Properties

Label 294.4.e.h.79.1
Level $294$
Weight $4$
Character 294.79
Analytic conductor $17.347$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,4,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, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.4.e.h.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-3.00000 + 5.19615i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-3.00000 + 5.19615i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(6.00000 + 10.3923i) q^{10} +(-6.00000 - 10.3923i) q^{11} +(6.00000 - 10.3923i) q^{12} +38.0000 q^{13} -18.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(63.0000 + 109.119i) q^{17} +(9.00000 + 15.5885i) q^{18} +(-10.0000 + 17.3205i) q^{19} +24.0000 q^{20} -24.0000 q^{22} +(-84.0000 + 145.492i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(44.5000 + 77.0763i) q^{25} +(38.0000 - 65.8179i) q^{26} -27.0000 q^{27} +30.0000 q^{29} +(-18.0000 + 31.1769i) q^{30} +(44.0000 + 76.2102i) q^{31} +(16.0000 + 27.7128i) q^{32} +(18.0000 - 31.1769i) q^{33} +252.000 q^{34} +36.0000 q^{36} +(-127.000 + 219.970i) q^{37} +(20.0000 + 34.6410i) q^{38} +(57.0000 + 98.7269i) q^{39} +(24.0000 - 41.5692i) q^{40} +42.0000 q^{41} -52.0000 q^{43} +(-24.0000 + 41.5692i) q^{44} +(-27.0000 - 46.7654i) q^{45} +(168.000 + 290.985i) q^{46} +(48.0000 - 83.1384i) q^{47} -48.0000 q^{48} +178.000 q^{50} +(-189.000 + 327.358i) q^{51} +(-76.0000 - 131.636i) q^{52} +(-99.0000 - 171.473i) q^{53} +(-27.0000 + 46.7654i) q^{54} +72.0000 q^{55} -60.0000 q^{57} +(30.0000 - 51.9615i) q^{58} +(330.000 + 571.577i) q^{59} +(36.0000 + 62.3538i) q^{60} +(269.000 - 465.922i) q^{61} +176.000 q^{62} +64.0000 q^{64} +(-114.000 + 197.454i) q^{65} +(-36.0000 - 62.3538i) q^{66} +(-442.000 - 765.566i) q^{67} +(252.000 - 436.477i) q^{68} -504.000 q^{69} +792.000 q^{71} +(36.0000 - 62.3538i) q^{72} +(-109.000 - 188.794i) q^{73} +(254.000 + 439.941i) q^{74} +(-133.500 + 231.229i) q^{75} +80.0000 q^{76} +228.000 q^{78} +(260.000 - 450.333i) q^{79} +(-48.0000 - 83.1384i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(42.0000 - 72.7461i) q^{82} -492.000 q^{83} -756.000 q^{85} +(-52.0000 + 90.0666i) q^{86} +(45.0000 + 77.9423i) q^{87} +(48.0000 + 83.1384i) q^{88} +(-405.000 + 701.481i) q^{89} -108.000 q^{90} +672.000 q^{92} +(-132.000 + 228.631i) q^{93} +(-96.0000 - 166.277i) q^{94} +(-60.0000 - 103.923i) q^{95} +(-48.0000 + 83.1384i) q^{96} +1154.00 q^{97} +108.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 6 q^{5} + 12 q^{6} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 6 q^{5} + 12 q^{6} - 16 q^{8} - 9 q^{9} + 12 q^{10} - 12 q^{11} + 12 q^{12} + 76 q^{13} - 36 q^{15} - 16 q^{16} + 126 q^{17} + 18 q^{18} - 20 q^{19} + 48 q^{20} - 48 q^{22} - 168 q^{23} - 24 q^{24} + 89 q^{25} + 76 q^{26} - 54 q^{27} + 60 q^{29} - 36 q^{30} + 88 q^{31} + 32 q^{32} + 36 q^{33} + 504 q^{34} + 72 q^{36} - 254 q^{37} + 40 q^{38} + 114 q^{39} + 48 q^{40} + 84 q^{41} - 104 q^{43} - 48 q^{44} - 54 q^{45} + 336 q^{46} + 96 q^{47} - 96 q^{48} + 356 q^{50} - 378 q^{51} - 152 q^{52} - 198 q^{53} - 54 q^{54} + 144 q^{55} - 120 q^{57} + 60 q^{58} + 660 q^{59} + 72 q^{60} + 538 q^{61} + 352 q^{62} + 128 q^{64} - 228 q^{65} - 72 q^{66} - 884 q^{67} + 504 q^{68} - 1008 q^{69} + 1584 q^{71} + 72 q^{72} - 218 q^{73} + 508 q^{74} - 267 q^{75} + 160 q^{76} + 456 q^{78} + 520 q^{79} - 96 q^{80} - 81 q^{81} + 84 q^{82} - 984 q^{83} - 1512 q^{85} - 104 q^{86} + 90 q^{87} + 96 q^{88} - 810 q^{89} - 216 q^{90} + 1344 q^{92} - 264 q^{93} - 192 q^{94} - 120 q^{95} - 96 q^{96} + 2308 q^{97} + 216 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −3.00000 + 5.19615i −0.268328 + 0.464758i −0.968430 0.249285i \(-0.919804\pi\)
0.700102 + 0.714043i \(0.253138\pi\)
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 6.00000 + 10.3923i 0.189737 + 0.328634i
\(11\) −6.00000 10.3923i −0.164461 0.284854i 0.772003 0.635619i \(-0.219255\pi\)
−0.936464 + 0.350765i \(0.885922\pi\)
\(12\) 6.00000 10.3923i 0.144338 0.250000i
\(13\) 38.0000 0.810716 0.405358 0.914158i \(-0.367147\pi\)
0.405358 + 0.914158i \(0.367147\pi\)
\(14\) 0 0
\(15\) −18.0000 −0.309839
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 63.0000 + 109.119i 0.898808 + 1.55678i 0.829019 + 0.559220i \(0.188899\pi\)
0.0697893 + 0.997562i \(0.477767\pi\)
\(18\) 9.00000 + 15.5885i 0.117851 + 0.204124i
\(19\) −10.0000 + 17.3205i −0.120745 + 0.209137i −0.920062 0.391773i \(-0.871862\pi\)
0.799317 + 0.600910i \(0.205195\pi\)
\(20\) 24.0000 0.268328
\(21\) 0 0
\(22\) −24.0000 −0.232583
\(23\) −84.0000 + 145.492i −0.761531 + 1.31901i 0.180530 + 0.983569i \(0.442219\pi\)
−0.942061 + 0.335441i \(0.891115\pi\)
\(24\) −12.0000 20.7846i −0.102062 0.176777i
\(25\) 44.5000 + 77.0763i 0.356000 + 0.616610i
\(26\) 38.0000 65.8179i 0.286631 0.496460i
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 30.0000 0.192099 0.0960493 0.995377i \(-0.469379\pi\)
0.0960493 + 0.995377i \(0.469379\pi\)
\(30\) −18.0000 + 31.1769i −0.109545 + 0.189737i
\(31\) 44.0000 + 76.2102i 0.254924 + 0.441541i 0.964875 0.262710i \(-0.0846163\pi\)
−0.709951 + 0.704251i \(0.751283\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 18.0000 31.1769i 0.0949514 0.164461i
\(34\) 252.000 1.27111
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) −127.000 + 219.970i −0.564288 + 0.977376i 0.432827 + 0.901477i \(0.357516\pi\)
−0.997115 + 0.0758992i \(0.975817\pi\)
\(38\) 20.0000 + 34.6410i 0.0853797 + 0.147882i
\(39\) 57.0000 + 98.7269i 0.234033 + 0.405358i
\(40\) 24.0000 41.5692i 0.0948683 0.164317i
\(41\) 42.0000 0.159983 0.0799914 0.996796i \(-0.474511\pi\)
0.0799914 + 0.996796i \(0.474511\pi\)
\(42\) 0 0
\(43\) −52.0000 −0.184417 −0.0922084 0.995740i \(-0.529393\pi\)
−0.0922084 + 0.995740i \(0.529393\pi\)
\(44\) −24.0000 + 41.5692i −0.0822304 + 0.142427i
\(45\) −27.0000 46.7654i −0.0894427 0.154919i
\(46\) 168.000 + 290.985i 0.538484 + 0.932681i
\(47\) 48.0000 83.1384i 0.148969 0.258021i −0.781878 0.623431i \(-0.785738\pi\)
0.930846 + 0.365410i \(0.119071\pi\)
\(48\) −48.0000 −0.144338
\(49\) 0 0
\(50\) 178.000 0.503460
\(51\) −189.000 + 327.358i −0.518927 + 0.898808i
\(52\) −76.0000 131.636i −0.202679 0.351050i
\(53\) −99.0000 171.473i −0.256579 0.444408i 0.708744 0.705466i \(-0.249262\pi\)
−0.965323 + 0.261058i \(0.915929\pi\)
\(54\) −27.0000 + 46.7654i −0.0680414 + 0.117851i
\(55\) 72.0000 0.176518
\(56\) 0 0
\(57\) −60.0000 −0.139424
\(58\) 30.0000 51.9615i 0.0679171 0.117636i
\(59\) 330.000 + 571.577i 0.728175 + 1.26124i 0.957654 + 0.287923i \(0.0929647\pi\)
−0.229478 + 0.973314i \(0.573702\pi\)
\(60\) 36.0000 + 62.3538i 0.0774597 + 0.134164i
\(61\) 269.000 465.922i 0.564622 0.977953i −0.432463 0.901652i \(-0.642355\pi\)
0.997085 0.0763018i \(-0.0243112\pi\)
\(62\) 176.000 0.360516
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −114.000 + 197.454i −0.217538 + 0.376787i
