Properties

Label 338.4.c.a.191.1
Level $338$
Weight $4$
Character 338.191
Analytic conductor $19.943$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [338,4,Mod(191,338)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(338, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("338.191");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 338 = 2 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 338.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.9426455819\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 191.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 338.191
Dual form 338.4.c.a.315.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{3} +(-2.00000 - 3.46410i) q^{4} -18.0000 q^{5} +(-4.00000 - 6.92820i) q^{6} +(-10.0000 - 17.3205i) q^{7} +8.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{3} +(-2.00000 - 3.46410i) q^{4} -18.0000 q^{5} +(-4.00000 - 6.92820i) q^{6} +(-10.0000 - 17.3205i) q^{7} +8.00000 q^{8} +(5.50000 + 9.52628i) q^{9} +(18.0000 - 31.1769i) q^{10} +(24.0000 - 41.5692i) q^{11} +16.0000 q^{12} +40.0000 q^{14} +(36.0000 - 62.3538i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-33.0000 - 57.1577i) q^{17} -22.0000 q^{18} +(8.00000 + 13.8564i) q^{19} +(36.0000 + 62.3538i) q^{20} +80.0000 q^{21} +(48.0000 + 83.1384i) q^{22} +(-84.0000 + 145.492i) q^{23} +(-16.0000 + 27.7128i) q^{24} +199.000 q^{25} -152.000 q^{27} +(-40.0000 + 69.2820i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(72.0000 + 124.708i) q^{30} +20.0000 q^{31} +(-16.0000 - 27.7128i) q^{32} +(96.0000 + 166.277i) q^{33} +132.000 q^{34} +(180.000 + 311.769i) q^{35} +(22.0000 - 38.1051i) q^{36} +(-127.000 + 219.970i) q^{37} -32.0000 q^{38} -144.000 q^{40} +(195.000 - 337.750i) q^{41} +(-80.0000 + 138.564i) q^{42} +(62.0000 + 107.387i) q^{43} -192.000 q^{44} +(-99.0000 - 171.473i) q^{45} +(-168.000 - 290.985i) q^{46} -468.000 q^{47} +(-32.0000 - 55.4256i) q^{48} +(-28.5000 + 49.3634i) q^{49} +(-199.000 + 344.678i) q^{50} +264.000 q^{51} +558.000 q^{53} +(152.000 - 263.272i) q^{54} +(-432.000 + 748.246i) q^{55} +(-80.0000 - 138.564i) q^{56} -64.0000 q^{57} +(-6.00000 - 10.3923i) q^{58} +(48.0000 + 83.1384i) q^{59} -288.000 q^{60} +(413.000 + 715.337i) q^{61} +(-20.0000 + 34.6410i) q^{62} +(110.000 - 190.526i) q^{63} +64.0000 q^{64} -384.000 q^{66} +(80.0000 - 138.564i) q^{67} +(-132.000 + 228.631i) q^{68} +(-336.000 - 581.969i) q^{69} -720.000 q^{70} +(210.000 + 363.731i) q^{71} +(44.0000 + 76.2102i) q^{72} +362.000 q^{73} +(-254.000 - 439.941i) q^{74} +(-398.000 + 689.356i) q^{75} +(32.0000 - 55.4256i) q^{76} -960.000 q^{77} +776.000 q^{79} +(144.000 - 249.415i) q^{80} +(155.500 - 269.334i) q^{81} +(390.000 + 675.500i) q^{82} +(-160.000 - 277.128i) q^{84} +(594.000 + 1028.84i) q^{85} -248.000 q^{86} +(-12.0000 - 20.7846i) q^{87} +(192.000 - 332.554i) q^{88} +(-813.000 + 1408.16i) q^{89} +396.000 q^{90} +672.000 q^{92} +(-40.0000 + 69.2820i) q^{93} +(468.000 - 810.600i) q^{94} +(-144.000 - 249.415i) q^{95} +128.000 q^{96} +(647.000 + 1120.64i) q^{97} +(-57.0000 - 98.7269i) q^{98} +528.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 36 q^{5} - 8 q^{6} - 20 q^{7} + 16 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 36 q^{5} - 8 q^{6} - 20 q^{7} + 16 q^{8} + 11 q^{9} + 36 q^{10} + 48 q^{11} + 32 q^{12} + 80 q^{14} + 72 q^{15} - 16 q^{16} - 66 q^{17} - 44 q^{18} + 16 q^{19} + 72 q^{20} + 160 q^{21} + 96 q^{22} - 168 q^{23} - 32 q^{24} + 398 q^{25} - 304 q^{27} - 80 q^{28} - 6 q^{29} + 144 q^{30} + 40 q^{31} - 32 q^{32} + 192 q^{33} + 264 q^{34} + 360 q^{35} + 44 q^{36} - 254 q^{37} - 64 q^{38} - 288 q^{40} + 390 q^{41} - 160 q^{42} + 124 q^{43} - 384 q^{44} - 198 q^{45} - 336 q^{46} - 936 q^{47} - 64 q^{48} - 57 q^{49} - 398 q^{50} + 528 q^{51} + 1116 q^{53} + 304 q^{54} - 864 q^{55} - 160 q^{56} - 128 q^{57} - 12 q^{58} + 96 q^{59} - 576 q^{60} + 826 q^{61} - 40 q^{62} + 220 q^{63} + 128 q^{64} - 768 q^{66} + 160 q^{67} - 264 q^{68} - 672 q^{69} - 1440 q^{70} + 420 q^{71} + 88 q^{72} + 724 q^{73} - 508 q^{74} - 796 q^{75} + 64 q^{76} - 1920 q^{77} + 1552 q^{79} + 288 q^{80} + 311 q^{81} + 780 q^{82} - 320 q^{84} + 1188 q^{85} - 496 q^{86} - 24 q^{87} + 384 q^{88} - 1626 q^{89} + 792 q^{90} + 1344 q^{92} - 80 q^{93} + 936 q^{94} - 288 q^{95} + 256 q^{96} + 1294 q^{97} - 114 q^{98} + 1056 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).

