Properties

Label 245.4.e.h.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.h.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 0.998263 0.0589190i \(-0.0187654\pi\)
−0.550157 + 0.835061i \(0.685432\pi\)
\(4\) −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 \(-0.393953\pi\)
0.327026 + 0.945015i \(0.393953\pi\)
\(14\) 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 0.702162 0.712017i \(-0.252218\pi\)
−0.967706 + 0.252082i \(0.918885\pi\)
\(18\) 14.3848 + 24.9152i 0.188362 + 0.326253i
\(19\) −40.1127 + 69.4772i −0.484341 + 0.838904i −0.999838 0.0179877i \(-0.994274\pi\)
0.515497 + 0.856891i \(0.327607\pi\)
\(20\) −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 \(0.198201\pi\)
0.0989050 + 0.995097i \(0.468466\pi\)
\(32\) −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 \(-0.493111\pi\)
0.0216405 + 0.999766i \(0.493111\pi\)
\(42\) 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 \(-0.643661\pi\)
0.997389 0.0722130i \(-0.0230061\pi\)
\(48\) −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 \(0.0711931\pi\)
−0.295462 + 0.955354i \(0.595474\pi\)
\(60\) −248.137 429.786i −0.533906 0.924752i
\(61\) −7.63247 + 13.2198i −0.0160203 + 0.0277479i −0.873924 0.486062i \(-0.838433\pi\)
0.857904 + 0.513810i \(0.171766\pi\)
\(62\) −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 0.919386 0.393356i \(-0.128686\pi\)
−0.800349 + 0.599534i \(0.795353\pi\)
\(74\) −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 \(-0.356125\pi\)
0.436761 + 0.899577i \(0.356125\pi\)
\(84\) 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 −0.852074 0.523421i \(-0.824655\pi\)
0.879333 + 0.476207i \(0.157989\pi\)
\(90\) 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 \(-0.157286\pi\)
0.880382 + 0.474265i \(0.157286\pi\)
\(98\) 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 0.952922 0.303217i \(-0.0980607\pi\)
−0.739054 + 0.673646i \(0.764727\pi\)
\(102\) 469.286 + 812.827i 0.455551 + 0.789038i
\(103\) −172.788 + 299.278i −0.165295 + 0.286299i −0.936760 0.349973i \(-0.886191\pi\)
0.771465 + 0.636272i \(0.219524\pi\)
\(104\) 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 \(0.366642\pi\)
−0.994530 + 0.104451i \(0.966691\pi\)
\(132\) 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 \(-0.519050\pi\)
−0.0598122 + 0.998210i \(0.519050\pi\)
\(140\) 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 0.706250 0.707963i \(-0.250385\pi\)
−0.966239 + 0.257649i \(0.917052\pi\)
\(158\) −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 \(-0.592028\pi\)
−0.285105 + 0.958496i \(0.592028\pi\)
\(168\) 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 \(-0.649245\pi\)
0.998503 0.0547040i \(-0.0174215\pi\)
\(174\) −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 \(-0.321230\pi\)
0.532561 + 0.846392i \(0.321230\pi\)
\(182\) 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 \(-0.967027\pi\)
0.407771 0.913084i \(-0.366306\pi\)
\(200\) −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 \(-0.464216\pi\)
0.112183 + 0.993688i \(0.464216\pi\)
\(224\) 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 0.718200 0.695837i \(-0.244966\pi\)
−0.961712 + 0.274061i \(0.911633\pi\)
\(228\) 3981.38 + 6895.95i 1.15646 + 2.00305i
\(229\) 3314.18 5740.32i 0.956362 1.65647i 0.225143 0.974326i \(-0.427715\pi\)
0.731219 0.682143i \(-0.238952\pi\)
\(230\) −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 \(0.151677\pi\)
−0.0470730 + 0.998891i \(0.514989\pi\)
\(242\) −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 \(-0.487513\pi\)
0.0392197 + 0.999231i \(0.487513\pi\)
\(252\) 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 \(-0.430206\pi\)
0.736535 0.676399i \(-0.236461\pi\)
\(258\) 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 0.784213 0.620491i \(-0.213067\pi\)
−0.929468 + 0.368903i \(0.879734\pi\)
\(270\) 2036.83 + 3527.89i 0.459102 + 0.795188i
\(271\) −2352.07 + 4073.91i −0.527226 + 0.913182i 0.472271 + 0.881453i \(0.343434\pi\)
−0.999497 + 0.0317282i \(0.989899\pi\)
\(272\) 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 \(0.0427585\pi\)
−0.379512 + 0.925187i \(0.623908\pi\)
\(284\) 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 \(-0.233830\pi\)
0.742100 + 0.670289i \(0.233830\pi\)
\(294\) 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 \(-0.522555\pi\)
−0.0707998 + 0.997491i \(0.522555\pi\)
\(308\) 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 \(-0.918207\pi\)
0.263490 0.964662i \(-0.415126\pi\)