\(66\) −36.0000 62.3538i −0.0671408 0.116291i
\(67\) −442.000 765.566i −0.805954 1.39595i −0.915645 0.401987i \(-0.868320\pi\)
0.109692 0.993966i \(-0.465014\pi\)
\(68\) 252.000 436.477i 0.449404 0.778391i
\(69\) −504.000 −0.879340
\(70\) 0 0
\(71\) 792.000 1.32385 0.661923 0.749572i \(-0.269740\pi\)
0.661923 + 0.749572i \(0.269740\pi\)
\(72\) 36.0000 62.3538i 0.0589256 0.102062i
\(73\) −109.000 188.794i −0.174760 0.302693i 0.765318 0.643652i \(-0.222582\pi\)
−0.940078 + 0.340959i \(0.889248\pi\)
\(74\) 254.000 + 439.941i 0.399012 + 0.691109i
\(75\) −133.500 + 231.229i −0.205537 + 0.356000i
\(76\) 80.0000 0.120745
\(77\) 0 0
\(78\) 228.000 0.330973
\(79\) 260.000 450.333i 0.370282 0.641347i −0.619327 0.785133i \(-0.712594\pi\)
0.989609 + 0.143786i \(0.0459277\pi\)
\(80\) −48.0000 83.1384i −0.0670820 0.116190i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 42.0000 72.7461i 0.0565625 0.0979691i
\(83\) −492.000 −0.650651 −0.325325 0.945602i \(-0.605474\pi\)
−0.325325 + 0.945602i \(0.605474\pi\)
\(84\) 0 0
\(85\) −756.000 −0.964703
\(86\) −52.0000 + 90.0666i −0.0652012 + 0.112932i
\(87\) 45.0000 + 77.9423i 0.0554541 + 0.0960493i
\(88\) 48.0000 + 83.1384i 0.0581456 + 0.100711i
\(89\) −405.000 + 701.481i −0.482359 + 0.835470i −0.999795 0.0202521i \(-0.993553\pi\)
0.517436 + 0.855722i \(0.326886\pi\)
\(90\) −108.000 −0.126491
\(91\) 0 0
\(92\) 672.000 0.761531
\(93\) −132.000 + 228.631i −0.147180 + 0.254924i
\(94\) −96.0000 166.277i −0.105337 0.182448i
\(95\) −60.0000 103.923i −0.0647986 0.112235i
\(96\) −48.0000 + 83.1384i −0.0510310 + 0.0883883i
\(97\) 1154.00 1.20795 0.603974 0.797004i \(-0.293583\pi\)
0.603974 + 0.797004i \(0.293583\pi\)
\(98\) 0 0
\(99\) 108.000 0.109640
\(100\) 178.000 308.305i 0.178000 0.308305i
\(101\) 309.000 + 535.204i 0.304422 + 0.527275i 0.977133 0.212631i \(-0.0682033\pi\)
−0.672710 + 0.739906i \(0.734870\pi\)
\(102\) 378.000 + 654.715i 0.366937 + 0.635554i
\(103\) −64.0000 + 110.851i −0.0612243 + 0.106044i −0.895013 0.446040i \(-0.852834\pi\)
0.833789 + 0.552084i \(0.186167\pi\)
\(104\) −304.000 −0.286631
\(105\) 0 0
\(106\) −396.000 −0.362858
\(107\) 738.000 1278.25i 0.666777 1.15489i −0.312023 0.950075i \(-0.601007\pi\)
0.978800 0.204817i \(-0.0656600\pi\)
\(108\) 54.0000 + 93.5307i 0.0481125 + 0.0833333i
\(109\) −595.000 1030.57i −0.522850 0.905603i −0.999646 0.0265892i \(-0.991535\pi\)
0.476796 0.879014i \(-0.341798\pi\)
\(110\) 72.0000 124.708i 0.0624085 0.108095i
\(111\) −762.000 −0.651584
\(112\) 0 0
\(113\) −462.000 −0.384613 −0.192307 0.981335i \(-0.561597\pi\)
−0.192307 + 0.981335i \(0.561597\pi\)
\(114\) −60.0000 + 103.923i −0.0492940 + 0.0853797i
\(115\) −504.000 872.954i −0.408680 0.707855i
\(116\) −60.0000 103.923i −0.0480247 0.0831811i
\(117\) −171.000 + 296.181i −0.135119 + 0.234033i
\(118\) 1320.00 1.02980
\(119\) 0 0
\(120\) 144.000 0.109545
\(121\) 593.500 1027.97i 0.445905 0.772331i
\(122\) −538.000 931.843i −0.399248 0.691517i
\(123\) 63.0000 + 109.119i 0.0461831 + 0.0799914i
\(124\) 176.000 304.841i 0.127462 0.220770i
\(125\) −1284.00 −0.918756
\(126\) 0 0
\(127\) −2536.00 −1.77192 −0.885959 0.463763i \(-0.846499\pi\)
−0.885959 + 0.463763i \(0.846499\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) −78.0000 135.100i −0.0532366 0.0922084i
\(130\) 228.000 + 394.908i 0.153822 + 0.266428i
\(131\) −1146.00 + 1984.93i −0.764324 + 1.32385i 0.176279 + 0.984340i \(0.443594\pi\)
−0.940603 + 0.339508i \(0.889739\pi\)
\(132\) −144.000 −0.0949514
\(133\) 0 0
\(134\) −1768.00 −1.13979
\(135\) 81.0000 140.296i 0.0516398 0.0894427i
\(136\) −504.000 872.954i −0.317777 0.550406i
\(137\) 363.000 + 628.734i 0.226374 + 0.392091i 0.956731 0.290975i \(-0.0939796\pi\)
−0.730357 + 0.683066i \(0.760646\pi\)
\(138\) −504.000 + 872.954i −0.310894 + 0.538484i
\(139\) 380.000 0.231879 0.115939 0.993256i \(-0.463012\pi\)
0.115939 + 0.993256i \(0.463012\pi\)
\(140\) 0 0
\(141\) 288.000 0.172014
\(142\) 792.000 1371.78i 0.468050 0.810687i
\(143\) −228.000 394.908i −0.133331 0.230936i
\(144\) −72.0000 124.708i −0.0416667 0.0721688i
\(145\) −90.0000 + 155.885i −0.0515455 + 0.0892794i
\(146\) −436.000 −0.247148
\(147\) 0 0
\(148\) 1016.00 0.564288
\(149\) −795.000 + 1376.98i −0.437107 + 0.757091i −0.997465 0.0711590i \(-0.977330\pi\)
0.560358 + 0.828251i \(0.310664\pi\)
\(150\) 267.000 + 462.458i 0.145336 + 0.251730i
\(151\) −1216.00 2106.17i −0.655342 1.13509i −0.981808 0.189877i \(-0.939191\pi\)
0.326466 0.945209i \(-0.394142\pi\)
\(152\) 80.0000 138.564i 0.0426898 0.0739410i
\(153\) −1134.00 −0.599206
\(154\) 0 0
\(155\) −528.000 −0.273613
\(156\) 228.000 394.908i 0.117017 0.202679i
\(157\) −307.000 531.740i −0.156059 0.270302i 0.777385 0.629025i \(-0.216546\pi\)
−0.933444 + 0.358723i \(0.883212\pi\)
\(158\) −520.000 900.666i −0.261829 0.453501i
\(159\) 297.000 514.419i 0.148136 0.256579i
\(160\) −192.000 −0.0948683
\(161\) 0 0
\(162\) −162.000 −0.0785674
\(163\) 926.000 1603.88i 0.444969 0.770709i −0.553081 0.833127i \(-0.686548\pi\)
0.998050 + 0.0624187i \(0.0198814\pi\)
\(164\) −84.0000 145.492i −0.0399957 0.0692746i
\(165\) 108.000 + 187.061i 0.0509563 + 0.0882589i
\(166\) −492.000 + 852.169i −0.230040 + 0.398441i
\(167\) −2136.00 −0.989752 −0.494876 0.868964i \(-0.664787\pi\)
−0.494876 + 0.868964i \(0.664787\pi\)
\(168\) 0 0
\(169\) −753.000 −0.342740
\(170\) −756.000 + 1309.43i −0.341074 + 0.590757i
\(171\) −90.0000 155.885i −0.0402484 0.0697122i
\(172\) 104.000 + 180.133i 0.0461042 + 0.0798548i
\(173\) −879.000 + 1522.47i −0.386296 + 0.669084i −0.991948 0.126646i \(-0.959579\pi\)
0.605652 + 0.795729i \(0.292912\pi\)
\(174\) 180.000 0.0784239
\(175\) 0 0
\(176\) 192.000 0.0822304
\(177\) −990.000 + 1714.73i −0.420412 + 0.728175i
\(178\) 810.000 + 1402.96i 0.341079 + 0.590766i
\(179\) 270.000 + 467.654i 0.112742 + 0.195274i 0.916875 0.399175i \(-0.130703\pi\)
−0.804133 + 0.594449i \(0.797370\pi\)
\(180\) −108.000 + 187.061i −0.0447214 + 0.0774597i
\(181\) 1982.00 0.813928 0.406964 0.913444i \(-0.366588\pi\)
0.406964 + 0.913444i \(0.366588\pi\)
\(182\) 0 0
\(183\) 1614.00 0.651969
\(184\) 672.000 1163.94i 0.269242 0.466341i
\(185\) −762.000 1319.82i −0.302829 0.524515i
\(186\) 264.000 + 457.261i 0.104072 + 0.180258i
\(187\) 756.000 1309.43i 0.295637 0.512059i
\(188\) −384.000 −0.148969
\(189\) 0 0
\(190\) −240.000 −0.0916391
\(191\) 1344.00 2327.88i 0.509154 0.881881i −0.490790 0.871278i \(-0.663292\pi\)
0.999944 0.0106027i \(-0.00337499\pi\)
\(192\) 96.0000 + 166.277i 0.0360844 + 0.0625000i
\(193\) 1151.00 + 1993.59i 0.429279 + 0.743533i 0.996809 0.0798198i \(-0.0254345\pi\)
−0.567531 + 0.823352i \(0.692101\pi\)
\(194\) 1154.00 1998.79i 0.427074 0.739714i
\(195\) −684.000 −0.251191
\(196\) 0 0
\(197\) 4374.00 1.58190 0.790951 0.611880i \(-0.209586\pi\)
0.790951 + 0.611880i \(0.209586\pi\)
\(198\) 108.000 187.061i 0.0387638 0.0671408i
