Properties

Label 147.6.e.o.79.1
Level $147$
Weight $6$
Character 147.79
Analytic conductor $23.576$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,6,Mod(67,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, base_ring=CyclotomicField(6))
 
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("147.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not 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: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(-4.61193 + 7.98809i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.6.e.o.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-5.11193 + 8.85412i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(11.8764 - 20.5705i) q^{5} -92.0147 q^{6} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(-5.11193 + 8.85412i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(11.8764 - 20.5705i) q^{5} -92.0147 q^{6} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +(121.423 + 210.310i) q^{10} +(-232.763 - 403.157i) q^{11} +(326.372 - 565.293i) q^{12} +1019.30 q^{13} +213.775 q^{15} +(-957.660 + 1658.72i) q^{16} +(280.878 + 486.496i) q^{17} +(-414.066 - 717.183i) q^{18} +(-693.789 + 1201.68i) q^{19} -1722.72 q^{20} +4759.47 q^{22} +(-2056.81 + 3562.50i) q^{23} +(1864.55 + 3229.49i) q^{24} +(1280.40 + 2217.72i) q^{25} +(-5210.59 + 9025.00i) q^{26} -729.000 q^{27} -2381.37 q^{29} +(-1092.80 + 1892.79i) q^{30} +(1475.33 + 2555.34i) q^{31} +(-3161.47 - 5475.84i) q^{32} +(2094.87 - 3628.42i) q^{33} -5743.32 q^{34} +5874.70 q^{36} +(4954.48 - 8581.40i) q^{37} +(-7093.20 - 12285.8i) q^{38} +(4586.85 + 7944.66i) q^{39} +(4920.92 - 8523.28i) q^{40} +4477.13 q^{41} +5181.48 q^{43} +(-16881.6 + 29239.9i) q^{44} +(961.989 + 1666.21i) q^{45} +(-21028.5 - 36422.5i) q^{46} +(-1560.80 + 2703.38i) q^{47} -17237.9 q^{48} -26181.3 q^{50} +(-2527.91 + 4378.46i) q^{51} +(-36963.5 - 64022.6i) q^{52} +(-570.499 - 988.133i) q^{53} +(3726.59 - 6454.65i) q^{54} -11057.6 q^{55} -12488.2 q^{57} +(12173.4 - 21085.0i) q^{58} +(13748.5 + 23813.2i) q^{59} +(-7752.26 - 13427.3i) q^{60} +(-10551.8 + 18276.2i) q^{61} -30167.1 q^{62} +3354.67 q^{64} +(12105.6 - 20967.6i) q^{65} +(21417.6 + 37096.4i) q^{66} +(27794.2 + 48141.0i) q^{67} +(20371.3 - 35284.2i) q^{68} -37022.6 q^{69} -6076.90 q^{71} +(-16780.9 + 29065.4i) q^{72} +(-8389.82 - 14531.6i) q^{73} +(50653.8 + 87735.0i) q^{74} +(-11523.6 + 19959.5i) q^{75} +100637. q^{76} -93790.5 q^{78} +(2422.63 - 4196.12i) q^{79} +(22747.1 + 39399.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-22886.7 + 39641.0i) q^{82} -60145.4 q^{83} +13343.3 q^{85} +(-26487.4 + 45877.5i) q^{86} +(-10716.2 - 18561.0i) q^{87} +(-96443.9 - 167046. i) q^{88} +(-31248.7 + 54124.4i) q^{89} -19670.5 q^{90} +298349. q^{92} +(-13277.9 + 22998.1i) q^{93} +(-15957.4 - 27639.0i) q^{94} +(16479.4 + 28543.2i) q^{95} +(28453.3 - 49282.5i) q^{96} +63653.8 q^{97} +37707.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 3 q^{2} + 36 q^{3} - 69 q^{4} - 54 q^{6} + 246 q^{8} - 324 q^{9} + 283 q^{10} - 402 q^{11} + 621 q^{12} - 924 q^{13} - 3273 q^{16} + 276 q^{17} - 243 q^{18} + 510 q^{19} - 9438 q^{20} + 2750 q^{22} - 6900 q^{23} + 1107 q^{24} - 2814 q^{25} - 15138 q^{26} - 5832 q^{27} + 1080 q^{29} - 2547 q^{30} - 6410 q^{31} - 15519 q^{32} + 3618 q^{33} - 42288 q^{34} + 11178 q^{36} - 15250 q^{37} - 41250 q^{38} - 4158 q^{39} - 8547 q^{40} - 8616 q^{41} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} - 15060 q^{47} - 58914 q^{48} - 14604 q^{50} - 2484 q^{51} - 47476 q^{52} - 13692 q^{53} + 2187 q^{54} - 146248 q^{55} + 9180 q^{57} - 52309 q^{58} + 34830 q^{59} - 42471 q^{60} - 5364 q^{61} - 32058 q^{62} - 146974 q^{64} - 66864 q^{65} + 12375 q^{66} + 5994 q^{67} - 58272 q^{68} - 124200 q^{69} + 178536 q^{71} - 9963 q^{72} + 59638 q^{73} + 185442 q^{74} + 25326 q^{75} - 42616 q^{76} - 272484 q^{78} + 44062 q^{79} - 33381 q^{80} - 26244 q^{81} + 57596 q^{82} + 416892 q^{83} + 72648 q^{85} + 136968 q^{86} + 4860 q^{87} - 87597 q^{88} - 77520 q^{89} - 45846 q^{90} + 316512 q^{92} + 57690 q^{93} - 73722 q^{94} + 221376 q^{95} + 139671 q^{96} + 377260 q^{97} + 65124 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.11193 + 8.85412i −0.903669 + 1.56520i −0.0809760 + 0.996716i \(0.525804\pi\)
−0.822693 + 0.568485i \(0.807530\pi\)
\(3\) 4.50000 + 7.79423i 0.288675 + 0.500000i
\(4\) −36.2636 62.8104i −1.13324 1.96282i
\(5\) 11.8764 20.5705i 0.212452 0.367977i −0.740030 0.672574i \(-0.765189\pi\)
0.952481 + 0.304597i \(0.0985219\pi\)
\(6\) −92.0147 −1.04347
\(7\) 0 0
\(8\) 414.344 2.28895
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 121.423 + 210.310i 0.383972 + 0.665059i
\(11\) −232.763 403.157i −0.580006 1.00460i −0.995478 0.0949934i \(-0.969717\pi\)
0.415472 0.909606i \(-0.363616\pi\)
\(12\) 326.372 565.293i 0.654275 1.13324i
\(13\) 1019.30 1.67280 0.836399 0.548121i \(-0.184657\pi\)
0.836399 + 0.548121i \(0.184657\pi\)
\(14\) 0 0
\(15\) 213.775 0.245318
\(16\) −957.660 + 1658.72i −0.935215 + 1.61984i
\(17\) 280.878 + 486.496i 0.235720 + 0.408279i 0.959482 0.281771i \(-0.0909219\pi\)
−0.723762 + 0.690050i \(0.757589\pi\)
\(18\) −414.066 717.183i −0.301223 0.521734i
\(19\) −693.789 + 1201.68i −0.440903 + 0.763667i −0.997757 0.0669438i \(-0.978675\pi\)
0.556853 + 0.830611i \(0.312009\pi\)
\(20\) −1722.72 −0.963032
\(21\) 0 0
\(22\) 4759.47 2.09653
