Properties

Label 162.6.c.d.55.1
Level $162$
Weight $6$
Character 162.55
Analytic conductor $25.982$
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] = [162,6,Mod(55,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.55");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 162.c (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: \(25.9821788097\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 162.55
Dual form 162.6.c.d.109.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 + 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-10.5000 - 18.1865i) q^{5} +(-37.0000 + 64.0859i) q^{7} +64.0000 q^{8} +O(q^{10})\) \(q+(-2.00000 + 3.46410i) q^{2} +(-8.00000 - 13.8564i) q^{4} +(-10.5000 - 18.1865i) q^{5} +(-37.0000 + 64.0859i) q^{7} +64.0000 q^{8} +84.0000 q^{10} +(-135.000 + 233.827i) q^{11} +(57.5000 + 99.5929i) q^{13} +(-148.000 - 256.344i) q^{14} +(-128.000 + 221.703i) q^{16} -861.000 q^{17} +1850.00 q^{19} +(-168.000 + 290.985i) q^{20} +(-540.000 - 935.307i) q^{22} +(-1809.00 - 3133.28i) q^{23} +(1342.00 - 2324.41i) q^{25} -460.000 q^{26} +1184.00 q^{28} +(-562.500 + 974.279i) q^{29} +(-2614.00 - 4527.58i) q^{31} +(-512.000 - 886.810i) q^{32} +(1722.00 - 2982.59i) q^{34} +1554.00 q^{35} +9917.00 q^{37} +(-3700.00 + 6408.59i) q^{38} +(-672.000 - 1163.94i) q^{40} +(-5379.00 - 9316.70i) q^{41} +(9857.00 - 17072.8i) q^{43} +4320.00 q^{44} +14472.0 q^{46} +(-4992.00 + 8646.40i) q^{47} +(5665.50 + 9812.93i) q^{49} +(5368.00 + 9297.65i) q^{50} +(920.000 - 1593.49i) q^{52} +36726.0 q^{53} +5670.00 q^{55} +(-2368.00 + 4101.50i) q^{56} +(-2250.00 - 3897.11i) q^{58} +(-13230.0 - 22915.0i) q^{59} +(26889.5 - 46574.0i) q^{61} +20912.0 q^{62} +4096.00 q^{64} +(1207.50 - 2091.45i) q^{65} +(6467.00 + 11201.2i) q^{67} +(6888.00 + 11930.4i) q^{68} +(-3108.00 + 5383.21i) q^{70} -4254.00 q^{71} -17521.0 q^{73} +(-19834.0 + 34353.5i) q^{74} +(-14800.0 - 25634.4i) q^{76} +(-9990.00 - 17303.2i) q^{77} +(18473.0 - 31996.2i) q^{79} +5376.00 q^{80} +43032.0 q^{82} +(38208.0 - 66178.2i) q^{83} +(9040.50 + 15658.6i) q^{85} +(39428.0 + 68291.3i) q^{86} +(-8640.00 + 14964.9i) q^{88} -45357.0 q^{89} -8510.00 q^{91} +(-28944.0 + 50132.5i) q^{92} +(-19968.0 - 34585.6i) q^{94} +(-19425.0 - 33645.1i) q^{95} +(-63787.0 + 110482. i) q^{97} -45324.0 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{2} - 16 q^{4} - 21 q^{5} - 74 q^{7} + 128 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{2} - 16 q^{4} - 21 q^{5} - 74 q^{7} + 128 q^{8} + 168 q^{10} - 270 q^{11} + 115 q^{13} - 296 q^{14} - 256 q^{16} - 1722 q^{17} + 3700 q^{19} - 336 q^{20} - 1080 q^{22} - 3618 q^{23} + 2684 q^{25} - 920 q^{26} + 2368 q^{28} - 1125 q^{29} - 5228 q^{31} - 1024 q^{32} + 3444 q^{34} + 3108 q^{35} + 19834 q^{37} - 7400 q^{38} - 1344 q^{40} - 10758 q^{41} + 19714 q^{43} + 8640 q^{44} + 28944 q^{46} - 9984 q^{47} + 11331 q^{49} + 10736 q^{50} + 1840 q^{52} + 73452 q^{53} + 11340 q^{55} - 4736 q^{56} - 4500 q^{58} - 26460 q^{59} + 53779 q^{61} + 41824 q^{62} + 8192 q^{64} + 2415 q^{65} + 12934 q^{67} + 13776 q^{68} - 6216 q^{70} - 8508 q^{71} - 35042 q^{73} - 39668 q^{74} - 29600 q^{76} - 19980 q^{77} + 36946 q^{79} + 10752 q^{80} + 86064 q^{82} + 76416 q^{83} + 18081 q^{85} + 78856 q^{86} - 17280 q^{88} - 90714 q^{89} - 17020 q^{91} - 57888 q^{92} - 39936 q^{94} - 38850 q^{95} - 127574 q^{97} - 90648 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 + 3.46410i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −8.00000 13.8564i −0.250000 0.433013i
\(5\) −10.5000 18.1865i −0.187830 0.325331i 0.756697 0.653766i \(-0.226812\pi\)
−0.944526 + 0.328436i \(0.893479\pi\)
\(6\) 0 0
\(7\) −37.0000 + 64.0859i −0.285402 + 0.494330i −0.972707 0.232039i \(-0.925460\pi\)
0.687305 + 0.726369i \(0.258794\pi\)
\(8\) 64.0000 0.353553
\(9\) 0 0
\(10\) 84.0000 0.265631
\(11\) −135.000 + 233.827i −0.336397 + 0.582657i −0.983752 0.179532i \(-0.942542\pi\)
0.647355 + 0.762188i \(0.275875\pi\)
\(12\) 0 0
\(13\) 57.5000 + 99.5929i 0.0943647 + 0.163444i 0.909343 0.416047i \(-0.136585\pi\)
−0.814979 + 0.579491i \(0.803251\pi\)
\(14\) −148.000 256.344i −0.201810 0.349544i
\(15\) 0 0
\(16\) −128.000 + 221.703i −0.125000 + 0.216506i
\(17\) −861.000 −0.722572 −0.361286 0.932455i \(-0.617662\pi\)
−0.361286 + 0.932455i \(0.617662\pi\)
\(18\) 0 0
\(19\) 1850.00 1.17568 0.587838 0.808979i \(-0.299979\pi\)
0.587838 + 0.808979i \(0.299979\pi\)
\(20\) −168.000 + 290.985i −0.0939149 + 0.162665i
\(21\) 0 0
\(22\) −540.000 935.307i −0.237869 0.412000i
\(23\) −1809.00 3133.28i −0.713048 1.23504i −0.963707 0.266961i \(-0.913981\pi\)
0.250659 0.968075i \(-0.419353\pi\)
\(24\) 0 0
\(25\) 1342.00 2324.41i 0.429440 0.743812i
\(26\) −460.000 −0.133452
\(27\) 0 0
\(28\) 1184.00 0.285402
\(29\) −562.500 + 974.279i −0.124202 + 0.215124i −0.921421 0.388567i \(-0.872970\pi\)
