Properties

Label 147.6.e.n.67.2
Level $147$
Weight $6$
Character 147.67
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 67.2
Root \(3.72311 + 6.44862i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.6.e.n.79.2

$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.949468 + 0.313863i \(0.101623\pi\)
−0.202921 + 0.979195i \(0.565043\pi\)
\(3\) 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 0.658906 0.752226i \(-0.271020\pi\)
−0.980899 + 0.194516i \(0.937686\pi\)
\(6\) 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 −0.989293 0.145945i \(-0.953378\pi\)
0.621038 + 0.783780i \(0.286711\pi\)
\(12\) 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 −0.563946 0.825811i \(-0.690718\pi\)
0.997147 + 0.0754862i \(0.0240509\pi\)
\(18\) 342.072 592.486i 0.248849 0.431019i
\(19\) 1054.26 + 1826.02i 0.669980 + 1.16044i 0.977909 + 0.209031i \(0.0670308\pi\)
−0.307929 + 0.951409i \(0.599636\pi\)
\(20\) 1416.19 0.791675
\(21\) 0 0
\(22\) −2496.45 −1.09968
\(23\) 320.494 + 555.112i 0.126328 + 0.218807i 0.922251 0.386591i \(-0.126347\pi\)
−0.795923 + 0.605398i \(0.793014\pi\)
\(24\) −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 −0.907663 0.419700i \(-0.862135\pi\)
0.817302 + 0.576210i \(0.195469\pi\)
\(32\) −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 0.914338 0.404953i \(-0.132712\pi\)
−0.807868 + 0.589363i \(0.799379\pi\)
\(38\) −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 −0.794222 0.607628i \(-0.792121\pi\)
−0.129110 0.991630i \(-0.541212\pi\)
\(48\) 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 −0.765850 0.643019i \(-0.777682\pi\)
0.939796 + 0.341736i \(0.111015\pi\)
\(54\) −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 −0.992484 0.122379i \(-0.960948\pi\)
0.602225 + 0.798327i \(0.294281\pi\)
\(60\) 6372.86 11038.1i 0.228537 0.395838i
\(61\) −11934.2 20670.6i −0.410646 0.711259i 0.584315 0.811527i \(-0.301363\pi\)
−0.994960 + 0.100268i \(0.968030\pi\)
\(62\) −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 −0.999479 0.0322646i \(-0.989728\pi\)
0.527682 + 0.849442i \(0.323061\pi\)
\(68\) 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 −0.937694 0.347461i \(-0.887044\pi\)
0.769757 + 0.638337i \(0.220377\pi\)
\(74\) −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 0.980995 + 0.194033i \(0.0621570\pi\)
−0.322460 + 0.946583i \(0.604510\pi\)
\(80\) 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 0.719658 0.694328i \(-0.244298\pi\)
−0.961135 + 0.276078i \(0.910965\pi\)
\(90\) −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 −0.292541 0.956253i \(-0.594501\pi\)
0.974410 0.224779i \(-0.0721659\pi\)
\(102\) 39238.8 67963.7i 0.373436 0.646810i
\(103\) −57962.7 100394.i −0.538339 0.932430i −0.998994 0.0448508i \(-0.985719\pi\)
0.460655 0.887579i \(-0.347615\pi\)
\(104\) −71165.6 −0.645188
\(105\) 0 0
\(106\) 60089.2 0.519436
\(107\) −41530.9 71933.6i −0.350681 0.607397i 0.635688 0.771946i \(-0.280716\pi\)
−0.986369 + 0.164549i \(0.947383\pi\)
\(108\) 14338.9 24835.8i 0.118293 0.204889i
\(109\) −22678.1 + 39279.7i −0.182827 + 0.316666i −0.942842 0.333240i \(-0.891858\pi\)
0.760015 + 0.649906i \(0.225192\pi\)
\(110\) 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 0.555043 0.831822i \(-0.312702\pi\)
−0.997900 + 0.0647701i \(0.979369\pi\)
\(132\) −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 0.0555168 + 0.998458i \(0.482319\pi\)
−0.892448 + 0.451150i \(0.851014\pi\)
\(138\) 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 0.919670 0.392692i \(-0.128456\pi\)
−0.799916 + 0.600112i \(0.795123\pi\)
\(150\) 69516.6 120406.i 0.252267 0.436939i
\(151\) 111889. 193797.i 0.399341 0.691678i −0.594304 0.804240i \(-0.702572\pi\)
0.993645 + 0.112562i \(0.0359057\pi\)
\(152\) −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 0.205706 + 0.978614i \(0.434051\pi\)
−0.950357 + 0.311161i \(0.899282\pi\)
\(158\) −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 0.791069 0.611727i \(-0.209525\pi\)
−0.925305 + 0.379223i \(0.876191\pi\)
\(164\) −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 0.538984 0.842316i \(-0.318808\pi\)
−0.998959 + 0.0456154i \(0.985475\pi\)
\(174\) 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 −0.746611 0.665261i \(-0.768320\pi\)
0.949438 + 0.313953i \(0.101653\pi\)
\(180\) −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 0.761939 0.647648i \(-0.224247\pi\)
−0.941850 + 0.336035i \(0.890914\pi\)