\(23\) −2056.81 + 3562.50i −0.810727 + 1.40422i 0.101630 + 0.994822i \(0.467594\pi\)
−0.912356 + 0.409397i \(0.865739\pi\)
\(24\) 1864.55 + 3229.49i 0.660762 + 1.14447i
\(25\) 1280.40 + 2217.72i 0.409729 + 0.709671i
\(26\) −5210.59 + 9025.00i −1.51166 + 2.61827i
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) −2381.37 −0.525814 −0.262907 0.964821i \(-0.584681\pi\)
−0.262907 + 0.964821i \(0.584681\pi\)
\(30\) −1092.80 + 1892.79i −0.221686 + 0.383972i
\(31\) 1475.33 + 2555.34i 0.275730 + 0.477579i 0.970319 0.241828i \(-0.0777471\pi\)
−0.694589 + 0.719407i \(0.744414\pi\)
\(32\) −3161.47 5475.84i −0.545776 0.945313i
\(33\) 2094.87 3628.42i 0.334866 0.580006i
\(34\) −5743.32 −0.852051
\(35\) 0 0
\(36\) 5874.70 0.755491
\(37\) 4954.48 8581.40i 0.594968 1.03051i −0.398584 0.917132i \(-0.630498\pi\)
0.993551 0.113382i \(-0.0361685\pi\)
\(38\) −7093.20 12285.8i −0.796862 1.38021i
\(39\) 4586.85 + 7944.66i 0.482895 + 0.836399i
\(40\) 4920.92 8523.28i 0.486291 0.842280i
\(41\) 4477.13 0.415949 0.207974 0.978134i \(-0.433313\pi\)
0.207974 + 0.978134i \(0.433313\pi\)
\(42\) 0 0
\(43\) 5181.48 0.427349 0.213675 0.976905i \(-0.431457\pi\)
0.213675 + 0.976905i \(0.431457\pi\)
\(44\) −16881.6 + 29239.9i −1.31457 + 2.27690i
\(45\) 961.989 + 1666.21i 0.0708172 + 0.122659i
\(46\) −21028.5 36422.5i −1.46526 2.53790i
\(47\) −1560.80 + 2703.38i −0.103063 + 0.178510i −0.912945 0.408082i \(-0.866198\pi\)
0.809882 + 0.586592i \(0.199531\pi\)
\(48\) −17237.9 −1.07989
\(49\) 0 0
\(50\) −26181.3 −1.48104
\(51\) −2527.91 + 4378.46i −0.136093 + 0.235720i
\(52\) −36963.5 64022.6i −1.89568 3.28341i
\(53\) −570.499 988.133i −0.0278975 0.0483198i 0.851740 0.523965i \(-0.175548\pi\)
−0.879637 + 0.475645i \(0.842215\pi\)
\(54\) 3726.59 6454.65i 0.173911 0.301223i
\(55\) −11057.6 −0.492893
\(56\) 0 0
\(57\) −12488.2 −0.509111
\(58\) 12173.4 21085.0i 0.475162 0.823005i
\(59\) 13748.5 + 23813.2i 0.514194 + 0.890610i 0.999864 + 0.0164678i \(0.00524209\pi\)
−0.485671 + 0.874142i \(0.661425\pi\)
\(60\) −7752.26 13427.3i −0.278003 0.481516i
\(61\) −10551.8 + 18276.2i −0.363078 + 0.628870i −0.988466 0.151444i \(-0.951608\pi\)
0.625387 + 0.780314i \(0.284941\pi\)
\(62\) −30167.1 −0.996676
\(63\) 0 0
\(64\) 3354.67 0.102376
\(65\) 12105.6 20967.6i 0.355389 0.615551i
\(66\) 21417.6 + 37096.4i 0.605217 + 1.04827i
\(67\) 27794.2 + 48141.0i 0.756428 + 1.31017i 0.944661 + 0.328047i \(0.106390\pi\)
−0.188234 + 0.982124i \(0.560276\pi\)
\(68\) 20371.3 35284.2i 0.534253 0.925353i
\(69\) −37022.6 −0.936146
\(70\) 0 0
\(71\) −6076.90 −0.143066 −0.0715330 0.997438i \(-0.522789\pi\)
−0.0715330 + 0.997438i \(0.522789\pi\)
\(72\) −16780.9 + 29065.4i −0.381491 + 0.660762i
\(73\) −8389.82 14531.6i −0.184266 0.319158i 0.759063 0.651017i \(-0.225657\pi\)
−0.943329 + 0.331859i \(0.892324\pi\)
\(74\) 50653.8 + 87735.0i 1.07531 + 1.86249i
\(75\) −11523.6 + 19959.5i −0.236557 + 0.409729i
\(76\) 100637. 1.99859
\(77\) 0 0
\(78\) −93790.5 −1.74551
\(79\) 2422.63 4196.12i 0.0436737 0.0756450i −0.843362 0.537345i \(-0.819427\pi\)
0.887036 + 0.461700i \(0.152760\pi\)
\(80\) 22747.1 + 39399.2i 0.397376 + 0.688275i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) −22886.7 + 39641.0i −0.375880 + 0.651043i
\(83\) −60145.4 −0.958313 −0.479156 0.877730i \(-0.659057\pi\)
−0.479156 + 0.877730i \(0.659057\pi\)
\(84\) 0 0
\(85\) 13343.3 0.200316
\(86\) −26487.4 + 45877.5i −0.386183 + 0.668888i
\(87\) −10716.2 18561.0i −0.151790 0.262907i
\(88\) −96443.9 167046.i −1.32760 2.29947i
\(89\) −31248.7 + 54124.4i −0.418174 + 0.724299i −0.995756 0.0920340i \(-0.970663\pi\)
0.577582 + 0.816333i \(0.303996\pi\)
\(90\) −19670.5 −0.255981
\(91\) 0 0
\(92\) 298349. 3.67498
\(93\) −13277.9 + 22998.1i −0.159193 + 0.275730i
\(94\) −15957.4 27639.0i −0.186269 0.322628i
\(95\) 16479.4 + 28543.2i 0.187341 + 0.324485i
\(96\) 28453.3 49282.5i 0.315104 0.545776i
\(97\) 63653.8 0.686903 0.343451 0.939170i \(-0.388404\pi\)
0.343451 + 0.939170i \(0.388404\pi\)
\(98\) 0 0
\(99\) 37707.6 0.386670
\(100\) 92863.9 160845.i 0.928639 1.60845i
\(101\) 92311.4 + 159888.i 0.900434 + 1.55960i 0.826932 + 0.562302i \(0.190084\pi\)
0.0735022 + 0.997295i \(0.476582\pi\)
\(102\) −25844.9 44764.7i −0.245966 0.426026i
\(103\) 26021.9 45071.2i 0.241683 0.418607i −0.719511 0.694481i \(-0.755634\pi\)
0.961194 + 0.275874i \(0.0889674\pi\)
\(104\) 422341. 3.82895
\(105\) 0 0
\(106\) 11665.4 0.100840
\(107\) −24088.9 + 41723.2i −0.203403 + 0.352304i −0.949623 0.313395i \(-0.898534\pi\)
0.746220 + 0.665700i \(0.231867\pi\)
\(108\) 26436.2 + 45788.8i 0.218092 + 0.377746i
\(109\) 18217.8 + 31554.1i 0.146869 + 0.254384i 0.930069 0.367386i \(-0.119747\pi\)
−0.783200 + 0.621770i \(0.786414\pi\)
\(110\) 56525.4 97904.9i 0.445412 0.771476i
\(111\) 89180.6 0.687010
\(112\) 0 0
\(113\) −96711.1 −0.712492 −0.356246 0.934392i \(-0.615944\pi\)
−0.356246 + 0.934392i \(0.615944\pi\)
\(114\) 63838.8 110572.i 0.460068 0.796862i
\(115\) 48855.0 + 84619.4i 0.344480 + 0.596658i
\(116\) 86357.1 + 149575.i 0.595872 + 1.03208i
\(117\) −41281.6 + 71501.9i −0.278800 + 0.482895i
\(118\) −281126. −1.85864
\(119\) 0 0
\(120\) 88576.5 0.561520
\(121\) −27831.7 + 48206.0i −0.172813 + 0.299321i
\(122\) −107880. 186853.i −0.656206 1.13658i
\(123\) 20147.1 + 34895.7i 0.120074 + 0.207974i
\(124\) 107001. 185332.i 0.624935 1.08242i
\(125\) 135054. 0.773093
\(126\) 0 0
\(127\) 23322.9 0.128314 0.0641568 0.997940i \(-0.479564\pi\)
