404738\pi\)
−0.817675 + 0.575680i \(0.804738\pi\)
\(684\) −278716. + 857799.i −0.0227783 + 0.0701044i
\(685\) 418413. + 2.39009e6i 0.0340705 + 0.194620i
\(686\) −2.85389e6 8.78337e6i −0.231540 0.712608i
\(687\) 4.05493e6 1.24798e7i 0.327787 1.00883i
\(688\) −196555. + 604934.i −0.0158312 + 0.0487233i
\(689\) −1.84909e6 5.69091e6i −0.148392 0.456703i
\(690\) −618283. 3.53181e6i −0.0494384 0.282406i
\(691\) −160479. + 493903.i −0.0127856 + 0.0393502i −0.957246 0.289276i \(-0.906586\pi\)
0.944460 + 0.328626i \(0.106586\pi\)
\(692\) 9.18059e6 + 6.67009e6i 0.728795 + 0.529500i
\(693\) −4.16461e6 −0.329414
\(694\) −1.01236e7 7.35521e6i −0.797876 0.579691i
\(695\) 709481. + 686823.i 0.0557158 + 0.0539365i
\(696\) −2.74161e6 + 1.99190e6i −0.214527 + 0.155863i
\(697\) −6.23380e6 + 4.52912e6i −0.486039 + 0.353128i
\(698\) −2.37401e6 7.30644e6i −0.184435 0.567633i
\(699\) −6.75618e6 −0.523008
\(700\) −148291. 4.56805e6i −0.0114385 0.352359i
\(701\) −1.23274e7 −0.947498 −0.473749 0.880660i \(-0.657100\pi\)
−0.473749 + 0.880660i \(0.657100\pi\)
\(702\) 641033. + 1.97290e6i 0.0490950 + 0.151099i
\(703\) 3.71681e6 2.70042e6i 0.283650 0.206084i
\(704\) −1.86388e6 + 1.35419e6i −0.141738 + 0.102979i
\(705\) −836955. 4.78092e6i −0.0634205 0.362276i
\(706\) −6.08262e6 4.41928e6i −0.459281 0.333687i
\(707\) −1.54236e7 −1.16048
\(708\) −2.53689e6 1.84316e6i −0.190204 0.138191i
\(709\) 916853. 2.82178e6i 0.0684990 0.210818i −0.910948 0.412522i \(-0.864648\pi\)
0.979447 + 0.201704i \(0.0646479\pi\)
\(710\) 1.55877e7 + 2.21023e6i 1.16048 + 0.164548i
\(711\) 1.01533e6 + 3.12488e6i 0.0753243 + 0.231824i
\(712\) −1.92532e6 + 5.92552e6i −0.142332 + 0.438053i
\(713\) 4.70895e6 1.44926e7i 0.346896 1.06764i
\(714\) 2.25377e6 + 6.93640e6i 0.165449 + 0.509200i
\(715\) 1.97630e7 1.04771e7i 1.44573 0.766436i
\(716\) −416894. + 1.28307e6i −0.0303909 + 0.0935336i
\(717\) 5.63665e6 + 4.09526e6i 0.409471 + 0.297498i
\(718\) −7.56128e6 −0.547374
\(719\) 6.33889e6 + 4.60547e6i 0.457289 + 0.332240i 0.792467 0.609915i \(-0.208796\pi\)
−0.335178 + 0.942155i \(0.608796\pi\)
\(720\) 1.14770e6 + 162735.i 0.0825080 + 0.0116991i
\(721\) 4.41179e6 3.20535e6i 0.316065 0.229635i
\(722\) −6.44547e6 + 4.68291e6i −0.460163 + 0.334328i
\(723\) −3.03532e6 9.34175e6i −0.215953 0.664634i
\(724\) 5.99872e6 0.425316
\(725\) −596528. 1.83758e7i −0.0421489 1.29838i
\(726\) −5.59163e6 −0.393728
\(727\) −2.94120e6 9.05210e6i −0.206390 0.635204i −0.999653 0.0263249i \(-0.991620\pi\)
0.793263 0.608879i \(-0.208380\pi\)
\(728\) 3.36696e6 2.44624e6i 0.235456 0.171068i
\(729\) −429945. + 312373.i −0.0299636 + 0.0217698i
\(730\) 3.20809e6 6.55712e6i 0.222812 0.455413i
