Properties

Label 147.6.e.j.67.1
Level $147$
Weight $6$
Character 147.67
Analytic conductor $23.576$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.6.e.j.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.00000 + 5.19615i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-39.0000 - 67.5500i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(3.00000 + 5.19615i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-39.0000 - 67.5500i) q^{5} +54.0000 q^{6} +168.000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(234.000 - 405.300i) q^{10} +(-222.000 + 384.515i) q^{11} +(18.0000 + 31.1769i) q^{12} -442.000 q^{13} -702.000 q^{15} +(568.000 + 983.805i) q^{16} +(63.0000 - 109.119i) q^{17} +(243.000 - 420.888i) q^{18} +(-1342.00 - 2324.41i) q^{19} +312.000 q^{20} -2664.00 q^{22} +(-2100.00 - 3637.31i) q^{23} +(756.000 - 1309.43i) q^{24} +(-1479.50 + 2562.57i) q^{25} +(-1326.00 - 2296.70i) q^{26} -729.000 q^{27} -5442.00 q^{29} +(-2106.00 - 3647.70i) q^{30} +(-40.0000 + 69.2820i) q^{31} +(-720.000 + 1247.08i) q^{32} +(1998.00 + 3460.64i) q^{33} +756.000 q^{34} +324.000 q^{36} +(2717.00 + 4705.98i) q^{37} +(8052.00 - 13946.5i) q^{38} +(-1989.00 + 3445.05i) q^{39} +(-6552.00 - 11348.4i) q^{40} +7962.00 q^{41} -11524.0 q^{43} +(-888.000 - 1538.06i) q^{44} +(-3159.00 + 5471.55i) q^{45} +(12600.0 - 21823.8i) q^{46} +(6960.00 + 12055.1i) q^{47} +10224.0 q^{48} -17754.0 q^{50} +(-567.000 - 982.073i) q^{51} +(884.000 - 1531.13i) q^{52} +(4797.00 - 8308.65i) q^{53} +(-2187.00 - 3788.00i) q^{54} +34632.0 q^{55} -24156.0 q^{57} +(-16326.0 - 28277.5i) q^{58} +(-13746.0 + 23808.8i) q^{59} +(1404.00 - 2431.80i) q^{60} +(-24739.0 - 42849.2i) q^{61} -480.000 q^{62} +27712.0 q^{64} +(17238.0 + 29857.1i) q^{65} +(-11988.0 + 20763.8i) q^{66} +(29678.0 - 51403.8i) q^{67} +(252.000 + 436.477i) q^{68} -37800.0 q^{69} +32040.0 q^{71} +(-6804.00 - 11784.9i) q^{72} +(30923.0 - 53560.2i) q^{73} +(-16302.0 + 28235.9i) q^{74} +(13315.5 + 23063.1i) q^{75} +10736.0 q^{76} -23868.0 q^{78} +(32888.0 + 56963.7i) q^{79} +(44304.0 - 76736.8i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(23886.0 + 41371.8i) q^{82} +40188.0 q^{83} -9828.00 q^{85} +(-34572.0 - 59880.5i) q^{86} +(-24489.0 + 42416.2i) q^{87} +(-37296.0 + 64598.6i) q^{88} +(3987.00 + 6905.69i) q^{89} -37908.0 q^{90} +16800.0 q^{92} +(360.000 + 623.538i) q^{93} +(-41760.0 + 72330.4i) q^{94} +(-104676. + 181304. i) q^{95} +(6480.00 + 11223.7i) q^{96} -143662. q^{97} +35964.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} - 78 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{2} + 9 q^{3} - 4 q^{4} - 78 q^{5} + 108 q^{6} + 336 q^{8} - 81 q^{9} + 468 q^{10} - 444 q^{11} + 36 q^{12} - 884 q^{13} - 1404 q^{15} + 1136 q^{16} + 126 q^{17} + 486 q^{18} - 2684 q^{19} + 624 q^{20} - 5328 q^{22} - 4200 q^{23} + 1512 q^{24} - 2959 q^{25} - 2652 q^{26} - 1458 q^{27} - 10884 q^{29} - 4212 q^{30} - 80 q^{31} - 1440 q^{32} + 3996 q^{33} + 1512 q^{34} + 648 q^{36} + 5434 q^{37} + 16104 q^{38} - 3978 q^{39} - 13104 q^{40} + 15924 q^{41} - 23048 q^{43} - 1776 q^{44} - 6318 q^{45} + 25200 q^{46} + 13920 q^{47} + 20448 q^{48} - 35508 q^{50} - 1134 q^{51} + 1768 q^{52} + 9594 q^{53} - 4374 q^{54} + 69264 q^{55} - 48312 q^{57} - 32652 q^{58} - 27492 q^{59} + 2808 q^{60} - 49478 q^{61} - 960 q^{62} + 55424 q^{64} + 34476 q^{65} - 23976 q^{66} + 59356 q^{67} + 504 q^{68} - 75600 q^{69} + 64080 q^{71} - 13608 q^{72} + 61846 q^{73} - 32604 q^{74} + 26631 q^{75} + 21472 q^{76} - 47736 q^{78} + 65776 q^{79} + 88608 q^{80} - 6561 q^{81} + 47772 q^{82} + 80376 q^{83} - 19656 q^{85} - 69144 q^{86} - 48978 q^{87} - 74592 q^{88} + 7974 q^{89} - 75816 q^{90} + 33600 q^{92} + 720 q^{93} - 83520 q^{94} - 209352 q^{95} + 12960 q^{96} - 287324 q^{97} + 71928 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.00000 + 5.19615i 0.530330 + 0.918559i 0.999374 + 0.0353837i \(0.0112653\pi\)
−0.469044 + 0.883175i \(0.655401\pi\)
\(3\) 4.50000 7.79423i 0.288675 0.500000i
\(4\) −2.00000 + 3.46410i −0.0625000 + 0.108253i
\(5\) −39.0000 67.5500i −0.697653 1.20837i −0.969278 0.245968i \(-0.920894\pi\)
0.271625 0.962403i \(-0.412439\pi\)
\(6\) 54.0000 0.612372
\(7\) 0 0
\(8\) 168.000 0.928078
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) 234.000 405.300i 0.739973 1.28167i
\(11\) −222.000 + 384.515i −0.553186 + 0.958146i 0.444856 + 0.895602i \(0.353255\pi\)
−0.998042 + 0.0625444i \(0.980079\pi\)
\(12\) 18.0000 + 31.1769i 0.0360844 + 0.0625000i
\(13\) −442.000 −0.725377 −0.362689 0.931910i \(-0.618141\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(14\) 0 0
\(15\) −702.000 −0.805581
\(16\) 568.000 + 983.805i 0.554688 + 0.960747i
\(17\) 63.0000 109.119i 0.0528711 0.0915754i −0.838379 0.545088i \(-0.816496\pi\)
0.891250 + 0.453513i \(0.149829\pi\)
\(18\) 243.000 420.888i 0.176777 0.306186i
\(19\) −1342.00 2324.41i −0.852842 1.47717i −0.878633 0.477498i \(-0.841544\pi\)
0.0257909 0.999667i \(-0.491790\pi\)
\(20\) 312.000 0.174413
\(21\) 0 0
\(22\) −2664.00 −1.17348
\(23\) −2100.00 3637.31i −0.827751 1.43371i −0.899799 0.436306i \(-0.856287\pi\)
0.0720476 0.997401i \(-0.477047\pi\)
\(24\) 756.000 1309.43i 0.267913 0.464039i
\(25\) −1479.50 + 2562.57i −0.473440 + 0.820022i
\(26\) −1326.00 2296.70i −0.384689 0.666301i
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) −5442.00 −1.20161 −0.600805 0.799396i \(-0.705153\pi\)
