Properties

Label 147.6.e.n.79.2
Level $147$
Weight $6$
Character 147.79
Analytic conductor $23.576$
Analytic rank $0$
Dimension $4$
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] = [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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{193})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(3.72311 - 6.44862i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.6.e.n.67.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.22311 - 7.31464i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-19.6693 - 34.0683i) q^{4} +(-18.0000 + 31.1769i) q^{5} +76.0160 q^{6} -61.9840 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(4.22311 - 7.31464i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-19.6693 - 34.0683i) q^{4} +(-18.0000 + 31.1769i) q^{5} +76.0160 q^{6} -61.9840 q^{8} +(-40.5000 + 70.1481i) q^{9} +(152.032 + 263.327i) q^{10} +(-147.785 - 255.971i) q^{11} +(177.024 - 306.615i) q^{12} +1148.13 q^{13} -324.000 q^{15} +(367.653 - 636.794i) q^{16} +(516.192 + 894.071i) q^{17} +(342.072 + 592.486i) q^{18} +(1054.26 - 1826.02i) q^{19} +1416.19 q^{20} -2496.45 q^{22} +(320.494 - 555.112i) q^{23} +(-278.928 - 483.117i) q^{24} +(914.500 + 1583.96i) q^{25} +(4848.67 - 8398.15i) q^{26} -729.000 q^{27} +7631.58 q^{29} +(-1368.29 + 2369.94i) q^{30} +(-483.488 - 837.426i) q^{31} +(-4097.03 - 7096.26i) q^{32} +(1330.06 - 2303.74i) q^{33} +8719.74 q^{34} +3186.43 q^{36} +(886.605 - 1535.65i) q^{37} +(-8904.48 - 15423.0i) q^{38} +(5166.58 + 8948.77i) q^{39} +(1115.71 - 1932.47i) q^{40} +11976.4 q^{41} -19802.9 q^{43} +(-5813.66 + 10069.6i) q^{44} +(-1458.00 - 2525.33i) q^{45} +(-2706.97 - 4688.60i) q^{46} +(-13983.1 + 24219.4i) q^{47} +6617.76 q^{48} +15448.1 q^{50} +(-4645.73 + 8046.64i) q^{51} +(-22582.9 - 39114.8i) q^{52} +(3557.16 + 6161.19i) q^{53} +(-3078.65 + 5332.37i) q^{54} +10640.5 q^{55} +18976.6 q^{57} +(32229.0 - 55822.3i) q^{58} +(-10434.8 - 18073.5i) q^{59} +(6372.86 + 11038.1i) q^{60} +(-11934.2 + 20670.6i) q^{61} -8167.30 q^{62} -45679.0 q^{64} +(-20666.3 + 35795.1i) q^{65} +(-11234.0 - 19457.9i) q^{66} +(-17335.8 - 30026.4i) q^{67} +(20306.3 - 35171.5i) q^{68} +5768.90 q^{69} -28413.2 q^{71} +(2510.35 - 4348.06i) q^{72} +(-7646.34 - 13243.8i) q^{73} +(-7488.46 - 12970.4i) q^{74} +(-8230.50 + 14255.6i) q^{75} -82946.0 q^{76} +87276.1 q^{78} +(36529.8 - 63271.4i) q^{79} +(13235.5 + 22924.6i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(50577.6 - 87603.0i) q^{82} +30340.9 q^{83} -37165.8 q^{85} +(-83630.0 + 144851. i) q^{86} +(34342.1 + 59482.3i) q^{87} +(9160.30 + 15866.1i) q^{88} +(-18044.7 + 31254.4i) q^{89} -24629.2 q^{90} -25215.6 q^{92} +(4351.39 - 7536.83i) q^{93} +(118104. + 204562. i) q^{94} +(37953.2 + 65736.9i) q^{95} +(36873.2 - 63866.3i) q^{96} +153963. q^{97} +23941.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} + 18 q^{3} - 37 q^{4} - 72 q^{5} + 54 q^{6} - 498 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} + 18 q^{3} - 37 q^{4} - 72 q^{5} + 54 q^{6} - 498 q^{8} - 162 q^{9} + 108 q^{10} - 480 q^{11} + 333 q^{12} + 2592 q^{13} - 1296 q^{15} + 1679 q^{16} - 936 q^{17} + 243 q^{18} + 216 q^{19} + 2664 q^{20} - 2984 q^{22} + 504 q^{23} - 2241 q^{24} + 3658 q^{25} + 8892 q^{26} - 2916 q^{27} + 12744 q^{29} - 972 q^{30} - 9936 q^{31} - 9039 q^{32} + 4320 q^{33} + 38880 q^{34} + 5994 q^{36} - 11124 q^{37} - 28116 q^{38} + 11664 q^{39} + 8964 q^{40} + 41904 q^{41} - 12528 q^{43} - 11196 q^{44} - 5832 q^{45} - 6160 q^{46} - 7920 q^{47} + 30222 q^{48} + 10974 q^{50} + 8424 q^{51} - 44820 q^{52} - 2220 q^{53} - 2187 q^{54} + 34560 q^{55} + 3888 q^{57} + 71318 q^{58} - 29736 q^{59} + 11988 q^{60} + 17280 q^{61} + 81360 q^{62} - 21758 q^{64} - 46656 q^{65} - 13428 q^{66} + 20680 q^{67} + 45216 q^{68} + 9072 q^{69} - 184560 q^{71} + 20169 q^{72} - 56592 q^{73} - 85218 q^{74} - 32922 q^{75} - 174744 q^{76} + 160056 q^{78} + 56096 q^{79} + 60444 q^{80} - 13122 q^{81} + 52272 q^{82} - 142704 q^{83} + 67392 q^{85} - 240996 q^{86} + 57348 q^{87} + 52812 q^{88} - 123192 q^{89} - 17496 q^{90} - 51072 q^{92} + 89424 q^{93} + 345384 q^{94} + 7776 q^{95} + 81351 q^{96} + 71712 q^{97} + 77760 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.22311 7.31464i 0.746548 1.29306i −0.202921 0.979195i \(-0.565043\pi\)
0.949468 0.313863i \(-0.101623\pi\)
\(3\) 4.50000 + 7.79423i 0.288675 + 0.500000i
\(4\) −19.6693 34.0683i −0.614667 1.06463i
\(5\) −18.0000 + 31.1769i −0.321994 + 0.557710i −0.980899 0.194516i \(-0.937686\pi\)
0.658906 + 0.752226i \(0.271020\pi\)
\(6\) 76.0160 0.862039
\(7\) 0 0
\(8\) −61.9840 −0.342416
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 152.032 + 263.327i 0.480767 + 0.832714i
\(11\) −147.785 255.971i −0.368255 0.637836i 0.621038 0.783780i \(-0.286711\pi\)
−0.989293 + 0.145945i \(0.953378\pi\)
\(12\) 177.024 306.615i 0.354878 0.614667i
\(13\) 1148.13 1.88422 0.942111 0.335302i \(-0.108838\pi\)
0.942111 + 0.335302i \(0.108838\pi\)
\(14\) 0 0
\(15\) −324.000 −0.371806
\(16\) 367.653 636.794i 0.359036 0.621869i
\(17\) 516.192 + 894.071i 0.433200 + 0.750325i 0.997147 0.0754862i \(-0.0240509\pi\)
−0.563946 + 0.825811i \(0.690718\pi\)
\(18\) 342.072 + 592.486i 0.248849 + 0.431019i
\(19\) 1054.26 1826.02i 0.669980 1.16044i −0.307929 0.951409i \(-0.599636\pi\)
0.977909 0.209031i \(-0.0670308\pi\)
\(20\) 1416.19 0.791675
\(21\) 0 0