\(731\) 4.45508e6 + 3.23680e6i 0.308363 + 0.224039i
\(732\) 5.77276e6 0.398204
\(733\) −7.26082e6 5.27529e6i −0.499144 0.362649i 0.309546 0.950884i \(-0.399823\pi\)
−0.808690 + 0.588235i \(0.799823\pi\)
\(734\) −591320. + 1.81990e6i −0.0405119 + 0.124683i
\(735\) −1.86865e6 + 3.81940e6i −0.127588 + 0.260781i
\(736\) −563776. 1.73512e6i −0.0383630 0.118069i
\(737\) 5.09972e6 1.56953e7i 0.345842 1.06439i
\(738\) −348086. + 1.07130e6i −0.0235259 + 0.0724052i
\(739\) −810143. 2.49336e6i −0.0545696 0.167948i 0.920057 0.391784i \(-0.128142\pi\)
−0.974627 + 0.223836i \(0.928142\pi\)
\(740\) −4.24231e6 4.10683e6i −0.284789 0.275694i
\(741\) 1.37692e6 4.23773e6i 0.0921221 0.283523i
\(742\) −2.48812e6 1.80773e6i −0.165906 0.120538i
\(743\) 1.31949e7 0.876865 0.438433 0.898764i \(-0.355534\pi\)
0.438433 + 0.898764i \(0.355534\pi\)
\(744\) 3.98563e6 + 2.89573e6i 0.263976 + 0.191790i
\(745\) 2.15954e7 1.14485e7i 1.42551 0.755715i
\(746\) 3.97610e6 2.88881e6i 0.261584 0.190052i
\(747\) 5.68787e6 4.13248e6i 0.372948 0.270963i
\(748\) 6.16366e6 + 1.89698e7i 0.402796 + 1.23968i
\(749\) −3.82860e6 −0.249365
\(750\) −4.22531e6 + 4.65806e6i −0.274287 + 0.302379i
\(751\) 2.48476e7 1.60763 0.803814 0.594881i \(-0.202801\pi\)
0.803814 + 0.594881i \(0.202801\pi\)
\(752\) −763170. 2.34880e6i −0.0492127 0.151461i
\(753\) 1.24291e7 9.03030e6i 0.798828 0.580383i
\(754\) 1.35442e7 9.84044e6i 0.867611 0.630357i
\(755\) −1.99412e7 + 1.05716e7i −1.27316 + 0.674950i
\(756\) 862570. + 626694.i 0.0548896 + 0.0398796i
\(757\) 4.69328e6 0.297671 0.148836 0.988862i \(-0.452447\pi\)
0.148836 + 0.988862i \(0.452447\pi\)
\(758\) 919646. + 668162.i 0.0581364 + 0.0422385i
\(759\) 2.78708e6 8.57775e6i 0.175608 0.540467i
\(760\) −1.78895e6 1.73182e6i −0.112348 0.108760i
\(761\) −7.15282e6 2.20141e7i −0.447730 1.37797i −0.879462 0.475969i \(-0.842098\pi\)
0.431732 0.902002i \(-0.357902\pi\)
\(762\) 3.34206e6 1.02858e7i 0.208510 0.641728i
\(763\) −4.54694e6 + 1.39940e7i −0.282754 + 0.870226i
\(764\) 2.84201e6 + 8.74680e6i 0.176154 + 0.542145i
\(765\) 4.41041e6 9.01458e6i 0.272474 0.556919i
\(766\) −3.71999e6 + 1.14489e7i −0.229071 + 0.705007i
\(767\) 1.25328e7 + 9.10564e6i 0.769239 + 0.558885i
\(768\) 589824. 0.0360844
\(769\) −9.06143e6 6.58351e6i −0.552562 0.401460i 0.276167 0.961110i \(-0.410936\pi\)
−0.828729 + 0.559650i \(0.810936\pi\)
\(770\) 5.05252e6 1.03270e7i 0.307101 0.627694i
\(771\) −3.04555e6 + 2.21272e6i −0.184514 + 0.134057i
\(772\) 9.34032e6 6.78614e6i 0.564051 0.409807i
\(773\) −8.12741e6 2.50136e7i −0.489219 1.50566i −0.825775 0.563999i \(-0.809262\pi\)
0.336556 0.941663i \(-0.390738\pi\)
\(774\) 805020. 0.0483008
