Properties

Label 150.6.g.b.31.3
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 31.3
Character \(\chi\) \(=\) 150.31
Dual form 150.6.g.b.121.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.23607 + 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-10.1537 + 54.9718i) q^{5} +(-29.1246 - 21.1603i) q^{6} +197.545 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +O(q^{10})\) \(q+(1.23607 + 3.80423i) q^{2} +(-7.28115 + 5.29007i) q^{3} +(-12.9443 + 9.40456i) q^{4} +(-10.1537 + 54.9718i) q^{5} +(-29.1246 - 21.1603i) q^{6} +197.545 q^{7} +(-51.7771 - 37.6183i) q^{8} +(25.0304 - 77.0356i) q^{9} +(-221.676 + 29.3220i) q^{10} +(161.561 + 497.233i) q^{11} +(44.4984 - 136.952i) q^{12} +(-218.957 + 673.882i) q^{13} +(244.179 + 751.507i) q^{14} +(-216.874 - 453.972i) q^{15} +(79.1084 - 243.470i) q^{16} +(1592.40 + 1156.95i) q^{17} +324.000 q^{18} +(444.204 + 322.733i) q^{19} +(-385.554 - 807.061i) q^{20} +(-1438.36 + 1045.03i) q^{21} +(-1691.89 + 1229.23i) q^{22} +(-1254.43 - 3860.75i) q^{23} +576.000 q^{24} +(-2918.81 - 1116.33i) q^{25} -2834.25 q^{26} +(225.273 + 693.320i) q^{27} +(-2557.08 + 1857.83i) q^{28} +(-428.905 + 311.617i) q^{29} +(1458.94 - 1386.18i) q^{30} +(-4479.93 - 3254.86i) q^{31} +1024.00 q^{32} +(-3806.74 - 2765.76i) q^{33} +(-2432.97 + 7487.91i) q^{34} +(-2005.81 + 10859.4i) q^{35} +(400.486 + 1232.57i) q^{36} +(2165.71 - 6665.38i) q^{37} +(-678.683 + 2088.77i) q^{38} +(-1970.62 - 6064.94i) q^{39} +(2593.67 - 2464.32i) q^{40} +(-5191.98 + 15979.3i) q^{41} +(-5753.43 - 4180.11i) q^{42} -14395.4 q^{43} +(-6767.54 - 4916.91i) q^{44} +(3980.64 + 2158.16i) q^{45} +(13136.6 - 9544.29i) q^{46} +(5415.84 - 3934.83i) q^{47} +(711.975 + 2191.23i) q^{48} +22217.2 q^{49} +(638.941 - 12483.7i) q^{50} -17714.8 q^{51} +(-3503.32 - 10782.1i) q^{52} +(-4396.47 + 3194.22i) q^{53} +(-2359.09 + 1713.98i) q^{54} +(-28974.2 + 3832.55i) q^{55} +(-10228.3 - 7431.31i) q^{56} -4941.59 q^{57} +(-1715.62 - 1246.47i) q^{58} +(-10595.5 + 32609.5i) q^{59} +(7076.69 + 3836.73i) q^{60} +(-1713.74 - 5274.35i) q^{61} +(6844.72 - 21065.9i) q^{62} +(4944.63 - 15218.0i) q^{63} +(1265.73 + 3895.53i) q^{64} +(-34821.3 - 18878.9i) q^{65} +(5816.19 - 17900.4i) q^{66} +(-16317.7 - 11855.5i) q^{67} -31493.0 q^{68} +(29557.3 + 21474.7i) q^{69} +(-43791.0 + 5792.43i) q^{70} +(62761.5 - 45598.9i) q^{71} +(-4193.94 + 3047.08i) q^{72} +(12030.2 + 37025.2i) q^{73} +28033.6 q^{74} +(27157.7 - 7312.49i) q^{75} -8785.05 q^{76} +(31915.6 + 98226.0i) q^{77} +(20636.6 - 14993.3i) q^{78} +(45766.3 - 33251.2i) q^{79} +(12580.8 + 6820.85i) q^{80} +(-5307.96 - 3856.46i) q^{81} -67206.4 q^{82} +(59276.9 + 43067.2i) q^{83} +(8790.46 - 27054.3i) q^{84} +(-79768.1 + 75789.8i) q^{85} +(-17793.7 - 54763.4i) q^{86} +(1474.44 - 4537.87i) q^{87} +(10339.9 - 31822.9i) q^{88} +(-42243.4 - 130012. i) q^{89} +(-3289.79 + 17810.9i) q^{90} +(-43254.0 + 133122. i) q^{91} +(52546.4 + 38177.2i) q^{92} +49837.4 q^{93} +(21663.3 + 15739.3i) q^{94} +(-22251.5 + 21141.8i) q^{95} +(-7455.90 + 5417.03i) q^{96} +(-81989.2 + 59568.7i) q^{97} +(27461.9 + 84519.1i) q^{98} +42348.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{2} - 54 q^{3} - 96 q^{4} + 30 q^{5} - 216 q^{6} - 212 q^{7} - 384 q^{8} - 486 q^{9} - 320 q^{10} + 578 q^{11} - 864 q^{12} + 964 q^{13} + 1312 q^{14} - 1350 q^{15} - 1536 q^{16} + 3318 q^{17} + 7776 q^{18} + 3240 q^{19} - 2400 q^{20} - 1998 q^{21} - 48 q^{22} - 2566 q^{23} + 13824 q^{24} + 16120 q^{25} - 2544 q^{26} - 4374 q^{27} - 3552 q^{28} + 2220 q^{29} + 4320 q^{30} + 12918 q^{31} + 24576 q^{32} - 108 q^{33} - 5968 q^{34} - 17190 q^{35} - 7776 q^{36} + 5738 q^{37} - 3600 q^{38} + 8676 q^{39} + 7680 q^{40} - 18732 q^{41} - 7992 q^{42} - 21176 q^{43} - 192 q^{44} + 6480 q^{45} + 20736 q^{46} + 37488 q^{47} - 13824 q^{48} + 62048 q^{49} + 7880 q^{50} - 32868 q^{51} + 15424 q^{52} + 49414 q^{53} - 17496 q^{54} - 83140 q^{55} - 14208 q^{56} - 42120 q^{57} + 8880 q^{58} - 37280 q^{59} + 11520 q^{60} + 65988 q^{61} - 20008 q^{62} + 26568 q^{63} - 24576 q^{64} - 62940 q^{65} + 20808 q^{66} + 38328 q^{67} - 58432 q^{68} + 46656 q^{69} + 33360 q^{70} + 199868 q^{71} - 31104 q^{72} - 50656 q^{73} + 2912 q^{74} - 82620 q^{75} - 74880 q^{76} - 83224 q^{77} - 23256 q^{78} + 132930 q^{79} + 20480 q^{80} - 39366 q^{81} + 15712 q^{82} - 304696 q^{83} + 47232 q^{84} + 12360 q^{85} + 9256 q^{86} + 93600 q^{87} + 36992 q^{88} - 343880 q^{89} + 9720 q^{90} + 453528 q^{91} + 82944 q^{92} - 142488 q^{93} + 149952 q^{94} + 321730 q^{95} - 55296 q^{96} + 153648 q^{97} + 125152 q^{98} - 91692 q^{99}+O(q^{100}) \) 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
\(5\) −10.1537 + 54.9718i −0.181635 + 0.983366i
\(6\) −29.1246 21.1603i −0.330280 0.239962i
\(7\) 197.545 1.52378 0.761889 0.647708i \(-0.224272\pi\)
0.761889 + 0.647708i \(0.224272\pi\)
\(8\) −51.7771 37.6183i −0.286031 0.207813i
\(9\) 25.0304 77.0356i 0.103006 0.317019i
\(10\) −221.676 + 29.3220i −0.701001 + 0.0927244i
\(11\) 161.561 + 497.233i 0.402582 + 1.23902i 0.922898 + 0.385045i \(0.125814\pi\)
−0.520316 + 0.853974i \(0.674186\pi\)
\(12\) 44.4984 136.952i 0.0892055 0.274546i
\(13\) −218.957 + 673.882i −0.359337 + 1.10592i 0.594116 + 0.804380i \(0.297502\pi\)
−0.953452 + 0.301545i \(0.902498\pi\)
\(14\) 244.179 + 751.507i 0.332958 + 1.02474i
\(15\) −216.874 453.972i −0.248874 0.520956i
\(16\) 79.1084 243.470i 0.0772542 0.237764i
\(17\) 1592.40 + 1156.95i 1.33638 + 0.970936i 0.999569 + 0.0293631i \(0.00934790\pi\)
0.336810 + 0.941573i \(0.390652\pi\)
\(18\) 324.000 0.235702
\(19\) 444.204 + 322.733i 0.282292 + 0.205097i 0.719916 0.694061i \(-0.244180\pi\)
−0.437625 + 0.899158i \(0.644180\pi\)
\(20\) −385.554 807.061i −0.215531 0.451161i
\(21\) −1438.36 + 1045.03i −0.711736 + 0.517106i
\(22\) −1691.89 + 1229.23i −0.745271 + 0.541471i
\(23\) −1254.43 3860.75i −0.494456 1.52178i −0.817802 0.575499i \(-0.804808\pi\)
0.323346 0.946281i \(-0.395192\pi\)
\(24\) 576.000 0.204124
\(25\) −2918.81 1116.33i −0.934018 0.357227i
\(26\) −2834.25 −0.822250
\(27\) 225.273 + 693.320i 0.0594703 + 0.183031i
\(28\) −2557.08 + 1857.83i −0.616381 + 0.447827i
\(29\) −428.905 + 311.617i −0.0947034 + 0.0688061i −0.634129 0.773227i \(-0.718641\pi\)
0.539426 + 0.842033i \(0.318641\pi\)
\(30\) 1458.94 1386.18i 0.295961 0.281201i
\(31\) −4479.93 3254.86i −0.837272 0.608314i 0.0843351 0.996437i \(-0.473123\pi\)
−0.921607 + 0.388124i \(0.873123\pi\)
\(32\) 1024.00 0.176777
\(33\) −3806.74 2765.76i −0.608511 0.442109i
\(34\) −2432.97 + 7487.91i −0.360943 + 1.11087i
\(35\) −2005.81 + 10859.4i −0.276771 + 1.49843i
\(36\) 400.486 + 1232.57i 0.0515028 + 0.158509i
\(37\) 2165.71 6665.38i 0.260074 0.800425i −0.732714 0.680537i \(-0.761746\pi\)
0.992787 0.119888i \(-0.0382535\pi\)
\(38\) −678.683 + 2088.77i −0.0762444 + 0.234656i
\(39\) −1970.62 6064.94i −0.207463 0.638506i
\(40\) 2593.67 2464.32i 0.256310 0.243527i
\(41\) −5191.98 + 15979.3i −0.482362 + 1.48456i 0.353403 + 0.935471i \(0.385024\pi\)
−0.835765 + 0.549087i \(0.814976\pi\)
\(42\) −5753.43 4180.11i −0.503273 0.365649i
\(43\) −14395.4 −1.18728 −0.593639 0.804731i \(-0.702309\pi\)
−0.593639 + 0.804731i \(0.702309\pi\)
\(44\) −6767.54 4916.91i −0.526986 0.382878i
\(45\) 3980.64 + 2158.16i 0.293036 + 0.158874i
\(46\) 13136.6 9544.29i 0.915352 0.665042i
\(47\) 5415.84 3934.83i 0.357619 0.259826i −0.394439 0.918922i \(-0.629061\pi\)
0.752058 + 0.659096i \(0.229061\pi\)
\(48\) 711.975 + 2191.23i 0.0446028 + 0.137273i
\(49\) 22217.2 1.32190
\(50\) 638.941 12483.7i 0.0361440 0.706182i
\(51\) −17714.8 −0.953699
\(52\) −3503.32 10782.1i −0.179668 0.552962i
\(53\) −4396.47 + 3194.22i −0.214988 + 0.156198i −0.690068 0.723745i \(-0.742419\pi\)
0.475080 + 0.879943i \(0.342419\pi\)
\(54\) −2359.09 + 1713.98i −0.110093 + 0.0799874i
\(55\) −28974.2 + 3832.55i −1.29153 + 0.170837i
\(56\) −10228.3 7431.31i −0.435847 0.316662i
\(57\) −4941.59 −0.201456
