Properties

Label 294.6.e.v.67.2
Level $294$
Weight $6$
Character 294.67
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: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.6.e.v.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 - 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-23.4645 - 40.6416i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(-2.00000 - 3.46410i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-23.4645 - 40.6416i) q^{5} -36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-93.8579 + 162.567i) q^{10} +(43.7279 - 75.7390i) q^{11} +(72.0000 + 124.708i) q^{12} +754.566 q^{13} -422.360 q^{15} +(-128.000 - 221.703i) q^{16} +(724.520 - 1254.90i) q^{17} +(-162.000 + 280.592i) q^{18} +(-1270.12 - 2199.91i) q^{19} +750.863 q^{20} -349.823 q^{22} +(456.124 + 790.030i) q^{23} +(288.000 - 498.831i) q^{24} +(461.338 - 799.060i) q^{25} +(-1509.13 - 2613.89i) q^{26} -729.000 q^{27} +173.217 q^{29} +(844.721 + 1463.10i) q^{30} +(-2265.57 + 3924.08i) q^{31} +(-512.000 + 886.810i) q^{32} +(-393.551 - 681.651i) q^{33} -5796.16 q^{34} +1296.00 q^{36} +(-3414.98 - 5914.92i) q^{37} +(-5080.48 + 8799.64i) q^{38} +(3395.55 - 5881.26i) q^{39} +(-1501.73 - 2601.07i) q^{40} +13069.3 q^{41} -12277.7 q^{43} +(699.647 + 1211.82i) q^{44} +(-1900.62 + 3291.97i) q^{45} +(1824.50 - 3160.12i) q^{46} +(-6746.40 - 11685.1i) q^{47} -2304.00 q^{48} -3690.70 q^{50} +(-6520.68 - 11294.1i) q^{51} +(-6036.52 + 10455.6i) q^{52} +(4838.85 - 8381.14i) q^{53} +(1458.00 + 2525.33i) q^{54} -4104.21 q^{55} -22862.1 q^{57} +(-346.434 - 600.041i) q^{58} +(-15184.6 + 26300.5i) q^{59} +(3378.88 - 5852.40i) q^{60} +(-366.236 - 634.340i) q^{61} +18124.5 q^{62} +4096.00 q^{64} +(-17705.5 - 30666.8i) q^{65} +(-1574.21 + 2726.60i) q^{66} +(-23200.0 + 40183.5i) q^{67} +(11592.3 + 20078.5i) q^{68} +8210.23 q^{69} -3295.39 q^{71} +(-2592.00 - 4489.48i) q^{72} +(-5119.09 + 8866.53i) q^{73} +(-13659.9 + 23659.7i) q^{74} +(-4152.04 - 7191.54i) q^{75} +40643.8 q^{76} -27164.4 q^{78} +(-49292.0 - 85376.2i) q^{79} +(-6006.90 + 10404.3i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-26138.5 - 45273.3i) q^{82} +87792.7 q^{83} -68001.9 q^{85} +(24555.4 + 42531.2i) q^{86} +(779.476 - 1350.09i) q^{87} +(2798.59 - 4847.29i) q^{88} +(34549.9 + 59842.2i) q^{89} +15205.0 q^{90} -14596.0 q^{92} +(20390.1 + 35316.7i) q^{93} +(-26985.6 + 46740.4i) q^{94} +(-59605.3 + 103239. i) q^{95} +(4608.00 + 7981.29i) q^{96} -42181.4 q^{97} -7083.92 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 \( 4 q - 8 q^{2} + 18 q^{3} - 32 q^{4} - 108 q^{5} - 144 q^{6} + 256 q^{8} - 162 q^{9} - 432 q^{10} + 124 q^{11} + 288 q^{12} + 1440 q^{13} - 1944 q^{15} - 512 q^{16} - 612 q^{17} - 648 q^{18} - 2088 q^{19} + 3456 q^{20} - 992 q^{22} - 772 q^{23} + 1152 q^{24} + 318 q^{25} - 2880 q^{26} - 2916 q^{27} - 9184 q^{29} + 3888 q^{30} - 9792 q^{31} - 2048 q^{32} - 1116 q^{33} + 4896 q^{34} + 5184 q^{36} + 5992 q^{37} - 8352 q^{38} + 6480 q^{39} - 6912 q^{40} + 40392 q^{41} - 2272 q^{43} + 1984 q^{44} - 8748 q^{45} - 3088 q^{46} - 36936 q^{47} - 9216 q^{48} - 2544 q^{50} + 5508 q^{51} - 11520 q^{52} + 16708 q^{53} + 5832 q^{54} - 12672 q^{55} - 37584 q^{57} + 18368 q^{58} - 74592 q^{59} + 15552 q^{60} + 18648 q^{61} + 78336 q^{62} + 16384 q^{64} - 33300 q^{65} - 4464 q^{66} - 67344 q^{67} - 9792 q^{68} - 13896 q^{69} + 153096 q^{71} - 10368 q^{72} - 47304 q^{73} + 23968 q^{74} - 2862 q^{75} + 66816 q^{76} - 51840 q^{78} - 140656 q^{79} - 27648 q^{80} - 13122 q^{81} - 80784 q^{82} + 188208 q^{83} + 115736 q^{85} + 4544 q^{86} - 41328 q^{87} + 7936 q^{88} + 17604 q^{89} + 69984 q^{90} + 24704 q^{92} + 88128 q^{93} - 147744 q^{94} - 91592 q^{95} + 18432 q^{96} + 170352 q^{97} - 20088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 4.50000 7.79423i 0.288675 0.500000i
\(4\) −8.00000 + 13.8564i −0.250000 + 0.433013i
\(5\) −23.4645 40.6416i −0.419745 0.727020i 0.576168 0.817331i \(-0.304547\pi\)
−0.995914 + 0.0903111i \(0.971214\pi\)
\(6\) −36.0000 −0.408248
\(7\) 0 0
\(8\) 64.0000 0.353553
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) −93.8579 + 162.567i −0.296805 + 0.514081i
\(11\) 43.7279 75.7390i 0.108963 0.188729i −0.806388 0.591387i \(-0.798580\pi\)
0.915350 + 0.402659i \(0.131914\pi\)
\(12\) 72.0000 + 124.708i 0.144338 + 0.250000i
\(13\) 754.566 1.23834 0.619168 0.785258i \(-0.287470\pi\)
0.619168 + 0.785258i \(0.287470\pi\)
\(14\) 0 0
\(15\) −422.360 −0.484680
\(16\) −128.000 221.703i −0.125000 0.216506i
\(17\) 724.520 1254.90i 0.608034 1.05315i −0.383530 0.923528i \(-0.625292\pi\)
0.991564 0.129617i \(-0.0413749\pi\)
\(18\) −162.000 + 280.592i −0.117851 + 0.204124i
\(19\) −1270.12 2199.91i −0.807161 1.39804i −0.914822 0.403857i \(-0.867669\pi\)
0.107661 0.994188i \(-0.465664\pi\)
\(20\) 750.863 0.419745
\(21\) 0 0
\(22\) −349.823 −0.154096
\(23\) 456.124 + 790.030i 0.179789 + 0.311404i 0.941808 0.336151i \(-0.109125\pi\)
−0.762019 + 0.647555i \(0.775792\pi\)
\(24\) 288.000 498.831i 0.102062 0.176777i
\(25\) 461.338 799.060i 0.147628 0.255699i
\(26\) −1509.13 2613.89i −0.437818 0.758323i
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) 173.217 0.0382468 0.0191234 0.999817i \(-0.493912\pi\)
0.0191234 + 0.999817i \(0.493912\pi\)
\(30\) 844.721 + 1463.10i 0.171360 + 0.296805i
