Properties

Label 294.6.e.x.79.1
Level $294$
Weight $6$
Character 294.79
Analytic conductor $47.153$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,6,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, 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("294.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.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: \(47.1528430250\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.6.e.x.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 - 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-51.7487 + 89.6314i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(2.00000 - 3.46410i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-51.7487 + 89.6314i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(206.995 + 358.526i) q^{10} +(-120.095 - 208.011i) q^{11} +(-72.0000 + 124.708i) q^{12} +805.477 q^{13} +931.477 q^{15} +(-128.000 + 221.703i) q^{16} +(646.633 + 1120.00i) q^{17} +(162.000 + 280.592i) q^{18} +(137.688 - 238.483i) q^{19} +1655.96 q^{20} -960.764 q^{22} +(-1898.29 + 3287.93i) q^{23} +(288.000 + 498.831i) q^{24} +(-3793.36 - 6570.30i) q^{25} +(1610.95 - 2790.26i) q^{26} +729.000 q^{27} +1227.52 q^{29} +(1862.95 - 3226.73i) q^{30} +(-2812.43 - 4871.27i) q^{31} +(512.000 + 886.810i) q^{32} +(-1080.86 + 1872.10i) q^{33} +5173.06 q^{34} +1296.00 q^{36} +(4539.25 - 7862.20i) q^{37} +(-550.754 - 953.933i) q^{38} +(-3624.65 - 6278.07i) q^{39} +(3311.92 - 5736.41i) q^{40} -18207.4 q^{41} -11708.2 q^{43} +(-1921.53 + 3328.18i) q^{44} +(-4191.65 - 7260.15i) q^{45} +(7593.15 + 13151.7i) q^{46} +(11524.3 - 19960.7i) q^{47} +2304.00 q^{48} -30346.9 q^{50} +(5819.70 - 10080.0i) q^{51} +(-6443.82 - 11161.0i) q^{52} +(-8831.40 - 15296.4i) q^{53} +(1458.00 - 2525.33i) q^{54} +24859.2 q^{55} -2478.39 q^{57} +(2455.04 - 4252.25i) q^{58} +(-9188.15 - 15914.3i) q^{59} +(-7451.82 - 12906.9i) q^{60} +(-5662.04 + 9806.95i) q^{61} -22499.5 q^{62} +4096.00 q^{64} +(-41682.4 + 72196.1i) q^{65} +(4323.44 + 7488.41i) q^{66} +(-18039.7 - 31245.6i) q^{67} +(10346.1 - 17920.0i) q^{68} +34169.2 q^{69} -63434.2 q^{71} +(2592.00 - 4489.48i) q^{72} +(26491.2 + 45884.1i) q^{73} +(-18157.0 - 31448.8i) q^{74} +(-34140.3 + 59132.7i) q^{75} -4406.03 q^{76} -28997.2 q^{78} +(24282.0 - 42057.7i) q^{79} +(-13247.7 - 22945.6i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-36414.8 + 63072.3i) q^{82} +113161. q^{83} -133850. q^{85} +(-23416.4 + 40558.5i) q^{86} +(-5523.83 - 9567.56i) q^{87} +(7686.11 + 13312.7i) q^{88} +(-54182.9 + 93847.6i) q^{89} -33533.2 q^{90} +60745.2 q^{92} +(-25311.9 + 43841.5i) q^{93} +(-46097.2 - 79842.7i) q^{94} +(14250.4 + 24682.4i) q^{95} +(4608.00 - 7981.29i) q^{96} +99641.2 q^{97} +19455.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{2} - 18 q^{3} - 32 q^{4} - 108 q^{5} - 144 q^{6} - 256 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{2} - 18 q^{3} - 32 q^{4} - 108 q^{5} - 144 q^{6} - 256 q^{8} - 162 q^{9} + 432 q^{10} - 124 q^{11} - 288 q^{12} + 1440 q^{13} + 1944 q^{15} - 512 q^{16} + 1260 q^{17} + 648 q^{18} - 360 q^{19} + 3456 q^{20} - 992 q^{22} - 6524 q^{23} + 1152 q^{24} - 4482 q^{25} + 2880 q^{26} + 2916 q^{27} + 14176 q^{29} + 3888 q^{30} - 5904 q^{31} + 2048 q^{32} - 1116 q^{33} + 10080 q^{34} + 5184 q^{36} + 6040 q^{37} + 1440 q^{38} - 6480 q^{39} + 6912 q^{40} - 34776 q^{41} - 1216 q^{43} - 1984 q^{44} - 8748 q^{45} + 26096 q^{46} + 30456 q^{47} + 9216 q^{48} - 35856 q^{50} + 11340 q^{51} - 11520 q^{52} - 3964 q^{53} + 5832 q^{54} + 48672 q^{55} + 6480 q^{57} + 28352 q^{58} - 40752 q^{59} - 15552 q^{60} + 1368 q^{61} - 47232 q^{62} + 16384 q^{64} - 82980 q^{65} + 4464 q^{66} + 16224 q^{67} + 20160 q^{68} + 117432 q^{69} - 6408 q^{71} + 10368 q^{72} - 23976 q^{73} - 24160 q^{74} - 40338 q^{75} + 11520 q^{76} - 51840 q^{78} + 82160 q^{79} - 27648 q^{80} - 13122 q^{81} - 69552 q^{82} + 347472 q^{83} - 267400 q^{85} - 2432 q^{86} - 63792 q^{87} + 7936 q^{88} - 200556 q^{89} - 69984 q^{90} + 208768 q^{92} - 53136 q^{93} - 121824 q^{94} + 25640 q^{95} + 18432 q^{96} + 503856 q^{97} + 20088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 3.46410i 0.353553 0.612372i
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) −8.00000 13.8564i −0.250000 0.433013i
\(5\) −51.7487 + 89.6314i −0.925710 + 1.60338i −0.135294 + 0.990806i \(0.543198\pi\)
−0.790416 + 0.612570i \(0.790136\pi\)
\(6\) −36.0000 −0.408248
\(7\) 0 0
\(8\) −64.0000 −0.353553
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 206.995 + 358.526i 0.654576 + 1.13376i
\(11\) −120.095 208.011i −0.299257 0.518329i 0.676709 0.736251i \(-0.263406\pi\)
−0.975966 + 0.217922i \(0.930072\pi\)
\(12\) −72.0000 + 124.708i −0.144338 + 0.250000i
\(13\) 805.477 1.32189 0.660944 0.750435i \(-0.270156\pi\)
0.660944 + 0.750435i \(0.270156\pi\)
\(14\) 0 0
\(15\) 931.477 1.06892
\(16\) −128.000 + 221.703i −0.125000 + 0.216506i
\(17\) 646.633 + 1120.00i 0.542670 + 0.939932i 0.998750 + 0.0499927i \(0.0159198\pi\)
−0.456080 + 0.889939i \(0.650747\pi\)
\(18\) 162.000 + 280.592i 0.117851 + 0.204124i
\(19\) 137.688 238.483i 0.0875011 0.151556i −0.818953 0.573860i \(-0.805445\pi\)
0.906454 + 0.422304i \(0.138779\pi\)
\(20\) 1655.96 0.925710
\(21\) 0 0
\(22\) −960.764 −0.423214
\(23\) −1898.29 + 3287.93i −0.748242 + 1.29599i 0.200423 + 0.979710i \(0.435769\pi\)
−0.948665 + 0.316284i \(0.897565\pi\)
