Properties

Label 245.4.e.i.226.1
Level $245$
Weight $4$
Character 245.226
Analytic conductor $14.455$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [245,4,Mod(116,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, 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("245.116");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.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: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.4.e.i.116.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.70711 + 4.68885i) q^{2} +(-2.32843 - 4.03295i) q^{3} +(-10.6569 - 18.4582i) q^{4} +(-2.50000 + 4.33013i) q^{5} +25.2132 q^{6} +72.0833 q^{8} +(2.65685 - 4.60181i) q^{9} +O(q^{10})\) \(q+(-2.70711 + 4.68885i) q^{2} +(-2.32843 - 4.03295i) q^{3} +(-10.6569 - 18.4582i) q^{4} +(-2.50000 + 4.33013i) q^{5} +25.2132 q^{6} +72.0833 q^{8} +(2.65685 - 4.60181i) q^{9} +(-13.5355 - 23.4442i) q^{10} +(26.1274 + 45.2540i) q^{11} +(-49.6274 + 85.9572i) q^{12} -30.6569 q^{13} +23.2843 q^{15} +(-109.882 + 190.322i) q^{16} +(18.6127 + 32.2381i) q^{17} +(14.3848 + 24.9152i) q^{18} +(40.1127 - 69.4772i) q^{19} +106.569 q^{20} -282.919 q^{22} +(-12.9167 + 22.3724i) q^{23} +(-167.841 - 290.708i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(82.9914 - 143.745i) q^{26} -150.480 q^{27} +20.9411 q^{29} +(-63.0330 + 109.176i) q^{30} +(-157.279 - 272.416i) q^{31} +(-306.593 - 531.035i) q^{32} +(121.672 - 210.741i) q^{33} -201.546 q^{34} -113.255 q^{36} +(-98.5736 + 170.734i) q^{37} +(217.179 + 376.165i) q^{38} +(71.3823 + 123.638i) q^{39} +(-180.208 + 312.130i) q^{40} -11.3625 q^{41} -33.8335 q^{43} +(556.872 - 964.531i) q^{44} +(13.2843 + 23.0090i) q^{45} +(-69.9340 - 121.129i) q^{46} +(-180.838 + 313.221i) q^{47} +1023.41 q^{48} +135.355 q^{50} +(86.6766 - 150.128i) q^{51} +(326.706 + 565.871i) q^{52} +(-76.5097 - 132.519i) q^{53} +(407.366 - 705.579i) q^{54} -261.274 q^{55} -373.598 q^{57} +(-56.6899 + 98.1897i) q^{58} +(-308.000 - 533.472i) q^{59} +(-248.137 - 429.786i) q^{60} +(7.63247 - 13.2198i) q^{61} +1703.09 q^{62} +1561.80 q^{64} +(76.6421 - 132.748i) q^{65} +(658.756 + 1141.00i) q^{66} +(83.2548 + 144.202i) q^{67} +(396.706 - 687.114i) q^{68} +120.303 q^{69} -952.000 q^{71} +(191.515 - 331.713i) q^{72} +(-74.2447 - 128.596i) q^{73} +(-533.698 - 924.393i) q^{74} +(-58.2107 + 100.824i) q^{75} -1709.90 q^{76} -772.958 q^{78} +(-428.862 + 742.812i) q^{79} +(-549.411 - 951.608i) q^{80} +(278.647 + 482.631i) q^{81} +(30.7595 - 53.2769i) q^{82} -660.528 q^{83} -186.127 q^{85} +(91.5908 - 158.640i) q^{86} +(-48.7599 - 84.4546i) q^{87} +(1883.35 + 3262.06i) q^{88} +(-22.8873 + 39.6420i) q^{89} -143.848 q^{90} +550.607 q^{92} +(-732.426 + 1268.60i) q^{93} +(-979.096 - 1695.84i) q^{94} +(200.563 + 347.386i) q^{95} +(-1427.76 + 2472.95i) q^{96} -1682.13 q^{97} +277.667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{2} + 2 q^{3} - 20 q^{4} - 10 q^{5} + 16 q^{6} + 96 q^{8} - 12 q^{9} - 40 q^{10} + 14 q^{11} - 108 q^{12} - 100 q^{13} - 20 q^{15} - 168 q^{16} - 50 q^{17} - 16 q^{18} + 36 q^{19} + 200 q^{20} - 368 q^{22} - 244 q^{23} - 496 q^{24} - 50 q^{25} + 216 q^{26} - 172 q^{27} - 52 q^{29} - 40 q^{30} - 120 q^{31} - 672 q^{32} + 498 q^{33} + 48 q^{34} - 272 q^{36} - 564 q^{37} + 320 q^{38} + 14 q^{39} - 240 q^{40} + 656 q^{41} - 520 q^{43} + 1164 q^{44} - 60 q^{45} - 704 q^{46} - 350 q^{47} + 2736 q^{48} + 400 q^{50} + 754 q^{51} + 628 q^{52} + 56 q^{53} + 648 q^{54} - 140 q^{55} - 1336 q^{57} + 8 q^{58} - 1232 q^{59} - 540 q^{60} + 336 q^{61} + 2400 q^{62} + 4256 q^{64} + 250 q^{65} + 1976 q^{66} + 152 q^{67} + 908 q^{68} - 2664 q^{69} - 3808 q^{71} + 800 q^{72} + 676 q^{73} - 2016 q^{74} + 50 q^{75} - 3536 q^{76} - 880 q^{78} - 1014 q^{79} - 840 q^{80} + 1454 q^{81} - 816 q^{82} + 752 q^{83} + 500 q^{85} + 768 q^{86} - 410 q^{87} + 4688 q^{88} - 216 q^{89} + 160 q^{90} + 528 q^{92} - 2760 q^{93} - 1928 q^{94} + 180 q^{95} - 2464 q^{96} - 5484 q^{97} + 1880 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70711 + 4.68885i −0.957107 + 1.65776i −0.227635 + 0.973746i \(0.573099\pi\)
−0.729472 + 0.684011i \(0.760234\pi\)
\(3\) −2.32843 4.03295i −0.448106 0.776142i 0.550157 0.835061i \(-0.314568\pi\)
−0.998263 + 0.0589190i \(0.981235\pi\)
\(4\) −10.6569 18.4582i −1.33211 2.30728i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 25.2132 1.71554
\(7\) 0 0
\(8\) 72.0833 3.18566
\(9\) 2.65685 4.60181i 0.0984020 0.170437i
\(10\) −13.5355 23.4442i −0.428031 0.741372i
\(11\) 26.1274 + 45.2540i 0.716156 + 1.24042i 0.962512 + 0.271239i \(0.0874333\pi\)
−0.246356 + 0.969179i \(0.579233\pi\)
\(12\) −49.6274 + 85.9572i −1.19385 + 2.06781i
\(13\) −30.6569 −0.654052 −0.327026 0.945015i \(-0.606047\pi\)
−0.327026 + 0.945015i \(0.606047\pi\)
\(14\) 0 0
\(15\) 23.2843 0.400798
\(16\) −109.882 + 190.322i −1.71691 + 2.97378i
\(17\) 18.6127 + 32.2381i 0.265544 + 0.459935i 0.967706 0.252082i \(-0.0811152\pi\)
−0.702162 + 0.712017i \(0.747782\pi\)
\(18\) 14.3848 + 24.9152i 0.188362 + 0.326253i
\(19\) 40.1127 69.4772i 0.484341 0.838904i −0.515497 0.856891i \(-0.672393\pi\)
0.999838 + 0.0179877i \(0.00572598\pi\)
\(20\) 106.569 1.19147
\(21\) 0 0
\(22\) −282.919 −2.74175