0.797219 + 0.603690i \(0.206304\pi\)
\(30\) 0 0
\(31\) −2614.00 4527.58i −0.488541 0.846178i 0.511372 0.859360i \(-0.329138\pi\)
−0.999913 + 0.0131811i \(0.995804\pi\)
\(32\) −512.000 886.810i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 1722.00 2982.59i 0.255468 0.442483i
\(35\) 1554.00 0.214428
\(36\) 0 0
\(37\) 9917.00 1.19090 0.595451 0.803392i \(-0.296973\pi\)
0.595451 + 0.803392i \(0.296973\pi\)
\(38\) −3700.00 + 6408.59i −0.415664 + 0.719952i
\(39\) 0 0
\(40\) −672.000 1163.94i −0.0664078 0.115022i
\(41\) −5379.00 9316.70i −0.499737 0.865571i 0.500262 0.865874i \(-0.333237\pi\)
−1.00000 0.000303132i \(0.999904\pi\)
\(42\) 0 0
\(43\) 9857.00 17072.8i 0.812968 1.40810i −0.0978093 0.995205i \(-0.531184\pi\)
0.910778 0.412897i \(-0.135483\pi\)
\(44\) 4320.00 0.336397
\(45\) 0 0
\(46\) 14472.0 1.00840
\(47\) −4992.00 + 8646.40i −0.329632 + 0.570940i −0.982439 0.186585i \(-0.940258\pi\)
0.652806 + 0.757525i \(0.273591\pi\)
\(48\) 0 0
\(49\) 5665.50 + 9812.93i 0.337092 + 0.583860i
\(50\) 5368.00 + 9297.65i 0.303660 + 0.525954i
\(51\) 0 0
\(52\) 920.000 1593.49i 0.0471823 0.0817222i
\(53\) 36726.0 1.79591 0.897954 0.440090i \(-0.145053\pi\)
0.897954 + 0.440090i \(0.145053\pi\)
\(54\) 0 0
\(55\) 5670.00 0.252741
\(56\) −2368.00 + 4101.50i −0.100905 + 0.174772i
\(57\) 0 0
\(58\) −2250.00 3897.11i −0.0878239 0.152115i
\(59\) −13230.0 22915.0i −0.494800 0.857019i 0.505182 0.863013i \(-0.331425\pi\)
−0.999982 + 0.00599391i \(0.998092\pi\)
\(60\) 0 0
\(61\) 26889.5 46574.0i 0.925248 1.60258i 0.134086 0.990970i \(-0.457190\pi\)
0.791162 0.611607i \(-0.209477\pi\)
\(62\) 20912.0 0.690902
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) 1207.50 2091.45i 0.0354490 0.0613994i
\(66\) 0 0
\(67\) 6467.00 + 11201.2i 0.176001 + 0.304843i 0.940507 0.339773i \(-0.110350\pi\)
−0.764506 + 0.644617i \(0.777017\pi\)
\(68\) 6888.00 + 11930.4i 0.180643 + 0.312883i
\(69\) 0 0
\(70\) −3108.00 + 5383.21i −0.0758116 + 0.131310i
\(71\) −4254.00 −0.100150 −0.0500751 0.998745i \(-0.515946\pi\)
−0.0500751 + 0.998745i \(0.515946\pi\)
\(72\) 0 0
\(73\) −17521.0 −0.384815 −0.192407 0.981315i \(-0.561630\pi\)
−0.192407 + 0.981315i \(0.561630\pi\)
\(74\) −19834.0 + 34353.5i −0.421047 + 0.729276i
\(75\) 0 0
\(76\) −14800.0 25634.4i −0.293919 0.509083i
\(77\) −9990.00 17303.2i −0.192017 0.332582i
\(78\) 0 0
\(79\) 18473.0 31996.2i 0.333020 0.576807i −0.650083 0.759863i \(-0.725266\pi\)
0.983102 + 0.183057i \(0.0585992\pi\)
\(80\) 5376.00 0.0939149
\(81\) 0 0
\(82\) 43032.0 0.706735
\(83\) 38208.0 66178.2i 0.608778 1.05443i −0.382664 0.923888i \(-0.624993\pi\)
0.991442 0.130547i \(-0.0416734\pi\)
\(84\) 0 0
\(85\) 9040.50 + 15658.6i 0.135720 + 0.235075i
\(86\) 39428.0 + 68291.3i 0.574855 + 0.995679i
\(87\) 0 0
\(88\) −8640.00 + 14964.9i −0.118934 + 0.206000i
\(89\) −45357.0 −0.606973 −0.303486 0.952836i \(-0.598151\pi\)
−0.303486 + 0.952836i \(0.598151\pi\)
\(90\) 0 0
\(91\) −8510.00 −0.107727
\(92\) −28944.0 + 50132.5i −0.356524 + 0.617518i
\(93\) 0 0
\(94\) −19968.0 34585.6i −0.233085 0.403716i
\(95\) −19425.0 33645.1i −0.220827 0.382483i
\(96\) 0 0
\(97\) −63787.0 + 110482.i −0.688340 + 1.19224i 0.284035 + 0.958814i \(0.408327\pi\)
−0.972375 + 0.233425i \(0.925007\pi\)
\(98\) −45324.0 −0.476720
\(99\) 0 0
\(100\) −42944.0 −0.429440
\(101\) 39435.0 68303.4i 0.384661 0.666253i −0.607061 0.794655i \(-0.707652\pi\)
0.991722 + 0.128403i \(0.0409849\pi\)
\(102\) 0 0
\(103\) 8744.00 + 15145.1i 0.0812114 + 0.140662i 0.903771 0.428017i \(-0.140788\pi\)
−0.822559 + 0.568680i \(0.807454\pi\)
\(104\) 3680.00 + 6373.95i 0.0333630 + 0.0577863i
\(105\) 0 0
\(106\) −73452.0 + 127223.i −0.634949 + 1.09976i
\(107\) −134364. −1.13455 −0.567275 0.823529i \(-0.692002\pi\)
−0.567275 + 0.823529i \(0.692002\pi\)
\(108\) 0 0
\(109\) −123487. −0.995531 −0.497766 0.867312i \(-0.665846\pi\)
−0.497766 + 0.867312i \(0.665846\pi\)
\(110\) −11340.0 + 19641.5i −0.0893576 + 0.154772i
\(111\) 0 0
\(112\) −9472.00 16406.0i −0.0713504 0.123583i
\(113\) −87019.5 150722.i −0.641092 1.11040i −0.985189 0.171470i \(-0.945148\pi\)
0.344097 0.938934i \(-0.388185\pi\)
\(114\) 0 0
\(115\) −37989.0 + 65798.9i −0.267863 + 0.463953i
\(116\) 18000.0 0.124202
\(117\) 0 0
\(118\) 105840. 0.699753
\(119\) 31857.0 55177.9i 0.206223 0.357189i
\(120\) 0 0
\(121\) 44075.5 + 76341.0i 0.273674 + 0.474018i
\(122\) 107558. + 186296.i 0.654249 + 1.13319i
\(123\) 0 0
\(124\) −41824.0 + 72441.3i −0.244271 + 0.423089i
\(125\) −121989. −0.698306
\(126\) 0 0
\(127\) −312982. −1.72191 −0.860954 0.508682i \(-0.830133\pi\)
−0.860954 + 0.508682i \(0.830133\pi\)
\(128\) −8192.00 + 14189.0i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 4830.00 + 8365.81i 0.0250662 + 0.0434160i