−0.600805 + 0.799396i \(0.705153\pi\)
\(30\) −2106.00 3647.70i −0.427224 0.739973i
\(31\) −40.0000 + 69.2820i −0.00747577 + 0.0129484i −0.869739 0.493512i \(-0.835713\pi\)
0.862263 + 0.506460i \(0.169046\pi\)
\(32\) −720.000 + 1247.08i −0.124296 + 0.215287i
\(33\) 1998.00 + 3460.64i 0.319382 + 0.553186i
\(34\) 756.000 0.112157
\(35\) 0 0
\(36\) 324.000 0.0416667
\(37\) 2717.00 + 4705.98i 0.326276 + 0.565127i 0.981770 0.190074i \(-0.0608727\pi\)
−0.655494 + 0.755201i \(0.727539\pi\)
\(38\) 8052.00 13946.5i 0.904575 1.56677i
\(39\) −1989.00 + 3445.05i −0.209398 + 0.362689i
\(40\) −6552.00 11348.4i −0.647476 1.12146i
\(41\) 7962.00 0.739712 0.369856 0.929089i \(-0.379407\pi\)
0.369856 + 0.929089i \(0.379407\pi\)
\(42\) 0 0
\(43\) −11524.0 −0.950456 −0.475228 0.879863i \(-0.657634\pi\)
−0.475228 + 0.879863i \(0.657634\pi\)
\(44\) −888.000 1538.06i −0.0691483 0.119768i
\(45\) −3159.00 + 5471.55i −0.232551 + 0.402790i
\(46\) 12600.0 21823.8i 0.877962 1.52068i
\(47\) 6960.00 + 12055.1i 0.459584 + 0.796022i 0.998939 0.0460561i \(-0.0146653\pi\)
−0.539355 + 0.842078i \(0.681332\pi\)
\(48\) 10224.0 0.640498
\(49\) 0 0
\(50\) −17754.0 −1.00432
\(51\) −567.000 982.073i −0.0305251 0.0528711i
\(52\) 884.000 1531.13i 0.0453361 0.0785244i
\(53\) 4797.00 8308.65i 0.234574 0.406294i −0.724575 0.689196i \(-0.757964\pi\)
0.959149 + 0.282902i \(0.0912971\pi\)
\(54\) −2187.00 3788.00i −0.102062 0.176777i
\(55\) 34632.0 1.54373
\(56\) 0 0
\(57\) −24156.0 −0.984777
\(58\) −16326.0 28277.5i −0.637250 1.10375i
\(59\) −13746.0 + 23808.8i −0.514098 + 0.890445i 0.485768 + 0.874088i \(0.338540\pi\)
−0.999866 + 0.0163567i \(0.994793\pi\)
\(60\) 1404.00 2431.80i 0.0503488 0.0872067i
\(61\) −24739.0 42849.2i −0.851251 1.47441i −0.880080 0.474825i \(-0.842511\pi\)
0.0288292 0.999584i \(-0.490822\pi\)
\(62\) −480.000 −0.0158585
\(63\) 0 0
\(64\) 27712.0 0.845703
\(65\) 17238.0 + 29857.1i 0.506062 + 0.876525i
\(66\) −11988.0 + 20763.8i −0.338756 + 0.586742i
\(67\) 29678.0 51403.8i 0.807695 1.39897i −0.106761 0.994285i \(-0.534048\pi\)
0.914456 0.404685i \(-0.132619\pi\)
\(68\) 252.000 + 436.477i 0.00660889 + 0.0114469i
\(69\) −37800.0 −0.955805
\(70\) 0 0
\(71\) 32040.0 0.754304 0.377152 0.926151i \(-0.376903\pi\)
0.377152 + 0.926151i \(0.376903\pi\)
\(72\) −6804.00 11784.9i −0.154680 0.267913i
\(73\) 30923.0 53560.2i 0.679164 1.17635i −0.296069 0.955166i \(-0.595676\pi\)
0.975233 0.221180i \(-0.0709907\pi\)
\(74\) −16302.0 + 28235.9i −0.346068 + 0.599408i
\(75\) 13315.5 + 23063.1i 0.273341 + 0.473440i
\(76\) 10736.0 0.213210
\(77\) 0 0
\(78\) −23868.0 −0.444201
\(79\) 32888.0 + 56963.7i 0.592884 + 1.02691i 0.993842 + 0.110809i \(0.0353441\pi\)
−0.400958 + 0.916097i \(0.631323\pi\)
\(80\) 44304.0 76736.8i 0.773959 1.34054i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 23886.0 + 41371.8i 0.392291 + 0.679469i
\(83\) 40188.0 0.640326 0.320163 0.947362i \(-0.396262\pi\)
0.320163 + 0.947362i \(0.396262\pi\)
\(84\) 0 0
\(85\) −9828.00 −0.147543
\(86\) −34572.0 59880.5i −0.504056 0.873050i
\(87\) −24489.0 + 42416.2i −0.346875 + 0.600805i
\(88\) −37296.0 + 64598.6i −0.513400 + 0.889234i
\(89\) 3987.00 + 6905.69i 0.0533545 + 0.0924127i 0.891469 0.453081i \(-0.149675\pi\)
−0.838115 + 0.545494i \(0.816342\pi\)
\(90\) −37908.0 −0.493315
\(91\) 0 0
\(92\) 16800.0 0.206938
\(93\) 360.000 + 623.538i 0.00431614 + 0.00747577i
\(94\) −41760.0 + 72330.4i −0.487462 + 0.844309i
\(95\) −104676. + 181304.i −1.18998 + 2.06110i
\(96\) 6480.00 + 11223.7i 0.0717624 + 0.124296i
\(97\) −143662. −1.55029 −0.775144 0.631784i \(-0.782323\pi\)
−0.775144 + 0.631784i \(0.782323\pi\)
\(98\) 0 0
\(99\) 35964.0 0.368791
\(100\) −5918.00 10250.3i −0.0591800 0.102503i
\(101\) 1353.00 2343.46i 0.0131976 0.0228589i −0.859351 0.511386i \(-0.829132\pi\)
0.872549 + 0.488527i \(0.162466\pi\)
\(102\) 3402.00 5892.44i 0.0323768 0.0560783i
\(103\) −65884.0 114114.i −0.611909 1.05986i −0.990918 0.134465i \(-0.957068\pi\)
0.379009 0.925393i \(-0.376265\pi\)
\(104\) −74256.0 −0.673206
\(105\) 0 0
\(106\) 57564.0 0.497607
\(107\) 64458.0 + 111645.i 0.544274 + 0.942710i 0.998652 + 0.0519010i \(0.0165280\pi\)
−0.454378 + 0.890809i \(0.650139\pi\)
\(108\) 1458.00 2525.33i 0.0120281 0.0208333i
\(109\) 50489.0 87449.5i 0.407034 0.705003i −0.587522 0.809208i \(-0.699896\pi\)
0.994556 + 0.104205i \(0.0332298\pi\)
\(110\) 103896. + 179953.i 0.818686 + 1.41800i
\(111\) 48906.0 0.376751
\(112\) 0 0
\(113\) 220146. 1.62186 0.810932 0.585140i \(-0.198960\pi\)
0.810932 + 0.585140i \(0.198960\pi\)
\(114\) −72468.0 125518.i −0.522257 0.904575i
\(115\) −163800. + 283710.i −1.15497 + 2.00046i
\(116\) 10884.0 18851.6i 0.0751006 0.130078i
\(117\) 17901.0 + 31005.4i 0.120896 + 0.209398i
\(118\) −164952. −1.09057
\(119\) 0 0
\(120\) −117936. −0.747641
\(121\) −18042.5 31250.5i −0.112030 0.194041i
\(122\) 148434. 257095.i 0.902888 1.56385i
\(123\) 35829.0 62057.6i 0.213536 0.369856i
\(124\) −160.000 277.128i −0.000934471 0.00161855i
\(125\) −12948.0 −0.0741187
\(126\) 0 0
\(127\) −74320.0 −0.408880 −0.204440 0.978879i \(-0.565537\pi\)
−0.204440 + 0.978879i \(0.565537\pi\)
\(128\) 106176. + 183902.i 0.572798 + 0.992115i
\(129\) −51858.0 + 89820.7i −0.274373 + 0.475228i
\(130\) −103428. + 179143.i −0.536760 + 0.929695i