\(775\) −2.51385e7 + 9.07983e6i −1.50344 + 0.543030i
\(776\) −3.75668e6 −0.223949
\(777\) −1.67824e6 5.16508e6i −0.0997242 0.306920i
\(778\) 8.21929e6 5.97167e6i 0.486839 0.353709i
\(779\) 1.95745e6 1.42217e6i 0.115571 0.0839670i
\(780\) −5.66990e6 803952.i −0.333687 0.0473144i
\(781\) 3.20390e7 + 2.32777e7i 1.87954 + 1.36556i
\(782\) −1.57950e7 −0.923641
\(783\) 3.46985e6 + 2.52099e6i 0.202258 + 0.146949i
\(784\) −668575. + 2.05766e6i −0.0388472 + 0.119559i
\(785\) 4.31777e6 2.28900e6i 0.250084 0.132578i
\(786\) 2.85019e6 + 8.77197e6i 0.164557 + 0.506455i
\(787\) 3.14264e6 9.67205e6i 0.180866 0.556650i −0.818986 0.573813i \(-0.805464\pi\)
0.999853 + 0.0171635i \(0.00546358\pi\)
\(788\) 1.59391e6 4.90554e6i 0.0914423 0.281430i
\(789\) 5.25279e6 + 1.61664e7i 0.300398 + 0.924531i
\(790\) −8.98058e6 1.27338e6i −0.511961 0.0725924i
\(791\) −431204. + 1.32711e6i −0.0245043 + 0.0754164i
\(792\) 2.35897e6 + 1.71389e6i 0.133632 + 0.0970892i
\(793\) −2.85188e7 −1.61045
\(794\) −4.63887e6 3.37034e6i −0.261132 0.189724i
\(795\) 729740. + 4.16848e6i 0.0409497 + 0.233916i
\(796\) −6.88575e6 + 5.00279e6i −0.385184 + 0.279853i
\(797\) 7.97603e6 5.79492e6i 0.444775 0.323148i −0.342754 0.939425i \(-0.611360\pi\)
0.787530 + 0.616277i \(0.211360\pi\)
\(798\) −707699. 2.17807e6i −0.0393406 0.121078i
\(799\) −2.13813e7 −1.18486
\(800\) −1.79593e6 + 2.64852e6i −0.0992118 + 0.146311i
\(801\) 7.88542e6 0.434254
\(802\) 5.77844e6 + 1.77842e7i 0.317230 + 0.976334i
\(803\) 1.48555e7 1.07931e7i 0.813013 0.590688i
\(804\) −3.41809e6 + 2.48339e6i −0.186485 + 0.135489i
\(805\) 6.54120e6 + 6.33230e6i 0.355769 + 0.344407i
\(806\) −1.96900e7 1.43056e7i −1.06760 0.775655i
\(807\) −1.93776e6 −0.104741
\(808\) 8.73643e6 + 6.34739e6i 0.470767 + 0.342032i
\(809\) −8.46418e6 + 2.60501e7i −0.454688 + 1.39939i 0.416813 + 0.908992i \(0.363147\pi\)
−0.871501 + 0.490393i \(0.836853\pi\)
\(810\) −252983. 1.44511e6i −0.0135481 0.0773905i
\(811\) 1.12030e7 + 3.44793e7i 0.598112 + 1.84080i 0.538580 + 0.842574i \(0.318961\pi\)
0.0595323 + 0.998226i \(0.481039\pi\)
\(812\) 2.65899e6 8.18354e6i 0.141523 0.435563i
\(813\) −1.99765e6 + 6.14813e6i −0.105997 + 0.326225i
\(814\) −4.58967e6 1.41256e7i −0.242784 0.747213i
\(815\) −1.66833e6 9.52994e6i −0.0879806 0.502570i
\(816\) 1.57798e6 4.85651e6i 0.0829613 0.255329i
\(817\) −1.39892e6 1.01638e6i −0.0733227 0.0532720i
\(818\) −1.96400e7 −1.02626
\(819\) −4.26130e6 3.09602e6i −0.221990 0.161285i
\(820\) −2.23420e6 2.16285e6i −0.116035 0.112329i
\(821\) −2.37158e7 + 1.72306e7i −1.22795 + 0.892158i −0.996735 0.0807444i \(-0.974270\pi\)
−0.231215 + 0.972903i \(0.574270\pi\)