\(58\) −1715.62 1246.47i −0.0669654 0.0486532i
\(59\) −10595.5 + 32609.5i −0.396269 + 1.21959i 0.531699 + 0.846933i \(0.321554\pi\)
−0.927969 + 0.372658i \(0.878446\pi\)
\(60\) 7076.69 + 3836.73i 0.253777 + 0.137589i
\(61\) −1713.74 5274.35i −0.0589686 0.181487i 0.917233 0.398350i \(-0.130417\pi\)
−0.976202 + 0.216864i \(0.930417\pi\)
\(62\) 6844.72 21065.9i 0.226139 0.695986i
\(63\) 4944.63 15218.0i 0.156958 0.483066i
\(64\) 1265.73 + 3895.53i 0.0386271 + 0.118882i
\(65\) −34821.3 18878.9i −1.02226 0.554233i
\(66\) 5816.19 17900.4i 0.164353 0.505828i
\(67\) −16317.7 11855.5i −0.444091 0.322651i 0.343167 0.939274i \(-0.388500\pi\)
−0.787258 + 0.616623i \(0.788500\pi\)
\(68\) −31493.0 −0.825927
\(69\) 29557.3 + 21474.7i 0.747382 + 0.543005i
\(70\) −43791.0 + 5792.43i −1.06817 + 0.141291i
\(71\) 62761.5 45598.9i 1.47757 1.07352i 0.499236 0.866466i \(-0.333614\pi\)
0.978330 0.207049i \(-0.0663861\pi\)
\(72\) −4193.94 + 3047.08i −0.0953436 + 0.0692712i
\(73\) 12030.2 + 37025.2i 0.264220 + 0.813186i 0.991872 + 0.127239i \(0.0406117\pi\)
−0.727652 + 0.685947i \(0.759388\pi\)
\(74\) 28033.6 0.595113
\(75\) 27157.7 7312.49i 0.557494 0.150111i
\(76\) −8785.05 −0.174466
\(77\) 31915.6 + 98226.0i 0.613445 + 1.88799i
\(78\) 20636.6 14993.3i 0.384062 0.279037i
\(79\) 45766.3 33251.2i 0.825046 0.599431i −0.0931073 0.995656i \(-0.529680\pi\)
0.918153 + 0.396225i \(0.129680\pi\)
\(80\) 12580.8 + 6820.85i 0.219777 + 0.119155i
\(81\) −5307.96 3856.46i −0.0898908 0.0653095i
\(82\) −67206.4 −1.10376
\(83\) 59276.9 + 43067.2i 0.944474 + 0.686201i 0.949493 0.313787i \(-0.101598\pi\)
−0.00501945 + 0.999987i \(0.501598\pi\)
\(84\) 8790.46 27054.3i 0.135929 0.418348i
\(85\) −79768.1 + 75789.8i −1.19752 + 1.13779i
\(86\) −17793.7 54763.4i −0.259430 0.798443i
\(87\) 1474.44 4537.87i 0.0208848 0.0642767i
\(88\) 10339.9 31822.9i 0.142334 0.438059i
\(89\) −42243.4 130012.i −0.565307 1.73984i −0.667038 0.745024i \(-0.732438\pi\)
0.101731 0.994812i \(-0.467562\pi\)
\(90\) −3289.79 + 17810.9i −0.0428117 + 0.231782i
\(91\) −43254.0 + 133122.i −0.547549 + 1.68518i
\(92\) 52546.4 + 38177.2i 0.647252 + 0.470256i
\(93\) 49837.4 0.597514
\(94\) 21663.3 + 15739.3i 0.252875 + 0.183724i
\(95\) −22251.5 + 21141.8i −0.252959 + 0.240343i
\(96\) −7455.90 + 5417.03i −0.0825700 + 0.0599906i
\(97\) −81989.2 + 59568.7i −0.884764 + 0.642819i −0.934508 0.355943i \(-0.884160\pi\)
0.0497435 + 0.998762i \(0.484160\pi\)
\(98\) 27461.9 + 84519.1i 0.288846 + 0.888975i
\(99\) 42348.5 0.434261
\(100\) 48280.4 13000.0i 0.482804 0.130000i
\(101\) 52175.3 0.508935 0.254467 0.967081i \(-0.418100\pi\)
0.254467 + 0.967081i \(0.418100\pi\)
\(102\) −21896.7 67391.2i −0.208391 0.641361i
\(103\) −41715.4 + 30308.0i −0.387439 + 0.281491i −0.764405 0.644736i \(-0.776967\pi\)
0.376966 + 0.926227i \(0.376967\pi\)
\(104\) 36687.2 26654.8i 0.332607 0.241653i
\(105\) −42842.5 89680.1i −0.379229 0.793821i
\(106\) −17585.9 12776.9i −0.152020 0.110449i
\(107\) 68308.0 0.576782 0.288391 0.957513i \(-0.406880\pi\)
0.288391 + 0.957513i \(0.406880\pi\)
\(108\) −9436.37 6855.93i −0.0778477 0.0565597i
\(109\) 18536.8 57050.4i 0.149441 0.459931i −0.848115 0.529813i \(-0.822262\pi\)
0.997555 + 0.0698819i \(0.0222622\pi\)
\(110\) −50394.0 105487.i −0.397097 0.831224i
\(111\) 19491.4 + 59988.4i 0.150154 + 0.462126i
\(112\) 15627.5 48096.5i 0.117718 0.362300i
\(113\) −50787.0 + 156306.i −0.374159 + 1.15154i 0.569885 + 0.821724i \(0.306988\pi\)
−0.944044 + 0.329819i \(0.893012\pi\)
\(114\) −6108.14 18798.9i −0.0440197 0.135479i
\(115\) 224969. 29757.7i 1.58628 0.209824i
\(116\) 2621.23 8067.32i 0.0180867 0.0556653i
\(117\) 46432.3 + 33735.0i 0.313585 + 0.227833i
\(118\) −137151. −0.906762
\(119\) 314571. + 228549.i 2.03634 + 1.47949i
\(120\) −5848.52 + 31663.8i −0.0370760 + 0.200729i
\(121\) −90845.6 + 66003.2i −0.564080 + 0.409828i
\(122\) 17946.5 13038.9i 0.109164 0.0793125i
\(123\) −46727.8 143813.i −0.278492 0.857110i
\(124\) 88599.9 0.517463
\(125\) 91003.5 149117.i 0.520934 0.853597i
\(126\) 64004.7 0.359158
\(127\) −51015.2 157009.i −0.280666 0.863802i −0.987664 0.156586i \(-0.949951\pi\)
0.706998 0.707216i \(-0.250049\pi\)
\(128\) −13254.9 + 9630.27i −0.0715077 + 0.0519534i
\(129\) 104815. 76152.7i 0.554562 0.402913i
\(130\) 28778.0 155804.i 0.149349 0.808573i
\(131\) 165415. + 120181.i 0.842163 + 0.611867i 0.922974 0.384862i \(-0.125751\pi\)
−0.0808108 + 0.996729i \(0.525751\pi\)
\(132\) 75286.3 0.376081
\(133\) 87750.3 + 63754.4i 0.430150 + 0.312522i
\(134\) 24931.2 76730.4i 0.119945 0.369152i
\(135\) −40400.4 + 5343.94i −0.190788 + 0.0252364i
\(136\) −38927.5 119807.i −0.180472 0.555435i
\(137\) 41021.4 126251.i 0.186728 0.574689i −0.813246 0.581920i \(-0.802302\pi\)
0.999974 + 0.00723096i \(0.00230171\pi\)
\(138\) −45159.6 + 138987.i −0.201861 + 0.621264i
\(139\) 81963.2 + 252257.i 0.359817 + 1.10740i 0.953163 + 0.302456i \(0.0978066\pi\)
−0.593346 + 0.804947i \(0.702193\pi\)
\(140\) −76164.4 159431.i −0.328422 0.687469i
\(141\) −18618.0 + 57300.3i −0.0788651 + 0.242722i
\(142\) 251046. + 182395.i 1.04480 + 0.759090i
\(143\) −370451. −1.51492
\(144\) −16775.8 12188.3i −0.0674181 0.0489821i
\(145\) −12775.2 26741.7i −0.0504601 0.105626i
\(146\) −125982. + 91531.3i −0.489132 + 0.355375i
\(147\) −161767. + 117530.i −0.617441 + 0.448597i
\(148\) 34651.4 + 106646.i 0.130037 + 0.400212i
\(149\) 159680. 0.589229 0.294615 0.955616i \(-0.404809\pi\)
0.294615 + 0.955616i \(0.404809\pi\)
\(150\) 61387.2 + 94275.5i 0.222766 + 0.342114i
\(151\) −37262.1 −0.132992 −0.0664960 0.997787i \(-0.521182\pi\)
−0.0664960 + 0.997787i \(0.521182\pi\)
\(152\) −10858.9 33420.3i −0.0381222 0.117328i
\(153\) 128984. 93712.6i 0.445460 0.323645i
\(154\) −334224. + 242828.i −1.13563 + 0.825082i
\(155\) 224413. 213221.i 0.750273 0.712854i
\(156\) 82546.3 + 59973.4i 0.271573 + 0.197309i
\(157\) −276977. −0.896799 −0.448400 0.893833i \(-0.648006\pi\)
−0.448400 + 0.893833i \(0.648006\pi\)
\(158\) 183065. + 133005.i 0.583396 + 0.423862i
\(159\) 15113.7 46515.2i 0.0474109 0.145916i
\(160\) −10397.4 + 56291.2i −0.0321088 + 0.173836i
\(161\) −247807. 762673.i −0.753441 2.31885i
\(162\) 8109.84 24959.5i 0.0242787 0.0747221i
\(163\) −174270. + 536347.i −0.513752 + 1.58116i 0.271791 + 0.962356i \(0.412384\pi\)
−0.785542 + 0.618808i \(0.787616\pi\)
\(164\) −83071.6 255668.i −0.241181 0.742279i
\(165\) 190691. 181181.i 0.545282 0.518087i
\(166\) −90567.0 + 278737.i −0.255094 + 0.785098i
\(167\) 2259.79 + 1641.84i 0.00627014 + 0.00455553i 0.590916 0.806733i \(-0.298766\pi\)
−0.584646 + 0.811289i \(0.698766\pi\)
\(168\) 113786. 0.311040
\(169\) −105792. 76862.4i −0.284929 0.207013i
\(170\) −386920. 209775.i −1.02683 0.556712i
\(171\) 35980.5 26141.4i 0.0940972 0.0683656i
\(172\) 186338. 135382.i 0.480264 0.348932i
\(173\) −78866.7 242727.i −0.200345 0.616599i −0.999872 0.0159690i \(-0.994917\pi\)
0.799527 0.600630i \(-0.205083\pi\)
\(174\) 19085.6 0.0477895
\(175\) −576596. 220526.i −1.42324 0.544334i
\(176\) 133842. 0.325695
\(177\) −95359.3 293486.i −0.228786 0.704132i
\(178\) 442379. 321407.i 1.04651 0.760336i
\(179\) 645966. 469322.i 1.50687 1.09481i 0.539333 0.842092i \(-0.318676\pi\)
0.967541 0.252716i \(-0.0813237\pi\)
\(180\) −71823.0 + 9500.34i −0.165227 + 0.0218553i
\(181\) −385985. 280434.i −0.875737 0.636260i 0.0563831 0.998409i \(-0.482043\pi\)
−0.932120 + 0.362149i \(0.882043\pi\)
\(182\) −559892. −1.25293
\(183\) 40379.7 + 29337.6i 0.0891323 + 0.0647584i
\(184\) −80283.7 + 247088.i −0.174817 + 0.538030i
\(185\) 344418. + 186731.i 0.739872 + 0.401133i
\(186\) 61602.5 + 189593.i 0.130562 + 0.401828i
\(187\) −318002. + 978710.i −0.665007 + 2.04668i
\(188\) −33098.6 + 101867.i −0.0682992 + 0.210203i
\(189\) 44501.7 + 136962.i 0.0906196 + 0.278898i
\(190\) −107932. 58517.1i −0.216904 0.117598i
\(191\) −201006. + 618632.i −0.398681 + 1.22701i 0.527377 + 0.849631i \(0.323175\pi\)