\(22\) −2496.45 −1.09968
\(23\) 320.494 555.112i 0.126328 0.218807i −0.795923 0.605398i \(-0.793014\pi\)
0.922251 + 0.386591i \(0.126347\pi\)
\(24\) −278.928 483.117i −0.0988471 0.171208i
\(25\) 914.500 + 1583.96i 0.292640 + 0.506867i
\(26\) 4848.67 8398.15i 1.40666 2.43641i
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) 7631.58 1.68508 0.842538 0.538637i \(-0.181060\pi\)
0.842538 + 0.538637i \(0.181060\pi\)
\(30\) −1368.29 + 2369.94i −0.277571 + 0.480767i
\(31\) −483.488 837.426i −0.0903611 0.156510i 0.817302 0.576210i \(-0.195469\pi\)
−0.907663 + 0.419700i \(0.862135\pi\)
\(32\) −4097.03 7096.26i −0.707284 1.22505i
\(33\) 1330.06 2303.74i 0.212612 0.368255i
\(34\) 8719.74 1.29362
\(35\) 0 0
\(36\) 3186.43 0.409778
\(37\) 886.605 1535.65i 0.106470 0.184411i −0.807868 0.589363i \(-0.799379\pi\)
0.914338 + 0.404953i \(0.132712\pi\)
\(38\) −8904.48 15423.0i −1.00034 1.73265i
\(39\) 5166.58 + 8948.77i 0.543928 + 0.942111i
\(40\) 1115.71 1932.47i 0.110256 0.190969i
\(41\) 11976.4 1.11267 0.556335 0.830958i \(-0.312207\pi\)
0.556335 + 0.830958i \(0.312207\pi\)
\(42\) 0 0
\(43\) −19802.9 −1.63327 −0.816636 0.577153i \(-0.804163\pi\)
−0.816636 + 0.577153i \(0.804163\pi\)
\(44\) −5813.66 + 10069.6i −0.452708 + 0.784113i
\(45\) −1458.00 2525.33i −0.107331 0.185903i
\(46\) −2706.97 4688.60i −0.188620 0.326700i
\(47\) −13983.1 + 24219.4i −0.923332 + 1.59926i −0.129110 + 0.991630i \(0.541212\pi\)
−0.794222 + 0.607628i \(0.792121\pi\)
\(48\) 6617.76 0.414580
\(49\) 0 0
\(50\) 15448.1 0.873879
\(51\) −4645.73 + 8046.64i −0.250108 + 0.433200i
\(52\) −22582.9 39114.8i −1.15817 2.00601i
\(53\) 3557.16 + 6161.19i 0.173946 + 0.301283i 0.939796 0.341736i \(-0.111015\pi\)
−0.765850 + 0.643019i \(0.777682\pi\)
\(54\) −3078.65 + 5332.37i −0.143673 + 0.248849i
\(55\) 10640.5 0.474303
\(56\) 0 0
\(57\) 18976.6 0.773627
\(58\) 32229.0 55822.3i 1.25799 2.17890i
\(59\) −10434.8 18073.5i −0.390259 0.675948i 0.602225 0.798327i \(-0.294281\pi\)
−0.992484 + 0.122379i \(0.960948\pi\)
\(60\) 6372.86 + 11038.1i 0.228537 + 0.395838i
\(61\) −11934.2 + 20670.6i −0.410646 + 0.711259i −0.994960 0.100268i \(-0.968030\pi\)
0.584315 + 0.811527i \(0.301363\pi\)
\(62\) −8167.30 −0.269835
\(63\) 0 0
\(64\) −45679.0 −1.39401
\(65\) −20666.3 + 35795.1i −0.606708 + 1.05085i
\(66\) −11234.0 19457.9i −0.317450 0.549839i
\(67\) −17335.8 30026.4i −0.471798 0.817178i 0.527682 0.849442i \(-0.323061\pi\)
−0.999479 + 0.0322646i \(0.989728\pi\)
\(68\) 20306.3 35171.5i 0.532548 0.922400i
\(69\) 5768.90 0.145871
\(70\) 0 0
\(71\) −28413.2 −0.668921 −0.334461 0.942410i \(-0.608554\pi\)
−0.334461 + 0.942410i \(0.608554\pi\)
\(72\) 2510.35 4348.06i 0.0570694 0.0988471i
\(73\) −7646.34 13243.8i −0.167937 0.290875i 0.769757 0.638337i \(-0.220377\pi\)
−0.937694 + 0.347461i \(0.887044\pi\)
\(74\) −7488.46 12970.4i −0.158969 0.275343i
\(75\) −8230.50 + 14255.6i −0.168956 + 0.292640i
\(76\) −82946.0 −1.64726
\(77\) 0 0
\(78\) 87276.1 1.62427
\(79\) 36529.8 63271.4i 0.658535 1.14062i −0.322460 0.946583i \(-0.604510\pi\)
0.980995 0.194033i \(-0.0621570\pi\)
\(80\) 13235.5 + 22924.6i 0.231215 + 0.400476i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 50577.6 87603.0i 0.830661 1.43875i
\(83\) 30340.9 0.483429 0.241715 0.970347i \(-0.422290\pi\)
0.241715 + 0.970347i \(0.422290\pi\)
\(84\) 0 0
\(85\) −37165.8 −0.557951
\(86\) −83630.0 + 144851.i −1.21931 + 2.11192i
\(87\) 34342.1 + 59482.3i 0.486440 + 0.842538i
\(88\) 9160.30 + 15866.1i 0.126096 + 0.218406i
\(89\) −18044.7 + 31254.4i −0.241477 + 0.418250i −0.961135 0.276078i \(-0.910965\pi\)
0.719658 + 0.694328i \(0.244298\pi\)
\(90\) −24629.2 −0.320512
\(91\) 0 0
\(92\) −25215.6 −0.310599
\(93\) 4351.39 7536.83i 0.0521700 0.0903611i
\(94\) 118104. + 204562.i 1.37862 + 2.38784i
\(95\) 37953.2 + 65736.9i 0.431459 + 0.747309i
\(96\) 36873.2 63866.3i 0.408351 0.707284i
\(97\) 153963. 1.66145 0.830724 0.556685i \(-0.187927\pi\)
0.830724 + 0.556685i \(0.187927\pi\)
\(98\) 0 0
\(99\) 23941.2 0.245503
\(100\) 35975.2 62310.9i 0.359752 0.623109i
\(101\) 69904.4 + 121078.i 0.681869 + 1.18103i 0.974410 + 0.224779i \(0.0721659\pi\)
−0.292541 + 0.956253i \(0.594501\pi\)
\(102\) 39238.8 + 67963.7i 0.373436 + 0.646810i
\(103\) −57962.7 + 100394.i −0.538339 + 0.932430i 0.460655 + 0.887579i \(0.347615\pi\)
−0.998994 + 0.0448508i \(0.985719\pi\)
\(104\) −71165.6 −0.645188
\(105\) 0 0
\(106\) 60089.2 0.519436
\(107\) −41530.9 + 71933.6i −0.350681 + 0.607397i −0.986369 0.164549i \(-0.947383\pi\)
0.635688 + 0.771946i \(0.280716\pi\)
\(108\) 14338.9 + 24835.8i 0.118293 + 0.204889i
\(109\) −22678.1 39279.7i −0.182827 0.316666i 0.760015 0.649906i \(-0.225192\pi\)
−0.942842 + 0.333240i \(0.891858\pi\)
\(110\) 44936.1 77831.5i 0.354090 0.613301i
\(111\) 15958.9 0.122941
\(112\) 0 0
\(113\) −355.533 −0.00261929 −0.00130965 0.999999i \(-0.500417\pi\)
−0.00130965 + 0.999999i \(0.500417\pi\)
\(114\) 80140.3 138807.i 0.577549 1.00034i
\(115\) 11537.8 + 19984.0i 0.0813538 + 0.140909i
\(116\) −150108. 259995.i −1.03576 1.79399i
\(117\) −46499.2 + 80538.9i −0.314037 + 0.543928i
\(118\) −176269. −1.16539
\(119\) 0 0
\(120\) 20082.8 0.127313
\(121\) 36844.8 63817.0i 0.228777 0.396253i
\(122\) 100799. + 174588.i 0.613133 + 1.06198i
\(123\) 53893.7 + 93346.7i 0.321200 + 0.556335i
\(124\) −19019.8 + 32943.2i −0.111084 + 0.192403i
\(125\) −178344. −1.02090
\(126\) 0 0