\(n\) \(171\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) −2.00000 + 3.46410i −0.384900 + 0.666667i −0.991755 0.128146i \(-0.959097\pi\)
0.606855 + 0.794812i \(0.292431\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −18.0000 −1.60997 −0.804984 0.593296i \(-0.797826\pi\)
−0.804984 + 0.593296i \(0.797826\pi\)
\(6\) −4.00000 6.92820i −0.272166 0.471405i
\(7\) −10.0000 17.3205i −0.539949 0.935220i −0.998906 0.0467610i \(-0.985110\pi\)
0.458957 0.888459i \(-0.348223\pi\)
\(8\) 8.00000 0.353553
\(9\) 5.50000 + 9.52628i 0.203704 + 0.352825i
\(10\) 18.0000 31.1769i 0.569210 0.985901i
\(11\) 24.0000 41.5692i 0.657843 1.13942i −0.323330 0.946286i \(-0.604802\pi\)
0.981173 0.193131i \(-0.0618643\pi\)
\(12\) 16.0000 0.384900
\(13\) 0 0
\(14\) 40.0000 0.763604
\(15\) 36.0000 62.3538i 0.619677 1.07331i
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −33.0000 57.1577i −0.470804 0.815457i 0.528638 0.848847i \(-0.322703\pi\)
−0.999442 + 0.0333902i \(0.989370\pi\)
\(18\) −22.0000 −0.288081
\(19\) 8.00000 + 13.8564i 0.0965961 + 0.167309i 0.910274 0.414007i \(-0.135871\pi\)
−0.813678 + 0.581317i \(0.802538\pi\)
\(20\) 36.0000 + 62.3538i 0.402492 + 0.697137i
\(21\) 80.0000 0.831306
\(22\) 48.0000 + 83.1384i 0.465165 + 0.805690i
\(23\) −84.0000 + 145.492i −0.761531 + 1.31901i 0.180530 + 0.983569i \(0.442219\pi\)
−0.942061 + 0.335441i \(0.891115\pi\)
\(24\) −16.0000 + 27.7128i −0.136083 + 0.235702i
\(25\) 199.000 1.59200
\(26\) 0 0
\(27\) −152.000 −1.08342
\(28\) −40.0000 + 69.2820i −0.269975 + 0.467610i
\(29\) −3.00000 + 5.19615i −0.0192099 + 0.0332725i −0.875471 0.483272i \(-0.839448\pi\)
0.856261 + 0.516544i \(0.172782\pi\)
\(30\) 72.0000 + 124.708i 0.438178 + 0.758947i
\(31\) 20.0000 0.115874 0.0579372 0.998320i \(-0.481548\pi\)
0.0579372 + 0.998320i \(0.481548\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 96.0000 + 166.277i 0.506408 + 0.877124i
\(34\) 132.000 0.665818
\(35\) 180.000 + 311.769i 0.869302 + 1.50567i
\(36\) 22.0000 38.1051i 0.101852 0.176413i
\(37\) −127.000 + 219.970i −0.564288 + 0.977376i 0.432827 + 0.901477i \(0.357516\pi\)
−0.997115 + 0.0758992i \(0.975817\pi\)
\(38\) −32.0000 −0.136608
\(39\) 0 0
\(40\) −144.000 −0.569210
\(41\) 195.000 337.750i 0.742778 1.28653i −0.208448 0.978033i \(-0.566841\pi\)
0.951226 0.308495i \(-0.0998254\pi\)
\(42\) −80.0000 + 138.564i −0.293911 + 0.509069i
\(43\) 62.0000 + 107.387i 0.219882 + 0.380846i 0.954772 0.297340i \(-0.0960995\pi\)
−0.734890 + 0.678186i \(0.762766\pi\)
\(44\) −192.000 −0.657843
\(45\) −99.0000 171.473i −0.327957 0.568038i
\(46\) −168.000 290.985i −0.538484 0.932681i
\(47\) −468.000 −1.45244 −0.726221 0.687461i \(-0.758725\pi\)
−0.726221 + 0.687461i \(0.758725\pi\)
\(48\) −32.0000 55.4256i −0.0962250 0.166667i
\(49\) −28.5000 + 49.3634i −0.0830904 + 0.143917i
\(50\) −199.000 + 344.678i −0.562857 + 0.974897i
\(51\) 264.000 0.724851
\(52\) 0 0
\(53\) 558.000 1.44617 0.723087 0.690757i \(-0.242723\pi\)
0.723087 + 0.690757i \(0.242723\pi\)
\(54\) 152.000 263.272i 0.383048 0.663458i
\(55\) −432.000 + 748.246i −1.05911 + 1.83443i
\(56\) −80.0000 138.564i −0.190901 0.330650i
\(57\) −64.0000 −0.148719
\(58\) −6.00000 10.3923i −0.0135834 0.0235272i
\(59\) 48.0000 + 83.1384i 0.105916 + 0.183453i 0.914112 0.405461i \(-0.132889\pi\)
−0.808196 + 0.588914i \(0.799556\pi\)
\(60\) −288.000 −0.619677
\(61\) 413.000 + 715.337i 0.866873 + 1.50147i 0.865176 + 0.501469i \(0.167207\pi\)
0.00169698 + 0.999999i \(0.499460\pi\)
\(62\) −20.0000 + 34.6410i −0.0409678 + 0.0709583i
\(63\) 110.000 190.526i 0.219979 0.381015i
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) −384.000 −0.716169
\(67\) 80.0000 138.564i 0.145874 0.252661i −0.783825 0.620982i \(-0.786734\pi\)
0.929699 + 0.368321i \(0.120067\pi\)
\(68\) −132.000 + 228.631i −0.235402 + 0.407729i
\(69\) −336.000 581.969i −0.586227 1.01537i
\(70\) −720.000 −1.22938
\(71\) 210.000 + 363.731i 0.351020 + 0.607984i 0.986428 0.164192i \(-0.0525016\pi\)
−0.635409 + 0.772176i \(0.719168\pi\)
\(72\) 44.0000 + 76.2102i 0.0720201 + 0.124743i
\(73\) 362.000 0.580396 0.290198 0.956967i \(-0.406279\pi\)
0.290198 + 0.956967i \(0.406279\pi\)
\(74\) −254.000 439.941i −0.399012 0.691109i
\(75\) −398.000 + 689.356i −0.612761 + 1.06133i
\(76\) 32.0000 55.4256i 0.0482980 0.0836547i
\(77\) −960.000 −1.42081
\(78\) 0 0
\(79\) 776.000 1.10515 0.552575 0.833463i \(-0.313645\pi\)
0.552575 + 0.833463i \(0.313645\pi\)
\(80\) 144.000 249.415i 0.201246 0.348569i
\(81\) 155.500 269.334i 0.213306 0.369457i
\(82\) 390.000 + 675.500i 0.525223 + 0.909713i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −160.000 277.128i −0.207827 0.359966i
\(85\) 594.000 + 1028.84i 0.757981 + 1.31286i
\(86\) −248.000 −0.310960
\(87\) −12.0000 20.7846i −0.0147878 0.0256132i
\(88\) 192.000 332.554i 0.232583 0.402845i
\(89\) −813.000 + 1408.16i −0.968290 + 1.67713i −0.267788 + 0.963478i \(0.586293\pi\)
−0.700503 + 0.713650i \(0.747041\pi\)
\(90\) 396.000 0.463801
\(91\) 0 0
\(92\) 672.000 0.761531
\(93\) −40.0000 + 69.2820i −0.0446001 + 0.0772496i
\(94\) 468.000 810.600i 0.513516 0.889436i
\(95\) −144.000 249.415i −0.155517 0.269363i
\(96\) 128.000 0.136083
\(97\) 647.000 + 1120.64i 0.677246 + 1.17303i 0.975807 + 0.218634i \(0.0701602\pi\)
−0.298560 + 0.954391i \(0.596506\pi\)
\(98\) −57.0000 98.7269i −0.0587538 0.101765i
\(99\) 528.000 0.536020
\(100\) −398.000 689.356i −0.398000 0.689356i
\(101\) −111.000 + 192.258i −0.109356 + 0.189409i −0.915509 0.402297i \(-0.868212\pi\)
0.806154 + 0.591706i \(0.201545\pi\)
\(102\) −264.000 + 457.261i −0.256273 + 0.443879i