−0.926058 + 0.377382i \(0.876825\pi\)
\(192\) −29823.6 21668.1i −0.0583858 0.0424197i
\(193\) 301171. 0.581997 0.290998 0.956724i \(-0.406013\pi\)
0.290998 + 0.956724i \(0.406013\pi\)
\(194\) −327957. 238275.i −0.625623 0.454541i
\(195\) 353410. 46747.0i 0.665567 0.0880374i
\(196\) −287585. + 208943.i −0.534719 + 0.388496i
\(197\) −526491. + 382518.i −0.966552 + 0.702241i −0.954663 0.297688i \(-0.903784\pi\)
−0.0118889 + 0.999929i \(0.503784\pi\)
\(198\) 52345.7 + 161103.i 0.0948894 + 0.292040i
\(199\) −193412. −0.346218 −0.173109 0.984903i \(-0.555381\pi\)
−0.173109 + 0.984903i \(0.555381\pi\)
\(200\) 109133. + 167601.i 0.192921 + 0.296279i
\(201\) 181528. 0.316923
\(202\) 64492.3 + 198487.i 0.111206 + 0.342258i
\(203\) −84728.1 + 61558.6i −0.144307 + 0.104845i
\(204\) 229305. 166600.i 0.385779 0.280285i
\(205\) −825692. 447661.i −1.37225 0.743986i
\(206\) −166862. 121232.i −0.273961 0.199044i
\(207\) −328814. −0.533365
\(208\) 146749. + 106619.i 0.235189 + 0.170875i
\(209\) −88707.5 + 273014.i −0.140474 + 0.432333i
\(210\) 288207. 273833.i 0.450979 0.428487i
\(211\) −122285. 376355.i −0.189090 0.581958i 0.810905 0.585178i \(-0.198975\pi\)
−0.999995 + 0.00321951i \(0.998975\pi\)
\(212\) 26868.8 82693.8i 0.0410591 0.126367i
\(213\) −215755. + 664025.i −0.325845 + 1.00285i
\(214\) 84433.3 + 259859.i 0.126032 + 0.387885i
\(215\) 146166. 791342.i 0.215651 1.16753i
\(216\) 14417.5 44372.5i 0.0210259 0.0647112i
\(217\) −884989. 642982.i −1.27582 0.926935i
\(218\) 239945. 0.341957
\(219\) −283459. 205945.i −0.399375 0.290163i
\(220\) 339007. 322100.i 0.472228 0.448677i
\(221\) −1.12831e6 + 819767.i −1.55399 + 1.12904i
\(222\) −204117. + 148300.i −0.277969 + 0.201956i
\(223\) 333029. + 1.02496e6i 0.448456 + 1.38020i 0.878649 + 0.477468i \(0.158445\pi\)
−0.430194 + 0.902737i \(0.641555\pi\)
\(224\) 202286. 0.269368
\(225\) −159056. + 196910.i −0.209457 + 0.259305i
\(226\) −657401. −0.856168
\(227\) −44504.6 136971.i −0.0573246 0.176427i 0.918294 0.395898i \(-0.129567\pi\)
−0.975619 + 0.219471i \(0.929567\pi\)
\(228\) 63965.3 46473.5i 0.0814906 0.0592064i
\(229\) 499839. 363154.i 0.629857 0.457618i −0.226494 0.974013i \(-0.572726\pi\)
0.856351 + 0.516395i \(0.172726\pi\)
\(230\) 391283. + 819052.i 0.487720 + 1.02092i
\(231\) −752004. 546363.i −0.927236 0.673677i
\(232\) 33929.9 0.0413869
\(233\) 337150. + 244954.i 0.406849 + 0.295593i 0.772325 0.635228i \(-0.219094\pi\)
−0.365476 + 0.930821i \(0.619094\pi\)
\(234\) −70942.2 + 218338.i −0.0846964 + 0.260669i
\(235\) 161314. + 337671.i 0.190548 + 0.398864i
\(236\) −169528. 521752.i −0.198135 0.609796i
\(237\) −157331. + 484214.i −0.181946 + 0.559972i
\(238\) −480622. + 1.47920e6i −0.549998 + 1.69272i
\(239\) −37055.1 114044.i −0.0419617 0.129145i 0.927881 0.372876i \(-0.121628\pi\)
−0.969843 + 0.243732i \(0.921628\pi\)
\(240\) −127685. + 16889.5i −0.143091 + 0.0189273i
\(241\) 492594. 1.51605e6i 0.546319 1.68140i −0.171515 0.985182i \(-0.554866\pi\)
0.717834 0.696215i \(-0.245134\pi\)
\(242\) −363382. 264013.i −0.398865 0.289792i
\(243\) 59049.0 0.0641500
\(244\) 71786.1 + 52155.7i 0.0771909 + 0.0560824i
\(245\) −225586. + 1.22132e6i −0.240103 + 1.29991i
\(246\) 489340. 355526.i 0.515552 0.374571i
\(247\) −314745. + 228676.i −0.328259 + 0.238494i
\(248\) 109516. + 337054.i 0.113070 + 0.347993i
\(249\) −659432. −0.674018
\(250\) 679762. + 161879.i 0.687871 + 0.163810i
\(251\) 518304. 0.519278 0.259639 0.965706i \(-0.416396\pi\)
0.259639 + 0.965706i \(0.416396\pi\)
\(252\) 79114.1 + 243488.i 0.0784789 + 0.241533i
\(253\) 1.71702e6 1.24749e6i 1.68646 1.22528i
\(254\) 534238. 388147.i 0.519578 0.377495i
\(255\) 179871. 973816.i 0.173225 0.937835i
\(256\) −53019.7 38521.1i −0.0505636 0.0367366i
\(257\) 895330. 0.845572 0.422786 0.906230i \(-0.361052\pi\)
0.422786 + 0.906230i \(0.361052\pi\)
\(258\) 419261. + 304611.i 0.392134 + 0.284902i
\(259\) 427827. 1.31671e6i 0.396295 1.21967i
\(260\) 628284. 83105.8i 0.576398 0.0762427i
\(261\) 13270.0 + 40840.8i 0.0120578 + 0.0371102i
\(262\) −252731. + 777827.i −0.227461 + 0.700052i
\(263\) 462047. 1.42203e6i 0.411904 1.26771i −0.503086 0.864236i \(-0.667802\pi\)
0.914991 0.403475i \(-0.132198\pi\)
\(264\) 93059.0 + 286406.i 0.0821767 + 0.252914i
\(265\) −130952. 274115.i −0.114551 0.239783i
\(266\) −134071. + 412627.i −0.116179 + 0.357564i
\(267\) 995353. + 723166.i 0.854474 + 0.620812i
\(268\) 322717. 0.274463
\(269\) 1.30360e6 + 947121.i 1.09841 + 0.798040i 0.980799 0.195020i \(-0.0624772\pi\)
0.117608 + 0.993060i \(0.462477\pi\)
\(270\) −70267.2 147087.i −0.0586602 0.122790i
\(271\) 1.60206e6 1.16397e6i 1.32512 0.962758i 0.325269 0.945621i \(-0.394545\pi\)
0.999853 0.0171362i \(-0.00545489\pi\)
\(272\) 407654. 296178.i 0.334095 0.242734i
\(273\) −389286. 1.19810e6i −0.316128 0.972941i
\(274\) 530992. 0.427279
\(275\) 83513.0 1.63168e6i 0.0665921 1.30108i
\(276\) −584558. −0.461907
\(277\) −87892.2 270505.i −0.0688258 0.211824i 0.910728 0.413007i \(-0.135521\pi\)
−0.979554 + 0.201183i \(0.935521\pi\)
\(278\) −858330. + 623613.i −0.666104 + 0.483953i
\(279\) −362874. + 263643.i −0.279091 + 0.202771i
\(280\) 512368. 486814.i 0.390559 0.371081i
\(281\) −1.80785e6 1.31348e6i −1.36583 0.992335i −0.998050 0.0624230i \(-0.980117\pi\)
−0.367782 0.929912i \(-0.619883\pi\)
\(282\) −240996. −0.180463
\(283\) −220467. 160179.i −0.163636 0.118888i 0.502954 0.864313i \(-0.332247\pi\)
−0.666590 + 0.745425i \(0.732247\pi\)
\(284\) −383564. + 1.18049e6i −0.282190 + 0.868492i
\(285\) 50175.4 271648.i 0.0365913 0.198105i
\(286\) −457903. 1.40928e6i −0.331023 1.01878i
\(287\) −1.02565e6 + 3.15663e6i −0.735013 + 2.26214i
\(288\) 25631.1 78884.4i 0.0182090 0.0560415i
\(289\) 758451. + 2.33427e6i 0.534174 + 1.64402i
\(290\) 85940.6 81654.4i 0.0600072 0.0570144i
\(291\) 281854. 867457.i 0.195115 0.600503i
\(292\) −503928. 366125.i −0.345869 0.251288i
\(293\) 1.04298e6 0.709755 0.354878 0.934913i \(-0.384523\pi\)
0.354878 + 0.934913i \(0.384523\pi\)
\(294\) −647066. 470121.i −0.436597 0.317206i
\(295\) −1.68502e6 913560.i −1.12733 0.611198i
\(296\) −362874. + 263644.i −0.240728 + 0.174899i
\(297\) −308346. + 224027.i −0.202837 + 0.147370i
\(298\) 197375. + 607458.i 0.128751 + 0.396256i
\(299\) 2.87636e6 1.86065
\(300\) −282767. + 350062.i −0.181395 + 0.224565i
\(301\) −2.84374e6 −1.80915
\(302\) −46058.5 141754.i −0.0290598 0.0894369i
\(303\) −379897. + 276011.i −0.237716 + 0.172711i
\(304\) 113716. 82619.6i 0.0705729 0.0512742i
\(305\) 307342. 40653.4i 0.189178 0.0250235i
\(306\) 515937. + 374850.i 0.314987 + 0.228852i
\(307\) 2.30792e6 1.39757 0.698786 0.715331i \(-0.253724\pi\)
0.698786 + 0.715331i \(0.253724\pi\)
\(308\) −1.33690e6 971312.i −0.803010 0.583421i
\(309\) 143405. 441355.i 0.0854413 0.262961i
\(310\) 1.08853e6 + 590163.i 0.643334 + 0.348793i
\(311\) 821865. + 2.52944e6i 0.481836 + 1.48294i 0.836511 + 0.547949i \(0.184591\pi\)
−0.354675 + 0.934989i \(0.615409\pi\)
\(312\) −126120. + 388156.i −0.0733493 + 0.225746i
\(313\) 28760.6 88515.9i 0.0165934 0.0510694i −0.942417 0.334440i \(-0.891453\pi\)
0.959010 + 0.283371i \(0.0914527\pi\)
\(314\) −342363. 1.05368e6i −0.195958 0.603096i
\(315\) 786356. + 426335.i 0.446522 + 0.242088i
\(316\) −279699. + 860825.i −0.157570 + 0.484950i
\(317\) 996653. + 724111.i 0.557052 + 0.404722i 0.830379 0.557199i \(-0.188124\pi\)
−0.273327 + 0.961921i \(0.588124\pi\)
\(318\) 195636. 0.108488
\(319\) −224241. 162920.i −0.123378 0.0896393i
\(320\) −226996. + 30025.8i −0.123921 + 0.0163915i
\(321\) −497361. + 361354.i −0.269407 + 0.195736i
\(322\) 2.59507e6 1.88543e6i 1.39479 1.01338i
\(323\) 333965. + 1.02784e6i 0.178113 + 0.548174i
\(324\) 104976. 0.0555556
\(325\) 1.39137e6 1.72250e6i 0.730692 0.904588i
\(326\) −2.25580e6 −1.17559
\(327\) 166831. + 513454.i 0.0862795 + 0.265541i
\(328\) 869938. 632047.i 0.446481 0.324388i
\(329\) 1.06987e6 777308.i 0.544932 0.395916i