\(131\) 52905.0 + 91634.1i 0.269351 + 0.466529i 0.968694 0.248256i \(-0.0798575\pi\)
−0.699343 + 0.714786i \(0.746524\pi\)
\(132\) 0 0
\(133\) −68450.0 + 118559.i −0.335540 + 0.581172i
\(134\) −51736.0 −0.248903
\(135\) 0 0
\(136\) −55104.0 −0.255468
\(137\) 142240. 246368.i 0.647473 1.12146i −0.336251 0.941772i \(-0.609159\pi\)
0.983724 0.179684i \(-0.0575076\pi\)
\(138\) 0 0
\(139\) 81164.0 + 140580.i 0.356309 + 0.617145i 0.987341 0.158612i \(-0.0507018\pi\)
−0.631032 + 0.775757i \(0.717368\pi\)
\(140\) −12432.0 21532.9i −0.0536069 0.0928499i
\(141\) 0 0
\(142\) 8508.00 14736.3i 0.0354084 0.0613292i
\(143\) −31050.0 −0.126976
\(144\) 0 0
\(145\) 23625.0 0.0933151
\(146\) 35042.0 60694.5i 0.136053 0.235650i
\(147\) 0 0
\(148\) −79336.0 137414.i −0.297725 0.515676i
\(149\) 135356. + 234443.i 0.499471 + 0.865109i 1.00000 0.000610783i \(-0.000194418\pi\)
−0.500529 + 0.865720i \(0.666861\pi\)
\(150\) 0 0
\(151\) 8426.00 14594.3i 0.0300732 0.0520882i −0.850597 0.525818i \(-0.823759\pi\)
0.880670 + 0.473730i \(0.157093\pi\)
\(152\) 118400. 0.415664
\(153\) 0 0
\(154\) 79920.0 0.271552
\(155\) −54894.0 + 95079.2i −0.183525 + 0.317875i
\(156\) 0 0
\(157\) −123686. 214231.i −0.400473 0.693639i 0.593310 0.804974i \(-0.297821\pi\)
−0.993783 + 0.111335i \(0.964487\pi\)
\(158\) 73892.0 + 127985.i 0.235480 + 0.407864i
\(159\) 0 0
\(160\) −10752.0 + 18623.0i −0.0332039 + 0.0575109i
\(161\) 267732. 0.814021
\(162\) 0 0
\(163\) −200116. −0.589947 −0.294973 0.955505i \(-0.595311\pi\)
−0.294973 + 0.955505i \(0.595311\pi\)
\(164\) −86064.0 + 149067.i −0.249869 + 0.432785i
\(165\) 0 0
\(166\) 152832. + 264713.i 0.430471 + 0.745598i
\(167\) −7059.00 12226.5i −0.0195863 0.0339244i 0.856066 0.516866i \(-0.172902\pi\)
−0.875652 + 0.482942i \(0.839568\pi\)
\(168\) 0 0
\(169\) 179034. 310096.i 0.482191 0.835179i
\(170\) −72324.0 −0.191938
\(171\) 0 0
\(172\) −315424. −0.812968
\(173\) 24199.5 41914.8i 0.0614740 0.106476i −0.833651 0.552292i \(-0.813753\pi\)
0.895124 + 0.445816i \(0.147087\pi\)
\(174\) 0 0
\(175\) 99308.0 + 172007.i 0.245126 + 0.424570i
\(176\) −34560.0 59859.7i −0.0840992 0.145664i
\(177\) 0 0
\(178\) 90714.0 157121.i 0.214597 0.371693i
\(179\) 375396. 0.875703 0.437852 0.899047i \(-0.355739\pi\)
0.437852 + 0.899047i \(0.355739\pi\)
\(180\) 0 0
\(181\) 440702. 0.999882 0.499941 0.866060i \(-0.333355\pi\)
0.499941 + 0.866060i \(0.333355\pi\)
\(182\) 17020.0 29479.5i 0.0380874 0.0659693i
\(183\) 0 0
\(184\) −115776. 200530.i −0.252101 0.436651i
\(185\) −104128. 180356.i −0.223687 0.387437i
\(186\) 0 0
\(187\) 116235. 201325.i 0.243071 0.421011i
\(188\) 159744. 0.329632
\(189\) 0 0
\(190\) 155400. 0.312296
\(191\) −243489. + 421735.i −0.482943 + 0.836482i −0.999808 0.0195849i \(-0.993766\pi\)
0.516865 + 0.856067i \(0.327099\pi\)
\(192\) 0 0
\(193\) 52092.5 + 90226.9i 0.100666 + 0.174358i 0.911959 0.410281i \(-0.134569\pi\)
−0.811293 + 0.584639i \(0.801236\pi\)
\(194\) −255148. 441929.i −0.486730 0.843041i
\(195\) 0 0
\(196\) 90648.0 157007.i 0.168546 0.291930i
\(197\) 39369.0 0.0722751 0.0361376 0.999347i \(-0.488495\pi\)
0.0361376 + 0.999347i \(0.488495\pi\)
\(198\) 0 0
\(199\) 952484. 1.70500 0.852501 0.522725i \(-0.175085\pi\)
0.852501 + 0.522725i \(0.175085\pi\)
\(200\) 85888.0 148762.i 0.151830 0.262977i
\(201\) 0 0
\(202\) 157740. + 273214.i 0.271997 + 0.471112i
\(203\) −41625.0 72096.6i −0.0708948 0.122793i
\(204\) 0 0
\(205\) −112959. + 195651.i −0.187731 + 0.325160i
\(206\) −69952.0 −0.114850
\(207\) 0 0
\(208\) −29440.0 −0.0471823
\(209\) −249750. + 432580.i −0.395494 + 0.685016i
\(210\) 0 0
\(211\) −220555. 382012.i −0.341044 0.590706i 0.643583 0.765377i \(-0.277447\pi\)
−0.984627 + 0.174671i \(0.944114\pi\)
\(212\) −293808. 508890.i −0.448977 0.777651i
\(213\) 0 0
\(214\) 268728. 465451.i 0.401124 0.694767i
\(215\) −413994. −0.610798
\(216\) 0 0
\(217\) 386872. 0.557722
\(218\) 246974. 427772.i 0.351974 0.609636i
\(219\) 0 0
\(220\) −45360.0 78565.8i −0.0631853 0.109440i
\(221\) −49507.5 85749.5i −0.0681852 0.118100i
\(222\) 0 0
\(223\) 412553. 714563.i 0.555543 0.962229i −0.442318 0.896858i \(-0.645844\pi\)
0.997861 0.0653703i \(-0.0208229\pi\)
\(224\) 75776.0 0.100905
\(225\) 0 0
\(226\) 696156. 0.906641
\(227\) −577851. + 1.00087e6i −0.744305 + 1.28917i 0.206213 + 0.978507i \(0.433886\pi\)
−0.950519 + 0.310668i \(0.899447\pi\)
\(228\) 0 0
\(229\) −671678. 1.16338e6i −0.846394 1.46600i −0.884405 0.466721i \(-0.845435\pi\)
0.0380105 0.999277i \(-0.487898\pi\)
\(230\) −151956. 263196.i −0.189408 0.328064i
\(231\) 0 0
\(232\) −36000.0 + 62353.8i −0.0439119 + 0.0760577i
\(233\) 1.07555e6 1.29790 0.648950 0.760831i \(-0.275208\pi\)
0.648950 + 0.760831i \(0.275208\pi\)
\(234\) 0 0
\(235\) 209664. 0.247659
\(236\) −211680. + 366641.i −0.247400 + 0.428509i
\(237\) 0 0