\(23\) −12.9167 + 22.3724i −0.117101 + 0.202825i −0.918618 0.395147i \(-0.870694\pi\)
0.801517 + 0.597973i \(0.204027\pi\)
\(24\) −167.841 290.708i −1.42751 2.47253i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) 82.9914 143.745i 0.625998 1.08426i
\(27\) −150.480 −1.07259
\(28\) 0 0
\(29\) 20.9411 0.134092 0.0670460 0.997750i \(-0.478643\pi\)
0.0670460 + 0.997750i \(0.478643\pi\)
\(30\) −63.0330 + 109.176i −0.383607 + 0.664426i
\(31\) −157.279 272.416i −0.911232 1.57830i −0.812327 0.583203i \(-0.801799\pi\)
−0.0989050 0.995097i \(-0.531534\pi\)
\(32\) −306.593 531.035i −1.69370 2.93358i
\(33\) 121.672 210.741i 0.641827 1.11168i
\(34\) −201.546 −1.01661
\(35\) 0 0
\(36\) −113.255 −0.524328
\(37\) −98.5736 + 170.734i −0.437984 + 0.758610i −0.997534 0.0701864i \(-0.977641\pi\)
0.559550 + 0.828797i \(0.310974\pi\)
\(38\) 217.179 + 376.165i 0.927133 + 1.60584i
\(39\) 71.3823 + 123.638i 0.293085 + 0.507638i
\(40\) −180.208 + 312.130i −0.712335 + 1.23380i
\(41\) −11.3625 −0.0432810 −0.0216405 0.999766i \(-0.506889\pi\)
−0.0216405 + 0.999766i \(0.506889\pi\)
\(42\) 0 0
\(43\) −33.8335 −0.119990 −0.0599948 0.998199i \(-0.519108\pi\)
−0.0599948 + 0.998199i \(0.519108\pi\)
\(44\) 556.872 964.531i 1.90799 3.30474i
\(45\) 13.2843 + 23.0090i 0.0440067 + 0.0762219i
\(46\) −69.9340 121.129i −0.224157 0.388251i
\(47\) −180.838 + 313.221i −0.561233 + 0.972084i 0.436156 + 0.899871i \(0.356339\pi\)
−0.997389 + 0.0722130i \(0.976994\pi\)
\(48\) 1023.41 3.07743
\(49\) 0 0
\(50\) 135.355 0.382843
\(51\) 86.6766 150.128i 0.237983 0.412199i
\(52\) 326.706 + 565.871i 0.871268 + 1.50908i
\(53\) −76.5097 132.519i −0.198291 0.343450i 0.749684 0.661796i \(-0.230206\pi\)
−0.947974 + 0.318347i \(0.896872\pi\)
\(54\) 407.366 705.579i 1.02658 1.77809i
\(55\) −261.274 −0.640549
\(56\) 0 0
\(57\) −373.598 −0.868145
\(58\) −56.6899 + 98.1897i −0.128340 + 0.222292i
\(59\) −308.000 533.472i −0.679630 1.17715i −0.975092 0.221800i \(-0.928807\pi\)
0.295462 0.955354i \(-0.404526\pi\)
\(60\) −248.137 429.786i −0.533906 0.924752i
\(61\) 7.63247 13.2198i 0.0160203 0.0277479i −0.857904 0.513810i \(-0.828234\pi\)
0.873924 + 0.486062i \(0.161567\pi\)
\(62\) 1703.09 3.48858
\(63\) 0 0
\(64\) 1561.80 3.05040
\(65\) 76.6421 132.748i 0.146251 0.253313i
\(66\) 658.756 + 1141.00i 1.22859 + 2.12799i
\(67\) 83.2548 + 144.202i 0.151809 + 0.262941i 0.931893 0.362735i \(-0.118157\pi\)
−0.780084 + 0.625675i \(0.784824\pi\)
\(68\) 396.706 687.114i 0.707465 1.22537i
\(69\) 120.303 0.209895
\(70\) 0 0
\(71\) −952.000 −1.59129 −0.795645 0.605763i \(-0.792868\pi\)
−0.795645 + 0.605763i \(0.792868\pi\)
\(72\) 191.515 331.713i 0.313475 0.542955i
\(73\) −74.2447 128.596i −0.119037 0.206178i 0.800349 0.599534i \(-0.204647\pi\)
−0.919386 + 0.393356i \(0.871314\pi\)
\(74\) −533.698 924.393i −0.838394 1.45214i
\(75\) −58.2107 + 100.824i −0.0896212 + 0.155228i
\(76\) −1709.90 −2.58078
\(77\) 0 0
\(78\) −772.958 −1.12205
\(79\) −428.862 + 742.812i −0.610770 + 1.05788i 0.380341 + 0.924846i \(0.375807\pi\)
−0.991111 + 0.133038i \(0.957527\pi\)
\(80\) −549.411 951.608i −0.767826 1.32991i
\(81\) 278.647 + 482.631i 0.382232 + 0.662045i
\(82\) 30.7595 53.2769i 0.0414246 0.0717494i
\(83\) −660.528 −0.873523 −0.436761 0.899577i \(-0.643875\pi\)
−0.436761 + 0.899577i \(0.643875\pi\)
\(84\) 0 0
\(85\) −186.127 −0.237509
\(86\) 91.5908 158.640i 0.114843 0.198914i
\(87\) −48.7599 84.4546i −0.0600875 0.104075i
\(88\) 1883.35 + 3262.06i 2.28143 + 3.95155i
\(89\) −22.8873 + 39.6420i −0.0272590 + 0.0472139i −0.879333 0.476207i \(-0.842011\pi\)
0.852074 + 0.523421i \(0.175345\pi\)
\(90\) −143.848 −0.168477
\(91\) 0 0
\(92\) 550.607 0.623965
\(93\) −732.426 + 1268.60i −0.816657 + 1.41449i
\(94\) −979.096 1695.84i −1.07432 1.86078i
\(95\) 200.563 + 347.386i 0.216604 + 0.375169i
\(96\) −1427.76 + 2472.95i −1.51792 + 2.62911i
\(97\) −1682.13 −1.76076 −0.880382 0.474265i \(-0.842714\pi\)
−0.880382 + 0.474265i \(0.842714\pi\)
\(98\) 0 0
\(99\) 277.667 0.281885
\(100\) −266.421 + 461.455i −0.266421 + 0.461455i
\(101\) −217.083 375.999i −0.213867 0.370429i 0.739054 0.673646i \(-0.235273\pi\)
−0.952922 + 0.303217i \(0.901939\pi\)
\(102\) 469.286 + 812.827i 0.455551 + 0.789038i
\(103\) 172.788 299.278i 0.165295 0.286299i −0.771465 0.636272i \(-0.780476\pi\)
0.936760 + 0.349973i \(0.113809\pi\)
\(104\) −2209.85 −2.08359
\(105\) 0 0
\(106\) 828.479 0.759142
\(107\) −108.559 + 188.030i −0.0980825 + 0.169884i −0.910891 0.412647i \(-0.864604\pi\)
0.812808 + 0.582531i \(0.197938\pi\)
\(108\) 1603.65 + 2777.60i 1.42880 + 2.47476i
\(109\) −867.205 1502.04i −0.762047 1.31990i −0.941794 0.336192i \(-0.890861\pi\)
0.179746 0.983713i \(-0.442472\pi\)
\(110\) 707.297 1225.07i 0.613074 1.06188i
\(111\) 918.086 0.785053
\(112\) 0 0
\(113\) −1854.20 −1.54362 −0.771809 0.635855i \(-0.780648\pi\)
−0.771809 + 0.635855i \(0.780648\pi\)
\(114\) 1011.37 1751.74i 0.830907 1.43917i
\(115\) −64.5837 111.862i −0.0523692 0.0907062i
\(116\) −223.167 386.536i −0.178625 0.309387i
\(117\) −81.4508 + 141.077i −0.0643601 + 0.111475i
\(118\) 3335.16 2.60191
\(119\) 0 0
\(120\) 1678.41 1.27681
\(121\) −699.784 + 1212.06i −0.525758 + 0.910639i
\(122\) 41.3238 + 71.5749i 0.0306662 + 0.0531155i
\(123\) 26.4567 + 45.8244i 0.0193945 + 0.0335922i