\(131\) 77658.0 + 134508.i 0.395374 + 0.684808i 0.993149 0.116856i \(-0.0372817\pi\)
−0.597775 + 0.801664i \(0.703948\pi\)
\(132\) −15984.0 −0.0798455
\(133\) 0 0
\(134\) 356136. 1.71338
\(135\) 28431.0 + 49243.9i 0.134263 + 0.232551i
\(136\) 10584.0 18332.0i 0.0490685 0.0849891i
\(137\) 132123. 228844.i 0.601419 1.04169i −0.391188 0.920311i \(-0.627936\pi\)
0.992606 0.121377i \(-0.0387310\pi\)
\(138\) −113400. 196415.i −0.506892 0.877962i
\(139\) 224612. 0.986043 0.493022 0.870017i \(-0.335892\pi\)
0.493022 + 0.870017i \(0.335892\pi\)
\(140\) 0 0
\(141\) 125280. 0.530682
\(142\) 96120.0 + 166485.i 0.400030 + 0.692873i
\(143\) 98124.0 169956.i 0.401269 0.695018i
\(144\) 46008.0 79688.2i 0.184896 0.320249i
\(145\) 212238. + 367607.i 0.838307 + 1.45199i
\(146\) 371076. 1.44072
\(147\) 0 0
\(148\) −21736.0 −0.0815690
\(149\) 41037.0 + 71078.2i 0.151429 + 0.262283i 0.931753 0.363092i \(-0.118279\pi\)
−0.780324 + 0.625376i \(0.784946\pi\)
\(150\) −79893.0 + 138379.i −0.289922 + 0.502159i
\(151\) 143516. 248577.i 0.512222 0.887194i −0.487678 0.873024i \(-0.662156\pi\)
0.999900 0.0141703i \(-0.00451071\pi\)
\(152\) −225456. 390501.i −0.791503 1.37092i
\(153\) −10206.0 −0.0352474
\(154\) 0 0
\(155\) 6240.00 0.0208620
\(156\) −7956.00 13780.2i −0.0261748 0.0453361i
\(157\) −64939.0 + 112478.i −0.210260 + 0.364181i −0.951796 0.306732i \(-0.900764\pi\)
0.741536 + 0.670913i \(0.234098\pi\)
\(158\) −197328. + 341782.i −0.628848 + 1.08920i
\(159\) −43173.0 74777.8i −0.135431 0.234574i
\(160\) 112320. 0.346862
\(161\) 0 0
\(162\) −39366.0 −0.117851
\(163\) −277642. 480890.i −0.818495 1.41768i −0.906791 0.421581i \(-0.861475\pi\)
0.0882955 0.996094i \(-0.471858\pi\)
\(164\) −15924.0 + 27581.2i −0.0462320 + 0.0800761i
\(165\) 155844. 269930.i 0.445636 0.771864i
\(166\) 120564. + 208823.i 0.339584 + 0.588177i
\(167\) 43512.0 0.120731 0.0603654 0.998176i \(-0.480773\pi\)
0.0603654 + 0.998176i \(0.480773\pi\)
\(168\) 0 0
\(169\) −175929. −0.473828
\(170\) −29484.0 51067.8i −0.0782464 0.135527i
\(171\) −108702. + 188277.i −0.284281 + 0.492388i
\(172\) 23048.0 39920.3i 0.0594035 0.102890i
\(173\) 9165.00 + 15874.2i 0.0232818 + 0.0403253i 0.877432 0.479702i \(-0.159255\pi\)
−0.854150 + 0.520027i \(0.825922\pi\)
\(174\) −293868. −0.735833
\(175\) 0 0
\(176\) −504384. −1.22738
\(177\) 123714. + 214279.i 0.296815 + 0.514098i
\(178\) −23922.0 + 41434.1i −0.0565910 + 0.0980185i
\(179\) 76662.0 132782.i 0.178833 0.309748i −0.762648 0.646814i \(-0.776101\pi\)
0.941481 + 0.337066i \(0.109434\pi\)
\(180\) −12636.0 21886.2i −0.0290689 0.0503488i
\(181\) −382066. −0.866846 −0.433423 0.901191i \(-0.642694\pi\)
−0.433423 + 0.901191i \(0.642694\pi\)
\(182\) 0 0
\(183\) −445302. −0.982940
\(184\) −352800. 611068.i −0.768217 1.33059i
\(185\) 211926. 367067.i 0.455255 0.788525i
\(186\) −2160.00 + 3741.23i −0.00457795 + 0.00792925i
\(187\) 27972.0 + 48448.9i 0.0584951 + 0.101316i
\(188\) −55680.0 −0.114896
\(189\) 0 0
\(190\) −1.25611e6 −2.52432
\(191\) 136704. + 236778.i 0.271143 + 0.469633i 0.969155 0.246453i \(-0.0792652\pi\)
−0.698012 + 0.716086i \(0.745932\pi\)
\(192\) 124704. 215994.i 0.244133 0.422852i
\(193\) −76801.0 + 133023.i −0.148414 + 0.257060i −0.930641 0.365933i \(-0.880750\pi\)
0.782228 + 0.622993i \(0.214083\pi\)
\(194\) −430986. 746490.i −0.822165 1.42403i
\(195\) 310284. 0.584350
\(196\) 0 0
\(197\) 154422. 0.283494 0.141747 0.989903i \(-0.454728\pi\)
0.141747 + 0.989903i \(0.454728\pi\)
\(198\) 107892. + 186874.i 0.195581 + 0.338756i
\(199\) 183428. 317707.i 0.328347 0.568714i −0.653837 0.756635i \(-0.726842\pi\)
0.982184 + 0.187922i \(0.0601752\pi\)
\(200\) −248556. + 430512.i −0.439389 + 0.761044i
\(201\) −267102. 462634.i −0.466323 0.807695i
\(202\) 16236.0 0.0279963
\(203\) 0 0
\(204\) 4536.00 0.00763128
\(205\) −310518. 537833.i −0.516062 0.893846i
\(206\) 395304. 684687.i 0.649028 1.12415i
\(207\) −170100. + 294622.i −0.275917 + 0.477902i
\(208\) −251056. 434842.i −0.402358 0.696904i
\(209\) 1.19170e6 1.88712
\(210\) 0 0
\(211\) 520244. 0.804453 0.402227 0.915540i \(-0.368236\pi\)
0.402227 + 0.915540i \(0.368236\pi\)
\(212\) 19188.0 + 33234.6i 0.0293218 + 0.0507868i
\(213\) 144180. 249727.i 0.217749 0.377152i
\(214\) −386748. + 669867.i −0.577289 + 0.999895i
\(215\) 449436. + 778446.i 0.663089 + 1.14850i
\(216\) −122472. −0.178609
\(217\) 0 0
\(218\) 605868. 0.863449
\(219\) −278307. 482042.i −0.392115 0.679164i
\(220\) −69264.0 + 119969.i −0.0964830 + 0.167113i
\(221\) −27846.0 + 48230.7i −0.0383515 + 0.0664267i
\(222\) 146718. + 254123.i 0.199803 + 0.346068i
\(223\) 304736. 0.410357 0.205178 0.978725i \(-0.434223\pi\)
0.205178 + 0.978725i \(0.434223\pi\)
\(224\) 0 0
\(225\) 239679. 0.315627
\(226\) 660438. + 1.14391e6i 0.860124 + 1.48978i
\(227\) −144294. + 249925.i −0.185859 + 0.321917i −0.943866 0.330330i \(-0.892840\pi\)
0.758007 + 0.652247i \(0.226173\pi\)
\(228\) 48312.0 83678.8i 0.0615486 0.106605i
\(229\) −386095. 668736.i −0.486525 0.842687i 0.513355 0.858177i \(-0.328403\pi\)
−0.999880 + 0.0154899i \(0.995069\pi\)
\(230\) −1.96560e6 −2.45005
\(231\) 0 0
\(232\) −914256. −1.11519
\(233\) −126117. 218441.i −0.152189 0.263599i 0.779843 0.625975i \(-0.215299\pi\)
−0.932032 + 0.362376i \(0.881966\pi\)
\(234\) −107406. + 186033.i −0.128230 + 0.222100i
\(235\) 542880. 940296.i 0.641260 1.11069i
\(236\) −54984.0 95235.1i −0.0642623 0.111306i
