Properties

Label 5.6.b.a.4.1
Level $5$
Weight $6$
Character 5.4
Analytic conductor $0.802$
Analytic rank $0$
Dimension $2$
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] = [5,6,Mod(4,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 5.b (of order \(2\), degree \(1\), 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: \(0.801919099065\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-11}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.1
Root \(0.500000 + 1.65831i\) of defining polynomial
Character \(\chi\) \(=\) 5.4
Dual form 5.6.b.a.4.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-6.63325i q^{2} +19.8997i q^{3} -12.0000 q^{4} +(-45.0000 - 33.1662i) q^{5} +132.000 q^{6} +59.6992i q^{7} -132.665i q^{8} -153.000 q^{9} +O(q^{10})\) \(q-6.63325i q^{2} +19.8997i q^{3} -12.0000 q^{4} +(-45.0000 - 33.1662i) q^{5} +132.000 q^{6} +59.6992i q^{7} -132.665i q^{8} -153.000 q^{9} +(-220.000 + 298.496i) q^{10} +252.000 q^{11} -238.797i q^{12} +119.398i q^{13} +396.000 q^{14} +(660.000 - 895.489i) q^{15} -1264.00 q^{16} +689.858i q^{17} +1014.89i q^{18} -220.000 q^{19} +(540.000 + 397.995i) q^{20} -1188.00 q^{21} -1671.58i q^{22} -2434.40i q^{23} +2640.00 q^{24} +(925.000 + 2984.96i) q^{25} +792.000 q^{26} +1790.98i q^{27} -716.391i q^{28} -6930.00 q^{29} +(-5940.00 - 4377.94i) q^{30} +6752.00 q^{31} +4139.15i q^{32} +5014.74i q^{33} +4576.00 q^{34} +(1980.00 - 2686.47i) q^{35} +1836.00 q^{36} -13969.6i q^{37} +1459.31i q^{38} -2376.00 q^{39} +(-4400.00 + 5969.92i) q^{40} -198.000 q^{41} +7880.30i q^{42} +417.895i q^{43} -3024.00 q^{44} +(6885.00 + 5074.44i) q^{45} -16148.0 q^{46} +10540.2i q^{47} -25153.3i q^{48} +13243.0 q^{49} +(19800.0 - 6135.76i) q^{50} -13728.0 q^{51} -1432.78i q^{52} +5823.99i q^{53} +11880.0 q^{54} +(-11340.0 - 8357.89i) q^{55} +7920.00 q^{56} -4377.94i q^{57} +45968.4i q^{58} -24660.0 q^{59} +(-7920.00 + 10745.9i) q^{60} -5698.00 q^{61} -44787.7i q^{62} -9133.98i q^{63} -12992.0 q^{64} +(3960.00 - 5372.93i) q^{65} +33264.0 q^{66} +43640.1i q^{67} -8278.30i q^{68} +48444.0 q^{69} +(-17820.0 - 13133.8i) q^{70} +53352.0 q^{71} +20297.7i q^{72} -70922.7i q^{73} -92664.0 q^{74} +(-59400.0 + 18407.3i) q^{75} +2640.00 q^{76} +15044.2i q^{77} +15760.6i q^{78} +51920.0 q^{79} +(56880.0 + 41922.1i) q^{80} -72819.0 q^{81} +1313.38i q^{82} +61841.8i q^{83} +14256.0 q^{84} +(22880.0 - 31043.6i) q^{85} +2772.00 q^{86} -137905. i q^{87} -33431.6i q^{88} -9990.00 q^{89} +(33660.0 - 45669.9i) q^{90} -7128.00 q^{91} +29212.8i q^{92} +134363. i q^{93} +69916.0 q^{94} +(9900.00 + 7296.57i) q^{95} -82368.0 q^{96} +101250. i q^{97} -87844.1i q^{98} -38556.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 24 q^{4} - 90 q^{5} + 264 q^{6} - 306 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 24 q^{4} - 90 q^{5} + 264 q^{6} - 306 q^{9} - 440 q^{10} + 504 q^{11} + 792 q^{14} + 1320 q^{15} - 2528 q^{16} - 440 q^{19} + 1080 q^{20} - 2376 q^{21} + 5280 q^{24} + 1850 q^{25} + 1584 q^{26} - 13860 q^{29} - 11880 q^{30} + 13504 q^{31} + 9152 q^{34} + 3960 q^{35} + 3672 q^{36} - 4752 q^{39} - 8800 q^{40} - 396 q^{41} - 6048 q^{44} + 13770 q^{45} - 32296 q^{46} + 26486 q^{49} + 39600 q^{50} - 27456 q^{51} + 23760 q^{54} - 22680 q^{55} + 15840 q^{56} - 49320 q^{59} - 15840 q^{60} - 11396 q^{61} - 25984 q^{64} + 7920 q^{65} + 66528 q^{66} + 96888 q^{69} - 35640 q^{70} + 106704 q^{71} - 185328 q^{74} - 118800 q^{75} + 5280 q^{76} + 103840 q^{79} + 113760 q^{80} - 145638 q^{81} + 28512 q^{84} + 45760 q^{85} + 5544 q^{86} - 19980 q^{89} + 67320 q^{90} - 14256 q^{91} + 139832 q^{94} + 19800 q^{95} - 164736 q^{96} - 77112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.63325i 1.17260i −0.810093 0.586302i \(-0.800583\pi\)
0.810093 0.586302i \(-0.199417\pi\)
\(3\) 19.8997i 1.27657i 0.769800 + 0.638285i \(0.220356\pi\)
−0.769800 + 0.638285i \(0.779644\pi\)
\(4\) −12.0000 −0.375000
\(5\) −45.0000 33.1662i −0.804984 0.593296i
\(6\) 132.000 1.49691
\(7\) 59.6992i 0.460494i 0.973132 + 0.230247i \(0.0739534\pi\)
−0.973132 + 0.230247i \(0.926047\pi\)
\(8\) 132.665i 0.732877i
\(9\) −153.000 −0.629630
\(10\) −220.000 + 298.496i −0.695701 + 0.943928i
\(11\) 252.000 0.627941 0.313970 0.949433i \(-0.398341\pi\)
0.313970 + 0.949433i \(0.398341\pi\)
\(12\) 238.797i 0.478714i
\(13\) 119.398i 0.195948i 0.995189 + 0.0979739i \(0.0312362\pi\)
−0.995189 + 0.0979739i \(0.968764\pi\)
\(14\) 396.000 0.539977
\(15\) 660.000 895.489i 0.757383 1.02762i
\(16\) −1264.00 −1.23438
\(17\) 689.858i 0.578945i 0.957186 + 0.289473i \(0.0934799\pi\)
−0.957186 + 0.289473i \(0.906520\pi\)
\(18\) 1014.89i 0.738306i
\(19\) −220.000 −0.139810 −0.0699051 0.997554i \(-0.522270\pi\)
−0.0699051 + 0.997554i \(0.522270\pi\)
\(20\) 540.000 + 397.995i 0.301869 + 0.222486i
\(21\) −1188.00 −0.587852
\(22\) 1671.58i 0.736326i
\(23\) 2434.40i 0.959561i −0.877388 0.479781i \(-0.840716\pi\)
0.877388 0.479781i \(-0.159284\pi\)
\(24\) 2640.00 0.935569
\(25\) 925.000 + 2984.96i 0.296000 + 0.955188i
\(26\) 792.000 0.229769
\(27\) 1790.98i 0.472804i
\(28\) 716.391i 0.172685i
\(29\) −6930.00 −1.53016 −0.765082 0.643932i \(-0.777302\pi\)
−0.765082 + 0.643932i \(0.777302\pi\)
\(30\) −5940.00 4377.94i −1.20499 0.888111i
\(31\) 6752.00 1.26191 0.630955 0.775820i \(-0.282663\pi\)
0.630955 + 0.775820i \(0.282663\pi\)
\(32\) 4139.15i 0.714556i
\(33\) 5014.74i 0.801610i
\(34\) 4576.00 0.678873
\(35\) 1980.00 2686.47i 0.273209 0.370690i
\(36\) 1836.00 0.236111
\(37\) 13969.6i 1.67757i −0.544464 0.838785i \(-0.683267\pi\)
0.544464 0.838785i \(-0.316733\pi\)
\(38\) 1459.31i 0.163942i
\(39\) −2376.00 −0.250141
\(40\) −4400.00 + 5969.92i −0.434813 + 0.589955i
\(41\) −198.000 −0.0183952 −0.00919762 0.999958i \(-0.502928\pi\)
−0.00919762 + 0.999958i \(0.502928\pi\)
\(42\) 7880.30i 0.689318i
\(43\) 417.895i 0.0344664i 0.999851 + 0.0172332i \(0.00548577\pi\)
−0.999851 + 0.0172332i \(0.994514\pi\)
\(44\) −3024.00 −0.235478
\(45\) 6885.00 + 5074.44i 0.506842 + 0.373557i
\(46\) −16148.0 −1.12519
\(47\) 10540.2i 0.695994i 0.937496 + 0.347997i \(0.113138\pi\)
−0.937496 + 0.347997i \(0.886862\pi\)
\(48\) 25153.3i 1.57577i
\(49\) 13243.0 0.787945
\(50\) 19800.0 6135.76i 1.12006 0.347091i