\(24\) 288.000 + 498.831i 0.102062 + 0.176777i
\(25\) −3793.36 6570.30i −1.21388 2.10250i
\(26\) 1610.95 2790.26i 0.467358 0.809488i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 1227.52 0.271040 0.135520 0.990775i \(-0.456730\pi\)
0.135520 + 0.990775i \(0.456730\pi\)
\(30\) 1862.95 3226.73i 0.377919 0.654576i
\(31\) −2812.43 4871.27i −0.525627 0.910413i −0.999554 0.0298489i \(-0.990497\pi\)
0.473927 0.880564i \(-0.342836\pi\)
\(32\) 512.000 + 886.810i 0.0883883 + 0.153093i
\(33\) −1080.86 + 1872.10i −0.172776 + 0.299257i
\(34\) 5173.06 0.767451
\(35\) 0 0
\(36\) 1296.00 0.166667
\(37\) 4539.25 7862.20i 0.545104 0.944148i −0.453496 0.891258i \(-0.649824\pi\)
0.998600 0.0528897i \(-0.0168432\pi\)
\(38\) −550.754 953.933i −0.0618726 0.107166i
\(39\) −3624.65 6278.07i −0.381596 0.660944i
\(40\) 3311.92 5736.41i 0.327288 0.566879i
\(41\) −18207.4 −1.69156 −0.845782 0.533528i \(-0.820866\pi\)
−0.845782 + 0.533528i \(0.820866\pi\)
\(42\) 0 0
\(43\) −11708.2 −0.965650 −0.482825 0.875717i \(-0.660389\pi\)
−0.482825 + 0.875717i \(0.660389\pi\)
\(44\) −1921.53 + 3328.18i −0.149629 + 0.259164i
\(45\) −4191.65 7260.15i −0.308570 0.534459i
\(46\) 7593.15 + 13151.7i 0.529087 + 0.916406i
\(47\) 11524.3 19960.7i 0.760974 1.31805i −0.181375 0.983414i \(-0.558055\pi\)
0.942349 0.334632i \(-0.108612\pi\)
\(48\) 2304.00 0.144338
\(49\) 0 0
\(50\) −30346.9 −1.71668
\(51\) 5819.70 10080.0i 0.313311 0.542670i
\(52\) −6443.82 11161.0i −0.330472 0.572395i
\(53\) −8831.40 15296.4i −0.431857 0.747998i 0.565176 0.824970i \(-0.308808\pi\)
−0.997033 + 0.0769720i \(0.975475\pi\)
\(54\) 1458.00 2525.33i 0.0680414 0.117851i
\(55\) 24859.2 1.10810
\(56\) 0 0
\(57\) −2478.39 −0.101038
\(58\) 2455.04 4252.25i 0.0958270 0.165977i
\(59\) −9188.15 15914.3i −0.343636 0.595194i 0.641469 0.767149i \(-0.278325\pi\)
−0.985105 + 0.171954i \(0.944992\pi\)
\(60\) −7451.82 12906.9i −0.267229 0.462855i
\(61\) −5662.04 + 9806.95i −0.194827 + 0.337450i −0.946844 0.321694i \(-0.895748\pi\)
0.752017 + 0.659144i \(0.229081\pi\)
\(62\) −22499.5 −0.743349
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −41682.4 + 72196.1i −1.22369 + 2.11948i
\(66\) 4323.44 + 7488.41i 0.122171 + 0.211607i
\(67\) −18039.7 31245.6i −0.490955 0.850359i 0.508991 0.860772i \(-0.330019\pi\)
−0.999946 + 0.0104130i \(0.996685\pi\)
\(68\) 10346.1 17920.0i 0.271335 0.469966i
\(69\) 34169.2 0.863996
\(70\) 0 0
\(71\) −63434.2 −1.49341 −0.746703 0.665158i \(-0.768364\pi\)
−0.746703 + 0.665158i \(0.768364\pi\)
\(72\) 2592.00 4489.48i 0.0589256 0.102062i
\(73\) 26491.2 + 45884.1i 0.581828 + 1.00776i 0.995263 + 0.0972215i \(0.0309955\pi\)
−0.413435 + 0.910534i \(0.635671\pi\)
\(74\) −18157.0 31448.8i −0.385447 0.667613i
\(75\) −34140.3 + 59132.7i −0.700832 + 1.21388i
\(76\) −4406.03 −0.0875011
\(77\) 0 0
\(78\) −28997.2 −0.539659
\(79\) 24282.0 42057.7i 0.437741 0.758189i −0.559774 0.828645i \(-0.689112\pi\)
0.997515 + 0.0704561i \(0.0224455\pi\)
\(80\) −13247.7 22945.6i −0.231427 0.400844i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) −36414.8 + 63072.3i −0.598058 + 1.03587i
\(83\) 113161. 1.80303 0.901513 0.432753i \(-0.142458\pi\)
0.901513 + 0.432753i \(0.142458\pi\)
\(84\) 0 0
\(85\) −133850. −2.00942
\(86\) −23416.4 + 40558.5i −0.341409 + 0.591337i
\(87\) −5523.83 9567.56i −0.0782424 0.135520i
\(88\) 7686.11 + 13312.7i 0.105803 + 0.183257i
\(89\) −54182.9 + 93847.6i −0.725083 + 1.25588i 0.233857 + 0.972271i \(0.424865\pi\)
−0.958940 + 0.283609i \(0.908468\pi\)
\(90\) −33533.2 −0.436384
\(91\) 0 0
\(92\) 60745.2 0.748242
\(93\) −25311.9 + 43841.5i −0.303471 + 0.525627i
\(94\) −46097.2 79842.7i −0.538090 0.931999i
\(95\) 14250.4 + 24682.4i 0.162001 + 0.280594i
\(96\) 4608.00 7981.29i 0.0510310 0.0883883i
\(97\) 99641.2 1.07525 0.537625 0.843184i \(-0.319321\pi\)
0.537625 + 0.843184i \(0.319321\pi\)
\(98\) 0 0
\(99\) 19455.5 0.199505
\(100\) −60693.8 + 105125.i −0.606938 + 1.05125i
\(101\) −82599.9 143067.i −0.805705 1.39552i −0.915814 0.401603i \(-0.868453\pi\)
0.110109 0.993920i \(-0.464880\pi\)
\(102\) −23278.8 40320.0i −0.221544 0.383725i
\(103\) 53623.6 92878.8i 0.498038 0.862628i −0.501959 0.864891i \(-0.667387\pi\)
0.999997 + 0.00226355i \(0.000720512\pi\)
\(104\) −51550.5 −0.467358
\(105\) 0 0
\(106\) −70651.2 −0.610738
\(107\) 48711.2 84370.2i 0.411310 0.712409i −0.583723 0.811953i \(-0.698405\pi\)
0.995033 + 0.0995431i \(0.0317381\pi\)
\(108\) −5832.00 10101.3i −0.0481125 0.0833333i
\(109\) −29653.6 51361.5i −0.239062 0.414068i 0.721383 0.692536i \(-0.243507\pi\)
−0.960445 + 0.278468i \(0.910173\pi\)
\(110\) 49718.3 86114.6i 0.391773 0.678571i
\(111\) −81706.4 −0.629432
\(112\) 0 0
\(113\) 157268. 1.15863 0.579313 0.815105i \(-0.303321\pi\)
0.579313 + 0.815105i \(0.303321\pi\)
\(114\) −4956.78 + 8585.40i −0.0357222 + 0.0618726i
\(115\) −196468. 340292.i −1.38531 2.39943i
\(116\) −9820.15 17009.0i −0.0677599 0.117364i
\(117\) −32621.8 + 56502.7i −0.220315 + 0.381596i
\(118\) −73505.2 −0.485974
\(119\) 0 0
\(120\) −59614.5 −0.377919
\(121\) 51679.7 89511.8i 0.320890 0.555798i
\(122\) 22648.2 + 39227.8i 0.137763 + 0.238613i
\(123\) 81933.4 + 141913.i 0.488313 + 0.845782i
\(124\) −44998.9 + 77940.4i −0.262814 + 0.455206i
\(125\) 461778. 2.64337
\(126\) 0 0
\(127\) −92477.3 −0.508775 −0.254387 0.967102i \(-0.581874\pi\)
−0.254387 + 0.967102i \(0.581874\pi\)
\(128\) 8192.00 14189.0i 0.0441942 0.0765466i