\(192\) −205555. + 356032.i −0.402416 + 0.697006i
\(193\) −482999. + 836579.i −0.933369 + 1.61664i −0.155851 + 0.987781i \(0.549812\pi\)
−0.777517 + 0.628861i \(0.783521\pi\)
\(194\) 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 −0.989950 0.141419i \(-0.954834\pi\)
0.617447 + 0.786612i \(0.288167\pi\)
\(200\) −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 0.233269 + 0.972412i \(0.425058\pi\)
−0.958768 + 0.284189i \(0.908276\pi\)
\(228\) −373257. + 646500.i −0.475523 + 0.823629i
\(229\) 155042. + 268541.i 0.195371 + 0.338393i 0.947022 0.321168i \(-0.104075\pi\)
−0.751651 + 0.659561i \(0.770742\pi\)
\(230\) 194902. 0.242938
\(231\) 0 0
\(232\) −473036. −0.576998
\(233\) −568268. 984268.i −0.685746 1.18775i −0.973202 0.229953i \(-0.926143\pi\)
0.287456 0.957794i \(-0.407190\pi\)
\(234\) 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 −0.677516 0.735508i \(-0.736944\pi\)
0.975727 + 0.218992i \(0.0702770\pi\)
\(242\) −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 0.537722 0.843122i \(-0.319285\pi\)
−0.999026 + 0.0441199i \(0.985952\pi\)
\(258\) −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 −0.443564 0.896243i \(-0.646286\pi\)
0.997951 0.0639842i \(-0.0203807\pi\)
\(264\) −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 −0.998785 0.0492716i \(-0.984310\pi\)
0.542063 + 0.840338i \(0.317643\pi\)
\(270\) −110831. + 191965.i −0.0925237 + 0.160256i
\(271\) −1.08314e6 1.87605e6i −0.895900 1.55174i −0.832687 0.553744i \(-0.813199\pi\)
−0.0632128 0.998000i \(-0.520135\pi\)
\(272\) 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 −0.911434 0.411446i \(-0.865024\pi\)
0.812040 + 0.583602i \(0.198357\pi\)
\(278\) −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 −0.956723 0.291001i \(-0.906012\pi\)
0.730376 + 0.683046i \(0.239345\pi\)
\(284\) 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 −0.242653 0.970113i \(-0.578018\pi\)
0.961469 0.274913i \(-0.0886491\pi\)
\(312\) −320245. + 554681.i −0.186250 + 0.322594i
\(313\) 917705. + 1.58951e6i 0.529471 + 0.917071i 0.999409 + 0.0343716i \(0.0109430\pi\)
−0.469938 + 0.882700i \(0.655724\pi\)
\(314\) −3.88503e6 −2.22367
\(315\) 0 0
\(316\) −2.87406e6 −1.61912
\(317\) −294980. 510920.i −0.164871 0.285565i 0.771738 0.635940i \(-0.219387\pi\)
−0.936609 + 0.350375i \(0.886054\pi\)
\(318\) 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 0.842929 0.538025i \(-0.180829\pi\)
−0.887408 + 0.460985i \(0.847496\pi\)
\(332\) −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 −0.458621 0.888632i \(-0.651656\pi\)
0.998888 0.0471388i \(-0.0150103\pi\)
\(348\) 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 −0.746510 0.665374i \(-0.768272\pi\)
0.949486 + 0.313809i \(0.101605\pi\)
\(354\) −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 −0.996461 0.0840524i \(-0.973214\pi\)
0.425439 0.904987i \(-0.360120\pi\)
\(360\) 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 −0.850731 0.525602i \(-0.823840\pi\)
0.880550 + 0.473954i \(0.157174\pi\)
\(368\) −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 0.997952 0.0639683i \(-0.0203757\pi\)
−0.554374 + 0.832268i \(0.687042\pi\)
\(374\) −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 0.990437 0.137967i \(-0.0440566\pi\)
−0.614701 + 0.788760i \(0.710723\pi\)
\(384\) −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 −0.376613 0.926371i \(-0.622911\pi\)
0.990567 0.137029i \(-0.0437553\pi\)
\(390\) −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 −0.987882 0.155205i \(-0.950396\pi\)
0.359529 0.933134i \(-0.382937\pi\)
\(398\) −3.51524e6 −1.11236
\(399\) 0 0
\(400\) 1.34488e6 0.420274
\(401\) −12508.0 21664.5i −0.00388444 0.00672804i 0.864077 0.503360i \(-0.167903\pi\)
−0.867961 + 0.496632i \(0.834570\pi\)
\(402\) −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 −0.797907 0.602780i \(-0.794060\pi\)
0.920977 + 0.389618i \(0.127393\pi\)
\(410\) 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 0.470708 + 0.882289i \(0.343999\pi\)
−0.999439 + 0.0334995i \(0.989335\pi\)
\(432\) −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 0.997540 + 0.0700959i \(0.0223305\pi\)
−0.438065 + 0.898943i \(0.644336\pi\)
\(440\) −659542. −0.162409
\(441\) 0 0
\(442\) 1.00114e7 2.43746
\(443\) 1.42628e6 + 2.47039e6i 0.345299 + 0.598075i 0.985408 0.170209i \(-0.0544443\pi\)
−0.640109 + 0.768284i \(0.721111\pi\)
\(444\) −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 0.678765 0.734355i \(-0.262515\pi\)