\(51\) −13728.0 −0.739064
\(52\) 1432.78i 0.0734804i
\(53\) 5823.99i 0.284794i 0.989810 + 0.142397i \(0.0454810\pi\)
−0.989810 + 0.142397i \(0.954519\pi\)
\(54\) 11880.0 0.554411
\(55\) −11340.0 8357.89i −0.505483 0.372555i
\(56\) 7920.00 0.337485
\(57\) 4377.94i 0.178477i
\(58\) 45968.4i 1.79428i
\(59\) −24660.0 −0.922281 −0.461140 0.887327i \(-0.652560\pi\)
−0.461140 + 0.887327i \(0.652560\pi\)
\(60\) −7920.00 + 10745.9i −0.284019 + 0.385357i
\(61\) −5698.00 −0.196064 −0.0980320 0.995183i \(-0.531255\pi\)
−0.0980320 + 0.995183i \(0.531255\pi\)
\(62\) 44787.7i 1.47972i
\(63\) 9133.98i 0.289941i
\(64\) −12992.0 −0.396484
\(65\) 3960.00 5372.93i 0.116255 0.157735i
\(66\) 33264.0 0.939971
\(67\) 43640.1i 1.18768i 0.804583 + 0.593840i \(0.202389\pi\)
−0.804583 + 0.593840i \(0.797611\pi\)
\(68\) 8278.30i 0.217104i
\(69\) 48444.0 1.22495
\(70\) −17820.0 13133.8i −0.434673 0.320366i
\(71\) 53352.0 1.25604 0.628022 0.778196i \(-0.283865\pi\)
0.628022 + 0.778196i \(0.283865\pi\)
\(72\) 20297.7i 0.461441i
\(73\) 70922.7i 1.55768i −0.627223 0.778840i \(-0.715808\pi\)
0.627223 0.778840i \(-0.284192\pi\)
\(74\) −92664.0 −1.96712
\(75\) −59400.0 + 18407.3i −1.21936 + 0.377865i
\(76\) 2640.00 0.0524288
\(77\) 15044.2i 0.289163i
\(78\) 15760.6i 0.293316i
\(79\) 51920.0 0.935981 0.467990 0.883734i \(-0.344978\pi\)
0.467990 + 0.883734i \(0.344978\pi\)
\(80\) 56880.0 + 41922.1i 0.993653 + 0.732350i
\(81\) −72819.0 −1.23320
\(82\) 1313.38i 0.0215703i
\(83\) 61841.8i 0.985342i 0.870216 + 0.492671i \(0.163979\pi\)
−0.870216 + 0.492671i \(0.836021\pi\)
\(84\) 14256.0 0.220445
\(85\) 22880.0 31043.6i 0.343486 0.466042i
\(86\) 2772.00 0.0404154
\(87\) 137905.i 1.95336i
\(88\) 33431.6i 0.460204i
\(89\) −9990.00 −0.133687 −0.0668437 0.997763i \(-0.521293\pi\)
−0.0668437 + 0.997763i \(0.521293\pi\)
\(90\) 33660.0 45669.9i 0.438034 0.594325i
\(91\) −7128.00 −0.0902328
\(92\) 29212.8i 0.359836i
\(93\) 134363.i 1.61092i
\(94\) 69916.0 0.816125
\(95\) 9900.00 + 7296.57i 0.112545 + 0.0829488i
\(96\) −82368.0 −0.912180
\(97\) 101250.i 1.09261i 0.837586 + 0.546305i \(0.183966\pi\)
−0.837586 + 0.546305i \(0.816034\pi\)
\(98\) 87844.1i 0.923948i
\(99\) −38556.0 −0.395370
\(100\) −11100.0 35819.5i −0.111000 0.358195i
\(101\) −109098. −1.06418 −0.532088 0.846689i \(-0.678592\pi\)
−0.532088 + 0.846689i \(0.678592\pi\)
\(102\) 91061.3i 0.866629i
\(103\) 70624.2i 0.655935i −0.944689 0.327967i \(-0.893636\pi\)
0.944689 0.327967i \(-0.106364\pi\)
\(104\) 15840.0 0.143606
\(105\) 53460.0 + 39401.5i 0.473212 + 0.348770i
\(106\) 38632.0 0.333951
\(107\) 97117.4i 0.820045i −0.912075 0.410022i \(-0.865521\pi\)
0.912075 0.410022i \(-0.134479\pi\)
\(108\) 21491.7i 0.177301i
\(109\) −21010.0 −0.169379 −0.0846895 0.996407i \(-0.526990\pi\)
−0.0846895 + 0.996407i \(0.526990\pi\)
\(110\) −55440.0 + 75221.1i −0.436859 + 0.592731i
\(111\) 277992. 2.14153
\(112\) 75459.8i 0.568422i
\(113\) 105018.i 0.773688i −0.922145 0.386844i \(-0.873565\pi\)
0.922145 0.386844i \(-0.126435\pi\)
\(114\) −29040.0 −0.209283
\(115\) −80740.0 + 109548.i −0.569304 + 0.772432i
\(116\) 83160.0 0.573812
\(117\) 18268.0i 0.123375i
\(118\) 163576.i 1.08147i
\(119\) −41184.0 −0.266601
\(120\) −118800. 87558.9i −0.753119 0.555069i
\(121\) −97547.0 −0.605690
\(122\) 37796.3i 0.229905i
\(123\) 3940.15i 0.0234828i
\(124\) −81024.0 −0.473216
\(125\) 57375.0 165002.i 0.328434 0.944527i
\(126\) −60588.0 −0.339985
\(127\) 87220.6i 0.479855i 0.970791 + 0.239927i \(0.0771236\pi\)
−0.970791 + 0.239927i \(0.922876\pi\)
\(128\) 218632.i 1.17947i
\(129\) −8316.00 −0.0439987
\(130\) −35640.0 26267.7i −0.184961 0.136321i
\(131\) 192852. 0.981852 0.490926 0.871201i \(-0.336659\pi\)
0.490926 + 0.871201i \(0.336659\pi\)
\(132\) 60176.8i 0.300604i
\(133\) 13133.8i 0.0643817i
\(134\) 289476. 1.39268
\(135\) 59400.0 80594.0i 0.280512 0.380599i
\(136\) 91520.0 0.424296
\(137\) 143570.i 0.653525i 0.945106 + 0.326763i \(0.105958\pi\)
−0.945106 + 0.326763i \(0.894042\pi\)
\(138\) 321341.i 1.43638i
\(139\) −318340. −1.39751 −0.698754 0.715362i \(-0.746262\pi\)
−0.698754 + 0.715362i \(0.746262\pi\)
\(140\) −23760.0 + 32237.6i −0.102453 + 0.139009i
\(141\) −209748. −0.888485
\(142\) 353897.i 1.47284i
\(143\) 30088.4i 0.123044i
\(144\) 193392. 0.777199
\(145\) 311850. + 229842.i 1.23176 + 0.907841i
\(146\) −470448. −1.82654
\(147\) 263532.i 1.00587i
\(148\) 167635.i 0.629088i
\(149\) 84150.0 0.310519 0.155260 0.987874i \(-0.450379\pi\)
0.155260 + 0.987874i \(0.450379\pi\)
\(150\) 122100. + 394015.i 0.443085 + 1.42983i
\(151\) −155848. −0.556236 −0.278118 0.960547i \(-0.589711\pi\)
−0.278118 + 0.960547i \(0.589711\pi\)
\(152\) 29186.3i 0.102464i
\(153\) 105548.i 0.364521i
\(154\) 99792.0 0.339074
\(155\) −303840. 223939.i −1.01582 0.748686i
\(156\) 28512.0 0.0938029
\(157\) 356643.i 1.15474i −0.816482 0.577371i \(-0.804079\pi\)
0.816482 0.577371i \(-0.195921\pi\)
\(158\) 344398.i 1.09753i
\(159\) −115896. −0.363560
\(160\) 137280. 186262.i 0.423943 0.575206i
\(161\) 145332. 0.441872
\(162\) 483027.i 1.44605i
\(163\) 144890.i 0.427139i 0.976928 + 0.213570i \(0.0685090\pi\)
−0.976928 + 0.213570i \(0.931491\pi\)
\(164\) 2376.00 0.00689822
\(165\) 166320. 225663.i 0.475592 0.645284i
\(166\) 410212. 1.15542
\(167\) 18102.1i 0.0502272i 0.999685 + 0.0251136i \(0.00799474\pi\)
−0.999685 + 0.0251136i \(0.992005\pi\)
\(168\) 157606.i 0.430824i
\(169\) 357037. 0.961604
\(170\) −205920. 151769.i −0.546482 0.402773i
\(171\) 33660.0 0.0880286
\(172\) 5014.74i 0.0129249i
\(173\) 492572.i 1.25128i 0.780112 + 0.625640i \(0.215162\pi\)
−0.780112 + 0.625640i \(0.784838\pi\)
\(174\) −914760. −2.29052
\(175\) −178200. + 55221.8i −0.439858 + 0.136306i
\(176\) −318528. −0.775115
\(177\) 490728.i 1.17736i
\(178\) 66266.2i 0.156762i
\(179\) 444420. 1.03672 0.518359 0.855163i \(-0.326543\pi\)
0.518359 + 0.855163i \(0.326543\pi\)
\(180\) −82620.0 60893.2i −0.190066 0.140084i
\(181\) 156902. 0.355985 0.177993 0.984032i \(-0.443040\pi\)
0.177993 + 0.984032i \(0.443040\pi\)
\(182\) 47281.8i 0.105807i
\(183\) 113389.i 0.250289i
\(184\) −322960. −0.703241
\(185\) −463320. + 628633.i −0.995295 + 1.35042i
\(186\) 891264. 1.88897
\(187\) 173844.i 0.363543i