0.0641568 + 0.997940i \(0.479564\pi\)
\(128\) 84018.4 145524.i 0.453262 0.785073i
\(129\) 23316.7 + 40385.7i 0.123365 + 0.213675i
\(130\) 123766. + 214369.i 0.642308 + 1.11251i
\(131\) −169379. + 293373.i −0.862345 + 1.49363i 0.00731374 + 0.999973i \(0.497672\pi\)
−0.869659 + 0.493653i \(0.835661\pi\)
\(132\) −303870. −1.51793
\(133\) 0 0
\(134\) −568328. −2.73424
\(135\) −8657.90 + 14995.9i −0.0408863 + 0.0708172i
\(136\) 116380. + 201576.i 0.539550 + 0.934528i
\(137\) 31438.4 + 54452.9i 0.143106 + 0.247867i 0.928665 0.370920i \(-0.120958\pi\)
−0.785559 + 0.618787i \(0.787624\pi\)
\(138\) 189257. 327802.i 0.845967 1.46526i
\(139\) −211927. −0.930356 −0.465178 0.885217i \(-0.654010\pi\)
−0.465178 + 0.885217i \(0.654010\pi\)
\(140\) 0 0
\(141\) −28094.3 −0.119007
\(142\) 31064.7 53805.6i 0.129284 0.223927i
\(143\) −237255. 410938.i −0.970233 1.68049i
\(144\) −77570.5 134356.i −0.311738 0.539947i
\(145\) −28282.2 + 48986.1i −0.111710 + 0.193488i
\(146\) 171553. 0.666062
\(147\) 0 0
\(148\) −718668. −2.69696
\(149\) −70136.4 + 121480.i −0.258808 + 0.448269i −0.965923 0.258830i \(-0.916663\pi\)
0.707115 + 0.707099i \(0.249996\pi\)
\(150\) −117816. 204063.i −0.427538 0.740518i
\(151\) 81995.7 + 142021.i 0.292650 + 0.506885i 0.974436 0.224667i \(-0.0721296\pi\)
−0.681785 + 0.731552i \(0.738796\pi\)
\(152\) −287467. + 497908.i −1.00920 + 1.74799i
\(153\) −45502.3 −0.157147
\(154\) 0 0
\(155\) 70086.4 0.234317
\(156\) 332671. 576203.i 1.09447 1.89568i
\(157\) 278272. + 481981.i 0.900990 + 1.56056i 0.826212 + 0.563360i \(0.190492\pi\)
0.0747781 + 0.997200i \(0.476175\pi\)
\(158\) 24768.6 + 42900.5i 0.0789331 + 0.136716i
\(159\) 5134.49 8893.19i 0.0161066 0.0278975i
\(160\) −150188. −0.463804
\(161\) 0 0
\(162\) 67078.7 0.200815
\(163\) 9863.32 17083.8i 0.0290773 0.0503634i −0.851121 0.524970i \(-0.824076\pi\)
0.880198 + 0.474607i \(0.157410\pi\)
\(164\) −162357. 281210.i −0.471368 0.816434i
\(165\) −49759.0 86185.1i −0.142286 0.246446i
\(166\) 307459. 532534.i 0.865998 1.49995i
\(167\) −94776.2 −0.262971 −0.131486 0.991318i \(-0.541975\pi\)
−0.131486 + 0.991318i \(0.541975\pi\)
\(168\) 0 0
\(169\) 667679. 1.79825
\(170\) −68210.0 + 118143.i −0.181020 + 0.313535i
\(171\) −56196.9 97335.9i −0.146968 0.254556i
\(172\) −187899. 325451.i −0.484288 0.838812i
\(173\) 169420. 293445.i 0.430379 0.745437i −0.566527 0.824043i \(-0.691713\pi\)
0.996906 + 0.0786055i \(0.0250468\pi\)
\(174\) 219121. 0.548670
\(175\) 0 0
\(176\) 891631. 2.16972
\(177\) −123737. + 214319.i −0.296870 + 0.514194i
\(178\) −319482. 553360.i −0.755782 1.30905i
\(179\) −388096. 672203.i −0.905330 1.56808i −0.820473 0.571685i \(-0.806290\pi\)
−0.0848573 0.996393i \(-0.527043\pi\)
\(180\) 69770.3 120846.i 0.160505 0.278003i
\(181\) 132697. 0.301067 0.150534 0.988605i \(-0.451901\pi\)
0.150534 + 0.988605i \(0.451901\pi\)
\(182\) 0 0
\(183\) −189932. −0.419247
\(184\) −852226. + 1.47610e6i −1.85571 + 3.21418i
\(185\) −117683. 203833.i −0.252804 0.437869i
\(186\) −135752. 235129.i −0.287715 0.498338i
\(187\) 130756. 226476.i 0.273438 0.473608i
\(188\) 226400. 0.467178
\(189\) 0 0
\(190\) −336967. −0.677178
\(191\) −3318.71 + 5748.17i −0.00658242 + 0.0114011i −0.869298 0.494289i \(-0.835429\pi\)
0.862715 + 0.505690i \(0.168762\pi\)
\(192\) 15096.0 + 26147.0i 0.0295535 + 0.0511882i
\(193\) −226295. 391954.i −0.437302 0.757430i 0.560178 0.828372i \(-0.310733\pi\)
−0.997480 + 0.0709425i \(0.977399\pi\)
\(194\) −325394. + 563598.i −0.620733 + 1.07514i
\(195\) 217901. 0.410368
\(196\) 0 0
\(197\) 816952. 1.49979 0.749896 0.661556i \(-0.230104\pi\)
0.749896 + 0.661556i \(0.230104\pi\)
\(198\) −192759. + 333868.i −0.349422 + 0.605217i
\(199\) 403208. + 698378.i 0.721767 + 1.25014i 0.960291 + 0.279000i \(0.0900031\pi\)
−0.238524 + 0.971137i \(0.576664\pi\)
\(200\) 530526. + 918899.i 0.937847 + 1.62440i
\(201\) −250148. + 433269.i −0.436724 + 0.756428i
\(202\) −1.88756e6 −3.25478
\(203\) 0 0
\(204\) 366684. 0.616902
\(205\) 53172.2 92096.9i 0.0883690 0.153060i
\(206\) 266044. + 460801.i 0.436802 + 0.756564i
\(207\) −166602. 288562.i −0.270242 0.468073i
\(208\) −976143. + 1.69073e6i −1.56443 + 2.70966i
\(209\) 645954. 1.02291
\(210\) 0 0
\(211\) 68773.9 0.106345 0.0531726 0.998585i \(-0.483067\pi\)
0.0531726 + 0.998585i \(0.483067\pi\)
\(212\) −41376.6 + 71666.5i −0.0632289 + 0.109516i
\(213\) −27346.1 47364.8i −0.0412996 0.0715330i
\(214\) −246281. 426572.i −0.367618 0.636734i
\(215\) 61537.4 106586.i 0.0907911 0.157255i
\(216\) −302057. −0.440508
\(217\) 0 0
\(218\) −372512. −0.530883
\(219\) 75508.4 130784.i 0.106386 0.184266i
\(220\) 400987. + 694529.i 0.558564 + 0.967461i
\(221\) 286299. + 495885.i 0.394312 + 0.682968i
\(222\) −455884. + 789615.i −0.620829 + 1.07531i
\(223\) 620227. 0.835196 0.417598 0.908632i \(-0.362872\pi\)
0.417598 + 0.908632i \(0.362872\pi\)
\(224\) 0 0
\(225\) −207425. −0.273152
\(226\) 494380. 856291.i 0.643857 1.11519i
\(227\) 501116. + 867959.i 0.645467 + 1.11798i 0.984193 + 0.177096i \(0.0566705\pi\)
−0.338727 + 0.940885i \(0.609996\pi\)
\(228\) 452867. + 784388.i 0.576944 + 0.999296i
\(229\) 442931. 767178.i 0.558145 0.966735i −0.439506 0.898239i \(-0.644847\pi\)
0.997651 0.0684960i \(-0.0218200\pi\)
\(230\) −998973. −1.24519
\(231\) 0 0
\(232\) −986707. −1.20356
\(233\) −298082. + 516293.i −0.359704 + 0.623026i −0.987911 0.155020i \(-0.950456\pi\)