\(127\) 168967. 0.929593 0.464797 0.885417i \(-0.346127\pi\)
0.464797 + 0.885417i \(0.346127\pi\)
\(128\) −61802.5 + 107045.i −0.333412 + 0.577486i
\(129\) −89113.2 154349.i −0.471485 0.816636i
\(130\) 174552. + 302333.i 0.905872 + 1.56902i
\(131\) −86984.6 + 150662.i −0.442858 + 0.767052i −0.997900 0.0647701i \(-0.979369\pi\)
0.555043 + 0.831822i \(0.312702\pi\)
\(132\) −104646. −0.522742
\(133\) 0 0
\(134\) −292843. −1.40888
\(135\) 13122.0 22728.0i 0.0619677 0.107331i
\(136\) −31995.6 55418.1i −0.148335 0.256924i
\(137\) −183862. 318458.i −0.836931 1.44961i −0.892448 0.451150i \(-0.851014\pi\)
0.0555168 0.998458i \(-0.482319\pi\)
\(138\) 24362.7 42197.4i 0.108900 0.188620i
\(139\) −217967. −0.956870 −0.478435 0.878123i \(-0.658796\pi\)
−0.478435 + 0.878123i \(0.658796\pi\)
\(140\) 0 0
\(141\) −251695. −1.06617
\(142\) −119992. + 207833.i −0.499381 + 0.864954i
\(143\) −169676. 293887.i −0.693873 1.20182i
\(144\) 29779.9 + 51580.3i 0.119679 + 0.207290i
\(145\) −137368. + 237929.i −0.542584 + 0.939783i
\(146\) −129165. −0.501492
\(147\) 0 0
\(148\) −69755.7 −0.261773
\(149\) 32453.0 56210.3i 0.119754 0.207420i −0.799916 0.600112i \(-0.795123\pi\)
0.919670 + 0.392692i \(0.128456\pi\)
\(150\) 69516.6 + 120406.i 0.252267 + 0.436939i
\(151\) 111889. + 193797.i 0.399341 + 0.691678i 0.993645 0.112562i \(-0.0359057\pi\)
−0.594304 + 0.804240i \(0.702572\pi\)
\(152\) −65347.0 + 113184.i −0.229412 + 0.397354i
\(153\) −83623.1 −0.288800
\(154\) 0 0
\(155\) 34811.1 0.116383
\(156\) 203246. 352033.i 0.668669 1.15817i
\(157\) −229986. 398348.i −0.744652 1.28977i −0.950357 0.311161i \(-0.899282\pi\)
0.205706 0.978614i \(-0.434051\pi\)
\(158\) −308538. 534404.i −0.983256 1.70305i
\(159\) −32014.5 + 55450.7i −0.100428 + 0.173946i
\(160\) 294986. 0.910964
\(161\) 0 0
\(162\) −55415.7 −0.165899
\(163\) −45534.3 + 78867.7i −0.134236 + 0.232504i −0.925305 0.379223i \(-0.876191\pi\)
0.791069 + 0.611727i \(0.209525\pi\)
\(164\) −235567. 408015.i −0.683921 1.18459i
\(165\) 47882.3 + 82934.6i 0.136919 + 0.237151i
\(166\) 128133. 221933.i 0.360903 0.625103i
\(167\) 314772. 0.873384 0.436692 0.899611i \(-0.356150\pi\)
0.436692 + 0.899611i \(0.356150\pi\)
\(168\) 0 0
\(169\) 946905. 2.55029
\(170\) −156955. + 271855.i −0.416537 + 0.721464i
\(171\) 85394.7 + 147908.i 0.223327 + 0.386813i
\(172\) 389510. + 674652.i 1.00392 + 1.73884i
\(173\) −181071. + 313625.i −0.459975 + 0.796701i −0.998959 0.0456154i \(-0.985475\pi\)
0.538984 + 0.842316i \(0.318808\pi\)
\(174\) 580122. 1.45260
\(175\) 0 0
\(176\) −217334. −0.528867
\(177\) 93912.9 162662.i 0.225316 0.390259i
\(178\) 152410. + 263982.i 0.360548 + 0.624487i
\(179\) 86948.1 + 150599.i 0.202828 + 0.351308i 0.949438 0.313953i \(-0.101653\pi\)
−0.746611 + 0.665261i \(0.768320\pi\)
\(180\) −57355.8 + 99343.1i −0.131946 + 0.228537i
\(181\) −134973. −0.306233 −0.153116 0.988208i \(-0.548931\pi\)
−0.153116 + 0.988208i \(0.548931\pi\)
\(182\) 0 0
\(183\) −214815. −0.474173
\(184\) −19865.5 + 34408.1i −0.0432569 + 0.0749231i
\(185\) 31917.8 + 55283.2i 0.0685652 + 0.118758i
\(186\) −36752.8 63657.8i −0.0778948 0.134918i
\(187\) 152571. 264260.i 0.319056 0.552622i
\(188\) 1.10015e6 2.27017
\(189\) 0 0
\(190\) 641123. 1.28842
\(191\) −90706.7 + 157109.i −0.179910 + 0.311614i −0.941850 0.336035i \(-0.890914\pi\)
0.761939 + 0.647648i \(0.224247\pi\)
\(192\) −205555. 356032.i −0.402416 0.697006i
\(193\) −482999. 836579.i −0.933369 1.61664i −0.777517 0.628861i \(-0.783521\pi\)
−0.155851 0.987781i \(-0.549812\pi\)
\(194\) 650202. 1.12618e6i 1.24035 2.14835i
\(195\) −371993. −0.700566
\(196\) 0 0
\(197\) −699058. −1.28336 −0.641679 0.766974i \(-0.721762\pi\)
−0.641679 + 0.766974i \(0.721762\pi\)
\(198\) 101106. 175121.i 0.183280 0.317450i
\(199\) −208095. 360432.i −0.372503 0.645194i 0.617447 0.786612i \(-0.288167\pi\)
−0.989950 + 0.141419i \(0.954834\pi\)
\(200\) −56684.4 98180.2i −0.100205 0.173560i
\(201\) 156022. 270238.i 0.272393 0.471798i
\(202\) 1.18086e6 2.03619
\(203\) 0 0
\(204\) 365513. 0.614933
\(205\) −215575. + 373387.i −0.358273 + 0.620546i
\(206\) 489566. + 847953.i 0.803791 + 1.39221i
\(207\) 25960.0 + 44964.1i 0.0421094 + 0.0729357i
\(208\) 422113. 731121.i 0.676504 1.17174i
\(209\) −623212. −0.986894
\(210\) 0 0
\(211\) −407152. −0.629580 −0.314790 0.949161i \(-0.601934\pi\)
−0.314790 + 0.949161i \(0.601934\pi\)
\(212\) 139934. 242373.i 0.213837 0.370377i
\(213\) −127860. 221459.i −0.193101 0.334461i
\(214\) 350779. + 607567.i 0.523600 + 0.906901i
\(215\) 356453. 617394.i 0.525903 0.910891i
\(216\) 45186.3 0.0658981
\(217\) 0 0
\(218\) −383089. −0.545957
\(219\) 68817.0 119195.i 0.0969584 0.167937i
\(220\) −209292. 362504.i −0.291538 0.504959i
\(221\) 592654. + 1.02651e6i 0.816246 + 1.41378i
\(222\) 67396.2 116734.i 0.0917810 0.158969i
\(223\) −882022. −1.18773 −0.593865 0.804565i \(-0.702398\pi\)
−0.593865 + 0.804565i \(0.702398\pi\)
\(224\) 0 0
\(225\) −148149. −0.195093
\(226\) −1501.45 + 2600.60i −0.00195542 + 0.00338690i
\(227\) −563251. 975579.i −0.725499 1.25660i −0.958768 0.284189i \(-0.908276\pi\)
0.233269 0.972412i \(-0.425058\pi\)
\(228\) −373257. 646500.i −0.475523 0.823629i
\(229\) 155042. 268541.i 0.195371 0.338393i −0.751651 0.659561i \(-0.770742\pi\)
0.947022 + 0.321168i \(0.104075\pi\)
\(230\) 194902. 0.242938
\(231\) 0 0
\(232\) −473036. −0.576998
\(233\) −568268. + 984268.i −0.685746 + 1.18775i 0.287456 + 0.957794i \(0.407190\pi\)