\(103\) 632.000 0.604590 0.302295 0.953214i \(-0.402247\pi\)
0.302295 + 0.953214i \(0.402247\pi\)
\(104\) 0 0
\(105\) −1440.00 −1.33838
\(106\) −558.000 + 966.484i −0.511300 + 0.885597i
\(107\) 474.000 820.992i 0.428255 0.741760i −0.568463 0.822709i \(-0.692462\pi\)
0.996718 + 0.0809490i \(0.0257951\pi\)
\(108\) 304.000 + 526.543i 0.270856 + 0.469136i
\(109\) 758.000 0.666085 0.333042 0.942912i \(-0.391925\pi\)
0.333042 + 0.942912i \(0.391925\pi\)
\(110\) −864.000 1496.49i −0.748902 1.29714i
\(111\) −508.000 879.882i −0.434389 0.752385i
\(112\) 320.000 0.269975
\(113\) −321.000 555.988i −0.267231 0.462858i 0.700914 0.713245i \(-0.252775\pi\)
−0.968146 + 0.250387i \(0.919442\pi\)
\(114\) 64.0000 110.851i 0.0525803 0.0910717i
\(115\) 1512.00 2618.86i 1.22604 2.12357i
\(116\) 24.0000 0.0192099
\(117\) 0 0
\(118\) −192.000 −0.149788
\(119\) −660.000 + 1143.15i −0.508421 + 0.880611i
\(120\) 288.000 498.831i 0.219089 0.379473i
\(121\) −486.500 842.643i −0.365515 0.633090i
\(122\) −1652.00 −1.22594
\(123\) 780.000 + 1351.00i 0.571791 + 0.990370i
\(124\) −40.0000 69.2820i −0.0289686 0.0501751i
\(125\) −1332.00 −0.953102
\(126\) 220.000 + 381.051i 0.155549 + 0.269419i
\(127\) 440.000 762.102i 0.307431 0.532485i −0.670369 0.742028i \(-0.733864\pi\)
0.977800 + 0.209543i \(0.0671975\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) −496.000 −0.338530
\(130\) 0 0
\(131\) 324.000 0.216092 0.108046 0.994146i \(-0.465541\pi\)
0.108046 + 0.994146i \(0.465541\pi\)
\(132\) 384.000 665.108i 0.253204 0.438562i
\(133\) 160.000 277.128i 0.104314 0.180677i
\(134\) 160.000 + 277.128i 0.103148 + 0.178658i
\(135\) 2736.00 1.74428
\(136\) −264.000 457.261i −0.166455 0.288308i
\(137\) −861.000 1491.30i −0.536936 0.930000i −0.999067 0.0431884i \(-0.986248\pi\)
0.462131 0.886812i \(-0.347085\pi\)
\(138\) 1344.00 0.829050
\(139\) 170.000 + 294.449i 0.103735 + 0.179675i 0.913221 0.407465i \(-0.133587\pi\)
−0.809485 + 0.587140i \(0.800254\pi\)
\(140\) 720.000 1247.08i 0.434651 0.752837i
\(141\) 936.000 1621.20i 0.559046 0.968295i
\(142\) −840.000 −0.496417
\(143\) 0 0
\(144\) −176.000 −0.101852
\(145\) 54.0000 93.5307i 0.0309273 0.0535676i
\(146\) −362.000 + 627.002i −0.205201 + 0.355418i
\(147\) −114.000 197.454i −0.0639630 0.110787i
\(148\) 1016.00 0.564288
\(149\) −375.000 649.519i −0.206183 0.357119i 0.744326 0.667816i \(-0.232771\pi\)
−0.950509 + 0.310697i \(0.899437\pi\)
\(150\) −796.000 1378.71i −0.433288 0.750476i
\(151\) 1748.00 0.942054 0.471027 0.882119i \(-0.343883\pi\)
0.471027 + 0.882119i \(0.343883\pi\)
\(152\) 64.0000 + 110.851i 0.0341519 + 0.0591528i
\(153\) 363.000 628.734i 0.191809 0.332223i
\(154\) 960.000 1662.77i 0.502331 0.870063i
\(155\) −360.000 −0.186554
\(156\) 0 0
\(157\) 614.000 0.312118 0.156059 0.987748i \(-0.450121\pi\)
0.156059 + 0.987748i \(0.450121\pi\)
\(158\) −776.000 + 1344.07i −0.390729 + 0.676763i
\(159\) −1116.00 + 1932.97i −0.556632 + 0.964116i
\(160\) 288.000 + 498.831i 0.142302 + 0.246475i
\(161\) 3360.00 1.64475
\(162\) 311.000 + 538.668i 0.150830 + 0.261245i
\(163\) 404.000 + 699.749i 0.194133 + 0.336249i 0.946616 0.322363i \(-0.104477\pi\)
−0.752483 + 0.658612i \(0.771144\pi\)
\(164\) −1560.00 −0.742778
\(165\) −1728.00 2992.98i −0.815301 1.41214i
\(166\) 0 0
\(167\) 1014.00 1756.30i 0.469854 0.813812i −0.529552 0.848278i \(-0.677640\pi\)
0.999406 + 0.0344662i \(0.0109731\pi\)
\(168\) 640.000 0.293911
\(169\) 0 0
\(170\) −2376.00 −1.07195
\(171\) −88.0000 + 152.420i −0.0393540 + 0.0681631i
\(172\) 248.000 429.549i 0.109941 0.190423i
\(173\) 597.000 + 1034.03i 0.262365 + 0.454429i 0.966870 0.255270i \(-0.0821644\pi\)
−0.704505 + 0.709699i \(0.748831\pi\)
\(174\) 48.0000 0.0209130
\(175\) −1990.00 3446.78i −0.859599 1.48887i
\(176\) 384.000 + 665.108i 0.164461 + 0.284854i
\(177\) −384.000 −0.163069
\(178\) −1626.00 2816.31i −0.684685 1.18591i
\(179\) 1410.00 2442.19i 0.588762 1.01977i −0.405633 0.914036i \(-0.632949\pi\)
0.994395 0.105729i \(-0.0337177\pi\)
\(180\) −396.000 + 685.892i −0.163978 + 0.284019i
\(181\) −754.000 −0.309637 −0.154819 0.987943i \(-0.549479\pi\)
−0.154819 + 0.987943i \(0.549479\pi\)
\(182\) 0 0
\(183\) −3304.00 −1.33464
\(184\) −672.000 + 1163.94i −0.269242 + 0.466341i
\(185\) 2286.00 3959.47i 0.908487 1.57355i
\(186\) −80.0000 138.564i −0.0315370 0.0546237i
\(187\) −3168.00 −1.23886
\(188\) 936.000 + 1621.20i 0.363111 + 0.628926i
\(189\) 1520.00 + 2632.72i 0.584993 + 1.01324i
\(190\) 576.000 0.219934
\(191\) 1164.00 + 2016.11i 0.440964 + 0.763772i 0.997761 0.0668766i \(-0.0213034\pi\)
−0.556797 + 0.830648i \(0.687970\pi\)
\(192\) −128.000 + 221.703i −0.0481125 + 0.0833333i
\(193\) −1225.00 + 2121.76i −0.456878 + 0.791336i −0.998794 0.0490969i \(-0.984366\pi\)
0.541916 + 0.840433i \(0.317699\pi\)
\(194\) −2588.00 −0.957771
\(195\) 0 0
\(196\) 228.000 0.0830904
\(197\) −2271.00 + 3933.49i −0.821330 + 1.42259i 0.0833617 + 0.996519i \(0.473434\pi\)
−0.904692 + 0.426066i \(0.859899\pi\)
\(198\) −528.000 + 914.523i −0.189512 + 0.328244i
\(199\) 332.000 + 575.041i 0.118266 + 0.204842i 0.919080 0.394070i \(-0.128933\pi\)
−0.800815 + 0.598912i \(0.795600\pi\)
\(200\) 1592.00 0.562857
\(201\) 320.000 + 554.256i 0.112294 + 0.194499i
\(202\) −222.000 384.515i −0.0773261 0.133933i
\(203\) 120.000 0.0414894
\(204\) −528.000 914.523i −0.181213 0.313870i
\(205\) −3510.00 + 6079.50i −1.19585 + 2.07127i
\(206\) −632.000 + 1094.66i −0.213755 + 0.370234i
\(207\) −1848.00 −0.620507
\(208\) 0 0
\(209\) 768.000 0.254180
\(210\) 1440.00 2494.15i 0.473188 0.819585i
\(211\) 2078.00 3599.20i 0.677988 1.17431i −0.297598 0.954691i \(-0.596186\pi\)