0.628207 + 0.778046i \(0.283789\pi\)
\(234\) −422057. 731025.i −0.503886 0.872755i
\(235\) 37073.3 + 64212.9i 0.0437917 + 0.0758495i
\(236\) 997143. 1.72710e6i 1.16541 2.01854i
\(237\) 43607.4 0.0504300
\(238\) 0 0
\(239\) 743111. 0.841509 0.420754 0.907175i \(-0.361765\pi\)
0.420754 + 0.907175i \(0.361765\pi\)
\(240\) −204724. + 354593.i −0.229425 + 0.397376i
\(241\) −587419. 1.01744e6i −0.651487 1.12841i −0.982762 0.184874i \(-0.940812\pi\)
0.331276 0.943534i \(-0.392521\pi\)
\(242\) −284548. 492851.i −0.312332 0.540975i
\(243\) 29524.5 51137.9i 0.0320750 0.0555556i
\(244\) 1.53058e6 1.64582
\(245\) 0 0
\(246\) −411961. −0.434029
\(247\) −707179. + 1.22487e6i −0.737542 + 1.27746i
\(248\) 611293. + 1.05879e6i 0.631132 + 1.09315i
\(249\) −270654. 468787.i −0.276641 0.479156i
\(250\) −690385. + 1.19578e6i −0.698621 + 1.21005i
\(251\) −352992. −0.353655 −0.176828 0.984242i \(-0.556584\pi\)
−0.176828 + 0.984242i \(0.556584\pi\)
\(252\) 0 0
\(253\) 1.91500e6 1.88090
\(254\) −119225. + 206504.i −0.115953 + 0.200837i
\(255\) 60044.9 + 104001.i 0.0578263 + 0.100158i
\(256\) 912666. + 1.58078e6i 0.870386 + 1.50755i
\(257\) 5006.34 8671.23i 0.00472811 0.00818932i −0.863652 0.504089i \(-0.831828\pi\)
0.868380 + 0.495900i \(0.165162\pi\)
\(258\) −476773. −0.445925
\(259\) 0 0
\(260\) −1.75597e6 −1.61096
\(261\) 96445.6 167049.i 0.0876357 0.151790i
\(262\) −1.73171e6 2.99940e6i −1.55855 2.69949i
\(263\) −840900. 1.45648e6i −0.749644 1.29842i −0.947993 0.318290i \(-0.896891\pi\)
0.198349 0.980131i \(-0.436442\pi\)
\(264\) 867995. 1.50341e6i 0.766492 1.32760i
\(265\) −27101.9 −0.0237075
\(266\) 0 0
\(267\) −562477. −0.482866
\(268\) 2.01584e6 3.49153e6i 1.71442 2.96947i
\(269\) −958587. 1.66032e6i −0.807702 1.39898i −0.914452 0.404694i \(-0.867378\pi\)
0.106750 0.994286i \(-0.465955\pi\)
\(270\) −88517.1 153316.i −0.0738955 0.127991i
\(271\) 1.14500e6 1.98320e6i 0.947069 1.64037i 0.195515 0.980701i \(-0.437362\pi\)
0.751554 0.659672i \(-0.229305\pi\)
\(272\) −1.07594e6 −0.881795
\(273\) 0 0
\(274\) −642843. −0.517283
\(275\) 596060. 1.03241e6i 0.475290 0.823226i
\(276\) 1.34257e6 + 2.32540e6i 1.06088 + 1.83749i
\(277\) 197401. + 341908.i 0.154579 + 0.267738i 0.932906 0.360121i \(-0.117265\pi\)
−0.778327 + 0.627859i \(0.783931\pi\)
\(278\) 1.08335e6 1.87642e6i 0.840734 1.45619i
\(279\) −239003. −0.183820
\(280\) 0 0
\(281\) −1.77699e6 −1.34252 −0.671259 0.741223i \(-0.734246\pi\)
−0.671259 + 0.741223i \(0.734246\pi\)
\(282\) 143616. 248751.i 0.107543 0.186269i
\(283\) 607622. + 1.05243e6i 0.450991 + 0.781139i 0.998448 0.0556949i \(-0.0177374\pi\)
−0.547457 + 0.836834i \(0.684404\pi\)
\(284\) 220370. + 381693.i 0.162128 + 0.280813i
\(285\) −148315. + 256889.i −0.108162 + 0.187341i
\(286\) 4.85133e6 3.50708
\(287\) 0 0
\(288\) 512159. 0.363851
\(289\) 552143. 956340.i 0.388872 0.673547i
\(290\) −289153. 500827.i −0.201898 0.349698i
\(291\) 286442. + 496132.i 0.198292 + 0.343451i
\(292\) −608490. + 1.05393e6i −0.417634 + 0.723364i
\(293\) 1.48897e6 1.01325 0.506627 0.862165i \(-0.330892\pi\)
0.506627 + 0.862165i \(0.330892\pi\)
\(294\) 0 0
\(295\) 653133. 0.436965
\(296\) 2.05286e6 3.55565e6i 1.36185 2.35879i
\(297\) 169684. + 293902.i 0.111622 + 0.193335i
\(298\) −717065. 1.24199e6i −0.467754 0.810174i
\(299\) −2.09651e6 + 3.63125e6i −1.35618 + 2.34898i
\(300\) 1.67155e6 1.07230
\(301\) 0 0
\(302\) −1.67662e6 −1.05784
\(303\) −830803. + 1.43899e6i −0.519866 + 0.900434i
\(304\) −1.32883e6 2.30160e6i −0.824679 1.42839i
\(305\) 250634. + 434111.i 0.154273 + 0.267209i
\(306\) 232604. 402883.i 0.142009 0.245966i
\(307\) −2.03109e6 −1.22994 −0.614968 0.788552i \(-0.710831\pi\)
−0.614968 + 0.788552i \(0.710831\pi\)
\(308\) 0 0
\(309\) 468394. 0.279071
\(310\) −358276. + 620553.i −0.211745 + 0.366754i
\(311\) 144892. + 250961.i 0.0849463 + 0.147131i 0.905368 0.424627i \(-0.139595\pi\)
−0.820422 + 0.571758i \(0.806261\pi\)
\(312\) 1.90053e6 + 3.29182e6i 1.10532 + 1.91447i
\(313\) 109105. 188976.i 0.0629484 0.109030i −0.832834 0.553523i \(-0.813283\pi\)
0.895782 + 0.444493i \(0.146616\pi\)
\(314\) −5.69002e6 −3.25679
\(315\) 0 0
\(316\) −351413. −0.197970
\(317\) −645315. + 1.11772e6i −0.360681 + 0.624718i −0.988073 0.153985i \(-0.950789\pi\)
0.627392 + 0.778704i \(0.284122\pi\)
\(318\) 52494.2 + 90922.7i 0.0291101 + 0.0504202i
\(319\) 554296. + 960068.i 0.304975 + 0.528233i
\(320\) 39841.4 69007.3i 0.0217500 0.0376721i
\(321\) −433600. −0.234870
\(322\) 0 0
\(323\) −779481. −0.415719
\(324\) −237925. + 412099.i −0.125915 + 0.218092i
\(325\) 1.30511e6 + 2.26052e6i 0.685393 + 1.18714i
\(326\) 100841. + 174662.i 0.0525526 + 0.0910237i
\(327\) −163960. + 283987.i −0.0847947 + 0.146869i
\(328\) 1.85507e6 0.952084
\(329\) 0 0
\(330\) 1.01746e6 0.514318
\(331\) 1.74280e6 3.01862e6i 0.874336 1.51439i 0.0168673 0.999858i \(-0.494631\pi\)
0.857469 0.514536i \(-0.172036\pi\)
\(332\) 2.18109e6 + 3.77776e6i 1.08600 + 1.88100i
\(333\) 401313. + 695094.i 0.198323 + 0.343505i
\(334\) 484489. 839160.i 0.237639 0.411603i
\(335\) 1.32038e6 0.642817
\(336\) 0 0
\(337\) 249198. 0.119528 0.0597641 0.998213i \(-0.480965\pi\)
0.0597641 + 0.998213i \(0.480965\pi\)
\(338\) −3.41313e6 + 5.91171e6i −1.62503 + 2.81463i
\(339\) −435200. 753788.i −0.205679 0.356246i
\(340\) −483876. 838098.i −0.227006 0.393186i
\(341\) 686803. 1.18958e6i 0.319850 0.553997i
\(342\) 1.14910e6 0.531241