\(330\) 924961. + 501481.i 0.467561 + 0.253495i
\(331\) 1.63491e6 + 1.18783e6i 0.820207 + 0.595915i 0.916772 0.399411i \(-0.130786\pi\)
−0.0965648 + 0.995327i \(0.530786\pi\)
\(332\) −1.17232e6 −0.583717
\(333\) −459263. 333674.i −0.226961 0.164897i
\(334\) −3452.66 + 10626.2i −0.00169351 + 0.00521208i
\(335\) 817404. 776637.i 0.397946 0.378099i
\(336\) 140647. + 432868.i 0.0679647 + 0.209174i
\(337\) 116766. 359370.i 0.0560071 0.172372i −0.919140 0.393932i \(-0.871115\pi\)
0.975147 + 0.221560i \(0.0711147\pi\)
\(338\) 161636. 497464.i 0.0769566 0.236848i
\(339\) −457083. 1.40676e6i −0.216021 0.664844i
\(340\) 319770. 1.73123e6i 0.150017 0.812189i
\(341\) 894642. 2.75342e6i 0.416642 1.28229i
\(342\) 143922. + 104565.i 0.0665368 + 0.0483418i
\(343\) 1.06875e6 0.490503
\(344\) 745352. + 541530.i 0.339598 + 0.246733i
\(345\) −1.48062e6 + 1.40677e6i −0.669723 + 0.636321i
\(346\) 825903. 600054.i 0.370885 0.269463i
\(347\) −3.20075e6 + 2.32548e6i −1.42702 + 1.03679i −0.436453 + 0.899727i \(0.643765\pi\)
−0.990563 + 0.137060i \(0.956235\pi\)
\(348\) 23591.1 + 72605.9i 0.0104424 + 0.0321384i
\(349\) −695664. −0.305729 −0.152864 0.988247i \(-0.548850\pi\)
−0.152864 + 0.988247i \(0.548850\pi\)
\(350\) 126220. 2.46609e6i 0.0550754 1.07607i
\(351\) −516541. −0.223788
\(352\) 165438. + 509166.i 0.0711671 + 0.219030i
\(353\) −2.93067e6 + 2.12925e6i −1.25178 + 0.909475i −0.998324 0.0578713i \(-0.981569\pi\)
−0.253460 + 0.967346i \(0.581569\pi\)
\(354\) 998616. 725537.i 0.423536 0.307717i
\(355\) 1.86939e6 + 3.91311e6i 0.787281 + 1.64798i
\(356\) 1.76952e6 + 1.28563e6i 0.739996 + 0.537639i
\(357\) −3.49948e6 −1.45323
\(358\) 2.58386e6 + 1.87729e6i 1.06552 + 0.774146i
\(359\) −788903. + 2.42800e6i −0.323063 + 0.994287i 0.649244 + 0.760580i \(0.275085\pi\)
−0.972307 + 0.233707i \(0.924915\pi\)
\(360\) −124920. 261488.i −0.0508012 0.106340i
\(361\) −671996. 2.06819e6i −0.271393 0.835262i
\(362\) 589732. 1.81501e6i 0.236529 0.727960i
\(363\) 312299. 961159.i 0.124395 0.382850i
\(364\) −692064. 2.12996e6i −0.273775 0.842591i
\(365\) −2.15749e6 + 285381.i −0.847651 + 0.112122i
\(366\) −61694.7 + 189877.i −0.0240738 + 0.0740916i
\(367\) 3.01143e6 + 2.18793e6i 1.16710 + 0.847948i 0.990659 0.136364i \(-0.0435415\pi\)
0.176441 + 0.984311i \(0.443542\pi\)
\(368\) −1.03921e6 −0.400023
\(369\) 1.10101e6 + 799934.i 0.420947 + 0.305836i
\(370\) −284644. + 1.54106e6i −0.108093 + 0.585214i
\(371\) −868502. + 631004.i −0.327594 + 0.238011i
\(372\) −645109. + 468699.i −0.241700 + 0.175605i
\(373\) 225214. + 693136.i 0.0838151 + 0.257956i 0.984178 0.177184i \(-0.0566987\pi\)
−0.900363 + 0.435140i \(0.856699\pi\)
\(374\) −4.11631e6 −1.52170
\(375\) 126230. + 1.56716e6i 0.0463536 + 0.575486i
\(376\) −428438. −0.156285
\(377\) −116081. 357262.i −0.0420639 0.129459i
\(378\) −466028. + 338589.i −0.167758 + 0.121883i
\(379\) 1.00364e6 729190.i 0.358907 0.260761i −0.393689 0.919244i \(-0.628801\pi\)
0.752596 + 0.658483i \(0.228801\pi\)
\(380\) 89200.6 482930.i 0.0316890 0.171564i
\(381\) 1.20204e6 + 873330.i 0.424233 + 0.308224i
\(382\) −2.60187e6 −0.912279
\(383\) −1.01616e6 738282.i −0.353968 0.257173i 0.396564 0.918007i \(-0.370203\pi\)
−0.750532 + 0.660834i \(0.770203\pi\)
\(384\) 45566.4 140239.i 0.0157695 0.0485334i
\(385\) −5.72373e6 + 757102.i −1.96801 + 0.260317i
\(386\) 372268. + 1.14572e6i 0.127171 + 0.391392i
\(387\) −360322. + 1.10896e6i −0.122296 + 0.376390i
\(388\) 501074. 1.54215e6i 0.168975 0.520051i
\(389\) 115744. + 356224.i 0.0387816 + 0.119357i 0.968573 0.248729i \(-0.0800130\pi\)
−0.929791 + 0.368087i \(0.880013\pi\)
\(390\) 614675. + 1.28667e6i 0.204637 + 0.428356i
\(391\) 2.46912e6 7.59916e6i 0.816770 2.51376i
\(392\) −1.15034e6 835771.i −0.378104 0.274708i
\(393\) −1.84018e6 −0.601005
\(394\) −2.10596e6 1.53007e6i −0.683456 0.496560i
\(395\) 1.36318e6 + 2.85348e6i 0.439603 + 0.920200i
\(396\) −548171. + 398270.i −0.175662 + 0.127626i
\(397\) −2.23833e6 + 1.62624e6i −0.712767 + 0.517855i −0.884065 0.467364i \(-0.845204\pi\)
0.171298 + 0.985219i \(0.445204\pi\)
\(398\) −239070. 735781.i −0.0756514 0.232831i
\(399\) −976189. −0.306974
\(400\) −502696. + 622332.i −0.157093 + 0.194479i
\(401\) 4.72070e6 1.46604 0.733020 0.680207i \(-0.238110\pi\)
0.733020 + 0.680207i \(0.238110\pi\)
\(402\) 224381. + 690574.i 0.0692502 + 0.213130i
\(403\) 3.17430e6 2.30627e6i 0.973612 0.707370i
\(404\) −675372. + 490686.i −0.205868 + 0.149572i
\(405\) 265892. 252631.i 0.0805504 0.0765331i
\(406\) −338912. 246234.i −0.102040 0.0741367i
\(407\) 3.66414e6 1.09644
\(408\) 917222. + 666400.i 0.272787 + 0.198191i
\(409\) −1.77290e6 + 5.45642e6i −0.524054 + 1.61287i 0.242126 + 0.970245i \(0.422155\pi\)
−0.766180 + 0.642627i \(0.777845\pi\)
\(410\) 682392. 3.69446e6i 0.200482 1.08540i
\(411\) 369192. + 1.13626e6i 0.107807 + 0.331797i
\(412\) 254942. 784631.i 0.0739943 0.227731i
\(413\) −2.09309e6 + 6.44186e6i −0.603827 + 1.85839i
\(414\) −406436. 1.25088e6i −0.116544 0.358687i
\(415\) −2.96936e6 + 2.82127e6i −0.846335 + 0.804126i
\(416\) −224212. + 690055.i −0.0635223 + 0.195502i
\(417\) −1.93124e6 1.40313e6i −0.543872 0.395146i
\(418\) −1.14825e6 −0.321438
\(419\) −3.09825e6 2.25101e6i −0.862147 0.626387i 0.0663211 0.997798i \(-0.478874\pi\)
−0.928468 + 0.371412i \(0.878874\pi\)
\(420\) 1.39797e6 + 757928.i 0.386699 + 0.209655i
\(421\) 1.01432e6 736947.i 0.278914 0.202643i −0.439530 0.898228i \(-0.644855\pi\)
0.718443 + 0.695585i \(0.244855\pi\)
\(422\) 1.28059e6 930401.i 0.350048 0.254325i
\(423\) −167562. 515702.i −0.0455328 0.140136i
\(424\) 347797. 0.0939532
\(425\) −3.35637e6 5.15455e6i −0.901357 1.38426i
\(426\) −2.79279e6 −0.745614
\(427\) −338542. 1.04192e6i −0.0898550 0.276545i
\(428\) −884197. + 642407.i −0.233313 + 0.169512i
\(429\) 2.69731e6 1.95971e6i 0.707600 0.514101i
\(430\) 3.19111e6 422102.i 0.832283 0.110090i
\(431\) 4.97192e6 + 3.61231e6i 1.28923 + 0.936682i 0.999790 0.0205136i \(-0.00653013\pi\)
0.289442 + 0.957195i \(0.406530\pi\)
\(432\) 186624. 0.0481125
\(433\) −5.99242e6 4.35375e6i −1.53597 1.11595i −0.952800 0.303597i \(-0.901812\pi\)
−0.583170 0.812350i \(-0.698188\pi\)
\(434\) 1.35214e6 4.16147e6i 0.344586 1.06053i
\(435\) 234484. + 127129.i 0.0594142 + 0.0322123i
\(436\) 296589. + 912806.i 0.0747203 + 0.229965i
\(437\) 688766. 2.11980e6i 0.172531 0.530997i
\(438\) 433087. 1.33291e6i 0.107867 0.331982i
\(439\) 1.05126e6 + 3.23545e6i 0.260345 + 0.801260i 0.992729 + 0.120369i \(0.0384076\pi\)
−0.732384 + 0.680892i \(0.761592\pi\)
\(440\) 1.64438e6 + 891522.i 0.404920 + 0.219533i
\(441\) 556104. 1.71151e6i 0.136163 0.419067i
\(442\) −4.51325e6 3.27907e6i −1.09884 0.798352i
\(443\) −3.65382e6 −0.884581 −0.442291 0.896872i \(-0.645834\pi\)
−0.442291 + 0.896872i \(0.645834\pi\)
\(444\) −816467. 593198.i −0.196554 0.142805i
\(445\) 7.57592e6 1.00210e6i 1.81357 0.239889i
\(446\) −3.48752e6 + 2.53383e6i −0.830194 + 0.603171i
\(447\) −1.16265e6 + 844717.i −0.275221 + 0.199960i
\(448\) 250040. + 769543.i 0.0588592 + 0.181150i
\(449\) 4.46825e6 1.04598 0.522988 0.852340i \(-0.324817\pi\)
0.522988 + 0.852340i \(0.324817\pi\)
\(450\) −945693. 361692.i −0.220150 0.0841991i
\(451\) −8.78423e6 −2.03359
\(452\) −812592. 2.50090e6i −0.187080 0.575772i
\(453\) 271311. 197119.i 0.0621187 0.0451319i
\(454\) 466059. 338611.i 0.106121 0.0771014i
\(455\) −6.87879e6 3.72943e6i −1.55770 0.844529i
\(456\) 255861. + 185894.i 0.0576225 + 0.0418652i
\(457\) 674951. 0.151176 0.0755878 0.997139i \(-0.475917\pi\)
0.0755878 + 0.997139i \(0.475917\pi\)
\(458\) 1.99936e6 + 1.45262e6i 0.445376 + 0.323584i
\(459\) −443409. + 1.36467e6i −0.0982364 + 0.302340i
\(460\) −2.63221e6 + 2.50093e6i −0.579997 + 0.551071i
\(461\) 672830. + 2.07076e6i 0.147453 + 0.453813i 0.997318 0.0731866i \(-0.0233169\pi\)
−0.849865 + 0.527000i \(0.823317\pi\)
\(462\) 1.14896e6 3.53614e6i 0.250438 0.770769i
\(463\) −46572.8 + 143336.i −0.0100967 + 0.0310745i −0.955978 0.293439i \(-0.905200\pi\)