\(31\) −2265.57 + 3924.08i −0.423421 + 0.733387i −0.996272 0.0862730i \(-0.972504\pi\)
0.572850 + 0.819660i \(0.305838\pi\)
\(32\) −512.000 + 886.810i −0.0883883 + 0.153093i
\(33\) −393.551 681.651i −0.0629095 0.108963i
\(34\) −5796.16 −0.859890
\(35\) 0 0
\(36\) 1296.00 0.166667
\(37\) −3414.98 5914.92i −0.410094 0.710304i 0.584805 0.811174i \(-0.301171\pi\)
−0.994900 + 0.100870i \(0.967838\pi\)
\(38\) −5080.48 + 8799.64i −0.570749 + 0.988567i
\(39\) 3395.55 5881.26i 0.357477 0.619168i
\(40\) −1501.73 2601.07i −0.148402 0.257040i
\(41\) 13069.3 1.21420 0.607102 0.794624i \(-0.292332\pi\)
0.607102 + 0.794624i \(0.292332\pi\)
\(42\) 0 0
\(43\) −12277.7 −1.01262 −0.506309 0.862352i \(-0.668990\pi\)
−0.506309 + 0.862352i \(0.668990\pi\)
\(44\) 699.647 + 1211.82i 0.0544813 + 0.0943643i
\(45\) −1900.62 + 3291.97i −0.139915 + 0.242340i
\(46\) 1824.50 3160.12i 0.127130 0.220196i
\(47\) −6746.40 11685.1i −0.445479 0.771592i 0.552606 0.833442i \(-0.313633\pi\)
−0.998085 + 0.0618499i \(0.980300\pi\)
\(48\) −2304.00 −0.144338
\(49\) 0 0
\(50\) −3690.70 −0.208778
\(51\) −6520.68 11294.1i −0.351049 0.608034i
\(52\) −6036.52 + 10455.6i −0.309584 + 0.536215i
\(53\) 4838.85 8381.14i 0.236621 0.409839i −0.723122 0.690721i \(-0.757293\pi\)
0.959742 + 0.280882i \(0.0906268\pi\)
\(54\) 1458.00 + 2525.33i 0.0680414 + 0.117851i
\(55\) −4104.21 −0.182946
\(56\) 0 0
\(57\) −22862.1 −0.932030
\(58\) −346.434 600.041i −0.0135223 0.0234213i
\(59\) −15184.6 + 26300.5i −0.567902 + 0.983634i 0.428872 + 0.903365i \(0.358911\pi\)
−0.996773 + 0.0802689i \(0.974422\pi\)
\(60\) 3378.88 5852.40i 0.121170 0.209873i
\(61\) −366.236 634.340i −0.0126019 0.0218272i 0.859656 0.510874i \(-0.170678\pi\)
−0.872258 + 0.489047i \(0.837345\pi\)
\(62\) 18124.5 0.598808
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −17705.5 30666.8i −0.519786 0.900295i
\(66\) −1574.21 + 2726.60i −0.0444838 + 0.0770481i
\(67\) −23200.0 + 40183.5i −0.631394 + 1.09361i 0.355873 + 0.934534i \(0.384183\pi\)
−0.987267 + 0.159072i \(0.949150\pi\)
\(68\) 11592.3 + 20078.5i 0.304017 + 0.526573i
\(69\) 8210.23 0.207603
\(70\) 0 0
\(71\) −3295.39 −0.0775821 −0.0387910 0.999247i \(-0.512351\pi\)
−0.0387910 + 0.999247i \(0.512351\pi\)
\(72\) −2592.00 4489.48i −0.0589256 0.102062i
\(73\) −5119.09 + 8866.53i −0.112431 + 0.194736i −0.916750 0.399462i \(-0.869197\pi\)
0.804319 + 0.594198i \(0.202530\pi\)
\(74\) −13659.9 + 23659.7i −0.289980 + 0.502261i
\(75\) −4152.04 7191.54i −0.0852331 0.147628i
\(76\) 40643.8 0.807161
\(77\) 0 0
\(78\) −27164.4 −0.505549
\(79\) −49292.0 85376.2i −0.888605 1.53911i −0.841525 0.540218i \(-0.818342\pi\)
−0.0470794 0.998891i \(-0.514991\pi\)
\(80\) −6006.90 + 10404.3i −0.104936 + 0.181755i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) −26138.5 45273.3i −0.429286 0.743545i
\(83\) 87792.7 1.39882 0.699412 0.714719i \(-0.253445\pi\)
0.699412 + 0.714719i \(0.253445\pi\)
\(84\) 0 0
\(85\) −68001.9 −1.02088
\(86\) 24555.4 + 42531.2i 0.358014 + 0.620099i
\(87\) 779.476 1350.09i 0.0110409 0.0191234i
\(88\) 2798.59 4847.29i 0.0385241 0.0667256i
\(89\) 34549.9 + 59842.2i 0.462351 + 0.800816i 0.999078 0.0429406i \(-0.0136726\pi\)
−0.536726 + 0.843756i \(0.680339\pi\)
\(90\) 15205.0 0.197870
\(91\) 0 0
\(92\) −14596.0 −0.179789
\(93\) 20390.1 + 35316.7i 0.244462 + 0.423421i
\(94\) −26985.6 + 46740.4i −0.315001 + 0.545598i
\(95\) −59605.3 + 103239.i −0.677604 + 1.17364i
\(96\) 4608.00 + 7981.29i 0.0510310 + 0.0883883i
\(97\) −42181.4 −0.455189 −0.227594 0.973756i \(-0.573086\pi\)
−0.227594 + 0.973756i \(0.573086\pi\)
\(98\) 0 0
\(99\) −7083.92 −0.0726417
\(100\) 7381.40 + 12785.0i 0.0738140 + 0.127850i
\(101\) −89237.0 + 154563.i −0.870445 + 1.50766i −0.00890797 + 0.999960i \(0.502836\pi\)
−0.861537 + 0.507695i \(0.830498\pi\)
\(102\) −26082.7 + 45176.6i −0.248229 + 0.429945i
\(103\) −17613.1 30506.8i −0.163585 0.283337i 0.772567 0.634933i \(-0.218972\pi\)
−0.936152 + 0.351596i \(0.885639\pi\)
\(104\) 48292.2 0.437818
\(105\) 0 0
\(106\) −38710.8 −0.334632
\(107\) −44980.4 77908.4i −0.379808 0.657847i 0.611226 0.791456i \(-0.290677\pi\)
−0.991034 + 0.133609i \(0.957343\pi\)
\(108\) 5832.00 10101.3i 0.0481125 0.0833333i
\(109\) −92501.2 + 160217.i −0.745729 + 1.29164i 0.204124 + 0.978945i \(0.434565\pi\)
−0.949853 + 0.312696i \(0.898768\pi\)
\(110\) 8208.42 + 14217.4i 0.0646812 + 0.112031i
\(111\) −61469.6 −0.473536
\(112\) 0 0
\(113\) −228275. −1.68175 −0.840877 0.541227i \(-0.817960\pi\)
−0.840877 + 0.541227i \(0.817960\pi\)
\(114\) 45724.3 + 79196.8i 0.329522 + 0.570749i
\(115\) 21405.4 37075.3i 0.150931 0.261421i
\(116\) −1385.74 + 2400.16i −0.00956170 + 0.0165614i
\(117\) −30559.9 52931.3i −0.206389 0.357477i
\(118\) 121477. 0.803134
\(119\) 0 0
\(120\) −27031.1 −0.171360
\(121\) 76701.2 + 132850.i 0.476254 + 0.824897i
\(122\) −1464.95 + 2537.36i −0.00891091 + 0.0154341i
\(123\) 58811.7 101865.i 0.350510 0.607102i
\(124\) −36249.1 62785.2i −0.211711 0.366693i
\(125\) −189953. −1.08735
\(126\) 0 0
\(127\) −343515. −1.88989 −0.944944 0.327232i \(-0.893884\pi\)
−0.944944 + 0.327232i \(0.893884\pi\)
\(128\) −8192.00 14189.0i −0.0441942 0.0765466i
\(129\) −55249.6 + 95695.1i −0.292318 + 0.506309i
\(130\) −70821.9 + 122667.i −0.367544 + 0.636605i
\(131\) 180636. + 312871.i 0.919657 + 1.59289i 0.799936 + 0.600085i \(0.204867\pi\)
0.119721 + 0.992808i \(0.461800\pi\)