\(199\) 800.000 + 1385.64i 0.284977 + 0.493595i 0.972604 0.232469i \(-0.0746806\pi\)
−0.687626 + 0.726065i \(0.741347\pi\)
\(200\) −356.000 616.610i −0.125865 0.218005i
\(201\) 1326.00 2296.70i 0.465318 0.805954i
\(202\) 1236.00 0.430518
\(203\) 0 0
\(204\) 1512.00 0.518927
\(205\) −126.000 + 218.238i −0.0429279 + 0.0743533i
\(206\) 128.000 + 221.703i 0.0432921 + 0.0749842i
\(207\) −756.000 1309.43i −0.253844 0.439670i
\(208\) −304.000 + 526.543i −0.101339 + 0.175525i
\(209\) 240.000 0.0794313
\(210\) 0 0
\(211\) 3332.00 1.08713 0.543565 0.839367i \(-0.317074\pi\)
0.543565 + 0.839367i \(0.317074\pi\)
\(212\) −396.000 + 685.892i −0.128290 + 0.222204i
\(213\) 1188.00 + 2057.68i 0.382162 + 0.661923i
\(214\) −1476.00 2556.51i −0.471483 0.816632i
\(215\) 156.000 270.200i 0.0494842 0.0857092i
\(216\) 216.000 0.0680414
\(217\) 0 0
\(218\) −2380.00 −0.739422
\(219\) 327.000 566.381i 0.100898 0.174760i
\(220\) −144.000 249.415i −0.0441294 0.0764344i
\(221\) 2394.00 + 4146.53i 0.728678 + 1.26211i
\(222\) −762.000 + 1319.82i −0.230370 + 0.399012i
\(223\) 2648.00 0.795171 0.397586 0.917565i \(-0.369848\pi\)
0.397586 + 0.917565i \(0.369848\pi\)
\(224\) 0 0
\(225\) −801.000 −0.237333
\(226\) −462.000 + 800.207i −0.135981 + 0.235527i
\(227\) −1122.00 1943.36i −0.328061 0.568218i 0.654066 0.756437i \(-0.273062\pi\)
−0.982127 + 0.188220i \(0.939728\pi\)
\(228\) 120.000 + 207.846i 0.0348561 + 0.0603726i
\(229\) 2825.00 4893.04i 0.815202 1.41197i −0.0939808 0.995574i \(-0.529959\pi\)
0.909183 0.416397i \(-0.136707\pi\)
\(230\) −2016.00 −0.577961
\(231\) 0 0
\(232\) −240.000 −0.0679171
\(233\) −2349.00 + 4068.59i −0.660464 + 1.14396i 0.320030 + 0.947407i \(0.396307\pi\)
−0.980494 + 0.196550i \(0.937026\pi\)
\(234\) 342.000 + 592.361i 0.0955438 + 0.165487i
\(235\) 288.000 + 498.831i 0.0799449 + 0.138469i
\(236\) 1320.00 2286.31i 0.364088 0.630618i
\(237\) 1560.00 0.427565
\(238\) 0 0
\(239\) −1200.00 −0.324776 −0.162388 0.986727i \(-0.551920\pi\)
−0.162388 + 0.986727i \(0.551920\pi\)
\(240\) 144.000 249.415i 0.0387298 0.0670820i
\(241\) 359.000 + 621.806i 0.0959553 + 0.166199i 0.910007 0.414593i \(-0.136076\pi\)
−0.814052 + 0.580793i \(0.802743\pi\)
\(242\) −1187.00 2055.94i −0.315303 0.546120i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) −2152.00 −0.564622
\(245\) 0 0
\(246\) 252.000 0.0653127
\(247\) −380.000 + 658.179i −0.0978900 + 0.169550i
\(248\) −352.000 609.682i −0.0901291 0.156108i
\(249\) −738.000 1278.25i −0.187827 0.325325i
\(250\) −1284.00 + 2223.95i −0.324829 + 0.562621i
\(251\) 6012.00 1.51185 0.755924 0.654659i \(-0.227188\pi\)
0.755924 + 0.654659i \(0.227188\pi\)
\(252\) 0 0
\(253\) 2016.00 0.500968
\(254\) −2536.00 + 4392.48i −0.626468 + 1.08507i
\(255\) −1134.00 1964.15i −0.278486 0.482351i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 1023.00 1771.89i 0.248300 0.430067i −0.714755 0.699375i \(-0.753462\pi\)
0.963054 + 0.269308i \(0.0867949\pi\)
\(258\) −312.000 −0.0752879
\(259\) 0 0
\(260\) 912.000 0.217538
\(261\) −135.000 + 233.827i −0.0320164 + 0.0554541i
\(262\) 2292.00 + 3969.86i 0.540459 + 0.936102i
\(263\) 3036.00 + 5258.51i 0.711817 + 1.23290i 0.964175 + 0.265269i \(0.0854606\pi\)
−0.252358 + 0.967634i \(0.581206\pi\)
\(264\) −144.000 + 249.415i −0.0335704 + 0.0581456i
\(265\) 1188.00 0.275390
\(266\) 0 0
\(267\) −2430.00 −0.556980
\(268\) −1768.00 + 3062.27i −0.402977 + 0.697976i
\(269\) 3465.00 + 6001.56i 0.785371 + 1.36030i 0.928777 + 0.370638i \(0.120861\pi\)
−0.143406 + 0.989664i \(0.545806\pi\)
\(270\) −162.000 280.592i −0.0365148 0.0632456i
\(271\) −676.000 + 1170.87i −0.151528 + 0.262454i −0.931789 0.362999i \(-0.881753\pi\)
0.780261 + 0.625454i \(0.215086\pi\)
\(272\) −2016.00 −0.449404
\(273\) 0 0
\(274\) 1452.00 0.320141
\(275\) 534.000 924.915i 0.117096 0.202816i
\(276\) 1008.00 + 1745.91i 0.219835 + 0.380765i
\(277\) 593.000 + 1027.11i 0.128628 + 0.222790i 0.923145 0.384451i \(-0.125609\pi\)
−0.794517 + 0.607241i \(0.792276\pi\)
\(278\) 380.000 658.179i 0.0819816 0.141996i
\(279\) −792.000 −0.169949
\(280\) 0 0
\(281\) 2442.00 0.518425 0.259213 0.965820i \(-0.416537\pi\)
0.259213 + 0.965820i \(0.416537\pi\)
\(282\) 288.000 498.831i 0.0608161 0.105337i
\(283\) −1414.00 2449.12i −0.297009 0.514435i 0.678441 0.734655i \(-0.262656\pi\)
−0.975450 + 0.220220i \(0.929323\pi\)
\(284\) −1584.00 2743.57i −0.330962 0.573242i
\(285\) 180.000 311.769i 0.0374115 0.0647986i
\(286\) −912.000 −0.188558
\(287\) 0 0
\(288\) −288.000 −0.0589256
\(289\) −5481.50 + 9494.24i −1.11571 + 1.93247i
\(290\) 180.000 + 311.769i 0.0364482 + 0.0631301i
\(291\) 1731.00 + 2998.18i 0.348705 + 0.603974i
\(292\) −436.000 + 755.174i −0.0873800 + 0.151347i
\(293\) 4758.00 0.948687 0.474344 0.880340i \(-0.342685\pi\)
0.474344 + 0.880340i \(0.342685\pi\)
\(294\) 0 0
\(295\) −3960.00 −0.781560
\(296\) 1016.00 1759.76i 0.199506 0.345555i
\(297\) 162.000 + 280.592i 0.0316505 + 0.0548202i
\(298\) 1590.00 + 2753.96i 0.309081 + 0.535345i
\(299\) −3192.00 + 5528.71i −0.617385 + 1.06934i
\(300\) 1068.00 0.205537
\(301\) 0 0
\(302\) −4864.00 −0.926794
\(303\) −927.000 + 1605.61i −0.175758 + 0.304422i
\(304\) −160.000 277.128i −0.0301863 0.0522842i
\(305\) 1614.00 + 2795.53i 0.303008 + 0.524825i
\(306\) −1134.00 + 1964.15i −0.211851 + 0.366937i
\(307\) −8476.00 −1.57574 −0.787868 0.615844i \(-0.788815\pi\)
−0.787868 + 0.615844i \(0.788815\pi\)
\(308\) 0 0
\(309\) −384.000 −0.0706958
\(310\) −528.000 + 914.523i −0.0967367 + 0.167553i
\(311\) −2316.00 4011.43i −0.422278 0.731406i 0.573884 0.818936i \(-0.305436\pi\)
−0.996162 + 0.0875302i \(0.972103\pi\)
\(312\) −456.000 789.815i −0.0827433 0.143316i
\(313\) 2411.00 4175.97i 0.435392 0.754122i −0.561935 0.827181i \(-0.689943\pi\)
0.997328 + 0.0730597i \(0.0232764\pi\)
\(314\) −1228.00 −0.220701
\(315\) 0 0
\(316\) −2080.00 −0.370282
\(317\) 1713.00 2967.00i 0.303507 0.525689i −0.673421 0.739259i \(-0.735176\pi\)
0.976928 + 0.213570i \(0.0685091\pi\)
\(318\) −594.000 1028.84i −0.104748 0.181429i
\(319\) −180.000 311.769i −0.0315927 0.0547201i
\(320\) −192.000 + 332.554i −0.0335410 + 0.0580948i
\(321\) 4428.00 0.769928
\(322\) 0 0
\(323\) −2520.00 −0.434107
\(324\) −162.000 + 280.592i −0.0277778 + 0.0481125i
\(325\) 1691.00 + 2928.90i 0.288615 + 0.499895i
\(326\) −1852.00 3207.76i −0.314640 0.544973i
\(327\) 1785.00 3091.71i 0.301868 0.522850i
\(328\) −336.000 −0.0565625
\(329\) 0 0
\(330\) 432.000 0.0720631
\(331\) 1394.00 2414.48i 0.231484 0.400942i −0.726761 0.686890i \(-0.758975\pi\)
0.958245 + 0.285948i \(0.0923086\pi\)
\(332\) 984.000 + 1704.34i 0.162663 + 0.281740i
\(333\) −1143.00 1979.73i −0.188096 0.325792i
\(334\) −2136.00 + 3699.66i −0.349930 + 0.606097i
\(335\) 5304.00 0.865040
\(336\) 0 0
\(337\) 434.000 0.0701528 0.0350764 0.999385i \(-0.488833\pi\)
0.0350764 + 0.999385i \(0.488833\pi\)
\(338\) −753.000 + 1304.23i −0.121177 + 0.209885i
\(339\) −693.000 1200.31i −0.111028 0.192307i