\(188\) 126483.i 0.260998i
\(189\) −106920. −0.217723
\(190\) 48400.0 65669.2i 0.0972661 0.131971i
\(191\) 332352. 0.659196 0.329598 0.944121i \(-0.393087\pi\)
0.329598 + 0.944121i \(0.393087\pi\)
\(192\) 258538.i 0.506140i
\(193\) 786120.i 1.51913i −0.650430 0.759566i \(-0.725411\pi\)
0.650430 0.759566i \(-0.274589\pi\)
\(194\) 671616. 1.28120
\(195\) 106920. + 78803.0i 0.201360 + 0.148408i
\(196\) −158916. −0.295480
\(197\) 59606.4i 0.109428i −0.998502 0.0547138i \(-0.982575\pi\)
0.998502 0.0547138i \(-0.0174247\pi\)
\(198\) 255752.i 0.463613i
\(199\) −395800. −0.708505 −0.354253 0.935150i \(-0.615265\pi\)
−0.354253 + 0.935150i \(0.615265\pi\)
\(200\) 396000. 122715.i 0.700036 0.216932i
\(201\) −868428. −1.51616
\(202\) 723674.i 1.24786i
\(203\) 413716.i 0.704631i
\(204\) 164736. 0.277149
\(205\) 8910.00 + 6566.92i 0.0148079 + 0.0109138i
\(206\) −468468. −0.769151
\(207\) 372464.i 0.604168i
\(208\) 150920.i 0.241873i
\(209\) −55440.0 −0.0877925
\(210\) 261360. 354614.i 0.408969 0.554890i
\(211\) −251548. −0.388969 −0.194484 0.980906i \(-0.562303\pi\)
−0.194484 + 0.980906i \(0.562303\pi\)
\(212\) 69887.9i 0.106798i
\(213\) 1.06169e6i 1.60343i
\(214\) −644204. −0.961588
\(215\) 13860.0 18805.3i 0.0204488 0.0277449i
\(216\) 237600. 0.346507
\(217\) 403089.i 0.581101i
\(218\) 139365.i 0.198615i
\(219\) 1.41134e6 1.98849
\(220\) 136080. + 100295.i 0.189556 + 0.139708i
\(221\) −82368.0 −0.113443
\(222\) 1.84399e6i 2.51117i
\(223\) 288765.i 0.388851i 0.980917 + 0.194425i \(0.0622842\pi\)
−0.980917 + 0.194425i \(0.937716\pi\)
\(224\) −247104. −0.329048
\(225\) −141525. 456699.i −0.186370 0.601415i
\(226\) −696608. −0.907230
\(227\) 1.16414e6i 1.49948i −0.661731 0.749741i \(-0.730178\pi\)
0.661731 0.749741i \(-0.269822\pi\)
\(228\) 52535.3i 0.0669290i
\(229\) 547670. 0.690129 0.345064 0.938579i \(-0.387857\pi\)
0.345064 + 0.938579i \(0.387857\pi\)
\(230\) 726660. + 535569.i 0.905757 + 0.667568i
\(231\) −299376. −0.369137
\(232\) 919368.i 1.12142i
\(233\) 48104.3i 0.0580489i −0.999579 0.0290245i \(-0.990760\pi\)
0.999579 0.0290245i \(-0.00924007\pi\)
\(234\) −121176. −0.144669
\(235\) 349580. 474311.i 0.412930 0.560264i
\(236\) 295920. 0.345855
\(237\) 1.03319e6i 1.19484i
\(238\) 273184.i 0.312617i
\(239\) −1.00584e6 −1.13903 −0.569514 0.821982i \(-0.692868\pi\)
−0.569514 + 0.821982i \(0.692868\pi\)
\(240\) −834240. + 1.13190e6i −0.934895 + 1.26847i
\(241\) 895202. 0.992838 0.496419 0.868083i \(-0.334648\pi\)
0.496419 + 0.868083i \(0.334648\pi\)
\(242\) 647054.i 0.710235i
\(243\) 1.01387e6i 1.10146i
\(244\) 68376.0 0.0735240
\(245\) −595935. 439221.i −0.634284 0.467485i
\(246\) −26136.0 −0.0275360
\(247\) 26267.7i 0.0273955i
\(248\) 895754.i 0.924825i
\(249\) −1.23064e6 −1.25786
\(250\) −1.09450e6 380583.i −1.10756 0.385123i
\(251\) 558252. 0.559301 0.279651 0.960102i \(-0.409781\pi\)
0.279651 + 0.960102i \(0.409781\pi\)
\(252\) 109608.i 0.108728i
\(253\) 613469.i 0.602548i
\(254\) 578556. 0.562680
\(255\) 617760. + 455306.i 0.594935 + 0.438483i
\(256\) 1.03450e6 0.986572
\(257\) 787924.i 0.744135i 0.928206 + 0.372067i \(0.121351\pi\)
−0.928206 + 0.372067i \(0.878649\pi\)
\(258\) 55162.1i 0.0515931i
\(259\) 833976. 0.772510
\(260\) −47520.0 + 64475.2i −0.0435956 + 0.0591506i
\(261\) 1.06029e6 0.963437
\(262\) 1.27924e6i 1.15132i
\(263\) 1.63173e6i 1.45465i 0.686291 + 0.727327i \(0.259238\pi\)
−0.686291 + 0.727327i \(0.740762\pi\)
\(264\) 665280. 0.587482
\(265\) 193160. 262080.i 0.168967 0.229255i
\(266\) −87120.0 −0.0754942
\(267\) 198798.i 0.170661i
\(268\) 523682.i 0.445380i
\(269\) −1.73637e6 −1.46306 −0.731529 0.681810i \(-0.761193\pi\)
−0.731529 + 0.681810i \(0.761193\pi\)
\(270\) −534600. 394015.i −0.446292 0.328930i
\(271\) −1.72005e6 −1.42271 −0.711357 0.702831i \(-0.751919\pi\)
−0.711357 + 0.702831i \(0.751919\pi\)
\(272\) 871980.i 0.714635i
\(273\) 141845.i 0.115188i
\(274\) 952336. 0.766326
\(275\) 233100. + 752211.i 0.185871 + 0.599802i
\(276\) −581328. −0.459355
\(277\) 1.27243e6i 0.996402i −0.867062 0.498201i \(-0.833994\pi\)
0.867062 0.498201i \(-0.166006\pi\)
\(278\) 2.11163e6i 1.63872i
\(279\) −1.03306e6 −0.794536
\(280\) −356400. 262677.i −0.271671 0.200229i
\(281\) 1.46500e6 1.10681 0.553404 0.832913i \(-0.313329\pi\)
0.553404 + 0.832913i \(0.313329\pi\)
\(282\) 1.39131e6i 1.04184i
\(283\) 1.65051e6i 1.22504i 0.790455 + 0.612521i \(0.209844\pi\)
−0.790455 + 0.612521i \(0.790156\pi\)
\(284\) −640224. −0.471016
\(285\) −145200. + 197008.i −0.105890 + 0.143672i
\(286\) 199584. 0.144281
\(287\) 11820.5i 0.00847089i
\(288\) 633290.i 0.449905i
\(289\) 943953. 0.664823
\(290\) 1.52460e6 2.06858e6i 1.06454 1.44437i
\(291\) −2.01485e6 −1.39479
\(292\) 851072.i 0.584130i
\(293\) 2.38772e6i 1.62485i −0.583064 0.812426i \(-0.698146\pi\)
0.583064 0.812426i \(-0.301854\pi\)
\(294\) 1.74808e6 1.17948
\(295\) 1.10970e6 + 817880.i 0.742422 + 0.547185i
\(296\) −1.85328e6 −1.22945
\(297\) 451326.i 0.296893i
\(298\) 558188.i 0.364116i
\(299\) 290664. 0.188024
\(300\) 712800. 220887.i 0.457261 0.141699i
\(301\) −24948.0 −0.0158716
\(302\) 1.03378e6i 0.652244i
\(303\) 2.17102e6i 1.35849i
\(304\) 278080. 0.172578
\(305\) 256410. + 188981.i 0.157828 + 0.116324i
\(306\) −700128. −0.427439
\(307\) 928264.i 0.562115i −0.959691 0.281058i \(-0.909315\pi\)
0.959691 0.281058i \(-0.0906852\pi\)
\(308\) 180531.i 0.108436i
\(309\) 1.40540e6 0.837346
\(310\) −1.48544e6 + 2.01545e6i −0.877912 + 1.19115i
\(311\) 568152. 0.333092 0.166546 0.986034i \(-0.446739\pi\)
0.166546 + 0.986034i \(0.446739\pi\)
\(312\) 315212.i 0.183323i
\(313\) 1.72244e6i 0.993766i 0.867818 + 0.496883i \(0.165522\pi\)
−0.867818 + 0.496883i \(0.834478\pi\)
\(314\) −2.36570e6 −1.35405
\(315\) −302940. + 411029.i −0.172021 + 0.233398i
\(316\) −623040. −0.350993
\(317\) 131643.i 0.0735785i −0.999323 0.0367893i \(-0.988287\pi\)
0.999323 0.0367893i \(-0.0117130\pi\)
\(318\) 768767.i 0.426311i
\(319\) −1.74636e6 −0.960853
\(320\) 584640. + 430896.i 0.319164 + 0.235233i
\(321\) 1.93261e6 1.04684
\(322\) 964023.i 0.518141i
\(323\) 151769.i 0.0809424i
\(324\) 873828. 0.462449
\(325\) −356400. + 110444.i −0.187167 + 0.0580006i
\(326\) 961092. 0.500865
\(327\) 418094.i 0.216224i
\(328\) 26267.7i 0.0134815i