0.945881 + 0.324513i \(0.105200\pi\)
\(464\) 41939.7 + 129077.i 0.00904337 + 0.0278326i
\(465\) −506034. + 2.73966e6i −0.108529 + 0.587575i
\(466\) −515120. + 1.58538e6i −0.109886 + 0.338195i
\(467\) −1.65348e6 1.20133e6i −0.350839 0.254899i 0.398382 0.917220i \(-0.369572\pi\)
−0.749221 + 0.662320i \(0.769572\pi\)
\(468\) −918295. −0.193806
\(469\) −3.22349e6 2.34200e6i −0.676696 0.491648i
\(470\) −1.08518e6 + 1.03106e6i −0.226599 + 0.215298i
\(471\) 2.01671e6 1.46523e6i 0.418882 0.304336i
\(472\) 1.77532e6 1.28984e6i 0.366793 0.266491i
\(473\) −2.32573e6 7.15787e6i −0.477977 1.47106i
\(474\) −2.03653e6 −0.416337
\(475\) −936267. 1.43787e6i −0.190399 0.292406i
\(476\) −6.22130e6 −1.25853
\(477\) 136023. + 418637.i 0.0273727 + 0.0842445i
\(478\) 388046. 281932.i 0.0776807 0.0564383i
\(479\) −853945. + 620427.i −0.170056 + 0.123553i −0.669558 0.742760i \(-0.733516\pi\)
0.499502 + 0.866313i \(0.333516\pi\)
\(480\) −222079. 464867.i −0.0439951 0.0920929i
\(481\) 4.01748e6 + 2.91887e6i 0.791755 + 0.575244i
\(482\) 6.37627e6 1.25011
\(483\) 5.83891e6 + 4.24222e6i 1.13884 + 0.827418i
\(484\) 555199. 1.70873e6i 0.107730 0.331558i
\(485\) −2.44211e6 5.11194e6i −0.471422 0.986805i
\(486\) 72988.6 + 224636.i 0.0140173 + 0.0431408i
\(487\) 166876. 513591.i 0.0318839 0.0981284i −0.933848 0.357670i \(-0.883571\pi\)
0.965732 + 0.259541i \(0.0835714\pi\)
\(488\) −109679. + 337559.i −0.0208485 + 0.0641652i
\(489\) −1.56843e6 4.82713e6i −0.296615 0.912886i
\(490\) −4.92501e6 + 651452.i −0.926652 + 0.122572i
\(491\) −1.62308e6 + 4.99533e6i −0.303834 + 0.935105i 0.676276 + 0.736649i \(0.263593\pi\)
−0.980110 + 0.198456i \(0.936407\pi\)
\(492\) 1.95736e6 + 1.42210e6i 0.364551 + 0.264862i
\(493\) −1.04351e6 −0.193366
\(494\) −1.25898e6 914704.i −0.232114 0.168641i
\(495\) −429994. + 2.32798e6i −0.0788767 + 0.427037i
\(496\) −1.14686e6 + 833243.i −0.209318 + 0.152078i
\(497\) 1.23982e7 9.00784e6i 2.25148 1.63580i
\(498\) −815103. 2.50863e6i −0.147278 0.453276i
\(499\) 6.38969e6 1.14876 0.574379 0.818590i \(-0.305244\pi\)
0.574379 + 0.818590i \(0.305244\pi\)
\(500\) 224408. + 2.78606e6i 0.0401434 + 0.498386i
\(501\) −25139.3 −0.00447465
\(502\) 640658. + 1.97174e6i 0.113466 + 0.349214i
\(503\) 3.44531e6 2.50317e6i 0.607168 0.441133i −0.241248 0.970464i \(-0.577557\pi\)
0.848416 + 0.529330i \(0.177557\pi\)
\(504\) −828494. + 601936.i −0.145282 + 0.105554i
\(505\) −529772. + 2.86817e6i −0.0924401 + 0.500469i
\(506\) 6.86809e6 + 4.98996e6i 1.19250 + 0.866405i
\(507\) 1.17690e6 0.203338
\(508\) 2.13695e6 + 1.55259e6i 0.367397 + 0.266929i
\(509\) −2.06489e6 + 6.35508e6i −0.353266 + 1.08724i 0.603742 + 0.797180i \(0.293676\pi\)
−0.957008 + 0.290062i \(0.906324\pi\)
\(510\) 3.92695e6 519434.i 0.668544 0.0884311i
\(511\) 2.37651e6 + 7.31415e6i 0.402613 + 1.23912i
\(512\) 81007.0 249314.i 0.0136568 0.0420312i
\(513\) −123690. + 380678.i −0.0207511 + 0.0638653i
\(514\) 1.10669e6 + 3.40604e6i 0.184764 + 0.568646i
\(515\) −1.24252e6 2.60091e6i −0.206437 0.432123i
\(516\) −640573. + 1.97148e6i −0.105912 + 0.325963i
\(517\) 2.83152e6 + 2.05722e6i 0.465900 + 0.338496i
\(518\) 5.53790e6 0.906820
\(519\) 1.85828e6 + 1.35012e6i 0.302826 + 0.220016i
\(520\) 1.09276e6 + 2.28741e6i 0.177221 + 0.370967i
\(521\) 511312. 371490.i 0.0825262 0.0599588i −0.545757 0.837943i \(-0.683758\pi\)
0.628283 + 0.777985i \(0.283758\pi\)
\(522\) −138965. + 100964.i −0.0223218 + 0.0162177i
\(523\) 1.02059e6 + 3.14107e6i 0.163154 + 0.502138i 0.998896 0.0469859i \(-0.0149616\pi\)
−0.835741 + 0.549124i \(0.814962\pi\)
\(524\) −3.27142e6 −0.520486
\(525\) 5.36489e6 1.44455e6i 0.849498 0.228736i
\(526\) 5.98086e6 0.942539
\(527\) −3.36814e6 1.03661e7i −0.528279 1.62588i
\(528\) −974526. + 708035.i −0.152128 + 0.110527i
\(529\) −8.12466e6 + 5.90291e6i −1.26231 + 0.917122i
\(530\) 880930. 836995.i 0.136223 0.129430i
\(531\) 2.24688e6 + 1.63246e6i 0.345816 + 0.251250i
\(532\) −1.73545e6 −0.265847
\(533\) −9.63131e6 6.99756e6i −1.46848 1.06691i
\(534\) −1.52076e6 + 4.68043e6i −0.230786 + 0.710285i
\(535\) −693577. + 3.75501e6i −0.104764 + 0.567188i
\(536\) 398900. + 1.22769e6i 0.0599724 + 0.184576i
\(537\) −2.22063e6 + 6.83440e6i −0.332308 + 1.02274i
\(538\) −1.99172e6 + 6.12989e6i −0.296670 + 0.913056i
\(539\) 3.58942e6 + 1.10471e7i 0.532173 + 1.63786i
\(540\) 472697. 449122.i 0.0697587 0.0662796i
\(541\) −1.52255e6 + 4.68594e6i −0.223656 + 0.688341i 0.774770 + 0.632243i \(0.217866\pi\)
−0.998425 + 0.0560975i \(0.982134\pi\)
\(542\) 6.40825e6 + 4.65586e6i 0.937003 + 0.680772i
\(543\) 4.29393e6 0.624965
\(544\) 1.63062e6 + 1.18471e6i 0.236241 + 0.171639i
\(545\) 2.94795e6 + 1.59827e6i 0.425137 + 0.230494i
\(546\) 4.07666e6 2.96187e6i 0.585225 0.425191i
\(547\) 4.21466e6 3.06213e6i 0.602274 0.437577i −0.244412 0.969672i \(-0.578595\pi\)
0.846685 + 0.532094i \(0.178595\pi\)
\(548\) 656342. + 2.02001e6i 0.0933639 + 0.287344i
\(549\) −449208. −0.0636088
\(550\) 6.31051e6 1.69917e6i 0.889525 0.239513i
\(551\) −291090. −0.0408459
\(552\) −722553. 2.22379e6i −0.100930 0.310632i
\(553\) 9.04092e6 6.56862e6i 1.25719 0.913400i
\(554\) 920419. 668724.i 0.127412 0.0925705i
\(555\) −3.49558e6 + 462376.i −0.481712 + 0.0637181i
\(556\) −3.43332e6 2.49445e6i −0.471007 0.342207i
\(557\) −775557. −0.105919 −0.0529597 0.998597i \(-0.516865\pi\)
−0.0529597 + 0.998597i \(0.516865\pi\)
\(558\) −1.45150e6 1.05457e6i −0.197347 0.143381i
\(559\) 3.15198e6 9.70080e6i 0.426633 1.31304i
\(560\) 2.48527e6 + 1.34743e6i 0.334892 + 0.181566i
\(561\) −2.86202e6 8.80839e6i −0.383942 1.18165i
\(562\) 2.76215e6 8.50103e6i 0.368899 1.13535i
\(563\) 456587. 1.40523e6i 0.0607089 0.186843i −0.916103 0.400944i \(-0.868682\pi\)
0.976812 + 0.214101i \(0.0686822\pi\)
\(564\) −297888. 916804.i −0.0394326 0.121361i
\(565\) −8.07677e6 4.37894e6i −1.06443 0.577096i
\(566\) 336844. 1.03670e6i 0.0441965 0.136023i
\(567\) −1.04856e6 761826.i −0.136974 0.0995171i
\(568\) −4.96496e6 −0.645720
\(569\) 2.53513e6 + 1.84188e6i 0.328261 + 0.238496i 0.739692 0.672945i \(-0.234971\pi\)
−0.411431 + 0.911441i \(0.634971\pi\)
\(570\) 1.09543e6 144898.i 0.141221 0.0186799i
\(571\) 5.73441e6 4.16629e6i 0.736035 0.534761i −0.155432 0.987847i \(-0.549677\pi\)
0.891467 + 0.453086i \(0.149677\pi\)
\(572\) 4.79522e6 3.48393e6i 0.612800 0.445225i
\(573\) −1.80905e6 5.56769e6i −0.230178 0.708416i
\(574\) −1.32763e7 −1.68189
\(575\) −648434. + 1.26691e7i −0.0817892 + 1.59800i
\(576\) 331776. 0.0416667
\(577\) −1.75448e6 5.39973e6i −0.219386 0.675200i −0.998813 0.0487073i \(-0.984490\pi\)
0.779427 0.626493i \(-0.215510\pi\)
\(578\) −7.94260e6 + 5.77064e6i −0.988879 + 0.718463i
\(579\) −2.19288e6 + 1.59322e6i −0.271843 + 0.197505i
\(580\) 416860. + 226007.i 0.0514542 + 0.0278966i
\(581\) 1.17099e7 + 8.50772e6i 1.43917 + 1.04562i
\(582\) 3.64839e6 0.446472
\(583\) −2.29857e6 1.67001e6i −0.280083 0.203492i
\(584\) 769933. 2.36961e6i 0.0934159 0.287505i
\(585\) −2.32594e6 + 2.20993e6i −0.281001 + 0.266987i
\(586\) 1.28920e6 + 3.96775e6i 0.155087 + 0.477309i
\(587\) −1.59149e6 + 4.89810e6i −0.190638 + 0.586722i −1.00000 0.000587432i \(-0.999813\pi\)
0.809362 + 0.587310i \(0.199813\pi\)
\(588\) 988629. 3.04269e6i 0.117921 0.362923i
\(589\) −939550. 2.89164e6i −0.111592 0.343444i
\(590\) 1.39258e6 7.53943e6i 0.164699 0.891679i
\(591\) 1.80991e6 5.57034e6i 0.213152 0.656014i
\(592\) −1.45150e6 1.05457e6i −0.170221 0.123672i
\(593\) −8.33120e6 −0.972906 −0.486453 0.873707i \(-0.661709\pi\)
−0.486453 + 0.873707i \(0.661709\pi\)
\(594\) −1.23338e6 896107.i −0.143428 0.104206i
\(595\) −1.57578e7 + 1.49719e7i −1.82475 + 1.73375i
\(596\) −2.06694e6 + 1.50172e6i −0.238348 + 0.173170i
\(597\) 1.40826e6 1.02316e6i 0.161714 0.117492i
\(598\) 3.55537e6 + 1.09423e7i 0.406567 + 1.25128i
\(599\) 6.43850e6 0.733192 0.366596 0.930380i \(-0.380523\pi\)
0.366596 + 0.930380i \(0.380523\pi\)