−0.973202 + 0.229953i \(0.926143\pi\)
\(234\) 392742. + 680250.i 0.468887 + 0.812136i
\(235\) −503391. 871898.i −0.594614 1.02990i
\(236\) −410490. + 710989.i −0.479758 + 0.830966i
\(237\) 657536. 0.760411
\(238\) 0 0
\(239\) 87506.8 0.0990940 0.0495470 0.998772i \(-0.484222\pi\)
0.0495470 + 0.998772i \(0.484222\pi\)
\(240\) −119120. + 206321.i −0.133492 + 0.231215i
\(241\) 268884. + 465721.i 0.298210 + 0.516515i 0.975727 0.218992i \(-0.0702770\pi\)
−0.677516 + 0.735508i \(0.736944\pi\)
\(242\) −311199. 539012.i −0.341586 0.591644i
\(243\) 29524.5 51137.9i 0.0320750 0.0555556i
\(244\) 938948. 1.00964
\(245\) 0 0
\(246\) 910397. 0.959164
\(247\) 1.21042e6 2.09651e6i 1.26239 2.18653i
\(248\) 29968.5 + 51907.0i 0.0309411 + 0.0535916i
\(249\) 136534. + 236484.i 0.139554 + 0.241715i
\(250\) −753167. + 1.30452e6i −0.762151 + 1.32008i
\(251\) −1.35353e6 −1.35607 −0.678036 0.735028i \(-0.737169\pi\)
−0.678036 + 0.735028i \(0.737169\pi\)
\(252\) 0 0
\(253\) −189457. −0.186084
\(254\) 713567. 1.23593e6i 0.693986 1.20202i
\(255\) −167246. 289679.i −0.161067 0.278976i
\(256\) −208866. 361766.i −0.199190 0.345007i
\(257\) −488450. + 846020.i −0.461304 + 0.799002i −0.999026 0.0441199i \(-0.985952\pi\)
0.537722 + 0.843122i \(0.319285\pi\)
\(258\) −1.50534e6 −1.40794
\(259\) 0 0
\(260\) 1.62597e6 1.49169
\(261\) −309079. + 535341.i −0.280846 + 0.486440i
\(262\) 734691. + 1.27252e6i 0.661229 + 1.14528i
\(263\) 621874. + 1.07712e6i 0.554387 + 0.960227i 0.997951 + 0.0639842i \(0.0203807\pi\)
−0.443564 + 0.896243i \(0.646286\pi\)
\(264\) −82442.7 + 142795.i −0.0728018 + 0.126096i
\(265\) −256116. −0.224038
\(266\) 0 0
\(267\) −324805. −0.278833
\(268\) −681966. + 1.18120e6i −0.579997 + 1.00458i
\(269\) −542042. 938844.i −0.456722 0.791066i 0.542063 0.840338i \(-0.317643\pi\)
−0.998785 + 0.0492716i \(0.984310\pi\)
\(270\) −110831. 191965.i −0.0925237 0.160256i
\(271\) −1.08314e6 + 1.87605e6i −0.895900 + 1.55174i −0.0632128 + 0.998000i \(0.520135\pi\)
−0.832687 + 0.553744i \(0.813199\pi\)
\(272\) 759119. 0.622139
\(273\) 0 0
\(274\) −3.10587e6 −2.49924
\(275\) 270299. 468171.i 0.215532 0.373313i
\(276\) −113470. 196536.i −0.0896622 0.155300i
\(277\) −126929. 219848.i −0.0993946 0.172157i 0.812040 0.583602i \(-0.198357\pi\)
−0.911434 + 0.411446i \(0.865024\pi\)
\(278\) −920497. + 1.59435e6i −0.714349 + 1.23729i
\(279\) 78325.1 0.0602407
\(280\) 0 0
\(281\) 1.14116e6 0.862143 0.431072 0.902318i \(-0.358136\pi\)
0.431072 + 0.902318i \(0.358136\pi\)
\(282\) −1.06294e6 + 1.84106e6i −0.795948 + 1.37862i
\(283\) −304959. 528204.i −0.226347 0.392045i 0.730376 0.683046i \(-0.239345\pi\)
−0.956723 + 0.291001i \(0.906012\pi\)
\(284\) 558870. + 967990.i 0.411164 + 0.712156i
\(285\) −341579. + 591632.i −0.249103 + 0.431459i
\(286\) −2.86624e6 −2.07204
\(287\) 0 0
\(288\) 663718. 0.471523
\(289\) 177020. 306608.i 0.124675 0.215943i
\(290\) 1.16024e6 + 2.00960e6i 0.810130 + 1.40319i
\(291\) 692833. + 1.20002e6i 0.479618 + 0.830724i
\(292\) −300797. + 520995.i −0.206450 + 0.357583i
\(293\) −156438. −0.106457 −0.0532283 0.998582i \(-0.516951\pi\)
−0.0532283 + 0.998582i \(0.516951\pi\)
\(294\) 0 0
\(295\) 751303. 0.502644
\(296\) −54955.3 + 95185.4i −0.0364570 + 0.0631453i
\(297\) 107735. + 186603.i 0.0708707 + 0.122752i
\(298\) −274106. 474765.i −0.178804 0.309698i
\(299\) 367968. 637340.i 0.238030 0.412281i
\(300\) 647554. 0.415406
\(301\) 0 0
\(302\) 1.89007e6 1.19251
\(303\) −629139. + 1.08970e6i −0.393677 + 0.681869i
\(304\) −775201. 1.34269e6i −0.481095 0.833281i
\(305\) −429630. 744141.i −0.264451 0.458042i
\(306\) −353150. + 611673.i −0.215603 + 0.373436i
\(307\) −293229. −0.177566 −0.0887831 0.996051i \(-0.528298\pi\)
−0.0887831 + 0.996051i \(0.528298\pi\)
\(308\) 0 0
\(309\) −1.04333e6 −0.621620
\(310\) 147011. 254631.i 0.0868853 0.150490i
\(311\) 1.22608e6 + 2.12363e6i 0.718816 + 1.24503i 0.961469 + 0.274913i \(0.0886491\pi\)
−0.242653 + 0.970113i \(0.578018\pi\)
\(312\) −320245. 554681.i −0.186250 0.322594i
\(313\) 917705. 1.58951e6i 0.529471 0.917071i −0.469938 0.882700i \(-0.655724\pi\)
0.999409 0.0343716i \(-0.0109430\pi\)
\(314\) −3.88503e6 −2.22367
\(315\) 0 0
\(316\) −2.87406e6 −1.61912
\(317\) −294980. + 510920.i −0.164871 + 0.285565i −0.936609 0.350375i \(-0.886054\pi\)
0.771738 + 0.635940i \(0.219387\pi\)
\(318\) 270401. + 468349.i 0.149948 + 0.259718i
\(319\) −1.12783e6 1.95346e6i −0.620537 1.07480i
\(320\) 822221. 1.42413e6i 0.448863 0.777454i
\(321\) −747556. −0.404931
\(322\) 0 0
\(323\) 2.17679e6 1.16094
\(324\) −129050. + 223522.i −0.0682963 + 0.118293i
\(325\) 1.04996e6 + 1.81859e6i 0.551399 + 0.955050i
\(326\) 384593. + 666134.i 0.200427 + 0.347151i
\(327\) 204103. 353517.i 0.105555 0.182827i
\(328\) −742344. −0.380996
\(329\) 0 0
\(330\) 808849. 0.408868
\(331\) −88659.2 + 153562.i −0.0444789 + 0.0770396i −0.887408 0.460985i \(-0.847496\pi\)
0.842929 + 0.538025i \(0.180829\pi\)
\(332\) −596785. 1.03366e6i −0.297148 0.514675i
\(333\) 71815.0 + 124387.i 0.0354899 + 0.0614703i
\(334\) 1.32932e6 2.30245e6i 0.652023 1.12934i
\(335\) 1.24817e6 0.607664
\(336\) 0 0
\(337\) −3.04781e6 −1.46189 −0.730943 0.682438i \(-0.760920\pi\)
−0.730943 + 0.682438i \(0.760920\pi\)
\(338\) 3.99888e6 6.92627e6i 1.90391 3.29767i
\(339\) −1599.90 2771.10i −0.000756124 0.00130965i
\(340\) 731027. + 1.26618e6i 0.342954 + 0.594014i
\(341\) −142904. + 247518.i −0.0665518 + 0.115271i