\(132\) 12593.6 0.0629095
\(133\) 0 0
\(134\) 185600. 0.892926
\(135\) 17105.6 + 29627.8i 0.0807800 + 0.139915i
\(136\) 46369.2 80313.9i 0.214972 0.372343i
\(137\) 152313. 263815.i 0.693325 1.20087i −0.277417 0.960750i \(-0.589478\pi\)
0.970742 0.240125i \(-0.0771883\pi\)
\(138\) −16420.5 28441.1i −0.0733986 0.127130i
\(139\) 129737. 0.569543 0.284772 0.958595i \(-0.408082\pi\)
0.284772 + 0.958595i \(0.408082\pi\)
\(140\) 0 0
\(141\) −121435. −0.514395
\(142\) 6590.79 + 11415.6i 0.0274294 + 0.0475091i
\(143\) 32995.6 57150.0i 0.134932 0.233710i
\(144\) −10368.0 + 17957.9i −0.0416667 + 0.0721688i
\(145\) −4064.44 7039.82i −0.0160539 0.0278062i
\(146\) 40952.7 0.159001
\(147\) 0 0
\(148\) 109279. 0.410094
\(149\) −186954. 323814.i −0.689873 1.19489i −0.971879 0.235482i \(-0.924333\pi\)
0.282006 0.959413i \(-0.409000\pi\)
\(150\) −16608.2 + 28766.2i −0.0602689 + 0.104389i
\(151\) 43319.9 75032.3i 0.154613 0.267797i −0.778305 0.627886i \(-0.783920\pi\)
0.932918 + 0.360089i \(0.117254\pi\)
\(152\) −81287.6 140794.i −0.285375 0.494283i
\(153\) −117372. −0.405356
\(154\) 0 0
\(155\) 212641. 0.710916
\(156\) 54328.7 + 94100.1i 0.178738 + 0.309584i
\(157\) 231087. 400254.i 0.748214 1.29594i −0.200465 0.979701i \(-0.564245\pi\)
0.948678 0.316243i \(-0.102421\pi\)
\(158\) −197168. + 341505.i −0.628338 + 1.08831i
\(159\) −43549.7 75430.2i −0.136613 0.236621i
\(160\) 48055.2 0.148402
\(161\) 0 0
\(162\) 26244.0 0.0785674
\(163\) −304516. 527437.i −0.897721 1.55490i −0.830401 0.557166i \(-0.811889\pi\)
−0.0673199 0.997731i \(-0.521445\pi\)
\(164\) −104554. + 181093.i −0.303551 + 0.525765i
\(165\) −18468.9 + 31989.1i −0.0528119 + 0.0914730i
\(166\) −175585. 304123.i −0.494559 0.856601i
\(167\) −127786. −0.354562 −0.177281 0.984160i \(-0.556730\pi\)
−0.177281 + 0.984160i \(0.556730\pi\)
\(168\) 0 0
\(169\) 198076. 0.533477
\(170\) 136004. + 235565.i 0.360935 + 0.625157i
\(171\) −102880. + 178193.i −0.269054 + 0.466015i
\(172\) 98221.5 170125.i 0.253154 0.438476i
\(173\) 71269.6 + 123443.i 0.181046 + 0.313581i 0.942237 0.334947i \(-0.108718\pi\)
−0.761191 + 0.648528i \(0.775385\pi\)
\(174\) −6235.81 −0.0156142
\(175\) 0 0
\(176\) −22388.7 −0.0544813
\(177\) 136661. + 236704.i 0.327878 + 0.567902i
\(178\) 138200. 239369.i 0.326932 0.566262i
\(179\) 148317. 256893.i 0.345986 0.599266i −0.639546 0.768753i \(-0.720878\pi\)
0.985532 + 0.169487i \(0.0542110\pi\)
\(180\) −30409.9 52671.6i −0.0699575 0.121170i
\(181\) −277654. −0.629952 −0.314976 0.949100i \(-0.601996\pi\)
−0.314976 + 0.949100i \(0.601996\pi\)
\(182\) 0 0
\(183\) −6592.25 −0.0145514
\(184\) 29191.9 + 50561.9i 0.0635650 + 0.110098i
\(185\) −160261. + 277581.i −0.344270 + 0.596293i
\(186\) 81560.4 141267.i 0.172861 0.299404i
\(187\) −63363.5 109749.i −0.132506 0.229507i
\(188\) 215885. 0.445479
\(189\) 0 0
\(190\) 476843. 0.958277
\(191\) 121292. + 210084.i 0.240574 + 0.416687i 0.960878 0.276972i \(-0.0893308\pi\)
−0.720304 + 0.693659i \(0.755998\pi\)
\(192\) 18432.0 31925.2i 0.0360844 0.0625000i
\(193\) 290762. 503615.i 0.561882 0.973208i −0.435451 0.900213i \(-0.643411\pi\)
0.997332 0.0729950i \(-0.0232557\pi\)
\(194\) 84362.8 + 146121.i 0.160933 + 0.278745i
\(195\) −318699. −0.600197
\(196\) 0 0
\(197\) 748916. 1.37489 0.687444 0.726237i \(-0.258733\pi\)
0.687444 + 0.726237i \(0.258733\pi\)
\(198\) 14167.8 + 24539.4i 0.0256827 + 0.0444838i
\(199\) 362846. 628468.i 0.649516 1.12500i −0.333722 0.942671i \(-0.608305\pi\)
0.983239 0.182324i \(-0.0583619\pi\)
\(200\) 29525.6 51139.9i 0.0521944 0.0904033i
\(201\) 208800. + 361652.i 0.364535 + 0.631394i
\(202\) 713896. 1.23100
\(203\) 0 0
\(204\) 208662. 0.351049
\(205\) −306663. 531156.i −0.509656 0.882750i
\(206\) −70452.3 + 122027.i −0.115672 + 0.200349i
\(207\) 36946.0 63992.4i 0.0599297 0.103801i
\(208\) −96584.4 167289.i −0.154792 0.268108i
\(209\) −222159. −0.351801
\(210\) 0 0
\(211\) 814718. 1.25980 0.629899 0.776677i \(-0.283096\pi\)
0.629899 + 0.776677i \(0.283096\pi\)
\(212\) 77421.6 + 134098.i 0.118310 + 0.204920i
\(213\) −14829.3 + 25685.1i −0.0223960 + 0.0387910i
\(214\) −179922. + 311634.i −0.268565 + 0.465168i
\(215\) 288089. + 498985.i 0.425041 + 0.736193i
\(216\) −46656.0 −0.0680414
\(217\) 0 0
\(218\) 740010. 1.05462
\(219\) 46071.8 + 79798.7i 0.0649120 + 0.112431i
\(220\) 32833.7 56869.6i 0.0457365 0.0792179i
\(221\) 546697. 946908.i 0.752950 1.30415i
\(222\) 122939. + 212937.i 0.167420 + 0.289980i
\(223\) −335874. −0.452288 −0.226144 0.974094i \(-0.572612\pi\)
−0.226144 + 0.974094i \(0.572612\pi\)
\(224\) 0 0
\(225\) −74736.7 −0.0984187
\(226\) 456550. + 790768.i 0.594589 + 1.02986i
\(227\) 32360.6 56050.2i 0.0416823 0.0721959i −0.844432 0.535663i \(-0.820062\pi\)
0.886114 + 0.463467i \(0.153395\pi\)
\(228\) 182897. 316787.i 0.233007 0.403581i
\(229\) −375394. 650202.i −0.473041 0.819332i 0.526483 0.850186i \(-0.323511\pi\)
−0.999524 + 0.0308542i \(0.990177\pi\)
\(230\) −171243. −0.213449
\(231\) 0 0
\(232\) 11085.9 0.0135223
\(233\) 693589. + 1.20133e6i 0.836974 + 1.44968i 0.892413 + 0.451220i \(0.149011\pi\)
−0.0554384 + 0.998462i \(0.517656\pi\)
\(234\) −122240. + 211725.i −0.145939 + 0.252774i
\(235\) −316601. + 548369.i −0.373975 + 0.647744i
\(236\) −242953. 420808.i −0.283951 0.491817i
\(237\) −887256. −1.02607
\(238\) 0 0
\(239\) −160907. −0.182213 −0.0911064 0.995841i \(-0.529040\pi\)