\(343\) 0 0
\(344\) 2.14692e6 0.978180
\(345\) −439695. + 761574.i −0.198886 + 0.344480i
\(346\) 1.73213e6 + 3.00014e6i 0.777840 + 1.34726i
\(347\) 753007. + 1.30425e6i 0.335719 + 0.581482i 0.983623 0.180240i \(-0.0576875\pi\)
−0.647904 + 0.761722i \(0.724354\pi\)
\(348\) −777214. + 1.34617e6i −0.344027 + 0.595872i
\(349\) −1.54370e6 −0.678423 −0.339212 0.940710i \(-0.610160\pi\)
−0.339212 + 0.940710i \(0.610160\pi\)
\(350\) 0 0
\(351\) −743070. −0.321930
\(352\) −1.47175e6 + 2.54914e6i −0.633107 + 1.09657i
\(353\) −838978. 1.45315e6i −0.358355 0.620689i 0.629331 0.777137i \(-0.283329\pi\)
−0.987686 + 0.156448i \(0.949996\pi\)
\(354\) −1.26507e6 2.19116e6i −0.536544 0.929322i
\(355\) −72171.8 + 125005.i −0.0303946 + 0.0526450i
\(356\) 4.53276e6 1.89556
\(357\) 0 0
\(358\) 7.93568e6 3.27248
\(359\) 1.24987e6 2.16483e6i 0.511832 0.886519i −0.488074 0.872802i \(-0.662300\pi\)
0.999906 0.0137165i \(-0.00436623\pi\)
\(360\) 398594. + 690385.i 0.162097 + 0.280760i
\(361\) 275363. + 476943.i 0.111208 + 0.192619i
\(362\) −678335. + 1.17491e6i −0.272065 + 0.471231i
\(363\) −500971. −0.199547
\(364\) 0 0
\(365\) −398564. −0.156591
\(366\) 970917. 1.68168e6i 0.378861 0.656206i
\(367\) −1.05371e6 1.82507e6i −0.408370 0.707318i 0.586337 0.810067i \(-0.300569\pi\)
−0.994707 + 0.102749i \(0.967236\pi\)
\(368\) −3.93945e6 6.82332e6i −1.51641 2.62649i
\(369\) −181324. + 314062.i −0.0693248 + 0.120074i
\(370\) 2.40634e6 0.913804
\(371\) 0 0
\(372\) 1.92602e6 0.721613
\(373\) −1.36612e6 + 2.36619e6i −0.508414 + 0.880599i 0.491538 + 0.870856i \(0.336435\pi\)
−0.999953 + 0.00974333i \(0.996899\pi\)
\(374\) 1.33683e6 + 2.31546e6i 0.494194 + 0.855970i
\(375\) 607742. + 1.05264e6i 0.223173 + 0.386547i
\(376\) −646706. + 1.12013e6i −0.235905 + 0.408600i
\(377\) −2.42733e6 −0.879581
\(378\) 0 0
\(379\) −2.04295e6 −0.730567 −0.365283 0.930896i \(-0.619028\pi\)
−0.365283 + 0.930896i \(0.619028\pi\)
\(380\) 1.19521e6 2.07016e6i 0.424604 0.735436i
\(381\) 104953. + 181784.i 0.0370410 + 0.0641568i
\(382\) −33930.0 58768.4i −0.0118967 0.0206056i
\(383\) 754497. 1.30683e6i 0.262821 0.455220i −0.704169 0.710032i \(-0.748680\pi\)
0.966991 + 0.254812i \(0.0820137\pi\)
\(384\) 1.51233e6 0.523382
\(385\) 0 0
\(386\) 4.62721e6 1.58071
\(387\) −209850. + 363471.i −0.0712249 + 0.123365i
\(388\) −2.30832e6 3.99812e6i −0.778423 1.34827i
\(389\) −2.25033e6 3.89768e6i −0.754000 1.30597i −0.945870 0.324546i \(-0.894788\pi\)
0.191870 0.981420i \(-0.438545\pi\)
\(390\) −1.11389e6 + 1.92932e6i −0.370837 + 0.642308i
\(391\) −2.31085e6 −0.764417
\(392\) 0 0
\(393\) −3.04882e6 −0.995751
\(394\) −4.17620e6 + 7.23339e6i −1.35532 + 2.34748i
\(395\) −57544.3 99669.7i −0.0185571 0.0321418i
\(396\) −1.36741e6 2.36843e6i −0.438189 0.758966i
\(397\) −1.76068e6 + 3.04958e6i −0.560665 + 0.971101i 0.436773 + 0.899572i \(0.356121\pi\)
−0.997439 + 0.0715292i \(0.977212\pi\)
\(398\) −8.24469e6 −2.60895
\(399\) 0 0
\(400\) −4.90476e6 −1.53274
\(401\) 453554. 785578.i 0.140853 0.243965i −0.786965 0.616998i \(-0.788349\pi\)
0.927818 + 0.373033i \(0.121682\pi\)
\(402\) −2.55748e6 4.42968e6i −0.789308 1.36712i
\(403\) 1.50380e6 + 2.60466e6i 0.461241 + 0.798893i
\(404\) 6.69508e6 1.15962e7i 2.04081 3.53479i
\(405\) −155842. −0.0472115
\(406\) 0 0
\(407\) −4.61287e6 −1.38034
\(408\) −1.04742e6 + 1.81419e6i −0.311509 + 0.539550i
\(409\) 2.15927e6 + 3.73996e6i 0.638260 + 1.10550i 0.985814 + 0.167839i \(0.0536790\pi\)
−0.347554 + 0.937660i \(0.612988\pi\)
\(410\) 543624. + 941585.i 0.159713 + 0.276630i
\(411\) −282945. + 490076.i −0.0826224 + 0.143106i
\(412\) −3.77458e6 −1.09553
\(413\) 0 0
\(414\) 3.40662e6 0.976838
\(415\) −714311. + 1.23722e6i −0.203595 + 0.352637i
\(416\) −3.22249e6 5.58152e6i −0.912974 1.58132i
\(417\) −953671. 1.65181e6i −0.268571 0.465178i
\(418\) −3.30207e6 + 5.71935e6i −0.924369 + 1.60105i
\(419\) 1.52041e6 0.423083 0.211541 0.977369i \(-0.432152\pi\)
0.211541 + 0.977369i \(0.432152\pi\)
\(420\) 0 0
\(421\) −4.42050e6 −1.21553 −0.607766 0.794116i \(-0.707934\pi\)
−0.607766 + 0.794116i \(0.707934\pi\)
\(422\) −351567. + 608932.i −0.0961008 + 0.166452i
\(423\) −126425. 218974.i −0.0343542 0.0595033i
\(424\) −236383. 409427.i −0.0638559 0.110602i
\(425\) −719274. + 1.24582e6i −0.193162 + 0.334567i
\(426\) 559164. 0.149285
\(427\) 0 0
\(428\) 3.49420e6 0.922016
\(429\) 2.13530e6 3.69844e6i 0.560164 0.970233i
\(430\) 629150. + 1.08972e6i 0.164090 + 0.284213i
\(431\) 3.42393e6 + 5.93041e6i 0.887833 + 1.53777i 0.842432 + 0.538803i \(0.181123\pi\)
0.0454009 + 0.998969i \(0.485543\pi\)
\(432\) 698134. 1.20920e6i 0.179982 0.311738i
\(433\) 3.99328e6 1.02355 0.511777 0.859119i \(-0.328988\pi\)
0.511777 + 0.859119i \(0.328988\pi\)
\(434\) 0 0
\(435\) −509079. −0.128992
\(436\) 1.32128e6 2.28853e6i 0.332874 0.576555i
\(437\) −2.85398e6 4.94324e6i −0.714904 1.23825i
\(438\) 771986. + 1.33712e6i 0.192276 + 0.333031i
\(439\) 742783. 1.28654e6i 0.183950 0.318611i −0.759272 0.650773i \(-0.774445\pi\)
0.943222 + 0.332162i \(0.107778\pi\)
\(440\) −4.58163e6 −1.12821
\(441\) 0 0
\(442\) −5.85416e6 −1.42531
\(443\) 2.81097e6 4.86874e6i 0.680528 1.17871i −0.294291 0.955716i \(-0.595084\pi\)
0.974820 0.222994i \(-0.0715831\pi\)
\(444\) −3.23401e6 5.60146e6i −0.778545 1.34848i
\(445\) 742245. + 1.28561e6i 0.177684 + 0.307757i
\(446\) −3.17055e6 + 5.49156e6i −0.754741 + 1.30725i
\(447\) −1.26246e6 −0.298846