\(822\) 1.26417e6 918471.i 0.0652567 0.0474117i
\(823\) −2.53601e6 7.80504e6i −0.130512 0.401676i 0.864353 0.502886i \(-0.167729\pi\)
−0.994865 + 0.101210i \(0.967729\pi\)
\(824\) −3.81811e6 −0.195898
\(825\) −1.48787e7 + 5.37407e6i −0.761080 + 0.274896i
\(826\) 7.96216e6 0.406051
\(827\) 4.75800e6 + 1.46436e7i 0.241914 + 0.744535i 0.996129 + 0.0879069i \(0.0280178\pi\)
−0.754215 + 0.656628i \(0.771982\pi\)
\(828\) −1.86804e6 + 1.35721e6i −0.0946915 + 0.0687974i
\(829\) 7.11417e6 5.16875e6i 0.359532 0.261216i −0.393325 0.919400i \(-0.628675\pi\)
0.752857 + 0.658184i \(0.228675\pi\)
\(830\) 3.34679e6 + 1.91178e7i 0.168629 + 0.963257i
\(831\) −4.10478e6 2.98230e6i −0.206199 0.149813i
\(832\) −2.91387e6 −0.145936
\(833\) 1.51538e7 + 1.10099e7i 0.756674 + 0.549756i
\(834\) 196509. 604792.i 0.00978288 0.0301086i
\(835\) 2.01560e7 + 2.85798e6i 1.00044 + 0.141855i
\(836\) −1.93543e6 5.95663e6i −0.0957770 0.294771i
\(837\) 1.92676e6 5.92995e6i 0.0950634 0.292575i
\(838\) −7.47180e6 + 2.29958e7i −0.367549 + 1.13120i
\(839\) 8.34015e6 + 2.56683e7i 0.409043 + 1.25891i 0.917472 + 0.397801i \(0.130227\pi\)
−0.508429 + 0.861104i \(0.669773\pi\)
\(840\) −2.60049e6 + 1.37861e6i −0.127162 + 0.0674130i
\(841\) 4.35801e6 1.34126e7i 0.212470 0.653916i
\(842\) 1.36898e7 + 9.94621e6i 0.665451 + 0.483479i
\(843\) −5.30480e6 −0.257099
\(844\) 9.63999e6 + 7.00387e6i 0.465823 + 0.338440i
\(845\) 7.46030e6 + 1.05782e6i 0.359430 + 0.0509646i
\(846\) −2.52873e6 + 1.83723e6i −0.121472 + 0.0882545i
\(847\) 1.14864e7 8.34533e6i 0.550141 0.399701i
\(848\) 665407. + 2.04791e6i 0.0317759 + 0.0977961i
\(849\) 1.26924e7 0.604329
\(850\) 1.70028e7 + 2.18730e7i 0.807184 + 1.03839i
\(851\) 1.17615e7 0.556723
\(852\) −3.13304e6 9.64250e6i −0.147865 0.455083i
\(853\) 6.61947e6 4.80932e6i 0.311495 0.226314i −0.421043 0.907041i \(-0.638336\pi\)
0.732538 + 0.680727i \(0.238336\pi\)
\(854\) −1.18585e7 + 8.61567e6i −0.556395 + 0.404245i
\(855\) −1.38490e6 + 2.83064e6i −0.0647892 + 0.132425i
\(856\) 2.16864e6 + 1.57561e6i 0.101159 + 0.0734962i
\(857\) −2.02079e6 −0.0939871 −0.0469935 0.998895i \(-0.514964\pi\)
−0.0469935 + 0.998895i \(0.514964\pi\)
\(858\) −1.16539e7 8.46704e6i −0.540446 0.392657i
\(859\) −4.97624e6 + 1.53153e7i −0.230101 + 0.708177i 0.767633 + 0.640890i \(0.221434\pi\)
−0.997734 + 0.0672875i \(0.978566\pi\)
\(860\) −976652. + 1.99621e6i −0.0450292 + 0.0920365i
\(861\) −883840. 2.72018e6i −0.0406318 0.125052i
\(862\) −6.81129e6 + 2.09630e7i −0.312220 + 0.960915i
\(863\) 5.09548e6 1.56823e7i 0.232894 0.716774i −0.764500 0.644624i \(-0.777014\pi\)
0.997394 0.0721498i \(-0.0229860\pi\)
\(864\) −230680. 709960.i −0.0105130 0.0323556i