\(340\) 1512.00 + 2618.86i 0.241176 + 0.417728i
\(341\) 528.000 914.523i 0.0838499 0.145232i
\(342\) −360.000 −0.0569198
\(343\) 0 0
\(344\) 416.000 0.0652012
\(345\) 1512.00 2618.86i 0.235952 0.408680i
\(346\) 1758.00 + 3044.95i 0.273152 + 0.473114i
\(347\) −3342.00 5788.51i −0.517026 0.895515i −0.999805 0.0197726i \(-0.993706\pi\)
0.482779 0.875742i \(-0.339628\pi\)
\(348\) 180.000 311.769i 0.0277270 0.0480247i
\(349\) 2630.00 0.403383 0.201692 0.979449i \(-0.435356\pi\)
0.201692 + 0.979449i \(0.435356\pi\)
\(350\) 0 0
\(351\) −1026.00 −0.156022
\(352\) 192.000 332.554i 0.0290728 0.0503556i
\(353\) 3711.00 + 6427.64i 0.559537 + 0.969147i 0.997535 + 0.0701707i \(0.0223544\pi\)
−0.437998 + 0.898976i \(0.644312\pi\)
\(354\) 1980.00 + 3429.46i 0.297276 + 0.514898i
\(355\) −2376.00 + 4115.35i −0.355225 + 0.615268i
\(356\) 3240.00 0.482359
\(357\) 0 0
\(358\) 1080.00 0.159441
\(359\) 5220.00 9041.31i 0.767412 1.32920i −0.171549 0.985176i \(-0.554877\pi\)
0.938962 0.344022i \(-0.111789\pi\)
\(360\) 216.000 + 374.123i 0.0316228 + 0.0547723i
\(361\) 3229.50 + 5593.66i 0.470841 + 0.815521i
\(362\) 1982.00 3432.92i 0.287767 0.498427i
\(363\) 3561.00 0.514887
\(364\) 0 0
\(365\) 1308.00 0.187572
\(366\) 1614.00 2795.53i 0.230506 0.399248i
\(367\) −5212.00 9027.45i −0.741319 1.28400i −0.951895 0.306425i \(-0.900867\pi\)
0.210575 0.977578i \(-0.432466\pi\)
\(368\) −1344.00 2327.88i −0.190383 0.329753i
\(369\) −189.000 + 327.358i −0.0266638 + 0.0461831i
\(370\) −3048.00 −0.428265
\(371\) 0 0
\(372\) 1056.00 0.147180
\(373\) −1639.00 + 2838.83i −0.227518 + 0.394073i −0.957072 0.289851i \(-0.906394\pi\)
0.729554 + 0.683923i \(0.239728\pi\)
\(374\) −1512.00 2618.86i −0.209047 0.362080i
\(375\) −1926.00 3335.93i −0.265222 0.459378i
\(376\) −384.000 + 665.108i −0.0526683 + 0.0912242i
\(377\) 1140.00 0.155737
\(378\) 0 0
\(379\) 6140.00 0.832165 0.416083 0.909327i \(-0.363403\pi\)
0.416083 + 0.909327i \(0.363403\pi\)
\(380\) −240.000 + 415.692i −0.0323993 + 0.0561173i
\(381\) −3804.00 6588.72i −0.511509 0.885959i
\(382\) −2688.00 4655.75i −0.360026 0.623584i
\(383\) 1536.00 2660.43i 0.204924 0.354939i −0.745184 0.666858i \(-0.767639\pi\)
0.950109 + 0.311919i \(0.100972\pi\)
\(384\) 384.000 0.0510310
\(385\) 0 0
\(386\) 4604.00 0.607092
\(387\) 234.000 405.300i 0.0307361 0.0532366i
\(388\) −2308.00 3997.57i −0.301987 0.523057i
\(389\) −3075.00 5326.06i −0.400794 0.694195i 0.593028 0.805182i \(-0.297932\pi\)
−0.993822 + 0.110987i \(0.964599\pi\)
\(390\) −684.000 + 1184.72i −0.0888095 + 0.153822i
\(391\) −21168.0 −2.73788
\(392\) 0 0
\(393\) −6876.00 −0.882566
\(394\) 4374.00 7575.99i 0.559287 0.968713i
\(395\) 1560.00 + 2702.00i 0.198714 + 0.344183i
\(396\) −216.000 374.123i −0.0274101 0.0474757i
\(397\) 53.0000 91.7987i 0.00670024 0.0116051i −0.862656 0.505791i \(-0.831201\pi\)
0.869356 + 0.494186i \(0.164534\pi\)
\(398\) 3200.00 0.403019
\(399\) 0 0
\(400\) −1424.00 −0.178000
\(401\) 879.000 1522.47i 0.109464 0.189598i −0.806089 0.591794i \(-0.798420\pi\)
0.915553 + 0.402197i \(0.131753\pi\)
\(402\) −2652.00 4593.40i −0.329029 0.569895i
\(403\) 1672.00 + 2895.99i 0.206671 + 0.357964i
\(404\) 1236.00 2140.81i 0.152211 0.263637i
\(405\) 486.000 0.0596285
\(406\) 0 0
\(407\) 3048.00 0.371213
\(408\) 1512.00 2618.86i 0.183469 0.317777i
\(409\) 1835.00 + 3178.31i 0.221846 + 0.384248i 0.955368 0.295417i \(-0.0954585\pi\)
−0.733523 + 0.679665i \(0.762125\pi\)
\(410\) 252.000 + 436.477i 0.0303546 + 0.0525757i
\(411\) −1089.00 + 1886.20i −0.130697 + 0.226374i
\(412\) 512.000 0.0612243
\(413\) 0 0
\(414\) −3024.00 −0.358989
\(415\) 1476.00 2556.51i 0.174588 0.302395i
\(416\) 608.000 + 1053.09i 0.0716578 + 0.124115i
\(417\) 570.000 + 987.269i 0.0669377 + 0.115939i
\(418\) 240.000 415.692i 0.0280832 0.0486416i
\(419\) −9660.00 −1.12631 −0.563153 0.826353i \(-0.690412\pi\)
−0.563153 + 0.826353i \(0.690412\pi\)
\(420\) 0 0
\(421\) 8462.00 0.979602 0.489801 0.871834i \(-0.337069\pi\)
0.489801 + 0.871834i \(0.337069\pi\)
\(422\) 3332.00 5771.19i 0.384358 0.665728i
\(423\) 432.000 + 748.246i 0.0496562 + 0.0860070i
\(424\) 792.000 + 1371.78i 0.0907144 + 0.157122i
\(425\) −5607.00 + 9711.61i −0.639952 + 1.10843i
\(426\) 4752.00 0.540458
\(427\) 0 0
\(428\) −5904.00 −0.666777
\(429\) 684.000 1184.72i 0.0769786 0.133331i
\(430\) −312.000 540.400i −0.0349906 0.0606056i
\(431\) −4896.00 8480.12i −0.547174 0.947733i −0.998467 0.0553572i \(-0.982370\pi\)
0.451293 0.892376i \(-0.350963\pi\)
\(432\) 216.000 374.123i 0.0240563 0.0416667i
\(433\) −7342.00 −0.814859 −0.407430 0.913237i \(-0.633575\pi\)
−0.407430 + 0.913237i \(0.633575\pi\)
\(434\) 0 0
\(435\) −540.000 −0.0595196
\(436\) −2380.00 + 4122.28i −0.261425 + 0.452801i
\(437\) −1680.00 2909.85i −0.183902 0.318528i
\(438\) −654.000 1132.76i −0.0713455 0.123574i
\(439\) −5320.00 + 9214.51i −0.578382 + 1.00179i 0.417283 + 0.908777i \(0.362982\pi\)
−0.995665 + 0.0930106i \(0.970351\pi\)
\(440\) −576.000 −0.0624085
\(441\) 0 0
\(442\) 9576.00 1.03051
\(443\) 8706.00 15079.2i 0.933712 1.61724i 0.156798 0.987631i \(-0.449883\pi\)
0.776914 0.629606i \(-0.216784\pi\)
\(444\) 1524.00 + 2639.65i 0.162896 + 0.282144i
\(445\) −2430.00 4208.88i −0.258861 0.448360i
\(446\) 2648.00 4586.47i 0.281136 0.486941i
\(447\) −4770.00 −0.504728
\(448\) 0 0
\(449\) −1710.00 −0.179732 −0.0898662 0.995954i \(-0.528644\pi\)
−0.0898662 + 0.995954i \(0.528644\pi\)
\(450\) −801.000 + 1387.37i −0.0839100 + 0.145336i
\(451\) −252.000 436.477i −0.0263109 0.0455718i
\(452\) 924.000 + 1600.41i 0.0961533 + 0.166542i
\(453\) 3648.00 6318.52i 0.378362 0.655342i
\(454\) −4488.00 −0.463948
\(455\) 0 0
\(456\) 480.000 0.0492940
\(457\) 323.000 559.452i 0.0330619 0.0572649i −0.849021 0.528359i \(-0.822807\pi\)
0.882083 + 0.471094i \(0.156141\pi\)
\(458\) −5650.00 9786.09i −0.576435 0.998414i
\(459\) −1701.00 2946.22i −0.172976 0.299603i
\(460\) −2016.00 + 3491.81i −0.204340 + 0.353928i
\(461\) −6018.00 −0.607996 −0.303998 0.952673i \(-0.598322\pi\)
−0.303998 + 0.952673i \(0.598322\pi\)
\(462\) 0 0
\(463\) −6712.00 −0.673722 −0.336861 0.941554i \(-0.609365\pi\)
−0.336861 + 0.941554i \(0.609365\pi\)
\(464\) −240.000 + 415.692i −0.0240123 + 0.0415906i
\(465\) −792.000 1371.78i −0.0789852 0.136806i
\(466\) 4698.00 + 8137.17i 0.467019 + 0.808900i
\(467\) −2682.00 + 4645.36i −0.265756 + 0.460303i −0.967761 0.251868i \(-0.918955\pi\)
0.702005 + 0.712172i \(0.252288\pi\)
\(468\) 1368.00 0.135119
\(469\) 0 0
\(470\) 1152.00 0.113059
\(471\) 921.000 1595.22i 0.0901007 0.156059i
\(472\) −2640.00 4572.61i −0.257449 0.445914i
\(473\) 312.000 + 540.400i 0.0303293 + 0.0525319i
\(474\) 1560.00 2702.00i 0.151167 0.261829i
\(475\) −1780.00 −0.171941
\(476\) 0 0
\(477\) 1782.00 0.171053
\(478\) −1200.00 + 2078.46i −0.114826 + 0.198884i
\(479\) −4920.00 8521.69i −0.469312 0.812873i 0.530072 0.847952i \(-0.322165\pi\)
−0.999385 + 0.0350799i \(0.988831\pi\)