−0.0911064 + 0.995841i \(0.529040\pi\)
\(240\) 54062.1 + 93638.4i 0.0605850 + 0.104936i
\(241\) 642408. 1.11268e6i 0.712473 1.23404i −0.251453 0.967870i \(-0.580908\pi\)
0.963926 0.266170i \(-0.0857583\pi\)
\(242\) 306805. 531402.i 0.336763 0.583290i
\(243\) 29524.5 + 51137.9i 0.0320750 + 0.0555556i
\(244\) 11719.6 0.0126019
\(245\) 0 0
\(246\) −470493. −0.495696
\(247\) −958388. 1.65998e6i −0.999537 1.73125i
\(248\) −144996. + 251141.i −0.149702 + 0.259291i
\(249\) 395067. 684276.i 0.403806 0.699412i
\(250\) 379906. + 658017.i 0.384438 + 0.665866i
\(251\) −481311. −0.482216 −0.241108 0.970498i \(-0.577511\pi\)
−0.241108 + 0.970498i \(0.577511\pi\)
\(252\) 0 0
\(253\) 79781.4 0.0783611
\(254\) 687029. + 1.18997e6i 0.668176 + 1.15732i
\(255\) −306008. + 530022.i −0.294702 + 0.510439i
\(256\) −32768.0 + 56755.8i −0.0312500 + 0.0541266i
\(257\) −16544.3 28655.6i −0.0156249 0.0270631i 0.858107 0.513470i \(-0.171640\pi\)
−0.873732 + 0.486407i \(0.838307\pi\)
\(258\) 441997. 0.413399
\(259\) 0 0
\(260\) 566575. 0.519786
\(261\) −7015.28 12150.8i −0.00637447 0.0110409i
\(262\) 722544. 1.25148e6i 0.650296 1.12635i
\(263\) −223100. + 386421.i −0.198889 + 0.344485i −0.948168 0.317768i \(-0.897067\pi\)
0.749280 + 0.662254i \(0.230400\pi\)
\(264\) −25187.3 43625.7i −0.0222419 0.0385241i
\(265\) −454164. −0.397281
\(266\) 0 0
\(267\) 621898. 0.533877
\(268\) −371199. 642936.i −0.315697 0.546803i
\(269\) 974269. 1.68748e6i 0.820915 1.42187i −0.0840873 0.996458i \(-0.526797\pi\)
0.905002 0.425407i \(-0.139869\pi\)
\(270\) 68422.4 118511.i 0.0571201 0.0989349i
\(271\) 48436.5 + 83894.5i 0.0400636 + 0.0693921i 0.885362 0.464903i \(-0.153911\pi\)
−0.845298 + 0.534295i \(0.820577\pi\)
\(272\) −370954. −0.304017
\(273\) 0 0
\(274\) −1.21851e6 −0.980510
\(275\) −40346.7 69882.5i −0.0321718 0.0557233i
\(276\) −65681.9 + 113764.i −0.0519006 + 0.0898945i
\(277\) −818393. + 1.41750e6i −0.640859 + 1.11000i 0.344382 + 0.938830i \(0.388088\pi\)
−0.985241 + 0.171171i \(0.945245\pi\)
\(278\) −259474. 449422.i −0.201364 0.348772i
\(279\) 367022. 0.282281
\(280\) 0 0
\(281\) −1.79558e6 −1.35656 −0.678281 0.734803i \(-0.737275\pi\)
−0.678281 + 0.734803i \(0.737275\pi\)
\(282\) 242870. + 420664.i 0.181866 + 0.315001i
\(283\) 640238. 1.10892e6i 0.475199 0.823068i −0.524398 0.851473i \(-0.675710\pi\)
0.999596 + 0.0284051i \(0.00904285\pi\)
\(284\) 26363.1 45662.3i 0.0193955 0.0335940i
\(285\) 536448. + 929155.i 0.391215 + 0.677604i
\(286\) −263965. −0.190823
\(287\) 0 0
\(288\) 82944.0 0.0589256
\(289\) −339929. 588774.i −0.239410 0.414671i
\(290\) −16257.8 + 28159.3i −0.0113518 + 0.0196619i
\(291\) −189816. + 328771.i −0.131402 + 0.227594i
\(292\) −81905.5 141864.i −0.0562155 0.0973680i
\(293\) −330814. −0.225120 −0.112560 0.993645i \(-0.535905\pi\)
−0.112560 + 0.993645i \(0.535905\pi\)
\(294\) 0 0
\(295\) 1.42519e6 0.953496
\(296\) −218559. 378555.i −0.144990 0.251130i
\(297\) −31877.7 + 55213.7i −0.0209698 + 0.0363208i
\(298\) −747816. + 1.29525e6i −0.487814 + 0.844918i
\(299\) 344175. + 596129.i 0.222639 + 0.385623i
\(300\) 132865. 0.0852331
\(301\) 0 0
\(302\) −346559. −0.218655
\(303\) 803133. + 1.39107e6i 0.502552 + 0.870445i
\(304\) −325150. + 563177.i −0.201790 + 0.349511i
\(305\) −17187.1 + 29768.9i −0.0105792 + 0.0183237i
\(306\) 234744. + 406589.i 0.143315 + 0.248229i
\(307\) 554088. 0.335531 0.167766 0.985827i \(-0.446345\pi\)
0.167766 + 0.985827i \(0.446345\pi\)
\(308\) 0 0
\(309\) −317035. −0.188891
\(310\) −425282. 736611.i −0.251347 0.435345i
\(311\) −879628. + 1.52356e6i −0.515701 + 0.893221i 0.484133 + 0.874995i \(0.339135\pi\)
−0.999834 + 0.0182260i \(0.994198\pi\)
\(312\) 217315. 376400.i 0.126387 0.218909i
\(313\) −1.16910e6 2.02493e6i −0.674512 1.16829i −0.976611 0.215012i \(-0.931021\pi\)
0.302099 0.953276i \(-0.402313\pi\)
\(314\) −1.84869e6 −1.05813
\(315\) 0 0
\(316\) 1.57734e6 0.888605
\(317\) 483696. + 837786.i 0.270349 + 0.468258i 0.968951 0.247252i \(-0.0795277\pi\)
−0.698602 + 0.715510i \(0.746194\pi\)
\(318\) −174199. + 301721.i −0.0966000 + 0.167316i
\(319\) 7574.41 13119.3i 0.00416747 0.00721827i
\(320\) −96110.5 166468.i −0.0524681 0.0908775i
\(321\) −809648. −0.438565
\(322\) 0 0
\(323\) −3.68090e6 −1.96313
\(324\) −52488.0 90911.9i −0.0277778 0.0481125i
\(325\) 348110. 602943.i 0.182813 0.316642i
\(326\) −1.21806e6 + 2.10975e6i −0.634784 + 1.09948i
\(327\) 832511. + 1.44195e6i 0.430547 + 0.745729i
\(328\) 836433. 0.429286
\(329\) 0 0
\(330\) 147752. 0.0746874
\(331\) 163904. + 283890.i 0.0822281 + 0.142423i 0.904207 0.427095i \(-0.140463\pi\)
−0.821979 + 0.569518i \(0.807130\pi\)
\(332\) −702341. + 1.21649e6i −0.349706 + 0.605708i
\(333\) −276613. + 479108.i −0.136698 + 0.236768i
\(334\) 255572. + 442664.i 0.125357 + 0.217124i
\(335\) 2.17750e6 1.06010
\(336\) 0 0
\(337\) 1.34052e6 0.642983 0.321491 0.946913i \(-0.395816\pi\)
0.321491 + 0.946913i \(0.395816\pi\)
\(338\) −396152. 686156.i −0.188613 0.326687i
\(339\) −1.02724e6 + 1.77923e6i −0.485480 + 0.840877i
\(340\) 544015. 942261.i 0.255219 0.442053i
\(341\) 198137. + 343183.i 0.0922741 + 0.159823i
\(342\) 823037. 0.380500
\(343\) 0 0
\(344\) −785772. −0.358014
\(345\) −192649. 333677.i −0.0871402 0.150931i
\(346\) 285078. 493770.i 0.128019 0.221735i
\(347\) 1.76687e6 3.06031e6i 0.787736 1.36440i −0.139615 0.990206i \(-0.544586\pi\)