\(865\) 2.84863e7 + 2.75766e7i 1.29448 + 1.25314i
\(866\) 5.42087e6 1.66837e7i 0.245626 0.755958i
\(867\) −2.54279e7 1.84745e7i −1.14885 0.834689i
\(868\) −1.25091e7 −0.563543
\(869\) −1.84586e7 1.34110e7i −0.829183 0.602437i
\(870\) −1.04610e7 + 5.54572e6i −0.468568 + 0.248405i
\(871\) 1.68862e7 1.22685e7i 0.754199 0.547958i
\(872\) 8.33461e6 6.05545e6i 0.371188 0.269684i
\(873\) 1.46923e6 + 4.52184e6i 0.0652463 + 0.200807i
\(874\) 4.95974e6 0.219624
\(875\) 1.72764e6 1.58748e7i 0.0762840 0.700951i
\(876\) −4.70100e6 −0.206981
\(877\) 2.79180e6 + 8.59228e6i 0.122570 + 0.377233i 0.993451 0.114262i \(-0.0364505\pi\)
−0.870880 + 0.491495i \(0.836450\pi\)
\(878\) −2.11390e7 + 1.53584e7i −0.925440 + 0.672372i
\(879\) 1.64704e7 1.19665e7i 0.719007 0.522389i
\(880\) −7.11186e6 + 3.77025e6i −0.309583 + 0.164121i
\(881\) −2.01438e7 1.46353e7i −0.874384 0.635277i 0.0573760 0.998353i \(-0.481727\pi\)
−0.931760 + 0.363076i \(0.881727\pi\)
\(882\) 2.73825e6 0.118523
\(883\) −1.64454e7 1.19483e7i −0.709813 0.515709i 0.173301 0.984869i \(-0.444557\pi\)
−0.883113 + 0.469160i \(0.844557\pi\)
\(884\) −7.79558e6 + 2.39923e7i −0.335520 + 1.03262i
\(885\) −7.87168e6 7.62029e6i −0.337839 0.327050i
\(886\) −4.61685e6 1.42092e7i −0.197588 0.608115i
\(887\) −1.34232e7 + 4.13124e7i −0.572859 + 1.76308i 0.0704966 + 0.997512i \(0.477542\pi\)
−0.643356 + 0.765567i \(0.722458\pi\)
\(888\) −1.17502e6 + 3.61633e6i −0.0500048 + 0.153899i
\(889\) 8.48597e6 + 2.61171e7i 0.360120 + 1.10834i
\(890\) −9.56662e6 + 1.95535e7i −0.404840 + 0.827465i
\(891\) 1.14039e6 3.50975e6i 0.0481236 0.148109i
\(892\) 1.32122e7 + 9.59924e6i 0.555986 + 0.403947i
\(893\) 6.71388e6 0.281738
\(894\) −1.27344e7 9.25209e6i −0.532887 0.387165i
\(895\) −2.07149e6 + 4.23398e6i −0.0864420 + 0.176681i
\(896\) −1.21162e6 + 880295.i −0.0504193 + 0.0366318i
\(897\) 9.22858e6 6.70495e6i 0.382960 0.278237i
\(898\) −8.13128e6 2.50255e7i −0.336487 1.03560i
\(899\) −5.03203e7 −2.07656
\(900\) 3.89036e6 + 1.12589e6i 0.160097 + 0.0463328i
\(901\) 1.86424e7 0.765049
\(902\) −2.41714e6 7.43919e6i −0.0989203 0.304446i
\(903\) −1.65368e6 + 1.20147e6i −0.0674888 + 0.0490335i
\(904\) 790403. 574262.i 0.0321683 0.0233716i
\(905\) 2.07511e7 + 2.94236e6i 0.842209 + 0.119419i
\(906\) 1.17590e7 + 8.54338e6i 0.475936 + 0.345788i
\(907\) 1.61338e6 0.0651204 0.0325602 0.999470i \(-0.489634\pi\)
0.0325602 + 0.999470i \(0.489634\pi\)
\(908\) −6.96033e6 5.05698e6i −0.280166 0.203553i
\(909\) 4.22342e6 1.29983e7i 0.169533 0.521769i
\(910\) 1.28470e7 6.81067e6i 0.514280 0.272638i
\(911\) −8.02186e6 2.46888e7i −0.320243 0.985606i −0.973542 0.228506i \(-0.926616\pi\)
0.653300 0.757099i \(-0.273384\pi\)