\(448\) 0 0
\(449\) 1.94883e6 0.456202 0.228101 0.973637i \(-0.426748\pi\)
0.228101 + 0.973637i \(0.426748\pi\)
\(450\) 1.06034e6 1.83657e6i 0.246839 0.427538i
\(451\) −1.04211e6 1.80499e6i −0.241253 0.417862i
\(452\) 3.50709e6 + 6.07446e6i 0.807422 + 1.39850i
\(453\) −737961. + 1.27819e6i −0.168962 + 0.292650i
\(454\) −1.02467e7 −2.33315
\(455\) 0 0
\(456\) −5.17441e6 −1.16533
\(457\) 1.33656e6 2.31499e6i 0.299363 0.518511i −0.676628 0.736325i \(-0.736559\pi\)
0.975990 + 0.217814i \(0.0698926\pi\)
\(458\) 4.52846e6 + 7.84352e6i 1.00876 + 1.74722i
\(459\) −204760. 354655.i −0.0453643 0.0785733i
\(460\) 3.54332e6 6.13720e6i 0.780756 1.35231i
\(461\) 4.65262e6 1.01964 0.509819 0.860282i \(-0.329713\pi\)
0.509819 + 0.860282i \(0.329713\pi\)
\(462\) 0 0
\(463\) −5.18586e6 −1.12426 −0.562132 0.827047i \(-0.690019\pi\)
−0.562132 + 0.827047i \(0.690019\pi\)
\(464\) 2.28055e6 3.95002e6i 0.491749 0.851735i
\(465\) 315389. + 546269.i 0.0676416 + 0.117159i
\(466\) −3.04754e6 5.27850e6i −0.650107 1.12602i
\(467\) −2.52990e6 + 4.38192e6i −0.536799 + 0.929763i 0.462275 + 0.886737i \(0.347033\pi\)
−0.999074 + 0.0430263i \(0.986300\pi\)
\(468\) 5.98808e6 1.26378
\(469\) 0 0
\(470\) −758064. −0.158293
\(471\) −2.50444e6 + 4.33783e6i −0.520187 + 0.900990i
\(472\) 5.69662e6 + 9.86684e6i 1.17696 + 2.03856i
\(473\) −1.20606e6 2.08895e6i −0.247865 0.429315i
\(474\) −222918. + 386105.i −0.0455720 + 0.0789331i
\(475\) −3.55331e6 −0.722603
\(476\) 0 0
\(477\) 92420.8 0.0185983
\(478\) −3.79873e6 + 6.57959e6i −0.760446 + 1.31713i
\(479\) −2.77543e6 4.80718e6i −0.552702 0.957308i −0.998078 0.0619642i \(-0.980264\pi\)
0.445377 0.895343i \(-0.353070\pi\)
\(480\) −675845. 1.17060e6i −0.133889 0.231902i
\(481\) 5.05010e6 8.74702e6i 0.995261 1.72384i
\(482\) 1.20114e7 2.35491
\(483\) 0 0
\(484\) 4.03711e6 0.783353
\(485\) 755979. 1.30939e6i 0.145934 0.252764i
\(486\) 301854. + 522827.i 0.0579704 + 0.100408i
\(487\) 3.43905e6 + 5.95661e6i 0.657077 + 1.13809i 0.981369 + 0.192133i \(0.0615405\pi\)
−0.324292 + 0.945957i \(0.605126\pi\)
\(488\) −4.37206e6 + 7.57262e6i −0.831067 + 1.43945i
\(489\) 177540. 0.0335756
\(490\) 0 0
\(491\) 7.44459e6 1.39360 0.696798 0.717267i \(-0.254607\pi\)
0.696798 + 0.717267i \(0.254607\pi\)
\(492\) 1.46121e6 2.53089e6i 0.272145 0.471368i
\(493\) −668876. 1.15853e6i −0.123945 0.214679i
\(494\) −7.23009e6 1.25229e7i −1.33299 2.30880i
\(495\) 447831. 775666.i 0.0821488 0.142286i
\(496\) −5.65145e6 −1.03147
\(497\) 0 0
\(498\) 5.53426e6 0.999968
\(499\) −1.07665e6 + 1.86481e6i −0.193563 + 0.335261i −0.946428 0.322914i \(-0.895338\pi\)
0.752866 + 0.658174i \(0.228671\pi\)
\(500\) −4.89754e6 8.48278e6i −0.876098 1.51745i
\(501\) −426493. 738707.i −0.0759132 0.131486i
\(502\) 1.80447e6 3.12543e6i 0.319588 0.553542i
\(503\) −8.61012e6 −1.51736 −0.758681 0.651463i \(-0.774156\pi\)
−0.758681 + 0.651463i \(0.774156\pi\)
\(504\) 0 0
\(505\) 4.38531e6 0.765195
\(506\) −9.78932e6 + 1.69556e7i −1.69972 + 2.94399i
\(507\) 3.00456e6 + 5.20404e6i 0.519111 + 0.899127i
\(508\) −845771. 1.46492e6i −0.145410 0.251857i
\(509\) 1.67100e6 2.89426e6i 0.285879 0.495157i −0.686943 0.726712i \(-0.741048\pi\)
0.972822 + 0.231554i \(0.0743810\pi\)
\(510\) −1.22778e6 −0.209024
\(511\) 0 0
\(512\) −1.32848e7 −2.23964
\(513\) 505772. 876023.i 0.0848519 0.146968i
\(514\) 51184.1 + 88653.4i 0.00854529 + 0.0148009i
\(515\) −618093. 1.07057e6i −0.102692 0.177867i
\(516\) 1.69109e6 2.92906e6i 0.279604 0.484288i
\(517\) 1.45318e6 0.239108
\(518\) 0 0
\(519\) 3.04957e6 0.496958
\(520\) 5.01589e6 8.68777e6i 0.813466 1.40896i
\(521\) −1.34152e6 2.32359e6i −0.216523 0.375029i 0.737220 0.675653i \(-0.236138\pi\)
−0.953743 + 0.300624i \(0.902805\pi\)
\(522\) 986046. + 1.70788e6i 0.158387 + 0.274335i
\(523\) −2.71178e6 + 4.69694e6i −0.433511 + 0.750863i −0.997173 0.0751429i \(-0.976059\pi\)
0.563662 + 0.826005i \(0.309392\pi\)
\(524\) 2.45692e7 3.90897
\(525\) 0 0
\(526\) 1.71945e7 2.70972
\(527\) −828775. + 1.43548e6i −0.129990 + 0.225149i
\(528\) 4.01234e6 + 6.94958e6i 0.626344 + 1.08486i
\(529\) −5.24276e6 9.08072e6i −0.814555 1.41085i
\(530\) 138543. 239963.i 0.0214237 0.0371070i
\(531\) −2.22726e6 −0.342796
\(532\) 0 0
\(533\) 4.56353e6 0.695798
\(534\) 2.87534e6 4.98024e6i 0.436351 0.755782i
\(535\) 572179. + 991044.i 0.0864266 + 0.149695i
\(536\) 1.15164e7 + 1.99469e7i 1.73142 + 2.99891i
\(537\) 3.49287e6 6.04983e6i 0.522693 0.905330i
\(538\) 1.96009e7 2.91958
\(539\) 0 0
\(540\) 1.25587e6 0.185336
\(541\) −1.09228e6 + 1.89188e6i −0.160450 + 0.277908i −0.935030 0.354568i \(-0.884628\pi\)
0.774580 + 0.632476i \(0.217961\pi\)
\(542\) 1.17063e7 + 2.02759e7i 1.71168 + 2.96471i
\(543\) 597135. + 1.03427e6i 0.0869106 + 0.150534i
\(544\) 1.77598e6 3.07609e6i 0.257301 0.445658i
\(545\) 865447. 0.124810
\(546\) 0 0
\(547\) −691437. −0.0988062 −0.0494031 0.998779i \(-0.515732\pi\)
−0.0494031 + 0.998779i \(0.515732\pi\)
\(548\) 2.28014e6 3.94931e6i 0.324347 0.561785i
\(549\) −854693. 1.48037e6i −0.121026 0.209623i
\(550\) 6.09403e6 + 1.05552e7i 0.859010 + 1.48785i
\(551\) 1.65217e6 2.86164e6i 0.231833 0.401547i
\(552\) −1.53401e7 −2.14279
\(553\) 0 0
\(554\) −4.03639e6 −0.558752
\(555\) 1.05914e6 1.83449e6i 0.145956 0.252804i
\(556\) 7.68523e6 + 1.33112e7i 1.05431 + 1.82612i
\(557\) −2.73828e6 4.74284e6i −0.373973 0.647740i 0.616200 0.787590i \(-0.288671\pi\)
−0.990173 + 0.139850i \(0.955338\pi\)