\(329\) −629244. −0.320501
\(330\) −1.49688e6 1.10324e6i −0.756662 0.557681i
\(331\) −1.58055e6 −0.792935 −0.396468 0.918049i \(-0.629764\pi\)
−0.396468 + 0.918049i \(0.629764\pi\)
\(332\) 742101.i 0.369503i
\(333\) 2.13735e6i 1.05625i
\(334\) 120076. 0.0588966
\(335\) 1.44738e6 1.96381e6i 0.704645 0.956063i
\(336\) 1.50163e6 0.725630
\(337\) 1.22885e6i 0.589419i −0.955587 0.294709i \(-0.904777\pi\)
0.955587 0.294709i \(-0.0952228\pi\)
\(338\) 2.36832e6i 1.12758i
\(339\) 2.08982e6 0.987667
\(340\) −274560. + 372523.i −0.128807 + 0.174766i
\(341\) 1.70150e6 0.792405
\(342\) 223275.i 0.103223i
\(343\) 1.79396e6i 0.823338i
\(344\) 55440.0 0.0252596
\(345\) −2.17998e6 1.60671e6i −0.986063 0.726756i
\(346\) 3.26735e6 1.46726
\(347\) 3.84224e6i 1.71301i 0.516137 + 0.856506i \(0.327370\pi\)
−0.516137 + 0.856506i \(0.672630\pi\)
\(348\) 1.65486e6i 0.732511i
\(349\) −1.59445e6 −0.700725 −0.350362 0.936614i \(-0.613942\pi\)
−0.350362 + 0.936614i \(0.613942\pi\)
\(350\) 366300. + 1.18205e6i 0.159833 + 0.515779i
\(351\) −213840. −0.0926448
\(352\) 1.04307e6i 0.448699i
\(353\) 295365.i 0.126160i 0.998008 + 0.0630802i \(0.0200924\pi\)
−0.998008 + 0.0630802i \(0.979908\pi\)
\(354\) −3.25512e6 −1.38057
\(355\) −2.40084e6 1.76949e6i −1.01110 0.745206i
\(356\) 119880. 0.0501328
\(357\) 819551.i 0.340334i
\(358\) 2.94795e6i 1.21566i
\(359\) 1.10484e6 0.452442 0.226221 0.974076i \(-0.427363\pi\)
0.226221 + 0.974076i \(0.427363\pi\)
\(360\) 673200. 913398.i 0.273771 0.371453i
\(361\) −2.42770e6 −0.980453
\(362\) 1.04077e6i 0.417430i
\(363\) 1.94116e6i 0.773206i
\(364\) 85536.0 0.0338373
\(365\) −2.35224e6 + 3.19152e6i −0.924165 + 1.25391i
\(366\) −752136. −0.293490
\(367\) 1.83760e6i 0.712174i 0.934453 + 0.356087i \(0.115889\pi\)
−0.934453 + 0.356087i \(0.884111\pi\)
\(368\) 3.07708e6i 1.18446i
\(369\) 30294.0 0.0115822
\(370\) 4.16988e6 + 3.07332e6i 1.58350 + 1.16709i
\(371\) −347688. −0.131146
\(372\) 1.61236e6i 0.604093i
\(373\) 2.93350e6i 1.09173i −0.837874 0.545864i \(-0.816202\pi\)
0.837874 0.545864i \(-0.183798\pi\)
\(374\) 1.15315e6 0.426292
\(375\) 3.28350e6 + 1.14175e6i 1.20575 + 0.419268i
\(376\) 1.39832e6 0.510078
\(377\) 827432.i 0.299832i
\(378\) 709227.i 0.255303i
\(379\) 5.09342e6 1.82143 0.910713 0.413040i \(-0.135533\pi\)
0.910713 + 0.413040i \(0.135533\pi\)
\(380\) −118800. 87558.9i −0.0422044 0.0311058i
\(381\) −1.73567e6 −0.612568
\(382\) 2.20457e6i 0.772976i
\(383\) 3.17485e6i 1.10593i −0.833205 0.552964i \(-0.813497\pi\)
0.833205 0.552964i \(-0.186503\pi\)
\(384\) −4.35072e6 −1.50568
\(385\) 498960. 676989.i 0.171559 0.232772i
\(386\) −5.21453e6 −1.78134
\(387\) 63937.9i 0.0217011i
\(388\) 1.21500e6i 0.409729i
\(389\) 1.79991e6 0.603083 0.301541 0.953453i \(-0.402499\pi\)
0.301541 + 0.953453i \(0.402499\pi\)
\(390\) 522720. 709227.i 0.174023 0.236115i
\(391\) 1.67939e6 0.555533
\(392\) 1.75688e6i 0.577467i
\(393\) 3.83771e6i 1.25340i
\(394\) −395384. −0.128315
\(395\) −2.33640e6 1.72199e6i −0.753450 0.555314i
\(396\) 462672. 0.148264
\(397\) 4.90405e6i 1.56163i 0.624760 + 0.780817i \(0.285197\pi\)
−0.624760 + 0.780817i \(0.714803\pi\)
\(398\) 2.62544e6i 0.830796i
\(399\) 261360. 0.0821877
\(400\) −1.16920e6 3.77299e6i −0.365375 1.17906i
\(401\) −642798. −0.199624 −0.0998122 0.995006i \(-0.531824\pi\)
−0.0998122 + 0.995006i \(0.531824\pi\)
\(402\) 5.76050e6i 1.77785i
\(403\) 806179.i 0.247268i
\(404\) 1.30918e6 0.399066
\(405\) 3.27686e6 + 2.41513e6i 0.992704 + 0.731650i
\(406\) −2.74428e6 −0.826254
\(407\) 3.52035e6i 1.05341i
\(408\) 1.82123e6i 0.541643i
\(409\) −2.05711e6 −0.608064 −0.304032 0.952662i \(-0.598333\pi\)
−0.304032 + 0.952662i \(0.598333\pi\)
\(410\) 43560.0 59102.3i 0.0127976 0.0173638i
\(411\) −2.85701e6 −0.834271
\(412\) 847490.i 0.245975i
\(413\) 1.47218e6i 0.424704i
\(414\) 2.47064e6 0.708450
\(415\) 2.05106e6 2.78288e6i 0.584599 0.793185i
\(416\) −494208. −0.140016
\(417\) 6.33489e6i 1.78402i
\(418\) 367747.i 0.102946i
\(419\) −2.93742e6 −0.817393 −0.408697 0.912670i \(-0.634017\pi\)
−0.408697 + 0.912670i \(0.634017\pi\)
\(420\) −641520. 472818.i −0.177454 0.130789i
\(421\) 2.71770e6 0.747303 0.373651 0.927569i \(-0.378106\pi\)
0.373651 + 0.927569i \(0.378106\pi\)
\(422\) 1.66858e6i 0.456106i
\(423\) 1.61266e6i 0.438219i
\(424\) 772640. 0.208719
\(425\) −2.05920e6 + 638119.i −0.553001 + 0.171368i
\(426\) 7.04246e6 1.88019
\(427\) 340166.i 0.0902862i
\(428\) 1.16541e6i 0.307517i
\(429\) −598752. −0.157074
\(430\) −124740. 91936.8i −0.0325338 0.0239783i
\(431\) 4.99435e6 1.29505 0.647524 0.762045i \(-0.275804\pi\)
0.647524 + 0.762045i \(0.275804\pi\)
\(432\) 2.26380e6i 0.583617i
\(433\) 2.08183e6i 0.533612i 0.963750 + 0.266806i \(0.0859684\pi\)
−0.963750 + 0.266806i \(0.914032\pi\)
\(434\) 2.67379e6 0.681402
\(435\) −4.57380e6 + 6.20574e6i −1.15892 + 1.57243i
\(436\) 252120. 0.0635172
\(437\) 535569.i 0.134156i
\(438\) 9.36180e6i 2.33171i
\(439\) −4.70404e6 −1.16496 −0.582478 0.812846i \(-0.697917\pi\)
−0.582478 + 0.812846i \(0.697917\pi\)
\(440\) −1.10880e6 + 1.50442e6i −0.273037 + 0.370457i
\(441\) −2.02618e6 −0.496114
\(442\) 546368.i 0.133024i
\(443\) 5.70103e6i 1.38021i 0.723711 + 0.690103i \(0.242435\pi\)
−0.723711 + 0.690103i \(0.757565\pi\)
\(444\) −3.33590e6 −0.803075
\(445\) 449550. + 331331.i 0.107616 + 0.0793162i
\(446\) 1.91545e6 0.455968
\(447\) 1.67456e6i 0.396399i
\(448\) 775613.i 0.182579i
\(449\) 6.20325e6 1.45212 0.726062 0.687630i \(-0.241349\pi\)
0.726062 + 0.687630i \(0.241349\pi\)
\(450\) −3.02940e6 + 938771.i −0.705221 + 0.218539i
\(451\) −49896.0 −0.0115511
\(452\) 1.26021e6i 0.290133i
\(453\) 3.10134e6i 0.710074i
\(454\) −7.72204e6 −1.75830
\(455\) 320760. + 236409.i 0.0726360 + 0.0535347i
\(456\) −580800. −0.130802
\(457\) 2.15371e6i 0.482388i 0.970477 + 0.241194i \(0.0775391\pi\)
−0.970477 + 0.241194i \(0.922461\pi\)
\(458\) 3.63283e6i 0.809248i
\(459\) −1.23552e6 −0.273727
\(460\) 968880. 1.31458e6i 0.213489 0.289662i
\(461\) −3.85130e6 −0.844024 −0.422012 0.906590i \(-0.638676\pi\)
−0.422012 + 0.906590i \(0.638676\pi\)
\(462\) 1.98584e6i 0.432851i
\(463\) 2.08213e6i 0.451394i 0.974198 + 0.225697i \(0.0724659\pi\)
−0.974198 + 0.225697i \(0.927534\pi\)