\(480\) −288.000 498.831i −0.0273861 0.0474342i
\(481\) −4826.00 + 8358.88i −0.457477 + 0.792374i
\(482\) 1436.00 0.135701
\(483\) 0 0
\(484\) −4748.00 −0.445905
\(485\) −3462.00 + 5996.36i −0.324126 + 0.561403i
\(486\) −243.000 420.888i −0.0226805 0.0392837i
\(487\) −712.000 1233.22i −0.0662501 0.114749i 0.830998 0.556276i \(-0.187770\pi\)
−0.897248 + 0.441527i \(0.854437\pi\)
\(488\) −2152.00 + 3727.37i −0.199624 + 0.345759i
\(489\) 5556.00 0.513806
\(490\) 0 0
\(491\) −4548.00 −0.418021 −0.209011 0.977913i \(-0.567024\pi\)
−0.209011 + 0.977913i \(0.567024\pi\)
\(492\) 252.000 436.477i 0.0230915 0.0399957i
\(493\) 1890.00 + 3273.58i 0.172660 + 0.299056i
\(494\) 760.000 + 1316.36i 0.0692187 + 0.119890i
\(495\) −324.000 + 561.184i −0.0294196 + 0.0509563i
\(496\) −1408.00 −0.127462
\(497\) 0 0
\(498\) −2952.00 −0.265627
\(499\) −3250.00 + 5629.17i −0.291563 + 0.505002i −0.974180 0.225775i \(-0.927509\pi\)
0.682616 + 0.730777i \(0.260842\pi\)
\(500\) 2568.00 + 4447.91i 0.229689 + 0.397833i
\(501\) −3204.00 5549.49i −0.285717 0.494876i
\(502\) 6012.00 10413.1i 0.534519 0.925815i
\(503\) 12168.0 1.07862 0.539308 0.842108i \(-0.318686\pi\)
0.539308 + 0.842108i \(0.318686\pi\)
\(504\) 0 0
\(505\) −3708.00 −0.326740
\(506\) 2016.00 3491.81i 0.177119 0.306779i
\(507\) −1129.50 1956.35i −0.0989405 0.171370i
\(508\) 5072.00 + 8784.96i 0.442980 + 0.767263i
\(509\) 10545.0 18264.5i 0.918269 1.59049i 0.116226 0.993223i \(-0.462920\pi\)
0.802043 0.597266i \(-0.203746\pi\)
\(510\) −4536.00 −0.393838
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 270.000 467.654i 0.0232374 0.0402484i
\(514\) −2046.00 3543.78i −0.175574 0.304104i
\(515\) −384.000 665.108i −0.0328564 0.0569090i
\(516\) −312.000 + 540.400i −0.0266183 + 0.0461042i
\(517\) −1152.00 −0.0979979
\(518\) 0 0
\(519\) −5274.00 −0.446056
\(520\) 912.000 1579.63i 0.0769112 0.133214i
\(521\) 2619.00 + 4536.24i 0.220231 + 0.381452i 0.954878 0.296998i \(-0.0959855\pi\)
−0.734647 + 0.678450i \(0.762652\pi\)
\(522\) 270.000 + 467.654i 0.0226390 + 0.0392120i
\(523\) −4294.00 + 7437.43i −0.359012 + 0.621828i −0.987796 0.155752i \(-0.950220\pi\)
0.628784 + 0.777580i \(0.283553\pi\)
\(524\) 9168.00 0.764324
\(525\) 0 0
\(526\) 12144.0 1.00666
\(527\) −5544.00 + 9602.49i −0.458255 + 0.793721i
\(528\) 288.000 + 498.831i 0.0237379 + 0.0411152i
\(529\) −8028.50 13905.8i −0.659859 1.14291i
\(530\) 1188.00 2057.68i 0.0973649 0.168641i
\(531\) −5940.00 −0.485450
\(532\) 0 0
\(533\) 1596.00 0.129701
\(534\) −2430.00 + 4208.88i −0.196922 + 0.341079i
\(535\) 4428.00 + 7669.52i 0.357830 + 0.619780i
\(536\) 3536.00 + 6124.53i 0.284948 + 0.493544i
\(537\) −810.000 + 1402.96i −0.0650914 + 0.112742i
\(538\) 13860.0 1.11068
\(539\) 0 0
\(540\) −648.000 −0.0516398
\(541\) −1531.00 + 2651.77i −0.121669 + 0.210737i −0.920426 0.390917i \(-0.872158\pi\)
0.798757 + 0.601654i \(0.205491\pi\)
\(542\) 1352.00 + 2341.73i 0.107146 + 0.185583i
\(543\) 2973.00 + 5149.39i 0.234961 + 0.406964i
\(544\) −2016.00 + 3491.81i −0.158888 + 0.275203i
\(545\) 7140.00 0.561182
\(546\) 0 0
\(547\) −8476.00 −0.662537 −0.331268 0.943537i \(-0.607477\pi\)
−0.331268 + 0.943537i \(0.607477\pi\)
\(548\) 1452.00 2514.94i 0.113187 0.196045i
\(549\) 2421.00 + 4193.30i 0.188207 + 0.325984i
\(550\) −1068.00 1849.83i −0.0827994 0.143413i
\(551\) −300.000 + 519.615i −0.0231950 + 0.0401749i
\(552\) 4032.00 0.310894
\(553\) 0 0
\(554\) 2372.00 0.181907
\(555\) 2286.00 3959.47i 0.174838 0.302829i
\(556\) −760.000 1316.36i −0.0579697 0.100407i
\(557\) 6273.00 + 10865.2i 0.477191 + 0.826520i 0.999658 0.0261400i \(-0.00832156\pi\)
−0.522467 + 0.852659i \(0.674988\pi\)
\(558\) −792.000 + 1371.78i −0.0600861 + 0.104072i
\(559\) −1976.00 −0.149510
\(560\) 0 0
\(561\) 4536.00 0.341373
\(562\) 2442.00 4229.67i 0.183291 0.317469i
\(563\) 6.00000 + 10.3923i 0.000449147 + 0.000777946i 0.866250 0.499611i \(-0.166524\pi\)
−0.865801 + 0.500389i \(0.833190\pi\)
\(564\) −576.000 997.661i −0.0430035 0.0744843i
\(565\) 1386.00 2400.62i 0.103203 0.178752i
\(566\) −5656.00 −0.420034
\(567\) 0 0
\(568\) −6336.00 −0.468050
\(569\) −9645.00 + 16705.6i −0.710614 + 1.23082i 0.254013 + 0.967201i \(0.418249\pi\)
−0.964627 + 0.263619i \(0.915084\pi\)
\(570\) −360.000 623.538i −0.0264539 0.0458196i
\(571\) 6074.00 + 10520.5i 0.445165 + 0.771048i 0.998064 0.0622005i \(-0.0198118\pi\)
−0.552899 + 0.833248i \(0.686478\pi\)
\(572\) −912.000 + 1579.63i −0.0666654 + 0.115468i
\(573\) 8064.00 0.587920
\(574\) 0 0
\(575\) −14952.0 −1.08442
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) 5183.00 + 8977.22i 0.373953 + 0.647706i 0.990170 0.139871i \(-0.0446687\pi\)
−0.616216 + 0.787577i \(0.711335\pi\)
\(578\) 10963.0 + 18988.5i 0.788929 + 1.36646i
\(579\) −3453.00 + 5980.77i −0.247844 + 0.429279i
\(580\) 720.000 0.0515455
\(581\) 0 0
\(582\) 6924.00 0.493143
\(583\) −1188.00 + 2057.68i −0.0843944 + 0.146175i
\(584\) 872.000 + 1510.35i 0.0617870 + 0.107018i
\(585\) −1026.00 1777.08i −0.0725126 0.125596i
\(586\) 4758.00 8241.10i 0.335412 0.580950i
\(587\) 7644.00 0.537482 0.268741 0.963213i \(-0.413393\pi\)
0.268741 + 0.963213i \(0.413393\pi\)
\(588\) 0 0
\(589\) −1760.00 −0.123123
\(590\) −3960.00 + 6858.92i −0.276323 + 0.478606i
\(591\) 6561.00 + 11364.0i 0.456656 + 0.790951i
\(592\) −2032.00 3519.53i −0.141072 0.244344i
\(593\) −4329.00 + 7498.05i −0.299782 + 0.519238i −0.976086 0.217385i \(-0.930247\pi\)
0.676304 + 0.736623i \(0.263581\pi\)
\(594\) 648.000 0.0447605
\(595\) 0 0
\(596\) 6360.00 0.437107
\(597\) −2400.00 + 4156.92i −0.164532 + 0.284977i
\(598\) 6384.00 + 11057.4i 0.436557 + 0.756139i
\(599\) −12900.0 22343.5i −0.879933 1.52409i −0.851414 0.524495i \(-0.824254\pi\)
−0.0285192 0.999593i \(-0.509079\pi\)
\(600\) 1068.00 1849.83i 0.0726682 0.125865i
\(601\) 16202.0 1.09966 0.549828 0.835278i \(-0.314693\pi\)
0.549828 + 0.835278i \(0.314693\pi\)
\(602\) 0 0
\(603\) 7956.00 0.537302
\(604\) −4864.00 + 8424.70i −0.327671 + 0.567543i
\(605\) 3561.00 + 6167.83i 0.239298 + 0.414476i
\(606\) 1854.00 + 3211.22i 0.124280 + 0.215259i
\(607\) 12068.0 20902.4i 0.806960 1.39770i −0.107999 0.994151i \(-0.534444\pi\)
0.914960 0.403546i \(-0.132222\pi\)
\(608\) −640.000 −0.0426898
\(609\) 0 0
\(610\) 6456.00 0.428518
\(611\) 1824.00 3159.26i 0.120771 0.209182i
\(612\) 2268.00 + 3928.29i 0.149801 + 0.259464i
\(613\) 2321.00 + 4020.09i 0.152927 + 0.264877i 0.932302 0.361680i \(-0.117797\pi\)
−0.779375 + 0.626557i \(0.784463\pi\)
\(614\) −8476.00 + 14680.9i −0.557107 + 0.964937i
\(615\) −756.000 −0.0495689
\(616\) 0 0
\(617\) −6726.00 −0.438863 −0.219432 0.975628i \(-0.570420\pi\)
−0.219432 + 0.975628i \(0.570420\pi\)
\(618\) −384.000 + 665.108i −0.0249947 + 0.0432921i
\(619\) 10610.0 + 18377.1i 0.688937 + 1.19327i 0.972182 + 0.234226i \(0.0752556\pi\)
−0.283245 + 0.959047i \(0.591411\pi\)
\(620\) 1056.00 + 1829.05i 0.0684032 + 0.118478i