\(600\) −1.68123e6 643008.i −0.190656 0.0729186i
\(601\) 8.56648e6 0.967423 0.483711 0.875228i \(-0.339288\pi\)
0.483711 + 0.875228i \(0.339288\pi\)
\(602\) −3.51506e6 1.08182e7i −0.395314 1.21665i
\(603\) −1.32173e6 + 960296.i −0.148030 + 0.107550i
\(604\) 482331. 350434.i 0.0537964 0.0390854i
\(605\) −2.70590e6 5.66412e6i −0.300554 0.629136i
\(606\) −1.51959e6 1.10404e6i −0.168091 0.122125i
\(607\) 9.15813e6 1.00887 0.504435 0.863450i \(-0.331701\pi\)
0.504435 + 0.863450i \(0.331701\pi\)
\(608\) 454864. + 330478.i 0.0499026 + 0.0362564i
\(609\) 291269. 896435.i 0.0318238 0.0979434i
\(610\) 534550. + 1.11895e6i 0.0581652 + 0.121754i
\(611\) 1.46578e6 + 4.51120e6i 0.158842 + 0.488865i
\(612\) −788282. + 2.42608e6i −0.0850752 + 0.261835i
\(613\) 3.27979e6 1.00941e7i 0.352529 1.08497i −0.604900 0.796301i \(-0.706787\pi\)
0.957429 0.288670i \(-0.0932130\pi\)
\(614\) 2.85274e6 + 8.77984e6i 0.305381 + 0.939865i
\(615\) 8.38014e6 1.10848e6i 0.893437 0.118179i
\(616\) 2.04260e6 6.28647e6i 0.216886 0.667505i
\(617\) −5.69471e6 4.13745e6i −0.602225 0.437542i 0.244443 0.969664i \(-0.421395\pi\)
−0.846668 + 0.532121i \(0.821395\pi\)
\(618\) 1.85627e6 0.195511
\(619\) −1.08927e7 7.91400e6i −1.14264 0.830175i −0.155153 0.987890i \(-0.549587\pi\)
−0.987485 + 0.157716i \(0.949587\pi\)
\(620\) −899615. + 4.87050e6i −0.0939891 + 0.508855i
\(621\) 2.39414e6 1.73945e6i 0.249127 0.181002i
\(622\) −8.60668e6 + 6.25312e6i −0.891989 + 0.648068i
\(623\) −8.34500e6 2.56833e7i −0.861402 2.65112i
\(624\) −1.63253e6 −0.167841
\(625\) 7.27323e6 + 6.51672e6i 0.744778 + 0.667312i
\(626\) 372285. 0.0379699
\(627\) −798367. 2.45712e6i −0.0811024 0.249608i
\(628\) 3.58527e6 2.60485e6i 0.362763 0.263563i
\(629\) 1.11602e7 8.10833e6i 1.12472 0.817156i
\(630\) −649883. + 3.51846e6i −0.0652355 + 0.353184i
\(631\) 6.01279e6 + 4.36855e6i 0.601177 + 0.436781i 0.846297 0.532712i \(-0.178827\pi\)
−0.245119 + 0.969493i \(0.578827\pi\)
\(632\) −3.62050e6 −0.360558
\(633\) 2.88132e6 + 2.09340e6i 0.285813 + 0.207655i
\(634\) −1.52275e6 + 4.68654e6i −0.150455 + 0.463052i
\(635\) 9.14904e6 1.21018e6i 0.900412 0.119101i
\(636\) 241819. + 744244.i 0.0237055 + 0.0729579i
\(637\) −4.86461e6 + 1.49717e7i −0.475007 + 1.46192i
\(638\) 342609. 1.05444e6i 0.0333232 0.102558i
\(639\) −1.94179e6 5.97622e6i −0.188127 0.578995i
\(640\) −394807. 826431.i −0.0381009 0.0797548i
\(641\) −304755. + 937938.i −0.0292958 + 0.0901632i −0.964635 0.263588i \(-0.915094\pi\)
0.935340 + 0.353751i \(0.115094\pi\)
\(642\) −1.98944e6 1.44542e6i −0.190500 0.138406i
\(643\) −1.23129e7 −1.17445 −0.587225 0.809424i \(-0.699780\pi\)
−0.587225 + 0.809424i \(0.699780\pi\)
\(644\) 1.03803e7 + 7.54172e6i 0.986268 + 0.716565i
\(645\) 3.12199e6 + 6.53511e6i 0.295483 + 0.618520i
\(646\) −3.49733e6 + 2.54096e6i −0.329727 + 0.239561i
\(647\) 1.30648e7 9.49214e6i 1.22699 0.891463i 0.230332 0.973112i \(-0.426019\pi\)
0.996661 + 0.0816491i \(0.0260187\pi\)
\(648\) 129757. + 399352.i 0.0121393 + 0.0373610i
\(649\) −1.79263e7 −1.67063
\(650\) 8.27261e6 + 3.16396e6i 0.767996 + 0.293730i
\(651\) 9.84515e6 0.910479
\(652\) −2.78832e6 8.58156e6i −0.256876 0.790582i
\(653\) −3.55421e6 + 2.58229e6i −0.326182 + 0.236985i −0.738809 0.673915i \(-0.764611\pi\)
0.412627 + 0.910900i \(0.364611\pi\)
\(654\) −1.74708e6 + 1.26933e6i −0.159723 + 0.116046i
\(655\) −8.28614e6 + 7.87288e6i −0.754656 + 0.717019i
\(656\) 3.47975e6 + 2.52819e6i 0.315710 + 0.229377i
\(657\) 3.15338e6 0.285011
\(658\) 4.27949e6 + 3.10923e6i 0.385325 + 0.279955i
\(659\) 3.63934e6 1.12007e7i 0.326444 1.00469i −0.644340 0.764739i \(-0.722868\pi\)
0.970784 0.239953i \(-0.0771322\pi\)
\(660\) −764433. + 4.13863e6i −0.0683093 + 0.369825i
\(661\) −4.67871e6 1.43996e7i −0.416507 1.28188i −0.910896 0.412636i \(-0.864608\pi\)
0.494389 0.869241i \(-0.335392\pi\)
\(662\) −2.49792e6 + 7.68780e6i −0.221530 + 0.681800i
\(663\) 3.87879e6 1.19377e7i 0.342699 1.05472i
\(664\) −1.44907e6 4.45978e6i −0.127547 0.392549i
\(665\) −4.39568e6 + 4.17646e6i −0.385454 + 0.366230i
\(666\) 701691. 2.15958e6i 0.0613000 0.188662i
\(667\) 1.74111e6 + 1.26499e6i 0.151534 + 0.110096i
\(668\) −44692.1 −0.00387516
\(669\) −7.84692e6 5.70112e6i −0.677851 0.492487i
\(670\) 3.96487e6 + 2.14961e6i 0.341226 + 0.185001i
\(671\) 2.34571e6 1.70426e6i 0.201126 0.146126i
\(672\) −1.47288e6 + 1.07011e6i −0.125818 + 0.0914123i
\(673\) −906128. 2.78878e6i −0.0771173 0.237343i 0.905065 0.425273i \(-0.139822\pi\)
−0.982182 + 0.187931i \(0.939822\pi\)
\(674\) 1.51145e6 0.128158
\(675\) 116447. 2.27515e6i 0.00983714 0.192199i
\(676\) 2.09226e6 0.176096
\(677\) 4.80539e6 + 1.47895e7i 0.402955 + 1.24017i 0.922591 + 0.385781i \(0.126068\pi\)
−0.519635 + 0.854388i \(0.673932\pi\)
\(678\) 4.78663e6 3.47769e6i 0.399904 0.290547i
\(679\) −1.61966e7 + 1.17675e7i −1.34818 + 0.979513i
\(680\) 6.98124e6 923439.i 0.578976 0.0765836i
\(681\) 1.04863e6 + 761876.i 0.0866474 + 0.0629530i
\(682\) 1.15805e7 0.953379
\(683\) 9.55425e6 + 6.94157e6i 0.783691 + 0.569385i 0.906084 0.423097i \(-0.139057\pi\)
−0.122394 + 0.992482i \(0.539057\pi\)
\(684\) −219893. + 676762.i −0.0179710 + 0.0553090i
\(685\) 6.52372e6 + 3.53693e6i 0.531213 + 0.288005i
\(686\) 1.32105e6 + 4.06577e6i 0.107179 + 0.329863i
\(687\) −1.71829e6 + 5.28837e6i −0.138901 + 0.427494i
\(688\) −1.13880e6 + 3.50486e6i −0.0917223 + 0.282292i
\(689\) −1.18989e6 3.66210e6i −0.0954901 0.293888i
\(690\) −7.18183e6 3.89373e6i −0.574265 0.311346i
\(691\) 1.90081e6 5.85010e6i 0.151441 0.466088i −0.846342 0.532640i \(-0.821200\pi\)
0.997783 + 0.0665521i \(0.0211999\pi\)
\(692\) 3.30361e6 + 2.40021e6i 0.262255 + 0.190539i
\(693\) 8.36576e6 0.661717
\(694\) −1.28030e7 9.30194e6i −1.00905 0.733119i
\(695\) −1.46992e7 + 1.94433e6i −1.15434 + 0.152689i
\(696\) −247049. + 179492.i −0.0193313 + 0.0140450i
\(697\) −2.67548e7 + 1.94385e7i −2.08603 + 1.51559i
\(698\) −859888. 2.64646e6i −0.0668041 0.205602i
\(699\) −3.75067e6 −0.290346
\(700\) 9.53758e6 2.56808e6i 0.735687 0.198091i
\(701\) −2.27525e7 −1.74878 −0.874389 0.485226i \(-0.838737\pi\)
−0.874389 + 0.485226i \(0.838737\pi\)
\(702\) −638480. 1.96504e6i −0.0488995 0.150497i
\(703\) 3.11315e6 2.26184e6i 0.237581 0.172613i
\(704\) −1.73249e6 + 1.25873e6i −0.131747 + 0.0957195i
\(705\) −2.96086e6 1.60527e6i −0.224360 0.121640i
\(706\) −1.17227e7 8.51701e6i −0.885145 0.643096i
\(707\) 1.03070e7 0.775503
\(708\) 3.99446e6 + 2.90215e6i 0.299485 + 0.217589i
\(709\) 3.08051e6 9.48084e6i 0.230148 0.708323i −0.767580 0.640953i \(-0.778539\pi\)
0.997728 0.0673699i \(-0.0214608\pi\)
\(710\) −1.25757e7 + 1.19485e7i −0.936235 + 0.889542i
\(711\) −1.41598e6 4.35792e6i −0.105047 0.323300i
\(712\) −2.70358e6 + 8.32076e6i −0.199866 + 0.615125i
\(713\) −6.94641e6 + 2.13789e7i −0.511725 + 1.57493i
\(714\) −4.32559e6 1.33128e7i −0.317541 0.977292i
\(715\) 3.76144e6 2.03644e7i 0.275163 1.48972i
\(716\) −3.94779e6 + 1.21501e7i −0.287787 + 0.885718i
\(717\) 873103. + 634346.i 0.0634260 + 0.0460817i
\(718\) −1.02118e7 −0.739248
\(719\) 2.07402e6 + 1.50686e6i 0.149620 + 0.108705i 0.660077 0.751198i \(-0.270524\pi\)
−0.510457 + 0.859903i \(0.670524\pi\)
\(720\) 840350. 798439.i 0.0604128 0.0573998i
\(721\) −8.24069e6 + 5.98721e6i −0.590372 + 0.428930i
\(722\) 7.03724e6 5.11285e6i 0.502411 0.365023i
\(723\) 4.43334e6 + 1.36444e7i 0.315417 + 0.970755i
\(724\) 7.63366e6 0.541235
\(725\) 1.59976e6 430750.i 0.113034 0.0304355i
\(726\) 4.04249e6 0.284647
\(727\) 1.17074e6 + 3.60316e6i 0.0821530 + 0.252841i 0.983693 0.179854i \(-0.0575626\pi\)
−0.901540 + 0.432695i \(0.857563\pi\)
\(728\) 7.24739e6 5.26554e6i 0.506820 0.368226i
\(729\) −429945. + 312373.i −0.0299636 + 0.0217698i
\(730\) −3.75246e6 7.85484e6i −0.260621 0.545544i
\(731\) −2.29232e7 1.66547e7i −1.58665 1.15277i
\(732\) −798593. −0.0550868
\(733\) −2.29938e6 1.67060e6i −0.158071 0.114845i 0.505938 0.862570i \(-0.331146\pi\)
−0.664009 + 0.747725i \(0.731146\pi\)