\(124\) −3352.20 + 5806.19i −2.42772 + 4.20493i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 1394.51 0.974352 0.487176 0.873304i \(-0.338027\pi\)
0.487176 + 0.873304i \(0.338027\pi\)
\(128\) −1775.22 + 3074.78i −1.22585 + 2.12324i
\(129\) 78.7788 + 136.449i 0.0537681 + 0.0931291i
\(130\) 414.957 + 718.726i 0.279955 + 0.484896i
\(131\) 881.209 1526.30i 0.587722 1.01796i −0.406808 0.913514i \(-0.633358\pi\)
0.994530 0.104451i \(-0.0333086\pi\)
\(132\) −5186.54 −3.41993
\(133\) 0 0
\(134\) −901.519 −0.581189
\(135\) 376.201 651.599i 0.239838 0.415412i
\(136\) 1341.66 + 2323.83i 0.845932 + 1.46520i
\(137\) 461.474 + 799.297i 0.287784 + 0.498457i 0.973281 0.229619i \(-0.0737481\pi\)
−0.685496 + 0.728076i \(0.740415\pi\)
\(138\) −325.672 + 564.081i −0.200892 + 0.347955i
\(139\) 196.039 0.119624 0.0598122 0.998210i \(-0.480950\pi\)
0.0598122 + 0.998210i \(0.480950\pi\)
\(140\) 0 0
\(141\) 1684.27 1.00597
\(142\) 2577.17 4463.78i 1.52303 2.63797i
\(143\) −800.984 1387.35i −0.468403 0.811298i
\(144\) 583.882 + 1011.31i 0.337895 + 0.585251i
\(145\) −52.3528 + 90.6777i −0.0299839 + 0.0519336i
\(146\) 803.954 0.455724
\(147\) 0 0
\(148\) 4201.94 2.33376
\(149\) −390.186 + 675.822i −0.214532 + 0.371580i −0.953128 0.302568i \(-0.902156\pi\)
0.738596 + 0.674149i \(0.235489\pi\)
\(150\) −315.165 545.882i −0.171554 0.297140i
\(151\) 1159.71 + 2008.68i 0.625008 + 1.08255i 0.988539 + 0.150964i \(0.0482377\pi\)
−0.363531 + 0.931582i \(0.618429\pi\)
\(152\) 2891.45 5008.15i 1.54295 2.67246i
\(153\) 197.805 0.104520
\(154\) 0 0
\(155\) 1572.79 0.815030
\(156\) 1521.42 2635.18i 0.780841 1.35246i
\(157\) 511.451 + 885.859i 0.259989 + 0.450314i 0.966239 0.257649i \(-0.0829478\pi\)
−0.706250 + 0.707963i \(0.749615\pi\)
\(158\) −2321.95 4021.74i −1.16914 2.02502i
\(159\) −356.294 + 617.120i −0.177711 + 0.307804i
\(160\) 3065.93 1.51489
\(161\) 0 0
\(162\) −3017.31 −1.46335
\(163\) 675.313 1169.68i 0.324507 0.562062i −0.656906 0.753973i \(-0.728135\pi\)
0.981412 + 0.191911i \(0.0614684\pi\)
\(164\) 121.088 + 209.731i 0.0576549 + 0.0998613i
\(165\) 608.358 + 1053.71i 0.287034 + 0.497157i
\(166\) 1788.12 3097.12i 0.836054 1.44809i
\(167\) 1230.58 0.570209 0.285105 0.958496i \(-0.407972\pi\)
0.285105 + 0.958496i \(0.407972\pi\)
\(168\) 0 0
\(169\) −1257.16 −0.572215
\(170\) 503.866 872.721i 0.227322 0.393733i
\(171\) −213.147 369.182i −0.0953203 0.165100i
\(172\) 360.558 + 624.506i 0.159839 + 0.276849i
\(173\) −1243.83 + 2154.37i −0.546626 + 0.946785i 0.451876 + 0.892081i \(0.350755\pi\)
−0.998503 + 0.0547040i \(0.982578\pi\)
\(174\) 527.993 0.230040
\(175\) 0 0
\(176\) −11483.8 −4.91830
\(177\) −1434.31 + 2484.30i −0.609093 + 1.05498i
\(178\) −123.917 214.630i −0.0521795 0.0903776i
\(179\) −810.589 1403.98i −0.338471 0.586248i 0.645675 0.763613i \(-0.276576\pi\)
−0.984145 + 0.177364i \(0.943243\pi\)
\(180\) 283.137 490.408i 0.117243 0.203071i
\(181\) −2593.69 −1.06512 −0.532561 0.846392i \(-0.678770\pi\)
−0.532561 + 0.846392i \(0.678770\pi\)
\(182\) 0 0
\(183\) −71.0866 −0.0287151
\(184\) −931.081 + 1612.68i −0.373044 + 0.646132i
\(185\) −492.868 853.672i −0.195872 0.339261i
\(186\) −3965.51 6868.47i −1.56326 2.70764i
\(187\) −972.603 + 1684.60i −0.380341 + 0.658770i
\(188\) 7708.66 2.99049
\(189\) 0 0
\(190\) −2171.79 −0.829253
\(191\) 911.539 1578.83i 0.345323 0.598116i −0.640090 0.768300i \(-0.721103\pi\)
0.985412 + 0.170184i \(0.0544362\pi\)
\(192\) −3636.54 6298.68i −1.36690 2.36754i
\(193\) 770.514 + 1334.57i 0.287372 + 0.497743i 0.973182 0.230038i \(-0.0738851\pi\)
−0.685810 + 0.727781i \(0.740552\pi\)
\(194\) 4553.70 7887.24i 1.68524 2.91892i
\(195\) −713.823 −0.262143
\(196\) 0 0
\(197\) 701.243 0.253612 0.126806 0.991928i \(-0.459527\pi\)
0.126806 + 0.991928i \(0.459527\pi\)
\(198\) −751.674 + 1301.94i −0.269794 + 0.467296i
\(199\) 1647.48 + 2853.52i 0.586868 + 1.01649i 0.994640 + 0.103402i \(0.0329727\pi\)
−0.407771 + 0.913084i \(0.633694\pi\)
\(200\) −901.041 1560.65i −0.318566 0.551773i
\(201\) 387.706 671.526i 0.136053 0.235651i
\(202\) 2350.67 0.818775
\(203\) 0 0
\(204\) −3694.80 −1.26808
\(205\) 28.4062 49.2010i 0.00967793 0.0167627i
\(206\) 935.514 + 1620.36i 0.316409 + 0.548037i
\(207\) 68.6358 + 118.881i 0.0230460 + 0.0399168i
\(208\) 3368.64 5834.66i 1.12295 1.94501i
\(209\) 4192.16 1.38746
\(210\) 0 0
\(211\) 4082.35 1.33195 0.665974 0.745975i \(-0.268016\pi\)
0.665974 + 0.745975i \(0.268016\pi\)
\(212\) −1630.70 + 2824.46i −0.528289 + 0.915023i
\(213\) 2216.66 + 3839.37i 0.713067 + 1.23507i
\(214\) −587.763 1018.04i −0.187751 0.325194i
\(215\) 84.5837 146.503i 0.0268305 0.0464718i
\(216\) −10847.1 −3.41691
\(217\) 0 0
\(218\) 9390.46 2.91744
\(219\) −345.747 + 598.851i −0.106682 + 0.184779i
\(220\) 2784.36 + 4822.65i 0.853280 + 1.47792i
\(221\) −570.607 988.320i −0.173679 0.300822i
\(222\) −2485.36 + 4304.76i −0.751379 + 1.30143i
\(223\) −747.161 −0.224366 −0.112183 0.993688i \(-0.535784\pi\)
−0.112183 + 0.993688i \(0.535784\pi\)
\(224\) 0 0
\(225\) −132.843 −0.0393608
\(226\) 5019.53 8694.08i 1.47741 2.55894i
\(227\) 832.837 + 1442.52i 0.243513 + 0.421776i 0.961712 0.274061i \(-0.0883670\pi\)
−0.718200 + 0.695837i \(0.755034\pi\)
\(228\) 3981.38 + 6895.95i 1.15646 + 2.00305i