\(621\) 2268.00 3928.29i 0.146557 0.253844i
\(622\) −9264.00 −0.597191
\(623\) 0 0
\(624\) −1824.00 −0.117017
\(625\) −1710.50 + 2962.67i −0.109472 + 0.189611i
\(626\) −4822.00 8351.95i −0.307869 0.533244i
\(627\) 360.000 + 623.538i 0.0229298 + 0.0397157i
\(628\) −1228.00 + 2126.96i −0.0780295 + 0.135151i
\(629\) −32004.0 −2.02875
\(630\) 0 0
\(631\) 29792.0 1.87956 0.939779 0.341783i \(-0.111031\pi\)
0.939779 + 0.341783i \(0.111031\pi\)
\(632\) −2080.00 + 3602.67i −0.130914 + 0.226751i
\(633\) 4998.00 + 8656.79i 0.313827 + 0.543565i
\(634\) −3426.00 5934.01i −0.214612 0.371718i
\(635\) 7608.00 13177.4i 0.475456 0.823513i
\(636\) −2376.00 −0.148136
\(637\) 0 0
\(638\) −720.000 −0.0446788
\(639\) −3564.00 + 6173.03i −0.220641 + 0.382162i
\(640\) 384.000 + 665.108i 0.0237171 + 0.0410792i
\(641\) 5079.00 + 8797.09i 0.312962 + 0.542066i 0.979002 0.203850i \(-0.0653455\pi\)
−0.666040 + 0.745916i \(0.732012\pi\)
\(642\) 4428.00 7669.52i 0.272211 0.471483i
\(643\) 29828.0 1.82940 0.914698 0.404138i \(-0.132429\pi\)
0.914698 + 0.404138i \(0.132429\pi\)
\(644\) 0 0
\(645\) 936.000 0.0571395
\(646\) −2520.00 + 4364.77i −0.153480 + 0.265835i
\(647\) −972.000 1683.55i −0.0590622 0.102299i 0.834982 0.550277i \(-0.185478\pi\)
−0.894045 + 0.447978i \(0.852144\pi\)
\(648\) 324.000 + 561.184i 0.0196419 + 0.0340207i
\(649\) 3960.00 6858.92i 0.239512 0.414848i
\(650\) 6764.00 0.408163
\(651\) 0 0
\(652\) −7408.00 −0.444969
\(653\) −13359.0 + 23138.5i −0.800579 + 1.38664i 0.118657 + 0.992935i \(0.462141\pi\)
−0.919236 + 0.393708i \(0.871192\pi\)
\(654\) −3570.00 6183.42i −0.213453 0.369711i
\(655\) −6876.00 11909.6i −0.410179 0.710452i
\(656\) −336.000 + 581.969i −0.0199979 + 0.0346373i
\(657\) 1962.00 0.116507
\(658\) 0 0
\(659\) 4260.00 0.251815 0.125907 0.992042i \(-0.459816\pi\)
0.125907 + 0.992042i \(0.459816\pi\)
\(660\) 432.000 748.246i 0.0254781 0.0441294i
\(661\) −11431.0 19799.1i −0.672639 1.16504i −0.977153 0.212537i \(-0.931827\pi\)
0.304514 0.952508i \(-0.401506\pi\)
\(662\) −2788.00 4828.96i −0.163684 0.283509i
\(663\) −7182.00 + 12439.6i −0.420703 + 0.728678i
\(664\) 3936.00 0.230040
\(665\) 0 0
\(666\) −4572.00 −0.266008
\(667\) −2520.00 + 4364.77i −0.146289 + 0.253380i
\(668\) 4272.00 + 7399.32i 0.247438 + 0.428575i
\(669\) 3972.00 + 6879.71i 0.229546 + 0.397586i
\(670\) 5304.00 9186.80i 0.305838 0.529727i
\(671\) −6456.00 −0.371432
\(672\) 0 0
\(673\) −32542.0 −1.86390 −0.931948 0.362592i \(-0.881892\pi\)
−0.931948 + 0.362592i \(0.881892\pi\)
\(674\) 434.000 751.710i 0.0248028 0.0429596i
\(675\) −1201.50 2081.06i −0.0685122 0.118667i
\(676\) 1506.00 + 2608.47i 0.0856850 + 0.148411i
\(677\) −7107.00 + 12309.7i −0.403463 + 0.698818i −0.994141 0.108089i \(-0.965527\pi\)
0.590679 + 0.806907i \(0.298860\pi\)
\(678\) −2772.00 −0.157018
\(679\) 0 0
\(680\) 6048.00 0.341074
\(681\) 3366.00 5830.08i 0.189406 0.328061i
\(682\) −1056.00 1829.05i −0.0592908 0.102695i
\(683\) 3546.00 + 6141.85i 0.198659 + 0.344087i 0.948094 0.317991i \(-0.103008\pi\)
−0.749435 + 0.662078i \(0.769675\pi\)
\(684\) −360.000 + 623.538i −0.0201242 + 0.0348561i
\(685\) −4356.00 −0.242970
\(686\) 0 0
\(687\) 16950.0 0.941314
\(688\) 416.000 720.533i 0.0230521 0.0399274i
\(689\) −3762.00 6515.98i −0.208013 0.360289i
\(690\) −3024.00 5237.72i −0.166843 0.288981i
\(691\) 6614.00 11455.8i 0.364122 0.630678i −0.624513 0.781015i \(-0.714702\pi\)
0.988635 + 0.150337i \(0.0480357\pi\)
\(692\) 7032.00 0.386296
\(693\) 0 0
\(694\) −13368.0 −0.731185
\(695\) −1140.00 + 1974.54i −0.0622197 + 0.107768i
\(696\) −360.000 623.538i −0.0196060 0.0339586i
\(697\) 2646.00 + 4583.01i 0.143794 + 0.249058i
\(698\) 2630.00 4555.29i 0.142617 0.247021i
\(699\) −14094.0 −0.762638
\(700\) 0 0
\(701\) 28062.0 1.51196 0.755982 0.654592i \(-0.227160\pi\)
0.755982 + 0.654592i \(0.227160\pi\)
\(702\) −1026.00 + 1777.08i −0.0551622 + 0.0955438i
\(703\) −2540.00 4399.41i −0.136270 0.236027i
\(704\) −384.000 665.108i −0.0205576 0.0356068i
\(705\) −864.000 + 1496.49i −0.0461562 + 0.0799449i
\(706\) 14844.0 0.791305
\(707\) 0 0
\(708\) 7920.00 0.420412
\(709\) 13625.0 23599.2i 0.721717 1.25005i −0.238594 0.971120i \(-0.576686\pi\)
0.960311 0.278932i \(-0.0899803\pi\)
\(710\) 4752.00 + 8230.71i 0.251182 + 0.435060i
\(711\) 2340.00 + 4053.00i 0.123427 + 0.213782i
\(712\) 3240.00 5611.84i 0.170540 0.295383i
\(713\) −14784.0 −0.776529
\(714\) 0 0
\(715\) 2736.00 0.143106
\(716\) 1080.00 1870.61i 0.0563708 0.0976371i
\(717\) −1800.00 3117.69i −0.0937549 0.162388i
\(718\) −10440.0 18082.6i −0.542643 0.939884i
\(719\) 7200.00 12470.8i 0.373456 0.646844i −0.616639 0.787246i \(-0.711506\pi\)
0.990095 + 0.140402i \(0.0448394\pi\)
\(720\) 864.000 0.0447214
\(721\) 0 0
\(722\) 12918.0 0.665870
\(723\) −1077.00 + 1865.42i −0.0553998 + 0.0959553i
\(724\) −3964.00 6865.85i −0.203482 0.352441i
\(725\) 1335.00 + 2312.29i 0.0683871 + 0.118450i
\(726\) 3561.00 6167.83i 0.182040 0.315303i
\(727\) 17984.0 0.917455 0.458727 0.888577i \(-0.348305\pi\)
0.458727 + 0.888577i \(0.348305\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 1308.00 2265.52i 0.0663168 0.114864i
\(731\) −3276.00 5674.20i −0.165755 0.287097i
\(732\) −3228.00 5591.06i −0.162992 0.282311i
\(733\) −8299.00 + 14374.3i −0.418186 + 0.724320i −0.995757 0.0920207i \(-0.970667\pi\)
0.577571 + 0.816341i \(0.304001\pi\)
\(734\) −20848.0 −1.04838
\(735\) 0 0
\(736\) −5376.00 −0.269242
\(737\) −5304.00 + 9186.80i −0.265095 + 0.459159i
\(738\) 378.000 + 654.715i 0.0188542 + 0.0326564i
\(739\) −730.000 1264.40i −0.0363376 0.0629386i 0.847285 0.531139i \(-0.178236\pi\)
−0.883622 + 0.468201i \(0.844902\pi\)
\(740\) −3048.00 + 5279.29i −0.151414 + 0.262258i
\(741\) −2280.00 −0.113034
\(742\) 0 0
\(743\) −30072.0 −1.48484 −0.742419 0.669936i \(-0.766322\pi\)
−0.742419 + 0.669936i \(0.766322\pi\)
\(744\) 1056.00 1829.05i 0.0520361 0.0901291i
\(745\) −4770.00 8261.88i −0.234576 0.406298i
\(746\) 3278.00 + 5677.66i 0.160880 + 0.278651i
\(747\) 2214.00 3834.76i 0.108442 0.187827i
\(748\) −6048.00 −0.295637
\(749\) 0 0
\(750\) −7704.00 −0.375080
\(751\) 9044.00 15664.7i 0.439441 0.761134i −0.558205 0.829703i \(-0.688510\pi\)
0.997646 + 0.0685686i \(0.0218432\pi\)
\(752\) 768.000 + 1330.22i 0.0372421 + 0.0645053i
\(753\) 9018.00 + 15619.6i 0.436433 + 0.755924i
\(754\) 1140.00 1974.54i 0.0550615 0.0953693i
\(755\) 14592.0 0.703387
\(756\) 0 0
\(757\) 24734.0 1.18755 0.593773 0.804633i \(-0.297638\pi\)
0.593773 + 0.804633i \(0.297638\pi\)
\(758\) 6140.00 10634.8i 0.294215 0.509595i
\(759\) 3024.00 + 5237.72i 0.144617 + 0.250484i
\(760\) 480.000 + 831.384i 0.0229098 + 0.0396809i
\(761\) 11139.0 19293.3i 0.530602 0.919030i −0.468760 0.883326i \(-0.655299\pi\)
0.999362 0.0357047i \(-0.0113676\pi\)
\(762\) −15216.0 −0.723383
\(763\) 0 0
\(764\) −10752.0 −0.509154
\(765\) 3402.00 5892.44i 0.160784 0.278486i
\(766\) −3072.00 5320.86i −0.144903 0.250980i