\(734\) −4.60106e6 + 1.41606e7i −0.315223 + 0.970156i
\(735\) −4.81833e6 1.00860e7i −0.328987 0.688651i
\(736\) −1.28454e6 3.95341e6i −0.0874083 0.269015i
\(737\) 3.25865e6 1.00291e7i 0.220988 0.680131i
\(738\) −1.68220e6 + 5.17728e6i −0.113694 + 0.349914i
\(739\) 255279. + 785667.i 0.0171951 + 0.0529209i 0.959286 0.282437i \(-0.0911428\pi\)
−0.942091 + 0.335358i \(0.891143\pi\)
\(740\) −6.21437e6 + 822002.i −0.417175 + 0.0551815i
\(741\) 1.08200e6 3.33005e6i 0.0723904 0.222795i
\(742\) −3.47401e6 2.52401e6i −0.231644 0.168299i
\(743\) −2.53458e7 −1.68435 −0.842177 0.539202i \(-0.818726\pi\)
−0.842177 + 0.539202i \(0.818726\pi\)
\(744\) −2.58044e6 1.87480e6i −0.170907 0.124172i
\(745\) −1.62134e6 + 8.77789e6i −0.107024 + 0.579428i
\(746\) −2.35847e6 + 1.71353e6i −0.155161 + 0.112731i
\(747\) 4.80143e6 3.48844e6i 0.314825 0.228734i
\(748\) −5.08803e6 1.56594e7i −0.332503 1.02334i
\(749\) 1.34939e7 0.878888
\(750\) −5.80580e6 + 2.41732e6i −0.376885 + 0.156921i
\(751\) 9.92024e6 0.641833 0.320917 0.947107i \(-0.396009\pi\)
0.320917 + 0.947107i \(0.396009\pi\)
\(752\) −529578. 1.62987e6i −0.0341496 0.105102i
\(753\) −3.77385e6 + 2.74186e6i −0.242548 + 0.176221i
\(754\) 1.21562e6 883200.i 0.0778699 0.0565758i
\(755\) 378348. 2.04837e6i 0.0241559 0.130780i
\(756\) −1.86411e6 1.35436e6i −0.118623 0.0861844i
\(757\) 7.72740e6 0.490110 0.245055 0.969509i \(-0.421194\pi\)
0.245055 + 0.969509i \(0.421194\pi\)
\(758\) 4.01458e6 + 2.91676e6i 0.253785 + 0.184386i
\(759\) −5.90260e6 + 1.81663e7i −0.371911 + 1.14462i
\(760\) 1.94743e6 257596.i 0.122301 0.0161772i
\(761\) −3.30177e6 1.01618e7i −0.206674 0.636076i −0.999641 0.0268115i \(-0.991465\pi\)
0.792967 0.609265i \(-0.208535\pi\)
\(762\) −1.83655e6 + 5.65231e6i −0.114582 + 0.352646i
\(763\) 3.66186e6 1.12700e7i 0.227714 0.700832i
\(764\) −3.21609e6 9.89811e6i −0.199340 0.613506i
\(765\) 3.84189e6 + 8.04203e6i 0.237351 + 0.496835i
\(766\) 1.55255e6 4.77826e6i 0.0956035 0.294237i
\(767\) −1.96550e7 1.42802e7i −1.20638 0.876488i
\(768\) 589824. 0.0360844
\(769\) 2.22976e7 + 1.62002e7i 1.35970 + 0.987880i 0.998464 + 0.0554053i \(0.0176451\pi\)
0.361236 + 0.932474i \(0.382355\pi\)
\(770\) −9.95510e6 2.08385e7i −0.605088 1.26660i
\(771\) −6.51904e6 + 4.73636e6i −0.394955 + 0.286952i
\(772\) −3.89844e6 + 2.83239e6i −0.235423 + 0.171045i
\(773\) −9.41382e6 2.89728e7i −0.566653 1.74398i −0.662988 0.748630i \(-0.730712\pi\)
0.0963345 0.995349i \(-0.469288\pi\)
\(774\) −4.66411e6 −0.279844
\(775\) 9.44253e6 + 1.45014e7i 0.564721 + 0.867272i
\(776\) 6.48603e6 0.386656
\(777\) 3.85044e6 + 1.18504e7i 0.228801 + 0.704177i
\(778\) −1.21209e6 + 880634.i −0.0717936 + 0.0521611i
\(779\) −7.46333e6 + 5.42242e6i −0.440645 + 0.320147i
\(780\) −4.13500e6 + 3.92877e6i −0.243354 + 0.231217i
\(781\) 3.28130e7 + 2.38401e7i 1.92495 + 1.39856i
\(782\) 3.19609e7 1.86897
\(783\) −312671. 227169.i −0.0182257 0.0132417i
\(784\) 1.75756e6 5.40922e6i 0.102122 0.314300i
\(785\) 2.81234e6 1.52260e7i 0.162890 0.881882i
\(786\) −2.27458e6 7.00045e6i −0.131324 0.404175i
\(787\) −3.50226e6 + 1.07788e7i −0.201563 + 0.620348i 0.798274 + 0.602295i \(0.205747\pi\)
−0.999837 + 0.0180532i \(0.994253\pi\)
\(788\) 3.21763e6 9.90283e6i 0.184595 0.568125i
\(789\) 4.15842e6 + 1.27983e7i 0.237813 + 0.731914i
\(790\) −9.17030e6 + 8.71295e6i −0.522776 + 0.496704i
\(791\) −1.00327e7 + 3.08776e7i −0.570135 + 1.75470i
\(792\) −2.19268e6 1.59308e6i −0.124212 0.0902452i
\(793\) 3.92953e6 0.221900
\(794\) −8.95331e6 6.50496e6i −0.504002 0.366179i
\(795\) 2.40357e6 + 1.30313e6i 0.134877 + 0.0731257i
\(796\) 2.50357e6 1.81895e6i 0.140048 0.101751i
\(797\) −1.21873e7 + 8.85462e6i −0.679615 + 0.493770i −0.873230 0.487308i \(-0.837979\pi\)
0.193615 + 0.981078i \(0.437979\pi\)
\(798\) −1.20664e6 3.71364e6i −0.0670763 0.206439i
\(799\) 1.31766e7 0.730189
\(800\) −2.98886e6 1.14312e6i −0.165113 0.0631493i
\(801\) −1.10729e7 −0.609791
\(802\) 5.83511e6 + 1.79586e7i 0.320341 + 0.985910i
\(803\) −1.64665e7 + 1.19636e7i −0.901183 + 0.654748i
\(804\) −2.34975e6 + 1.70719e6i −0.128198 + 0.0931413i
\(805\) 4.44417e7 5.87849e6i 2.41713 0.319725i
\(806\) 1.26972e7 + 9.22506e6i 0.688447 + 0.500186i
\(807\) −1.45020e7 −0.783872
\(808\) −2.70149e6 1.96275e6i −0.145571 0.105763i
\(809\) −9.50281e6 + 2.92467e7i −0.510483 + 1.57110i 0.280871 + 0.959745i \(0.409377\pi\)
−0.791354 + 0.611358i \(0.790623\pi\)
\(810\) 1.28973e6 + 699244.i 0.0690693 + 0.0374469i
\(811\) −6.72384e6 2.06938e7i −0.358976 1.10481i −0.953668 0.300860i \(-0.902726\pi\)
0.594693 0.803953i \(-0.297274\pi\)
\(812\) 517812. 1.59366e6i 0.0275602 0.0848215i
\(813\) −5.50740e6 + 1.69500e7i −0.292227 + 0.899382i
\(814\) 4.52913e6 + 1.39392e7i 0.239582 + 0.737356i
\(815\) −2.77145e7 1.50258e7i −1.46155 0.792400i
\(816\) −1.40139e6 + 4.31303e6i −0.0736773 + 0.226755i
\(817\) −6.39449e6 4.64587e6i −0.335159 0.243507i
\(818\) −2.29489e7 −1.19916
\(819\) 9.17248e6 + 6.66420e6i 0.477834 + 0.347167i
\(820\) 1.48980e7 1.97063e6i 0.773739 0.102346i
\(821\) 2.19663e7 1.59595e7i 1.13736 0.826343i 0.150614 0.988593i \(-0.451875\pi\)
0.986750 + 0.162249i \(0.0518748\pi\)
\(822\) −3.86623e6 + 2.80898e6i −0.199576 + 0.145001i
\(823\) −6.88480e6 2.11892e7i −0.354317 1.09047i −0.956405 0.292045i \(-0.905664\pi\)
0.602088 0.798430i \(-0.294336\pi\)
\(824\) 3.30004e6 0.169317
\(825\) 8.02363e6 + 1.23223e7i 0.410427 + 0.630315i
\(826\) −2.70935e7 −1.38170
\(827\) −3.08700e6 9.50080e6i −0.156954 0.483055i 0.841400 0.540413i \(-0.181732\pi\)
−0.998354 + 0.0573587i \(0.981732\pi\)
\(828\) 4.25626e6 3.09235e6i 0.215751 0.156752i
\(829\) −7.49293e6 + 5.44393e6i −0.378674 + 0.275123i −0.760798 0.648988i \(-0.775192\pi\)
0.382125 + 0.924111i \(0.375192\pi\)
\(830\) −1.44031e7 7.80884e6i −0.725705 0.393451i
\(831\) 2.07094e6 + 1.50463e6i 0.104032 + 0.0755835i
\(832\) −2.90227e6 −0.145355
\(833\) 3.53786e7 + 2.57040e7i 1.76656 + 1.28348i
\(834\) 2.95068e6 9.08125e6i 0.146895 0.452096i
\(835\) −113200. + 107554.i −0.00561863 + 0.00533841i
\(836\) −1.41932e6 4.36822e6i −0.0702368 0.216167i
\(837\) 1.24745e6 3.83926e6i 0.0615474 0.189423i
\(838\) 4.73370e6 1.45688e7i 0.232858 0.716663i
\(839\) −1.46070e6 4.49557e6i −0.0716401 0.220485i 0.908825 0.417177i \(-0.136980\pi\)
−0.980465 + 0.196691i \(0.936980\pi\)
\(840\) −1.15535e6 + 6.25503e6i −0.0564956 + 0.305866i
\(841\) −6.25144e6 + 1.92400e7i −0.304783 + 0.938024i
\(842\) 4.05728e6 + 2.94779e6i 0.197222 + 0.143290i
\(843\) 2.01117e7 0.974718
\(844\) 5.12235e6 + 3.72160e6i 0.247522 + 0.179835i
\(845\) 5.29945e6 5.03515e6i 0.255322 0.242589i
\(846\) 1.75473e6 1.27489e6i 0.0842917 0.0612415i
\(847\) −1.79461e7 + 1.30386e7i −0.859532 + 0.624487i
\(848\) 429901. + 1.32310e6i 0.0205295 + 0.0631834i
\(849\) 2.45261e6 0.116778
\(850\) 1.54604e7 1.91397e7i 0.733960 0.908634i
\(851\) −2.84501e7 −1.34667
\(852\) −3.45208e6 1.06244e7i −0.162923 0.501424i
\(853\) 2.12613e7 1.54472e7i 1.00050 0.726906i 0.0383050 0.999266i \(-0.487804\pi\)
0.962195 + 0.272360i \(0.0878042\pi\)
\(854\) 3.54525e6 2.57578e6i 0.166342 0.120855i
\(855\) 1.07170e6 + 2.24334e6i 0.0501371 + 0.104950i
\(856\) −3.53679e6 2.56963e6i −0.164977 0.119863i
\(857\) 4.14445e7 1.92759 0.963795 0.266643i \(-0.0859144\pi\)
0.963795 + 0.266643i \(0.0859144\pi\)
\(858\) 1.07892e7 + 7.83884e6i 0.500349 + 0.363525i
\(859\) 1.19934e7 3.69117e7i 0.554572 1.70680i −0.142500 0.989795i \(-0.545514\pi\)
0.697072 0.717001i \(-0.254486\pi\)
\(860\) 5.55021e6 + 1.16180e7i 0.255896 + 0.535654i
\(861\) −9.23086e6 2.84097e7i −0.424360 1.30605i
\(862\) −7.59642e6 + 2.33794e7i −0.348210 + 1.07168i
\(863\) −5.75723e6 + 1.77189e7i −0.263140 + 0.809861i 0.728976 + 0.684539i \(0.239996\pi\)
−0.992116 + 0.125322i \(0.960004\pi\)
\(864\) 230680. + 709960.i 0.0105130 + 0.0323556i
\(865\) 1.41439e7 1.87088e6i 0.642732 0.0850169i
\(866\) 9.15561e6 2.81781e7i 0.414851 1.27678i
\(867\) −1.78709e7 1.29839e7i −0.807416 0.586622i