\(229\) −3314.18 + 5740.32i −0.956362 + 1.65647i −0.225143 + 0.974326i \(0.572285\pi\)
−0.731219 + 0.682143i \(0.761048\pi\)
\(230\) 699.340 0.200492
\(231\) 0 0
\(232\) 1509.50 0.427172
\(233\) 216.215 374.496i 0.0607929 0.105296i −0.834027 0.551723i \(-0.813970\pi\)
0.894820 + 0.446427i \(0.147304\pi\)
\(234\) −440.992 763.821i −0.123199 0.213387i
\(235\) −904.190 1566.10i −0.250991 0.434729i
\(236\) −6564.62 + 11370.3i −1.81068 + 3.13619i
\(237\) 3994.30 1.09476
\(238\) 0 0
\(239\) 5580.44 1.51033 0.755165 0.655535i \(-0.227557\pi\)
0.755165 + 0.655535i \(0.227557\pi\)
\(240\) −2558.53 + 4431.50i −0.688135 + 1.19188i
\(241\) −3148.43 5453.25i −0.841529 1.45757i −0.888602 0.458679i \(-0.848323\pi\)
0.0470730 0.998891i \(-0.485011\pi\)
\(242\) −3788.78 6562.36i −1.00641 1.74316i
\(243\) −733.864 + 1271.09i −0.193734 + 0.335557i
\(244\) −325.352 −0.0853629
\(245\) 0 0
\(246\) −286.485 −0.0742504
\(247\) −1229.73 + 2129.95i −0.316785 + 0.548687i
\(248\) −11337.2 19636.6i −2.90287 5.02793i
\(249\) 1537.99 + 2663.88i 0.391431 + 0.677978i
\(250\) −338.388 + 586.106i −0.0856062 + 0.148274i
\(251\) −311.921 −0.0784393 −0.0392197 0.999231i \(-0.512487\pi\)
−0.0392197 + 0.999231i \(0.512487\pi\)
\(252\) 0 0
\(253\) −1349.92 −0.335451
\(254\) −3775.09 + 6538.64i −0.932559 + 1.61524i
\(255\) 433.383 + 750.642i 0.106429 + 0.184341i
\(256\) −3364.23 5827.02i −0.821346 1.42261i
\(257\) −3930.69 + 6808.16i −0.954046 + 1.65246i −0.217511 + 0.976058i \(0.569794\pi\)
−0.736535 + 0.676399i \(0.763539\pi\)
\(258\) −853.050 −0.205847
\(259\) 0 0
\(260\) −3267.06 −0.779285
\(261\) 55.6375 96.3670i 0.0131949 0.0228543i
\(262\) 4771.06 + 8263.71i 1.12503 + 1.94860i
\(263\) −2613.55 4526.80i −0.612769 1.06135i −0.990772 0.135542i \(-0.956722\pi\)
0.378003 0.925804i \(-0.376611\pi\)
\(264\) 8770.48 15190.9i 2.04464 3.54143i
\(265\) 765.097 0.177357
\(266\) 0 0
\(267\) 213.166 0.0488596
\(268\) 1774.47 3073.47i 0.404451 0.700530i
\(269\) 640.854 + 1109.99i 0.145255 + 0.251589i 0.929468 0.368903i \(-0.120266\pi\)
−0.784213 + 0.620491i \(0.786933\pi\)
\(270\) 2036.83 + 3527.89i 0.459102 + 0.795188i
\(271\) 2352.07 4073.91i 0.527226 0.913182i −0.472271 0.881453i \(-0.656566\pi\)
0.999497 0.0317282i \(-0.0101011\pi\)
\(272\) −8180.82 −1.82366
\(273\) 0 0
\(274\) −4997.04 −1.10176
\(275\) 653.185 1131.35i 0.143231 0.248084i
\(276\) −1282.05 2220.57i −0.279602 0.484286i
\(277\) −4479.28 7758.34i −0.971603 1.68286i −0.690719 0.723123i \(-0.742706\pi\)
−0.280883 0.959742i \(-0.590627\pi\)
\(278\) −530.698 + 919.195i −0.114493 + 0.198308i
\(279\) −1671.47 −0.358668
\(280\) 0 0
\(281\) −370.904 −0.0787412 −0.0393706 0.999225i \(-0.512535\pi\)
−0.0393706 + 0.999225i \(0.512535\pi\)
\(282\) −4559.51 + 7897.30i −0.962818 + 1.66765i
\(283\) −2911.13 5042.22i −0.611479 1.05911i −0.990991 0.133926i \(-0.957241\pi\)
0.379512 0.925187i \(-0.376092\pi\)
\(284\) 10145.3 + 17572.2i 2.11977 + 3.67155i
\(285\) 933.995 1617.73i 0.194123 0.336231i
\(286\) 8673.40 1.79325
\(287\) 0 0
\(288\) −3258.29 −0.666655
\(289\) 1763.63 3054.71i 0.358973 0.621760i
\(290\) −283.449 490.949i −0.0573956 0.0994121i
\(291\) 3916.71 + 6783.94i 0.789009 + 1.36660i
\(292\) −1582.43 + 2740.85i −0.317140 + 0.549302i
\(293\) −7443.79 −1.48420 −0.742100 0.670289i \(-0.766170\pi\)
−0.742100 + 0.670289i \(0.766170\pi\)
\(294\) 0 0
\(295\) 3080.00 0.607880
\(296\) −7105.51 + 12307.1i −1.39527 + 2.41667i
\(297\) −3931.66 6809.83i −0.768142 1.33046i
\(298\) −2112.55 3659.04i −0.410660 0.711284i
\(299\) 395.987 685.869i 0.0765903 0.132658i
\(300\) 2481.37 0.477540
\(301\) 0 0
\(302\) −12557.9 −2.39280
\(303\) −1010.93 + 1750.97i −0.191670 + 0.331983i
\(304\) 8815.35 + 15268.6i 1.66314 + 2.88064i
\(305\) 38.1623 + 66.0991i 0.00716449 + 0.0124093i
\(306\) −535.479 + 927.477i −0.100037 + 0.173269i
\(307\) 761.674 0.141600 0.0707998 0.997491i \(-0.477445\pi\)
0.0707998 + 0.997491i \(0.477445\pi\)
\(308\) 0 0
\(309\) −1609.30 −0.296278
\(310\) −4257.72 + 7374.58i −0.780071 + 1.35112i
\(311\) 3859.35 + 6684.58i 0.703677 + 1.21880i 0.967167 + 0.254142i \(0.0817929\pi\)
−0.263490 + 0.964662i \(0.584874\pi\)
\(312\) 5145.47 + 8912.21i 0.933669 + 1.61716i
\(313\) 4278.00 7409.72i 0.772546 1.33809i −0.163617 0.986524i \(-0.552316\pi\)
0.936163 0.351565i \(-0.114350\pi\)
\(314\) −5538.21 −0.995348
\(315\) 0 0
\(316\) 18281.3 3.25444
\(317\) 3890.48 6738.50i 0.689309 1.19392i −0.282753 0.959193i \(-0.591248\pi\)
0.972062 0.234725i \(-0.0754189\pi\)
\(318\) −1929.05 3341.22i −0.340176 0.589202i
\(319\) 547.138 + 947.670i 0.0960308 + 0.166330i
\(320\) −3904.51 + 6762.81i −0.682089 + 1.18141i
\(321\) 1011.09 0.175805
\(322\) 0 0
\(323\) 2986.42 0.514455
\(324\) 5939.00 10286.7i 1.01835 1.76383i
\(325\) 383.211 + 663.740i 0.0654052 + 0.113285i
\(326\) 3656.29 + 6332.88i 0.621175 + 1.07591i
\(327\) −4038.45 + 6994.79i −0.682956 + 1.18291i
\(328\) −819.045 −0.137879
\(329\) 0 0
\(330\) −6587.56 −1.09889
\(331\) 2466.06 4271.34i 0.409507 0.709288i −0.585327 0.810797i \(-0.699034\pi\)
0.994835 + 0.101510i \(0.0323673\pi\)
\(332\) 7039.15 + 12192.2i 1.16363 + 2.01546i
\(333\) 523.791 + 907.233i 0.0861970 + 0.149298i
\(334\) −3331.31 + 5769.99i −0.545751 + 0.945269i
\(335\) −832.548 −0.135782
\(336\) 0 0