0.927351 0.374193i \(-0.122080\pi\)
\(348\) 12471.6 + 21601.5i 0.00552045 + 0.00956170i
\(349\) 3.98108e6 1.74959 0.874796 0.484491i \(-0.160995\pi\)
0.874796 + 0.484491i \(0.160995\pi\)
\(350\) 0 0
\(351\) −550078. −0.238318
\(352\) 44777.4 + 77556.7i 0.0192620 + 0.0333628i
\(353\) 22139.6 38346.8i 0.00945654 0.0163792i −0.861258 0.508167i \(-0.830323\pi\)
0.870715 + 0.491788i \(0.163657\pi\)
\(354\) 546645. 946817.i 0.231845 0.401567i
\(355\) 77324.6 + 133930.i 0.0325647 + 0.0564037i
\(356\) −1.10560e6 −0.462351
\(357\) 0 0
\(358\) −1.18654e6 −0.489299
\(359\) 875569. + 1.51653e6i 0.358554 + 0.621034i 0.987719 0.156238i \(-0.0499366\pi\)
−0.629166 + 0.777271i \(0.716603\pi\)
\(360\) −121640. + 210686.i −0.0494674 + 0.0856801i
\(361\) −1.98835e6 + 3.44393e6i −0.803019 + 1.39087i
\(362\) 555308. + 961821.i 0.222721 + 0.385765i
\(363\) 1.38062e6 0.549931
\(364\) 0 0
\(365\) 480467. 0.188769
\(366\) 13184.5 + 22836.2i 0.00514471 + 0.00891091i
\(367\) −1.98557e6 + 3.43911e6i −0.769521 + 1.33285i 0.168302 + 0.985735i \(0.446172\pi\)
−0.937823 + 0.347114i \(0.887162\pi\)
\(368\) 116768. 202248.i 0.0449473 0.0778510i
\(369\) −529305. 916783.i −0.202367 0.350510i
\(370\) 1.28209e6 0.486871
\(371\) 0 0
\(372\) −652483. −0.244462
\(373\) −1.11980e6 1.93955e6i −0.416743 0.721820i 0.578867 0.815422i \(-0.303495\pi\)
−0.995610 + 0.0936023i \(0.970162\pi\)
\(374\) −253454. + 438995.i −0.0936958 + 0.162286i
\(375\) −854789. + 1.48054e6i −0.313892 + 0.543677i
\(376\) −431769. 747847.i −0.157501 0.272799i
\(377\) 130703. 0.0473624
\(378\) 0 0
\(379\) −4.25421e6 −1.52132 −0.760661 0.649149i \(-0.775125\pi\)
−0.760661 + 0.649149i \(0.775125\pi\)
\(380\) −953685. 1.65183e6i −0.338802 0.586822i
\(381\) −1.54582e6 + 2.67743e6i −0.545564 + 0.944944i
\(382\) 485169. 840337.i 0.170112 0.294642i
\(383\) −809417. 1.40195e6i −0.281952 0.488355i 0.689913 0.723892i \(-0.257649\pi\)
−0.971865 + 0.235537i \(0.924315\pi\)
\(384\) −147456. −0.0510310
\(385\) 0 0
\(386\) −2.32610e6 −0.794621
\(387\) 497246. + 861256.i 0.168770 + 0.292318i
\(388\) 337451. 584482.i 0.113797 0.197102i
\(389\) 676577. 1.17187e6i 0.226696 0.392648i −0.730131 0.683307i \(-0.760541\pi\)
0.956827 + 0.290659i \(0.0938744\pi\)
\(390\) 637397. + 1.10400e6i 0.212202 + 0.367544i
\(391\) 1.32188e6 0.437271
\(392\) 0 0
\(393\) 3.25145e6 1.06193
\(394\) −1.49783e6 2.59432e6i −0.486097 0.841944i
\(395\) −2.31322e6 + 4.00662e6i −0.745975 + 1.29207i
\(396\) 56671.4 98157.7i 0.0181604 0.0314548i
\(397\) 214028. + 370707.i 0.0681545 + 0.118047i 0.898089 0.439814i \(-0.144956\pi\)
−0.829934 + 0.557861i \(0.811622\pi\)
\(398\) −2.90277e6 −0.918555
\(399\) 0 0
\(400\) −236205. −0.0738140
\(401\) 59114.1 + 102389.i 0.0183582 + 0.0317973i 0.875059 0.484017i \(-0.160823\pi\)
−0.856700 + 0.515814i \(0.827489\pi\)
\(402\) 835199. 1.44661e6i 0.257765 0.446463i
\(403\) −1.70952e6 + 2.96097e6i −0.524338 + 0.908180i
\(404\) −1.42779e6 2.47301e6i −0.435223 0.753828i
\(405\) 307901. 0.0932767
\(406\) 0 0
\(407\) −597320. −0.178740
\(408\) −417323. 722825.i −0.124114 0.214972i
\(409\) −604871. + 1.04767e6i −0.178795 + 0.309682i −0.941468 0.337102i \(-0.890553\pi\)
0.762673 + 0.646784i \(0.223886\pi\)
\(410\) −1.22665e6 + 2.12463e6i −0.360381 + 0.624199i
\(411\) −1.37082e6 2.37433e6i −0.400291 0.693325i
\(412\) 563619. 0.163585
\(413\) 0 0
\(414\) −295568. −0.0847534
\(415\) −2.06001e6 3.56804e6i −0.587149 1.01697i
\(416\) −386338. + 669156.i −0.109455 + 0.189581i
\(417\) 583816. 1.01120e6i 0.164413 0.284772i
\(418\) 444317. + 769580.i 0.124381 + 0.215433i
\(419\) 4.12593e6 1.14812 0.574059 0.818814i \(-0.305368\pi\)
0.574059 + 0.818814i \(0.305368\pi\)
\(420\) 0 0
\(421\) 3.12374e6 0.858953 0.429477 0.903078i \(-0.358698\pi\)
0.429477 + 0.903078i \(0.358698\pi\)
\(422\) −1.62944e6 2.82227e6i −0.445406 0.771466i
\(423\) −546458. + 946493.i −0.148493 + 0.257197i
\(424\) 309687. 536393.i 0.0836580 0.144900i
\(425\) −668496. 1.15787e6i −0.179526 0.310948i
\(426\) 118634. 0.0316728
\(427\) 0 0
\(428\) 1.43937e6 0.379808
\(429\) −296960. 514350.i −0.0779032 0.134932i
\(430\) 1.15236e6 1.99594e6i 0.300550 0.520567i
\(431\) −557293. + 965260.i −0.144507 + 0.250294i −0.929189 0.369605i \(-0.879493\pi\)
0.784682 + 0.619899i \(0.212826\pi\)
\(432\) 93312.0 + 161621.i 0.0240563 + 0.0416667i
\(433\) 266138. 0.0682161 0.0341080 0.999418i \(-0.489141\pi\)
0.0341080 + 0.999418i \(0.489141\pi\)
\(434\) 0 0
\(435\) −73159.9 −0.0185375
\(436\) −1.48002e6 2.56347e6i −0.372865 0.645820i
\(437\) 1.15866e6 2.00686e6i 0.290238 0.502706i
\(438\) 184287. 319195.i 0.0458997 0.0795007i
\(439\) −1.23023e6 2.13083e6i −0.304668 0.527700i 0.672519 0.740079i \(-0.265212\pi\)
−0.977187 + 0.212379i \(0.931879\pi\)
\(440\) −262669. −0.0646812
\(441\) 0 0
\(442\) −4.37358e6 −1.06483
\(443\) 605404. + 1.04859e6i 0.146567 + 0.253861i 0.929956 0.367670i \(-0.119844\pi\)
−0.783390 + 0.621531i \(0.786511\pi\)
\(444\) 491757. 851748.i 0.118384 0.205047i
\(445\) 1.62139e6 2.80833e6i 0.388139 0.672277i
\(446\) 671749. + 1.16350e6i 0.159908 + 0.276969i
\(447\) −3.36517e6 −0.796596
\(448\) 0 0
\(449\) −3.66337e6 −0.857561 −0.428781 0.903409i \(-0.641057\pi\)
−0.428781 + 0.903409i \(0.641057\pi\)
\(450\) 149473. + 258896.i 0.0347963 + 0.0602689i
\(451\) 571492. 989853.i 0.132303 0.229155i