\(558\) 1.22177e6 2.11616e6i 0.166113 0.287715i
\(559\) 5.28149e6 0.714869
\(560\) 0 0
\(561\) 2.35361e6 0.315739
\(562\) 9.08386e6 1.57337e7i 1.21319 2.10131i
\(563\) 199488. + 345523.i 0.0265244 + 0.0459416i 0.878983 0.476853i \(-0.158223\pi\)
−0.852459 + 0.522795i \(0.824889\pi\)
\(564\) 1.01880e6 + 1.76462e6i 0.134863 + 0.233589i
\(565\) −1.14858e6 + 1.98940e6i −0.151370 + 0.262181i
\(566\) −1.24245e7 −1.63019
\(567\) 0 0
\(568\) −2.51793e6 −0.327471
\(569\) 2.11556e6 3.66426e6i 0.273934 0.474467i −0.695932 0.718108i \(-0.745008\pi\)
0.969866 + 0.243641i \(0.0783418\pi\)
\(570\) −1.51635e6 2.62640e6i −0.195485 0.338589i
\(571\) −4.37551e6 7.57861e6i −0.561615 0.972746i −0.997356 0.0726734i \(-0.976847\pi\)
0.435741 0.900072i \(-0.356486\pi\)
\(572\) −1.72075e7 + 2.98042e7i −2.19901 + 3.80879i
\(573\) −59736.7 −0.00760072
\(574\) 0 0
\(575\) −1.05342e7 −1.32871
\(576\) −135864. + 235323.i −0.0170627 + 0.0295535i
\(577\) −883558. 1.53037e6i −0.110483 0.191362i 0.805482 0.592620i \(-0.201906\pi\)
−0.915965 + 0.401258i \(0.868573\pi\)
\(578\) 5.64503e6 + 9.77748e6i 0.702824 + 1.21733i
\(579\) 2.03665e6 3.52759e6i 0.252477 0.437302i
\(580\) 4.10245e6 0.506376
\(581\) 0 0
\(582\) −5.85709e6 −0.716761
\(583\) −265582. + 460001.i −0.0323614 + 0.0560516i
\(584\) −3.47627e6 6.02107e6i −0.421775 0.730536i
\(585\) 980555. + 1.69837e6i 0.118463 + 0.205184i
\(586\) −7.61153e6 + 1.31835e7i −0.915646 + 1.58595i
\(587\) 8.65009e6 1.03616 0.518078 0.855333i \(-0.326648\pi\)
0.518078 + 0.855333i \(0.326648\pi\)
\(588\) 0 0
\(589\) −4.09426e6 −0.486281
\(590\) −3.33877e6 + 5.78292e6i −0.394872 + 0.683939i
\(591\) 3.67628e6 + 6.36751e6i 0.432953 + 0.749896i
\(592\) 9.48941e6 + 1.64361e7i 1.11285 + 1.92750i
\(593\) 7.72568e6 1.33813e7i 0.902194 1.56265i 0.0775549 0.996988i \(-0.475289\pi\)
0.824640 0.565659i \(-0.191378\pi\)
\(594\) −3.46965e6 −0.403478
\(595\) 0 0
\(596\) 1.01736e7 1.17316
\(597\) −3.62888e6 + 6.28540e6i −0.416712 + 0.721767i
\(598\) −2.14344e7 3.71254e7i −2.45108 4.24540i
\(599\) 1.92400e6 + 3.33247e6i 0.219098 + 0.379489i 0.954533 0.298107i \(-0.0963552\pi\)
−0.735434 + 0.677596i \(0.763022\pi\)
\(600\) −4.77474e6 + 8.27009e6i −0.541466 + 0.937847i
\(601\) −1.27578e7 −1.44075 −0.720376 0.693583i \(-0.756031\pi\)
−0.720376 + 0.693583i \(0.756031\pi\)
\(602\) 0 0
\(603\) −4.50266e6 −0.504285
\(604\) 5.94691e6 1.03004e7i 0.663284 1.14884i
\(605\) 661082. + 1.14503e6i 0.0734289 + 0.127183i
\(606\) −8.49400e6 1.47120e7i −0.939574 1.62739i
\(607\) −6.81033e6 + 1.17958e7i −0.750233 + 1.29944i 0.197476 + 0.980308i \(0.436726\pi\)
−0.947709 + 0.319135i \(0.896608\pi\)
\(608\) 8.77359e6 0.962539
\(609\) 0 0
\(610\) −5.12489e6 −0.557648
\(611\) −1.59092e6 + 2.75555e6i −0.172403 + 0.298611i
\(612\) 1.65008e6 + 2.85802e6i 0.178084 + 0.308451i
\(613\) −7.67372e6 1.32913e7i −0.824812 1.42862i −0.902063 0.431605i \(-0.857948\pi\)
0.0772508 0.997012i \(-0.475386\pi\)
\(614\) 1.03828e7 1.79835e7i 1.11145 1.92510i
\(615\) 957099. 0.102040
\(616\) 0 0
\(617\) 1.18485e7 1.25300 0.626500 0.779421i \(-0.284487\pi\)
0.626500 + 0.779421i \(0.284487\pi\)
\(618\) −2.39439e6 + 4.14721e6i −0.252188 + 0.436802i
\(619\) −437230. 757304.i −0.0458652 0.0794408i 0.842181 0.539194i \(-0.181271\pi\)
−0.888047 + 0.459753i \(0.847938\pi\)
\(620\) −2.54158e6 4.40215e6i −0.265537 0.459924i
\(621\) 1.49941e6 2.59706e6i 0.156024 0.270242i
\(622\) −2.96272e6 −0.307054
\(623\) 0 0
\(624\) −1.75706e7 −1.80644
\(625\) −2.39730e6 + 4.15225e6i −0.245484 + 0.425190i
\(626\) 1.11548e6 + 1.93206e6i 0.113769 + 0.197054i
\(627\) 2.90679e6 + 5.03471e6i 0.295287 + 0.511453i
\(628\) 2.01823e7 3.49567e7i 2.04207 3.53697i
\(629\) 5.56642e6 0.560983
\(630\) 0 0
\(631\) −4.43859e6 −0.443784 −0.221892 0.975071i \(-0.571223\pi\)
−0.221892 + 0.975071i \(0.571223\pi\)
\(632\) 1.00380e6 1.73864e6i 0.0999667 0.173147i
\(633\) 309483. + 536040.i 0.0306992 + 0.0531726i
\(634\) −6.59761e6 1.14274e7i −0.651873 1.12908i
\(635\) 276992. 479764.i 0.0272605 0.0472165i
\(636\) −744780. −0.0730104
\(637\) 0 0
\(638\) −1.13341e7 −1.10239
\(639\) 246115. 426283.i 0.0238443 0.0412996i
\(640\) −1.99567e6 3.45661e6i −0.192593 0.333580i
\(641\) −406276. 703690.i −0.0390549 0.0676451i 0.845837 0.533441i \(-0.179101\pi\)
−0.884892 + 0.465796i \(0.845768\pi\)
\(642\) 2.21653e6 3.83915e6i 0.212245 0.367618i
\(643\) 1.17941e7 1.12496 0.562481 0.826810i \(-0.309847\pi\)
0.562481 + 0.826810i \(0.309847\pi\)
\(644\) 0 0
\(645\) 1.10767e6 0.104837
\(646\) 3.98465e6 6.90162e6i 0.375672 0.650683i
\(647\) −1.21690e6 2.10773e6i −0.114286 0.197950i 0.803208 0.595699i \(-0.203125\pi\)
−0.917494 + 0.397749i \(0.869791\pi\)
\(648\) −1.35925e6 2.35430e6i −0.127164 0.220254i
\(649\) 6.40031e6 1.10857e7i 0.596471 1.03312i
\(650\) −2.66866e7 −2.47748
\(651\) 0 0
\(652\) −1.43072e6 −0.131806
\(653\) 4.73332e6 8.19835e6i 0.434393 0.752391i −0.562853 0.826557i \(-0.690296\pi\)
0.997246 + 0.0741664i \(0.0236296\pi\)
\(654\) −1.67630e6 2.90344e6i −0.153253 0.265442i
\(655\) 4.02323e6 + 6.96843e6i 0.366413 + 0.634647i
\(656\) −4.28756e6 + 7.42628e6i −0.389001 + 0.673770i
\(657\) 1.35915e6 0.122844
\(658\) 0 0
\(659\) 1.40662e7 1.26172 0.630860 0.775896i \(-0.282702\pi\)
0.630860 + 0.775896i \(0.282702\pi\)
\(660\) −3.60888e6 + 6.25076e6i −0.322487 + 0.558564i
\(661\) −8.58029e6 1.48615e7i −0.763832 1.32300i −0.940862 0.338791i \(-0.889982\pi\)