\(337\) −7121.13 −1.15108 −0.575538 0.817775i \(-0.695207\pi\)
−0.575538 + 0.817775i \(0.695207\pi\)
\(338\) 3403.26 5894.62i 0.547671 0.948594i
\(339\) 4317.38 + 7477.92i 0.691704 + 1.19807i
\(340\) 1983.53 + 3435.57i 0.316388 + 0.548000i
\(341\) 8218.60 14235.0i 1.30517 2.26062i
\(342\) 2308.05 0.364927
\(343\) 0 0
\(344\) −2438.83 −0.382246
\(345\) −300.757 + 520.926i −0.0469339 + 0.0812919i
\(346\) −6734.34 11664.2i −1.04636 1.81235i
\(347\) −4770.29 8262.39i −0.737991 1.27824i −0.953399 0.301713i \(-0.902442\pi\)
0.215408 0.976524i \(-0.430892\pi\)
\(348\) −1039.25 + 1800.04i −0.160086 + 0.277277i
\(349\) −1281.65 −0.196576 −0.0982880 0.995158i \(-0.531337\pi\)
−0.0982880 + 0.995158i \(0.531337\pi\)
\(350\) 0 0
\(351\) 4613.25 0.701530
\(352\) 16021.0 27749.1i 2.42591 4.20180i
\(353\) 2899.03 + 5021.27i 0.437110 + 0.757097i 0.997465 0.0711552i \(-0.0226686\pi\)
−0.560355 + 0.828253i \(0.689335\pi\)
\(354\) −7765.67 13450.5i −1.16593 2.01946i
\(355\) 2380.00 4122.28i 0.355823 0.616304i
\(356\) 975.627 0.145247
\(357\) 0 0
\(358\) 8777.40 1.29581
\(359\) −1133.65 + 1963.53i −0.166662 + 0.288666i −0.937244 0.348674i \(-0.886632\pi\)
0.770583 + 0.637340i \(0.219965\pi\)
\(360\) 957.574 + 1658.57i 0.140190 + 0.242817i
\(361\) 211.443 + 366.230i 0.0308271 + 0.0533940i
\(362\) 7021.38 12161.4i 1.01944 1.76571i
\(363\) 6517.58 0.942381
\(364\) 0 0
\(365\) 742.447 0.106470
\(366\) 192.439 333.314i 0.0274835 0.0476027i
\(367\) −3686.42 6385.07i −0.524332 0.908169i −0.999599 0.0283274i \(-0.990982\pi\)
0.475267 0.879842i \(-0.342351\pi\)
\(368\) −2838.64 4916.67i −0.402104 0.696465i
\(369\) −30.1885 + 52.2879i −0.00425894 + 0.00737670i
\(370\) 5336.98 0.749883
\(371\) 0 0
\(372\) 31221.4 4.35150
\(373\) −3223.57 + 5583.39i −0.447480 + 0.775059i −0.998221 0.0596176i \(-0.981012\pi\)
0.550741 + 0.834676i \(0.314345\pi\)
\(374\) −5265.88 9120.78i −0.728054 1.26103i
\(375\) −291.053 504.119i −0.0400798 0.0694203i
\(376\) −13035.4 + 22578.0i −1.78790 + 3.09673i
\(377\) −641.989 −0.0877032
\(378\) 0 0
\(379\) −4247.57 −0.575680 −0.287840 0.957678i \(-0.592937\pi\)
−0.287840 + 0.957678i \(0.592937\pi\)
\(380\) 4274.75 7404.09i 0.577079 0.999531i
\(381\) −3247.01 5623.99i −0.436613 0.756236i
\(382\) 4935.27 + 8548.13i 0.661021 + 1.14492i
\(383\) −3340.93 + 5786.66i −0.445727 + 0.772022i −0.998103 0.0615735i \(-0.980388\pi\)
0.552375 + 0.833595i \(0.313721\pi\)
\(384\) 16533.9 2.19725
\(385\) 0 0
\(386\) −8343.45 −1.10018
\(387\) −89.8906 + 155.695i −0.0118072 + 0.0204507i
\(388\) 17926.2 + 31049.1i 2.34553 + 4.06257i
\(389\) 3185.89 + 5518.12i 0.415247 + 0.719229i 0.995454 0.0952400i \(-0.0303619\pi\)
−0.580207 + 0.814469i \(0.697029\pi\)
\(390\) 1932.39 3347.00i 0.250899 0.434570i
\(391\) −961.661 −0.124382
\(392\) 0 0
\(393\) −8207.33 −1.05345
\(394\) −1898.34 + 3288.02i −0.242733 + 0.420427i
\(395\) −2144.31 3714.06i −0.273144 0.473100i
\(396\) −2959.06 5125.24i −0.375500 0.650386i
\(397\) 2123.96 3678.81i 0.268510 0.465074i −0.699967 0.714175i \(-0.746802\pi\)
0.968477 + 0.249101i \(0.0801353\pi\)
\(398\) −17839.6 −2.24678
\(399\) 0 0
\(400\) 5494.11 0.686764
\(401\) 4416.81 7650.14i 0.550038 0.952693i −0.448234 0.893916i \(-0.647947\pi\)
0.998271 0.0587765i \(-0.0187199\pi\)
\(402\) 2099.12 + 3635.78i 0.260434 + 0.451086i
\(403\) 4821.69 + 8351.41i 0.595993 + 1.03229i
\(404\) −4626.85 + 8013.94i −0.569788 + 0.986902i
\(405\) −2786.47 −0.341879
\(406\) 0 0
\(407\) −10301.9 −1.25466
\(408\) 6247.93 10821.7i 0.758134 1.31313i
\(409\) −159.602 276.439i −0.0192954 0.0334206i 0.856216 0.516617i \(-0.172809\pi\)
−0.875512 + 0.483197i \(0.839476\pi\)
\(410\) 153.797 + 266.385i 0.0185256 + 0.0320873i
\(411\) 2149.02 3722.21i 0.257916 0.446723i
\(412\) −7365.53 −0.880761
\(413\) 0 0
\(414\) −743.218 −0.0882298
\(415\) 1651.32 2860.17i 0.195326 0.338314i
\(416\) 9399.17 + 16279.8i 1.10777 + 1.91871i
\(417\) −456.462 790.615i −0.0536044 0.0928455i
\(418\) −11348.6 + 19656.4i −1.32794 + 2.30006i
\(419\) 12789.2 1.49115 0.745577 0.666420i \(-0.232174\pi\)
0.745577 + 0.666420i \(0.232174\pi\)
\(420\) 0 0
\(421\) −6747.40 −0.781112 −0.390556 0.920579i \(-0.627717\pi\)
−0.390556 + 0.920579i \(0.627717\pi\)
\(422\) −11051.4 + 19141.5i −1.27482 + 2.20805i
\(423\) 960.921 + 1664.36i 0.110453 + 0.191310i
\(424\) −5515.07 9552.38i −0.631687 1.09411i
\(425\) 465.317 805.953i 0.0531087 0.0919870i
\(426\) −24003.0 −2.72992
\(427\) 0 0
\(428\) 4627.60 0.522625
\(429\) −3730.07 + 6460.67i −0.419789 + 0.727095i
\(430\) 457.954 + 793.200i 0.0513593 + 0.0889570i
\(431\) 2592.37 + 4490.12i 0.289722 + 0.501813i 0.973743 0.227649i \(-0.0731038\pi\)
−0.684021 + 0.729462i \(0.739770\pi\)
\(432\) 16535.1 28639.6i 1.84154 3.18964i
\(433\) 4242.03 0.470806 0.235403 0.971898i \(-0.424359\pi\)
0.235403 + 0.971898i \(0.424359\pi\)
\(434\) 0 0
\(435\) 487.599 0.0537439
\(436\) −18483.3 + 32014.1i −2.03026 + 3.51651i
\(437\) 1036.25 + 1794.84i 0.113434 + 0.196473i
\(438\) −1871.95 3242.31i −0.204213 0.353707i
\(439\) −2717.06 + 4706.08i −0.295394 + 0.511638i −0.975077 0.221869i \(-0.928784\pi\)
0.679682 + 0.733507i \(0.262118\pi\)
\(440\) −18833.5 −2.04057
\(441\) 0 0
\(442\) 6178.77 0.664919
\(443\) 5746.89 9953.91i 0.616350 1.06755i −0.373796 0.927511i \(-0.621944\pi\)