\(452\) 1.82620e6 3.16307e6i 0.420438 0.728220i
\(453\) −389879. 675291.i −0.0892657 0.154613i
\(454\) −258885. −0.0589477
\(455\) 0 0
\(456\) −1.46318e6 −0.329522
\(457\) 4.36934e6 + 7.56792e6i 0.978645 + 1.69506i 0.667340 + 0.744754i \(0.267433\pi\)
0.311306 + 0.950310i \(0.399234\pi\)
\(458\) −1.50158e6 + 2.60081e6i −0.334491 + 0.579355i
\(459\) −528175. + 914825.i −0.117016 + 0.202678i
\(460\) 342487. + 593204.i 0.0754656 + 0.130710i
\(461\) 1.23476e6 0.270602 0.135301 0.990805i \(-0.456800\pi\)
0.135301 + 0.990805i \(0.456800\pi\)
\(462\) 0 0
\(463\) −4.07764e6 −0.884008 −0.442004 0.897013i \(-0.645732\pi\)
−0.442004 + 0.897013i \(0.645732\pi\)
\(464\) −22171.8 38402.6i −0.00478085 0.00828068i
\(465\) 956886. 1.65737e6i 0.205224 0.355458i
\(466\) 2.77435e6 4.80532e6i 0.591830 1.02508i
\(467\) −2.62510e6 4.54681e6i −0.556999 0.964750i −0.997745 0.0671184i \(-0.978619\pi\)
0.440746 0.897632i \(-0.354714\pi\)
\(468\) 977917. 0.206389
\(469\) 0 0
\(470\) 2.53281e6 0.528881
\(471\) −2.07978e6 3.60228e6i −0.431981 0.748214i
\(472\) −971814. + 1.68323e6i −0.200784 + 0.347767i
\(473\) −536878. + 929900.i −0.110337 + 0.191110i
\(474\) 1.77451e6 + 3.07354e6i 0.362771 + 0.628338i
\(475\) −2.34381e6 −0.476639
\(476\) 0 0
\(477\) −783894. −0.157747
\(478\) 321813. + 557397.i 0.0644220 + 0.111582i
\(479\) −843534. + 1.46104e6i −0.167982 + 0.290954i −0.937710 0.347418i \(-0.887059\pi\)
0.769728 + 0.638372i \(0.220392\pi\)
\(480\) 216249. 374553.i 0.0428401 0.0742012i
\(481\) −2.57682e6 4.46319e6i −0.507834 0.879595i
\(482\) −5.13927e6 −1.00759
\(483\) 0 0
\(484\) −2.45444e6 −0.476254
\(485\) 989763. + 1.71432e6i 0.191063 + 0.330931i
\(486\) 118098. 204552.i 0.0226805 0.0392837i
\(487\) −2.19760e6 + 3.80635e6i −0.419881 + 0.727255i −0.995927 0.0901621i \(-0.971261\pi\)
0.576046 + 0.817417i \(0.304595\pi\)
\(488\) −23439.1 40597.8i −0.00445545 0.00771707i
\(489\) −5.48129e6 −1.03660
\(490\) 0 0
\(491\) 2.13582e6 0.399817 0.199909 0.979815i \(-0.435935\pi\)
0.199909 + 0.979815i \(0.435935\pi\)
\(492\) 940987. + 1.62984e6i 0.175255 + 0.303551i
\(493\) 125499. 217371.i 0.0232554 0.0402795i
\(494\) −3.83355e6 + 6.63991e6i −0.706780 + 1.22418i
\(495\) 166220. + 287902.i 0.0304910 + 0.0528119i
\(496\) 1.15997e6 0.211711
\(497\) 0 0
\(498\) −3.16054e6 −0.571067
\(499\) 967196. + 1.67523e6i 0.173885 + 0.301178i 0.939775 0.341794i \(-0.111034\pi\)
−0.765890 + 0.642972i \(0.777701\pi\)
\(500\) 1.51962e6 2.63207e6i 0.271839 0.470838i
\(501\) −575037. + 995993.i −0.102353 + 0.177281i
\(502\) 962622. + 1.66731e6i 0.170489 + 0.295296i
\(503\) 9.47334e6 1.66949 0.834744 0.550639i \(-0.185616\pi\)
0.834744 + 0.550639i \(0.185616\pi\)
\(504\) 0 0
\(505\) 8.37559e6 1.46146
\(506\) −159563. 276371.i −0.0277048 0.0479862i
\(507\) 891343. 1.54385e6i 0.154002 0.266738i
\(508\) 2.74812e6 4.75988e6i 0.472472 0.818346i
\(509\) 5.27947e6 + 9.14431e6i 0.903225 + 1.56443i 0.823282 + 0.567632i \(0.192140\pi\)
0.0799428 + 0.996799i \(0.474526\pi\)
\(510\) 2.44807e6 0.416771
\(511\) 0 0
\(512\) 262144. 0.0441942
\(513\) 925917. + 1.60373e6i 0.155338 + 0.269054i
\(514\) −66177.3 + 114622.i −0.0110484 + 0.0191365i
\(515\) −826563. + 1.43165e6i −0.137328 + 0.237858i
\(516\) −883994. 1.53112e6i −0.146159 0.253154i
\(517\) −1.18002e6 −0.194162
\(518\) 0 0
\(519\) 1.28285e6 0.209054
\(520\) −1.13315e6 1.96267e6i −0.183772 0.318302i
\(521\) 3.76595e6 6.52282e6i 0.607827 1.05279i −0.383770 0.923429i \(-0.625375\pi\)
0.991598 0.129359i \(-0.0412921\pi\)
\(522\) −28061.1 + 48603.3i −0.00450743 + 0.00780710i
\(523\) 3.66658e6 + 6.35071e6i 0.586148 + 1.01524i 0.994731 + 0.102517i \(0.0326896\pi\)
−0.408583 + 0.912721i \(0.633977\pi\)
\(524\) −5.78035e6 −0.919657
\(525\) 0 0
\(526\) 1.78480e6 0.281271
\(527\) 3.28289e6 + 5.68614e6i 0.514909 + 0.891848i
\(528\) −100749. + 174503.i −0.0157274 + 0.0272406i
\(529\) 2.80207e6 4.85333e6i 0.435352 0.754051i
\(530\) 908329. + 1.57327e6i 0.140460 + 0.243284i
\(531\) 2.45990e6 0.378601
\(532\) 0 0
\(533\) 9.86162e6 1.50359
\(534\) −1.24380e6 2.15432e6i −0.188754 0.326932i
\(535\) −2.11088e6 + 3.65616e6i −0.318845 + 0.552256i
\(536\) −1.48480e6 + 2.57174e6i −0.223231 + 0.386648i
\(537\) −1.33485e6 2.31204e6i −0.199755 0.345986i
\(538\) −7.79415e6 −1.16095
\(539\) 0 0
\(540\) −547379. −0.0807800
\(541\) 6.29893e6 + 1.09101e7i 0.925281 + 1.60263i 0.791109 + 0.611676i \(0.209504\pi\)
0.134173 + 0.990958i \(0.457162\pi\)
\(542\) 193746. 335578.i 0.0283292 0.0490676i
\(543\) −1.24944e6 + 2.16410e6i −0.181851 + 0.314976i
\(544\) 741908. + 1.28502e6i 0.107486 + 0.186172i
\(545\) 8.68197e6 1.25206
\(546\) 0 0
\(547\) −4.21767e6 −0.602704 −0.301352 0.953513i \(-0.597438\pi\)
−0.301352 + 0.953513i \(0.597438\pi\)
\(548\) 2.43702e6 + 4.22104e6i 0.346663 + 0.600437i
\(549\) −29665.1 + 51381.5i −0.00420064 + 0.00727572i
\(550\) −161387. + 279530.i −0.0227489 + 0.0394023i
\(551\) −220006. 381062.i −0.0308713 0.0534707i
\(552\) 525455. 0.0733986
\(553\) 0 0
\(554\) 6.54715e6 0.906312
\(555\) 1.44235e6 + 2.49823e6i 0.198764 + 0.344270i
\(556\) −1.03790e6 + 1.79769e6i −0.142386 + 0.246619i
\(557\) 4.78265e6 8.28379e6i 0.653176 1.13133i −0.329171 0.944270i \(-0.606769\pi\)
0.982348 0.187064i \(-0.0598972\pi\)
\(558\) −734044. 1.27140e6i −0.0998013 0.172861i
\(559\) −9.26432e6 −1.25396
\(560\) 0 0