0.975586 0.219618i \(-0.0704811\pi\)
\(212\) −1116.00 1932.97i −0.361543 0.626211i
\(213\) −1680.00 −0.540431
\(214\) 948.000 + 1641.98i 0.302822 + 0.524503i
\(215\) −1116.00 1932.97i −0.354003 0.613151i
\(216\) −1216.00 −0.383048
\(217\) −200.000 346.410i −0.0625663 0.108368i
\(218\) −758.000 + 1312.89i −0.235497 + 0.407892i
\(219\) −724.000 + 1254.00i −0.223394 + 0.386931i
\(220\) 3456.00 1.05911
\(221\) 0 0
\(222\) 2032.00 0.614319
\(223\) 1646.00 2850.96i 0.494279 0.856117i −0.505699 0.862710i \(-0.668765\pi\)
0.999978 + 0.00659300i \(0.00209863\pi\)
\(224\) −320.000 + 554.256i −0.0954504 + 0.165325i
\(225\) 1094.50 + 1895.73i 0.324296 + 0.561698i
\(226\) 1284.00 0.377922
\(227\) −1176.00 2036.89i −0.343850 0.595565i 0.641294 0.767295i \(-0.278398\pi\)
−0.985144 + 0.171730i \(0.945064\pi\)
\(228\) 128.000 + 221.703i 0.0371799 + 0.0643974i
\(229\) 686.000 0.197957 0.0989785 0.995090i \(-0.468442\pi\)
0.0989785 + 0.995090i \(0.468442\pi\)
\(230\) 3024.00 + 5237.72i 0.866942 + 1.50159i
\(231\) 1920.00 3325.54i 0.546869 0.947205i
\(232\) −24.0000 + 41.5692i −0.00679171 + 0.0117636i
\(233\) 1818.00 0.511164 0.255582 0.966787i \(-0.417733\pi\)
0.255582 + 0.966787i \(0.417733\pi\)
\(234\) 0 0
\(235\) 8424.00 2.33839
\(236\) 192.000 332.554i 0.0529582 0.0917263i
\(237\) −1552.00 + 2688.14i −0.425372 + 0.736766i
\(238\) −1320.00 2286.31i −0.359508 0.622686i
\(239\) −540.000 −0.146149 −0.0730747 0.997326i \(-0.523281\pi\)
−0.0730747 + 0.997326i \(0.523281\pi\)
\(240\) 576.000 + 997.661i 0.154919 + 0.268328i
\(241\) 431.000 + 746.514i 0.115200 + 0.199532i 0.917860 0.396905i \(-0.129916\pi\)
−0.802660 + 0.596437i \(0.796583\pi\)
\(242\) 1946.00 0.516916
\(243\) −1430.00 2476.83i −0.377508 0.653864i
\(244\) 1652.00 2861.35i 0.433436 0.750734i
\(245\) 513.000 888.542i 0.133773 0.231702i
\(246\) −3120.00 −0.808634
\(247\) 0 0
\(248\) 160.000 0.0409678
\(249\) 0 0
\(250\) 1332.00 2307.09i 0.336972 0.583653i
\(251\) −2418.00 4188.10i −0.608059 1.05319i −0.991560 0.129649i \(-0.958615\pi\)
0.383501 0.923540i \(-0.374718\pi\)
\(252\) −880.000 −0.219979
\(253\) 4032.00 + 6983.63i 1.00194 + 1.73540i
\(254\) 880.000 + 1524.20i 0.217386 + 0.376524i
\(255\) −4752.00 −1.16699
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −705.000 + 1221.10i −0.171116 + 0.296381i −0.938810 0.344435i \(-0.888070\pi\)
0.767695 + 0.640816i \(0.221404\pi\)
\(258\) 496.000 859.097i 0.119688 0.207306i
\(259\) 5080.00 1.21875
\(260\) 0 0
\(261\) −66.0000 −0.0156525
\(262\) −324.000 + 561.184i −0.0763999 + 0.132329i
\(263\) −4152.00 + 7191.47i −0.973473 + 1.68610i −0.288586 + 0.957454i \(0.593185\pi\)
−0.684886 + 0.728650i \(0.740148\pi\)
\(264\) 768.000 + 1330.22i 0.179042 + 0.310110i
\(265\) −10044.0 −2.32829
\(266\) 320.000 + 554.256i 0.0737611 + 0.127758i
\(267\) −3252.00 5632.63i −0.745390 1.29105i
\(268\) −640.000 −0.145874
\(269\) 1317.00 + 2281.11i 0.298509 + 0.517033i 0.975795 0.218687i \(-0.0701774\pi\)
−0.677286 + 0.735720i \(0.736844\pi\)
\(270\) −2736.00 + 4738.89i −0.616695 + 1.06815i
\(271\) −3718.00 + 6439.76i −0.833404 + 1.44350i 0.0619197 + 0.998081i \(0.480278\pi\)
−0.895323 + 0.445417i \(0.853056\pi\)
\(272\) 1056.00 0.235402
\(273\) 0 0
\(274\) 3444.00 0.759342
\(275\) 4776.00 8272.27i 1.04729 1.81395i
\(276\) −1344.00 + 2327.88i −0.293113 + 0.507687i
\(277\) 2537.00 + 4394.21i 0.550302 + 0.953150i 0.998253 + 0.0590922i \(0.0188206\pi\)
−0.447951 + 0.894058i \(0.647846\pi\)
\(278\) −680.000 −0.146704
\(279\) 110.000 + 190.526i 0.0236040 + 0.0408834i
\(280\) 1440.00 + 2494.15i 0.307344 + 0.532336i
\(281\) −1638.00 −0.347740 −0.173870 0.984769i \(-0.555627\pi\)
−0.173870 + 0.984769i \(0.555627\pi\)
\(282\) 1872.00 + 3242.40i 0.395305 + 0.684688i
\(283\) 2294.00 3973.32i 0.481852 0.834592i −0.517931 0.855422i \(-0.673298\pi\)
0.999783 + 0.0208301i \(0.00663091\pi\)
\(284\) 840.000 1454.92i 0.175510 0.303992i
\(285\) 1152.00 0.239434
\(286\) 0 0
\(287\) −7800.00 −1.60425
\(288\) 176.000 304.841i 0.0360101 0.0623713i
\(289\) 278.500 482.376i 0.0566863 0.0981836i
\(290\) 108.000 + 187.061i 0.0218689 + 0.0378780i
\(291\) −5176.00 −1.04269
\(292\) −724.000 1254.00i −0.145099 0.251319i
\(293\) 1425.00 + 2468.17i 0.284128 + 0.492123i 0.972397 0.233332i \(-0.0749627\pi\)
−0.688270 + 0.725455i \(0.741629\pi\)
\(294\) 456.000 0.0904573
\(295\) −864.000 1496.49i −0.170522 0.295353i
\(296\) −1016.00 + 1759.76i −0.199506 + 0.345555i
\(297\) −3648.00 + 6318.52i −0.712722 + 1.23447i
\(298\) 1500.00 0.291586
\(299\) 0 0
\(300\) 3184.00 0.612761
\(301\) 1240.00 2147.74i 0.237450 0.411275i
\(302\) −1748.00 + 3027.62i −0.333067 + 0.576888i
\(303\) −444.000 769.031i −0.0841820 0.145807i
\(304\) −256.000 −0.0482980
\(305\) −7434.00 12876.1i −1.39564 2.41732i
\(306\) 726.000 + 1257.47i 0.135630 + 0.234917i
\(307\) 8120.00 1.50955 0.754777 0.655982i \(-0.227745\pi\)
0.754777 + 0.655982i \(0.227745\pi\)
\(308\) 1920.00 + 3325.54i 0.355202 + 0.615228i
\(309\) −1264.00 + 2189.31i −0.232707 + 0.403060i
\(310\) 360.000 623.538i 0.0659569 0.114241i
\(311\) −3528.00 −0.643262 −0.321631 0.946865i \(-0.604231\pi\)
−0.321631 + 0.946865i \(0.604231\pi\)
\(312\) 0 0
\(313\) −6982.00 −1.26085 −0.630425 0.776250i \(-0.717119\pi\)
−0.630425 + 0.776250i \(0.717119\pi\)
\(314\) −614.000 + 1063.48i −0.110350 + 0.191132i
\(315\) −1980.00 + 3429.46i −0.354160 + 0.613423i
\(316\) −1552.00 2688.14i −0.276287 0.478544i
\(317\) 9270.00 1.64245 0.821223 0.570608i \(-0.193292\pi\)
0.821223 + 0.570608i \(0.193292\pi\)
\(318\) −2232.00 3865.94i −0.393599 0.681733i