\(238\) 127428. + 220712.i 0.145822 + 0.252571i
\(239\) −18048.0 31260.1i −0.0204378 0.0353993i 0.855626 0.517595i \(-0.173173\pi\)
−0.876063 + 0.482196i \(0.839839\pi\)
\(240\) 0 0
\(241\) −36437.5 + 63111.6i −0.0404116 + 0.0699949i −0.885524 0.464594i \(-0.846200\pi\)
0.845112 + 0.534589i \(0.179534\pi\)
\(242\) −352604. −0.387034
\(243\) 0 0
\(244\) −860464. −0.925248
\(245\) 118976. 206072.i 0.126632 0.219332i
\(246\) 0 0
\(247\) 106375. + 184247.i 0.110942 + 0.192158i
\(248\) −167296. 289765.i −0.172725 0.299169i
\(249\) 0 0
\(250\) 243978. 422582.i 0.246888 0.427623i
\(251\) −1.65869e6 −1.66181 −0.830906 0.556413i \(-0.812177\pi\)
−0.830906 + 0.556413i \(0.812177\pi\)
\(252\) 0 0
\(253\) 976860. 0.959469
\(254\) 625964. 1.08420e6i 0.608787 1.05445i
\(255\) 0 0
\(256\) −32768.0 56755.8i −0.0312500 0.0541266i
\(257\) 397090. + 687781.i 0.375022 + 0.649557i 0.990330 0.138729i \(-0.0443018\pi\)
−0.615308 + 0.788287i \(0.710969\pi\)
\(258\) 0 0
\(259\) −366929. + 635540.i −0.339885 + 0.588699i
\(260\) −38640.0 −0.0354490
\(261\) 0 0
\(262\) −423240. −0.380920
\(263\) −795396. + 1.37767e6i −0.709078 + 1.22816i 0.256121 + 0.966645i \(0.417555\pi\)
−0.965200 + 0.261515i \(0.915778\pi\)
\(264\) 0 0
\(265\) −385623. 667919.i −0.337325 0.584264i
\(266\) −273800. 474236.i −0.237263 0.410951i
\(267\) 0 0
\(268\) 103472. 179219.i 0.0880006 0.152422i
\(269\) 1.57975e6 1.33109 0.665545 0.746358i \(-0.268199\pi\)
0.665545 + 0.746358i \(0.268199\pi\)
\(270\) 0 0
\(271\) −415762. −0.343892 −0.171946 0.985106i \(-0.555005\pi\)
−0.171946 + 0.985106i \(0.555005\pi\)
\(272\) 110208. 190886.i 0.0903214 0.156441i
\(273\) 0 0
\(274\) 568962. + 985471.i 0.457833 + 0.792990i
\(275\) 362340. + 627591.i 0.288925 + 0.500432i
\(276\) 0 0
\(277\) −281203. + 487058.i −0.220202 + 0.381400i −0.954869 0.297027i \(-0.904005\pi\)
0.734667 + 0.678427i \(0.237338\pi\)
\(278\) −649312. −0.503897
\(279\) 0 0
\(280\) 99456.0 0.0758116
\(281\) 1.21331e6 2.10152e6i 0.916657 1.58770i 0.112200 0.993686i \(-0.464210\pi\)
0.804457 0.594011i \(-0.202456\pi\)
\(282\) 0 0
\(283\) 601466. + 1.04177e6i 0.446421 + 0.773225i 0.998150 0.0607992i \(-0.0193649\pi\)
−0.551729 + 0.834024i \(0.686032\pi\)
\(284\) 34032.0 + 58945.2i 0.0250375 + 0.0433663i
\(285\) 0 0
\(286\) 62100.0 107560.i 0.0448928 0.0777566i
\(287\) 796092. 0.570504
\(288\) 0 0
\(289\) −678536. −0.477890
\(290\) −47250.0 + 81839.4i −0.0329919 + 0.0571436i
\(291\) 0 0
\(292\) 140168. + 242778.i 0.0962037 + 0.166630i
\(293\) 336236. + 582377.i 0.228810 + 0.396310i 0.957456 0.288581i \(-0.0931833\pi\)
−0.728646 + 0.684891i \(0.759850\pi\)
\(294\) 0 0
\(295\) −277830. + 481216.i −0.185876 + 0.321947i
\(296\) 634688. 0.421047
\(297\) 0 0
\(298\) −1.08284e6 −0.706359
\(299\) 208035. 360327.i 0.134573 0.233088i
\(300\) 0 0
\(301\) 729418. + 1.26339e6i 0.464045 + 0.803750i
\(302\) 33704.0 + 58377.0i 0.0212649 + 0.0368320i
\(303\) 0 0
\(304\) −236800. + 410150.i −0.146960 + 0.254541i
\(305\) −1.12936e6 −0.695156
\(306\) 0 0
\(307\) −2.79488e6 −1.69245 −0.846226 0.532823i \(-0.821131\pi\)
−0.846226 + 0.532823i \(0.821131\pi\)
\(308\) −159840. + 276851.i −0.0960083 + 0.166291i
\(309\) 0 0
\(310\) −219576. 380317.i −0.129772 0.224772i
\(311\) 1.52980e6 + 2.64968e6i 0.896876 + 1.55344i 0.831465 + 0.555577i \(0.187503\pi\)
0.0654112 + 0.997858i \(0.479164\pi\)
\(312\) 0 0
\(313\) −1.31737e6 + 2.28175e6i −0.760059 + 1.31646i 0.182760 + 0.983157i \(0.441497\pi\)
−0.942820 + 0.333304i \(0.891837\pi\)
\(314\) 989492. 0.566354
\(315\) 0 0
\(316\) −591136. −0.333020
\(317\) −404188. + 700075.i −0.225910 + 0.391288i −0.956592 0.291430i \(-0.905869\pi\)
0.730682 + 0.682718i \(0.239202\pi\)
\(318\) 0 0
\(319\) −151875. 263055.i −0.0835621 0.144734i
\(320\) −43008.0 74492.0i −0.0234787 0.0406663i
\(321\) 0 0
\(322\) −535464. + 927451.i −0.287800 + 0.498484i
\(323\) −1.59285e6 −0.849510
\(324\) 0 0
\(325\) 308660. 0.162096
\(326\) 400232. 693222.i 0.208578 0.361267i
\(327\) 0 0
\(328\) −344256. 596269.i −0.176684 0.306025i
\(329\) −369408. 639833.i −0.188155 0.325895i
\(330\) 0 0
\(331\) 426839. 739307.i 0.214138 0.370898i −0.738867 0.673851i \(-0.764639\pi\)
0.953006 + 0.302953i \(0.0979724\pi\)
\(332\) −1.22266e6 −0.608778
\(333\) 0 0
\(334\) 56472.0 0.0276992
\(335\) 135807. 235225.i 0.0661165 0.114517i
\(336\) 0 0
\(337\) −148939. 257970.i −0.0714387 0.123735i 0.828093 0.560590i \(-0.189426\pi\)
−0.899532 + 0.436855i \(0.856092\pi\)
\(338\) 716136. + 1.24038e6i 0.340960 + 0.590560i
\(339\) 0 0
\(340\) 144648. 250538.i 0.0678602 0.117537i
\(341\) 1.41156e6 0.657375
\(342\) 0 0
\(343\) −2.08221e6 −0.955630
\(344\) 630848. 1.09266e6i 0.287428 0.497839i
\(345\) 0 0
\(346\) 96798.0 + 167659.i 0.0434686 + 0.0752899i
\(347\) −44373.0 76856.3i −0.0197831 0.0342654i 0.855964 0.517035i \(-0.172964\pi\)