\(129\) 52687.0 + 91256.5i 0.278759 + 0.482825i
\(130\) 166730. + 288784.i 0.865276 + 1.49870i
\(131\) 36164.2 62638.2i 0.184120 0.318905i −0.759160 0.650904i \(-0.774390\pi\)
0.943280 + 0.331999i \(0.107723\pi\)
\(132\) 34587.5 0.172776
\(133\) 0 0
\(134\) −144317. −0.694315
\(135\) −37724.8 + 65341.3i −0.178153 + 0.308570i
\(136\) −41384.5 71680.1i −0.191863 0.332316i
\(137\) −112831. 195429.i −0.513602 0.889585i −0.999876 0.0157784i \(-0.994977\pi\)
0.486273 0.873807i \(-0.338356\pi\)
\(138\) 68338.3 118365.i 0.305469 0.529087i
\(139\) −327971. −1.43979 −0.719894 0.694084i \(-0.755810\pi\)
−0.719894 + 0.694084i \(0.755810\pi\)
\(140\) 0 0
\(141\) −207437. −0.878697
\(142\) −126868. + 219743.i −0.527999 + 0.914521i
\(143\) −96734.2 167548.i −0.395585 0.685173i
\(144\) −10368.0 17957.9i −0.0416667 0.0721688i
\(145\) −63522.5 + 110024.i −0.250904 + 0.434579i
\(146\) 211930. 0.822829
\(147\) 0 0
\(148\) −145256. −0.545104
\(149\) −82005.4 + 142038.i −0.302606 + 0.524128i −0.976725 0.214494i \(-0.931190\pi\)
0.674120 + 0.738622i \(0.264523\pi\)
\(150\) 136561. + 236531.i 0.495563 + 0.858340i
\(151\) −31154.4 53961.0i −0.111193 0.192592i 0.805059 0.593195i \(-0.202134\pi\)
−0.916251 + 0.400604i \(0.868800\pi\)
\(152\) −8812.06 + 15262.9i −0.0309363 + 0.0535832i
\(153\) −104755. −0.361780
\(154\) 0 0
\(155\) 582159. 1.94631
\(156\) −57994.4 + 100449.i −0.190798 + 0.330472i
\(157\) 119903. + 207679.i 0.388224 + 0.672423i 0.992211 0.124571i \(-0.0397555\pi\)
−0.603987 + 0.796994i \(0.706422\pi\)
\(158\) −97128.0 168231.i −0.309529 0.536121i
\(159\) −79482.6 + 137668.i −0.249333 + 0.431857i
\(160\) −105981. −0.327288
\(161\) 0 0
\(162\) −26244.0 −0.0785674
\(163\) 218397. 378275.i 0.643841 1.11516i −0.340727 0.940162i \(-0.610673\pi\)
0.984568 0.175002i \(-0.0559933\pi\)
\(164\) 145659. + 252289.i 0.422891 + 0.732469i
\(165\) −111866. 193758.i −0.319881 0.554051i
\(166\) 226322. 392001.i 0.637466 1.10412i
\(167\) 38846.7 0.107786 0.0538931 0.998547i \(-0.482837\pi\)
0.0538931 + 0.998547i \(0.482837\pi\)
\(168\) 0 0
\(169\) 277501. 0.747390
\(170\) −267700. + 463669.i −0.710437 + 1.23051i
\(171\) 11152.8 + 19317.1i 0.0291670 + 0.0505188i
\(172\) 93665.7 + 162234.i 0.241412 + 0.418139i
\(173\) −198139. + 343186.i −0.503331 + 0.871795i 0.496661 + 0.867944i \(0.334559\pi\)
−0.999993 + 0.00385097i \(0.998774\pi\)
\(174\) −44190.7 −0.110652
\(175\) 0 0
\(176\) 61488.9 0.149629
\(177\) −82693.4 + 143229.i −0.198398 + 0.343636i
\(178\) 216732. + 375390.i 0.512711 + 0.888041i
\(179\) −121942. 211209.i −0.284459 0.492698i 0.688019 0.725693i \(-0.258481\pi\)
−0.972478 + 0.232995i \(0.925147\pi\)
\(180\) −67066.4 + 116162.i −0.154285 + 0.267229i
\(181\) −299273. −0.679002 −0.339501 0.940606i \(-0.610258\pi\)
−0.339501 + 0.940606i \(0.610258\pi\)
\(182\) 0 0
\(183\) 101917. 0.224967
\(184\) 121490. 210427.i 0.264544 0.458203i
\(185\) 469800. + 813718.i 1.00922 + 1.74801i
\(186\) 101248. + 175366.i 0.214586 + 0.371675i
\(187\) 155315. 269014.i 0.324796 0.562563i
\(188\) −368778. −0.760974
\(189\) 0 0
\(190\) 114003. 0.229104
\(191\) 388498. 672899.i 0.770558 1.33465i −0.166699 0.986008i \(-0.553311\pi\)
0.937257 0.348639i \(-0.113356\pi\)
\(192\) −18432.0 31925.2i −0.0360844 0.0625000i
\(193\) −138211. 239388.i −0.267084 0.462603i 0.701023 0.713138i \(-0.252727\pi\)
−0.968108 + 0.250535i \(0.919393\pi\)
\(194\) 199282. 345167.i 0.380159 0.658454i
\(195\) 750284. 1.41299
\(196\) 0 0
\(197\) −131615. −0.241624 −0.120812 0.992675i \(-0.538550\pi\)
−0.120812 + 0.992675i \(0.538550\pi\)
\(198\) 38910.9 67395.7i 0.0705356 0.122171i
\(199\) −282480. 489270.i −0.505656 0.875822i −0.999979 0.00654355i \(-0.997917\pi\)
0.494322 0.869279i \(-0.335416\pi\)
\(200\) 242775. + 420499.i 0.429170 + 0.743344i
\(201\) −162357. + 281211.i −0.283453 + 0.490955i
\(202\) −660799. −1.13944
\(203\) 0 0
\(204\) −186230. −0.313311
\(205\) 942211. 1.63196e6i 1.56590 2.71221i
\(206\) −214494. 371515.i −0.352166 0.609970i
\(207\) −153761. 266322.i −0.249414 0.431998i
\(208\) −103101. + 178576.i −0.165236 + 0.286197i
\(209\) −66143.0 −0.104741
\(210\) 0 0
\(211\) 313637. 0.484977 0.242489 0.970154i \(-0.422036\pi\)
0.242489 + 0.970154i \(0.422036\pi\)
\(212\) −141302. + 244743.i −0.215928 + 0.373999i
\(213\) 285454. + 494421.i 0.431109 + 0.746703i
\(214\) −194845. 337481.i −0.290840 0.503750i
\(215\) 605886. 1.04942e6i 0.893911 1.54830i
\(216\) −46656.0 −0.0680414
\(217\) 0 0
\(218\) −237229. −0.338085
\(219\) 238421. 412957.i 0.335918 0.581828i
\(220\) −198873. 344459.i −0.277025 0.479822i
\(221\) 520848. + 902136.i 0.717349 + 1.24248i
\(222\) −163413. + 283039.i −0.222538 + 0.385447i
\(223\) −279483. −0.376351 −0.188176 0.982135i \(-0.560257\pi\)
−0.188176 + 0.982135i \(0.560257\pi\)
\(224\) 0 0
\(225\) 614525. 0.809251
\(226\) 314535. 544791.i 0.409636 0.709511i
\(227\) 611754. + 1.05959e6i 0.787974 + 1.36481i 0.927206 + 0.374551i \(0.122203\pi\)
−0.139232 + 0.990260i \(0.544463\pi\)
\(228\) 19827.1 + 34341.6i 0.0252594 + 0.0437505i
\(229\) −127387. + 220641.i −0.160523 + 0.278034i −0.935056 0.354499i \(-0.884651\pi\)
0.774533 + 0.632533i \(0.217985\pi\)
\(230\) −1.57174e6 −1.95912
\(231\) 0 0
\(232\) −78561.2 −0.0958270
\(233\) −373086. + 646204.i −0.450215 + 0.779794i −0.998399 0.0565630i \(-0.981986\pi\)
0.548184 + 0.836357i \(0.315319\pi\)