\(342\) 1.44253e6 0.666896
\(343\) 0 0
\(344\) 1.22747e6 0.559259
\(345\) −103840. + 179856.i −0.0469697 + 0.0813538i
\(346\) 1.52937e6 + 2.64895e6i 0.686787 + 1.18955i
\(347\) 1.21180e6 + 2.09891e6i 0.540268 + 0.935771i 0.998888 + 0.0471388i \(0.0150103\pi\)
−0.458621 + 0.888632i \(0.651656\pi\)
\(348\) 1.35097e6 2.33995e6i 0.597996 1.03576i
\(349\) 2.67690e6 1.17644 0.588218 0.808702i \(-0.299830\pi\)
0.588218 + 0.808702i \(0.299830\pi\)
\(350\) 0 0
\(351\) −836985. −0.362619
\(352\) −1.21096e6 + 2.09744e6i −0.520921 + 0.902262i
\(353\) 475206. + 823081.i 0.202976 + 0.351565i 0.949486 0.313809i \(-0.101605\pi\)
−0.746510 + 0.665374i \(0.768272\pi\)
\(354\) −793209. 1.37388e6i −0.336418 0.582694i
\(355\) 511438. 885837.i 0.215388 0.373064i
\(356\) 1.41971e6 0.593711
\(357\) 0 0
\(358\) 1.46877e6 0.605683
\(359\) −1.39441e6 + 2.41518e6i −0.571022 + 0.989039i 0.425439 + 0.904987i \(0.360120\pi\)
−0.996461 + 0.0840524i \(0.973214\pi\)
\(360\) 90372.7 + 156530.i 0.0367520 + 0.0636563i
\(361\) −984862. 1.70583e6i −0.397747 0.688919i
\(362\) −570007. + 987282.i −0.228617 + 0.395977i
\(363\) 663206. 0.264169
\(364\) 0 0
\(365\) 550536. 0.216299
\(366\) −907187. + 1.57129e6i −0.353993 + 0.613133i
\(367\) 76940.7 + 133265.i 0.0298189 + 0.0516478i 0.880550 0.473954i \(-0.157174\pi\)
−0.850731 + 0.525602i \(0.823840\pi\)
\(368\) −235662. 408178.i −0.0907129 0.157119i
\(369\) −485044. + 840120.i −0.185445 + 0.321200i
\(370\) 539169. 0.204749
\(371\) 0 0
\(372\) −342356. −0.128269
\(373\) 1.19191e6 2.06444e6i 0.443578 0.768299i −0.554374 0.832268i \(-0.687042\pi\)
0.997952 + 0.0639683i \(0.0203757\pi\)
\(374\) −1.28865e6 2.23200e6i −0.476381 0.825117i
\(375\) −802548. 1.39005e6i −0.294709 0.510450i
\(376\) 866727. 1.50121e6i 0.316164 0.547612i
\(377\) 8.76203e6 3.17506
\(378\) 0 0
\(379\) 3.65191e6 1.30594 0.652969 0.757385i \(-0.273523\pi\)
0.652969 + 0.757385i \(0.273523\pi\)
\(380\) 1.49303e6 2.58600e6i 0.530407 0.918692i
\(381\) 760352. + 1.31697e6i 0.268350 + 0.464797i
\(382\) 766129. + 1.32697e6i 0.268623 + 0.465269i
\(383\) 1.07865e6 1.86827e6i 0.375736 0.650794i −0.614701 0.788760i \(-0.710723\pi\)
0.990437 + 0.137967i \(0.0440566\pi\)
\(384\) −1.11245e6 −0.384991
\(385\) 0 0
\(386\) −8.15904e6 −2.78722
\(387\) 802019. 1.38914e6i 0.272212 0.471485i
\(388\) −3.02835e6 5.24525e6i −1.02124 1.76883i
\(389\) 1.83236e6 + 3.17373e6i 0.613954 + 1.06340i 0.990567 + 0.137029i \(0.0437553\pi\)
−0.376613 + 0.926371i \(0.622911\pi\)
\(390\) −1.57097e6 + 2.72100e6i −0.523006 + 0.905872i
\(391\) 661746. 0.218902
\(392\) 0 0
\(393\) −1.56572e6 −0.511368
\(394\) −2.95220e6 + 5.11336e6i −0.958087 + 1.65946i
\(395\) 1.31507e6 + 2.27777e6i 0.424089 + 0.734543i
\(396\) −470906. 815634.i −0.150903 0.261371i
\(397\) −1.97324e6 + 3.41775e6i −0.628353 + 1.08834i 0.359529 + 0.933134i \(0.382937\pi\)
−0.987882 + 0.155205i \(0.950396\pi\)
\(398\) −3.51524e6 −1.11236
\(399\) 0 0
\(400\) 1.34488e6 0.420274
\(401\) −12508.0 + 21664.5i −0.00388444 + 0.00672804i −0.867961 0.496632i \(-0.834570\pi\)
0.864077 + 0.503360i \(0.167903\pi\)
\(402\) −1.31780e6 2.28249e6i −0.406708 0.704439i
\(403\) −555106. 961472.i −0.170260 0.294900i
\(404\) 2.74994e6 4.76304e6i 0.838244 1.45188i
\(405\) 236196. 0.0715542
\(406\) 0 0
\(407\) −524107. −0.156832
\(408\) 287961. 498763.i 0.0856412 0.148335i
\(409\) 416350. + 721139.i 0.123069 + 0.213163i 0.920977 0.389618i \(-0.127393\pi\)
−0.797907 + 0.602780i \(0.794060\pi\)
\(410\) 1.82079e6 + 3.15371e6i 0.534935 + 0.926535i
\(411\) 1.65476e6 2.86612e6i 0.483203 0.836931i
\(412\) 4.56035e6 1.32360
\(413\) 0 0
\(414\) 438528. 0.125747
\(415\) −546136. + 945935.i −0.155661 + 0.269613i
\(416\) −4.70391e6 8.14741e6i −1.33268 2.30827i
\(417\) −980850. 1.69888e6i −0.276225 0.478435i
\(418\) −2.63190e6 + 4.55858e6i −0.736763 + 1.27611i
\(419\) −3.95178e6 −1.09966 −0.549828 0.835278i \(-0.685307\pi\)
−0.549828 + 0.835278i \(0.685307\pi\)
\(420\) 0 0
\(421\) 4.72285e6 1.29867 0.649336 0.760502i \(-0.275047\pi\)
0.649336 + 0.760502i \(0.275047\pi\)
\(422\) −1.71945e6 + 2.97817e6i −0.470011 + 0.814084i
\(423\) −1.13263e6 1.96177e6i −0.307777 0.533086i
\(424\) −220487. 381895.i −0.0595619 0.103164i
\(425\) −944115. + 1.63526e6i −0.253544 + 0.439150i
\(426\) −2.15986e6 −0.576636
\(427\) 0 0
\(428\) 3.26754e6 0.862207
\(429\) 1.52708e6 2.64499e6i 0.400608 0.693873i
\(430\) −3.01068e6 5.21465e6i −0.785224 1.36005i
\(431\) −2.03905e6 3.53174e6i −0.528731 0.915789i −0.999439 0.0334995i \(-0.989335\pi\)
0.470708 0.882289i \(-0.343999\pi\)
\(432\) −268019. + 464223.i −0.0690966 + 0.119679i
\(433\) 1.79927e6 0.461186 0.230593 0.973050i \(-0.425933\pi\)
0.230593 + 0.973050i \(0.425933\pi\)
\(434\) 0 0
\(435\) −2.47263e6 −0.626522
\(436\) −892127. + 1.54521e6i −0.224756 + 0.389288i
\(437\) −675766. 1.17046e6i −0.169275 0.293193i
\(438\) −581244. 1.00674e6i −0.144768 0.250746i
\(439\) 2.25913e6 3.91293e6i 0.559475 0.969039i −0.438065 0.898943i \(-0.644336\pi\)
0.997540 0.0700959i \(-0.0223305\pi\)
\(440\) −659542. −0.162409
\(441\) 0 0
\(442\) 1.00114e7 2.43746
\(443\) 1.42628e6 2.47039e6i 0.345299 0.598075i −0.640109 0.768284i \(-0.721111\pi\)
0.985408 + 0.170209i \(0.0544443\pi\)
\(444\) −313901. 543692.i −0.0755675 0.130887i
\(445\) −649611. 1.12516e6i −0.155508 0.269348i
\(446\) −3.72488e6 + 6.45168e6i −0.886696 + 1.53580i
\(447\) 584155. 0.138280