\(237\) 591984. 0.684603
\(238\) 0 0
\(239\) −1.45114e6 −1.64329 −0.821643 0.570002i \(-0.806942\pi\)
−0.821643 + 0.570002i \(0.806942\pi\)
\(240\) −398736. 690631.i −0.446845 0.773959i
\(241\) 73199.0 126784.i 0.0811825 0.140612i −0.822576 0.568656i \(-0.807464\pi\)
0.903758 + 0.428043i \(0.140797\pi\)
\(242\) 108255. 187503.i 0.118825 0.205812i
\(243\) 29524.5 + 51137.9i 0.0320750 + 0.0555556i
\(244\) 197912. 0.212813
\(245\) 0 0
\(246\) 429948. 0.452979
\(247\) 593164. + 1.02739e6i 0.618632 + 1.07150i
\(248\) −6720.00 + 11639.4i −0.00693809 + 0.0120171i
\(249\) 180846. 313234.i 0.184846 0.320163i
\(250\) −38844.0 67279.8i −0.0393074 0.0680824i
\(251\) 607860. 0.609003 0.304501 0.952512i \(-0.401510\pi\)
0.304501 + 0.952512i \(0.401510\pi\)
\(252\) 0 0
\(253\) 1.86480e6 1.83160
\(254\) −222960. 386178.i −0.216842 0.375581i
\(255\) −44226.0 + 76601.7i −0.0425919 + 0.0737714i
\(256\) −193664. + 335436.i −0.184692 + 0.319897i
\(257\) −47793.0 82779.9i −0.0451369 0.0781794i 0.842574 0.538580i \(-0.181039\pi\)
−0.887711 + 0.460401i \(0.847706\pi\)
\(258\) −622296. −0.582033
\(259\) 0 0
\(260\) −137904. −0.126515
\(261\) 220401. + 381746.i 0.200268 + 0.346875i
\(262\) −465948. + 807046.i −0.419357 + 0.726348i
\(263\) 1.10017e6 1.90555e6i 0.980779 1.69876i 0.321410 0.946940i \(-0.395843\pi\)
0.659370 0.751819i \(-0.270823\pi\)
\(264\) 335664. + 581387.i 0.296411 + 0.513400i
\(265\) −748332. −0.654605
\(266\) 0 0
\(267\) 71766.0 0.0616085
\(268\) 118712. + 205615.i 0.100962 + 0.174871i
\(269\) −885123. + 1.53308e6i −0.745801 + 1.29177i 0.204019 + 0.978967i \(0.434600\pi\)
−0.949820 + 0.312798i \(0.898734\pi\)
\(270\) −170586. + 295464.i −0.142408 + 0.246658i
\(271\) 111752. + 193560.i 0.0924341 + 0.160101i 0.908535 0.417809i \(-0.137202\pi\)
−0.816101 + 0.577910i \(0.803869\pi\)
\(272\) 143136. 0.117308
\(273\) 0 0
\(274\) 1.58548e6 1.27580
\(275\) −656898. 1.13778e6i −0.523801 0.907250i
\(276\) 75600.0 130943.i 0.0597378 0.103469i
\(277\) 171389. 296854.i 0.134210 0.232458i −0.791086 0.611705i \(-0.790484\pi\)
0.925295 + 0.379248i \(0.123817\pi\)
\(278\) 673836. + 1.16712e6i 0.522928 + 0.905739i
\(279\) 6480.00 0.00498384
\(280\) 0 0
\(281\) 480378. 0.362925 0.181463 0.983398i \(-0.441917\pi\)
0.181463 + 0.983398i \(0.441917\pi\)
\(282\) 375840. + 650974.i 0.281436 + 0.487462i
\(283\) 14990.0 25963.4i 0.0111259 0.0192706i −0.860409 0.509604i \(-0.829792\pi\)
0.871535 + 0.490334i \(0.163125\pi\)
\(284\) −64080.0 + 110990.i −0.0471440 + 0.0816558i
\(285\) 942084. + 1.63174e6i 0.687033 + 1.18998i
\(286\) 1.17749e6 0.851219
\(287\) 0 0
\(288\) 116640. 0.0828641
\(289\) 701990. + 1.21588e6i 0.494409 + 0.856342i
\(290\) −1.27343e6 + 2.20564e6i −0.889159 + 1.54007i
\(291\) −646479. + 1.11973e6i −0.447530 + 0.775144i
\(292\) 123692. + 214241.i 0.0848955 + 0.147043i
\(293\) −198066. −0.134785 −0.0673924 0.997727i \(-0.521468\pi\)
−0.0673924 + 0.997727i \(0.521468\pi\)
\(294\) 0 0
\(295\) 2.14438e6 1.43465
\(296\) 456456. + 790605.i 0.302810 + 0.524482i
\(297\) 161838. 280312.i 0.106461 0.184395i
\(298\) −246222. + 426469.i −0.160615 + 0.278193i
\(299\) 928200. + 1.60769e6i 0.600432 + 1.03998i
\(300\) −106524. −0.0683352
\(301\) 0 0
\(302\) 1.72219e6 1.08659
\(303\) −12177.0 21091.2i −0.00761963 0.0131976i
\(304\) 1.52451e6 2.64053e6i 0.946121 1.63873i
\(305\) −1.92964e6 + 3.34224e6i −1.18776 + 2.05725i
\(306\) −30618.0 53031.9i −0.0186928 0.0323768i
\(307\) −1.04564e6 −0.633191 −0.316595 0.948561i \(-0.602540\pi\)
−0.316595 + 0.948561i \(0.602540\pi\)
\(308\) 0 0
\(309\) −1.18591e6 −0.706572
\(310\) 18720.0 + 32424.0i 0.0110637 + 0.0191629i
\(311\) −918588. + 1.59104e6i −0.538542 + 0.932783i 0.460441 + 0.887691i \(0.347691\pi\)
−0.998983 + 0.0450920i \(0.985642\pi\)
\(312\) −334152. + 578768.i −0.194338 + 0.336603i
\(313\) 182747. + 316527.i 0.105436 + 0.182621i 0.913916 0.405903i \(-0.133043\pi\)
−0.808480 + 0.588523i \(0.799709\pi\)
\(314\) −779268. −0.446029
\(315\) 0 0
\(316\) −263104. −0.148221
\(317\) 14169.0 + 24541.4i 0.00791938 + 0.0137168i 0.869958 0.493126i \(-0.164146\pi\)
−0.862039 + 0.506843i \(0.830812\pi\)
\(318\) 259038. 448667.i 0.143647 0.248803i
\(319\) 1.20812e6 2.09253e6i 0.664714 1.15132i
\(320\) −1.08077e6 1.87195e6i −0.590007 1.02192i
\(321\) 1.16024e6 0.628473
\(322\) 0 0
\(323\) −338184. −0.180363
\(324\) −13122.0 22728.0i −0.00694444 0.0120281i
\(325\) 653939. 1.13266e6i 0.343423 0.594825i
\(326\) 1.66585e6 2.88534e6i 0.868145 1.50367i
\(327\) −454401. 787046.i −0.235001 0.407034i
\(328\) 1.33762e6 0.686510
\(329\) 0 0
\(330\) 1.87013e6 0.945337
\(331\) −966958. 1.67482e6i −0.485107 0.840230i 0.514746 0.857342i \(-0.327886\pi\)
−0.999854 + 0.0171123i \(0.994553\pi\)
\(332\) −80376.0 + 139215.i −0.0400204 + 0.0693173i
\(333\) 220077. 381185.i 0.108759 0.188376i
\(334\) 130536. + 226095.i 0.0640271 + 0.110898i
\(335\) −4.62977e6 −2.25397
\(336\) 0 0
\(337\) −1.88817e6 −0.905664 −0.452832 0.891596i \(-0.649586\pi\)
−0.452832 + 0.891596i \(0.649586\pi\)
\(338\) −527787. 914154.i −0.251285 0.435239i
\(339\) 990657. 1.71587e6i 0.468192 0.810932i
\(340\) 19656.0 34045.2i 0.00922142 0.0159720i
\(341\) −17760.0 30761.2i −0.00827098 0.0143258i
\(342\) −1.30442e6 −0.603050
\(343\) 0 0
\(344\) −1.93603e6 −0.882097
\(345\) 1.47420e6 + 2.55339e6i 0.666820 + 1.15497i