0.990146 0.140039i \(-0.0447228\pi\)
\(444\) −9783.91 16946.2i −1.04577 1.81133i
\(445\) −114.437 198.210i −0.0121906 0.0211147i
\(446\) 2022.65 3503.32i 0.214742 0.371944i
\(447\) 3634.08 0.384532
\(448\) 0 0
\(449\) −16849.3 −1.77098 −0.885489 0.464661i \(-0.846176\pi\)
−0.885489 + 0.464661i \(0.846176\pi\)
\(450\) 359.619 622.879i 0.0376725 0.0652507i
\(451\) −296.872 514.198i −0.0309959 0.0536865i
\(452\) 19760.0 + 34225.3i 2.05626 + 3.56155i
\(453\) 5400.62 9354.15i 0.560140 0.970191i
\(454\) −9018.32 −0.932270
\(455\) 0 0
\(456\) −26930.2 −2.76561
\(457\) −7674.25 + 13292.2i −0.785528 + 1.36057i 0.143155 + 0.989700i \(0.454275\pi\)
−0.928683 + 0.370875i \(0.879058\pi\)
\(458\) −17943.7 31079.3i −1.83068 3.17083i
\(459\) −2800.84 4851.20i −0.284820 0.493322i
\(460\) −1376.52 + 2384.20i −0.139523 + 0.241661i
\(461\) −14038.4 −1.41830 −0.709148 0.705059i \(-0.750920\pi\)
−0.709148 + 0.705059i \(0.750920\pi\)
\(462\) 0 0
\(463\) −8661.23 −0.869377 −0.434689 0.900581i \(-0.643142\pi\)
−0.434689 + 0.900581i \(0.643142\pi\)
\(464\) −2301.06 + 3985.55i −0.230224 + 0.398760i
\(465\) −3662.13 6343.00i −0.365220 0.632580i
\(466\) 1170.64 + 2027.60i 0.116371 + 0.201560i
\(467\) 3507.35 6074.91i 0.347539 0.601956i −0.638272 0.769811i \(-0.720351\pi\)
0.985812 + 0.167855i \(0.0536839\pi\)
\(468\) 3472.04 0.342938
\(469\) 0 0
\(470\) 9790.96 0.960901
\(471\) 2381.75 4125.32i 0.233005 0.403576i
\(472\) −22201.6 38454.4i −2.16507 3.75001i
\(473\) −883.981 1531.10i −0.0859313 0.148837i
\(474\) −10813.0 + 18728.7i −1.04780 + 1.81484i
\(475\) −2005.63 −0.193737
\(476\) 0 0
\(477\) −813.100 −0.0780488
\(478\) −15106.9 + 26165.8i −1.44555 + 2.50376i
\(479\) 9067.34 + 15705.1i 0.864922 + 1.49809i 0.867125 + 0.498091i \(0.165965\pi\)
−0.00220344 + 0.999998i \(0.500701\pi\)
\(480\) −7138.79 12364.8i −0.678833 1.17577i
\(481\) 3021.96 5234.18i 0.286464 0.496171i
\(482\) 34092.6 3.22173
\(483\) 0 0
\(484\) 29830.0 2.80146
\(485\) 4205.32 7283.82i 0.393719 0.681941i
\(486\) −3973.30 6881.95i −0.370848 0.642328i
\(487\) −8268.92 14322.2i −0.769405 1.33265i −0.937886 0.346944i \(-0.887219\pi\)
0.168480 0.985705i \(-0.446114\pi\)
\(488\) 550.173 952.928i 0.0510352 0.0883955i
\(489\) −6289.67 −0.581654
\(490\) 0 0
\(491\) 220.608 0.0202768 0.0101384 0.999949i \(-0.496773\pi\)
0.0101384 + 0.999949i \(0.496773\pi\)
\(492\) 563.891 976.687i 0.0516710 0.0894969i
\(493\) 389.771 + 675.103i 0.0356073 + 0.0616736i
\(494\) −6658.02 11532.0i −0.606393 1.05030i
\(495\) −694.167 + 1202.33i −0.0630313 + 0.109173i
\(496\) 69128.8 6.25801
\(497\) 0 0
\(498\) −16654.0 −1.49856
\(499\) −2969.52 + 5143.36i −0.266401 + 0.461419i −0.967930 0.251222i \(-0.919168\pi\)
0.701529 + 0.712641i \(0.252501\pi\)
\(500\) −1332.11 2307.28i −0.119147 0.206369i
\(501\) −2865.31 4962.86i −0.255514 0.442564i
\(502\) 844.403 1462.55i 0.0750748 0.130033i
\(503\) 11604.8 1.02869 0.514345 0.857584i \(-0.328035\pi\)
0.514345 + 0.857584i \(0.328035\pi\)
\(504\) 0 0
\(505\) 2170.83 0.191289
\(506\) 3654.39 6329.59i 0.321062 0.556096i
\(507\) 2927.20 + 5070.06i 0.256413 + 0.444121i
\(508\) −14861.1 25740.2i −1.29794 2.24810i
\(509\) −933.836 + 1617.45i −0.0813193 + 0.140849i −0.903817 0.427919i \(-0.859247\pi\)
0.822498 + 0.568769i \(0.192580\pi\)
\(510\) −4692.86 −0.407457
\(511\) 0 0
\(512\) 8025.75 0.692757
\(513\) −6036.17 + 10454.9i −0.519500 + 0.899800i
\(514\) −21281.6 36860.8i −1.82625 3.16316i
\(515\) 863.942 + 1496.39i 0.0739220 + 0.128037i
\(516\) 1679.07 2908.23i 0.143250 0.248116i
\(517\) −18899.3 −1.60772
\(518\) 0 0
\(519\) 11584.6 0.979786
\(520\) 5524.62 9568.91i 0.465905 0.806970i
\(521\) 3058.60 + 5297.66i 0.257197 + 0.445479i 0.965490 0.260440i \(-0.0838676\pi\)
−0.708293 + 0.705919i \(0.750534\pi\)
\(522\) 301.233 + 521.752i 0.0252579 + 0.0437480i
\(523\) −8342.80 + 14450.2i −0.697524 + 1.20815i 0.271798 + 0.962354i \(0.412382\pi\)
−0.969322 + 0.245793i \(0.920952\pi\)
\(524\) −37563.7 −3.13164
\(525\) 0 0
\(526\) 28300.6 2.34594
\(527\) 5854.78 10140.8i 0.483944 0.838215i
\(528\) 26739.1 + 46313.5i 2.20392 + 3.81730i
\(529\) 5749.82 + 9958.97i 0.472575 + 0.818523i
\(530\) −2071.20 + 3587.42i −0.169749 + 0.294014i
\(531\) −3273.24 −0.267508
\(532\) 0 0
\(533\) 348.338 0.0283081
\(534\) −577.062 + 999.501i −0.0467639 + 0.0809975i
\(535\) −542.797 940.151i −0.0438638 0.0759744i
\(536\) 6001.28 + 10394.5i 0.483612 + 0.837640i
\(537\) −3774.79 + 6538.13i −0.303341 + 0.525403i
\(538\) −6939.44 −0.556097
\(539\) 0 0
\(540\) −16036.5 −1.27796
\(541\) −4654.51 + 8061.86i −0.369895 + 0.640677i −0.989549 0.144198i \(-0.953940\pi\)
0.619654 + 0.784875i \(0.287273\pi\)
\(542\) 12734.6 + 22057.0i 1.00922 + 1.74802i
\(543\) 6039.21 + 10460.2i 0.477288 + 0.826686i
\(544\) 11413.0 19768.0i 0.899504 1.55799i
\(545\) 8672.05 0.681596
\(546\) 0 0
\(547\) 10894.7 0.851598 0.425799 0.904818i \(-0.359993\pi\)
0.425799 + 0.904818i \(0.359993\pi\)
\(548\) 9835.73 17036.0i 0.766718 1.32799i
\(549\) −40.5567 70.2463i −0.00315286 0.00546091i
\(550\) 3536.49 + 6125.37i 0.274175 + 0.474885i
\(551\) 840.005 1454.93i 0.0649463 0.112490i
\(552\) 8671.81 0.668654
\(553\) 0 0
\(554\) 48503.6 3.71971
\(555\) −2295.21 + 3975.43i −0.175543 + 0.304050i