\(561\) −1.14054e6 −0.153005
\(562\) 3.59116e6 + 6.22008e6i 0.479617 + 0.830721i
\(563\) 4.69593e6 8.13359e6i 0.624382 1.08146i −0.364278 0.931290i \(-0.618684\pi\)
0.988660 0.150172i \(-0.0479826\pi\)
\(564\) 971481. 1.68266e6i 0.128599 0.222740i
\(565\) 5.35635e6 + 9.27747e6i 0.705908 + 1.22267i
\(566\) −5.12190e6 −0.672032
\(567\) 0 0
\(568\) −210905. −0.0274294
\(569\) −5.19337e6 8.99517e6i −0.672463 1.16474i −0.977204 0.212304i \(-0.931903\pi\)
0.304741 0.952435i \(-0.401430\pi\)
\(570\) 2.14579e6 3.71662e6i 0.276631 0.479138i
\(571\) −2.21480e6 + 3.83614e6i −0.284279 + 0.492385i −0.972434 0.233178i \(-0.925087\pi\)
0.688155 + 0.725563i \(0.258421\pi\)
\(572\) 527929. + 914400.i 0.0674661 + 0.116855i
\(573\) 2.18326e6 0.277791
\(574\) 0 0
\(575\) 841709. 0.106168
\(576\) −165888. 287326.i −0.0208333 0.0360844i
\(577\) 6.00910e6 1.04081e7i 0.751398 1.30146i −0.195747 0.980654i \(-0.562713\pi\)
0.947145 0.320805i \(-0.103953\pi\)
\(578\) −1.35971e6 + 2.35509e6i −0.169289 + 0.293217i
\(579\) −2.61686e6 4.53254e6i −0.324403 0.561882i
\(580\) 130062. 0.0160539
\(581\) 0 0
\(582\) 1.51853e6 0.185830
\(583\) −423186. 732979.i −0.0515656 0.0893142i
\(584\) −327622. + 567458.i −0.0397503 + 0.0688496i
\(585\) −1.43414e6 + 2.48401e6i −0.173262 + 0.300098i
\(586\) 661628. + 1.14597e6i 0.0795921 + 0.137858i
\(587\) 6.97624e6 0.835653 0.417826 0.908527i \(-0.362792\pi\)
0.417826 + 0.908527i \(0.362792\pi\)
\(588\) 0 0
\(589\) 1.15102e7 1.36708
\(590\) −2.85039e6 4.93701e6i −0.337112 0.583894i
\(591\) 3.37012e6 5.83722e6i 0.396896 0.687444i
\(592\) −874234. + 1.51422e6i −0.102524 + 0.177576i
\(593\) 890739. + 1.54281e6i 0.104019 + 0.180167i 0.913337 0.407204i \(-0.133496\pi\)
−0.809318 + 0.587371i \(0.800163\pi\)
\(594\) 255021. 0.0296558
\(595\) 0 0
\(596\) 5.98253e6 0.689873
\(597\) −3.26562e6 5.65622e6i −0.374998 0.649516i
\(598\) 1.37670e6 2.38452e6i 0.157430 0.272676i
\(599\) −801823. + 1.38880e6i −0.0913085 + 0.158151i −0.908062 0.418836i \(-0.862438\pi\)
0.816753 + 0.576987i \(0.195772\pi\)
\(600\) −265730. 460259.i −0.0301344 0.0521944i
\(601\) −1.51165e7 −1.70712 −0.853562 0.520991i \(-0.825562\pi\)
−0.853562 + 0.520991i \(0.825562\pi\)
\(602\) 0 0
\(603\) 3.75839e6 0.420929
\(604\) 693119. + 1.20052e6i 0.0773064 + 0.133899i
\(605\) 3.59951e6 6.23453e6i 0.399811 0.692493i
\(606\) 3.21253e6 5.56427e6i 0.355358 0.615498i
\(607\) −5.25833e6 9.10769e6i −0.579263 1.00331i −0.995564 0.0940863i \(-0.970007\pi\)
0.416301 0.909227i \(-0.363326\pi\)
\(608\) 2.60120e6 0.285375
\(609\) 0 0
\(610\) 137497. 0.0149612
\(611\) −5.09060e6 8.81718e6i −0.551653 0.955491i
\(612\) 938977. 1.62636e6i 0.101339 0.175524i
\(613\) −1.35649e6 + 2.34951e6i −0.145802 + 0.252537i −0.929672 0.368388i \(-0.879910\pi\)
0.783870 + 0.620925i \(0.213243\pi\)
\(614\) −1.10818e6 1.91942e6i −0.118628 0.205470i
\(615\) −5.51994e6 −0.588500
\(616\) 0 0
\(617\) 1.14961e7 1.21573 0.607864 0.794041i \(-0.292026\pi\)
0.607864 + 0.794041i \(0.292026\pi\)
\(618\) 634071. + 1.09824e6i 0.0667831 + 0.115672i
\(619\) −5.49749e6 + 9.52194e6i −0.576684 + 0.998846i 0.419172 + 0.907907i \(0.362320\pi\)
−0.995856 + 0.0909396i \(0.971013\pi\)
\(620\) −1.70113e6 + 2.94644e6i −0.177729 + 0.307836i
\(621\) −332514. 575932.i −0.0346004 0.0599297i
\(622\) 7.03702e6 0.729312
\(623\) 0 0
\(624\) −1.73852e6 −0.178738
\(625\) 3.01547e6 + 5.22294e6i 0.308784 + 0.534829i
\(626\) −4.67639e6 + 8.09974e6i −0.476952 + 0.826105i
\(627\) −999714. + 1.73156e6i −0.101556 + 0.175901i
\(628\) 3.69739e6 + 6.40406e6i 0.374107 + 0.647972i
\(629\) −9.89687e6 −0.997405
\(630\) 0 0
\(631\) −4.19503e6 −0.419432 −0.209716 0.977762i \(-0.567254\pi\)
−0.209716 + 0.977762i \(0.567254\pi\)
\(632\) −3.15469e6 5.46408e6i −0.314169 0.544157i
\(633\) 3.66623e6 6.35010e6i 0.363672 0.629899i
\(634\) 1.93478e6 3.35114e6i 0.191165 0.331108i
\(635\) 8.06039e6 + 1.39610e7i 0.793271 + 1.37399i
\(636\) 1.39359e6 0.136613
\(637\) 0 0
\(638\) −60595.3 −0.00589369
\(639\) 133463. + 231165.i 0.0129303 + 0.0223960i
\(640\) −384442. + 665873.i −0.0371006 + 0.0642601i
\(641\) 5.31352e6 9.20329e6i 0.510784 0.884704i −0.489138 0.872207i \(-0.662688\pi\)
0.999922 0.0124978i \(-0.00397826\pi\)
\(642\) 1.61930e6 + 2.80470e6i 0.155056 + 0.268565i
\(643\) 1.54228e6 0.147108 0.0735538 0.997291i \(-0.476566\pi\)
0.0735538 + 0.997291i \(0.476566\pi\)
\(644\) 0 0
\(645\) 5.18561e6 0.490795
\(646\) 7.36181e6 + 1.27510e7i 0.694070 + 1.20216i
\(647\) 6.40851e6 1.10999e7i 0.601861 1.04245i −0.390678 0.920527i \(-0.627759\pi\)
0.992539 0.121926i \(-0.0389072\pi\)
\(648\) −209952. + 363648.i −0.0196419 + 0.0340207i
\(649\) 1.32798e6 + 2.30013e6i 0.123760 + 0.214359i
\(650\) −2.78488e6 −0.258537
\(651\) 0 0
\(652\) 9.74452e6 0.897721
\(653\) 1.42275e6 + 2.46427e6i 0.130570 + 0.226155i 0.923897 0.382642i \(-0.124986\pi\)
−0.793326 + 0.608797i \(0.791652\pi\)
\(654\) 3.33004e6 5.76780e6i 0.304443 0.527310i
\(655\) 8.47705e6 1.46827e7i 0.772043 1.33722i
\(656\) −1.67287e6 2.89749e6i −0.151775 0.262883i
\(657\) 829293. 0.0749540
\(658\) 0 0
\(659\) −2.04185e7 −1.83151 −0.915755 0.401736i \(-0.868407\pi\)
−0.915755 + 0.401736i \(0.868407\pi\)
\(660\) −295503. 511826.i −0.0264060 0.0457365i
\(661\) −1.09464e7 + 1.89597e7i −0.974467 + 1.68783i −0.292786 + 0.956178i \(0.594582\pi\)
−0.681681 + 0.731649i \(0.738751\pi\)