\(448\) 0 0
\(449\) −1.90246e6 −0.445348 −0.222674 0.974893i \(-0.571478\pi\)
−0.222674 + 0.974893i \(0.571478\pi\)
\(450\) −625650. + 1.08366e6i −0.145646 + 0.252267i
\(451\) −1.76993e6 3.06561e6i −0.409746 0.709700i
\(452\) 6993.09 + 12112.4i 0.00160999 + 0.00278859i
\(453\) −1.00700e6 + 1.74417e6i −0.230559 + 0.399341i
\(454\) −9.51468e6 −2.16648
\(455\) 0 0
\(456\) −1.17625e6 −0.264903
\(457\) −1.32417e6 + 2.29353e6i −0.296588 + 0.513705i −0.975353 0.220650i \(-0.929182\pi\)
0.678765 + 0.734355i \(0.262515\pi\)
\(458\) −1.30952e6 2.26815e6i −0.291708 0.505253i
\(459\) −376304. 651778.i −0.0833695 0.144400i
\(460\) 453881. 786146.i 0.100011 0.173224i
\(461\) −1.09031e6 −0.238944 −0.119472 0.992838i \(-0.538120\pi\)
−0.119472 + 0.992838i \(0.538120\pi\)
\(462\) 0 0
\(463\) −2.50851e6 −0.543831 −0.271916 0.962321i \(-0.587657\pi\)
−0.271916 + 0.962321i \(0.587657\pi\)
\(464\) 2.80578e6 4.85975e6i 0.605004 1.04790i
\(465\) 156650. + 271326.i 0.0335968 + 0.0581914i
\(466\) 4.79971e6 + 8.31335e6i 1.02388 + 1.77342i
\(467\) −1.60468e6 + 2.77938e6i −0.340483 + 0.589734i −0.984522 0.175259i \(-0.943924\pi\)
0.644040 + 0.764992i \(0.277257\pi\)
\(468\) 3.65843e6 0.772112
\(469\) 0 0
\(470\) −8.50350e6 −1.77563
\(471\) 2.06988e6 3.58513e6i 0.429925 0.744652i
\(472\) 646789. + 1.12027e6i 0.133631 + 0.231456i
\(473\) 2.92657e6 + 5.06898e6i 0.601460 + 1.04176i
\(474\) 2.77685e6 4.80964e6i 0.567683 0.983256i
\(475\) 3.85647e6 0.784252
\(476\) 0 0
\(477\) −576260. −0.115964
\(478\) 369551. 640081.i 0.0739784 0.128134i
\(479\) 1.15731e6 + 2.00452e6i 0.230468 + 0.399182i 0.957946 0.286949i \(-0.0926410\pi\)
−0.727478 + 0.686131i \(0.759308\pi\)
\(480\) 1.32744e6 + 2.29919e6i 0.262973 + 0.455482i
\(481\) 1.01794e6 1.76312e6i 0.200612 0.347471i
\(482\) 4.54211e6 0.890513
\(483\) 0 0
\(484\) −2.89885e6 −0.562486
\(485\) −2.77133e6 + 4.80009e6i −0.534976 + 0.926605i
\(486\) −249370. 431922.i −0.0478911 0.0829497i
\(487\) 2.31867e6 + 4.01606e6i 0.443014 + 0.767322i 0.997911 0.0645962i \(-0.0205759\pi\)
−0.554898 + 0.831919i \(0.687243\pi\)
\(488\) 739727. 1.28124e6i 0.140612 0.243547i
\(489\) −819618. −0.155003
\(490\) 0 0
\(491\) 5.02151e6 0.940007 0.470003 0.882665i \(-0.344253\pi\)
0.470003 + 0.882665i \(0.344253\pi\)
\(492\) 2.12011e6 3.67213e6i 0.394862 0.683921i
\(493\) 3.93936e6 + 6.82317e6i 0.729976 + 1.26436i
\(494\) −1.02235e7 1.77076e7i −1.88487 3.26469i
\(495\) −430941. + 746411.i −0.0790505 + 0.136919i
\(496\) −711024. −0.129772
\(497\) 0 0
\(498\) 2.30639e6 0.416735
\(499\) −1.68911e6 + 2.92562e6i −0.303673 + 0.525978i −0.976965 0.213399i \(-0.931546\pi\)
0.673292 + 0.739377i \(0.264880\pi\)
\(500\) 3.50791e6 + 6.07587e6i 0.627514 + 1.08689i
\(501\) 1.41648e6 + 2.45341e6i 0.252124 + 0.436692i
\(502\) −5.71610e6 + 9.90057e6i −1.01237 + 1.75348i
\(503\) −5.03743e6 −0.887747 −0.443873 0.896090i \(-0.646396\pi\)
−0.443873 + 0.896090i \(0.646396\pi\)
\(504\) 0 0
\(505\) −5.03311e6 −0.878230
\(506\) −800097. + 1.38581e6i −0.138921 + 0.240617i
\(507\) 4.26107e6 + 7.38039e6i 0.736205 + 1.27515i
\(508\) −3.32347e6 5.75642e6i −0.571390 0.989677i
\(509\) 3.36233e6 5.82373e6i 0.575236 0.996338i −0.420780 0.907163i \(-0.638244\pi\)
0.996016 0.0891752i \(-0.0284231\pi\)
\(510\) −2.82520e6 −0.480976
\(511\) 0 0
\(512\) −7.48361e6 −1.26164
\(513\) −768553. + 1.33117e6i −0.128938 + 0.223327i
\(514\) 4.12556e6 + 7.14568e6i 0.688771 + 1.19299i
\(515\) −2.08666e6 3.61420e6i −0.346684 0.600473i
\(516\) −3.50559e6 + 6.07187e6i −0.579612 + 1.00392i
\(517\) 8.26595e6 1.36009
\(518\) 0 0
\(519\) −3.25929e6 −0.531134
\(520\) 1.28098e6 2.21872e6i 0.207747 0.359828i
\(521\) 2.21385e6 + 3.83450e6i 0.357317 + 0.618892i 0.987512 0.157546i \(-0.0503582\pi\)
−0.630194 + 0.776437i \(0.717025\pi\)
\(522\) 2.61055e6 + 4.52161e6i 0.419330 + 0.726301i
\(523\) 4.47955e6 7.75882e6i 0.716111 1.24034i −0.246418 0.969164i \(-0.579254\pi\)
0.962529 0.271178i \(-0.0874131\pi\)
\(524\) 6.84372e6 1.08884
\(525\) 0 0
\(526\) 1.05050e7 1.65551
\(527\) 499145. 864545.i 0.0782889 0.135600i
\(528\) −978005. 1.69395e6i −0.152671 0.264434i
\(529\) 3.01274e6 + 5.21822e6i 0.468082 + 0.810742i
\(530\) −1.08161e6 + 1.87340e6i −0.167255 + 0.289694i
\(531\) 1.69043e6 0.260173
\(532\) 0 0
\(533\) 1.37504e7 2.09652
\(534\) −1.37169e6 + 2.37583e6i −0.208162 + 0.360548i
\(535\) −1.49511e6 2.58961e6i −0.225834 0.391156i
\(536\) 1.07454e6 + 1.86116e6i 0.161551 + 0.279815i
\(537\) −782533. + 1.35539e6i −0.117103 + 0.202828i
\(538\) −9.15641e6 −1.36386
\(539\) 0 0
\(540\) −1.03240e6 −0.152358
\(541\) 5.02337e6 8.70073e6i 0.737907 1.27809i −0.215529 0.976498i \(-0.569147\pi\)
0.953436 0.301595i \(-0.0975192\pi\)
\(542\) 9.14840e6 + 1.58455e7i 1.33766 + 2.31690i
\(543\) −607380. 1.05201e6i −0.0884018 0.153116i
\(544\) 4.22970e6 7.32606e6i 0.612791 1.06139i
\(545\) 1.63282e6 0.235477
\(546\) 0 0
\(547\) −1.31426e7 −1.87808 −0.939039 0.343811i \(-0.888282\pi\)
−0.939039 + 0.343811i \(0.888282\pi\)
\(548\) −7.23287e6 + 1.25277e7i −1.02887 + 1.78205i
\(549\) −966667. 1.67432e6i −0.136882 0.237086i
\(550\) −2.28300e6 3.95427e6i −0.321810 0.557391i
\(551\) 8.04564e6 1.39355e7i 1.12897 1.95543i
\(552\) −357579. −0.0499487
\(553\) 0 0
\(554\) −2.14415e6 −0.296811
\(555\) −287260. + 497549.i −0.0395861 + 0.0685652i
\(556\) 4.28726e6 + 7.42575e6i 0.588156 + 1.01872i
\(557\) −4.53376e6 7.85270e6i −0.619185 1.07246i −0.989635 0.143607i \(-0.954130\pi\)