\(556\) −2089.16 3618.52i −0.159352 0.276006i
\(557\) 3936.95 + 6818.99i 0.299486 + 0.518725i 0.976019 0.217688i \(-0.0698514\pi\)
−0.676532 + 0.736413i \(0.736518\pi\)
\(558\) 4524.85 7837.27i 0.343284 0.594585i
\(559\) 1037.23 0.0784796
\(560\) 0 0
\(561\) 9058.55 0.681733
\(562\) 1004.08 1739.11i 0.0753638 0.130534i
\(563\) 10885.4 + 18854.0i 0.814854 + 1.41137i 0.909433 + 0.415851i \(0.136516\pi\)
−0.0945786 + 0.995517i \(0.530150\pi\)
\(564\) −17949.1 31088.7i −1.34006 2.32105i
\(565\) 4635.51 8028.94i 0.345163 0.597841i
\(566\) 31522.9 2.34100
\(567\) 0 0
\(568\) −68623.3 −5.06931
\(569\) 6190.63 10722.5i 0.456106 0.790000i −0.542645 0.839962i \(-0.682577\pi\)
0.998751 + 0.0499628i \(0.0159103\pi\)
\(570\) 5056.85 + 8758.72i 0.371593 + 0.643618i
\(571\) 2884.19 + 4995.56i 0.211383 + 0.366126i 0.952148 0.305639i \(-0.0988700\pi\)
−0.740765 + 0.671764i \(0.765537\pi\)
\(572\) −17071.9 + 29569.5i −1.24793 + 2.16147i
\(573\) −8489.81 −0.618965
\(574\) 0 0
\(575\) 645.837 0.0468405
\(576\) 4149.48 7187.12i 0.300165 0.519901i
\(577\) 2366.69 + 4099.23i 0.170757 + 0.295759i 0.938685 0.344777i \(-0.112045\pi\)
−0.767928 + 0.640536i \(0.778712\pi\)
\(578\) 9548.70 + 16538.8i 0.687151 + 1.19018i
\(579\) 3588.17 6214.89i 0.257546 0.446083i
\(580\) 2231.67 0.159767
\(581\) 0 0
\(582\) −42411.8 −3.02066
\(583\) 3998.00 6924.74i 0.284014 0.491927i
\(584\) −5351.80 9269.59i −0.379211 0.656813i
\(585\) −407.254 705.385i −0.0287827 0.0498531i
\(586\) 20151.1 34902.8i 1.42054 2.46044i
\(587\) 8441.67 0.593569 0.296785 0.954944i \(-0.404086\pi\)
0.296785 + 0.954944i \(0.404086\pi\)
\(588\) 0 0
\(589\) −25235.6 −1.76539
\(590\) −8337.89 + 14441.6i −0.581806 + 1.00772i
\(591\) −1632.79 2828.08i −0.113645 0.196839i
\(592\) −21663.0 37521.4i −1.50396 2.60493i
\(593\) 9469.94 16402.4i 0.655791 1.13586i −0.325904 0.945403i \(-0.605669\pi\)
0.981695 0.190460i \(-0.0609979\pi\)
\(594\) 42573.7 2.94077
\(595\) 0 0
\(596\) 16632.6 1.14312
\(597\) 7672.08 13288.4i 0.525958 0.910987i
\(598\) 2143.96 + 3713.44i 0.146610 + 0.253936i
\(599\) −11327.7 19620.1i −0.772681 1.33832i −0.936089 0.351764i \(-0.885582\pi\)
0.163407 0.986559i \(-0.447752\pi\)
\(600\) −4196.02 + 7267.71i −0.285503 + 0.494505i
\(601\) 15947.4 1.08237 0.541187 0.840902i \(-0.317975\pi\)
0.541187 + 0.840902i \(0.317975\pi\)
\(602\) 0 0
\(603\) 884.784 0.0597532
\(604\) 24717.8 42812.5i 1.66516 2.88413i
\(605\) −3498.92 6060.31i −0.235126 0.407250i
\(606\) −5473.36 9480.15i −0.366898 0.635486i
\(607\) −12996.6 + 22510.8i −0.869053 + 1.50524i −0.00608748 + 0.999981i \(0.501938\pi\)
−0.862966 + 0.505263i \(0.831396\pi\)
\(608\) −49193.1 −3.28132
\(609\) 0 0
\(610\) −413.238 −0.0274287
\(611\) 5543.93 9602.36i 0.367076 0.635794i
\(612\) −2107.98 3651.13i −0.139232 0.241157i
\(613\) −332.704 576.260i −0.0219213 0.0379689i 0.854857 0.518864i \(-0.173645\pi\)
−0.876778 + 0.480895i \(0.840312\pi\)
\(614\) −2061.93 + 3571.37i −0.135526 + 0.234738i
\(615\) −264.567 −0.0173470
\(616\) 0 0
\(617\) 18401.3 1.20066 0.600330 0.799752i \(-0.295036\pi\)
0.600330 + 0.799752i \(0.295036\pi\)
\(618\) 4356.55 7545.77i 0.283570 0.491157i
\(619\) −5575.30 9656.70i −0.362020 0.627037i 0.626273 0.779604i \(-0.284579\pi\)
−0.988293 + 0.152567i \(0.951246\pi\)
\(620\) −16761.0 29030.9i −1.08571 1.88050i
\(621\) 1943.71 3366.61i 0.125602 0.217548i
\(622\) −41790.6 −2.69397
\(623\) 0 0
\(624\) −31374.6 −2.01280
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 23162.0 + 40117.8i 1.47882 + 2.56139i
\(627\) −9761.15 16906.8i −0.621727 1.07686i
\(628\) 10900.9 18880.9i 0.692665 1.19973i
\(629\) −7338.88 −0.465215
\(630\) 0 0
\(631\) 5381.79 0.339534 0.169767 0.985484i \(-0.445699\pi\)
0.169767 + 0.985484i \(0.445699\pi\)
\(632\) −30913.8 + 53544.3i −1.94570 + 3.37006i
\(633\) −9505.46 16463.9i −0.596854 1.03378i
\(634\) 21063.9 + 36483.7i 1.31948 + 2.28541i
\(635\) −3486.27 + 6038.40i −0.217872 + 0.377365i
\(636\) 15187.9 0.946918
\(637\) 0 0
\(638\) −5924.64 −0.367647
\(639\) −2529.33 + 4380.92i −0.156586 + 0.271215i
\(640\) −8876.12 15373.9i −0.548218 0.949542i
\(641\) 9727.53 + 16848.6i 0.599398 + 1.03819i 0.992910 + 0.118869i \(0.0379267\pi\)
−0.393512 + 0.919320i \(0.628740\pi\)
\(642\) −2737.13 + 4740.84i −0.168265 + 0.291443i
\(643\) 14695.8 0.901317 0.450658 0.892696i \(-0.351189\pi\)
0.450658 + 0.892696i \(0.351189\pi\)
\(644\) 0 0
\(645\) −787.788 −0.0480917
\(646\) −8084.56 + 14002.9i −0.492388 + 0.852842i
\(647\) −6347.41 10994.0i −0.385691 0.668037i 0.606174 0.795332i \(-0.292704\pi\)
−0.991865 + 0.127295i \(0.959370\pi\)
\(648\) 20085.8 + 34789.6i 1.21766 + 2.10905i
\(649\) 16094.5 27876.5i 0.973442 1.68605i
\(650\) −4149.57 −0.250399
\(651\) 0 0
\(652\) −28786.8 −1.72911
\(653\) 6192.82 10726.3i 0.371124 0.642805i −0.618615 0.785694i \(-0.712306\pi\)
0.989739 + 0.142889i \(0.0456393\pi\)
\(654\) −21865.0 37871.3i −1.30732 2.26435i
\(655\) 4406.05 + 7631.50i 0.262837 + 0.455248i
\(656\) 1248.54 2162.53i 0.0743096 0.128708i
\(657\) −789.030 −0.0468539
\(658\) 0 0
\(659\) −2072.18 −0.122489 −0.0612447 0.998123i \(-0.519507\pi\)
−0.0612447 + 0.998123i \(0.519507\pi\)
\(660\) 12966.4 22458.4i 0.764720 1.32453i