\(234\) 130487. + 226011.i 0.155786 + 0.269829i
\(235\) 1.19274e6 + 2.06588e6i 1.40888 + 2.44026i
\(236\) −147010. + 254630.i −0.171818 + 0.297597i
\(237\) −437076. −0.505459
\(238\) 0 0
\(239\) 321036. 0.363546 0.181773 0.983341i \(-0.441816\pi\)
0.181773 + 0.983341i \(0.441816\pi\)
\(240\) −119229. + 206511.i −0.133615 + 0.231427i
\(241\) −621268. 1.07607e6i −0.689027 1.19343i −0.972153 0.234348i \(-0.924705\pi\)
0.283125 0.959083i \(-0.408629\pi\)
\(242\) −206719. 358047.i −0.226904 0.393008i
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) 181185. 0.194827
\(245\) 0 0
\(246\) 655467. 0.690578
\(247\) 110905. 192093.i 0.115667 0.200341i
\(248\) 179996. + 311762.i 0.185837 + 0.321880i
\(249\) −509225. 882003.i −0.520489 0.901513i
\(250\) 923555. 1.59964e6i 0.934572 1.61873i
\(251\) 690235. 0.691532 0.345766 0.938321i \(-0.387619\pi\)
0.345766 + 0.938321i \(0.387619\pi\)
\(252\) 0 0
\(253\) 911902. 0.895668
\(254\) −184955. + 320351.i −0.179879 + 0.311560i
\(255\) 602324. + 1.04326e6i 0.580069 + 1.00471i
\(256\) −32768.0 56755.8i −0.0312500 0.0541266i
\(257\) −6893.35 + 11939.6i −0.00651024 + 0.0112761i −0.869262 0.494351i \(-0.835406\pi\)
0.862752 + 0.505627i \(0.168739\pi\)
\(258\) 421496. 0.394225
\(259\) 0 0
\(260\) 1.33384e6 1.22369
\(261\) −49714.5 + 86108.0i −0.0451733 + 0.0782424i
\(262\) −144657. 250553.i −0.130192 0.225500i
\(263\) −287417. 497820.i −0.256226 0.443796i 0.709002 0.705206i \(-0.249146\pi\)
−0.965228 + 0.261411i \(0.915812\pi\)
\(264\) 69175.0 119815.i 0.0610857 0.105803i
\(265\) 1.82806e6 1.59910
\(266\) 0 0
\(267\) 975293. 0.837253
\(268\) −288635. + 499930.i −0.245477 + 0.425179i
\(269\) 559464. + 969020.i 0.471402 + 0.816492i 0.999465 0.0327131i \(-0.0104147\pi\)
−0.528063 + 0.849205i \(0.677081\pi\)
\(270\) 150899. + 261365.i 0.125973 + 0.218192i
\(271\) −347435. + 601775.i −0.287376 + 0.497749i −0.973183 0.230034i \(-0.926116\pi\)
0.685807 + 0.727784i \(0.259449\pi\)
\(272\) −331076. −0.271335
\(273\) 0 0
\(274\) −902648. −0.726343
\(275\) −911131. + 1.57813e6i −0.726523 + 1.25837i
\(276\) −273353. 473462.i −0.215999 0.374121i
\(277\) 418827. + 725429.i 0.327971 + 0.568062i 0.982109 0.188313i \(-0.0603019\pi\)
−0.654138 + 0.756375i \(0.726969\pi\)
\(278\) −655942. + 1.13613e6i −0.509042 + 0.881687i
\(279\) 455614. 0.350418
\(280\) 0 0
\(281\) −917687. −0.693312 −0.346656 0.937992i \(-0.612683\pi\)
−0.346656 + 0.937992i \(0.612683\pi\)
\(282\) −414875. + 718584.i −0.310666 + 0.538090i
\(283\) 207632. + 359629.i 0.154109 + 0.266924i 0.932734 0.360565i \(-0.117416\pi\)
−0.778625 + 0.627489i \(0.784083\pi\)
\(284\) 507474. + 878971.i 0.373352 + 0.646664i
\(285\) 128254. 222142.i 0.0935314 0.162001i
\(286\) −773873. −0.559442
\(287\) 0 0
\(288\) −82944.0 −0.0589256
\(289\) −126340. + 218828.i −0.0889809 + 0.154119i
\(290\) 254090. + 440097.i 0.177416 + 0.307293i
\(291\) −448386. 776627.i −0.310398 0.537625i
\(292\) 423859. 734145.i 0.290914 0.503878i
\(293\) −1.21491e6 −0.826752 −0.413376 0.910561i \(-0.635650\pi\)
−0.413376 + 0.910561i \(0.635650\pi\)
\(294\) 0 0
\(295\) 1.90190e6 1.27243
\(296\) −290512. + 503181.i −0.192723 + 0.333807i
\(297\) −87549.6 151640.i −0.0575921 0.0997525i
\(298\) 328022. + 568150.i 0.213974 + 0.370615i
\(299\) −1.52903e6 + 2.64835e6i −0.989093 + 1.71316i
\(300\) 1.09249e6 0.700832
\(301\) 0 0
\(302\) −249235. −0.157250
\(303\) −743399. + 1.28761e6i −0.465174 + 0.805705i
\(304\) 35248.2 + 61051.7i 0.0218753 + 0.0378891i
\(305\) −586007. 1.01499e6i −0.360706 0.624761i
\(306\) −209509. + 362880.i −0.127908 + 0.221544i
\(307\) −2.60119e6 −1.57517 −0.787584 0.616207i \(-0.788668\pi\)
−0.787584 + 0.616207i \(0.788668\pi\)
\(308\) 0 0
\(309\) −965225. −0.575085
\(310\) 1.16432e6 2.01666e6i 0.688125 1.19187i
\(311\) 409582. + 709417.i 0.240126 + 0.415911i 0.960750 0.277415i \(-0.0894778\pi\)
−0.720624 + 0.693326i \(0.756144\pi\)
\(312\) 231977. + 401797.i 0.134915 + 0.233679i
\(313\) 440970. 763782.i 0.254418 0.440665i −0.710319 0.703880i \(-0.751449\pi\)
0.964737 + 0.263215i \(0.0847828\pi\)
\(314\) 959226. 0.549031
\(315\) 0 0
\(316\) −777024. −0.437741
\(317\) 802191. 1.38944e6i 0.448363 0.776587i −0.549917 0.835219i \(-0.685341\pi\)
0.998280 + 0.0586323i \(0.0186740\pi\)
\(318\) 317930. + 550672.i 0.176305 + 0.305369i
\(319\) −147419. 255338.i −0.0811106 0.140488i
\(320\) −211963. + 367130.i −0.115714 + 0.200422i
\(321\) −876801. −0.474940
\(322\) 0 0
\(323\) 356135. 0.189937
\(324\) −52488.0 + 90911.9i −0.0277778 + 0.0481125i
\(325\) −3.05547e6 5.29223e6i −1.60461 2.77927i
\(326\) −873589. 1.51310e6i −0.455264 0.788540i
\(327\) −266882. + 462254.i −0.138023 + 0.239062i
\(328\) 1.16527e6 0.598058
\(329\) 0 0
\(330\) −894929. −0.452381
\(331\) −501540. + 868693.i −0.251614 + 0.435809i −0.963970 0.266009i \(-0.914295\pi\)
0.712356 + 0.701818i \(0.247628\pi\)
\(332\) −905288. 1.56801e6i −0.450756 0.780733i
\(333\) 367679. + 636839.i 0.181701 + 0.314716i
\(334\) 77693.4 134569.i 0.0381082 0.0660053i
\(335\) 3.73412e6 1.81793
\(336\) 0 0
\(337\) −2.62317e6 −1.25821 −0.629103 0.777322i \(-0.716578\pi\)
−0.629103 + 0.777322i \(0.716578\pi\)
\(338\) 555001. 961290.i 0.264242 0.457681i
\(339\) −707705. 1.22578e6i −0.334467 0.579313i
\(340\) 1.07080e6 + 1.85468e6i 0.502355 + 0.870104i
\(341\) −675521. + 1.17004e6i −0.314596 + 0.544896i
\(342\) 89222.1 0.0412484
\(343\) 0 0