\(912\) −495495. + 1.52498e6i −0.0197266 + 0.0607122i
\(913\) −1.50866e7 + 4.64316e7i −0.598981 + 1.84347i
\(914\) 2.20463e6 + 6.78516e6i 0.0872912 + 0.268655i
\(915\) 1.99694e7 + 2.83153e6i 0.788521 + 0.111807i
\(916\) 7.20877e6 2.21863e7i 0.283872 0.873668i
\(917\) −1.89468e7 1.37656e7i −0.744067 0.540596i
\(918\) −6.46284e6 −0.253114
\(919\) 9.95182e6 + 7.23042e6i 0.388699 + 0.282407i 0.764922 0.644123i \(-0.222777\pi\)
−0.376223 + 0.926529i \(0.622777\pi\)
\(920\) −1.09917e6 6.27877e6i −0.0428149 0.244571i
\(921\) −1.16697e6 + 847854.i −0.0453326 + 0.0329361i
\(922\) −1.14304e7 + 8.30469e6i −0.442828 + 0.321733i
\(923\) 1.54780e7 + 4.76362e7i 0.598011 + 1.84049i
\(924\) −7.40376e6 −0.285281
\(925\) −1.26608e7 1.62874e7i −0.486528 0.625890i
\(926\) 1.61182e7 0.617717
\(927\) 1.49326e6 + 4.59578e6i 0.0570737 + 0.175655i
\(928\) −4.87397e6 + 3.54115e6i −0.185786 + 0.134982i
\(929\) 1.07298e7 7.79566e6i 0.407899 0.296356i −0.364852 0.931066i \(-0.618880\pi\)
0.772751 + 0.634710i \(0.218880\pi\)
\(930\) 1.23670e7 + 1.19720e7i 0.468874 + 0.453900i
\(931\) −4.75838e6 3.45717e6i −0.179922 0.130721i
\(932\) −1.20110e7 −0.452938
\(933\) −1.23796e7 8.99433e6i −0.465590 0.338271i
\(934\) 1.41446e6 4.35325e6i 0.0530545 0.163285i
\(935\) 1.20170e7 + 6.86446e7i 0.449539 + 2.56790i
\(936\) 1.13961e6 + 3.50737e6i 0.0425175 + 0.130856i
\(937\) 1.50739e7 4.63927e7i 0.560889 1.72624i −0.118973 0.992897i \(-0.537960\pi\)
0.679862 0.733340i \(-0.262040\pi\)
\(938\) 3.31509e6 1.02028e7i 0.123023 0.378627i
\(939\) −2.08533e6 6.41797e6i −0.0771809 0.237538i
\(940\) −1.48792e6 8.49942e6i −0.0549237 0.313740i
\(941\) 8.86206e6 2.72746e7i 0.326257 1.00412i −0.644612 0.764510i \(-0.722981\pi\)
0.970870 0.239608i \(-0.0770188\pi\)
\(942\) −2.54611e6 1.84985e6i −0.0934866 0.0679220i
\(943\) 6.19418e6 0.226832
\(944\) −4.51003e6 3.27673e6i −0.164721 0.119677i
\(945\) 2.67646e6 + 2.59098e6i 0.0974947 + 0.0943811i
\(946\) −4.52251e6 + 3.28580e6i −0.164305 + 0.119375i
\(947\) 9.62296e6 6.99149e6i 0.348685 0.253335i −0.399632 0.916676i \(-0.630862\pi\)
0.748317 + 0.663341i \(0.230862\pi\)
\(948\) 1.80504e6 + 5.55534e6i 0.0652328 + 0.200766i
\(949\) 2.32241e7 0.837092
\(950\) −5.33898e6 6.86827e6i −0.191933 0.246910i
\(951\) 5.78904e6 0.207566
\(952\) 4.00671e6 + 1.23314e7i 0.143283 + 0.440980i
\(953\) −4.02922e7 + 2.92740e7i −1.43710 + 1.04412i −0.448466 + 0.893800i \(0.648030\pi\)
−0.988638 + 0.150317i \(0.951970\pi\)
\(954\) 2.20479e6 1.60188e6i 0.0784326 0.0569846i
\(955\) 5.54094e6 + 3.16514e7i 0.196596 + 1.12301i
\(956\) 1.00207e7 + 7.28047e6i 0.354612 + 0.257641i
\(957\) −2.97830e7 −1.05121