\(319\) 144.000 + 249.415i 0.0252741 + 0.0437761i
\(320\) −1152.00 −0.201246
\(321\) 1896.00 + 3283.97i 0.329671 + 0.571007i
\(322\) −3360.00 + 5819.69i −0.581508 + 1.00720i
\(323\) 528.000 914.523i 0.0909557 0.157540i
\(324\) −1244.00 −0.213306
\(325\) 0 0
\(326\) −1616.00 −0.274546
\(327\) −1516.00 + 2625.79i −0.256376 + 0.444056i
\(328\) 1560.00 2702.00i 0.262612 0.454857i
\(329\) 4680.00 + 8106.00i 0.784245 + 1.35835i
\(330\) 6912.00 1.15301
\(331\) 3860.00 + 6685.72i 0.640981 + 1.11021i 0.985214 + 0.171328i \(0.0548057\pi\)
−0.344233 + 0.938884i \(0.611861\pi\)
\(332\) 0 0
\(333\) −2794.00 −0.459791
\(334\) 2028.00 + 3512.60i 0.332237 + 0.575452i
\(335\) −1440.00 + 2494.15i −0.234853 + 0.406777i
\(336\) −640.000 + 1108.51i −0.103913 + 0.179983i
\(337\) −1726.00 −0.278995 −0.139497 0.990222i \(-0.544549\pi\)
−0.139497 + 0.990222i \(0.544549\pi\)
\(338\) 0 0
\(339\) 2568.00 0.411430
\(340\) 2376.00 4115.35i 0.378990 0.656430i
\(341\) 480.000 831.384i 0.0762271 0.132029i
\(342\) −176.000 304.841i −0.0278275 0.0481986i
\(343\) −5720.00 −0.900440
\(344\) 496.000 + 859.097i 0.0777399 + 0.134649i
\(345\) 6048.00 + 10475.4i 0.943807 + 1.63472i
\(346\) −2388.00 −0.371040
\(347\) 2010.00 + 3481.42i 0.310958 + 0.538595i 0.978570 0.205914i \(-0.0660168\pi\)
−0.667612 + 0.744509i \(0.732683\pi\)
\(348\) −48.0000 + 83.1384i −0.00739388 + 0.0128066i
\(349\) −955.000 + 1654.11i −0.146476 + 0.253703i −0.929922 0.367756i \(-0.880126\pi\)
0.783447 + 0.621459i \(0.213460\pi\)
\(350\) 7960.00 1.21566
\(351\) 0 0
\(352\) −1536.00 −0.232583
\(353\) −2721.00 + 4712.91i −0.410267 + 0.710603i −0.994919 0.100681i \(-0.967898\pi\)
0.584652 + 0.811284i \(0.301231\pi\)
\(354\) 384.000 665.108i 0.0576536 0.0998589i
\(355\) −3780.00 6547.15i −0.565131 0.978836i
\(356\) 6504.00 0.968290
\(357\) −2640.00 4572.61i −0.391383 0.677895i
\(358\) 2820.00 + 4884.38i 0.416317 + 0.721083i
\(359\) −9324.00 −1.37076 −0.685379 0.728187i \(-0.740363\pi\)
−0.685379 + 0.728187i \(0.740363\pi\)
\(360\) −792.000 1371.78i −0.115950 0.200832i
\(361\) 3301.50 5718.37i 0.481338 0.833703i
\(362\) 754.000 1305.97i 0.109473 0.189613i
\(363\) 3892.00 0.562747
\(364\) 0 0
\(365\) −6516.00 −0.934419
\(366\) 3304.00 5722.70i 0.471866 0.817295i
\(367\) −2260.00 + 3914.43i −0.321447 + 0.556762i −0.980787 0.195083i \(-0.937503\pi\)
0.659340 + 0.751845i \(0.270836\pi\)
\(368\) −1344.00 2327.88i −0.190383 0.329753i
\(369\) 4290.00 0.605226
\(370\) 4572.00 + 7918.94i 0.642397 + 1.11266i
\(371\) −5580.00 9664.84i −0.780860 1.35249i
\(372\) 320.000 0.0446001
\(373\) 2969.00 + 5142.46i 0.412142 + 0.713851i 0.995124 0.0986343i \(-0.0314474\pi\)
−0.582982 + 0.812485i \(0.698114\pi\)
\(374\) 3168.00 5487.14i 0.438004 0.758645i
\(375\) 2664.00 4614.18i 0.366849 0.635401i
\(376\) −3744.00 −0.513516
\(377\) 0 0
\(378\) −6080.00 −0.827305
\(379\) −1108.00 + 1919.11i −0.150169 + 0.260101i −0.931290 0.364280i \(-0.881315\pi\)
0.781120 + 0.624381i \(0.214649\pi\)
\(380\) −576.000 + 997.661i −0.0777584 + 0.134681i
\(381\) 1760.00 + 3048.41i 0.236660 + 0.409907i
\(382\) −4656.00 −0.623617
\(383\) −1914.00 3315.15i −0.255355 0.442287i 0.709637 0.704567i \(-0.248859\pi\)
−0.964992 + 0.262280i \(0.915526\pi\)
\(384\) −256.000 443.405i −0.0340207 0.0589256i
\(385\) 17280.0 2.28746
\(386\) −2450.00 4243.52i −0.323061 0.559559i
\(387\) −682.000 + 1181.26i −0.0895814 + 0.155160i
\(388\) 2588.00 4482.55i 0.338623 0.586513i
\(389\) 5022.00 0.654564 0.327282 0.944927i \(-0.393867\pi\)
0.327282 + 0.944927i \(0.393867\pi\)
\(390\) 0 0
\(391\) 11088.0 1.43413
\(392\) −228.000 + 394.908i −0.0293769 + 0.0508823i
\(393\) −648.000 + 1122.37i −0.0831737 + 0.144061i
\(394\) −4542.00 7866.97i −0.580768 1.00592i
\(395\) −13968.0 −1.77926
\(396\) −1056.00 1829.05i −0.134005 0.232104i
\(397\) −3043.00 5270.63i −0.384695 0.666311i 0.607032 0.794677i \(-0.292360\pi\)
−0.991727 + 0.128367i \(0.959027\pi\)
\(398\) −1328.00 −0.167253
\(399\) 640.000 + 1108.51i 0.0803009 + 0.139085i
\(400\) −1592.00 + 2757.42i −0.199000 + 0.344678i
\(401\) −561.000 + 971.681i −0.0698629 + 0.121006i −0.898841 0.438275i \(-0.855589\pi\)
0.828978 + 0.559281i \(0.188923\pi\)
\(402\) −1280.00 −0.158807
\(403\) 0 0
\(404\) 888.000 0.109356
\(405\) −2799.00 + 4848.01i −0.343416 + 0.594814i
\(406\) −120.000 + 207.846i −0.0146687 + 0.0254070i
\(407\) 6096.00 + 10558.6i 0.742426 + 1.28592i
\(408\) 2112.00 0.256273
\(409\) −181.000 313.501i −0.0218823 0.0379013i 0.854877 0.518831i \(-0.173633\pi\)
−0.876759 + 0.480930i \(0.840299\pi\)
\(410\) −7020.00 12159.0i −0.845593 1.46461i
\(411\) 6888.00 0.826667
\(412\) −1264.00 2189.31i −0.151148 0.261795i
\(413\) 960.000 1662.77i 0.114379 0.198110i
\(414\) 1848.00 3200.83i 0.219382 0.379981i
\(415\) 0 0
\(416\) 0 0
\(417\) −1360.00 −0.159711
\(418\) −768.000 + 1330.22i −0.0898663 + 0.155653i
\(419\) 1158.00 2005.71i 0.135017 0.233856i −0.790587 0.612350i \(-0.790225\pi\)
0.925604 + 0.378494i \(0.123558\pi\)
\(420\) 2880.00 + 4988.31i 0.334594 + 0.579534i
\(421\) 5006.00 0.579519 0.289760 0.957099i \(-0.406425\pi\)
0.289760 + 0.957099i \(0.406425\pi\)
\(422\) 4156.00 + 7198.40i 0.479410 + 0.830362i
\(423\) −2574.00 4458.30i −0.295868 0.512458i
\(424\) 4464.00 0.511300
\(425\) −6567.00 11374.4i −0.749521 1.29821i
\(426\) 1680.00 2909.85i 0.191071 0.330945i
\(427\) 8260.00 14306.7i 0.936134 1.62143i
\(428\) −3792.00 −0.428255
\(429\) 0 0
\(430\) 4464.00 0.500635
\(431\) 5622.00 9737.59i 0.628311 1.08827i −0.359579 0.933115i \(-0.617080\pi\)
0.987891 0.155153i \(-0.0495869\pi\)
\(432\) 1216.00 2106.17i 0.135428 0.234568i