\(767\) 12540.0 + 21719.9i 0.590343 + 1.02250i
\(768\) 384.000 665.108i 0.0180422 0.0312500i
\(769\) 16130.0 0.756388 0.378194 0.925726i \(-0.376545\pi\)
0.378194 + 0.925726i \(0.376545\pi\)
\(770\) 0 0
\(771\) 6138.00 0.286712
\(772\) 4604.00 7974.36i 0.214639 0.371766i
\(773\) −14859.0 25736.5i −0.691386 1.19752i −0.971384 0.237515i \(-0.923667\pi\)
0.279998 0.960000i \(-0.409666\pi\)
\(774\) −468.000 810.600i −0.0217337 0.0376439i
\(775\) −3916.00 + 6782.71i −0.181506 + 0.314377i
\(776\) −9232.00 −0.427074
\(777\) 0 0
\(778\) −12300.0 −0.566808
\(779\) −420.000 + 727.461i −0.0193172 + 0.0334583i
\(780\) 1368.00 + 2369.45i 0.0627978 + 0.108769i
\(781\) −4752.00 8230.71i −0.217721 0.377103i
\(782\) −21168.0 + 36664.1i −0.967987 + 1.67660i
\(783\) −810.000 −0.0369694
\(784\) 0 0
\(785\) 3684.00 0.167500
\(786\) −6876.00 + 11909.6i −0.312034 + 0.540459i
\(787\) −4762.00 8248.03i −0.215689 0.373584i 0.737797 0.675023i \(-0.235866\pi\)
−0.953485 + 0.301439i \(0.902533\pi\)
\(788\) −8748.00 15152.0i −0.395475 0.684983i
\(789\) −9108.00 + 15775.5i −0.410968 + 0.711817i
\(790\) 6240.00 0.281024
\(791\) 0 0
\(792\) −864.000 −0.0387638
\(793\) 10222.0 17705.0i 0.457748 0.792842i
\(794\) −106.000 183.597i −0.00473778 0.00820608i
\(795\) 1782.00 + 3086.51i 0.0794981 + 0.137695i
\(796\) 3200.00 5542.56i 0.142489 0.246798i
\(797\) −33906.0 −1.50692 −0.753458 0.657496i \(-0.771616\pi\)
−0.753458 + 0.657496i \(0.771616\pi\)
\(798\) 0 0
\(799\) 12096.0 0.535577
\(800\) −1424.00 + 2466.44i −0.0629325 + 0.109002i
\(801\) −3645.00 6313.33i −0.160786 0.278490i
\(802\) −1758.00 3044.95i −0.0774029 0.134066i
\(803\) −1308.00 + 2265.52i −0.0574823 + 0.0995623i
\(804\) −10608.0 −0.465318
\(805\) 0 0
\(806\) 6688.00 0.292276
\(807\) −10395.0 + 18004.7i −0.453434 + 0.785371i
\(808\) −2472.00 4281.63i −0.107630 0.186420i
\(809\) 315.000 + 545.596i 0.0136895 + 0.0237109i 0.872789 0.488098i \(-0.162309\pi\)
−0.859099 + 0.511809i \(0.828976\pi\)
\(810\) 486.000 841.777i 0.0210819 0.0365148i
\(811\) −20788.0 −0.900081 −0.450040 0.893008i \(-0.648590\pi\)
−0.450040 + 0.893008i \(0.648590\pi\)
\(812\) 0 0
\(813\) −4056.00 −0.174969
\(814\) 3048.00 5279.29i 0.131244 0.227321i
\(815\) 5556.00 + 9623.27i 0.238795 + 0.413606i
\(816\) −3024.00 5237.72i −0.129732 0.224702i
\(817\) 520.000 900.666i 0.0222674 0.0385683i
\(818\) 7340.00 0.313737
\(819\) 0 0
\(820\) 1008.00 0.0429279
\(821\) 21549.0 37324.0i 0.916036 1.58662i 0.110658 0.993859i \(-0.464704\pi\)
0.805378 0.592762i \(-0.201962\pi\)
\(822\) 2178.00 + 3772.41i 0.0924166 + 0.160070i
\(823\) 7136.00 + 12359.9i 0.302242 + 0.523499i 0.976644 0.214866i \(-0.0689315\pi\)
−0.674401 + 0.738365i \(0.735598\pi\)
\(824\) 512.000 886.810i 0.0216461 0.0374921i
\(825\) 3204.00 0.135211
\(826\) 0 0
\(827\) 13644.0 0.573698 0.286849 0.957976i \(-0.407392\pi\)
0.286849 + 0.957976i \(0.407392\pi\)
\(828\) −3024.00 + 5237.72i −0.126922 + 0.219835i
\(829\) 1205.00 + 2087.12i 0.0504842 + 0.0874412i 0.890163 0.455642i \(-0.150590\pi\)
−0.839679 + 0.543083i \(0.817257\pi\)
\(830\) −2952.00 5113.01i −0.123452 0.213826i
\(831\) −1779.00 + 3081.32i −0.0742633 + 0.128628i
\(832\) 2432.00 0.101339
\(833\) 0 0
\(834\) 2280.00 0.0946642
\(835\) 6408.00 11099.0i 0.265578 0.459995i
\(836\) −480.000 831.384i −0.0198578 0.0343948i
\(837\) −1188.00 2057.68i −0.0490601 0.0849746i
\(838\) −9660.00 + 16731.6i −0.398209 + 0.689718i
\(839\) 23160.0 0.953006 0.476503 0.879173i \(-0.341904\pi\)
0.476503 + 0.879173i \(0.341904\pi\)
\(840\) 0 0
\(841\) −23489.0 −0.963098
\(842\) 8462.00 14656.6i 0.346342 0.599882i
\(843\) 3663.00 + 6344.50i 0.149656 + 0.259213i
\(844\) −6664.00 11542.4i −0.271782 0.470741i
\(845\) 2259.00 3912.70i 0.0919668 0.159291i
\(846\) 1728.00 0.0702244
\(847\) 0 0
\(848\) 3168.00 0.128290
\(849\) 4242.00 7347.36i 0.171478 0.297009i
\(850\) 11214.0 + 19423.2i 0.452514 + 0.783777i
\(851\) −21336.0 36955.0i −0.859446 1.48860i
\(852\) 4752.00 8230.71i 0.191081 0.330962i
\(853\) 32078.0 1.28761 0.643804 0.765190i \(-0.277355\pi\)
0.643804 + 0.765190i \(0.277355\pi\)
\(854\) 0 0
\(855\) 1080.00 0.0431991
\(856\) −5904.00 + 10226.0i −0.235741 + 0.408316i
\(857\) 7203.00 + 12476.0i 0.287106 + 0.497282i 0.973118 0.230308i \(-0.0739735\pi\)
−0.686012 + 0.727590i \(0.740640\pi\)
\(858\) −1368.00 2369.45i −0.0544321 0.0942792i
\(859\) −15310.0 + 26517.7i −0.608115 + 1.05329i 0.383436 + 0.923567i \(0.374741\pi\)
−0.991551 + 0.129718i \(0.958593\pi\)
\(860\) −1248.00 −0.0494842
\(861\) 0 0
\(862\) −19584.0 −0.773821
\(863\) −8784.00 + 15214.3i −0.346478 + 0.600118i −0.985621 0.168970i \(-0.945956\pi\)
0.639143 + 0.769088i \(0.279289\pi\)
\(864\) −432.000 748.246i −0.0170103 0.0294628i
\(865\) −5274.00 9134.84i −0.207308 0.359068i
\(866\) −7342.00 + 12716.7i −0.288096 + 0.498997i
\(867\) −32889.0 −1.28831
\(868\) 0 0
\(869\) −6240.00 −0.243587
\(870\) −540.000 + 935.307i −0.0210434 + 0.0364482i
\(871\) −16796.0 29091.5i −0.653399 1.13172i
\(872\) 4760.00 + 8244.56i 0.184855 + 0.320179i
\(873\) −5193.00 + 8994.54i −0.201325 + 0.348705i
\(874\) −6720.00 −0.260077
\(875\) 0 0
\(876\) −2616.00 −0.100898
\(877\) 10853.0 18797.9i 0.417879 0.723787i −0.577847 0.816145i \(-0.696107\pi\)
0.995726 + 0.0923577i \(0.0294403\pi\)
\(878\) 10640.0 + 18429.0i 0.408978 + 0.708371i
\(879\) 7137.00 + 12361.6i 0.273862 + 0.474344i
\(880\) −576.000 + 997.661i −0.0220647 + 0.0382172i
\(881\) −14958.0 −0.572018 −0.286009 0.958227i \(-0.592329\pi\)
−0.286009 + 0.958227i \(0.592329\pi\)
\(882\) 0 0
\(883\) −32812.0 −1.25052 −0.625261 0.780415i \(-0.715008\pi\)
−0.625261 + 0.780415i \(0.715008\pi\)
\(884\) 9576.00 16586.1i 0.364339 0.631054i
\(885\) −5940.00 10288.4i −0.225617 0.390780i
\(886\) −17412.0 30158.5i −0.660234 1.14356i
\(887\) 19428.0 33650.3i 0.735432 1.27381i −0.219101 0.975702i \(-0.570312\pi\)
0.954533 0.298104i \(-0.0963542\pi\)
\(888\) 6096.00 0.230370
\(889\) 0 0
\(890\) −9720.00 −0.366084
\(891\) −486.000 + 841.777i −0.0182734 + 0.0316505i
\(892\) −5296.00 9172.94i −0.198793 0.344319i
\(893\) 960.000 + 1662.77i 0.0359744 + 0.0623096i
\(894\) −4770.00 + 8261.88i −0.178448 + 0.309081i
\(895\) −3240.00 −0.121007
\(896\) 0 0
\(897\) −19152.0 −0.712895
\(898\) −1710.00 + 2961.81i −0.0635450 + 0.110063i
\(899\) 1320.00 + 2286.31i 0.0489705 + 0.0848194i
\(900\) 1602.00 + 2774.75i 0.0593333 + 0.102768i
\(901\) 12474.0 21605.6i 0.461231 0.798876i
\(902\) −1008.00 −0.0372092
\(903\) 0 0
\(904\) 3696.00 0.135981
\(905\) −5946.00 + 10298.8i −0.218400 + 0.378279i
\(906\) −7296.00 12637.0i −0.267542 0.463397i
\(907\) 14138.0 + 24487.7i 0.517579 + 0.896474i 0.999792 + 0.0204194i \(0.00650015\pi\)
−0.482212 + 0.876055i \(0.660167\pi\)
\(908\) −4488.00 + 7773.44i −0.164030 + 0.284109i
\(909\) −5562.00 −0.202948
\(910\) 0 0
\(911\) 8112.00 0.295019 0.147510 0.989061i \(-0.452874\pi\)
0.147510 + 0.989061i \(0.452874\pi\)