0.370450 0.928853i \(-0.379204\pi\)
\(558\) 330775. 572920.i 0.0449726 0.0778948i
\(559\) −2.27363e7 −3.07744
\(560\) 0 0
\(561\) 2.74627e6 0.368414
\(562\) 4.81923e6 8.34715e6i 0.643631 1.11480i
\(563\) −5.25898e6 9.10882e6i −0.699247 1.21113i −0.968728 0.248126i \(-0.920185\pi\)
0.269481 0.963006i \(-0.413148\pi\)
\(564\) 4.95068e6 + 8.57483e6i 0.655340 + 1.13508i
\(565\) 6399.59 11084.4i 0.000843395 0.00146080i
\(566\) −5.15150e6 −0.675916
\(567\) 0 0
\(568\) 1.76117e6 0.229050
\(569\) −3.66153e6 + 6.34196e6i −0.474114 + 0.821189i −0.999561 0.0296373i \(-0.990565\pi\)
0.525447 + 0.850826i \(0.323898\pi\)
\(570\) 2.88505e6 + 4.99706e6i 0.371934 + 0.644209i
\(571\) 3.48990e6 + 6.04469e6i 0.447943 + 0.775861i 0.998252 0.0591007i \(-0.0188233\pi\)
−0.550309 + 0.834961i \(0.685490\pi\)
\(572\) −6.67483e6 + 1.15611e7i −0.853002 + 1.47744i
\(573\) −1.63272e6 −0.207743
\(574\) 0 0
\(575\) 1.17237e6 0.147875
\(576\) 1.85000e6 3.20429e6i 0.232335 0.402416i
\(577\) 2.90605e6 + 5.03343e6i 0.363382 + 0.629397i 0.988515 0.151122i \(-0.0482886\pi\)
−0.625133 + 0.780518i \(0.714955\pi\)
\(578\) −1.49515e6 2.58968e6i −0.186151 0.322423i
\(579\) 4.34699e6 7.52921e6i 0.538881 0.933369i
\(580\) 1.08078e7 1.33403
\(581\) 0 0
\(582\) 1.17036e7 1.43223
\(583\) 1.05139e6 1.82106e6i 0.128113 0.221898i
\(584\) 473951. + 820906.i 0.0575044 + 0.0996005i
\(585\) −1.67397e6 2.89940e6i −0.202236 0.350283i
\(586\) −660654. + 1.14429e6i −0.0794750 + 0.137655i
\(587\) −7.37446e6 −0.883355 −0.441677 0.897174i \(-0.645616\pi\)
−0.441677 + 0.897174i \(0.645616\pi\)
\(588\) 0 0
\(589\) −2.03888e6 −0.242161
\(590\) 3.17284e6 5.49552e6i 0.375247 0.649948i
\(591\) −3.14576e6 5.44862e6i −0.370473 0.641679i
\(592\) −651927. 1.12917e6i −0.0764530 0.132420i
\(593\) −4.73264e6 + 8.19717e6i −0.552671 + 0.957254i 0.445410 + 0.895327i \(0.353058\pi\)
−0.998081 + 0.0619274i \(0.980275\pi\)
\(594\) 1.81991e6 0.211633
\(595\) 0 0
\(596\) −2.55332e6 −0.294435
\(597\) 1.87286e6 3.24388e6i 0.215065 0.372503i
\(598\) −3.10794e6 5.38311e6i −0.355402 0.615575i
\(599\) 4.26098e6 + 7.38023e6i 0.485224 + 0.840432i 0.999856 0.0169788i \(-0.00540478\pi\)
−0.514632 + 0.857411i \(0.672071\pi\)
\(600\) 510159. 883622.i 0.0578532 0.100205i
\(601\) −657065. −0.0742031 −0.0371016 0.999311i \(-0.511813\pi\)
−0.0371016 + 0.999311i \(0.511813\pi\)
\(602\) 0 0
\(603\) 2.80839e6 0.314532
\(604\) 4.40155e6 7.62371e6i 0.490923 0.850303i
\(605\) 1.32641e6 + 2.29741e6i 0.147330 + 0.255182i
\(606\) 5.31385e6 + 9.20386e6i 0.587798 + 1.01810i
\(607\) −2.93443e6 + 5.08257e6i −0.323260 + 0.559902i −0.981159 0.193204i \(-0.938112\pi\)
0.657899 + 0.753106i \(0.271445\pi\)
\(608\) −1.72773e7 −1.89547
\(609\) 0 0
\(610\) −7.25750e6 −0.789700
\(611\) −1.60544e7 + 2.78070e7i −1.73976 + 3.01336i
\(612\) 1.64481e6 + 2.84890e6i 0.177516 + 0.307467i
\(613\) −1.92201e6 3.32902e6i −0.206588 0.357820i 0.744050 0.668124i \(-0.232902\pi\)
−0.950637 + 0.310304i \(0.899569\pi\)
\(614\) −1.23834e6 + 2.14486e6i −0.132562 + 0.229603i
\(615\) −3.88035e6 −0.413698
\(616\) 0 0
\(617\) 6.44660e6 0.681739 0.340869 0.940111i \(-0.389279\pi\)
0.340869 + 0.940111i \(0.389279\pi\)
\(618\) −4.40609e6 + 7.63158e6i −0.464069 + 0.803791i
\(619\) −3.36870e6 5.83476e6i −0.353375 0.612063i 0.633464 0.773772i \(-0.281633\pi\)
−0.986838 + 0.161709i \(0.948299\pi\)
\(620\) −684712. 1.18596e6i −0.0715367 0.123905i
\(621\) −233640. + 404677.i −0.0243119 + 0.0421094i
\(622\) 2.07115e7 2.14652
\(623\) 0 0
\(624\) 7.59804e6 0.781160
\(625\) 352380. 610339.i 0.0360837 0.0624987i
\(626\) −7.75114e6 1.34254e7i −0.790551 1.36927i
\(627\) −2.80446e6 4.85746e6i −0.284892 0.493447i
\(628\) −9.04736e6 + 1.56705e7i −0.915425 + 1.58556i
\(629\) 1.83063e6 0.184491
\(630\) 0 0
\(631\) −9.14514e6 −0.914360 −0.457180 0.889374i \(-0.651140\pi\)
−0.457180 + 0.889374i \(0.651140\pi\)
\(632\) −2.26426e6 + 3.92181e6i −0.225493 + 0.390566i
\(633\) −1.83219e6 3.17344e6i −0.181744 0.314790i
\(634\) 2.49147e6 + 4.31534e6i 0.246168 + 0.426376i
\(635\) −3.04141e6 + 5.26787e6i −0.299323 + 0.518443i
\(636\) 2.51881e6 0.246918
\(637\) 0 0
\(638\) −1.90518e7 −1.85304
\(639\) 1.15074e6 1.99313e6i 0.111487 0.193101i
\(640\) −2.22489e6 3.85362e6i −0.214713 0.371894i
\(641\) 520442. + 901432.i 0.0500296 + 0.0866538i 0.889956 0.456047i \(-0.150735\pi\)
−0.839926 + 0.542701i \(0.817402\pi\)
\(642\) −3.15701e6 + 5.46811e6i −0.302300 + 0.523600i
\(643\) −9.08713e6 −0.866761 −0.433381 0.901211i \(-0.642679\pi\)
−0.433381 + 0.901211i \(0.642679\pi\)
\(644\) 0 0
\(645\) 6.41615e6 0.607261
\(646\) 9.19284e6 1.59225e7i 0.866699 1.50117i
\(647\) −1.10356e6 1.91141e6i −0.103641 0.179512i 0.809541 0.587064i \(-0.199716\pi\)
−0.913182 + 0.407551i \(0.866383\pi\)
\(648\) 203339. + 352193.i 0.0190231 + 0.0329490i
\(649\) −3.08420e6 + 5.34199e6i −0.287429 + 0.497842i
\(650\) 1.77364e7 1.64658
\(651\) 0 0
\(652\) 3.58252e6 0.330042
\(653\) 9.18048e6 1.59011e7i 0.842524 1.45929i −0.0452296 0.998977i \(-0.514402\pi\)
0.887754 0.460318i \(-0.152265\pi\)
\(654\) −1.72390e6 2.98588e6i −0.157604 0.272978i
\(655\) −3.13145e6 5.42382e6i −0.285195 0.493972i
\(656\) 4.40316e6 7.62649e6i 0.399489 0.691935i
\(657\) 1.23871e6 0.111958
\(658\) 0 0
\(659\) 6.21208e6 0.557216 0.278608 0.960405i \(-0.410127\pi\)
0.278608 + 0.960405i \(0.410127\pi\)
\(660\) 1.88363e6 3.26254e6i 0.168320 0.291538i
