Properties

Label 294.6.e.z.79.2
Level $294$
Weight $6$
Character 294.79
Analytic conductor $47.153$
Analytic rank $0$
Dimension $4$
Inner twists $2$

Related objects

Downloads

Learn more

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 79.2
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.6.e.z.67.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 - 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(51.7487 - 89.6314i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(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 \(-0.456802\pi\)
0.790416 0.612570i \(-0.209864\pi\)
\(6\) 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 \(-0.729844\pi\)
−0.660944 + 0.750435i \(0.729844\pi\)
\(14\) 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 \(-0.984080\pi\)
0.456080 0.889939i \(-0.349253\pi\)
\(18\) 162.000 + 280.592i 0.117851 + 0.204124i
\(19\) −137.688 + 238.483i −0.0875011 + 0.151556i −0.906454 0.422304i \(-0.861221\pi\)
0.818953 + 0.573860i \(0.194555\pi\)
\(20\) −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 \(0.00950261\pi\)
−0.473927 + 0.880564i \(0.657164\pi\)
\(32\) 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 \(-0.179134\pi\)
0.845782 + 0.533528i \(0.179134\pi\)
\(42\) 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 \(0.441945\pi\)
−0.942349 + 0.334632i \(0.891388\pi\)
\(48\) −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 0.985105 0.171954i \(-0.0550082\pi\)
−0.641469 + 0.767149i \(0.721675\pi\)
\(60\) −7451.82 12906.9i −0.267229 0.462855i
\(61\) 5662.04 9806.95i 0.194827 0.337450i −0.752017 0.659144i \(-0.770919\pi\)
0.946844 + 0.321694i \(0.104252\pi\)
\(62\) 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 \(-0.969004\pi\)
0.413435 0.910534i \(-0.364329\pi\)
\(74\) −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 \(-0.857542\pi\)
−0.901513 + 0.432753i \(0.857542\pi\)
\(84\) 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 \(-0.575135\pi\)
0.958940 0.283609i \(-0.0915318\pi\)
\(90\) 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 \(-0.680679\pi\)
−0.537625 + 0.843184i \(0.680679\pi\)
\(98\) 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 \(0.131547\pi\)
−0.110109 + 0.993920i \(0.535120\pi\)
\(102\) −23278.8 40320.0i −0.221544 0.383725i
\(103\) −53623.6 + 92878.8i −0.498038 + 0.862628i −0.999997 0.00226355i \(-0.999279\pi\)
0.501959 + 0.864891i \(0.332613\pi\)
\(104\) 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 −0.943280 0.331999i \(-0.892277\pi\)
0.759160 + 0.650904i \(0.225610\pi\)
\(132\) −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 \(-0.244190\pi\)
0.719894 + 0.694084i \(0.244190\pi\)
\(140\) 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 0.603987 0.796994i \(-0.293578\pi\)
−0.992211 + 0.124571i \(0.960244\pi\)
\(158\) −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 \(-0.517163\pi\)
−0.0538931 + 0.998547i \(0.517163\pi\)
\(168\) 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 \(-0.665441\pi\)
0.999993 0.00385097i \(-0.00122580\pi\)
\(174\) 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 \(-0.389742\pi\)
0.339501 + 0.940606i \(0.389742\pi\)
\(182\) 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 \(0.00208289\pi\)
−0.494322 + 0.869279i \(0.664584\pi\)
\(200\) 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 \(-0.439743\pi\)
0.188176 + 0.982135i \(0.439743\pi\)
\(224\) 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 \(-0.877797\pi\)
0.139232 0.990260i \(-0.455537\pi\)
\(228\) 19827.1 + 34341.6i 0.0252594 + 0.0437505i
\(229\) 127387. 220641.i 0.160523 0.278034i −0.774533 0.632533i \(-0.782015\pi\)
0.935056 + 0.354499i \(0.115349\pi\)
\(230\) 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 \(0.0752954\pi\)
−0.283125 + 0.959083i \(0.591371\pi\)
\(242\) −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 \(-0.612381\pi\)
−0.345766 + 0.938321i \(0.612381\pi\)
\(252\) 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 −0.862752 0.505627i \(-0.831261\pi\)
0.869262 + 0.494351i \(0.164594\pi\)
\(258\) −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 0.528063 0.849205i \(-0.322919\pi\)
−0.999465 + 0.0327131i \(0.989585\pi\)
\(270\) 150899. + 261365.i 0.125973 + 0.218192i
\(271\) 347435. 601775.i 0.287376 0.497749i −0.685807 0.727784i \(-0.740551\pi\)
0.973183 + 0.230034i \(0.0738839\pi\)
\(272\) 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 0.778625 0.627489i \(-0.215917\pi\)
−0.932734 + 0.360565i \(0.882584\pi\)
\(284\) 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 \(-0.364350\pi\)
0.413376 + 0.910561i \(0.364350\pi\)
\(294\) 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 \(-0.211332\pi\)