\(346\) −54990.0 + 95245.5i −0.0246941 + 0.0427715i
\(347\) −1.45969e6 + 2.52825e6i −0.650782 + 1.12719i 0.332151 + 0.943226i \(0.392226\pi\)
−0.982933 + 0.183962i \(0.941108\pi\)
\(348\) −97956.0 169665.i −0.0433594 0.0751006i
\(349\) −780682. −0.343092 −0.171546 0.985176i \(-0.554876\pi\)
−0.171546 + 0.985176i \(0.554876\pi\)
\(350\) 0 0
\(351\) 322218. 0.139599
\(352\) −319680. 553702.i −0.137518 0.238188i
\(353\) −667185. + 1.15560e6i −0.284977 + 0.493594i −0.972604 0.232470i \(-0.925319\pi\)
0.687627 + 0.726064i \(0.258653\pi\)
\(354\) −742284. + 1.28567e6i −0.314820 + 0.545284i
\(355\) −1.24956e6 2.16430e6i −0.526243 0.911479i
\(356\) −31896.0 −0.0133386
\(357\) 0 0
\(358\) 919944. 0.379362
\(359\) −508716. 881122.i −0.208324 0.360828i 0.742863 0.669444i \(-0.233468\pi\)
−0.951187 + 0.308616i \(0.900134\pi\)
\(360\) −530712. + 919220.i −0.215825 + 0.373821i
\(361\) −2.36388e6 + 4.09436e6i −0.954679 + 1.65355i
\(362\) −1.14620e6 1.98527e6i −0.459715 0.796249i
\(363\) −324765. −0.129361
\(364\) 0 0
\(365\) −4.82399e6 −1.89528
\(366\) −1.33591e6 2.31386e6i −0.521283 0.902888i
\(367\) −418840. + 725452.i −0.162324 + 0.281154i −0.935702 0.352792i \(-0.885232\pi\)
0.773378 + 0.633946i \(0.218566\pi\)
\(368\) 2.38560e6 4.13198e6i 0.918286 1.59052i
\(369\) −322461. 558519.i −0.123285 0.213536i
\(370\) 2.54311e6 0.965742
\(371\) 0 0
\(372\) −2880.00 −0.00107903
\(373\) 759965. + 1.31630e6i 0.282827 + 0.489871i 0.972080 0.234650i \(-0.0753943\pi\)
−0.689253 + 0.724521i \(0.742061\pi\)
\(374\) −167832. + 290694.i −0.0620434 + 0.107462i
\(375\) −58266.0 + 100920.i −0.0213962 + 0.0370593i
\(376\) 1.16928e6 + 2.02525e6i 0.426529 + 0.738770i
\(377\) 2.40536e6 0.871620
\(378\) 0 0
\(379\) 2.64465e6 0.945737 0.472869 0.881133i \(-0.343219\pi\)
0.472869 + 0.881133i \(0.343219\pi\)
\(380\) −418704. 725217.i −0.148747 0.257637i
\(381\) −334440. + 579267.i −0.118034 + 0.204440i
\(382\) −820224. + 1.42067e6i −0.287590 + 0.498121i
\(383\) −1.00668e6 1.74362e6i −0.350667 0.607373i 0.635700 0.771936i \(-0.280712\pi\)
−0.986366 + 0.164564i \(0.947378\pi\)
\(384\) 1.91117e6 0.661410
\(385\) 0 0
\(386\) −921612. −0.314833
\(387\) 466722. + 808386.i 0.158409 + 0.274373i
\(388\) 287324. 497660.i 0.0968930 0.167824i
\(389\) 363117. 628937.i 0.121667 0.210733i −0.798758 0.601652i \(-0.794509\pi\)
0.920425 + 0.390919i \(0.127843\pi\)
\(390\) 930852. + 1.61228e6i 0.309898 + 0.536760i
\(391\) −529200. −0.175056
\(392\) 0 0
\(393\) 1.39784e6 0.456538
\(394\) 463266. + 802400.i 0.150345 + 0.260406i
\(395\) 2.56526e6 4.44317e6i 0.827255 1.43285i
\(396\) −71928.0 + 124583.i −0.0230494 + 0.0399228i
\(397\) −2.28789e6 3.96274e6i −0.728549 1.26188i −0.957496 0.288446i \(-0.906861\pi\)
0.228947 0.973439i \(-0.426472\pi\)
\(398\) 2.20114e6 0.696529
\(399\) 0 0
\(400\) −3.36142e6 −1.05045
\(401\) 16935.0 + 29332.3i 0.00525926 + 0.00910930i 0.868643 0.495438i \(-0.164993\pi\)
−0.863384 + 0.504548i \(0.831659\pi\)
\(402\) 1.60261e6 2.77581e6i 0.494610 0.856690i
\(403\) 17680.0 30622.7i 0.00542275 0.00939248i
\(404\) 5412.00 + 9373.86i 0.00164970 + 0.00285736i
\(405\) 511758. 0.155034
\(406\) 0 0
\(407\) −2.41270e6 −0.721966
\(408\) −95256.0 164988.i −0.0283297 0.0490685i
\(409\) 2.93089e6 5.07645e6i 0.866346 1.50056i 0.000641640 1.00000i \(-0.499796\pi\)
0.865704 0.500556i \(-0.166871\pi\)
\(410\) 1.86311e6 3.22700e6i 0.547367 0.948067i
\(411\) −1.18911e6 2.05959e6i −0.347229 0.601419i
\(412\) 527072. 0.152977
\(413\) 0 0
\(414\) −2.04120e6 −0.585308
\(415\) −1.56733e6 2.71470e6i −0.446726 0.773751i
\(416\) 318240. 551208.i 0.0901616 0.156164i
\(417\) 1.01075e6 1.75068e6i 0.284646 0.493022i
\(418\) 3.57509e6 + 6.19223e6i 1.00080 + 1.73343i
\(419\) 302748. 0.0842454 0.0421227 0.999112i \(-0.486588\pi\)
0.0421227 + 0.999112i \(0.486588\pi\)
\(420\) 0 0
\(421\) −5.36708e6 −1.47582 −0.737909 0.674900i \(-0.764187\pi\)
−0.737909 + 0.674900i \(0.764187\pi\)
\(422\) 1.56073e6 + 2.70327e6i 0.426626 + 0.738938i
\(423\) 563760. 976461.i 0.153195 0.265341i
\(424\) 805896. 1.39585e6i 0.217703 0.377073i
\(425\) 186417. + 322884.i 0.0500626 + 0.0867109i
\(426\) 1.73016e6 0.461915
\(427\) 0 0
\(428\) −515664. −0.136068
\(429\) −883116. 1.52960e6i −0.231673 0.401269i
\(430\) −2.69662e6 + 4.67068e6i −0.703312 + 1.21817i
\(431\) −588528. + 1.01936e6i −0.152607 + 0.264323i −0.932185 0.361982i \(-0.882100\pi\)
0.779578 + 0.626305i \(0.215433\pi\)
\(432\) −414072. 717194.i −0.106750 0.184896i
\(433\) −3.66249e6 −0.938766 −0.469383 0.882995i \(-0.655524\pi\)
−0.469383 + 0.882995i \(0.655524\pi\)
\(434\) 0 0
\(435\) 3.82028e6 0.967994
\(436\) 201956. + 349798.i 0.0508792 + 0.0881254i
\(437\) −5.63640e6 + 9.76253e6i −1.41188 + 2.44545i
\(438\) 1.66984e6 2.89225e6i 0.415901 0.720362i
\(439\) 1.26837e6 + 2.19688e6i 0.314113 + 0.544059i 0.979248 0.202663i \(-0.0649597\pi\)
−0.665136 + 0.746722i \(0.731626\pi\)
\(440\) 5.81818e6 1.43270
\(441\) 0 0
\(442\) −334152. −0.0813558
\(443\) −3.00752e6 5.20917e6i −0.728113 1.26113i −0.957680 0.287836i \(-0.907064\pi\)
0.229566 0.973293i \(-0.426269\pi\)
\(444\) −97812.0 + 169415.i −0.0235470 + 0.0407845i
\(445\) 310986. 538644.i 0.0744459 0.128944i
\(446\) 914208. + 1.58345e6i 0.217625 + 0.376937i
\(447\) 738666. 0.174856
\(448\) 0 0
\(449\) 5.65965e6 1.32487 0.662436 0.749119i \(-0.269523\pi\)
0.662436 + 0.749119i \(0.269523\pi\)