\(464\) 8.75952e6 1.88880
\(465\) 4.45632e6 6.04634e6i 0.955749 1.29676i
\(466\) −319088. −0.0680684
\(467\) 1.30822e6i 0.277579i −0.990322 0.138790i \(-0.955679\pi\)
0.990322 0.138790i \(-0.0443212\pi\)
\(468\) 219216.i 0.0462655i
\(469\) −2.60528e6 −0.546919
\(470\) −3.14622e6 2.31885e6i −0.656968 0.484204i
\(471\) 7.09711e6 1.47411
\(472\) 3.27152e6i 0.675919i
\(473\) 105309.i 0.0216429i
\(474\) 6.85344e6 1.40108
\(475\) −203500. 656692.i −0.0413838 0.133545i
\(476\) 494208. 0.0999752
\(477\) 891071.i 0.179315i
\(478\) 6.67199e6i 1.33563i
\(479\) −6.76368e6 −1.34693 −0.673464 0.739220i \(-0.735194\pi\)
−0.673464 + 0.739220i \(0.735194\pi\)
\(480\) 3.70656e6 + 2.73184e6i 0.734291 + 0.541193i
\(481\) 1.66795e6 0.328716
\(482\) 5.93810e6i 1.16421i
\(483\) 2.89207e6i 0.564080i
\(484\) 1.17056e6 0.227134
\(485\) 3.35808e6 4.55625e6i 0.648241 0.879534i
\(486\) −6.72527e6 −1.29157
\(487\) 6.67193e6i 1.27476i −0.770549 0.637381i \(-0.780018\pi\)
0.770549 0.637381i \(-0.219982\pi\)
\(488\) 755925.i 0.143691i
\(489\) −2.88328e6 −0.545273
\(490\) −2.91346e6 + 3.95299e6i −0.548175 + 0.743764i
\(491\) −6.87575e6 −1.28711 −0.643556 0.765399i \(-0.722542\pi\)
−0.643556 + 0.765399i \(0.722542\pi\)
\(492\) 47281.8i 0.00880605i
\(493\) 4.78072e6i 0.885881i
\(494\) −174240. −0.0321241
\(495\) 1.73502e6 + 1.27876e6i 0.318267 + 0.234572i
\(496\) −8.53453e6 −1.55767
\(497\) 3.18507e6i 0.578400i
\(498\) 8.16312e6i 1.47497i
\(499\) 6.94010e6 1.24771 0.623856 0.781539i \(-0.285565\pi\)
0.623856 + 0.781539i \(0.285565\pi\)
\(500\) −688500. + 1.98002e6i −0.123163 + 0.354198i
\(501\) −360228. −0.0641185
\(502\) 3.70302e6i 0.655839i
\(503\) 921007.i 0.162309i −0.996702 0.0811546i \(-0.974139\pi\)
0.996702 0.0811546i \(-0.0258607\pi\)
\(504\) −1.21176e6 −0.212491
\(505\) 4.90941e6 + 3.61837e6i 0.856645 + 0.631371i
\(506\) −4.06930e6 −0.706550
\(507\) 7.10495e6i 1.22755i
\(508\) 1.04665e6i 0.179946i
\(509\) 4.97979e6 0.851955 0.425977 0.904734i \(-0.359930\pi\)
0.425977 + 0.904734i \(0.359930\pi\)
\(510\) 3.02016e6 4.09776e6i 0.514167 0.697623i
\(511\) 4.23403e6 0.717302
\(512\) 134151.i 0.0226161i
\(513\) 394015.i 0.0661027i
\(514\) 5.22650e6 0.872575
\(515\) −2.34234e6 + 3.17809e6i −0.389163 + 0.528017i
\(516\) 99792.0 0.0164995
\(517\) 2.65614e6i 0.437043i
\(518\) 5.53197e6i 0.905848i
\(519\) −9.80206e6 −1.59735
\(520\) −712800. 525353.i −0.115600 0.0852007i
\(521\) −147798. −0.0238547 −0.0119274 0.999929i \(-0.503797\pi\)
−0.0119274 + 0.999929i \(0.503797\pi\)
\(522\) 7.03317e6i 1.12973i
\(523\) 1.23884e7i 1.98043i −0.139543 0.990216i \(-0.544563\pi\)
0.139543 0.990216i \(-0.455437\pi\)
\(524\) −2.31422e6 −0.368194
\(525\) −1.09890e6 3.54614e6i −0.174004 0.561509i
\(526\) 1.08237e7 1.70573
\(527\) 4.65792e6i 0.730576i
\(528\) 6.33863e6i 0.989488i
\(529\) 510027. 0.0792417
\(530\) −1.73844e6 1.28128e6i −0.268825 0.198132i
\(531\) 3.77298e6 0.580695
\(532\) 157606.i 0.0241431i
\(533\) 23640.9i 0.00360451i
\(534\) −1.31868e6 −0.200118
\(535\) −3.22102e6 + 4.37028e6i −0.486529 + 0.660123i
\(536\) 5.78952e6 0.870423
\(537\) 8.84385e6i 1.32344i
\(538\) 1.15178e7i 1.71559i
\(539\) 3.33724e6 0.494783
\(540\) −712800. + 967128.i −0.105192 + 0.142725i
\(541\) −9.99810e6 −1.46867 −0.734335 0.678787i \(-0.762506\pi\)
−0.734335 + 0.678787i \(0.762506\pi\)
\(542\) 1.14095e7i 1.66828i
\(543\) 3.12231e6i 0.454440i
\(544\) −2.85542e6 −0.413688
\(545\) 945450. + 696823.i 0.136348 + 0.100492i
\(546\) −940896. −0.135070
\(547\) 1.18580e7i 1.69451i −0.531189 0.847253i \(-0.678255\pi\)
0.531189 0.847253i \(-0.321745\pi\)
\(548\) 1.72284e6i 0.245072i
\(549\) 871794. 0.123448
\(550\) 4.98960e6 1.54621e6i 0.703330 0.217953i
\(551\) 1.52460e6 0.213933
\(552\) 6.42682e6i 0.897736i
\(553\) 3.09958e6i 0.431013i
\(554\) −8.44034e6 −1.16838
\(555\) −1.25096e7 9.21995e6i −1.72390 1.27056i
\(556\) 3.82008e6 0.524065
\(557\) 904550.i 0.123536i −0.998091 0.0617681i \(-0.980326\pi\)
0.998091 0.0617681i \(-0.0196739\pi\)
\(558\) 6.85252e6i 0.931676i
\(559\) −49896.0 −0.00675361
\(560\) −2.50272e6 + 3.39569e6i −0.337242 + 0.457571i
\(561\) −3.45946e6 −0.464088
\(562\) 9.71772e6i 1.29785i
\(563\) 8.68719e6i 1.15507i 0.816366 + 0.577535i \(0.195985\pi\)
−0.816366 + 0.577535i \(0.804015\pi\)
\(564\) 2.51698e6 0.333182
\(565\) −3.48304e6 + 4.72579e6i −0.459026 + 0.622807i
\(566\) 1.09482e7 1.43649
\(567\) 4.34724e6i 0.567879i
\(568\) 7.07794e6i 0.920526i
\(569\) −2.27007e6 −0.293940 −0.146970 0.989141i \(-0.546952\pi\)
−0.146970 + 0.989141i \(0.546952\pi\)
\(570\) 1.30680e6 + 963148.i 0.168470 + 0.124167i
\(571\) 1.43807e7 1.84582 0.922908 0.385021i \(-0.125806\pi\)
0.922908 + 0.385021i \(0.125806\pi\)
\(572\) 361061.i 0.0461414i
\(573\) 6.61372e6i 0.841510i
\(574\) −78408.0 −0.00993300
\(575\) 7.26660e6 2.25182e6i 0.916562 0.284030i
\(576\) 1.98778e6 0.249638
\(577\) 5.63943e6i 0.705173i −0.935779 0.352586i \(-0.885302\pi\)
0.935779 0.352586i \(-0.114698\pi\)
\(578\) 6.26148e6i 0.779574i
\(579\) 1.56436e7 1.93928
\(580\) −3.74220e6 2.75811e6i −0.461910 0.340440i
\(581\) −3.69191e6 −0.453744
\(582\) 1.33650e7i 1.63554i
\(583\) 1.46765e6i 0.178834i
\(584\) −9.40896e6 −1.14159
\(585\) −605880. + 822059.i −0.0731976 + 0.0993146i
\(586\) −1.58383e7 −1.90531
\(587\) 1.28473e6i 0.153893i −0.997035 0.0769464i \(-0.975483\pi\)
0.997035 0.0769464i \(-0.0245170\pi\)
\(588\) 3.16239e6i 0.377200i
\(589\) −1.48544e6 −0.176428
\(590\) 5.42520e6 7.36092e6i 0.641632 0.870566i
\(591\) 1.18615e6 0.139692
\(592\) 1.76576e7i 2.07075i
\(593\) 7.00943e6i 0.818552i −0.912411 0.409276i \(-0.865781\pi\)
0.912411 0.409276i \(-0.134219\pi\)
\(594\) 2.99376e6 0.348138
\(595\) 1.85328e6 + 1.36592e6i 0.214609 + 0.158173i
\(596\) −1.00980e6 −0.116445
\(597\) 7.87632e6i 0.904456i
\(598\) 1.92805e6i 0.220478i
\(599\) −8.80020e6 −1.00213 −0.501067 0.865409i \(-0.667059\pi\)
−0.501067 + 0.865409i \(0.667059\pi\)
\(600\) 2.44200e6 + 7.88030e6i 0.276928 + 0.893644i
\(601\) −1.07670e7 −1.21593 −0.607965 0.793964i \(-0.708014\pi\)
−0.607965 + 0.793964i \(0.708014\pi\)
\(602\) 165486.i 0.0186110i
\(603\) 6.67694e6i 0.747798i
\(604\) 1.87018e6 0.208588
\(605\) 4.38962e6 + 3.23527e6i 0.487571 + 0.359353i
\(606\) −1.44009e7 −1.59298