\(344\) 749326. 0.341409
\(345\) −1.76821e6 + 3.06263e6i −0.799809 + 1.38531i
\(346\) 792555. + 1.37274e6i 0.355909 + 0.616452i
\(347\) −113117. 195924.i −0.0504317 0.0873503i 0.839708 0.543039i \(-0.182726\pi\)
−0.890139 + 0.455689i \(0.849393\pi\)
\(348\) −88381.3 + 153081.i −0.0391212 + 0.0677599i
\(349\) −1.46280e6 −0.642866 −0.321433 0.946932i \(-0.604165\pi\)
−0.321433 + 0.946932i \(0.604165\pi\)
\(350\) 0 0
\(351\) 587193. 0.254398
\(352\) 122978. 213004.i 0.0529017 0.0916285i
\(353\) −1.40479e6 2.43316e6i −0.600031 1.03928i −0.992816 0.119653i \(-0.961822\pi\)
0.392785 0.919630i \(-0.371512\pi\)
\(354\) 330773. + 572916.i 0.140289 + 0.242987i
\(355\) 3.28264e6 5.68570e6i 1.38246 2.39449i
\(356\) 1.73385e6 0.725083
\(357\) 0 0
\(358\) −975534. −0.402286
\(359\) 1.84950e6 3.20343e6i 0.757388 1.31183i −0.186790 0.982400i \(-0.559808\pi\)
0.944178 0.329435i \(-0.106858\pi\)
\(360\) 268265. + 464649.i 0.109096 + 0.188960i
\(361\) 1.20013e6 + 2.07869e6i 0.484687 + 0.839503i
\(362\) −598546. + 1.03671e6i −0.240063 + 0.415802i
\(363\) −930234. −0.370532
\(364\) 0 0
\(365\) −5.48354e6 −2.15441
\(366\) 203834. 353050.i 0.0795377 0.137763i
\(367\) −584623. 1.01260e6i −0.226574 0.392438i 0.730216 0.683216i \(-0.239419\pi\)
−0.956791 + 0.290778i \(0.906086\pi\)
\(368\) −485961. 841710.i −0.187061 0.323998i
\(369\) 737400. 1.27721e6i 0.281927 0.488313i
\(370\) 3.75840e6 1.42725
\(371\) 0 0
\(372\) 809980. 0.303471
\(373\) 2.28845e6 3.96371e6i 0.851666 1.47513i −0.0280372 0.999607i \(-0.508926\pi\)
0.879704 0.475523i \(-0.157741\pi\)
\(374\) −621262. 1.07606e6i −0.229665 0.397792i
\(375\) −2.07800e6 3.59920e6i −0.763075 1.32168i
\(376\) −737555. + 1.27748e6i −0.269045 + 0.466000i
\(377\) 988738. 0.358284
\(378\) 0 0
\(379\) −2.35520e6 −0.842229 −0.421114 0.907007i \(-0.638361\pi\)
−0.421114 + 0.907007i \(0.638361\pi\)
\(380\) 228006. 394919.i 0.0810006 0.140297i
\(381\) 416148. + 720789.i 0.146871 + 0.254387i
\(382\) −1.55399e6 2.69159e6i −0.544867 0.943738i
\(383\) −1.51973e6 + 2.63225e6i −0.529382 + 0.916916i 0.470031 + 0.882650i \(0.344243\pi\)
−0.999413 + 0.0342662i \(0.989091\pi\)
\(384\) −147456. −0.0510310
\(385\) 0 0
\(386\) −1.10568e6 −0.377714
\(387\) 474183. 821309.i 0.160942 0.278759i
\(388\) −797130. 1.38067e6i −0.268813 0.465597i
\(389\) 229637. + 397742.i 0.0769426 + 0.133269i 0.901929 0.431883i \(-0.142151\pi\)
−0.824987 + 0.565152i \(0.808818\pi\)
\(390\) 1.50057e6 2.59906e6i 0.499567 0.865276i
\(391\) −4.90998e6 −1.62419
\(392\) 0 0
\(393\) −650956. −0.212603
\(394\) −263231. + 455929.i −0.0854272 + 0.147964i
\(395\) 2.51313e6 + 4.35286e6i 0.810441 + 1.40373i
\(396\) −155644. 269583.i −0.0498762 0.0863882i
\(397\) −2.71250e6 + 4.69819e6i −0.863761 + 1.49608i 0.00451026 + 0.999990i \(0.498564\pi\)
−0.868272 + 0.496089i \(0.834769\pi\)
\(398\) −2.25984e6 −0.715106
\(399\) 0 0
\(400\) 1.94220e6 0.606938
\(401\) −1.05564e6 + 1.82841e6i −0.327833 + 0.567824i −0.982082 0.188456i \(-0.939652\pi\)
0.654248 + 0.756280i \(0.272985\pi\)
\(402\) 649428. + 1.12484e6i 0.200432 + 0.347158i
\(403\) −2.26535e6 3.92370e6i −0.694821 1.20346i
\(404\) −1.32160e6 + 2.28908e6i −0.402853 + 0.697761i
\(405\) 679047. 0.205713
\(406\) 0 0
\(407\) −2.18057e6 −0.652506
\(408\) −372461. + 645121.i −0.110772 + 0.191863i
\(409\) −1.27872e6 2.21481e6i −0.377980 0.654680i 0.612788 0.790247i \(-0.290048\pi\)
−0.990768 + 0.135567i \(0.956714\pi\)
\(410\) −3.76884e6 6.52783e6i −1.10726 1.91783i
\(411\) −1.01548e6 + 1.75886e6i −0.296528 + 0.513602i
\(412\) −1.71595e6 −0.498038
\(413\) 0 0
\(414\) −1.23009e6 −0.352725
\(415\) −5.85594e6 + 1.01428e7i −1.66908 + 2.89093i
\(416\) 412404. + 714305.i 0.116840 + 0.202372i
\(417\) 1.47587e6 + 2.55628e6i 0.415631 + 0.719894i
\(418\) −132286. + 229126.i −0.0370317 + 0.0641407i
\(419\) 2.17401e6 0.604959 0.302480 0.953156i \(-0.402186\pi\)
0.302480 + 0.953156i \(0.402186\pi\)
\(420\) 0 0
\(421\) −5.47930e6 −1.50668 −0.753338 0.657633i \(-0.771558\pi\)
−0.753338 + 0.657633i \(0.771558\pi\)
\(422\) 627274. 1.08647e6i 0.171465 0.296987i
\(423\) 933468. + 1.61681e6i 0.253658 + 0.439349i
\(424\) 565210. + 978972.i 0.152684 + 0.264457i
\(425\) 4.90583e6 8.49714e6i 1.31747 2.28192i
\(426\) 2.28363e6 0.609680
\(427\) 0 0
\(428\) −1.55876e6 −0.411310
\(429\) −870607. + 1.50794e6i −0.228391 + 0.395585i
\(430\) −2.42354e6 4.19770e6i −0.632091 1.09481i
\(431\) 3.08437e6 + 5.34229e6i 0.799785 + 1.38527i 0.919756 + 0.392491i \(0.128387\pi\)
−0.119971 + 0.992777i \(0.538280\pi\)
\(432\) −93312.0 + 161621.i −0.0240563 + 0.0416667i
\(433\) 4.89596e6 1.25493 0.627463 0.778647i \(-0.284093\pi\)
0.627463 + 0.778647i \(0.284093\pi\)
\(434\) 0 0
\(435\) 1.14341e6 0.289719
\(436\) −474458. + 821785.i −0.119531 + 0.207034i
\(437\) 522744. + 905419.i 0.130944 + 0.226802i
\(438\) −953683. 1.65183e6i −0.237530 0.411414i
\(439\) 1.77294e6 3.07082e6i 0.439069 0.760489i −0.558549 0.829471i \(-0.688642\pi\)
0.997618 + 0.0689822i \(0.0219752\pi\)
\(440\) −1.59099e6 −0.391773
\(441\) 0 0
\(442\) 4.16679e6 1.01448
\(443\) −3.02826e6 + 5.24510e6i −0.733134 + 1.26983i 0.222403 + 0.974955i \(0.428610\pi\)
−0.955537 + 0.294871i \(0.904723\pi\)
\(444\) 653651. + 1.13216e6i 0.157358 + 0.272552i
\(445\) −5.60780e6 9.71299e6i −1.34243 2.32516i
\(446\) −558966. + 968158.i −0.133060 + 0.230467i
\(447\) 1.47610e6 0.349419
\(448\) 0 0