−0.875747 + 0.482769i \(0.839631\pi\)
\(348\) 0 0
\(349\) −1.18087e6 + 2.04533e6i −0.518967 + 0.898877i 0.480790 + 0.876836i \(0.340350\pi\)
−0.999757 + 0.0220413i \(0.992983\pi\)
\(350\) −794464. −0.346660
\(351\) 0 0
\(352\) 276480. 0.118934
\(353\) 1.93038e6 3.34352e6i 0.824530 1.42813i −0.0777471 0.996973i \(-0.524773\pi\)
0.902278 0.431156i \(-0.141894\pi\)
\(354\) 0 0
\(355\) 44667.0 + 77365.5i 0.0188112 + 0.0325819i
\(356\) 362856. + 628485.i 0.151743 + 0.262827i
\(357\) 0 0
\(358\) −750792. + 1.30041e6i −0.309608 + 0.536257i
\(359\) −3.74852e6 −1.53505 −0.767527 0.641017i \(-0.778513\pi\)
−0.767527 + 0.641017i \(0.778513\pi\)
\(360\) 0 0
\(361\) 946401. 0.382215
\(362\) −881404. + 1.52664e6i −0.353512 + 0.612300i
\(363\) 0 0
\(364\) 68080.0 + 117918.i 0.0269318 + 0.0466473i
\(365\) 183970. + 318646.i 0.0722796 + 0.125192i
\(366\) 0 0
\(367\) 1.33170e6 2.30657e6i 0.516107 0.893924i −0.483718 0.875224i \(-0.660714\pi\)
0.999825 0.0187000i \(-0.00595273\pi\)
\(368\) 926208. 0.356524
\(369\) 0 0
\(370\) 833028. 0.316341
\(371\) −1.35886e6 + 2.35362e6i −0.512555 + 0.887772i
\(372\) 0 0
\(373\) −479935. 831272.i −0.178612 0.309365i 0.762793 0.646642i \(-0.223827\pi\)
−0.941405 + 0.337277i \(0.890494\pi\)
\(374\) 464940. + 805300.i 0.171877 + 0.297700i
\(375\) 0 0
\(376\) −319488. + 553369.i −0.116543 + 0.201858i
\(377\) −129375. −0.0468810
\(378\) 0 0
\(379\) −193780. −0.0692964 −0.0346482 0.999400i \(-0.511031\pi\)
−0.0346482 + 0.999400i \(0.511031\pi\)
\(380\) −310800. + 538321.i −0.110413 + 0.191242i
\(381\) 0 0
\(382\) −973956. 1.68694e6i −0.341492 0.591482i
\(383\) −2.77696e6 4.80984e6i −0.967327 1.67546i −0.703228 0.710965i \(-0.748259\pi\)
−0.264100 0.964495i \(-0.585075\pi\)
\(384\) 0 0
\(385\) −209790. + 363367.i −0.0721328 + 0.124938i
\(386\) −416740. −0.142363
\(387\) 0 0
\(388\) 2.04118e6 0.688340
\(389\) 2.41398e6 4.18113e6i 0.808833 1.40094i −0.104839 0.994489i \(-0.533433\pi\)
0.913672 0.406451i \(-0.133234\pi\)
\(390\) 0 0
\(391\) 1.55755e6 + 2.69775e6i 0.515228 + 0.892402i
\(392\) 362592. + 628028.i 0.119180 + 0.206426i
\(393\) 0 0
\(394\) −78738.0 + 136378.i −0.0255531 + 0.0442593i
\(395\) −775866. −0.250204
\(396\) 0 0
\(397\) 313409. 0.0998011 0.0499005 0.998754i \(-0.484110\pi\)
0.0499005 + 0.998754i \(0.484110\pi\)
\(398\) −1.90497e6 + 3.29950e6i −0.602809 + 1.04410i
\(399\) 0 0
\(400\) 343552. + 595050.i 0.107360 + 0.185953i
\(401\) −2.64145e6 4.57512e6i −0.820316 1.42083i −0.905447 0.424459i \(-0.860464\pi\)
0.0851315 0.996370i \(-0.472869\pi\)
\(402\) 0 0
\(403\) 300610. 520672.i 0.0922021 0.159699i
\(404\) −1.26192e6 −0.384661
\(405\) 0 0
\(406\) 333000. 0.100260
\(407\) −1.33880e6 + 2.31886e6i −0.400616 + 0.693887i
\(408\) 0 0
\(409\) −2.29406e6 3.97342e6i −0.678104 1.17451i −0.975551 0.219772i \(-0.929469\pi\)
0.297448 0.954738i \(-0.403865\pi\)
\(410\) −451836. 782603.i −0.132746 0.229923i
\(411\) 0 0
\(412\) 139904. 242321.i 0.0406057 0.0703312i
\(413\) 1.95804e6 0.564867
\(414\) 0 0
\(415\) −1.60474e6 −0.457387
\(416\) 58880.0 101983.i 0.0166815 0.0288932i
\(417\) 0 0
\(418\) −999000. 1.73032e6i −0.279656 0.484379i
\(419\) 1.18349e6 + 2.04986e6i 0.329328 + 0.570413i 0.982379 0.186901i \(-0.0598444\pi\)
−0.653051 + 0.757314i \(0.726511\pi\)
\(420\) 0 0
\(421\) 227398. 393864.i 0.0625289 0.108303i −0.833066 0.553173i \(-0.813417\pi\)
0.895595 + 0.444870i \(0.146750\pi\)
\(422\) 1.76444e6 0.482309
\(423\) 0 0
\(424\) 2.35046e6 0.634949
\(425\) −1.15546e6 + 2.00132e6i −0.310301 + 0.537457i
\(426\) 0 0
\(427\) 1.98982e6 + 3.44647e6i 0.528135 + 0.914756i
\(428\) 1.07491e6 + 1.86180e6i 0.283637 + 0.491274i
\(429\) 0 0
\(430\) 827988. 1.43412e6i 0.215950 0.374036i
\(431\) 1.26286e6 0.327462 0.163731 0.986505i \(-0.447647\pi\)
0.163731 + 0.986505i \(0.447647\pi\)
\(432\) 0 0
\(433\) 5.48900e6 1.40693 0.703467 0.710728i \(-0.251634\pi\)
0.703467 + 0.710728i \(0.251634\pi\)
\(434\) −773744. + 1.34016e6i −0.197185 + 0.341534i
\(435\) 0 0
\(436\) 987896. + 1.71109e6i 0.248883 + 0.431078i
\(437\) −3.34665e6 5.79657e6i −0.838314 1.45200i
\(438\) 0 0
\(439\) 3.05822e6 5.29699e6i 0.757369 1.31180i −0.186819 0.982394i \(-0.559818\pi\)
0.944188 0.329407i \(-0.106849\pi\)
\(440\) 362880. 0.0893576
\(441\) 0 0
\(442\) 396060. 0.0964285
\(443\) −369600. + 640166.i −0.0894793 + 0.154983i −0.907291 0.420503i \(-0.861854\pi\)
0.817812 + 0.575486i \(0.195187\pi\)
\(444\) 0 0
\(445\) 476249. + 824887.i 0.114008 + 0.197467i
\(446\) 1.65021e6 + 2.85825e6i 0.392828 + 0.680398i
\(447\) 0 0
\(448\) −151552. + 262496.i −0.0356752 + 0.0617913i
\(449\) 7.31432e6 1.71221 0.856107 0.516799i \(-0.172876\pi\)
0.856107 + 0.516799i \(0.172876\pi\)
\(450\) 0 0
\(451\) 2.90466e6 0.672441
\(452\) −1.39231e6 + 2.41156e6i −0.320546 + 0.555202i
\(453\) 0 0