\(607\) 1.51219e7i 1.66584i 0.553391 + 0.832921i \(0.313333\pi\)
−0.553391 + 0.832921i \(0.686667\pi\)
\(608\) 910613.i 0.0999021i
\(609\) 8.23284e6 0.899511
\(610\) 1.25356e6 1.70083e6i 0.136402 0.185070i
\(611\) −1.25849e6 −0.136379
\(612\) 1.26658e6i 0.136695i
\(613\) 8.31622e6i 0.893871i 0.894566 + 0.446936i \(0.147485\pi\)
−0.894566 + 0.446936i \(0.852515\pi\)
\(614\) −6.15740e6 −0.659139
\(615\) −130680. + 177307.i −0.0139323 + 0.0189033i
\(616\) 1.99584e6 0.211921
\(617\) 1.21083e7i 1.28047i −0.768178 0.640237i \(-0.778836\pi\)
0.768178 0.640237i \(-0.221164\pi\)
\(618\) 9.32240e6i 0.981875i
\(619\) 9.73238e6 1.02092 0.510461 0.859901i \(-0.329475\pi\)
0.510461 + 0.859901i \(0.329475\pi\)
\(620\) 3.64608e6 + 2.68726e6i 0.380932 + 0.280757i
\(621\) 4.35996e6 0.453684
\(622\) 3.76869e6i 0.390584i
\(623\) 596395.i 0.0615622i
\(624\) 3.00326e6 0.308768
\(625\) −8.05437e6 + 5.52218e6i −0.824768 + 0.565471i
\(626\) 1.14254e7 1.16529
\(627\) 1.10324e6i 0.112073i
\(628\) 4.27972e6i 0.433028i
\(629\) 9.63706e6 0.971220
\(630\) 2.72646e6 + 2.00948e6i 0.273683 + 0.201712i
\(631\) −8.60145e6 −0.859999 −0.430000 0.902829i \(-0.641486\pi\)
−0.430000 + 0.902829i \(0.641486\pi\)
\(632\) 6.88797e6i 0.685959i
\(633\) 5.00574e6i 0.496546i
\(634\) −873224. −0.0862785
\(635\) 2.89278e6 3.92493e6i 0.284696 0.386276i
\(636\) 1.39075e6 0.136335
\(637\) 1.58119e6i 0.154396i
\(638\) 1.15840e7i 1.12670i
\(639\) −8.16286e6 −0.790842
\(640\) 7.25120e6 9.83844e6i 0.699777 0.949459i
\(641\) −6.42440e6 −0.617572 −0.308786 0.951132i \(-0.599923\pi\)
−0.308786 + 0.951132i \(0.599923\pi\)
\(642\) 1.28195e7i 1.22753i
\(643\) 3.64721e6i 0.347883i −0.984756 0.173941i \(-0.944350\pi\)
0.984756 0.173941i \(-0.0556503\pi\)
\(644\) −1.74398e6 −0.165702
\(645\) 374220. + 275811.i 0.0354183 + 0.0261043i
\(646\) −1.00672e6 −0.0949134
\(647\) 3.78036e6i 0.355036i −0.984118 0.177518i \(-0.943193\pi\)
0.984118 0.177518i \(-0.0568068\pi\)
\(648\) 9.66053e6i 0.903782i
\(649\) −6.21432e6 −0.579138
\(650\) 732600. + 2.36409e6i 0.0680117 + 0.219473i
\(651\) −8.02138e6 −0.741816
\(652\) 1.73868e6i 0.160177i
\(653\) 1.66957e7i 1.53223i 0.642706 + 0.766113i \(0.277812\pi\)
−0.642706 + 0.766113i \(0.722188\pi\)
\(654\) −2.77332e6 −0.253545
\(655\) −8.67834e6 6.39618e6i −0.790375 0.582529i
\(656\) 250272. 0.0227066
\(657\) 1.08512e7i 0.980761i
\(658\) 4.17393e6i 0.375821i
\(659\) −1.22166e6 −0.109581 −0.0547907 0.998498i \(-0.517449\pi\)
−0.0547907 + 0.998498i \(0.517449\pi\)
\(660\) −1.99584e6 + 2.70796e6i −0.178347 + 0.241981i
\(661\) 1.62789e7 1.44918 0.724589 0.689182i \(-0.242030\pi\)
0.724589 + 0.689182i \(0.242030\pi\)
\(662\) 1.04842e7i 0.929799i
\(663\) 1.63910e6i 0.144818i
\(664\) 8.20424e6 0.722135
\(665\) −435600. + 591023.i −0.0381974 + 0.0518263i
\(666\) 1.41776e7 1.23856
\(667\) 1.68704e7i 1.46829i
\(668\) 217226.i 0.0188352i
\(669\) −5.74636e6 −0.496395
\(670\) −1.30264e7 9.60083e6i −1.12108 0.826270i
\(671\) −1.43590e6 −0.123117
\(672\) 4.91731e6i 0.420053i
\(673\) 1.43928e7i 1.22492i −0.790503 0.612459i \(-0.790181\pi\)
0.790503 0.612459i \(-0.209819\pi\)
\(674\) −8.15126e6 −0.691155
\(675\) −5.34600e6 + 1.65665e6i −0.451616 + 0.139950i
\(676\) −4.28444e6 −0.360602
\(677\) 2.62429e6i 0.220059i −0.993928 0.110030i \(-0.964905\pi\)
0.993928 0.110030i \(-0.0350946\pi\)
\(678\) 1.38623e7i 1.15814i
\(679\) −6.04454e6 −0.503140
\(680\) −4.11840e6 3.03538e6i −0.341552 0.251733i
\(681\) 2.31661e7 1.91419
\(682\) 1.12865e7i 0.929177i
\(683\) 1.03039e7i 0.845184i −0.906320 0.422592i \(-0.861120\pi\)
0.906320 0.422592i \(-0.138880\pi\)
\(684\) −403920. −0.0330107
\(685\) 4.76168e6 6.46065e6i 0.387734 0.526078i
\(686\) 1.18998e7 0.965449
\(687\) 1.08985e7i 0.880998i
\(688\) 528219.i 0.0425444i
\(689\) −695376. −0.0558048
\(690\) −1.06577e7 + 1.44604e7i −0.852197 + 1.15626i
\(691\) 4.50285e6 0.358751 0.179375 0.983781i \(-0.442592\pi\)
0.179375 + 0.983781i \(0.442592\pi\)
\(692\) 5.91086e6i 0.469230i
\(693\) 2.30176e6i 0.182066i
\(694\) 2.54865e7 2.00868
\(695\) 1.43253e7 + 1.05581e7i 1.12497 + 0.829136i
\(696\) −1.82952e7 −1.43157
\(697\) 136592.i 0.0106498i
\(698\) 1.05764e7i 0.821672i
\(699\) 957264. 0.0741035
\(700\) 2.13840e6 662662.i 0.164947 0.0511148i
\(701\) −4.88090e6 −0.375150 −0.187575 0.982250i \(-0.560063\pi\)
−0.187575 + 0.982250i \(0.560063\pi\)
\(702\) 1.41845e6i 0.108636i
\(703\) 3.07332e6i 0.234541i
\(704\) −3.27398e6 −0.248969
\(705\) 9.43866e6 + 6.95655e6i 0.715217 + 0.527134i
\(706\) 1.95923e6 0.147936
\(707\) 6.51307e6i 0.490046i
\(708\) 5.88873e6i 0.441508i
\(709\) −9.96961e6 −0.744839 −0.372420 0.928064i \(-0.621472\pi\)
−0.372420 + 0.928064i \(0.621472\pi\)
\(710\) −1.17374e7 + 1.59254e7i −0.873831 + 1.18561i
\(711\) −7.94376e6 −0.589321
\(712\) 1.32532e6i 0.0979765i
\(713\) 1.64371e7i 1.21088i
\(714\) −5.43629e6 −0.399077
\(715\) 997920. 1.35398e6i 0.0730013 0.0990482i
\(716\) −5.33304e6 −0.388770
\(717\) 2.00160e7i 1.45405i
\(718\) 7.32868e6i 0.530536i
\(719\) −1.19167e7 −0.859675 −0.429838 0.902906i \(-0.641429\pi\)
−0.429838 + 0.902906i \(0.641429\pi\)
\(720\) −8.70264e6 6.41409e6i −0.625633 0.461109i
\(721\) 4.21621e6 0.302054
\(722\) 1.61035e7i 1.14968i
\(723\) 1.78143e7i 1.26743i
\(724\) −1.88282e6 −0.133494
\(725\) −6.41025e6 2.06858e7i −0.452929 1.46160i
\(726\) −1.28762e7 −0.906664
\(727\) 1.38269e6i 0.0970264i 0.998823 + 0.0485132i \(0.0154483\pi\)
−0.998823 + 0.0485132i \(0.984552\pi\)
\(728\) 945636.i 0.0661296i
\(729\) 2.48079e6 0.172890
\(730\) 2.11702e7 + 1.56030e7i 1.47034 + 1.08368i
\(731\) −288288. −0.0199541
\(732\) 1.36067e6i 0.0938585i
\(733\) 6.09661e6i 0.419110i 0.977797 + 0.209555i \(0.0672016\pi\)
−0.977797 + 0.209555i \(0.932798\pi\)
\(734\) 1.21893e7 0.835099
\(735\) 8.74038e6 1.18590e7i 0.596777 0.809707i
\(736\) 1.00764e7 0.685660
\(737\) 1.09973e7i 0.745793i
\(738\) 200948.i 0.0135813i
\(739\) 6.16946e6 0.415562 0.207781 0.978175i \(-0.433376\pi\)
0.207781 + 0.978175i \(0.433376\pi\)
\(740\) 5.55984e6 7.54360e6i 0.373236 0.506406i
\(741\) 522720. 0.0349723
\(742\) 2.30630e6i 0.153782i
\(743\) 1.57574e7i 1.04716i 0.851978 + 0.523578i \(0.175403\pi\)
−0.851978 + 0.523578i \(0.824597\pi\)
\(744\) 1.78253e7 1.18060