\(449\) −1.20801e6 −0.282783 −0.141392 0.989954i \(-0.545158\pi\)
−0.141392 + 0.989954i \(0.545158\pi\)
\(450\) 1.22905e6 2.12878e6i 0.286113 0.495563i
\(451\) 2.18663e6 + 3.78735e6i 0.506213 + 0.876787i
\(452\) −1.25814e6 2.17917e6i −0.289657 0.501700i
\(453\) −280390. + 485649.i −0.0641972 + 0.111193i
\(454\) 4.89403e6 1.11436
\(455\) 0 0
\(456\) 158617. 0.0357222
\(457\) 2.73275e6 4.73326e6i 0.612082 1.06016i −0.378807 0.925476i \(-0.623666\pi\)
0.990889 0.134681i \(-0.0430011\pi\)
\(458\) 509549. + 882565.i 0.113507 + 0.196600i
\(459\) 471396. + 816481.i 0.104437 + 0.180890i
\(460\) −3.14349e6 + 5.44468e6i −0.692655 + 1.19971i
\(461\) 1.15956e6 0.254121 0.127061 0.991895i \(-0.459446\pi\)
0.127061 + 0.991895i \(0.459446\pi\)
\(462\) 0 0
\(463\) −4.31335e6 −0.935108 −0.467554 0.883964i \(-0.654865\pi\)
−0.467554 + 0.883964i \(0.654865\pi\)
\(464\) −157122. + 272144.i −0.0338800 + 0.0586818i
\(465\) −2.61972e6 4.53748e6i −0.561852 0.973156i
\(466\) 1.49235e6 + 2.58482e6i 0.318350 + 0.551398i
\(467\) 2.99462e6 5.18683e6i 0.635403 1.10055i −0.351027 0.936365i \(-0.614167\pi\)
0.986430 0.164184i \(-0.0524992\pi\)
\(468\) 1.04390e6 0.220315
\(469\) 0 0
\(470\) 9.54189e6 1.99246
\(471\) 1.07913e6 1.86911e6i 0.224141 0.388224i
\(472\) 588042. + 1.01852e6i 0.121494 + 0.210433i
\(473\) 1.40610e6 + 2.43544e6i 0.288978 + 0.500524i
\(474\) −874152. + 1.51408e6i −0.178707 + 0.309529i
\(475\) −2.08921e6 −0.424862
\(476\) 0 0
\(477\) 1.43069e6 0.287905
\(478\) 642073. 1.11210e6i 0.128533 0.222626i
\(479\) −1.77326e6 3.07138e6i −0.353129 0.611638i 0.633667 0.773606i \(-0.281549\pi\)
−0.986796 + 0.161968i \(0.948216\pi\)
\(480\) 476916. + 826043.i 0.0944798 + 0.163644i
\(481\) 3.65626e6 6.33283e6i 0.720567 1.24806i
\(482\) −4.97015e6 −0.974432
\(483\) 0 0
\(484\) −1.65375e6 −0.320890
\(485\) −5.15631e6 + 8.93099e6i −0.995370 + 1.72403i
\(486\) 118098. + 204552.i 0.0226805 + 0.0392837i
\(487\) 4.39160e6 + 7.60648e6i 0.839074 + 1.45332i 0.890669 + 0.454651i \(0.150236\pi\)
−0.0515950 + 0.998668i \(0.516430\pi\)
\(488\) 362371. 627645.i 0.0688817 0.119307i
\(489\) −3.93115e6 −0.743443
\(490\) 0 0
\(491\) −586608. −0.109811 −0.0549053 0.998492i \(-0.517486\pi\)
−0.0549053 + 0.998492i \(0.517486\pi\)
\(492\) 1.31093e6 2.27060e6i 0.244156 0.422891i
\(493\) 793754. + 1.37482e6i 0.147085 + 0.254759i
\(494\) −443619. 768371.i −0.0817887 0.141662i
\(495\) −1.00680e6 + 1.74382e6i −0.184684 + 0.319881i
\(496\) 1.43997e6 0.262814
\(497\) 0 0
\(498\) −4.07380e6 −0.736082
\(499\) 4.79886e6 8.31187e6i 0.862753 1.49433i −0.00650801 0.999979i \(-0.502072\pi\)
0.869261 0.494353i \(-0.164595\pi\)
\(500\) −3.69422e6 6.39858e6i −0.660842 1.14461i
\(501\) −174810. 302780.i −0.0311152 0.0538931i
\(502\) 1.38047e6 2.39104e6i 0.244494 0.423475i
\(503\) −7.21481e6 −1.27147 −0.635733 0.771909i \(-0.719302\pi\)
−0.635733 + 0.771909i \(0.719302\pi\)
\(504\) 0 0
\(505\) 1.70978e7 2.98340
\(506\) 1.82380e6 3.15892e6i 0.316666 0.548482i
\(507\) −1.24875e6 2.16290e6i −0.215753 0.373695i
\(508\) 739818. + 1.28140e6i 0.127194 + 0.220306i
\(509\) −2.19210e6 + 3.79682e6i −0.375029 + 0.649569i −0.990331 0.138722i \(-0.955701\pi\)
0.615302 + 0.788291i \(0.289034\pi\)
\(510\) 4.81859e6 0.820342
\(511\) 0 0
\(512\) −262144. −0.0441942
\(513\) 100375. 173854.i 0.0168396 0.0291670i
\(514\) 27573.4 + 47758.5i 0.00460344 + 0.00797339i
\(515\) 5.54991e6 + 9.61272e6i 0.922078 + 1.59709i
\(516\) 842992. 1.46010e6i 0.139380 0.241412i
\(517\) −5.53606e6 −0.910909
\(518\) 0 0
\(519\) 3.56650e6 0.581197
\(520\) 2.66768e6 4.62055e6i 0.432638 0.749351i
\(521\) −1.03291e6 1.78905e6i −0.166712 0.288753i 0.770550 0.637380i \(-0.219982\pi\)
−0.937262 + 0.348626i \(0.886648\pi\)
\(522\) 198858. + 344432.i 0.0319423 + 0.0553258i
\(523\) −3.98285e6 + 6.89850e6i −0.636707 + 1.10281i 0.349444 + 0.936957i \(0.386371\pi\)
−0.986151 + 0.165852i \(0.946963\pi\)
\(524\) −1.15725e6 −0.184120
\(525\) 0 0
\(526\) −2.29933e6 −0.362358
\(527\) 3.63722e6 6.29985e6i 0.570484 0.988107i
\(528\) −276700. 479258.i −0.0431941 0.0748143i
\(529\) −3.98881e6 6.90882e6i −0.619732 1.07341i
\(530\) 3.65611e6 6.33257e6i 0.565366 0.979242i
\(531\) 1.48848e6 0.229090
\(532\) 0 0
\(533\) −1.46657e7 −2.23606
\(534\) 1.95059e6 3.37851e6i 0.296014 0.512711i
\(535\) 5.04148e6 + 8.73210e6i 0.761507 + 1.31897i
\(536\) 1.15454e6 + 1.99972e6i 0.173579 + 0.300647i
\(537\) −1.09748e6 + 1.90088e6i −0.164233 + 0.284459i
\(538\) 4.47571e6 0.666663
\(539\) 0 0
\(540\) 1.20719e6 0.178153
\(541\) −4.11712e6 + 7.13105e6i −0.604784 + 1.04752i 0.387302 + 0.921953i \(0.373407\pi\)
−0.992086 + 0.125563i \(0.959926\pi\)
\(542\) 1.38974e6 + 2.40710e6i 0.203205 + 0.351962i
\(543\) 1.34673e6 + 2.33260e6i 0.196011 + 0.339501i
\(544\) −662152. + 1.14688e6i −0.0959314 + 0.166158i
\(545\) 6.13815e6 0.885209
\(546\) 0 0
\(547\) 5.20365e6 0.743601 0.371800 0.928313i \(-0.378741\pi\)
0.371800 + 0.928313i \(0.378741\pi\)
\(548\) −1.80530e6 + 3.12686e6i −0.256801 + 0.444793i
\(549\) −458626. 794363.i −0.0649423 0.112483i
\(550\) 3.64453e6 + 6.31250e6i 0.513729 + 0.889805i
\(551\) 169015. 292743.i 0.0237163 0.0410778i
\(552\) −2.18683e6 −0.305469
\(553\) 0 0
\(554\) 3.35061e6 0.463821
\(555\) 4.22820e6 7.32346e6i 0.582671 1.00922i
\(556\) 2.62377e6 + 4.54450e6i 0.359947 + 0.623447i
\(557\) 2.04583e6 + 3.54347e6i 0.279403 + 0.483940i 0.971236 0.238117i \(-0.0765302\pi\)
−0.691834 + 0.722057i \(0.743197\pi\)