\(454\) −2.31140e6 4.00347e6i −0.526303 0.911584i
\(455\) 89355.0 + 154767.i 0.0202344 + 0.0350470i
\(456\) 0 0
\(457\) 3.84452e6 6.65890e6i 0.861096 1.49146i −0.00977649 0.999952i \(-0.503112\pi\)
0.870872 0.491509i \(-0.163555\pi\)
\(458\) 5.37343e6 1.19698
\(459\) 0 0
\(460\) 1.21565e6 0.267863
\(461\) 2.96968e6 5.14365e6i 0.650816 1.12725i −0.332110 0.943241i \(-0.607760\pi\)
0.982925 0.184005i \(-0.0589063\pi\)
\(462\) 0 0
\(463\) 227978. + 394869.i 0.0494243 + 0.0856054i 0.889679 0.456586i \(-0.150928\pi\)
−0.840255 + 0.542192i \(0.817595\pi\)
\(464\) −144000. 249415.i −0.0310504 0.0537809i
\(465\) 0 0
\(466\) −2.15110e6 + 3.72582e6i −0.458877 + 0.794798i
\(467\) −5.97097e6 −1.26693 −0.633465 0.773771i \(-0.718368\pi\)
−0.633465 + 0.773771i \(0.718368\pi\)
\(468\) 0 0
\(469\) −957116. −0.200924
\(470\) −419328. + 726297.i −0.0875607 + 0.151660i
\(471\) 0 0
\(472\) −846720. 1.46656e6i −0.174938 0.303002i
\(473\) 2.66139e6 + 4.60966e6i 0.546960 + 0.947363i
\(474\) 0 0
\(475\) 2.48270e6 4.30016e6i 0.504882 0.874482i
\(476\) −1.01942e6 −0.206223
\(477\) 0 0
\(478\) 144384. 0.0289034
\(479\) −2.12420e6 + 3.67921e6i −0.423015 + 0.732683i −0.996233 0.0867198i \(-0.972362\pi\)
0.573218 + 0.819403i \(0.305695\pi\)
\(480\) 0 0
\(481\) 570228. + 987663.i 0.112379 + 0.194646i
\(482\) −145750. 252446.i −0.0285753 0.0494939i
\(483\) 0 0
\(484\) 705208. 1.22146e6i 0.136837 0.237009i
\(485\) 2.67905e6 0.517163
\(486\) 0 0
\(487\) −1.04048e6 −0.198797 −0.0993985 0.995048i \(-0.531692\pi\)
−0.0993985 + 0.995048i \(0.531692\pi\)
\(488\) 1.72093e6 2.98073e6i 0.327125 0.566596i
\(489\) 0 0
\(490\) 475902. + 824286.i 0.0895421 + 0.155091i
\(491\) −2.77849e6 4.81248e6i −0.520122 0.900877i −0.999726 0.0233925i \(-0.992553\pi\)
0.479605 0.877485i \(-0.340780\pi\)
\(492\) 0 0
\(493\) 484312. 838854.i 0.0897446 0.155442i
\(494\) −851000. −0.156896
\(495\) 0 0
\(496\) 1.33837e6 0.244271
\(497\) 157398. 272621.i 0.0285830 0.0495073i
\(498\) 0 0
\(499\) 176639. + 305948.i 0.0317567 + 0.0550042i 0.881467 0.472246i \(-0.156556\pi\)
−0.849710 + 0.527250i \(0.823223\pi\)
\(500\) 975912. + 1.69033e6i 0.174576 + 0.302375i
\(501\) 0 0
\(502\) 3.31739e6 5.74588e6i 0.587539 1.01765i
\(503\) 4.21978e6 0.743651 0.371826 0.928303i \(-0.378732\pi\)
0.371826 + 0.928303i \(0.378732\pi\)
\(504\) 0 0
\(505\) −1.65627e6 −0.289003
\(506\) −1.95372e6 + 3.38394e6i −0.339224 + 0.587552i
\(507\) 0 0
\(508\) 2.50386e6 + 4.33681e6i 0.430477 + 0.745608i
\(509\) −173067. 299761.i −0.0296087 0.0512838i 0.850841 0.525423i \(-0.176093\pi\)
−0.880450 + 0.474139i \(0.842759\pi\)
\(510\) 0 0
\(511\) 648277. 1.12285e6i 0.109827 0.190226i
\(512\) 262144. 0.0441942
\(513\) 0 0
\(514\) −3.17672e6 −0.530361
\(515\) 183624. 318046.i 0.0305078 0.0528411i
\(516\) 0 0
\(517\) −1.34784e6 2.33453e6i −0.221775 0.384125i
\(518\) −1.46772e6 2.54216e6i −0.240335 0.416273i
\(519\) 0 0
\(520\) 77280.0 133853.i 0.0125331 0.0217080i
\(521\) 1.90025e6 0.306703 0.153351 0.988172i \(-0.450993\pi\)
0.153351 + 0.988172i \(0.450993\pi\)
\(522\) 0 0
\(523\) −5.16589e6 −0.825831 −0.412915 0.910769i \(-0.635489\pi\)
−0.412915 + 0.910769i \(0.635489\pi\)
\(524\) 846480. 1.46615e6i 0.134675 0.233265i
\(525\) 0 0
\(526\) −3.18158e6 5.51067e6i −0.501394 0.868440i
\(527\) 2.25065e6 + 3.89825e6i 0.353006 + 0.611424i
\(528\) 0 0
\(529\) −3.32679e6 + 5.76217e6i −0.516876 + 0.895255i
\(530\) 3.08498e6 0.477049
\(531\) 0 0
\(532\) 2.19040e6 0.335540
\(533\) 618585. 1.07142e6i 0.0943151 0.163359i
\(534\) 0 0
\(535\) 1.41082e6 + 2.44362e6i 0.213102 + 0.369104i
\(536\) 413888. + 716875.i 0.0622259 + 0.107778i
\(537\) 0 0
\(538\) −3.15950e6 + 5.47241e6i −0.470611 + 0.815123i
\(539\) −3.05937e6 −0.453586
\(540\) 0 0
\(541\) 4.15125e6 0.609797 0.304899 0.952385i \(-0.401377\pi\)
0.304899 + 0.952385i \(0.401377\pi\)
\(542\) 831524. 1.44024e6i 0.121584 0.210590i
\(543\) 0 0
\(544\) 440832. + 763543.i 0.0638669 + 0.110621i
\(545\) 1.29661e6 + 2.24580e6i 0.186990 + 0.323877i
\(546\) 0 0
\(547\) −4.56262e6 + 7.90269e6i −0.651998 + 1.12929i 0.330640 + 0.943757i \(0.392735\pi\)
−0.982637 + 0.185536i \(0.940598\pi\)
\(548\) −4.55170e6 −0.647473
\(549\) 0 0
\(550\) −2.89872e6 −0.408601
\(551\) −1.04062e6 + 1.80242e6i −0.146021 + 0.252916i
\(552\) 0 0
\(553\) 1.36700e6 + 2.36772e6i 0.190089 + 0.329243i
\(554\) −1.12481e6 1.94823e6i −0.155706 0.269691i
\(555\) 0 0
\(556\) 1.29862e6 2.24928e6i 0.178154 0.308572i
\(557\) −3.78858e6 −0.517415 −0.258707 0.965956i \(-0.583297\pi\)
−0.258707 + 0.965956i \(0.583297\pi\)
\(558\) 0 0
\(559\) 2.26711e6 0.306862
\(560\) −198912. + 344526.i −0.0268035 + 0.0464250i
\(561\) 0 0
\(562\) 4.85325e6 + 8.40608e6i 0.648174 + 1.12267i
\(563\) −2.84333e6 4.92479e6i −0.378056 0.654812i 0.612723 0.790297i \(-0.290074\pi\)