\(745\) −3.78675e6 2.79094e6i −0.249963 0.184230i
\(746\) −1.94586e7 −1.28016
\(747\) 9.46179e6i 0.620400i
\(748\) 2.08613e6i 0.136329i
\(749\) 5.79784e6 0.377626
\(750\) 7.57350e6 2.17803e7i 0.491636 1.41387i
\(751\) −1.51816e7 −0.982243 −0.491122 0.871091i \(-0.663413\pi\)
−0.491122 + 0.871091i \(0.663413\pi\)
\(752\) 1.33229e7i 0.859118i
\(753\) 1.11091e7i 0.713987i
\(754\) −5.48856e6 −0.351585
\(755\) 7.01316e6 + 5.16889e6i 0.447761 + 0.330012i
\(756\) 1.28304e6 0.0816461
\(757\) 652274.i 0.0413705i 0.999786 + 0.0206852i \(0.00658478\pi\)
−0.999786 + 0.0206852i \(0.993415\pi\)
\(758\) 3.37859e7i 2.13581i
\(759\) 1.22079e7 0.769194
\(760\) 968000. 1.31338e6i 0.0607913 0.0824817i
\(761\) 4.51420e6 0.282566 0.141283 0.989969i \(-0.454877\pi\)
0.141283 + 0.989969i \(0.454877\pi\)
\(762\) 1.15131e7i 0.718300i
\(763\) 1.25428e6i 0.0779980i
\(764\) −3.98822e6 −0.247199
\(765\) −3.50064e6 + 4.74967e6i −0.216269 + 0.293434i
\(766\) −2.10596e7 −1.29681
\(767\) 2.94437e6i 0.180719i
\(768\) 2.05862e7i 1.25943i
\(769\) −1.20799e7 −0.736625 −0.368312 0.929702i \(-0.620064\pi\)
−0.368312 + 0.929702i \(0.620064\pi\)
\(770\) −4.49064e6 3.30973e6i −0.272949 0.201171i
\(771\) −1.56795e7 −0.949939
\(772\) 9.43344e6i 0.569674i
\(773\) 1.04245e7i 0.627492i 0.949507 + 0.313746i \(0.101584\pi\)
−0.949507 + 0.313746i \(0.898416\pi\)
\(774\) −424116. −0.0254467
\(775\) 6.24560e6 + 2.01545e7i 0.373525 + 1.20536i
\(776\) 1.34323e7 0.800750
\(777\) 1.65959e7i 0.986163i
\(778\) 1.19393e7i 0.707177i
\(779\) 43560.0 0.00257184
\(780\) −1.28304e6 945636.i −0.0755099 0.0556529i
\(781\) 1.34447e7 0.788721
\(782\) 1.11398e7i 0.651421i
\(783\) 1.24115e7i 0.723467i
\(784\) −1.67392e7 −0.972620
\(785\) −1.18285e7 + 1.60489e7i −0.685104 + 0.929549i
\(786\) 2.54565e7 1.46974
\(787\) 3.45366e7i 1.98766i −0.110913 0.993830i \(-0.535378\pi\)
0.110913 0.993830i \(-0.464622\pi\)
\(788\) 715277.i 0.0410354i
\(789\) −3.24711e7 −1.85697
\(790\) −1.14224e7 + 1.54979e7i −0.651163 + 0.883498i
\(791\) 6.26947e6 0.356279
\(792\) 5.11503e6i 0.289758i
\(793\) 680333.i 0.0384183i
\(794\) 3.25298e7 1.83118
\(795\) 5.21532e6 + 3.84384e6i 0.292660 + 0.215698i
\(796\) 4.74960e6 0.265689
\(797\) 2.09287e7i 1.16707i 0.812089 + 0.583533i \(0.198330\pi\)
−0.812089 + 0.583533i \(0.801670\pi\)
\(798\) 1.73367e6i 0.0963736i
\(799\) −7.27126e6 −0.402942
\(800\) −1.23552e7 + 3.82871e6i −0.682535 + 0.211508i
\(801\) 1.52847e6 0.0841735
\(802\) 4.26384e6i 0.234080i
\(803\) 1.78725e7i 0.978131i
\(804\) 1.04211e7 0.568558
\(805\) −6.53994e6 4.82012e6i −0.355700 0.262161i
\(806\) 5.34758e6 0.289948
\(807\) 3.45533e7i 1.86770i
\(808\) 1.44735e7i 0.779910i
\(809\) 2.48797e7 1.33651 0.668257 0.743930i \(-0.267041\pi\)
0.668257 + 0.743930i \(0.267041\pi\)
\(810\) 1.60202e7 2.17362e7i 0.857936 1.16405i
\(811\) −3.95415e6 −0.211106 −0.105553 0.994414i \(-0.533661\pi\)
−0.105553 + 0.994414i \(0.533661\pi\)
\(812\) 4.96459e6i 0.264237i
\(813\) 3.42285e7i 1.81619i
\(814\) −2.33513e7 −1.23524
\(815\) 4.80546e6 6.52005e6i 0.253420 0.343841i
\(816\) 1.73522e7 0.912282
\(817\) 91936.8i 0.00481875i
\(818\) 1.36453e7i 0.713018i
\(819\) 1.09058e6 0.0568132
\(820\) −106920. 78803.0i −0.00555296 0.00409268i
\(821\) −3.43550e6 −0.177882 −0.0889410 0.996037i \(-0.528348\pi\)
−0.0889410 + 0.996037i \(0.528348\pi\)
\(822\) 1.89512e7i 0.978269i
\(823\) 3.94833e6i 0.203195i 0.994826 + 0.101598i \(0.0323954\pi\)
−0.994826 + 0.101598i \(0.967605\pi\)
\(824\) −9.36936e6 −0.480720
\(825\) −1.49688e7 + 4.63863e6i −0.765688 + 0.237277i
\(826\) −9.76536e6 −0.498010
\(827\) 3.38176e7i 1.71941i 0.510791 + 0.859705i \(0.329353\pi\)
−0.510791 + 0.859705i \(0.670647\pi\)
\(828\) 4.46956e6i 0.226563i
\(829\) 1.52015e7 0.768244 0.384122 0.923282i \(-0.374504\pi\)
0.384122 + 0.923282i \(0.374504\pi\)
\(830\) −1.84595e7 1.36052e7i −0.930091 0.685503i
\(831\) 2.53210e7 1.27198
\(832\) 1.55123e6i 0.0776903i
\(833\) 9.13579e6i 0.456177i
\(834\) −4.20209e7 −2.09194
\(835\) 600380. 814596.i 0.0297996 0.0404321i
\(836\) 665280. 0.0329222
\(837\) 1.20927e7i 0.596635i
\(838\) 1.94846e7i 0.958478i
\(839\) 2.89012e7 1.41746 0.708729 0.705481i \(-0.249269\pi\)
0.708729 + 0.705481i \(0.249269\pi\)
\(840\) 5.22720e6 7.09227e6i 0.255606 0.346806i
\(841\) 2.75138e7 1.34140
\(842\) 1.80272e7i 0.876290i
\(843\) 2.91532e7i 1.41292i
\(844\) 3.01858e6 0.145863
\(845\) −1.60667e7 1.18416e7i −0.774077 0.570516i
\(846\) −1.06971e7 −0.513857
\(847\) 5.82348e6i 0.278917i
\(848\) 7.36153e6i 0.351543i
\(849\) −3.28446e7 −1.56385
\(850\) 4.23280e6 + 1.36592e7i 0.200946 + 0.648452i
\(851\) −3.40077e7 −1.60973
\(852\) 1.27403e7i 0.601285i
\(853\) 2.02107e7i 0.951062i 0.879699 + 0.475531i \(0.157744\pi\)
−0.879699 + 0.475531i \(0.842256\pi\)
\(854\) −2.25641e6 −0.105870
\(855\) −1.51470e6 1.11638e6i −0.0708617 0.0522270i
\(856\) −1.28841e7 −0.600992
\(857\) 1.70522e7i 0.793101i −0.918013 0.396550i \(-0.870207\pi\)
0.918013 0.396550i \(-0.129793\pi\)
\(858\) 3.97167e6i 0.184185i
\(859\) 1.95505e7 0.904015 0.452008 0.892014i \(-0.350708\pi\)
0.452008 + 0.892014i \(0.350708\pi\)
\(860\) −166320. + 225663.i −0.00766829 + 0.0104043i
\(861\) 235224. 0.0108137
\(862\) 3.31288e7i 1.51858i
\(863\) 2.70896e7i 1.23816i −0.785330 0.619078i \(-0.787507\pi\)
0.785330 0.619078i \(-0.212493\pi\)
\(864\) −7.41312e6 −0.337844
\(865\) 1.63368e7 2.21657e7i 0.742379 1.00726i
\(866\) 1.38093e7 0.625716
\(867\) 1.87844e7i 0.848692i
\(868\) 4.83707e6i 0.217913i
\(869\) 1.30838e7 0.587741
\(870\) 4.11642e7 + 3.03392e7i 1.84383 + 1.35896i
\(871\) −5.21057e6 −0.232723
\(872\) 2.78729e6i 0.124134i
\(873\) 1.54912e7i 0.687940i
\(874\) 3.55256e6 0.157312
\(875\) 9.85050e6 + 3.42524e6i 0.434949 + 0.151242i
\(876\) −1.69361e7 −0.745682
\(877\) 1.98285e6i 0.0870545i −0.999052 0.0435272i \(-0.986140\pi\)
0.999052 0.0435272i \(-0.0138595\pi\)
\(878\) 3.12031e7i 1.36603i
\(879\) 4.75150e7 2.07424
\(880\) 1.43338e7 + 1.05644e7i 0.623955 + 0.459872i
\(881\) −4.22840e7 −1.83542 −0.917712 0.397247i \(-0.869966\pi\)
−0.917712 + 0.397247i \(0.869966\pi\)
\(882\) 1.34402e7i 0.581745i
\(883\) 134502.i 0.00580535i −0.999996 0.00290267i \(-0.999076\pi\)
0.999996 0.00290267i \(-0.000923951\pi\)