\(312\) 5145.47 + 8912.21i 0.933669 + 1.61716i
\(313\) −4278.00 + 7409.72i −0.772546 + 1.33809i 0.163617 + 0.986524i \(0.447684\pi\)
−0.936163 + 0.351565i \(0.885650\pi\)
\(314\) 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 \(-0.468663\pi\)
0.0982880 + 0.995158i \(0.468663\pi\)
\(350\) 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 0.560355 0.828253i \(-0.310665\pi\)
−0.997465 + 0.0711552i \(0.977331\pi\)
\(354\) −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 \(0.00901809\pi\)
−0.475267 + 0.879842i \(0.657649\pi\)
\(368\) −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 −0.552375 0.833595i \(-0.686279\pi\)
0.998103 + 0.0615735i \(0.0196119\pi\)
\(384\) −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 −0.968477 0.249101i \(-0.919865\pi\)
0.699967 + 0.714175i \(0.253198\pi\)
\(398\) 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 0.875512 0.483197i \(-0.160524\pi\)
−0.856216 + 0.516617i \(0.827191\pi\)
\(410\) 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 \(-0.767826\pi\)
−0.745577 + 0.666420i \(0.767826\pi\)
\(420\) 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 \(-0.575641\pi\)
−0.235403 + 0.971898i \(0.575641\pi\)
\(434\) 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 −0.679682 0.733507i \(-0.737882\pi\)
0.975077 + 0.221869i \(0.0712156\pi\)
\(440\) 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 \(-0.249080\pi\)
0.709148 + 0.705059i \(0.249080\pi\)
\(462\) 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 −0.985812 0.167855i \(-0.946316\pi\)
0.638272 + 0.769811i \(0.279649\pi\)
\(468\) −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 \(-0.834035\pi\)
0.00220344 0.999998i \(-0.499299\pi\)
\(480\) −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 \(-0.671965\pi\)
−0.514345 + 0.857584i \(0.671965\pi\)
\(504\) 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 −0.822498 0.568769i \(-0.807420\pi\)
0.903817 + 0.427919i \(0.140753\pi\)
\(510\) 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 0.708293 0.705919i \(-0.249466\pi\)
−0.965490 + 0.260440i \(0.916132\pi\)
\(522\) 301.233 + 521.752i 0.0252579 + 0.0437480i
\(523\) 8342.80 14450.2i 0.697524 1.20815i −0.271798 0.962354i \(-0.587618\pi\)
0.969322 0.245793i \(-0.0790484\pi\)
\(524\) 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 \(-0.863484\pi\)
0.0945786 0.995517i \(-0.469850\pi\)
\(564\) −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 0.767928 0.640536i \(-0.221288\pi\)
−0.938685 + 0.344777i \(0.887955\pi\)
\(578\) 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 \(-0.595914\pi\)
−0.296785 + 0.954944i \(0.595914\pi\)
\(588\) 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 \(0.394331\pi\)
−0.981695 + 0.190460i \(0.939002\pi\)
\(594\) −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 \(-0.682025\pi\)
−0.541187 + 0.840902i \(0.682025\pi\)
\(602\) 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 \(-0.498062\pi\)
0.862966 0.505263i \(-0.168604\pi\)
\(608\) 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 0.988293 0.152567i \(-0.0487540\pi\)
−0.626273 + 0.779604i \(0.715421\pi\)
\(620\) −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 \(-0.648811\pi\)
−0.450658 + 0.892696i \(0.648811\pi\)
\(644\) 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 0.991865 0.127295i \(-0.0406296\pi\)
−0.606174 + 0.795332i \(0.707296\pi\)
\(648\) 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 0.849788 0.527125i \(-0.176730\pi\)
−0.881397 + 0.472375i \(0.843397\pi\)
\(662\) 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 −0.799753 0.600329i \(-0.795036\pi\)
0.919777 + 0.392442i \(0.128370\pi\)
\(678\) 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 \(-0.463690\pi\)
0.803486 0.595324i \(-0.202976\pi\)
\(692\) −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 −0.742113 0.670275i \(-0.766176\pi\)
0.951532 + 0.307551i \(0.0995095\pi\)
\(720\) 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 \(-0.529831\pi\)
−0.0935794 + 0.995612i \(0.529831\pi\)
\(728\) 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 −0.613259 0.789882i \(-0.710142\pi\)
0.990687 + 0.136157i \(0.0434751\pi\)
\(734\) −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 −0.891241 0.453529i \(-0.850165\pi\)
0.838389 + 0.545073i \(0.183498\pi\)
\(762\) −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 \(-0.676592\pi\)
−0.526758 + 0.850015i \(0.676592\pi\)
\(770\) 0 0
\(771\) 36609.3 1.71006
\(772\) 16422.5 28444.6i 0.765620 1.32609i