0.177029 0.984206i \(-0.443351\pi\)
\(662\) 1.78182e7 + 3.08620e7i 1.58022 + 2.73702i
\(663\) −2.57669e6 + 4.46296e6i −0.227656 + 0.394312i
\(664\) −2.49209e7 −2.19353
\(665\) 0 0
\(666\) −8.20592e6 −0.716872
\(667\) 4.89803e6 8.48364e6i 0.426292 0.738359i
\(668\) 3.43692e6 + 5.95293e6i 0.298009 + 0.516166i
\(669\) 2.79102e6 + 4.83419e6i 0.241100 + 0.417598i
\(670\) −6.74969e6 + 1.16908e7i −0.580894 + 1.00614i
\(671\) 9.82424e6 0.842350
\(672\) 0 0
\(673\) 5.87113e6 0.499671 0.249836 0.968288i \(-0.419623\pi\)
0.249836 + 0.968288i \(0.419623\pi\)
\(674\) −1.27388e6 + 2.20643e6i −0.108014 + 0.187086i
\(675\) −933413. 1.61672e6i −0.0788523 0.136576i
\(676\) −2.42124e7 4.19372e7i −2.03785 3.52966i
\(677\) 6.96368e6 1.20614e7i 0.583938 1.01141i −0.411069 0.911604i \(-0.634844\pi\)
0.995007 0.0998062i \(-0.0318223\pi\)
\(678\) 8.89884e6 0.743462
\(679\) 0 0
\(680\) 5.52872e6 0.458513
\(681\) −4.51005e6 + 7.81163e6i −0.372660 + 0.645467i
\(682\) 7.02178e6 + 1.21621e7i 0.578077 + 1.00126i
\(683\) −9.15503e6 1.58570e7i −0.750945 1.30067i −0.947365 0.320155i \(-0.896265\pi\)
0.196421 0.980520i \(-0.437068\pi\)
\(684\) −4.07580e6 + 7.05950e6i −0.333099 + 0.576944i
\(685\) 1.49350e6 0.121613
\(686\) 0 0
\(687\) 7.97275e6 0.644490
\(688\) −4.96210e6 + 8.59461e6i −0.399663 + 0.692237i
\(689\) −581509. 1.00720e6i −0.0466669 0.0808294i
\(690\) −4.49538e6 7.78622e6i −0.359454 0.622593i
\(691\) −8.83583e6 + 1.53041e7i −0.703967 + 1.21931i 0.263096 + 0.964770i \(0.415256\pi\)
−0.967063 + 0.254537i \(0.918077\pi\)
\(692\) −2.45752e7 −1.95088
\(693\) 0 0
\(694\) −1.53973e7 −1.21351
\(695\) −2.51693e6 + 4.35945e6i −0.197656 + 0.342350i
\(696\) −4.44018e6 7.69062e6i −0.347438 0.601781i
\(697\) 1.25753e6 + 2.17810e6i 0.0980473 + 0.169823i
\(698\) 7.89131e6 1.36681e7i 0.613070 1.06187i
\(699\) −5.36547e6 −0.415351
\(700\) 0 0
\(701\) 8.22993e6 0.632559 0.316279 0.948666i \(-0.397566\pi\)
0.316279 + 0.948666i \(0.397566\pi\)
\(702\) 3.79852e6 6.57922e6i 0.290918 0.503886i
\(703\) 6.87472e6 + 1.19074e7i 0.524646 + 0.908714i
\(704\) −780843. 1.35246e6i −0.0593789 0.102847i
\(705\) −333660. + 577916.i −0.0252832 + 0.0437917i
\(706\) 1.71552e7 1.29534
\(707\) 0 0
\(708\) 1.79486e7 1.34570
\(709\) −1.23183e7 + 2.13360e7i −0.920314 + 1.59403i −0.121386 + 0.992605i \(0.538734\pi\)
−0.798929 + 0.601426i \(0.794600\pi\)
\(710\) −737874. 1.27803e6i −0.0549334 0.0951474i
\(711\) 196233. + 339886.i 0.0145579 + 0.0252150i
\(712\) −1.29477e7 + 2.24261e7i −0.957179 + 1.65788i
\(713\) −1.21379e7 −0.894167
\(714\) 0 0
\(715\) −1.12710e7 −0.824510
\(716\) −2.81475e7 + 4.87530e7i −2.05191 + 3.55401i
\(717\) 3.34400e6 + 5.79197e6i 0.242923 + 0.420754i
\(718\) 1.27784e7 + 2.21329e7i 0.925053 + 1.60224i
\(719\) −9.41269e6 + 1.63033e7i −0.679034 + 1.17612i 0.296238 + 0.955114i \(0.404268\pi\)
−0.975272 + 0.221007i \(0.929066\pi\)
\(720\) −3.68503e6 −0.264917
\(721\) 0 0
\(722\) −5.63055e6 −0.401983
\(723\) 5.28677e6 9.15696e6i 0.376136 0.651487i
\(724\) −4.81205e6 8.33472e6i −0.341180 0.590942i
\(725\) −3.04911e6 5.28122e6i −0.215441 0.373155i
\(726\) 2.56093e6 4.43566e6i 0.180325 0.312332i
\(727\) −6.77607e6 −0.475491 −0.237745 0.971328i \(-0.576408\pi\)
−0.237745 + 0.971328i \(0.576408\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 2.03743e6 3.52893e6i 0.141506 0.245096i
\(731\) 1.45537e6 + 2.52077e6i 0.100735 + 0.174478i
\(732\) 6.88760e6 + 1.19297e7i 0.475106 + 0.822908i
\(733\) −8.61136e6 + 1.49153e7i −0.591986 + 1.02535i 0.401978 + 0.915649i \(0.368323\pi\)
−0.993965 + 0.109701i \(0.965011\pi\)
\(734\) 2.15459e7 1.47613
\(735\) 0 0
\(736\) 2.60102e7 1.76990
\(737\) 1.29389e7 2.24109e7i 0.877465 1.51981i
\(738\) −1.85383e6 3.21092e6i −0.125293 0.217014i
\(739\) 8.82669e6 + 1.52883e7i 0.594548 + 1.02979i 0.993610 + 0.112864i \(0.0360023\pi\)
−0.399062 + 0.916924i \(0.630664\pi\)
\(740\) −8.53520e6 + 1.47834e7i −0.572973 + 0.992418i
\(741\) −1.27292e7 −0.851641
\(742\) 0 0
\(743\) −1.36977e7 −0.910281 −0.455141 0.890420i \(-0.650411\pi\)
−0.455141 + 0.890420i \(0.650411\pi\)
\(744\) −5.50163e6 + 9.52911e6i −0.364384 + 0.631132i
\(745\) 1.66594e6 + 2.88549e6i 0.109968 + 0.190471i
\(746\) −1.39670e7 2.41916e7i −0.918877 1.59154i
\(747\) 2.43589e6 4.21908e6i 0.159719 0.276641i
\(748\) −1.89668e7 −1.23948
\(749\) 0 0
\(750\) −1.24269e7 −0.806698
\(751\) −5.80446e6 + 1.00536e7i −0.375545 + 0.650463i −0.990408 0.138171i \(-0.955878\pi\)
0.614864 + 0.788633i \(0.289211\pi\)
\(752\) −2.98943e6 5.17784e6i −0.192772 0.333890i
\(753\) −1.58846e6 2.75130e6i −0.102092 0.176828i
\(754\) 1.24083e7 2.14919e7i 0.794851 1.37672i
\(755\) 3.89526e6 0.248696
\(756\) 0 0
\(757\) 6.25226e6 0.396550 0.198275 0.980146i \(-0.436466\pi\)
0.198275 + 0.980146i \(0.436466\pi\)
\(758\) 1.04434e7 1.80885e7i 0.660191 1.14348i
\(759\) 8.61748e6 + 1.49259e7i 0.542970 + 0.940452i
\(760\) 6.82815e6 + 1.18267e7i 0.428814 + 0.742728i
\(761\) −1.51063e7 + 2.61648e7i −0.945574 + 1.63778i −0.190977 + 0.981595i \(0.561166\pi\)
−0.754597 + 0.656188i \(0.772168\pi\)
\(762\) −2.14605e6 −0.133891
\(763\) 0 0
\(764\) 481393. 0.0298378
\(765\) −540404. + 936007.i −0.0333860 + 0.0578263i
\(766\) 7.71386e6 + 1.33608e7i 0.475007 + 0.822736i
\(767\) 1.40139e7 + 2.42728e7i 0.860142 + 1.48981i
\(768\) −8.21400e6 + 1.42271e7i −0.502518 + 0.870386i
\(769\) 2.58756e7 1.57788 0.788940 0.614470i \(-0.210630\pi