\(450\) 719037. + 1.24541e6i 0.167386 + 0.289922i
\(451\) −1.76756e6 + 3.06151e6i −0.409198 + 0.708752i
\(452\) −440292. + 762608.i −0.101367 + 0.175572i
\(453\) −1.29164e6 2.23719e6i −0.295731 0.512222i
\(454\) −1.73153e6 −0.394267
\(455\) 0 0
\(456\) −4.05821e6 −0.913949
\(457\) 3.23080e6 + 5.59590e6i 0.723634 + 1.25337i 0.959534 + 0.281593i \(0.0908629\pi\)
−0.235900 + 0.971777i \(0.575804\pi\)
\(458\) 2.31657e6 4.01242e6i 0.516038 0.893804i
\(459\) −45927.0 + 79547.9i −0.0101750 + 0.0176237i
\(460\) −655200. 1.13484e6i −0.144371 0.250058i
\(461\) −3.37353e6 −0.739320 −0.369660 0.929167i \(-0.620526\pi\)
−0.369660 + 0.929167i \(0.620526\pi\)
\(462\) 0 0
\(463\) −4.54974e6 −0.986358 −0.493179 0.869928i \(-0.664165\pi\)
−0.493179 + 0.869928i \(0.664165\pi\)
\(464\) −3.09106e6 5.35387e6i −0.666518 1.15444i
\(465\) 28080.0 48636.0i 0.00602233 0.0104310i
\(466\) 756702. 1.31065e6i 0.161421 0.279589i
\(467\) −1.00568e6 1.74189e6i −0.213386 0.369596i 0.739386 0.673282i \(-0.235116\pi\)
−0.952772 + 0.303686i \(0.901783\pi\)
\(468\) −143208. −0.0302240
\(469\) 0 0
\(470\) 6.51456e6 1.36032
\(471\) 584451. + 1.01230e6i 0.121394 + 0.210260i
\(472\) −2.30933e6 + 3.99987e6i −0.477123 + 0.826402i
\(473\) 2.55833e6 4.43115e6i 0.525779 0.910676i
\(474\) 1.77595e6 + 3.07604e6i 0.363066 + 0.628848i
\(475\) 7.94196e6 1.61508
\(476\) 0 0
\(477\) −777114. −0.156383
\(478\) −4.35341e6 7.54032e6i −0.871484 1.50946i
\(479\) 3.80201e6 6.58527e6i 0.757137 1.31140i −0.187168 0.982328i \(-0.559931\pi\)
0.944305 0.329071i \(-0.106736\pi\)
\(480\) 505440. 875448.i 0.100131 0.173431i
\(481\) −1.20091e6 2.08004e6i −0.236673 0.409930i
\(482\) 878388. 0.172214
\(483\) 0 0
\(484\) 144340. 0.0280074
\(485\) 5.60282e6 + 9.70437e6i 1.08156 + 1.87332i
\(486\) −177147. + 306828.i −0.0340207 + 0.0589256i
\(487\) −336556. + 582932.i −0.0643035 + 0.111377i −0.896385 0.443277i \(-0.853816\pi\)
0.832081 + 0.554654i \(0.187149\pi\)
\(488\) −4.15615e6 7.19867e6i −0.790027 1.36837i
\(489\) −4.99756e6 −0.945117
\(490\) 0 0
\(491\) −2.47170e6 −0.462692 −0.231346 0.972872i \(-0.574313\pi\)
−0.231346 + 0.972872i \(0.574313\pi\)
\(492\) 143316. + 248231.i 0.0266920 + 0.0462320i
\(493\) −342846. + 593827.i −0.0635304 + 0.110038i
\(494\) −3.55898e6 + 6.16434e6i −0.656158 + 1.13650i
\(495\) −1.40260e6 2.42937e6i −0.257288 0.445636i
\(496\) −90880.0 −0.0165869
\(497\) 0 0
\(498\) 2.17015e6 0.392118
\(499\) −3.04076e6 5.26675e6i −0.546677 0.946873i −0.998499 0.0547648i \(-0.982559\pi\)
0.451822 0.892108i \(-0.350774\pi\)
\(500\) 25896.0 44853.2i 0.00463242 0.00802358i
\(501\) 195804. 339142.i 0.0348520 0.0603654i
\(502\) 1.82358e6 + 3.15853e6i 0.322972 + 0.559405i
\(503\) −846216. −0.149129 −0.0745644 0.997216i \(-0.523757\pi\)
−0.0745644 + 0.997216i \(0.523757\pi\)
\(504\) 0 0
\(505\) −211068. −0.0368293
\(506\) 5.59440e6 + 9.68979e6i 0.971353 + 1.68243i
\(507\) −791680. + 1.37123e6i −0.136782 + 0.236914i
\(508\) 148640. 257452.i 0.0255550 0.0442626i
\(509\) 3.83392e6 + 6.64055e6i 0.655917 + 1.13608i 0.981663 + 0.190625i \(0.0610514\pi\)
−0.325746 + 0.945457i \(0.605615\pi\)
\(510\) −530712. −0.0903511
\(511\) 0 0
\(512\) 4.47130e6 0.753804
\(513\) 978318. + 1.69450e6i 0.164129 + 0.284281i
\(514\) 286758. 496679.i 0.0478749 0.0829217i
\(515\) −5.13895e6 + 8.90093e6i −0.853801 + 1.47883i
\(516\) −207432. 359283.i −0.0342966 0.0594035i
\(517\) −6.18048e6 −1.01694
\(518\) 0 0
\(519\) 164970. 0.0268835
\(520\) 2.89598e6 + 5.01599e6i 0.469665 + 0.813483i
\(521\) 4.84469e6 8.39125e6i 0.781937 1.35435i −0.148875 0.988856i \(-0.547565\pi\)
0.930812 0.365499i \(-0.119102\pi\)
\(522\) −1.32241e6 + 2.29047e6i −0.212417 + 0.367916i
\(523\) 3.75839e6 + 6.50972e6i 0.600824 + 1.04066i 0.992696 + 0.120639i \(0.0384943\pi\)
−0.391872 + 0.920020i \(0.628172\pi\)
\(524\) −621264. −0.0988435
\(525\) 0 0
\(526\) 1.32021e7 2.08055
\(527\) 5040.00 + 8729.54i 0.000790504 + 0.00136919i
\(528\) −2.26973e6 + 3.93128e6i −0.354315 + 0.613691i
\(529\) −5.60183e6 + 9.70265e6i −0.870343 + 1.50748i
\(530\) −2.24500e6 3.88845e6i −0.347157 0.601294i
\(531\) 2.22685e6 0.342732
\(532\) 0 0
\(533\) −3.51920e6 −0.536570
\(534\) 215298. + 372907.i 0.0326728 + 0.0565910i
\(535\) 5.02772e6 8.70827e6i 0.759429 1.31537i
\(536\) 4.98590e6 8.63584e6i 0.749604 1.29835i
\(537\) −689958. 1.19504e6i −0.103249 0.178833i
\(538\) −1.06215e7 −1.58208
\(539\) 0 0
\(540\) −227448. −0.0335659
\(541\) −3.67162e6 6.35944e6i −0.539343 0.934169i −0.998940 0.0460415i \(-0.985339\pi\)
0.459597 0.888128i \(-0.347994\pi\)
\(542\) −670512. + 1.16136e6i −0.0980411 + 0.169812i
\(543\) −1.71930e6 + 2.97791e6i −0.250237 + 0.433423i
\(544\) 90720.0 + 157132.i 0.0131433 + 0.0227649i
\(545\) −7.87628e6 −1.13587
\(546\) 0 0
\(547\) 2.18296e6 0.311945 0.155973 0.987761i \(-0.450149\pi\)
0.155973 + 0.987761i \(0.450149\pi\)
\(548\) 528492. + 915375.i 0.0751774 + 0.130211i
\(549\) −2.00386e6 + 3.47079e6i −0.283750 + 0.491470i
\(550\) 3.94139e6 6.82668e6i 0.555575 0.962284i
\(551\) 7.30316e6 + 1.26495e7i 1.02478 + 1.77498i
\(552\) −6.35040e6 −0.887061
\(553\) 0 0
\(554\) 2.05667e6 0.284702
\(555\) −1.90733e6 3.30360e6i −0.262842 0.455255i
\(556\) −449224. + 778079.i −0.0616277 + 0.106742i
\(557\) −6.27328e6 + 1.08656e7i −0.856755 + 1.48394i 0.0182524 + 0.999833i \(0.494190\pi\)
−0.875007 + 0.484110i \(0.839144\pi\)