\(958\) 690745. + 501856.i 0.0243167 + 0.0176671i
\(959\) −1.22607e6 + 3.77346e6i −0.0430496 + 0.132493i
\(960\) 2.04035e6 + 289307.i 0.0714541 + 0.0101317i
\(961\) 1.37587e7 + 4.23450e7i 0.480585 + 1.47909i
\(962\) 5.80486e6 1.78655e7i 0.202234 0.622412i
\(963\) 1.04838e6 3.22657e6i 0.0364294 0.112118i
\(964\) −5.39612e6 1.66075e7i −0.187020 0.575590i
\(965\) 3.56391e7 1.88936e7i 1.23200 0.653125i
\(966\) 1.81175e6 5.57600e6i 0.0624677 0.192256i
\(967\) 1.25547e7 + 9.12153e6i 0.431758 + 0.313691i 0.782352 0.622837i \(-0.214020\pi\)
−0.350593 + 0.936528i \(0.614020\pi\)
\(968\) −9.94067e6 −0.340979
\(969\) 1.12308e7 + 8.15965e6i 0.384239 + 0.279166i
\(970\) −1.29953e7 1.84264e6i −0.443463 0.0628799i
\(971\) 2.13835e7 1.55361e7i 0.727833 0.528801i −0.161044 0.986947i \(-0.551486\pi\)
0.888877 + 0.458146i \(0.151486\pi\)
\(972\) −764346. + 555330.i −0.0259492 + 0.0188532i
\(973\) 498964. + 1.53565e6i 0.0168961 + 0.0520009i
\(974\) 9.66319e6 0.326380
\(975\) −1.92193e7 5.56215e6i −0.647479 0.187383i
\(976\) 1.02627e7 0.344855
\(977\) −6.64302e6 2.04451e7i −0.222653 0.685256i −0.998521 0.0543610i \(-0.982688\pi\)
0.775868 0.630895i \(-0.217312\pi\)
\(978\) −5.04058e6 + 3.66219e6i −0.168513 + 0.122432i
\(979\) −4.42994e7 + 3.21854e7i −1.47721 + 1.07325i
\(980\) −3.32205e6 + 6.79004e6i −0.110495 + 0.225843i
\(981\) −1.05485e7 7.66393e6i −0.349959 0.254260i
\(982\) −3.47410e7 −1.14964
\(983\) −1.12183e7 8.15055e6i −0.370290 0.269032i 0.387041 0.922062i \(-0.373497\pi\)
−0.757331 + 0.653031i \(0.773497\pi\)
\(984\) −618820. + 1.90453e6i −0.0203740 + 0.0627047i
\(985\) 7.91988e6 1.61877e7i 0.260093 0.531612i
\(986\) 1.61177e7 + 4.96053e7i 0.527973 + 1.62493i
\(987\) 2.45252e6 7.54810e6i 0.0801347 0.246629i
\(988\) 2.44786e6 7.53374e6i 0.0797801 0.245538i
\(989\) −1.36794e6 4.21010e6i −0.0444711 0.136868i
\(990\) 7.31963e6 + 7.08587e6i 0.237356 + 0.229776i
\(991\) 1.14117e7 3.51214e7i 0.369117 1.13603i −0.578245 0.815863i \(-0.696262\pi\)
0.947362 0.320163i \(-0.103738\pi\)
\(992\) 7.08557e6 + 5.14797e6i 0.228610 + 0.166095i
\(993\) −5.23709e6 −0.168546
\(994\) 2.08271e7 + 1.51317e7i 0.668593 + 0.485761i
\(995\) −2.62734e7 + 1.39285e7i −0.841315 + 0.446011i
\(996\) 1.01118e7 7.34664e6i 0.322983 0.234661i
\(997\) 3.79259e7 2.75548e7i 1.20837 0.877929i 0.213285 0.976990i \(-0.431584\pi\)
0.995081 + 0.0990609i \(0.0315839\pi\)
\(998\) −6.78438e6 2.08802e7i −0.215617 0.663602i
\(999\) 4.81245e6 0.152564
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.c.31.1 24
25.21 even 5 inner 150.6.g.c.121.1 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.6.g.c.31.1 24 1.1 even 1 trivial
150.6.g.c.121.1 yes 24 25.21 even 5 inner