\(433\) −6553.00 11350.1i −0.727291 1.25971i −0.958024 0.286688i \(-0.907446\pi\)
0.230733 0.973017i \(-0.425888\pi\)
\(434\) 800.000 0.0884821
\(435\) 216.000 + 374.123i 0.0238078 + 0.0412364i
\(436\) −1516.00 2625.79i −0.166521 0.288423i
\(437\) −2688.00 −0.294244
\(438\) −1448.00 2508.01i −0.157964 0.273601i
\(439\) 6740.00 11674.0i 0.732762 1.26918i −0.222936 0.974833i \(-0.571564\pi\)
0.955698 0.294348i \(-0.0951026\pi\)
\(440\) −3456.00 + 5985.97i −0.374451 + 0.648568i
\(441\) −627.000 −0.0677033
\(442\) 0 0
\(443\) 14508.0 1.55597 0.777986 0.628281i \(-0.216241\pi\)
0.777986 + 0.628281i \(0.216241\pi\)
\(444\) −2032.00 + 3519.53i −0.217195 + 0.376192i
\(445\) 14634.0 25346.8i 1.55892 2.70012i
\(446\) 3292.00 + 5701.91i 0.349508 + 0.605366i
\(447\) 3000.00 0.317439
\(448\) −640.000 1108.51i −0.0674937 0.116902i
\(449\) 3783.00 + 6552.35i 0.397619 + 0.688696i 0.993432 0.114427i \(-0.0365033\pi\)
−0.595813 + 0.803123i \(0.703170\pi\)
\(450\) −4378.00 −0.458624
\(451\) −9360.00 16212.0i −0.977262 1.69267i
\(452\) −1284.00 + 2223.95i −0.133616 + 0.231429i
\(453\) −3496.00 + 6055.25i −0.362597 + 0.628036i
\(454\) 4704.00 0.486277
\(455\) 0 0
\(456\) −512.000 −0.0525803
\(457\) −2701.00 + 4678.27i −0.276471 + 0.478863i −0.970505 0.241080i \(-0.922498\pi\)
0.694034 + 0.719942i \(0.255832\pi\)
\(458\) −686.000 + 1188.19i −0.0699884 + 0.121223i
\(459\) 5016.00 + 8687.97i 0.510080 + 0.883485i
\(460\) −12096.0 −1.22604
\(461\) 2325.00 + 4027.02i 0.234894 + 0.406848i 0.959242 0.282587i \(-0.0911924\pi\)
−0.724348 + 0.689435i \(0.757859\pi\)
\(462\) 3840.00 + 6651.08i 0.386695 + 0.669775i
\(463\) −17188.0 −1.72526 −0.862629 0.505838i \(-0.831183\pi\)
−0.862629 + 0.505838i \(0.831183\pi\)
\(464\) −48.0000 83.1384i −0.00480247 0.00831811i
\(465\) 720.000 1247.08i 0.0718047 0.124369i
\(466\) −1818.00 + 3148.87i −0.180724 + 0.313023i
\(467\) −14580.0 −1.44472 −0.722358 0.691520i \(-0.756941\pi\)
−0.722358 + 0.691520i \(0.756941\pi\)
\(468\) 0 0
\(469\) −3200.00 −0.315058
\(470\) −8424.00 + 14590.8i −0.826745 + 1.43196i
\(471\) −1228.00 + 2126.96i −0.120134 + 0.208079i
\(472\) 384.000 + 665.108i 0.0374471 + 0.0648603i
\(473\) 5952.00 0.578590
\(474\) −3104.00 5376.29i −0.300784 0.520973i
\(475\) 1592.00 + 2757.42i 0.153781 + 0.266356i
\(476\) 5280.00 0.508421
\(477\) 3069.00 + 5315.66i 0.294591 + 0.510246i
\(478\) 540.000 935.307i 0.0516716 0.0894978i
\(479\) 1050.00 1818.65i 0.100158 0.173479i −0.811592 0.584225i \(-0.801398\pi\)
0.911750 + 0.410746i \(0.134732\pi\)
\(480\) −2304.00 −0.219089
\(481\) 0 0
\(482\) −1724.00 −0.162917
\(483\) −6720.00 + 11639.4i −0.633065 + 1.09650i
\(484\) −1946.00 + 3370.57i −0.182757 + 0.316545i
\(485\) −11646.0 20171.5i −1.09035 1.88853i
\(486\) 5720.00 0.533878
\(487\) 6002.00 + 10395.8i 0.558473 + 0.967304i 0.997624 + 0.0688910i \(0.0219461\pi\)
−0.439151 + 0.898413i \(0.644721\pi\)
\(488\) 3304.00 + 5722.70i 0.306486 + 0.530849i
\(489\) −3232.00 −0.298888
\(490\) 1026.00 + 1777.08i 0.0945917 + 0.163838i
\(491\) −6618.00 + 11462.7i −0.608281 + 1.05357i 0.383242 + 0.923648i \(0.374807\pi\)
−0.991524 + 0.129926i \(0.958526\pi\)
\(492\) 3120.00 5404.00i 0.285895 0.495185i
\(493\) 396.000 0.0361764
\(494\) 0 0
\(495\) −9504.00 −0.862976
\(496\) −160.000 + 277.128i −0.0144843 + 0.0250875i
\(497\) 4200.00 7274.61i 0.379066 0.656561i
\(498\) 0 0
\(499\) 18560.0 1.66505 0.832525 0.553988i \(-0.186895\pi\)
0.832525 + 0.553988i \(0.186895\pi\)
\(500\) 2664.00 + 4614.18i 0.238275 + 0.412705i
\(501\) 4056.00 + 7025.20i 0.361694 + 0.626472i
\(502\) 9672.00 0.859925
\(503\) −6216.00 10766.4i −0.551009 0.954376i −0.998202 0.0599387i \(-0.980909\pi\)
0.447193 0.894438i \(-0.352424\pi\)
\(504\) 880.000 1524.20i 0.0777744 0.134709i
\(505\) 1998.00 3460.64i 0.176059 0.304943i
\(506\) −16128.0 −1.41695
\(507\) 0 0
\(508\) −3520.00 −0.307431
\(509\) 3957.00 6853.73i 0.344579 0.596829i −0.640698 0.767793i \(-0.721355\pi\)
0.985277 + 0.170964i \(0.0546882\pi\)
\(510\) 4752.00 8230.71i 0.412592 0.714631i
\(511\) −3620.00 6270.02i −0.313384 0.542798i
\(512\) 512.000 0.0441942
\(513\) −1216.00 2106.17i −0.104654 0.181267i
\(514\) −1410.00 2442.19i −0.120997 0.209573i
\(515\) −11376.0 −0.973372
\(516\) 992.000 + 1718.19i 0.0846325 + 0.146588i
\(517\) −11232.0 + 19454.4i −0.955479 + 1.65494i
\(518\) −5080.00 + 8798.82i −0.430893 + 0.746328i
\(519\) −4776.00 −0.403937
\(520\) 0 0
\(521\) −14742.0 −1.23965 −0.619826 0.784739i \(-0.712797\pi\)
−0.619826 + 0.784739i \(0.712797\pi\)
\(522\) 66.0000 114.315i 0.00553399 0.00958515i
\(523\) 1250.00 2165.06i 0.104510 0.181016i −0.809028 0.587770i \(-0.800006\pi\)
0.913538 + 0.406754i \(0.133339\pi\)
\(524\) −648.000 1122.37i −0.0540229 0.0935704i
\(525\) 15920.0 1.32344
\(526\) −8304.00 14382.9i −0.688349 1.19226i
\(527\) −660.000 1143.15i −0.0545542 0.0944906i
\(528\) −3072.00 −0.253204
\(529\) −8028.50 13905.8i −0.659859 1.14291i
\(530\) 10044.0 17396.7i 0.823176 1.42578i
\(531\) −528.000 + 914.523i −0.0431511 + 0.0747399i
\(532\) −1280.00 −0.104314
\(533\) 0 0
\(534\) 13008.0 1.05414
\(535\) −8532.00 + 14777.9i −0.689478 + 1.19421i
\(536\) 640.000 1108.51i 0.0515742 0.0893292i
\(537\) 5640.00 + 9768.77i 0.453229 + 0.785016i
\(538\) −5268.00 −0.422155
\(539\) 1368.00 + 2369.45i 0.109321 + 0.189349i
\(540\) −5472.00 9477.78i −0.436069 0.755294i
\(541\) 17894.0 1.42204 0.711020 0.703172i \(-0.248234\pi\)
0.711020 + 0.703172i \(0.248234\pi\)
\(542\) −7436.00 12879.5i −0.589305 1.02071i
\(543\) 1508.00 2611.93i 0.119180 0.206425i
\(544\) −1056.00 + 1829.05i −0.0832273 + 0.144154i
\(545\) −13644.0 −1.07238
\(546\) 0 0