−0.990779 + 0.135485i \(0.956741\pi\)
\(564\) 0 0
\(565\) −1.82741e6 + 3.16517e6i −0.240832 + 0.417134i
\(566\) −4.81173e6 −0.631335
\(567\) 0 0
\(568\) −272256. −0.0354084
\(569\) 5.25194e6 9.09663e6i 0.680048 1.17788i −0.294918 0.955522i \(-0.595292\pi\)
0.974966 0.222354i \(-0.0713742\pi\)
\(570\) 0 0
\(571\) −3.50496e6 6.07077e6i −0.449876 0.779208i 0.548502 0.836149i \(-0.315198\pi\)
−0.998377 + 0.0569418i \(0.981865\pi\)
\(572\) 248400. + 430241.i 0.0317440 + 0.0549822i
\(573\) 0 0
\(574\) −1.59218e6 + 2.75774e6i −0.201704 + 0.349361i
\(575\) −9.71071e6 −1.22485
\(576\) 0 0
\(577\) −3.54196e6 −0.442898 −0.221449 0.975172i \(-0.571079\pi\)
−0.221449 + 0.975172i \(0.571079\pi\)
\(578\) 1.35707e6 2.35052e6i 0.168960 0.292647i
\(579\) 0 0
\(580\) −189000. 327358.i −0.0233288 0.0404066i
\(581\) 2.82739e6 + 4.89719e6i 0.347493 + 0.601875i
\(582\) 0 0
\(583\) −4.95801e6 + 8.58753e6i −0.604138 + 1.04640i
\(584\) −1.12134e6 −0.136053
\(585\) 0 0
\(586\) −2.68988e6 −0.323586
\(587\) −7.63892e6 + 1.32310e7i −0.915032 + 1.58488i −0.108178 + 0.994132i \(0.534502\pi\)
−0.806854 + 0.590751i \(0.798832\pi\)
\(588\) 0 0
\(589\) −4.83590e6 8.37602e6i −0.574366 0.994832i
\(590\) −1.11132e6 1.92486e6i −0.131434 0.227651i
\(591\) 0 0
\(592\) −1.26938e6 + 2.19862e6i −0.148863 + 0.257838i
\(593\) −278457. −0.0325178 −0.0162589 0.999868i \(-0.505176\pi\)
−0.0162589 + 0.999868i \(0.505176\pi\)
\(594\) 0 0
\(595\) −1.33799e6 −0.154939
\(596\) 2.16569e6 3.75108e6i 0.249735 0.432555i
\(597\) 0 0
\(598\) 832140. + 1.44131e6i 0.0951576 + 0.164818i
\(599\) 5.03181e6 + 8.71535e6i 0.573003 + 0.992471i 0.996255 + 0.0864590i \(0.0275551\pi\)
−0.423252 + 0.906012i \(0.639112\pi\)
\(600\) 0 0
\(601\) −6.82889e6 + 1.18280e7i −0.771194 + 1.33575i 0.165715 + 0.986174i \(0.447007\pi\)
−0.936909 + 0.349574i \(0.886326\pi\)
\(602\) −5.83534e6 −0.656259
\(603\) 0 0
\(604\) −269632. −0.0300732
\(605\) 925586. 1.60316e6i 0.102808 0.178069i
\(606\) 0 0
\(607\) 4.47969e6 + 7.75905e6i 0.493487 + 0.854745i 0.999972 0.00750376i \(-0.00238854\pi\)
−0.506484 + 0.862249i \(0.669055\pi\)
\(608\) −947200. 1.64060e6i −0.103916 0.179988i
\(609\) 0 0
\(610\) 2.25872e6 3.91221e6i 0.245775 0.425695i
\(611\) −1.14816e6 −0.124423
\(612\) 0 0
\(613\) 529958. 0.0569627 0.0284813 0.999594i \(-0.490933\pi\)
0.0284813 + 0.999594i \(0.490933\pi\)
\(614\) 5.58975e6 9.68173e6i 0.598372 1.03641i
\(615\) 0 0
\(616\) −639360. 1.10740e6i −0.0678881 0.117586i
\(617\) 2.98514e6 + 5.17041e6i 0.315683 + 0.546779i 0.979582 0.201043i \(-0.0644330\pi\)
−0.663899 + 0.747822i \(0.731100\pi\)
\(618\) 0 0
\(619\) 585668. 1.01441e6i 0.0614363 0.106411i −0.833671 0.552261i \(-0.813765\pi\)
0.895108 + 0.445850i \(0.147099\pi\)
\(620\) 1.75661e6 0.183525
\(621\) 0 0
\(622\) −1.22384e7 −1.26837
\(623\) 1.67821e6 2.90674e6i 0.173231 0.300045i
\(624\) 0 0
\(625\) −2.91287e6 5.04523e6i −0.298277 0.516632i
\(626\) −5.26949e6 9.12702e6i −0.537443 0.930879i
\(627\) 0 0
\(628\) −1.97898e6 + 3.42770e6i −0.200236 + 0.346820i
\(629\) −8.53854e6 −0.860512
\(630\) 0 0
\(631\) −1.49126e7 −1.49101 −0.745504 0.666501i \(-0.767791\pi\)
−0.745504 + 0.666501i \(0.767791\pi\)
\(632\) 1.18227e6 2.04776e6i 0.117740 0.203932i
\(633\) 0 0
\(634\) −1.61675e6 2.80030e6i −0.159743 0.276682i
\(635\) 3.28631e6 + 5.69206e6i 0.323426 + 0.560190i
\(636\) 0 0
\(637\) −651532. + 1.12849e6i −0.0636191 + 0.110192i
\(638\) 1.21500e6 0.118175
\(639\) 0 0
\(640\) 344064. 0.0332039
\(641\) −3.94252e6 + 6.82864e6i −0.378991 + 0.656431i −0.990916 0.134485i \(-0.957062\pi\)
0.611925 + 0.790916i \(0.290395\pi\)
\(642\) 0 0
\(643\) −929020. 1.60911e6i −0.0886130 0.153482i 0.818312 0.574774i \(-0.194910\pi\)
−0.906925 + 0.421292i \(0.861577\pi\)
\(644\) −2.14186e6 3.70980e6i −0.203505 0.352481i
\(645\) 0 0
\(646\) 3.18570e6 5.51779e6i 0.300347 0.520217i
\(647\) −1.54147e6 −0.144768 −0.0723841 0.997377i \(-0.523061\pi\)
−0.0723841 + 0.997377i \(0.523061\pi\)
\(648\) 0 0
\(649\) 7.14420e6 0.665797
\(650\) −617320. + 1.06923e6i −0.0573095 + 0.0992630i
\(651\) 0 0
\(652\) 1.60093e6 + 2.77289e6i 0.147487 + 0.255454i
\(653\) −2.06668e6 3.57959e6i −0.189666 0.328512i 0.755473 0.655180i \(-0.227407\pi\)
−0.945139 + 0.326669i \(0.894074\pi\)
\(654\) 0 0
\(655\) 1.11100e6 1.92432e6i 0.101184 0.175256i
\(656\) 2.75405e6 0.249869
\(657\) 0 0
\(658\) 2.95526e6 0.266092
\(659\) 8.54102e6 1.47935e7i 0.766118 1.32696i −0.173535 0.984828i \(-0.555519\pi\)
0.939653 0.342128i \(-0.111148\pi\)
\(660\) 0 0
\(661\) 3.07322e6 + 5.32298e6i 0.273584 + 0.473861i 0.969777 0.243994i \(-0.0784576\pi\)
−0.696193 + 0.717855i \(0.745124\pi\)
\(662\) 1.70736e6 + 2.95723e6i 0.151419 + 0.262265i
\(663\) 0 0
\(664\) 2.44531e6 4.23540e6i 0.215236 0.372799i
\(665\) 2.87490e6 0.252098
\(666\) 0 0
\(667\) 4.07025e6 0.354247