\(558\) 19440.0 + 33671.1i 0.00264308 + 0.00457795i
\(559\) 5.09361e6 0.689439
\(560\) 0 0
\(561\) 503496. 0.0675443
\(562\) 1.44113e6 + 2.49612e6i 0.192470 + 0.333368i
\(563\) −2.57986e6 + 4.46845e6i −0.343025 + 0.594136i −0.984993 0.172595i \(-0.944785\pi\)
0.641968 + 0.766731i \(0.278118\pi\)
\(564\) −250560. + 433983.i −0.0331676 + 0.0574480i
\(565\) −8.58569e6 1.48709e7i −1.13150 1.95981i
\(566\) 179880. 0.0236016
\(567\) 0 0
\(568\) 5.38272e6 0.700053
\(569\) −5.87260e6 1.01717e7i −0.760414 1.31708i −0.942637 0.333819i \(-0.891663\pi\)
0.182223 0.983257i \(-0.441671\pi\)
\(570\) −5.65250e6 + 9.79042e6i −0.728708 + 1.26216i
\(571\) 3.77364e6 6.53614e6i 0.484362 0.838940i −0.515476 0.856904i \(-0.672385\pi\)
0.999839 + 0.0179636i \(0.00571829\pi\)
\(572\) 392496. + 679823.i 0.0501586 + 0.0868772i
\(573\) 2.46067e6 0.313089
\(574\) 0 0
\(575\) 1.24278e7 1.56756
\(576\) −1.12234e6 1.94394e6i −0.140951 0.244133i
\(577\) −4.64242e6 + 8.04090e6i −0.580503 + 1.00546i 0.414916 + 0.909859i \(0.363811\pi\)
−0.995420 + 0.0956015i \(0.969523\pi\)
\(578\) −4.21194e6 + 7.29530e6i −0.524400 + 0.908288i
\(579\) 691209. + 1.19721e6i 0.0856866 + 0.148414i
\(580\) −1.69790e6 −0.209577
\(581\) 0 0
\(582\) −7.75775e6 −0.949354
\(583\) 2.12987e6 + 3.68904e6i 0.259526 + 0.449513i
\(584\) 5.19506e6 8.99811e6i 0.630317 1.09174i
\(585\) 1.39628e6 2.41842e6i 0.168687 0.292175i
\(586\) −594198. 1.02918e6i −0.0714804 0.123808i
\(587\) 1.47623e6 0.176831 0.0884155 0.996084i \(-0.471820\pi\)
0.0884155 + 0.996084i \(0.471820\pi\)
\(588\) 0 0
\(589\) 214720. 0.0255026
\(590\) 6.43313e6 + 1.11425e7i 0.760838 + 1.31781i
\(591\) 694899. 1.20360e6i 0.0818376 0.141747i
\(592\) −3.08651e6 + 5.34600e6i −0.361963 + 0.626938i
\(593\) 6.20034e6 + 1.07393e7i 0.724067 + 1.25412i 0.959357 + 0.282196i \(0.0910629\pi\)
−0.235289 + 0.971925i \(0.575604\pi\)
\(594\) 1.94206e6 0.225837
\(595\) 0 0
\(596\) −328296. −0.0378573
\(597\) −1.65085e6 2.85936e6i −0.189571 0.328347i
\(598\) −5.56920e6 + 9.64614e6i −0.636854 + 1.10306i
\(599\) 1.84564e6 3.19674e6i 0.210174 0.364032i −0.741595 0.670848i \(-0.765930\pi\)
0.951769 + 0.306816i \(0.0992636\pi\)
\(600\) 2.23700e6 + 3.87460e6i 0.253681 + 0.439389i
\(601\) 9.12223e6 1.03018 0.515092 0.857135i \(-0.327758\pi\)
0.515092 + 0.857135i \(0.327758\pi\)
\(602\) 0 0
\(603\) −4.80784e6 −0.538464
\(604\) 574064. + 994308.i 0.0640277 + 0.110899i
\(605\) −1.40732e6 + 2.43754e6i −0.156316 + 0.270747i
\(606\) 73062.0 126547.i 0.00808184 0.0139981i
\(607\) 2.83957e6 + 4.91828e6i 0.312810 + 0.541803i 0.978970 0.204007i \(-0.0653964\pi\)
−0.666160 + 0.745809i \(0.732063\pi\)
\(608\) 3.86496e6 0.424020
\(609\) 0 0
\(610\) −2.31557e7 −2.51961
\(611\) −3.07632e6 5.32834e6i −0.333372 0.577416i
\(612\) 20412.0 35354.6i 0.00220296 0.00381564i
\(613\) 7.00529e6 1.21335e7i 0.752966 1.30417i −0.193414 0.981117i \(-0.561956\pi\)
0.946379 0.323057i \(-0.104711\pi\)
\(614\) −3.13691e6 5.43328e6i −0.335800 0.581623i
\(615\) −5.58932e6 −0.595897
\(616\) 0 0
\(617\) −253686. −0.0268277 −0.0134139 0.999910i \(-0.504270\pi\)
−0.0134139 + 0.999910i \(0.504270\pi\)
\(618\) −3.55774e6 6.16218e6i −0.374716 0.649028i
\(619\) −2.15017e6 + 3.72420e6i −0.225552 + 0.390667i −0.956485 0.291782i \(-0.905752\pi\)
0.730933 + 0.682449i \(0.239085\pi\)
\(620\) −12480.0 + 21616.0i −0.00130387 + 0.00225837i
\(621\) 1.53090e6 + 2.65160e6i 0.159301 + 0.275917i
\(622\) −1.10231e7 −1.14242
\(623\) 0 0
\(624\) −4.51901e6 −0.464603
\(625\) 5.12841e6 + 8.88267e6i 0.525149 + 0.909585i
\(626\) −1.09648e6 + 1.89916e6i −0.111832 + 0.193699i
\(627\) 5.36263e6 9.28835e6i 0.544765 0.943561i
\(628\) −259756. 449911.i −0.0262825 0.0455226i
\(629\) 684684. 0.0690023
\(630\) 0 0
\(631\) 1.04150e7 1.04132 0.520662 0.853763i \(-0.325685\pi\)
0.520662 + 0.853763i \(0.325685\pi\)
\(632\) 5.52518e6 + 9.56990e6i 0.550242 + 0.953048i
\(633\) 2.34110e6 4.05490e6i 0.232226 0.402227i
\(634\) −85014.0 + 147249.i −0.00839977 + 0.0145488i
\(635\) 2.89848e6 + 5.02031e6i 0.285257 + 0.494079i
\(636\) 345384. 0.0338579
\(637\) 0 0
\(638\) 1.44975e7 1.41007
\(639\) −1.29762e6 2.24754e6i −0.125717 0.217749i
\(640\) 8.28173e6 1.43444e7i 0.799229 1.38430i
\(641\) −2.26357e6 + 3.92062e6i −0.217595 + 0.376885i −0.954072 0.299577i \(-0.903154\pi\)
0.736477 + 0.676462i \(0.236488\pi\)
\(642\) 3.48073e6 + 6.02880e6i 0.333298 + 0.577289i
\(643\) 1.49687e7 1.42776 0.713882 0.700266i \(-0.246935\pi\)
0.713882 + 0.700266i \(0.246935\pi\)
\(644\) 0 0
\(645\) 8.08985e6 0.765669
\(646\) −1.01455e6 1.75726e6i −0.0956518 0.165674i
\(647\) 8.65098e6 1.49839e7i 0.812465 1.40723i −0.0986691 0.995120i \(-0.531459\pi\)
0.911134 0.412110i \(-0.135208\pi\)
\(648\) −551124. + 954575.i −0.0515599 + 0.0893043i
\(649\) −6.10322e6 1.05711e7i −0.568784 0.985163i
\(650\) 7.84727e6 0.728509
\(651\) 0 0
\(652\) 2.22114e6 0.204624
\(653\) −2.03735e6 3.52880e6i −0.186975 0.323850i 0.757265 0.653107i \(-0.226535\pi\)
−0.944240 + 0.329258i \(0.893202\pi\)
\(654\) 2.72641e6 4.72227e6i 0.249256 0.431725i
\(655\) 6.05732e6 1.04916e7i 0.551668 0.955516i
\(656\) 4.52242e6 + 7.83305e6i 0.410309 + 0.710676i
\(657\) −5.00953e6 −0.452776
\(658\) 0 0
\(659\) −3.79475e6 −0.340384 −0.170192 0.985411i \(-0.554439\pi\)
−0.170192 + 0.985411i \(0.554439\pi\)
\(660\) 623376. + 1.07972e6i 0.0557045 + 0.0964830i