\(547\) 17444.0 1.36353 0.681766 0.731571i \(-0.261212\pi\)
0.681766 + 0.731571i \(0.261212\pi\)
\(548\) −3444.00 + 5965.18i −0.268468 + 0.465000i
\(549\) −4543.00 + 7868.71i −0.353170 + 0.611709i
\(550\) 9552.00 + 16544.5i 0.740543 + 1.28266i
\(551\) −96.0000 −0.00742239
\(552\) −2688.00 4655.75i −0.207262 0.358989i
\(553\) −7760.00 13440.7i −0.596725 1.03356i
\(554\) −10148.0 −0.778244
\(555\) 9144.00 + 15837.9i 0.699353 + 1.21132i
\(556\) 680.000 1177.79i 0.0518677 0.0898374i
\(557\) 501.000 867.757i 0.0381114 0.0660109i −0.846341 0.532642i \(-0.821199\pi\)
0.884452 + 0.466631i \(0.154532\pi\)
\(558\) −440.000 −0.0333812
\(559\) 0 0
\(560\) −5760.00 −0.434651
\(561\) 6336.00 10974.3i 0.476838 0.825908i
\(562\) 1638.00 2837.10i 0.122945 0.212946i
\(563\) 2370.00 + 4104.96i 0.177413 + 0.307289i 0.940994 0.338424i \(-0.109894\pi\)
−0.763581 + 0.645713i \(0.776560\pi\)
\(564\) −7488.00 −0.559046
\(565\) 5778.00 + 10007.8i 0.430234 + 0.745187i
\(566\) 4588.00 + 7946.65i 0.340721 + 0.590146i
\(567\) −6220.00 −0.460697
\(568\) 1680.00 + 2909.85i 0.124104 + 0.214955i
\(569\) −4341.00 + 7518.83i −0.319832 + 0.553965i −0.980453 0.196755i \(-0.936960\pi\)
0.660621 + 0.750720i \(0.270293\pi\)
\(570\) −1152.00 + 1995.32i −0.0846526 + 0.146623i
\(571\) 5492.00 0.402510 0.201255 0.979539i \(-0.435498\pi\)
0.201255 + 0.979539i \(0.435498\pi\)
\(572\) 0 0
\(573\) −9312.00 −0.678908
\(574\) 7800.00 13510.0i 0.567188 0.982398i
\(575\) −16716.0 + 28953.0i −1.21236 + 2.09986i
\(576\) 352.000 + 609.682i 0.0254630 + 0.0441031i
\(577\) −17278.0 −1.24661 −0.623304 0.781980i \(-0.714210\pi\)
−0.623304 + 0.781980i \(0.714210\pi\)
\(578\) 557.000 + 964.752i 0.0400833 + 0.0694263i
\(579\) −4900.00 8487.05i −0.351705 0.609170i
\(580\) −432.000 −0.0309273
\(581\) 0 0
\(582\) 5176.00 8965.09i 0.368646 0.638514i
\(583\) 13392.0 23195.6i 0.951355 1.64780i
\(584\) 2896.00 0.205201
\(585\) 0 0
\(586\) −5700.00 −0.401817
\(587\) 7620.00 13198.2i 0.535794 0.928022i −0.463330 0.886186i \(-0.653346\pi\)
0.999124 0.0418368i \(-0.0133210\pi\)
\(588\) −456.000 + 789.815i −0.0319815 + 0.0553936i
\(589\) 160.000 + 277.128i 0.0111930 + 0.0193869i
\(590\) 3456.00 0.241155
\(591\) −9084.00 15733.9i −0.632260 1.09511i
\(592\) −2032.00 3519.53i −0.141072 0.244344i
\(593\) −9198.00 −0.636959 −0.318479 0.947930i \(-0.603172\pi\)
−0.318479 + 0.947930i \(0.603172\pi\)
\(594\) −7296.00 12637.0i −0.503971 0.872903i
\(595\) 11880.0 20576.8i 0.818542 1.41776i
\(596\) −1500.00 + 2598.08i −0.103091 + 0.178559i
\(597\) −2656.00 −0.182082
\(598\) 0 0
\(599\) 7200.00 0.491125 0.245563 0.969381i \(-0.421027\pi\)
0.245563 + 0.969381i \(0.421027\pi\)
\(600\) −3184.00 + 5514.85i −0.216644 + 0.375238i
\(601\) 7235.00 12531.4i 0.491051 0.850526i −0.508896 0.860828i \(-0.669946\pi\)
0.999947 + 0.0103025i \(0.00327944\pi\)
\(602\) 2480.00 + 4295.49i 0.167902 + 0.290816i
\(603\) 1760.00 0.118860
\(604\) −3496.00 6055.25i −0.235514 0.407922i
\(605\) 8757.00 + 15167.6i 0.588467 + 1.01926i
\(606\) 1776.00 0.119051
\(607\) 10412.0 + 18034.1i 0.696227 + 1.20590i 0.969765 + 0.244040i \(0.0784728\pi\)
−0.273538 + 0.961861i \(0.588194\pi\)
\(608\) 256.000 443.405i 0.0170759 0.0295764i
\(609\) −240.000 + 415.692i −0.0159693 + 0.0276596i
\(610\) 29736.0 1.97373
\(611\) 0 0
\(612\) −2904.00 −0.191809
\(613\) −4303.00 + 7453.01i −0.283518 + 0.491068i −0.972249 0.233950i \(-0.924835\pi\)
0.688731 + 0.725017i \(0.258168\pi\)
\(614\) −8120.00 + 14064.3i −0.533708 + 0.924409i
\(615\) −14040.0 24318.0i −0.920565 1.59447i
\(616\) −7680.00 −0.502331
\(617\) 4827.00 + 8360.61i 0.314956 + 0.545519i 0.979428 0.201793i \(-0.0646770\pi\)
−0.664472 + 0.747313i \(0.731344\pi\)
\(618\) −2528.00 4378.62i −0.164549 0.285007i
\(619\) 14384.0 0.933993 0.466997 0.884259i \(-0.345336\pi\)
0.466997 + 0.884259i \(0.345336\pi\)
\(620\) 720.000 + 1247.08i 0.0466385 + 0.0807803i
\(621\) 12768.0 22114.8i 0.825060 1.42905i
\(622\) 3528.00 6110.68i 0.227428 0.393916i
\(623\) 32520.0 2.09131
\(624\) 0 0
\(625\) −899.000 −0.0575360
\(626\) 6982.00 12093.2i 0.445778 0.772110i
\(627\) −1536.00 + 2660.43i −0.0978340 + 0.169453i
\(628\) −1228.00 2126.96i −0.0780295 0.135151i
\(629\) 16764.0 1.06268
\(630\) −3960.00 6858.92i −0.250429 0.433755i
\(631\) −730.000 1264.40i −0.0460552 0.0797700i 0.842079 0.539354i \(-0.181332\pi\)
−0.888134 + 0.459584i \(0.847998\pi\)
\(632\) 6208.00 0.390729
\(633\) 8312.00 + 14396.8i 0.521915 + 0.903984i
\(634\) −9270.00 + 16056.1i −0.580692 + 1.00579i
\(635\) −7920.00 + 13717.8i −0.494954 + 0.857285i
\(636\) 8928.00 0.556632
\(637\) 0 0
\(638\) −576.000 −0.0357430
\(639\) −2310.00 + 4001.04i −0.143008 + 0.247697i
\(640\) 1152.00 1995.32i 0.0711512 0.123238i
\(641\) 6231.00 + 10792.4i 0.383946 + 0.665015i 0.991622 0.129170i \(-0.0412314\pi\)
−0.607676 + 0.794185i \(0.707898\pi\)
\(642\) −7584.00 −0.466225
\(643\) 4976.00 + 8618.68i 0.305186 + 0.528597i 0.977303 0.211848i \(-0.0679482\pi\)
−0.672117 + 0.740445i \(0.734615\pi\)
\(644\) −6720.00 11639.4i −0.411188 0.712199i
\(645\) 8928.00 0.545023
\(646\) 1056.00 + 1829.05i 0.0643154 + 0.111398i
\(647\) −13044.0 + 22592.9i −0.792601 + 1.37282i 0.131751 + 0.991283i \(0.457940\pi\)
−0.924352 + 0.381542i \(0.875393\pi\)
\(648\) 1244.00 2154.67i 0.0754150 0.130623i
\(649\) 4608.00 0.278705
\(650\) 0 0
\(651\) 1600.00 0.0963271
\(652\) 1616.00 2798.99i 0.0970666 0.168124i
\(653\) −1947.00 + 3372.30i −0.116680 + 0.202096i −0.918450 0.395537i \(-0.870559\pi\)
0.801770 + 0.597633i \(0.203892\pi\)
\(654\) −3032.00 5251.58i −0.181285 0.313995i
\(655\) −5832.00 −0.347901