\(884\) 988416. 0.0425411
\(885\) −1.62756e7 + 2.20828e7i −0.698520 + 0.947753i
\(886\) 3.78164e7 1.61844
\(887\) 3.87668e6i 0.165444i −0.996573 0.0827219i \(-0.973639\pi\)
0.996573 0.0827219i \(-0.0263613\pi\)
\(888\) 3.68798e7i 1.56948i
\(889\) −5.20700e6 −0.220970
\(890\) 2.19780e6 2.98198e6i 0.0930065 0.126191i
\(891\) −1.83504e7 −0.774374
\(892\) 3.46518e6i 0.145819i
\(893\) 2.31885e6i 0.0973070i
\(894\) 1.11078e7 0.464819
\(895\) −1.99989e7 1.47397e7i −0.834543 0.615081i
\(896\) −1.30522e7 −0.543141
\(897\) 5.78414e6i 0.240026i
\(898\) 4.11477e7i 1.70277i
\(899\) −4.67914e7 −1.93093
\(900\) 1.69830e6 + 5.48039e6i 0.0698889 + 0.225530i
\(901\) −4.01773e6 −0.164880
\(902\) 330973.i 0.0135449i
\(903\) 496459.i 0.0202611i
\(904\) −1.39322e7 −0.567019
\(905\) −7.06059e6 5.20385e6i −0.286563 0.211205i
\(906\) −2.05719e7 −0.832635
\(907\) 2.87363e7i 1.15988i 0.814660 + 0.579939i \(0.196924\pi\)
−0.814660 + 0.579939i \(0.803076\pi\)
\(908\) 1.39697e7i 0.562306i
\(909\) 1.66920e7 0.670037
\(910\) 1.56816e6 2.12768e6i 0.0627750 0.0851732i
\(911\) 1.87675e6 0.0749223 0.0374611 0.999298i \(-0.488073\pi\)
0.0374611 + 0.999298i \(0.488073\pi\)
\(912\) 5.53372e6i 0.220308i
\(913\) 1.55841e7i 0.618736i
\(914\) 1.42861e7 0.565650
\(915\) −3.76068e6 + 5.10249e6i −0.148496 + 0.201479i
\(916\) −6.57204e6 −0.258798
\(917\) 1.15131e7i 0.452137i
\(918\) 8.19551e6i 0.320974i
\(919\) −6.76852e6 −0.264366 −0.132183 0.991225i \(-0.542199\pi\)
−0.132183 + 0.991225i \(0.542199\pi\)
\(920\) 1.45332e7 + 1.07114e7i 0.566098 + 0.417230i
\(921\) 1.84722e7 0.717579
\(922\) 2.55466e7i 0.989706i
\(923\) 6.37015e6i 0.246119i
\(924\) 3.59251e6 0.138426
\(925\) 4.16988e7 1.29219e7i 1.60239 0.496560i
\(926\) 1.38113e7 0.529306
\(927\) 1.08055e7i 0.412996i
\(928\) 2.86843e7i 1.09339i
\(929\) 1.15356e7 0.438530 0.219265 0.975665i \(-0.429634\pi\)
0.219265 + 0.975665i \(0.429634\pi\)
\(930\) −4.01069e7 2.95599e7i −1.52059 1.12072i
\(931\) −2.91346e6 −0.110163
\(932\) 577252.i 0.0217684i
\(933\) 1.13061e7i 0.425214i
\(934\) −8.67772e6 −0.325491
\(935\) 5.76576e6 7.82299e6i 0.215689 0.292647i
\(936\) −2.42352e6 −0.0904184
\(937\) 3.92632e7i 1.46096i −0.682936 0.730478i \(-0.739297\pi\)
0.682936 0.730478i \(-0.260703\pi\)
\(938\) 1.72815e7i 0.641319i
\(939\) −3.42762e7 −1.26861
\(940\) −4.19496e6 + 5.69173e6i −0.154849 + 0.210099i
\(941\) 2.94919e7 1.08575 0.542874 0.839814i \(-0.317336\pi\)
0.542874 + 0.839814i \(0.317336\pi\)
\(942\) 4.70769e7i 1.72855i
\(943\) 482012.i 0.0176514i
\(944\) 3.11702e7 1.13844
\(945\) 4.81140e6 + 3.54614e6i 0.175264 + 0.129174i
\(946\) 698544. 0.0253785
\(947\) 2.09628e7i 0.759581i −0.925072 0.379791i \(-0.875996\pi\)
0.925072 0.379791i \(-0.124004\pi\)
\(948\) 1.23983e7i 0.448067i
\(949\) 8.46806e6 0.305224
\(950\) −4.35600e6 + 1.34987e6i −0.156595 + 0.0485268i
\(951\) 2.61967e6 0.0939281
\(952\) 5.46368e6i 0.195386i
\(953\) 1.64122e7i 0.585375i 0.956208 + 0.292687i \(0.0945495\pi\)
−0.956208 + 0.292687i \(0.905451\pi\)
\(954\) −5.91070e6 −0.210265
\(955\) −1.49558e7 1.10229e7i −0.530643 0.391099i
\(956\) 1.20701e7 0.427135
\(957\) 3.47521e7i 1.22660i
\(958\) 4.48652e7i 1.57941i
\(959\) −8.57102e6 −0.300944
\(960\) −8.57472e6 + 1.16342e7i −0.300291 + 0.407435i
\(961\) 1.69604e7 0.592416
\(962\) 1.10639e7i 0.385454i
\(963\) 1.48590e7i 0.516325i
\(964\) −1.07424e7 −0.372314
\(965\) −2.60726e7 + 3.53754e7i −0.901295 + 1.22288i
\(966\) 1.91838e7 0.661443
\(967\) 4.71911e7i 1.62291i 0.584416 + 0.811454i \(0.301324\pi\)
−0.584416 + 0.811454i \(0.698676\pi\)
\(968\) 1.29411e7i 0.443897i
\(969\) 3.02016e6 0.103329
\(970\) −3.02227e7 2.22750e7i −1.03135 0.760130i
\(971\) 3.84771e7 1.30965 0.654823 0.755783i \(-0.272743\pi\)
0.654823 + 0.755783i \(0.272743\pi\)
\(972\) 1.21665e7i 0.413046i
\(973\) 1.90047e7i 0.643544i
\(974\) −4.42566e7 −1.49479
\(975\) −2.19780e6 7.09227e6i −0.0740417 0.238932i
\(976\) 7.20227e6 0.242016
\(977\) 2.70184e7i 0.905572i −0.891619 0.452786i \(-0.850430\pi\)
0.891619 0.452786i \(-0.149570\pi\)
\(978\) 1.91255e7i 0.639389i
\(979\) −2.51748e6 −0.0839478
\(980\) 7.15122e6 + 5.27065e6i 0.237856 + 0.175307i
\(981\) 3.21453e6 0.106646
\(982\) 4.56086e7i 1.50927i
\(983\) 2.88475e7i 0.952192i −0.879393 0.476096i \(-0.842051\pi\)
0.879393 0.476096i \(-0.157949\pi\)
\(984\) −522720. −0.0172100
\(985\) −1.97692e6 + 2.68229e6i −0.0649230 + 0.0880876i
\(986\) −3.17117e7 −1.03879
\(987\) 1.25218e7i 0.409142i
\(988\) 315212.i 0.0102733i
\(989\) 1.01732e6 0.0330726
\(990\) 8.48232e6 1.15088e7i 0.275060 0.373201i
\(991\) −5.21596e7 −1.68714 −0.843569 0.537021i \(-0.819550\pi\)
−0.843569 + 0.537021i \(0.819550\pi\)
\(992\) 2.79475e7i 0.901704i
\(993\) 3.14525e7i 1.01224i
\(994\) 2.11274e7 0.678235
\(995\) 1.78110e7 + 1.31272e7i 0.570336 + 0.420353i
\(996\) 1.47676e7 0.471696
\(997\) 9.78148e6i 0.311650i 0.987785 + 0.155825i \(0.0498036\pi\)
−0.987785 + 0.155825i \(0.950196\pi\)
\(998\) 4.60354e7i 1.46307i
\(999\) 2.50193e7 0.793161
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 5.6.b.a.4.1 2
3.2 odd 2 45.6.b.b.19.2 2
4.3 odd 2 80.6.c.a.49.1 2
5.2 odd 4 25.6.a.c.1.2 2
5.3 odd 4 25.6.a.c.1.1 2
5.4 even 2 inner 5.6.b.a.4.2 yes 2
7.6 odd 2 245.6.b.a.99.1 2
8.3 odd 2 320.6.c.g.129.2 2
8.5 even 2 320.6.c.f.129.1 2
12.11 even 2 720.6.f.f.289.2 2
15.2 even 4 225.6.a.n.1.1 2
15.8 even 4 225.6.a.n.1.2 2
15.14 odd 2 45.6.b.b.19.1 2
20.3 even 4 400.6.a.t.1.2 2
20.7 even 4 400.6.a.t.1.1 2
20.19 odd 2 80.6.c.a.49.2 2
35.34 odd 2 245.6.b.a.99.2 2
40.19 odd 2 320.6.c.g.129.1 2
40.29 even 2 320.6.c.f.129.2 2
60.59 even 2 720.6.f.f.289.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.6.b.a.4.1 2 1.1 even 1 trivial
5.6.b.a.4.2 yes 2 5.4 even 2 inner
25.6.a.c.1.1 2 5.3 odd 4
25.6.a.c.1.2 2 5.2 odd 4
45.6.b.b.19.1 2 15.14 odd 2
45.6.b.b.19.2 2 3.2 odd 2
80.6.c.a.49.1 2 4.3 odd 2
80.6.c.a.49.2 2 20.19 odd 2
225.6.a.n.1.1 2 15.2 even 4
225.6.a.n.1.2 2 15.8 even 4
245.6.b.a.99.1 2 7.6 odd 2
245.6.b.a.99.2 2 35.34 odd 2
320.6.c.f.129.1 2 8.5 even 2
320.6.c.f.129.2 2 40.29 even 2
320.6.c.g.129.1 2 40.19 odd 2
320.6.c.g.129.2 2 8.3 odd 2
400.6.a.t.1.1 2 20.7 even 4
400.6.a.t.1.2 2 20.3 even 4
720.6.f.f.289.1 2 60.59 even 2
720.6.f.f.289.2 2 12.11 even 2