\(662\) 655617. 1.13556e6i 0.0581440 0.100708i
\(663\) −4.92028e6 8.52217e6i −0.434716 0.752950i
\(664\) 5.61873e6 0.494559
\(665\) 0 0
\(666\) 2.21291e6 0.193320
\(667\) 79008.4 + 136847.i 0.00687636 + 0.0119102i
\(668\) 1.02229e6 1.77065e6i 0.0886405 0.153530i
\(669\) −1.51143e6 + 2.61788e6i −0.130564 + 0.226144i
\(670\) −4.35500e6 7.54308e6i −0.374801 0.649175i
\(671\) −64059.0 −0.00549255
\(672\) 0 0
\(673\) −992084. −0.0844327 −0.0422164 0.999108i \(-0.513442\pi\)
−0.0422164 + 0.999108i \(0.513442\pi\)
\(674\) −2.68104e6 4.64370e6i −0.227329 0.393745i
\(675\) −336315. + 582515.i −0.0284110 + 0.0492094i
\(676\) −1.58461e6 + 2.74462e6i −0.133369 + 0.231002i
\(677\) 3.91748e6 + 6.78528e6i 0.328500 + 0.568979i 0.982214 0.187763i \(-0.0601235\pi\)
−0.653714 + 0.756741i \(0.726790\pi\)
\(678\) 8.21790e6 0.686573
\(679\) 0 0
\(680\) −4.35212e6 −0.360935
\(681\) −291245. 504452.i −0.0240653 0.0416823i
\(682\) 792548. 1.37273e6i 0.0652476 0.113012i
\(683\) 3.70591e6 6.41883e6i 0.303979 0.526507i −0.673055 0.739593i \(-0.735018\pi\)
0.977033 + 0.213086i \(0.0683515\pi\)
\(684\) −1.64607e6 2.85108e6i −0.134527 0.233007i
\(685\) −1.42958e7 −1.16408
\(686\) 0 0
\(687\) −6.75710e6 −0.546221
\(688\) 1.57154e6 + 2.72199e6i 0.126577 + 0.219238i
\(689\) 3.65123e6 6.32412e6i 0.293016 0.507519i
\(690\) −770595. + 1.33471e6i −0.0616174 + 0.106724i
\(691\) −5.02584e6 8.70502e6i −0.400418 0.693545i 0.593358 0.804939i \(-0.297802\pi\)
−0.993776 + 0.111394i \(0.964468\pi\)
\(692\) −2.28063e6 −0.181046
\(693\) 0 0
\(694\) −1.41350e7 −1.11403
\(695\) −3.04421e6 5.27272e6i −0.239063 0.414069i
\(696\) 49886.5 86405.9i 0.00390355 0.00676114i
\(697\) 9.46894e6 1.64007e7i 0.738277 1.27873i
\(698\) −7.96215e6 1.37908e7i −0.618574 1.07140i
\(699\) 1.24846e7 0.966455
\(700\) 0 0
\(701\) 1.59518e7 1.22607 0.613034 0.790057i \(-0.289949\pi\)
0.613034 + 0.790057i \(0.289949\pi\)
\(702\) 1.10016e6 + 1.90553e6i 0.0842581 + 0.145939i
\(703\) −8.67486e6 + 1.50253e7i −0.662024 + 1.14666i
\(704\) 179110. 310227.i 0.0136203 0.0235911i
\(705\) 2.84941e6 + 4.93533e6i 0.215915 + 0.373975i
\(706\) −177116. −0.0133736
\(707\) 0 0
\(708\) −4.37316e6 −0.327878
\(709\) 1.91312e6 + 3.31361e6i 0.142931 + 0.247563i 0.928599 0.371085i \(-0.121014\pi\)
−0.785668 + 0.618648i \(0.787681\pi\)
\(710\) 309299. 535721.i 0.0230267 0.0398834i
\(711\) −3.99265e6 + 6.91548e6i −0.296202 + 0.513036i
\(712\) 2.21119e6 + 3.82990e6i 0.163466 + 0.283131i
\(713\) −4.13352e6 −0.304506
\(714\) 0 0
\(715\) −3.09690e6 −0.226549
\(716\) 2.37308e6 + 4.11029e6i 0.172993 + 0.299633i
\(717\) −724080. + 1.25414e6i −0.0526003 + 0.0911064i
\(718\) 3.50228e6 6.06612e6i 0.253536 0.439137i
\(719\) −3.96365e6 6.86525e6i −0.285939 0.495261i 0.686897 0.726754i \(-0.258972\pi\)
−0.972836 + 0.231493i \(0.925639\pi\)
\(720\) 973118. 0.0699575
\(721\) 0 0
\(722\) 1.59068e7 1.13564
\(723\) −5.78167e6 1.00142e7i −0.411347 0.712473i
\(724\) 2.22123e6 3.84728e6i 0.157488 0.272777i
\(725\) 79911.5 138411.i 0.00564630 0.00977968i
\(726\) −2.76124e6 4.78262e6i −0.194430 0.336763i
\(727\) −3.24519e6 −0.227722 −0.113861 0.993497i \(-0.536322\pi\)
−0.113861 + 0.993497i \(0.536322\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −960934. 1.66439e6i −0.0667400 0.115597i
\(731\) −8.89542e6 + 1.54073e7i −0.615706 + 1.06643i
\(732\) 52738.0 91344.9i 0.00363786 0.00630096i
\(733\) 2.98840e6 + 5.17605e6i 0.205437 + 0.355827i 0.950272 0.311422i \(-0.100805\pi\)
−0.744835 + 0.667249i \(0.767472\pi\)
\(734\) 1.58846e7 1.08827
\(735\) 0 0
\(736\) −934142. −0.0635650
\(737\) 2.02897e6 + 3.51428e6i 0.137596 + 0.238324i
\(738\) −2.11722e6 + 3.66713e6i −0.143095 + 0.247848i
\(739\) 1.30032e6 2.25222e6i 0.0875870 0.151705i −0.818904 0.573931i \(-0.805418\pi\)
0.906491 + 0.422226i \(0.138751\pi\)
\(740\) −2.56418e6 4.44129e6i −0.172135 0.298147i
\(741\) −1.72510e7 −1.15417
\(742\) 0 0
\(743\) −2.29585e7 −1.52571 −0.762854 0.646571i \(-0.776203\pi\)
−0.762854 + 0.646571i \(0.776203\pi\)
\(744\) 1.30497e6 + 2.26027e6i 0.0864305 + 0.149702i
\(745\) −8.77355e6 + 1.51962e7i −0.579141 + 1.00310i
\(746\) −4.47920e6 + 7.75820e6i −0.294682 + 0.510404i
\(747\) −3.55560e6 6.15848e6i −0.233137 0.403806i
\(748\) 2.02763e6 0.132506
\(749\) 0 0
\(750\) 6.83831e6 0.443911
\(751\) −2.30159e6 3.98647e6i −0.148911 0.257922i 0.781914 0.623386i \(-0.214244\pi\)
−0.930825 + 0.365464i \(0.880910\pi\)
\(752\) −1.72708e6 + 2.99139e6i −0.111370 + 0.192898i
\(753\) −2.16590e6 + 3.75145e6i −0.139204 + 0.241108i
\(754\) −261407. 452770.i −0.0167451 0.0290034i
\(755\) −4.06591e6 −0.259592
\(756\) 0 0
\(757\) 4.78695e6 0.303612 0.151806 0.988410i \(-0.451491\pi\)
0.151806 + 0.988410i \(0.451491\pi\)
\(758\) 8.50843e6 + 1.47370e7i 0.537869 + 0.931616i
\(759\) 359016. 621835.i 0.0226209 0.0391805i
\(760\) −3.81474e6 + 6.60733e6i −0.239569 + 0.414946i
\(761\) −1.14221e7 1.97836e7i −0.714962 1.23835i −0.962974 0.269593i \(-0.913111\pi\)
0.248013 0.968757i \(-0.420223\pi\)
\(762\) 1.23665e7 0.771544
\(763\) 0 0
\(764\) −3.88135e6 −0.240574
\(765\) 2.75408e6 + 4.77020e6i 0.170146 + 0.294702i
\(766\) −3.23767e6 + 5.60780e6i −0.199370 + 0.345319i
\(767\) −1.14578e7 + 1.98454e7i −0.703253 + 1.21807i
\(768\) 294912. + 510803.i 0.0180422 + 0.0312500i
\(769\) −1.02787e7 −0.626793 −0.313397 0.949622i \(-0.601467\pi\)
−0.313397 +