\(661\) −7.71149e6 1.33567e7i −0.686491 1.18904i −0.972966 0.230950i \(-0.925817\pi\)
0.286475 0.958088i \(-0.407517\pi\)
\(662\) 748835. + 1.29702e6i 0.0664112 + 0.115028i
\(663\) −5.33389e6 + 9.23857e6i −0.471260 + 0.816246i
\(664\) −1.88065e6 −0.165534
\(665\) 0 0
\(666\) 1.21313e6 0.105980
\(667\) 2.44588e6 4.23638e6i 0.212873 0.368707i
\(668\) −6.19136e6 1.07238e7i −0.536840 0.929834i
\(669\) −3.96910e6 6.87468e6i −0.342868 0.593865i
\(670\) 5.27118e6 9.12995e6i 0.453650 0.785745i
\(671\) 7.05475e6 0.604889
\(672\) 0 0
\(673\) −2.27201e7 −1.93362 −0.966811 0.255491i \(-0.917763\pi\)
−0.966811 + 0.255491i \(0.917763\pi\)
\(674\) −1.28713e7 + 2.22937e7i −1.09137 + 1.89030i
\(675\) −666670. 1.15471e6i −0.0563186 0.0975467i
\(676\) −1.86250e7 3.22594e7i −1.56758 2.71513i
\(677\) −6.80867e6 + 1.17930e7i −0.570940 + 0.988897i 0.425530 + 0.904944i \(0.360088\pi\)
−0.996470 + 0.0839525i \(0.973246\pi\)
\(678\) −27026.2 −0.00225793
\(679\) 0 0
\(680\) 2.30369e6 0.191052
\(681\) 5.06926e6 8.78021e6i 0.418867 0.725499i
\(682\) 1.20700e6 + 2.09059e6i 0.0993682 + 0.172111i
\(683\) −1.19993e6 2.07833e6i −0.0984245 0.170476i 0.812608 0.582810i \(-0.198047\pi\)
−0.911033 + 0.412334i \(0.864714\pi\)
\(684\) 3.35931e6 5.81850e6i 0.274543 0.475523i
\(685\) 1.32380e7 1.07795
\(686\) 0 0
\(687\) 2.79076e6 0.225595
\(688\) −7.28061e6 + 1.26104e7i −0.586404 + 1.01568i
\(689\) 4.08408e6 + 7.07383e6i 0.327753 + 0.567684i
\(690\) 877057. + 1.51911e6i 0.0701302 + 0.121469i
\(691\) 701824. 1.21560e6i 0.0559156 0.0968487i −0.836713 0.547642i \(-0.815526\pi\)
0.892628 + 0.450793i \(0.148859\pi\)
\(692\) 1.42462e7 1.13093
\(693\) 0 0
\(694\) 2.04703e7 1.61334
\(695\) 3.92340e6 6.79553e6i 0.308106 0.533656i
\(696\) −2.12866e6 3.68695e6i −0.166565 0.288499i
\(697\) 6.18211e6 + 1.07077e7i 0.482009 + 0.834864i
\(698\) 1.13048e7 1.95806e7i 0.878266 1.52120i
\(699\) −1.02288e7 −0.791831
\(700\) 0 0
\(701\) −5.78991e6 −0.445017 −0.222509 0.974931i \(-0.571425\pi\)
−0.222509 + 0.974931i \(0.571425\pi\)
\(702\) −3.53468e6 + 6.12225e6i −0.270712 + 0.468887i
\(703\) −1.86942e6 3.23793e6i −0.142665 0.247103i
\(704\) 6.75066e6 + 1.16925e7i 0.513351 + 0.889150i
\(705\) 4.53052e6 7.84708e6i 0.343301 0.594614i
\(706\) 8.02739e6 0.606126
\(707\) 0 0
\(708\) −7.38882e6 −0.553977
\(709\) 5.65716e6 9.79849e6i 0.422652 0.732055i −0.573546 0.819173i \(-0.694433\pi\)
0.996198 + 0.0871187i \(0.0277659\pi\)
\(710\) −4.31972e6 7.48198e6i −0.321595 0.557020i
\(711\) 2.95891e6 + 5.12498e6i 0.219512 + 0.380206i
\(712\) 1.11848e6 1.93727e6i 0.0826857 0.143216i
\(713\) −619821. −0.0456607
\(714\) 0 0
\(715\) 1.22167e7 0.893692
\(716\) 3.42042e6 5.92435e6i 0.249343 0.431875i
\(717\) 393781. + 682048.i 0.0286060 + 0.0495470i
\(718\) 1.17775e7 + 2.03992e7i 0.852591 + 1.47673i
\(719\) 1.36890e7 2.37101e7i 0.987529 1.71045i 0.357420 0.933944i \(-0.383656\pi\)
0.630109 0.776507i \(-0.283010\pi\)
\(720\) −2.14415e6 −0.154143
\(721\) 0 0
\(722\) −1.66367e7 −1.18775
\(723\) −2.41996e6 + 4.19149e6i −0.172172 + 0.298210i
\(724\) 2.65484e6 + 4.59831e6i 0.188231 + 0.326026i
\(725\) 6.97908e6 + 1.20881e7i 0.493121 + 0.854110i
\(726\) 2.80079e6 4.85111e6i 0.197215 0.341586i
\(727\) −9.86471e6 −0.692226 −0.346113 0.938193i \(-0.612499\pi\)
−0.346113 + 0.938193i \(0.612499\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 2.32498e6 4.02698e6i 0.161477 0.279687i
\(731\) −1.02221e7 1.77052e7i −0.707534 1.22548i
\(732\) 4.22527e6 + 7.31837e6i 0.291458 + 0.504820i
\(733\) −1.93938e6 + 3.35911e6i −0.133322 + 0.230921i −0.924955 0.380076i \(-0.875898\pi\)
0.791633 + 0.610997i \(0.209231\pi\)
\(734\) 1.29972e6 0.0890448
\(735\) 0 0
\(736\) −5.25229e6 −0.357400
\(737\) −5.12393e6 + 8.87490e6i −0.347483 + 0.601859i
\(738\) 4.09679e6 + 7.09584e6i 0.276887 + 0.479582i
\(739\) 3.97749e6 + 6.88922e6i 0.267916 + 0.464044i 0.968323 0.249699i \(-0.0803318\pi\)
−0.700408 + 0.713743i \(0.746998\pi\)
\(740\) 1.25560e6 2.17477e6i 0.0842894 0.145994i
\(741\) 2.17876e7 1.45768
\(742\) 0 0
\(743\) 1.65977e7 1.10300 0.551500 0.834175i \(-0.314056\pi\)
0.551500 + 0.834175i \(0.314056\pi\)
\(744\) −269717. + 467163.i −0.0178639 + 0.0309411i
\(745\) 1.16831e6 + 2.02357e6i 0.0771200 + 0.133576i
\(746\) −1.00671e7 1.74367e7i −0.662304 1.14714i
\(747\) −1.22881e6 + 2.12835e6i −0.0805716 + 0.139554i
\(748\) −1.20039e7 −0.784453
\(749\) 0 0
\(750\) −1.35570e7 −0.880056
\(751\) −7.55359e6 + 1.30832e7i −0.488713 + 0.846475i −0.999916 0.0129846i \(-0.995867\pi\)
0.511203 + 0.859460i \(0.329200\pi\)
\(752\) 1.02818e7 + 1.78087e7i 0.663020 + 1.14838i
\(753\) −6.09088e6 1.05497e7i −0.391464 0.678036i
\(754\) 3.70030e7 6.40911e7i 2.37033 4.10553i
\(755\) −8.05598e6 −0.514341
\(756\) 0 0
\(757\) 5.80923e6 0.368450 0.184225 0.982884i \(-0.441022\pi\)
0.184225 + 0.982884i \(0.441022\pi\)
\(758\) 1.54224e7 2.67124e7i 0.974944 1.68865i
\(759\) −852556. 1.47667e6i −0.0537178 0.0930420i
\(760\) −2.35249e6 4.07464e6i −0.147739 0.255891i
\(761\) −1.27135e7 + 2.20204e7i −0.795799 + 1.37836i 0.126531 + 0.991963i \(0.459616\pi\)
−0.922331 + 0.386402i \(0.873718\pi\)
\(762\) 1.28442e7 0.801346
\(763\) 0 0
\(764\) 7.13656e6 0.442340
\(765\) 1.50522e6 2.60711e6i 0.0929919 0.161067i
\(766\) −9.11050e6 1.57798e7i −0.561010 0.971697i
\(767\) −1.19804e7 2.07507e7i −0.735334 1.27364i
\(768\) 1.87979e6 3.25589e6i 0.115002 0.199190i
\(769\) 1.53909e7