\(668\) −112944. + 195625.i −0.00979314 + 0.0169622i
\(669\) 0 0
\(670\) 543228. + 940898.i 0.0467515 + 0.0809759i
\(671\) 7.26016e6 + 1.25750e7i 0.622501 + 1.07820i
\(672\) 0 0
\(673\) −4.36248e6 + 7.55604e6i −0.371275 + 0.643067i −0.989762 0.142728i \(-0.954413\pi\)
0.618487 + 0.785795i \(0.287746\pi\)
\(674\) 1.19151e6 0.101030
\(675\) 0 0
\(676\) −5.72909e6 −0.482191
\(677\) −5.92244e6 + 1.02580e7i −0.496625 + 0.860180i −0.999992 0.00389267i \(-0.998761\pi\)
0.503367 + 0.864073i \(0.332094\pi\)
\(678\) 0 0
\(679\) −4.72024e6 8.17569e6i −0.392907 0.680534i
\(680\) 578592. + 1.00215e6i 0.0479844 + 0.0831114i
\(681\) 0 0
\(682\) −2.82312e6 + 4.88979e6i −0.232417 + 0.402559i
\(683\) 4.03085e6 0.330632 0.165316 0.986241i \(-0.447136\pi\)
0.165316 + 0.986241i \(0.447136\pi\)
\(684\) 0 0
\(685\) −5.97410e6 −0.486459
\(686\) 4.16442e6 7.21299e6i 0.337866 0.585201i
\(687\) 0 0
\(688\) 2.52339e6 + 4.37064e6i 0.203242 + 0.352026i
\(689\) 2.11174e6 + 3.65765e6i 0.169470 + 0.293531i
\(690\) 0 0
\(691\) −1.61461e6 + 2.79658e6i −0.128639 + 0.222809i −0.923149 0.384441i \(-0.874394\pi\)
0.794511 + 0.607250i \(0.207727\pi\)
\(692\) −774384. −0.0614740
\(693\) 0 0
\(694\) 354984. 0.0279776
\(695\) 1.70444e6 2.95218e6i 0.133851 0.231836i
\(696\) 0 0
\(697\) 4.63132e6 + 8.02168e6i 0.361096 + 0.625437i
\(698\) −4.72349e6 8.18133e6i −0.366965 0.635602i
\(699\) 0 0
\(700\) 1.58893e6 2.75210e6i 0.122563 0.212285i
\(701\) 1.34398e7 1.03300 0.516499 0.856288i \(-0.327235\pi\)
0.516499 + 0.856288i \(0.327235\pi\)
\(702\) 0 0
\(703\) 1.83464e7 1.40012
\(704\) −552960. + 957755.i −0.0420496 + 0.0728321i
\(705\) 0 0
\(706\) 7.72153e6 + 1.33741e7i 0.583031 + 1.00984i
\(707\) 2.91819e6 + 5.05445e6i 0.219566 + 0.380299i
\(708\) 0 0
\(709\) 1.04150e7 1.80393e7i 0.778114 1.34773i −0.154913 0.987928i \(-0.549510\pi\)
0.933028 0.359805i \(-0.117157\pi\)
\(710\) −357336. −0.0266030
\(711\) 0 0
\(712\) −2.90285e6 −0.214597
\(713\) −9.45745e6 + 1.63808e7i −0.696707 + 1.20673i
\(714\) 0 0
\(715\) 326025. + 564692.i 0.0238499 + 0.0413092i
\(716\) −3.00317e6 5.20164e6i −0.218926 0.379191i
\(717\) 0 0
\(718\) 7.49704e6 1.29852e7i 0.542723 0.940024i
\(719\) 2.57779e7 1.85963 0.929813 0.368032i \(-0.119968\pi\)
0.929813 + 0.368032i \(0.119968\pi\)
\(720\) 0 0
\(721\) −1.29411e6 −0.0927115
\(722\) −1.89280e6 + 3.27843e6i −0.135133 + 0.234058i
\(723\) 0 0
\(724\) −3.52562e6 6.10655e6i −0.249970 0.432961i
\(725\) 1.50975e6 + 2.61496e6i 0.106674 + 0.184765i
\(726\) 0 0
\(727\) 3.62246e6 6.27428e6i 0.254195 0.440279i −0.710481 0.703716i \(-0.751523\pi\)
0.964677 + 0.263437i \(0.0848561\pi\)
\(728\) −544640. −0.0380874
\(729\) 0 0
\(730\) −1.47176e6 −0.102219
\(731\) −8.48688e6 + 1.46997e7i −0.587428 + 1.01745i
\(732\) 0 0
\(733\) 2.82136e6 + 4.88674e6i 0.193954 + 0.335938i 0.946557 0.322536i \(-0.104535\pi\)
−0.752603 + 0.658474i \(0.771202\pi\)
\(734\) 5.32678e6 + 9.22626e6i 0.364943 + 0.632100i
\(735\) 0 0
\(736\) −1.85242e6 + 3.20848e6i −0.126050 + 0.218326i
\(737\) −3.49218e6 −0.236825
\(738\) 0 0
\(739\) 1.72501e7 1.16193 0.580967 0.813927i \(-0.302674\pi\)
0.580967 + 0.813927i \(0.302674\pi\)
\(740\) −1.66606e6 + 2.88569e6i −0.111843 + 0.193718i
\(741\) 0 0
\(742\) −5.43545e6 9.41447e6i −0.362431 0.627749i
\(743\) −6.46732e6 1.12017e7i −0.429786 0.744412i 0.567068 0.823671i \(-0.308078\pi\)
−0.996854 + 0.0792596i \(0.974744\pi\)
\(744\) 0 0
\(745\) 2.84247e6 4.92329e6i 0.187631 0.324986i
\(746\) 3.83948e6 0.252595
\(747\) 0 0
\(748\) −3.71952e6 −0.243071
\(749\) 4.97147e6 8.61084e6i 0.323802 0.560842i
\(750\) 0 0
\(751\) −2.84905e6 4.93469e6i −0.184332 0.319272i 0.759019 0.651068i \(-0.225679\pi\)
−0.943351 + 0.331796i \(0.892345\pi\)
\(752\) −1.27795e6 2.21348e6i −0.0824081 0.142735i
\(753\) 0 0
\(754\) 258750. 448168.i 0.0165749 0.0287086i
\(755\) −353892. −0.0225945
\(756\) 0 0
\(757\) 3.72388e6 0.236187 0.118093 0.993002i \(-0.462322\pi\)
0.118093 + 0.993002i \(0.462322\pi\)
\(758\) 387560. 671274.i 0.0245000 0.0424352i
\(759\) 0 0
\(760\) −1.24320e6 2.15329e6i −0.0780741 0.135228i
\(761\) −8.84733e6 1.53240e7i −0.553797 0.959205i −0.997996 0.0632765i \(-0.979845\pi\)
0.444199 0.895928i \(-0.353488\pi\)
\(762\) 0 0
\(763\) 4.56902e6 7.91377e6i 0.284126 0.492121i
\(764\) 7.79165e6 0.482943
\(765\) 0 0
\(766\) 2.22157e7 1.36801
\(767\) 1.52145e6 2.63523e6i 0.0933833 0.161745i
\(768\) 0 0
\(769\) −8.32902e6 1.44263e7i −0.507900 0.879708i −0.999958 0.00914603i \(-0.997089\pi\)
0.492058 0.870562i \(-0.336245\pi\)
\(770\) −839160. 1.45347e6i −0.0510056 0.0883443i
\(771\) 0 0
\(772\) 833480. 1.44363e6i 0.0503329 0.0871791i
\(773\) 2.04852e6 0.123308 0.0616539 0.998098i \(-0.480362\pi\)
0.0616539 + 0.998098i \(0.480362\pi\)
\(774\) 0 0
\(775\) −1.40320e7 −0.839197
\(776\) −4.08237e6 + 7.07087e6i −0.243365 + 0.421520i