\(558\) 911228. 1.57829e6i 0.123892 0.214586i
\(559\) −9.43070e6 −1.27648
\(560\) 0 0
\(561\) −2.79568e6 −0.375042
\(562\) −1.83537e6 + 3.17896e6i −0.245123 + 0.424565i
\(563\) 1.79526e6 + 3.10948e6i 0.238702 + 0.413444i 0.960342 0.278824i \(-0.0899447\pi\)
−0.721640 + 0.692269i \(0.756611\pi\)
\(564\) 1.65950e6 + 2.87434e6i 0.219674 + 0.380487i
\(565\) −8.13841e6 + 1.40961e7i −1.07255 + 1.85771i
\(566\) 1.66105e6 0.217943
\(567\) 0 0
\(568\) 4.05979e6 0.527999
\(569\) −4.89858e6 + 8.48459e6i −0.634293 + 1.09863i 0.352372 + 0.935860i \(0.385375\pi\)
−0.986665 + 0.162767i \(0.947958\pi\)
\(570\) −513014. 888567.i −0.0661367 0.114552i
\(571\) 1.10902e6 + 1.92088e6i 0.142347 + 0.246552i 0.928380 0.371632i \(-0.121202\pi\)
−0.786033 + 0.618185i \(0.787868\pi\)
\(572\) −1.54775e6 + 2.68078e6i −0.197792 + 0.342587i
\(573\) −6.99297e6 −0.889764
\(574\) 0 0
\(575\) 2.88036e7 3.63309
\(576\) −165888. + 287326.i −0.0208333 + 0.0360844i
\(577\) 1.32767e6 + 2.29959e6i 0.166016 + 0.287548i 0.937016 0.349288i \(-0.113576\pi\)
−0.771000 + 0.636836i \(0.780243\pi\)
\(578\) 505361. + 875310.i 0.0629190 + 0.108979i
\(579\) −1.24390e6 + 2.15449e6i −0.154201 + 0.267084i
\(580\) 2.03272e6 0.250904
\(581\) 0 0
\(582\) −3.58708e6 −0.438969
\(583\) −2.12122e6 + 3.67406e6i −0.258473 + 0.447688i
\(584\) −1.69544e6 2.93658e6i −0.205707 0.356295i
\(585\) −3.37628e6 5.84788e6i −0.407895 0.706495i
\(586\) −2.42982e6 + 4.20857e6i −0.292301 + 0.506280i
\(587\) −2.62690e6 −0.314665 −0.157332 0.987546i \(-0.550289\pi\)
−0.157332 + 0.987546i \(0.550289\pi\)
\(588\) 0 0
\(589\) −1.54896e6 −0.183972
\(590\) 3.80380e6 6.58838e6i 0.449871 0.779199i
\(591\) 592269. + 1.02584e6i 0.0697510 + 0.120812i
\(592\) 1.16205e6 + 2.01272e6i 0.136276 + 0.236037i
\(593\) 5.75310e6 9.96467e6i 0.671839 1.16366i −0.305543 0.952178i \(-0.598838\pi\)
0.977382 0.211481i \(-0.0678287\pi\)
\(594\) −700397. −0.0814475
\(595\) 0 0
\(596\) 2.62417e6 0.302606
\(597\) −2.54232e6 + 4.40343e6i −0.291941 + 0.505656i
\(598\) 6.11611e6 + 1.05934e7i 0.699394 + 1.21139i
\(599\) −3.23132e6 5.59681e6i −0.367970 0.637343i 0.621278 0.783590i \(-0.286614\pi\)
−0.989248 + 0.146247i \(0.953281\pi\)
\(600\) 2.18498e6 3.78449e6i 0.247781 0.429170i
\(601\) 8.55332e6 0.965937 0.482968 0.875638i \(-0.339559\pi\)
0.482968 + 0.875638i \(0.339559\pi\)
\(602\) 0 0
\(603\) 2.92243e6 0.327303
\(604\) −498470. + 863376.i −0.0555964 + 0.0962958i
\(605\) 5.34871e6 + 9.26425e6i 0.594102 + 1.02901i
\(606\) 2.97360e6 + 5.15042e6i 0.328928 + 0.569720i
\(607\) −1.49521e6 + 2.58978e6i −0.164714 + 0.285293i −0.936554 0.350524i \(-0.886003\pi\)
0.771840 + 0.635817i \(0.219337\pi\)
\(608\) 281986. 0.0309363
\(609\) 0 0
\(610\) −4.68806e6 −0.510115
\(611\) 9.28256e6 1.60779e7i 1.00592 1.74231i
\(612\) 838036. + 1.45152e6i 0.0904450 + 0.156655i
\(613\) 885724. + 1.53412e6i 0.0952023 + 0.164895i 0.909693 0.415281i \(-0.136317\pi\)
−0.814491 + 0.580177i \(0.802984\pi\)
\(614\) −5.20239e6 + 9.01080e6i −0.556906 + 0.964589i
\(615\) −1.69598e7 −1.80814
\(616\) 0 0
\(617\) 1.40871e7 1.48974 0.744869 0.667210i \(-0.232512\pi\)
0.744869 + 0.667210i \(0.232512\pi\)
\(618\) −1.93045e6 + 3.34364e6i −0.203323 + 0.352166i
\(619\) 5.67152e6 + 9.82336e6i 0.594940 + 1.03047i 0.993555 + 0.113348i \(0.0361574\pi\)
−0.398616 + 0.917118i \(0.630509\pi\)
\(620\) −4.65727e6 8.06663e6i −0.486578 0.842778i
\(621\) −1.38385e6 + 2.39690e6i −0.143999 + 0.249414i
\(622\) 3.27666e6 0.339590
\(623\) 0 0
\(624\) 1.85582e6 0.190798
\(625\) −1.20421e7 + 2.08576e7i −1.23312 + 2.13582i
\(626\) −1.76388e6 3.05513e6i −0.179901 0.311597i
\(627\) 297643. + 515534.i 0.0302362 + 0.0523707i
\(628\) 1.91845e6 3.32286e6i 0.194112 0.336211i
\(629\) 1.17409e7 1.18325
\(630\) 0 0
\(631\) −2.32628e6 −0.232588 −0.116294 0.993215i \(-0.537102\pi\)
−0.116294 + 0.993215i \(0.537102\pi\)
\(632\) −1.55405e6 + 2.69169e6i −0.154765 + 0.268060i
\(633\) −1.41137e6 2.44456e6i −0.140001 0.242489i
\(634\) −3.20876e6 5.55774e6i −0.317040 0.549130i
\(635\) 4.78558e6 8.28887e6i 0.470978 0.815758i
\(636\) 2.54344e6 0.249333
\(637\) 0 0
\(638\) −1.17935e6 −0.114708
\(639\) 2.56909e6 4.44979e6i 0.248901 0.431109i
\(640\) 847851. + 1.46852e6i 0.0818219 + 0.141720i
\(641\) 1.28193e6 + 2.22036e6i 0.123230 + 0.213441i 0.921040 0.389468i \(-0.127341\pi\)
−0.797809 + 0.602910i \(0.794008\pi\)
\(642\) −1.75360e6 + 3.03733e6i −0.167917 + 0.290840i
\(643\) −5.95343e6 −0.567858 −0.283929 0.958845i \(-0.591638\pi\)
−0.283929 + 0.958845i \(0.591638\pi\)
\(644\) 0 0
\(645\) −1.09059e7 −1.03220
\(646\) 712271. 1.23369e6i 0.0671528 0.116312i
\(647\) 767611. + 1.32954e6i 0.0720909 + 0.124865i 0.899818 0.436266i \(-0.143699\pi\)
−0.827727 + 0.561132i \(0.810366\pi\)
\(648\) 209952. + 363648.i 0.0196419 + 0.0340207i
\(649\) −2.20691e6 + 3.82248e6i −0.205671 + 0.356233i
\(650\) −2.44437e7 −2.26926
\(651\) 0 0
\(652\) −6.98871e6 −0.643841
\(653\) 9.97909e6 1.72843e7i 0.915815 1.58624i 0.110112 0.993919i \(-0.464879\pi\)
0.805703 0.592319i \(-0.201788\pi\)
\(654\) 1.06753e6 + 1.84902e6i 0.0975968 + 0.169043i
\(655\) 3.74290e6 + 6.48290e6i 0.340883 + 0.590427i
\(656\) 2.33055e6 4.03663e6i 0.211446 0.366235i
\(657\) −4.29157e6 −0.387885
\(658\) 0 0
\(659\) −1.05477e7 −0.946119 −0.473060 0.881030i \(-0.656850\pi\)
−0.473060 + 0.881030i \(0.656850\pi\)
\(660\) −1.78986e6 + 3.10013e6i −0.159941 + 0.277025i