\(661\) −8.21307e6 + 1.42255e7i −0.731142 + 1.26638i 0.225253 + 0.974300i \(0.427679\pi\)
−0.956395 + 0.292075i \(0.905654\pi\)
\(662\) 5.80175e6 1.00489e7i 0.514534 0.891199i
\(663\) 250614. + 434076.i 0.0221422 + 0.0383515i
\(664\) 6.75158e6 0.594272
\(665\) 0 0
\(666\) 2.64092e6 0.230712
\(667\) 1.14282e7 + 1.97942e7i 0.994634 + 1.72276i
\(668\) −87024.0 + 150730.i −0.00754567 + 0.0130695i
\(669\) 1.37131e6 2.37518e6i 0.118460 0.205178i
\(670\) −1.38893e7 2.40570e7i −1.19535 2.07040i
\(671\) 2.19682e7 1.88360
\(672\) 0 0
\(673\) 5.50675e6 0.468660 0.234330 0.972157i \(-0.424710\pi\)
0.234330 + 0.972157i \(0.424710\pi\)
\(674\) −5.66452e6 9.81124e6i −0.480301 0.831906i
\(675\) 1.07856e6 1.86811e6i 0.0911136 0.157813i
\(676\) 351858. 609436.i 0.0296142 0.0512934i
\(677\) −9.19787e6 1.59312e7i −0.771286 1.33591i −0.936858 0.349709i \(-0.886280\pi\)
0.165572 0.986198i \(-0.447053\pi\)
\(678\) 1.18879e7 0.993185
\(679\) 0 0
\(680\) −1.65110e6 −0.136931
\(681\) 1.29865e6 + 2.24932e6i 0.107306 + 0.185859i
\(682\) 106560. 184567.i 0.00877270 0.0151948i
\(683\) −879174. + 1.52277e6i −0.0721146 + 0.124906i −0.899828 0.436245i \(-0.856308\pi\)
0.827713 + 0.561151i \(0.189641\pi\)
\(684\) −434808. 753110.i −0.0355351 0.0615486i
\(685\) −2.06112e7 −1.67833
\(686\) 0 0
\(687\) −6.94971e6 −0.561791
\(688\) −6.54563e6 1.13374e7i −0.527206 0.913148i
\(689\) −2.12027e6 + 3.67242e6i −0.170155 + 0.294717i
\(690\) −8.84520e6 + 1.53203e7i −0.707270 + 1.22503i
\(691\) 2.68157e6 + 4.64462e6i 0.213646 + 0.370045i 0.952853 0.303433i \(-0.0981329\pi\)
−0.739207 + 0.673478i \(0.764800\pi\)
\(692\) −73320.0 −0.00582046
\(693\) 0 0
\(694\) −1.75162e7 −1.38052
\(695\) −8.75987e6 1.51725e7i −0.687916 1.19151i
\(696\) −4.11415e6 + 7.12592e6i −0.321927 + 0.557594i
\(697\) 501606. 868807.i 0.0391094 0.0677394i
\(698\) −2.34205e6 4.05654e6i −0.181952 0.315150i
\(699\) −2.27011e6 −0.175733
\(700\) 0 0
\(701\) −2.12606e7 −1.63411 −0.817054 0.576561i \(-0.804394\pi\)
−0.817054 + 0.576561i \(0.804394\pi\)
\(702\) 966654. + 1.67429e6i 0.0740335 + 0.128230i
\(703\) 7.29243e6 1.26309e7i 0.556524 0.963928i
\(704\) −6.15206e6 + 1.06557e7i −0.467831 + 0.810307i
\(705\) −4.88592e6 8.46266e6i −0.370232 0.641260i
\(706\) −8.00622e6 −0.604527
\(707\) 0 0
\(708\) −989712. −0.0742037
\(709\) −1.03864e6 1.79898e6i −0.0775980 0.134404i 0.824615 0.565694i \(-0.191392\pi\)
−0.902213 + 0.431290i \(0.858058\pi\)
\(710\) 7.49736e6 1.29858e7i 0.558165 0.966770i
\(711\) 2.66393e6 4.61406e6i 0.197628 0.342302i
\(712\) 669816. + 1.16016e6i 0.0495171 + 0.0857662i
\(713\) 336000. 0.0247523
\(714\) 0 0
\(715\) −1.53073e7 −1.11979
\(716\) 306648. + 531130.i 0.0223541 + 0.0387185i
\(717\) −6.53011e6 + 1.13105e7i −0.474376 + 0.821643i
\(718\) 3.05230e6 5.28673e6i 0.220961 0.382716i
\(719\) −2.11810e6 3.66865e6i −0.152800 0.264657i 0.779456 0.626457i \(-0.215496\pi\)
−0.932256 + 0.361800i \(0.882162\pi\)
\(720\) −7.17725e6 −0.515973
\(721\) 0 0
\(722\) −2.83665e7 −2.02518
\(723\) −658791. 1.14106e6i −0.0468708 0.0811825i
\(724\) 764132. 1.32352e6i 0.0541779 0.0938388i
\(725\) 8.05144e6 1.39455e7i 0.568890 0.985347i
\(726\) −974295. 1.68753e6i −0.0686039 0.118825i
\(727\) 2.14524e7 1.50536 0.752678 0.658389i \(-0.228762\pi\)
0.752678 + 0.658389i \(0.228762\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −1.44720e7 2.50662e7i −1.00513 1.74093i
\(731\) −726012. + 1.25749e6i −0.0502517 + 0.0870384i
\(732\) 890604. 1.54257e6i 0.0614337 0.106406i
\(733\) 7.44459e6 + 1.28944e7i 0.511777 + 0.886424i 0.999907 + 0.0136528i \(0.00434594\pi\)
−0.488130 + 0.872771i \(0.662321\pi\)
\(734\) −5.02608e6 −0.344341
\(735\) 0 0
\(736\) 6.04800e6 0.411545
\(737\) 1.31770e7 + 2.28233e7i 0.893612 + 1.54778i
\(738\) 1.93477e6 3.35111e6i 0.130764 0.226490i
\(739\) −3.49662e6 + 6.05632e6i −0.235525 + 0.407941i −0.959425 0.281963i \(-0.909014\pi\)
0.723900 + 0.689905i \(0.242348\pi\)
\(740\) 847704. + 1.46827e6i 0.0569069 + 0.0985656i
\(741\) 1.06770e7 0.714335
\(742\) 0 0
\(743\) 1.90428e6 0.126549 0.0632745 0.997996i \(-0.479846\pi\)
0.0632745 + 0.997996i \(0.479846\pi\)
\(744\) 60480.0 + 104754.i 0.00400571 + 0.00693809i
\(745\) 3.20089e6 5.54410e6i 0.211290 0.365966i
\(746\) −4.55979e6 + 7.89779e6i −0.299984 + 0.519587i
\(747\) −1.62761e6 2.81911e6i −0.106721 0.184846i
\(748\) −223776. −0.0146238
\(749\) 0 0
\(750\) −699192. −0.0453882
\(751\) −9.76806e6 1.69188e7i −0.631988 1.09463i −0.987145 0.159828i \(-0.948906\pi\)
0.355157 0.934807i \(-0.384427\pi\)
\(752\) −7.90656e6 + 1.36946e7i −0.509851 + 0.883087i
\(753\) 2.73537e6 4.73780e6i 0.175804 0.304501i
\(754\) 7.21609e6 + 1.24986e7i 0.462247 + 0.800635i
\(755\) −2.23885e7 −1.42941
\(756\) 0 0
\(757\) 1.25183e6 0.0793973 0.0396986 0.999212i \(-0.487360\pi\)
0.0396986 + 0.999212i \(0.487360\pi\)
\(758\) 7.93396e6 + 1.37420e7i 0.501553 + 0.868715i
\(759\) 8.39160e6 1.45347e7i 0.528738 0.915801i
\(760\) −1.75856e7 + 3.04591e7i −1.10439 + 1.91286i
\(761\) −1.02236e7 1.77078e7i −0.639944 1.10841i −0.985445 0.169997i \(-0.945624\pi\)
0.345501 0.938418i \(-0.387709\pi\)
\(762\) −4.01328e6 −0.250387
\(763\) 0 0
\(764\) −1.09363e6 −0.0677857
\(765\) 398034. + 689415.i 0.0245905 + 0.0425919i
\(766\) 6.04008e6 1.04617e7i 0.371938 0.644216i
\(767\) 6.07573e6 1.05235e7i 0.372915 0.645908i
\(768\) 1.74298e6 + 3.01892e6i 0.106632 + 0.184692i
\(769\) 2.21064e6