\(868\) 1.75025e7 0.788498
\(869\) 2.39276e7 + 1.73844e7i 1.07486 + 0.780928i
\(870\) −193789. + 1.04917e6i −0.00868022 + 0.0469946i
\(871\) 1.15621e7 8.40035e6i 0.516406 0.375191i
\(872\) −3.10592e6 + 2.25658e6i −0.138324 + 0.100499i
\(873\) 2.53669e6 + 7.80711e6i 0.112650 + 0.346701i
\(874\) 8.91558e6 0.394794
\(875\) 1.79773e7 2.94574e7i 0.793788 1.30069i
\(876\) 5.60600e6 0.246827
\(877\) −8.89454e6 2.73746e7i −0.390503 1.20185i −0.932409 0.361406i \(-0.882297\pi\)
0.541906 0.840439i \(-0.317703\pi\)
\(878\) −1.10090e7 + 7.99848e6i −0.481959 + 0.350164i
\(879\) −7.59412e6 + 5.51745e6i −0.331517 + 0.240861i
\(880\) −1.35899e6 + 7.35756e6i −0.0591576 + 0.320278i
\(881\) 1.56908e7 + 1.14000e7i 0.681089 + 0.494840i 0.873719 0.486431i \(-0.161702\pi\)
−0.192630 + 0.981272i \(0.561702\pi\)
\(882\) 7.19836e6 0.311575
\(883\) 2.75683e7 + 2.00295e7i 1.18989 + 0.864507i 0.993253 0.115969i \(-0.0369973\pi\)
0.196639 + 0.980476i \(0.436997\pi\)
\(884\) 6.89563e6 2.12226e7i 0.296786 0.913413i
\(885\) 1.71017e7 2.26212e6i 0.733975 0.0970860i
\(886\) −4.51637e6 1.39000e7i −0.193288 0.594880i
\(887\) −1.69166e6 + 5.20641e6i −0.0721947 + 0.222192i −0.980643 0.195805i \(-0.937268\pi\)
0.908448 + 0.417998i \(0.137268\pi\)
\(888\) 1.24745e6 3.83926e6i 0.0530874 0.163386i
\(889\) −1.00778e7 3.10163e7i −0.427673 1.31624i
\(890\) 1.31766e7 + 2.75819e7i 0.557606 + 1.16721i
\(891\) 1.06000e6 3.26234e6i 0.0447313 0.137669i
\(892\) −1.39501e7 1.01353e7i −0.587036 0.426507i
\(893\) 3.67563e6 0.154242
\(894\) −4.65061e6 3.37887e6i −0.194610 0.141393i
\(895\) 1.92405e7 + 4.02753e7i 0.802897 + 1.68066i
\(896\) −2.61845e6 + 1.90242e6i −0.108962 + 0.0791654i
\(897\) −2.09432e7 + 1.52161e7i −0.869084 + 0.631426i
\(898\) 5.52306e6 + 1.69982e7i 0.228554 + 0.703417i
\(899\) 2.93573e6 0.121148
\(900\) 207017. 4.04471e6i 0.00851921 0.166449i
\(901\) −1.06965e7 −0.438964
\(902\) −1.08579e7 3.34172e7i −0.444355 1.36758i
\(903\) 2.07057e7 1.50436e7i 0.845029 0.613949i
\(904\) 8.50957e6 6.18257e6i 0.346327 0.251621i
\(905\) 1.93352e7 1.83709e7i 0.784741 0.745603i
\(906\) 1.08525e6 + 788477.i 0.0439246 + 0.0319131i
\(907\) 2.51321e7 1.01441 0.507203 0.861827i \(-0.330680\pi\)
0.507203 + 0.861827i \(0.330680\pi\)
\(908\) 1.86423e6 + 1.35445e6i 0.0750388 + 0.0545189i
\(909\) 1.30597e6 4.01936e6i 0.0524231 0.161342i
\(910\) 5.68496e6 3.07783e7i 0.227575 1.23209i
\(911\) 3.01546e6 + 9.28063e6i 0.120381 + 0.370494i 0.993031 0.117851i \(-0.0376006\pi\)
−0.872650 + 0.488346i \(0.837601\pi\)
\(912\) −390921. + 1.20313e6i −0.0155633 + 0.0478990i
\(913\) −1.18376e7 + 3.64324e7i −0.469988 + 1.44647i
\(914\) 834285. + 2.56767e6i 0.0330331 + 0.101665i
\(915\) −2.02274e6 + 1.92186e6i −0.0798707 + 0.0758873i
\(916\) −3.05475e6 + 9.40154e6i −0.120292 + 0.370220i
\(917\) 3.26769e7 + 2.37412e7i 1.28327 + 0.932350i
\(918\) −5.73960e6 −0.224789
\(919\) −2.70968e7 1.96869e7i −1.05835 0.768935i −0.0845660 0.996418i \(-0.526950\pi\)
−0.973782 + 0.227483i \(0.926950\pi\)
\(920\) −1.27677e7 6.92219e6i −0.497328 0.269634i
\(921\) −1.68043e7 + 1.22090e7i −0.652786 + 0.474277i
\(922\) −7.04597e6 + 5.11920e6i −0.272969 + 0.198324i
\(923\) 1.69862e7 + 5.22780e7i 0.656283 + 2.01983i
\(924\) 1.48725e7 0.573064
\(925\) −1.37621e7 + 1.70373e7i −0.528847 + 0.654706i
\(926\) −602851. −0.0231038
\(927\) 1.29064e6 + 3.97219e6i 0.0493296 + 0.151821i
\(928\) −439198. + 319096.i −0.0167414 + 0.0121633i
\(929\) −1.23035e7 + 8.93902e6i −0.467724 + 0.339821i −0.796554 0.604568i \(-0.793346\pi\)
0.328830 + 0.944389i \(0.393346\pi\)
\(930\) −1.10478e7 + 1.46133e6i −0.418858 + 0.0554042i
\(931\) 9.86894e6 + 7.17021e6i 0.373161 + 0.271117i
\(932\) −6.66785e6 −0.251447
\(933\) −1.93650e7 1.40695e7i −0.728306 0.529145i
\(934\) 2.52630e6 7.77515e6i 0.0947584 0.291636i
\(935\) −5.05726e7 2.74187e7i −1.89185 1.02569i
\(936\) −1.13508e6 3.49340e6i −0.0423482 0.130334i
\(937\) 8.78445e6 2.70357e7i 0.326863 1.00598i −0.643730 0.765253i \(-0.722614\pi\)
0.970593 0.240727i \(-0.0773860\pi\)
\(938\) 4.92505e6 1.51577e7i 0.182769 0.562506i
\(939\) 258845. + 796643.i 0.00958023 + 0.0294849i
\(940\) −5.26375e6 2.85382e6i −0.194301 0.105343i
\(941\) 2.03561e6 6.26496e6i 0.0749411 0.230645i −0.906568 0.422059i \(-0.861307\pi\)
0.981509 + 0.191414i \(0.0613074\pi\)
\(942\) 8.06686e6 + 5.86092e6i 0.296195 + 0.215198i
\(943\) 6.82049e7 2.49768
\(944\) 7.10127e6 + 5.15937e6i 0.259362 + 0.188437i
\(945\) −7.98092e6 + 1.05567e6i −0.290719 + 0.0384546i
\(946\) 2.43554e7 1.76952e7i 0.884845 0.642877i
\(947\) −1.24664e7 + 9.05738e6i −0.451717 + 0.328192i −0.790273 0.612754i \(-0.790061\pi\)
0.338556 + 0.940946i \(0.390061\pi\)
\(948\) −2.51729e6 7.74742e6i −0.0909730 0.279986i
\(949\) −2.75847e7 −0.994266
\(950\) 4.31271e6 5.33908e6i 0.155039 0.191936i
\(951\) −1.10874e7 −0.397537
\(952\) −7.68995e6 2.36672e7i −0.274999 0.846359i
\(953\) 9.58409e6 6.96325e6i 0.341837 0.248359i −0.403600 0.914936i \(-0.632241\pi\)
0.745436 + 0.666577i \(0.232241\pi\)
\(954\) −1.42446e6 + 1.03493e6i −0.0506732 + 0.0368162i
\(955\) −3.19664e7 1.73310e7i −1.13419 0.614917i
\(956\) 1.55218e6 + 1.12773e6i 0.0549285 + 0.0399079i
\(957\) 2.49459e6 0.0880479
\(958\) −3.41578e6 2.48171e6i −0.120248 0.0873649i
\(959\) 8.10358e6 2.49403e7i 0.284532 0.875698i
\(960\) 1.49396e6 1.41945e6i 0.0523190 0.0497097i
\(961\) 628753. + 1.93510e6i 0.0219620 + 0.0675920i
\(962\) −6.13816e6 + 1.88913e7i −0.213846 + 0.658150i
\(963\) 1.70977e6 5.26214e6i 0.0594118 0.182851i
\(964\) 7.88150e6 + 2.42568e7i 0.273159 + 0.840698i
\(965\) −3.05800e6 + 1.65559e7i −0.105711 + 0.572316i
\(966\) −8.92107e6 + 2.74562e7i −0.307591 + 0.946668i
\(967\) −2.77102e7 2.01326e7i −0.952956 0.692363i −0.00145172 0.999999i \(-0.500462\pi\)
−0.951504 + 0.307636i \(0.900462\pi\)
\(968\) 7.18665e6 0.246512
\(969\) −7.86898e6 5.71715e6i −0.269221 0.195601i
\(970\) 1.64284e7 1.56090e7i 0.560615 0.532656i
\(971\) 3.08919e6 2.24443e6i 0.105147 0.0763937i −0.533969 0.845504i \(-0.679300\pi\)
0.639116 + 0.769110i \(0.279300\pi\)
\(972\) −764346. + 555330.i −0.0259492 + 0.0188532i
\(973\) 1.61915e7 + 4.98322e7i 0.548282 + 1.68744i
\(974\) 2.16009e6 0.0729581
\(975\) −1.01864e6 + 1.99022e7i −0.0343170 + 0.670487i
\(976\) −1.41972e6 −0.0477066
\(977\) −2.83455e6 8.72386e6i −0.0950054 0.292397i 0.892250 0.451542i \(-0.149126\pi\)
−0.987255 + 0.159146i \(0.949126\pi\)
\(978\) 1.64248e7 1.19333e7i 0.549102 0.398946i
\(979\) 5.78213e7 4.20097e7i 1.92811 1.40085i
\(980\) −8.56592e6 1.79306e7i −0.284911 0.596389i
\(981\) −3.93093e6 2.85599e6i −0.130413 0.0947509i
\(982\) −2.10096e7 −0.695247
\(983\) −1.65336e7 1.20123e7i −0.545736 0.396501i 0.280475 0.959861i \(-0.409508\pi\)
−0.826211 + 0.563361i \(0.809508\pi\)
\(984\) −2.99058e6 + 9.20406e6i −0.0984617 + 0.303034i
\(985\) −1.56819e7 3.28261e7i −0.515001 1.07803i
\(986\) −1.28985e6 3.96975e6i −0.0422520 0.130038i
\(987\) −3.67790e6 + 1.13194e7i −0.120173 + 0.369854i
\(988\) 1.92355e6 5.92009e6i 0.0626920 0.192946i
\(989\) 1.80581e7 + 5.55770e7i 0.587057 + 1.80678i
\(990\) −9.38765e6 + 1.24175e6i −0.304417 + 0.0402666i
\(991\) −4.57772e6 + 1.40888e7i −0.148069 + 0.455711i −0.997393 0.0721618i \(-0.977010\pi\)
0.849323 + 0.527873i \(0.177010\pi\)
\(992\) −4.58744e6 3.33297e6i −0.148010 0.107536i
\(993\) −1.81877e7 −0.585336
\(994\) 4.95929e7 + 3.60314e7i 1.59204 + 1.15668i
\(995\) 1.96384e6 1.06322e7i 0.0628852 0.340459i
\(996\) 8.53587e6 6.20167e6i 0.272646 0.198089i
\(997\) 3.26641e7 2.37319e7i 1.04072 0.756126i 0.0702924 0.997526i \(-0.477607\pi\)
0.970426 + 0.241401i \(0.0776068\pi\)
\(998\) 7.89809e6 + 2.43078e7i 0.251013 + 0.772538i
\(999\) 5.10912e6 0.161969
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.b.31.3 24
25.21 even 5 inner 150.6.g.b.121.3 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.6.g.b.31.3 24 1.1 even 1 trivial
150.6.g.b.121.3 yes 24 25.21 even 5 inner