\(661\) 6.10220e6 + 1.05693e7i 0.543229 + 0.940900i 0.998716 + 0.0506576i \(0.0161317\pi\)
−0.455487 + 0.890242i \(0.650535\pi\)
\(662\) 2.00616e6 + 3.47477e6i 0.177918 + 0.308164i
\(663\) 4.68763e6 8.11922e6i 0.414162 0.717349i
\(664\) −7.24231e6 −0.637466
\(665\) 0 0
\(666\) 2.94143e6 0.256964
\(667\) −2.33018e6 + 4.03599e6i −0.202803 + 0.351266i
\(668\) −310774. 538276.i −0.0269466 0.0466728i
\(669\) 1.25767e6 + 2.17836e6i 0.108643 + 0.188176i
\(670\) 7.46824e6 1.29354e7i 0.642734 1.11325i
\(671\) 2.71994e6 0.233213
\(672\) 0 0
\(673\) −7.97959e6 −0.679114 −0.339557 0.940585i \(-0.610277\pi\)
−0.339557 + 0.940585i \(0.610277\pi\)
\(674\) −5.24634e6 + 9.08693e6i −0.444843 + 0.770491i
\(675\) −2.76536e6 4.78975e6i −0.233611 0.404625i
\(676\) −2.22001e6 3.84516e6i −0.186847 0.323629i
\(677\) −2.54190e6 + 4.40271e6i −0.213151 + 0.369188i −0.952699 0.303915i \(-0.901706\pi\)
0.739548 + 0.673104i \(0.235039\pi\)
\(678\) −5.66164e6 −0.473007
\(679\) 0 0
\(680\) 8.56639e6 0.710437
\(681\) 5.50578e6 9.53629e6i 0.454937 0.787974i
\(682\) 2.70208e6 + 4.68014e6i 0.222453 + 0.385299i
\(683\) 8.01654e6 + 1.38850e7i 0.657559 + 1.13893i 0.981246 + 0.192762i \(0.0617445\pi\)
−0.323686 + 0.946165i \(0.604922\pi\)
\(684\) 178444. 309074.i 0.0145835 0.0252594i
\(685\) 2.33554e7 1.90179
\(686\) 0 0
\(687\) 2.29297e6 0.185356
\(688\) 1.49865e6 2.59574e6i 0.120706 0.209069i
\(689\) −7.11349e6 1.23209e7i −0.570867 0.988770i
\(690\) 7.07284e6 + 1.22505e7i 0.565550 + 0.979562i
\(691\) 5.50657e6 9.53766e6i 0.438719 0.759883i −0.558872 0.829254i \(-0.688766\pi\)
0.997591 + 0.0693705i \(0.0220991\pi\)
\(692\) 6.34044e6 0.503331
\(693\) 0 0
\(694\) −904935. −0.0713212
\(695\) 1.69721e7 2.93965e7i 1.33283 2.30852i
\(696\) 353525. + 612324.i 0.0276629 + 0.0479135i
\(697\) −1.17735e7 2.03923e7i −0.917961 1.58996i
\(698\) −2.92560e6 + 5.06728e6i −0.227288 + 0.393674i
\(699\) 6.71555e6 0.519863
\(700\) 0 0
\(701\) −3.10660e6 −0.238776 −0.119388 0.992848i \(-0.538093\pi\)
−0.119388 + 0.992848i \(0.538093\pi\)
\(702\) 1.17439e6 2.03410e6i 0.0899431 0.155786i
\(703\) −1.25000e6 2.16507e6i −0.0953943 0.165228i
\(704\) −491911. 852015.i −0.0374072 0.0647911i
\(705\) 1.07346e7 1.85929e7i 0.813418 1.40888i
\(706\) −1.12383e7 −0.848571
\(707\) 0 0
\(708\) 2.64619e6 0.198398
\(709\) 6.90180e6 1.19543e7i 0.515640 0.893115i −0.484195 0.874960i \(-0.660887\pi\)
0.999835 0.0181549i \(-0.00577922\pi\)
\(710\) −1.31306e7 2.27428e7i −0.977547 1.69316i
\(711\) 1.96684e6 + 3.40667e6i 0.145914 + 0.252730i
\(712\) 3.46771e6 6.00625e6i 0.256355 0.444021i
\(713\) 2.13552e7 1.57319
\(714\) 0 0
\(715\) 2.00235e7 1.46479
\(716\) −1.95107e6 + 3.37935e6i −0.142230 + 0.246349i
\(717\) −1.44466e6 2.50223e6i −0.104947 0.181773i
\(718\) −7.39800e6 1.28137e7i −0.535554 0.927607i
\(719\) 6.49275e6 1.12458e7i 0.468389 0.811273i −0.530959 0.847398i \(-0.678168\pi\)
0.999347 + 0.0361248i \(0.0115014\pi\)
\(720\) 2.14612e6 0.154285
\(721\) 0 0
\(722\) 9.60107e6 0.685451
\(723\) −5.59141e6 + 9.68461e6i −0.397810 + 0.689027i
\(724\) 2.39418e6 + 4.14685e6i 0.169751 + 0.294017i
\(725\) −4.65642e6 8.06516e6i −0.329009 0.569860i
\(726\) −1.86047e6 + 3.22242e6i −0.131003 + 0.226904i
\(727\) −8.61224e6 −0.604338 −0.302169 0.953254i \(-0.597711\pi\)
−0.302169 + 0.953254i \(0.597711\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −1.09671e7 + 1.89956e7i −0.761700 + 1.31930i
\(731\) −7.57092e6 1.31132e7i −0.524029 0.907645i
\(732\) −815334. 1.41220e6i −0.0562416 0.0974134i
\(733\) −3.01000e6 + 5.21348e6i −0.206922 + 0.358400i −0.950743 0.309979i \(-0.899678\pi\)
0.743821 + 0.668379i \(0.233011\pi\)
\(734\) −4.67698e6 −0.320424
\(735\) 0 0
\(736\) −3.88769e6 −0.264544
\(737\) −4.33297e6 + 7.50492e6i −0.293844 + 0.508952i
\(738\) −2.94960e6 5.10886e6i −0.199353 0.345289i
\(739\) 46846.3 + 81140.1i 0.00315547 + 0.00546543i 0.867599 0.497265i \(-0.165662\pi\)
−0.864443 + 0.502730i \(0.832329\pi\)
\(740\) 7.51681e6 1.30195e7i 0.504608 0.874007i
\(741\) −1.99629e6 −0.133560
\(742\) 0 0
\(743\) −1.29874e7 −0.863081 −0.431541 0.902094i \(-0.642030\pi\)
−0.431541 + 0.902094i \(0.642030\pi\)
\(744\) 1.61996e6 2.80585e6i 0.107293 0.185837i
\(745\) −8.48735e6 1.47005e7i −0.560250 0.970381i
\(746\) −9.15380e6 1.58549e7i −0.602219 1.04307i
\(747\) −4.58302e6 + 7.93803e6i −0.300504 + 0.520489i
\(748\) −4.97009e6 −0.324796
\(749\) 0 0
\(750\) −1.66240e7 −1.07915
\(751\) 318720. 552040.i 0.0206210 0.0357166i −0.855531 0.517752i \(-0.826769\pi\)
0.876152 + 0.482035i \(0.160102\pi\)
\(752\) 2.95022e6 + 5.10993e6i 0.190244 + 0.329511i
\(753\) −3.10606e6 5.37985e6i −0.199628 0.345766i
\(754\) 1.97748e6 3.42509e6i 0.126673 0.219403i
\(755\) 6.44880e6 0.411729
\(756\) 0 0
\(757\) −4.86768e6 −0.308732 −0.154366 0.988014i \(-0.549334\pi\)
−0.154366 + 0.988014i \(0.549334\pi\)
\(758\) −4.71040e6 + 8.15866e6i −0.297773 + 0.515758i
\(759\) −4.10356e6 7.10757e6i −0.258557 0.447834i
\(760\) −912026. 1.57967e6i −0.0572760 0.0992050i
\(761\) −2.90894e6 + 5.03842e6i −0.182084 + 0.315379i −0.942590 0.333952i \(-0.891618\pi\)
0.760506 + 0.649331i \(0.224951\pi\)
\(762\) 3.32918e6 0.207706
\(763\) 0 0
\(764\) −1.24319e7 −0.770558
\(765\) 5.42092e6 9.38930e6i 0.334903 0.580069i
\(766\) 6.07891e6 + 1.05290e7i 0.374329 + 0.648358i
\(767\) −7.40085e6 1.28186e7i −0.454248 0.786781i
\(768\) −294912. + 510803.i −0.0180422 + 0.0312500i