0.787584 + 0.616207i \(0.211332\pi\)
\(308\) 0 0
\(309\) −965225. −0.575085
\(310\) 1.16432e6 2.01666e6i 0.688125 1.19187i
\(311\) −409582. 709417.i −0.240126 0.415911i 0.720624 0.693326i \(-0.243856\pi\)
−0.960750 + 0.277415i \(0.910522\pi\)
\(312\) 231977. + 401797.i 0.134915 + 0.233679i
\(313\) −440970. + 763782.i −0.254418 + 0.440665i −0.964737 0.263215i \(-0.915217\pi\)
0.710319 + 0.703880i \(0.248551\pi\)
\(314\) −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 \(-0.395835\pi\)
0.321433 + 0.946932i \(0.395835\pi\)
\(350\) 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 \(0.0381783\pi\)
−0.392785 + 0.919630i \(0.628488\pi\)
\(354\) 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 0.956791 0.290778i \(-0.0939141\pi\)
−0.730216 + 0.683216i \(0.760581\pi\)
\(368\) −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 \(-0.655757\pi\)
0.999413 0.0342662i \(-0.0109094\pi\)
\(384\) 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 \(-0.501436\pi\)
0.868272 0.496089i \(-0.165231\pi\)
\(398\) 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 0.990768 0.135567i \(-0.0432856\pi\)
−0.612788 + 0.790247i \(0.709952\pi\)
\(410\) −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 \(-0.597814\pi\)
−0.302480 + 0.953156i \(0.597814\pi\)
\(420\) 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 \(-0.715907\pi\)
−0.627463 + 0.778647i \(0.715907\pi\)
\(434\) 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 −0.997618 0.0689822i \(-0.978025\pi\)
0.558549 + 0.829471i \(0.311358\pi\)
\(440\) 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 \(-0.540554\pi\)
−0.127061 + 0.991895i \(0.540554\pi\)
\(462\) 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 \(0.385833\pi\)
−0.986430 + 0.164184i \(0.947501\pi\)
\(468\) −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 0.986796 0.161968i \(-0.0517843\pi\)
−0.633667 + 0.773606i \(0.718451\pi\)
\(480\) 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 \(-0.280698\pi\)
0.635733 + 0.771909i \(0.280698\pi\)
\(504\) 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 −0.615302 0.788291i \(-0.710966\pi\)
0.990331 + 0.138722i \(0.0442994\pi\)
\(510\) −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 0.937262 0.348626i \(-0.113352\pi\)
−0.770550 + 0.637380i \(0.780018\pi\)
\(522\) 198858. + 344432.i 0.0319423 + 0.0553258i
\(523\) 3.98285e6 6.89850e6i 0.636707 1.10281i −0.349444 0.936957i \(-0.613629\pi\)
0.986151 0.165852i \(-0.0530373\pi\)
\(524\) 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 0.721640 0.692269i \(-0.243389\pi\)
−0.960342 + 0.278824i \(0.910055\pi\)
\(564\) 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 0.771000 0.636836i \(-0.219757\pi\)
−0.937016 + 0.349288i \(0.886424\pi\)
\(578\) 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 \(-0.449711\pi\)
0.157332 + 0.987546i \(0.449711\pi\)
\(588\) 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 \(0.401162\pi\)
−0.977382 + 0.211481i \(0.932171\pi\)
\(594\) 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 \(-0.660441\pi\)
−0.482968 + 0.875638i \(0.660441\pi\)
\(602\) 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 −0.771840 0.635817i \(-0.780663\pi\)
0.936554 + 0.350524i \(0.113997\pi\)
\(608\) −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 \(-0.963843\pi\)
0.398616 0.917118i \(-0.369491\pi\)
\(620\) −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 \(-0.408362\pi\)
0.283929 + 0.958845i \(0.408362\pi\)
\(644\) 0 0
\(645\) −1.09059e7 −1.03220
\(646\) 712271. 1.23369e6i 0.0671528 0.116312i
\(647\) −767611. 1.32954e6i −0.0720909 0.124865i 0.827727 0.561132i \(-0.189634\pi\)
−0.899818 + 0.436266i \(0.856301\pi\)
\(648\) 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 \(-0.983868\pi\)
0.455487 0.890242i \(-0.349465\pi\)
\(662\) 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 −0.739548 0.673104i \(-0.764961\pi\)
0.952699 + 0.303915i \(0.0982940\pi\)
\(678\) 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 −0.997591 0.0693705i \(-0.977901\pi\)
0.558872 + 0.829254i \(0.311234\pi\)
\(692\) −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 −0.999347 0.0361248i \(-0.988499\pi\)
0.530959 + 0.847398i \(0.321832\pi\)
\(720\) −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 \(-0.402289\pi\)
0.302169 + 0.953254i \(0.402289\pi\)
\(728\) 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 −0.743821 0.668379i \(-0.766989\pi\)
0.950743 + 0.309979i \(0.100322\pi\)
\(734\) 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 −0.760506 0.649331i \(-0.775049\pi\)
0.942590 + 0.333952i \(0.108382\pi\)
\(762\) −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
\(769\) −1.94310e7 −1.18490 −0.592448