\(661\) 537.182 + 930.427i 0.0316096 + 0.0547495i 0.881397 0.472375i \(-0.156603\pi\)
−0.849788 + 0.527125i \(0.823270\pi\)
\(662\) 13351.8 + 23126.0i 0.783885 + 1.35773i
\(663\) −2657.23 + 4602.46i −0.155654 + 0.269600i
\(664\) −47613.0 −2.78275
\(665\) 0 0
\(666\) −5671.84 −0.329999
\(667\) −270.491 + 468.504i −0.0157023 + 0.0271972i
\(668\) −13114.1 22714.3i −0.759580 1.31563i
\(669\) 1739.71 + 3013.27i 0.100540 + 0.174140i
\(670\) 2253.80 3903.69i 0.129958 0.225094i
\(671\) 797.667 0.0458921
\(672\) 0 0
\(673\) 26195.2 1.50037 0.750186 0.661226i \(-0.229964\pi\)
0.750186 + 0.661226i \(0.229964\pi\)
\(674\) 19277.7 33389.9i 1.10170 1.90821i
\(675\) 1881.00 + 3257.99i 0.107259 + 0.185778i
\(676\) 13397.3 + 23204.9i 0.762252 + 1.32026i
\(677\) −2114.22 + 3661.93i −0.120024 + 0.207887i −0.919777 0.392442i \(-0.871630\pi\)
0.799753 + 0.600329i \(0.204964\pi\)
\(678\) −46750.4 −2.64814
\(679\) 0 0
\(680\) −13416.6 −0.756624
\(681\) 3878.40 6717.59i 0.218239 0.378001i
\(682\) 44497.3 + 77071.5i 2.49837 + 4.32730i
\(683\) −13762.8 23837.8i −0.771036 1.33547i −0.936996 0.349341i \(-0.886405\pi\)
0.165960 0.986133i \(-0.446928\pi\)
\(684\) −4542.96 + 7868.63i −0.253954 + 0.439861i
\(685\) −4614.74 −0.257402
\(686\) 0 0
\(687\) 30867.3 1.71421
\(688\) 3717.70 6439.24i 0.206012 0.356822i
\(689\) 2345.55 + 4062.60i 0.129693 + 0.224634i
\(690\) −1628.36 2820.41i −0.0898416 0.155610i
\(691\) −16662.2 + 28859.8i −0.917309 + 1.58883i −0.113823 + 0.993501i \(0.536310\pi\)
−0.803486 + 0.595324i \(0.797024\pi\)
\(692\) 53021.1 2.91266
\(693\) 0 0
\(694\) 51654.8 2.82534
\(695\) −490.097 + 848.872i −0.0267488 + 0.0463303i
\(696\) −3514.77 6087.76i −0.191418 0.331546i
\(697\) −211.486 366.305i −0.0114930 0.0199065i
\(698\) 3469.56 6009.45i 0.188144 0.325875i
\(699\) −2013.77 −0.108967
\(700\) 0 0
\(701\) −33262.9 −1.79219 −0.896094 0.443864i \(-0.853607\pi\)
−0.896094 + 0.443864i \(0.853607\pi\)
\(702\) −12488.6 + 21630.8i −0.671439 + 1.16297i
\(703\) 7908.11 + 13697.2i 0.424267 + 0.734852i
\(704\) 40805.9 + 70677.9i 2.18456 + 3.78377i
\(705\) −4210.68 + 7293.12i −0.224941 + 0.389609i
\(706\) −31392.0 −1.67345
\(707\) 0 0
\(708\) 61141.0 3.24551
\(709\) −6851.52 + 11867.2i −0.362926 + 0.628606i −0.988441 0.151606i \(-0.951555\pi\)
0.625515 + 0.780212i \(0.284889\pi\)
\(710\) 12885.8 + 22318.9i 0.681122 + 1.17974i
\(711\) 2278.85 + 3947.08i 0.120202 + 0.208196i
\(712\) −1649.79 + 2857.52i −0.0868378 + 0.150408i
\(713\) 8126.14 0.426825
\(714\) 0 0
\(715\) 8009.84 0.418953
\(716\) −17276.7 + 29924.0i −0.901758 + 1.56189i
\(717\) −12993.7 22505.7i −0.676788 1.17223i
\(718\) −6137.80 10631.0i −0.319026 0.552569i
\(719\) −4037.47 + 6993.10i −0.209419 + 0.362724i −0.951532 0.307551i \(-0.900491\pi\)
0.742113 + 0.670275i \(0.233824\pi\)
\(720\) −5838.82 −0.302222
\(721\) 0 0
\(722\) −2289.59 −0.118019
\(723\) −14661.8 + 25395.0i −0.754188 + 1.30629i
\(724\) 27640.5 + 47874.8i 1.41886 + 2.45753i
\(725\) −261.764 453.389i −0.0134092 0.0232254i
\(726\) −17643.8 + 30559.9i −0.901959 + 1.56224i
\(727\) 3668.70 0.187159 0.0935794 0.995612i \(-0.470169\pi\)
0.0935794 + 0.995612i \(0.470169\pi\)
\(728\) 0 0
\(729\) 21881.9 1.11172
\(730\) −2009.88 + 3481.22i −0.101903 + 0.176501i
\(731\) −629.732 1090.73i −0.0318625 0.0551875i
\(732\) 757.559 + 1312.13i 0.0382516 + 0.0662538i
\(733\) −7490.15 + 12973.3i −0.377428 + 0.653725i −0.990687 0.136157i \(-0.956525\pi\)
0.613259 + 0.789882i \(0.289858\pi\)
\(734\) 39918.2 2.00737
\(735\) 0 0
\(736\) 15840.7 0.793338
\(737\) −4350.47 + 7535.23i −0.217438 + 0.376613i
\(738\) −163.447 283.098i −0.00815252 0.0141206i
\(739\) −3265.30 5655.66i −0.162538 0.281525i 0.773240 0.634114i \(-0.218635\pi\)
−0.935778 + 0.352589i \(0.885301\pi\)
\(740\) −10504.8 + 18194.9i −0.521846 + 0.903863i
\(741\) 11453.3 0.567812
\(742\) 0 0
\(743\) 25952.0 1.28141 0.640704 0.767788i \(-0.278643\pi\)
0.640704 + 0.767788i \(0.278643\pi\)
\(744\) −52795.7 + 91444.8i −2.60159 + 4.50609i
\(745\) −1950.93 3379.11i −0.0959416 0.166176i
\(746\) −17453.1 30229.7i −0.856573 1.48363i
\(747\) −1754.93 + 3039.62i −0.0859564 + 0.148881i
\(748\) 41459.6 2.02662
\(749\) 0 0
\(750\) 3151.65 0.153443
\(751\) 7046.97 12205.7i 0.342407 0.593066i −0.642472 0.766309i \(-0.722091\pi\)
0.984879 + 0.173243i \(0.0554246\pi\)
\(752\) −39741.8 68834.8i −1.92717 3.33796i
\(753\) 726.285 + 1257.96i 0.0351491 + 0.0608801i
\(754\) 1737.93 3010.19i 0.0839414 0.145391i
\(755\) −11597.1 −0.559024
\(756\) 0 0
\(757\) −2554.41 −0.122644 −0.0613220 0.998118i \(-0.519532\pi\)
−0.0613220 + 0.998118i \(0.519532\pi\)
\(758\) 11498.6 19916.2i 0.550987 0.954338i
\(759\) 3143.20 + 5444.18i 0.150317 + 0.260357i
\(760\) 14457.3 + 25040.7i 0.690027 + 1.19516i
\(761\) 1109.54 1921.78i 0.0528527 0.0915435i −0.838389 0.545073i \(-0.816502\pi\)
0.891241 + 0.453529i \(0.149835\pi\)
\(762\) 35160.1 1.67154
\(763\) 0 0
\(764\) −38856.5 −1.84003
\(765\) −494.512 + 856.520i −0.0233714 + 0.0404805i
\(766\) −18088.5 31330.2i −0.853217 1.47781i
\(767\) 9442.31 + 16354.6i 0.444514 + 0.769921i
\(768\) −15666.7 + 27135.6i −0.736100 + 1.27496i
\(769\) 22466.2 1.05352 0.526758 0.850015i \(-0.323408\pi\)
0.526758 + 0.850015i \(0.323408\pi\)
\(770\) 0 0
\(771\) 36609.3 1.71006
\(772\) 16422.5