−0.975353 + 0.220650i \(0.929182\pi\)
\(458\) −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 0.644040 0.764992i \(-0.277257\pi\)
−0.984522 + 0.175259i \(0.943924\pi\)
\(468\) 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 −0.727478 0.686131i \(-0.759308\pi\)
0.957946 + 0.286949i \(0.0926410\pi\)
\(480\) 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 −0.554898 0.831919i \(-0.687243\pi\)
0.997911 + 0.0645962i \(0.0205759\pi\)
\(488\) 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 0.673292 0.739377i \(-0.264880\pi\)
−0.976965 + 0.213399i \(0.931546\pi\)
\(500\) 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 0.996016 + 0.0891752i \(0.0284231\pi\)
−0.420780 + 0.907163i \(0.638244\pi\)
\(510\) −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 −0.630194 0.776437i \(-0.717025\pi\)
0.987512 + 0.157546i \(0.0503582\pi\)
\(522\) 2.61055e6 4.52161e6i 0.419330 0.726301i
\(523\) 4.47955e6 + 7.75882e6i 0.716111 + 1.24034i 0.962529 + 0.271178i \(0.0874131\pi\)
−0.246418 + 0.969164i \(0.579254\pi\)
\(524\) 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 0.953436 + 0.301595i \(0.0975192\pi\)
−0.215529 + 0.976498i \(0.569147\pi\)
\(542\) 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 0.370450 + 0.928853i \(0.379204\pi\)
−0.989635 + 0.143607i \(0.954130\pi\)
\(558\) 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 0.269481 + 0.963006i \(0.413148\pi\)
−0.968728 + 0.248126i \(0.920185\pi\)
\(564\) 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 0.525447 0.850826i \(-0.323898\pi\)
−0.999561 + 0.0296373i \(0.990565\pi\)
\(570\) 2.88505e6 4.99706e6i 0.371934 0.644209i
\(571\) 3.48990e6 6.04469e6i 0.447943 0.775861i −0.550309 0.834961i \(-0.685490\pi\)
0.998252 + 0.0591007i \(0.0188233\pi\)
\(572\) −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 −0.625133 0.780518i \(-0.714955\pi\)
0.988515 + 0.151122i \(0.0482886\pi\)
\(578\) −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 −0.998081 0.0619274i \(-0.980275\pi\)
0.445410 0.895327i \(-0.353058\pi\)
\(594\) 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 −0.514632 0.857411i \(-0.672071\pi\)
0.999856 + 0.0169788i \(0.00540478\pi\)
\(600\) 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 0.657899 0.753106i \(-0.271445\pi\)
−0.981159 + 0.193204i \(0.938112\pi\)
\(608\) −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 −0.950637 0.310304i \(-0.899569\pi\)
0.744050 + 0.668124i \(0.232902\pi\)
\(614\) −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 −0.986838 0.161709i \(-0.948299\pi\)
0.633464 + 0.773772i \(0.281633\pi\)
\(620\) −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 −0.839926 0.542701i \(-0.817402\pi\)
0.889956 + 0.456047i \(0.150735\pi\)
\(642\) −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 −0.913182 0.407551i \(-0.866383\pi\)
0.809541 + 0.587064i \(0.199716\pi\)
\(648\) 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 0.887754 + 0.460318i \(0.152265\pi\)
−0.0452296 + 0.998977i \(0.514402\pi\)
\(654\) −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 0.286475 + 0.958088i \(0.407517\pi\)
−0.972966 + 0.230950i \(0.925817\pi\)
\(662\) 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 −0.996470 0.0839525i \(-0.973246\pi\)
0.425530 0.904944i \(-0.360088\pi\)
\(678\) −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 −0.911033 0.412334i \(-0.864714\pi\)
0.812608 + 0.582810i \(0.198047\pi\)
\(684\) 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 0.892628 0.450793i \(-0.148859\pi\)
−0.836713 + 0.547642i \(0.815526\pi\)
\(692\) 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 0.996198 0.0871187i \(-0.0277659\pi\)
−0.573546 + 0.819173i \(0.694433\pi\)
\(710\) −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 0.630109 + 0.776507i \(0.283010\pi\)
0.357420 + 0.933944i \(0.383656\pi\)
\(720\) −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 0.791633 0.610997i \(-0.209231\pi\)
−0.924955 + 0.380076i \(0.875898\pi\)
\(734\) 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 −0.700408 0.713743i \(-0.746998\pi\)
0.968323 + 0.249699i \(0.0803318\pi\)
\(740\) 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 0.511203 0.859460i \(-0.329200\pi\)
−0.999916 + 0.0129846i \(0.995867\pi\)
\(752\) 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 −0.922331 0.386402i \(-0.873718\pi\)
0.126531 0.991963i \(-0.459616\pi\)
\(762\) 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