\(656\) 3120.00 + 5404.00i 0.185694 + 0.321632i
\(657\) 1991.00 + 3448.51i 0.118229 + 0.204778i
\(658\) −18720.0 −1.10909
\(659\) 11910.0 + 20628.7i 0.704018 + 1.21939i 0.967045 + 0.254606i \(0.0819458\pi\)
−0.263027 + 0.964788i \(0.584721\pi\)
\(660\) −6912.00 + 11971.9i −0.407650 + 0.706071i
\(661\) −3871.00 + 6704.77i −0.227783 + 0.394531i −0.957151 0.289590i \(-0.906481\pi\)
0.729368 + 0.684122i \(0.239814\pi\)
\(662\) −15440.0 −0.906484
\(663\) 0 0
\(664\) 0 0
\(665\) −2880.00 + 4988.31i −0.167942 + 0.290885i
\(666\) 2794.00 4839.35i 0.162561 0.281563i
\(667\) −504.000 872.954i −0.0292578 0.0506760i
\(668\) −8112.00 −0.469854
\(669\) 6584.00 + 11403.8i 0.380496 + 0.659039i
\(670\) −2880.00 4988.31i −0.166066 0.287634i
\(671\) 39648.0 2.28106
\(672\) −1280.00 2217.03i −0.0734778 0.127267i
\(673\) −10585.0 + 18333.8i −0.606273 + 1.05010i 0.385576 + 0.922676i \(0.374003\pi\)
−0.991849 + 0.127420i \(0.959331\pi\)
\(674\) 1726.00 2989.52i 0.0986395 0.170849i
\(675\) −30248.0 −1.72481
\(676\) 0 0
\(677\) 17982.0 1.02083 0.510417 0.859927i \(-0.329491\pi\)
0.510417 + 0.859927i \(0.329491\pi\)
\(678\) −2568.00 + 4447.91i −0.145462 + 0.251948i
\(679\) 12940.0 22412.7i 0.731357 1.26675i
\(680\) 4752.00 + 8230.71i 0.267987 + 0.464166i
\(681\) 9408.00 0.529391
\(682\) 960.000 + 1662.77i 0.0539007 + 0.0933588i
\(683\) 8760.00 + 15172.8i 0.490764 + 0.850029i 0.999943 0.0106317i \(-0.00338425\pi\)
−0.509179 + 0.860661i \(0.670051\pi\)
\(684\) 704.000 0.0393540
\(685\) 15498.0 + 26843.3i 0.864450 + 1.49727i
\(686\) 5720.00 9907.33i 0.318354 0.551405i
\(687\) −1372.00 + 2376.37i −0.0761937 + 0.131971i
\(688\) −1984.00 −0.109941
\(689\) 0 0
\(690\) −24192.0 −1.33474
\(691\) 14048.0 24331.8i 0.773388 1.33955i −0.162308 0.986740i \(-0.551894\pi\)
0.935696 0.352807i \(-0.114773\pi\)
\(692\) 2388.00 4136.14i 0.131182 0.227214i
\(693\) −5280.00 9145.23i −0.289424 0.501297i
\(694\) −8040.00 −0.439761
\(695\) −3060.00 5300.08i −0.167011 0.289271i
\(696\) −96.0000 166.277i −0.00522826 0.00905562i
\(697\) −25740.0 −1.39881
\(698\) −1910.00 3308.22i −0.103574 0.179395i
\(699\) −3636.00 + 6297.74i −0.196747 + 0.340776i
\(700\) −7960.00 + 13787.1i −0.429800 + 0.744435i
\(701\) 18342.0 0.988256 0.494128 0.869389i \(-0.335487\pi\)
0.494128 + 0.869389i \(0.335487\pi\)
\(702\) 0 0
\(703\) −4064.00 −0.218032
\(704\) 1536.00 2660.43i 0.0822304 0.142427i
\(705\) −16848.0 + 29181.6i −0.900046 + 1.55893i
\(706\) −5442.00 9425.82i −0.290103 0.502472i
\(707\) 4440.00 0.236186
\(708\) 768.000 + 1330.22i 0.0407672 + 0.0706109i
\(709\) 18665.0 + 32328.7i 0.988687 + 1.71246i 0.624244 + 0.781230i \(0.285407\pi\)
0.364443 + 0.931226i \(0.381259\pi\)
\(710\) 15120.0 0.799216
\(711\) 4268.00 + 7392.39i 0.225123 + 0.389925i
\(712\) −6504.00 + 11265.3i −0.342342 + 0.592954i
\(713\) −1680.00 + 2909.85i −0.0882419 + 0.152840i
\(714\) 10560.0 0.553499
\(715\) 0 0
\(716\) −11280.0 −0.588762
\(717\) 1080.00 1870.61i 0.0562529 0.0974329i
\(718\) 9324.00 16149.6i 0.484636 0.839414i
\(719\) −2400.00 4156.92i −0.124485 0.215615i 0.797046 0.603918i \(-0.206395\pi\)
−0.921532 + 0.388303i \(0.873061\pi\)
\(720\) 3168.00 0.163978
\(721\) −6320.00 10946.6i −0.326448 0.565425i
\(722\) 6603.00 + 11436.7i 0.340358 + 0.589517i
\(723\) −3448.00 −0.177362
\(724\) 1508.00 + 2611.93i 0.0774094 + 0.134077i
\(725\) −597.000 + 1034.03i −0.0305821 + 0.0529698i
\(726\) −3892.00 + 6741.14i −0.198961 + 0.344611i
\(727\) 23960.0 1.22232 0.611160 0.791507i \(-0.290703\pi\)
0.611160 + 0.791507i \(0.290703\pi\)
\(728\) 0 0
\(729\) 19837.0 1.00782
\(730\) 6516.00 11286.0i 0.330367 0.572213i
\(731\) 4092.00 7087.55i 0.207043 0.358608i
\(732\) 6608.00 + 11445.4i 0.333659 + 0.577915i
\(733\) −21418.0 −1.07925 −0.539626 0.841905i \(-0.681434\pi\)
−0.539626 + 0.841905i \(0.681434\pi\)
\(734\) −4520.00 7828.87i −0.227297 0.393691i
\(735\) 2052.00 + 3554.17i 0.102978 + 0.178364i
\(736\) 5376.00 0.269242
\(737\) −3840.00 6651.08i −0.191924 0.332423i
\(738\) −4290.00 + 7430.50i −0.213980 + 0.370624i
\(739\) −2692.00 + 4662.68i −0.134001 + 0.232097i −0.925215 0.379442i \(-0.876116\pi\)
0.791214 + 0.611539i \(0.209449\pi\)
\(740\) −18288.0 −0.908487
\(741\) 0 0
\(742\) 22320.0 1.10430
\(743\) 762.000 1319.82i 0.0376246 0.0651677i −0.846600 0.532230i \(-0.821354\pi\)
0.884225 + 0.467062i \(0.154688\pi\)
\(744\) −320.000 + 554.256i −0.0157685 + 0.0273119i
\(745\) 6750.00 + 11691.3i 0.331947 + 0.574950i
\(746\) −11876.0 −0.582857
\(747\) 0 0
\(748\) 6336.00 + 10974.3i 0.309715 + 0.536443i
\(749\) −18960.0 −0.924944
\(750\) 5328.00 + 9228.37i 0.259401 + 0.449296i
\(751\) 9656.00 16724.7i 0.469178 0.812640i −0.530201 0.847872i \(-0.677884\pi\)
0.999379 + 0.0352321i \(0.0112170\pi\)
\(752\) 3744.00 6484.80i 0.181555 0.314463i
\(753\) 19344.0 0.936168
\(754\) 0 0
\(755\) −31464.0 −1.51668
\(756\) 6080.00 10530.9i 0.292497 0.506619i
\(757\) −17623.0 + 30523.9i −0.846128 + 1.46554i 0.0385102 + 0.999258i \(0.487739\pi\)
−0.884638 + 0.466278i \(0.845595\pi\)
\(758\) −2216.00 3838.22i −0.106186 0.183919i
\(759\) −32256.0 −1.54258
\(760\) −1152.00 1995.32i −0.0549835 0.0952342i
\(761\) −6261.00 10844.4i −0.298241 0.516568i 0.677493 0.735529i \(-0.263066\pi\)
−0.975734 + 0.218961i \(0.929733\pi\)
\(762\) −7040.00 −0.334688
\(763\) −7580.00 13128.9i −0.359652 0.622935i
\(764\) 4656.00 8064.43i 0.220482 0.381886i
\(765\) −6534.00 + 11317.2i −0.308807 + 0.534869i
\(766\) 7656.00 0.361126
\(767\) 0 0
\(768\) 1024.00 0.0481125
\(769\) −12025.0 + 20827.9i −0.563892 + 0.976689i 0.433260 + 0.901269i \(0.357363\pi\)
−0.997152 + 0.0754200i \(0.975970\pi\)
\(770\)