\(912\) 480.000 831.384i 0.0174281 0.0301863i
\(913\) 2952.00 + 5113.01i 0.107007 + 0.185341i
\(914\) −646.000 1118.90i −0.0233783 0.0404924i
\(915\) −4842.00 + 8386.59i −0.174942 + 0.303008i
\(916\) −22600.0 −0.815202
\(917\) 0 0
\(918\) −6804.00 −0.244625
\(919\) 13040.0 22585.9i 0.468063 0.810709i −0.531271 0.847202i \(-0.678285\pi\)
0.999334 + 0.0364931i \(0.0116187\pi\)
\(920\) 4032.00 + 6983.63i 0.144490 + 0.250265i
\(921\) −12714.0 22021.3i −0.454876 0.787868i
\(922\) −6018.00 + 10423.5i −0.214959 + 0.372320i
\(923\) 30096.0 1.07326
\(924\) 0 0
\(925\) −22606.0 −0.803547
\(926\) −6712.00 + 11625.5i −0.238197 + 0.412569i
\(927\) −576.000 997.661i −0.0204081 0.0353479i
\(928\) 480.000 + 831.384i 0.0169793 + 0.0294090i
\(929\) −24585.0 + 42582.5i −0.868254 + 1.50386i −0.00447392 + 0.999990i \(0.501424\pi\)
−0.863780 + 0.503870i \(0.831909\pi\)
\(930\) −3168.00 −0.111702
\(931\) 0 0
\(932\) 18792.0 0.660464
\(933\) 6948.00 12034.3i 0.243802 0.422278i
\(934\) 5364.00 + 9290.72i 0.187918 + 0.325484i
\(935\) 4536.00 + 7856.58i 0.158656 + 0.274800i
\(936\) 1368.00 2369.45i 0.0477719 0.0827433i
\(937\) 48314.0 1.68447 0.842236 0.539110i \(-0.181239\pi\)
0.842236 + 0.539110i \(0.181239\pi\)
\(938\) 0 0
\(939\) 14466.0 0.502748
\(940\) 1152.00 1995.32i 0.0399724 0.0692343i
\(941\) −17391.0 30122.1i −0.602477 1.04352i −0.992445 0.122692i \(-0.960847\pi\)
0.389968 0.920828i \(-0.372486\pi\)
\(942\) −1842.00 3190.44i −0.0637108 0.110350i
\(943\) −3528.00 + 6110.68i −0.121832 + 0.211019i
\(944\) −10560.0 −0.364088
\(945\) 0 0
\(946\) 1248.00 0.0428922
\(947\) 12558.0 21751.1i 0.430919 0.746373i −0.566034 0.824382i \(-0.691523\pi\)
0.996953 + 0.0780087i \(0.0248562\pi\)
\(948\) −3120.00 5404.00i −0.106891 0.185141i
\(949\) −4142.00 7174.15i −0.141681 0.245398i
\(950\) −1780.00 + 3083.05i −0.0607903 + 0.105292i
\(951\) 10278.0 0.350460
\(952\) 0 0
\(953\) −15462.0 −0.525565 −0.262782 0.964855i \(-0.584640\pi\)
−0.262782 + 0.964855i \(0.584640\pi\)
\(954\) 1782.00 3086.51i 0.0604763 0.104748i
\(955\) 8064.00 + 13967.3i 0.273241 + 0.473267i
\(956\) 2400.00 + 4156.92i 0.0811941 + 0.140632i
\(957\) 540.000 935.307i 0.0182400 0.0315927i
\(958\) −19680.0 −0.663708
\(959\) 0 0
\(960\) −1152.00 −0.0387298
\(961\) 11023.5 19093.3i 0.370028 0.640907i
\(962\) 9652.00 + 16717.8i 0.323485 + 0.560293i
\(963\) 6642.00 + 11504.3i 0.222259 + 0.384964i
\(964\) 1436.00 2487.22i 0.0479776 0.0830997i
\(965\) −13812.0 −0.460750
\(966\) 0 0
\(967\) −736.000 −0.0244759 −0.0122379 0.999925i \(-0.503896\pi\)
−0.0122379 + 0.999925i \(0.503896\pi\)
\(968\) −4748.00 + 8223.78i −0.157651 + 0.273060i
\(969\) −3780.00 6547.15i −0.125316 0.217053i
\(970\) 6924.00 + 11992.7i 0.229192 + 0.396972i
\(971\) 14634.0 25346.8i 0.483653 0.837712i −0.516170 0.856486i \(-0.672643\pi\)
0.999824 + 0.0187737i \(0.00597621\pi\)
\(972\) −972.000 −0.0320750
\(973\) 0 0
\(974\) −2848.00 −0.0936918
\(975\) −5073.00 + 8786.69i −0.166632 + 0.288615i
\(976\) 4304.00 + 7454.75i 0.141155 + 0.244488i
\(977\) −8337.00 14440.1i −0.273003 0.472856i 0.696626 0.717434i \(-0.254684\pi\)
−0.969629 + 0.244579i \(0.921350\pi\)
\(978\) 5556.00 9623.27i 0.181658 0.314640i
\(979\) 9720.00 0.317316
\(980\) 0 0
\(981\) 10710.0 0.348567
\(982\) −4548.00 + 7877.37i −0.147793 + 0.255985i
\(983\) 15636.0 + 27082.3i 0.507336 + 0.878731i 0.999964 + 0.00849130i \(0.00270290\pi\)
−0.492628 + 0.870240i \(0.663964\pi\)
\(984\) −504.000 872.954i −0.0163282 0.0282812i
\(985\) −13122.0 + 22728.0i −0.424469 + 0.735201i
\(986\) 7560.00 0.244178
\(987\) 0 0
\(988\) 3040.00 0.0978900
\(989\) 4368.00 7565.60i 0.140439 0.243248i
\(990\) 648.000 + 1122.37i 0.0208028 + 0.0360315i
\(991\) 7964.00 + 13794.1i 0.255282 + 0.442162i 0.964972 0.262352i \(-0.0844982\pi\)
−0.709690 + 0.704514i \(0.751165\pi\)
\(992\) −1408.00 + 2438.73i −0.0450646 + 0.0780541i
\(993\) 8364.00 0.267295
\(994\) 0 0
\(995\) −9600.00 −0.305870
\(996\) −2952.00 + 5113.01i −0.0939134 + 0.162663i
\(997\) −21007.0 36385.2i −0.667300 1.15580i −0.978656 0.205505i \(-0.934116\pi\)
0.311356 0.950293i \(-0.399217\pi\)
\(998\) 6500.00 + 11258.3i 0.206166 + 0.357090i
\(999\) 3429.00 5939.20i 0.108597 0.188096i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 294.4.e.h.79.1 2
3.2 odd 2 882.4.g.i.667.1 2
7.2 even 3 6.4.a.a.1.1 1
7.3 odd 6 294.4.e.g.67.1 2
7.4 even 3 inner 294.4.e.h.67.1 2
7.5 odd 6 294.4.a.e.1.1 1
7.6 odd 2 294.4.e.g.79.1 2
21.2 odd 6 18.4.a.a.1.1 1
21.5 even 6 882.4.a.n.1.1 1
21.11 odd 6 882.4.g.i.361.1 2
21.17 even 6 882.4.g.f.361.1 2
21.20 even 2 882.4.g.f.667.1 2
28.19 even 6 2352.4.a.e.1.1 1
28.23 odd 6 48.4.a.c.1.1 1
35.2 odd 12 150.4.c.d.49.1 2
35.9 even 6 150.4.a.i.1.1 1
35.23 odd 12 150.4.c.d.49.2 2
56.37 even 6 192.4.a.i.1.1 1
56.51 odd 6 192.4.a.c.1.1 1
63.2 odd 6 162.4.c.c.109.1 2
63.16 even 3 162.4.c.f.109.1 2
63.23 odd 6 162.4.c.c.55.1 2
63.58 even 3 162.4.c.f.55.1 2
77.65 odd 6 726.4.a.f.1.1 1
84.23 even 6 144.4.a.c.1.1 1
91.44 odd 12 1014.4.b.d.337.2 2
91.51 even 6 1014.4.a.g.1.1 1
91.86 odd 12 1014.4.b.d.337.1 2
105.2 even 12 450.4.c.e.199.2 2
105.23 even 12 450.4.c.e.199.1 2
105.44 odd 6 450.4.a.h.1.1 1
112.37 even 12 768.4.d.n.385.2 2
112.51 odd 12 768.4.d.c.385.2 2
112.93 even 12 768.4.d.n.385.1 2
112.107 odd 12 768.4.d.c.385.1 2
119.16 even 6 1734.4.a.d.1.1 1
133.37 odd 6 2166.4.a.i.1.1 1
140.23 even 12 1200.4.f.j.49.2 2
140.79 odd 6 1200.4.a.b.1.1 1
140.107 even 12 1200.4.f.j.49.1 2
168.107 even 6 576.4.a.r.1.1 1
168.149 odd 6 576.4.a.q.1.1 1
231.65 even 6 2178.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6.4.a.a.1.1 1 7.2 even 3
18.4.a.a.1.1 1 21.2 odd 6
48.4.a.c.1.1 1 28.23 odd 6
144.4.a.c.1.1 1 84.23 even 6
150.4.a.i.1.1 1 35.9 even 6
150.4.c.d.49.1 2 35.2 odd 12
150.4.c.d.49.2 2 35.23 odd 12
162.4.c.c.55.1 2 63.23 odd 6
162.4.c.c.109.1 2 63.2 odd 6
162.4.c.f.55.1 2 63.58 even 3
162.4.c.f.109.1 2 63.16 even 3
192.4.a.c.1.1 1 56.51 odd 6
192.4.a.i.1.1 1 56.37 even 6
294.4.a.e.1.1 1 7.5 odd 6
294.4.e.g.67.1 2 7.3 odd 6
294.4.e.g.79.1 2 7.6 odd 2
294.4.e.h.67.1 2 7.4 even 3 inner
294.4.e.h.79.1 2 1.1 even 1 trivial
450.4.a.h.1.1 1 105.44 odd 6
450.4.c.e.199.1 2 105.23 even 12
450.4.c.e.199.2 2 105.2 even 12
576.4.a.q.1.1 1 168.149 odd 6
576.4.a.r.1.1 1 168.107 even 6
726.4.a.f.1.1 1 77.65 odd 6
768.4.d.c.385.1 2 112.107 odd 12
768.4.d.c.385.2 2 112.51 odd 12
768.4.d.n.385.1 2 112.93 even 12
768.4.d.n.385.2 2 112.37 even 12
882.4.a.n.1.1 1 21.5 even 6
882.4.g.f.361.1 2 21.17 even 6
882.4.g.f.667.1 2 21.20 even 2
882.4.g.i.361.1 2 21.11 odd 6
882.4.g.i.667.1 2 3.2 odd 2
1014.4.a.g.1.1 1 91.51 even 6
1014.4.b.d.337.1 2 91.86 odd 12
1014.4.b.d.337.2 2 91.44 odd 12
1200.4.a.b.1.1 1 140.79 odd 6
1200.4.f.j.49.1 2 140.107 even 12
1200.4.f.j.49.2 2 140.23 even 12
1734.4.a.d.1.1 1 119.16 even 6
2166.4.a.i.1.1 1 133.37 odd 6
2178.4.a.e.1.1 1 231.65 even 6
2352.4.a.e.1.1 1 28.19 even 6